Power Plants and Power Systems Control 2006: A Proceedings Volume from the IFAC Symposium on Power Plants and Power Systems Control, Kananaskis, Canada, 2006 (IFAC Proceedings Volumes)

POWER PLANTS AND POWER SYSTEMS CONTROL 2006 A Proceedings Volume from the IFAC Symposium on Power Plants and Power Systems Control, Kananaskis, Canada, 2006

Edited by

Dr. DAVID WESTWICK Department of Electrical and Computer Engineering University of Calgary Calgary, T2N 1N4 Canada

Published for the

International Federation of Automatic Control By

ELSEVIER LTD

Elsevier The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, UK 30 Corporate Drive, Suite 400, Burlington, MA 01803, USA First edition 2007 Copyright © 2007, IFAC. Published by Elsevier 2007. All rights reserved No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means electronic, mechanical, photocopying, recording or otherwise without the prior written permission of the publisher Permissions may be sought directly from Elsevier’s Science & Technology Rights Department in Oxford, UK: phone (+44) (0) 1865 843830; fax (+44) (0) 1865 853333; email: [email protected]. Alternatively you can submit your request online by visiting the Elsevier web site at http://elsevier.com/locate/permissions, and selecting Obtaining permission to use Elsevier material Notice No responsibility is assumed by the publisher for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein. Because of rapid advances in the medical sciences, in particular, independent verification of diagnoses and drug dosages should be made British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress ISBN–13: 978-0-08-046620-0 ISBN–10: 0-08-046620-6 ISSN: 1474-6670 Printed and bound in Great Britain 07 08 09 10 11 10 9 8 7 6 5 4 3 2 1

Table of Contents A Novel Concept for Stabilization of AC/DC Network with UPFC R.K. Pandey

1

Limitation Control Procedures Required for Power Plants and Power Systems Possibility for Reducing Future Blackouts E. Welfonder and M. Kurth

7

SISO Extended Predictive Control – Formulation and Robust Analysis M. Abu-Ayyad and R. Dubay

17

Robust Decentralized H∞ Controller Design for Power Systems: A Matrix 23 Inequality Approach using Parameter Continuation Method G.K. Befekadu and I. Erlich Self-Tuning PI Controller I. Boiko

29

Development of an Extended Predictive Controller for a Speed Control System M. Abu-Ayyad and R. Dubay

35

Power System Stabilizer Design for Multimachine Power System using 41 Population-Based Incremental Learning K.A. Folly Development of Educational Web-Based Simulator for the Electricity Spot 47 Market in Korea J.W. Lee, K.M. Yang, Y.W. Jeong, J.B. Park and J.R. Shin A Cooperative Power Trading System based on Satisfaction Space Technology

53

K. Matsumoto, T. Maruo, and N. Mori Influence of Wind Energy on the Power Station Park and the Grid H. Weber, T. Hamacher, and T. Haase

59

An Approach to Optimal Dispatch of Bilateral Electricity Contracts Regarding 65 Voltage Stability B. Mozafari, A.M. Ranjbar, A. Mozafari and T. Amraee Identification of Synchronous Generators using “4SID” Identification Method 71 and Neural Networks M. Karrari, W. Rosehart, O.P. Malik and A.H. Givehchi Parameter Estimation of Power System Oscillations based on Phasor Measurements T. Hashiguchi, Y. Ota, H. Ukai, Y. Mitani, O. Saeki and M. Hojo

77

Identification of Electric Parameters of Synchronous Generator using InputOutput Data Set S.A. Saied, S.M. Bathaee, M. Karrari, W. Rosehart and O.P. Malik

83

iii

Estimation of Moisture Content in Coal in Coal Mills P.F. Odgaard and B. Mataji

89

Simplified Fuel Cell System Model Identification S. Caux, W. Hankache, D. Hissel and M. Fadel

95

An Affine Geometrical Approach to Power Systems Problems E.D. Crainic and A.I. Petroianu

101

Discrete-Time Model Reference Adaptive Regulation of Nodal Voltage Amplitude in Power Systems G. Fusco and M. Russo

107

Determination of Transmission Transfer Capability with Security and Voltage Stability D. Hur and H.J. Lee

113

Voltage Stability Assessment and Enhancement of the Thailand Power System A. Sode-Yome, N. Mithulananthan and K.W. Lee

119

Design, Implementation and Testing of an Artificial Neural Network Based 125 Admittance Relay G. Chawla, M.S. Sachdev and G. Ramakrishna A New Numerical Algorithm for Fault Location Estimation using TwoTerminal Synchronized Voltage and Current Phasors C.J. Lee, Z. Radojevic, H.H. Kim, J.B. Park and J.R. Shin Complete Fault Analysis for Long Transmission Line using Synchronized Sampling N. Zhang and M. Kezunovic

131

137

Study on the Establishment of Dynamic Performance Test Environment for 143 the Digital Protective Relay using RTDS B.T. Jang, C.Y. Choe and G. Jung Hybrid HVDC Converters and their Impact on Power System Dynamic Performance B. Qahraman, A.M. Gole and I.T. Fernando

147

Predicting Transient Instability of Power Systems based on Hybrid System 153 Reachability Analysis Y. Susuki, H. Ebina and T. Hikihara Stability Analysis of an Islanded Generator P. Lilje and A. Petroianu

159

Primary Control System and Stability Analysis of a Hydropower Plant M.R.G. Zoby and J.I. Yanagihara

165

Observer-Based Coal Mill Control using Oxygen Measurements P. Andersen, J.D. Bendtsen, T.S. Pedersen, J.H. Mortensen and R.J. Nielsen

171

iv

Fault Detection in Coal Mills used in Power Plants P.F. Odgaard and B. Mataji

177

Control Performace of Large Scale Steam Power Plants and Improvements T. Weissbach, M. Kurth, E. Welfonder, D. Haake and R. Gudat

183

Intelligent Start-Up Schedule Optimization System for a Thermal Power Plant M. Shirakawa, K. Kawai, M. Arakawa and H. Nakayama

189

A Fault Diagnosis and Operation Advising Cooperative Expert System Based 195 on Multi-Agent Technology W. Zhao, X. Bai, J. Ding, Z. Fang and Z. Li Model Based Fleet Optimisation and Master Control of a Power Production 201 System C. Joergensen, J.H. Mortensen, T. Moelbak and E.O. Nielsen Reliability Enhancement Scheme for IEC61850 based Substation Automation 207 System S.I. Lim, D.H. Park, S.J. Lee, S.S. Han and M.S. Choi Modeling Voltage Regulation in Object-Oriented Analysis of Distribution Systems Including Dispersed Generation G.M. Casolino, A. Losi and M. Russo

213

Service Restoration Considering Load Balancing in Distribution S.Y. Choi, J.S. Cha, C.D. Yoon and M.C. Shin

219

Real-Time Volt/VAR Control in a Distribution System using Multi-Stage Method J.Y. Park and J.K. Park

225

Development of the Automatic Recognition System for Distribution Facility 231 Map B.J. Yi, J.I. Song, J.H. Shin, J.I. Lee and S.K. Cho Sensor Dynamics Compensator for Temperature Measurement in Combustion 237 Chambers of Utility Boiler and Incinerators I. Boiko, and V. Mkrttchian Sub-Space Principal Component Analysis for Power Plant Monitoring L. Pan, D. Flynn and M. Cregan

243

Combustion Plant Monitoring and Control using Infrared and Video Cameras S. Zipser, A. Gommlich, J. Matthes and H.B. Keller

249

Enhancement of Electric Motor Reliability through Condition Monitoring K.E. Holbert, K. Lin and G.G. Karady

255

Performance of H∞ -PSSs as Affected by the Parameters of the Bilinear Transform K.A. Folly and K. Mocwane

261

v

Dual Input Quasi-Optimal PSS for Generating Unit with Static Excitation 267 System Z. Lubosny Experimental Studies on a Proto-Type Power System using an Adaptive PSS G. Ramakrishna and O.P. Malik

273

Extended Phase Compensation Design of Power System Stabilizer for Bisotoun 279 Power Plant G. Zafarabadi, M. Parniani, M. Rasouli and P. Ansarimehr Robust Control Design of PSS in Wide Area Power System Considering Information Reliability H. Ukai, G. Toyosaki, Y. Nakachi and S.C. Verma

285

Analytical Investigation of the Effect of Generator Modelling on Electromechanical Load Damping K. Kaberere, A. Petroianu and K. Folly

291

Comparison of Methods for Oscillation Detection – Case Study on a Coal-Fired 297 Power Plant P.F. Odgaard and K. Trangbaek Low Load Model of a Once-Through Boiler with Recirculation K. Trangbaek

303

Semigroup based Neural Network Architecture for Extrapolation of Mass Unbalance for Rotating Machines in Power Plants B.H. Kim, J.P. Velas and K.Y. Lee

309

MGP: A Tool for Wide Range Temperature Modeling A.F. Kuri-Morales and L.V. Seisdedos

315

Simulation as a Tool for Process Design and Disturbance Analysis in Industrial 321 Power Plants Y. Majanne Operator Guidance Simulator, A New Power Plant Training Tool Concept U. Tomschi, H. Jackisch and R. Newald

327

Application of Affine Transformations to Real-Time Power System EMS Functions E.D. Crainic and A.I. Petroianu

333

Autonomous Power Networks Based Power System A. Jokic and P.P.J. van den Bosch

339

Importance of the Selfregulating Effect within Power Systems M. Kurth and E. Welfonder

345

Optimal Power System Management via Mixed Integer Dynamic Programming H.G. Kwatny, E. Mensah D. Niebur and C. Teolis

353

vi

Static Characteristics Analysis of Power Systems Through a Hermitian Approach J. Zhou and Y. Ohsawa

359

Economic Dispatch Algorithm by λ-P Tables Reflecting Actual Fuel Cost 365 Curves K.I. Min, J.G. Lee, S.J. Kim, H.S. Hong and Y.H. Moon Power System Maximum Loadability with Generation Constraints C.E.M Fernandes, R.S. Salgado and L.V. Barboza

371

Optimal Allocation of Static VAR Compensators using Modal Analysis, Simulated Annealing and TABU Search S. Ebrahimi, M.M. Farsangi, H. Nezamabadi-Pour and K.Y. Lee

377

Distributed MPC Strategies for Automatic Generation Control A.N. Venkat, I.A. Hiskens, J.B. Rawlings and S.J. Wright

383

Modelling and Optimization of a Micro Combined Heat and Power Plant D. Faille, C. Mondon and L. Henckes

389

The Way of District Heating Output Control by Means of Hydrothermal Power 395 Systems - Three Modifications J. Balate, P. Jenik, B. Chramcov and P. Navratil Weighted Fouling Model for Power Plant Condenser Monitoring M. Cregan and D. Flynn

401

A Multi-Agent System-Based Reference Governor for Multiobjective Power 407 Plant Operation J.S. Heo and K.Y. Lee Adaptive Governor Control and Load Shedding Scheme for an Incinerator 413 Plant Y.D. Lee, C.S. Chen and C.T. Hsu Author Index

419

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Foreword IFAC Symposium on Power Plants and Power Systems is sponsored and organized by the IFAC Technical Committee on Power Plants and Power Systems. It is held every three years and the latest Symposium in this series was held June 25-28, 2006 in Kananaskis, Alberta, Canada. Out of 110 papers submitted for presentation at the Symposium, 76 papers were accepted for presentation after independent peer review. Session Chairs were asked to evaluate the papers in their individual sessions. Based on paper quality and presentation, the Session Chairs recommended a total of 69 papers that are included in the Proceedings of the Symposium. Control plays a very important role in all aspects of power plants and power systems. The papers included in the Proceedings are by authors from a large number of countries around the world. They encompass a wide spectrum of topics in the control of practically every aspect of power plants and power systems.

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Copyright 0Power Plants and Power Systems Control. Kananaskis, Canada 2006

ELSEVIER

A Novel Concept for Stabilization of AC/DC Network with UPFC R.K. Pandey Department o j Electrical Engineering Institute of Technology Banaras IIindu University, Varanasi, INDIA

Abstract: This paper presents a novel concept for stabilization of AC/DC network with Unified Power Flow Controller (LJPFC). The system considered has the structure of two areas connected by HVDC link. 'The investigation for perturbation in ac bus voltages has been carried out and the effect on the stability deterioration has been analyzed. The new concept of control has been proposed by embedding UPFC and then generating the control decisions adequately which stabilizes the earlier one. The concept of including the Unified Power Flow Controller (UPFC) in AC/ DC network especially where a DC link is embedded to connect the two AC Systems is proposed. The proposed control design has been done utilizing a Novel Discrete -Time model of ACiDC system. The complete system stability has been studied in which the individual controller such as HVDC-SVC and HVDC-SVC-UPFC performance under varying perturbation of ac system voltage has been widely analyzed. Tht: results show that in situations the HVDC-SVC alone is unable to reject the perturbation, the UPFC along with the HVDC - SVC damps the oscillations, thus matching the real and reactive power demands adequately. This novel combination can effectively be utilized in situations when the ac system bus voltage undergoes the fluctuations due to changing P and Q requirements. Copyright 02006 IFAC Keywords: - HVDC, SVC, UPFC, Discrete-time, continuous time, multirate sampling

1. INTRODUCTION

In case of power oscillations, the converters will function by their firing angle controls. As the firing angle can vary within a certain limit as directed by the control, the Static VAR Compensator will also act accordingly. But, when the HVDC converter controls along with SVC are not sufficient enough to damp the oscillations, i.e., reactive power mismatch is not met, and then the AC system voltage will come down from normal 1 p.u. value. As this is noticed by the network. it will first land to converter control instability and associated afterwards failure and then may enter to ACI DC system interaction. Moreover, if the voltage in the AC side of the corridor becomes low, then DC link voltage, as well as the power transfer through the DC link will come down undesirably. Now, providing an UPFC block, in between the AC switchyards, parallel to the A C tie line, and the DC link. the real and reactive power both can be modulated adequately, by their multifunctional and coordinated control. The capability of UH;C has been demonstrated (Hingorani Narain G, 1999; Wang H.F.. 2000) in damping oscillations. In case, there is reactive power drop in the network, which cannot be met by SVS, etc. then, the UPFC will pump that power to the AC corridor; immediately. and thus stability of the power network can be maintained. Depending on the rating of UPFC and SVS, the real and reactive power can be modulated and the whole network can be made stable, up to a certain extent. Thus. chances of' network tripping, due to large. sudden and sustained power mismatch can be minimized a lot and stability of the AC/DC system can adcquatcly bc cnhanccd.

The HVDC transmission technology is well established nowadays. So, many schemes all over the world are running well including back-to-back, pointto-point and multi-terminal. The basic operational requirement of the HVDC schemes is adequate control action, depending upon the power ordcr for damping thc power network oscillations. Sometimes, the inadequate control action such as. absence of adequate control of Static VAR Compensator (SVC) at the converter bus. might result in unstable system behaviour. So far. no remedy has been reported in literature, where there is a variation of the AC switchyard line-to-line voltage because of external reasons; which might ultimately affect the operation of converter. A new approach has been proposed for the network in which DC link is embedded. When AC bus voltages of converter station fluctuate, the SVC may not be in a position to help to damp this and so the converter may land to control instability. This is very detrimental for the system. To alleviate this novel concept of Unified Power Flow Controller (UPFC) in between the AC switchyard has been proposed which acts as a supplementary controller for the AC network and thus regulates the system dynamics adequately in situations of perturbations in AC switchyard voltages either side, which in turn improves the overall system stability as desired. In the power system network, two regional grids can be interconnected by HVDC back-to-back. I he two converter stations are connected through the DC link and the converters have their individual controls.

1

From the results shown in this uork, it can be said that this proposed HVDC-SVC-UPFC compact system (Fig.1) is far better to design the effective control strategy for HVDC link. suited to restore stability in a wry short time, which is csscntial to ciibure bettcr stability for. a dynamically varying power network But. IJPFC also cannot sustain a ver)' large amount o f power oscillations because its DC link capacitor has a maximum limit to support the required VAR. So. this proposed model may not guaranty power network stabilization for a very high amount of perturbation. but it can definitely give a higher level of confidence to the power system researchers. In earlier research studies, no such concept has been proposed yet. so this proposed conccpt will be intercsting to powcr cnginecrs and rcscarchcrs worldwidc.

Aar(kT+T3)+ A / , [AI&(k+l)T

Inverter Side

Fig.1 HVDC-SVC-IJPFC system representation 11 DISCRETE-TIME MODEL, OF

HVDC-SVC-UPFC In standard practice stability investigations are performed using IineariLed perturbation models in which the system is linearized around a nominal operating point l o achieve [his objeclive. il is important that the behaviour of various components o f the HVDC system be appropriately represented in a linear domain

where A , to A,? and R, to R12 are linearized scalar constants. The relation ship between the DC current Id and the overlap angle IJ are derived for both the cases of rectifier and inverter (Pandey, et u1.,199O). The linearized values of the overlap angles, ;c and U, in terms of DC currents and firing angles are given as,

2.1 Discrete-time HVDC System Model

Continuous-time (Carrol and Krause. 1970) and discrete-time system representation hake been described in the literatures (Pandey, et a l , I990). Discrete-time equations for convcrtcrs in HVDC sy5tem (Pundey, et a1 , 1990) are given below Rectifier Side

(kT+Ti)]/d, Combining the transmission line and current controller model, state space expression is obtained (Since it has been assumed that. the predictive type control at inverter end, the variable Aa) has been represented in terms of the variable A/,, )

AV,,(k7;T,)

-

A-[A&(kT-Tz) + AIJ,] +A,?

2

A

=

Fig.11 Static var corripeiibator The equation for the equivalent reactance for a standard SVC circuit is given below.

This state space model represents continuous- time nature o f thc both transmission line and thc controllers. To combine the continuou+time models of the transmission line and controllen with the discrete-time model of converter, the thcory of multirate sampling has been applied (Pundey et ul

1990).

Suaceplance.

dx(kT+T/) @ T / ) d x ( k T ) + Q(1,) AC;(kT) Ax(kT T?) = q T 2 - T / )Ax (kT I T / ) I Q(T2-T,) AV, ( k 7 + f / ) h ( k T T3) = @T3-T2) AX(kT 1 T2) 1 6(T3-T2) AVd((kTt Tr ) A~x[(k+I)l= l q 1 - 7 3 ) A ~(kf l 1 3 ) + O ( 1 -13) A[/,(kTT T,) (3) where @( I @(T z- I ,), @( 1 3 - 12). @(T - I 3) are the state transition matrices evaluated at the four discrete instants. while $(TI). 8(Tz-Tl).8(T3-T2).8(T-T3) are the corresponding input matrices. Thererore. combined equation &[(k+l)T] = @(T/ ) @(T2-T/) @(T3-T2) @(T-T3) AX( k f ) + @ ( f 2 - f / ) q f 3 1 2 ) q ( T - f 3 ) B ( T / )Al’dkf) +@(Tj-TZ) (yT-T3) @T:-T/) AV,(kT+T/) +@(T-T,) H ( I 3 I,) AC’d(kT4 T z ) + B(T-7.3) AL>(/LT+T3) (4) The kector AV, in this expression can be substituted by the appropriate a\ erage expressions derived at different time instdnt5 as given in ( 1 a d 2) After simplification (4), can be converted into the lollowing homogeneous state eqn A x ( k l I ) I ’ ] = MHVDL MkO (5) This expression represents the combined DC Iinh modcl. Where MIIvDLis the closcd loop matrix o f the entire two terminal HVDC \ystem

Putting the value o f & in (8) following results

Now, linearizing (9) the perturbation equation is obtained as

(10) Therefore. the reactive power equation for Static Var Compensator, connected in the rectifier side. is AQ,,

f

= 4 ,(A%

f

1 s, +

7

W

l

I

1

(11)

Rectifier Reactive Power Equation For the rectifier. the reactive power equation is, Q, = 1.35V” I , S W Z ( ~ , ) (12) Linearizing equation (12) AG? = R,l(A%)+ R & ~ , r ) + R , , ( A V L , ) (‘3) Reactive power injectedhithdrawn in case of power imbalance in the network can be expresied as below for suitable controller design,

IIVDC-SF’C Svslem Model In the model of HVDC-SVC, thc linearized statc equations of the HVDC are taken from above. The above closed loop equation of HVDC is combined with the linearixd state equations of SVC. which are developed in the following part Calculation &Reactive Power (0)in Static VAR Comnensator

AQR,,,‘,

=A Q

AQR,,

= R, I(A% 1+ U M ‘ , ,1+ h ( A C f r )- &I

-

AQ,,,

(A%,

1

(14 At steady state, reactive power perturbation must =0 be zero, i.e. Therefore, from ( I 4)

The standard Static VAR Compensator (SVC) circuit can be represented as in figure below,

3

'This expression rcprescnts the completc HVDC-SVC model. Where, M/,vJjc.~yvc is the closed loop matrix of this system. Here also the eigen values of matrix MHvD,,.sr,c- indicate the system stability, i.e., for the stable system operation, the eigen values must lie within the unit circle.

h ( A ? ) = * ~ p l ( A ~ ,1-l Av,Ic

l1

AU = [Amc Amb Ad,,]' The final state equation of UPFC connected in a two machine system can be written as,

AX = MtrpFC AX The diagram of the proposed compact model, where UPFC is combined with the HVDC-SVC system is

E7,"I.O

P.U.

Excitation system 2: K2A=20.0,T2,4=0.01secs. 111 PERFORMANCE EVALUATION The perturbation of AC line-line voltage is increased from 0.074074 p u. to 1 p.u.(i.e., approximately 25%). In this case, as the perturbation is increased considerably. the SVC will not able to sustain it and finally it will lead to 5ystem collapse (Fig. V). Some of the states have been shown below. The detailed study has been given in Table I.

4 . .

h A

A1

Fig.lV Proposed IHVDC-SVC-UPFC system

II

The state equation for the HVDC-SVC and UPFC comDact model can be written as

I

wherc, [ ~ H I . D c ~ ~ s r . c ~ - r . c= ~l

[ A c ~ s v ~ AIdF ., Aid, AVJ,L AVci A 6 AID, A w ~El,,' / ) , I > AE2q' &,ii AvdL.1 'Thus, the I-IVIIC-SVC-UPFC compact model is developed in a discrete time framework and stability study has been perlormed using this model through cigcn-valuc analysis.

a

I11 SIMUl.AT1ON OF SAMPLE SYSTEM The simulation study is carried out using MA'I1,AB software package. The parameters of the sample system are given below, No load rectifier direct voltage, F;Fo=l p.u. No load inverter direct voltage, Vd,rl=l p.u. Frequency = 50 Hz. Direct Current, 4j,.=Id,=0.25p.u. Link length=500 meter Commutating inductancc, Lc=4.99c-O4 p.u. Line inductance, L=O.0399 p.u. Line resistance, R=0.25 PSI.

I )

a

4

fj"

5

1

1

,

~

converter control. Under this siiuation. ihe concept of employing UPFC as supplementary controller for damping the oscillations has been thoroughly examined and it has been found that the induction of UPFC drastically improves the overall system stability that too in minimum time. 1he complete system model of HVDC-SVC-UPFC fi-amework has been developed in the discrete time domain and the system stability has bcen examined. wherc it has been observed that the variation of AC line-to-line bus voltage does not deteriorate the overall system stability. rhis has been reflected so because the basic feature of UPFC in the AC network is to control the power flow dynamics verj fast using VSC technology having vcry fist control of- both rcal and reactive power. UPFC has been incorporated at the back to back HVDC link to demonstrate the concept. where it has been intentionally presumed that the DC link length and the AC transmission line length (the distance between the two AC switchyards has been asumed to be 500 meters).

L

;.

8

[

113:

[:I::

I

,

:I):

CCI

"I;

13:

31::

,

CCI

]:I:

:I:#:

Tune (sec.)

(c) Fig.V Response of state variables for HVDC-SVC model by making initial perturbation of 25%; (a) AG,, , (b) A , (c) A bTable I: ComDarison between HVDC-SVC model and I-IVUC-SVC-UPFC compact model for 10% perturbation and relatively IarPe Derturbation. (25%)

perturhat'on 25%) Peak Overshoot

;:

Settling

Overshoot(p,u,)

Pandey R. K., Ghosh A and Sachchidanand (1999), Development of Novel IHVDC System Model for Control Design. Electric Machines and Power Syutem Research, 27, pp.1243-1257. Carol D.P. and Krause P.C. (1970), StabiliQ analqsis of a DC power system, PAS-89, pp. 1 I 12- I I 19. Hingorani Narain G (1999) , Gyugyi Laszlo, Ckderstanding FACTS Concepts and Technologv of Fkxible AC Transmission SyAtems. IEEE Press, New York. Wang H.F.,Swifi F.J. and Li M (1998) A un@d model for the analysis of FACTS devices in damping power systems.IEEE Trans. on Powe Delivery. No. 4. Claudio A. Canizares and Zcno T Faur (1999) Analysis of SL'C and TCSC Controllers in Lbltage Collapse, IEEE 'Irans.on Power Systems, Vo1.14. ppS8-hS. Pandey R K and Tripathi S B Mani (ZOOS), Design of Unified Power Flow Controller with State Predominant Approach, Sixth International Conjerence on Power Electronics (e Drives Systems, Kuala Lumpur, Malaysia Wang H.F. (2000). A uni$ed model for the analysis of FACTS devices in damping out system oscillations Part 111 Unij?ed Power Flow Controller. IEEE Trans. on PWRD. No. 3. Saeed Arabi, Prabhashankar Kundur and Rambabu Adapa (2000), Innovative techniques in modelling tiPFC' for power bystem analysis, IEEE Trans. on Power Systems. V01.15, pp.336-340. Wang H.F. (1999) , Selection of r o h t installing locations and feedback signals of FAC'TS -based stabilizers in multi-machine power systems, IEEE Trans. on PWRS. No. 2,. Gjugyi. L. . Schauder C.D. , Williams S.L. . Keitman '1.R. , rorgerson D.K. . Edris A. (1995) . The [JniJied Power Flow Controller il New Approach to Power Transmission Control, IEFE Trans. Power Delivery, Vol.10, pp.1085-1093.

Relaticely large

Operating Point Domain( 10% perturbation)

Control Strategies; System

REFERENCES

settling time

~

I

I

II Idi

0 489

100107 I

0 474

0 012

I

IV. CONCLUSION An investigation has been carried out of a network whcre HVDC is having back to back link and also the stability characteristics has been found deteriorating when the line-to-line voltage of the AC system is varied, because of some system disturbance. The HVDC-SVC alone could not handle the perturbation of line to line voltage change alter a certain value and this is because of the fact that SVC can not support for the external reactive power variation as this is meant to regulate the Var requirements during the

6

Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

PUBLlCATlONS

LIMITATION CONTROL PROCEDURES, REQUIRED FOR POWER PLANTS AND POWER SYSTEMS POSSlR11,I'I'Y FOR REEDLICING FUTURE RI.ACKOLITS

E. Welfonder and M. Kurth

Department for Power Generation and Automatic Control, IF'D, L'niversiv of Stuttgart Pfaffenwaldring 23, 70550 Stuttgart, Germany Tel t49 711 685-6214, Fax +49 711685-6590 welfonderQivd uni-stuttgart de

Abstract: For maintaining the reliability of interconnected power systems also in cases of extreme power transits the protective system devices should not become active when ever possible. For this reason, it is necessary to provide for limitation control procedures, and this not only on the side of power plant and system, where it has been common practice for many years to keep at least the main manipulated and controlled variables uithin their foreseen operation arcas. but also uithin the grid to contain the transmission flows of heavily overloaded system components within their maximum allowable transmission capacity. In this respect. manual short-term bottlcncck management on the system operation side turns out to be not sufficient enough, in the case of unexpected events caused by increased power transits.. Copyright 02006 IFAC' Keyuords: Power plants. poi%er systems, power transits, bottleneck management, limitatiorr control, protectiori, blackouts..

1. TNTRODUCTION

Thc original objective of interconnected power networks aimed - above all - at a joint spinning reserve power. Also with the first cross-border power transmits inside of Europe the interconnected power system was loaded only to little extent. s. in Figure 1 '.from about 1970. These power transmits were i s . caused by the purchase of seasonally lowprice naturally generated electrical power from highhead hydropower stations in the Alpine countrics and the transmission o\ er long distances to the large industrial centres such as the Ruhr area in NorthWest Germany. Since the mid 1980s. however, spccific non-seasonal power transits more often occur fiom countries with a high amount of low-price generator output into countries with a lack in inexpensive generator output. So, for example. Italy from the mid 1990s on - i s . before the liberalihon of the electrical energy market - continuouslq purchased 4 to 6 GW power from France.

Caused by these power transits speci tic high-voltage transmission lines concerned within the European pouer system have already been strongly loaded at that time, s. in I'igurc 1 "from about 1985". With the change to a liberalized energy market. the trade intensifies the use of the interconnected power sqstem as a transport network. uhere not seldom individual transmission lines are loaded to full capacity (Kaupa and Pohorny, 2004: Reyer and Weis, 2004). s. in Figure I "from about 2000". This development is verified quantitatively by the strong power ex- and import from and to Germany plotted in Figure 2 (Schnug and Fleischer. 1999; Welfonder. 2000). As the diagram shows, the power transits in 2003 already reach = 5 G W. averaged over the year.

*

Figures 3 and 4 show detail considerations for 2003, on the basi? of power ex- and import? on the third Wedncsday ofcach month (UCTE, 2005):

/

~

1970

-

I

~

2000

1985

~

t

\ 1980

1990

2000 from 1991 incl East-Germany

Fig. 1 lncreasc of maximum powcr transits within

Fig. 2 Increase of the mean power transits within Germany since the second hall' ofthe 1980s

thc European intcrconnected power system => trend behalriour

7f;"-'

a) night ( 3 : O O a.m.) 10

P [GWl 5

b) day (1 I :00 a.m.)

Export

10

P [GWI 5

0

0

-5

-5 -10

-10

1

2

3

4

5

6

7

8

1

9 101112

2

3

4

6

5

month

7

8

9 101112

8

9

month

Fig. 3 Load ex- and imports on the third Wednesda) of each month in Germany in 2003 a) night (3:OO a.m.)

1

2

3

b) day ( 1 1:00 a.m.)

4

5

6

7

8

9

101112

1

2

3

4

month

5

6

7

month

Fig. 4 Load ex- and imports on the third Wednesday of each month in Italy in 2003

8

101112

From Figure 3 can bc secn that in Germany at night (3 a.m.), power cxports of 10 GW have already been effected. and in the morning ( 1 1 a.m.), power imports of -8 GW have already been reached. Similarly Italy, as describcd in Figure 4, purchases 6 i 7 G W day and night in most of the months. Also power imports of up to 10 GW should have been occurred occasionally. In this contcxt, thc load-dcpcndinghighcr dcmand during the day is balanced out in Italy by employing pumped storage power from hydropower stations with nightly pumping capacities u p to 3 GW. Due to this ongoing development, limitation control procedures arc requircd in powcr systcms, too. Thus an installing of additional powerful transmission lines will not be realizable in foreseeable time, due to environmental and recently also economical reasons, and scheduled power transits cannot generally be reduced as for liberalized market reasons.

2. EXAMPLES FOR ALREADY IMPLEMENTED I ,IMITATION CONTROI, PROCEDURES The following examples shall illustrate the importance of already implemeiited limitation control procedures for the reliability of the electric energy supply.

2. I Power Plant Limitation Control As "the pouer plants are the actuators of the povler systcm". the individual power plant units are mostly operated during the whole day at the upper limit and. at night, often at the lower limit of their duty range. see Figure 5a. So, on the power plant side, numerous limitation control proccdurcs havc alrcady bccn implemcnted. comp. the separate I&C function "limitation control" in Figure 5b. The necessity of such limitation control measures is, among others. verified by VDIIVDE guideline no. 3500 published

in German already in 1996 and overtaken as TEC Technical Report in 2002.

2 I I Limitation Control for Steam Boilers and Turbines For economical reasons, fossil-fired and nuclear steam power plants are operated in the case of high system load at nominal power if ever possible. Thus also the live-steam is produced at as high pressure as possible. i.e. near the plant's upper limit. see Figure 5a. To prevent that, in cases of a sudden increase of the live steam pressure pD be it through increased throttling in the case of network disturbances with surplus active power or also through internal power plant malfunctions with excess heat flux overpressure protection devices do respond, modern steam pomer plant uniti are employed with overpressure limitation control, see Figure 6. centre. By means of this procedure excess steam is conducted into the condenser via the high-pressure steam b y p a s station (VDl/VDF, 1996; Welfonder, 1992: Sattinger and Welfbnder, 1993). ~

Correspondingly, at off-peak load the power outputs of fossil-fired steam power plants are often run down as far as possible. In this case. minimum load limitation control makes sure that the load does not fall below the lower limits, such 0 referring to live-steam pressure and feedwater flow (=' to ensure a still sufficient flow through the numerous heating surl'ace tube banks), and 0 referring to the fuel flou (=> to ensure a still stable combustion in the furnace), see Figure 5a "Lower Limitation Range". Uy this way. a response of the relevant protective equipment is avoided at low load operation (VDIIVDE. 1996). In addition. steam powcr plant units. to prevent excessive thermal stress in thick-walled construction components, may be started up and shut down on14 with definedload change rates. For these reasons also suitable limitation control procedures are applied, cf. "Limitation Control at StartIJpiShutdown" in Figure 5a and velocity limitation in guiding function for the reference power output" in Figure 6. top.

a) Lood dependent operotion oreos and I&C functlons of power plonts 3 wiih typical opemiion points

.Frequency voltages PrernureP

. Temperotvre~

of steam power plants

f

u

*

Q

ThWrnd =tress

g

oxygen contents pn-wiues

pz

.

@ 8.9.

g&~

Fig. 5 Functional layout of I&C-systems with limitation control

9

b) Interaction of the different l&C functions

[7

normally 380kV down to less than 50% the high-voltage transmission (Zimmermann. 1990).

I90 k V in network

Also. the blackouts occurred in vast areas of the LJSA and Canada (14 Aug. 2003). as well as in Scandinavia (23 Sept. 2003), were caused by power line di\connections mainly due to reduced boltage at high load flow (UCTC. 2004; ETG. 2003). In this context, the inciease ofthe load flow is caused on the one hand by the fact. that after some generators had broken down, the missing acti\ e and reacti\ e power has to be provided by other, partly far distant system areas. On the other hand, with decreasing voltage on the high-voltage side. the current flows in thc high voltage transmission network increases because without appropriate countermeasures - the voltage on the low voltage side and therefore the power demand remains constant due to the re-adjustment of the tap changer transformers within the distributing nctworks. A pre-condition for the applicability of this limitation control measure on the generator side is that the machine transformers will be equipped with step changers. rhis additional actuation possibility is normally given in the case of feeding-in of large generators to the German high-voltage network. In

'G,dei "!

I

-

I Fig. 6 Overpressure limitation control in fossil-fired steam power plants =>Opening ofswitches S, and S2i f p > 1;

the other case, as soon as i, = i, is reached, a stepping up of the transformers on the distribution sidc is required which causes a decrease of the inductive power demand. Should this not be sufficient, motors have selectively to be taken out of service. i.e. a regional inductive load shedding has to be activated by means of limitation control (=> opening ofswitch S4 in Figure 7).

2 1 2 Limitation Contipol for Generators At high load generators are mostly operated mith high overexcitation due to high reactive power demand caused by motor load\ m d heavily loaded transmission lines. In order that in cases ofpoucr system incidents, such as dropout of one power plant unit. the overexciting protection depices of neighbouring power plant units do not respond additionally. the larger generators in Germany have already in the 1990s been equipped with excitation currcnt limitation control. Due to this in the case of limitation control activation the respective excitation currcnt gets adjusted to its allowable upper limit value. u hile the generator voltage and depending on that the auxiliary voltage is kept on its setpoint by appropriate atepping down of the belonging machine trarisrorrner, s. Figures 7a and b. Due to the decreasing voltage on thc uppcr side of the machine transformer5 and thus in the highvoltage network the motors in the distribution systems need less reactive power. I'or retaining this effect - as accompanying procedure - the tap changer transformers on the distribution side have to he blocked temporarily (Welfonder. 1992; Zimmermann, lYYO), s. Figure 7c. c3 This excitation current limiting procedure substantially helps to restrict the danger of possible voltage collapses. Thus such a voltage collapse occurred in 1988 in north-western France when in the Normandy. after the failure of one power plant unit. numerous adjoining units were overloaded themselves by trying to keep their voltage and were due to this shut down one after another. like a domino effect. I his resulted for several hours in a drop of the nominal voltage of

a ) Hiah voltaoe transmission svstem

A

L

380 k V I

I

I

380 k V

c ) Load port system

Fig. 7 1 imitation procedure referring to the generator: - Change-over of controller K,, to i e limitation control - Change-over of controller Ru2 to control the generator voltage UG and - Blocking of controller Ru3

10

,

Correspondingly, for regulating the line voltage rising at low load - compensation coils are automatically switched on as soon as the respective generators reach their lower excitation level. This limitation control mcasurc has already been state of the art in system operation for many years.

w,ci

stage 1 A l w i o y o f perso’irie.. srlieUuliii(~ E a t i h e p w e r stciian capccty n r y e t nitivnted

49,i Inctnntanmtis i h r l d i i g o f s y s w m lond

2 2 Low Frequency Limitation Control

Stme 2

49.c

10 -15%

It is within the scope of the transmisvion system

operators to provide sufficient spinning resen e power in order that the drop of the \).\tern frequency remains within the allowable range of control - also in case of the maximal power outage taken into account (VDN. 2003). Should these boundarj conditions fail. be it because of insufficient reserve power, or a suddenly occurring great deficit i n active power - such as through the breakdown of entire power-generating areas within the interconnected system - or in case of high overload in a systcm area after sudden separation from the interconnected power system stagcd load shedding comcs into forcc as a limitation control measure to avoid a too great frequency drop, s. Figure 8. All partners of power \ystem\ habe already decades ago accepted this low fiequencg limiting measure as an urgent necessity to prevcnt the separation of power plants at f I 47,5 HI from the grid and due to this \ystem blackouts (VDN, 2003).

Stme 3

lu.:lier 10-159/,

4 8.5

Staue 4 fu-ther

‘520%

4

ZAP:,= 35 - 5c ”/, I=?

4a.c

Stria

47.5

C t z o n i e c t on o i p w c r s / c : ~ s i i s f r o m -he n e t w o r k

S n u L oowr o f power dnnt m * s

Fig. 8 5-stage plan for low l‘requency dependent load shedding regulations ofVDN (2003), UCTE

Therein the protection mechanism can e.g. be activated by delayed response 01’ installed overcurrent relays or through an increased sagging of thermally overstressed high-voltage power lines, which in turn on touching tree tops for instance cause disconnections by earth fault or short-circuit. Such a direct or indirect diwmnection through an overloaded transmission line can have in consequence the overloading and disconnection of further transmission lines and hence cause the separation of s> stem areas or even the break-down of the entire power system. Thus the blackout in ltaly (28 Sept. 2003) was caused by high-level power transits (UCTE, 2004: ETG, 2003). -

3. LIMITATION PROCEDURES REQUIRED FOR SYSTEM AREAS WITH HIGH POWER TRANSITS

To

prevent the protective disconnection of overloadcd transmission lines and consequently the weakening o f the transmission s j stem limitation procedures are requires a1 least in syslem areas with a high and thus specifically directed power transit, cf. Figurc 9. n

Active power flow Reactive power flaws

141

ALine voltage angles

IAg,

Voltages and

f

Frequency

Generator powers

IG,Q

Consumer loads

_Pv,Q

4

Transformer steppings Switching ”On/Off” S of lines

I

I

Acfuafion

50

Zero-load

7

Peak off load

I t Peak load

,,,L

L

Fig. 9 Load-dependcnt normal. borderlinc, and risk ranges of high-voltage lines and high-voltage transmission system => Minimum limitation ranges referring to voltage U and frequency fsee Fig. 5a

11

3. I 1,oadKurrying Capabiliw qf Transmission Lines

High- Voltage

The capabilitj of transmission power lines to carq load, depends on the one hand on weather effects such as outside temperature and wind speed. see Figures 10a and b. On the other hand. it is dependent on the topography "Ilere. we have lowland uith fields and meadows and. in consequence, welldefined conductoriground distances, and there are mountainous landscape with inaccessible forests and gorges and therefore highlq variable conductoriground distances.". The minimum vertical distances to treetops to be kept in the case of 380kV high-voltage power lines are according to EST1 (2003): 6.3 m for fruit-trees, and 5.3 m for othcr trccs, wherc normally nobody will climb up. According to the German standard DIN 48204 thermal limit values for the mavimum currentcarrying capacitq of typical conductors were established. in dependence of specified parameters for weather and power line conditions. see state values on grey background in Figure 10 (Hutte, 1988), as well as for compulsory conductoriground distances. These current limits are associated with corresponding thermal limit values for the various voltage levels. Ilo\+ever. as these limit values were cstablishcd fix a vcry wmmcry ambicnt tcmpcraturc of 35" C, the! may be cxcceded also stationwill, at least in winter months. cC Figure lob. The same i s true for the mid-span sag of transmission lines depending on load flow and weather conditions. Therein the sag is mainly influenced by the conductor temperature. In order that this temperature does not rise too high, the respective allowable maximum thermal load should not be exceeded if

an) possible. Thus the 380kV "San Rernardino" power line from Switzerland to Italy was "heated up" to ullne= 103" C, due to excessive north-south load flom (at Ion wind speed of vw = 0.6 mis and night air temperature of u,,, = 12" C). As a consequence. a greater mid-span sag up to Ah = 3 m ( ! ) occurred (ESTI, 2003). Independent from the general specifications, pointed out above concerning the load-carrq ing capability of high voltage transmission lines. each qyytem operator has to specify within his congestion management the maximum loads. which the individual transmission lines may bear depending on weather and landscape and based on this to which values the relevant monitoring and protection response criteria have seasonably to be set. These place- and time-variant limit \ alues should also be tahen as the bmis for parameteri~ing additional limitation control measures.

3.2 Two-Step Procedure For the activation of the respective necessarj limitation control measures, a staggered two-step procedure can be applied. This is possible because of the delayed thermal effect of power overload. In the first step, as soon as the allowable transmission load is exceeded, the fast bottleneck management gets promptly activated (Rrauner. 2004). This means that - starting out from the (n-1) calculations of reliability which have already bcen done the day before as part of the day-ahead congestion forecasting (Reyer and Weis, 2004: Zimmermann. et,al., 2001) - the transmission system operators concerned check which limitation control measures are adequate to reduce the excessive b) Decreasing outside temperature aumg

a) Increasing wind speed Vwlnd

uG

5

-

15

20

25 m/s 30

-19 0 10 20 30 35 10 'C 50 0,6 4, Fig. 10 Increase of the continuous current-carrying capacity of conductors, here: Al1St 265135 mm2 (DIN 48204) 10

Gins

-

12

Concerning the latter limitation control measure. uncritical consumers have to be shut down where possible, which means e.g. - in case of providing appropriate ripple control s> stems - temporary disconnections such as switching off washing machines and dish washers in households, reducing pumping and fan capacities in the supply engineering sector. and taking out of operation industrial plants with intermediate storage capacities, foreseen within the operation flow of production andlor manufacturing factories.

transmission load to the allowable reference power value and this as well as in a fast as well as supplyand cost-effective way. Iiowever should no countermeasures have been taken or measures taken not succeed within a specified yaiting time of e.g. Tu = 10 min, in the second step the automatic limitation control responds without any hrther delay.

3.3 Possible Limitation Control li4easures a) Load Flow Shgt In the case of highly different loaded transmission lines taking part in the transit, load flow shifting provides an effective solution and thus the possibility to reduce the exce\sive tran\mission load by means of cross regulators and corrective switching actions to increase the effective transmission impedance. As far as available also FACTS can be used for correqmnding load flow shifting rhe\e measures, already widely used within the framework of daq -ahead congestion forecasting. are especially effective when the special action is taken in a wide range and thus spreading control Lones.

The setting criteria for the required load shedding in each case have to be specilied a priori. This may simply be done in such a manner that overloaded transmission lines become sufficiently relieved by switching constant high amounts of load. However, such a simplified procedure to be always on the safe side. usually results in excessive load shedding. For this reason. it will he better to start out from calculations of load flow and (n-I) reliability carried out each time the day before as part of day-ahead congestion forecasting. Building up on this. the setting criteria for the respective necessarq load shedding can be specified online. varying in place and time e.g. by an hourly period split, depending on the predicted power transit and the respecti\ e network structure.

b) Reduction of Power Transits IT the excessive transmission load cannot be reduced sufficiently by load flow shifting, the only possibility that remains is to reduce the transit power correspondingly. Ihis should - if possible - be done on both sides. i.e. not only by the power importing netu orks, but also by the exporting networks. in the latter case through reducing the generator output concerned. The required import power can be reduced in various ways. taking as an example the power import for Italy; thus by: increasing the generation output of "highei -cost" pouer plant units which are not yet turned up to full output (if'possible). putting into operation quick-starting gas turbines (if possible). rising the power output of storage power stations in the case ofturbines operation (ifpossible). or stopping storage pumping operation (if being active) and going over to turbine operation, or last but not least by load reduction in the power importing network. All of these measures can - if applicable - be taken manually within the framework of f a t bottleneck management.

Figure 11 shows as an example the reduction of the transmission flows to Italy for the case of load reduction of 3 GW. I his value was chosen because in Italy up to 3 GMI of industrial supplies can be shed by remote control. An additional reason was that, at the Italian disturbance. in spitc of extremcly high import 3 GW power were still needed for the pumping operation during night time m ithin storage power stations. As to be seen in rigure 11 a) from data uritten in straight characters - in the case of load shedding as evenly shared as possible - the load flows on the 380kV transmission lines to France and Switzerland, decrease by AP = 400 MW each and, on the respcctive 220kV transmission lines. by AP zz 90MW each.

3.4 Automatic Limitation qf Power Transits In case the fast bottleneck management measures do not take effect at all or not in time. the only actions remaining for the automatic limitation control are the shut down of pumps operated in storage power stations - if possible - and otherwise or in addition regional load shedding, and this immediately after exceeding the foreseen waiting time of e.g. Tw = 10 min.

b) P , v p l m r i s!-eridrng in !\of+* l r d j a ) Load s h e d d i r g evenly sha-ed 1 7 Italy

Fig. 11

13

Load reduction on the transmission lines from France, Su itzerland. Austria and Slovcnia in casc of CAP\, = -3 CW load shed in Italy

O n the few - higher loaded - transmission lines to Austria and Slovenia, load tlou changes are up to 1.5 times as high. In Figure I1 b) the corresponding behaviour is shown - by the data writtcn in italics - when 3 CW of pumping capacity are switched off regionally. here in Northern Italy. As can be seen from the diagram no essential load flow change occurs. due to the specific longitudinal structure o f the Italian transmission network. As to be seen. the transmis5ion lines toward5 Frdnce are unloaded by about 10% more and in consequence the other transmission lines correspondingly less so. The calculations made are based on a detailed model ol' the European interconnected power system (Kurth and Welfonder. 2005).

4. SUMMARY 1 or economic reasons. power stations are mostly operated at the limits o f their respective normal operating range. As liberalization of the electrical energy market increases, high-voltagc transmission lines partlj are operated eien at the limit of their transmission capacity. In order that these capacities in cases of raised actual load, p o u e r plant outage or failure of transmission line -are not taken out o f service by overload protection or because of cascading fault?. it is nccessary to provide for limitation control procedures also o n the side o f the network. In the case of suddenly occurring transmission bottlenecks these procedures have the task to limit power transits superimposed to the normal interconncctcd systcm opcration to thc allowable maximum. This is done bj automatic decreasing of generator output in the exporting network section o f the intei connected powei systcm and by correspondingly increasing the generation of more expensive power units or if that is not posyible bq appropriate load shedding in the importing network section. Such mostly regional load shedding seems legitimate becauce by thih way the blackout of network sections or even the entire network system can be avoided. Then the (n-1)-reliability of normal system operation must not be impaired by superimposed high load transits. So in bottleneck situations. high load tranyits arc only possiblc to limitcd cxtcnt and thus only with reduced reliability. Due to the slow thermal effect of line overloads. the limitation control procedures - also considered absolutely necessary within the high-voltage transmission sqstem - need not respond spontaneously. but after a certain waiting timc of c.g. 1 a = 10 min. Up to this time it can be tried by means of fast bottleneck management, to activate appropriate countermeasures manually.

5. REFERENCES

,.Engpassmanagement und Intra-DayEnergiedustausch". 15.-16. Juni 2004, Miinchen. DIN 48204 ,,Leiterseile; Aluminium-Stahl-Seile" EST1 (2003). ..Berich1 des Eidgeniissischen SLarkstrominspektordtes zum Ereignis vom 28. September 2003 (Strompanne in ltalien und in schweizerischen Grenzregionen)". ETG (2002). Freileitungsnorm in neuer Gestalt EN 50341 (VDE 0210). Vortriige dcr ETG-Fachtagung vom 15. bis 16. Mai 2002 in Wiirzburg. VDE-Verlag. ETG (2003). ETG-Task-Force ,,Blackout", Nov. 2003. Iiiitte (19%). Taschenbuch dcr Technik: Elektrische Energietechnik. Band 3, Netze Springer-Verlag Berlin Heidelberg New York. Kaupa, H. und E Pokorny (2004). Nelztopologie und Abhilfe ,,Seilakt ohne Netz". Internationale Dreiliinder-Tagung D/A/CH 2004 ,,Engpassmanagement und Intra-Day-Energieaustausch. 15.16. Juni 2004, Miinchen. KieBling, F., P. Nefzger und U. Kaintzyk (2001). Freileitungen, Planung, Berechnung, Ausfihrung. Springerverlag. Kurth, M. and E. Welfonder (2005). Oscillation Behaviour of the Enlarged European Power System under Deregulated Energy Market Conditions. Control Engineering Practice, Special Section on Power plants and Power Systems Control, Volume 13, Issue 12, pp. 1455-1558;December 2005. Reyer, F. und 0. Weis (2004). Day-Ahead Congestion Forecast. Internationale Dreilander-Tagung D/A/CI I 2004 ,,Engpassmanagement und Intra-DayEnergieauslausch'. 15.-16. Juni 2004, Munchen. Sattinger. W and E. Welfonder (1993) Control Behaviour of Isolated Part Power Systems after Separation from the Interconnected Grid. 1111i PSCC. Aug 30 - Sep 4, 1993, Avignon, France. Schnug. A. and I,. Fleischer (1999). Components for Electric Europe - A chronicle of electric interDVG Deutsche connection in Germany. VerbundgesellschaAe.V., Heidelberg. UCTE (2004). Final Report of-the Investigation Committee on the 28 Septemher 2003 Blackout in Italy. U C I E (2005). http://www ucte.org/statistics/exchange/ e-default. asp VDI/VDE ( 1996). Richtlinie 3500 ,,Begrenzungsregelungen in konventionellen Damplkraftwerken-, September 1996. Transferred in IEC Tcchnical Report 62140-1 ,,Fossil-fired steam power stations - Part 1: Limiting controls", 2002. VDN (2003). Transmission Code 2003: ,,Network and System Rules of the German Trdnsnlission System Operators'.. VDN, Berlin, August 2003 Welfonder, E. (1992). Constrained Control Concepts in Power Plants and Power Systems for Avoiding Emergency Conditions. IFAC-Symposium Symposium on "Control of Power Plants and Power Systems", 9.-1 I. March, 1992, Munich, Germany. Welfonder, E. (2000) Unbundling and Safe Operation of Power Systems - Solutions for the Practice. IFAC Symposium on "Power Plants & Power Systems Control 2000", 26.-29. April 2000, Brussels. Ziniiiieimani. H (1990). Netzzus~iiiiieiibrclieaufgrund von Blindleistungs-Mangel oder -herschuss. 2. GMAETG Fachtdgung "Netzregelung", 22.-23. Mai 1990, Baden-Baden VDl Berichte 801, S 79-88. Zimmermann, D., K. lmhof and M. Emery (2001). Modular Day-Ahead Congestion Forecast as a first Step of a Congestion Management Process. 1st Balkan Power Conference, BPC 2001. Bled, SLOVENIA

Brauner, G (2004) Ursachen von Engpassen Internationale Dnelander-Tagung D/A/Cl-1 2004

14

6. ANNEX: LOAD DEPENDENT MID-SPAN SAG OF CONDUCTOR LINES In the following the correlation between loading, heat-up and sag of conductor lines are pointed out with the example of a simplified assessment. The study is done with the example of the 380-kV power linc "San-Bcrnardino", which was thc sccond to break down due to overload during the power failure in Italy. According to the Swiss fault report (ESTI, 2003) the lines concerned consists of double-bundle conductors and was loaded with I = 2703 A after the preceeding failure of the first power line called Lukmani er . Ihe necessary parameters and state variables of power linesare compiled in Tables l a and 2. The data - as far as not already published in ESTI (2003) - were put at our disposal by &!ktrzzrtutJGescllschaft I,azifenburg (Ctl). the operator of the high-voltage power line. and by the Lumpi Company (A), the high-voltage power line manufacturer. AI

Equating thc power output relations (1) and (3) and solving - taking eq. 2 into account the power line temperature results in general form to ~

1 + l 2 -R,,,

(l-pth 20°C) n (4) 1 anlrd + 1 2 - R L 2 0 Bth n and with the data according to Table l a to QLllJ,n,Stgt = 84" c. By substituting 9, in eq. 2 , the power loss per conductor and kilometre results to PLloSs= 269.5 kWikm.

annd9,

9,

=

h) Determination of the surface coefJicient The authors have determined the surface coefficient - to be given in eq. 4 - by equating eqs. 1 and 2 and wlving to

Heat-Up of Conductor(s)

a) Calculation Procedure

The power losses occurred for each double conductor line along the high-voltage power line of the length 1 are

K ' , ( 9 L ) = R ' , ( 9 L = 2 0 0 C ) ~ [ 1 + ~ t ~ ( 9 L - 2 0 0 C(2). )]

For each conductor line. this power loss has to be dissipaled 10 [he environmenl in the Corm ol' waste heat

84" C for the San Bernardino power line, cf. Table 1 .

2703 A

horizontal distance

I between towers

current resistance (at 9 I T =20"C) 0.0036 liK resistance (jth increase as a function of temperature conductor 9, Result of eq. 4 temperature ambient tempcraturc

0.0036 l/K

Table 1:

d

30.6 mm

22.4 mm

n

2

1

W

a

I

I

vertical differcnce of b tower height I conductor cross IA section modulus ol'elasticity E

1-

conductor diameter wires per cond 11 cto r wind speed surface coefficient

Based on the example case referring to the allowable maximum thermal load (Hulle. 1998) considered in Figure 10. taken as a basis in that figure, a surface coefficient of a - 19.6 W/(m2K) results. when substituting the state variables and parameters of the power line according to I able 1b. This value was taken as a basis for the above calculation of the power line temperature 9LlUn,Sts -

conductor weight per meter weightlmass conversion factor thermal conductor expansion factor conductor line tcmperature

0,6 mls I 0.6 m l s 19.6 W/(m2K) (see eq. 5)

Table 2:

Electrical and thermal conductor line parameters and state variables

15

393 m

I

100 m

I

550 mm'l 57000 N/mm2

m

1.514 kg/m

E

9.81 Nikg

cth

2.3,10-5K-'

9 L2

103OC

Mechanical conductor line parameters and state variables

c) Comparing Consideralion The h m p i Co. determined a power line temperature of 9 , "mp, = 103" C bq special calculation program

(ESTI. 2003). taking into account further influencing parameters. which do mainly actuate variables concerning heat transfer. Thus in the calculation, for the emission coefficient that depends on the extent of darkening on the wire surface, a mean value of y = 0.55 (for an oxidized conductor of average dirtiness) was assumed (for new. shiny conductor lines the value that holds is y = 0.09 and for blackened conductors exposed to weather for many qears the value is y = 0.9). By correspondingly increasing this - not quite exactly speciliable coefficient. the values determined under eqs. 5 and 4 would result as well. The reason is that the effects of the other parameters. such as wind direction and solar radiation. can be neglected in the considered case of predominantly low w ind speed (w = 0.6 mis) and at night (3 a.m.). A2

Increased Mid-Span Sag of Conduclov Lines

The following shows, again with the example of simplified mathematical relations. based on ETG (2002) and KieDling (200 I), how the higher sag of a conductor line Af, - increasing by rising conductor temperature 9, - can be estimated. This estimation i\ b a x d on the power line i conductor temperature 9, = 103" C calculated by L u m p and on the data in Table 2. Regarding the different line clearance from the ground, the conductor length y ields to

dm=

a,, = 405.1 m (6). This corresponds to a ground incline of b cp = arctg - = 15.9". a I he horizontal tensile force H2 at 9,, = 103" C can be calculated by means of the conductor state equation according to KieBling (2001). eq. 14.36. In standardired form with h, = H,/H1 this equation results to h2-1 = B/h?-(B+C) (7) a) Variant sag of a conductor line

f

=

I-(],,

IY,

W,

Therein the belonging coefficients are: E A (a . m .g) EA B= .c=--c th (9 L2 -'Ll) 24H: H1 By iterative solution of eq. 7 the tensile force H2 results for 9,, = 103" C to 1H2 = h2 HI = 0.885 . 17355 = 15363 N According to KielJling (2001), eq. 14.9. the midspan sag ofthe conductor results b)

and. for the tensile forces HI and H2, amounts to fS2 = 19.87m at 9,, = 40°C fs 1 = 17.59 m at 9, = 103" C Thus the increa5e of sag amounts to AfS2,,ISt3t = 2.28 m In comparison to this, the increased mid-span sag of the conductor line determined by EGL by means of a detailed calculation program according to ESTI (2003) amounts to: Afs2 IIEGL = 2-96 m The difference of good 20 per ccnt between the t u o calculations are mainly caused b j the simplified assumptions made by the authors: parabolic sag o f a conductor line, calculation of the conductor length as a function of the different line clearance from the ground according to simplified Pythagorean relation, regarding of only one conductor between two towers. i.e. neglecting the interferences by neighboured conductor sections, neglect of possible thermal deformations cffects.

A3

Resume

The objective of the above simplified but therefore easily understandable calculations is on the one hand to demonstrate the essential physical correlations, on the other hand, to point out the high parameter dependence of the individual results.

H, ...-

a)

..--

' ---. '

ILi Llrnit load, / -

tower " i f ? "

b) Security distance of 380-kV lines: tower

",'.

1.0 = 6,3 rn :o : ~ L I L trees = 5,3m :o other :lees

Fig. L1: Basic illustration of the sag of conductor lines

16

Copyright 0Power Plants and Power Systems Control. Kananaskis, Canada 2006

PUBLlCATlON$ SISO EXTENDED PREDICTIVE CONTROL - FORMULATION AND ROBUST ANALYSIS Ma'moun Abu-Ayyad and Rickey Dubay Department of Mechanical Engineering The University of New Brimswick Fredericton, New Brunswick, Canada

Manioun.AhuAyyad~unb.ca,[email protected]

Abstract: A new predictive controller is developed that represents a significant change from conventional model predictive control (MPC). The method termed extended predictive control (EPC) uses one tuning parameter, the condition number (CN) of the system matrix to provide a easy-to-follow tuning procedure. The control performance of EPC is compared with the original move suppressed and recently derived shifted predictivc controllers, with improved rcsults. Copyright 02006 IFAC Keywords: Modeling, Simulation, Control Methods, and Real-Time Operation.

to industrial plants. One of the major problems of the existing MPC controllers is the limitation on the use of nu >2 which could lead to undesirable closed loop response oscillations in the plant output. In order to overcome the problem of providing fast closed loop responses, larger values of nLican be used.

1. INTRODUCTION

Several algorithms of model predictive control (MPC) havc been established as bcing important and useful methods of advanced control in industry (Cutler, 1980; Gupta, 1987; Morari, 1993). These applications of MPC in industry can be found in (Garcia, 1987; Meadows, 1997; Morari, 1993). The reason of their popularity in the industrial and academic world is that MPC offers a good relationship between simplicity and performance.

Previous investigations have attempted to improve thc closcd loop rcsponsc by focusing on lowcring thc CN of the system matrix without considering the effect of the determinant of the system matrix (Dubay, 2004; Shridhar et al., 1997). Also, lowering of the CN in these investigations did not account for the influence of the control horizon. This work focuses on developing a new control strategy that can be applied to control a wide range of processes such as servo valve control circuits requiring high-speed in power plant systems.

Tuning of constrained and unconstrained singleinput single-output (SISO) and multi-input multioutput (MIMO) MPC have been addressed by an array of researches. Cutler proposed a systematic trial-and-error move suppression tuning procedure (Cutler, 1980). Simplified Predictive Control (SPC) was proposed by (Gupta, 1987) in which the error is minimized at one point on the prediction horizon and only one control move is calculated. The drawback of SPC is that by restricting the control h01'kon to one the closed-loop response can become unstable if the number of unstable modes in the process is greater than one.

2. EXTENDED PREDICTIVE CONTROL 2.1 Initial Consideration

The general predictive control law is based on the solution of a quadratic cost function which is formulated as a least-squares problem with weighting factors on the manipulated variable moves (Dougherty, 2003)

An analytical expression for move suppression coefficient 2 was derived by Shridhar et al. (1997). The proposed method by Shridhar and Cooper still involve an iterative procedure to determine the optimal value of the CN. The most recent work on tuning MPC was done by Dubay et al. (2004). Here, the second column of the dynamic matrix A is shifted downwards by m>l, where rn is thc shifting factor, followed by the same for subsequent columns. Beside the restriction of using n , = 2, shifted DMC demands very good understanding for its application

min J = [e - AAu]' [e - AAu]+ AuTWo,(/ Au ( I ) ALI

In Ey. (I), e is the vector of tracking difference between the reference trajectory and the prediction of the process, A is the dynamic matrix, Au is the vector of manipulatcd variablc movcs, and thc paramctcr W,,," = LI, where A is move suppression coefficient. 17

The closed form solution of the unconstrained MPC law without weighting on A'A is (Marchetti, 2003)

3. ANAT,YTICAI, OVERVIEW

In this section, a mathematical formulation for the determinant and the CN for A] and A2 as a function of n,, and 1 are presented for suppressed MPC and EPC. It is assumed that the plant to be controlled is a first order plus dead time (FOPDT) model with a process gain K,,, time constant t and dead time 0, with a transfer function of the form

2.2 Extended Move Suppression

The formulation of the new control strategy begins by introducing a ncw wcighting movc supprcssion matrix W,,,, of the form

r o

-

41

-

The system matrix ArA in MPC can be approximatcd as follows (Shridhar, 1997) By introducing the error vector 2 = e - AAu in Eq. ( I ) , the general form of the cost function with W,,,,, is

A'A=K;

a,)= P - k

a,,= A , =a,, ~ =... Furthermore, it is necessary to reduce the number of move suppression coefficients in Eq. (3) that are necded to be tuned. Another stipulation is that the diagonal elements of W,,,,, should have the same increasing effect on I A'A+ W,,,,, I. At this stage, the EPC structure of the W,,,,, matrix is designed to have 3 parameters R I , R2 and d for any (nu 1 3). Thc W,,,. matrix using these parameters is now termed WkIMS where the subscript EMS is extended inove suppression. Consider a control horizon of n,,=5, the weighting matrix WE,Ms is

0

-R,A

-A

-R,A

-A

a21

a22

.

.

... .

where

The paramctcr P in Eq.(4) is thc prediction horizon. To achieve fast response with minimal oscillations, Au must be evaluated from a well conditioned systcm matrix. In order to increase M'A+W,,,J to obtain lower values of the CN, it is assumed that the even elements of the first row of W,,,,. are equal.

[

l

1

32 --+3--(z 2T

1

2

.

+ J .)

i,j= 1,2;..,n, (8)

The parameter k is the discrete dead time calculated as k=O/T+I, and T is the sampling time. Marchetti et al. (2003) showed that the AA ' matrix is singular when n,>3. Therefore, it is assumed that a5 the prediction horimn P-m, q I E q2E . .. . 3.1 Move Suppressed MPC

A general expression is needed for IA,I as a function of 1, nu and a, where a is the first element of A'A ( a = K : a , , ) . T h e A I matrixfornL,=2is

L

J

The condition number can be computed by dividing the largest singular value over the smallest singular value. 'lhen,y - g + l (where y is the CN). As 4

2-q

-

/z

yA, + 1 . This is impractical as large values

of 1 can result in very undesirable sluggish plant dynamic responses, even though

For clarity, define A, = A'A+W,,l,,, A2 = AIA+W,,,, and A3 = A'A+WbM5 which will be all used in the following section.

yA,is unity.

3.2 Neb!Move Suppressed MPC The analysis is repeated for the new extended move suppression matrix as shown in Eq. (3).

18

2a 1 . As /1 >a,yA, - 1 . This R implies that unity CN can be reached faster than the old structure. The general expressions for the determinant and CN for move suppressed MPC and EPC are given in Table 1. Similarly,

rA,

-

results shown in Fig. 2 were obtained from the dynamic matrix of a FOPDT plant with unity gain, time constant and dead time. Figure 2 shows that increasing R, while maintaining a constant value of1, a relatively lower CN and higher determinant can be achieved simultaneously. ',lo[,\!'

'

Table 1. General form of determinant and condition number equations.

'

'

'

'

'

'

'

I

h

Figure 1 shows the approximate and exact CN of A, as 1 varies from 0.1 to I . The result5 were obtained from a simulation for Process 1 (Shndhar er al. 1997)

GI ($1 =

e

-50r

(1 1)

(1 50s + 1)(25s+ 1)

Fig, 2. Importance of the weight factor Rl on the condition number and determinant of matrix A'A.

Exact Table 1

3. EPC ( 4 2 3 )

The determinant and CN of A3 will be calculated in terms of (2, R,, R2)as

01

02

03

04

05

06

07

08

09

1

Move suppression coefficient, h

yA,can be improvcd by eliminating the second

Fig. 1. The exact and approximate condition number of ArA based on Eq. (7) and General Form of Table 1 for small values of A.

element of its first row in bq. (13) by assuming RI1=a. Also, define R2 as R2=rRI,Eq. (13) becomes

The plots based on Eq. (7) deviate from the exact plots for highcr valucs of n?,. Howevcr, the plots based on the general form of the newly developed CN equations in Table I show good agreement with the exact plots. The tuning parameters P=54 and T= 16 arc used in thc simulation.

yA3is obtained by multiplying the no1111

3.3 The Structure ofEPC

norm of (A,>l. Consider RI=lO,Eq. (15)becomes

Plot yn, vs r using the derived expression and

yA4= l + . \ / r 2 -2v+1.81

(16)

Figure 3 shows the relationship between

superimpose this result with yruic,. From these plots, select the value of r that exists on the overlapped regions of the plots.

yA, and r,

uung the dynamic rnalrix of Proces5 1 and Eq. (1 6).

y[

3)

25-

T

Upto 1502 2"

2

-

t

,

5. SISO SIMULATION CONTROL

UD to

2172

A computer simulation was performed to compare

the propoyed method with the move suppressed and shifted MPC The process used tor compdrisons involved time delay and inverse response behavior (Shridhar et a1 1997)

i5-

n =3 in

G, (s) = "1

-1

"

,

?

5

4

A

7

6

I

and

4. GENERAL TUNING STRATEGY FOR SISO EPC

1

-1

Rl 1

Control Scheme

Tun. Par.

2 MPC rn MPC EPC

I =4 m=21

I

1 r = 3

IA,,,,,

I

Y?i , } , [A,,], \ and 1

B2 =drag{Bzl,B,2,..., B , , )

.

Consider the following decentralized output feedback controller for the system given in (2): L(t)=&,

x,,(t)+ B,, Y , W

Hence, the overall extended system can be rewritten in a compact form as follows. ;(t)=A

(3)

u,(l)=C,, x , , ( t ) + D , , Y ,U )

where x , , ( t ) t W is the state of the ith-local controller, n,, is a specified dimension, and

where

(6)

=0,

- - -

- - -

A,, = A + B , K , C , ,

B,, =B, +B,K,,D,,,

C,,=C, +D,,K,Cb,

D,,=D,, +D,,K,D>,

- . -

are constant matrices to be determined during the actual design step. In this paper, the design procedure deals with nonzero D,, , A,,, B,, , C , , , D,, , i=1,2;.., N

however, it can be set to zero, i.e., D,, ith-local is strictly proper controller.

, x(t)+B,,w(z)

~ (= tC ) ' , x ( t ) +D,,w ( t )

- - .

Considcr the following dcsign approach whcre the controller strategy in (3) internally stabilizes the closed-loop of the transfer function r,,,( 3 ) from w to z and moreover satisfies a certain prescribed disturbance attenuation level y > o , i e , IT,,, (s)Il= < y

so that the

c

In the following, the design procedure assumes that the system in (2) is stabilizable with the same prescribed disturbance attenuation level y via a centralized H , controller of dimension equal to or greater than n, := ~ ~ l inn which ~ T each controller input U, is determined by the corresponding measured outputs y , , 1 5 J 5 N . The significance of

v,,L8, PG 8

w, An n,,th-order

this assumption lies on the fact that the decentralized controllers cannot achieve better performances than that of centralized controllers. In this paper, the centralized fIz controller is used for the initial boundary value in the two-stage iterative matrix inequality optimization method.

Fig. 1. General structure of the ith-generator together with the PSS in the multimachine power system. After augmenting the decentralized controller (3) in the system, the state space equation for ith-extended subsystem will have the following form

- - -

:,(t)= (4+B,, K , C > O % ( f )

+

6, +B,, K , C , , ) w , ( t ) + Z k , x , W

2 2 Decentralized H , outputfeedback controller design using parameterized continuation method

(4)

J*f Y

x

Y

z, ( t ) = ( C , +, D I 2 K , ~

-

c ,Ox, ( t ) + ( D ,

I,

x

+ D,:, K , J),,

M ,( t ) Designing a decentralized H , output feedback controller for the system is equivalent to that of finding the matrix K,] that satisfies an H , norm bound condition on the closed-loop transfer function T,,, ( 7 ) = C , , ( ~ I - A , , ) B ,+D,, , from disturbance w to measured output z , i e IT,,^ (&)I], < y (for a given scalar constant y >O ) Moreover, the transfer functions I,,, (s) must be stable (Gahinet & Apkanan, 1994) The following proposition is instrumental in establishing the cxrstcnce o f decentralized control strategy (3) for the system (2)

where ? , ( T I = [ x i ( t ) x:, (t)f is the augmented state variable for the ith-subsystem and

Moreover, the overall extended system equation for the system can be rewritten in one state-space equation form as x(t)=

(A +B,K,

Proposition. The system (2) is stabilizable with the disturbance attenuation level y > o via a decentralized controller (3) composed of N n,, - dimensional local

c,);(t)+ (B, +B,K,,C,)w(t)

z(t)=(?, +D,,K,,?,

)x(l)+(;,,

t f i , , K , , D , ,) w ( t )

(5)

controllers if there exist a matrix K,, and a positivedefinite matrix 6 that satisfy the following matrix inequality:

where

25

( 2 ) Compute PICthat satisfies

-

@((I

2-1, ) K F + 3-kK

-

, Pi, . Ak )

0

End do

Remark 1: If the problem in Step-I of the above Algorithm fails to be feasible, then the step-length should be changed in order to compute K , , ~ that satisfies 6 ( K r j h,FA-,,A,l as (Abu-Ayyad, 2006)

:

-

Equation (8) indicates that the CN of A3 is independent of the tuning variables P, T and other parametcrs z, k and Kp. Using EPC, the modified equation for the manipulated variable moves Eq. (2) becomes

Au = (A3)-'A T e where R, and R2 are the weighting factors It was shown (Abu-Ayyad, 2006) that the CN 0fA'A can be furthcr improved by eliminating thc sccond clcmcnt Thcreforc, iL of thc first row by assuming R,/Z= ~2

(9)

3. EFFECT OF R, ON EPC The condition number o r A j using n , = 3 is (AbuAyyad, 2006)

is no longer a tuning parameter Also, define the weighting factor R2 as R2=rR, Then, Eq (4) becomes

It is to be noted that the matrix A3 becomes a singular matrix for the special case of R,-m.

IA31 is calculated as follows

36

This case of R* m is to be avoided since the EPC structure is valid only for nci = 3. A simulation was performed using Process 1 (Shridhar, 1997) in order to demonstrate as an example the effect of using a relatively large value of R I which was chosen arbitrarily. Process 1 has a relatively large dead time and has a transfcr function of the form p

G, (s) =

R, = 15

s

(150s + 1)(25s+ 1)

(13) 51

I -

The results shown in Figs. 1 and 2 using Eq. (8) illustrate the contours of yAd(extracted from a 3-D plot) [or n,,= {3,4} with P = 54 and T = 16. The plot in Fig. 1 illustrates that yAs at a specific r is independent of RI for n,, = 3. In Fig. 2 the general result is that RI decreases as r increases in order to maintain the same value of YA:, . This trend is the same [or higher nuvalues. , ,y

0

1

2

3

1

1

5

6

i

R

S

r

Fig. 3. The relationship between Process 1 ( n , = 3)

yA,

and r for

Figure 3 illustrates the exact and approximate yA3for Process 1 using Eqs. 8 and 10 respectively, with the overlapping region starting at r 2.7. Figure 4 illustratcs the closcd-loop responses for RI = 15 and R I = 100 with n,, values varying from 3 to 7 using r = 3.6 from (Fig. 3) and the same P and T values The noted result i s that R I does not affect the closed-loop response for nu = 3 since the overlapping region of YA, is independent of Ri as shown in Fig. 3. However, minor differences in transient behavior occur for higher n,,values.

contour lines

, 7 8 2

14

........

12

r

Fig. 1. A contour plot of y A I for different values of R , and r on Process 1 (nL,= 3)

I

I / 0

500

,.;:

141

,,y

1000

,500

Timc (scc)

contour lines 3'

( 0 1

I

...., _--

----

._>.l._,_.:l__.-.

PO8

R, = 100

$0 6

m

mod 02 500

3000

1500

Time (sec)

Fig. 4. The effect of R, on the closed loop response for large and small values of R , for Process 1 The closed-loop response for nu = 3 illustrates zero overshoot since yAdat nu= 3 has the smallest value as compared to higher n , as shown in Table 1. The differences in y A I in Table 1 can be explained using Fig. 5 which shows that YA3 gets larger a5 RI increases at a specific r.

nzr

R,=15 R,=100

3 3.8 3.82

4 76.7 444.2

5 6 108.9 133.3 730.5 897.6

7 161.9 1092

Table 1 . CN for different n,, values - Process 1

37

4. THE EFFECR OF Y ON THE CLOSED-LOOP RESPONSE

EPC uses the stable yAJregion directly as only tuning mechanism in order to obtain a desired closed-loop response. In this section the rclation between Y and the closed-loop performance parameters such as percent overshoot ,8 and settling time Ts is presented. Using incremental values of Y starting ~ 2 . from 5 Fig. 3, which is the starting point of the overlapping region, closed-loop results for Process 1 are shown in Fig. 6 using the previous P and T values. Also, a decrease in r values causes the manipulated variables to be more aggressive with an underdamped closed-loop response. Figure 7 shows four regions for the CN and its relation to the process closed-loop performance for a higher value ofn,,= 5. The division or the yA1 into four regions is very important and useful for tuning the closed-loop response in order to achieve various control performance settings.

-4

Fig. 7 . The relationship between yA?and the closedloop performance (n,,= 5 )

A more detailed set of relations can be obtained as itemized in Table 2 for PZ, = 5 as the example. The results in Table 2 can be generated for any n , >2, showing a direct relationship between closed-loop specifications and r. The % overshoot parameter is and the settling time s'7 in sec.

; Ts

464

1189

560

624

656

Table 2. Closed-loop specifications for different values of Y - Process 1 ( M , = 5 ) Regarding the general form of the AJ matrix in Eq. (S), as the tuning parameter r approaches a,the invcrse matrix ofA3 becomes Fig. 5. The relationship between Process 1 (nu= 4)

?A3

and

I*

a

260

460

600

8bO

loo0

1MO

for

r 1

1%

Y

O ... O

1

This form of (A3)-' which is now a scalar quantity demonstrates that EPC and SPC (Guptd, 1987) algorithms become the same in terms of the number of manipulated variable being one. An important feature of this result is that EPC produces the same closed-loop response at large r values for any n , with zero overshoot and without sacrificing the rise time. This is not the case [or other MPC algorithms where increasing the tuning parameter leads to an increasingly sluggish closed-loop response.

l

Time (sec)

Fig. 6. The responses for different values of Process 1 ( n u = 5)

1

for

38

5. EPC VERSUS SPC

EPC, while the point D=3S i s chosen for SPC. The responses arc almost identical while EPC reaching the setpoint faster by 100 sec. Simulation results for Process 3 are shown in Fig. 9 where the values of P=50 and T=O.1 were used in the simulation (Kember et al. 2003). The tuning parameters ~ 2 . 4 5 , R1=10 and n,=4 are used for EPC, while the point D=6 is chosen for SPC. EPC shows a better responsc comparing with that of SPC reaching the setpoint in a shorter time.

Control simulation comparison between EPC and SPC was carried out since the latter has the best conditionality of having a CN of unity. A higherorder process with sluggish open-loop dynamics (Shridhar, 1997) and first-order process are used for comparing the closed-loop responses. The processes are

6. DC MOTOR SPEED CONTROL

A practical application of EPC was carried out on an electric DC motor coupled with a tachogenerator speed transducer. The performance of the EPC method was compared to move suppressed MPC. The closed-loop results are experimental studies on the DC motor system.

Process 3

1 G, (s)= s+l

The dynamic matrix A was obtained from an open loop test of the motor. Using RI=10 and following the EPC tuning procedure (Abu-Ayyad, 2006), closed-loop tests were conducted using 5 values of r equally spaced starting just where the overlapping region starts. Using thcsc r values, closed-loop control using EPC was conducted on the DC motor as shown in Fig. 10.

0-

I

0

1400-

100

200

400

300

5W

600

700

Time (sec)

1200.

i

\

Fig. 8. Performance comparison of EPC and SPC controller for Process 2.

1

05

2

15

25

i

0

i

2

'2 n 125

S

.. is an upward convex function, then (1 2) is satisfied:

For this typc of customers, the auctioncer estimates their satisfaction less than real values Therefore, they get rewdrd more than necessary to be paid to them If thc other customcr's g,, is a downward convex function, then ( I 3 ) IS satisfied:

If market price is p, initial power demand rd,, and reduced power demand then the reward wdl given to customer] is defined as ( 5 ) in this model

We define a degree of satisfaction of customer J as 1); (p,r,w), and also define ,q, as a satisfaction function of thc reward at a market pricc p In this case.

For this type of customers, the auctioneer estimates their satisfaction more than real values. Therefore, they will not get enough reward to maintain the degree of satisfaction. 3 . SATISFACTION SPACE We have developed a satisfaction space technology that solves the problem stated in the previous chapter.

3. I Dgfinition qf Evuluation Function Where, g,;' is an inverse function of g,,, L'd,(p,r) is a satisfaction function with regards to the power quantity r under the conditions of the market price p, which is defined as (8).

Supplier's and consumer's evaluation functions are defined as satisfaction functions like (14) and (15) respectively.

The following equation i s derived in the same way: Where, p is a market price, r i , supplier i's power supply, and w,,the amount of reward to pay. On the other hand, 7'4 is customerj's power demand, and wd, the amount of reward to be paid. Substituting (7) and (9) for (4), we get (10): Moreover, a total evaluation function of the coopcrative power trading systcm is defincd as (I 6),

Mapping ( 1 0) using g,, ( 1 I ) is derived as a constraint of this model. Where a, and bJ are weights of suppliers and coiisuincrs rcspccti vely.

54

3.2 Trading Procedure Dealings are done with the cooperative power trading system according to the following processes:

Price Decision Process 1) Suppliers and customers submit their bids for initial power trading quantities rrrlst,rdllsrand expected unit prices p.,,,p6,/respectively. 2 ) The auctioneer decides a market price p1 based on the values of the bidding. In our simulation, (1 7) is uscd to determine the pricc p , .

----____

PPP2

Power -

Id

Fig. 2. Satisfaction Space. Power ieduction is caiiied out i n the following sequences Customers present some trading points ( { ( / " d j k W d k ) I ydk< rdj2nd, "Vdrk'O, k-1, 2, 1) that they can make deals as shown in Fig 2. Using this presented information, power reduction is formulated into a combinatorial problem that determines the best power reduction plan under the condition of minimizing the total amount of rewards and maintaining thc degree of satisfaction of each customer.

Power Reduction Process 1) Getting the market price pl, suppliers and customers submit their second bids for expected ,,~ power trading quantities r,r2nd,r ~ / 2respectively 2 ) The auctioneer makes a power reduction plan to balancc thc amount of powcr supply and demand by means of evaluation functions of customers. In this process, each customer's rd and reward wd, are determined by solving the following constrained minimization problem to maintain the degree of satisfaction of every customer: Objective function:

This method can be applied to the customers whose evaluation functions can't be estimated beforehand, and it is also possible to collect the trading information of the customers necessary for estimating their evaluation functions. 4. EXPERIMENTAL RESULTS

subject to

Some simulations were carried out to examine the validity of the proposed technique. 4. I Evaluation Functions of Suppliers and Customers

Supplier's evaluation function is shown in ( 2 3 ) ,

3 ) Quantity of supplying power rsr that each supplicr actually supplies is dctermincd by (21):

Quantity of reward w,, that each supplier actually pays is dctermincd by (22):

where f is sensitivity to the power at the time when demand quantity goes over tbe optimal operating point, e, i s sensitivity to the price, and a is a satisfaction conversion factor of reward into the degree of satisfaction of the electric power.

3.3 Comhinatorial Optimization Technique for Power Reduction

As an example, the following three kinds of functions were used as the evaluation functions of customers:

You must use some information of customers to estimate the customer's evaluation functions This section dcscribcs a mcthod to make an clcctric powcr reduction plan under the conditions that sufficient infomiation can't be obtained to estimate the c ustomcrs ' cv al uat I on funct I ons

where (J&I, r ) is a satisfaction function with regards

55

to the power quantity r under the conditions of the market pricep, and it is defined as (27). U&,r)=a-bexp

(-cr)-dr-e,-

P- Pd,

On the other hand, the proposed method can make a proper power reduction plan for all customers. This means that the new method can handle properly various kinds of customers.

(27)

p4 a, b, c and d are parameters on the electric power, and e, is sensitivity to the price. Real values of the parameters a, b, c and d are estimated by means of Newton-Raphson method using initial values established in advance and the bid information of every customer.

4.2 Simulation I All customers’ evaluation functions are assumed to be known in this simulation. Comparative experiments were carried out for the previous model and the proposcd model to verify their abilities of making suitable power reduction plans. “Suitable” means that the auctioneer could reduce the power demand while inaiiitaiiiing the degree of satisfaction of customers Total power demand is reduced to the total power supply, and each customer’s demand is reduced in proportion to the amount of initial demand. Reward is determined by the calculation method of each model. Detail data arc shown in the following: Total number of customers: 90 (Linear type:30 , Logarithmic type:30 , Exponential type:30) Initial power demand: l00KW f 10% (determined by uniform random numbers) Initial parameters: a = b = 2.624, c = 0.00882, d = 0.00616 Pricing scnsitivity parameter: el =0.005 Reward sensitivity parameter: a=OS I .0 (determined by uniform random numbers) Total number of suppliers: 5 Initial power supply: IOOOKW i 10% (determined by uniform random numbers) Sensitivity parameter for excess over optimal operating point:p6 Pricing sensitivity parameter: e, =0.00 I 10) Reward sensitivity parameter: a=0.5 1.0 (determined by uniform random numbers)

-

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4.3 Simulation 2 For 100 customers and 5 suppliers, we have mdde power reduction plans using the combinatonal optimization technique and checked the efficiency of the market control and the necessary information of the customers I ) Total number of customers: 100 (Linear type 30 , Logarithmic type 60 , Exponential type 10) 2) Total number of suppliers 5 Calculating the market price and the amount of each expected power supply and demand, making power reduction plans were tried 100 times for each case, which corresponds to the number of trading points (from 1 to 4) that customers should present to the auctioneer. Every customer presented the specified number of trading points that were made at random at every time of the 100 trials The power reduction rate of this scenario is shown in Table 2 Excess amount of power supply and maximum error ratc are shown in Table 3 If the nuinbei of the trading points 15 two, five times out of 100 could not reduce power less than the total expected power supply If the number of trading points is more than three, all 100 times could reduce power less than the total expected power supply Generally, the more the number of the trading points presented hy customer? increase?, the more the burdens of the customers increase Therefore, considering the burden of the customers and stable market control, it is necessary to make power reduction plans with the necessary and sufficient amount of information The values of the total evaluation function increase with the number of trading points as shown in Table 4. This means that the power reduction plans do not always reach a perfect equilibrium point, but they are Table 2 Power reduction rate in the simulation 2

Table 1 shows the degree of satisfaction of every customer. This table shows that the previous model can deal with correctly only the type of customer IL1.

Vajl (Linear) C’d~2(Logarithmic)

VG? (Fxponential)

Before reducing

Previous method

Proposed method

0955 0 957 0 964

0955 1 194 0 887

0955 0957 0 964

Total expected power supply

Reduction ratc

9717404kW

7300941kW

24 8%

Table 3 Excess amount of suuulv and error rate

Table I Change of satisfaction of each customer Type of customers

Total expected power demand

Number of trdding points 1 2

3 4

56

Excess

amount of power supply 795 70’3 103.410 0 0

Maximum error rate 10 9 Yo 1.41 ‘% 0% 0%

Table 4 The values of the total evaluation function Number o f trading points

Before reducing

1 2 3 4

0 223 0 223 0 223 0 223

6. CONCLUSIONS

Average of

This paper proposed a cooperative power trading system that could cope with various kinds of customers by modeling them on a satisfaction space In the cooperative power trading system, it is not necessary to find the price that supply corresponds with demand of power because there is adjustment by rewards If it tries to find the price at which supply and demand correspond strictly, it will cause a price jump since price elasticity of electnc power is low.

100 trials 0 709 0 820 0 912 0 945

very close to the equihbrium point Moreover, increasing of the total evaluation function implies that the trading system can make efficient reduction plans.

This system can be applied to customers whose evaluation functions cannot be estiirrakcl beforehand. When evaluation functions of consumers can't be cstimatcd, auctioneer makcs a dcalings plan by untying a combination problem based on the information bid by consumers. The most efficient power reduction point is chosen one by one for every consumer, and this simulation is searched for a solution using the maximum steep slope method for performing electric power reduction gradually.

5. NETWORK MODEL We have developed a network model for the proposed cooperative power trading system that works on the Internet. A schematic view of the nctwork model is shown in Fig. 3. The proposed system is built on a Web server, and trading data are managed in the form of XML (extensible Markup Language) A customer inputs bid information through the Web browser The inputted information is processed on the Web server and stored in the form of XML The proposed system conducts electric power dealings based on this stored XML information

LIf-

-

view HTML/JSP

REFERENCES Dy-Liacco, T. E. (2002). Control centers are here to stay. IEEE Comput. Appl. Power, vol. 15, pp.1823. Matsumoto K., N. Mori, M. Kitayama and Y . Izui, (2001). An interactive demand side management system using utility functions. In: Proc. International Conference on Intelligent System Application to Power Systems (Isill> ZOOl), pp.197-201, Budapest, Hungary. Matsumoto K., T. Maruo, N. Mori, M. Kitayama and Y. Izui. (2003). A communication network model of electric power trading systems using Web services. In: Proc. IEEE Bologna Power Tech Conference, Paper number #49, Bologna, Italy. Stoft S. (2002). Power Syslem Economics: Designing Mai4ets for Electricity. Wiley,. New York. Vaahedi E. and M. Shahidehpour (2004). Decision support tools in restructured electricity systems: an overview. IEEE Trans. Power Systems, vol. 19, no. 4, pp. 1999-2005. Vojdani A. F. (2003). Tools for real-time business integration and collaboration. IEEE l>ans. Power Systems, vol. 18, no. 2, pp.555-562.

Power Trading System \

- Controller -

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As a future task, we should develop an cstimating method of customers' evaluation functions on the basis of the collected customer information.

Servlet

Model XML Colltrol Real,

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H

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XSL r txtensible Style5heet L anguage rransfomdtion SMTP Simple Mail Transfer Protocol

Fig. 3. Architecture of thc network model.

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Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

PUBLICATIONS

INFLUENCE OF WIND ENERGY ON THE POWER STATION PARK AND THE GRID H. Weber" T. Harnacher"" T. Haase"

"University ofRostock

""Mu~-Plunck-lr~sti~ut fur Pkusmuphysik Gurching

Abstract: The cncrgy supply in Germany was stecrcd by thc current demand of the consumers till now. It will change in an adjustment process to an energy supply led by stochastically arising energy offer by wind power stations. The development of the wind energy is pushed at suitable onshore and offshore sites. Up to the year 2030 onshore wind parks are expected with an installed power of approx. 22 GW and offshore wind parks with 26 GW installed power. The planned offshore wind parks with partly more Giga watts of power must bc connected to the existing high-voltage transmission system. Another problem is that the wind energy is mostly produced in northern Germany, but is mainly needed in the middle and Southern part of Germany such as the Rhine-Main and Ruhr district. In order to compensate for the fluctuating feeding from the wind power stations backup power plants are needed. They must be able to provide reserve power. A simplified model of the German cncrgy generation and transmission system was used for this investigation. Based on this model a conceivable scenario of the energy supply in Germany in the year 2030 will be discussed in this paper. Cop,vright 02006 IFAC Keywords: Renewable energy, bottlenecks, load management, congestion management, substitution of conventional power.

1. DEVELOPMENT OF THE OFFSHORE AND

ONSHORE WIND ENERGY UNTIL 2030 An enormous boom for the construction of onshore wind power plants was caused by an attractive remuneration of the wind energy fed into the grid as well as the obligation to accept delivery of wind energy according to the renewable energy law (Geiinan abbreviation EEG) and the rdpid technical development starting afterwards By the end of 2003 wind power stations with an output of 14 315 MW were installed in Germany By far the greatest shares hereof belonged to the energy supply companies of Vattenfall Europe ( 5 400 MW) and E ON (6 250 MW) The Geman wind energy production amounted to approx 18,6 TWh (E ON 8,5 TWh and Vattenfall Europe 6,7 TWh) in the year 2003 This devclopment will continue and the dnnual rates of increase will turn out lower due to the restricted productive onshore sites Starting from the year 20 10

saturation will occur. By then the rise of the wind energy production will be caused only by the replacement of older plants by more efficient and more productive plants. For the year 2030 an installed onshore wind power with approx. 22 GW is forecasted. The difficulty will be to maintain the extension of the wind energy use in Germany on high standard even though there will be a saturation in the onshorc arca. Thc solution will bc to gradually acquire suitable sites at sea. For these sites in the North Sea and the Baltic Sea investors have applied for 18 wind parks which partly consist of several hundred single wind power plants. At present, wind parks are planned with an installed power of 21.561 MW in the North Sea and 4.437 MW in the Baltic Sea. Also, 800 MW shall be used for the production of hydrogen directly offshore. Figure 1 gives an overview over the historic and expected development of the German onshore and offshore wind energy capacity.

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1990 1995 2000 2005 2010 2015 2020 2025 2030

Fig. 1 : Historic and expected development of the German onshore and offshore wind energy capacity

3 . WIND MODEL Wind power shows very special characteristics, which diffcrs considerable from conventional power plants. The following investigations are based on wind data collected on the world wind atlas (Sander + Partner GmbH, Swit7erland). The data presented on the world wind atlas has only a six hour time resolution. By special random methods also data with one hour time resolution were produced. The transformation from wind velocity to active-power output was done with data from modern existing wind turbines for onshore sites (1 MW, 1,5 MW. 2 MW) and offshore sites (2,5 MW, 3 MW).

2. SIJBJECI OF EXAMINATION

The challenge for the next years will be to develop a power station park which brings in line the different political interests and specifications. particularly the reduction of the greenhouse gases and the generation of electricity of local lignite and hard coal. With a model of the German energy generation and transmission system a scenario of the energy supply in the year 2030 w.ith an installation of 26 GW offshore and 22 GW onshore wind power is analysed. The investigation is based on the conditions that thc wind powcr plants will producc nothing but electrical power (no hydrogen) and there will be no further development of the pumpedstorage power stations. 'The power station park and the transmission system should adapt optimally to the characteristics of the wind and ensure the balance between generation and consumption. Starting from these expectations the paper will address technical and economic problems related to the integration of 48 GW wind powcr into thc German clectricity grid. Basis of the analysis are two models: engineering and an economic model. The economic model is calibrated with the help of the engineering model. The analysis will be made on two levels: 1) An economic level, which will address the possible development of the costs of wind turbines and the costs related to the installation of extra transport capacities: increased demand of control power and back-up power. The conventional part of the power system will be described in two scenarios: A business as usual scenario, with a power plant structure which is similar to the current one and a wind scenario, in which the rest of the power system is more seen as a system to balance the stochastic power supply ofthe wind plants. 2) A technical level, which will address all questions related to the bottlenecks in the transport infrastructure. 'l'here are several results of the optimization in level 1. Firstly the capacities of baseload and peak-load power plants. Secondly the optimal behaviour of the power station park related to the influence of wind power. The transport capacities between the nodes in the grid are a further outcome ol' the model. These results of optimipation are the input data for had flow calculation in level 2. The following questions shall be answered:

Are the wind power plants able to cover the base-load in the year 2030 and thereby substitute the thermal power station capacity? How much fuel can be saved by means ofthls substitution and can this lead to a considerably reduction of the C 0 2 emissions? At which sites in the transmission system can new power stations for lignite, hard coal or gas be installed cost-effectively? Where do bottlenecks arise in the high-voltage transmission system and how many transmission capacities must be built then?

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Fig. 3: Character ofan onshore site in Southern Germany Supply of power from wind turbines is stochastically in nature, the actual active-power output is more or less proportional to the third power of the actual wind velocitj. The wind velocity depends on the location and the actual meteorological situation. which itself depends strongly on the season. A

60

;

2 3

5%

Fig. 2: Character of an offshore site in the North Sea

5

6 s -

comparison between two onshore sites in the North Sea and in Southern Germany is depicted in figures 2,3. The average wind velocities and the active power related to the installed nominal power are represented for a typical year. When comparing the figures 2 and 3 it is noticeable, that the average wind velocity in the North Sea is considerably grcatcr thcn in Southcrn Gcrmany. Duc to thc characteristics of the wind power plants (P-v’) the active-power output is significantly smaller. This means, a profitable and economic wind energy production is possible only in the north part of Germany, especially offshore. On the other hand in Southern Gemany this is hardly imaginable. The German Wind Energy institute (DEWI) updates the details on the wind power installations for the single Gcrman fcderal states each month. The wind powcr plants installed in December 2003 in the German federal states were distributed among the network nodes. It was scaled to the onshore installation of 22 GW in the year 2030. Thc estimated offshore installation of 26 GW in 2030 was distributed to the network nodes in the immediate coastal area. In the year 2030 the wind current production would amount to 118,6 TWh with an offshore share of 69,2 TWh. Then the quota of wind cnergy in the total electricity generation of Germany will be up to 21 YO. 4. NETWORK MODEL The transmission systems and the power station parks of the four big German energy supply companies were united, as there are EnBW, RWE, E O N and Vattenfall Europe. In the network model the German production and consumption centrcs are represented by 30 substitute nodes. The power stations belonging to the consumption centres were summarized and subdivided according to their sources of energy or their mode of operation (lignite, hard coal, gas, pumped-storage, run-of-river). The nuclear power stations were replaced by lignite and hard coal power plants as well as natural gas fired power stations. Special attention was paid to the modelling of the pumped-storage power stations because these plants are the only ones which are presently able to store energy with a high efficiency (> 75 %). Exact data were provided by the operators of the pumpedstorage power stations in order to be able to determine the energy capability as well as the average power in the pump and turbine operating mode. The calculated total energy capability of the pumped-storage power stations in the turbine operating mode amounts to approx. 43,3 GWh and in the pump operating mode to approx. 56,7 GWh. The electrical consumer loads were taken from a UCTE data set and assigned to the respective substitute nodes. The consumer loads of every node were subdivided into 84 typical diurnal variations. These variations represent one week of each month of the year. It was calculated from Monday to Sunday because every day of the week has a specific characteristic. In order to model these characteristics the calculation was realized in a one-hour resolution. Among other things the calculation of the curves was

61

based on the load of the four German energy supply companies of the year 2003 Then they were scaled to the consumption expected for the year 2030. The transmission capacities between the substitute nodes in the 3801220-kV level wcre determined and summarized from d detailed model of the UCTE net. The surrounding UCTE net was modelled in simplificd tcrms into tcn nctwork nodcs Thc production and consumption of each UCTE member were summari7ed in one network node The transmission capacities between the European network operators were taken from the statirtical yearbook of the UCTE. Thereby a calculation of the European powcr flow IS possible in which the monthly changes are considered 1 his is particularly important since the German net is charged by power transits both to east-west duection and to north-south direction Power exports in the winter and power imports in the summer are distinctivc for Germany

5 OPTIMIZATION The optimization of the model was carried out with a linear cost optimization. The investment costs are distributed over the economic life time of the power stations with the annuity method. The optimal power stations and transmission capacities as well as the optimal schedule of the power station park result from the optimization. However, the linear optimization is not able to consider the lower efficiencies in the operating mode with partial loads of the thermal power stations. The optimization was realized with the CAMS (General Algebraic Modelling System) software package. The optimization was executed with the values of twelve randomly selected days in one year, one typical day for each month. It was calculated with a time resolution of one our. The result was projected onto the whole year with 8760 hours. This simplification was necessary because the available memory capacity of the computer was fully occupied. Additionally it was intended to reduce the computation time. In the future however these problems will be solved by way of better and faster algorithm of optimization. Besides the parameters length and efficiency of the 380-kV transmission lines the costs for investments and maintenance were also implemented in the model. Parameters like efficiency, C 0 2 emissions, fuel costs, investment costs as well as variable costs and operating costs, were assigned to the individual power station types. The calculation of the current-dependent COz emission is based on the assumption that the coal fired power stations will have an efficiency of 50 % in the year 2030. The ratio of the electricity generation between lignite and hard coal amounts 45 O/o to 55 o/. Due to this mixture the thermal emission factor results in 360 g C02/kWh. The gas fired power stations will have an efficiency of 40 % in the year 2030 and the thermal emission factor of the natural gas will amount to 200 g COz/kWh. Two scenarios were defined and examined, scenario I (without wind power installation) and scenario 11 (with a sum of 48 GW wind power installation, onshore and offshore).

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Output Data For The Optimization . . . . . . . . . . .I . . . . .......

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Fig. 4: lnput and Output data for the optimization 6. SCENARIOS

6.1 Results of the optimization with a power station park without windpower (Scenario 4 The currcnt dcmand of 571,2 TWh will be met by coal fired power stations at 84,7 %, by natural gas fired power stations at 13,l 9'0 and by hydroelectric power stations at 2,2 YO.In detail hydroelectric power stations will provide a capacity of 8.500 MW which was used as a constant value in the optimization. In addition coal fired power stations will contribute a capacity of 57.070 MW and natural gas fired power stations will have a capacity of 26.970 MW. Both capacities were determined by the optimization. The coal fired power stations shall cover the base-load whercas the gas fired power stations are designcd for the peak-load. Taking this power station mix the current-dependent C 0 2 emissions would amount to approx. 473,l million tons per annum. The then existing power supply system would be sufficient to transport the energy which will be needed. As a further result the optimization does not add any new transmission capacities. 6.2 Results of the optimization with a power station park with windpower (Scenario /()

I

A

a capacity of 45.170 MW and natural gas fired power stations will have a capacity of 36.500 MW. Both capacities were determined by the optimization. The coal fired power stations shall cover the base-load whereas the gas fired power stations are designed for the peak-load. Taking this power station mix the current-dependent COz emissions would amount to approx. 358,4 million tons per aimum. The then existing power supply system would not be sufficient to transport the energy which will be needed. In the model a 2.600 MVA transmission line between Hamburg and Rostock which will be built until the year 2030 was assumed. As a further result the optimization inserted new transmission capacities in the net model. Bottlenecks will occur at the lines which go from the coastal area of the North Sea to the south. The is caused by the fact that the electricity generation centre will be then in the north part, especially in the Hamburg area and the consumption centres will be located in the west and south part (Rhine-Main and Ruhr district). The programme inserted transmission capacities of 6.500 MVA between the nodes Bremen and Muenster as well as capacities of 5.200 MVA between Kiel and Hamburg. The total length of the new transmission capacities would amount to approx. 1.000 km based on a 380-kV Wansmission line with a 1.300 MVA transfer capability.

7 . NETWORK CALCULATION The current demand of 571,2 TWh will be met by wind power stations at 21,3 %, by coal fired power stations at 6 1,l %, by natural gas fired power stations at 15,4 % and by hydroelectric power stations at 2,2 %. In detail wind power will provide a capacity of 48 000 MW and hydroelectric power stations will plovide a capacity of 8 500 MW which both were used as constant values in the optimization In addition coal fired power stations will contribute

Various cases were investigated with the DIgSILENT software. Input quantities of the power flow calculation are the optimized power station capacities and line capacities from scenario 11. For the whole German net the optimized power station capacities are represented in figure 4 which is subdivided into seven regions. The concentration of the wind power plants in the north is clearly

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Behaviour of the power station park during a week with strong wind power; grey (base load), yellow (peak-load), green (wind onshore), red (wind offshore), blue (run-of-river), purple (pumped-storage)

recognizable This means that about 80% of the German wind energy would be produced in the north It i s also outstanding, that hardly any baseload power plants but considerably more peak-load power plants would be installed in the north. Hydroelectric power stations are only available in the southern regions due to the geographical conditions. The main consumer centres are in the western and southern part where, according to the consumer behaviour, more base-load and peak-load power stations would be installed Furthermore the power stations where operated in a minimum-cost schedule. In figure 5 a strong feeding from wind energy for the German net is represented for one week from Monday till Sunday On Monday practically no wind fceding was offered Thc figure shows thc gencration schedule as known so far. The schedule i s designed for the hourly changing consumer power. The baseload power stations would cover the power up to approximately half of the expected peak-load The peak-load power stations then would follow the consumers in their diurnal variation The pumpedstorage plants regulate the need for peak-load With thc feeding of wind energy increasing on Tucsday it was noticeable that at first the power of the pumpedstorage plants and the peak-load power plants were throttled down In the night from Wednesday to Thursday the power of the base-load power stations would have to be reduced, too During the day on Friday very few peak-load power stations continue to fced cnergy into thc net The consumer dcmand then i s covered only by the base-load power stations and thc wind power stations The pumpcd-storagc plants reguldte the need for peak-load With the feeding of wind energy increasing on Tuesday it was noticeable that at first the power of the pumped-storage plants and the peak-load power plants was throttled down. In the night from Wednesday to Thursday the power

63

of the base-load power stations would have to be reduced, too. During the day on Friday very few peak-load power stations continue to feed energy into the net. The consumer demand then is covered only by the base-load power stations and the wind power stations. During the weekend the consumer demand diminishes substantially. The wind feeding, however, remains constantly high. Further base-load power stations would have to be switched off after that. The generation schedule then would be dependent almost only on the feeding of wind energy. The consumer would play a completely subordinate role in this. The load flow investigation aims at the following: - Up to which amount of wind energy feeding can the net be operated stably? - Is the transmission grid able to transport several Giga watts of wind energy through the net? These questions shall be answered by a rough estimation with the help of a simplified German network model. Figure 6 represents the active power load flow in the German as well as European net during the feeding of 25 GW wind power. A further shifting o f the load flow in north-south direction as consequence can be clearly recognized. The width of the lines corresponds to the active power flowing over the tie lines. About 113 of the consumer load is covered by wind energy at this time. The situation in the western part of the German grid system which is characterized substantially by the high feeding of wind energy from the North Sea has to be judged considerably critically. The shifting of the power flow i s carried out under the unavoidable demand on the net of the Benelux states as well as France and the Czech Republic. This here represented 25 GW case is a theoretical borderline case. At increasing feeding of wind energy in this range the transmission lines are charged extremely and the voltage cannot be kept in its operating limits any more.

-------------p n d ow F F e e d i n g X s h o r e Wind P o w e r Feeding O f f s h o r e

10.414 MW 14.988 MW

Consumption Germany

I

75.086 MW

I

Interchange Power France

* 6.011 MW

Poland

i

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1.126MW

Czechia Denmark

+ 35MW

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- 6 083MW

Benelux S t a t e

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28 MW

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10 012 MW

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South-West South-East

- 5 843MW - 1 4 4 7 MW - 3 313 MW - 1113 MW - 1.719 MW

Germany

This paper was based on economic power plant models which have been provided with realistic parameters. In this study the minimal costs for the investments and for the operation of the German integrated grid for the year 2030 including the wind energy have been calculated with a linear minimumcost model. Afterwards, the technical feasibility o f the optimised power station park and of the optimised German grid was investigated by means of net calculation and simulation. At first it is obvious, that the installation of 22 GW onshore and 26 GW offshore wind energy does not lead to any significant reduction of the capacities of thermal power stations. The primary benefit of this heavy wind energy installation will be to save fuel, about 8,9 million of tons per annum of hard coal and about 18,2 million of tons per annum of lignite. But the operational availability of wind power generation is poor. Secondly a considerable number of new high voltage transmission lines will have to be built to transport the wind energy from the north part to the south and west parts of Germany. The used synthetic network model is sufficiently exact for the general estimation of the network extension. In the comparison with the dena-study similar results were obtained. By comparing the scenarios I and I1 in terms of the COz emissions, then a reduction by approx. 114,7 million of tons will occur in scenario TI. This value is still much higher than in the year 2000. In neither case there would be any reduction of the greenhouse gas emissions. Regarding the installed power station capacities one has to recognize that although fewer

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8. CONCLUSIONS AND OUTLOOK

146 MW

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Fig. 6: Load Flow situation by feeding of 25 GW wind power

3 L83 MW

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base-load power stations will have to be built (20,9 YO)on the other hand more peak-load power stations will be needed (35,3 %) in scenario 11. This seems logical since the wind can cover a certain base-load for a large area. Yet the considerable fluctuation of the wind can be compensated only with the fast natural gas fired power stations which then must be available in large numbers. However, seen absolutely the potential reduction amounts to only 2,8 % of conventional power station capacity (coal and gas) if 48 GW of wind power plants were installed. In principle, one can state as follows: If in Germany 22 GW Onshore and 26 GW offshore wind power capacity were installed, the COz emissions on the side of the power stations could be kept approximately at today's level. Numerous technical and economic questions will have to be answered before there can be a considerable development of wind energy in Germany. Therefore further research and examinations are required in order to determine the necessary measures for the maintaining of today's standards as regards supply reliability. REFERENCES ETG (2005). Elelctrische Energieversorgung 2020 Perspektiven und Handlungs bedarf: dena (2005). EnergiewirtschajUiche Planung jur die Netzintegration von Windenergie in Deutschland an Land und Offshore bis Zuni Jahr 2020. Haase, T., T. Hamacher, H. Weber (2004). EinJluss der Einspeisung von Windenergie auf die Struktur des Krajherkparks und des Uhertragungsnetzes. In: ETG Konferenz 2004, Berlin Wcbcr, Il., T. Ilaasc, T. Ilamachcr (2003). Network Requirements Of Future Energy Conversion Technologies. In: IFAC Conference 2003, Seoul

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Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

PUBLlCATlONS

AN APPROACH TO OPTIMAL DISPATCH OF BILATERAL ELECTRICITY CONTRACTS REGARDING VOLTAGE STABILITY B. Mozafarf, A. M. Ranjbar*, A. Mozafari'*, T. Amraee*

of Electrical* * Engineering, Sharif University of 7 echnology, Iehran, Iran k t i o n a l Petrochemical ('ornpany Emails mozafari-babakf2yahoo corn, ranjbargsharif edu, a mozafari@gmail corn

* Department

Abstract: This paper proposes a methodology for optimal dispatch of bilateral electricity contracts, which may endanger the system voltage stability in light of short-term operational planning of a deregulated power system. In this framework the value that each owner of a transaction is willing to pay will reflect how much the electricity contract is important to be implemented physically. The proposed model dispatches optimally the bilateral transactions regarding the prices offered by owners of bilateral contracts for reactive power and transmission capacity utilization in one hand and, the total operational costs of reactive power resources in the other hand. The model also includes the limits imposed by the physical constraints on the power system such as nodal power flow equations, limits on capacity of resources, voltage stability constraint and etc. The proposed framework is formulated as an AC-OPF problem and is implemented over the IEEE 14 bus test system using CONOPT solver (GAMS) to illustrate the feasibility of the approach. Copyright 02006 IFAC Keywords: Bilateral contracts, Deregulation, Reactive power, Voltage stability, OPF.

Optimal reactive power management can quite increase the available transmission capability as a consequence of the improvement of the network voltage profiles as well as reduction of active and reactive power losses. Therefore in an open electricity market, reactive power support is an ancillary service that plays a significant role in facilitating power transportation (Bhattacharya and Zhong, 2001). This ancillary service becomes very important when the loadability margin of the network diminishes due to high volume or transactions. Iri this situation I S 0 needs to follow a transparent procedure for rcadjusting rcactivc powcr rcsourccs to providc enough security level in the network. However the electrical transactions should be curtailed at least in some part, once the available reactive power resources are inadequate to achieve this goal. It is important to note that reasonably reactive power resources have different utilization prices in a deregulated power system, which may influence the ISO's selection of reactive power resources to meet

1 . INTRODUCTION Competition in purchasing and selling of a commodity so-called electricity is a new interesting paradigm in deregulated power industries which many countries around the world have found it necessary with their long run economic strategies. The prevalent market models for trading of electricity can be summarized into three groups; decentralized markets, pool or centralized markets and hybrid markets (Cafiizares, et al., 2001). The existence of an independent entity named System Operator (SO or ISO) or in some models Market Operator (MO) who should adapt market activities regarding the available transmission network capability is a common feature among the market models. In practice, the transmission capability of power systems is usually restricted by some factors such as equipment thermal limits; available active and reactive power capacities and the limits associated with the network stability problems.

65

system requirements. Up to now some standpoints toward competitive reactive power procurement have been presented in numerous research articles, which can be categorized into three groups. In the first approach, ISO, on the behalf the consumers purchase reactive energy based on the purpose of minimizing the reactive power procurement costs (Lamont and Fu, 1999; Danachi et al., 1996). In this methodology, active power transactions usually are kept constant. Recently a method that incorporates voltage stability criterion into the reactive power market formulation is presented in (Lin, 2003). In the second approach, active and reactive energy are dispatched simultaneously to meet some purposes such as minimizing active power generation costs (Baughman and Siddiqi, 1991), maximizing social welfare of active power market (Cafiizares, et al., 2001), or minimi7ing total incurred costs of active and reactive power generation (Xie, et al, 2000). This mechanism is usually proposed for hybrid or OPFbased market structure. From the point of this view, a security constraint optimal power flow is used to determine the approved transactions regarding the voltage stability criterion (Cafiizares, et al., 2001). Active and reactive marginal prices can also be determined at each location as by-product of optimal dispatch problem. In the third approach, a reactive power market is designed for a structure in which energy is totally traded through bilateral contracts (Zhong and Bhattacharya, 2003). In this structure, reactive power cost is determined independent of energy market activities with the aim of minimizing deviations from transaction requests and real power loss minimization. In this model, IS0 acts on behalf of the consumer in purchasing the reactive power. Transactions are assumed to have the same priority and hence no clear competition can be distinguished among the owners of transactions. Voltage stability problem has not yet been established in this reactive market structure. In this paper we make an attempt to develop the ideas proposed in (Lin, 2003, Zhong and Bhattacharya, 2003) and, introduce a competitive market structure for reactive power supporting in an open access electricity framework. The optimal power flow equations of the market are modified so as to include voltage stability criterion. The performance of reactive power market structure is evaluated by performing different case studies on the IEEE 14-bus test system and for each case, Locational Marginal Prices of reactive power are calculated at each node.

Synchronous generators are the main sources of active power generation in a power system, however they are also able to provide reactive power to fulfill transmission requirements. Active power generation cost of a generator is usually approximated by a second-order polynomial as a function of active power output of the generator. However it is very difficult to determine the cost of reactive power supported by a generator because no fuel is consumed for reactive power production. Reactive power cost determination for a generator is still an open issue for research, which needs further investigation, but we use here the model proposed by (Rider and Paucar, 2004) for generators’ reactive power cost calculations as following:

2. REACTIVE POWER COSTS

3. THE PROPOSED MARKET FOR REACTIVE

c:g P ( P‘9 ) = o pgz2 + b$ + c cost. Qgr :

is reactive power output of generator i.

sg1 :

is apparent power output of generator i.

K~~ :

is profit rate of active power generation, usually between 0.05-0.1

2.2

Static compensators

In general, static reactive devices are used to regulate voltage magnitudes throughout the power network. They have different characteristics in term of dynamics and speed of regulation. Switched capacitors as well as reactors have low installation and operation costs but they are slow in response to a reactive requirement. Static VAR compensators in contrast to fixed reactive devices are able to response to a reactive requirement rapidly, however their installation and operation costs are moderately high. Regardless of considering reactive power quality, in this paper static VAR compensator’s costs are modelled in term of their reactive outputs as following (Rider and Paucar, 2004): CCl(YCJ) =

ec.

Where: r . is unit cost of reactive power in $IMVAR. CJ . Q, : is amount of

supplied reactive power in MVAR.

In above equation, it is assumed that a reactive compensator is installed at bus j. POWER

Reactive power cost analysis ahs been reported in detail in (Lamont and Fu, 1999; Danachi et al., 1996). Synchronous generators and static VAR compensators are the equipment that their associated reactive power generation costs are reviewed briefly. 21

is active power production

3. I Electricity market structure

Nowadays electrical energy is provided through electricity market. Market transparency mainly depends on its clearing mechanism. In centralized electricity market, the pool would be the only place for the participants to bid for electricity and ancillary

Synchronous Generators

66

$/M W. As different transactions have different effects on the power system operation and stability problem, by this way it seems that transactions can compete with each other for using available transmission system capacity and limited reactive power resources. TFB is reported to IS0 and IS0 will not share this information with other participants. IS0 can organize TFB value into a matrix as following:

services. The IS0 clears the market taking into account the bids information and the system capacity. In this procedure, electricity and ancillary services are dispatched simultaneously. On the other hand, the bilateral market provides a good opportunity for sellers and buyers to negotiate bilateral contracts directly for the purchase and sale of electricity in a decentralized manner. To have a feasible and secure operating condition, the electricity contracts need to be adapted on the basis of the available ancillary services. Among different types of ancillary services, in this paper, we are dealing with the efficient provision of reactive power for bilatcral contracts. It is assumcd that thc 1SO has only information about amount of transactions and organize them into the Bilateral Transaction Matrix (BTM) as following: -

BTM =

w,,WI2

rm=

- 1

w, w'2 .

. .

. .

-

Y,, 'Yh,

.

-Y,wi:

(5)

.

.

fVmn -

-

TI1

TI2

.

.

TI,

72,

7i2

.

.

T2n

-T,I

3.3 Reactive power market: A competitive model

(3)

,

TN2

.

.

In general, a market operates best when there is a free and simple environment for competition. Maximizing the social welfare value in competitive electricity markets follows this purpose. For reactive power, it is nearly impossible to establish a market based on the concept of demand and supply theory because reactive power losses in transmission system are very high and the loss varies nonlinearly with the change of power system operating condition. Nevertheless, one can propose the following structure for competitive procurement of reactive power, which aims to maximize the value of the contracted transactions and simultaneously to minimize the costs of dispatching reactive power.

.,

/??In -

3.2 Transactions reqziiremenls ,for entering to competitive reactive power market

sf : r

In the absence of any constraint or congestion on the electric power system or shortcoming of reactive power resources all transactions are deemed to be accepted by the ISO. However this situation may not frequently occur in practice. To preserve voltage levels and stability margin, each transaction should be supported by efficient reactive power compensation. However, when the reactive power demand increases due to the high volume of transactions or changing power system operating conditions, there is a need to allocate reactive power resources to each bilateral transaction through a competition mechanism. In such cases, just knowing the importance of each transaction can be used by the IS0 in optimal dispatch mechanism. Prom economical points of view, it is a rational way to measure the importance of each transaction with the cost that the owners are willing to pay for approval of each MW fraction of their electricity contracts. Therefore in the proposed structure, transaction's owners are required to submit their offers to the IS0 which is called, "Transaction Firmness Bid" (TFB) in

1

Where: N is set of bus numbers; n E { N f ; {aG)c N;

67

rsm( .),g"'"( .)

represent nodal active and reactive power flow equations under stress conditions where the base load and generation have been increased by the factor ( I + C'SM); C, and @ are the vector of bus voltage magnitudes and angles; 7;, is a bilateral

Necessary condition of I .agrange equation implies that: ^.

transaction negotiated between bus i and bus j . q,'is the ij element of the transposed matrix. Qbl,Stands for reactive power generation at bus n and finally cpon indicates the load power factor angle at bus n. In this formulation, the amounts of power transactions form the control variables. Generator voltage magnitudes are assumed to be constant. In this modelling, the IS0 attempts to make an economic equilibrium between the utilization cost o f reactive power and transmission capacity in one hand and accepting bilateral contracts as closely as possible to the values obtained as results of electricity bilateral market. Lagrange theory is used for achieving equilibrium point. Equations (6) can be transformed into of following Lagrange form:

Equation (8) can be extended to:

As it is clear, offering prices, Wi, s, have a key role in

dispatch mechanism and hence competition procedure. Solving (9) gives Lagrange multipliers and slack variables. 3.4 The reactive power prices

Similar to other standard market, the price of reactive power at every bus can be determined by Lagrange multiplicr associatcd with rcactivc powcr flow equations. In this manner, marginal reactive price is dL obtained from -= 0 at generation buses. 3Q,,, 4. SIMULATION AND RESULTS

4.I The test system r

1

r

1

r

1

IEEE 14 bus standard system is used to test the proposed methodology for analyzing of the reactive power marginal price and transactions modification process. IEEE 14 bus test system has a special characteristic where generation area is rather far from the load area. This makes it suitable for voltage stability study. The one line diagram is shown in Figl. Transmission line parameters as well as generation and load consumptions are reported in (Power System Test Case Archive) in detail. However power flow solutions at normal operation are tabulated in Tables 1&2. The parameters of generation cost function are listed in Table 3. THREE

WlMIIN6

T W S F W E R EQUlV4LENT

T'

Lagrange multipliers of equality and non equality constraints. Slack variables associated with inequality constraints are:

I

lLul

-&)

Cd? Ed).

operational point for t,he ~aria~bles in t,he model are fourid for a number of intervals covering the entire operational range for the c o d mill, q ( t ) is the normal distributed process disturbances; r(t) is the normal distributed measurement noises. 7kl(b) i s the measured ternpera.ture and

3.2 Opttmal unknown snpul observer The optimal unknown input observer is described in (Chen and Patton 1.999). For discrete time systems with unknowii inputs and disturbances which can be represented by

an optimal unknown input observer of the following form can be derived.

B=

+ I]

X[TL

Z[TL

+ I] + H , + L N +[ ~I].

(17)

The basic idea in this observer is to elirninate the deperidency of the unknown input from the estimation error by matrix transforms, and subsequeritly design a. Kalman est,iniator for the transin. A posit.ive side effect of this, is that the estimator gain is recomput.etl a,t ea,ch sample, meaning the model can be changed such that the point of operation can be updated. The schemes for computing the matrices in tlie optimal unknown input observer can be seen in Appendix

3.2 Model wth, moisture This lincar model is subsequently modificd for the estimation of the coal moisture content. An additional state is introduced for representing the coal moisture content. ~ [ T L ] .instead of the input 'I'his state is driven by the unknown input. deiioted m[n]. In addition the static estimate of the moistiire content ir cniisidered iis A very noisy ineasurernent, (8-13).

A. The varia,nce of the disturbance and measurement noises Q[n]arid R[n]:as well a.s the internal fault model parameter p are all found by trial arid error, ba.sed on experimenta.1 data, in the way that, tlie observer est,iinates the inoistrire conl,ent in the coal. The results can he seen in Section 4. From Fig. 4-7 in Section 4 it can be seen that the observer estimates the coal moisture content u7rl1, and it, is hereby concluded that t,he observer and niodel are well tuned.

rm[n].

(9)

4. RESULTS

where yn(t) is the generic unknown input which is low-pass filtered in order to represent tlie coal inoirtiire content. a r i d

'l'he designed moisture est,irna.tor is a.pplied t o measured da.ta from the coal mill described in Sect,ion 2. Since t,he rnoist,iire cont,rnt,is not rnea.siired

92

"I

I

II

I

0 125

1500

SO0

Sanlples I"]

lo00

1

11""

sarnpics I"]

Figure 6 . Example 3 , comparison of observer estimated, static measiired/estimated coal moisture content. 'l'he sta,tic estimate reacts on the load cha.nge at sample 1230>which the observer estimate does not.

Figure 4. Example I , comparison of' observer estimated and static measuredleslirnated coal moisture content,. Notice the static measurement is influenced by a plant load change at sample 66 and 450.

"I

' I

0105

0136-

0134 0

500

100

200

300

400

100

600

700

OW

800

, 10

1000

SnrnplPsln]

Figure 7 . Example 4,comparison of observer estimated, static niea.sured/estiinated moisture coiiterit. The third exa.mplr shown in Fig. 6 contains a load change a.pproximately at sample 1230. 'The observer estimated coal moisture content shows the increa.se in coal moist.ure cont.erit without i-ea.ctiiig011 the load change a.t sample 1230. which the static estimated moisture content: on the other hand, does.

Figure 5 . Example 2 ; comparison of observer estimated aiid static iiieasured/estirnated coal moisture content. The observer estimate does not react on the load change at sa.mple 900, which t.he sta.tic estirnat.e does. it is impossible to comparc the cslimatcd moisture content with the real rnoistuie content I-Iowevei it can be compared mitli a static estimate l'his comparison has been done for four diffeient sets of rnedsi~rernentsarid can be seen in Fig 4-7

The fiist example shown in Fig 4 contains two changes of the plant load at sainple 66 aiid 450 These load changes are influencing the static measured but not the one estiniakd by the use the proposed scheme Ex( ept from the the plant load changes both methods are following lhe increases and decreases of the moisture content

'l'he fourth example which is illustration by Fig. 7, has a, variating moisture content and plant load change approximately at sample 146. The conclusion which can be inade of this example is similar to the three others. 'l'he observer based estirna.tion gives the moisture content without reacting on tlie plant load changes, which tlie ic estimate, on the other hand, does.

The second example shown In Fig 5 contains one load change approximately at sainple 900 Again the static measuren~ent/estiniate reacts on the load changes whereas the proposed scheme does no1 Both estimates follow the iricreased moisture ( ontent well

From these four examples, illustrated by Figs. 47, it can be seen that the observer estirna.tes the moisture content of the coal well in all four ca.ses. On the other hand this estimate does not react on load changes as the static estimate does. It can hereby be concluded that the observer and model

93

Appendix A. OP‘L‘IMAL UNKNOWN INPUT

are well tuned, and the estimator can be used to estimate the moisture content dynamically.

OBSERVER A necessary arid sufficicnt condition for the existence of a solution to the given observer problem is i ~ (i C h i and Palton 1999) given as: an optimal unkiiown input observer solution exists if arid only if. rank (Cn+lEn)= rank (En).

5. CONCLTJSION ‘l’liis paper introduces a method for estimating moisture content in the coal in coal mills used in power plants. The eslimation is performed by using a simple linearized dynamic energy balance model, and an optimal unknown input observer. The designed observer is tested on four sets of cxpcrimcntal dala from a. coal mill, and it is concluded that the observer estimates the coal moist,ure content, in all these cases wit,li different moisture content.

The computation of the matrices in the observer is also givcn in (Chen and Pattoii 1999) as:

(I) Set initial values: Pg

P(O), zo CoEo (CoEo)+Yo, Ho = 0. (2) C h i p u t e H,+, = E, (C,+lE,)+. (3) Compute =

=

xg

~

+

AA+,P,C: (C,P,C: R,)-’, T and Pk+l = P,, - KA+lCILPIL (4) Cornputp TrL+l= I - Hn+lC,+I, F,+i = An - Hn+iCn+iAn - KA+lCn, K;+l = Fn+lHn, a d Kn+I = K,I,+, + K?L+l KA,,

6. ACKNOWLEDGMENT

The authors acknowledge the Danish Ministry of Science Technology and Innovation, for support to the research program CMUC (Center for Model Based Control), grant no 2002-603/400 1-93.

=

(5) Now compute

+

+

+

11 = F,+lz[n] T,+~B,u[nl Kn +1Y and x[n 11 = ~ [ n11 H,+ly[n 11. T . (6) Compute Pk+, = P,L-KA+LC,LP,L and following P , + ~= A;+, (AA+~)~+T,+~Q,,T +;+, HrL+lRn+lH:+l z[n

REFERENCES Clien, Jie and R. J. Patton (1999). Rob,ust modelbased fault diagnosis for dynamic systems. first ed.. Kliiwer academic publisliers. Fukayarria, Y., K. Hirasawa, I J. Wang, G. Oluwande, 1). Matts and X. X.Zhou (2002). Coal mill modeling by inacliine learning based on oiisite measurements. IEEE Tmnsactions on Energy

I.[

( 7 ) Set ri

Conversion 17, 549-555.

94

+

= ri

+ +

+ 1 arid jump t o step 2.

+

me

Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

ELSEVIER

PUBLICATIONS

SIMPLIFIED FUEL CELL SYSTEM MODEL IDENTIFICATION S.Caux', W. Hankache'. ', D. Hissel', M.Fadel' 'Laboratoire d'Electrotechnique et d 'Electronique Industrielle, LEEI li1\41? I N P T C N R S 2 rue Camichel31071 Toulozise cedex 7-France hankache,fadei,cazixx/cr,leeienreeihl fi. 2 Laboratoire de recherche en Electronrqzie, Electrotechnique et SystBmes, L2ES EA i'IiUlJ7BM, 13 ride zlieg 90010 Belforf I ,>

The output voltage expression is:

u ! = Ere, + V a t - &n

.I

Fuel Cell System

Fuel cell needs also some ancillaries to control the different gas loops and different important values as: pressure, flow and temperature. So adding compressor, pump, radiator and valves with their own control, a fuel cell system given in Fig I is obtained and modeled for simulation in Matlab/Simulink. In the hydrogen loop there is no special control because an ideal source of hydrogen is considered represented by only an infinite tank and a passive reducer to fix the 2bar absolute pressure in this compartment whatever the flow is.

To obtain this expression some assumptions are made: - For control purpose and simplified modelling, a uniform current density is considered in the stack. - A uniform temperature equal to the temperature of the outlet cooling water is considered. Moreover, with an effective control law being established, this temperature is maintained constant during the work of the fuel cell. - Non significant anodic activation voltage is assumed.

96

- The damping air-blower unit, which recuperates

feed the converter so: Ir,eL=lfc-lrux.This consumption is represented by a varying resistance R a m . Resistance of the Fuel Cell is represented by r. r, R a m and PO2 must be computed to have an accurate representation of the controlled fuel cell system behavior (figure 2). - F R ' * ( ~ e1.S) With "V586 the number of based-cell used, e=50pm width ol" the membrane, S-O,1 956m2 the equivalent surface and p depends on air humidity injected and temperature (if both are regulated p = 72.4mQ.m) - Raux=Ulcz/Pcomp. Pcomp is computed with the compressor characteristics depending on its velocity and the PO2 pressure.

water and ensures that the air has a high humidity level, has been designed and modelled ideally. So, the humidity is adequate, saturation in water vapour (thus a relative humidity of 100 %) is ensured in the cathode compartment, while the anode is supposed to be supplied with dry hydrogen. - The partial pressures of gases are considered constants inside the stack and this, by neglecting the pressure drop in the gas distribution channels due to the gas / membrane and gas I gas interactions whereas the pressures used in the Amphlett equations are on the interface electrode / gas level. - Same as temperature, the pressure at the entry of the anode and cathode compartments is supposed to be controlled and maintained constant. - The pure delays related to the progress of gases in the distribution channels are considered to be negligible compared to the system time-constants. - The inlet air flow is controlled and in particular a cathode stoichiometric ratio is maintained constant. - The tlooding phenomenon ofthe membrane due to water excess is not taken into consideration. - The migration of oxygen and nitrogen molecules from the cathode towards the anode throughout the membrane is supposed to be negligible.

r

Hc r

lelec

-

r

IdllX

Kaux Ufc

Pcoinp

0.. I

I

Fig 2. Simplified Fuel Cell Model

3I

The air pressure is fixed to 1 .Sbar so the compressor map can be read from data sheet to obtain the equivalent Pconzp to deliver the current If'. In real time U, is the previous computed voltage value. If no compressor is used Razlx disappears and C'oz law can be a little different. PO2 also varies and depends on the fuel cell behavior, so identification is first made with the complete physical fuel cell model provided by our partner (CEA).The oxygen partial pressure is computed by the number of mole presents inside the compartment, so the calculus is made in 3 steps:

Simulation based approach

To compute voltage behavior U, the current I and pressures POZ and PHZ behaviors under current solicitation must be known. 1 - If temperature Tfc and hydrogen pressure PH2are constant (inside pressure is constant because input pressure is fixed and Tfi fixes the saturated pressure in the cell), a constant source U, representing the constant voltage of the fuel cell is computed by: LJo= a ,+a, (T,-298 15)+a, 7fi +,O, +,B, q' (7) 2 - The fuel cell voltage depends on the current delivered Ir, so a varying voltage source Cr, can be detailed by writing:

* The flow in the controlled loop can be seen as a second order transfer function:

3 - The last voltage source corresponds to the voltage due to the fuel cell parameters and the oxygen pressure PO2 and the temperature of the fuel cell ipfL, so, U,i2 is written as:

with : s=Laplace operator, qhfthe flow time constant fixed in the closed loop controller (zfh70.02s), X02r,,.=21Y~the oxygen ration in ambient air at the beginning and Fret computed by faraday's law NI F = L a n d IJL is known using the power ?if

cx, and PI coefficients are the same defined above.

4F

reference: Ilc-PreJlofL A part of the current produced by the fuel cell is consumed by its ancillaries. The current needed for ancillaries (compressor, pump.. .) is consumed before providing the usable current le,i.c to its exit to

* So number of mole is known by integration: 1

nO2 (s) = -

P

97

(s)

with initial condition IC,

current profile tests of 3-cell stack are provided on Figure 4.

adjusted after a first simulation using the complete model to track the fuel cell behavior. IC depends on the fuel cell characteristics, using prefect gaz law: IC'=PcarhVcarh/R.5'). xo2,nir With: .Yo2,,,,,=8.21% oxygen ratio in the cathode; 1 lm3; R=8.1 JiKimol; Tfc=298'K PcOth=2bar;Vcati2=0.

* Inside pressure behavior can be described by transfer function ( 1 1) after parameters identification : RTj'

Po2 (s) = (no2 (s)

20L

-

(1 1)

)(Peat/?- ~ l n t L v & ) )

pcati? vcath

With K,,, a coefficient describing the fuel cell behavior which must be identified by measures made with our simulator to compute the ratio from entry and interne pressure on the compressor flow: K,,,=Ka.Fcomp+ Kb (12) And after simulation: Kb=996.2 and Ka= -0.28

Time (s)

Fig 4. Actual current demand measured and used for current demand. Due to experimental constraints adaptations, some expressions have been changed to be representative of the experimental setup and to adapt the formulation with the available sensors. The reversible voltage expression is relative to the oxydo-reduction reaction and is considered constant. The ohmic resistance and the activation over voltage are considered specific to each fuel cell and should be meawred. The relation providing qoet must be identified replacing pi by experimentally identified coefficient

This simple model is compared to the complete model which takes into account all electromechanico-chimical phenomena (fluid behavior, chemical reaction, gas propagation, direct and reverse flow see Birdl960). This simplified model generates little relative error but is 100 times faster (Lachaize2005) and details are also in section 4.

3.2

Experimental approach

Two types of tests were used, a set of static tests on a 20 cells stack with an active surface of 100cm2and a nominal power of 700W and dynamic tests on a 3 cells stack of the German manufacturer ZSW with a membrane GORE MESGA Primea Series 5.510.

No problem to compute ,Z : With the fuel cell stack feeding its own ancillaries, in particular the compressor, the current output will be the sum ,~ of the current consumed by these auxiliaries I " ~ and

Polarization curve 19

I

I

the load current (the static converter for example) I',, . The reference air flow is calculated according

I

I

to Faraday's law as a hnction of I,, and

st,, .

No problem to compute P J ~ For ~ : the anode compartment and using the simplification hypothesis stated before, p15,can be expressed as: PH2 ( t )= Punode ( t )- P H 2 0 t a l (Tf' 14 ~

0

l

p

5

l

~

! 10

p

l

p

15

l

~

20

I

25

1

(14)

30

FC current (A)

Fig 3 . Polarization curve measured on the actual 20based-cell fuel cell at Belfort.

With P~,~(,,,/( T ) ~is ~the saturation pressure of water vapour (in Pascal), pa,,,,, the pressure of the anodic

During the dynamic test, the fuel cell is subjected to a specific currenthime profile resulting from measurements of speed recovered on the course of a vehicle in urban environment and after having carried out a homothety on the power in order to make it compatible with the tested fuel cell stack. An example of the polarization curve of the 20-cells stack is given on Figure 3, in addition dynamic

compartment considered to be constant (in Pascal). As for the calculation of the inlet hydrogen flow in the compartment, F,. ( t ) , we have :

41 (4=(4,

98

(4

+(~//'),u,ui

(16)

Where ( F ~ ~is )the~ hydrogen ~ , ~ ~flow consumed by Consequently, the value of

the chemical reaction of oxydo reduction (mol/s) and (FH2)f,t,rse ( t ) the flow of the purge valve (mol/s).

Special PO2 computation: Let 4, ,~, be the oxygen

Table I : Parameters identified

reference flow, as air is a constant mixture of l?40) refei ence flow is: oxygen and nitrogen (XoZ=2

4

Fr e / =

7 he term

I

st,

(18)

x,,.4.F

ce/"i'r'

Iz',t,h

corresponds to the total number of

= Pcuih.vLarh

K.Tf(

EXPERIMENTAL VALIDATION AND COMPARISION

To test the behavior of the proposed model, actual measurements have been used to prove the accuracy of the computed behavior. The full 400kW power is used in simulation and an artificial repetition of 54s of a most varying tramway profile is used. An urban cycle is used for actual tests and simple homothetic coefficient provides reachable values.

moles in the cathodic compartment at pressureeoth, : V

Alstom-CEA-LEEI: “Interest of using Fuel Cells in bus, tramways, shunting loco.”, FDFC 2002 October 7- 10 2002 - Forbach - France. J. C. Amphlett, R. M. Baumert and al. : “Performance Modeling of the Rallard Mark IV Solid Polymer Electrolyte Fuel Cell’: Jour. Electrochemical Society, Vol. 142, No. I, ppl-8, 1995. Bird, Stewart, Lightfoot: book, “Transport Phenomena” p48 I , Wiley international edition 1960, ISBN: 0-471-07395-4 D. Corgier: “Hydrogen air fuel cell vehicle technology FEVER demonstration project”, proceedings of EVS 14 - Orlando, Florida 1997. W. Friede, S Rael, B Davat: “PEM JzIel cell models jor supply of an electric loaaP’, proceedings of Electrimacs 2002, August 18- 19, Canada. S. Jemei’, D. Hissel and al: “Black-box modeling oJ Proton Exchange Membrane Fuel Cell Generators.“, proceedings of 2Sth Int Conf on Ind. Electronics, [ECON 2002, 10-518 SevillaSpain. J. Lachaize, M. Fadel, S. Caux and al: “Energy Management of Fuel Cell System and Supercaps Elements”, proceedings of IFAC 2005, power plant and power system, 4-8 july- Prague Tcheque Republic. J. Lachaize, S. Caux, M. Fadel, P. Shott, L. Nicod : ”Pressure, Flow and Thermal control of a Fuel Cell system f o r Electrical Rail Transport.”, proceedings of International Symposium Industrial Electronics ISIE 2004- Ajaccio France- 05-417 2004 L. Solero, A. Di Napoli, and al. : “Fuel cell FIEV’s assisted by ultracapacitor and battery storage syJtem”, FISITA-Helsinki, Finland - June 2-7 200 1.

24

U 0

5u

I00

1 150

Time (s)

Fig 6. Simplified model exit voltage tuned after parameters identification compared to actual fuel cell voltage behavior measured. 5.

CONCLUSIONS

A simplified fuel cell model is established to have an accurate voltage behavior without prohibitive simulation time. The model is based on physical main phenomena in the different controlled loops which compose the Fuel Cell System. In the three voltage sources model-circuit proposed, there are little calculus to make and few parameters to identifji. Considering effective control of &el cell’s main variables (mainly pressures, temperature) and focusing on main electro chemical phenomena, three voltages sources have been specified and linked to fuel cell parameters. Each fuel cell must be identified to obtain a n accurate set of coefficients to be used in the simplified model due to specific conception and type of fuel cell. Using actual classic static and dynamic measurements a simple least square algorithm allows to identify the six most important parameters. The simplified model obtained is under some classical assumptions, but all the actual current demand used did not always respect these assumptions. To have a better direct identification,

100

Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

PUBLlCATlONS

AN A W I N E CEOME'I'KICAL AYYKOACH '1'0YOWEK SYS'I'EMS YKOSLEMS Emmanuel D. Crainic", Alexander I. Petroianub' Logiciels de r b e a u x , lnstitut de recherche d'Hydro-QuCbec,IREQ, 1800 Blvd Lionel Boulet, Larennes, QC, Canada, J3X IS1 Department of Electrical Engineering, IJniveriity of Cape Town, iJniver5ity Private Bag, Rondebosch 7701. Republic ofSouth Afvica

Abstract: I he paper introduces modern concepts and tools from affine geometry into power system analysis. It i s shown that such an approach allows: I) a new non linear formulation of such classical problems as load flow and state estimation, ii) a more efficient way of solving such problems through non itei ative methods. The new appioach i s illustrated for a small but representative example of a load flow for a two-bus network. Copyright 02006 IbAC Keywords: affine geometry. affine transformations, linear methods, algebraic and geometric invariants, power systems load flow.

1 . AFFlNE GEOMETRY: AN INTRODUCTION

A 2-dimensional affine space E is a space of points associated to a vector space E of the same dimension, in the sense that: i) for each pair of point5 (a, b) E 15,the difference (a-b) betmeen them is a vector AH in the vector space E ,ii) For each vector in the vector space and for each point in the affine spacc E, adding the vector to this point results in an another point in the affine space E, iii) every triplet of points (a, b, c) E E satisries the relationship fa-b) + (b-c) - (a-b). Tlierehre. there is ail one-to-one mapping of the elements of the two associated spaces (BcklCmichev, 1988).

In many power system applications, some of the physical quantities involved in the formulation and the solution of the related problems are expressed either as complex numbers of a I-dimensional complex space C' or as vectors of a 2-dimensiona1 real space RZ.Both approaches have their proper merit. In the complex space C' all the four arithmetic operations among the set o r its complex numbers i.e.: addition. subtraction. multiplication and division are allowcd. The clemcnts of a rcal spacc RZ. called vectors, are regarded as entities involved in linear operations. i.e.: multiplication of a vector by a scalar and the addition of two vectors. This vector space is a linear space. Ilowever. this may constitute a limitation, since a vector space contains only vectors of the same naturc (for instancc, power, or voltagc or currcnt vcctors, ctc.. but not a combination of two or more vectors of different nature). In this paper, the authors emphasize the geometric aspects and the physical meaning of the affine space associated with the vector space usually used in the investigation of power system load flow problem (Petroianu. 1969).

An affine space E may be visualized itself as a linear space by choosing in it an arbitrary point 0, called the origin, and in the appropriate vector space E a basis (el. e2). If a is an arbitrary point in E , together with the coordinate origin 0, it defines a vector 02 E k , the radius vector of the point a, which in terms of the basis (el, e2), may be expressed as oci= xiel + x2e2. The coefficients x I , x2 are called the afline coordinates of the point a. As any space, the affine spacc is dcfincd by its gcomctry. In thc spirit of thc Erlangen Progranzm, insisting on the concept of the group rather than that of the space. Klein (1 974) saw any geometry, including the affine geometry, as the study of invariants under a group of transformations. An afine transfornzation, as linear mapping From an

* Corresponding author: Alexander I. Petroianu, E-mail address. al7etroianu/u:ebe.uct.ac.ra

101

affine space to another affine space (or to itself), is any transformation that preserves parallelism of lines and the ratio of distances between colinear points. In a 2-dimensional affine space, to map a point (x; y) to a point (x'. y') four main affine transformations. or linear combinations of them, may be used (Klein, 2004): I,

- rotation

S'mk = S m k - i0.5V2mBC"mk S'km

=

x coscp + y sincp -x sincp + y coscp

(2)

2.

A,, =V,(V*, -V*,)(gmk+ib,,,,)

(5)

where

S -km

(6)

=

= P m k +iQ,, (12) V (V" V ' )( +ibmk)= Pkm+iQkm (13) -k -k -m %k

giuk = Rini /(R2d +

bmk

(7) (8)

Pkm=-V,,,VkcOs~mkgmk-VmVkSin~mkb,,,k+v2kg~~k (1 8) Q,,= VmVksin~mkgm,-VmV,co~~,"kbm,+v2,b, ( 19) From the above expressions. the active and reactive powers in (9) and (10) are: -

Pm,

(20)

p'km = Pkm

(21)

P'mk

Q Q,,,k0.5V2mBCap",k Q km = Qk,,- 0.5V2LBc"P,k

By taking into account (14) and (1 5). the angle Ymk is defined as: tany,, = 'mk grnk (24) Pmk

Pmk =

Fig. 1. Electrical line representation:

7c

(23)

2.2 Bus voltage module

With the radius expressed as:

I

(22)

With a known voltage (module and angle) at a chosen reference bus. the system to be solved has 2(N-1) non linear equations of bus power injections, expressed as sums of ad.jacent power transit 01' type (16) to ( I Y ) , and (N-I) voltage modules and (N-1) voltage angles as variables. Its iterative solution is a well known proccdurc (for a dctailcd trcatmcnt of it, scc Dcbs (1988) or Eremia, et al, (2000)).

In power system analysis, the class of problems related to load flow (planning and operating versions) is of a mathematically non-linear type. In planning environment. the load flow problem assumes the knowledge of power in.jections and values of electrical parameters of network elements. The solution consists in finding the nodal voltages (module and angle). For a component of the network, for example a line (Figure I), the apparent power flows are expressed as follows:

wd

(14) (15)

Pmk=-V,VkcosOmkgmk+VmVksinOmkbmk+VZmgmk ( 16) Qmk = -VmVksinOmkgmk-VmVkcosOmkbmkfV2,bmk ( 1 7)

2 1 Power system loadflow formulution

k5B

x2nii)

= x m k /(R2mk+ X'mk)

In (12) and ( I 3) Pmk, Pkm are the active and Qmk, Qkm the reactive powers. They represent the real and the imaginary parts ofthe complex numbers Lkand &,:

2 AFFINE GEOMETRICAL APPROACH TO THE LOAD FLOW PROBLEM

@.5B"",

( 1 1)

(3) (4)

The affine transformations make the general affine group GA (2, R). which i s a semidirect product of the general linear group and the translations in E by vectors of . The essential difference between an affine and a vector space consists in the fact that in the affine space the operation of adding a vector to a point is allowed. The operations solely on points are also possible. but only under certain conditions: this is the subject of barycentric calculus (see MBbius (1827) or Dclodc (2000)). An affine space, not being dependent on a specitic choice of a coordinate system. is the appropriate framework in dealing with motions, trajectories, and physical or electromagnetical forces. among other things.

f

- 6k

considered to be positive (all over this paper the hypothesis is made that m is the sending and k the receiving nodes of the active power). Analytically; are as follows: the complex powers &k and

(1)

-reflection in the x axis, x' = x y' = - y 3. - scaling, x ' = Lx y'= & Y 4. - translation, x' = x + px Y5 = Y + PY

6,

Omk

the origin. =

(9) (10)

In the equations (9) and ( 1 0) the voltages are complex numbers represented by their modulcs and angles, i.e. V , , Vk respectively, 6 , , 6k with the difference:

by an angle cp counter clockwise about x' y'

- i0.5V2kBCaPmk

= &m

I t

of the circle (see Figure 2)

d

m

(25)

the foliou ing trigonometric functions may be derived for the angle 2ymk:

model

102

Fig. 2. Electrical line base angles

If the electrical state on the m-side of the line, defined by the triplet of quantities [Pmk, Qmk,and Vm], is known. the equations (30). (31) and (32) allow for the evaluation of the elecfricul state, defined by the triplet of quantities [PkmrQ k m , and Vk], on the k-side of the line.

In the arline approach to the load llou problem the notion of topological spannzng tree, that is a trec having (N-1 ) edges (lines, transformers. etc.) linking all the N nodes of the network. plays a central role. What is required to be known is one of the pairs (P& or (Pkm, Q k m ) of active and reactive power at the extremities m or k of each of (N-I) edges of the spanning tree and one voltage at the arbitrary chosen reference bus. With this information, and starting from thc reference bus, the formulae of type (32) or (37) are used to obtain thc vollage rriodule(sj at neighbouring node(s), and the formulae of type (40) or (41) to obtain its affine pair (Pkm. (Skm), respectively, (Pn+ Q m k ) Qmk)

Keciprocally. the equations ( 3 5 ) . (36) and (37) allow evaluating the electrical state [Pmk. Qmk,and V,] on the rn-side of the line when the elcctrical state [Pkm, Qkm,and Vk] on the k-side of the line is known. In other words. the systems (30), (31) and ( 3 5 ) , (36) of linear equations represent @ne transformations, each one the inverse of the other. This property is the main result put forward in this paper. For expressing the translation transformation (see (7). (8)) in a matrix form, it is necessary to use the homogeneous coordinates (which were first introduced by Mobius ( 1 827)). In these coordinates, the matrix A of the affine transformation (30). (31) is defined as:

2 3 Bus voltage angle

For any (m, k) edges belonging to the spanning tree, three basic formulae (42). (43) and (44) allow evaluating the angle difference &,,h betvceen the voltagcs at the buses m and k: taIf)rnh= ( b m h P m h - g m h Q m h ) / ( ( P ~ ~ h ~ r n ) z - ( g ~ ~ ~ h ~ ~ ~ ~ h +(42) b~~hQ~~h))

tm%h= -(bmhP~,,-g,hQ~,)/((PmhVb)2-(GmhPh,+b,,~Qh,u))

If thc values ofthe active and reactive power Pmk.Qmk and Pkl,,. Qkm are known, the following formula should be used.

This matrix A is invertible. i.e.: A A-‘ = I

(43)

(39) tmQ,, = ( P m k Q k m

Consequently, the cquations (30). (3 1 ) and, respectively. the equations (35). (36) may be written as follows:

- PkmQmk)/(PmkPkm

+ QmkQkm) (44)

Once the bus voltage have been evaluated. they are used to calculate the active and reactive transit

103

powers on the remaining (L-N+I) edges not belonging to the spanning tree of the network and. consequently. to calculate the active and reactive power injections to the N buses o f the network (Table 1).

the equations (47), (48) and (49), (50) may be expressed in homogeneous coordinates form, as follows:

Table 1 Power system load flow problem. a comoarison

Jt is to be mentioned that the matrices Bmkand are riot arfine tranaforniationa.

Line

From the equations (48) and (47) it results that (see also (24)): (54) OQmk/ ~pmk b m k / gmk tanynk

data Bus

voltage

therefore, the vector ((sP,k, OQmk)is colinear with the axis A'A (Figure 2).

md po\+ei data

Bkrn

in~ectlonsP,,, , Q,,,

transits P,,,L.Q,,,h on

(m=2,3,.. ,N)

branches forming a

2.5 Active and reactive powers between buses rn and k.

Variables

In the transient stability studies, the approximate formula for the active power between buses m and k is expressed as: (p,l,L)t r a n c m t ? t a h i l q = ((VmVk)/Xmk)sinomk (55)

Prohlein Solut~on ,

power transits

power transits on

Main

and the role of the reactive power is practically ignored. However, in the context of a competitive environment. any quantity of the reactive power, influencing network voltage Stdbility. is very important and should be accounted for.

hy-

products

2.4 Active power requirements.

losses

and

reactive

By definition, the active power between the sending and the receiving ends m and k of a line is expressed as: EPIIIh= o . j ( P m k - Pkm) (56)

power

By definition, the active power losses for the line (m, k) are: OPmh =

P m k + Pkm

and the reactive power exchanged is

(45)

EQ,,

and the reactive power requirements are

=0mmk

Qkm)

(57)

In terms of the sending end m, the equations ( 5 6 ) , (57) may be written as: &Pmk= Sln2yII&Prnk-0.5Sln2y,,,LQ,k -0.5(V2k-V2,,Jg,k (58) &Qmk=-0.5Sil12y,,hPrnk+c0S'Y,bV,k -0.5(V'k-V',)bmk (59) and in terms ofthe receiving end k as: &Pink= -sin2ymLPkln+0.5Sin2ymhQk, -0.5(V2~-v2,)g,k (60) &Q,,k= 0.5Sin2y,,kPkn, -COSZY,,,~Qkm -~.5(V2~-V',,)b,k(6 1) By introducing the matrices C,,,k and Ckj,l defined as:

104

3. AN EXAMPLE

Expressed in homogeneous coordinates the equations (58). (59) and, respectively, (60). (61) become:

In a large power utility, a transmission line 734.6 km long operates at 765 kV. The constructive parameters are as follows: 1) conductor type - Zebra, 2) number of conductors per phase - six, 3) distance between the conductors (bundle spacing) 0.4 m. ~

It is to be mentioned that the matrices Cmkand Ckl,,

In Table 2, the electrical parameters are calculated for 100 and Vhace= 765 kV. In Table 3 the results are presented that corresponds to v, = vk = 1.0 pu and to a surge impedance load of 22 15 MW.

are not affine transformations.

Pha<e =

c

Table 2 Line data

It is to be mentioned that the ratio between line rcactivc power rcquiremcnts (10.658) / (active power losses (0.485) is equal to 21.98 and the value of the line angle is equal to 27.0.55 degrees, which corresponds to the line surge impedance load in (see Tdbk 3 column 1 1 ) .

Lmc

parametel

Starting with the triplet [Pmk= 22.393. Q m k = 4.32, V, 1.01. the expression (32) gives the value Vk = 1.0; by taking into account the values of sin2ymk and Cos27,k rrom Table 2: columns 11 and 12, the expressions (30), (31) yield for Pkm and Qkm the following values: =

Table 3 Netuork element-based load flow Vi = 1 00 pu, V,,

=

1 00 pu

PI,,,= (-0.9959)(22.39)+ (0.0908)(4.32)= -21.908PU, Qim= (0.0908)(22.39) - (-0.9959)(4.32) = 6.34

PU

In Table 4, for Vk = 0.98 pu and V, = 1.02 pu and in Table 5 , for Vk = 1.02 pu and V, = 0.98 pu, similar results are presented by imposing the transit angle O m k to be the same as in the previous case, that is equal to 27.055 degrees.

Table 4 Network element-based load flo\+ VI = 0,98 pu, V,,

=

It is to be mentioned the invariant nature with the product VmVkof active power losses o P , ~= 0.488 pu (Table 4, column 5 and Table 5, column 5) and of line reactive power requirements (TQ,,~ = 10.73 pu (Table 4, column 12 and Table 5. column 12) for the two different cases of line operating conditions.

1.02 pu

4. GEOMETRIC AND ALGEBRAIC INVARIANTS OF THE ELECTRICAL LINE

Table 5 Nctwork elcment-based load flou VL 1 02 pu, V,, ~

~

7 he geometric and algebraic invariants related to afline transformations as applied to the load flow problem, are important for a better understanding of the power system and for a more efficient problem solving. Some of'them arc presented in this section.

0 98 pu

the affine transformation matrix A defined in (38), whose determinant is equal to -1, has one eigenvalue h, equal to -1, and two eigenvalues k Z 3equal to I . The two non trivial corresponding eigenvectors are orthogonal (they form a base) and are expressed as:

105

the relationship between the electrical line base angles is an invariant: 0mk = 2 x

where

(Pkm, (Pmk

- ((Pkm - (Pmk)

(75)

are used to define the power factor of

Smk and Lmr the sending, respectively, the receiving apparent powers.

-

the normal h to the axis A’A from the point m and from the point k, may be expressed either as:

All these formulae may be verified by using the information given in the Tables 2 to 5.

Fig. 3. Electrical line: some geometric and algebraic invariants 5 . CONCLUSION

or: in normalized form: U t ( h = I ) =[cos”fmk

= [siny,k

v‘(k

sinymk 01 -cosymk 01

The paper demonstrates the advantages of an affine geometrical approach for power system analysis. For a real-time and on-line operator load flow (a classical non linear problem), an appropriate affine transformation allows a linear reformulation and a faster direct solution. Other on-line applications such as parameter estimation, bad data detection and identification, and state estimation (particularly state estimation for distributed networks) are likely to benefit riom a similar ar‘finegeometrical approach.

(67) (68)

The eigenvector it is colinear to the axis A’A and the eigenvector v is colinear to the axis Y ’ \y normal to it (Figure 3). the aria.. taken counter clockwise. of (he parallelogram formed by the points Omok (Figure 3) is an invariant to any change of basis it is submitted to, i.e.: 12mk P m k Qkm - P k m Qmk (69) It is known as the standard symplectic form Q on

6. REFERENCES

RZ, and it is antisymmctric: fikm =

%k

= P k m Qmk

P m k Qkm

Beklkmichev, D.V. ( 1 988).

where

+P(k.k) .U : the positive-, negative-, and zero sequence phase current of the h-th harmonic at both ends of the lines, 't;, ,, n : the positive-, negative-, and zero sequence faulted phase voltage of the h-th harmonic at the fault point, i('*): the positive- or negative sequence line impedance for the h-th harmonic, zOi'') : the zero sequence line impedance for the h-th harmonic. no

Fig. 1. Single-phase to ground fault on transmission line.

By adding the above equations and using the basic symmetrical component equations, the phase voltage and current of the h-th harmonic can be obtained:

The three-phase circuit from Figure 1 can be presented by the three qingle-phase equivalent sequence circuits of the faulted lines as shown in Figure 2. The three single-phase equivalent circuits are a positive (p), negative (n), and zero (0) sequence circuits, respectively.

and

The phase voltage of the h-th harmonic of sendingand receiving end is given by:

Fig. 2. Equivalent sequence network connection of the faulted line. For the equivalent sequence network depicted in Fig. 2, the following equations can be obtained:

and

where, i;") = (if)- i("))/ i(")is the zero sequence compensation factor, which can be calculated in advance. In this paper only fundamental harmonic fault model will be used for algorithm development because minimal number of harmonics needed for algorithm development is the first harmonic. Subtracting cquation (13) from (12), thc cquation for fundamental harmonic can be obtained:

The fault location t calculated as follows:

132

from equation (8) can be

Subtracting equation (18) from ( 1 9), one equation for fundamental harmonic can be obtained:

Equation ( 1 5 ) is the explicit fault location expression for the a-phase to ground fault on transmission line.

The known parameter (" from equations (16), (17), and (20) can be calculated as follows:

3. LONG LINE APPLICATION

If the fault location algorithm does not compensate for shunt capacitance in long line model, error of the fault location estimation may be increased. To estimate the more accurate fault location on transmission lines, the n line model is adopted to the long line application. The n line model is shown in Figure 3.

Equation (21) is the explicit fault location expression in long line model for the a-phase arcing ground fault on transmission lines.

Bus R

BUSS Transmission Lines

4. COMPUTER SIMULATED TESTS

}/

To test the validity of the proposed algorithm for the fault location estimation, the test was performed using the Electromagnetic Transient Program (EMTP). The schematic diagram of the power system on which the tests are based is shown in Fig. 4. Here v(t) and i(t) are digitized voltages and currents, and D is the line length.

Network .A

.1

D

I.

Network B

Fig. 3. Schematic diagram of the faulted system with shunt capacitance. In Figure 3 the unknown parameter !* is the fault distance away from sending end considering the shunt capacitance and is shunt admittance. Here the fault location t is calculated using the approximated formula (15).

From Figure 3 the positive sequence phase current of the h-th harmonic at both terminals of the lines can be obtained as follows:

where, i('*)"and i:: 5,

are the positive sequence

phase current of the h-th harmonic in the series impedance at the sending- and receiving ends, respectively. The positive sequence phase voltage of the h-th harmonic at sending- and receiving end is given by:

Fig. 4. Test power system. In this computer simulation, a synchronization error of 0 degrees is added to the test input data and the pre-fault load is present on the line. Single-phase to ground faults are simulated at different points on the transmission line. The left line terminal voltages and currents are sampled with the sampling frequency .h = 3840 Hz. 4.1 Cuse 1: short line model (without shunt)

In case of the short line model, the line parameters I' =0.0325 R k m , x =0.36 Rikm, are D = 100 h, ro = 0.0975 !2 /km and xo = 1.08 !2 /km. Data for network A are: R A = 1 C2, LA =0.064 H, R A O = 2C2 and LAO = 0.128 H. Data for network B are: RH = 0.5 R,LR = 0.032 H, RRO=1Rand LBO=0.064 H. The equivalent electromotive forces of networks A and B are E4 = 400 kV and EB = 395 kV, respectively. The fault resistance is Rr= 2 R and the fault inception is 33ms. 133

Results obtained by processing an example of short circuit with different fault point = 10, 20, 50, 80, 90 km) will be demonstrated. In Figs. 5 and 6 the faulted a-phase voltages and currents obtained by changing the fault location are presented, respectively.

(e

By processing input data, the calculated fault locations according to the variation of fault point are plotted in Fig.7.

- Sending End

zaB-;

i= 20km

0 16

36

57

77

97

117

137

157

I77

197

tlrre[ns]

Fig. 7. Calculated fault distances (exact values used by EMTP are 10,20,50,80,90km) Fig. 7 demonstrates clearly that the proposed algorithm i s not affected by different fault locations. Also, the calculated fault distances converge fast to the correct value after fault inception. For the purpose of fine analysis of the error and speed of convergence, Fig. 8 presents the relative errors for the cases depicted in Fig. 7.

J

time [rns 1

Fig. 5. Input faulted a-phase voltages and currents generated by EMTP at the sending end (! = 10, 20, 50, 80,90 km).

I

- Keceviiig Fnd

tirdmsl Fig. 8. Rclativc crrors in calculating fault location. As shown in Fig. 8, the relative errors obtained by changing the fault location are less than 0.01%. The reliable information of the fault dktance can be obtained in 20 ms after the fault inception.

I

I

‘I I

15 time Ims I

Fig. 6. Input faulted a-phase voltages and currents generated by EMTP at the receiving end (0 = 10, 20, 50, 80, 90 km).

To investigate the impact of different synchronization errors on the estimation of the fault distance, six synchronization errors are tested. The synchronization errors of 0, 0.125, 0.25, 0.5, 0.75, and 1 ms are added to the test input data. Fig. 9 shows the estimated the fault location with various synchronized errors. Here, the exact value of fault location used by EMTP is set as 10 km away from BUS S.

134

Table 1 Calculated fault distance for the different

002 Om OM

Om

00'

OCB OM 011 012 013 015 Olh 017 319 02C Ir l E I I B C 1

Fig. 9. Estimated fault location with various synchronized errors. As shown in Fig. 9, in spite of the synchronization error with 0.25rns, the fault distance is calculated almost correctly. Since a GPS receiver provides time synchronization to f Ip accuracy, the proposed algorithm for the fault location estimation is suitable for practical applications. From the algorithm speed and accuracy point of view, the results obtained confirm that the algorithm is useful for the application to real overhead line protection.

I I

1 1

250 280

2578580 2875740

I I

26193 25247

I I

2489560 2788860

I I

03480 03713

In Table 1 the maximum and minimum error calculated by considering the shunt capacitance are approximately 0.3 and 0.003%, respectively. Thc crrors of cstimatcd fault location with long linc are shown in Fig. 10. 3c3

,

4.2 Case 2: long line model (with shunt) In case of the long line model, the line parameters are D = 3 0 0 km, r = 0.1 Rikm, x = 0.36 Rikm, ro= 0.25 Rikm, ?co = 0.6 Rikm, c = 3.0 ,uF , and co = 2 . 0 , ~ f. Sequence impedance of network A are: ZAP - 5+j13 R , Z,, - 4+j10 R, and ZA0 3+j6 R . Sequence impedance of network B are: Z= , 5+j18 R, Z,, = 4+j 14 R,and Z,, = 3+j 19 R.The equivalent electromotive forces of networks A and B are E4= 133 kV and En = 100 kV, respectively. Here, network A and B are equivalent power system connected to sending- and receiving end of transmission line.

10

20

50

100

150

200

233

280

line leng:h[tml

Fig. 10. Errors of estimated fault location (D=300km).

~

For the long line (D=300km), the simulation results for the different fault points on transmission lines are shown in Table 1. Here, the first column of the table specifies the exact values used by EMTP. The second column is the calculated fault distance obtained by using a simple lumped impedance model and the last column is the calculated fault distance obtained by using a n line model. The fault location error to evaluate the algorithm accuracy, in percentage terms, is calculated using the following equation:

were, t , and C, represent the actual fault location and the calculated fault location, and D denotes the whole line length.

Since the shunt capacitances parallel to the fault resistance affect the accuracy of the fault location estimation, accurate compensation for long lines should be considered to develop the fault location estimation algorithm. From the test results, the proposed algorithm for the fault location estimation can be applied to the long line model. 6. CONCLUSION

This paper presents the two-terminal numerical algorithm for fault location estimation based on the synchronized phasors measured from the PMUs which are installed at both sides of the transmission lines. The proposed algorithm is based on the spectral analysis of the input phase voltages and line currents signals measured by numerical relay. Only findamental harmonic phasors calculated by Discrete Fourier Technique are needed for algorithm development. In case of the short line model, the proposed algorithm is extremely robust and fast. From the algorithm speed and accuracy point of view, the proposed algorithm is useful for the application to real transmission line protection. In case of the long line model, the shunt capacitance in order to obtain the more accurate result is considered. The proposed algorithm for long line model is relatively simple and easy to be implemented in the on-line application.

135

I I

ACKNOWLEDGEMENT This work is supported by the Korea Ministry of Commerce, lndustry and Energy (MOCIE) and Korea Electric Power Research Instituted (KEPRIj through IERC program. REFERENCES M.Sachdev (19971, Advancements in Microprocessor Based Protection and Communication, lEEE Tutorial Course Text, Publication No. 97 TP120-0. T. Takagi, et al (1 982), Development of a New Fault Locator Using the One-Terminal Voltage and Current Data, IEEE Transaction on PAS, 101, pp. 2892-2898. I. Zamora, J.F. Minambres, A.J Mazon, R. Alvarezlsasi, and J. Lazaro (1996), Fault location on two-terminal transmission lines based on voltages, IEE Proc. Gen., Trans., und Dist., 143, pp. 1-6.

RadojeviC, Z., Lj. Popovic, (2002j, Digital Algorithm for Distance Relay Including Grounding Impedance at Fault Place, European Transactions on Electrical Power(ETEP), 12, pp. 269-274. Chi-Shan Yu, Chih-Wen Liu, Sun-Li Yu, and JoeAir Jiang (2002), A New PMU-Based Fault Location Algorithm for Series Compensated Lines, IEEE Trans. on Power Delivevy, 17, pp. 33-46. J.A. Jiang, J.Z. Yang, Y.11. Lin, C.W. Liu, and J.C. Ma, (2000), An adaptive PMU based fault detectionAocation technique for transmission lines part I: Theory and algorithms, IEEE Tvuns. on Power Delivery, 15, pp. 486-493.

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Copyright 8Power Plants and Power Systems Control, Kananaskis, Canada 2006

PUBLlCATlON$

COMPLETE FAULT ANALYSIS FOR LONG TRANSMISSION LINE USING SYNCHRONIZED SAMPLING Nail Zhang * Mladen Kezuiiovic * * Texas A&M UrLiverszt:y, Department o,f Electrical and Computer Engineering, College Sla,tion, 1;. 77843-3128,

U.S.A.

Abstract A complete fault analysis scheme for long transniission line represented with distributed parameters is proposed in this paper. The syiichronized samples from both ends of the transmission line are thc data sources for this scheme. The paper derives a speci c feature which equals to zero for normal situation and external faults, and is close to fault current diiriiig the internal faults. 1his feature is uscd for fault dctcction and classi cation Fault location is then implcnicntcd by selecting di ereiit methods according to the classi ed fault type. The results from a comprehensive evaluation study demonstrate an excellent performance of entire fault analysis. Copyrzght @2006 IFAC Keywords: fanlt analysis, fault detection. fault classi cation. fault location, synchronized sampling.

1. INTRODITC'I'ION

Aiitoniated fault analysis tool for transmission lines is vcry useful for on-line con rniatiori and o -line lrouble-slioot,ing. When it is used on-line, the system operator can obtain the detailed information about t he disturbances before he issues corrective coritrols. It ca,ri help correct the relay rnisoperalions a.s soon as possible to prevent tlie occurrence of a large-scale blackout. When used o -line, tlie disturbmces can be fully analyzed and the relay syst ern operat ions can be assessed in a very detailed way Wit,h the lasl development of signa.1 processing, computer and communication technologies, new approaches have been deployed in the fault analysis providing better solutions in faull delection, classi cation arid location. An expert system b a e d a,pproach is described in (Girgis a,nd .Johns, 1996) a.nd a phasor measnremeiit unit (P1cITJ) based a.pproach is described in (Jia,ng el

id., 2003). 'l'hose approaches depend 011 the phasor calculation. A neural network based fault a.nalysis tool is developed in (Oleskovicz et al., 200l), but it is hard to prcciscly obtain a, fault location since neural network is not good at precisely c l a sifying the continuous va,ria,bles. NIethods based on traveling waves and recently based on faultgenerated high-frequency transients have been used extensively in protection schemes (Chamia and Liberman. 1978; Ro et al.! 2000). Most of those techniques require very high-speed sampling rate which is still not widely used in existing devices. A time-domain fault lomtion techniqi.ie wa.s tleveloped at Texas A & N IJniversity (Keziniovic et al., 1.994). The digital fault recorder with Global Positioning Systerri (GPS) satellite receiver is the source of the data for this approach. Data from both ends of transmission line a.re used to achieve high accuracy of the fault location. This method will be more attractive when the concept of Wide

137

Area Measurcnicnl Syst,em (WAMS) and Phasor Measurement Unit (PAIU) are further developed. Previous e orts were aimed at implenient ing accurate fault location algorithms for short line represent.ed with lumped parameters aiid long liiie represented with distributed parameters (Kezuiiovic el d.,1994; Gopalakrishiian aiid Kezunovic: 2000). A conrplete fault analysis tool was proposed for sliort line (I<exunovic and Perunicic, 1996). Due to the e ect of shunt capacitances in long line, t,he wave propagation and t,he fa,ult, analysis principle is quite di erent from those in the short, line a.lgoritlnn. 'lhe developrnerit of fault a.nalysis schcrne can not shift to thc long line model directly. In this paper, a complete fault analysis scheme including fault detection, classi cat,ion and location is developed specially for long tra.nsmission line iriodel. 'lhe paper rst derives the tlieoret,ical basis in detail, and then designs the complete fa.ult a.nalysis scheme according to the derivat,ion in the 1-heoretical basis. At the end: a. comprehensive evaluation study is implemented to evaluate the statisticad performance of the proposed approach.

Fig. 1. A homogeneous transmission line

Fig. 2 . A faulted trmsmission line transmission line with the distance of Ax, as shown in Fig. 1. Corribiriirig (2) a.nd ( 3 ) to e1irninat.e ~ ~ - ~1)(and k i j P l ( k 1) we get

+

+

(4)

When there is no internal fault 011 the line, which means the line pa.rameters are lionlogeneous; equation (4) can be expressed as t h e relation hctwccn t,hc scriding end a.nd receiving crid samples. Sihstitutc j - I with S and j witahR and not,e t,hr tiirect,iori of 1, . Eqiia.t,ion (4) is clianged t.0

2. TIIEOKETIC'AL BASIS

where d i s the length of tlie trarismission line, P is tlie sample di ererice if the wave travels from tlie sending end to the receiving end with the time of PA2 I>e ne

For long transmission line represented by distributed parameters, the voltage a.nd current along the line a.re functions of tlie dista.nce li' and the time t ,

Similarly, we can get another form of equation (5)

mliere R,L , C are per-unit-length resistance, inductance and capacit,ance respectively. A discrete form of the solution of (1) is derived as follows (Gopalakrishnan and Kezunovic, 2000):

as

I

l',(k)

And de nc

= -[v7-l(k-I)+?,7-l(k+1)] 2

27,. +[Z,-l(k 2

- I) - i,-l(k

+ l)]

*

KAx [z,-l(~--I)+~,-I(k+1)]--

(2)

-Ki )A( xk ) 2

iL [G)-l(k 22

!,(k)=

1 +5[7,-,(k-

+

- 1) - G , - l ( k

I)+l,-l(k+l)]

R A5 ~

4 2

+ I)]

[Z,-l(k

When there is no internal fa.ult on the line, obviously & ( k ) and & ( k ) should equal to zero.

(3)

Now consider tihe situation of an internal fault. As shown in Fig. 2, at a certain time, the fault current and voltage at the fault point can be expressed a,s the signals from sending end and receiving end:

+ 1) - L1-1(k - I)]

where An: = A t / m i s the distance that tlie wave travels with a sampling time step At; .Zc =

+

z r . ( k ) = z,..s(k) Zi..]l(k) v p ( k ) = u , . , y ( k ) = ?,.),(A")

IS the surge inipcdancc. Subscript J is the position of the discretized point of the line and k is the sample point.

(9)

Note t h t , for long t,ra.nsmission line; i s ( k ) f i ~ ~ ( kand . ) i ~ ( k )# i ~ ~ ( due k . )to the traveling wavc issue. According to cquat,ion ( 5 ) , if we note

'lhe two equations de ne the relation of voltage and current samples between two poinls on the

138

the current direction for each current signal shown in Fig. 2, we have

wheie F‘s arid F‘R are the sample di eiences i f the wavr t iavels from the fault point to tlie sending end with the time of PsAt and to the receiving end with t h r tiinc of PRAf respectivrly d~ and CjR are the dirtiincr\ froin the fault point to the sending end and to the recriving end respectively

Substitute k with k - PR in equation ( l o ) , and rniriiis equation (11) to elirnindte ~ > F ( ~ - I ’ Note R) that P = P5 PR and d = d5 + d ~ then . the lefth m d side i s changed to

+

1s(k-P)

[

z.1

1 - - +z,q(k)

[If- 3+ ?: ~

P)>Rd 2 2,

First of all, use transformation rna,trix 7’ to transfer the line parameters and the measured phase values into tlie modal donmin,

It is noted that the translhrnmation matrix T and its inverse matrix have the unsymmetrical form. From equation (19); we can get the modal components with respect to the reference phase “a”. Siinilarly, we call get the rriodal conipoiients with respect t,o tlie pliases “b” and “c” bjr rothtiou. Note that the O-inode has the same form irrespective wlmt the reference phase is. We can get seven sets of modal components: [Zi(k).z ( k ) ] , ,[;u ( k ) .i ( k ) ] , , - , , 2 : [v(k).i ( k ) ] b L l 2 : [u(k).Z(II:)]‘--1,2 (20)

And the right-hand side is changed t o

For realistic transmission line, 2 RdIi 2,. tf) the fault, is cleared. Tlic dynamics are tlicn govcrncd by t,lie post-fault differeiitial equation fpost. In addition, by re-closiiig operation, at t = t,(> t c ) tlie network t,opology rct,iirns to t,lic prc-fault one. The differential equat,ion is t.2ien fixed at. j,,, .

2. PREDICTING TRANSIENT INSTABILITY: A NOVEL METHOD This section proposes a iiiethotl for predictring traiisierit iiist,a.bilitybased on reachability analysis of nonlinear hybrid automat>a.Note that, the authors (IIikihara. 2005, Susuki et al. 2005) show a geiieral framework for power system stability analysis based on 1iyk)rid systcin thcory.

2.1 Nonlinear hybrid autommtori H

A nonlinear hybrid automatoii H (Tomlin 1998) is clefiiirtl to be the collrction

The nonlinear hybrid automatori can combine the transient, tiyiiamics cvitli line switching operations. In H the vect,or field f is descrihed by the diffcrential equations Jpre. Jon, and fposl: in (2). On the ot.her hand5discrete variables { q?} are assigned t,o the above system st,at>es: pre-fault,, fault-on. and post.-fault oi~cs.Tlic discrctc transition E ca,ntlieii describe the t,opological change of tlie constedby { u ( . ) E PCO I E VT E R} andD A { d ( . ) E PCo I d ( ~ E) DVT E X } . PC" denotes t,he space of piecewise contiiiuous fiiiictions over R; Z,u x E d i s tlie product of the finit,e set of ete control act,ions antl t,he finit,e set, of d iscret.e d ist.11rlmnce a.c1 ions:

u

f : 0 x X x U x D + Y'X is the vect,or field which associat.es a nonlinear control system f ( q ,x,'IL, d ) with each discrete statr: q E &: E : Q x X x Zu x Z d 2QXx is the discrete t,raiisit,ion fimct,iori; Inzl C Q x X i s t~heinva.riant associatcd with each disc;ret,e state, meaning t,liat the system evolves according t,o k = f(y, x . u,d ) only if ( q , x ) E Jnv; I & Q x X is the set of initial states; E is tkic t,rajoctory ac:ccpt~ancocondition .

u

bd = Obt.' for b' CJ x X . 0 denotes a map, called property, from the set of all executions of II t o {True,False} (1,ygeros ~t n i . 1990).

154

power systems siich a s d c links by ? I ( . ) E T i arid unrcgulatcd powcxr flow duc to clcctricity trading as d(.) E D . Hence {he nonlinear hybrid auloinaton H is applicable to modeling of the transient dynamics with taking thc relay opcrwtioiis into account.

EeJo

EeJs

generator

transmission line

infinite

bus Fig. 2. Single machine-infinite bus (ShlIB) system

EeJs Pm

The present subscction int,roduccsa novel nictliod

for predictsingtlic transicnt, instability. Now tlcfinc an unsafe set G c Q x X for t,he hybrid automaton €3. The unsafe set is interpreted as a subset, of the systein states in which a power system shou~s iinaccept a.hleopera.t,ions:for esu.mples, occiirrence of large rotor speed deviation and stepping- out^ of generators. A reachable set &(G) for the time t ( < 0) in the hybrid autornalon H is then defined by a subset of Q x X in wliicli aiiy systein state readies the bountlary UG of G in It1 time despite of any control ( , u ( . ) , g u [ . ] ) Fig. . 1 shows t,he concept of reachable set,s in contiiiuous st ate space. The concept of reachable set,s is much important for estiniat,ing tlie transient instability of power syst,em. If a. system st,a.t,eexists in X t ( G ) , then we call evaluate tliat the power xysterri will reach unacceptable operation in It1 t,irnc.Thc esiirnation is possible at any onset, of discret,e transit,ions such as acciclerit,alfaults, clea.ring and re-closing operations. Namely7 by evaluating the roachable set>s, we caii tliscuss at, t,he onset of accidental faults whet,l-ier t h e power system goes t,o iinucceptable opcrat,ions or not. Thc reac:liabilitjyanalysis t,liiis makes it possible to predict the transient, instabil-

(a) fault-on

4 3 (b) one line operation

( c ) two lines operation

Fig. 3. Fault condition following control sequence of relay devices

3.1 Fault condition The subsection gives us a fa,ult condition for t~he analysis of ShlIB system and model it via. the hybrid automaton H . Fig. 3 shcxvs t~hefmlt cnndition following control sequence of relay devices. The thrcc modes in t,hc figure arc represented :is follows:

Fig. 1. Conccpt of rcachable set for continuous state space. G is an unsafc set in which a power systcni slio~.vsunacceptable operations.

3. APPLICATION T O SINGLE hf ACHINE-INFINITE BUS SYSTEhI

This section applies the proposed iiiet,liod to an a.nalysis of siiigle iriachirie-irifiiiite bus (SMIB) systeni in Fig. '2. Tlie SMIB syst,em consists of it syixlironous mactiine, an iiifiiiit,e bus, and two parallel transmission lines. An infinite bus is a. source of voltage constant in phase, magnit,ude, and frequency, and is not, affect,ed by t,lie amount, of current, wilhdrawn from ii (Kimba.rk 1947).

0

0

fault-on (a) is the state during a sustained fault, on one line. Tlicn tlic generator cannot supply it,s electric power output to the ac transmission; one line operation (b) is th ing the falilt, line by protective relay operation; and two lines operation (c) is tlic statc: after reclosing the faull; line.

The fault-clearing time t, and the reclosing time as cmnf.rol pat-a,meters in i,he following The onsetr of acciclent,al faultr is fixed at, zero in t.his paper.

3.2 Descr'pt'on osf '-I Tlie fault condition and a,ssociated transient dynamics are now modeled via the following iionlinea,r hybrid aiiiomai.on H :

155

Go - {qi.qz,q3} x { ( S . U , Z ) dG I

G

= ( q i . q 2 , ~ 3 }x ( ( ~ , w , zE ) = (41) x

X ; X;

> wC}.

~ w I =wC},

((6.w, z ) E x;121 < w,, z

= 0>,

(4)

wlicre w, = 2.0. h y st&c in G physically iniplies unaccept>al)leopera,tions of the SMIB syst,em tjecarLse I , L ~occurrelice r o ~ o rspred dcvia.tion and stepping-out of gcncmtor. dt

Note that the tiefinit,ioii of unsafe sets is crucial for t,he proposed metfhod i n this paper. The estimation of instability strongly depends on how TVC fix iinacccpt,ablc st,atcs of powor syst,cins. In the present automat.on H , continuous dynamics are described by tlie swing equation system. The system represent.s the stepping-out state of generat>oras a stable limit cycle of the second kind (hlinorskg 1947). The location of limit cycle is w M plr,/k (Hasegawa and Ueda 1999). Therefore. to avoid t Iic largc rot.or spccd deviation and stepping-out,:in t,liispaper, w, is &xed a.t,the above value which does no{, exc

cv = 0.5 if q = 4 2 .

q q 1 , (4d.tJT. a l ) = ( q 2 , (6, JJ. t J T ) . q q z , ( b J . t r ) T , a 2 ) = (qd. ( b J , t r ) T ) . 3

Inv \

=

U(n&.x), $=I

The above descriplion is based on (Tomlin 1998). Table 1 shows t lie phvsical rricming of variables and parameters in N. The variables and paramctcrs are in per unit system. In H the discrete variablc ql is assigncd to tlic fault-on stat,q2 to the one line operation, and q3 to the two lines operation. Tlic clraring a i d redosing operations are also regarded nit,ransicnt, st abilit,y malysis. nmtica 3 5 ( 3 ) , 349-370. csuctions o n Ci7%'2L%t.s urcd Systems Minorsky, M. (1947). Inlroductiorc to Non-L%rzear CAS-34(2), 160-173. M e c h m i c s . Edwards Brothers. Arin Arbor, Dehlarco, C. L. (2001). A plia.se t,ransit,ionmodel USA. for ca.scading network failure. IEBE Control Mitchell, I. and C. Tomlin (2000). Lcvcl set mcthSgstems Magazine 21(6), 40-51. ods for comput,at,ion in hybrid systems. In: Dobson, I., B. A. Carreras, V. E. Lynch and Hybrid Systems: Cornputation und Conikol n. E. Nemiman (2004). Complex syst,emsanal(B. Krogli iiiicl N. Lyiicli, Ecls.). Lecture N o h ysis of scrics of blackoi&: Casca,tling failin Comput,cr Scierice 1790. Springer-Verlag. ure, crit,icalit,y,and self-orgmization. 111: Propp. 310 323. ceedings of the Bulk Power System Dynamics Sakiyama, T., T. Uerriiira,: T. Ochi, T. Hikiand CovitroZ-VI. Cortiria. tl'hmpezzo? Italy. liara. Y. Susuki arid €I. Ebiria (2006). Appp. 438-451. plic.at,ion of hybrid system theory t c Domenica., NI., Beiiedett,o, D. and Sangiovannisyst,eim analysis (TV). In: An,nmal Vincentelli, A., Eds. (2001). Hybrid Systems: Record I.E.E.Japan. Vol. 6. pp. 269Computation und Control. Lecture Notes in Japaiiosc). Comput>erScience 2034. Springer-Verlag. Susuki, Y . a.nd T. Hikihara (2006). Application Ebina,, €I., Y. Susuki and T. Hikiliara (2005). of hybrid system theory to power system Aii aiialysis of transient. dynamics of voltage stabilit,y malysis. In: 9th Intern.atina2 tric power systmri based on reachable Workshop on Hybrid Systems: Computation Technical Report NLP2005-31. IEICE. (in a71.d Control. Santa Ba.rabala., USA. (post,er Japaiiesc). present a,t.ion). Fairlcy, P. (2001). The unruly power grid. IEEE Susuki, Y., H. Ebiiia arid T. Hikihara (2005). ApSpectrum 41(8), 22-27. Aicat,ion of hybrid system theory to power Vorir1;ts~ G. K.: K. J . Kyriakopoulos antl C. D. tern stability aiialysis. In: Proceedings o f Vouriias (2004). Hybrid systems inocleliiig for the 2005 International Symposium on Nonlinpower systems. IEEE Circuits and Systems ea,r Th,eory and its Application,s. Bruge, BelMugazine 4(3). 16-23. gium. pp. 202-205. Gellings, C. W. and K. E, Yeager (2004). TransTalukdar: S. N., J. Apt, M. Ilk, L. 13. Lave and forming the electric infrastructure. Physics M. G. Morgan (2003). Cascarliilg failures: Toda?/ 57(12)!45-51. Survival wrsiis prevent ion. Thr N e c k i c i l y Geyer. T., &I. Larsson arid M. Morari (2003). Journ,cd 16(9), 25-31. Hybrid emcrgency voltage control in power Tomlin, C. J. (1998). Hybrid control of air t.raffic systems. In: Pro(;ecddinp o f the Europeun management systems. PhD disserhtion. UniContial Confereme 2003. Cambridge, UK. vr:rsit,y of California. at, Bcrkclcy. Hasegawa; Y. and Y. U(-:da (1999). Global basin 'Lbmlin, C. J., I. Mit,chell. A. L.1. Bayen and st,ruct>ureof att,raction of two degrees of freeId. Oishi (2003). Cornputjational techniques dom swing equation system. Intemakional for the verificat,ion of hybrid J o ~ ofd Bifurcnr'ion and CI~ao.9 9(8), 1549ceedings of the IEEE 91(7), 986-1001. 1569. Henzinger, T. A. (1996). The t,heory of hybrid autoinat,a.. In: Prnccetlings of the 11th Rn,n,ual

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Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

STABILITY ANALYSIS OF AN ISLANDED GENERATOR P. Lilje', A. Petroianu2 'PhD Candidale; 'Univevsily ($Cape Town Abstract: The authors investigate the stability of an islanded generator. They examine the effect of a predominantly resistive load on small-signal (frcqucncy) stability of' an islanded gcncrator. Thc authors derive a new linear generator modcl for the islanded power station, and pcrform small-sibma1 arialyscs usiiig tliis rnodel. The analyses arc also pcrkmcd using Lwo industrial -grade soflwarz packages, and thc results arc compared. The authors show that prcdominantly rcsistivc loads lead to poor damping of the spccd rcsponse, and that an increase in the L/R ratio further dccrcascs the damping. The use of a power system stabilizer is proposed to increase the damping of the speed response by varying the generator terminal voltage in response to speed changes. In this sense the PSS is also contributing to frequency control. Finally, the authors study the effect of the turbine and its control system on stability. Copyright 02006 WAC Keywords: Generator modeling, small-signal analysis, islanded power station

1

lNTRODUCTION

Major power system disturbances can result in the formation of islands in which one or more generators supply local load. A conventional power system has a self-regulating characteristic, i.e. the load dccrcascs Qncrcascs) if thc frcquency decreases (increases). This is not the case in a power system with a resistive load- in such a power system the load power is independent o f frequency, If the load voltage is constant the generator electrical power is also constant, but the electrical torque decreases (increases) with an increase (decrease) in speed (Lilje et a/., 2004). Resistive loads can &crease damping, and are therefore of particular interest. One example of a resistive load is a smelter Another conceivable example is that of a high-energy resistor used to dissipate some of the excess energy produced by a power plant when it is disconncctcd from thc power system (Lil~cet a1 ,2004) Such a resistor can be used to mitigate problems occurring in a power plant (e g blades overheating) following the disconnection The long-term operation of an islanded power station with a predotnnantly resistive load needs to be investigated from the small-signal stability viewpoint

generator does not represent a typical power system for which generator models are developed (IEEE Std 11 101991). The linear generator models found in the literature (Kundur, 1993, de Mello et n l 1969, de Mello et 01, 1975) do not include the effects o f speed variation on generator voltage. To include the relationship between electrical torque and frequency a? described above it is necessary to include thc effects of speed variation on voltage for the power system studied in this paper The linear model is used in small-signal stability studies. In these studies thc effect on damping of various combinations of resistance and inductance is determined. A power system stabilizer is proposed to increase the damping by varying excitation in response to speed changes. The PSS is similar to a conventional power system stabilizer, but in this case it is specifically used to aid in frequency control. Lastly the effect on stability of the turbine and its control system is investigated.

2

DERIVATION OF A LINEAR MODEL

This section presents a summary o f the derivation of a linear model of an islanded generator supplying a resistive load. The structure of the model is shown in Fig. I.

In this paper the authors study the dynamics, and specifically the frequency control, of a single generator supplying a resistive load The calculation o f damping is conservative as it ignore5 the damping that would be iiitroduced by inductioii motor loads. A new linear model of an islanded generator supplying a resistive load was developed. This was done to aid in the understanding of the dynamics, and since a small-signal analysis using two commercially available software packages yielded slightly different results. The islanded

. Fig. 1 : Structure of linear modcl

159

2 1 Linear model ofgenerator, excitation and load The model includes: Shaft dynamics Core saturation; The dynamics of the field circuit; and The dynamics of the excitation system.

ed = idRE- X E i q e, = i, RE + XEid

The model is based on the following assumptions The fast statoi tiansieiits iepreseiited by the pll/ tcrmv in the stator voltage equations may be neglected, The effects of the damper windings may be neglected, and The external impedance R, + j x b is con-

A linear form of (6) was obtained by differentiating with respect to W and The partial derivatives (at !he

v,d.

initial operating point) of

and i, were

derivatives (at the initial operating point) of the stator currents, the paramctcrs u,b,c and d were introduced

The proccss followed in deriving a linear modcl is similar to that used in deriving a linear single-machine i n h i t e bus model (Kundur 1993; de Mello et a/., 1969; de Mello et a/., 1975). The critical difference is that the effects of speed variation on terminal voltage are consdered.

in thc derivation:

Aid = d UK ld. vfd Aiq = cAo+ d A V ,

The shaft dynamics are described by the following firstorder differential equation:

K,

V u d V,,, , id

calculated using equations (3), (4) and (7). The partial derivatives were then expressed in terms of the perturbed variables A@ and A v f d .In !he case of the partial

stant

In (I),

(7)

Finally, the perturbed electrical torque was expressed as a function of Am and A V , d ,

accounts for mechanical damping, i.e. bearing

where the parameters

K2 and K7 depend 011 the initial

operating point.

friction and windage. It is noted that the term K,p.I approximates the true mechanical characteristics, since although bearing friction is a function of 0 , windage is a

It was assumed that the same saturation characteristic applies to both the d-axis and the q-axis, i.e. = Krq,

Yd

function of 0 2The . linearized form of (1) is:

The perturbed field flux was expressed as a function of the perturbed field voltage and perturbed shaft speed:

AT,, -ATF = 2 H d A w + ~ , ~ w(2) dt The model is based on the synchronous machine equations (3)-(6), and the circuit constraints (7).

ed =-my, - R,id e, = +myd - Ruiq

AE, (3)

is obtained from the excitation system transfer

function, GL,(s) and the perturbed terminal voltage,

Ae, which I S approximatcd as follows.

The resulting linear model is shown in Fig. 4, where the parameters are defincd in cquations (16)-(38).

160

2.2 Linear model of turbine and its control system Typical models of turbines and turbine control systems are presented in (Kundur, 1993; IEEE, 1991). The model used apply to a 3000 rprn, single-reheat, tandem corn pound steam turbine with an clectrornechanical control system- see the block diagrams in Fig. 2 and Fig. 3. Linear models were derived by reducing these block diagrams. Note that the output of the turbine model was modeled as mechanical torque, not power. This is a conservative choice as it will lead to a lower calculated damping than if the output were modeled as mechanical power. Throlle

3

presI"re

STABILITY ANALYSlS

In this section the eigenvalues of the islanded generator supplying a resistive load are calculated.

3.1 Anulysis neglecting turbine control system The transfer function A 0 was obtained from the

CVP

/AT

model of Fig. 4 The transfer function

Fig. 2 : Turbine model

AOIATnl was

then derived using equation (2), and the roots were calculatcd from its dcnominator (in this scction thc turbinc output is assumed to remain constant, hence hcrc ATn

is represents a disturbance torque). Table 1 shows the results. Also shown are the eigenvalues as obtained from two analysis software programs. The results are almost identical in the three cases.

Fig. 3 :Turbine control systcm modcl

Equation (12) shows the linear model of the turbine control system. Similarly, (13) shows the linear model of the turbine. Multiplying (12) and (13) yields the transfer function ATm/ A m .

The system is unstable, because although the turbine torque is constant, the electrical torque decreases (increases) with an increase (decrease) in speed.

Fig 4 Linear model of single generator supplying a resistivc load

161

pole of the transfer function

Table I heenvalues for a load o f 0.826 + 10D U (turbine controls excluded) MATLAB

DIgSLENT

0 -24.496 +2 1.2991 0.198

0 -25.190 k17.3991 0.202

Linear model

3.2 Analysis including turbine control system

-25.38 izj25.10 0.199

The effect of the turbine and turbine control system were investigated using the linear models presented in section 2 and MATLAB’s ‘sisotool’ function. The load power was set to 0.826i~j0.3pu, and the PSS gain was 2. Fig. 6 shows the root locus and bode diagram of the system with an increasing turbine control system gain, K G .The system is stable even if K , = 0 due to the

PSS. Increasing this gain iinpmves the system danipiiig, although thc systcm bccomcs unstablc again at vcry large gains.

Table 2 Unstable ciescnvaluc from linear model for loads of different LE l R , ratios

LE i R,

0.826+J0

0.826+J0.3 0.826+j0.6

into the

stable region (from 10.25 ris to -0.58 r/s).

The introduction of a series load inductancc further decreases the damping, as shown in Table 2 At higher (lower) frequencies the higher (lower) reactance reduces the voltage applied to the resiqtor, thereby reducing (increasing) the electrical torque in the generator

Load power (PU)

AwiAT,,, well

The squares in Fig. 6 show the closed loop pole positions for a gain K , = 25. The system has a significant

Unstable eirrenvalue 0 0.205 0.363 0.247 0.726 0.339

phase inargiii and gain margin, as indicated in the bode diagrams. Root Locus Editor (Cl

O P ~ ~ C OBode O P Editor (Cl

5

A PSS adds damping to the system, and stabilizes the inner loop (i,e, the electrical loop in Fig. 1). The authors proposc a PSS shown in Fig. 5. In the invcstigations of this paper no phase lead was included in the PSS, i.e.

. . . ...*.. . . . ..

4 3

2

Ti =Z, = 0 , because:

1

a) at frequencies of up to about loris the clectrical loop

0

and mechanical loop act in unison. h) at higher frequencies the gain of the electrical loop is about 50dB more than that of the mechanical loop.

1

Fieq 4 01 radisec

-150

Sllbb im(?

1

0

2

10

-90

3 -180

4

Points a) and b) above can be verified by comparing the bode plots of the following two transfer functions:

5

3

1

-2 Real Axis

-270 0 0.0001

1 10

ImW

Frequency(radlsw;)

€ig.6 :Root locus and bode diagrams for system including turbine controls

4

Fig 5 Power system stabilizer The gain

CONCLUSION

The authors studied the stability of an islanded generator that supplies a resistive load A linear model has been developed It wa5 used to calculate the system’s eigenvalues The model differs from other linear models found in the literature- i t includes the effect of speed variations on the terminal voltages. The dominant pole was found to be unstable, and the damping decreases with an increase in the LIR ratio. The PSS can provide suffj~ientdamping to StdbiliZe the islanded generator supplying a resistive load In this case the PSS is used specifically to improve frequency control. This differs from the Conventional use of a PSS

K, determines the additional damping

introduced by the controller. In the case of a load of K, = 2 moves the unstable

0 826+jO 3 pu, a gain of

162

to increase the damping of oscillations in multi-machine power systems.

E,ci field voltage in pu

K , mechanical damping constant in pu a,b, C , d variables used in the calculation of the constants K2,K, ,K, ,K,,K,

The authors further studied the effect of the turbine and its control system on the damping The turbine control systcm provides additional damping to the specd R sponse As the gain of the turbine control system is increased the system becomes oscillatory. If the gain is increased too much the system becomes unstable

Ro,R , armature resistance, field resijtance all in pu R,, RE series equivalent resistance and external resstancc of high-cncrgy rcsistor, all in pu

x,, xTqtotal d - and q-axis reactances L,, x, external inductance and reactance, pu

SYMBOLS constants used in describing the generator

A, B

CVP i, j

L, ,L,,

saturation characteristic control valve position complex operaton

tance

,Layssaturated values o f d - and q-axis mutual

vd,vCl d- and q-axis stator flux linkages in pu y ',

inductances

Ladzrunsaturated value of d-axis mutual indutance Ge.y(s) linear transfer function of excitation system K, ,s,,, ,s,, stabilizing controller gain and limts

field flux linkage in pu

id,i, d- and q-axis stator currents in pu

. .

zdc1, lye, initial d- and q-axis armaturc currents in pu

i,

initial armature current in pu,

zd, + zqO .J?L

APPENDIX A: EQUATIONS D E F M G THE PARAMETERS OF THE LINEAR MODEL

ed,eq per unit d- and q-axis stator voltages

edO,e4, initial d- and q-axis armature voltages

e terminal voltage in pu,

The parameters for the model of Fig. 4are calculated using the following equations:

,/=

e, initial terminal voltage in pu,

Jm

@(, initial powcr factor angk

6,, initial internal machine angle, in radians 6 rotor angle relative to infinite bus, in radians

n

p operator dt

c,,mechanical power in pu A refers to a perturbation in a variable

h ' shaft inertia constant in seconds K , excitation system gain K , ,KAqsaturation constants

KVn,incremental

slope of the non-linear valve charac-

teristic Z, field circuit time constant in seconds

s Laplace operator (complex frequency) electrical torque in pu

T,n mechanical

torque in pu

u) rotational speed in pu W , ratcd rotational speed in pu, W ,

leakage inductance and field circuit induc-

=1

W , rated rotational speed in rs.'

163

APPENDIX B GENERATOR PARAMETERS The parameters o r the generator used in the paper are given below. Unless otherwise indicated, all values are in per unit.

S=211.7MVA

U , =13.2kV

Ld =2.01

L:, =0.24 L, =1.96 L, =0.14

Ra = 0.001 K,=0.01 K , = 200

z,' = 11 o,,~ = 1 0 0 ~ H = 2.0 A=0.03 B z 6 . 9 ~,~=0.8 Z, = 0.02

REFERENCES de Mello F. P., C. Concordia (April 1969). Concepts o f Synchronous Machine Stability as Affected by Excit ation Control, IEEE Trans. PAS, Vol. 88, No. 4, pp. 316329 deMello F. P., T. F. Laskowski (May/ June 1975). Concepts of power system dynamic stability, IEEE Trans., Vol. PAS-94, No. 3 IEEE Std. I 1 10-1991, Power Engineering Society, IEEE Guide for Synchronous Generalor Modeling Praclices in Stability Analyses

K , = L [ - b R u +d(Luyr+ I,

,,)I+ (35)

IEEE Working Group on Prime Mover and Energy Supply Models for System Dynamic Performance Studies, (May 1991). Dynamic Models for Fossil Fuelled Steam Units in Power System Studies, IEEE Trans. Power Systems, Vol. 6, No. 2 Kundur P. (1993). Power System Stability and Control, Electric Power Research Institute, MGraw-Hill Inc., ISBN 0-07-035958-X Lilje P., A. Petroianu (2004),Power plant islanding with the aid o f a controlled resistor, IEEE Afiicon Conference, Vol. 2, pp. 775-781

164

Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

PUBLICATIONS

PRIMARY CONTROL SYSTEM AND STABILITY ANALYSIS OF A HYDROPOWER PLANT Maria Regina Gomes Zoby, Jurandir Itizo Yanagihara Department ojMechanica1 Engineering - Polytechnic School of the University ofS60 Paulo

Abstract: The objective of this work is to study the primary control system of a hydropower plant operating isolated. The plant is modeled by differential equations and the results are compared with Geld data from an actual hydropowcr plant, with dcviations lowcr than 1 .O%. The study of thc primary control systcm is conducted in order to define optimal parameters for the controllers. Four controllers are studied: traditional, PI, PID and PIPD. The controllers’ performances are evaluated by stability criteria and a performance index. For the hydropower plant studied, the PI controller has the best performance. Copyright 02006 IFAC Key words: modcling, hydroelcctric systems, primary regulation, optimal control, stability

1.

INTRODUCTION

This work deals with the operation and control of hydropower plants and its basic equipments and presents an analysis of the dynamic behavior of an actual hydropower plant. The main objectives are to model an actual plant using a nonlinear model based on differential equations with parameters that can be easily estimated or obtained from field tests and to study the primary control system for the plant in isolatcd operation in order to define the optimal parameters for the chosen controllers. The power plants have particular control systems to ensure stable operation. The satisfactory operation of a power system rcquires a frequcncy control that keeps it to acceptable liinits when the system is submitted to significant load variation. As the frequency is common to all the system, a change on the active power at one point will be reflected on the net as a frequency variation (KUNDUR, 1994).

1.1. Primary Control System The primary control system is composed of the speed sensor, the controller, the actuator and the hydraulic supply system. Its main functions are to maintain the

angular speed constant and equal to its nominal value and to change the distributor position when the load varies or the operation conditions (as head) changes. Each operation condition has its requirements so the controller parameters that are adequate to one condition may not be adequate to another one. The use of adaptive control is an option to satisfy different operating conditions. Otherwise, the usual procedure to define the controller parameters is to considcr thc isolated condition that imposcs thc most severe operation requirements and guarantees that the stability will be sustained in this case (SILVA, 2000). This procedure is adopted in the stability study of this work.

2.

MODEL EQUATIONS

2. I . Hydraulic Circuit The model is based on the assumption that water is as an incompressible fluid and that the penstocks are rigid. Two kinds of plants are presented: single penstock and multiple penstocks with a common conduit.

165

For the individual penstock,

Single Penstock. A single pcnstock plant has onc conduit wpplying each turbine. From the laws of momentum, the rate of change of flow in the penstock is (IEEE, 1992):

(h, - h , - h )-=gA dq I dt

’

(1)

h, =jq2

(2)

In this equation h,, is the static pressure of the water column at the turbine’s admission [m], h,, is the pressure at the turbine’s admission [m],h,, is the friction loss on the individual conduit [in] and T,,,, is the time constant of each individual penstock [s].

In these equations ho is the static pressure of the water column [m], hL is the pressure at the turbine admission [m], h, is the friction pressure loss [m], g is the gravitational force [ m / s 2 ] , A is the conduit’s transversal section [m’], 1 is the conduit’s length [m], q is the flow rate [m’/s] and f is the loss coeficient of the conduit. In per unit it becomes,

The equation can then be written as,

2.2. Equipmcnts

The basic equipments on a stability study of a hydropower plant are the turbine and the generator. The following models represent their operation and the distributor action.

The water starting time is defined as: (4)

Distributor. The equation 12 represents the relation between the gate position (Y) and the prime control system signal, K Y= (12)

If the penstock presents different sections then,

(T,s+ l)(T,s + 1)

Multiple Pemtocks with a Common Conduit. A plant with multiple penstocks with a common conduit is rcpresented on the fol 1owing fi gurc .

where T, and T2 are the actuator’s time consCants.

Turbine. The turbine can be modeled by its valve characteristic,

T

Common Conduit

/

u

, # , /

r

cr=G&

b

G(s) =

G is defined as,

(13)

Go

(14)

~

1+T,s

G , ( y )= d o + d , y + d , y 2 Fig. 1 . Multiple Penslocks supplied rrom a Common Conduit

(15)

where y, is the gate position ( y = 1 for nominal position and J = 0 for closed position) and T2, is the gate time constant. The gate time constant in this work is considered 1.0 second.

From the equations presented, the rate of flow change in the penstocks is (IEEE, 1992),

The mechanical power can be writen as (IEEE, 1992),

P,

= pgh,q

-

K

0’

(16)

where P,, i s the mechanical power [W], p the water density [kg/m3] and wthe angular speed [Hz]. The turbine’s loss coefficient (Kl) is defined a5 a sccond order equation,

K , = a l q 2 + b, q+ c +

where h,, is the static pressure of the water column at the bifurcation [m], k , is the pressurc at the bifurcation [m], hfcis the friction loss on the common conduit [m], T,, i s the water starting time constant of thc common conduit [s] according to equation 4, q( is the flow rate in the common conduit [m’/\l and qLis the flow rate i n the individual penstock [irr’/s].

(17)

Generator. The difference between the values of the mechanical power (P,n) and electrical power ( P p ) causes a variation on the axis torque which genearates the angular speed variation. If we define the constant H a s , 166

1

5

2

Jwo H = kinetic.energy.at.nan.speed-nominal.aparent. power

S,

(18)

whcrc J is the generator inertia [kg.m2], q,is the nominal speed [Hz] and S, is the nominal apparent power [V.A], then we can write,

or, in per unit,

Proportional Integral and Proportional Derivative. This controller is the combination of a proportional integral controllcr and a proportional derivative controllcr and is shown in the following figurc.

Fig. 3. Controllcr - PI-PD - Proportional Integral and Proportional Derivative

We can also define,

Proportional Integral and Derivative. This controller has the following transfer function,

G, (s) = K , 1+

The electrical powcr can be writtcn a5 function of the load power (PG)as (Kundur , 1994),

hp, = AFG+ FGD,,floo.AiB

(22)

As result, we obtain,

-AFti = ~H.S.AW+?~,;,,,~CO~.AW (23)

@?,

3.

+ T,s

~

K

s

1

FIELD TESTS RESULTS OF ACTUALHYDROPOWER STATION

(27)

AN

Field tests results of an actual hydropower station with three Francis turbines built in Brazil are used to evaluate the model and to calculate its parameters. Fig. 4 shows the plant circuit and Tab. 1 presents its main geometric characteristics.

2.3. Controllers The four controllers studied in this work are represented i n Fig. 2. Fig. 4. Hydropower plant hydraulic circuit

Fig. 2. Schematic View of the Control System Traditional Controller. The traditional controller has the following transfer function (CEPEL, 1999),

The head water level (hM)is 479.2 metera and the tail water level (h,) varies from 303.7 to 3 1 1.8 meters. So the net head varies approximately from 165.4 to 173.5 meters. The inertia of the generator is 600 ton.m2. The optimal operation conditions are, speed: 450 rpm; power: 32.37 MW; flow rate: 2 1.O mz/s; net head: 168 m. Tablc I . Hvdraulic Circuit

where r is the transient droop and T, is the controller zcro parameter.

Circuit

Proportional IuLtegrutive. The transfer function of this controller is,

whcrc T, is thc intcgral constant.

167

L [m] d [ml A [m2] T, I turbine 0.74 29.84

Conduit 1

1728.0 6.16

Conduit2

355.0

4.00

12.57

0.36

Individual 1.2.3 Spiral Case 1.2.3 Draft tube 1.2.3

40.0 16.6 10.9

2.20 1 .Ill 2.36

3.80 2.57 4.37

0.13

Total

1.34

0.08 0.03

[F]

The net head is calculated by,

h, = h,w - h,

- 0.000964

Cq 2

(28)

Table 2. Operation points - 167m net head

Y [pul 0.5 0.6 0.7 0.8 0.9 1.0

Table 5. Base Values used to Calculate the Paramctcrs in Der unit [mi/sl Flow rate at the optimal point 21.0

qbase

Q [m3/sl q [“h] P [MWI 15.2 18.0 20.9 23.3 25.3 27.4

91.5 93.5 94.4 94.0 93.5 92.7

22.6 27.4 32.0 35.6 38.5 41.4

hba\e [m] Gross head at the nominal point 168.4

[Hz]

[kWl Nominal Apparent Power

Nominal Sped

35966.7

7.5

Pbare

Table 6. Model Parameters in per unit Tw [s] f‘ d, + d , y + d , y ’

1.34

0.002524 -0.570+ 2 . 0 2 3 ~ -0.142~~

Table 3. Operation points - I68m net head Y [pul 0.5 0.6 0.7 0.8 0.9

Q lm3/sl 15.3 18.0 21.0 23.4 25.4 27.5

1.0

q [“/.I 91.5 93.6 94.4 94.1 93.5 92.8

Table 4. Operation points

Y [pul 0.5 0.6 0.7 0.8 0.9

Q lm3/sl 15.3 18.2 21.0 23.4 25.6 27.7

1 .o

-

P [MWI 23.0 28.0 32.4 36.0 39.0 42.0

0.469

7.407

6.95 1

0.197G2- 3490+ 0.204

The gate time con5tarit 1 5 estimated a5 1 .Os. For the actuator it is considered that T2 is zero and Tl represents the time necessary to open the gate from y=0 to y=0.632, which is 5.94s. This yields the following first order equation,

169m net head

Y=

q [“h] P [MWl 91.5 23.0 93.6 28.0 94.4 32.6 94.0 36.3 93.5 39.3 92.8 42.2

1

(5.94s

(28)

+ 1)

4.2. Model Results The model results for different gate positions with the condition of one turbine operating are compared to the field results. The deviations were very low, varying from -0.54% to 0.7607, as shown in Tab. 7. These results were considered satisfactory to validate the model of this hydropower plant.

The stability study is conducted based on the range of operation close to thc optimal conditions. This range comprises net head varying from 167 to 169 meters (operating conditions shown in Tabs. 2, 3 and 4). Thc loss coefficient Ks is determined by the results on the graphic shown in Fig. 5. The gate opening time is 9.4 seconds.

Table 7. Model Deviations compared to Real Results

ym1 q m 1 hL[%O] Pm[%I PG [%’.I Awlpul 0.7 0.8 0.9 1.0

K ~ Qx 7 6Ei03

0.60% 0.38% -0.54% 0.04%

-0.01% -0.03% 0.01% 0.06%

0.76% 0.29% -0.15% 0.49%

0.76% 0.29% -0.15% 0.49%

0.0006 0.0004 0.0010 0.0045

F 65E+03

2 p

55E+03

5 . PRIME CONTROL SYSTEM ANALYSIS

45E+03

3 5E+03 150

175

zoo

225

2511

275

The controllers studied are the traditional, PI, PID and PI-PD. To compare their performances and to determine the optimal parameters, a performance index is introduced to evaluate the speed deviation when the system is submitted to a load variation represented by a ramp from 0.779 to 1.009pu in 10 seconds. It is also required that when the system is submitted to load variation, the third peak of the speed variation is not higher than 5.0% of the ramp or 25% of the value of the first peak. The permanent droop is considered constant and equal to 5%. The performance index is defined as,

300

P [m31sl

Fig. 5. Turbine loss coeficient as a function of the flow rate for different net head conditions

4.

MODEL SIMULATION

4. I . Parameters Calculation The base values used to calculate the model parameters are presented in Tab. 5. Thc parameters of the model are listed in Tab. 6. 168

5. I . Traditional Controller

5.3. Proportional Controller

The range of values studied is T, varying from 0.5 lo 2.5, and r varying from 1.0 to 20. The performance index calculated in this range shows that the lower both parameters are, highcr is the index. The lower value of the performance index is 1,=0.664, for T I = 0.5 and r = I .0 m (Fig. 6). TRADITIONAL CONTROLLER

Integral

Derivative

(PID)

T o the PID controller the range is also the recommcndcd by Hovey (1988). The proportional gain (P=K,) varies from de 0 to 20, the integral ( I = K f l l ) from 0 to 40 and the derivative (D=K,.T,J from 0 to 20. The best performance index is 1,,=0.457, obtained Tor P= 2.0, I = 40 e D = I .0 (Fig. 8). PID CONTRQLLER 0 85, /

0 80

0.75 0 70 0.65: 0 60,

25

05

Fig. 6. performance Index as function of TI and r ’I raditional Controller Fig. 8. Performance Index as function of D and I PID Controller - P=4.0

5.2. Proportionul Integrul ( P I ) Controller The proportional (P=K,) and intcgral (I=K,/T,) gains are evaluated for P varying from 0 to 20, and I varying from 0 to 40, which is the range os values proposed by Hovey (1988).

S.4. Proportional Integral (PI-PD) Controller

-

Proportional Derivative

In this work PI is considered 1.0. The adjustable parameters are P2, I e D , and Pz varies from 0 to 20, I , from 0 to 40 and D, from 0 to 15. The results in Fig. 9 show that for higher values of D, the system has a lower performance index. For valuer over D= 15 the response bccames too oscillatory and stability is not achieved. The minimum value of the index is 1,=0.657, for P,=l.0, D=15, P2=5.0 and

PI CONTROLLER 1.0

0.91

1=40. 0.5

PI-PD CONTROLLER

20

I

Fig. 7. Performance Index as function of P and I PI Controller The lower value of the performance index for the PI controller is 1,,=0.456, for P= 4.0 and I = 40.0. In Fig. 7 , the surface shows that for higher values for the integral parameter there is a significant reduction of the index when these values vary from 0 to 25. However for values higher than 25 the reduction is not significant and we verify that for values higher than 40, the system performance is no more influenced by this parameter. Besides, for low values of the integral parameter, higher values of the proportional parameter reduce the performance index. On the other hand, for high values of the integral parameter, the proportional gain does not influence significantly the system’s performancc.

Fig. 9. Perrormance Index as runction of P2 e I - PIPD Controller - PI=1.0 e D=9.45

5.5. Controllers Cornparison

After analysing each controller submitted to different values of its adjustable parameters, the optimal system’s performance is presented on Tab. 8. The lower performance index is for the PI controller and the higher is for the Traditional Controller.

169

Table 8. Ootimal Values of the Performance Index Traditional 0.664

PI 0.456

PID 0.457

Figure 12 presents the speed variation when the system is submitted to the demand curve. The speed is kept to stability limits and the system has a good dynamic behavior with the PI optimal controller.

PI-PD 0.658

Controllers Performance

--2 8

6. CONCLUSIONS

0 02

This work combines the nonlinear model analysis with a primary control optimization. The main objectives, the model’s validation and the definition of the vptiinal parameters, ale achieved.

0

002 004

D a6 0 08 200

210

220

230

240

2511

2611

270

The model’s results with its parameters calculated based on an actual hydropower plant operating with one turbine are satisfactory and present flow, power and speed deviations lower than 1.0%. These deviations are due to approximations on thc model parameters.

Time Is1

Fig. 10. Comparison of the controller5 when the system is submittcd to a ramp AP(, = + 0.23 pzi Figure 10 shows that for all controllers the system becomes stable in about 50 seconds. The traditional controller’s response is the most oscillatory and presents the higher initial peak of -0.07 pu. The responses of the PI and PID controllers are very close to cach other. They present an initial peak of -0.68 p u and are damped and not oscillatory. The PIPD controller has also a not very oscillatory response but the system stabilizes slowly and has an initial peak of 0.60 pii.

The analysis shows that the PI controller presents the best performance index (Zd,,,,,,,=0.456) and the traditional controller has the worst performance (1,,,,,,,,=0.664). The model response with thc optimal PI controller for a real demand curve presents a behavior within the stability criteria for this kind of power plants and the mechanical power follows the demand power.

5.6. Optimal Controller Behavior ,for a Demand

REFERENCES

Curve

Centro de Pesquisa de Energia ElBtrica - CEPEL (1999). Electroinechanic Transients Analysis ANATEM - Handbook. Research Center of Electrical Energy (in Portuguese). Dorf, R. C. and R. H. Bishop. (2000) Modern Control Systems. Prentice Hall, New Jersey. Hovey, L. M. et a1 (1988). IEEE Recommended Practice for Preparation of Equipment Spcifcationsfor Speed-Governing of Hj~druulic Turbines Intended to Drive Electric Generators. The Institute of Electrical and Electronics Engineers. IEEE Working Group on Prime Mover and Energy Supply Models for System Dynamic Performance Studies (1992). Hydraulic Turbine and Turbine Control Models for System Dynamic Studies. IEEE Transactions on Power Systcms, Vol. 7, No 1 . Kundur, P. (1994). Power System Stability and Control. Mc Graw-Hill Inc., Ncw York. Ohishi, T., Soares, S., Cicogna, M., Laudanna, P., Lopes, J. (2002). Optimization of the Dispatch of Paranapanema’s River Machines. University of Campinas. (in Portuguese). Silva, A. S., Costa, A. J. S. (2000). Control and Stability on Electrical Power Systems. Federal University of Santa Catarina. Available in: (in Portuguese).

To verify the dynamic behavior of the PI controller with best performance (optimal controller) the demand curvc presented in Fig. 11 for one day is chosen. The curve’s critical stability regions are those with higher demand vaiiation. Demand Curve 12

-2

1 08

g 08

Y

g

04

02

0 1 2 3 4 5 6 7 8 9 101112131415161718192021222324

Hours

1 0Demand 1

Fig. 1 I . Demand curve (Ohishi et al., 1999) for one day Response to the Demand Curve

1 2 3 4 I 6 7 8 9 10111L1314151617181Y2021222324

Hours

Fig. 12. Speed variation when the system is submitted to a power demand curve

170

Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

PUBLlCATlONS

OBSERVER-BASED COAL MILL CONTROL USING OXYGEN MEASUREMENTS Palle Andersen, Jan Dimon Bendtsen and Tom Sandergaard Pedersen * Jan Henrik Mortensen and Rene Just Nielsen **

* Aalhorg Universio, Department of Control Engineering, Fredrik Bajers Vej 7, DK-9220 Aalborg 0, Dentnark c-inail: {pa,dimon,tom}@contrt,l.aau.dk ** Elsanz Engineering Krafivct.rk5ve.j 70, DK-7000 Skarbct.k, Denmark e-mail: {jhm,rejnl @els~am-mg.com

Abstract: This paper proposes a novel approach to coal flow estimation i n pulverized coal mills, which utilizes ineasurenients of oxygen content in the flue gas. Pulverized coal mills are typically not equipped with sensors that detect the amount of coal injected into the fui-nace.This makes control of the coal flow difficult, causing stability problems and limits the plant’s load following capabilities. To alleviate this problem without having to rely on expensive flow measurement equipment, a novel observer-based approach is investigated. A Kalman filter based on measurements of combustion air flow led into the furnace and oxygen concentration in the flue gas is designed to estimate the actual coal flow injected into the furnace. With this estimate, it becomes possible to close an inner loop around the coal mill itself, thus giving a better disturbance rejection capability. The approach is validated against a fairly detailed, nonlinear differential equation model of the furnace and the steam circuit using data measured at a Danish power plant. Keywords: Coal mills, Kalman filters, flue gas measurements, observer design

1. INTRODUCTION

In the power generation industry, the current trend toward market deregulation, coupled with increasing demands for maximization of natural resources and minimization of environmental impact, places greater and greater locus on elfective plant-wide operation and conirol systems. I m z f Jdlowing, i.e., ihe ability of the power plant to meet the power production demands at all times is becoming a major concern due to the growing competition between power companies and other market forces (Garduno-Ramirez and Lee, 2001).

’ The work presented in ths paper w;t) sponiored by Vwrneforsk

Scrvice AB, 101 53 Stockholm, Sweden.

However, when modern coal fired power plants are forced to operate under many different operating conditions, effects of variations in behavior of the coal mills supplying fuel to the plants tend to cause disturbances in both the furnace and steam systems, forcing thc power plant control to be inore cautious than what could be hoped for during load changes in order to avoid undesired transients, oscillations etc. If, on the other hand, the coal mills can be controlled precisely, it is possible to input exactly the required amount of coal into the furnace at the required time, thus improving the transient behavior dunng load changes and enabling the power plant to “ramp up” (or down) to a new operating point in a rapid manner.

Tn principle, tight control of the coal mills would bc possiblc by closing a local loop around thc coal

171

Live steam pressure

Fig. 1. Overview of Benson Boiler including control system. Only parts of the steam circuit are shown. mills; under normal circumstances, however, there is no sen,sor equipment available to measure the coal flow leaving the mill and hence no local feedback can be made. Specific coal flow measurement equipment is available on the market, but is highly expensive and not straightforward to employ in practice. Methods to detect thc coal flow using the available sensors are thus desirable, which motivates the work presented in this paper.

and finally, Section 6 sums up the main points of the work and discusses possibilities for future work.

2. CONVENTIONAL COAL MILL CONTROL Figure 1 shows a sketch of the combustion control scheme cmployed at CHP plant Nordjyllandsvmket, unit 3 (NJV3). The figure uses a mix of simplified control notation and simplified process drawing symbols in order to explain only the most essential components. The combustion control scheme consists of two control loops, a live steam pressure (LSP) loop and an oxygen concentration (CO,)control loop. The LSP loop functions as an outer loop while the Co, loop produces a correction to the excess air ratio to the LSP loop.

The main contribution of this work is the design of a state estimator for the actual coal flow that utilizes the total air flow and oxygen sensor measurement as inputs to a Kalman filter, which estimates the amount of coal combusted in the furnace. Based on this estimated coal flow, it is possible to close an inner loop around the coal mill to reject disturbances. In (Flynn, 2003) a siinilar method to estimate the pulverised coal flow using a Kalman filter approach is presented. In (Flynn, 2003), however, the coal flow estimate mainly relies on measurements from the steam path of the boiler whereas the work in the present article uses measurements "closer" to the coal mills, seen from a process technicaudynamical point of vicw.

When a deviation between the LSP and LSP reference (P5s,,-q-) occurs, the PID controller changes the reference uiit/.,,,,j to the coal inills in combination with the boiler load signal. Furthermore, this signal is fed into the air controller where the total amount of combusand the excess air tion air is calculated from rizg,,f ratio.

The outline of the rest of this paper is as follows. First, in Section 2 we review the conventional approach to Benson boiler operation and coal mill control, focusing on available measurements etc. Then, in Section 3 we present a Kalman filter-based estimator design that utilizes measurements of oxygen content in flue gas, which enables a much faster feedback, and hence more efficient control, than conventional approaches. In Section 4, the concept is validated using actual measurement data from a Danish power plant together with a fairly dctailcd simulation model. Next, Scction 5 discusses a potential observer based control scheme, which utilizcs thc novcl obscrvcr in a cascadc sctup,

Of the total combustion air approximately one fourth

(called primary air) is used to convey the pulverised coal from the coal mills to the burner nozzles. The reinaining air is injected through three inlets positioned around each of the 16 burners (burner air) and above Lhe Pour highest positioned burners (over$re air). With the introduction of overfire air and quadruple burner air inlets, including the primary air, it is possible to reduce the generation of NO,, by staging the combustion. The purpose of the Co9control is to maintain a slightly lean combustion in the furnace to ensure that all carbon oxides are spent. The concentration of oxygen in

172

explained in the previous section. The oxygen concentration in the flue gas duct at the furnace outlet, Co,, is influenced in the positive direction by contributions from the inflow of primary air and in the negative direction by the (stoichiomctric) combustion and the outflow of flue gas to the smoke stack. Next we will present the equations necessary to observe coal flow using measurements of oxygen and the total air flow. Fig. 2. Setup for fuel observer design. the flue gas i s measured at the boiler outlet immediatcly after the top pass and is compared to thc refcrence value Co2r e f , which is a l-unction of the current boiler load and the number of coal mills in operation. From thc Co? dcviation a PI controllcr produce\ a correction sigiial to be multiplied with the flow reference signals to the burner and overfire air.

2.1 Coal nzrll control In the vertical roller mills used at NJV3, the raw coal from the coal bunkers is dropped through a chute onto a rotating grinding table. The centrifugal action forces the coal outwards under three static rollers where it is pulverised, and hot primary air passing the rim of thc grinding tablc from bclow drags thc pulvcriscd coal upwards. Immediately the heavy grains drop back on the grinding table while the light particles are dried and swept on to the rotating classifier vanes. Here a further filtration process occurs where only the finest particles will be conveyed to the burners via the primary air, and the remaining coal particles return to the grinding table for re-grinding. In order to control the mass flow of coal leaving the mill, three control signals are used, the primary air p o w , the raw coal ,flow and the classij?er rotational speed.The three inputs affect the net coal flow in different ways: obviously the flow of raw coal affects the amount of pulverised coal inside the mill. However, if the primmy air pow is not supplied accordingly over time, the mill will either choke or exhaust, and thus the air flow call be used for teiniporarily release or retaining coal from the mill. Likewise, the classifier rotational speed can be used for increase or decrease of the net coal flow. Because no measurement of the flow of pulverized coal is available these three inputs are controlled in a feedforward manner in dependency of *.fu,re,f with the aim to give correct steady state behaviour with dynamic compensation in order to give proper transient responses. In this paper this adjustmciit will not be considered, but we will use estimations of the coal flow in order to manipulate the coal flow reference.

3. KALMAN FILTER-BASED ESTIMATION OF COAL FLOW Figure 2 shows a block diagram of the combustion system with eiiiphasis on the oxygen control loop, as

The oxygen mass balance of the furnace can be written on state space form as

- f uCU:.fu )

co, = xo2

(1)

(2)

where V is the volume and pjs is the density of the flue gas. Co2 and Colair are the concentrations of oxygen in the flue gas duct and atmospheric air, respectively, while CO?,J,is the amount of oxygen consumed by stoichiometric combustion of 1 kg coal.2 We note that although (1) is a nonlinear model that lumps the contributions from several subsystems together, it can be considered a "well-behaved" system, i.e., the parameters do not ch<mgesignificantly over time and the nonlinearities are smooth. The coal flow r i ? ~ is , ~ described ~ using a simple linear second-order model:

(4) =Xff,]

(5)

where ao,al,ho and hl are scalar parameters. This model reflects the coal mill dynamics as well as the overall behavior of the existing control system. Using such a simple model is obviously a gross oversimplification, but since the focus in this work is on estimating the fuel flow for control purposes and not on estimating internal states in the coal mill itself, this is deemed acceptable within the scope of this work. The performance of the entire concept can likely be improved by replacing (3)-(4) with a more detailed model. inair denotes the

total air flow governed by the following first-order air fan model:

&,, = xnzo

(7)

This simplified model reprcsents the behavior of the regulated air supply system. It is noted that the model will yicld biascd cstimatcs of thc air flow in thc prcsences of disturbances such as leakages. In this plant

' In this paper, we use SI units for all physical quantities.

173

it is supposed lhat leakage flows are of minor importance since the furnace pressure is regulated to only slightly below ambient pressure, such that the the small differential pressure yields negligible leakage flow through unintcndcd openings etc. The 0 2 control block is composed of a fuel reference feedforward given by

aid a PI controller providing an aidfuel ratio correction signal, which is multiplied by the fuel reference feedforward signal and used as a reference to the air fans. The integral state of the 0 2 controller is given by

where Kl,,O, IS the conlrol gain and 7;,02is the inlegration time of the PI-controller. This implies that the air fan reference signal is XPIX f ~ L J

%.teJ

(10)

Equalions (I), ( 3 ) , (4), (6), (8) and (9) represent the model of the oxygen control loop used here. The equations can be combined into a single state space model of the form dx/dt = f ( x ,u ) , y = Cx, where

are the skate, input and output vectors of the system, respectivcly.

approximation. The model matrices ( A , B ,C) thus depend on the operating point, and it can be expected that if the load changes significantly, new model matrices may be required. In this case, linearizations in a fcw more load conditions can be evaluated, and the model matrices for a given load can be approximated by interpolation. F and G are constructed according to observations of the noise levels obtained from measurement data. In the general Kalman filter theory, F and G represent thc intcractions bctwccn thc Gaussian noisc and cach individual state or output. In our approach, we chose F and G to be diagonal, with each entry on the main diagonal representing the standard deviation of a corresponding noise channel: F = diag(1, 1,

lop3}

G = diag(3.2, lop3} Finally, K was found by solving a steady-state Riccati equation.

4. VERIFICATION OF CONCEPT In order to evaluate the potential ability of the Kalinan filter to improve control of pressure in the LSP loop of the power plant, the estimated coal flow is used as an input to a fairly detailed nonlinear simulation model. This nonlinear model was derived from energy and mass balance equations and has been validated against actual power plant measurements (Andersen et al., 2004).

To estimate the states in the above state space equations, we employ a Kalman filter. The general form of a Kalirian filler for a liiiear sy\lein

dx

- =Ax+Bu+Fv

dt y=Cx+Gw

where F and G are weighting matrices and v and w are white, zero-mean Gaussian noise sequences with standard deviations of I , is

dP =Ax^ Bu + K ( y - C.?) dt

-

9 = c.t

+

(13)

(14)

Here, K is the so-called Kalman gain, which essentially acts as a measurement feedback control driving the prediction el-rory - C.f to zero. The theory is well established, and will thus not be discussed any further here; refer to e.g., (Grewal and Andrews, 2001) for further treatment of the subject. The model equations are linearized around an appropriate operating point (&G); using a standard Taylor

Fig. 3. Nonlinear model structure. Figure 3 shows the structure of the nonlinear model. Note that the figure does not \how all states and ineasureinent points in the model, only the mosl important ones. The primary inputs to the model are the fuel reference infu,refto the coal mill and the feedwater flow &,,. The primary outputs are the pressure Pye and the enthalpy h,, = h(Pse.Ge)of the steam leaving the evaporator. All signals indicated by arrows going into the block diagram, e.g. the feedwater temperature c,,and the recirculation air flow &ca,f, are external inputs that must be supplied through measurements.

174

Figure 4 shows a simulation performed using this model along with actual power plant data acquired during the spring of 2004 from the Danish power plant I/S Nordjyllandsvaxket Unit 3 (Nordjyllandsvzrket, 1998). For most of thc scqucncc, thc plant opcratcs at a load of around 85%,but around the middle of the sequence it changes operation to almost full load, then back to 85%.

3 32-

0

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8

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7

8

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7

8

I

I

$2 0

- - Measured

6)

The second and third plots in the figure show that the estimated oxygen concentralion and air flow correspond well to the measured values, which is quite natural, since they are outputs fi-om the Kalinan filter.

From this figure, it is obvious that the estimated coal flow varies rapidly during the one-hour sequence, although the reference is entirely conslant. Furthermore. it is noticed from the lower two plots that the plant dynainics observed in the ineasuremeiit data are captured better by using the estimated coal flow than by using the coal flow reference. In parlicular, the variations in the estimated fuel flow from around 1.2 to 1.6 hours are clearly reflected in both the estimated furnace temperature and live steam pressure, while the simulation using simply the coal flow rcfercncc docs not reflect these details. The peak seen in the simulated furnace temperature at 1 .I5 hours is obviously caused by the corresponding peak in the recirculation air flow. Since the peak does not occur in the measured furnace temperature, this is in fact likely to be a single outlier in the recirculation air flow measurement data. Furthermore, it is noted that the slow variation in the recirculation air flow, which appears to be reflected in the measured furnace temperature, is apparently not reflected fully in the model.

.

F

In figure 4 the results of a Kalman observer estimation of the coal flow are shown in the top plot along with the reference coal flow to the mill. It may be noticed that the observer estimates a flow that matches the fuel reference around the low operating point, but is slightly lower at full load. More importantly, the variations reflecting the state in the furnace can be seen. Note that the variations are more interesting than the steady state behavior, because they can be used in an inner cascade control loop controlling the coal mill. The steady state behavior is of less interest because the LSP loop will invariably contain integral action and hence remove any steady state errors.

The last two plots in the figure each show one measured and two simulated data sets. The first simulation was performed using the coal flow reference as input to the simulation model explained above, whereas the second simulation was performed using the coal flow estimated by the Kalman filter. Figure 5 shows a zoomed view of Figure 4 during a part of the sequence during which the coal flow reference was kept constant. Note that in Figure 5 , the plot of the oxygen percentage is replaced by the recirculation air flow in order to explain some of the variations observed in the data.

Estimatedtl

-.-. ~ i r n u l a t e d tfuel ~ , ref.

I

4

8

I

2 3501 - -Measure

id"

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6

7

Time (hours) Fig. 4. Simulated and actual measurements. 5. OBSERVER-BASED CONTROL SCHEME

The estimated value of the coal flow may be used in the existing control scheme as illustrated in figure 6, where the estimated value is used in an inner loop feedback (cascade) in the LSP loop. This inner loop is able to reject variations caused by e.g. variations in the humidity, fuel grain size and calorific value or the coal. Furthermore it has a stabiliLing effect on the outer pressure control loop when the coal mill dynamics vary. It should be noticed that a prefilter is added in the controller in order to compensate for the new dynamic response of the controlled coal mill, so that the dynamics of the prefilter in series with the controlled coal mill has a response similar to the coal mill operated in open loop. Using this prefiller, the LSP loop will not have to be re-luned. The design of the cascade controller should reject fuel disturbances in a frequency area where the disturbances propagate to the watedsteam circuit. Observations from figures 4 and 5 indicate that the observer estimate variations in the frequency range froin 0.01 to 0.1 rad/sec, which may also be seen in the measurements of Tip2.Only the lower fi-equencerange propa-

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26.5

8 5 9

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LL

25.5'

501

' 0.8

1

1

1.2

I .4

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i.4

1.6

Fig. 7. Coal flow disturbance rejection, assuming sinusoidal disturbances. 6. CONCLUSION AND FUTURE WORK I""

0.8

1

264 262

1.2

\

1

1.6

I .4

1.6

-r 3 -

0.8

I .4

i

1.2

Time (hours)

Fig. 5. Zoomed view of Figure 4.

i

In this paper, a novel fuel flow observer for pulverized coal mills, which utilizes mcasuremcnts of oxygen content in the flue gas, was suggested. A Kalman filter based on measurements of combustion air flow led into the furnace and oxygen concentration in the flue gas was designed to estimate the actual coal flow injected into the furnace. The Kalman filter was derived from a simple model oP the coal mill and the combustion in the power plant furnace. The approach was validated against a fairly detailed, nonlinear differential equation model of the furnace and the steam circuit using data measured at a Danish power plant. Furthermore. a cascade control scheme was proposed, which utilizes the estimated coal flow. Closing the loop around the coal mill in this way exhibits potential for better disturbance rejection and load following capabilities of the plant.

O1 Control

I N

' I

I I

Fig. 6. Cascade control scheme based on fuel flow observer. gate to Pse and h,s, due to the dynamics of the cvaporator. This indicates that a bandwidth of 0.1 radtsec would be more than sufficient. In figure 7 a bode plot of the disturbance rejection ratio of a controller with a bandwidth of 0.07 rad/sec is shown. Another way of using the idea of a Kalman filter is to regard the system from the air Bow and coal flow inputs to the oxygen content and steam pressure outputs as a 2 x 2 system and design a multivariable state space controller for this system. In this set-up an observer for the system will include an estimation o f the coal flow. The advantage of a multivariable controller compared to the two SISO controllers where the airflow controls the oxygen content and the coal flow conlrols the stream pressure is lhat both inputs are active in controlling each output, making a more optimal control possible.

From here, the plan is to test the concept on an actual power plant. In this contcxt, it will be an interesting problem to devise a performance measure that can indicate the relative improvement of introducing the concept outlined in this paper. This is far from trivial, since the operating conditions of an actual power plant are difficult to reproduce.

REFERENCES Andersen, l?, J. D. Bendtsen, J. H. Mortensen, K. J. Niclsen and T. S. Pcderrcn (2004). Obscrverbased fuel control using oxygen measurement. Technical report. Vrirmeforsk Service AB. Flynn, D., Ed. (2003). Therrnul Power Plant Simulution and Control. LEE. Carduno-Rainirez, R. and K.Y. Lee (2001). Overall control of fossil-fuel power plants. In: Proc. cf the 2001 Wititer Meeting of [he IEEE Power Engineering Society. Grewal, M. and A. Andrews (2001). Kultnun Filtering. 2 ed.. John Wiley & Sons. Nordjyllandsvaxkct, IS (1998). Nordjyllandsvmkct unit 3 - advanced technology and high efficiency.

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Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

PUBLlCATlONS

FAULT DETECTION IN COAL MILLS USED IN POWER PLANTS Peter Fogh Odgaard Babak Mataji s s

* Department of Control En,g%n,ecring,Aalborg Universitg,

Aalboy, Denmark, od,[email protected] ** Elsam Engineermg A / S , Kraftverksvej 53, DK-7000 Fredericia, Denmark, [email protected]

Abst rac t In order t,o achieve high performance and efficiency of coal-fired power plant.s, it. is highly important to control the coal flow into the furna.ce in the power plant. This means suppression of disturbances and force the coal mill to deliver the required coal flow, as well as monitor tlie coal mill in order to detect faults in the coal mill when they emerge. This paper deals with the second objective. Based on a sirnple dynamic rriodel of the energy balance a residual is formed for the coal mill. An opt.irria.1unknown input observer is designed to estirrmte this residual. The estimated residual is following tested on nieasrired data. of a fault in a coal mill, it can hereby be concluded tliat this residual is verj' useful for detect,ing faults ill the coal mill. Copyright @ 2006 IFAC. Keywords: Fault Detection, Coa.l-fired Power Plants, Optimal Unknown Input Observer

1. IN'I'RODUC'L'TON Thc performance of a. coal-lircd powcr plant is highly dependent on the supplied coal flow into tlie furnace. In order to achieve good performance or the power plant, this coal flow should be known and controllable. In other words the performance requirements of the power plant can be trarisfered to the coal mill wliicli delivers the pulverized coal to the burners inside tlie power plant furnace. One thing is to guarantee the required coal flow, in terms of suppressing pla.nt disturbaiices. It isl however, another thing to monitor tlie coal mill for detecting faults. In order to avoid additional failures and decreased performance in the power plant unit,, it is important to dctcct any fault as soon as possible, and hopefully as the fault emerges. In most coal mills it is not possible to measure the pulverized coal flow out of the mill. 'lhe coal flow into the mill is only indirectly mea-

sura.ble. Implying that the ea.rly fault detection based on detection of drops in the coal flow of the coal mill, is iiot so sirriple as it. seeins. A critical example on a f h l t in the coal mill is caused by a blocking in the raw coal inlet pipe, a coal mill is illustrated in Fig. 1. This blocking of tlie raw coal inlet, pipe will with t,ime result in a. stopped coal flow from the coal mill to the furnace, and since the actual coal flow into tlie furnace cannot be measured, the fault in the coal mill cannot he directly detected. Dynamic: rnodeliiig and nominal control of these coal mills have been tlie topic of ninneroiis of publicatioiis. Soinr examples dealing with modeling of coal rriills are (Rees arid Flzri 2003), (Zharig et u6. 2002) a ~ i d(Tigges e l d.1998). Coriirollers fur the coal mill are designed in (Kees and Fan 2003) and (Hassclbaclicr et ul. 1992). High order clyIianiic models a.nd observer design for coal mills

177

are the topics in ( h k a y a m a et al. 2004). However, the interest has not, previously been addressed on the monitoring of the coal mills wit,h the purpose of detecting any emerging faults. ‘lhe temperature of coal dust, flow after the classificr is a good indicat,or OF the “health” of t,he coal mill, since a non-intendanl change in tlie in and out flows of the coal mill will result in a va.ria.tion i n the temperature. However, the measured ternpcralure caririol be uscld to detect faulls directly: sirice a coritrol loop is foriried to keep (,lie irieasured temperature at lOO”C! in order t o evaporate the nioist,ure in the coal. Meaning that, the fault can be seen by combining the temperature and the energy in tlie primary air. 1.e. it might be iisefiil to moriit,or an energy balance state space model of the coal mill, which lias the cricrgy flows in and out of the coal mill as inputs, a.nd the tcmpcraturc as out.put. A fault in the coal mill is in this setting an extra energy input to t,liis model. If this extra energy input could he estimated, it would be a useful residual for monitoring the coal mill, wit-11 the intension of detecting cvcntual faults in the coal mill. This residual can be estimated by inlroducing a. slate representing t,lie fault in the energy model. This state is driven by a.n unknown input which is filtered through the fa.ult model. This described estimation problem cim he solved by t,he use of a.11 opt,iinal imknown inpiit observer, see (Chen and Patton 1999). Such an optimal unknown input observer is as a consequence designed for estimating the residuallfault signal arid the temperature. A threshold method is subsequently applied to the residual with the purpose of detect.irig the fault in coal mill. It is A.S well int.eresting t.o invest.igate t.he sign of this energy balance, sirice it can be used to separate the possible faults into two cla.sses which help in the fault isolation. The fault detection method is subsequently applied to data sampled during a fault in a coal mill. This experinlent shows the potential of the proposed residual estimated based on the energy balance niodel of the coal mill.

2. THE COAL MILL

The work presented in this paper, is based 011 a Babcock MPS 212 coal mill used at Elsam’s Nordjyllandsv~rkt.et TJnit 3 . However, the method proposcd in thc papcr is so gcncric that it ca.n be a.pplied to other types of coal mills. The coal mill is illustra,ted in principles in Fig. 1. ‘The coal is fed to the coal mill through the central inlet pipe. The coal is pulverized on the rotating grinding table by tlic rollers. The pulverized coal is then blown up and the moisture content, is evaporakd by the hot primary air. The primary air is mixed by cold outside air and heated outside air, which is heated

Pulverized coal A

Grinding table

\Primary

Air

/

Figure 1. An illustration of the coal mill. by the furnace. The ratio of these air flows are used to control t,lie t,emperatiire of the primary air flow. Coal particles which in the pulverizing have becri sma.11 cnough will pass through the classificr a n d out through t.he out,let pipes int,o the fiirnace.

2.1 Conlrol arid measurements References to coal flow a,nd priina,ry air flow are given by the general power plant controller, as well a.s rotational speed of the classifier. The temperature of tlie primary air is used to control the t,emperatiire in t,he coal mill at t,he classifier. . L ’ k temperature controller is often required t o kccp tcmpcraturc constant at 100°C in order to evaporate the moisture content in the coal. A coal mill is a harsh environment in which it is difficult to perform measurements, this niearis t1ia.t all the variables are not measurable. l3.g. the actual coal flows in and out of the coal mill are not measurable. However, the primary air flow and temperature are, as well as the temperature at the classifier.

178

102

Figure 2 . An illustration of energy balance in the coal inill, where Y ' ( t ) is the temperature in the mill, Qair(t) is the energy in the primary air flow, Prnotor ( t ) denotes the power delivered by the roller motors, Qcoal(t)is the energy in the coal flow, and QInoisture(t) is tlie energy in the coal rrioistuie. ~tn,,deriot,es the inass of the mill.

0

05

1

2

15

25

Salnplas I"]

2.2Faults A number of different hults can occur in t,he coal mill, aiid if the fault leads to a decrease in the o u l p u l coal [low Liorri Llie coal mill, Lliis ca,ri lead to drop out of t h e entire power p h n t unit. Some examples on critical fa.ults are: choking of tlie raw coa,l irilct, faults iri primary a i r supply both the fan a.nd the t,emperat,iire contmller, arid finally all the sensors, etc. All these ase fa.ults which it are urgent: t:o detect.

x to(

Figure 3. A plot of the non-linear and linear inodel response compared wit,li measiireineiit,s of a p response on the coal mill. are different, however the model error due to heat of steam to a conple of degrees above 100°C is neglectable in this context.

The t3yn a.inic rion-1 inra.r model i s siibseqiientl y given by 7rLII1Crn?(t) =7fLpa(t)Cair( T P A ( t )

-

T(t))

+ h C ( t ) C C(& q q ) + 7(t)7iz,(t)Cnr. Y; '

3. ENERGY BALANCE MODEL OF THE COAL MILL

-

(2)

~ ( t ) f n , ( t ) I & tT ( t ) + Prnotor ( t ) -

'

i

A simple energy balance model of the coal mill is derived based on (Rers and Fan 2003) In this rnodcl the LO^ inill is seen {(TI, S4)> (T2, S J I , {(TI, Si), (T2, %)I> {(TI, Si), (T*, S J t , {(TI, S3), (TI, S,)) But when TI and Tz are used simultaneously, the switching option {(TI, S1), (Tz, S,)} is not a feasible one due to radial structure constraint.

220

If the results of these feasible options are examined, thcn the corresponding sub-tree of figure.3 IS obtained. In figure.3, both TI and T2 are tie switches of isolated feeder section and dotted line represents switching options.

Level 1 w

4

Fig 4. The first Step of best-first search In the end, nodes {6~,@,6),,@,@} are found by best-first search. By always expanding the most likely node, it is possible to get to a goal node or a solution quickly. But tbis procedure achieves the trade-off between optimality and computational speed. It is possible that unexplored path would have yielded a solution. Therefore, optimality is sacrificed for the sake of increased speed in best-first search. But, in cyclic best-first search, with circulatory reevaluating the unexplored nodes and path, more effective solution for feeder load balance could be found. Although the search space of cyclic best-first search is slightly larger than that of best-first search, the computation difference is negligible due to using heuristic based sub-tree. The cyclic best-first search process is as follows:

Level 2

Fig 3. Sub tree with two backup feeders 3.2 Cyclic best-first search An exhaustive search evaluates all feasible switching options o j the above sub-tree and it guarantees optimal solution. But this is probab[y not realizable jor large sub-tree because of heavy computation. On the other hand, by using heuristic search, time and effbrt can be saved by finding reasonable solution promptly. There ure usually three heuristic search way,s to find optimal(or nearoptinzal) switching pairs on the above sub-tree : depth-first, breadth-first, best-first. The advantage of the best-fivst search usually, but not alway.s, yields solution faster than any other heuristic search. Rut the problem is thut it does not always give the optinzal solution: unexplored path would have given an optimal solution. To overconie this defect, the new methodology (so called cyclic bestTfirst search) is presented in this paper. This methodology is based on best-first search. But, by using cyclic methodology, it can usually find more effective solution than best-first search. As an e-rample for a best-Jirst search, consider is the start node and node @ figure 4, where node is a goal node. Node 0i.s e.rpnnded into it.7 rhildwn node @ @ @ 0. Since the losses of node @ is 1e.w than other nodes, node @ is chosen jbr expansion. This is continued until a goal node has been found.

First step: nodes are selected by using best-first search.

Second step: Constructing the reversed sub-tree and a search is proceed by using best-first search. Reversed sub-tree is constructed by reversing levels of sub-tree that was previously constructed. As an example, consider figure 5 , the level-4 of the subtree in first step becomes the level-0 of the reversed sub-tree in second step, and the level-3 in first step becomes the level-1 in second step. After reversed sub tree is constructed, a best-first search is used to select near-optimal nodes in a reversed sub-tree

/

r''o

Y

6

((f

.O

0

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Fig 5 . The second step of best-first search

22 1

Level 4

In the second step of best-first search. nodes in each level are evaluated on condition that nodes in the lower levels are already chosen by the first step of best-first search. As an example, node @ is are already selected on condition that nodes 8,0,0 detcrmined from first step. Similarly, node (8 in levcl-2 is selected on condition that nodcs arc already determined from first step. : In the first step of best-first search, the nodes in level-2 are evaluated on condition that node 8 in level-3 and node 63 in level-4 are not selected by expansion. On the contrary, in second step, nodes @ @ was already selected before evaluating nodes in level-2, and nodes was also determined from first step. Due to using near-optimal solution from first step, more effective solution can be found in second step. After the second step of best first search, are selected. a new nodes {

Q,a

@,a)

( FAULT ON FEEDER SECTION 80)

When feeder fault is detected on section 80, The first step of best-first search for initial sub-tree is shown in figure 7. Initial sub-tree level is defined by T114, T111, T117, T118, T119, T124, T123, T122, T115, T116, T118 sequentially due to the different voltagc across

Level 0

T114

Level 1

TI11

Level 2

TI17

Level 3

TI 18

Level 4

TI19

Level 5

T124

Level 6

T I 23

Level 7

Ti 22

Level 8

TI15

Level 9

T t 16

Level t o

Tt13

Level 11

@,@,@,a,a] 4. TEST RESULT

The distribution network for KEPCO 108 bus system is used to demonstrate the validity and effectiveness of the proposed algorithm. The network consisting of two feeders with 108 busbars and 14 tie switches as shown in figure.6. The total load are 72.27[MW], 32,78[MVAR] . Table 1 shows initial feeder loadings

Fig.7. First step of best-first search for restoration on fault line section 80

L

Fig. 6. Initial configuration of 108 bus system Table 1. Feeder loading5 for 108 bu5 system

Feeder

Feeder

14.47

5.17

Feeder 13.04

Feeder

Feeder

Feeder

Feeder

8.38

14.34

9.88

13.80

In figure 7, the selected (close, open) switching pair for level 1 is (TI 14, 19) and feeder balance index is 2.579 foi the switching operation. In the process of checking nodes of each level, if checked nodes would increases index then the rest of unchecked nodes are ignored and searching proceeds to next level By pruning of the most unlikely nodes, this procedure makes it possible to get a solution much faster even if it deep down in the tree After the fir\t step of be\t-first search, selected (close, open) switching pairs are {(Tl14,19), (TI 11,26), (TI 17,44), (T118,73), (T119,77), (T115,50), (T116,42), (T113,36)) This solution seems feasible but it is only locally optimal, because the first step of best-first search dose not examines all the possible nodes. Therefore, it is possible that unexplored path

222

would have presented more feasible solution Thus, to find more feasible solution, reversed sub-tree IS constructed by reversing the level of sub-tree that was constructed in first step The second step of bestfirst search is executed in figure 8

Level 1

T116

Leva 2

T115

LeYel 3

TI22

Level 4

LeYel

T123 !

!

2

5

1 1 188

T124

Level 6

7119

LeYel 7

-a

T118

5 CONCLUSION In this paper, a new heuristic algorithm and feeder load balance index was presented for service restoration considering feeder load balance in distribution networks. The proposed search algorithm adopts the concept of sub-tree proposed by reference J. S. Wu Et.al 1991, and utilizes cyclic best-first search and feeder load balance index developed by the authors. Cyclic best-first search is using best-first search that gets a solution much faster even if it lies deep down in the tree. And, by using revered sub tree, it compensates best-first search for not obtaining the best solution eveiy time. Feeder load balance index is presented in order to distributing feeder loadings with respect to their nominal capacities in the proportional manner. Test results on the KEPCO‘s 108 bus distribution system show that the performance is efficient and robust.

Level 0

r i i 3

nominal capacities.

ACKNOWLEDGEMENTS This work was financially supported by MOCTE through ElRC program.

Level 8

1149

T117

Level 9

7111

Lrval 10

T114

Level 11

REFERENCES

Fig 8. The second step of cyclic best-first search After the second step of best first search, switching pairs((TI14,19), (TI 11,26), (TI 17,44), (TI 18,72), (T 1 19,77), (TI 15,50), (TI 16,42), (TI 13,36)) arc sclected to minimize feeder balance index. Comparing feeder loadings before service restoration with those of after service restoration is presented as below table 2 and 3. Table 2 Feeder loadings before service rewxation when T 120 i\

closcd to cncrgizc ibolated section Feeder loading [MVA] Feeder1 Fecded Feedcd Feeder( Fcedei Feeded 1 5 I 6 1 1 2 1 9 1 4 14.47 5.17 13.04 8.38 26.06 0

1

I

1

1

I

I 1

Feede 7

13.80

rable 1 Feeder loadings after service restoration when T 120 I$ clo\ed to energize i\olated section Feeder loading [MVA] Feeder1 Fecded Feedcd Feeder( Fcedei Feeded Feede 1 5 I 6 1 1 2 1 9 1 4 13.171 11.291 13.04 11.701 17.911 0

1

I 1

7

13.80

The above comparison indicates that loadings on feeder 5 IS decreased after service restoration, therefore loadings on isolated feeder section after fault are distributed in proposition to adjacent feeder

223

T. Taylor, D. Lubkeman, “Implementation of heuristic search strategies for distribution feeder reconfiguration”, lEEE Trans. on Power Delivery, Vol. 5 , No. 1, pp. 239 - 246. January 1990. J. S. Wu. K. L. Tomsovic, C. S. Chen, “A heuristic search approach to feeder switching operations for overload, fault, unbalanced flow and maintenance”, IEEE Trans. on Power Delivery, Vol. 6, No. 4, pp.1579 - 1585, October 1991. M. E, Baran, F. F. Wu, “Network reconfiguration in distribution systems for loss reduction and load balancing”, TEEE Trans. on Power Delivery, Vol. PWRD-4, 1989, pp. 1401-1 407, April 1989. D. Shirmohammandi, H.W. Hong, “Reconfiguration of electrical distribution networks for resistive line losses reduction”, IEEE Trans. On Power Delivery, 1989, Vol. 4, N0.2, April, 1989. W-M.Lin, et al“ Distribution feeder reconfiguration with refined genetic Algorithm” IEE ProcGener. Trdnsm.Distrib,Vol. 147, Noh, November.2000

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Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

PUBLlCATlONS

REAL-TIME VOLTNAR CONTROL IN A DISTRIBUTION SYSTEM USING MULTI-STAGE METHOD

Jong-young Park, Jong-keun Park School of Electrical Engineering, Seoul National University, Korea

Abstract: This paper proposes a method for real-time control of both capacitors and ULTC in a distribution system to reduce the total power loss and to improve the voltage profile over a day. Multi-stage consists of the off-line stage to determine dispatch schedule based on a load forecast and the on-line stage to generate the time and control sequences at each sampling time. It is then determined whether one of the control actions in the control sequence is performed at the present sampling time. The proposed method is presented for a typical radial distribution system with a single ULTC and capacitors. Copyright 02006 IFAC Keywords: VolWAr control, Distribution system, Real-time control, Under-load tap changer (ULTC), Capacitor

I . INTRODUCTION

VoltiVAr control is important to the daily operation of distribution systems, because the proper dispatch of voltNAr devices not only reduces the total power loss, but also improves the voltage profile for distribution feeders. With the development of communication and power electronic technologies, integrated control of all the available Volt/VAr devices, including the under-load tap changer (ULTC) and capacitor banks installed at substations or distribution feeders, becomes available for distribution systems. Over the last two decades, several techniques have been proposed to deal with the voltNAr control problems in distribution systems. Most of the previous techniques have been accomplished in the off-line environment by finding dispatch schedules for capacitors and ULTCs based on the load forecast for the day ahead. Some papers have proposed a dynamic programming approach for voltiVAr control problems [ 1-31, Some researchers used neural-netbased methods to control the voltiVAr devices [4-61. In [7], a time-interval base volt/VAr control method used a genetic algorithm to divide the daily load into several load levels and to find the optimal tap positions for each load level and the dispatch schedule of capacitors. Since the loads in real distribution systems are subject to non-simultaneous variation, the control of

volt/VAr devices should follow the often changing load conditions to reduce total power loss and to improve the voltage profile. For this purpose, this paper proposes a real-time voltiVAr control method based on the difference between the measured and forecasted loads. In the off-line stage, a dispatch schedule is determined using the hourly load profile available from load forecasting and then the load profile at each sampling time is calculated by applying a cubic spline interpolation to the hourly data. In the on-line stage, the time and control sequences at each sampling time are generated based on the off-line dispatch schedule. To reflect the power system conditions at each sampling time, the generated time sequence is adjusted based on the difference between the measured and forecasted loads. It is then determined whether one of the control actions in the control sequence should be moved up to the present sampling time. The proposed algorithm is demonstrated in a typical radial distribution system and compared with the off-line control method. 2 . PROBLEM FORMULATION

The distribution system under study is shown in Fig. 1. The main transformer is installed with a ULTC to keep its secondary bus voltage close to the preset value under changing load conditions. Since the primary bus voltage changes slightly over a day

225

(1). For this minimization, this paper uses the timeinterval base voltiVAr control algorithm presented in [7]. During the minimization, the voltage profile at hour h, Vh, is obtained by solving the following equation: 18

-

9

15

28

2i

29 30

-e

IG 17

where P,l,/,, QjTi1 are forecasted active and reactive loads of node n at hour h and,L7is load flow equation of node n including the consideration of the operation of voltIVAr devices.

Fig. 1. Distribution system under study compared to the secondary bus and feeder voltages, the primary bus voltage is assumed to be a constant. Two shunt capacitors are installed at the secondary bus to compensate the reactive power flow through the main transformer. In addition, some capacitors are installed at feeder buses to maintain the voltage profile within the acceptable limits and to minimize the power loss. In this paper, it is assumed that the proposed algorithm will be applied to this central unit.

3.2 Interpolation of the forecasted load data

Although the proposed algorithm requires load data at each sampling time, ollly hourly data are available from the load forecast, In order to determine the load data at each sampling time, a cubic spline interpolation is applied to the hourly data and then the interpolated load data are discretized with the sampling interval At,:

To minimize the total power loss in a distribution

system and bus voltage deviation from the desired value, the dispatch problem can be formulated as follows:

where iv,, iv2 are weighting factors for the power loss and voltage profile, IV is total number of nodes in the distribution system, L h is total percent loss in the distribution system at hour h, and &/, is voltage deviation of node n from 1 .O pu at hour h. The objective function of (1) is subject to the following inequality constraints:

where P,(t) and Qj,(t) are interpolated active and reactive load of node n at time t. Then, the forecasted voltage profile without any voltage control during a day, vll], is obtained by solving the following equation:

where f,: is load flow equation of node n without considering the operation of voltiVAr devices.

4. ON-LINE STAGE

(3) h=2

At sampling time io, the future dispatch schedule can be divided into time sequence T o [ i o ] and control sequence C, [io] , as shown in the equation

where V,, is voltage of node n at hour h, V,,,, Vmm are nodal voltage limits, 7Af'h is tap position at hour h, MK, is maximum operating number of the ULTC, C, h is status of capacitor m (on or off) at hour h, and MKC, is maximum operating numbers ol"capacitor m. 3. OFF-LINE STAGE

where jk is k-th scheduled time, ck is k-th scheduled control action, and K is total operating number of all volt/VAr devices after io. In this step, it is important to reduce computational burdens to perform the proposed method in real-time. For this purpose, the following assumption is made:

3. I Ofi-line dispatch schedule

With the day-ahead load profile available from a load forecast, the off-line dispatch schedule of the voltiVAr devices is determined from minimizing J in

Lon4 ass~mmption:The future difference between the measured and interpolated loads is the same as the present difference.

226

This assumption originates from the fact that when the measured load exceeds the forecasted one, the load in the future is more likely to also be larger than the forecasted load. In addition to the time sequence in (10), the control sequence is also adjusted for on-line control. Considering the computational burden, the following constraint is used in this step: Control constraint: only one element of the control sequence can be moved up to the present sarnpling time and the order of the others should be preserved without any change. When the p-th control action, c/,, is moved up to iO, the schedule of (10) is changed to

J3

- 'G

11

I,

According to the schedule of ( I l ) , the voltage profile at the sampling time j k ,qrf,],which corresponds to the voltage profile just after ck is performed at is obtained by solving the following equation: V[y,] such that

flllli

Fig. 2. Example of re-forecasted voltage

.J. = number of branch points = 60%) AND (Length of longest connected line >=20) AND (the number of connected lines >= 2)) Recognize as low-voltage line; Else ignore; } If(not ignored) { cLine = new ELinc; Set the parameter value to eline, add to the wire recognition result list; Delete the pixels on branch point and the straight line; Modifji the hasELine value of ith and jth pole in candidate poles to TRUE;)

Input image was scanned with Vidar TruScan 500 of 300 DPI, and image size is 7568 x 5433 pixels with 256 colors.

Fig.8. Result ofAutomatic Recognition Figurc 8 shows rccognition rcsult of thc randomly selected image hom distribution facility map of Daejeon area. The threshold value 123 was obtained by histogram analysis. In this experiment, we focus on two aspects. First thing is the changes in performance with the quality of input drawings. We classi@ input drawings into "good", "normal", and "bad" groups and calculate average recognition ratio of each group. Secondly we evaluate recognition ratio with target facilities. Table 3 shows experimental results. Tablc 3 Statistics of rccognition ratio Quality

Good

1 As poles and wires are always connected, candidates with wire are recognized as real poles. But there are some cases that the wire is unrecognized in recognition process, so if the candidate poles without wire have large circularity (about 95%) is recognized as poles.

Normal

Bad

6. EXPERIMENTSAND PERFORMANCE EVALUATION In this section, we address the result of experiment pcrforrned and performancc evaluation. For the experiments, IBM-PCi586 with 450CPU is used and the program is coded with Visual C*.

Fsi$r: Pole HVC LVC

2.10 3.92 3.45

Unrec Recog ognize nition d ratio Ratio 1.02 96.88 1.85 94.23 11.70 84.85

SL

6.50

13.50

80.00

Subtotal Pole HVC LVC SL Subtotal Pole HVC LVC SL Subtotal

3.80 1.70 1.44 6.23 4.17 4.18 1.33 7.83 11.66 14.00 2.64

3.04 3.95 14.51 16.66 21.33 7.98 8.66 15.07 15.97 26.81 16.99

93.16 94.35 84.05 77.11 74.50 87.84 90.01 77.10 72.37 59.19 80.37

As shown in Table 3, while recognition ratio of poles is high with bad drawing quality, recognition ratio of HV circuit gradually declines as the quality get worse.

235

Table 4. Recognition ratio using probabilistic relaxation method (presented data) Drawings for experiment Symbols Lines

Dl

D2

D3

D4

92.8 98.8 96.9 94.9 80.1 92.1 86.6 87.4

Table 5. Recognition ratio using probabilistic relaxation method (experimental result) Quality of Drawings Good Normal Bad

Error Ratio 5.98 7.04 9.45

Unrecogni Recognitio zed ratio n Ratio 2.91 91.30 7.12 85.84 10.54 80.01

While recognition ratio which was got by using CREIPI tcchniqucs [8] is shown in tablc 4, the actual result from experiment with our distribution facility map is shown in table 5. Wc can notc thc followings from thc comparison of table 3 and table 5. The error ratio of our method was smaller than mcthod in [8], but unrecognized ratio of [8] is smaller than ours. 7. CONCLUSION AND FURTHER RESEARCH

In this paper we proposed a technique based on circularity and connectivity for recognizing clcctric poles, hi&-voltage circuits, low-voltage circuits and subsistence line in power distribution facility map. Experimental study of proposed method with 30 randomly sampled drawings. To evaluate the pcrformance, we examine the changes in recognition ratio related with quality of drawings and types of facilities. In case of poles and high-voltage circuit, recognition ratio appears good but in other cases, we did not get an accurate recognition result. Therefore, techniques for enhancing recognition ratio by extracting only facility drawings from input images efficiently can be proposed as a further research.

117, Jan. 1996. [3] Akio Okazaki, Takashi Kondo, Kazihiro Mori, Shou Tsunckawa, and Fiji Kawamoto, "An automatic circuit diagram reader with loopstructure-based symbol recognition," TEEE Transaction on Pattern Recognition and Machine Intelligence, Vol. 10, No. 3, pp. 331-341, May 1988. [4] S. H. Joseph and T. P. Pridmore, "Knowledge-Directed Interpretation of Mechanical Engineering Drawings," TEEE Transaction on Pattern Analysis and Machine Intelligence, Vol. 14, No. 9, pp. 928-940, Sept. 1992. [5] Wei Wu, Wei Lu, Masao Sakauchi, " A n Object-Oriented Model for Drawing Understanding and Its Ability of Noise Absorption", Proceedings of Third International Conference on Document Analysis and Recognition, pp, 261-264, 1995. [6] YUhong Yu, Ashok Samal, and Sharad Seth, "Isolating symbol from connection lines in a class of engineering drawings," Pattern Recognition, V01.27,NO.3, pp. 391-404, 1994. [7] Satoshi Suzuki and Toyomichi Yamada, "MARTS: Map recognition input system," Pattern Recognition, Vo1.23, No.8, pp.919-933, 1990. [Sl Osamu Hori, Shigeyoshi Shimotsuji, Fumlhiko Hoshino, and Toshiaki Ishii, "Line-drawing interpretation using probabilistic relaxation," Machine Vision and Applications, Vol. 6, pp. 100109,1993. [9] P. K. Sahoo, S. Soltani, and A. K. C. Wong,"A survey of thresholding Techniques" Computer Vision, Graphics, and Lmages Processing, Vol.41, pp. 233-260, 1988. [ 101 Louisa Lam, Seong-Whan Lee, and Ching Y. Suen, "Thinning Methodologies-A comprehensive survey," lEEE Transaction on Pattern Analysis and Machine Intelligencc, Vol. 14, No. 9, pp. 869-885, September 1992.

8. REFERENCES

[1] Gerd Maderlechner and Hclmut Mayer, "Conversion of high level information horn scanned maps into geographic information systems," Proceedings of the third international conference on document analysis and recognition, pp. 253-256, 1995. [2] J. E. Den Hartog, "Knowledge-based intcrprctation of utility maps," Computcr Vision and Images Processing, Vol. 63, No. 1, pp. 105-

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Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

SENSOR DYNAMICS COMPENSATOR FOR TEMPERATURE MEASUREMENT IN COMBUSTION CHAMBERS OF UTILITY BOILERS AND INCINERATORS

Igor Boiko", Vardan Mkrttchian"" *SNC-Lavalin, 909 5th Avenue SW, Calgary, Alberta, T2P 3G5, Canada, **All Armenian Internet (Jniversity, Armenia

Abstract A sliding mode compcnsation scheme for the dynamics of the sensors used for temperature measurements in the combustion chambers of utility boilers and incinerators is proposed. The proposed compensator can be used as a part of the electronics of temperature transmitters Analysis and design are carned out in the frequcncy domain with the use of the locus of a perturbed relay system (LPRS) method. Frequency-domain characteristics or the compensator dynamics are derived An example of design is provided Copyvzght 02006 IFAC Keywords sliding mode control, dynamic compensators, active sensing, dynamic observers

1. INTRODUCTION

Precise temperature measurements in the combustion chambers of modern utility boilers, incinerators, and Claus burners in various transient processes is an important technical problem. Accurate temperature measurement would allow one to know relatively fast fluctuations of this important internal process parameter and implement some more sophisticated control schemes to achieve a better quality of control. The same also applies to the measurement of water and steam temperature in utility boilers. However, unless the pyrometer measurements are used (which is an expensive option), the dynamics of the sensor due to the heat transfer in the thermowell and sensor matcnal would not allow one to read the process temperature instantaneously. The lag may be significant preventing the device rrom sensing rast temperature changes and fluctuations in a transient mode. The combined themowell-sensor time constant may range from a few seconds to a few minutes. A possible means or compensating for the sensor lag effect would be the application of the sliding mode (SM) principle (Utkin, 1992). This application can be

considered a special type of the SM observer, which would allow one to obtain the variable that cannot be measured directly, via matching the measured variablcs, subject to the sensor dyiiaiiiic model being available. This compensation would be used within the electronics of temperature transmitters. The theory of SM observers that can be utiliLed for the purpose outlined is presented in (Utkin, 1992; Edwards and Spurgeon, 1998). However, this theory does not provide any other than ideal quantitative characteristics of a SM observer in a transient mode, under harmonic excitation for example. It is assumed that once the SM is established an ideal observation occurs. With the recently developed frequency-domain method of analysis of real SMs (Boiko, 2005b), which considers parasitic dynamics and their effects being the "chattcring" phcnomenon and non-ideal response to external inputs and disturbances, one is able 10 do a quantilalive asessirienl of the compensator quality in various transient modes. The present paper uses the locus of a perturbed relay system (LPRS) method (Uoiko, 2005a) for analysis and design of thc SM compcnsator for the sensor

237

dynamics. The dynamical characteristics of the compensator can be assessed in the frequency domain as a response to the harmonic inputs at various frequencies. The paper is organued as follows At first the principle of the SM compensator is discussed, and it is shown that the SM compensator is essentially a relay servo systcm Thcn application of the LPRS method to the SM compensator along with the LPRS method fundamentals are given Finally, an example or analysis and design or a SM compensator is provided 2. SLIDING MODE COMPENSATOR

Let the dynamics of the temperature sensor be described by the following transfer function (Coughanowr and Koppel, 1965):

where TI is the time constant due to the thermowell heat transfer, T, i s the sensor time constant, T,(s) i s the temperature signal provided by the sensor (in the Laplace domain), Ti(s) is the true combustion temperature (in the Laplace domain). Let us design a SM compensator using the same idea as of the SM observer design (Utkin, 1992) The SM observer will include a model, which should be the same dynamics as the dynamics of the thermowellsensor This model will have a discontinuous control input that should enforce the output of the model to match the measured temperature This will be achicved on thc account of the discontinuous SM control, which will act in the direction of eliminating the mismatch between the measured temperature provided by the sensor and the output of the model

T,

=-

[*-(TI + T 2 ) i A-T,

TI T2

u={

+c

if

CT20

-c

if

oies and process condit,ions. The process control is sct up robust but t.liis is not opt.ima1 undcr ;dl conditions. Bc.caa.isc of following reasons only fcvv advanced ada,ptive control schemes are report,ed. - Combustions arc' dist,ribut.ed. time variant,,

nonlinear! a.nd niiilt,iva,riali)leprocesses. Ma t,hemat,icalmodels simulat,iiigt,he overall process or plant bchavior arc often not available. That a,pplies already for processes with time constant, and homogeneous fuels like fuel oil and even more so in case of time varying and het,crogcnous fuels like municipal waste.

- The dcvclopmciit of motlcls suitablc for a model-based control design without having an owrall proccss model is elaborat c, time consuming, and has t o be done a t the real plant. This usually prevents a systematic i.e.

249

I. e. they superpose or absorb the radiat,ion of interest, e.g. the IR emission of a solid fuel bed. Therefore we siiggest, a cornbinat,ion of short and long t,erin filtering which performs a detection and rcconstruct,ion of disturbed irn8g.e arms. This rcsults in a filt,ered image suit~ablefor the pa,ra.meter calculation. But. t,he recoiist,ruct,ion of disturbed image areas uses past image data. Obviously the validity of the filtered imagc and the succxxdiiig calculations d c creases if t,he dist,urbances effect a. la.rgeimage area and/or last long. Therefor, especially at closed loop coiit,roI,a proper aut,omat,icimage valitlat'iuii is required (Zipser et ul.? 2004).

model-based control design aiid leads to a more heuristic-int uitiv cont,rol. - The lack of rnodels describing t,he plant. r e x tion on fuel changes makes the development of ada.ptive control st,rat>egicsdifficult. - In most) cases the changing fuel propert,ies can not, be mea,surecl online (esp. solid fiiels). Furt,herrnore process variables charackizing the process condition like t.lie local oxygen coimntmtion or t,he temperature are riot known precisely. The missing knowlcdgc about, the current, and local different process state is one of the main reasons preveiiting the cleveloprnent of suitable niodcls arid advanccd control. Therefore as TV cameras and la,t!erinfrared cameras became available they were used for a det,ailed combust ion a,nalysis. This paper is locused on t.lie pot,ent,ialof VTS (visuell) a.nd TR (infrared) camera conibust,ion inoiiitoriiig wit,lirespect, to control. In dct,adl we tliscuss, prima.rily based on t he example of a grate firing, followiiig issues:

3. hlEASURING PRINCIPLE

- sclieme of camera aided combustion coiitiol, - measuring principle of VIS and IR cameras. - camera based temperature iiieasurernent,

- image parameters describing certain combustion features, aiid - camera aided combustion control with the

help of the sofLware system INSPECT. 2. CAMERA AIDED CONTROL Fig. 1 clepict,~a sket,cli of a camera. aided control. The control comprises an automalic part, whereas soloctd irnagc aiialysis rcsult>s(refcrrctl AS parameters) are used directly in t,he closed loop control and a inariual part whereas 1 he plant engineers adapt the contml s ings wit,h respect. to the displayed camera image and parameter charts.

0 Validation

I H I TI 4 Parameter

3

Display

Control

4

process Control System

I

For the combustion moiiit,oring in the VIS mostly single chip CCD (Charge Coupled Device) rolour video camera.s wit,h ail arialoge int,erface a.re used. Advant.ages are a good linearity? an approved and hexpensive t,ecliriology,arid a, high pixel resolution of c.g. 768x 576. Disadva,ntagcs arc tJhe low grey value resolut,ioii of only 8 bit, and the small exposure seiisit ivit,y rimge. Therefore 3-chip CCD sensors wit,h channel selective exposure or CMOS (Complementary Met a1 Oxide Serriicoiiductor) ca~merasbecoinc comiiion. 'I'hc latter liavc a 1ogarit.hiiiicchara,cterist.icand a wide serisitivit,y range. Hence t,hey enable lovv and high exposed irnagc areas without, saturation art>efrrcts. IR cameras are build with yuant,mn or bolometer sensors. Like the CCD sensors the quantuni sensors accumulate t,he charge carriers set free by the photons of t,lie IR irratlia,tion or iiicidcrit, light rcspcct,ivcly.To rcduce tlicrmic noisc IR quantum sensors need to be cooled. Bolomeler sensors m c k r the irradiat iori induced temperature increase of an absorber via t,liermo resistance or thermo voltage. Modern bolometer carncms operate with uiicoolcd bolometcr arrays, they are low-maiiit,enance, provide a resolntiori of 320x240 pixel, a measure rangc of 400-1500°C, and likc advaiiccd VIS camcras, a,digital intcrfxc. IR cameras for st,andard applications are sensitiv a.t a wavclcngt,hof 3-5 or 8-12 prn, t,hc rangc of thc so-called atmospheric transparency windows. For solid body t,eniperwt,uremea.siirenient,sin combustion chambers a band pass a t 3.8-4prn is required (Hoffniann et ul., 2005).

4. TEMPERATURE SIEASUREhIENT Cornhurtions arc' characterized cssciitially by the temperature level and distribution. Due to the limitations of therim couplc based measurcinents camera based approaches were iiivestigated rxtens i d y . After a skc>tch o€ thr. measuring principle the capnhilitim aiid limitations will be oiitliiiecl. Rvery horly with a icmperature T > O ° K m i i t 5

Fig. 1. Caniera a.ided coinbustion control scheme at. the exaniple of a grate firing plant After image capturing an image filtering is necessary, which minimizes t,hc influence of inevit.ably dist,iirbances likc whirlccl iip solid pxticles and flmnes. Pa,rt.iclesclist,url-,VIS or IR images siniilar.

250

with calculations bascd on c2 modcl describing the overall heat transfer including absorption and reflection effects (hlanca and Rovaglio. 2002). VIS based measurements are not reported because tlic light ciiiission rcquircs tciripcrat i r e s abovci 650°C and the light cmission of glowing fuel is oft eii superposed bv flames.

4.2 Gas and flame temperature measurement IS Wavclcngth ~nKin

Fig. 2. Black body emission vcrsus wavclcngth A: sensitivity of visuell and infrared canieias (ktromngnetic radiation. The Stcfan-Boltzmnnn law describes the emission (the spectral energy dcnsity L A ) of an ideal black body at thc wavelength X as a function of its temperature T , Fig. 2. Real bodies are often referred as grey bodies at least at certain tcmperatures and wavclcngths. Compared with the black body the grey body emission is lowcred by tlic mat crial dcpcndcnt emisqivity factor 5 with 0 < E < 1. For the grey body temperat lire rneasurenients usiially the W e n approximation

of the Stefan-Boltzmann law is used. The object tempcraturc. T can be t1cmvc.d from tlie emitted LA,] metered at the wavelength (spectral pyroinctcr), tlir ratio L A , ~ / L A at, two ~ wavclengths XI and A, (colour pyroineter) or the integral of L A between X I and A2 (band pyroriieter). 4.1 ,Wid furl tcrnpimtiirr rn~nsiircmrnt

The t,eunpcratjurcof solid bodies like the solid fuel or t,he boiler wall are measured with IR cameras scnsitiv at, 3.8-4pn (band pyroiii tra.nsparency window t,hc distjurbing absorpt>ion and emission from combust,ion ga.s comporieiits like carbon monoxide (CO), carbon dioxide (CO,) or water vapor (I3,O) are minimized. The other dominating gas components nitrogen (N,) and oxygen (0,)arc IR-transpa.rcnt. Unlike the gases with gas specific emission bands (H,Oz 2.9, CO,= 4.55! and C O z 4.8prn) soot has a continuous emission characteristic: (simi1a.r to l-he black body emission shown in Fig. 2). Therefore soot) is referred a.s grey body. If soot emission occurs it is present, in t,he camera images and requires image processing (whereat soot has a largcr cfftxtJin t,lic VIS tJhanin tlic IR). IR,-based kmperature measurement.s regarding a fuel bed of il waste combustion t,he relative error is despite disturbances and a changing emissivity less than 10%. The accuracy can be inc;reased 1

(7,

and

are constant,s,

Ro i s the solid angle

As mentioned abovt: hot) gases like CO, CO,, and H,O are visible at cert~airiwavelengths in the IR but. not- in tlic VIS. Flarncs arc visiblc bccausc they corit,aiii glowing soot, part,icles wit>h light emission. For flame temperature measurements it is a.ssumed t>ha.tt,hc gas and the soot, have t~he same temperature. Up to now it was implied that, the radiation is ernit,t,edhy a solid siirface. But in case of gases or flames the emission and the (re)absorption occurs in t>heMirnensional (3D) space. Therefor a point. of e.g. a. flame image represents the resultant, emission alorig a lim-of-siglit8across the fiamc. A t,empcraturo calculated Ixised on this is therefore called he-of-sight temperature. It describes t,he mean tempera,t,urealorig a, line approxima,tely because t,lic emission is relat,cd to both t,hc soot temperature and tlic soot, volume fraction. However t,he line-of-sight temperature of t,he flue gas (using an IR bolometer sensit.ive at the maximum cmissivit,y of CO,) providcs a fast signal for power control purposes. To determine t.lie 3D temperahre distribution regarding the 3D gas or soot c:oncent.rationrequires elaborate tomographic measurements and calculat,ions (hbel t~rnnsforniation).Applicat,ions work with colour \'IS carrieras (Cignolio et nl., 2005) or (Lu el ul., 2005) a d assume s~ableaxially symmet,ric soot flames (oil burner). Because a colow ca.niera,provides a mea.surement at 3 wavelengths barids coloiir pyrornctry can bo performed. Usually t,he red and the grcen cha.nnel are a.nalyzcd. Because of technical restrict~ionand the difficult,ies liandling t,hc fast changing fiaincs the VIS bascd t,einpera.turerneasurernent is past>ially1irnit)ed.Yet other non-tcinpcrsturc bascd information dcrivcd froin tlie VIS can be used cspccially for an enhanced gas burn out, cont>rol. For control purposes tlie t eniperature of' the burning solid fuel is of greater interest because t,his process dominates the combustion. Flames are in esseiice a result. of the solid firel c;oinbust.ion, alt hough flames themselves effect a.gabn t,he solid fuel combiistion via ratliat',ion. 5 . EXAMPLE GRATE FIRING PLANT

Fig. 1 dcpicts the consirlcrcd type of a grate fircd ( ombii\tion plant which rims typically with changing fiiels like hiomas5 or waste The file1

25 1

Table 1. Improwments due to IR-based process control

1200

3in

C

I process variable

1000

builer cEiciettcy steam variat.ion

900

iinproveinerit

+

2 7%. rcldlive -10 to -30 'lo, relative

800

-0,s 'it , absolute

700

variation Oa

600 500

-2 to -5 54,relative to -50 %, absolute to -80 % '

ture, ,..) Tor every line as well as the whole grate ase used (Schreiner aiid Jansen, 1997). The last, it,em implies a detect>ioiiof the burning zone a.s an object. 'Ibensure a reliable aut,onia.t,icburning zone det,ect,ioii an adaptjive approach has been developed arid patented (Zipser and Keller , 200.5). In detail the coiit,rol t,rics t,o achieve a proper shaped a,nd compact) ma,in burning zone a.t the grate middle, with a corist,ant' heat production, corresponding with t,licmain burning zonc properties. and a certain flue gas 0, content,. Manipulate variables are t,he fuel inass flow, the primary air flow and distribut>ion,the secondary air and t>he lrarisporl atiori speed. hlea.surenients from MARTIN GmbH Germany at different combustion plantis show tihe advant,uge of the IR-c,arncra based process control. In t,ahlc 1 the most import,ant, improvements a,rc summarized (Schreiner, 2005).

Fig. 3 . Top view inhared inmge of a grate firing fuel bcd; drawn in the gra,t,csegments aiid t,lic del ecled burning zones ent'ers the grat)eand pass t>lirougha drying, pyrolysis, arid igiiit,ion pliascs bcforc tlic birrriing down bcgins from tlic fucl hcd surfam Thc: gratc is subdivided into controllable zones and lines, see Fig. 3. The primary air flows t'hrougli the grate from below. Because t~heprimary air does not c~isurccomplclc gas burning out secondary air is injoct.c-:da,bove tho fuel bcd. The main cont,rol object,ives are: - an energy efficient combustion with low ex-

cess air, a.nd a constant heat production, - a complete solid fuel buriiing out. and a high

slag qiialit,y as well a.s - a complcte fluo gas burning oirt and a low polliit,nnt,fornia.t.ioni~.ndemission.

A VIS camera rrionnted at posit~iori( 3 ) is a standard configuration. It. monitors t'lie solid fuel burning out by the recognition of glowing or burning fuel after ti. given burning out, line. IR ca,nicra,sa,re not expedient at posit,ion ( 3 ) because the inforniat,ioii derivable are relat,ively small anyhow. To control the solid fuel burning out t,he transport,ation speed and primary air supply in t.he last grate segmenls a.re adapted.

Tlicsc objcct,ivcs are couiit,cra.ctcd by changing and heterogen fuel properties which lead to an local tliffercnt and non-stat,ionary conit)ust,ion.E. g. docs an incrcasc in t,he licat,iiig value causc a, cornbustion zone shift t,o the fuel feed. A drop causes a shift, t>othe fuel bed end. But. t,he process only operates properly if the main cornbustion takes place around t~liehalf grate length. In t~lie first case t.hc fuel can ignitc a,lrea,tlyin tlie fccder, iri (.he second case a, corriplek solid Tuel burriirig d. In both cases the pollritarit forriiat>ioriincreases. In case of niixecl liet~erogenous fuels several conihstion zones can emerge. From the cont-rolpoint, of vicw a, cl-iasactcrizatiori of t,he input fuel (on basis of the drying arid igriit,ionbehavior) is of great inkrest,, beeairse t.liis enables a prediction of combustion behavior. For that an IR camcra has t-o bc placed at position (1) in Fig. 1. Preliminary investigations for an IR irnage based heating value estima.tion are described in (1Llullc.r a,nd Keller, 1999). Placing a.n IR camera, on position ( 2 ) thc hirning zonc and depending on tlie plant geoniet,ry the ignition and the burning out) can bc monitored. For an opt,iniized process control up to 50 parameters likc (Fig. 3 ) t!hc nican sagmcnt, t,emperatiircs, t.hc longitudinal tc?mpcraturc profilcs, ;ml t,lic criicial hi.irning zone properf ies (areaj position, tempera-

G . EXAMPLE ROTARY KILN PLANT Fig. 4 shows a plant) sket,cli with t!he inclined rot8at,ingkiln for tlhe solid fuel coinbustlion and the post combustion cliamber to ensure a complete gas burning out. The solid fuel e.g. the hazardous wast,e enters the kiln via a chute. The combustion in the kiln can be controlled via the fuel and priinary air mass flow, perhaps the rotat,ional speed and tlie lieat, input. by a burnor. For t,he post, combirst,ioncontrol a secondary air input and again burners are provided. Rotary kilns work with solid fiicls a s wdl as licjiiids aiid gases. As will be discussed lat,er t,hey are also used for the conibust ion of high-calorific wwte in drums. Plant cont,rol object,ives arc' the same as ment,ioned above in case of grate firing. An additjiorial demand is to ensurc a prot,ect,ing slag layer on tlie expensive kiln lining snrfxe. Recaiise t.he sla,g

252

I

I Post combustion Oil burner

Oil burner

IR camera

I

Fuel bed

Rotary kiln

Slag

Fig. 4. Rotary kiln with IR camera monitoring fuel bed, kiln lining, and gaseous pliase (layer) behavior is closely relat.ed to t,he t.emperat,ure, an IR caniera monitoring the inner kiln temperat,ure is recomineizded. Of special int,erest, are longitudinal t,ernperature profiles m d hot, spot ion. An IR camera. ba 1 approach for lining t,ion is described in ( steen ct nl.. 2002). Wit,hin the scope of R&D projects at t,lie semiindustrial scalc rotary kiln plant. THERESA of the Research Centre Karlsruhe the fuel bed, the lining temperature, and t,he changes of t,lieg. pha.se in t,he rotary kiln were invest>iga,ted. Therefor a novel niultispectral IR camera was built up equipped wit11 bandpass filters at t.hc maxiniuni eniissivit,y of tlie gases I-120!CO,, and CO (2.9 i0.1; 4.55 f0.1, and 4.8i0.1pm) beside the coniinon filter a,t the akmospheric window for solid st,a . k t,emper at lire mea siir ement>s(3.9 i0.1pna ) . A result obtained rising wood chips as model fuel shows the t,emperature image of tlie kiln inside of Fig. 5. For a simpler analysis Ihe perspeclive

Y

1235 YinT

520

Fig. 5. Infrared temperature image of the kiln inside; right camera in Fig. 4 camera view was miippetl on basis of the geometric kiln model, Fig. G. The longitudinal temperatine profile (A) describes Ihe lining temperature, profile (B) the fucl hcat up drid ignition, and profile (C) the burning zone. The temperature charts sliow tlial hcrc tlic solid iiicl burning out is ( ornplete at = 40% of the kiln length. Investigations were also made with fuel oil filled drums as i-nodcl fuel for a rapid fucl change (Gommlich. 2005). Fig. 7 show the results of putting i-spectralIR camera inonit,oring a rotary kiln were presented. Finally, the software tool INSPECT was presenkd which was successfully applied as partr of the camera aided combustion control at several indust,ria,l phiits.

Zipser, S., A. Cornmlich, J. Mat,thes. H.B. Keller, Ch. Fo~icla and R. Schreirier (2004). On t.he optknizat,ion of intlust,rial combustion processes iisiiig infra,red t,hennography. Proc. 23rd IASTED eonf., 2.?.-25.2.2004 pp. 386391. Zipser, S. and H.B. Keller (2005). Verfahren zur Erkennung und Ident4fikation vvn Brennzoncn. gcriimn patent DE 103 02 175 A l , 712005; european palent applied for 8/2005.

REFERENCES Cignolio, F., S. De Liiliis and G. Zizak (2005). T~~r(~-dirnc.!nsioii~iI two-wavclcngth omission

254

Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

ENHANCEMENT OF ELECTRIC MOTOR RELIABILITY THROUGH CONDITION MONITORING Keith E. Holbert, Kang Lin, George G . Karady Department of Electrical Engineering, Arizona State University, Tenzpe, AZ, USA

Abstract: Diagnostic servicc offerings, such as condition monitoring (CM) of electric motors, for industrial customers are a potential market for electric utilities. This paper reviews the mechanisms of major motor component failures along with the existing techniques for detecting these defects. Whereas other researchers have focused on singular methods for fault diagnosis, we scck to develop an integrated CM systcm for induction motors. Our approach combines the diverse information from motor magnetic fields, vibration signals, and acoustic emissions into a more robust and comprehensive CM approach. Such a multi-faceted methodology using diverse measurement signals will allow inter comparisons of diagnostic information. Copyright 02006 IFAC Keywords: condition monitoring, failure detection, electric motors, motor bearing failure, predictive maintenance, online equipment health monitoring.

1. INTRODUCTION

I n the competitive, deregulated environment, electric utilities are continuing to expand their product line by offering value-added services to customers. For example, utilities are providing power quality monitoring for commercial customers and telecommunication services for residential consumers (Newbury, 1996). One potential market i s diagnostic services for industrial customers. Such diagnostics could include condition monitoring (CM) of electrical equipment such as motors. A CM program can reduce both costs and eqiiipment downtime, primarily by eliminating unnecessary maintenance and refurbishment actions. CM can also provide a technical basis for extending a motor’s qualified lifc, an advantagc that can provide very significant cost savings. Finally, CM can allow the utility to selectively focus attention on motors that, for reasons of loading conditions, operating patterns (is., onioff cycles, run time), or environmental considerations, are more susceptible to degradation.

Scientific literature is ripe with instances in which CM has been applied to equipment within power

plants and systems (McGrail, 1998) and other significant infrastructures (e.g., bridges). For example, Birlasekaran et al. (1998) review examples of condition monitoring applied to transformers, power cables, switchgear, bushings and insulators. Over the past 10 years. sophisticated online monitors, which are sensitive to many motor problems that can occur, have been developed. In particular, these methods include (Stone and Kapler, 1997): vibration monitoring to detect bearing problems, stator current harmonic analysis to detect induction rotor problems, and flux probes to detect synchronous rotor problems. These techniques have been applied to find various problems before catastrophic failure occurs, thereby enabling repairs to be made, often at a fraction of the cost that would be incurred if failure did happen. In one case, electric power plant operators reported avoided costs of $1.2 million over three years for -30 motors using prcdictive maintcnance techniques (EPRI, 1999a); in another plant, a cost savings of $182,000 was realized with four electric motors (EPRI, 1999b).

255

2. TYPES OF ELETRIC MOTOR FAULTS AND THEIR DETECTION TECHNIQUES The major faults of electrical machines can be broadly classified as (Nandi and Toliyat, 1999): stator faults resulting in the opening or shorting of one or more of the stator phase windings; abnormal connection of the stator windings; broken rotor bar or cracked rotor end-rings: static and/or dynamic air-gap irregularities; bent shaft (akin to dynamic eccentricity) which can result in rubbing between the rotor and stator, causing serious damage to the stator core and windings; shorted rotor field winding; and bearing and gearbox failures. Industry reliability surveys suggest that ac motor failurcs may be divided into five categories, including (IEEE, 1997): bearing: 44%; stator winding: 26%; rotor: 3%; shaft: 5%; and others: 22%. Because bearing, stator, and rotor failure account for over 70% of all motor failures, much work has bcen done to identify ways to reduce operational conditions that may cause failure of these components. For instance, motor bearing failures would be significantly diminished if the driven equipment was properly aligned when installed and remained aligned regardless of changes in operating conditions. A motor coupled to a misaligncd pump load, or a load with rotational unbalance, will likely fail prematurely due to stresses imparted upon the bearings. Based upon the above information, bearing, stator turn, and rotor bar failures are the most prevalent ones and thus demand special attention. These faults and their diagnosis arc briefly discussed below. Subsequently, Table 1 provides a comprehensive comparison of the induction motor failure types and the existing techniques for their detection.

2.1 Bearing jkults. The majority of the electrical machines use ball or rolling element bearings. The main components of rolling bearings are the inner ring, the outer ring, and the rolling elements (see Fig. 1). Typically, the inner ring of thc bcaring is mounted on a rotating shaft, and the outer ring is mounted to a stationary housing. The rolling elements may be balls or rollers. The balls in a ball bearing transfer the load over a very small surface (ideally, point contact) on the raceways Radial ball bearings are simple in design, suitable for high and even very high speeds, and robust in operation and require little maintenance. Angularcontact ball bearings have an angle between the inner

and outer rings, as shown in Fig. 1 , which enables them to support both radial and axial loads.

Inner ring out& ring Fig. I Angular contact ball bearings (McInerny and Dai, 2003). There arc a number of mcchanisms that can lead to bearing failure, including mechanical damage, crack damage, wear damage, lubricant deficiency, and corrosion. Abusive handling can induce nicks and dents, which are especially harmfiil when located in areas trackcd by the rolling elemcnts. Even under normal operating conditions with balanced load and good alignment, fatigue failures may take place. These faults may lead to increased vibration and noise levels. Flaking or spalling of bearings might occur when fatigue causes small pieces to break loose from the bearing. Though almost 40%-50% of all motor failures are bcaring relatcd, very littlc has been rcportcd in literature regarding bearing related fault dctcction. Bearing faults might manifest themselves as rotor asymmetry faults (Kliman and Stein, 1990), which are usually covered under the category of eccentricity related faults. Otherwise, the ball bearing related defects can be categorized as (Devaney and Eren, 2004) outer bearing race, inner bearing race, ball, and train defects. The vibration frequencies to detect these faults are given by analytical expressions. Although bearing faults account for nearly half of all induction motor failures, Kliman et al. (1997) noted that a review of scientific literature reveals dozens of papers addrcssing rotor bars bul only a few papers employing motor current signature analysis to detect bcaring faults. Motor bearing damage detection using a stator current signal is a useful application area (Schoen et al., 1995; Yazici and Kliman, 1999; Lindh et al., 2002). In stator current monitoring, the condition is often scrutinized at pre-calculated characteristic frequencies at which faults are likely to cause changes. However, such information is not necessarily available or easily discovered and, thus, a generic method which can determine the significant frequencies of interest would be of considerable value. Ilonen et al (2005) have proposed a method and a general diagnosis tool The method can discriminate bctwecn two classes of signals using statistical discrimination measures for time-frequency features, I P , Gahor filter iesponses The method utili7es

256

global information, namely, power spectra of the filter responses. The tool is intended to bc uscd by engineering researchers to analyze differences between signals of normal and damaged motors and to identify the present condition. In experiments, the tool was successfully applied to detect bearing damage in 15 kW induction motors using measurements of the stator current or vibration.

2.2 Stator,faults. Bearings and rotors are only two of the main components of a motor. In a survey of over 7500 motor failures, 37% of significant forced outages were found to have been caused by the third major component: stator windings (Stone and Kapler, 1997). Stator faults are usually related to insulation failure. In common terms they are generally known as phase-to-ground or phase-to-phase faults. It is believed that these faults start as undetected turn-toturn faults that finally grow and culminate into major ones (Kliman et a/., 1996). Almost 30%-40% of all reported induction motor failures fall in this category (Kliman et al., 1996). Armature or stator insulation can fail duc to several reasons. Primary among these are (Nandi and Toliyat, 1999): high stator core or winding temperatures, slack core lamination, slot wedges and joints, loose bracing for end winding, contamination due to oil, moisture and dirt, short circuit or starting stresses, electrical discharges, and leakage in cooling systems. There arc a number of techniques to detect these faults. Turn-to-turn faults can be detected by analyzing the axial flux component of the machine using a large coil wound concentrically around the shaft of the machine (Penman et a/., 1994). Even the fault position could be detected by mounting four coils symmetrically in the four quadrants of the motor at a radius of about half the distance from the shaft to the stator end winding. The frequency components to detect in the axial flux component is given by [k* n (1 - s ) l ~ 1 . f ; (1) where p is the number of pole pairs, ,f; is the fundamental frequency, k = 1,3 and n = 1,2, 3, ...,(2p l), and s is the slip. Research beginning in 1977 indicated that patterns of features extracted from three-phase voltage and current phasors arc present during incipient stages of electrical-component deterioration. Research in these areas showed that a small voltage unbalance greatly reduces the effectiveness of the deteriorationdetection system because the unbalance alters the line currents and any subsequent features extracted from them. A result of the research in this area has been the identification of the effective negativesequence impedance as such an indicator. This impedance can be acquired easily, and has exhibited

a sensitivity to minor winding problems. The development of this indicator applied in the small motors (< 200 hp) that operate at low voltage (< 1000 V) is presented by Sottile and Kohler (1993). Stone and Kapler (1997) review the development of an expert system which analyzes all common on-line and off-line tests together with operating data to estimate an overall indicator of the risk of winding failure. They also examine an online partial discharge measurement system that can be used by plant personnel to detect most of the deterioration mechanisms that can occur in stator windings rated 4 kV and above.

2.3 Broken rotor bar and end ving faults. Cage rotors are of two types: cast and fabricated. Previously, cast rotors were only used in small machines. However, with the advent of cast ducted rotors; casting technology can be used even for the rotors of machines in the range of 3000 kW. Fabricated rotors are generally found in larger or special application machines. Cast rotors though more rugged than the fabricated type, can almost never be repaired once faults like cracked or broken rotor bars develop in them. The rotor bar and end ring breakage can be caused by (Nandi and Toliyat, 1999): thermal stresses due to thermal overload and unbalance, hot spots or excessive losses, and sparking (mainly fabricated rotors); magnetic stresses caused by electromagnetic forces, unbalanced magnetic pull, electromagnetic noise and vibration; residual stresses due to manufacturing problems; dynamic stresses arising from shaft torques, centrifugal forces and cyclic stresses; environmental stresses caused by for example contamination and abrasion of rotor material due to chemicals or moisture; and mcchanical strcsscs duc to loosc laminations, fatigued parts, bearing failure, and so forth. Motor current signature analysis is used to detect broken bar faults (Elkasabgy et al., 1992; Filippetti et ul., 1996). They investigate the sideband components,j,, around the fundamental frequency V;) for detecting broken bar faults .h,=(1 2s)fi. (2) While the lower sideband is specifically due to a broken bar, the upper sideband is due to consequential speed oscillation. In fact, broken bars actually give rise to a sequence of such sidebands given by (Elkasabgy et al., 1992) , ~ ~ = ( l i 2 k s ) f ; , k = 1 , 2,... ,3 (31 The motor-load inertia also affects the magnitude of these sidebands. Other spectral Components that can be observed in the stator line current arc given by (Nandi and Toliyat, 1999) ,fi= [(kiP)(l s) SIJi (4) where ,J, are the detectable broken bar frequencies, and kip = 1,3,5...

*

~

257

*

Table 1 AC Motor Faults and Techniques for Their Detection

Major Components Percent of failures (IEEE, 1997) Fault types

Bearing 44 % 0

0

Major cause of failure (Beck et a/., 1996) Techniques for fault detection

0

0

Structural defects (outer and inncr rings, rolling elements, and cage) Lubricant (high friction) Overheating Mcchanical damagc Acoustic emission (Miettinen et d., 2001) Current signature analysis (Benbouzid, 2000) Vibration monitoring (Thorsen and Dalva, 1997)

Stator Turn 26 ?/o

Rotor Bar 3

Phase-to-phase Phase-to-ground

0 0

0

0

0

Overheating Insulation breakdown Current signature analysis (Benbouzid, 2000) Magnetic flux (Sin eta/., 2003) Vibration monitoring (Trutt eta/., 2002)

0

Broken bar

0

Mechanical damage

0

Current signature analysis (Benbouzid, 2000) Magnetic flux (Sin eta/., 2003)

techniques will allow inter comparisons of diagnostic information. This strategy can be likened to the plugand-play modules of today’s computer industry as illustrated in Fig. 2.

3. AN INTEGRATED CONDITION MONITORING SYSTEM The capability to detect faults and to replace the components just prior to failure is desired by industry. By doing so, the consequences of unexpected equipment failures can be avoided. Online component monitoring can yield higher availability, extended life, and reduced costs. Incipient failure detcction not only serves to avoid catastrophic failure, but also to assist in planning corrective actions (e.g., predictive maintenance). Incipient failure detection has the ability to assist in achieving condition-based maintenance objectives.

I

I

Within the previous section a variety of fault detection techniques have been presented. Each of these approaches has advantages and disadvantages. Reliable commercial implementations favour those mcthods with low misscd and falsc alarm ratcs. In order to improve the overall reliability of motor CM, the use of various methods to address the diverse failure mechanisms (categories) and the implementation of multiple techniques within a failure category is promoted here to improve the fault detection (i.e., the robustness).

I

lnput Measurements I

I

Y Y Y $t $-

I

I

Y $-

Condition Monitor Decision Maker

Fig. 2 Architecture for integrated condition monitoring system, where the diverse measurements are input to the various signal processing modules from which thcir outputs arc assimilatcd into a decision regarding the electric motor health.

3.1 Diverse signals and fault detection techniques. Electric motor failures are a cause of critical system malfunctions and the interruption of large system operations. We propose the development of an integrated CM system for induction motors. In particular, other researchers have focused on singular methods for fault diagnosis. Instead, our monitor will combine the diverse information from motor magnetic fields, vibration signals, and acoustic emissions into a more robust and comprehensive CM approach. Such a multi-faceted methodology using diverse measurement signals along with novel or existing (Sin et a/., 2003) signal processing

As an example of utilizing diverse measurcments for integrated fault diagnosis, consider the use of magnetic field transducers. Vibration in the motor should be observable using magnetic field sensors placed at the peripheiy of the motor. In particular, consider lateral motor vibration with sensors mounted to the left and right; vibration-induced movement toward the right will result in a larger magnetic field in the right sensor, and a smaller measured field in the left sensor. A similar approach was successfully developed for nuclear reactor core barrel vibration

258

monitoring using neutron flux detectors, for which 0.02 to 0.06 mm motions were measured using detectors that were placed nearly 4 m from one another (Thie, 1981).

3.2 System simulation and testing

A salient feature of the approach presented in this paper is that it builds upon proven fault detcction and A challenge to the isolation (FDI techniques. integrated CM system is the combining of the diverse results from the signal processing modules into a final status decision. To accomplish this, we employ a rule-based fuzzy logic decision maker. The rules are established by first noting the failure mode(s) that a specific module is capable of detecting. Weights can be assigned to quantify the level of confidence that one has for a specific module in detecting a given anomaly type. By having multiple modules capable of detecting a given failure mode, we seek to decrease the missed alarm rate. Likewise, the rule-base is constructcd to dccrcasc thc falsc alarm ratc by using knowledge between modules. For example, from Table 1 we note that current signature analysis (CSA) is capable of detecting all three failure modcsbearing, stator, and rotor. Therefore, the rules are created such that the CSA module results do not falsely indicate a non-existent failure mode, while properly activating those rules pertaining to the failure mode which is truly occurring. In terms of motor health monitoring, this approach can be likened to the manner in which a physician employs multiple measures to diagnosis a patient’s illness. Over time, experience may demonstrate the need to remove a module due to poor performance, or if a new state-ofthe-art technique becomes available, then it can be inserted into the existing integrated health monitor.

Studies relating to the detection of electrical winding faults in rotating machines have normally been oriented toward the measurement and analysis of electrical parameters such as current, voltage and magnetic flux. Conversely, efforts to apply mechanical vibration technology in the CM of ac motors and generators have generally been focused on areas relating to unbalance, bearing condition, eccentricities, and other mechanical phenomena. However, theory predicts that current changes due to electrical winding deterioration in rotating machines will altcr intcrnal magnctic forccs which will thcn cause a modification in vibration characteristics. The monitoring of mechanical vibration should therefore be a useful indicator of electrical winding conditionyet another instance of employing diverse measurements for incipient fault detection through inter comparisons. While the application of these concepts in the protection of rotating machinery has been considered for many years, the major emphasis has been to study the relationships between winding faults and electrical parameters. However, an understanding of the relationships between mechanical vibrations and electrical winding deterioration could provide a means for supplemental monitoring of electrical winding integrity as well as information that might be used to discriminate between electrical and mechanical problcms.

In order to validate the developed methods for large motors, an clcctromechanical modcl of a largc induction motor for computer simulation of both fault-free and faulty conditions is nccdcd. Internal faults account for around 70% of the induction motor failures. A key challenge is to find a quantificational analysis tool for studying the diagnosis and protection of induction motor faults. Conventional methods make use of test machines; however, the machines must be damaged to orchestrate interior fault experiments. This is relatively easy for small motors, but difficult for repeated experiments and expensive to implement on larger capacity motors. Simulation models based on EMTDC (EMTP) in combination with internal faults, including both stator and rotor faults of induction motors, havc becn established to provide a virtual environment for researching induction motor interior faults (Cai et al., 2003). Such a computer model might be used to validate the developed signature analysis techniques.

Trutt et al. (1999) made a theoretical review of the relationships that should exist between electrical winding currents and the mechanical vibration of machine elements under normal and faulted operating conditions. Data from an cxpcrimcntal study that relates stator vibration and bearing vibration to selected winding faults in a synchronous machine were presented. Results demonstrated a measurable relationship between electrical deterioration and mechanical vibration and thus provide the motivation for additional study and a basis for monitoring applications.

In contrast to traditional acoustic emission (AE) analyses that simply examine wave peak amplitude, we propose to incorporate AE waveform analysis which makes use of information such as wave shape, arrival time and amplitude. For example, the high frequency components of waveforms originating from flexural events arrive first, whereas for extensional waveforms, the low frequencies are quicker to arrive at the detector. Modal AE analysis requires the use of broadband versus resonant sensors. Here we are referring to acoustic signals within both the audible and ultrasonic frequency ranges. Proper placement and monitoring of multiplc acoustic cmission scnsors provides the ability to perform three-dimensional source determination (i.e.,fault location).

REFERENCES Beck, C.E., B. Hussain, A.K. Behera, and A.J. Alsammarae (1996). Condition monitoring of 4 kV induction motors used in nuclear generating stations. Conference Record of IEEE Nuclear Science Symposium, 2, pp. 970-973. Benbouzid, M.E.H. (2000). A review of induction motors signature analysis as a medium for faults

259

Miettinen, J., P. Anderson, and V. Wikstroem (2001). Analysis of grease lubrication of a ball bearing using acoustic emission measurement. Proceedings of'the I MECH E Part J Journal of' Engineering Tribologv, 215(6), pp. 535-544. Nandi, S. and H.A. 'I'oliyat (1999). Condition monitoring and fault diagnosis of electrical machines-a review. IEEE Industry Applicutions Confkrence, Phoenix, pp. 197-204. Newbury, J. (1996). Development for the electric es networks towards the national information infrastructure. IEEE Trans. Power Delivery, 11(3),pp. 1209-1213. Penman, J., H.G. Sedding, B.A. Lloyd, W.T. Fink (1994). Dctection and location of interturn short circuits in the stator windings of operating motors. IEEE Trans. Energy Conv., 9(4), pp. 652-658. Schoen, R., T. Habetler, F. Kamran, and R. Bartfield (1995). Motor bearing damage detection using stator current monitoring. Applicat., 31(6), pp. 1274-1279. Sin, M.L., W.L. Soong, and N. Ertugrul (2003). Induction machine on-line condition monitoring and fault diagnosis A survey. Australasian Universities Power Engincering Conference, Christchurch, New Zealand. Sottile, J. and J.L. Kohler ( I 993). An on-line method to detect incipient failure of turn insulation in random-wound motors. IEEE Trans. Energy Conversion, 8(4), pp. 762-768. Stone, G.C. and J. Kapler (1997). Condition-based maintenance for the electrical windings of large motors and generators. Pulp and Paper Industry Technical Conference, Cincinnati, pp. 57-63. Thie, J.A. (1981). Power Reactor Noise, American Nuclear Society, pp. 1 1 5- I2 1 . Thorsen, O.V., and M. Dalva (1997). Condition monitoring mcthods, failurc idcntification and analysis for high voltage motors in petrochemical industry. Eighth International Conference on Electrical Machines and Drives, pp. 109-1 13. Trutt, F.C., J. Sottile, and J.L. Kohler (1999). Detection of A-C machine winding deterioration using electrically excited vibrations. IEEE 34'" Industry Application Conference, 3, pp. 19031907. Truii, F.C., J. Soitile, and J.L. Kohler (2002). Condition monitoring of induction motor stator windings using clcctrically excitcd vibrations. Conjerence Record of' the 37Ih Ind. Applicat. Conjkrence, 4, pp. 2301-2305. Yazici, B., and G. Kliman (1999). An adaptive statistical time-frequency method for detection of broken bars and bearing faults in motors using stator current. IEEE Tr*ans. Ind. Applicat., 35(2), pp. 442452.

detection. IEEE Trans. Ind. Electronics, 47(5), pp. 984-993. Birlasekaran, S., S.S. Choi, and A.C. Liew (1998). Overview of diagnostic and conditioning monitoring techniques for in-service power apparatus. International Conference on Energy Management and Power Delivery, 2, pp. 673-678. Cai, Z., A. Gao, and J. Jiang (2003). Modeling for interior faults of induction motors and its simulation on EMTDC. International Conference on Power Systems Transients, pp. 1-5. Devancy, M.J., and L. Eren (2004). Detecting motor bearing faults. IEEE Instrumentation & Measurement Magazine, 7(4), pp. 30-50. EPRI (1999a). Predictive maintenance tools and techniques help LG&E avoid costly motor failures. EPRIInnovators, IN-1 10285. EPRI (1 999b). Electric motor predictive maintenance tools and techniques increase motor reliability while reducing costs. EPRl Innovators, IN1 11769. Elkasabgy, N.M., A.R. Eastham, and G.E. Dawson (1 992). Detection of broken bars in the cage rotor on an induction machine. IEEE Trans. Ind. Applns., IA-22(6), pp. 165-171. Filippetti, F., G. Franceschini, C. Tassoni, and P. Vas (1 996). A1 techniques in induction machines diagnosis including the speed ripple effect. IEEEIAS Annual Meeting Con$', pp. 655-662. IEEE STD 493- 1997. IEEE recommended practice for the design qf reliable industrial and commercial power systems. App. H, Table XI. Ilonen J., J.-K. Kamarainen, T. Lindh, J. Ahola, H. Kalvianen, and J. Partanen (2005). Diagnosis tool for motor condition monitoring. IEEE Trans. Ind. Applicat., 41(4), pp. 963-971. Kliman, G.B., and J. Stein (1990). Induction motor fault detection via passive current monitoring. Intern. Con$ on Electrical Machines, pp. 13-17. Kliman, G.B., W. J. Premerlani, R. A. Koegl, and D. Hoeweler (1996). A new approach to on-line fault detection in ac motors. IEEE-IAS Annual Meeting Conference, pp. 687-693. Kliman, G.B., W.J. Premerlani, B. Yazici, R.A. Koegl, and J. Mazereeuw (1997). Sensorless, online motor diagnostics. IEEE Comp. App. Pwr.,10(2), pp. 39-43. Lindh, T., J. Ahola, and J. Partanen (2002). Evaluation of condition monitoring of bearings of 15 kW induction motor based on stator currcnt measurement. Proc. of' ICEM'O2, Brugges, Belgium. McGrail, T. (1998). Condition monitoring a user perspective. IEE Colloquium on HV Measurements, Condition Monitoring and Associated Database Handling Strategies, pp. 1 I1- 113. McInerny, S.A., and Y. Dai (2003). Basic vibration signal processing for bearing fault detection. IEEE Trans. Education, 46(1), pp. 149-156. ~

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Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

PERFORMANCE OF HW-PSSS AS AFFECTED BY THE PARAMETERS OF THE BILINEAR TRANSFORMATION

K A Folly, K Mocwane Universily of Cape Town, Dept. of Electrical Engineering, Cape Town South Africa

Abstract: This paper investigates the effect of the parameters of the bilinear transformation on the performance of H,-PSSs. The bilinear transformation is used together with H, optimal control to design H, based Power System Stabilizers (PSSs) that are robust with respect to system's uncertainty. Two cases of the bilinear transformation are investigated. Namely, the Simple Case (SC) where only one parameter Cpl) of the bilinear transformation is used and the Complex Case (CC) where two parameters (PI and p2) are used. It is shown that for the controller to perform satisfactory in the Simple Case (SC), the absolute value of p i should be set high enough to give adequate damping without exciting the high-frequency modes. For the Complex Case (CC), a medium value of p 1 togcthcr with a rclativcly high value of p 2 should bc used to achieve a good performance of the controller. In this case, a trade-off is required in setting the values of p 1 andp2. Copyright 02006 IFAC Keywords: Power System Stabilizer (PSS), bilinear transformation, H m optimal control, robustness.

I . INTRODUCTION The bilinear transformation also known as the j w axis poles shifting transform technique (Chiang and Safonov 2001), has recently attracted a significant interest in power systems because of its ability to deal with the pole-zero cancellation phenomenon that is inherent with the H,-PSS (Folly et al., 1998). H, optimal control is a frequency-domain optimization and synthesis theory that was developed to explicitly address the problem of uncertainties. It deals with the minimization of the peak value of certain closed-loop system functions (Chiang ef al., 1990). A common design formulation in H, optimal control involves the so-called mixed-sensitivity weighting strategy where frequency dependent weighting functions are used to shapc thc various sensitivity functions such as the sensitivity function (8,the complementary sensitivity function (7) andor the input sensitivity function ( R ) (Chiang et al., 1990), (Chiang and Safonov, 2001). It is known that in the weighted mixed sensitivity problem formulation, the H, controller always cancels the stable poles of the

system (Chiang and Safonov, 2001; Bosgra and Kwakernaak, 1997). If lightly damped poles are cancelled, the closed-loop system will behave like an open-loop system. This issue becomes critical when designing power system stabilizers (PSSs), where the main objective is to add damping to the lightly damped electromechanical modes. Therefore, polezero cancellation phenomenon in H,-PSS design leads to poor robustness and performance (Folly, et al., 1998). To prevent this phenomenon, Chiang and Safonov (2001) have proposed the use of the bilinear transformation in combination with the H, optimal control. This approach has a number of advantages over the standard H m optimal control. First, it allows the designer to reassign dominant poles of the closed-loop system at desired locations in the s-plane. This means that time domain requirements such as the settling time, overshoots and rise time, which cannot be specified in the standard approach, can now be specified and achieved.

26 I

Second, it can remove the ill-conditioning inherent in some augmented plants (e.g., nominal system and weights). In other words, the bilinear transformation can deal with situations in which singularities arise in the equations that determine the state-space realization of the H, control law (Chiang and Safonov, 2001).

finite bus

e - p

'

,w

w-

Fig. 1 System model also vary. This variation is likely to affect the dynamic characteristics of the system.

Xu and Mansour (1988), Chiang and Safonov (2001); Folly et al. (2004) have shown the effectiveness of this approach. However, in the literature, the advantages and disadvantages of using the Simple Case (SC) bilinear transformation over the Complex Case (CC) and vice-versa is not discusscd. No clear guidelines can be found on how to choose the parameters of the bilinear transformation to achieve good damping at low frequcncics without scarifying thc robustncss of the system at high frequencies. While it clear that the parameters pl can be used to control the locations of the dominant poles, the role ofp2 is not clear.

2.2 Design Specijications

The objective in this study is to design a robust controller that stabilizes not only the nominal system G&) but also a set of system models that lie in the true plant G(s). Since the model of the true plant is not known exactly, the off-nominal conditions are used to model it. Table 1 shows the range of possible operating conditions considered in the design. The various operating conditions are obtained by varying the transmission line reactance Xe, the active power P, and reactive power Qe.

In this paper, we investigate the effect that the paramctcrs of thc bilincar transformation have on the performance of the Hm-PSS. Two bilinear cases are compared, i.e. the Simple Case (SC) where only one parameter (pi) of the bilinear transformation is used and the Complex Case (CC) where all the parameters (pi) and pz) are used. It found that the controller based on the Complex Case could perform better than the Simple Case if the parameters of the bilinear transformation are chosen such that the controller can attenuate disturbances at low-frequency without exciting high frcquency unmodelled dynamics.

The specifications of the design are: 1.

2.

3.

2 . SYSTEM MODEL AND DESIGN

Stabilization of the system despite the variations in the system's parameters (Folly el al., 1998; Travichandran, and Quintana 1996). Robustness in the presence of uncertainties such neglected high-frequency dynamics, unmodelled dynamics, noises, etc. (Chiang el a1 , 1998; Chiang, and Safonov, 2001, Folly et al., 2004) Settling time should be less than 2sec for the nominal closed-loop system, less than 3ec for off-nominal systems and acceptable maximum overshoot and undershoot (say bout 4.5%)

SPECIFICATIONS Specification 1 means that we should achieve a good disturbance attenuation at the frequency of oscillations, i.e., the sensitivity function S should be small at low frequencies.

2. I System Model

The system model used is a single machine infinite bus as shown in figure 1. The synchronous generator is modeled by a third-order differential equations (damper winding neglected), and it has a standard AVR which is modeled by a first order differential equation (Kundur, 1994; Folly el ul., 2004). To improve the stability of the system, a PSS is added to the excitation control (this is not shown in Fig.1). The nonlinear equations are linearized around the nominal operating condition and the system is rcprcscntcd in the frequency domain as:

where G, (s) = C, (SI - AO)-'B, + D o , y is the system output and ZI is the system input. A,,, Bo, C,, and Do are constant matrices of appropriate dimensions. It should be mentioned that ( 1 ) i s only valid for one operating condition (i.e., the nominal operating condition). As the operating point is varying, the matrices A,, B,,, C,, and D, will

Specification 2 means that the cornplerrieritary sensitivity function 7':= I-S and /or the input sensitivity R ;- KS (where K is the controller) should be small at high frequencies to prevent the highfrequency modes from being excited. This means a good roll-off of the controller Specification 3 is related to the damping of the dominant closed-loop poles. For the system that is considered in this study, this means a damping ratio of at least 0.25. This requirement can only be achieved by using the bilinear transformation. Table 1 Possible operating conditions Parameters

xe pe Qe

262

Minimum 0.25 0.80 -0.30

Nominal 0.50 0.80 0.30

Maximum 1.OO 1.04 0.40

It should be mentioned that uncertainty weighting functions are chosen by trial and error to represent the maximum multiplicative andior additive uncertainty. The disturbance weighting function should reflect the disturbance attenuation specification. During the design, these weighting functions are used to penalize the various sensitivity functions. Thc focus of this paper is not the weighting functions, so we will not discuss how the weights have been chosen. Interested reader can see Chiang and Safonov (2001), Chiang et al.. (1990), Folly et al. (1998, 2004).

3. BILINEAR TRANSFORMATION

-s = - s + p ,

(3)

S ~1

P2 where p l < 0 and p2< 0 arc the end-points of the diameter of a circle in the left s-plane as shown in Fig. 2 (b). Note that both the poles and zeros are affected by the transformation. With the Complex Case, we have two parameters to choose. This adds more flexibility in the design at the expense of complexity because the parameters interact with each other.

3.2 Simple Case (SC)

The bilincar transformation can be formulated as j l y axis polc shifting transformation. Let the pole-zero configuration of the nominal system Go@) be as shown in Fig. 2 (a). This system has a jo axis zero and a pair of lightly damped poles. If the standard H, approach is used to design the controller based on this model, the lightly damped poles will reappear as closed-loop poles due to the pole-zero cancellation phenomenon. Consequently, the damping of the closed-loop system will not be improved. This will lead to poor robustness and performance. To prevent this, we apply the bilinear transformation.

By simplifying the Complex Case, we obtain the Simple Case. The assumption made for the SC is that p 2 = m. Therefore, we are left with only one parameter y l which can take any value depending on the design requirements. Fig.3 illustrates this case.

In the following sections, we discuss the two types of the bilinear transformation: the Complex Case (CC) and the Simple Case (SC). Since the SC is a simplification of CC we start with CC.

a. Open-loop

4

s-plane

s--plane

x

............................................................

:.....................

.i..&jv\7L

x ....................................................................................................... b. Transformed open-loop

t

t

r--planc

s-planc

3.1 Complex Case (CC)

In the Complex Case, the two parameters of the p l and p 2 of the bilincar transformation of ( 2 ) are used to shift the poles of the nominal system G&) in the s-plane such that G,,(s) is transformed it into a tictitious unstable system Go(?) in the new F plane as shown in Fig. 2 (b). Because of the internal stability requirement in H, design, unstable poles cannot be cancelled; instead, they are shifted approximately to their mirror images once the fecdback loop is closed with the H, controller as shown in Fig. 2 (c). Thc controller K(s) corresponding to the original system is found by using the inverse bilinear transformation (3). It should be mentioned that K(s) is sub-optimal solution of the original H, control problem. When the original lightly damped nominal system GJs) is closed with this sub-optimal controller, the closedloop modes will move further in the left half s-plane as shown in Fig. 2 (d).

c. Closed-loop is s--plane

1 h, .

d. Closed-loop in s-plane

Fig.2 Bilinear Transformation- Complex Case (CC)

,

s--plane

.........................................................................................................

's-

1?2

x . .........................................................................................

a. Open-loop

c. Closed-loop is s--plane

+K

b. Transformed open-loop

d. Closed-loop in s-plane

Fig.3 Bilinear Transformation- Simple Case (SC)

263

4. POWER SYSTEM STABILIZER DESIGN

5.1 Time Domain Simulations

4.I Simple Case (SC) For all the simulations, a step response is applied to the voltage reference Vref Note that one could also apply a step response in the mechanical input, the results would have been the same. The responses shown in Figs. 4 and 5 are those of the output of the system (i.e., speed deviation). Thus, the input signal to the 11-PSS is thc speed deviation Aw.

For this design, we fixed p2 to infinity while p , is varied from -0.5 to -20. 'lhe rule-of-thumb for choosingpl is given as (Chiang and Safonov 2001):

I PI I

=

son

(4)


the condition (6) will be fulfilled when:

This requirement is in fact related to the voltage controller time constants T,, T c ~and to the plant’s field circuit time constant T,? but not directly to the PSS. This means that the optimal PSS requires modification of the AVR time constant values. Unfortunately, when the values of the PSS time constants have been chosen to satisfy (6) and (8), it is impossible to satisfy at the same time condition (7). But fortunately, for a typically small value of the voltage controller time constant TA , the difference

268

between coefficients a2 and hZlends to be small. This is because the absolute error is proportional here to a2-b2= TITA. This causes in fact that the imaginary part of the transfer function Tps5 is not equal to zero but fortunately it is very close to 7ero. In that senw the PSS can be named as the quasi-optimal one.

l=

0 9, computed for plant (described in Appendix) operating at rated load is presented in Fig. 2. 1.5

i

To makc the PSS defined by (1 0) implementable, thc transfer function GP5\has to be transferred to the following form: 0

1

2

3

Frequency (Hz)

Then the quasi-optimal PSS (and AVK) time constants can be defined as: m

T, = T, = T3 + T, Values of the time constants T, and Tl should be chosen small (i.e. T, = Tf = 0.005 s) so as to not introduce meaningful shift to the CP,)(s) transfer function phase, for frequencies in the electromechanical oscillation5 range, i.e. 0.1-2.5 Hz.

2.2 PSS gain design

Fig. 2. PSS gain and real Tcr, and imaginary T,, parts of transfer function T < i u ) - measure of the s ynchronising and damping torque. We can see here that for a given plant, keeping the PSS gain equal to 20 to allow us to keep the damping ratio not lower than 0.9 for the all range of frcqucncies of electromechanical oscillations. When reactive load of the plant decreases the Kpss required to keep the given damping ratio also decreases. That can suggests that KP,, can be defined as equal to the maximum value needed to keep given damping ratio computed for the plant's rated operating point. For simplification purpose the following equation was used for the PSS gain calculation:

The PSS gain definition, in a considered case, is a separate task, not related to the time constants definition. In general the PSS gain definition, especially for the multi-machine power system is not an easy task, but can be done by utilisation of various known methods. Below the simple way of the PSS gain definition is proposed. For plant from Fig. 1 the equation of motion, taking into account ( 1 ) and assuming that T,~,s.s(s) transfer function has only a real part (ix. the PSS is optimal), can be written in the form:

where 77 = 2.5, is a constant coefficient comprising nonlinearity of the synchronising torque component ThcARMA parsmcters on-line (c.f. (1)).It consists of two layers: a. hidden layer consisting of radially syrnmet,ric basis functions aiid a. liiicar output layer. The hidden nodes consist, of REF ccrit,crsantl cadculnt~c the Euclidean distancc bctwccn t,hc ccrkcrs arid the network input vector. The result is passed through a Gaussian funct>ion,&(:rj>given by:

A variety of dist,urbanccs can be q p l i c d to t,lie system. Using t,he switch shown in t~heexcit,alion circuit of t.lie DC mot,or, Fig. 1, a st,ep change in input, torque of I,he generator can be applied. Similarly, t,lic input rcfcrcncc volt,itgc of t,hc -4VR can bc st,cppcd up or down. In addition, diffcrcnt, types of faults can be applied to simulate large dist,urbances. The faults are ximrilat,ed using relays cont,rolled by short circuit siniulat,ion logic (Fig. 1). The operating coiiditioii of the generator, i.c. active power and power fa.ct>or,can also be changed by changing the armature current of DC motor and terniinal voltage of the generator. rcspect.ivcly.

The overall input-output response of the network is given by

274

RBF

Transmission Line

W Circuit Tesf Three Interkkcked Breakers AdlirslahleTime Sequence

Manual

-

Fig. 1. St,ructurc of t,lic power syst,crn niodcl In ( 8 ) , x p is the input vector, w, is the biasing t,crni, w, is t,lic weight, bctwceii the hidden nodcs a.rid the out,put, c7&is t,he center of the hidden node, a is the widt,h of the hidden node, N is tho number of liitldcn nodcs aiid @(.)tlcriot,cs the Gaussian function. For on-line identification of a. power system using t8he RBF net'mrk t'lie centers have to suitably sample tho input domain. The n,-ineuns clustering t~cchniyueof pattern classification is an effectjive procedure t,o updat~ethe RBF centers. Because the response of t,he iiet>workis linear with respect, t>o its .i?leight,s.recursive least squares (RLS) inet,hod is proposed for atljust,ing t,hc mights. ~ 1 1 weight ~ : vect,or, I@, is c:rlculateti by t,he following RLS eqiiai-ions:

1 P(t + 1) = -[P(t)

dt)

W(t

+ 1)= W ( t )

-

KT(t)P(t)k(t)] (10)

+K ( t )[,y ( t )- Mir ( t )W (t)] ;I( t )

(11)

where p ( t ) is the €orgelting factor. P(t) is the covariance matrix and K(t) is the modifying gain vector. W ( t )is a vcctor consisting of tlic following elemenls (outputs of RBF-Identifier hidden layer)

13(t) a tracking constrained coefficient (G.P. Chen a r i d O.P. Malik and G.S. Hope imd Y.H. (tin aiid G.Y. Xu, 1993). The RBF represrnts a NARIVIAX modrl (S. Chen, S.A. Billings and P.M. Grant, 1992). '10 obtain the linear paramc~tcr~ (c.f. (5) ) of tlic standard ARlCIh model, the output of thc RBF, y(t) = f(z/(t- c), u(t - L ) ) . is liiieariaed using thc Taylor series expansion. Retaining only the linear t e r m

The partial derivative terms, [ay/i)x,] are the clerneilts ol' the RBF network Jacobian [.Iy] and are given by

iV rcprcscnts tlic total number of hidtien nodcs. is the node number.

12

The ARhIA model parameters are used in the PS coiit roller to calcula t c llic control.

9.2 RBF-Identifier Training A two-stage learning procedure is nsed for the proposed RBF-Identifier. The RBF-1dent)ifieris first. tra.ined off-line usiiig a. simulated model of t,he generating unit. The t,raining data set, coiisists of iiiput,-output tlat,a. for a. variety of operat,ing conditions asid disturbances. The operating condition changes iii the range of 0.3 p u to 1.1pu power output and 0.75 p f lag to 0.9 p f lead. The disturbances used are the voltage reference and input torque reference dist,urbances arid three phiise to ground fa,iilt. Scvciit>ccnRBF ccnt,crs arc obt,aiiicd duriiig offline training using the n-means clustering procedure a.s shown in Fig. 3. St,art>ingwit,h off-line w l -

275

ues for RBF centers, it requires small computation time to update tlie weights on-line.

.

.

0.05

-

"4.05-

Fig. 4. Stabilit,y proof for tJhe PS control: polepattern for T ( 2 - l )

0

To consider the time domain performance of t,lic cont,rollcd syst,cni, a pcrforrnancc index J is formed to measure the diEerence between the predicted system output, ?j(t+ I) and it~sreference. !h(t 1):

4.151

+

Fig. 3. Plot of y(t) k 7 4 t ) for training vectors and the centers

+

3.3 PS-Controller

The self-optimizing PS control algorithm (G.P. Chen arid O.P. Malik arid G.S. Hopc and Y.H. Qin and G.Y. Xu. 1993) is eniployed to generate tlie control signal. Assunie that the feedback has the form

From rqns. (1) and (15) the closrd-loop charactcristir polynomiaI T ( z - l ) ran h tlcrivctl as

A(z-')F(z-')

+ I?(z-')G(z-l)

= T(2-l). (16)

In the pole-assignment (PA) algorithm T(2-l) is prescribcd (PAL Mills arid Tadc, 1996). However, tlie PS control algorithm makes T ( 2 - l ) take tlie form of A(%-') but the pole locations are shifted by a factor a , i.c. T(z-') = A(~r2-l).

(17)

In tlie 1's algorithm, a , a scalar, is the only par to bc tlctcrmincd tLnd its value rcfl the stability of the closed-loop system. Suppose X is the absolute valuc of the largest cliaracteristic root of A ( z - l ) , then 0 . X is tlie largest characteristic root of Y'(2-l). 'lo guarantee the stability of the closed-loop system. a ought to satisfy the following inequality (stability constraint):

E is the expectation operator. G(t 1) is dctcrrniricd by system paramctcr polynomials A(.-'), B(2-l) and past ~ ( tand ) u ( t ) signal sequeiice. Coiisidcririg that u ( t ) is a fwiction of the pole shifting factor N , thc pcrformancc iiidcx J bccomes nzzn,J

= r [ A ( . ) ,El(.). u ( t ) , y ( t ) , yr(i

+ I)].

(20)

In (20) F[.] denotes function. The polc-shiftirig factor a is the only unknown variable in (20) and thus can be delerrniricd by minimizing J . The stabilizer must keep the closed loop system stable. It implies that all roots of the closedloop cliaracteristic polynomial (A(az-'))must lie within the unit circle in the z-planc (c.f. 18). Thcl pole-patterns of T ( 2 - l ) are shown in Fig. 4 for a tlrirecpliase fault.

4. DSP IMPLEMENTATION

Thc structure of the digital control system is shownin Fig. 1. Thc RBF-Idcntificr/PS-Controller is iniplcmcnted on a Texas Instruments (TI) ThIS320C30 Digital Signal Proccssing (DSP) Board mouiited on a Peiitium I11 PC. The DSP board provides requiiite computdtional power (33.3MHz) for iinplcmcntiiig the APSS. I/O signals are transferred between AVR and DSP througli A/D channels. A conimcrcial ABB PHSC (ABB Proqrammnblc Hzqh Speed Controller - System Dcscriptmn, 19'30) Excitation System providcs tlic AVR function. The ThIS320C30 DSP chip contains integer and floating-point arithmetic units. For data acquisition purposes. thc board is cquippcd with two 200 k H z . 16-bit analog 1/0 channel\ on h o x d to a11 4eria1 and parallel coiipled with direct ;1

It can hc seen that once T ( 2 - l ) is specified, F ( z P 1 )and G'(7-l) can be dctcrrniricd by (16), and thii.; thc control sigiial n(t)can br calciilatrd from ( I 5 ) .

276

T/O cha.rinels of DSP chip. The :32-bit, on-chip t,inier is programmed by soft,\varet,oa resolution of 120 ns. The board is mourit,ed inside Pentiuni 111 PC (Fig. 1) with tlic corresponding dcvclopnient software arid debugging applica.t,ionprogram. Comrniiiiicat~ioiibet,ween the DSP and t>hePHSCZ programmable logic controller is through analog signals, as sliown in Pig. 1. The AVR calculatcs (,lie gerierator a.ct.ive power, Pc, based 011 (lie measured instant,aneous voltages and current,s. The P, signal is t,lieii tra,nsferretl t,o DSP board t,hrough tlic A/D channel. This A/D channel samples tlic signal at 50 ms interval. The samplcd signal goes through a filt,er, which liinit,s the noise and provides ant,i-aliasingprot,cction. Tlic filtered signal is then stored in a. buffer. Thc DSP chip rends the buffcr and coinputcs the control signal, U,,,,. The coniput,ed U,,, is placed into the output D/A channel. This out,put signal is connect>edto the analog input of the PHSC2. The AVR receives thc PSS cont,rol signad as a supplcmcnt.ary input and adds it, to the volt,age reference signal. The combined signal Lhen goes tlirougli t,he AVR block in order t,o obtain the required field cont,rol signal. Dimensionality of t,he network can become a problem with t~heRBF-Identifier (S. Haykin, 1994). This problem is circiimvc:ntjed by sc;lec%ing the centers Erom the input, vector rather than using rantlonily init,ializcd ccnt,crs. Using t~liisprocetlurc 9 centers and linear weights were obt,ained from off-line computer simulations and are directly at1optc:d for t,he 1nbora.t~ory studies in t.his paper. Thr: ovcr;ill calculat,ion t,ima on t kit: DSP for R.BFIdent,ifier/PS-Controller is 24112s (with a maximum of 27ms during disturbance). This comput,at.ion time is within the 50m.s sampling interval chosen in t~heAPSS iniplenient,at~ion. For coinparison, a CI'SS wit,li t.lie following transfer fimct>ion(IEEE,Working Group on Sp bility Controls, Power System Engineering Committcc, 1087) was irriplcrncntod digit~ally.

was irnplemexit,ed in the same erivironnienl. Since t,he cont,rol environment is for the developmerit, of digital controllers; t.lic CPSS t,ransfcr function is discretized. Because of t>liecomputationa.1 simplicity of the CPSS, a sampling rate of T = 1ms is chosen in the st>utlies.

Fig. 5, AP, response for 0.20p.u. input torque reference Step change with APSS

4i

-"'I -"

5

10

15

iim.z

20

25

3

Fig. 6. AP, response for 0.1Op.e1. input torque refwence step clia.nge wit,h APSS in t!orque reference is applied at, 10s and removed at 20.7. Tlic AP, rcsponsc wit'li no PSS (OPEN), CPSS anti APSS is shown iii Fig. 5 . The pararnet>ersof t,he CPSS are tuned using t,he Zieger-Nichols rules for t,unirig PID cont,rollers (K. Ogaia., 1990) to givc t,hc hcst rcsponsc for t,hc operating conditions of this test.

To further test the performance of t,he APSS, the operating contlit,ion is ckiangctl to P = 0.6pu, p f = 0.92pi~(lend),V = 0.99pu. A 0.1Opu decrease in t,oryue reference is applied again and removed at, 20s. The genera.tor is operating at lower voltage (leading p f ) hence the stability margin is redimxi. Response is shown in Fig. 6. Alt,hough t>hcsta.bility niargiri is rcduccd in t,he new opera(irig coridiliori, (,lie APSS slill prwides a good performance.

5.2 Stnbility Maryin Tcsf

5. EXPERIMENTAL STUDIES 5.1 Input torque reference step churige

0

PSSs are primarily used to provide extra damping to gcncmting units to d a m p low frcquciicy oscillations, and thm increase the stability margin of t h e power system. JVith PSS in operation. a power

277

Ada.ptive Power Sysbem St>abilizerlor Damping of Activc Power Swings. Proceedings of The IEEE Power Engineering Society, Sumvier Meeting, Seattle, Washington. pp. 122126. ABB Pro,qrammable High Speed Controller - Systern Description (1990). IAR. Excitation System Training Manual, ABB 1ndust)rie AG, Turgi, Schweiz. E.V. Larsen and D.A. Swann (1981). Applying Power System Stabilizers, Part 1-111. IEEE Pans. on, Power Appuratzis and system..^. pp. 3017-3046. G.P. Chen and O.P. nlalik and G.S. Hope and Y.H. Qiri and G.Y. Xu (1993). An Ada,ptlivc Power Syst,ern Stabilizer Based on the SelfOptimizing Pole Shifting Control Strategy. IEEE Paas. on, Energy Contwxion. pp. 639-

OM

0 02

c

a‘

0

4 02

4 04

Fig. 7. Stability niargiiz tcst, APSS syst,em can operate at, higher levels of load even if it is not stahlc witliout a PSS or wit,li R poor PSS. The test) starts with t,he gencmting unit, operating at a stable condition wit.h APSS. The load is gradually incrcascd. At opcrating condition 0 . 9 7 ~ 7power, ~ 0.925p.f (lead) tlie APSS is st,able. The operating condition indicates approximat,ely t~liernaximurn stability rria,rgiri reached wit,h t~he APSS. At approximat,cly lOs, t,he APSS is replaced by tlie CPSS. Tlie systcin begiris to oscillate wit,hout,any ext,ernal tlist,urbance. This mea.ns that the CPSS is unable to maintain t.lie saine 1t:vcl of systmri st ability for tlic abovc opcrat.ing conditions. The APSS is switched ba.ck again and the system stabilizes again. The results are given in Figs. 7.

646. IEE,E W’orking Group on Special Stabilit,y Cunt,rols, Power System Engineering Committ,ee (1987). Bibliography on the Application of Discret,e Supy1ernent)ar.yControls to Improve Power System Stabilit,y. IEEE Trans. on Power Systems. pp. 474-485. K. Ogata (1990). 1VIodern Control Engzneerzng. Prentice-Hall. Englewood Cliffs, N.J. O.P. Madik, G.S. Hopo and S.J. Cliciig (1991). Some Issues on the Practical use of RLS Ident,ification in Self-Tuning Control. Inl. J. Control. pp. 1021-1033. P.M. Mills, A.Y. Zoinaya a.nd M.0. Tade (1996). Neuro-Adaptkue Process Control - A Pmcticul Appruuch. JuEiri Wiley & Suns. NY, U.S.A. S. Chen, S.A. Billings and l’.hl. Grant (1992). Re cursive IIyhrid Algorithm for Noii-Linea,r Syst e r n Ident,ifiic:ation Using Radial Basis Funct,ion Networks. h t . .J. &7i,tr01. pp. 1051-1070. S. Haykin (1994). Neural Networks: A Cornyehensiiie Foundation. klncniillan. New York.

6. CONCLUSIONS of APSS iisirig an RBF-Identificx Irriplernenl,i~.t,ion ant3 PS-Controller arid real-t,iine test resiiks on a. physical model of a power syst,emitre present,ed in this papcr. A conimcrcial ACB PIISC2 Excit,at,ion Syst,ern provided the AV-R function.

A. PHYSICAL MODEL OF POWER SYSTEM

The RBF-Ident,ifier is first, trained off-line. The RBF-Ident>ifieris furt,lier updated on-line at, every sampling interval to t,rack the dynamic coiidit ions. Tlie PS cont,rol iiscs tlic ARMA paramt t airiecl oil-line froni tlie lineurimtion of tlic ideritiiier Lo compute the control signal.

A . l Thc paramctcrs of tlic micro-altcrnator in p.u. arc 2,L - 1.20 1’,] - 1.20 r d - 0.0026 I’q = 0.0026 XTnd = 1.I 29 XnZq 1.129 T & = 1.25 xhq = 1.25 r’hd = 0.0083 rkq = 0.0083 xf = 1.27 rf = 0.000747 H = 4.75s A.2 Each transmission line consists of six 50 km equivalent rr-sections. For each i.r-vction, the parameters in p.u. are

Experimental results with the proposed APSS are comparcd t,o t~lioscof tlic CPSS. It- is dcmonstratal that APSS exhibits good performance over a wide rung; of operating condit,ions wit,hoiit requiring any taming unlike t,he CPSS. CPSS can provide similar performance as the APSS for the power system configurat~ioriarid operat,ing conditions for which it, is designed.

R = 0.036

X

= 0.0706.

Lz

= 18.779

A.3 Paranieters of the CPSS are

REFERENCES

K,

A . Eichniarni. A. Kohler. O.P. Malik and J . Tahorda (2000). h Prototype Svlf-Tuning

278

= -0.5

TI = 0.065s T3 = 0.065s

T2 = 0.08s T d = 0.08s

Copyright 8 Power Plants and Power Systems Control. Kananaskis. Canada 2006

PUBLlCATlONS

EXTENDED PHASE COMPENSATIONDESIGN OF POWER SYSTEM STABILIZER FOR BISOTOUN POWER PLANT G. Zafarabadi, It M. Parniani, M. Rasouli and P. Ansarimehr I . Power System Operation Department, Niroo Research Institute (NRI), 2. Sharij'University of Technology

Abstract: In this papcr, pcrformance of power systcm stabilizer (PSS) of a largc thermal power plant, as tuned by the manufacturer, is investigated. Then, the stabilizer is redcsigncd bascd on extended phase compensation of thc excitcr input - elcctrical torque transfcr function and root locus analysis; and its cffcct on local, intcrplant and intcr-arca clcctromcchanical oscillations is thoroughly analyzcd. As Bisotoun PSS has a special structure with two inputs, frequency and power, its performance is compared with power-speed PSS. The effect of PSS with existing and new tunings on transient stability is also studied. Simulation results are verified by experimental test records. Keywords: Electromechanical oscillations, Power system stability, Power system stabilizer, PSS tuning

1. INTRUDUCTION

YNAMIC stability is onc of the mosl important issues in powcr systcm opcration. Sufficicnt damping and stability margin is required to utilize maximum capacity of the system. Power system stabilizer (PSS) is a complementary controller installed on the excitation system to improve damping of electromechanical oscillations. In addition to the initial design and commissioning stages, PSS parameters may need to bc rctuncd after somc ycars of operation, bccausc of changes in thc structurc of powcr systcm and its paraincters. Bisotoun powcr plant has two 400 MVA stcam turbinc gcneraling units, and is located in the west area of Iran. This power plant is connected to electrical grid of Iran through six 230 KV transmission lines. Each generator is equipped with a PSS, connected to a static excitation system. In this paper, pcrformance of thc stabilizer is thoroughly invcstigatcd. Then, it is redcsigncd for ncar-optimal opcration under various conditions and in a widc range of oscillation frcqucncics. Excitation systcm and gcncrator data arc identified physically and experimentally during the work, and the whole Tran EHV system i s modeled for the analysis and design. PSS design is carried out based on phase compensation in a desired range of frequencies and root locus analysis eundur, et al., 1989, Kundur, 1999). Dynamic pcrformancc of the power plant and its cffcct on differcnt clectromcchanical oscillation modes, with and without PSS, is cvaluatcd. Also, as Bisotoun PSS has a special structure with frequency and power inputs, its performance is compared with a power-speed PSS. Besides,

D

influence of the PSS with existing and new tunings on transient stability is studied. On-sitc test results arc presented for cxpcrimcntal verification of the simulations, and showing the cffcctivcness of thc stabilizer on damping thc local and inter-area oscillations. 2. MODELING BTSOTOUN POWER PLANT AND THE INTERCONNECTEDPOWER SYSTEM

2.I Generalor Model Generator model parameters werc derived from identification cxpcrimcnts. DC currcnt decay tcst, according to IEC 34-4 standard was pcrformcd for thc idcntification. The gcncrator model used for dynamic stability studies is the 7th order twoaxis model (dqo) of IEEE standard. Generator data is given in Ref. (PSOD, 2002). 2.2 Excitation System Model Figure 1 shows a simplified modcl of the static excitation system at Bisotoun powcr plant. As shown in thc figurc, AVR is of PI typc. Its paramctcrs werc obtained from identification tests (PSOD, 2003). ".F'dllh

v, (PW

Fig. 1. Block diagram of Bisotoun excitation system

279

00471

P

I ~

1+0.0161S+2.48e4Sz

_I

1+0.086S ~

1 C0.018S t3 98e-5SZ

I

7.1s

1+7.1$

Fig. 2. Block diagram of thc PSS 2.3 PSS Model PSS of Bisotoun powcr plant has two inputs: active power and frequency. Figure 2 shows the block diagram of this PSS. PSS gains in either of the power and frequency paths arc tunable.

2.4 Modeling EHVPower Nehoork For modcling of Iranian EHV powcr grid, all lincs, transformers and compensators of transmission network are directly modeled. For modeling of gcncrators, according to thcir significancc in thc analyses, three kinds of models arc considered. Subtransicnt modcl is considered for Bisotoun gcncrators, which are of primc influcnce in the studies. Excitation systems of Bisotoun and ncarby plants arc also modelcd. Exccpt for Bisotoun generators, similar units in each plant are merged and an equivalent unit is replaced to represent them. For power plants near Bisotoun, transient model is used, and remote plants arc rcprcscnkd with classic model. With this approach, 48 generators arc rctained in thc system modcl. Plant parameters are taken from Ref. (Parniani, 2002).

3. DESIGNOF POWER SYSTEM STABILIZER For the PSS design, thc worst condition in which electromechanical oscillations have minimum damping should be considcrcd. This is known as "performance condition" and is accomplished in thc ratcd activc powcr and maximum equivalent impcdance of thc network (Larscn, 1981). Maximum anticipated impedance in the study system is obtained when two transmission lincs betwccn Bisotoun and East K e m s h a h buses are disconnected. 3. I Phase Compensation Thc basic principlc in PSS dcsign for incrcasing damping torquc is that the phasc lag of GEP(s) (transfer function between cxciter input and thc clcctrical torquc as a function of frcqucncy) in a

frcqucncy rangc including local, intcrplant and intcrarca modes should be calculatcd and compcnsated by proper selcction of PSS parameters. For this purpose, the two Bisotoun units were represented as a single equivalent generator having a large inertia, and the gcnerators at all other stations wcrc modeled as infinite buses (Kundur, et al., 1989). Phasc of PSS should bc as ncar as possiblc to thc phasc lag of GEP(s). It is important to avoid overcompensation, is.the phasc compensation of PSS should not bc more than phasc lag of GEP(s), sincc il results in a negative synchronizing torque, which is undesirable. With the above approach, in addition to improving the damping of local mode, thc stabilizer produces some positivc damping torquc at inter-area frcqucncics. Range of frequency that contains local, inlcrplant and intcr-tic oscillations in tbc study systcm is bctwccn 0.4 to 1.5 Hz. To calculatc the phase characteristic of the PSS depicted in Figure 2, with due attention to swing equation and considering ATm= 0, electrical power is: dt

-

2H

(AT,-AT,

-DAmr)

Thcrefore, noting the proportion of frcqucncy and rotor specd, block diagram of PSS is rcdrawn as Figure 3. Figurc 4 illustrates thc ideal phasc compensation characteristics in diffcrent operating conditions (curvcs 2-5) as well as actual phase compcnsation providcd by the designed PSS (curve 1). Curve 2 shows the phase lag of GEP(s) as a function of frequency, in

-

I+C 086s ~

Ix).018S+3.98c-SS

7.1s

I

lr7.lS

Fig. 3. Block diagram of PSS for calculating phase compensation

280

I

8,

84

8,.

~

8,

,

,

.

I :

11,

> /

1

Fig. 4. Phasc charactcristicsof PSS "performance condition". Curve 3 of the figure shows thc phase lag of GEP(s) at peak load and normal system condition. Curves 4 and 5 corrcspond to similar cascs as curves 2 and 3 with only onc unit of Bisotoun connected to the network. It is seen that curves 2 to 5 are all above curve 1, but the phase difference between them is less than 35" degrecs, which is acccptable. By the above phase compensation dcsign, the ratio of thc two PSS gains is obtained as: K, K,

=

0.2 15

(3)

For finding the absolute values of K, and K, root locus method is employed.

3.2 Determining the PSS Gain The gain of PSS has direct cffcct on damping of electromcchanical oscillations. It is desired to attain maximum damping of thcsc oscillations without destabilizing other modes. Since the ratio & is

Ic

constant, gains K, and K, arc increased from zero and root locus is drawn. The proccdure is carried out once for PSS with power and rotor speed inputs, and once with powcr and frequency inputs. Figurc 5 is thc root locus for thc performance condition. The root loci for another conditions is in (Zafarabadi, 2004). In this figurc, part "a" is for PSS with powerspeed input and part "b" is for PSS with powerfrcqucncy input. Arrows show thc direction of motion of some modes with increasing gains. Too much increase of K, and K, has a negative erfect on other modes (such as control modes). Based on these results, gain values of K, = 0.874 and K, = 8.625 arc selcctcd.

4.PLWORMANCE EVALUATION THROUGHSIMULATION The effect of Bisotoun Plant stabilizer on three types of oscillations (local, intcrplant and inter-area modes) is investigated. For identification of these modcs, mode shapes and participation factors associated with rotor speed and rotor angle arc employed (Kundur, 1994). To ease the demonstration, generators are numbered from 1 to 48, and Bisotoun is denoted by 3 . Moreover,

Fig. 5. Root locus with'two units connected to the network with full load and maximum impedance, (a) PSS with power-frequency input, (b) PSS with power-speed input. plants near Bisotoun are numbered from 1 to 14.

4.1 Effect of PSS on Damping of Local Oscillation Modes Local modes are associated with the swing of units at one generating station with respect to the rest of power system. State matrix of the system in performance condition comprises 110 complex eigenvalues. By studying these eigenvalues and the corresponding participation factors it is observed that 6 modes are affected by Bisotoun rotor speed. These modes (1 to 6 ) are depicted in Figure 5. Bisotoun generator speed has maximum participation in modes 2 and 5. Figure 6 shows mode shape components corresponding to the rotor ofthe turbine generators for mode 2. Local nature of this mode is evident from the figure. Investigation of participation matrix shows that after employing the PSS, (with the settings specified in the previous section) mode numbers which are most affected by Risotoun speed, change to modes 5 , 7 and 8. Among these modes, Bisotoun speed has the most participation in modes 5 and 7. The mode shapes also confirm this result. The mode shape components associated with the speed of all machines for mode 7 are depicted in Figure 7. It is observed that the effect and participation of Bisotoun on the oscillation modes also depends on PSS gain. This result is confmed in other conditions

281

Power uarizdtlon iou 8'

Fig. 6 . Mode shape components associated with speed of generators for mode 2 (without PSS) 1%

I

h

l

U

Fig. 8. Active power variations of one unit aftcr 2% change in voltage reference when 2 units working at full load are connected to the network.

r

1

Fig. 7 Mode shape components associated with the speed of generators for mode 7 (with PSS) (not presented here for the sake of brevity). Table I shows the effect of PSS with power-speed and powerfrequency inputs on damping of local mode in different conditions. It is observed from the table that the damping decreases as the impcdance or active power increase. Anotlicr result is that P-f PSS yields a little morc damplng than P-w PSS. Figures 8 and 9 show the variations of active power, when a 2% change in voltage reference IS applied to the generator. Each

"re

wax,

1.490

Min.

-0.944f 10.08i

1.605

figure contains thrcc curves: PSS off, P-w PSS and P-f PSS, with max and min impedance conditions shown in figurcs a and b respectively. It is observed that the PSS always has satisfactory performance, and P-f PSS slightly outperform the other type. 4.2 PSS Efects on Interplant Mode Damping Mode shape components corresponding to the rotor speed of 2 units arc in opposite direction for interplant mode and are unidirectional for local mode. PSS effect on damping of interplant mode is shown in Table 11.

PSS

0.066

P-W Eigenvalue of interplant mode -2.8721 12.24

1.955

0.093

-3.30+ 13.071i

2.080

Without PSS Eigenvalue of interplant mode -0,6171 9.3621

Impedance

Fig. 9. Active power variations after 2% change in voltage reference when 1 unit working at full load is connected to the network.

(

282

Freq. (Hz)

P-f PSS

0,228

Eigenvalue of interplant mode -3.781+ 11.08i

Freq. (Hz) 1.763

0.323

0.245

-4.251f 11.83i

1.883

0.338

Damping

Damping

The main result is alike local mode behavior: PSS improves the damping of interplant oscillation considerably and P-f PSS is a little better than P-w PSS. Also, it is obvious that the network structure and impedance has negligible effect on interplant damping. 4.3 PSS Ejfectson Inter-Area Modes Damping ContTibution of each power plant in inter-area oscillations mainly depends upon its situation in the network, its nominal power and inertia. Frequencies of these oscillations are less than local mode. In the analyses camed out on the study network, three interarca modcs wcrc idcntificd. Thcir frcqucncics arc 0.436,0.583 and 0.746 respectively. According to components of mode shapes associated with rotor speeds, Bisotoun is most effective on mode 2 and has no effect on mode 3. Investigations of the effect of Bisotoun PSS on theinter-area eigenvalues damping reveal that the designed PSS slightly improves damping of modes 1 and 2 but mode 3 remains unchanged. This result is confirmed by their mode shapes that are not shown (Zafarabadi, 2004).

5. MODELVALIDATION AND TESTRESLJJTS According to the results obtaincd from excitation system identification, present adjustments of the PSS gains set by the manufacturer were: K,=1.575 (4) K, =0.513 , The main result of this section is that unlike local and interplant modes, PSS is less effective on inter-area oscillations. Moreover, its effect on different inter-area modes depends upon the position and characteristics of a power plant. Figure 10 shows phase compensation of the existing PSS as compared to the desired compensation in different operating conditions. Notations of different curves are similar to Figure 4. Considerable overcompensation provided by the existing PSS is evident. So, these adjustments are expected to yield undesirable effects on synchronizing torque, and to decrease oscillation frequency. To investigate the performanccs of existing and designed PSS tunings, some safe disturbances like tap .,

.r>.,.

, . ?,...(,.”,

n:

Pm.m

r

III

pu 011 s j s t t i n base

1

‘ i

I Fig 11. Active power vanatlons of unit 1, PSS OFF

:r,

.,r.,

. ,. ,

r

changing of the generator transformer and turbine valve position changing (about 2%) were cc applied, and necessary signals like active power; frequency and PSS output were recorded using a Data Acquisition System (DAS). Figures 11 and 12 show active power variations of unit 1 without and with PSS. In both figures, unit 2 is paralleled and is operating at P=160 [MW] and Q=O [MVAR], while the operating point of unit 1 is P=310 [MW] and Q=130 [MVAR]. Also all transmission lines in the area are in service (normal condition). Applied disturbance in the simulations is voltage reference changing (1.7% of nominal value). Each figure consists of two signals: a- measured, and b- simulatcd activc powcr. It is evident from both simulation and test results that the existing PSS improves oscillation damping. However, as it was expected, oscillation frequency decreased considerably because of PSS operation. For example, in Figure 11, f= 1.33 [Hz] but in Figure 12, e0.75 [Hz]. Therefore, the present tuning is not desired from transient stability point of view. After implementation of the new adjustments, sufficient damping of the local mode was achieved without compromising transient stability (Zafarabadi, 2004). I-Iowever, somc higher frcqucncy (about 6 Hz), damped oscillations were observed. Therefore, a fine-tuning was performed to avoid these oscillations. Active power variations at P 3 2 0 [MW] and Q=l20 [MVAR] for both units with the final tuning are depicted in Fig. 13.

r,i

.s

.,

.”.

I

, .,

2

, I

,+

,~

1

,,,L,r:

Fig. 12. Active power variations of unit I, PSS ON (existing tuning)

Fig. 10. Desired and present phase characteristicsof the PSS

283

,

, / .

,

Fig. 13. Active power variations ofunit 1, PSS ON (final tuning) 6. CONCLUSION In this paper, extended phase compensation method and root locus analysis was successfilly used for PSS design. Experimental test results and nonlinear simulations verified lmearized eigcnvalue analyses. Participation factors and mode shapes were effectively employed to identify local, interplant and inter-area modes and their characteristics. The following observations were also made: Adjustment of PSS parameters set by the manufacturer possessed an overcompensation characteristic, and had negative impact on transient stability. The PSS designed with extended phase compensation improves the damping of local and interplant oscillation modes considerably, and has some positive damping effect on inter-area oscillations. Fine-tuning during on-site tests was necessary to achieve satisfactoryperformance. P-f PSS slightly outperforms P-w PSS in damping electromechanical oscillations. Participation of Bisotoun generators in the oscillatory modes also depends on PSS operation. ACKNOWLEDGMENT

This work was part OF the PONBROl projcct conducted by the Department of Power System Operation, Niroo Research Institute (NRI), Iran. Tavanir Organization and Bakhtar Regional Electric Company in Iran supported the project. The authors would like l o thank management and technical staff of Bisotoun Generating Station for their assistance.

REFERENCES

Kundur, P., M. Klein, G. J. Rogers, M. S. Zywno (1 989). Application of Power Systcm Stahilizcrs for

PSOD (power Systcm Operation Dcpartmcnt) (2002). Proper Model for Generators of Bisotoun Power Plant and Offering Proper Method for Its Parameters Identification, part of project PONBROl, Niroo Research Institute (NRI). PSOD (power System Operation Department) (2003). Modeling of Excitation System of Bisotoun Power Plant. part of project PONBROl, Niroo Research Institute (NRI) Parniani, M. (2002). Dala of Electrical Power Grid of Iran in Years 2004 and 2009. First Report of the Contract No. 275-76-lot3 with Tavanir, Sharif University of Technology. Larsen, E. V., D. A. Swan (1981). Applying Power System Stabilizers, Parts 1, TI and TTT. 1EIX Trans. Vol. PAS-100, pp. 3017-3046.6 Zafarabadi, G. (2004). Design of Power System Stabilizer for Bisotoun Power Plant. MS. Thesis, Sharif University of Technology. Kundur, P. (1994). Power System Stability and Control. McGraw-Hill. Gholambasan Zafarabadi received his B.Sc. degree in Electrical Power engineering from Mazandaran Univesity in 2001. In 2003, he received his MSc. drgree in Power Engineering from Sharif University of Technoloby, Tehran, Irdn. Since 2002, he has been with thc Department of Powcr Systcm Opcration at Nuoo Research Institute (NRI) in Tehran. He has been working for the Iranian Academic Center for Education, culture and Research (ACECR) Sharif Branch in Tehran since 2003. Mostafa Parniani (Senior Member, IEEE) reccived Ius B.Sc. degree from Amrkabir University of Technology in 1987, and the M.Sc. degree from Sharif University of Technology in 1989, both in Electrical Power Engineering. He worked for Ghcds-Niroo Consulting Engineers Co. and for Electric Power Research Center in Tehran during 1988-90. Then, he obtained the Ph.D. degree in Electrical Engineering from the University of Toronto, Canada, in 1995. Currently, he is an assistant professor at Lhe EE Dept., Sharif University of Technohgy, Tehau, ban. IIe also worked as a consultant for the Department of Power System Operation, NRI during 2002-2005. His research interests include power system dynamics and control, and power electronics applications in power. Mohammad Rasouli received his B.Sc. degree in Electrical Engineering fmm Power and Water Institute of Technology (P.W.I.T.) in 1997, and his MSc. degree in Control Engineering from Amii-kabir University, Tehran, Iran, in 2000. He worked in the Department of Power System Operation at NRI during 2000-2005 where he conducted or supervised several projects on dynamic model identification of large turbine -generators and tuning of their controllers. Currently, he is studying his PFID at Calgaq University. Pooya Ansarimehr received his BSc. degree in Control Engineeringand M.Sc. degree in Power System Engineering from the Sharif University of Technology in 1995 and 1998, respectively. Since 1998, he worked at Eleckical Power System Research Center, NRI. He has been head of Power System Operation Dcpartmcnt since 2000. His main research interests include power system operation, dynamics and control.

Enhancement of Overall Systcm Stability. IEEE Tram. Vo1.4, No.2, pp. 614-626.1 Kundur, P. (1999). Effective Use of Power System Stabilizers for Enhancement of Power System Reliability. Power Engineering Society Summer Meeting, IEEE, Vol. 1, pp. 96 - 103.

284

Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

PUBLlCATlONS

ROBUST CONTROL DESIGN OF PSS IN WIDE AREA POWER SYSTEM CONSIDERING INFORMATION RELIABILITY IIiroyuku Ukai *Goh Toyosaki * Yoshiki Nakachi "Surech Chand Verma **

* Nagoya Institute of Technology, Gokiso, Showa, Nagoya, 466-8555, JAPAN * * Electric Poiuer R&D Center, Chubu Electric Power Co. Inc., 20- 1 Kitasekiyama, Odaka-cho, Madori-ku, Nagoya 4 59-8522, JAPAN

Abstract: In recent years, electric power system becomes larger and more complex due to the enlargement of power flow in wide area, the deregulation of electric utilities and thc full-scale cntry of Power Product Companies. Utidcr the background both inter-area a i d local oscillations are significant. In order to cope with these problems, the advancement of the PSS(Power Stabilizing System) are expected. In this paper, we propose the control system on basis of the robust control theory, which can improve stability of power system in wide area. The proposed control system is based on the "hierarchical power and inforination network"; that is: the feedback control system is hierarchically constructed by using information of wide area system in correspondence with the level of reliability. In particular, we idcnt,ify the dynamic impedance niodel of large power system by measuriiig voltage and current at the interconnection node. Copyright (c) 2006 IFAC. Kcywords: power system stabilixr, wide area power system. systcm identification. PMU, reliability

1. INTRODUCTION

Power syst,ern stabilizer(PSS) has beeii a costefficient measure to improve stability in power systems. The conventional PSS is designed on the basis of classical control theory for the linearizcd modcl around a certain opcrating condition. Therefore, it is adequate only for a narrow range around a design point. Since a, wide area power system is highly nonlinear and the network operating condition frequently changes, it brings discrepancies between the mathematical

linearized model and the real nonlinear system. Moreover it. cannot compensate Tor t,he miltimodes of power oscillation in wide area power system. Under these backgrounds inany robust control techniques have been applied with incrcasing demands for high quality electricity supply(Qihua Zhao, 1995)(S.Chen, 1995)(S.Cui et al., 1999). However, niost, of these robust controllers are designed on basis of a single machine and a infinite bus model. Therefore, even if it i s robustly designed for uncertainties of oscillation modes, it is difficult to compensate for both the local and the

285

inter-area modes of power oscillation. Moreover, when t,he operating condition undergoes large variations, it is often impossible to achieve high perforinaiice over an entire operatiiig range.

duced for designing the control model. Lastly the effectiveness of t,he proposed met,hod is confirmed by soine numerical simulations.

On the other hand, in recent years, phasor ineasureinent unit(Pb1U) in power system by using GPS(Global Positioning System) was iiitroduced aiid applied to a, st,atic state estimation, various protections, and so on(R..O.Burnett. et al., 1994)(M.Hojoel; al., 2003). One of the authors is carrying 011 a research project among uiiiversities in Japan for dcvcloping an oiiliiic global monitoring system for power system dynamics by usirig llie PMU. Iri tlie iiear lulure, it is expecled applying the Pl\iIU based technologies to various fields in power system. In stabihing control of power system, power inforination which are ineasured or estimated at rmilti-points by using the PMU will be aggressively utilized.

2. HIERARCHICAL FEEDBACK CONTROL SYSTEM

In that case, however, it is iiriportaiit to consider the reliability of various power data measured in a wide area power system. In other words! it is necessary to properly use several information data in a wide area according the level of reliability. Reliability of inforination used in this paper implies two meanings. One is the measure of degratlat,ion of power data owing to the lack of data in acquisition systems, time delay of transmitted data, traiisrnission noise, aiid so 011. The other is parameter uiicertainties of mathematical model used for designing controllers. In this paper, the design method of the advanced PSS is proposed to coinpelisate for multiple oscillation inodes in wide area power system. The mathematical model representing the total system is constructed by the generator to be controlled, the local power system, and the large power systein connected to the local power system. It is inodeled by taking accouiit of the information reliability of data used iii tlie model. 111 this way, thc proposed method provides both the local and the inter-area oscillation inodes in the control design model. As the result,: the feedback control configuration is coiistructed by takiiig accouiit of reliability of power information. In the following chapter, t.hc concept, of the proposed design method of controllers based on the level of iiiforinatioii reliability is shown. In the third chapter, the constructioii of coiitrol model based oii this idea aiid the design iiiethod based on Ifm control theory are presented. In particular, in this paper, the dynainical impedance model for the interconnected large power system is intro-

In this section, the concept of the proposed control design method based on the hierarchical feedback cont,rol syst,em is explained. The configurai,ion of t,he system is shown in Fig. 1. The basic idea is to coiist,ruct feedback control loops according to reliability of iiiforinatioii fed back from inultipoints in a wide area power system. As mentioned before, the reliability of information used in this paper iinplies two meanings. One is tlie measure of degradation of power data owing to the lack of data in acquisition systems, time delay of transmitted data, transmission noise, and so on. The other is parameter uncertainties of inatheinatical inoclel used for designing controllers. The power information of the generator to be controlled is highly reliable, highly frequent, and has large data iiumbers in which generator speed, active power, teriniiial voltage, aiid so oii are iiicluded. Moreover almost parameters of the generator are able to be known in advance. The reliability, the frequency, and data number of power inforination in the local area belong to the inediuin level, and the parameters of generators, network impedance, and load are somewhat uncertain. Moreover, in case that, t,here are many generators and load in a local area, they should be aggregated. Therefore t,he local area power system is forced to include parameter uncertainty. On the other hand, the power information of a large power systeiii or ariothcr powcr system area connectcd to the intcrconnection node is poor, that is, at most only information at the interconnection node can be useful. Moreover, its reliability and frequency belong to the low level. As the result, the feedback data to be directly used for the PSS inputs are divided to thrcc categories according to the information reliability and acquisition frequency. Moreover, the model parameters to be used l o design the coiitroller are cat,egorized t,o three levels.

3. CONTROL DESIGN METHOD In this section, the control model is constructed based on the idea of the hierarchical feedback coiitrol system. hheover, the H O0 controller to stabilize the total power system is designed based on t,he a,ggregat,edcont,rol model.

286

with the governor and AVR as shown in Fig.2 and Fig.3 On the other hand, for othei generatois in

Fig. 2. Block diagram of the governor

(

Large Powersystem

)

Fig. 1. Hierarchical feedback control system

3.1 System model for control design First of all, let GI be a generator to be controlled, and let G2 Gk be geiicrators belonging a local area power system. It may be assumed that the generator group is aggregated in a local area power system. Then state space inodel for k generators is defined by

-

Fig. 3. Block diagram of AVR local power system the simplified models are used, where the same model of generator is used aiid the governor aiid the AVR are reduced to first order models.

These generator models are not connected to power network. In order to embedding the network iinpednnce a i d load in the local power syswhere tem to the above system models, it is necessary to give the impedance characteristics of both the local power system and the large power system connected to the local power system. The local power system is constriicted by appropriately aggreagted generaors and loads. The local oscillatioii modes are reprcsentcd in this way. On the other hand, thc large power systcrn includes many generators and loads. As mentioned above, however, the impedance characteristics of the large power where. Z L % is a stale variable for each generator, u,, is a control input froin PSS, and @.zdL, AzClIL system is uncertain. Thus it is necessay to model the inter-area oscillation inode between the genare d - q axis terminal currents of generator a. erators in the local power system and those in The percise model of the generator to be coiitroled the other large power system. In this paper, it is derived by linesrlidng the following nonlinear is proposed that the network impedance of the model. large power system is presented as the dynamical iriodel by applying the system identification = w n ( w - 1) method. Therefore, the effects from other power 1 ;j = - [T, - T, - D(u l)] systems coniiected to the considered local power 2H system c'm be cmhedded in t,hc c o n h l design model.

s

-

Let the sniall deviations of node voltage and cur, rent at the interconnection point be Avn, & a d the deviation of the frequency at this node be w ~ If .thcrc arc sevral nodes connected to the considered local power sgtern, the identification is done at, each connect,ion node. Then the dy-

287

nainical inodel for each connected power system is idcnt ificd as follows: Subst,itut,ing Eqs.(9) and (10) to Eq.(12), we have

+

AVL = K L Z L K R X R

(13)

and

Then the following relation is finally obtained.

whcrc, t>heinput signal for the identification is A7.R aiid the outJput signals the A ~ R and AWR at the interconnected iiode, respectively. hi this paer, the 4SID(SubSpace based State Space model IDentificatioii method) is used to identify the system model. This method is the effective identification algorithm to identify the state space niodel and is easily available using MATLAB "Identification Toolbox". Main features are as follows;

As the result, by substituting the above relation to (1) and (8), the control desgiii model of the

total power system is given by

+ [ B;'] ucz.

(15)

(1) It can be applied to unstable and/or closed loop systems. (2) It provides a high acciiracy by virtue of SVD and QR decomposition algorithm. (3) It provides simple iiurnerical algorit,hin (4) It is easy to extend to multi-inputs arid multioutput systems.

whcre, K 7 ,i = 1,. . . , 4 are suitable coefficient matrices constructed by network impedances.

In this way, it is possible to represent the t d a l systerri rriotlel iriclutliiig the inter-area oscillation mode.

Each output is fed back to PSS according to thier information levels. In this paper, the output to be controlled is defined by the generator power outputs ill local power system.

Now we embed the network equation to the system model. In this paper, loads are assumed to be coiist ant iinpedaiice for simplicity. The local power systcin is appropriately aggregated. T h a i the volt>agesand currents at generator nodes and the iiitercoiinectioii iiode are expressed b y network impedance as follows;.

where I L , VL are currents a d voltages at generator nodes aiid Y,, are aggregated admittances in the local power system, rcspcctivcly. On the other hand. the terrniiial currents AZL iii Eq.(1) are expressed by t eriiiirial voltages of aggregated geiierators ud,, uYZin the local system and the voltages Avdrz. Av,rz at the interconnection nodes. Coilsidered with the trsiisforinatioii of the phase angle froin the standard D - C2 axis to the geiirator d - 4 axis, the linearized equation is represent cd by

In the similar manner, the deviation of the terininal voli age VL are expressed by

On the other haiid, the ineaured output is defined by y = [Aw,, Aw2, . . . . A W k , Awn]

z

=

[AP,l, LIP,,,

' ' '

, Ar-',,I

(16)

(17)

3.2 Control design The controller is designed based on this mathematical model of the total system by applying the H W control theory. 111 this paper, tlie coiitrol problem is foriiiulated by the 1obust stabilization problem of HO" control. Thc weight functions are designed by considering the model errors due to the aggregation of generators iii local power system, the identification error, and tlie data error of frequency at each measuring point. The solution to this problem is obtained by using MATLAB "Robust control toolbox".

4. KUMERICAL SIMULATION RESULTS

In this section, the numerical simulation results are shown by applying the proposed method to the 1EE.J WEST10-inachiiies system in Fig.4, which consists of 10 machines and 30 nodes. It is generally known that the longitudinal structure produces t.he typical long term oscillat.ion a,nd local

288

Fig. 4. IEEJ WEST10-machines system generator oscillations. It is assumed that the generator to be controlled i s GI, and generators in the local area power system is aggregated to the generator G2. The iritercoiiriectsioiinode is the tie line bet,ween G2 and G3.

Bode Diagram From U l l r

0

-100

First of all: t,he identificatioii result is shown in F i g 5 The input and output data are used in case that the three phase-to-ground fault occurs at the transrriissioii line iieitr the generator 9. It. is found that the estimated frequency well coincides with the measured one. The order of t,he identified system model is five. In order to X10" 540

in

c 0.0 -1.5

10"

10

Frcwenry I H d

0

10

20 time [ s e c ]

30

40

Fig. 5. Identification rcsult confirm tlie effectiveness of the proposed method, the nonlinear simulation is done when the three phase-t>o-grouiidfault, occurs at t,he transmission line near the generator 1 as shown in Fig.5 The simulation is achieved under the conditions; (1) superimpose the random noise of inaxiinuiri &lo% to the frequencies of the generator G2 aiid the iiiterconncction node, (2) assume the time delay 80[msec]for the transmitted data, (3) and thin the data acyuisitioii of the freyuencies of G2 and the intercoiiiiection node coinparcd with thc oiic of gcncrator G1.

The bode diagrams from the control input to each generator active power are shown in Fig. 6. It is found that each transfer function has resonance

Fig. 6. Bode diagram from control input to each generator active power modes at 0 . 4 H ~and ~ H LThe . former corresponds to the inter-area oscillation mode, and the latter local mode. The controller is designed to suppress these resonance modes against modeling errors. The transient responses of the active power and the freqiieiiry of each generator are Show11 in Flg.7 aiid Fig.8. In both figures. tlie solid line represents the case of proposed controller and the broken line the case that only the frequency of G1 is fed back. In the latter case, the 11O0control iiiethod is applied to a single rriacliiiie arid irifiriite bus iriodel with respect to the generator 1. It is found that the proposed method improves the transient stability compared with the case of the conventional 11" control case against parameter uncertainty. Moreover, the frequency at the intcrconnection node is shown in Fig.9. It is also the oscillation of the frequency at the interconiiectioii node is well suppressed.

289

5. CONCLUSIONS

..__......_ COfl "en1 l O l l d l ad van ce

In this paper the design method of the advanced PSS is proposed to compensate for rnultiple oscillation modes in a wide area power system. The main ideas and results of the proposed method [lllne

the feedback cont;roller is designed by taking account of informatioil reliability in power system. To do this, tlie control sign model is derived in correspoiidarice with three levels of information reliability. The first is exact model of tlie controlled generator, the second is reduced model of the local generators, and third is the estiinatioii model of the large power system connected to t,he considered local power system. The dyiiainical iinpedaiice model of a large power system connected to the considered local power syst,ems is obt,ained by using the system identification method. The 4SID method is applied to obtain the dynninical iinpedaiice model. This inethod can be realized based on the PMU system. Tlic simulation results show the good performance of the proposed rncthod compared with the conventional H m applied to control design model b a e d on a single niachiiie and infinite bus system.

30

-0.0I

I

1 0 8 -

s

4

I

I

I -

-

.,: :. : , 1 0

,

20

30

40

I - Gl+ciP*Aw

1-

-

-

&. Zhm aiid J . .Jiaiig (1995), Robust Controller

ltimej

0

1

30

iiit.ercoiinectioii node REFERENCES

-

-0.15

I

20

0 2 -

-0 4

I

I

10

0 4 -

-0 7

-

0 . 15 I

.. .. ,

0 6 -

9 E

I

;

*

Fig. 8. Transieiit respoiises of the frequencies of G l j G2, and G10

I

0.1

.

I timc I

advance

- 0.05 -

40

I time I

. _ _ . . _c _ _ _ _I o n_ ventiona I

I

40

Itime I

Fig. 7. Transient responses of thc activc powers of G1, G2, and G10

Design for Generator Excitation Systems, IEEE Trans. on Energy Conv, Vol. 10, No.2, pp. 201-209. S. Cheii aiid O.P. Malik (1995),Power System Stabilizer Design Using p Synthesis, IEEE Trans. on Energy Conv. Vol.10, KO. 2 , pp.175181. S.Cui, H.Uk;ti. et al. (1999), Decent,ralized Control of Large Power System by H X Control Based Excitation Coiitrol System, Proc. of IFAC'99, Vol. 0 , pp.255-260. R.O.Burnett Jr, M.M.Butts, T.W.Cease, V.Centeno, G.Miche1, R..J.Miirphy, a i d A.G.Phadke (1994), Synchronized Phasor Measurements of a power system event, Trans. IEEE Powcr Syst., 9, No.3, pp.16431649. M.Hojo, T.Ohiiishi, Y.Mitani, O.Saeki, and H.Ukai (2003), OBservatin of Frequency Oscillation in Western ,Japan 6OHz Power System Based on Multiple Synchronized Phasor Measurement Proc. Powertech '03.

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Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

ANALYTICAL INVESTIGATION OF THE EFFECT OF GENERATOR MODELLING ON ELECTROMECHANICAL MODE DAMPING Keren Kaberere’, Alexander Petroianu’, Komla Folly’ University of Cape Town, Dept ofElectncu1 Engineering, Cape Town, South Apicu ‘kkunulhu@ehe uct uc zu, 2upetvoiunu@ehe uct uc. zu, ‘kjolly@ehe uc.1 uc zu

Abstract: Power system analytical tools differ in their components modelling. The differences affect electromechanical modes damping. This paper investigates the effect of including rotor speed deviation in stator voltage calculation -with the stator transients neglected- and the modelling of turbine output, on electromechanical mode damping of a single machine infinite bus system. We use a sixth order generator model with different excitation control configurations. We analyse results obtained with EUROSTAG and compare these with results obtained with three other industrial-grade tools. Our results show that: (i) if rotor speed deviation is included in the stator voltage calculation, the results are more conservative than those obtained if speed deviation is neglected. (ii) if the turbine model output is torque, the results are more conservative than those obtained if the output model is power. Copyright 02006 IFAC Keywords: Eigenvalue analysis, electromechanical mode, speed deviation, turbine model output.

1

INTRODUCTION

The advancement of computer technology has facilitated the development of several power system analytical tools. Hence, decision makers increasingly rely on digital simulations for planning and operation. One important function of these tools is eigenvalue analysis. System stability is deduced from the eigenval tie resti It s. The analytical tools differ in their components modelling and numerical methodology; therefore, for the same benchmark network, different tools give different results. From experience (Kaberere, et al., 2005a; 2005b) the differences in results, obtained using different tools, are mainly due to differences in components modelling. The results obtained with different tools differ in damping but agree on frequency of oscillation (Kaberere, et al., 20053; Slootweg, et al., 2002). Kyriakides and Farmer (2004) acknowledge the need for carrying out studies to determine the modelling aspects that result in “damping errors”. Kaberere, et al. (2005a) highlighted the following generator modelling aspects as causes of variations in eigenvalue results obtained using different tools; i) Stator voltage calculation; include (rotor angular velocity, a, # 1) or neglect (q = 1) speed deviation. ii) Representation or turbine model output; mechanical torque, T, or mechanical power, P,.

aspects. We use a sixth order generator model with different excitation control configurations. With the tools at our disposal (PSS/E, PowerFactory, EUROSTAG, and SSAT), it was not possible to investigate the modelling aspects using only one tool. Only EUROSTAG and PowerFactory include rotor speed deviation in stator voltage calculation, but none of the two tools allows the user to neglect the speed deviation. The A matrix is therefore important for investigating the effect of speed deviation. The A matrix in PowerFactory is not accessible Therefore we use EUROSTAG and MATLAB to investigate the effect of including rotor speed deviation on the electromechanical mode We compare the EUROSTAGIMATLAB results with results obtained using PSSIE, PowerFactoiy and SSAT Our investigation reveals that: (i) if the stator transients are neglected, results obtained with rotor speed deviation included in the stator voltage calculation are more conservative than those obtained with speed deviation neglected, (ii) results obtained with T,,, turbine model output are more conservative than those obtained with P,, turbine model output. The paper is organisecl as follows. In section 2 , we discuss the linearised system equations; section 3, stator voltage calculation; section 4, turbine model output; section 5 , case study; section 6, conclusions.

We investigate the efrect of the two generator modelling aspects listed above on electromechanical modes. We use a single machine infinite bus (SMIB) system to demonstrate the effect of the two modelling 29 1

2

1979; TREE Std 1 1 10, 1991; Kundur, 1994). Moreover, the Power System Damping Ad Hoc Task Force (1999) reports that even if speed deviation is neglected in stator voltage calculation, it is important to include the effect of speed deviation in the value of terminal voltage fed back to the voltage regulator.

LTNEARTSED SYSTEM EQUATIONS

The dynamic behaviour of the power system is expressed through a system of non-linear differential and algebraic equations (DAE). To study the system's response to a small disturbance, these equations are linearised around an equilibrium point.

From the foregoing, various authors agree that it i s necessary to neglect stator transients and if stator transients are neglected, rotor speed deviation should also be neglected in stator voltage calculation.

For a S M B system with the generator on manual control represented using a 6'h order model, one form of expiessing the liiiearised system equations is 1' 3

1' 4

'15

a23

'24

a25 a2h

'33

034 ' 3 5

0

'VId

*VI~

'36

............................................. 043 044 045 046 ............................................. 0 5 3 '54 0 5 5 056

0 ru;, 0

One of the recommendations of the Power System Damping Ad Hoc Task Force (1999) is that research should be carried out to establish the effect on system damping, of neglecting stator transients without neglecting speed deviation in stator voltage calculation. From the available literature, little has been done in this respect.

"fd

'16-

. 4 2 ,

i

Aw, *b'

where: A

- denotes a small deviation

yffd

- field flux linkage

VJ/~

- d-axis amortisseur flux linkage

A study by Slootweg, et al. (2002) shows that the real part of the electromechanical mode is influenced by the inclusion or omission of rotor speed deviation in the stator voltage calculation. However, the authors do not state whether the influence is detrimental to damping or otherwise.

v2q- q-axis amortisseur flux linkage w, - rotor angular velocity 6 - rotor angle YJ,~,

.element

a,

of the A matrix for i , j =I, .... 6

- base angular velocity

wo

Johansson, et al. (2002) report that the inclusion of rotor speed deviation in stator voltage calculation results in conservative results. Their results were obtained using a 2"d order (classical) generator model.

The dimension of the A matrix increases as generator controllers are added. 3

All the tools that we use in our investigation neglect stator transicntc Table 1 gives a summary of thc representation of rotor speed deviation in four industrial-grade tools

STATOR VOLTAGE CALCULATION

Based on the dq-axis machine representation, the per unit (pu) stator terminal voltage, E, is expressed as E, = ed + j e ,

Table I : Representation of rotor speed deviation in stator voltage calculation in four industrial-grade tools Tool PSSIE PowerFactory EUROSTAG SSAT

where: ed, eq - d- and y-axis components of terminal voltage Y , Y, - d- and q-axis components of stator flux linkage - d- and q-axis components of stator current id, i, y - rotor angular velocity R, - stator resistance

Speed deviation Neglected Included Included Neglected

If rotor speed deviation is neglected, elements aI5,azi, equal to Lero.

u3irand ud5in (1 ) are all

4

In stability studies, network transients are neglected because they decay very l'ast. Therefore, for modelling consistency, the terms representing stator transients (d Y/dt terms in (2)) are also neglected.

TURBINE MODEL OUTPUT

From literature, it is not clear whether the turbine model output should be mechanical power Pm or mechanical torque T,. For example, Kundur (1994) represents the turbine model with T, output whereas IEEE Committee Report (1973) and Rogers (2000) represent the models with P,, output. Different analytical tools model the turbine output differently.

Several studies have found that in so far as low frequency oscillations are concerned, neglecting rotor speed deviation (co. = 1 in (2)) in stator voltage calculation counterbalances the el'fect of neglecting the stator transients (Dandeno, et al., 1974; Krause et al.,

If speed deviation is neglected (a. = 1 pu), then T, = P, pu; T,, and P,,, can be used interchangeably in the

292

Table 2 gives a summary of the turbine model output used in four industrial-grade tools.

swing equation. However, if speed deviation is considered (a,# 1 pu), T, # P, pu. The eigenvalue analysis results obtained with T, output are different from the results obtained with P,?,output.

Table 2: Turbine model output in four industrial-grade

tools

In section 4.1 and 4.2 we analyse the linearised swing equation with different turbine model outputs. We assume the following: i) Rotor speed deviation is neglected in stator voltage calculation. Thus electrical torque T, is a function of V J ~ , VIM, vlq,~2~~ and 6. ii) Rotor speed deviation is not neglected in the power-torque relationship (T,,?# P,,, pu). iii) The governor is not modelled

Tool

Turbine model output PSSE Pm PowerFactory P, T,,l EUROSTAG EUROSTAG’ P, SqAT p,,, SSAT~ T*,

5

Elernent uis ofA matrix

-&+ Pn&H -KD+ P d 2 H -KD/2H -(fG+ P,,o)I2H -(KO + P,,t0)/211 -KL>I2H

CASE STUDY - SINGLE MACHINE INFINITE BUS SYSTEM

4. I

Linearised swing equation T, turbine model output The linearised swing equation is

5.1

(3)

System model

We used the single machine infinite bus (SMIB) system as shown in Fig. 1 (Kundur, 1994) for our case study. For GI we used the 6‘h order generator model. We neglected saturation. vt

where: A - denotes a small deviation N - inertia constant (s) w,. - rotor angular velocity - turbine model mechanical torque output T, - electrical torque T, KD - damping torque coefficient.

P +

c!+ Figure I : SMIB system network representation

The mechanical torque is constant (AT,n = 0).

We sirnulaled the syskin with the following excitation control configurations: i) Manual control ii) AVR iii) AVR and power system stabiliser (PSS)

Equation (3) corresponds to row 5 , shown dotted in (1). From ( 3 ) , we deduce that element ass of the A matrix is equal to -K&2H.

Linearisedswing equation - P,x turbine model output Whenever the turbine model output is P,, and speed deviation is not neglected, equation (4) is used to calculate the turbine output torque.

4.2

Figure 2 shows the block diagram of the generator excitation system. We did not model the turbine-governor set.

(4)

System data are given in the appendix.

Lineansing (4),

(5) A l , = M,, t P,,,Ao, Subslituhng ( 5 ) in (3), the linearised swing equation becomes dAq I (hp, - A T - ( K O +P,,)Am,)

transducer

-

dt

2H

where P,, is the steady state mechanical power output.

Power system stablliset

Figure 2: Block diagram of excitation system with AVR and PSS

The mechanical power is constant (AP,, = 0). From (6), we deduce that element uJ5 of the A matrix is equal to -(K,,+Pm,,)/2H.

We used the following tools for eigenvalue analysis: (i) PSS/E, (ii) PowerFactory, (iii) EUROSTAG, (iv) SSAT.

Hence, from a theoretical viewpoint, we expect the electromechanical mode damping to be higher if the turbine model output i s PnIand rotor speed deviation is considered than with T, output.

’

The program’s default turbine model output is Kx. We modified the output for the purposes of this study. Power option - specd dcviation ncglcctcd (T,x= PM).

293

+

1Jsing ElJROSTAG and SSAT, we ran two sets o f simulations for each excitation control configuration: (i) T, turbine model output, (ii) P, turbine model output.

5.2

EUROSTAG results are more conservative than EUROMAT results.

Simulation results and discussion

To exclude the effect of speed deviation on stator voltage, we exported the A matrix from EUROSTAG into MATLAB and set elements uI5, uj5,and u45in ( I ) equal to zero. We set element a55equal to -KJ2H and -(K,+P,,)RH for T,, and P, turbine model output respectively. We calculated the eigenvalues of the resultant matrix.

FT methods appear most viable. The choice depends on the need for detecting oscillatiorw during transients versus avoiding false detections.

5 . ACKNOWLEDGMENI'

o.

-

~

'I'he authors acknowledge the Danish illillistry of Sciencc Technology and Innovation. for support to the research program CMBC (Center for Model Based Control), grant 110 2002-603/4001-93

~~~~~~~~~~~~~

REFERENCES Harris. T. J.: C . 'I?. Seppala and L. D. Desborough (1999). A review of performance monitoring a.nd assessment techniques for univariate and te control systems. Journal of Process Control 9(1)>1-17. Mallat, S. (1999). A mavelet tour of szgmd processing. 2nd ed.. Academic Press. Miao, 1'. and D.E. Seborg (1999). Automatic dctcctian of cxccssivcly oscillatory fccdhack control loops. In: IEEE Inlernational Conferen,ce o n Control Applications. Hawaii, 1JSA. pp. 359-364. Odgaard. P.F. and M V . Wickerhanser (2005). Karhunen-lo2ve based detection of multiple oscillations in multiple measurement signals from large-scale process plants. Submitted for publicat ion. 'I'honihill, N.F., B. Huang and H.Z21a.ng (2003). Detection of multiple oscillations in control loops. Journal o.f Process Control 13, 91-100.

4. CONCLUSION Thcsc cxpcrimcnts with thcsc diffcrcnt oscillation detection methods, have given sonie interesting results. Two methods could not in the given data set detect the oscillations, thrse are WIV and ACF KL responds strongly enough on the oscillation in the test data to detect it, hut responds even stronger on the transients Ilowevei. this method does as the only method give similar results for both window lengths DF'I' responds to the oscillation and not to the transients, However, as a consequence of t h e occi~rrenceof transients it cannot detect

302

Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

LOW LOAD MODEL OF A ONCE-THROUGH BOILER WITH RECIRCULATION Klaus Trangbaek

Abstract: A dynamic sirnulation rnodel of a. once-t,hrough boiler in low to medium load is developed. When the syst.em is in low load; water from the evaporator is recirculated t-hrough a hott-lc. 'l'his recircnla,tion system is includcd in thc model, which is then shown to fit closed-loop data. from a real plant nicely. Copyright 0 2 0 0 6 IFAC Kcywords: Hydrothermal powcr systems, model approxiination, simulation.

1. INTRODUC?'ION The increasing liberalisation of the energy markets has led to a, grea,ter need for operating power pla.nts in ways for wliicli tlicy were not designed. For instance, plants designed to work a.t base load for most of the tirne are suddenly required to take part in 1oa.d regulation a.nd to operate at low 1oa.d for extended periods of t.irne. 'I% leads to a. rieed for i.econsidwing the cont,id strnctnre at, lorn 1oa.d. In order to do this it is nece simple dynamic model of the plant which is able to simulate 1oe.d hansients in low to niediuni 1oe.d. In this paper a model is developed for a 400 MW once-through boiler. When opera.ting this plant in low load, feed wat,er is recirculated leading to a, dynamic behaviour very different from tlie oiie in riiediurrr to high load, cspecially if t . 1 eritlialpy ~ of llie recircrrlated water is nirrch higher than (,hatof tile rresil reed water. Apart froin (Eitelberg and Boje, 2004), it seems t.liere are no dynamical models of this syst.eni described in 1it.erature. In this paper eniphasis is

' Supported by Eltra PSO grant 02-4114. The author would like t,o thank Babak hlataji et al. of Elsarn Erigirieering for kind support, and Prof. Edward Boje of U. of KwaZulu-Natal for useful advice.

put on acliieving a simple nonlinpar niodcl that will work in the range from low to medium load.

2. LOW LOAD OPERATION

'l'his section describes the system modelled in this paper. Some of the details are specific to the particiilar plant and may not hold in general for once-t,lirorigh boilers.

T h e boiler system considered is shown in Figure 1, where 3 syrribolises a hea,t input. In rriedium

to high loa.d, the boiler operates in once-through mode (O'ILI) meaning that the feed water passes through the high pressure pre-hea.ters (HPPH) and economiser to the evaporator where it fully evaporates int,o stearn. The stearn then passes to the superheaters: where it is 2iea.ted before passing t,hrough the (fully open) t,urbine valve to t,he high pressure turbine. and Loosely speaking, the outlet pressure, PhlL, temperature, 2 $ h , are controlled by the fuel flow ri?,fuei to t,he furnace and the feed water flow ri?fUl.

When tlie load and hence the Fuel flow is decreased, tlie feed water flow i s also decreased in order to maintain the desired stearn temperature and flow. However! a certain rninirnum Aow, rhmin! of' feed water is required in order to prevent dam-

303

some we,ter can be returned to the bottle throi.igh

m

--"(

lSh

s'h

5

To HP turbine "turb

'"out

&++ -x?- uperheater 2

~ R M F .

'l'here is a significmt difference in the dynainica,l bchaviours of the systcai in Ol'M and in RCM. In particuhr, if' tlie recirculated water is much warmer than the fresh feed water, non-minimum phase behaviour is iritrodnced, since iricreased recirculation in order to lower thc water lcvcl in thc bollle lends lo waririer ked waler (will] it larger specific volume); which in the short term increases the output flow from the evaporator, leading to an increased bottle level. Furthermore the systeni in H.CILI is less c o n t r o l l d e since the fresh water flow is bound by the minimum flow restriction, arid less obscrvablc since the cvaporator output temperature is given by the pressure and tlms contn.ins no informtition on thc st.cnm cnt.halpy.

3 . SIILIULATIO1v hlODEL

In this section the development of a simulation model of the above system is discussed. 'The aim is to obtain a simulator on which to examine different control stra.tegies for a pa.rticular plant. The pasarneters of the model are tuned using a. few easily obtn.ined physical parameters and measurement da.ta from closed-loop operation. Since the aim is controller design, the focns is on dymmic behaviour rat.her than stat.ic characteristics being exact. Furthermore, the model is required to be of rehtively low order and reasonably hst.

Feed water pump

'l'he model is required to operate from the lowest practical load (15%$)to aicdium load (50%) and to be able to handle transitions between RC'M and O1'1CI. Supercritical operation is not required.

Fig. 1. Y'he high pressure steam system. age t,o the evaporat,or tubes. Thus, at some point rj2pu, is mainhined a,t kmin even though the steam temperature is lower t,han desired. This also rneaiis that the stearn leaving the emporator is not. fully evaporated. The separator extracts the water, so that only saturated stenni is led to tlie superheaters. The ext,ract,ed wat,er is led t,o the bottle which acts as a srrrall buffer. In recirculation mode (RCM) t.he water in the bottle is recirculated to the feed water.

I f . '-

the

r,

I he main components of the recirculation system are the recirculation pump a.nd the recirculation valve wT. rl'he pump operates a t consta,nt speed and the valve controls the water level in tlie bottle through the recircula.tion flow fn,. Since the water leaving the bottle is close to saturation, it is irecessary to a.dd coolairt through w l y p s ~ , which is always fully open when t,he pump is on. Furthermore, in order to mainta.in a. suficient flow in the pump, when the required r j l , is low,

Fig. 2. A basic control volume.

The econoniiser, evaporator and superheaters are each modelled by a. lumped parameter control volume as shown in Figure 2. A control volunie IC has three state variables: steam mass AT,, steam enthalpy I/, , and wall temperature Ti,,,. The steam pressure P, and temperature 2; are determined by steam tables (Wagner. 2000) from the specific etitlia.lpy h, = f f , / h f , a,nd specific volume w, = K T / M , where KT is the steam volume. 'l'he niass flow between two volumes is determined by the pressure difference between them, i.e ~&-,+1 = c,,,+l(P, - 9,+1); where c is some constant. In a sense, this ineans that

3 04

the coiitrol volumes a.re split into a voluine with a inass and energy balance and a pipe across which the pressure drop occurs. 'l'he specific enthalpy of lhe steam flow oul of a. control volume is given by the specific enthalpy in that particular volume, whereas t,he input flow will have an eritlialpy specified by tlie preceding volume. This type of spatial discretisation has several advantages wlieii the objective is to rnodel dynarriic behaviour; it is simple a.nd leads to ordinary differential equations. Furtlieriiiore, using a biliiiea,r discretisation such as a ceiit.ra1 difference schenie tends t.o introduce unrealistic non-minirnuin phase bel-iaviour. This is not a problem when using a, backwards difference type scheme as the above. On the ot.lier hand, it may be difficult to obtain a good static fit in a. widc range of operating points, but this is considered as a minor problem here. A further simplification is the heat input from the furnace to the wall. 'l'he energy flow is simply modelled as the fuel flow multiplied by a coiist.ant gain for each control volume.

3. I Separator and bottle

Ideally, when steam in a 2-phase condition enters lhc (cyclone) scparalor, saturalcd water is separated and led to the bottle, whereas the reinainiiig saturdled steam IS led to the superheaters. To compensate for pressure differences, there is a lube from lhc lop of the botllc to tlic inlct of the superheater. as illustrated in Figure 3 I

r&hIe

= ritchtc

+ riJt,z.

(2)

In general? this results iii a steam flow from sepa.rator to bottle and then into tlie superheater. In steady state the resulting net flows are the same as with perfect separation, and the transient behaviour is almost the same! but this method tends to be softer on the eqimtion solver. Another issue is the output flow a.t the bottom of the bottle. When there is a flow of coolant through the L'RArJ7 valve to the bottom of the bot,t>le,the specific ent,halpy a.t the bottle out,let, can be considerably below saturation enthalpy. To model this properly it i s necessa.ry to split the bot,t,le model i1it.o a.t least t,wo control volumes. Here, we let the hott,le model consist, of t,wocorit,rol volnrnes, one at the top with the same steam volume a.s the actual bottle ha.ving steam inass a.nd eritlialpy as state variables, and a smaller oiie at the bottom with only enthalpy as the sta.te variable, liavirig a constant mass. Thus the mass flow from the top to the bottom volunie equals the net flow out of the bottom, i.e %r minus the coolant flow.

3.8 Parameter adjustment

I

i: separa

Fig. 3. T h e separator Assuming perfect separation, we would have (referring to Figure 3) m,h,

t,he pressure drop from evaporator to superhea,ter and bottle, respectively. The specific ent,halpies are then determined from he, i.e. if the dryness fraction a,t the evapora,tor outlet is higher than & / ~ c then the flow into the superhea.ter will have specific entha.lpy hz: and h, will be giveii by

+ m,hz,

= mlLhl

(1)

where hi and h~ are the saturation etithalpies at the appropriate pressure. Thus if for instance riz, or riz, 15 known, then the other two flows will be given. I'hus. one approach would bc to compute the evaporator outlet flow from tlir pressure drop from evaporator to superheater aiid then get mA or rkul from (1). However, this approach tends to be a bit rigid, inakiiig the differential equations hard to solve Instead, we will take a different approach letting the flows Ij%, or riz, be controlled by

The model is adjusted to fit a set of closed-loop data froin a 400 MW gas fired plant. 'l'he plant is a.n important part in compensa.ting for changes in elcctricity consumption on the nct,, nrcaning that there is a dearth of steady state data, especia.lly at low load. However: fitting the &tic characteristics acciirately is less important than getting the dynamic behaviour right.. A bigger problem is the closed-loop iiature of the data, but since no open-loop data are available, a choice mist be made on where to break the loop when simulating, i.e. which controllers should be included and what should act as exteriial sigiials when trying to make a siniula~tionfit the data.

In RCM the system is open-loop unstable, but is stabilised if a. feed water flow controller keeps r i z f w at rizman (or at some other reference, e.g. from a temperature control) and a bottle level controller keeps riz, proportional to the bottle level L. 'Therefore, all water flow controllers are applied in the simulation when tuning the parameters. As noted in (Eit.elherg and Boje; 2004), t.l-iese loops interact heavily and improper tuning can lead to insta.bility. However, since the ba.ndwidt1is of these

305

loops are fairly high, this issue is riot relemnt, in t,he frequency range or int,erest. In ot,her words, any sufficiently fast and stabilising flow loop controllers will do.

it is noted that the outlet, pressure follows the rnea.surernents nicely. The same goes for the evaporator outlet temperature, which is unsurprising, since it merely the saturation temperature in this mode. Thus, in order to evaluate the evapora.tor model it is necessary to look at the bottle level or the recirculation flow. Unfortunately these rneasurements are extremely rioisy, so it is bcttcr t,o look a t thc valvc positions vT and V R A I F . Note that. no effort has been put into a,djusting the valve models, so steady state levels should not be expected t.ofit. However, the general shapes fit nicely indicating t,hat t,hc evaporator and recirculation system are modelled correct.ly, The superheater outlet temperatures a.re not fully satisfact.ory. Achieving a, better fit would probably require a more thorough nonlinear model of he& tmiisfer from furnace to wall, or possibly splitting the superheater into several control volumes.

Essentially the fnel flow, feed water flow, a.iid turbine valve are nsed for controlling pressure, temperature, and flow at t,lie outlet. 'l'hese cont.ro1 signals contaiii both feedback p a t s from disturbarice corripcrisatiori arid feed-forward p a r k frorn load changes. When fitting to closed-loop data it is of course irnportant to kecp in mind that, some mcasurcmcnts, e.g. superheater outlet temperatures: are in reality controlled outputs. If' the controller is included in the simulation then of course the simulated out.put will fit the measurement. What should then he evaluated is if the control input, e.g. t.he feed water flow, looks like t,he rrieasiired input. If' the model is simulated withont the controller present, the simulated output should not be expected to fit the rneasnred outpnt nicely.

Figure 5 shows a siniula.tion in OThl at medium load. Here, the inputs to the simulator ase the measured fuel flow and feed water flow, where tlie latter is wed as a reference for the feed water flow control. Both the evaporator outlet temperature and the outlet, pressure fit very nicely. The SIIperheat.er t,emperat,iirt.s fit reasonably well. These a,re essentially coni.rolled oi.iiput.s, so a hei.ter fit) should probably not be expected from this openloop siniulation.

Since the objective is a model for controller design, it is chosen to let, the three signals act as openloop inputs in the simulation when fit,t-ingto data. Thus, the only part. of the cont,rol syst,cm, which h a s been included in the model is the water flow loops. Acting as inputs (boundary conditions) are feed water flow reference, fuel Row, injection flows, and turbine valve set,ting.

The transition between modes also works satisfactorily, but, it is difficult to do a direct comparison with nieasurement data, since the exact timing of achieving full evaporation is crncial to the overall bcliaviour .

The ma,in paraaiet,ers t,o adjust ade the hea,t input gains, pressure drop to flow gains, stea.m volumes, arid wall lieat capacities, where the first two are nia,irrly acljuslcd to fil stcady slate siluations arid llie l a t k two are irsetl lor i-tdju s h g (,lie tlyriairiic behavionr .

Finally! a few reinarks on experiences frorn the modelling:

Evaluating the evaporator model is somewhat difficult, sincc when in OTM the fccd water flow arid fiiel flow are heavily correlated. We can therefore not be entirely certadn that the model will work for inputs that are riot correlated in t,he same way. When in RCM, tlie measured ev-apora.tor out.let temperature is useless, sirice it is merely the satura,tion t,ernperature. There are no flow measnremerits showing the fraction of steam that flows to the superheater, so we have to rely on the bott.le level rneasnremerit, which is quite noisy.

r ,

1lie recirculation coolant flow can be large arid, since it is quite cold, significantly a.ffects the system behaviour. Getting the flow right in the simulation is difficult, since it has to be estimated from terriperaturr rneasurernents, and these tend to give unreliable estirnafes. Adding the small volume at the bottom of tlie bottle results in a correct outlet temperature most of the time, but perhaps splitting the bottle into a stearn volume and a wall with heat capacity would achieve the same, arid possibly even make the transient response more correct. The proposed model is not very flexible in terms of being a.blr to modify the dyiiamic behaviour by adji.isiing t h e parameters. Tf the xhieved behaviour is not acceptable, it is probably necessary to split the individual control volumes into two or more sma,ller volumes. This wonltl make it possible to motlify the transient behaviour without affecting

3.3 Sirnulutron model results

1 ' he tuned model is tested with dnt D sets not nsed for tlie tuning. Fignre 4 slio~vsa sininlation in RCM. where tlie input to the sirnulation model. shown in the first two plots, is the measured hie1 flow (scaled for confidentiality) and turbine valve setting (fully open). The remaining plots compare the simulation result to rneasurernents

3 06

fuel

bottle level [m]

turbine valve [0-I]

1.27 -1 I 4.5

0.8 25

O'g

I

recirc. flow [kg/s]

4

0.8

3.5

recirc. flow temp. [K]

bottle outlet temp. [K]

550

7

500 450 I

400 I

evap. outlet temp. [K] 595 I

superheater 1 outlet temp. [K] 800

700 0

I

50

100

150

superheater 2 outlet pressure [Bar] 1051

90' 0

Time [min]

50

100

'

150

superheater 2 outlet temp. [K] I

740' 0

50

Time [min]

100

I

150

Time [min]

Fig. 4. Siiniilation in RCM. Solid, blue: siinidation. Dashed, red: measuremriits. Ilhdtiple measurement lines are due to parallel superheater strings. Fuel measurernent scaled for reasons of confidentiality

feed water flow [kg/s]

fuel

evap. outlet temp. [K]

* 7 140

0.5 I superheater 1 outlet temp. [K] 900 1 -

700 I*--

I '

80' 550 superheater 2 outlet pressure [Bar] superheater 2 outlet temp. [K] 900 850

800 800 700 I 0

I

200 400 Time [min]

600

0

200 400 Time [min]

600

750

0

Fig. 5 . Simulation in O'lM. Solid, blue: simulation. Das'ried, red: measurements

307

200 400 Time [min]

600

r l

Ihis approach works very well in the small load range a.bove. Closed-loop simulation results with the EI'V inodel are practically iridistirigiiisha.hle from those of the nonli~iearmodel. However, extending the method to a wider load range causes problems. rna.inly in choosiiig a suitable scheduling pa.rameter. Using the reference pressure works fine for the above range and for O'lM, but the significant differences bctwccn the two modes makes it dificult t o perform a smooth transition. Another problem a.rises when moving to a lower load. Here, the pressure is kept above a minimum by pa,rtially closing the turbine valve. Thus, t,hc pressure is no longer useful a.s a scheduling parmieter. These problems remain a.s yet nnsolved. Employing ve1ocit.y-based 1inea)risations (Leit h and Leithead, 1999) may be part of' the solution.

the steady state performance. but would of course makc tlie model slower. The model has been verified with closedloop data only. There i s no way to tell if it will behave correctly if the control system is significantly altered

4. LINEARISEL) MODEL APPHOXII\/IA"lOn'

The niodel is of the 15th order and somewhat slow (approxirnately 4 times fa.ster than real- time). For extensive studies of cont,rol strategies a much faster model would be an a.dva.nta.ge.Possibly, it could be made faster rising singular pertrirba.tion techrriyues (Kokotovic et ul., 1976) or quasi steady statc modelling as dcscribcd i n (Eitclbcrg and Boje, 2003), but the slowness seems to be caused by the bottle, making it difficult to separate fast and slow dyirarrrics. A inore geireral nuinerically based nonlinear model order reduction method (e.g. (Fujinioto a.nd Schrrpen, 2004)) might be considered instead.

5 . CONCLUSIONS

A simple dynamic simulation riiodel of a oncethrough boiler has been developed to fit inea.suremerit data well both in recirculation and in oncethrough mode. Further work will focus on making the model execute faster, since the current speed is riot entirely satisfactory. A first step was taken by a local 1inea.risation approach, but it is unc1ea.r if' this will work i n general and how to perform rriode cliariges lo arid l'rurri OTM. Apart frorri the relative slowness, the model has already proven very useful in trying out new control methods.

As a first step on the way t o a faster model, a local lineasisation approach has been tested in a relatively sniall load range, where the system is in RCh.1 with a fully open turbine valve. 'lhe simulation model including flow controllers is liriearised at reference pressures 90,92,94.96:98.100, and 102 bar, resulting in 7 linear models with corresponding equilibrium points (zo.~, ~ 0 , ~ Even ) . for this relat.ively small load range, studying these linearisat ions show that there a.re significant nonlinearities.

REFERENCES

A linear time varying (LTV) niodel is now constructed from the linear models. 'I'he schedulr is chosen as tlie reference pressure

rather than the actual (simulated) pressure in order to avoid some of the problems of hidden feedbacks. For R given reference pressure P,. we will then select t,he two nearest linearisations A l l = ( A l . 5 1 ) and A12 = (Az,R2) given by their individual sta,te space matrices, a,nd a scheduling gain r ( t ) bet,ween 0 and 1, so t,hat we have the interpolated linearisation ( A ( t )B , ( t ) )= r ( t ) ( A lB,1) (1 - r ( t ) ) ( A 2H2) , with corresponding cyuilibrium point ( ~ g ( t ) . u g ( t ) ) = y(t)(.xg,l,ug.l) (1 ~(t))(x0,2 ~ ,0 . 2 ) .Note that this only inakes sense because the state variables have a specific meaning common to the two linearisations. The nonlinear model can now be approximated by the linear t.irne varying model

+

+

--

d2'(t) dt

~

+ B(t)(u(C)

A(t)zl(t)

-

uo(f))

-

dZo ( t ) $t'(")

where the state in global variables will be z ( t )= ~ [ ( +t ~) g ( t ) . Tlir last term in ( 3 ) niay have to be discretised in time ill order t o implement it.

Eitelberg, Eduard and Edward Boje (2003). Quasi steady state modelling of an evaporator. Proc. African Control Confe Eitelberg, Eduard a.nd Edward Boje (2004). Water circulation cont.rol during once-through boiler start-up. Control Engineering Practice 12(6), 677-685. Fujimoto, I(. and J.M.A. Scherpen (2004). Ralancing and model reduction for discrete-time nonlinear systems ba,sed on hankel singular value analysis. Proc. 16th Int. Syrnp. Malhem u t k a l yy~eoryof Networ.ks a d Systems. Kokol,ovic, P. V.: R.E. O'hlalley a i d I). Sannuti (1976). Singular perturbations and order reduct,ion in control theory. Autovimtica 12. 123-132. I,eit.h, D. J. and W. E. Lcithead (1999). Aiialyt.ic fra.mework for blended multiple model syst.cms using linear local modcls. Intcmationul Journal of Control 72(7-8), 605-619. Wagiier. W. et al. (2000). 'l'he IAPWS industrial formulation 1997 for the thermodynaniic properties of water and steam. A S M E Journal of Eng. Gas I'urbines and Power 122! 150182.

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Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

PUBLICATIONS

SEMICROUP BASED NEURAL NETWORK ARCHITECTURE FOR EXTRAPOLATION OF MASS UNBALANCE FOR ROTATING MACHINES IN POWER PLANTS Byoung-Hee Kim, John P. Velas, and Kwang Y. Lee

Department of Electi+icalEngineering, The Pennsylvania State IJniversity University Park, PA 16802, IJSA Abstract: In this paper we focus on an investigation of a mathematical approach to extrapolation, using a combination of a modified neural network architecture and the semigroup theory. Semigroup theory provides a unified and powerful tool for the study of differential equations, partial differential equations and combinations thereof. The target of this investigation will be the prediction (by way of extrapolation) of the mass unbalance of the rotating component in a power plant. Simple mass unbalance system is considered for the simulation purpose. A new technique is proposed for measurement of vibration directly from rotating component using extrapolation. Copyright 0 2006 IFAC Keywords: mass unbalance, vibration, neural network, extrapolation, power plant, semigroup.

1. INTRODUCTION Avoiding destructive vibration is of major imporlance in the lurbine-generalor in a power planl. Mass unbalance is the most common source of vibration in machincs with rotating parts. Balancing of rotors prevents excessive loading of bearings and avoids fatigue failure, thus increasing the useful life of machinery. There are many studies on the vibration subject and most of those studies are hased on linear modeling (Florjancic, et al., 1998; Selig and Ding, 2000; Ahmad, et al., 2001). It was found, however, that linear rotor dynamics cannot account for an unbalance as it had occurred. In addition, a linear model is not sufficient at high frequencies (Florjancic, et al., 1998). During transient loads, furthermore, extreme conditions have been observed and efficient methods and tools to analyze such cases are of primary interest to the industry. Vibration has been notoriously difficult to measure, and most reported measurements have used accelerometers attached to a stationary housing carried by a retrofitted bearing mounted on the shaft of interest. Thus, the theory may not well predict the coupling of rear axle motion and bending resonances in the drive shaft. Furthermore, it is difficult to take vibration measurement if a shaft is rotating. The objective of this research is to develop a method of estimating the rotational mass unbalance, which is the most common source of vibration as it pertains to the turbine portion of a power plant, by introducing a

system-type neural network architecture from a sparse set of test data. One of the most important applications of vibration analysis is the solution of balancing problcms. An unbalanced rotor or driveshaft will cause vibration and stress in the rotating part and in its supporting stmcturc. Balancing of a rotating part is therefore highly imperative in order to minimize structural stresses, minimize operator annoyance and fatigue, increase bearing life, or minimize power loss. In this paper, a new method of estimating vibration on a turbine-generator is proposed using mass unbalance extrapolation based on a system-type neural network architecture, i.e., the semigroup based neural network architecture. Essentially, rather than relying on inaccurate vibration measurements, this method extrapolates a set of reliable mass unbalance readings from a common source of vibration. Concerning the issue o f extrapolation, a global need for extrapolation exists in many diverse areas (which will be highlighted in Section 2). In the case of the power plant, the opportunity for extrapolation of temperature inside of boiler furnace (Kim, et al., 2005a) and enthalpy in steam delivery section (Kim, et al., 2005b) also exists in a unique way. In Section 2, the general approach for extrapolation will be presented and the newly proposed approach will be presented in Section 3. In Section 4, the proposed approach will be simulated on empirical data. Finally, we make some conclusions in Section 5.

309

2. BASIC THEORY 2.1. The General Problem of Extrapolation Concerning the general problem of extrapolation, there are two points to be made. One, the need exists for a universal type of extrapolation; two, at present, each extrapolation problem is solved by developing a tcchniquc specific to thc problem. For cxample, referring to (Jangamshetti and Guruparasada, 19991, the authors extrapolate a set of capacity factors (at the ground level) for a wind turbine generator in the altitude direction. In this case, the extrapolation is based partly on the assumption that the power law, which describes the distribution of capacity with height at low altitudes, also applies in a modified form at high altitudes. The extrapolation is also based partly on the use of the Weibull statistical distribution model. As a final example, in (He, et al., 1994), the authors develop a method for extrapolating in frequency a set of radar readings, based upon the use of the Papoulis-Gerchberg iterative method. In summary, there are numerous applications for extrapolation but, at present, there is no universal method. As a contrast, the proposed method can be applied generally; there is no need for individual customization (Kim, et al., 2005a, b). 2.2 The Specific Problem of Extrupolation Jbr a Turbine-generator in a Power Plant

Fin. 1. Simnle mass unbalance svstem. engine speed, Because of abnormalities in the normal manufacturing process, some irregularities in the mass distribution are always present, which become the origin of mass unbalance. As a result of the above, variable disturbing forces occur which produce vibrations. To remove these vibrations and establish safe and quiet operation, balancing becomes necessary.

3. PROPOSED METHOD

In this paper, a new mass unbalance extrapolation mcthod is developed. Very bricfly, the method is implemented with a new neural network ( N N ) architecture which consists of two cooperating NN’s, one of which develops a functlon space and the other one of which selects a particular function from within that space. 3.1. PhiluresiShortcomings of Conventional iVN k

There are various sources of vibration and there are various vibration models. The most common and the most important source of vibration for rotating equipment is mass unbalance, and to illustrate the proposed procedure, the most elementary physical model will be assumed. The physical system consists of a shaft carrying a mass at its midspan and having a small mass unbalance, as shown in Fig. 1 . In general, the resulting vibrations can be complex, depending primarily on the geometry of the system. In this case only the simplest forms of transverse vibrations along the longitudinal axis of the shaft are being considered. As one example of a more complex vibration that’s being ignored, mass unbalance can be coupled to shaft whirling. If a shaft, driven at constant angular spccd w, also deflects bccausc of shaft resonance, the centroidal axis of the shaft will break down. In general, it takes a long time to startup thc turbinc in a powcr systcm. That is, thc start-up proceeds in a series of steps, along each of which the speed is held constant. The total start-up time may take up to 18 hours. Therefore, if at any point during the start-up, we can anticipate the mass unbalance at a future step, we can balance it to avoid vibration.

Recently, a Shift has occurred in the overall architecture of neural nctworks from simple or component-type networks to system-type architectures. The most popular architecture seems to be the one advocated by Jacobs and Jordan (1 99 1j, called the “Modular Connectionist Architecture,” one example of which is shown in Fig. 2 (Atiya, et al., 1998). It consists of a collection of expert components, each being trained independently, tied together by a component called the “gating logic” element, whose function is to decide on the relative contributions to be made by each expert component, such that when they are added, they provide the correct output for a given input. The present proposed method represents an adaptation of Fig. 2. The most serious flaw in the design of system-type neural networks is the lack of a cohesive discipline in the architectural design and in the design of the

For simulation purposes, the simple mass unbalance system will be considered to be one integral mass, M, which represents the rotor mass, along with a small mass unbalance offset (mr) mounted on a stubby shaft and supported at the two ends by its own bearings which have nonlinearity, as shown in the Fig. I . The damping (C) is assumed linear.

L

“lt,llfI”f”

t --- j ‘

7-~”(I)YO)

Fig. 2. Modular connectionist architecture. The unbalance force presents itself as a harmonic forcing function with a frequency that matches the

learning algorithm. Virtually, the entire design is done on an intuitive basis. As a contrast to intuition, 310

the proposed method relies on semigroup theory for the design of the semigroup channel. To illustrate the lack of a cohesive discipline, in (Atiya, et al , 1998), the partitioning of components corresponds to the separation of variables, which works if the variables are separated and does not work if the variables are not separated (Lee, el al., 2004, Kim, et al., 2005a, b).

The similarity between the mapping F(co, A ) proposed architecture (Fig. 3) and that of Fig 2 anses from the fact that the function channel is implemented as N “expert” systems The function channel can have a Radial Basis Function (RBF) architecture (Haykin, 1999). It consist^ of n RBF networks, each one of which implements one orthonormal vector of an n-

3.2. lielationship qf semigroup theory to A I W design

IA

The semigroup approach begins by asserting that certain functions are to be re-interpreted as follows: under certain circumstances, the function F ( w ,A ) should be thought of not as one map, but rather, as one family of maps: ( F 9 ( A ) , uG[O,Q]} which, in turn, is produced by a second family of maps ( @ ( w ) } where the two families are related by the following:

I

!

1 -

Function Channel

Semi-group Channel (”2) I

I

!

Fig. 3. System-type architecture. dimensional basis set of vectors E ( A ) . The outputs of the orthonormal vectors are (internally) linearly summed so that the channel spans an n-dimensional function space. The coefficients which determine the linear sum and thereby define the specific function being implemented is supplied by the semigroup channel. Up to this point, the operation of the RBF channel parallels the idea used by Phan and Fmeh (1996).

where

This interpretation suggests that the mapping must be achieved with a pair of neural networks, one that selects a given function at each value of o and another that then implements the chosen function. This interpretation also places severe constraints on the “selecting” neural component, forcing it to take on the generic semigroup behavior (3).

One of the essential differences between their approach and the present proposed approach is that the former requires prior engineering knowledge for selecting the basis vectors, and the latter approach requires no such knowledge. One advantage that RBF networks have over other architectures is that their functionality can be given an explicit mathematical expression in which the neuron activation functions act as Green’s functions (Tikhonov, 1973). This makes these networks amenable to design rather than training. Another advantage is that they function as universal approximators (Haykin, 1999). Thc scmigroup channel can be adapted from the Diagonal Neural Network (DRNN) (Ku, et a/., 1992; Ku and Lee, 1995), the Time-Lagged Recurrent Network (TLRN) (David and Donald, 1992) or Simple Recurrent Netwrok (SRN) (Elman, 1990; Haykin, 1999), in which the input is split into a dynamic scalar component w and one static vector component, the vector C ( 0 ) .The output is a vector C ( W ) ,which is related to the dynamic input w and to the static input c‘(0) by the semigroup property.

If a given system behavior (expressed as a set of data) possesses a semigroup property, the extrapolation of that data set is achieved by a neural network (the semigroup channel) which itself acquires its own semigroup property. The semigroup property is ultimately achieved within the semigroup channel as a sequence of weight changes that occur after weight convergence has taken place.

3.3. Proposed N N Architecture Neural networks are being used for systems described by PDE’s (Padhi and Balakrishnan, 2002). Thc system-type attribute of thc neural network architecture is shown in Fig. 3, implementing an arbitrary function I.’(@,A ) . Unlike conventional neural network architectures that would attempt to achieve the mapping J(’(u,A) with one neural network, the proposed architecture reflects a systemtype approach using two neural network channels, a filnction channel and a semigroup channel, in an adaptation of the connectionist architecture (Fig. 2). During use, the semigroup channel supplies the function channcl with a coefficient vector C(w) as a function of the index OJ. The coefficient vector, when applied to thc basis sct E ( A ) of the function channel, causes the function channel to operate as one specific function from within a vector space of functions. Jointly, these two channels realize a semigroup-based implementation of the

3.4. Proposed Learning Algorithm

Since it is composed of RBF components, the first component of the system, namely the function channel, can be designed, rather than trained The second component, the semigroup channel, can be trained in the new way illustrated below. Dunng training, the scmigroup channel rcceives as input a preliminary coefficient vector C ( u ) and produces a 311

develop an analytic model for the data, and then extrapolate the model along one specific axis. System modeling is achieved through a technique referred to as algebraic decomposition. Algebraic decomposition is an operation which is applied to a given function F ( w , R ) , for the purpose of representing it in a form that contains a semigroup: F ( w , A ) = qJ( A ) = C(w)‘ E( A ) , where E( A ) providcs the algebraic basis for thc rcprcscntation of each member of the parameterized function {f.:u(24)j . The essential value of algebraic decomposition is that when it is applied to the class of functions that will be considercd in this paper, it always produces a semigroup property for the coefficient vector.

smoothened coefficient vector ? ( w ) . That is, the primary objective of training is to replicate (and, if necessary, to smoothen) the vector C(w) with a vector c ( w ) which has the following semigroup property: C ( w ) = CD(w)i;(O),

(4)

where C ( w ) = [E, ( w ) , Er (O)),

’..,En ( w ) ] ’

@(w) : an n x n matrix that satisfies (3).

However, there is a secondary objective of training; thc channel must also “replicatc” thc semigroup property of the trajectory by gradually acquiring a semigroup property of its own in the weight space. The existence of this acquired semigroup property in the weight space becomes the basis for extrapolation (Lee, et a/., 2004). In order to elicit this gradual acquisition of the semigroup property, it is necessary that the training in this second step (semigroup tracking) occur in a gradual manner, as shown in Fig. 4. It must be noted that there are two concepts of convergence that occur. First, to acquire a given weight, for example, weight W3, requires conventional training convergence, which in turn may require 500 training iterations. Second, after all . . ., W,) have been obtained, a search weights (W,, W,, begins for a convergence within this weight stream alone.

3.6. Extrapolation

Extrapolation involves only the coefficient vector and the recurrent neural network (the semigroup channel). At the uppermost level, the idea is to train the neural network to replicate the coefficient vector in such a way that it is additionally rcplicating the semigroup property. And this is responsible for generating the coefficient vector by acquiring a semigroup property of its own in weight space. As a comparison, some other recent extrapolation attempts are given in (Altman and Mittra, 1999). One current method, which also attempts to build a universal framework for extrapolation, occurs in various forms in nonlinear control theory and is collectively called “continuation methods.” These methods have been in existence for some time, but are only recently receiving attention (Richter and de Carlo, 1983). These “continuation methods,” however. require advanced mathematics. 4. SIMULATION RESULTS

data point

Fig. 4. Ovcrvicw of ncw training algorithm.

The following illustrates simulation results of the application of the proposed mcthod to thc prediction (extrapolation) of mass unbalance data. In its simplest form, assuming cubic nonlinearity in the spring, the vibration in Fig. 1. is expressed by the following equation:

Unlike conventional neural network training which would repeatedly present the entire trajectory as a target, the proposed method begins by slicing the entire trajectory into a nested sequence of trajectories. In the nested sequence a given trajectory includes the previous trajectory and adds one additional data point. Each sub-trajectory is trained by a conventional (batch) method, and the resulting weight is recorded. After all sub-trajectories have been trained (culminating in the last sub-trajectory being the entire trajectory), the sequence of resulting weights is examined for convergence. Again, unlike conventional neural networks which require large data sets for training, the proposed method has been applied to sparse data sets (Lee, et al., 2004; Kim, et a/., 2005a, b). If thc data contains noisc, this will be removed by the semigroup channel as part of the smoothing process.

M x + CX + Kx3= F ( t ) = nzrw’ cos wt

(5)

By scaling this last equation properly, the following equation is obtained, which is one of the classic Duffing equations: X+yX+((ax+,Bx3)= FW2cosWt

(6)

where w = engine speed, F = mr = normalized mass unbalance. It can be shown that Eq. (6) has the following approximate solution (Stoker, 1950).

3 5 Sy.yten? Modeling

The modeling and extrapolation problem is formulated as follows. Given a set of empirical data for which there is no analytic description, first

where, 312

w = engine speed, a,b,y = constant, and A

vibration magnitude. This will be simulated on the domain: w ~ [ 1 0 0 , 1 5 0 ] x 2 ~A~[0.01,0.10] ; , using the following pardmcter VdlUcs: a = 900; = 0.75; y = 0.75. (Vance, 1988). =

The extrapolation will be simulated in the region, which is assumed thcrc is no data. Thc results of the extrapolation will be compared to given raw data in that region. The mass unbalance raw data profile is shown in Fig. 5. The preliminary (rough) coefficient vector and the basis vectors produced by the RBF

I.

=

I

I1

I

160

01

140 0 02

Mass Unbalance Vlbiatlon Analysis alysls

Frequency (radisec)

0 06

0 04

120

loo

Vibration Amplitude

Fig. 8. Error between empirical and computed unbalancc profilc.

01 008 1

5

006

I

I

06

160

140

0

120

-

Frequency (radlsec)

006

, 100

0 02

0

0 04

01

on

0 595

..

0 59

V#biat#onamplitude

Fig. 5. Mass unbalance profilc

I

0 585

Coefficient vector

I

0 SR

l

100

105

110

120 125 130 Frequency (radsec)

115

135

145

140

150

Fig. 9. Comparison of original and smoothened coefficients.

--

Integral of lnpul Weight

x 10'

-p 4-

0 1958

Integral of weight conwrgence IS shown foithe first 15 weights 3~

o 1958 0 g,571ppppppppppI 100

105

110

115

125 130 120 Frequency (radlsec)

135

140

145

Fig. 6. Preliminary (rough) coefficient vector. Basis Vector I

I

r

I

1

r

r

I

1

150

:

1

2

0

5

10

15

20

25

30

35

5

40

Frequency (radlsec)

Fig. 10. Integral of input weights. Cnlrapoleled C1 coefficient 0 61

Extrapolallon Tesl

0 05 001

l pmpmpmp pmpmpmp p p

002

003

004

005 006 007 Vibration amplitude

008

009

01

1

Extrawlatlon

Observation

0 605

I

t-*

06

I

4 1

U

011

-

Fig. 7. Basis vectors. network arc shown in Fig. 6. and Fig. 7, rcspcctively. The use of this rough coefficient vector together with the basis set of vectors can produce the computed mass unbalance profile. The error between empirical and computed unbalance profile is shown in Fig. 8. The recurrent neural network then smoothens the prcliminary coefficicnt vector, as shown in Fig. 9. The possibility Tor extrapolation begins by checking for weight convergence as training is performed

0 595 0 59

o 585 0 58

. 100

105

110

115

120 125 130 Frequcnoy (mdlscc)

. 135

I 140

145

150

Fig. 11. Extrapolation. along the coefficient vector. In this case, weight convergence occurs as this training is repeated over 313

successively longer intervals (refer to Fig. 10). In this case, because of the smoothness, the possibility for extrapolation exists and the next step is to apply an extrapolation test in which the trailing end of the weight change sequence (produced by training) is replaced by an equivalent weight change sequence based on a rule that generates a semigroup. Based upon an observation of the weight change sequence on the interval from 125 radsec to 130 radsec, a semigroup-based rule for weight change is formulated and applied to the interval from 130 rad/sec to 135 r.ad/sec, as a test. Extrapolation, from 135 radsec to 150 radisec, consists of the autonomous continuation of the rule for weight change, which was derived during the extrapolation test. These results are shown in Fig. 1 1 . 5. CONCLUSIONS In this paper, a mathematical approach is investigated to extrapolation o f the mass unbalance which i s a common source o f vibration on a turbine-generator in a power plant, using a combination of a modified neural network architecture and semigroup theory. Given a set of empirical data with no analytic expression, we first develop an analytic description and then extend that model along a single axis. This can be achieved by using algebraic decomposition to obtain an analytic description of empirical data in a specific form, called the semigroup form, which involves the product of a coefficient vector and a basis set of vectors. The concept can also be tested in many other engineering and non-engineering problems. REFERENCES Ahmad, S. M., A. J. Chipperfield and M.O. Tokhi (2000). Modelling and control of a twin rotor multi-input multi-output system. Proceeding of American Control Conference, 3, pp. 1720- 1724. Altman, Z. and R. Mittra (1999). A tcchniquc for extrapolating numerically rigorous solutions of electromagnetic scattering problems to higher frequencies and their scaling properties. IEEE Transactions on Antennas and Propagation, 47, pp. 744-75 1. Atiya, A., R. Aiyad and S. Shaheen (1998). A practical gated expert system neural network. IEEE International Joint Conference on .Neural Nefivorks, 1, pp. 419-424. David, A. W. and A. S. Donald (1992). Handbook of Intelligent Control, Van Nostrand Reinhold, N.Y. Elman, J. (1990). Finding structure in time. Journal of Cognitive Science, 14, pp. 179-21 1. Florjancic, S. S., N. Livcly and G. R. Thomas (1 998). Mechanical behavior of an industrial gas turbine under fault conditions, a case history. Proceedings of ISROMAC- 7 Conference, A, pp. 373-382. Haykin, S. (1999). .Neural Networks, 2nd ed. Prentice Hall, N.J. He, S., W. Sun and G. Guo (1994). A new data extrapolation algorithm with application in

guidance and target recognition. Proceedings of the IEEE Aerospace and Electronics Conference, 1 , pp. 89-92. Jacobs, R. and M. Jordan (1991). A competitive modular connectionist architecture. Advances in Neural Information Processing Systems, 3, pp. 767-773. Jangamshetti, S. H. and R. V. Guruprasada (1999). Height extrapolation of capacity factors for wind turbine generators. IEEE Power Engineering Review, 19, pp. 48-49. Kim, B. H., J. P. Velas and K. Y. Lee (2005a). Development of intelligent monitoring system for fossil-fuel power plants using system-type neural networks and semigroup theory. IEEE Poiver Engineering Society General Meeting, pp. 2949-2954. Kim, B. H., J. P. Velas and K. Y. Lce (2005h). Semigroup based neural network architecture for extrapolation of enthalpy in a power plant. Proceedings ofthe ISAP, pp. 291-296. Ku, C. C. and K. Y. Lee (1995). Diagonal recurrent neural networks for dynamic systems control. IEEE Transactions on M w a l Networkr, 6, pp. 144-156. Ku, C. C., K. Y. Lee and R. M. Edwards (1992). Improved nuclear reactor temperature control using diagonal recurrent neural networks. IEEE 7kansactions on h'uclear Science, 39, pp. 22982308. Lee, I Sucesi-~ee n e r g y transformations

Fig.1 Fossil fueled generation unit The thermal energy transferred depends on the discrete and continuous combined control actions This process section can be identified as hybrid system The term “hybrid’, sec (Antsaklis, 2000), refers to the combination of continuous and discrete par15 In this w i s e a hybrid dyriarriical system is understood to mean a dynamical system where the bchaviour of intcrcst is dctcrmincd by thc intcracting continuous and discrete dynamics 2.2 The thermal sub process in the real plant. The physical thermal process to be modelled is shown in Fig. 11. S e n s o r locations

I

I

I

I

I

I

I

I

I

I

I

I

Cont.ro1 e

2. DYNAMIC MODELING

2.1 The real plant: review of jossil fired power plant based in boiler with dome. The heat generation process, see the section a) in Fig. I identifies parts functioning as discrete such as; the Induced Draft Fan (IDF), the Forced Draft Fan (FDF), the Regenerative Draft Fan (RDF) and the number of Burners. Also, the Soot Blowers (SB) are only activated when the fluid resistance increases due to the excessive soot.

De-vices for manoeurabikty Fig. I1 Theinid sub process c o n s i d e r e d .

Therc we have singled out the placement of sensor’s locations; ‘d’ stands for dome’s outlet, ‘1’ for Primary Atemperator inlet, ‘2’ for Primary SuperHeater inlet (coincident with Ap’s outlet), ‘3’ for Secondary Atemperator inlet (coincident with SHp’s outlet), ‘4’ for Secondary SuperHeater inlet

3 16

Heat suurces: Combustion gas +Flatne!flue! htion + comctlon , Metd + Sink:Superheated s t e . m Always convection

(coincident with A,’s outlet), ’v’ for control valve inlet (coincident with SH,’s outlet). We single out, as manoeuvrability or driving vanables, ‘(ILp’ and ‘qc,’ which are the cooling water mass flows on the attemperator primary and secondary control valves.

irlrirrirrii

2.3 Basic assumptions for temperature dynamic modeling

1

I

n Y

Superheaters (and also reheaters) are large heat exchangers with steam flowing into the tubes, and gas crossing the tube banks in cross flow. Thc following are some general properties (Maffeuoni, 1997) worth recalling:

Temperature profiles SOLTRCES

SINK (1) The hcat transfcr cocfficient on thc gas sidc is much smaller than on the steam side, so that steady state behavior is nearly independent of steam side coefficients. (2) The dynamics of these heat exchangers is essentially due to the considerable energy storage in the rnctal wall, because flue gas has negligible density and steam has much lower capacitance that the corresponding metal wall. (3) Mass storage determines much faster dynamics with respect to energy storage, because only steam is involved. (4) It is known that adequate modeling of superheaters and reheaters requires a distributed parameter approach. However, it turns out (Keflenz, 1986) that reasonable approximations by lumped parameters may be used. (5) The temperature dynamic is nonlinear, because the time constant is nearly proportional to the inverse of the load. (6) Temperature dynamics are affected by multiple lags, which vary with the load. In addition, the transducers for steam temperature are generally affected by a small (a few seconds) and a larger (some tens of seconds) time lag due to the thermal inertia of the cylinder where thc sensor is placed.

2.4 Practical considerations,for model building

I

x

t

Gradient of Temperatwe

I Fig. I11 Temperat.1.m profiles.

t x

For wide-range temperature modeling (for fossilfired power plants based in boiler with dome) as per the GMP approach, three temperature range arc defined (while keeping a wide prcssurc range). For cnthalpy polynomial curvc fitting, the following three temperature ranges arc considered Low range: [325 - 4001 “C Medium range: [460 - 4751 “C High range: [5 10 - 5401 “C Full range: [280 5401 “C ~

Polynomial curve fitting with GMPs is obtained for a wide pressure range as follows: Pressure range: [70 - 1401 Bar. The equations sets for lumped parameters temperature modcl for wide range pressure (power) operation are the following:

2.4.I Superheuter

The superheater is assumed to be a heat exchanger of the cross flow type. The tubes are represented by one tube with constant dimensions throughout the whole length. The main features for its modeling are revisited on Fig. 111

a. Empirical heat transfer equation in superheaters, see (Anderson, et. Al., 1968). b. Enthalpy polynomial curve fitting with GMPs:

c. Heuristic criteria (where, implicitly, the thermal energy loss factor is taken into account):

Where, ‘kcon,’can bc taken as, either

317

a) A constant. Which was implicitly taken to be k=1.8 in (Eklund, 1971). b) A load function.

superheater's ends. Thus, the heat transfer characteristics are implicitly included. Then, from the MGP approach, we may find an accurate polynomial which fits the whole operation range. We consider the Heuristic criterion, QMs = k,,,,. ( H s s ~ ,- Hss,+i) qs. Temperatures, pressure and steam mass rate are recorded on a central computer. The fuel calorific energy can be taken as Q G =~ kcombqf. Two possibilities on the simulated data (see Fig. IV) have been introduced. The reference is taken from real plant database (see, Table 3). Familiarity both on multivariate algebraic curve fitting and process modeling is assumed.

d. The superheater is divided into N sections (index 'n' refers to variables in section n); the equations governing heat dynamics for section n then are:

The pressure drop over a superheater can be taken according to the following momentum equation: p,, - pw= k,l%

1 Enthalpy polynomial curve fitting by MGP

2

2.4.2 Attemperator

A spray type attemperator is considered. The cooling of thc stcam is simply achicvcd by injccting water into the steam flow. The volume and material masses of such an attemperator are small (since the attemperator has a very small volume, storages in it are negligible). Therefore all dynamics of the attemperator are disregarded.

The algorithm and the corresponding software (see Kuri et Al., 1998) allow us to find the polynomial's coefficients according to any of the following three optimization criteria: The best minimax curve fitting (TRN) over the training set, the best (smallest) maximum absolute error (TSTM) over the test set or the best RMS error (TSTR) over the test set. In this paper, we report on the TRN results. We wish to point out, however, that the more stringent TSTR errors were also remarkably satisfactory. Table 1 shows the polynomial equations for different ranges.

Energy, mass and momentum equations yield:

'I'able 1: Enthalpv polvnomial curve fitting bv GMP. Range LR (fi)

The pressure drop is lumped to the end of the attemperator The drop is small and when it i s desirable to set it to zero, thc constant kp2 is made equal to zero The enthalpy of the coolant is assumed to be constant Often this is justified since the water supplied to the attemperators is feedwater taken at the outlet of the economiser For conveniencc wc present the nomenclature used in what follows in an appendix at the end of the paper

MR (f2)

HR (f3)

FR (f4) TSTR

3. EXPERIMENTS AND SIMULATION

Enthalpy obtained equation by MGP (h,,) 0.7581016 - O.5O798Pn,- 0.47261 P,: + 0.501973 T,, + 0.177947 T,, P,, + 1.189684 T,, P:, - 1.14979 Tn: P,: 0.09417 T:, - 0.00949 T:, P,, i 0.430308 T,,' P,: 0.780182 0.70817 P,, 0.06857P,: + 0.220623 T,,+0.047924 TnrPnr+0.018766 T,,,P,,,2-0.00348P,1,4- 0.00094 T,,,' 0.0073 1 T,: P:, + 0.0017 13 T,: P:, 0.0976-0.60736 P,,-0.041 59 P,: +0.406946 T,, - 0.00906 T,: P,, 0.00198 P,,' - 0.00035 T,: - 0.00025 T:, P,,, + 0.073059 T,,, P,,+0.014104 T,, P,,2 0.210735-0.2634 P,, - 0.67839P,: + 1.1 84068 T,, + 3.035704 T,, Pn:+ 0.27573 Tn: + 0.788859 T,: P,, - 4.15317 T,: P i - 0.35015 T:, P,, - 0.25692 Tnr Pnr- 0.67414 T,: + 1.775461 T,: P,; Table 2: Variable normahzation range.

In this paper, basically concerned with a primary superheater, thc following csscntial considerations hold:

Range LR

For the superheated steam, stating the energy balance by enthalpy thermodynamic property is the best way to include, implicitly, the heat transfer characteristic. Indeed, the quantity of calorific energy taken by the steam mass flow per time unit may be completely calculated by measuring temperature and prcssurc at both

MR HR

318

Normalization. T,, = 0.01333(T-325) P,,,= 0.1 1765(P-70) h= 560.026(hn,0.5018)+2880.13 T,, = 0.006666(T-460) P,,, = 0.1 1765(P-70) h= 168.65hn,+3181.55 T,,= 0.003333(T-510)

Coef. Error 0.0212

5.73 x 1 O-s 7.15

FR

P,, = 0.10526(P-60) h= 174.47hn,+3333.13 T,, = 3.84615x10 (T-280) P,, = 0.010526(P-60) h= 918.476(hnr0.224418)+2805.24

3.2 Simulation estimations

model for

21 T a ~ n , 358 TsSHo 470 TV, 495

Xl0j

4f

0.0249

static

U

Function Q M ~ (fs) TssHo (fc)

~

Once it is possible to describe analytically the static characteristic on a whole operation range, and knowing the dyiiaiiiic modeling aspects which were summarized in 2.4, a dynamic simulation on a wide range can be conducted. For example, Fig. V shows a TMOresponse when an 'qs' negative step forcing function (from 320 Tonlh to 322 Tonlh) excites thc simulation model (for Pd= 120 Bar and TISM,= 370 "C)

TSS1-l"

To illustrate the G M P approach a wide static range for temperature modeling data set was collected. When considering the the Primary SuperHeater from an Electrical Power Unit of 100 MWs we took advantagc of thc data recorded aftcr major maintenance procedures A special test was performed during these procedures. its temperature regulator was closed in the control loop with the basic purpose of recording the diagnostic variables listed on Table 4 A five MWs constant step on the active powcr was set and a range from 50 MW to 95 MW was swept.

Fig V

9s (If

T,,ix, ."._. TsSHo

TMo

Var.

75

MW Pd a.

112 300

'Tmo' dynamic r e s p o n s e w h e n t h e

simulation model is excit.sd by 'qs' .

Table 3: Primary superheater data report. 65 MW 95 247 18.7 350 470 495

Polynomial description. 0.960679q5,,- 0.820386 P d n l T \ ~ ~ l n r + 0.8586 Pdnr qsn? 0.941957 T,, + 0.001574 T s s ~TM,i 0.00136 Ts& + 2.6710~10"T,SH?Tuo - 1.lX10-j qs TM, - 0.75373 TsSHi+ 3.77 x 10.' qs TsSwl TMo 3.8 x qs T M ~ 6.0636q; - 621.0580 q: + 12.4995~10~ q; - 4.9361 x105 q: + 4.7869 x106qf13082 x107

QGM (f7)

Fig. IV Simulation model for data generation

Pd

27 374 470 495

Table 4: Wide range static functions for the Primary superheater.

4

qs_ IU l

55 60 MW MW 80 90 238 242 I6 17 345 347 470 470 495 495 Continued 80 85 MW MW 120 128 320 328

26 370 470 495

parameter

3.2.1 Simulation inodel for a superheater btep. The essential idea for the advanced simulation tool is bascd in Fig. IV.

50 MW 73 232 14 343 470 495

24.5 366 470 495

Wide range static functions obtained by GMP:

On the steam line between dome and control valve, the superheater modeling is much more complex than the attemperator's. Hence, the static parameter estimations by MGP (for the temperature modeling on a wide real plant operation) stem from data corresponding to this kind of thermoelectric subprocess.

Var.

23.2 362 470 495

4. CONCLUSIONS

70 MW 103 280 20 355 470 495

90

95

MW

MW

133 335

140 340

The application of thc reportcd mcthodology may bc very useful for the industrial and university sectors. In fact, a relative unified approach is now being proposed which will simulate and emulate the dynamic of steam temperature for each section's attemperator- superheater. Our methodology may be extended to the whole electrical generation unit. Indeed, its application can be applied to cach sub-process. As an 'off-line' approach, for 'real' plants, the functions should be updated periodically. At any rate, it can be a very useful software tool for both industrial and

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educational sectors which are interested in the design of control systems, the evaluation of dynamic performance on a day-to-day basis aimed at optimal plant maintenance, etc.

of Hybrid Systems. In: Proceedings ofthe IEEE, Vol. 88. NO 7, July 2000, pp. 879 - 887. Balchen, J. and Larsen G. (1997). Control of a steam boiler by elementary nonlinear decoupling (END). In: Proceedings of the NATO Advanced Study Institute on Nonlinear Model Based Process Control (Ridvan Berber and Costas Kravaris), pp. 749 - 779. Kluwer Academic Publishers. Bell, R.D. and Astrom K.J. (1979). ‘A Low Order Nonlinear Dynamic Model for Drum Boiler Turbine - Alierndior Uniis’. Repori LUTFD2 (TFRT-7162/1-039). Lund Institute of Tcchnology, Swccdcn. Chen - Kuo, W and Asok Ray, (1997). Robust Wide - Range Control of Steam - Electric Power Plants. IEEE Transactions on Control System Twhno/ogy, Vol. 5, No. 1, January 1997, pp. 74 88. Eklund K (1971). ‘Linear drum boiler-turbine models’. PhD thesis. Lund Institute of Technology, Sweeden. Klefenz, G. (1986). Automatic conlrol of steam powerplants. Bibliographisches Institut, Zurich. Kuri, A., Villegas, C., (1998) A Universal Genetic Algorithm far Constrained Optimization., EUFIP’ ?W, 6th European Congress on Intelligent Techniques and Sofi Computing, Aachen, Germany. Kuri, A, Alinaraz, F., (2005). Genetic Multivariate Polynomials: An Alternative Tool to Neural Networks. Lecture Notes in Computer Science, No. 3773, pp. 262-270, Springer-Verlag. Maffezzoni C, (1 997). ‘Boiler - Turbine Dynamics in Power - Plant’ Control. Control Eng. Praclice, Vol 5, No 3, pp 301 312. Elsevier Science Lid. Moclbak, T., and Mortensen, J. H.(2003): ‘Steam temperature control’ in Thermal power plant simulation and control, pp 131 - 160, edited by Flynn, D. IEE, London. Working Group on Prime Mover and Energy Supply Models for System Dynamic Performance Studies (1991). ‘Dynamic models for fossil fueled steam units in power system studies’. IEEE Transactions on Power Systems, Vo1.6, NO. 2, pp 753-761. Usoro P.B., (1977). ‘Modeling and simulation of a drum boiler-turbine power plant under emergency state control’. M.S. thesis, Massachusetts Inst. of Tech., USA. Vande Wouwer, A. et al. (2000). An approach to the selection of the optimal sensor locations in distributed paramctcr systems. .lournal of PROCESS CONTROL, Vol. 10 (2000), pp. 291 -

Appendix Nomenclature

LR, MR, LR and FR refer to Low, Medium, High and Full temperature’s range. SH, A, C: SuperHeaier, Aiiemperaior and Coolani. i, o: input and output rcspcctivcly. nr: normalized range. The symbols used are the following: T, P: Temperature [“C], Pressurc [bar]. C,: Heal capacitance for superheater tubes [kJikg “C]. M,: Mass of superheater metal tubes [kg] QGM:Heat flow from gases to superheater metal tubes [kJ/s]

QMs: Heal flow rrorn superheater meial lubes to steam [kJ/s]

Thl: Superheater metal tube temperature [“C] qs: Steam flow [kgis]

~

qc:Coolant flow in attemperator [kgis] qf: Fuel flow [kgis] Pd:

Drum pressure [bar]

Ps0: Steam pressure outlet [bar] hsSH1: Steam enthalpy at SH’s inlet [kJ/kg] hsSHo:Steam enthalpy at SH’s outlet [kJ/kg] hsA,:Steam enthalpy at A’s inlet [kJ/kg] hsAo: Steam enthalpy at A’s outlet [kJikg] h,: Coolant water enthalpy [kJ/kg] REFERENCES

300 Anderson, J. H., Kwan, H.W., Quallrough, G.H., Dynamic models for power station boilers. Item 9.1: The governing laws of fluid dynamics and some empirical heat transfer relationships. Paper presented at Third U.K.A.C. Control Convention, April 1968. Anisaklis, P.J (2000). Theory arid Applications. A brief introduction to the Theory and Application

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Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

SIMULATION AS A TOOL FOR PROCESS DESIGN AND DISTURBANCE ANALYSIS IN INDUSTRIAL POWER PLANTS

Yrjo Majanne

Tampere University of Technology, Institute ofAutomation and Control P.O. BOX692, FIN-33101 TAMPERE, FINLAND [email protected] Abstract: Industrial power plant is a large scale system. During evcry day operation thc plant is cxposcd to large load disturbanccs caused by trips and start ups of steam consuming processes. Pressure stability of the plant must be maintained also during the disturbances in order to ensure the trouble free and efficient operation of the production system. The required stability is achieved by using load leveling components for balancing the loads in the steam network. In large scale systems the dynamic simulation i s the only possibility to analyze the responses caused by the disturbances and design the process and control system to meet the requirements set for the plant. Copyright 02006 IFAC. Keywords: Dynamic simulation, Power plant control. Load level control

feed water tanks, auxiliary condensers, condensing turbines, and blow out valves (Majanne, 2005).

1. INTRODUCTION During the last few years the role of the dynamic simulation as a part of the process and control design has incrcascd rcmarkably. Benefits of thc dynamic simulation are the most evident in the analysis of the dynamic behavior of the large scale systems. An industrial power plant is a good example of a large scale dynamic system exposed large disturbances during an every day operaiion of ihe plani.

Modeling of the power plant process may be approachcd from different points of view dcpcnding on the purpose of the use of the model (Leva and Maffezzoni, 2003). For the disturbance analysis of the plant the simulation model should be valid for a rather wide range of operation (non-linear model) and should be based on the firsi principle phenomena (laws of conservation of mass, energy, and momcnium) and thc dcsign data. This spccification leads to a model structuring approach based on the representation of plant components and their interconnections with variables and parameters corresponding to well-defined measurements or physical entities. For simulation models representing an entire power plant, it is quite common to seek model accuracy over an intermediate time-scale, i.e. in the range from a few tenths up to a few thousands of seconds, (Leva and Maffezzoni ,2003).

Load charactcristics of thc industrial powcr plant differs remarkably from that of a condensing power plant producing electricity to nationaliintemational power grids or a CHP (combined heat and power) plant producing heat and electricity to the electric and district heating networks. The main output of the industrial power plants is process steam. These plants are typically exposed to large and rapid load changes caused by trips and start ups of steam consuming processes. Pressure disturbances in process steam network may lead to a trip of a large capacity production process causing great economical losses. E.g. a 30 min trip of a paper machine will cause about 8 000 € (10 000 USD) loss.

Modeling of the power plant process has a history dating back to the pioneering work of Chien et a!. (1958), the earlier engineering-oriented works of Caseau et al. (1970), McDonald and Kwatny (1970), Weber et ul. (1976), Lausterei et al. (1984), Maffezzoni et aE. (1984), and h t r o m and Bell (1988). In the boiler area, there are many well documcntcd models ranging from complex knowledge based models to experimental models

Besides steam generators and back pressure turbines the industrial power plants are equipped with load balancing components stabilizing the operation of the steam network during rapid load changes. Typical load balancing components are steam accumulators,

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denvcd from special plant tests In the middle of this range there are so-called interpretation models. These modcls are complex enough to capturc the essential physics whilst at the same time they have good control dcsign features. 2. DYNAMIC CHARACTERISTICS OF THE INDUSTRIAL POWER PLANT In process industry the steam generating units are typically dimensioned so that changes in production capacity (typically enlargement) lead also changes in cncrgy production cquipmcnt. To build a ncw boilcr results often to build a new turbine plant, and because of these modifications the structure and the dynamics of the steam network will be changed.

Fig. 1. Typical structure of the industrial power plant with three pressure level steam network.

The capacity of the boiler units does not tell directly how difficult or easy task it is to stabilize the steam network. That is because part of the steam generating units can be constant load boilers such as chemical recovery boilers or combined cycle plants without controllable supplementary firing. These constant load units reduce the control range of the steam generating power of the plant. The increasing capacity of the steam consuming processes leads to increasing size of the load disturbances caused by the trips of these units. E.g. a web break in a paper machine causes typically a 10 30 kgls load change within 1 - 2 minutes corresponding 20 - 40 YOof the controllable load capacity of the steam generation.

The boiler dynamics dominates the dynamic characieristics of the sieam network. Time constanis of the boilers are in the minute range whereas the time constants of the turbines and pressure reduction valvcs arc in thc range of a couple of seconds. Furthermore the boiler dynamics can be asymmetric; e.g. for a grate fired boiler and a fluidized bed boiler the ratio of the time constants for increasing load and decreasing load can be 1:2.

~

Typical load balancing components in the industrial power plant are a steam accumulator, a feed water tank, an auxiliary condenser, a condensing turbine, and a blow out valve. These components have different operation expenses and to optimize the efficiency of the plant the use of these components should be prioritized

The steam consumers are typically connected to the intermediate (IP) and low pressure (LP) networks and the boilers are connected to the high pressure (HP) network The networks are connected together by a back pressure turbine equipped with a required number of extraction outlets. The back pressure turbine controls pressures in consumer networks by manipulating steam flows from HP network to LP and 1P networks. The controlled load boilers stabilize steam pressure in the HP network by balancing steam generation and consumption in the network. This is possible only in a long run, because a typical control speed (inax.) of the boilcr is about 5%/iiiiii and the rate of the load change caused by the trip of the paper machine can be 10 20 % Imin or even more of the controllable power generating capacity. This unbalance between the generated and the consumed steam flows effects on the pressure of the HP network.

The most efficient load leveling components are the steam accumulator and the condensing turbine. The steam accumulator is typically charged from IP network and discharged to LP network. Both energy and process water are recovered. With the condensing turbine it i s possible to compensate the disturbances in the steam load by adjusting the generated electric power. The problem with these components is the investment cost. Steam accumulator is a 100 - 300 m3 pressurized tank which is not nomally included to the equipment of thc industrial power plant. Also the condcnsing turbine is not very often included in the industrial power plant. Thc problem with the use of the feed water tank for load leveling is the asymmetric leveling capacity. It can receive a good amount of excessive steam from the nctwork but it can not release extra steam to the network. Big changes in heating steam flow to the feed water tank may also effect on the deaeration of the condensate leading problems with the quality of the boiler water.

Pressure fluctuations in the HP network should not exceed 5 % of the nominal pressure of the header. Frequent pressure fluctuations exceeding this level may damage the boiler structures (pressure fluctuation -> temperature fluctuation) and even temporary fluctuations exceeding this level may trip the boiler due to the loss of the drum level. E.g. a tripping of a recovery boiler will disturb severely the opcration of both the pulp inill and the papcr mill.

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With the auxiliary condenser only the process water is recovered. Active use of auxiliary condenser for load balancing requires that the cooling pumpsifans must be running all the time causing energy losses. The blow out valve has the highest operation expenses as a load leveling component. Both energy and process water are lost. The effective use of ihe indusinal power plant requires an automatic scheduling of load leveling operations The use of different load levcling cornponcnts ahould be ataggered horn the rnoai economic one to the worst one In practice this is achieved by biasing the control errors for controllcrs controlling the operation of these load leveling components

Fig. 2. Staggered operation of the steam leveling components during a web breaks in a paper machine. 3. SIMULAI'ION BASbD ANALYSIS

The simulation study is especially useful when an exisiing production system is modernized and the production capacity, e.g. a capacity of a paper machine is increased, a new turbine-generator unit is installed, a boiler capacity is increased ctc. Reconstruction of any component of the process effects on the required capacity and control performance of the remaining components. With the simulation study it is possible to analyze the effects of the modernization to the remaining part of the system and design the possible changes and improvements needed for the rest of the process. Simulation study of a new, nonexisting plant gives a lot of valuable design information for process and control design, but the results are more suggestive than for the exisiing p h i , because the simulation model cannot be validated against the measured process data. The third case for simulation is to study the possibilities to improve the operation of the existing plant. Implemented studies have shown that it is possible to get annual savings about 200 000 1000 000 euros (250 000 - 1 200 000 USD) in energy costs by improving the control strategy of the existing plant. The savings are coming from the

reduced need of energy and make up water. This i q the case when the steam consumers are tripping frequently and the load balancing is carried out by blowing out the excessive steam during the trips. When designing the structure and the control concept of the industrial power plant, simulation is used to study, how the load disturbances should be handled. A portion of ihe load disturbance in IPiLP network will be transferred to the HP network by the turbine controller. The prcssure disturbance in HP network will be cornpensated by the controlled boilers. In the HP network the storage capacity of the boilers is utilized. Also the constant load boilers stabilize steam pressure in the HP neiwork because of the storage capacity of their steam and water volumes connected with the HP network. The operation of the turbine controller must be constrained so that the disturbance in the HP network will not exceed the +- 5% limit from the nominal pressure. The rest of the disturbance must be compensated with the load balancing components in the IP and LP networks. If the simulation study shows that the steam accumulator is needed, also the capacity (volumc and capacity of chargc and discharge lines) of the accumulator can be defined. Simulation results are also used for dimensioning the turbine parameters, capxity of extraction outlets etc., and properties of turbine controller unit.

4. POWER PLANT SIMULATOR The industrial power plant simulator is programmed in MatlabiSimulinkO environment. Modelling of the power plant components is bascd mainly on the first principle models. The dynamic models are based on the energy and the mass balances. The momentum balance is neglected and the flow dynamics is embedded into the actuator dynamics. The rcason for this is that physical parameters like friction coefficients for pipe lines are needed to parametrize the momentum balance equations, and this kind of information is typically noi available. The nonlinear thermodynamics is applied by using nonlinear lookup tables to determine the state variables of superheated and saturated steam. The model library consists of steam generators, turbines, load leveling components, stcam consumers, controllers, and miscellaneous components like valves for different media with different type of actuators (pneumatic, hydraulic, electric). 4.1 Boiler models

The mosi important features of the boiler model for the purposes of disturbance analysis are the load change rate and the storage capacity. The boiler model includes steam and water volumes and

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When charging the accumulator the 1P $team condenses into the saturated water in the tank increasing the temperature and the pressure in the tank The accumulator can be charged as long as the pressure in the tank is less than the IP network pressure When discharging the accumulator, tank pressure is dropped and saturated water is vaporized Pressure and temperature drops due to the required vaporization energy and the accumulator can be discharged to the LP network until the tank pressure equals with the LP pressurc

dynamic4 for fuel feeding (2 \eparate fuels, e g oil and bio mass), combustion, and heat transfer The dynamics of the heat transfer can be determined either by the mass of the heat transfer structures or by using experimental results measured from an existing boiler. Increasing and decreasing the load can be modeled with different combustion dynamics. Normally the drum level and the steam temperature controls are supposed to work ideally, and they are excluded from the model. Howevcr, thcrc IS an altcrnative model including drum dynamics and stcarn temperature control available, but it is not normally used

Auxiliary condenser and blow out valve are modeled as steam valvcs. Only the mass balance and actuator dynamics are modeled.

4.2 Turbine models

The main variables of the turhinc model arc the inlet and the outlet steam mass and energy flows. The inlet flow is modeled as a control valve operating under critical flow conditions. The flow dynamics is embcdded to thc actuator model. The energy balance of the steam expansion is modeled to determine the outlet steam enthalpy. The enthalpy is needed to calculate the amount of cooling water required to cool the steam to the set point temperature of the back prcssurc hcadcr. Stcam cooling is supposed to work ideally. In extraction turbines steam expansion is divided in stages, and each stage has been modeled as an individual turbine

4.4 Vulves

The main variable of the valve models is mass flow through the valve. Throttling has no effect on the enthalpy. The model library contains control valves for steam and water flows with the dynamics of pneumatic (1 order dynamics) or electric motor operated (constant velocity) actuators. The capacities of the valves can be determined by Cv or Kv values or by inlct and outlet prcssurcs and maximum flow. The flow models are referred from the Flow Control book by Neles Jamesbury. Pressure reduction valve is used to reduce the steam pressure and temperature to the next lower network level (HP -> IP, 1P -> LP). Pressure reduction valves are typically used to by pass the steam turbine if it is not available. The model of the pressure reducing valve includes both the mass and the energy balance equations. Energy balance is needed to calculate the cooling water amount nccded to cool the steam to thc desired outlet temperature. Temperature control is supposed to work ideally.

I

i

'.

4.5 Controllers The controller library contains a PID controller and a controller module with parallel connected PID controllers with the selection of the active controller according to the minimum or maximum selection of the controller outputs These parallel connected controllers are used in multi criteria control, where the actuator is connected with different controllers according to the operation state of the process In the steam networks e g the control of the charge and diqcharge valves of the steam accumulator requires this kind of controller structure

Fig. 3. Model library for turbine models and rcduction valvc models. 4.3 Load leveling component5

The controller outputs can also be forced to the predetermined positions and controllers can be forced to manual mode freezing the output to its present value. These options are needed e.g. in turbine controller where the operation of the controller must be able to be constrained if steam pressure in the HP network is disturbed too much (overriding control).

The main variables of the models of load leveling componcnts are mass flows to and from the component. In the models of the steam accumulator and the feed water tank also energy balance is included. The energy balance is needed to determine the pressure of the tank and further to calculate the charging or discharging flows to/from the tank.

3 24

4 6 Model huikding A simulation model is built by dragging model components from the library window to the application window. The components are connected together and parameterized according to thc initial state of the simulaied process. The model blocks are built so that the required parameters can be found easily from the technical documents of the plant. The initialization scnpts calculate initial values for the proccss states and the controllcr outputs and actuators so that the simulation can be starled horn d steady state without any transients In a typical project the customer fills up the coupons where the capacity and volume information of the examined process is determined. At the same time ihe control specialist of the consulting company drafts the proposed control scheme. After receiving the coupons the programmer sets up the simulator with the proposed control structure. Next simulation runs are executed and the performance of the controlled process during the load disturbances is analyzed. According to the simulation results it is evaluated if any changes to the process or control structure arc rcquircd.

operated by the frequency control of the electric network and turbine generator TG2346 (in practice 4 separate turbines) is controlling steam pressures in 12 bar (extraction outlet) and 4 bar headers (back pressure ouilet). Beside the turbines the headers are connected together with pressure reduction valves. A paper machine is connected to the 4 bar network. The operation of the process was studied during the disturbances originating from the steam load of the paper machine and from thc frequency control caused by the change of the eleclnc lodd At the rrioirienl there is no steam accumulator in process, but the rcsponse of thc proccss was simulated also with a 250 m3 accumulator connected between the 12 and the 4 bar headers Figures 5 and 6 show the simulated pressure stability in the 4 bar header during the load disturbance caused by the paper machine connecied to the 4 bar network. Fig. 5 shows the results without the steam accumulator and fig.6 with the accumulator. With the accumulator pressure fluctuations stay within 0.05 bar and no steam need to be blown out. Without accumulator fluctuation is -0.3 ... 0.1 bar and app. 1500 kg stcam is blown out

5 SIMULATlON CASE

A simulated power plant consists of 2 HP headers, 140 and 82 bar, 12 bar IP header, and 4 bar LP header. Steam is generated by two controlled power boilers controlling pressures in 140 (PB2) and 82 bar (PB1) headers and a constant load recovery boiler RB123 (actually 3 separate boilers) connected to 82 bar header. Turbine generators TGI and TG5 are

Fig. 4.

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important role when designing the process and the control structure to result a system with good disturbance attenuation.

4 t a r header [bar]

0

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20 30 Blmv oui [kgis]

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The simulation models included in the presented simulator are a compromise between the accuracy and thc complexity. Especially thc flow dynamics is simplified and embedded to the dynamics of the actuators. Compared with the accuracy achieved with more detailed model structures with a number of unknown model parameters which must be guessed, there is no big difference between the final accuracy achieved. However, the computational effort and the time required to tune up the simulator are minor compared with the more complex models.

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Load [kgis]

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The results gathered from over 20 simulation projects has shown the usability of this simulation bascd analysis concept.

c

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REFERENCES

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Time [min]

Astrom, K., Bell, R.: Simple Drum Boiler Models. Proceedings of the IFAC Power Systems Modeling and Control Applications. Brussels, Belgium, 1988, pp. 123 - 127. Caseau, P., Godin, P., and Malhouitre, G.: Numerical Simulation of a Steam Generator. Journees de I'AIM, Liege, 1970 (in French) Chien, K.L., Ergin, E l . , Ling, C., and Lee, A,: Dynamic Analysis of a Boiler. Trans. ASME, 1958 80, pp. 1809 - 1819 Flow Control Manual. Neles-Jamesbury, ISBN 95 195409-9-7. Helsinki 1992 Lausterer, G.K., Franke, J., Eitelberg, E.: Modular Modeling Applied to a Benson Boiler. Proceedings First IFAC Workshop on Modeling and Contiaol of Electric Power Plants. Pergamon, 1984 Leva, A., Maffezzoni, C. Modelling of Power Plants. Thermal Power Plant Sirnulation and Control. Damian Flynn (Ed.). IEEE Power and Energy Series 43. ISBN 0852964196,2003 Maffezzoni, C., Magnani, G., Marcocci, L.: Computer Aided Modeling of Large Power Plants. Proceedings First IFAC Workshop on Modeling and Control of Electric Power Plants. Pergamon, 1984ings Majanne Y .: Model Predictive Pressurc Control of Steam Networks. Control Eng. Practice, Vol. 13 (2005), FF. 1499 - 1505 McDonald, J., Kwatny, H.: A Mathematical model for Reheat Boiler-Turbine-Generator system. Proceedings of the IEEE PES Winter Power Meeting, January 25 30, 1970, New York, pp. 1 - 19. Weber, D.S., Konopacki, W.A., Massimo, F.M.: Modeling and Simulation of Hanfort K-Area Boiler-Turbine-Generator Sysytem. Technical report ERDA 76- 151, 1976

Fig. 5. 4 bar header pressure and blow out steam flow during the load disturbance without the steam accumulator. 4 t a r header [bar]

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20 30 Blah, oui [kgls]

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----1 5 -

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5 0

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6. CONCLUSIONS

~

Simulation is a good and pcrhaps thc only way to examine the cffects of load disturbanccs in a largc scale system having strong interactions between several process variables. Simulation has also an

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Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

PUBLlCATlONS

Operator Guidance Simulator: A New Power Plant Training Tool Concept

Ulrich Tomschi Siemen:, Power Generation , E912 Plant Design, Erlangen, Germuny Horst Jackisch Siemens Industrial Solutions and Services, IS L B C Simulation Center, Lrlungeri, Germany Rainer Newald Siemens Power Generation , E912 Plant Design, Erlungen, Germany

Ahstract: The improvements and developments o f power plant automation syslems make operation easier. This comcs along with an increased tendency for the operator of losing knowledge about his plant. The consequential need for effective training possibilities led to the development of a new well-priced simulation tool "Operator Guidance Simulator" which combines early availability with high plant similarity. It is based on Siemens' longtime experience in simulation of power plant processes, which ranges from steady state performance simulations, dynamic plant and automation simulations to Operator Training Simulators. Copyright 02006 IFAC. Keywords: Simulators. Operation. Training, Power Generation. Automation

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1. NEED FOR TRAlNJNG

During the last years the market structures of electricity supply systems have been changing in many countries. Liberali7ation. in particular the scparation of gcncration and transmission of electricity. leads to increased challenges for the power plants regarding operational flexibility, e g. l‘requcnt fast plant start-ups and shut downs (cycling capability), often several times a week. lhere is a considerable economic benefit of such flexibility for the plant owner.

. . traininD

training at Site

training

courses

This development leads to a permanently increasing and optimiLed automation level covering these demands. Such highly automated processes ideally require only very few interaction with the power plant operator. As an extreme case he can start up the plant from cold condition to I‘ull output by pressing only one button. Nevertheless the operator should still be able to perform such procedures manually or react to disturbances, failures or any unexpected situations correctly.

Figure 1 : Effect of operator training

A description of the requirements and the characteristics of an OTS for fossil fuel power plants is given by ANSI/ISA [ 11. An OTS can therein be categorized into the following main types:

1) The “generic” simulator: A generic OTS, based on a generic process simulation model, instructs the trainee in the general process characteristics of the type of power plant he is going to work on (e.g. a steam power plant or a Combined Cycle Power Plant). Such an OTS can be used long before the operator starts working on -’his“ plant, but unavoidably it is generic not only in the process. but also in the automation and control system. Even if the simulated process is close to the real plant, there might be considerable differences in the automation and control concept. The familiarization with details of equipment. plant control and its graphical representation can be done only when he starts to operate “his” plant. Therefore such an generic OTS is applicable in particular for operators to be instructed in the fundamentals of the power plant process and - in case the HMl system is the same as used in the real plant in the principle handling of the system.

However, the lcss an operator has to intcract with his plant during undisturbed operation. the higher the probability that the detailed knowledge about the power plant process and the automation mechanism? gcts lost with time or ncvcr has bcen obtained comprchcnsively . Since critical damages to plant or personnel are avoided by several safety systems, the consequence of incorrect operator actions or reactions is not necessarily damage to the facility. What might happcn is an incorrect rcaction in situations which arc not covered by thc automation system. E.g. if by some reason a control loop has to be operated manually and the operator does not realize the impact of his actions, in the worst case the plant might trip. The negative effect of untrained personnel therefore is to the greatest extent on thc economical side. Unplanned outages lead to high opportunity costs as energy is not provided to the grid as contracted or the missing energy has to be bought on the control energy market on high tariffs. Additionally. any trip of the plant can lead to high thermal stress on critical plant components reducing their economical lifetime. This increases also the costs for the plant service and maintenance program.

2) The full scooc. high realism simulator At the other end, an OTS can bc developed individually for the specific plant, simulating the complete plant process and auxiliary systems together with the dynamic rcsponscs of any kind of normal and abnormal operation. Resides the laborious process modeling. this also requires representation of thc complctc functionality of the automation s j stem. One solution would be the use of the original automation hardware. This solution of course would be expensive due to thc hardware and space demand. An alternative is the emulation of the automation system which allows the use 01‘ the original application software or the simulation of the automation logic either in the process simulation tool or elseu here. Ideallj, the trainee should not see anj difference helween the sirnulator and the real plant in terms of‘

2. OPERATOR TRAINING SIMIJLATORS Operator Training Simulators (OTS) have been used for many years to train the power plant perxonnel iu operation of the plant and to avoid the negative effects as described above. The positive result of such training - if performed regularly - often is illustrated as shown in figure I .

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operation and behaviour. Such an OTS therefore needs to include the specific automation and control philosophy and the specific graphical HMI (human machine interface), embedded into the control room ambience, and requires a thorough model tuning once the plant has been put into operation. This kind of OTS, in combination with training features on the instructor side as e.g. programmed malfunctions, special scenarios, trainee monitoring and diagnosis tools is very useful for an effective training of the operator, but the main disadvantage beside the high expenses - is the long lead time which according to ANSIiISA indicatively is hvo to three years. Considering the present short lead time of the whole power plant, which in case of a Combined Cycle Power Plant during the last years could be reduced to less than 24 months, it is more than questionable that a customer would accept such an OTS lead time. In fact, in current power plant specifications. the availability of a training simulator is nften required even before the scheduled start of plant commissioning. in order to start operation with well trained personell.

3. OGS CONCEPT The targets of a contemporary power plant training tool can be summarized as follows:

. =

availability before handover of the plant to the customer same “look and feel” as in the real plant correct operation and automation philosophy affordable investment

In particular, the possibility to have a plant specific training tool allowing an effective initial operator training in due time appears to become more and more important, whereas the need for replication of the control room seems to be secondary since the control rooms themselves tend to be less representative and reduced to a few PC terminals. These requirements led to the development of a new concept of training tool, called Operator Guidance Simulator (OGS). The OGS is based on the project specific Automation System (AS) Plant Shop Test which is performed by Siemens Power Generation for virtually all new power plants, being an essential quality assurance for the process arid autornation engineering. This plant shop test integrates the complete original plant specific A S hardware and software (“hardware in the loop”), which will be used later in the real plant. with a process simulator reflecting the project specific power plant, see Fig. 2.

3) The reduced-scope. high realism simulator In this type of simulator thc simulated process arcas are limited to the major systems. Auxiliary systems are included only if relevant for the main operation. There is no complete replica of the control room required. However. the training effects should be similar to those of the full scope simulator. Price and lead time of such simulator of course depend a lot on the completeness. depth and fidelity of the simulation. The lead time of such a simulator is indicated by ANSILSA with one to two years. llcnce even with such a reduced scope simulator the above mentioned early availability can not be obtained.

Process Simulator

TXP AS

TXP HMl

Figure 2: Plant shop test with “hardware in the loop” As such it allows testing of the most important functionalities of the power plant, mainly in the f-leat Recovery Stcam Generator (HRSG) and wateristeam cycle areas: as slart-up, shul-down and normal operation. In case of a Combined Cycle Power Plant. (CCPP) in particular the unit control, i s . the integrating controls of the main components gas turhine, steam turbine and HRSG, is heing tested thoroughly. This test is done before the automation system will be delivered to site. The process simulation used for this plant shop test is based on the prqject specific P&IDs (Piping & lnstrumentation Diagrams), heat flow diagrams and equipment data sheets and hence shows a high consistency with the projected power plant. The OGS uses the automation software which was tested together with the process model in the plant shop test. In contrast to a conventional OTS, this OGS concept, making use of a direct high quality engineering output, allows early availability before PAC (Preliminary Acceptance Certificate) of a highly

In the ANSIiISA Standard there are only few indications given about the required representation of the automation and control system. Modern I&C systems allow effective engineering on a graphical interface with modular “drag and drop“ functionalities rather than building the logics from zero. The resulting functional diagrams do not always show all details of the correspoding internal logic. Therefore, a correct representation of the automation logics i n the simulation tool ofen is difficult or even impossible, if based only on the logic diagrams. In particular, simulated processes with a high automation lcvel bear thc risk of wrong responses even if the process itself is simulated correctly.

I n the view of the operator, the yardstick o f the quality o r the sirnulalor are riol onlj the correct process values but maybe rather the correct actions and messages he sees on the HMI in comparison to the real plant.

329

The focus of the simulation model in the OGS is the correct technological representation of the dynamic behaviour of the plant rather than compliance with all thermodynamic principles. which is necessary in other applications as e.g. process design or calculation of performance data. but would enhance unnecessarily the complexity of the model and might reduce the dynamic performance of the simulation. The simulation scope of the OGS comprises in the basic version the IIRSG and the wateristeam cycle with steam turbine (see Fig. 5 ) . The gas turbine is represented in a simplified way, but can also be simulated in detail if required.

consistent process model and automation and control software. PAC

Commissioning Plant Shop

,npvtto06s

Tested simulation model tested application s o h a r e

Figure 3 : Integration o f OGS in project handling

t,

4 '

The main components of the OGS system are (see also Figure 4): ,

..

.+.:

process simulation emulation/simulation o f the AS stimulated human machine interface (HMI)

d Automation

Figure 5: Example for a CCPP heat flow diagram This modular system of the OGS allows extension to other process areas and auxiliary systems as needed by the customer.

Simulation

The process simulation is implemented with the SIMIT test and simulation platform by Siemens I&S. SIMIT facilitates fine grained solutions for testing of automation software: from simple signal tests or tests on the actuator-sensor level to the entire automation system test with process models. It is widely used for Simatic automation testing in various industries. SIMIT either provides the electronic interface to the real automation hardware (CPUs). to emulated CPUs (SoTtPLCs in case or S 7 ) or it allows implementation of automation and control functions dircctly to thc simulation.

Emulation

Fig. 6 shows an example of the process oriented view of the simulatoriinstructor intcrface in the OGS:

HMI

Stimulated HMI

Figure 4: From plant to OGS

Process Simulation:

330

between the HMI in the training and the HMI in the plant. For the process parts which are simulated dynamically, all actions by the operator will have the correct effect on the process. Process signals which are not dynamically simulated appear as a static value. Other features which are part of the licensed HMI as e.g. trends are also available.

4. OGS CHARACTERISTICS IN COMPARISON ’1‘0 AN 0 1 S The OGS allows quite some of the functionalities which are known from an OTS:

Fig. 6: SIMIT simulation interface

.

Emulationisimulation of automation: One big advantage of the OGS is the high congruence with the automation used in thc real plant. Instead of the automation processors used in the real plant and in the Plant Shop Test, the OGS makes use of a software emulation of the AS which allows running the original plant specific automation software as if it was loadcd to the real system. This emulation communicates via a bus protocol with the process simulator using the signals defined in the P&IDs as liOs between process and AS Only in case when the emulation of some AS components is technically not possible, the relevant automation logics will be implemented into the simulator. In case ol‘ the Siemens power plant Automation System Teleperm XP, the emulation h as been used in many training simulation projccts, c.g. the OTS for Santa Rita Power Plant on the Philippines. Teleperm XP is based on S5 automation language and components and is used in virtually all large fossil power plants built by Siemens during the last years This automation system now is being followed by the new system SPPA-T3000, which is based on S7 components. The emulation software for S7 application code has been developed and proved successfully in several training simulator projects. The specifics for SPPA-T3000 are currently in a pilot phase. Here it is a big advantage to have the detail knowledge about the automation system within one company in ordcr to cmulatc thc complete functionality of the system.

.

The instructor h a access to all signals which are available in the simulator and hence has the possibility to manipulate them. Although this is not like a programmed malfunction or a scenario as known in an OTS, this allows training of the operator in detection. analysis and reaction to failures. Furthermore, in every moment during the training the instructor can make a “snapshot” of the current situation and reload it for Further training or analysis at a later time.

However, reflected at the AN SI/ISA standard, there are a couple of’differences, as e.g:

. .

Normal operation is limited to start up, shut down and load changes. Component or plant trips of course will happen according to the protective automation system. However. the plant dynamic response is not necessarily exactly the same as in reality in every case and it might not be available for a Fat restart. The initial conditions are limited to cold start and full load. No backtrack. slow time or fast time is foreseen in the OGS. Due to the early availability, no update to the real plant is part of the OGS scope. However, this could be supplied as an additional option i.e. after end of hot commissioning. Also due to the early availability. the issue of accuracy doesn’t apply as no data for comparison is available at that point in time.

The OGS therefore is close to a reduced-scope simulator within the ANSlilSA structure, with a limited scope of simulation and instructor features, but with a high realism automation representation. It has the same structure and is based on the same principles as an OTS. Therefore according to the needs of the customer, extensions to a full scale O’I’S are possible at any time and to any extend by implementing functionalities like malfunctioiis, scenarios or by applying a model tuning in order to

Stimulated HMI The I-IMI system and the graphical displays are identical to those used in the real plant. Thc information to be exchanged with the process i s obtained from and sent to the AS emulation (“stimulation”). Thcrcforc the training cffcct is maximized since the trainee sees no difference

33 1

Fossil Fuel Power Plant Simulators Requirements. ISA, North Carolina. May 1994

improve the dynamic representation and to implement later changes. as illustrated in figure 5.

t

Customer benefit

Malfunctions, scenarios, model tuning

PST Simulator

OTS

Complexity and cost

Fig. 7: OGS between Plant Shop Test (PSr) and 01s This staggered approach complies with the targets of a training tnol of being available already for initial training of the operator. being as realistic as reasonably possible and being extendable to a full scale OTS if required for a later extended and continuous training.

5 . SIJMMARY

The Operator Guidance Simulator was developed in order to meet the customer's demand for an early available and pro-ject specific training tool for initial and continuous training of the operational staff of a new power plant. The close linkage of the OGS to the project specific engineering of the process automation allows performing the training already at a time before hand-over of the plant to the client. Thus thc plant can be operated right from the beginning with well-trained personnel. Due to the same reason there is maximum congruence between OGS and the real plant regarding automation and HMI. This allows highest training efficiency. Since the development of the OGS i s highly integrated into the project execution. it can be offered at an attractive price together with the power plant. For further training quality the OGS can be upgraded to a plant specific 0 TS.

Rel'ercrices

ANSI/ISA-S77.20- 1993

332

-

Functional

Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

PUBLlCATlONS

APPLICATION O F AFFINE TRANSFORMATIONS T O REAL-TIME POWER SYSTEM EMS FUNCTIONS Emmanuel D. Crainic a ', Alexander 1. Petroianub de rheuux Inytitut de recherche d'Hydro-Que'hec, IRCQ, 1800 Blvd Lionel Boubt, Chrennes, QC, Cunudu,.J3X I SI Department ofElectrica1 Engineering, bniversity oJCape rown, University Private Bag, Rondebosch 7701, Republic of Soulh Africa

a Logicieh

Abstract: The paper introduces the concepts of affine transformations in the methodology and in the algorithms for real-time power system EMS functions. It demonstrates the advantages of this new conceptual approach. The advantages are: i) a new formulation of the state estimation problem and related applications. ii) a faster and more reliable solution obtained through direct. non-combinatorial techniques. Copyright 82006 IFAC Keywords: affine transformations, power systems, online applications, state estimation, bad data detection and identification, measurement and parameter validation.

I . AFFINE TRANSFORMATIONS: AN

Basically, the state estimation and the related E M S functions arc nonlinear problems; thcrefore. the algorithms used to solve them must be robust, fast, and ensure a feasible solution. The need €or improving the algorithms used in solving real time power system problems is very strong. In this paper, the authors introduce an affine geometrical approach for the solution of the state estimation and other functions related to it, like bad data detection and identification, and measurement and parameter validation.

INTRODUCTlON

Power systems are operating nowadays under much more difficult conditions than in the past. These difficulties are due to the following new factors: competitive operating conditions, higher fuel costs, environmental, institutional, and societal constraints. Even in the previous developed energy management systems (EMS), the state estimators were considered as suffering from the following major drawbacks (Handschin and Petroianu, 1991): i) slow response time i.e.: snapshot or static instead of 'tracking' or dynamic estimation, ii) poor quality of solution, especially with regards to reactive power flows, voltages, and tap positions. iii) lack o€ a strong local, busbar oriented validation.

Most of the physical quantities involved in the state cstimation modcl arc complcx numbcrs bclonging to the 1-dimensional complex space C'. This complex space is mapped into a 2-dimensional vector space 2, whose elements are involved in linear operations, i.e.: multiplication of a vector by a scalar and addition of two vectors. Of interest are not only the operations performed on these vectors, but also their mutual position and the geometric properties of the figures made of these vectors on the plane (Petroianu, 1969).

As of a result of such weaknesses, in some utilities the state estimator did not operate properly. results for reactive power being disregarded. In other utilities the state estimator was not really implemented. A large utility (Tokyo Electric Power-TEPCO) does not even have a state estimator; instead of it a double system control and data acquisition system (SCADA) hardware and software solution is utilized for obtaining the reliable real-time data base.

For this reason the aftlne space E. a space of points, is introduced and which is associated to a vector space ~. E of the same dimension. in the sense that: i) for each pair of points (u, h) E E, the difference (u-h) between them is a vector AB in the vector space E , ii) for each vector in the vector space and rhr each point in the affine space E, adding the vector to this point results in an anothcr point in the affine space E,

* Corresponding author: Emmanuel D. Crainic, E-mail address: c ra in ic.em man uel(@ req .ca

333

iii) every triplet of points (a, b, c) relationship fa-b) + (b-c) = fa-h).

EE

satisfies the

In the spirit of his 1872-Erlangen Programnz, Klein ( I 974) regarded any geometry as the study of those properties of figures on a given space which are invariant under all the transformations of a specified transformation. is any group. An @ne transformation that preserves parallelism of lines and the ratio of distances between colinear points. In matrix notation and using the homogeneous coordinates, first introduced by Mobius (1 827): the following main affine transformations in a 2dimensional space, i.e.: rotation by an angle cp counter clockwise about the origin (position of axes unchanged): I coscp -sin9 0 I R,= I sincp coscp 0 I (1) I 0 0 11

I:ig. 1 Electrical line II model representation 111the equations (5) and ( 6 ) the voltages a e complex numbers representcd by their modules V,, vk and by their angles 6,. fik with the difference: Omk = 6, - 61, (7) considered to be positive (all over this paper the hypothesis is made that m is the sending and k the receiving nodes of the active porn er). Analytically. the complex powers &,k and Skmare as follows:

reflection in the x axis:

M,=IO

-1

01 01

10

0

II

0

I1

0

scaling:

IL S1=l0

)y

01 01

10

0

II

I1 T,=IO 10

0

PXI

1

PSI

0

II

(3)

In (8) and (9) Pmk.Pk, are the active and Qmk, Qkm the reactive powers. They represent the real and the imaginary parts of the complex numbers Smk and &,:

trunslution: (4)

form the general affine group GA (2. R) which is a semi direct product of the general linear group GL ( 2 , R) and the translations in E by vectors o f E .Given a group G acting on elements o r an affine space E, a real value runciion I depending or1 these elernenls is called an invariant of G if, whenever a transformation g E G changes I into I*= f (g) I, where f is a function of g alone. i.e. does not depend on the element which is transformed. If f = 1, I is called an absolute invariant. In the case of the 2-dimensional space the general affine group GA (2. R) preserves the rutios (absolute invariants) between arias of subsets of E, or of E , while the arias themselves are relative invariants ofthe group (Olver, 1995).

From the above expressions, the active and reactive power5 in (5), (6) and in Figure 1 are: mk = Pm, (16) km = 'km (1 7) Q = Ql,,k- 0.5V',,,B'"'n,k (18) Q km = Qkm- 0.5V2~BCapmk (19) The module of voltage difference dYmk and, respcctively, the aria AVmkof the voltagcs triangle (Figure 2) are given by: dV,k

2. POWER SYSTEM LOAD FLOW MODEL

= (V2,

+ V*k - 2V,Vk cosO,k)

AVmk

2. I Power system loadflow equations

= 0.5V,Vk

sinemk

For an clectrical transmission line, the most common component ol' a power system (Figure l), the apparent power flows, expressed as complex numbers, are

Fig. 2 Electrical line voltage diagram

334

(20) (21)

The radius Pmk of the circle in Figure 3 is defined as: Pmk = (g*mk+ b * m d

()

'

cos2ymk= (g2,, - b 2 d 1 dnli sin2Ymk (2gmkbmk) / P2mL

(22)

By taking into account the equations (12)-(15) and (20). the active power losses for the line (rn, h) are. by definition: GPrn= ~ Plllk + Pkm= gmk dV2mr (23)

the angle (omk defined as: (Pmk = atan (vmk

+ Qkm= bmk

dV2mk

/V,ndVmk (32) cos (Ymk - (Pmk) = (V2m-vmvhcos~n,k) sin (ymk - q m k ) = V,Vk sinBmk/V,dV,k (33)

(24)

the angle (&,I

2.2 Electrical line base angles

defined as: (Pkm = atan (Qkm

In the next section the following electrical line angles and relationships between them will be extensively used: the angle &k between the voltages ym,&Three basic formulae (25), (26) and (27) allow evaluating it:

/ Pkm)

(34)

The following trigonometric functions may be derived for the difference of angles (qkm- ymk),i.e : (vkm - Ymk)

= (V'h

sin (qkm- ymk) =

tan%!,= (b,LP,L-g,hO~)/((P,,Lv~n)2;(g,hpmhfb~Vma)) ( 2 5 ) tanOnik= -(bnikPk,~-g,hVlm)i((Pnikv~) -(siii~Priii+bmhVhi,i)) (26)

-vmvh~Ose,,,,)/VhdVmk (35) V,Vk sinBmk/VhdVmk (36)

Iwo other points on the circle of radius Pn,k are of interest: the point g", at an angular distance equal to 0,k counter clockwise from the point gd. and the point gk,at an angular distance equal to 0,k clockwise from the point gd

tanemk = ( P m k Q k m - PkmQmk) 1( P m k P k m + QmkQkm) (27) the angle l/n& expressed as: Yink = atan (bmk / gmk)

(31)

The following trigonometric functions may be derived for the difference of angles (ymk - (Pmk), i.e.:

and the reactive power requirements are: K ? r n ~= Qmk

Pmk)

(29)

(30)

(28)

From (23) and (24) it may be seen that the vector

ci

3. AFFINE TRANSFORMATIONS ACTION

(oPmh,OQ,,,~)makes an angle Ymk with the x-axis: it is colinear with axis A A (Figure 4). The axis A' A

intersects the circle of radius P m k in two points (Figure 3). g"whose coordinates are (&k. bmk)and gd whose coordinates are (-gml,-hmk). These two points, together with the origin 0, are the fixedpoints and the line II'D (Figure 6). tangent in the point gd to the circle of radius P,,,k and which makes an angle with the x-axis equal to (yrnk-x), is the fixed line of some of the affine transformations used in the next section. The following trigonometric functions may be derived for the angle 2ymk,i t . :

where V, in (40) and (41) is given by the formula: vin= ((Pkin-v'kgmk)

f

(Qkm-V'kbnd ')" '/ PinkVk

(42)

The systems of linear equations (37), (38) and (40), (4 I ) represent afjne transformations, from one to another, of the electrical states (Plnh.Qmh,V,) and (PkmrV k m , Vk) at the extremities m and k of the line. With the matrix A defined as:

Fig. 3 Electrical line base angles

335

the equations (37), (38) and. respectively. the equations (40). (41) may be written as follows: Ik’km

IPm,

I

IQkml

A

I

Ik’km

(A) A-’ l Q k m l

IQmkl =

I l l

I l l

I (44) ‘The coefficients matrix Bgk of the right side of equations (48), (49) represents the af$ne transformation of point g”to point k (Figure 5), bcing the product of a rotation of angle (qkm-ymk) counter clockwise (see equations (35), (36)). followed by a scaling equal to (VkAVmk), i.e.:

I l l

The aria, taken counter clockwise. of the triangle formed by the points Omk (Figure 4) is an affine relative invariant, i.e.: %k=

0.5(pmk

Qkm

- Pkm

(45 1

Qmk)

Fig. 5 Fixed point to electrical transformation

Fig. 4 Electrical state to electrical state affine transformation

32

Fured

point transjornzation

to

electrical

slate

state

affine

I ( ~ ~ , - v ~ , V ~ c o s 0 , ~ ,-Vn,VksinBmk ) 01 Bgk = I VmVksinemk (V2,-VmVkcosAmk) 01 ( 5 2 ) 0 11 1 0

ajfine

?he systems of equations (12). (13) and (14). (15) may be rearranged as follows:

7 he matrix Bgk has the determinant = (vkAV,nk)* and it is invertible. Consequentlj, the equations (48), (49) may be written as follows:

Pmk= (V’, -VmVkcosOm,)gmk + VmVksinOm,bmk(46)

Om,= -VmV,sinem,gmh+ (V2m-VmVhcosBm,)b,,,h (47)

lPkm

I

lQkml

Pkn,= (V2k-VmVkCOS0mk)gmk - VmV,sinOn,,bm, (48) Qkm = VmVkSln0mkgmk + (V2k-VmVkCoS0,,,k)brnk(49)

I 1 I l l

lPkrn

lEnik

I (53)

= Bgk lbmk = (Bgk) B-’gk lQkml

I l l

I l l

The aria, taken counter clockwise. of the triangle Omg” (Figure 5 ) is given by the formula:

The coefficients matrix B,, o f the right side of’ equations (46), (47) represents the afine transformation of point g”to point m (Figure 5 ) , being the product o f a rotation of angle (Yd&mk) clockwise (see equations (32), ( 3 3 ) ) followed by a scaling equal to (V,nAVmk).i.e.:

d,g=

0.5(Pmkbmk-Qmkgmk)= O.jVmVkSitlt),kP’”k(54)

and the aria, taken clockwise, of the triangle Okg” (Figure 5 ) is given by the formula.

nkg= - o . s ( P ~ ~ =~ O~ . ~S -V Q~ V~ ~~ S~~ ~~( 5~~5 ),)~ P * ~ ~ 3 3 Electrical trunsforma tion Ihe matrix Bgmhas the determinant = (VmAVmk)’and it is invertible. Consequently, the equations (46), (47) may be cvrillen as hl~ocvs

state

to

parallel

line

affine

The systems of equations (12), (13) and (14), (15) may be rearranged a5 follows:

336

-VZrngm,) /VmVk (56) -CoSO,&nk +SlnOmrbmk = = (Qmk -VZmbm,)/VmV,(57) -sinOmkgmk -cosOmkbmk /VmVk (58) -cosBmkgmk-sinOmkbd = (Pkm-V2kgmk) Sinemhgmh-cosomhbrnk = (Qkm -VZkb,,,,)~VmVh(59) The right side of equations (56). (57) represents the .fine transformation of point m to point g" (Figure 6):

I glnmkl

I 'mk 1

I bmmkl= r m a I Qmkl I l l I l l

(60)

with the matrix Tmgdefined as:

Fig. 6 Electrical state to parallel line affine transformation 4.AN EXAMPIE In a large power utility, a transmission line 734.6 km long operates at 765 kV. The constructive parameters are as follous: 1) conductor type - Zebra, 2 ) number of conductors per phase - six, 3 ) distance between the conductors (bundle spacing) - 0.4 m.

Table I Line data

3.4 Relative and absolute invariants of the afine transformations The affine transformations approach to the power system load flow equations is an open subject; not all possible affinc transformations were treated in this paper, and for those selected, only a part of the relative and absolute invariants were presented. They play a major role especially in measurement and data validation. For instance, the ratio of the arias of the triangles Omg, Okg (Figure 5 ) , which is an absolute invariant: (Pmkbmk-Qmkgmk) 1(-Pmkbmk+Qmkgmk) 1 (66)

Table 2 AMine tramformation invariants VI, V,,

and links only the active and reactive power measurements. The following ratio, which is also an absolute invariant: (Amg Akg) /' (Amm Akk) = 1 (67) allows validating the voltage at one side of the line when the electrical state o f the other side is known.

337

=

1.00 [pu]

line. iii) the fact that in the affine space E, these triplets are afine transformations of each other (see matrix A, section 3.1)

Table 3 Aftine transformation in\ ariants Vk= 0,98 .V,,, = 1,02 [pu]

Lm

Qknl

Qknl

-3,33

1,78

Akk

Ak

U 2

15)

5.3 Parameter estimation

Pkni

If the triplets of measurements (P”’”,k, Q , k , Vmem) and ( P t n c k m . Q“2km. Vlllck)are consistent for a fair amount of time, one may proceed to better, or dynamic. parameter estimation. This may be done by using the matrices of type B-Imgor / and B-lkgwhich are matrices of electrical state to fixed point a f f i x transformations (section 3.2). This type of parameter estimation may be seen as a localized (per network elemcnt) dynamic or tracking statc estimation: potentially, it may be adapted or extended as parallel state estimation.

U 2

16

390,33 406,26

6. CONCLUSlON

In rablc I , the clcctrical parameters are calculated for Pbaie = 100 and Vbarc = 765 kV In Table 2 are presented the results that correspond to V,,, = Vk = 1 0 pu and in rable 3 those that that correspond to V,, = I 02 and Vk = 0.98 pu. All the formulae developed in the paper ma) be checked based on the information presented in these Tables

The affine transformations constitute powerful tools in dealing with and solving the linearized models of nonlinear problems encountered in power systems. ‘They are especially helpful in the context of on-line power system applications, where speed and robustness are critical constraints. This novel approach was shown to be adequate to various modern requirements of an EMS: state estimation, bad data detection and identification. measurement validation and parameter estimation and correction. Also new in this approach is the treatment of SCADA measurements. not as individual measurements, but as coherent triplets of measurements. dething a physical reality, i.e.: the electrical state of the extremities of a line,

5. ON-LINE POWER SYSTEM APPLICATIONS 5.1 State estimation for distribution networks In the affine approach solution to the state estimation problem the notion of topological spanning tree, which is a tree having (N-1) edges (lines. transformers, etc.) linking all the N nodes of the network plays a central role. In the case of distribution networks, which are predominantly radial, the topological spanning tree is self-evident. What is required to be known is one of the pairs (P,,, Qmk)or (Pkm.Qkm)of active and reactive power at the extremities m or k of each o i (N-I) edges of the spanning tree and one voltage at the arbitrary chosen reference bus. With this information, and starting from the refercncc bus, the formulae of type (39) or (42) are used to obtain the voltage module(s) at neighbouring node(s), and the formulae of type (43) to obtain its affine pair (Pkm,Qkm),respectively, (Pmk. Qmk). It is, basically, the same strategy as that developed in the first state estimator based on line flow measurement (Dopazo. et al. 1970), but instead of non linear systems of equations of type (12)-( H), systems of linear equations of type (37)-(38) or (40)(41) are used.

7. REFERENCES Dopazo, .1.1:., O.A. Klitin, G.W. Stagg and L.S. Van Slyck. (1970). State Calculation of Power Systems from Line Flow Measurements. IEEE Trans. Power App. Syst., Vol. PAS-89, No.7, 1698-1716. Handschin, E. and A.I. Petroianu. (1991). Energy Management Systems: Operation and Control o j Electric Energy Transmission Systenzs. Springer Verlag, Berlin Klein. F. (2004). Elementaipy Mathematics from an Advanced Standpoint: Geometry. Dover Publications. Mineola, New York. Mobius, A.F. (1827). Der harycentrische Calcul: ein news FlilJrmittel zur analytisrhen Hehandlung der Geonzetrie, Leipzig. Olver, P.J. (1995). Equivalence, Invariants and Symmetry. Cambridge University Press, Cambridge. Petroianu, P.I. (1969). A Geometrical Approach to the Steady State Problem of Electrical Networks. Rev. Roum. Sci. Techn.-Electrotechn. Et Energ., Vol. 14, NO. 4.623-630.

j . 2 Multiple bad data detection and identification It is known that grossly erroneous measurements and topological errors (e.g., breaker’s false status) cause state estimation‘s failure. The authors propose a direct method based on: i) the use of triplets of measurements (Pmemk, Q”lernk, V C m and ) (P”lekrn, Qmnekm, Vmck).defining the electrical state at the extremities of the line, ii) the fact that any one of these two triplets describes entirely the internal electrical state of the

338

Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

ELSEVIER

PU CATI BL o N SI AUTONOMOUS POWER NETWORKS BASED POWER SYSTEM A. Jokic, P.P.J. van den Bosch Eindhoven [Jniversity of Technolom, Department of Electrical Engineering, Postbus 513,5600 MB Eindhoven, The Netherlands Tel t 3 1 40 247 3307, e-mail A Jokic@tue nl

Abstract: I'he operation of future power systems will be more challenging and demanding than present systems owning to increased uncertainties (renewables, dispersed generation), less inertia in the system, replacement of centralized coordinating activities by decentralized parties and the reliance on dynamic markets for both power balancing and system reliability/security. The paper presents the concept of Autonomous Networks to cope with this increased complexity while enhancing market-based operation. Power balance problem and system reliability through provision of ancillary services are formulated as an optimisation problem for the overall autonomous networks based power system. Copyright Cj2006 IFAC Keywords: power systems, power distribution, renewable energy systems, reliability, economics

I . INTRODUCTlON Power systems are going through significant changes in many aspects. Central to the many of the changes are two major paradigm shifts occurring in the structure and operation of power systems. Major structural changes are caused by large-scale integration of privately owned Distributed Generators (DG) in all levels of traditional, vertically structured power system. In operational sense, there is a shift towards the use of competitive markets as rriechariisrris for both balaricirig power production and consumption and for ensuring system's rcliability. Indeed, these two major changes are coupled and one is supporting the other. Introduction of de-regulated, open-access markets should encourage investment in DG by creating new business opportunities. On the other hand, non-dependence on fossil fuels and environmental issues supporting renewable based DG together with high efficiency of some DG units, like for instance combined heat and power units, are introducing novel players having an impact on power system economics and creating a rich playground for existence of competitive markets. All this as well results in enormous changes on the more technical side of power systems. Network, as a dynamical system, is changing its characteristics on all time scales. Introduction of large amount of DG is a change towards the system with striking characteristics as large time and space heterogeneity, low inertia, extremely large uncertainties, and extreme increase in number of generators in comparison to traditional power systems.

Large variety of DG technologies (micro-turbines, fuel cells, wind turbines, photovoltaic (PV) arrays, to name a few) makes the system more heterogeneom with respect to the traditional power system that was completely relying on large-scale synchronous generators. Across the set of these different DG technologies, there is a huge variety of possible time responses to the changes in reference values for power outputs. Further more, many of the technologies, like fuel cells or PV, are inertia-less, and all the renewables, like wind turbines and PV, are practically uncontrollable in their power outputs and are introducing large production fluctuations and large uncertainties in any future system state predictions. It is the major challenge of managing the system of such an underlying technical complexity, even more since the solution has to enhance the major driving force causing the change - the existence of unbundled, competitive markets as central mechanisms for system operation and reliability. It is also evident that the efficient solution necessarily needs to be based on large amount of players capable of competition in all the markets. One of novel paradigms for defining the operation of distributed generation that has gained significant attention in power system society is the concept of microgrids (Lasseter, 2002; Venkataramanan, and Illindala, 2002). There is no simple or rather complete definition for a microgrid that in concise way presents its major characteristics and objectives. The papers of Lasseter (2002) and Venkataramanan and Illindala (2002), which are among the first references on the topic, present a microgrid as a

339

cluster of loads and microsources (DG units) operating as a single controllable system that provides both power and heat to its local area. To the utility the microgrid can be thought of as a controlled cell of a power system, while to the customer inside the microgrid, it can be designed to meet customers special needs; such as, enhance local reliability, reduce feeder losses, support local voltages, provide increased efficiency through use of waste heat, or provide uninterruptible power supply functions. As in those two papers, in most of the references dealing with microgrids (Lasseter, and Piagi, 2004; Kueck, e/ a/, 2003), the major emphasis is on microgrid’s internal objectives, problems and their solutions. One of those objectives that has been widely studied (Pecas Lopes, e/ al, 2003) is the possibility of a microgrid to efficiently operate in an island mode, i.e. disconnected from the rest of the power system. Much less attention has been paid to the relationship between the microgrid and the local utility, and the main feature of this relationship is often summarized in the statement that a microgrid is a well behaved, “good citizen” or “model citized” (Lasseter, et al, 2002) in the overall power system. By “good” behaviour, it is in most cases thought of a low impact, or more importantly on absence of a negative impact, that a microgrid has on the electricity network, despite a potentially significant level of generation by intermittent renewable sources (AbuSharkh, e t a / , 2004). This low impact is attained by a good match between generation and load inside microgrids, even for a faster time scales (seconds). What is however less clear is the reward that would encourage the microgrid to behave in this way, especially in the case when the outside system is rather strong and the microgrid’s total installed capacity is relatively small so that even the worst case, sudden internal imbalances would have rather low impact on the outside system. In the case of a significant number of microgrids in the system, their mutual and overall system impacts will indeed become significant, and “good citizen” behaviour would not only be desirable but is also a necessity. To the best of our knowledge, some more detailed elaboration of the overall system’s operation in such a microgrids-based system has not yet been presented. Still, several references are addressing this topic. I n (Dimeas, and Hatziargyriou, 2005) the operation of a multiagent system for control of microgrids in a market environment is presented. Only the real power market has been considered, and the emphasis of the paper is on the details of an auction algorithm and the operation of negotiations agents. In (Abu-Sharkh, et al, 2004) the possibility of the creation of local ancillary services markets has been addressed as an important issue. Similarly (Kueck, et al, 2003) refers to provision of ancillary services from microgrids as a future research need. The purpose of this paper is to take one step further from the microgrid concept. It presents the concept of autonomous power networks as a realistic approach to dealing with increased complexity and uncertainty of the future power systems while enabling markets-based operation for both dispatch (economic) and ancillary services (reliability).

2. AUTONOMOUS POWER NETWORKS Although it shares many of the objectives and characteristics with the microgrid, an Autonomous power Network (AN) has an additional property: it is a major building block of a power system in all of its layers, i.e. physical, economic and reliability. The idea of the overall system being a network of ANs is crucial. With the strong emphasis on this, which is the central idea to the AN concept, in this section we continue with presenting the concept of AN. I n a more formal and detailed way, this is further continued in the next section. An AN is the aggregation of networked producers and consumers in a relatively small area with respect to overall system, whose operation is coordinatedicontrolled with one central unit acting as an interface in between internal producerslconsumers and the rest of the power system. The goal of such a unit is efficient deployment of internal recourses and active involvement in overall system competitive markets where it reflects the preferences of its owners, i.e. of its internal producersiconsumers. In the physical as well as in the economical layer (power and ancillary service markets) each AN is presented as one producerlconsumer. It is this requirement for the active involvement in all of the layers of the system that defines AN to be a major building block. For power balance and reliability issues (ancillary services) this implies that AN is obliged to provide, in an appropriate form, the information of its own actions and to take the responsibility for those actions. Note that the “good citizen” behaviour, if defined as within the microgrid concept, implies high uniformity of microgids in some of their characteristics, e.g. each microgrid has well controlled power exchange with the rest of the network, even for the time scale of seconds. In the AN concept, there are no such a priori characterizations (constraints) of an AN, and different ANs can have significantly different characteristics. However, it is crucial that all those, possibly different and time varying characteristics are taken into account on the global level, so that the overall system will operate efficiently and reliably. Good citizen behaviour for an AN is therefore defined by the requirement for its active and responsible involvement in the energy and ancillary service markets, as well as for following a set of predefined rules in provision of the commodities sold in those markets. Energy and ancillary services markets provide global coordination and time synchronization of ANs actions. They have a central role in keeping the power balance in between ANs, and in ensuring the overall system’s reliability by accumulating sufficient levels of ancillary services, e.g. regulation capacity, spinning, non-spinning or operational reserves, etc. As presented in the next section, ANs can be both producers and consumers of ancillary services. This is a novel and unique feature, and is in the line with the driving forces for the power system restructuring since it introduces a large amount of well defined players in ancillary service markets. In

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AN based power systems, spare capacities for ancillary services are treaded in a equivalent way as energy in energy markets. As a result, the operational structure of ancillary service markets becomes analogous to energy market. With the increase of uncertainties in the future power systems, e.g. due to the increased penetration of renewable sources, it is expected that the value of transactions in those markets will increase as well. To summarize, an AN is seen as an intrinsically local co-operative venture. Each of its internal members accepts the AN as its operational authority and in return shares the benefits of this co-operation. The AN is therefore the highest authority for those members. Each unit (producericonsumer) can also act as an isolated player, but it is then required to take responsibilities in all layers of the system, i.e. it iq preqented in the overall syqtem as an AN. This especially holds for large-scale synchronous generator based producers or large-scale costumers, e.g. large factories, that are by themselves capable of efficient involvement in markets. For a price inelastic consumers inside some AN (e.g. residential loads), AN becomes a market agent acting on their behalf. Furthermore, for those consumers, an AN offers a possibility of their efficient involvement in ancillary service markets if they agree on a certain level of interruptions in power supply. In contrast to the microgrids, that are usually associated with a "small community", like for instance typical housing estate, isolated rural communities, academic or public communities such as universities and schools, commercial areas, trading estates and similar, what implicitly defines a microgrid as a very small cell of a power system, we do not restrict to any particular sizes of networks candidates for AN. Possible different sizes of coexisting ANs are a result of their efficiency in a competitive market environment. For existence of efficient overall markets, it is important that large amounts of ANs are mutually interconnected. A well-meshed topology of transmission networks fits well for this purpose. In that network topology the candidate areas for ANs are all medium and low voltage networks with aggregated DG units and corresponding loads. An illustration of an AN-based power system is presented in Fig. 1 .

3. POWER BALANCE AND RELIABILITY By treating ancillary services (regulation capacity, spinning, non-spinning or operational reserves, etc.) as market commodities, the objectives of the corresponding markets are to ensure a required reliability level of power system. This required level of reliability is prescribed by the required total accumulated amount of each of the commodities. For instance, hourly spinning reserve requirements are usually defined to be the grater of a fixed percentage of total forecast demand and the largest on-line unit. To simplify mathematical formulations we will consider only one ancillary service and denote it with A, but other ancillary services B, C, ... could easily be included. Generally, A is a capacity that is available as a power injection, or load reduction, in the system within some specified time interval. The systems required reliability level at some time t is then defined with

1A, ( t ) 2 Afey( t ) ,

(1)

I

where A, is available capacity at bus i, and A""(t) is required capacity that has to account for an uncertainty in power productionldemand and can be different for different t. Assume that for a certain autonomous network n it is required to have AF1(t) for a reliable operation of that AN. For simplicity, further in the text we will leave out time dependence i n the notation, although we will consider all the quantities being time dependent. Then for some autonomous network n it is necessary to have 4,

A,,

-

2 A,yq

A:

(2)

r=l

where A,,l is capacity [W] available from unit i inside AN,

mrz

is total number of units inside '41

autonomous network n, so

.4,,

is total capacity

1-1

available in the AN, and A,:* is the capacity that the AN sells to the outside system, i.e. to other ANs. Note that if A>: is negative, the AN is buying that amount from the outside system. Now, for the overall system we can write

11=1

i=1

,,=I

11=l

Since we assume the overall system being a network of ANs (i.e. any consumer or producer is in some AN), we can take A'"'" =CAT' , i.e. required n

overall system capacity is sum of required capacity levels for each AN. From (3), for the reliability of the overall system, one of the goals for the outside A: = 0 . market is to achieve I?

Fig. 1. Autonomous networks based power system

Note that with this formulation, capacity from ancillary services is traded in an equivalent way as real power. All ANs are either "producers" or "consumers" of spare capacity for ancillary services and the overall balance has to be achieved. This is in contrast with today's power systems where the 341

required capacity for system's reliability is determined by ISO. In an AN-based power system, trading with ancillary services capacities is closer to the trading in PX. Attaining the required overall system reliability level becomes a decentralized decision and each AN contributes. This decentralisation is desirable due to the overall system's complexity and its large-scale, since for AN it is easier to assess its internal required capacity level based on local predictions and on generally better insight into its internal situation. The power balance within some autonomous network n is given with

c m,,



1,s

[WYO]

This quantitative equation agrees with the real frequencylpower behaviour of the European power system as proved by the lot of measurements in Fig. 3a. As to be seen there, all measuring points are laying above the maximal frequency dropioutage power characteristic for kpp)= 2,O %I%. 111. EVIDENCE OF THE HIGH SYSTEM SELFREGULATING EFFECT The exiqtence of the hidden - induqtrial and municipal - selfregulating effect, based on the speed control of the corresponding steam power plants, is documented in the following on the hand of three examples.

Exaniple 1: Comprehenbive experimental investigation, concerning a real power system Before the East European Centre1 power system together with the East German VEAG power system was connected to the West European power system thc cvidcncc of thc controllability of thc ncw accessory power systems had to be provided. For that, the in synchrony operating Centre1 and VEAC power systems performed comprehensive experimental investigations, which, as can be seen in Fig. 4e2, induced a much higher controllability as expected during the test planning [91.

This was based in the fact that not only the 500- and 200-MW power plant units, which were upgraded with up-to-date primary control equipment, kept spinning reserve power ready during operation, but also the older 100-MW power plant units, s. Fig. 4el, as well as further municipal and industrial power plant units, s. Fig. 4d2, which were equipped with simple speed governors. Based on this, the system selfregulating effect summed up to:

347

system selfregulating effect

k $)

This lead to a system selfregulating effect of

consumer influence speed selfregulating + governed power plant effect units )k: + k(lnd PP) + k(’OOMW PP) =

Pf

sy stem

selfiegulating effect

Pf

consumer =

selfregulating + effect

influence speed governed power

plant units

fl

=> Above parameter values see also Fig 4 d l , d2, el 3)

a) Pump storage power plant Forbflch

Seconoary controlled power p l u n k of VEAG

A K’( i )

V5

V6

area

b) ?ice

Murqtal”

7 c ) V o l t o g e dependence o f t h e lood

A K’(i)t

v7

v7

v5

Vh

v1

v3

vs

:

v

c

consumer

v4

d l ) Frequency deoeqdence of t h e lood

02) S p e w c o i r r o l l e d

P ) Speed cnnrrolleC 100 UW u o ta e 2 ) P r n o y controlled 506 MLll ond 210 N S un i s

i

6,4

I L2 VL

VG

VI

l

l

vs V9

I VR

1

industrial power plant (paper mill)

Fig. 5: Control tests during isolated operation

tndustrzal paver plants

AK’(i)‘

v7

u

I b4

I

c

J

lest runs ( V )

Fig. 4: Representation of shares of the power plants, consumers and power system in the normalized power-frequency characteristic derived from test run (“yersuch”) V1 - V9.

Example 2: Industrial procesJ power plant, generating steam j o r a paper nzill During tests of isolated operation within the part system “Badenwerk”, situated in the South West of Germany, initially two pump storage driven generators supplied the service area “Murgtal”, s. Fig 5. After disconnecting the smaller second generator the frequency dropped quite less than expected. Instead of an expected consumer selfregulating effect of k(c)pi= I%/% a system selfregulating effect of k(s)pf = 4,4%/% resulted. A s aimed inquiries have shown, a speed governed industrial power plant, build to supply a paper mill with process steam, fed in the running isolated power system as well.

Example 3: Industrial process power plant, generuting steanz for a sugar refinery A comprehensive study carried out by the University of Stuttgart assigned by the DVG to determine the consumer selfregulating effect k(‘lpi seven load areas nearly equally distributed over the West German power system were equipped with numerous automatic data logging systems [ 7 ] . 1his had been carried out mainly in substations on the 110- and 220-kV level, supplying sub-systems, whereby in cases of distributed feed-ins more than one datalogging system were required. Within the underlying 150-MW load area of the EVS with two feed-ins in the sub-stations “Heilbronn” and “Kupferzell”, situated in the South of Germany, an unexpected high consumer selfregulating effect of k(C)p,{Jan I)ec = 1,6 %I% resulted as annual average value, which had been determined by the lot of measurings. Aimed investigations have shown that during I 5th September and 23th December of the considered year an industrial power plant unit with PG, = 15 MW, equipped with a speed governed turbine valve, was in operation to supply a sugar refinery with process steam. Also the operation times within the two M o w i n g years were clearly fixed €or evaluation. For this duration the measurements had been recorded by the two data logging systems. The carried out semi-annual analysis of the acquired measurements APc(t) and Af(t) yield to the results shown in Fig. 6db. When the industrial power plant

348

was out of operation the alone effective consumer selfregulating effect yields to kpf(L)= 0,9 %I%. In the other case the resulting system selfregulating effect yields to kpf(s) = 3,4 %I%. As can be seen, the speed governed power plant unit contributed with k(lndPP)pf = 2,5%/% to the effective system selfregulating effect. This fact looks feasible because it applies: 15MW 100 2.5 150MW 4 with 6,: drop of the speed governor. ppp

Pf

- PG,N 100 --.-=-.-=

PCN 6,

This result is essential for the spinning reserve power to be kept ready qualitatively and quantitatively not only concerning the power plants but also concerning the whole power system.

In addition no agreement between transient measurements and corresponding simulations can be achieved without regarding the existing system selfregulating effect in full size (e.g. [ 101). A. Advantages,for the power system

Assuming a system selfregulating effect according to the Transmission Code [ 11 of sq stem

consumer

selfregulating effect

=

influence speed

selSregulating + governed power eSfect plant units

0.0

0.5

U ) 2IDec.

13.SFPJ

2'1 Dec

i

1 4 Sepi

_I

i

a) ldentiiicction o i load scliqulatinq eiiecr

i

b) loer!ificalion

3i

sysierri selfrequlatinq eliec!

0.9 t

2.5

Fig. 6: Long term evaluation ofthe consumer and system selfregulating effect

Example 4: Global Estimation Assuming an amount of only 5% of smaller speed controlled industrial and municipal power plant units, which feed in additionally into the interconnected power system having a speed controller gain of V, = 1000//5% = 20, then the hidden selfregulating effect already results to k p t n dpp) = I ,O%/%.

1V. ADVANTAGES OF THE EFFECTIVE SYSTEM SELFREGULATING EFFECT As proved in Chapter 2 by means of measurements in the interconnected power system and underlined in Chapter 3 by experimental investigations carried out on the example of individual part syqtems behaviour, the existing system selfregulating effect of the European power system must be in practice at least equal kpf(s)= 1,5 %I%.

the system frequency will arduously decrease in the case of disturbances greater than the spinning reserve power of 3 GW to be kept during operation. This theoretically bad behaviour can clearly be seen in Fig. 3a. Thus the lower frequency border from 49,O Hz, i.e. the first step of load shedding, would already be reached with an outage power of AP*z = 2,2% 2 3,3 GWII5O GW during peak-off time, as shown by the dotted line5 in Fig. 3a. However, in practice, where a realistic selfregulating effect of system selfregulating

consumer =

eSSect

k(") Pf

-

influence speed

selfregulating + effect k(C)

Pf

+

governed powcr plant units k(PPu) Pf

AP ~

+ 2 l,o

L"/dYO]

will be effective, the lower frequency border of 49,O Hz will still be reached at a disturbance power of AP*Z=3,7%; 5,s GWIISO G W . A corresponding worst case consideration was carried out in [ I l l . Assuming a system self regulating effect of kpf(i)= kpf(L)+ kPf('"') = 1 ,O + 0 = 1 ,O %I% the lower frequency border of 49,O Hz will be reached at a disturbance of AP*z= 3%; 6,O GWI200 GW. Thiq rewlt agree4 almo4t with the eqtimation in Fig. 3.

349

The reason is that the system selfregulating effect caused - on the one hand by a greater frequency dependence of the load and - on the other hand by smaller, not regarded municipal and industrial power plant units being operated with underlaying speed controllers is much higher as assumed by the transmission operators when deriving the guide lines for the required spinning reserve power to be kept ready by the primary controlled power plant units. The advantages of the higher existing selfregulating effect are - on the power system side the frequency will decrease much smaller in emergency cases when the outage power will be higher than the spinning reserve power to be kept ready, and - on the power plant side the steam power plant units have not to be throttled so much any more. As they have not to hlfil the Transmission Code guide lines dynamically exactly they can be operated more economically.

B. Advantagesfor power plants

For fulfilling the requirements of [ I ] also dynamically, a relatively high throttling of the turbine valve is continuously necessary in case of a system disturbance of AP*z = 2% and a participation of kp, 2 50% of power plants at the mimary control. The reason for this is, that during the considered time space of 0 < t I 30s nearly only the high pressure turbine-parts of the primary controlled thermal power plant units are active with a power share of about clHp = 40%. With proceeded time the low pressure turbine power share delayed up to 50s through the reheater -becomes active, too. However, as the steam storage capacity is limited with a storage time constant of up to 80s, the live steam pressure decreases, until the fuel-sided increased heat supply becomes effective after some minutes. As both influences are pointed in contrary and almost compensate each other, an uneconomically high throttling of the turbine valve of Ay*7 2 10% is needed round the clock. ~

6. REFERENCES

Neglecting this only transiently acting fact, that during the first minutes only the high pressure part of the steam turbine is effective, the throttling of the turbine valves can be reduced from Ay*l = 10% to A Y * ~= 4%. Doing this, the resulting frequency behaviour has been simulated in Fig. 8 by means of a simplified system model, sketched in Fig. 7. There all primary controlled power plant units are gathered to one equivalent steam power plant unit of corresponding size. Furtheron in both simulation cases a power outage of PZ= 2% has been considered.

VDN (2003). ‘Transmission Code 2003: ,.Network and Sjstem Rules o f the German Transmission System Operators“. Berlin, August 2003. DVC (1 996). Anforderungen an die Primarregelung im UCPTr-Verbundbetricb. I lcidclbcrg. UCTE (1998). Ground rules concerning primary and secondary control of frequency and active power control within the UCTE. Paris Welfonder (2002). Interaction o f power plants and power systems within the deregulated energy market. VGR PowerTech (82) 2002, Issue 3 and 4. Welfonder, k.(1997). Lcast Cost Dynamic Interaction of‘ Powcr Plants and Power Systems. 13th IFAC World Congress. June 30 - July 5, 1996, San Francisco, IJSA. Control Engineering Practice, Vol. 5, NO. 9, pp. 1203-1216, 1997. DVG ( 1980). Leistungsregelung im Verbundnetz. Heidelberg Welfonder, E.. Hall, B.. Glaunsinger, W.. Heueck, R. (1994). Study of the Dependence of Consumer Subsystems on Frequencq and Voltage CIGRE 1994 Session, 28.08.-03.09 1994, Paris. VDI/VDE 3508 (2003). Unit control o f thermal power stations. Reuth Verlag, Berlin. [lo] WelFonder, E.; NeiFer, R.; Sattinger, W.; Spanner, M. and Tillmann, H.-B.; Kranhold. M. and Svarc, L. (1996). Control Behaviour of the VEAG and CENTREL Power System determined by comprehensive experimental investigations and additional simulation. CIGRE 1996 Session; 25.31.08.1996, Paris [ I l l Kurth, M. and E. Welfonder (2005). Oscillation Rehaviour of the Enlarged European Power System under Deregulated Energy Market Conditions. Control Engineering Practice, Special Section on Power plants and Power Systems Control, Volume 13, Issue 12. pp. 1455-1558, December 2005. [12] Asal. 1I.P.; Bath, P.; Grebe. E.; Quadflieg, D. (1998). Dynamic System Studies of new Requirements and Strategies for the Primary Control in the UCP‘TE/CENTREL, Power System. ClGKE 1998 Session, 30.08.-05.09.98. Paris.

As to be seen by Fig. S1 the frequency will strongly drop by -1200 mHz to less than 49 Hz in case of a system selfregulating effect of only k,?) = 0,s %I% as assumed by [6] and [I] up to now. However, in the real case, where - as pointed out - a selfregulating effect of kpJs)2 1,5 %/% exists, the frequency will only decrease by -360 mHz to > 49,6 Hz, as shown in Fig. SI1.That means, the frequency will clearly remain within the permitted system operation range of 49,O 5 f 5 5 1,0 Hz [ l]! Therefore keeping the necessary system dynamics further on, the steam power units have not to be throttled so much any more and can be operated much more economically.

5. SUMMARY Within the European power systerri the frequency drops resulting in reality in the case of power outages are much smaller than expected by the transmission system operators [ 1,3].

350

a Grid

............................ b) Equivalent steam pawer plant unit

Fig. 7: Simplified summary model of the power system under consideration of the steam generation dynamics I) kb;' = 0,5%/%

II) k$'

a) DisturbanceAP;

= I$%/%

a) Disturbance AP*,

.....................................................................

i

b) Frequency

49

c) Generatooutput&

c ) Generator output

P,

PGsDI,~

PG '

0.96--

0.96-

d) Fuel mass flow

e) Fuel mass flow

0,96

e) Valve position

i) Valve position 1.04

ll::i1T**

A

f) Live steam pressure p * " q

09d

09d h) Turbine steam flow live steam flow difference

g) Turbine steam flow live steam flow difference 1 04 m*, I ~ I [

1 04

.-

,----

by---.

o,g5--

................................................ _ ..i......-..'-.......... ->........... ,

,

t

[S]

0,961- .-",., 2000

Fig. 8: Simulation results for kpE(S)= 0,5 %/% and kpf(s)= I 1,5 %I%

351

......*,............

........................................................ t [S]2000

7. APPENDIX : INDUSTRIAL AND MUNICIPAL POWER PLANT UNITS

I

I n the appendix the block diagrams of industrial and municipal power plant units are illustrated. The dynamic behaviour of the overlaid process pressure control or heatwater temperature control respectively is normally slow in comparison to power system caused actions of the underlaid speed controllers, which will last only a few minutes, until the normal primary controlled steam power plant units will have increased their generator power already to their enlarged reference values.

Psir*

A 1 Industrial process power plunt unit with underlaid speed control

'-1

,. , I

I

1.... I

I

I

Turbine valve

'----I-' apenurecontml

Q

Fig. A111 : Unit control of steam power in a process steam network

Figurc A111 shows an cxamplc of thc control of a unit, generating process steam. The steam pressure in the process steam network, pPSt, is the back-pressure of the turbine pBp. This pressure is adjusted to a specified value; the turbine valve aperture yI is the assigned manipulated variable. By adding the actuating signal of the turbine speed controller to that of the back-pressure controller, the unit also temporarily contributes to frequency drops in the electrical power network. As the process steam network is very inert, steam generation is at first adapted to steam consumption by adjusting the live steam pressure prsr to a fixed setpoint pLSlset, see left side of Figure A 111.

I

A 2 Municipal heatingpowerplant unit with underluid speed control retwn

FigureA211 shows an example of the control of a unit generating district heat. The district heat supply temperature QDll is set to the setpoint QDLise, by adjusting the turbine valve aperture y r . The actuating signal of the turbine speed controller - added to that of the heating-water supply temperature controller - causes the unit to contribute to the frequency control in the electrical power network, utilising the large storage capacity of the district heat network. Steam generation is adapted to steam consumption by adjusting the live steam pressure pLst to a fixed setpoint pLStset.The thermal output Qb of the fuel

Fig. A211 : Unit control of a combined heating and power station using hot water as heat carrier

mass flow m g is the manipulated variable. The control response to changes in output is improved using the PD-TI feedforward signal derived from the turbine steam mass flow m, .

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Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

PUBLlCATlONS

OPTIMAL POWER SYSTEM MANAGEMENT VIA MIXED INTEGER DYNAMIC PROGRAMMING Harry G. Kwatny * Edoe Mensah * Dagmar Niebur ** Carole Teolis *** * Department of Meclmnical Engineering arid Mechan,ics, Drezcl UrriversitzJ, Philadclphiu. PA 19104. USA ** Department of Electrical an,d Computer Engineering.

Dyezel [Jniuersity. Philadelphia, PA 19104, USA *** Tech,no-Sc,lences. Inc..lOOOI Derekwood Lane Lunham, M D ,20706, USA

Abst,ract: Power systems involve both continuous and discrete acting components and subsyst,erns.In this work a logical specification is used to define the traasit,ion dynamics of the discrete subsystem. A computational tool that. reduces t,he logical specification to a set of' incqualities and tlic use of t,he transforrned inodel in a dyiiarnic progrnrnining approach to the design of optimal feedback controls are described. An example of optinial load shcddiiig for a power system with aggregate induction motor and const,aiit>admit t,a,iiceloa,cis is g,'wen. Keywords: power syst,em mantgerncnt., liybritl systems, dynamic: progra.mmiiig, mixcd intcgcr progmnming

1. INTRODUCTION In thib papei we seek to design poivci inailagement systems that optimize tlie discrete actions of protcctivc device5 in order to insure continuity of service to vital loads. lye describe a modeling approach that captures both the discrete and continuous aspects of the power syskm and show how dynamic prograrnniirig can be applied to derivcl optimd control 5trdtcgic5. Tlic coiiiputational tools iire summarized and an example is given.

A power systeni's continuous and discrete dynamics can be iiitcgratcd in ct hybrid nulornaton rnodcl thnt i b coinposrd of a deswiption of the discrete transition behavior from one discrete state (or mode) to another along with model5 of continuoub This rcscarch was supported by tlic Office of Naval Rcseilrcli Contrxt Number N00014-04-LI-0285 mid the No.-

behavior wit>liincach iiiodc. It has provccl to be an important theoret,ical t,ool and is a key coiicept,ual devicc for modcl building. However, ot,licr forms of models are far more convenient for coiitrol system design. Such models include the 'mixed logical dgiiamic systcin' (MLD) (Bcmpor8.d and hlomri, 1999: Geyer eC a,l., 2003). The ability t>o corivcrt, from one form of iriodel t,o another are import tint.

In our approach, we model the transition dynamics by a logical statement (or specification). We have developed a tool in hfuthernuticu, that) converts any logical specification into a set of niixcd-int,cgcr forrriulas (IP formulas). Thus, t,hc transition specificat,ionfor the automaton is converted into a set of iiieyualities involving Boolean variables. The IP formulas iire used in comput,iiig the opt>imalcontrol strat'egy.Our approach derives

tional Science Foundation Contract Nuinher ECS-0400391.

353

a feedback policy based on finite horizon dynamic programming.

events and p to represent uncontrollable events. Thus, C = S x P where s E S and p E P. A g i i ~ r dis a siibset, of the continuoils &ate space X that. enables a transit,ion. A transition enabled by a guard might rcprcsent a, prot,cction device. Not, all t,raiisitions have guards and some transit,ions might require simultaneous satisfaction ol a guard antl the occurrence of a.n event. The gua.rd assignment function is G : E 4 2x.

The basic idea was out.lined in (Kwatny et al.. 2005) where we gave several simple rxa.mples that illustrated t.he conversion of logical specifications to IP formulas. We also gave im cxaniple of 01)I.irria1 periodic corilrol o r sirrrple power elechiiic device. In this paper we design an opt,imal load shedding coiitmller for a power system with aggregated induction motors and const.ant admittame loatis. Because this simple syst,ern ex1iibit)s typical power syst,ein nonlinear dyna.inics, it has h.xpicnl~lybccn used to articula1,c behaviors associat,ed with volt,age collapse, e.g., (Ohtsuki et al., 1991; Pal, 1993; Bao et al.; 2000).

We consider each discret,e state label, q E Q , and each event,.(T E C , t,o be logical va.ria.blest>ha.tt,a,ke the values True or Fa,lse. Guards also a.re specified as logical conditions. In t,his way t he transition system, iiicluding gua,rds, can be defined by a. logical specification (€ormula) C.

In Sect>ion2 we provide a specific definit,ion of the problems considered herein. S ions 3 antl 4 describe t,he comput,ational tools. The opt,imal load shedding example is given in Sectlion 5.

For computa,t,ionalpurposes it is useful to a,ssocia.t,ewit,li each logical Val-iable, say a , a, Boolean variable or indica.t,or function, ha, such t,ha.t 6, aSsiinies tlie values 1 or 0 corresponding respectively t,o 0 being True or False. It is convenient to define t.he discret~est,a.t,evector 6, = [6,, , . . . 6,,n]. tlic cont,rol event, vector J , ~ = fi,, , . . . ,h.3wls],and

2 . PROBLEM DEFINITION

[

bpL,.

t,he exogenous event vector 6, = . . ,6 ? h P ] . l’rccisely one of the clenients of 6, will be unity and all others will be zero.

2.1 Modeling

The class of hybrid systems t,o be consitlcrcd is defined as follows. The syst,em operates in one of m modes denoted ql, . . . , qm,. We refer t,o the set^ of modes Q = (91. . . . , q m } as t,lie cliscrete state space. The discrete time diEercncc-algebraic equalioii (DAE) describiiig opcratiun iri motle q,

Notice t1ia.t with the int.rodiict,ionof the Boolem variables we can replacc the set of dynamical cquations (1) with t,hc single rclat.iori

is

iii cont,innous st nt,c,

y EY

2 Rp is the vector of algebraic variables and

u E U Rrnis the continuous cont,rol. Transitions caii occur only Mween cert,adn modes. The set of admissible transitions is E C (2 x Q. It, is convcnient, to view the rnotle transition systom a,s a graph with elements of t,he set Q being the nodes and t,he elements of E being the edges. We assume that^ transit~ionsare instant,aneous a.nd t,akeplace at thc beginning of a t,imeinlerval. So, if a, syst.em transitions from mode ql to 92 at)time k we would writ>eq ( k ) = 41%q(k+) = q 2 . m7edo allow resek. State traject,ories are assumed cont,inuous t,lirough cvcnts, i.c., x ( k ) = x(k+), unlcss a rcsct’ is specified.

2.2 The Control problem

FVc asunic hat, t,he syst cin is observed in operat’ionover some finit.et , i m horizon T that is divided into N discrete t,irne intervals of equal length. A cont,rol policy is a. sccpcncc of functions 7i-

= {PO (To. 6,o)

3..

.

1

P X - 1 (%-I,

6y(N--l))}

such that, [Uk.6d.3 = pk. (Xk,6&)

Transitions are triggered by ext>ernal events and grcards. We dcwote the finit convenient to part,ition the those tha.t, are conlrollable (t,hey can be assigned a value by the cont,roller), and t,hosc that arc not. The lat,terare exogenous and occur spont,anc>ously. Such an cvcnt rniglit corrrspond t,o a. component, failiire>or a. high level change of opera.tiona1mode. We will use the symboIs .s t,o represent!cont,roIIabIe

354

Thus, p~k.genera,tsesthe continuous cont.rol U k and t,he discrete control 61, t,hat. are to be applied at. i-imc k , based on the st,at,c (xl;,h41;)obscrvcd at. t,inie k .

Consider tlie set of m-tuples (0: 1}ln. Let, A,,,, denot,e the subset of elements S E { O . l } r r L that. satisfy 61 . . . S, = 1. Dcnot,c by II t,hc set. of sequences of fii /“k ; x + u x isc. con1,inuous on X. (0,.I}”” t.hat. are p

+

+

x a,,,

Now, given the init,ial st,a,t,e ( 2 0 , h,o) t,he pi-ohlem is to find a policy, T* G n, that minimizes tlic cost functional J7r

(xo, 6,o) =

+

G,v (rn;? 6,~)

E56,++Eed 5 E0+Eiz+~~'26,+E~6,+E~~~ (6)

(3)

Specific ally, the Optancal Feedbad Coritr 01 Problem is defincd a5 follows. For e;icli .xg E X , Sqo E A,, determine the control policv T* E TI that minirni7cs tlie cost ( 3 ) subject to tlie constraints (I) and thc logical spccification. i.c>.,

A* (zo. 6,o) 5 J ,

exogenous events. They also involve a set of auxiliary Boolean variables; d. introduced during the t,raiisforination process, and t,he contiiluous st,ate variables, T . The general form is

( T o . 6,o)

wherc t,hc matrices havc appropriate dimensions. As we will see in examples below, wit,h x,6,, 6,, 6, given these inequalities typically provide a unique solubion for tion,the cliscrcte state after trmsition, t.he controllable event.s, the

4-1 ( Z % - d q ( % - L ) ) =

{LL ( z ~ - ~ , ~ ~ ( ~ - I ~ +J,* , P - I( )~ , 6 ~ ~ ) }

in111 !J-1

(7)

Equation (7) provides a mcchaiiism for backward recursive solution of the optimization problem. To begin the backward recursion, we nccd to solve tlic single stage problern with z = N . The elid point ZN.b q i5~ free, 50 wc begin at a gencml terminal point

Once the pair pi--l, JAr-l is obtaincd, wc com.Ti,-,. Coiitiniiing in this way we obtain piite

for 2

2 i 2 N.

VTe need t.o solve (9) recimively backward, for i = 2 . . . . , 1V aftcr iriit>ializingwit>h(8). We begin by construct,iiig a discrete grid on the continuous slat,e space. The tliscrele space is denoted Atj each it>crationthe optimal control arid the optimal cost are evaluated at, discrete poiilts in Q x 2. To cont inuc with the next, sta,gc we need to set, up an interpolation function to cover a.11points in Q x X .

x.

We exploit the fact that, the syst,em is liiglily constrained and almost all of the constraint,s are linear in Boolean varia.bles. The basic approach is a s follows:

355

(1) Identify the binary and real variables and separate the inequalities into binary and real sets, biiiary equations contain only binary variables, real equations can contain bot.11 binary and real variables. ( 2 ) Usc the Ilfathernaticn function Reduce to obtain all feasible solutions of the binary inequalities: a list of possible solutions of pairs (Sq+, d ) . Reduce is a very efficient solver, espccisllg- wlieii thc inequalitics are linear although it is not limited to linear inequalities. In gerieral, if there A r c N binary variables then t2icrc arc ZN corntinations tliat need to I)e evaluatcc1if one were to attempt to optimize by enumeration. But the feasible combinations are almost certainly much fewer. ( 3 ) Use Reduce to solve the real inequalities for tlie real variables for every feasible combination of binary variables. Many of tliese conilinations of binary variables will not admit feasible real variables. so they can be dropped. The reinailling combinations typically produce unique values for the real variables. (4) Enumerate the values of the cust for cach feasiblc pair uf binary and real variables and select the ininirnuin.

Fig. 1. System configimtion. impedance depends on the aggregate induction motor slip. The ncl work equut ions are cwsily obtainrd. Suppose 61.62denote thc voltage anglcs at bus 1 aiid 2. Define the relative angle iictwork equations arc I'dJ03 = r.,

-

0 2 = 62 - 61. The

cv,2

0 = ( u / n )E f i sin 82 + cV; 0 = ( ( ~ / / tEV2 ) cos 02 dV; From the last two equation5 we obtain

+

5. EXAA1PLE: OPTlAlAL LOAD SHEDDLNG In this section we provide a simple illustration of t he formu1;ttion ;tnd solution of a powcr managcinent opt,imal control problem. 'L'he primary mechanism for w h g e cont,rol is the corit,inuousvariation of field vokage wit)hinit,s bounds. 111 addition, we consider load shedding as a discrele control means, specifically for acconmlotla.til?g.~ini~[la~t,iiigtransinission line faaults.

The power absorbed by the load is PL = -v, 2 c.

(2,

= V,"d

Now, let 11s t u n to t'he induct,ioii motors. An equivalent circuit for a.n induction motor is shown in Figure 2. Here, l.he parameters R,, X , dciiote the resistance and inductance of t,he stator, X , denotes the magnet>izinginductance, and R,, X , t,he rotor resistance ;tiid inductance. Thc rcsist a.nce R, (1. - s) / s represents the motor electrical output. power. We will neglect, t,hc small stator resist>anceand inductance. We also assume t,he a,pproximat,ionof large magnetizing inductance is accept'able.

5.1 Network and Load D ~ ~ n a m i c s

A rc1at)ivoly simple tcin that) is known to cshibit. interesting vohage stability charxteristlcs is a single generator feeding an aggregated load composed of constant iinpedance loads a.nd induction motors. The syst.erii lias beer1 used to study thr: offcct of tap changing transformers antl capacitor banks in voltage control, e.g., (Ohtsuki et al., 1991; Pal, 1993: Bao et al., 2000). Considcr t,lic system shown in Figure 1. Tlic syst,em consists of a generator, a transmission line, an on-load t,ap changing transformer (OLTC) and an aggregat)ed load. The generat,or is c1iaract)erized by a 'const>antvoltage behind reactance' model. Tlic gcIicrat,or interrial bus voltage E is used t,o maintairi the voltage at bus 2 ; so long as E remains within the liniits iniposed by [,heescit,a,t,ion cnrrent, limits. The OLTC ordinarily rrioves in smdl discrete steps over a narrow range. The load is an aggregate coiiiposed of parallel induction 1110tors antl constant impeda,nce loads. An induction motor can be characterized as an impedance with slowly varying rcsist,ancc; conscxpmit,ly.t,hc aggmgate load is represent,ed hy const,a.ntinipcda.iico actually, a slowly wrying irnpedance, where t h e

jx,

jx,

R,

R,

Fig. 2 . Induction niotoi equivalent circuit. Undm Lliesc toridit ions we obt ain t lie following. Thc real power tlclivcrctl to the rotor, Pd, and thc power delivered to the shaft, P?. are

r, =

R,S If:

R; + s 2 X ?

p, = r d (1- S )

The dynamic a1 equation for tlic motor (Newton's law) is 1

(P,- Pn,) I,, iU'0 Introducing the slip, s, s = ( L U ~- wff,)/wo, tlie motor dynamics take the form Gm =

356

______

5.2 System Operation

In t,he following, we allow for shedding a fraction, I', of the loatl. In the present example, we allow three different values of q including zero, so E (0, r l l , ria} . ConseqiientJy, there is normal operat,ioii a.nd two priorit,ized blocks of load that, can bc droppcd in wcorde.ncc with tlic tmnsition behavior defined in Figure 3. The corresponding logical specificat>ionis = eXactl?J (1, {41 ( t ) ,(Z" ( t ) ,43 ( t ) } A) P r a 4 Y (I, (41 ( t i - ) ,42 ( t + ) > ( I 3( t ' ) } )

(M

A

( t ) A (51 v 7 3 2 ) =+ r12 ( f ' ) ) A ( t )A 32 + ~a ( f ' ) ) A (43 ( t )A 7

(43

V2. Wc will assume that it. is dcsirctl to niaint,ain V2 = 1. If we ignore tlie exciter dyna.rriics, t.lieri (11) allows Ihe delemiination of Lhe field voltage that, yields the desired load bus voltage. However, the field voltage is st-rict>lylimit,ed, 0 < E < 2 . If we assume tliat, only t hc uppcr limit is a binding const,raint,,there are two possibilities for sat,isfying (11):

752

+ 43 (t'))

Equation (12) represents the aggregated 1110tor tlvnaniics. and tlic load atlinittancc is givcn by the last t\+o equations. The system data is RL = 2, R, = 0.25, X , = 0.125, u = 1 (nominal) Imcji = 4.

.

5.3 The Oplimal Control Problem WLL~OUL OLTC. TL = 1

Fig. 3 . Transit ion diagram €or load shedding optimization. In the present case. n7e asslime the blocks are sized sucl1 that 41

*

= U,

41

* 7 = U.4,

q3

+ rl = 0.8

Wc 0:

06:)

ti::)

'

Stcp 2. Sutx,titutc v(")for ( 3 ) or (5) to compute p ( n ~ )= [P:"', ... aIic1 ~ ( 7 1 2 ) =

where AP, a.nd AQ7, denot,es t,lie nodal act ive/react,ive power iiicrerrieiih, respeclively, corresponding to tlie nodal act,ive/react,ive powers P, a n d (2,. Hence we call AP a.nd AQ t h e nodal

,pg)l*

[Qj""'*.. . , Q$"]', and tlicn i i 5 ~R. A1 and V('") in (17) to compute J$$ and J)$: then determine A ~ ( . J=) p s - p(7n) and ~ ~ ( n=t (2 )s - ( ~ ( m ) ;

361

rminc the solution AV('".'') by siibst,itutiiigR, A P ( ~ ~ALQ)(,~ T&~) ) , and for 1,he first, ecpiatjionof (16) as appropriately;

.~g)

nr,

Step 4. By the second equat>ioiiof (16), compute V("'+') = V('") + AV(mi-*) and t,est if I lAV("'+') I I 5 c: i f the tolerance inequality condition is satisfied, talienstop; ot,herwise,let, ni = ,rn+ 1 and return to Step 2. In t,lic Jacobian eynations (16) and (17), an underlying assumplion is that, all tlie nodal act,ivc/rcact ivc powrs a.rc spccifictl. Howcvcr, t his is not the case a.s always. If there are nodes in t.he power syst,em either (or both) of whose nodal active and reactive powers is (or are) not given but whose nodal voltages are specified, t.he NewtonRaplisori algorithm must be modified.

4. VOLTAGE EVALUATION VIA QUADRATIC EXPRESSIONS Here we develop eigen~.alue/signLilar vahe inecliialities between the nodal voltages L$, (or t,he nodal voltage vect,or V and t,he nodal voltage increment vector LV) and tlie ac:t,ivc/rea.ctive power indices Pt%Qi (or the nodal act,ive/rea.ctive power index increment. vectors A P , LQ).Tliese inequalities allow us t,o evaluate nodal voltage st,a.lr,ility wit,h or withiit, power flows.

One can assert a similar result on YgY&. Using tliese facts back to (18). we obtain lPfI

Secondly, we est ablisli inequalities by working or1 t,he Hermitian power eqiiat,ion (9). Obviously, we can have from (9) and the C'auchy-Scliwarz inequality that .

+

N

Since Y p k YFk and U,, eack k , it follows that

+Y& are Hermitian for

(i). Inequalities &(.ween V, (or V) and P,i, Q,

First,ly, we establish inequalit,ies by working on t.he quadratic power equat,ion (8). By the specific , obt aiii from niat,rix cxpressioiis of lip, and Y ; J ~we the well-known Caucliy-Schwarz inequality that

0twioiisly, we can cla.irn some sirnilas results on IICr=lmi,,(Y~k+Y$k)l I. By thcso iiiequalitics, we can verify t,lic following two iiiequalit,ics.

Note that Ypl; and

are square. Then,

miix k

Now assiimc that R = Af = IL\r.In this spwiitl case of R and A f . we have that

Now let) 11s consider the case when all t,he entries 01 1,he weiglil irig coefficierit irialrices R arid A 1 are 1. H,ecalling the discussions around (10) and (1 1) a,nd t h e eigenvalue rules a,hout, Kronecker

362

prodiirts of matrices (see Propertv 2.4(1 l)(e) of Lukkcpohl (1996), we are led by (20) tliat

+

Thirdly, again by tlie [act that Ypk Y& and Y Q ~Y& are Hermitian for eack k , tlie following inequalitics can bc clainicd by applying RayleighRitz tlieorrin (Lutkepohl, 1996) to (9).

+

s

claim that t,he IIerniitian power equations reveal t,lie statsic structural cliaractreristics of power systerns better than t,he coiiventional polar power equa.tion.

(b). In vicw of (20) and ( 2 2 ) : it should also be poiritxd out) t,liat by choosing R a.nd AP in ccrt,ain ways one can evalmtc nodal volt,age stability through tlie cliiatlra.tic a n d 1Ierinitia.n power equations (8) arid (9) but, in tcrrns of diffcrcnt, lowcr/upper bounds. (ii). Inequalities bctwccri Au,~,Av,, (or AV) and

AP,A Q

Now we develop inequalities between nodal voltage fact>orincrements Au,i and A.U:,, (or t,lie nodal volt age increment, vector AV) and power index incrcrncnt vcctors AP and A Q by mcans of thc Jacobian eqiiat,ion (14). Different, from t,he inequalities (18). (20) and ( 2 2 ) , these inequalities involve t,lie power flow knowledge. To derivc these inequalities, assume t,hat the Jacohian mahrix J defined in (14) i s non-singular. By t,he definitions of the infinite vector norms 1 1 . I I m and the EL^clidean vect,or norm I I 11, it is evident, t,ha.t, 11 . [ I m I1 1 . 1 1 for any vector (.).

-

Firstly, we obt.ain by (14) t,hat From Properly 5.3.2(2) of Lutkepohl (199G). ( 2 2 ) yields that

Sccondly, if J is non-singular, we obtain from the

+

generahed matrix inverse theory that [ J & J p v J & , J ~ V ] I [&,. J,&]J = 12x, wlicrc (.)+ is tkic

generalized matrix inverse of tionship in (14), we obtain

(A).

1Jsing this rela-

Again let us consider the case when all the entries of the weighting coefficient matrices R and A1 arc 1. Repeating some discussions similar to those around (21), T.VP are led by (22) that

Suriiniarizing tlic above argunicnts. wc liitvc tlic following results.

Theorem 1. Assume that the power system is in the steady stat?. Thcn, the eigcrivalue/singularvalue inequalities (I$), (19), (20). (21), ( 2 2 ) . (Z), and (24) are always satisfied. Also under the non-singiilarity assuniption on JpvJ&/ and J Q ~ ~ J Q ' ,it. . is clear to see that Sornc rcmarlis about the rcsults of Thcorcm 1. .J&<Jp,, J&JQv is also non-singular. Hence, (a). From the above arginiicnts, we can scc that the generalized matrix inverse theory yields that il fioultl be hard lo tlrrivr (lie irieqiiali~irsol Theoreiii 1 witliout the Hcrniitian power equation (9) Tn a mathematical sense it i i reasmahle to

+

363

(b). Since the iiieqiialities in Theorem 2 can be expresied also through the nodal active/reactive power incrcment vectors A P and Ad) via (Is), the inequalities of Theorem 2 can be used for estimating nodal voltage variations quantitatively through eigenvalues and/or singular values of Ja cobian matrices at a givcln working point V and with prescribed weighting coeIGcients matrices R and ill, wlieii nodal iiiput active and/or reactive powers arc changed minutelv.

Now we obscrve by tlic singular valucs thcory (Zhou, K and J. C. Doyle, 1998) again that

5. CONCLTJSIONS

In t,he pasper we suggest a Hermit>ia,iiapproac,h in power systems t,hat are running in t,hc steady &ate through quadrat,ic funtion forms in terms of iiodal v o h g e factors. This brings us theoretic and niinieric advantages in dealing with probleins of power syst,einsover the coiivciit,ioiial po1a.r power equations can provide. In particular, we have paid our a,ttent,ioiit~o:(i) suggest.ing Newt~onRaplison iteralive a.lgoritlims four powcr flows Ihal include adjust~ableweighting coefficieat,s; (ii) deriving c:igc~nvitIiir./singiilas-valii~? incqiialities for nodal voltage stability evaluat,ion wit.h or without power flows.

+

Lel us define A x . = Ai;, ~ A 1 - 1which ~ ~ . means tlicx nodal voltage incrcment of V , at tlie i-th iiodc in thc polar expression scrisc. It i s obvious that niax,=1,2, ,L%r{lA&I} 5 IlAVll. This, together with (23) and (as), yields the following resiilts.

Theorem 2. In the power system that is in the steady statc with the nodal voltagc vector V . Assuinc that the Jacohiaii mdtrix J = [J&, J&IT defined in (14) is rloli-5i11gUh' at V . Then

REFERENCES

Furt lierrnore, if J ~ non-singular . then

~ ~ - I ,and T,

Aclia, E. bi: M. Ma.drigal (2001). Power Systems Ha.rmonic.s, Wiley. Hasegawa, J. k e t al. (2002). Pozrier Systems Enqineerzng, Denkigakkai (in Japaness). Horn, R. A. & and C. R. Johnson (1985). Mo,tyi:r An,a,ly.sis, Ca.mbridge Uiiiv. Press. Lulkepohl, I1 (1996). fIa7idbocik: of Mutr-ices, John

JQ\/JQT, are also

(in Japsness). Pavella,, 11.& P.C. I\;lurtrhy(1994). Transient Sta.bilitg of Power Syslems- T h e o ~ yarid Praclice, John Wiley & Sons, Chichest,er. Taylor, C. W. (1994). Po,uier System Voltage Slabilit?~, McGrew-Hill, Inc., New York. Tiranuchit, A. bi: R. J . Tliornas (1988). A posturing st~rategyagaiiist voltage instabilities in eleclric: power syslerns, IEEE Truns. orb Power. Systems, vol. 3, pp. 87-93. Rockafellar, R. T. (1 970). Conrier Annlysis, Princeton Universky P r Nejdawi, K.A. Clements An efficient interior poiiit method for sequeiitial quadratic programming based optimal power flow, IEEE Tram. on Power Systems, vol. 15, 111). 1179-1183. Zhou, J. & Y. Ohsawa (2003). Iterative singu1a.r inequalit,y evaluation of stat,ic voltage stability in power systems, Proc rtuiccd Rleetirry o'ri Pvuier Systems Engineering. IEE Japan, pp. 25-30 (in Japaiiess). Zhou, J. bi: Y. Ohsawa (2004). Volt>agestability evaluation of power systems under convex analysis fra,mework. Proceedi.n.ys oef Intcrnatiorid Corifereiice on Pomer Systern.s (ICPS2004). K:rthmunthi, Ncpal. pp. 125-130. Zhoir, K. 6c J. C. Doyle (1998). E.ssentials of Robust Control, Prentice Ball.

Sonic rcniarks a.bout (26) and Tlinorcm 2 .

(a). Eq. ( 2 6 ) indicaaes t,lia.t,bot>liact,ivo a~iitlreactive power variations have irnpactJs 011 the nodal v o h g e s . The struct,ural fca.tures in the qmlitative a.spects of tliese impacts a,re t,lie same, while tlie quantit,alive aspects of 1hese inipacts may be di€ferent,. In ot,lier -words, struct>ural;i.djust~~iient~ nieasiires in order t.o improve the active (respectively, reactive) power performance in a power system bring a similar a,ffcct on llie react,ive (respectively, adive) power perlorrriawe, iii the seiise ol 111erelationship between AP and AV a i d that, between A Q and AV.

364

Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

ECONOMIC DISPATCH ALGORlTHM BY 2.-P TABLES REFLECTING ACTUAL FUEL COST CURVES Kyung-11 Min, Jong-Gi Lee, Suk-Joo Kim, Hyo-Sik Hong, Young-Hyun Moon Dept. of Electrical Engineering, Yonsei Univ., Seoul, 120-749, Korea

Abstract: This paper presents a new approach to economic dispatch (ED) problems with actual fiiel cost curves using a L P table method. Conventional ED algorithms are developed on the basis of approximated fuel cost function, which cannot be adapted to actual fuel cost curves properly. In this paper, a A-Ptable method is proposed to improve accuracy of ED solution. It is noled that the proposed algorithm is very simple and has some advantages in considering the must-run condition and modifying the ED solution associated with generator addition/elimination. Numerical results of the proposed algorithm are compared with those of the conventional algorithms. Copyright 0 2006 IFAC Keywords: generalion cosl runclion, h-P table meihod, P-h LdbleS, aclual rue1 cosl curve, nonlinear cost function, economic dispatch (ED), unit commitment (UC), must-run condition

1. INTRODUCTION

Power industries are faced with rapid renovations in the whole world. Past power industries characterized by monopoly, excessive regulation and public property have been transferring to a new paradigm characterized by competition, deregulation and structural reform, and participation of private funds. It needs new economic dispatch (ED) algorithm for transitional systems of which concepts of economic operation is changed as compared with the rormer. Due to introduction of power market systems ED should be able to admit various types of fuel cost curves with frequent alteration by power market bidding. Conventional ED algorithms cannot apply to actual fuel cost curves because they have to use approximated cost functions such as second ordcr polynomial, piecewire linear function, and so on For accuracy, nonlinearity of fuel cost curves should be considered NLP (Nonlinear Programming) (Kuhn and Tuckcr, 1951) may allow using nonlincar cost functions, but it has reliability problems in convergence which make it complex to implement ED In order to overcome the reliability problem, LP (Linear Programming) (Waight, et al., 1981) has

been widely applied to solve the ED problem. Thc LP algorithms allow adopting only piecewise linearized functions, and it is necessary to divide fuel cost curve into so many linear sectors in order to rcflect fucl cost function accurately. However, the more linear sectors create the more inequality conditions, which significantly degrade the merits of LP algorithms. Recently, it has been attempted to apply ANN (Artificial Neural Network) and GA (Genetic Algorithm) based on AI(Artificia1 Intelligence) to ED problems. Some of the interesting methods are GA (Walter and Sheble, 1992), SA (Simulated Annealing) (Wong and Fung, 1993) and PSO (Particle Swarm Optimization) (Park, et al., 2005), which are considered the most advanced. These methods have a severe defect that drastic increase in the number of genes or particles with the system size increasing guarantce neither optimality nor convergence. Up to date, ED algorithms havc developed on the basis of smooth continuous fuel cost functions. However, due to introduction of power market systems, the fuel cost functions presented by electric power company at bidding may be artificially manipulated different from the actual. In this reason, it is necessary that the ED algorithms

365

be able to accept various types o f the fiiel cmt functions, that is, step, linear, piecewise linear, and smooth function as well. On the othcr hand, it is supposed in the power market systems that gencrators are subjected to frequent onioff switchings Some generator maintains minimum output with must-run condition, while some generators are shut off when the market price goes down under a certain value This situation can be well treated by using the proposed h-P table method This paper proposes a new ED algorithm using a h-P table which is obtained by inverting the P-h curve. Hcre it is noted that the h-P tablc accommodates any kind or rue1 cost function and enables us to adopt the actual cost data obtained in the field test.

Especially, as Fig. 1 (h) depicts, discontinuities due to valve switchings makc the error larger. In order to reduce the approximation error, the cost curve is approximated to one-piece or two-piece linear functions, or higher order polynomials in economic dispatch. In order to obtain a precise incremental cost function close to the actual, one may use linearization of five or ten sectors or higher order of polynomials for approximation. Main idea of the proposed algorithm by h-P tables is to use sampling data of the incremental fuel cost curves instead of approximatcd ones, and to utilize the h-P table, which is obtained by inverting thc P-h table Details will be examined further in the next section Fig 2 illustrates the sampling and inverting process of the incremental fuel cost function.

2. THE P-h TABLES REFLECTING ACTUAL FUEL COST CURVE Conventional ED algorithms have been developed on the basis of incremental fuel cost functions which arc approximated to Iincar, piccewisc linear and/or higher ordcr polynomials However, adopting approximated cost functions always involves some approximation error? The errors are illustrated in Fig I(a>

I L ‘1‘ \ Inverting

Fig. 2. Curve Data Sampling and Inverting process P-h data can be obtained by table sampling from the field measurement data. This h-P table reduces the approximation error. Sampling error can be minimized by selecting properly small sampling interval. Here, it should be noted that the proposed approach is developed under a premise that each of the incremental fuel cost curves must be nondecreasing. Actual incremental fuel cost may show decreasing trend in very low generation but keeps nondecreasing trend for regular generating interval. Since minimum of generation is assumed for each generation, this premise can be generally accepted in the ED problem. If the P-h table are inverted to the h-P table for the same interval and values, generation output is determined by the function of h, pG,(A).

Poweroulput. M W

(a) Actual and approximatcd curvcs 14.006

5 13.000

8

E 12wo g,

-

2’- 11000

3. ED ALGORITHM USING THE h-P TABLE WlTHOUT LOSS CONSIDERATlON

z

-P

10000

50

60

70

!XI Net generation (mw)

90

1W

In order to develop a new ED algorithm, we utilize thc fact that each output power of all gencrators is determined by the incremental cost h. The total generating power is given by summation of each generating power. That is, total generating power, PGttl, is a function of h given by

110

(b) Including discontinuities due to valves Fig. 1. Incremental fuel cost curves

3 66

where PD is the total demand including estimated system loss. Since PGI,,(A)is nondecreasing, we can solve (1) to obtain A* with bisectional or linear interpolation methods, etc. In this method, it is noted that KuhnTucker conditions need not be considered since PGz(A)provides all information for minimum and maximum generation outputs (Madrigal and Quintana, 2000; Moon and Park, 2000).

optimal output is determined by substituting A*,that If generator 2 is added or eliminated, is, PG!(A*). PGIIi (A) is modified by adding or subtracting PG2(A) from P~,,, (A).

3.3 Proposed ED algorithm In this section, the proposed ED algorithm will be explained by using the main idea described in the previous section. The proposed algorithm is composed of the following 5 steps roughly. Siep 1) Take sample data for the incremenial fuel cost curve and construct the P-h table for each generator. Step 2) Establish h-P tables by inverting the P-h tables. Step 3) Consiruct the total generation function PGrr,(A)by summing up the h-P tablcs for all generators. Step 4) Calculate optimal A* by solving (1) by using the bisectiondl method andor linear inierpolation. Step 5 ) Calculate optimal dispatch for each generator with PG,(A*).

Fig. 3 shows an illustrative example with a 3generator system.

In the subsequent sections, the detailed implementation strategies of the proposed method are described.

Fig. 3. The summation of three generators’ ouiput power 3.I Must-run condition

Fig. 3 shows graphical analysis for three generators. Generator 1 and generator 3 are operated in the must-run condition which must generate its minimum output, while generator 2 is stopped for economical elkiency below a certain marginal cost. Conventional methods have no efficient algorithm to deal with this situation including must-run or not conditions. However, the condition can be easily applied into h-P tables by filling actual generator output below the minimum marginal cost for both cases.

In step 1, the measurement data obtained from field test can bc directly used without approximation. If the measured values are discrete, those values can be direcily used to construct P-h tables. In step 3, linear interpolation can be applied to obtain generation power for every generator at arbiirary h. In step 4, the optimal A- can be calculated by the bisectional method. Generally, this method is known to degrade the computational specd. However, the bisectional algorithm does not take much time to find Abecause it finishes within only n times for 2“ points of h. The proposed algorithm can be efficiently applied to the modules which need repeated ED computations as in UC. In step 5 , it calculates power generation for each generator with A* obtained in the previous step. Interpolation is also adopted for calculaiing the exact generation. Remarks

i) It can be applied to any type of incremental fuel cosi curves which may have nonlinearity, high order terms or discretc jump points as long as each of the Pc,(A) satisfies the nondecreasing assumption.

3.2 Arbitrary generator’s addition and elimination

The proposed algorithm can also be applied to ED associatcd with UC(Unit Commitmcnt) assuming rrequent onioff operations Tor each generator Total ), summation of generating power, P ~ ~ ~ ! (isAsimple three generators.

Afier selecting arbitrary

11) Once

A:,,,,,,

&,!(A) is constructed, modification of

P‘,,!(A) can bc pcrformcd with simple process in association with addition or elimination of arbitrary generators.

optimal incremental cost, A*,can be easily obtained by bisectional or linear interpolation method Each

367

iii) Arbitrary changcs in PG,(A) can bc casily takcn into account with the simple modification of

In this case, modified P-h table should be used instead

4. ED BY h-P DATA TABLE REFLECTING SYSTEM LOSS In thc previous scction, thc system loss has bcen neglected to explain the concepts of the main idea. Howevcr, thc system loss i s considcrcd to be an important factor in the ED problem in practice. The ED problem with losses can be also solved by using the h-P table? with slight modification The total generating power with losses is expressed as

.

.*-.--

Modify

,.

...- -...~ ., ,

,

Inverting

Fig. 4. Construction process of modified h-P tables considering losses

5. EXAMPLES

The loss-considered optimal condition is given by

PF, , IC, = PF, . IC, = 6 = PF, . IC,, = A" (3 )

Test is executed by using the proposed h-P table method. It is assumed that actual fuel cost curve is third order polynomial because it is difficult to gather thc data and obtain real solution. Actual fuel cost curve is assumed as ( 5 ) and its coefficients arc given in table 1.

where

F ( 4 )= A + B e

+ Ce' + D e 3 (5)

Table 1 Coefficients of actual fuel cost curves assumed by third order polynomial

The penalty coefficient for generator I , PF , can be calculated by the power flow calculation. The penalty factors can be slightly changed by the results or ED. However, this study uses approximated penalty factors calculated in the similar previous operation condition. By substituting (3) into (2), the total generating power is rewritten as

1

320

XO0

74955

695

9 6 8 E 04

127r 07

2

300

1200

12x5

7 051

738E-04

h 4 5 k 08

3

275

1100

1531

6 531

104E-03

998E-08

The h-P table is constructed by sampling actual incremental fuel cost curve from ( 5 ) by lambda interval o r 0.01. LineariLed incremental fuel cost function is one-line approximated as (6). Table 2 represents its coefficients.

(4) Table 2

Each of the optimal generating power is determined by A* divided by Pe . In this facts, modified h-P tables, P p d ( A ) ,can be obtained. Once PFd(/l)is constructed, optimal h can be found out by bisectional or linear interpolation methods in the same manner of the neglecting loss case. Fig. 4 illustrates the construction process of

e;,'"d (A).

First, P-h tables are modified by multiplying each penalty factor to h. And then, modified P-h tables arc invcrtcd to h-P tables. Process of thc considering loss case is the same as the neglecting except step 2.

One-line approximated incremental fuel cost function coefficients

I

320

800

6.837879

0.002363

2

qno

I200

6955216

0no176s

3

275

1100

6.40653

0.002492

5. I Comparison ojresults of each method

The results of the conventional and the h-P table mcthod are compared to the actual results. Total demand for test is set as 2300MW, 2500MW and 2700MW. Results are represented in Table 3.

368

Table 3 Generating Dowers and costs (Demand=2300MW) [MW] (;en, No.

Actual curve

Linearized h.

h-P ldbk

1

1j64.6849

667.2822

1j64.6849

2

828.0756

826.8844

828.0756

3

807 2395

805.8334

807 2395

Coat

21,033 4659

21,033 4779

21,033 4659

generators respectively. The system demand is set as 8000MW. In this problem, must-run condition considering case is compared with not considering case. Must-run condition is applied to 14 generators. Results are shown in Table 7 Table 7 Generations and costs in 50-generator system (Demand=XOOOMW) 1h8w1

Must-run-not-considered

(;en. N,\

Table 4 Generating powers and costs (Demand=2500MW)

1

2 3 4

r ~ w i Gen.No.

Actual cuwe

Linearized th

1-P table

5

1

724.9915

728.1 272

724.9915

2

910.1533

908.3442

910.1 533

3

864.8552

863.5287

864.8552

Cost

22.729.3246

22.729.3421

22.729.3246

6 7 8 9 10 I1 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 13 14 35 36 17 38 39 40 11 42 43 44 45 46 47 48 49

Table 5 Generating powers and costs (Demand=2700MW) Gen. No.

Actual curve

1,inrarred h.

h-P table

1

785.1824

788.9721

785.1824

2

992.1608

989.8040

992.1608

3

922.6568

92 1.2239

922.6568

Cost

24,455 1679

24,455 1940

24,455 1679

The conventional method results in some errors. On the contrary, the h-P table method shows exact results in all c a m . Results o f Cost also show that the h-P table method remarkablely improvcs the solution accuracy. 5.2 1-P table method considering losses

The h-P table mcthod is also tested in the lossconsidered case. In the test, the power demand is 2S00MW and losses are set to be 7SMW, 3 percent of the total demand. Penalty factors are given in Each generating powers are also Table 6. represented in Table 4. Generator 3 is taken as the slack bus. Table 6 h-P table method with losses (Demand=2300MW, Losses=75MW(3%))

5. 0 .

lMWl

Gen No

q

A,(= IC, PF,)

Total

PF,

I

764 5398

8 6529

10450

2

846 2951

8 6529

10255

1

758 I 6 5 0

8 6529

I 0000

Cost

21,629.0986

aldck

5.3 Example with 50-generator considering various types of incrementalfuel cost jiinctions

The proposed method has also been applied to the ED problem with SO-generator system which has various incremental fuel cost function types. The type of second order incremental fuel cost function is from generator I to 20. From generator 2 1 to 50, the function types are third order polynomial, two-piece linear function, and step function every ten

Must-run-considered

Genera11on

Cost

Cieneralioll

cost

130 130 460 465 160 455 455 470 80 80 0 300 162 I62 0 100 0 0 0 0

2884.66 2884.66

130 130 460 465 160 455 455 470 80 0 0 0 0 162 0 0 1x o 210 210 210 0 0 100 100 155

2884 66 2884 66

lll29.91 I1 120.36 4066.02 8544.62 8887.28 11205.19 2197.37 2720.1 I 7704.60 4253.40 3741.25 3041 .SO

0 0

100 100 155 I55 197 197 197 400

2077.89 2088.77 1902.56 1905.94 4867.75 4887.96 4908.19 3460.00

0

0 80 80 0

197 136 0 400

1112036 4066 02 854462 888728 11205 19 2197 37

0 0 0 0 0

3741.25

5702.75 6616.67 6648.07 6490.40

0 0 0 0

2077.89 2088.77 1902.56 1905.94 4867.75 3438 23 3460.00

0

0

0 3112.88 3076.57

0 0

300 300 335 70 70 120 120 120 210 210 210 2x0 3x5 8000

I55

1112991

MI1

10x14 63 11202.98 15990.35 1868.71 3868.74 2774.20 2774.20 2774.20 51 17.33 5177.33 5177.33 6584.94 9717.21 198577.60

80 80 0 0 0 300 300 425 70 70 120 120 120

210 210 210 2x0 385 8000

3 112.88 3076.57

10x1463 11202.98 18291.59 1868.71 1868.74 2774.20 2774.20 2774.20 5 117.33 5 177.33 5177.33 6584.94 9717.21 202259.20

0 0 0

0 0

From Table 7, it is known that the proposed algorithm can efficiently deal with must-run condition and mixed types of incremental fuel cost in the ED problem. In comparison with considering must-run condition case, not considering case is a little cheaper.

6. CONCLUSIONS This paper has presented a new approach to the ED problem bascd on a h-P table mcthod reflecting actual fuel cost curve. In order to apply actual fuel cost curve to the ED problem, the h-P table method uses sampling data obtained fioni field tests or

3 69

Programming S/ati,stir.s und Prohahility, University of California Press, Berkeley Park, J. B., Lee, K. S. (200.5). A particle swarm optimization for economic dispatch with nonsmooth cost functions, IEEE Transaclions on power systems, Vol. 20, No. 1, pp. 34-42 Madrigal, M., Quintana, V. H. (2000). An analytical solution to the economic dispatch problem, IEEE Power Engineering Review, Vol. 20, pp. 52-55 Moon, Y. H., Park, J. D. (2001). A new economic dispatch algorithm considering any higher order generation cost functions, International Journal ojElectrica1 Power & Energy System, Vol. 23, pp. 113-1 18 Waight, J. G., Bose, A., Shcblc, G. B. (1981) Generation dispatch with reserve margin constraints using linear programming, ZEEE Transaction on Power Apparatus and Sjntems, Vol. PAS-100, NO. l,pp252-258 Walter, D. C., Sheble, G. B. (1992). Genetic algorithm solution of economic dispatch with valve point loading, IEEE PAS summer meeting, Seattle, paper 92 SM 4 14-3 PWRS Wong, K. P., Fung, C. C. (1993). Simulatedannealing based economic dispatch algorithm, IEE Proceedings. C, Vol. 140, issue 6, pp. 509-

operations. Main idea of the proposed algorithm is very simple and very easy to apply to the ED problem. The proposed method has some advantages in must-run condition and arbitrary generator’s additionielimination. Test shows that the proposed method provides much-improved calculation results very close to the optimal solution compared with the conventional methods. It has been shown that the proposed method can nicely handle the lossconsidered case with slight modification in algorithm. REFERENCES

Allen J Wood, Bruce F. Wollenberg (1996). Power generation, operation, and control, John Wilcy & Sons John J Grainger, William D Stevenson, Jr (1994) Power system analysis, chapter 13, McGrawHill. Leon K. Kirehmayer (1958) Economic operation oJ power systems, chapter 2, John Wiley & Sons, New York Kuhn, H. W , Tucker, A. W (1951). Nonlinear Programming, in Second Berkeley Symp0.c rum on Mathematical Progruinming Statistics and

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Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

PUBLlCATlONS

POWER SYSTEM MAXIMUM LOADABILITY WITH GENERATION CONSTRAINTS C. E. M. Fernandes* R. S. Salgado* L. V. Barboza**

*

Uni~~er.siclaile Federal rle Santa Catcmna

CTC - EEL - LARSPOT Flot ioaripolas. SC. Brnzzl * * Un,*ioer.s.irladeCato'lica cLc relotas Gentro Federal de Educnpio Tecnolbyica Pelotas, RS, Brazil

Abstract: Thc control of reactive power aims at bot>h iiicroasing tlic limit of power t,ra.nsfer between areas ant1 monitoring the bus volt,a,ge ma,gnitiide. In order to increase tlie amount, of' energy transfer, suppliers must, produce reactive power close t,o t,lic p1;~ccwhere it, is nccdcd. Additionally, extra reactive power capacity niust, be kept to protect, the int,egrity of the system against, unforeseeable corihgencies and sitdden cliariges of powcr load levels. Tlie present work is addressed to the cletermination of operational solutions (that is, t>hosesatisfying all operat,ioiial h i t s ) of iiiaxiiiium loadability considering the reactive power reserve. A constraint) related to tlic quadratic dcviat,ioii of a pre-spccificd level of reac:tive power generation is included in h e stal.ic opt~imizat,ionproblem t,haf, models f he computation of t>liemaxiinurn loaclabilit,ysolution. This iiiodified problem is solved t,hrough t,he nonlinear version of t,lie Interior Point met,hod. It is shown how the crit,ical loadability arid the reactive power margins are modified as the priority of reactjive powcr rcscrvc changcs. Numerical rcsults obt,aincd .with a 57-biiscs system ilhistrat,e the app1icat)ioiiof the proposed approach. Keywords: Maxirnurri loadability, rcnct,ivc power gcnoration rcscrvc, opt,irnizabion.

1. INTRODUCTION

Ovcr tlic. last decadcs, economic prcssurc ha,i led to the continuous interconnection of bulk power systems and full use of existing facilities. This brought about more complexity to the power networks. such as to require theni to operate closer to thc limits. It also contributed to incrcasc the importance of problems associated with the maximum loadability of power systems, traditionally limited by transient stability or thermal condi-

tions. Besides. the problems of voltage stability and voltage collapse faccd by heoperation of power netrworkscan be foiincl in the literatiire. Approaches such as (Alvarado and Overbye, 1999) a.rc fociwcd on t,l-ie issues related to tlic rcactivc power ma.rket. Reference (Hao and Papalexopoulos, 1997) proposes mea,sures relating tlie reactive power requirements of the el( ric ixkwork t,o the cliange in the power demand. A few studies found in the 1it)cratiu-cconsidcr t>liciiiflueiicc of the rcactive power margins iii t.he critical operational power demand. This compromise provides addit.ional argument>sfor understanding t,he react,ive power c1ist)ribution;which is essent,ial t.o the assessment of tlic rcquiremcnt,s of power transactions. The loadability ma.rgin a.nd the reactive power reserve can be seen as very mance indexes whicli can be s efficient,QV cont,rolnieasurement.s. The guara,ntee of miiiimurn values t,o these aiiiount,s reduces the risk of 1oa.d shedding in t,he normal opera.t>ioiia.nd under cont,iiigencyconditions (Bao et al., 2003).

If' all operational coiistraink are considered, the optimimtion tcclmiqucs arc tlic iiiost suitablc strategy to solvc this problem. The predictorcorrector dlgorithin of the Interior Point Method is applied in (Irisarri cf al., 1997) to obtain the operational solution corresponding to the critical opcrational demand. The problem to bcl solved is analytically expreqsed as Mar p 3.t. pv, - (p,g P A p d , ) - PJ(v.6,a ) = 0

The research described in this paper is focused on the applicatjioii of sta.t,ic optimization met>liods t,o deterniine the critical opera,t,ional 1oa.dabilit~yof a power system, increasing simultaneously t,hc rcactivc power magins. Analytically, the proposed strategy consists of iiicluding an addit iond inequ;rlit,y constraint, relat,etl indirectly t~ot,he react,ive power reserve. This const,raJnt is expressed in tcrins of t,hc squascd deviation from a pre-specified levcl of reactive power gciieration. The new aspect of the proposed approach is the use of a variable limit to t,he definition of this inequality const,raint. The proposed methodology provides stcady statc powcr network solutions in which the power demand is maximized together with the reactive power reserve. Numerical resnits obtaiiicd wit.h t,he IEEE 57 buses lest-system arc iised to illustrat>etrhe applicat,ion of the proposed met liodologp.

+

- (62:J 4- PAQd, I - Q3 Pg","5 Pg, 5 P ; OgJ

v,"' 5 v,5 by)'

&I

a;i: 5 a k j 5 akJ (1) where the optirnimtion variables are: the voltage magnitude at all buses (K), the voltage angle at all buses except the reference bus (&). the transforines taps of tlic Load T,ip C h a n g ~trcinsforniers ( o n [ ) and the load parameter p. The equality wiislrairils represeiil the power balnrict. equdtioii at the load buses. The inequalities represent the upeiatioiial constraints on the power generation, voltage magnitudc dnd transformcr tap of thc LTCs. The power generation is represented equation (1) provides:

whcrc, Pj6 and QO,, are the active and rcactivc power load at the bus z, respectively, for a base caw: APdt arid AQd, rcprescnt the tliicction of activc and reactive power load change and p is t h e w-rallrd load p a m m P f w

0

372

t he opcr ational solution of t lie power nci work in steady state corrrsponcling to the maxii-nurn 1mwc.r load supply (voltage angle

0

0

and iriagiiitude at each bus. tap of the UI’C translormers and load parameter p, wkli all the ineqiialit,y constradnts satisfied; t,he Lagrange mult,ipliers corresponding t,o t,hc active a.nd rcxt,ivc powcr balance cquat>ionsat, the load buses, which are iilterpret)ed as instant,aneous sensitivity relationships bet>weeiithe load para.mct,er ziiid tlie power iiijeclions at the load buses; t>hc dual multipliers corresponding to tlic act,ive inequality constraints, which represent^ t,he instantaneous sensitivity rela.tions1iip of t>hcload parameter wit,li respect to the limit that, was reached.

In (Dai et al., ZOOO), the first order optimalit,y condit,ions of the optimization problem solved to determine the critical power loadability are simplified, providing a reduced and efficient. model which providcs thc critical power demand and/or the minimal load curtailment and the available transfer capability between t>he producers aid the costlimes. In these approaches the iiiaximuin power demand t.o he supplied is the only ta.rget. taken into account to establisli t,he tlispatcli of tlie power generation. The comhina.t,ionof t,he Continuation Method with the iionlinear version of the primal-dual int,erior point, algorit,hm is proposed in (Almeida and Salgado, 2000) to the determi1i:rtion of a sequence of opt,imnl solut,ions from a, base case t,o t,he point) of maximuin operat,ioiial loadabilit,y. Although ail act,ivcpower distribution of minimum cost, is cieterminecl for ea.ch solution, a high cornpittatiorial effort is required to determine this sequence.

3 . I\IAXTkKJkT T,OADARTT,TTY WTTH GENERATION CONSTRAINTS The modified version of the problem of the inaxinium operational powcr demand proposed in the prcsc~~t work consists of tlic inclusion of a constraint related to the squared deviation of the rcartive power generation from a pre-specified geiieratioii level. It is analytically expressed as 2

Q;‘) 5 Pq 1=1

wlicrc cyq, is t,lic pcnalty fa,ctor corrcspondiiig t,o the deviation of t,he react,ive power generat’ion from the prc-spec:ified value QiLaiid pq is the liiiiit of t,he t>otalweighted sum of the reactive power dcviat ion. Several alternatives are available to specily Ihe generation level a i d the associated penalty factors. The guarantee of a power margin is related to the prc-spccificd \ d u e s of t,l-ic powcr gcmcration. For exa.mple, if QE:” = Qby is selrrt,ed, t,he rve corresponding i.o t,he upper

limit is maximized. Thus, in order to liave these margins accordingly with the gencration capacity, tlie penalty factors are selected as

(3) Therefore, the optimization problem considering tlic iiiclusion of tlic constraint associated to tlie rcactivc powcr tlcviation is cxpresscd as 1Zla.7

-3.f.

wop - +pq

Pg3- (P:? f p a P d J ) - Pj(v, 6. 0,) d?gJ -

(@fJ

+ Pad?,

-0 3

=0

(v,fi, a ) = 0

i=l

(4) where, pq is the limit. associa,tedto the constraint, t,o be included; wo is the weight,ing factor assigned t,o t>lie1oa.d parameter aiitl wq represent,s the weighting faclor ributed to the power deviation const.raint,s. c ncgativc signal in the term of the objective fuiict,ion ensures that the non-negat,ive variable prl is minimized. The weigliting factors i~()and u4a,redirectly associat,cd tmothc im,por.tance of t8herespectlive performance indexes. They allow to obt aiii solutions favorable t,o t,he loadability margin or t>ot,he reasctfivepower reserve. Equation (4) could be also interpreled as a niult,i-objcctivc optimization problem, wlicro the a.im is to maximize the power demand and sirriultaneously to rriiriirnize t.he deviation of a prespecified power generation level. The iiiodeling of tliis problem can be seen as a conibinatAon of tlic rnct,kiodologicswhich iisc vvc:igkitjingfactors as well a.s inequality const mints to deal hierarchically with tlie performance indexes t>obe optimized. Observe that fixed values selected wrongly could make impossible to satisfy the constraint on the deviation of t,lic power gcncration. Tlius, in order t,o faci1itat)ethe scarch for t,he optimal solut,ion of blem expressed by equat,ion (4), the papq is coiisiciered im opt irnization mriable. hdditiona.lly, in order to limit tlie incursions of tliis ~iewvariable, a rion-riegativity coristrainit is a.dded to the opt~imizationproblem. 4. KUMERICAL RESULTS

In order to illustratc the application of the proposed methodology, numeriral results obtained with thc IEEE 57 buscs systcrn arc prcscntctl in this section. The Predictor-Corrector of the Primal-Dual Tnterior Point mrl hod WRS iisc~lto

373

l'able 2. Variation of the weighting factor d q - powcr demand and power inargins.

solve the optirnization problem r epresentecl by equation (4). In all casc5, the prc-spccificd valuc of the reactive power generation was Q6pJ' =

w.

The main objectives of tlicsc tests wcrc:

css t,lic sohitjions obtaincd t,lirougli t~lic at,tribut,ion of different, weighting fa,ct'or to the loadabilit8yand reactive power devia,tion; to vcri& t,he margins of rcact,ivc power rcserve determined with different penaky factors; to observe the coniproinise beheen t,he critical operational demand and t,he maintenance of a prc-specified rcactivc power margin: t,o assess the effect, of the transformer tsapsiri the constrained loadability problem proposed here; to observe the coInput,ational effort. added to the it.crat>iveprocess of tlie ma,ximurn loada,bility problem due to the inclusion of the reactive power constraint.

30 f

\

m

Unity Weighthg Factor Tablcs 1 and 2 sumniarizc t,hr: rcsults obt,a,inctl with cvq = 1 for five values of uq = 0. The s o l u h n oblainecl wit,h wq = 0 corresponds l,o the conventional maximum loadability problem of equa,t,ioii(1). The increase of the factor wq (I, 10, 100 and 1000) means tliat, a liiglicx priority i s given to the minimum deyiat ion Gorri the reactive power level. This results in sniallcr critical loadability (1612.43 t.o 1300.12 MW and 433.16 ho 349.25 hfvar), reactive power geiieratiori levels (391.02 to 249.69 kIvar) and deviations (148.53 to 7.20 M w r ) and 1a.rger reactive power masgins (93.97 t,o 235.30 Mvar).

[

Total generation

Po

100 1000

I 1

111:3 51 1311.40

]

I

302.02 249.69

I I

I I

I

800

1wo

In this ca.sc, the weighting factors aqi are as cxpressed by equation ( 3 ) . Nunierical rcsuks prcsented in tables 5 and 6 show the active and rcact,ivc power generation, t,he active and reactive power margin arid tlic pcrccnt 1oa.dabilitv (wit,li rcspcct to thc uppcr powcr gciicration limit) of each generating unit. It can be observed that, if the capacity of t,he gcmerat'or is t,aken into account t,o assign the weighting factor, as the priority of the minimum reactive power deviation increases (w,) t,he loadability of each generating unit knds to be more proportional to the capacity of the generator. wit,h a better distribution of t.lie reactive power margin.

Power deviation

182.19 50.35

€00 weights

upper power generation limit) of each generating unil. Since the capacity of llic generator is not taker1 irito accoiiiit to assign tlic weighting fxtoib the reactive power deviation (aq= I ) , some units opciatc at the upper ieactive power limit without any power margin (units 2. 3, 9 dnd 12).

I

I

400

P"

Fig. 1. Variation of the parameters p and prl

Table 1, Varia.tion of the weighting factor uq - power generation a,nd deviation from it. prc-spccificd level. Weight

-x-

59.53 7.20

~

Figure 1 shows the parameters associated to tlie 1oa.d ( p ) and t,o t'he reactive power deviation (p,). As t>hef x t o r wq beconies higher, one of t.liese two parameters increases ( p q ) as the ot,her dccrcascs ( p ), showing the compromise bctwccn the inaxiiiium loadability and the ma.intenaiice of a reactive power margin.

4.3 Effect of the Transformer Taps Tables 7 and 8 shows the influence of the transformer taps in t.he critical loadability- arid reactive power reservc. These resiilts were ohtaincxl by fixing a,i1 transfoririw ta,ps iii t,he valiie corresponding

Tablcs 3 and 3 show Ihc activc and reactive power generat,ion, t,he act,ive arid react.ive power margin and the percent loadw,bility (wit.h respect to t h e

3 74

d C iari , =

Table 4. Variation of

d4,

Generation 71.97 49.99

50

Margin 27.03 0.01 0

1.0

uq = 1.0.

w q - 100

BUS

1 2 3

Table 3. Variation of

up- 1000

% Load. 72.7 100.0 100.0

Generation 73.18 49.99

50

Margin 25.82 0.01 0

%) Load.

Q""

Qerp

73.9 100.0 100.0

99

99 50 50

50 50

Table 5. Variation o f d q , a4 = Q"'1-9". 1

Bus ~~

1 2 3 6 8 9 12 Total

1

= 0. i Margin 32.61 0.02 0.01 8.03 52.31 0 0 92.08

I

Wn

Generation 66.39 49.98 49.99 26.07 47.60 80 70 391.02

96 Load. 67.1 100.0 100.0 77.1 47.7 100.0 100.0

=1 Margin 32.57 0.06 0.01 8.03 52.3 0

I

*'n

Generation 66.43 d9.94 49.99 26.97 47.7 80 70 391.03

n 92.97

Table 6. Variation of

to the conventional maxiinurn loadability problem. It can be observed that the reactive powcr margins are modified with some generating units rcacliing tlicir reactive power limits. Tlic total amotmt of' reactivc powcr dclivcrcd by the generators is bigger, indicating that there is a larger ainount of reactive powcr circulating in tlie power network and how effective the transformers are to better dislribut e the reactive power margins.

% Load.

aq =

dJq.

67.1 99.9 100.0 77.1 47.7 100.0 1no.o

= 10 Margin 24.13 0.07 1.66

I

Wn

Generation 74.87

49.93 48.31 27.65 60.6 62.02

m i l

386.81

7.55 39.4 17.98 6. Ci 97.19

'% Load. 75.6 99.9 96.7 79.0 60.6 77.5 90.6

6.

tlie reactive power deviation. The values presented in this table correspond to thc coniputatiorial time in seconds. Tliese results were obtained in a personal computer AMD ATHLON 1.2 GHz. In both cabes, an incrcase in the computational effort is noted, mainly for d J q2 100. However. as previously pointed out, there is no considerable changes in the maximum power demand to the solutions obtained to d q 2 100 and thus. the computational effort addcd by the inclusion of the reactive power constraint is relatively small, as can be observed by coniparing ~ o w s2 and 5 of tablc 9.

Table 9 shows the computational effort required bv the iriclirsion of the inequality const rairit 011

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Table 7. Results for fixed tra.risforrrier taps, a,* = &.

Table 8. R,esults for fixed transformer t,a,ps,ctq = &. Bus 1 2

(Jq

Gencration 81.79 -49.98

= 100 Margin 17.21 0.02

1000 Ma.rgin 17.15 0.02

dq =

'X Load.

Gencration 81.85

82.6 100.0

-49.98

'X Load. 82.7 100.0

Q" 99 50

Qesp

99 50

Table 9. Computational effort.

I

100 1000

1

1.792 1.542 1.932 3.224

1.392 1.782 1.452 2.914 5.237

I

dit>ions. IEEE Transactions on Power Sgsterns 15(4), 1204-1211. hlvaratio, F. and T. Ovcrbyc (1999). Mea,suring reactive power mahket. In: Proceedings o,f the IEEE/PES Winler Meeting. Vol. 1. pp. 294296. Bao, L., Z. H~iarigand W. Xu (2003). Online volt,age st>abilit,ymonitoring using va,r reserves. 1EEE Transactions on, Po,wer Systems 18(4), 1461-1469. Ca.nizares, C. A. and F. L. Alvarado (1993). Point of collapse and cont,iriuat,ioriniet,liod for large ac/tlc systems. IEEE Trunsactions o n Power Systems 8(1), 1-8. Dai, Y., J. D. McCalley and V. Vittal (2000). Sirnplificatioii, expalision and enliaiiceiiieiit of tlircct iiit>eriorpoint algorit hnr for powcr system maximum lodabilily. IEEE Transnckions on Power Systcms 15(3), 1014-1021. Hao, S. and A. hpalcxopoulos (1997). Rcactivc power pricing a.nd management. IEEE Truri.9acb,ions on Power Sysbem,s 12(1), 95-104. Trisarri. G. D., X. Wang, J. Tong arid S. Mokhtari (1997). hfaximum 1oadahilil.y of power t,crns using noii linear iiit,crior point, rriethod. IEEE Transactions on Power Syst r r / ~12(1), s 162-172. SeycM, R. (1994). Pmrtacd Bifurcation i d Stobility Analysis - From Epu,il?;briumto Chaos. Springer - Verlag New York Inc.

5. CONCLUSIONS Alt'ernat,iveoperat'ional solutions can be obtained t-odifferent levels of crit>icaldemand. Ea.ch of these solutions sabisfies the power balance a i d bhc operat,ional const,raint>s.The use of tliese solutions depends on the desi.red operational condition of the power system. If the choice for the adequate operational solution t,akcs into a.ccount not only the conventional criteria like the volt,age magnitude level, powcr loss in the traiisniission system etc, the proposed met,hodology can he useful t.o take int,o account the react,ive power margin as the tlccisioii c,rit>cria.The a,ddit,ionof a const,ra.int related to the reactive power deviation, represerikd by an inequality: rcsrilt,s in an increase in t.he cornput,at,ioiialeffort, to reach the convergence ol the ikralive process, mainly i i high values are attributed to thc a-cightiiig fa.cturs. Future works ilecl arialysis of (,lieileralive prucess.

REFERENCES Ajjarapii. V. aiicl C. Christy (1991). The coiitinuation power flow: A tool for strady state volt-

age stability analysis.. IEEE Transactions on Poapr S y s t e m s 10, 30;1-310. Almcitla, K. C. and R. Salgado (2000). Optimal power flow solutions under variable load con-

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OPTIMAL ALLOCATION OF STATIC VAR COMPENSATORS USING MODAL ANALYSIS, SIMULATED ANNEALING AND TABU SEARCH Somayeh Ebrahimi", Malihe Maghfoori Farsangi*, Hosien Nezamabadi-Pour", and Kwang Y. Lee**

"Department of Electrical Engineering, Kerman University, Kernzan, Iran ""Departnzent of Electrical Engineering, The Pennsylvania State University, Uriiversily Purk, PA 16802, USA

Abstract: This paper investigates the ability of tabu search (TS) and simulated annealing (SA) optimization methods to deal with optimal placement of Static Var Compensators (SVC) in a large power system based on its primary function, where the optimization is made on two parameters: its location and size. 'I'he primary function of an SVC is improving transmission system voltage, thereby enhancing the maximum power transfer limit. Modal analysis is used to place several SVCs in the power system and the results obtained are compared with the results of applied TS and SA techniques. The results show that SA can give a good suboptimal placement while TS gives an optimal solution. Since by using the modal analysis alone SVCs may not be placed optimally in the power system, the study is carried out in two steps. In the first step, by using the modal analysis, the critical area of the power system is identified in view of the voltage instability. In the second step, once the weak area is identified, the SA technique is applied to get the level of compensation by the SVCs. Copyright 02006 IFAC Keywords: S v c , modal analysis, simulated annealing, tabu search, voltage Stability.

1. lNTRODUCTlON The daily operation of a power system requires that the voltage protile be within pre-specified limits. Due to a continuous growing on demand for electricity and system interconnections, and also due to economic and environmental considerations to expand the generation and transmission capacities, power systems worldwide are operating closer to their transfer capability limits that results in a higher possibility of voltage collapse. Due to several major blackouts that have happened around the world, voltage collapse phenomena in power systems have become one of the important concerns in the power industry over the last two decades. In the last decades, efforts have been made to find the ways to assure the security of the system in terms of voltage stability. It is found that FACTS devices arc good choices to improve the voltage profile in

power systems that operate near their steady-state stability limits and may result in voltage instability. Many studies have becn carried out on thc use of FACTS devices in voltage and angle stability. Taking advantages of the FACTS devices depends greatly on how these devices are placed in the power system, namely on their location and size. In a practical power system, allocation of the devices depends on a comprehensive analysis of steady-state stability, transient stability, small signal stability and voltage stability. Moreover, other practical factors such as cost and installation conditions also need to be considered. A great deal of work has been carried out to develop analytical and control synthesis tools to detect and avoid voltage instability. In the literature a tool has been reported based on the determination of critical modes known as modal analysis. Modal analysis has

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been used to locate SVCs and other shunt compensators to avoid voltage instability. The work carried out by Mansour, et al. (1994) is one of the works about using of modal analysis. Over the last decades there has been a growing interest in algorithms inspired by the observation of natural phenomenon. It has been shown by many researches that these algorithms are viable candidates as tools to solve complcx computational problcms. For example, various heuristic approaches have been adopted, including genctic algorithm, tabu search, simulated annealing, ant colony, particle swarm, etc.

power in a power system. For this, several SVCs are placed in a large power system based on their primary function, which is the voltage stability. To locate SVCs based on the voltage stability, modal analysis is used. However, using the modal analysis, the SVC cannot be placed in the power system optimally due to the unknown optimal size of SVC. For this reason, to place SVC efficiently, two heuristic methods are used; simulated annealing and tabu search, that are considered as global optimization tcchniques. A bricf description about the modal analysis, SA and TS are given in the next section.

Tabu search (TS) and simulated annealing (SA) has been paid attcntion on different applications in powcr systems since 1995 and 1990, respectively. Among these applications a few work has been done on FACTS devices. Bhasaputra and Ongsakul (2003)proposed a hybrid tabu search and simulated annealing approach to determine optimal settings of the FACTS parameters for different loading levels, and then find the optimal placement of the multi-type FACTS devices by solving optimal power flow to minimize the total generator fuel cost. Cerbex, et al. (2003) used three heuristic methods, simulated annealing, tabu search and genetic algorithm, to locate FACTS devices in a power system to enhance the power system security. Parallel tabu search was applied by Mori and Goto (2000) for the optimal allocation of UPFCs to maximize the available transfer capability. Mori (2UUI) placed SVC in distribution system using parallel tabu system. Tabu search was used by Kim, et al. (2001)to tune the input and output gain of a Fuzzy Logic Controller (FLC) for thyristor controlled series compensator (TCSC) for a low frequency oscillation in a power system. Similar study was done by Hwang, et al. (2004). Simulated annealing was used by Chen, et al. (1998) to design output feedback controllers for TCSCs in a power system to damp the critical modes. A twostage optimization method using an expert system and simulated annealing to solve the SVC placement problem is carried out by Jwo, et al. (1999). Hsiao, et al. (1994) developed a computer package based on SA for multiobjective SVC planning of large-scale power systems. In the above methods, the attention has been focused upon 1R2 losses. Relatively little effort has been directly involved with voltage stability improvement. Similar study was carried out by Chang and Huang ( 1 998). Simulated annealing algorithm was used by Abido (2000) for robust power system stabilizer (PSS) design to get optimal settings of the PSS parameters. Also, tabu search and simulated annealing have been applied to several power systcm problcms such as planning, economic dispatch, unit commitment, network reconfiguration, ete., which can be found in the literature. In this paper, SVCs are used to maintain the nodal voltage magnitudes. The problem formulation is how to place SVCa that provide compensation for reactive

2. VOLTAGE STABILlTY ANALYSIS Voltage stability is the ability of a power system to maintain acceptable voltages at all buses in the system under normal operation as well as following disturbances. Voltage stability can be categorized to large-disturbance and small-disturbance voltage stabilities. Large-disturbance voltage stability is the ability of the system to control the voltage after being subjected to large disturbances such as system faults, loss of load or generation. Small signal voltage stability is the ability of the system to control voltage after being subjected to small perturbations, such as gradual changcs in loads. In this paper three techniques are used for analysis of voltage stability, which are briefly explained.

2. I Placenzent Lking Critical Modes of Instability (Modal Analysis)

Voltage

Modal or eigenvalue analysis of the system Jacobian matrix near the point of voltage collapse can he used to identify buses vulnerable to voltage collapse. When modal analysis is used, there is no need to drive the system precisely to its “nose point” to ensure that a maximum level of stress is reached. The eigenvector of the critical eigenvalue gives information about the loads responsible for the voltage collapse. The main conclusion from this is that voltage collapse is actually the collapse of a modal voltage. In which case, the power system cannot support a particular combination of reactive power loads.

2.2 Siniulated Annealing

Simulated annealing is a derivative-free optimization technique that simulates the physical annealing process in the field of combinatorial optimization. Annealing is the physical process of heating up a solid until it melts, followed by slowly cooling it down by decreasing the temperature of the environment in steps to obtain a perfect structure corresponding to a minimum energy state. SA is a global search strategy, which tries to avoid local minima by accepting worsc solutions with a

378

probability. The probability to accept a solution is defined according to the Metropolis distribution:

I' where x and y are an initial and new solutions, respectively, and A,) is the evaluation of the objective function at a solution. SA starts from an initial solution x and then a solution y is generated. If y has been improved from x, it will be accepted; otherwise, y will be accepted as the current configuration with a probability proportional to the difference in the value of the objective function,f(x)fcv), on temperature Tas shown in (1). 2.3 Tabu Search

Tabu search (TS) algorithm is used to solve combinatorial optimization problem (COP). This mechanism is somewhat similar to SA, but the main difference between the two search algorithms is that TS uses a flexible memory to store the information and data of the solutions in each iteration. This is to get to the lower objective function values with the hclp of the information stored, whilc spccial features are added to escape from being trapped in the local minima. TS searches the neighbourhood of the current solution to find the next solution with more improvement in the value of objective function. In order to avoid returning to the local optimum, TS uses a list which is called Tabu List. The elements of the tabu list are called tabu moves. Tabu list stores the moves in a data structure such as finite length and restricts the local search algorithm in reusing those moves for some iteration. The number of iteration a move is kept in the list is called tabu list size. Since the tabu list may forbid certain worthy or interesting moves found so far, this tabu moves will be accepted as the next move and will be released from the tabu list if they are judged to be worthy. This override of the tabu list is called aspiration criterion.

regions of the solution space so far to diversify the search solution. If there is a better solution in the outer spaces of the local search the search space changes it's place to that new region. It should be mentioned that a frequency counter denotes the number of times the solution having been visited throughout the solution process. 3. STUDY SYSTEM A 5-area-16-machine system: The system shown in Fig. 1 consists of 16 machines and 68 buses. This is a reduced order model of the New England (NE) New York (NY) interconnected system. The first nine machines are the simple representation of the New England system generation. Machines 10 to 13 represent the New York power system. The last three machines are the dynamic equivalents of the three large neighboring areas interconnected to the New York power system.

Modal analysis, simulated annealing and tabu search are used to locate SVCs optimally in the power system shown in Fig. 1. Starting from an initial load, the SA is applied. All loads are increased gradually ncar to the point of collapse. To locatc SVC by simulated annealing, suitable buses are selected based on 30 test runs. Thc obtaincd rcsults by SA arc as follows: 27% of results show that the first SVC should be placed at bus 48 with 156 Mvar (the bestso-far), 13% of results show that a 186 Mvar SVC should be placed at bus 47, and 7% of results show that the first SVC should be placed at bus 40 with the size of 145 Mvar. Bus voltage magnitude profile of stressed system after placing SVC at buses 40, 47 and 48 are shown in Figs. 2-4, respectively. Using modal analysis, it is found that the weakest area in this power system is in the N Y system near bus 40, as illustrated in Fig. 5. Fig. 6 shows the profile of the voltage when system is heavily stressed and is reached to the point of collapse. Based on modal aidysis, bus 40 is a good candidate to place the first SVC. Using the modal analysis, only the weak area can be determined. However, it cannot give any information regarding the size of SVC.

The Tabu search algorithm used in this paper follows a rather straight forward pattern. As soon as a trial solution is generated, it is checked to see if it's in the tabu list or not. If so, the search algorithm will then searches for the frequency counter related to this trial solution. If the frequency counter is smaller than a threshold, it will add up the frequency counter by one, and starts to search for the next move from the neighbourhood of the current solution. This mechanism is called intensqication. And if the frequency counter was more than the threshold the move will be penalized for some iteration and the search will therefore be directed to unexplored

Fig. 1. Single line diagram of a 5-area study system.

3 79

Fig. 2. Bus voltage magnitude profile of stressed system after placing SVC at bus 40 with the size of 145 Mvar.

Fig.

5. The critical eigenvector corresponding bus number.

and the

Fig. 6. Bus voltage magnitude profile when system is heavily stressed. Fig. 3. Bus voltage magnitude profile of stressed system after placing SVC at bus 47 with the size of 186 Mvar.

Fig. 4. Bus voltage magnitude profile of stressed system after placing SVC at bus 48 with the size of 156 Mvar. Since the size is playing an important role for the SVC to be effective, simulated annealing is used to find the Mvar size needed for SVC. To find the optimal compensation level, first, the SVC is placed in the power system at bus 40, and then using simulated annealing, the Mvar size of SVC is obtained, which is 145. The obtained level of compensation is the same as the 7% of the results obtained by simulated annealing when bus 40 was selected. After placing the first SVC at bus 40, once again the loads are gradually increased. Based on Figs. 2-4, the best recovery of the voltage profiles is when SVC is

located at bus 40. On the other hand the obtained Mvar size of the SVC when located at bus 40 is less. It means that SA is a good tool to get promising suboptimal results. Therefore, since the SA failed to identify bus 40, which is vulnerable to voltage collapse, only the modal analysis is used to place the second SVC. Then SA is used to find the level of compensation for the SVC. Using the modal analysis, as shown in Fig. 7, the second worst bus is identified which is bus 50. Fig. 8 shows the voltage profile when system is under stress. Again simulated annealing is used to find the optimal size of the SVC at bus 50. The obtained Mvar size is 155 Mvar. Now, tabu search is applied to find the best place of SVC in the power system shown in Fig. 1. Once again, all loads will increase gradually near to the point of collapse. As in the case of simulated annealing, to locate SVC by tabu search, suitable buses are selected based on 30 test runs. The obtained results by tabu search are as follows: 86.66% of results show that the first SVC should be placed at bus 40 with 138 Mvar, 6.66% of results show that a 136.4 Mvar SVC should be placed at bus 48, and 6.66% of results show other buses to place SVC. The results show that tabu search has the ability of finding the optimal location better than SA. The fitness and the level of compensation are shown in Figs. 9-1 0. Also, by applying modal analysis and then placing SVC at bus 40, TS finds the level of compensration to be 138 Mvar.

380

Fig. 7. The critical eigenvector and the corresponding bus number.

Fig. 9. Convergence characteristics of TS in finding the solution, 145 Mvar SVC at bus 40.

Fig. 8. Bus voltage magnitude profile when svstem is heavilv stressed.

Fig. 10. Search process for finding the level of compensation.

4. CONCLUSIONS In order to take of the advantages of the FACTS devices in the power systems, two SVCs are placed optimally in a large power system. For this purpose, the location and size of SVCs are obtained using modal analysis, simulated annealing and tabu search. In finding the best place based on their primary function, both modal analysis and tabu search give the same results. While simulated annealing gives a suboptimal solution. The work carried out by other researches with simulated annealing as reviewed in section 1 reported promising results, but in this study, although choosing of the objective function was done carefully, simulated annealing did not identify optimal place of SVC. In placing the SVC by simulated annealing, the results are not the same as those obtained by modal analysis and tabu search, and it was shown that the result obtained by SA is not the best. However, SA gives a good suboptimal result (choosing bus 48), and the best sizes of SVCs can be found by SA (by placing SVC at bus 40 and 50). Although, the obtained size of SVC by SA and TS are not the same but they are close. This inconsistency is due to the tuning of parameters in SA and TS. Taking the advantages of the FACTS devices depends greatly on how these devices are placed in the power system, namely on their location and size. Therefore as shown in the results, by

placing SVC based on the modal analysis and then finding the level of compensation by simulated annealing or tabu search, SVC can be placed optimally (sub-optimally) in the power system. REFERENCES Abido, M.A. (2000). Robust design of multimathchine power system stabilier using simulated annealing. IEEE. Trans. Power Systems, 15 (3), pp. 297-3043. Bhasaputra, P. and W. Ongsakul, (2003). Optimal placement of multi-type FACTS devices by hybrid TSISA approach. Proceedings of the 2003 International Symposium on Circuits and Systems, 3, pp. 285-290. Chang, C.S. and J.S.Huang (1998). Optimal multiobjective SVC planning for voltage stability edhancement. TEE Proc.-Gener. Transm. Distrib., 145 (2). Chen, X.R, N.C. Pahalawaththa, U.D.Annakkage and C.S.Kumble (1998). Design of decentralized output feedback TCSC damping controllers by using simulated annealing. TEE Proc.-Gener. Transm. Distrib., 145 (5), pp.553 558. Gerbex, S., K.,Cherkaoui, and A.J Germond (2003). Optimal location of FACTS devices to enhance ~

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power system security. Power Tech Conference Proceedings, 3. Hsiao, Y.T. , H.D Chiang, C.C. Liu, and Y.L. Chen (1994). A computer package for optimal multiobjective VAR planning in large scale power systems. IEEE Trans. Power Sys., 9 (2), pp. 668-676. Hwang, G.H., J.H. Park; K.J. Mun and H. T. Kang (2004). Design of fuzzy logic controller for firing angle of TCSC using real-type tabu search. The 30th Annual Conference of IEEE Industrial Electronics Society, 3, 2-6 Nov. 2004, pp.2182-2187. Jwo, W.S. , C.C. Liu and Y.T. Hsiao (1999). Hybrid expert system and simulated annealing approach to optimal reactive planning. 1EE €‘roc.-Gener. Transm. Distrib., 142 (4), pp.381-385. Kim, W.G.; G.H. Hwang; H.T. Kang; S.O. Lee and J.H. Park (2001). Design of fuzzy logic controller for firing angle of TCSC using realtype tabu search. IEEE International Symposium on Industrial Electronics, 1, 12-16 June 2001, pp. 575 - 580. Mansour, Y., W. Xu, F. Alvarado and C. Rinzin( 1994). SVc placement using critical modes of voltage instability. IEEE Trans. Power Systems, 9 (2), pp. 757-763. Mori, H. and Y. Goto (2000). A parallel tabu search based method [or determining oplimal allocation of FACTS in power systems. International Confcrcncc on Powcr Systcm Tcchnology, 2, pp. 1077 1082. Mori,H. (2001); Optimal allocation of FACTS devices in distribution systems, IEEE Power Engineering Society Winter Meeting, 2, pp.936 - 937. ~

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Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

PUBLlCATlONS

DISTRIBUTED MPC STRATEGIESFOR AUTOMATIC GENERATION CONTROL Aswin N. Venkat * James B. Rawlings *

Ian A. Hiskens **,I Stephen J. Wright ***

* Dcrpartment of Chemical and Biological Engineering,

University of Wisconsin, Madison, WI-53706

** Drpartinerz f of Electrical and Computer Engineering, ***

University of Wisconsin, Madison, WI-53706 Computer Sciences Department, University of Wisconsin, Madison, WI-53706

Abstract: The paper considers distributed model predictive control (MPC)strategies that are appropriate for controlling large-scale systems such as power systems. The overall system is decomposed into subsystems, each with its own MPC controller. To achieve performance equivalent to centralized MPC, these distributed regulators must work iteratively and cooperatively towards satisfying a common, systemwide control objective. Automatic generator control (AGC) provides a practical example for contrasting the performance of centralized and decentralized controllers. Keywords: Distributed model predictive control; automatic generation control; power system control.

1. INTRODUCTION

Model predictive control (MPC) is emerging as a sophisticated, yet practical, control technology. This model-based control strategy uses a prediction of system behaviour to establish an appropriate control response. A number of benefits follow from using MPC, including the ability to account systematically for process constraints. The effectiveness of MPC depends on models Of

accuPacy and 'On the

ity of sufficiently fast computational resourcesrequirements that limit the application base for MPC' Even so/ abound in the Process industries, and are becoming more wide2003; Carnacho and spread (Qin and BadP"ellf Bordons, 2004).

often perform poorly when the subsystem interactions are significant. Centralized MPC, on the other hand, is impractical for control of largescale, geographically expansive systems, such as power systems. A distributed MPC framework is appealing in this context, but must be designed to take account of interactions between subsystems. Interaction issues are crucial to the success of distributed MPC, and are discussed further in Section 3. Automatic generation control (AGC) provides a topical example for illustra ting the performance of distributed MPC in a powep syqtem setting. The purpose of AGC is to regulate the real power output of generators, with the aim of controlling system frequency and tie-line interchange (Wood and Wollenbere, 1996). AGC must account for various limits, including restrictions on the amount and rate of generator power deviations. VI

Traditionally, control of large, networked systems is achieved by designing local, subsystembased controllers that ignore the interactions between the different subsystems.These controllers Correspondingauthor. Email : hiskens@ e n g r .wisc .e m

Flexible AC transmission system (FACTS) devices allow control of the real power flow over selected paths through a transmission network

383

(Hingorani and Gyugyi, 2000). As transmission systems become more heavily loaded, such controllability offers economic benefits (Krogh and Kokotovic, 1984).However FACTS controls must be coordinated with each other, and with AGC. Distributed MPC oflers an ellective ineaiis ol achieving such coordination, whilst alleviating the organizational and computational burden associated with centralized control. 2. MODELS Distributed MPC relies on decomposingthe overall system model into appropriate subsystem models. A system comprised ol hl interconnected subsystems will be used to establish these concepts.

2.1 Centralized model The overall system model is represented as a discrete, linear time-invariant (LTI) model of the form .r(k

+ 1) = AT(L)+ B u ( k ) dk)= W k ) .

(1)

in which I; denotes discrete time and

3. DISTRIBUTED MPC FOR POWER SYSTEM CONTROL 3.1 Preliminaries Given the PM for each subsystem 1 = I , . . . , A l , we consider two formulations for distributed MPC: communication-based MPC and cooperationbased MPC. The suitability of either distributed MPC framework for systemwide control is assessed in the sequel. In both approaches, an optimization and exchange of variables between subsystems is performed during a sample time. We may choose not to iterate to convergence. The set of admissible controls for subsystem z. [it C R”&% is assumed to be a non-empty, compact, convex set containing the origin in its interior. The set of admissible controls for the whole plant I1 is defined to be the Cartesian product of the admissible control sets of each of the subsystems. For subsystem / at time k, the predicted state vector at time t > k is denoted by ~ ~ ( t l k ) . We havex.,(klk) = r L ( k ) . The cost function for subsystem 1 is defined over an infinite horizon as follows: & (G,,%,T?,(k)) =

2

2k(tlk)’Q,(t).&(tlk)

+ ut(tlk)’Rz(t)u,(tlk),

(4)

t=k

where Q7 > 0, R,> 0 are symmetric weighting matrices and xt(k)7 [ z , ( k + l l k ) ’ , z , ( k . . .]‘, u,(I;)= [u,(I;lI;)’, .,(I; + Ilk)’, . note the infinite horizon state and input trajectories, respectively, for subsystem L. C .

=

[21‘

2Af’]

22‘

‘

z/ = [VI‘

1/2’

7J\J‘]

‘

For each subsystem 7 = l . . . .,AP, the triplet ( u z2, , . g l ) represents the subsystem input, state and output vector respectively. 2.2 Decentralized model

3.2 Communication-based MPC For communication-basedMPC, the optimal stateinput trajectory (z$(k),uf(k)) for subsystem i at iteration p is obtained as the solution to the following optimization problem

In the decentralized modeling framework, the effect of the external subsystems on the local subsystem is assumed to be negligible. The decentralized model for subsystem i , 7 = 1,.. . , M is written as ct(k

+ 1) = A t r t ( k ) + Bttut(k) uz(k) = C d % ( k ) .

+

(2)

2.3 Partitioned model (PM) The PM for each subsystem z incorporates the eflect ol the local subsystem variables as well as the effect of the states and inputs of the interconnected subsystems. The PM for subsystem 2, as the name suggests, is obtained by consideringan appropriate partition of (l),as follows: xz(k

J f 7

u,(tlh) E R,,k 5 t 5 I, ut(tlk)= 0, k N 5 t.

+ n.- 1 (5)

The integer N denotes the control horizon. For notational simplicity, we drop the time de en dence of ( z p ( k ) .uf(A))and represent it as (2,. $ uf-). For each subsystem i at iteration p, only the subsystem input sequence uf is optimized and updated. The other subsystems’ inputs are not altered during the solution of (5); they remain at their values from iteration p - 1. The objective function is the one for subsystem i only. In the communication-based MPC framework, each subsystem’s MPC has no information about

+ 1) = & & ( k ) + Bttut(k) + C ( A % J Z J +( ~B)‘ J ~ ’ J ( ~ ) ) Jf r

Yz(k) = Ct%G(k).

Similar strategies have been proposed by (Jia and Krogh, (3)

2001; Camponogara r i ni., 2002)

384

the objectives of the interconnected subsystems’ MPCs. Convergence of the exchanged state and input trajectories must therefore be assumed-a drawback of this formulation. Not uncommonly, this MPC formulation leads to unstable closedloop behavior, so i t is an unreliable strategy for systemwide control.

a),(.) is obtained by eliminating the state trajectory 2,from (4), using (3). For this case, the FC-MPC optimization problem for each subsystem z = 1... . , 111 can be explicitly written as the finite horizon optimization

in which each cost function

FC-MPC, A

3.3 Feasible cooperation-basedMPC (FC-MPC) To arrive at a reliable, distributed, systemwide MPC framework, we modify the objectives of the subsystems’ MPCs to provide a means for cooperative behaviour among the controllers. Each local controller objective b, is replaced by one that measures the systemwide impact of local control actions. Here, we choose the simplest such measure - a strong convex combination of the individual subsystems‘ objectives z.e., 4 = C7uto,, where tit, are the weights. We set w, = l / A 1 for all z = 1.. . . ,111 in our discussion below, but our results hold for any combination of weights satisfying ui, > 0, C u‘, = 1. In large-scale implementations,the system sampling interval may be insufficient for the convergence of the iterative, Cooperation-based algorithm. In such cases, the algorithm has to be terminated prior to convergence of the state and input trajectories and the last calculated input trajectories used to compute a suitable control law. To facilitate intermediate termination, it is imperative that all iterates generated by the cooperation-based algorithm are systemwide feasible (i.e., satisfy all model and inequality constraints) and the resulting distributed control law is closed-loop stable. We define the finite horizon state and input trajectories for subsystem I as Z,(.k)’ = [x,(k + Ilk)’, . . . , ~ ~ ( k + ~ V l andu,(k)’ k)’] = [u,(klk)’.u,(k+ 1I k)’ , . . . u, (A + 11: - 1I k ) ’ ] .For convenience, we in thei follow, drop the k dependence of Z7and % ing discussion. It is shown in Appendix A that for each L = 1. . . . .M , Z, can be expressed a s follows:

.

+ S L L ~ L (+k :C[Ez3uJ ) + ft3zJ(k:)] (6)

% = EZ,%

3fZ

The infinite horizon input trajectory u,is obtained by augmenting u,with the input sequence u t( tlk) = 0 for all t 2 k + K . The infinite horizon state trajectory z,is derived from Zzby propagating the terminal state r , ( k + iVlk) using (3) and u,(tlk) = 0, t 2 k + N , ti z = 1,.. . , M . For subsystem (, the FC-MPC optimization problem is uf‘*)(k)g

in which FC-MPC,

arg(FC-MPC,)

(7a)

in which

j=1

s# j

j=1

=diag(Q,(l) , . . . ,C2i(N-1),aZ)>

Q%

M,,] = diag ( 0 , . . . , O,aij) , R, = diag (R,(O),R c ( l ) ,. . . , R,(N

-

1)) ,

nr j=l

while

is a suitable terminal penalty matrix. Restricting attention to open-loop stable systems simplifies the choice of Q.For each i = 1,.. . , M , let Q L ( 0 = ) Q t ( l ) = ... = Q,(,V - 1) = Q,. The terminal penalty can be obtained as the solution to the centralized Lyapunov equation

~’o~-(re=-~

(10)

in which Q = diag(Q1,( 2 2 . . . . ,CJ-bf).

3.4 FC-MPC algorithm and properties The state trajectory for subsystem i generated by the set of subsystem input trajectories u1,. . . ,Z L L ~ and initial state z i s represented as 2,( u ~. .,,ul1~ ; 2). For notational simplicity, we drop the functional dependence of the state trajectory and write z,+ z , ( u l , .. . ,ulxf; z ) . The following algorithm is employed for cooperation-based distributed MPC.

.

Algorithm 1. Given (u:, xL(k)), Q, 2 0, R, 2 0. L = 1,.. . M pmax(k)L 0 and E > 0 p + i , p , +rE,r >> 1 while p, > f for some i = 1,. .. , 111and p 5 pmax for I = 1,.. . . A l uF(*)E arg(FC-MPC,),(see (7), (8)) I’ - 1 P ( * ) (1 - &) uf-1 21, - xut p 1 . -- lluP1 - uP-l L II

+

385

end (for) Transmit up, i = 1,.. . , M to interconnected subsystems. Calculate zz(u:',. . . ,ugl;t(kj), I = 1,.. . , ?il. P+P+l

in which 1L(2(k))

= [tL:'("(k;;,:(k))':... ,,u;r)(k:z(k))t] '

forallx(kj ~ X a n d a n y p ( k ) =1 , 2,...

end (while)

Remark 4. If ( A ,Qij is detectable and Qz 2 0 for After p iterates, denote the cooperation-based . . ,u : ~~;( k ) The ) . followcost functionby @(uy,. ing properties ciin be estiiblished for the FC-MPC formulation (8) employing Algorithm 1.

.

all i = 1,. . . M , then the closed-loop system is asymptotically stable under the distributed MPC control law.

4. EXAMPLES Lemma 1. Given the distributed MPC formulation FC-MPC, defined in (7), (8), V i = 1,.. . AI, the sequence of cost functions {@(uy,. . . , u : ~~; ( k ) ) }4.1 Performance comparison generated by Algorithm 1 is a non-increasing

.

function of the iteration number p. Using Lemma 1and the fact that a(.)is bounded below assures convergence with iteration number p.

The examples use the cumulative stage cost as an index for comparing the performance of different controller paradigms. Accordingly, define

k=O

z=1

Lerrirm 2 . All limit points ol Algorithm 1 are optimal.

4.2 Two area power system network

Lemma 2 implies that the solution obtained at convergence of Algorithm 1is Pareto optimal i.e., the solution at convergence is identical to the centralized MPC solution.

We consider an example with two control areas interconnected through a tie line. For a 25% load increase in area 2, the load disturbance rejection performance of the FC-MPC formulation is evaluated and coinpared against the performance of centralized MPC (cent-MPC), decentralized MI'C (decent-MK), communicationbased MPC (comm-MPC) and the standard automatic generation control (AGC) with anti-reset windup. The load reference setpoint in each area is constrained between 1 0 3.

3.5 Distributed MPC control law Let X represent the constrained stabilizable set for the system under the set of input constraints x x . . . x Rbr. At time I;, let the FC-MPC algorithm (Algorithm 1)be terminated after p ( k ) = I iterates, with u',(.(k)) =

+ l,.L(k))', . . ,] 0

[UE(k,L(k))/,UI(k

z=l..

(11) ,PI

representing the solution to Algorithm 1 after I cooperation-based iterates. The distributed MPC control law is obtained through a receding horizon implementation of optimal control whereby the input applied to subsystem L at time k , u , ( k ) , is & ( k ) = uf(k,.c(k))

(12)

The relative performance of standard AGC, centMPC and FC-MPC (terminated after just 1cooperation-based iteration) is depicted in Fig. 1,where the transient responses of the tie-line power flow and the area 2 load reference setpoint are shown. Under standard AGC, the system takes more than 400 sec to drive the tie-line power flow deviation to zero. With cent-MPC or FC-MPC (termninated after just 1 ileration), the tie-line power flow disturbance is rejected in less than 100 sec. The closed-loop performances of the various control formulations are compared in Table 1. Table 1. Performance of different control formulations w.r.t. cent-MPC,

Lemmas 1and 2 lead to the following theorem on closed-loop stability of the nominal system.

=

standard AGC decent-MPC comm-MPC FC-MPC (1iterate) FC-MPC (5iterates) cent-MPC

Theorem 3. Let Algorithm 1, the distributed MPC formulation (7), (8) with N 2 1, and the distributed control law defined in (12) be given. If A is stable, is obtained from (lo), and Qi(0) = Qi(1) = . . . = Q i ( N - 1) = Qi > 0 &(0) = Ri(1)= . . . = R I ( N - 1)= R,

>0 . . . .M

i=1,

then the origin is an exponentially stable equilibrium for the closed-loop system .(k

+ 1)= Az(k) + B u ( z ( k ) )

hioiifxg-'~cent h n t

x 100.

A 39.26 17683 17.42 15.24 N

15.2

15.2

Ah% 158.32 164 1462 0.24 N

0

-

In practice, such a large load change would result in curtailment of AGC, and activation of other, more drastic controls such as load sheddhig. This exaggerated disturbance is useful, however, for exploring the influence of constraints on the various control strategies.

386

~.

0.2,

cent-MPC =point-

----

0.1

~

-I r"i

----0.05O :

-0.1 1 , 0

20

40

60

80 100 120 140

I

10

0

Time (sec)

I

20

I

I

I

30

40

50

I

Time (sec)

comm-MPC - - - -

0.2

..--.--

,--._

,'

0

20

target cent-MPC .......~. standard AGC - - - FC-MPC (1iterate) ------

_,-.__--

40

-0.5j1;

-1 0

60 80 100 120 140 Time (sec)

i

,

,

,

~

...

10

20

30

Time (sec)

40

50

Fig. 1. Change in tie line power flow (LIP,',,") and load reference setpoint (APrCt2).

Fig. 3. Change in tie line flow (LIP,',,"), and load reference setpoint (APrcfl).

4.3 Four arm power system netwovk

4.4 True men power system with FACTS device

An example with four control areas is shown in Fig. 2. Power flows through tie-line connections 1 - 2, 2 - 3, and 3 - 4 are the sources of interactions between the control areas. The relative performance of cent-MPC, comm-MPC and FCMPC is analyzed for a 25% load increase in area 2 and a simultaneous 25% load drop in area 3. In the comm-MPC and FC-MPC formulations, in each area is the load reference setpoint (Pref) manipulated independently to reject the load disturbances and drive the deviations in frequencies (Aw,) and tie-line power flows ( A P i i )to zero. In the cent-MPC framework, a single MPC controls the entire power network. The load reference setpoint for each area is constrained between il.

This example returns to the two area network. In this case, the interconnection between the two areas incorporates a FACTS device that is employed by area 1 to manipulate the effective impedance of the tie line. We investigate the relative performance of the cent-MPC, comm-MPC, and FC-MPC formulations, in response to a 25% increase in the load of area 2.

Fig. 3 shows the performance of cent-MPC, commMPC and FC-MPC (terminated after 1cooperationbased iterate.) Based on calculated closed-loop control costs, the performance of comm-MPC is worse than that of cent-MPC by about 25%. The closed-loop performance of the FC-MPC formulation, terminated after just 1 cooperation-based iterate, is within 3.2%) of cent-MPC performance. Perforinance of the FC-MPC framework can be driven to within any pre-specified tolerance of cent-MPC performance by allowing the cooperation-based iterative process to converge.

Under the comm-MPC formulation, the system takes about 300 sec to reject the load disturbance. The comm-MPC formulation incurs a performance loss of 192.51% relative to cent-MPC. Under the FC-MPC formulation, terminated after 1 iterate, the performance loss is only 6.2% compared to cent-MPC. The system rejects the load disturbance in less than half the time required by comm-MPC. Fig. 4 shows the relative phase deviation in the two areas, and the change in impedance due to the FACTS device, for the different MPC frameworks. 5 . CONCLUSIONS

Centralized MPC is not well suited for control of large-scale, geographically expansive systems such as power systems. However, the performance benefits obtained with centralized MPC can be realized through distributed MPC strategies. Such strategies rely on decomposition of the overall system into interconnected subsystems, and iterative exchange of information between these subsystems. An MPC optimization problem is solved within each subsystem, using local measurements and the latest available external information. Various forms of distributed MPC have been defined. Feasible cooperation-based MPC (FCMPC) assigns a common, system-wide objective

Fig. 2. Four area power network.

387

in which 0.05 comm-MPC - - - FC-MPC (1 iterate) ------

O -0.01

-I

...................

I--

0

20

40

[

0

-'J 9 .I

1

- 4 zN1 - 2

60 80 100 120 140 Time (sec)

:I'

0 0

...... 0 0 ... 0

;

.... .

A,, Azl-3A,, . . . . . . 0

Combining the models in (A.1)/b' i = I,... , M , gives the following system of equations A;c = E u + Bz(k)

(A4

in which ,

-0.1 0

20

40

,

I

60

80 100 120 140 Time (sec)

. . ......

Fig. 4. Relative phase difference (A& - A&)/ and change in FACTS impedance (AX,,).

Thc papcr has prcscntcd a numbcr of powcr system examples that have applied distributed MPC to automatic generation control (AGC).MPC outperforms standard AGC, due to its ability to account for process constraints. FC-MPC achieves performance that is equivalent to centralized MPC, and superior to other forms of distributed MI'C. The FC-MI'C framework also allows coordination of FACTS controls with AGC. In this case, the cooperative aspect of FC-MPC was very important for achieving acceptable response. 6. ACKNOWLEDGMENT The authors gratefully acknowledge the financial support of the industrial members of the TexasWisconsin Modeling and Control Consortium, and NSF through grant #CTS-0456694. Appendix A. MODEL MANIPULATION To simplify the development of the FC-MPC algorithm, it is convenient to eliminate the states z t ,2 = 1 , , 91 using the PM (3). Propagating the model for each subsystem through the control horizon ,V gives

=EtZuP +??,~zZ(k) + C[ZZJZJ+gLJzJ+?,~xCj(k)] J#L

V7=1>...,AI

u=

xM

I

UbT

(A.3)

to all subsystem problems, and has the property that the converged solution is identical to centralized MPC. In addition, the FC-MPC algorithm can be terminated prior to convergence without compromising feasibility or closed-loop stability of the resulting distributed controller. This feature allows the practitioner to terminate the algorithm at the end of the sampling interval, even if convergence is not achieved.

%

x=

.

(Al)

388

Since the system is LTI, a solution to the system (A.2) exists for each permissible RHS. Matrix A is therefore invertible and consequently, we can write for each i = 1,.... M ZL= &,Ti,

+ j i i z i ( k ) + c [ E i j . U j+ fijxJ(k)].

(A.4)

I.#
111 boiler house No KJ, M ; -~ prcdictcd ~ mass flow in time RT, A$/liiied approach to balaiice t,lie t,echnical, economic, environmcntal and oft.cn times political forces! that influence the decision making process. This paper presents a method for quantifying the economic impact of condenser maintenance based on plant thermodynamics, condenser modelling arid market forces in the form of power purchase agreernent,s. An opcrat,ing cost. function is forrnu1at)cd which is ablc to cst,imatc opcratiiig costs based on current plant da,t,a and opemting paramet purchase cont>racts.The results highlight the financial iniplic ions. Due t,o t,lic coniplcx, mult~i-modaland discont,inuous nature of tlric: cost funchion, conventional optimisation techniques struggle with this scheduling problem. However, using genet,ic algorithms, it is possible to search arid iderkify a range of feasible least cost maintenance schedules. As a result, key sclieclules arid their associated costs are quickly liigliliglitetl. allowirig the user to make a more informed decision regarding future maintenance. Kcymwds: genetic algorithms, stcani plants. physical rnodc4s

1. INTRODUCTION The environment in which nmny power stations opcrahe has changed considerably over the past t,wo decades. No longer is t,lie pursuit. of unit, cfficioncy the sole arbiter. In its place is a multit ride of economic and environmental forces which only exacerbat,ethe already difficult ta.sk of power st~ationoperation. On one side t.here may be shareholders anticipating a. profit~ableret,iirn on investment,, and on t,he other, new legiskion enforcing capital investment in emissions reducing plant. It, is within this compctitive environment, that mana,genientjcont~inuallyendeavour t,obalance t,he opposing economics of gcncrat,ion and niaint,c> naiicc. While producing electricity is funtlaancntal to generating revenue, maintenance can not be ignored, as the physical healill of‘ the plant) is

paramount, to both t,he ability t,o generate electricity arid also rclia,bility. It is oftcn the case t,hat,unt,irnely pla.nt failures ca.n have drama.t,ic financial penakies, especially if t>lieyoccur at t,iines when thc systcni dcnianil for clcct,ricity is high.

At tjhc heart of a, convent,ional power plant, are the boiler and condenser, whose respective tasks govern the efficiency of the generating unit, as represented by t,he Rankine steani cycle. This paper preseilts a. methodology to improve unit efficiency and profitability for a steam turbine genera,t,or. by targeting tlic largcst, single cncrgy loss wit,hin the Rarikine cycle, t,lie condenser.

It. is in t,hc condcnscr t,liat, latent heat from t2hc st,ca.ni is lost t,o the cooling water, arid where inefficiencies in the heat transfer process impact on t.he overall efficiency of the generating unit.

40 1

Unfort,unat~ely,process control on the condenser

--

is usually limited t,o the number of cooling water

o,9.

feed pumps in operation and the rate of air ext,raction, neit>lierof which have a major impact on heat t,ra,nsfer, except, when t,hey fail t.o operate. Consccpently~condenser performance relics heavily on rout,ine maintenance such as cleaning and t,ube repair. Present>edin this paper is a novel method for modelling condenser losses. This is a.chiewd by idcnt,irying t hc fouling processes at work within tlie condenser a,nd motlelliiig their non-1inea.r variat,ion over t,ime. In so doing, previously uiiaccounted variations in seasoiial and eiivironrnc+iit,al conditions are incorporated, as well as time of ycar dependent cont,rac:t,u;tlc:onst,rairit,s.This combination of operating rosts permits accrirate performance estiniat,es for any specified time period. The resiilts highlighted in this paper are a development, of work originally presented by Cregan and Flynn (2003). Sincc t,licii t,he focus 1ia.s been on pra.ctical implementation, dealing with issiics sucli a.s computer interfacing, graphical uscr int,crfa.ccdcvclopiiimt~and physical niotlcl custoniisaliori. Decisions regartlirig sollware desigri arid inil.)lementat,ionwere t,aken in consultation with plant operators and engineering staff. The result of t,his was that complex GA and costing parameters have been hidcleii from the operator, model t,uiiing has been simplified and where appropriate simplc: graphics havc rcplacc: text, in t,hc user inter face.

2 . CONVENTIONAL hIAINTENANCE APPROACH Tra,dit,ionally, condenser ma,intena,nce has been based on simple thermodynamic perforriia.nce estimaks, as presented by BE1 (1991). hIaiiit,enance schedules based on these techniques, as described by Put'maii (2000), liave ignored non-linear seasonal variations in performmce as well a.s cont.ractual cost s and constrabnts. This conventional approa.ch is liniit,cd tjo cfficiciicy rcla.t>ctlcosts. which for a modern power station are only one of a multitude of different costs which may influence the maintenance planning program. In the t,echniyue described by Putman a simple linear relat,ionship between condenser fouling and t,ime is a.ssmned. Hence, the c:urriulat,ive fuel costs are calculat~edby int.egraling with respect to lime. Subsequently, t,lie specific cost of n sclietluletl out,ages at, times tl to t , are added t.o the cumulative addkional hiel cost). A typical graph, Figure 1, plots t,he cumulat,ive costs stret,ching over twelve months and iiichdes three planned outages at tiiiics 11 to t 3 .

0.8-

Zero Maintenance

- - One Outage - TWO Outages

Zero Maintenance

,'

Fig. 1. Operating Cost for Lineu Fouling TypicaJly, t.he aim is to find tlie least. cost solution to t,he problem by 'experimenting' with various maintenance schedules. Figure 1 demonstrat,es this by highlightzingthree possible schedules. The first, and most, expensive opt.ion is to ignore maint,ena,iicewit,h a subsequent, coiit iiiiial incrcasc in plant fouling. Hcrc, thr: cxponcntial increase in cost indicates that this is not a sensible approach. Also plotted a,re two other schedules, with one a.nd two o i h g e s respect~ively,where two outages represent's t>hebet>t'eror least cost scliedule. This graph is only illiistrative and does not necessarily show t8hebest, solution.

To find tlic lr:ast, cost solut,ion, as tlcmonst3ra,t,cd by Putman, t,lie maintenmce window is recursively divided into equally spaced periods, wit,li thc nurnbor of outages incrcasing by one diiring each iteration. Eventually, a series of schedules are calciilat ed am1 from t,hese a. least cost,maintenance plan may be det,ermined. This simple costing technique however does not provide a triie representation, because ra,rely is condenser fouling liiiear - inst,ead it vxies wit,li tirric of ycar, unit loading, ctc. In itddition many of (he o(,lier market -driven economic a r i d conlritcl iial costs have been cornplet,ely ignored. This simple approach may have been sufficient when the economics of' operating a geiierat>iiigunit were limited tfo unit efficiency, but. in today's competit,ive environment,, gcncra~t>ing conipanics ncctl a. new and morc comprchcnsivc approach. 3. COhlPOSITE FOULING MODEL

The composit.e fouling inotlel presenkd here l.enipls to a.dtlress the weaknesses of the linear model by ideiitifiing t,lie various fouling processes act,ive and iiiodelling their non-linear beliaviour. One of the early attenipk at modelling the thermal resistance due t.o fouling ( r f) was proposed by Kern and Seaton (1959), using t~hefollowing simple mat>crialbalancc cyuat>ion,

402

%

where the rate of fouling, is the difference bet.ween, &> t,he rate of deposit.ion and, $,, the rate of removal. The composite model contends tha,t,a I ogicr?1 tievc:loprnent of t,his si ni ple foi 1 I irig ni ode1 is tlie ide1it)ification and analysis of individual incchanisms at, work wit,liin tlic contlcnscr. Thcsc would be represented a s sub-models for particulat,e fouling, bio-fouling, scaaiag/crystalliza.tion, tube blockages?etc. Most recent work by Putriiaii (2000) and Zubair (2000) identified various fouling mecha.nisins,which are listed in Table 1 t,ogether with a brief description. Table 1. Coniposit>eFouling Sub-Models Sub Model sml

Dcscription

= Altl/"l

Power law

r1

Asymptotic Falling rat,e Linear

r g = r,(l - e-61'2 r:i = A 3 log( R3t)

smg

Exponential

rs = A;,tB5

rq

= Aqt

1

+ Bq

Ai and Bzare constants, r s = Sat,uration fouling limit. t = t,ixne.

where:-

0 < IVi

< 1,

where i is t,he nuniber of sub-models and t is time. It is also assumed that, t,liere are no ext,crna.lt,herinal resisCances impeding heat transfer. Therefore, rf = r,, whcrc rf is t,hc tot.al fouling r~sist~aiicc.

3.1 Composite Sub-Models

Format

sirs2 sm,g smg

The weights. I f / , . allocated to the sub-models may vary between zero and one, to reflect the changes in seasoiial and environmental conditions. Hence. the coiiiposite fouling resistance, rc, is the sum of is the fouling all weighted sub-models, u hile rate for each sub-model.

In ortlcr to highlight the rclntis-e time dependent properties for ~ a c hsub-model, cach has bcen norrn~disedand plotted on a single axis, spalining twelve months, in Figure 2. It IS notcd that thc falling rate inodel (rg),and power law model ( T I ) , look similar. However, with the falling rate model is always decreasing, the rate of deposition, ~6 hich is not true of the power law model.

9.

('Omel

Each of the sub-models 1ist.ed in Table 1 has been ideiit.ifiec1as representing a, particular type of fouling found in heat, exchangers and condensers. The following is a. brief description of cach, highligliting t,hcir particular chara.cteristics.

Power Law n/Iodel (sm

Documented hy Klian,

cb al. (199G) whilc investigating t.hc deposit,ion of

CaC03 in heat exchangers operating at, relatively high temperatures (2 50°C). Consequently, this may be employed t.o represent, the build up of crystalline deposits, commonly associa.ted with condensers opera.t,ingat, high ai-nbient, temperat,ures. Asymptotic Model (.sm2) It was obsc:rvcictl by Zubair (2000) that hea.t, exchanger fouling from cooling water at, t,einperatures 5 25°C caii be represented as an a.symptot~icmodel. This is because at lower temperat>uresthe deposition of different shaped salt crystals and suspended pa.rt,iclescreates a,relatively weak layer. As the thickness of the deposit, lwpr incrcascs so docs thr: rt:moval rnto, and cvciitmlly t,lie reizioval rat,e approaches that of t.hc deposit ion ratc arid sat.iiration is reached. Such a modcl may bc used to represent the condenser deposits encountered during the cooler seasons in both coastal arid inland power stat,ions.

0

60

120

180

240

300

360

Time (days)

Fig. 2. Coniposit,c Fouling Sub-Modcls In practice, siiriulating the non-linear fouling processes requires a collection of sub-models, tailored to each condenser or power st,atioii. Each of the sub-models is chosen to reflect, t,he fouling niechanisms act,ive in the condenser ant1 weighted according to their relativc eflcct.

Fa,lling Rate Model (srn,y) The falling rate curve represenh a process where t,lie deposition mte is always greater tfliatst>lieremoval rat>e. Bot,h nluller-Steinhaga.n (1988) and Bansal (1993) have iclc~it~ified this fouling proccss. In thc lattcr it was representative of tallisa.tion: while in the former it was pa,rt.iculat,efouling. Putman (2000) highlighted t,he process as being typical of that observed in coastal power stat,ioiis. It represents the particulat~enature of organic fouling deposit,s that, build up in coa.st,al condensers, especially problematic during tbc sunirncr montbs.

403

Li.n,cti,r Model (‘qrn.1) T,inea.r foiiling i - r q be included to represent unidentifiable deposits that arc not represented by the otlrcr sub-models. It may also be employed when the operat,or is unavare of what fouling processes are a.t work. Even wit,h the simple linear sub-model t,he composite niodcl can wary its weighting to rcprc sonal changes in fouling, which is still a dramatic improvement over the conventional linear fouling model.

Exponential Model (sms) An exponential model m a y be employed t>orepresent, air ingress int>othe midcnscr. It is lrnown that trhc prcscncc of a.ir can drast>icallyreduce condtmser performance by reducing lieat) ixmsfer t>ot>liecooling wat,er. For examplc, an air blanket of 1 mm is equivalcnt~t,o a slab of copper 16.5 In thick. It was remarked by Putmari (2000) that the thernial resistance of entrapped air in t.he condenser has an almost exponmt,id effect on heat traiisfer.

3.2 Pal-anreter. Selection Given t,hat there a,re several sub-models each with their own unknown parameters a i d weight~s it is initially assumcd that, all the sub-modcls arc cqually wcig1it)cd. antl tlrc cocfficicnts for each sub-model, A, and B,, are chosen so tjliat, each sub-model produces zero foiding at, zero t inic, ~ ~ & ~,. , In and a, thermal resistance, T ~ ~ ,at,. tirnc Figure 2 t,he target end point is represented by point. A , where rtargetis the annual accurnulat~ed fouling under normal operat,ing condit~ions.

t,o derrioiist,rate the strengths of t,he composite modelling process. Visual inspect,ion of t~liecondenser during routine cloaning idcntified t,wo scpa.rat,e fouliiig t,ypcs as beirig pretloinina.rit, Duriiig the waruier rrioiit,lis, organic fouling due t>osea mussels restricts cooling wat,er Bow, an(l during the wint,er, silt.ing on condenser tubes reduces heat, iransfer. In t,he composite model, these fouling mechaiiisms are represented by submodels s7n2 and s n ~ ,3 m-here sm,2 corrcsponds t,o the t,licrmal rcsistsncc of a weakly boiidecl low temperature deposit. In submodel s m 3 the depositmionrate is alm-ays greater that>t hc rcmoval rate, a result of thc parliculat,e nat.urc of organic fouling.

Is was determined, based on recorded LhITD (log mean temperat,ure difference) data, €rom t,he power st,at.ion and extrapolated over t,welve mont,hs, that the fouling resistance increased by almost. t,wo thirds in a year. Assuming, r,leala.the therante of t,lic coiiticnscr whcii clean is m’K/W, the target)re 40 x m’K/W. Figure 3 plots tpheestimated thcrnial rc;sist,anccsfor thc: t,wo sub-models over a. Lwelve riiori(,h period.

p is t,o allocate weights t,o each submodel. Aga.in t>osimpli€y select>ion,weigh1.s are either maiiitaincd constant, or varicd t,o reflect. sc~sorialvariations. It) was ,judged that a gaussian funct,ion, g ( l ) , or t,he form,

Fig. 3. Coastal Power Station Sub-Models where, cj, is the centre of t!he function, antl, F ? , is t,he spread or width of the function, would allow summer or aut,umn peaks t,o gent,ly fade with t,inic and rise again t,hc following year. In the following soct,ioii, this process of paramct,cr selection is illustmted by employing t,lie cxcmple of a costal power station.

The A a,nd B coefficients €or t>hethermal resist.ancc curves in Figure 3 were calculated bascd on t>hcassiimptjion that. the condcriscr is iiiit,ially clean. Ilence, both curves pass through t.he origin. Additionally, the target time was set at twelve mont,hs. T h e weights applied to each of the sub-models re-

flect,sthe impwt ca.ch has on t,he condenser. Sincc 3.3 Composite Model for Coa,stcrl Potucr Station,

This example utilises data froin a coastal power station on the north cast coast of Ireland. For commercial reasons, the specific plant performance details are not disclosed. This, however, docs not detract from tlic potential of tlic example

organic fouling. rcprcseiitctl by 57113, is afkxt~etl by sea water temperature then the sub-model weight., 7113, should reflect variations in t,he cooling wat,er inlet t,emperature. Dat.a collected from the plant, indicated t,hat, t,he cooling water t,emperat.ure peaked in late September, followed by a gradual decrease until a low in March. However, in the winter pcriocl of Novcnibcr tjo February,

404

- w3 Parltculate

o,9

-

0.7 3E 0.6 I

wliere C,, are performance relat,ed costs, C, are contract, related costs and C,, are direct ma,interiance costs. The negative sign applied to C, indicates an iiiward flow of revenue, compared t,o the remaining terms which m e all out,wa.rd expenditures. A full description of t,hese costs is dcscri1)ed by Crcgan and Flynri (2003).

-

0.3. 0.2.

Fig. 4. Coastal Power Station Sub-hlodel Weights Finally. c.orrhining the fouling resistance, r, . from Figure 3, aiid sub-model viieiglit5, wZrin Figure 4. rcsults in tlic wciglitcd fouling plot cli,r in Figure 5. This graph liigliliglits tlic strength of tlicl composite rriodcl bv dciiioiistiat iiig the nun-liiicar fouling cxpcctcd in t hc condenser.

The effect of the non-linear coniposit e fouling model is expressed in C, as the cost, of addit>ional fuel required to conipensat>efor condenser fouling. Thc comp1cxit.y of t,hc cost function is furthcr coinpouiitled by t.he many tliscoiitiiiiious regions int,roduced by restrictions and fluctuations in the contract cost,s, Cc. For example, imit,s are given an availability payment and during a winter wcck day tlie payment. during peak t,irnes (4-7 pm), is foiir times greater t.han that, al; riiglit t.irne. The aim of the cost function is to determine the operating cost, based on a specific maintenance schedule. Many of the parameters assocjat,ed wit,h arc fixed, for examplc, the physical dimensions of the condenser, heat load, etc. while others arc wsiable - fouling rate, opera.ting times, niaint,onancc tinics, ctc. In ordcr to find a lmst, cost rriaiiileriarice scliedule only (,lie rriairileria.rice t,inies should he perrnit,ted t>ovary while t,lie ot,her parameters reiiiain constant. This will allow ail optimisat,ion routine to utilise the cost funct,ion in it,s search for least cost solutions.

5. MAINTENANCE SCHEDULING

2006

Fig. 5. Coastal Power Station Sub-Model Fouling The umisual ‘hump’which occiiis during Februaiy niid LIarcli is prirrilie s l i m of three distinct wmponents such that,

Advnnces within the domain of condenser ma.intenance have been very limited Ma & Epnteiri (198l),and more recently, Wolff, et. al. (1996) approached the problem by applying mixed integer linear programming (hIILP). This technique, like most others, breaks down when large discontinuities are encountered in tlie cost function. Alternatively. tlie success of genet,ic a1gorit)hms (GA) with NP (noii-d rrninist,ic polynomial) t>ypcsr:hcduling problniiis such a.s t,hc ‘t,ra,vclling salesman’ is well documented. The GA eiiiploys an intdligent, search of a h r g e hut firiit,e soliition space, wliich converges towards minima.. Nonlinearities or discontinuities in the cost. funct,ion do not significant>lyhinder the search. Using hlatlah’s graphical interface and toolboxes: a n integrated software package was creat>edfor the power shlion. By employing a s l a n d a d binary encoding chromosome t,o represent, rnairit,enance schedules. Each schedule evaluatsed by tlie cost function would return an estimate for the operat.ing cost over a specific period such t,hat, maintenance cost. = f ( t 1 , t 2 .

405

where N is tlie niiiiiber of oiitages and t is the time between maintenance outages.

The GA optimisation routine u.oiild search for soliit,ioiis using tlic cost, function and presentj t,o tlie operator a raiige of kmt, cost, solutixis a s illustra,ted in Figure 6. The bar chart, presented in this grap1iic:al user interrace liiglilight~st-he t o t d cost for each schedule by combining the maintenance, contract and perforniance costs. For this example the least cost soliition generat,ed by the CA rccommcnds a iivc out~agcschcdulc. b'.. ,'

A

d

HmtenmnrL S*Ldulmm

approaches, where many of t,hese subtle differences would go iinrecognised, the composite model can identify the significant, effect. of changing sea and air temperatures on condeiiser fouling. Wlien planiiing future rna.iiiteriarice scliedules identifying variations in condenser fouling can especially wlien iiit,egrated into an overall cost^ function. By combining cont,ra.c:tual, performance and rriaintenance costs into a single function, it is then feasible to search for minima. Howcvcr, thc process of opbimisation, wl-lerc. least, cost so1ut)ioiisare located, tlepends great,ly on the complexit,y of t,he cost) funct,ion.

.

It hiis been denionstrat ed t,liat dcspitc the cornplexities of the cost fimct>ion,stja.ndardGA algorithms are able t,o effectively search and return valid, least, cost,, condenser niaint,enance schedules. T&%h these solutions the key times and schedules are quickly highlighted. permit.ting a well informed decision on fiitlture maintenance.

REFE,RENCES Fig. G. Scheduling Costs Operator Display By selecting onc of the schcdulcs in Figure 6 tlic opcraior is ihlc? to analysc in detail a.ny of the range of possible solutions. In this example Figure 7 plots a breakdown of component costs against time for the five outage schcdulc. - Combined (Cmo,) o.5.

- - Performance(cJ (CJ - - Contract Maintenance(Cm) ,

Feb. Mar. Apr. May h 11

i2

e July pug. Sap. Oct. Nbv. Dec. Jan. 2o06

t3

14

t5

Fig. 7. Component Cost,s for Opt,irniim Schcdule Furtlier opt.ions in software permit. existing planned oiitages to be incorporated by fixing t,he time of one or more outages. In each instance t,he program highlights a range of opt,irnal scheduling solut,ions.

6. CONCLUSIONS The composite fouling model presented enables the noii-linear antl time dependent variations in condenser fouling to be reprotliiced antl quant ificd. Compared with convcntional linear modelling

BiLnsal, B. a n d H. Midlcr-St.einliagac1??ii(1993). C:rystallizat,ioiifouling in plate heat, exchangers. ASWE +J. Heut Trmsfer. 115, pp. 584591. BET (1991). Modern Power Sta.tion Practice. Perganion Press, London, UK. Crcgan, nl.and D. Flyrin (2003). Condenscr maintenance cost optimisation using genetic algorit,lims. IFAC Puuier Plants and Power Syst e m Control Con~fSeoul, Korea. Kern, D.Q. and R.E. Scaton (1959). A t.heoret'ica1 analysis of tlierrrial surface foiiling. Cli,errrical ETLY.,4(6). pp. 258-262. Kha.n, M.S., SAL. Zuba.ir, M.O. Biida.ir, A.K. S1ir:ikh and A. Qutidus (1996). Fouling r e sist~mcemodel for prediction of C n C 0 3 scaling in AIAI 316 t.ubcs. Heat Muss Tmn.sfer, 32, pp. 73-80. 1CIa, R,.S.T. and W. Epstein (1981). Opt,imum cycles for falling rate Ixocesses. Cu,nadinn J . Chemical Eng.. 59, pp. 631-633. h/ruller-St,eirihageri, H., F. Reif, N. Epsteiri arid A.P. Watkinson (1988). Influeiice of operating conclit,ionson particiila.trefouling. Can,. JUYT. Cficrri. Erg., 66, pp. 42-50. I'utman, R (2000). Steam Surjnce Condensers. ASME. Wolff, P.J., P.A.March and 1I.S. Pearson (1996). Using condenser performance measurements to optimise condenser cleaning. EPRI Heut Rute Con,! Dallas,USA. Zubair. S. hl.. A. K. Sheikh, hl. Younas and M.O. Biidair (2000). A risk based. lieat exchanger analysis subject, t,o fouling - part 1 - performa~nccevaluation. Errer

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Copyright 0Power Plants and Power Systems Control. Kananaskis, Canada 2006

PUBLlCATlON$

A MULTI-AGENT SYSTEM-BASED REFERENCE GOVERNOR FOR MULTIOBJECTIVE POWER PLANT OPERATION

Jin S. Heo and Kwang Y. Lee

Department of Electrical Engineeuing, The Pennsylvania State University, University Park, PA 16802, U.S.A. (email:juh [email protected]) (email: kwunglee@jpsu,edu)

Abstract: A large-scale power plant requires optimal set-points, namely references, for optimal operation. In a 600 MW oil-fired drum-type boiler power unit, the set-points considered are for the main steam pressure and reheaterhperheater steam temperatures. Thc set-points should bc mapped with varying unit load dcmand and satisfy the conflicting operation requirements of the power plant. The conflicting requirements are tackled by multiobjective optimization problem to produce the optimal mapping. In general, the set-points obtained by using a fixed nonlinear function cannot provide optimal power plant operation. This paper presents a methodology, Multi-Agent Systembased Reference Governor (MAS-RG), to realize the optimal mapping by searching for the best solution to the multiobjective Optimization problem. In searching for the optimal set-points, a heuristic optimization tool, Particle Swarm Optimization (PSO), is utilized to solve the multiobjective optimization problem. Moreover, the approach provides the means to specify optimal set-points for controllers under a diversity o f operating scenarios on-line. Copyright 02006 IFAC Keywords: Reference governor, multi-agent system, multiobjective optimization, power plant control, set-points, particle swarm optimization.

1. INTRODUCTION While the demand in power is increasing, powcr plants are getting more complex and expansive to run. Power plant is a large-scale system consisting of many subsystems. It is no longer the best solution to manage the large-scale system by using only strictly centralized or loosely decentralized schemes. The data processing and operational requirements of the large-scale system have been excessive, especially for optimal operation. Moreover, it has been challenged to generate power while minimizing loadtracking error, fuel consumption, heat loss rate and

pollutant emission, and maximizing duty life on equipment. Recently, there has been a growing interest in MultiAgent System (MAS) to deal with the complexity and distributed problems in power systems. Each agent system has special functions to solve the distributed problems. Moreover, in the multi-agent system the agents can work together to solve problems, which are beyond the capabilities or knowledge of an individual agent (Woodridge, 2002). On ilie other hand, a modern heurisiic method, Particle Swarm Optimization (PSO), has become a favorite topic for multiobjcctivc optimal power plant

407

Fig. 1. The large-scale power plant model and MAS. operation (Heo, et ul., 2005). The PSO provides high quality solution with simple implementation and fast convergence as reported in many references (Kcnncdy and Eberhart 1995: Lce and El-Sharkawi, 2002; Park, et al., 2003). In the power plants, the optimal operation can be achieved by various approaches such as optimal control, optimal set-points scheduling, and other optimal techniques for the power plant (Ghezelayagh and Lee, 2002). In a small-scale power plant, which is a low-order system, the optimal set-points can be obtained by analytical approaches (Gaduno-Ramires and Lee, 2001). However, a large-scale distributed powcr plant rcquircs gcncrating optimal sct-points using an intelligent method such as MAS. The MAS is described as a group activity of individual distributed intelligent agents (Wittig, et al., 1994). This paper presents a methodology, Multi-Agent System-based Reference Governor (MAS-RG), to realize the optimal mapping between set-points and varying unit load dcmand by searching for the best solution to the multiobjective optimization problem. The set-points considered are for the main steam pressure and reheated superheater steam temperatures in a 600 MW oil-fired drum-type boiler power unit. The optimal set-points are determined by solving the multiobjcctive optimization problem with conflicting requirements such as load following, fuel conservation, life extension of equipments, reducing pollution, etc. Following the introduction, the power plant and Multi-Agent System (MAS) are described in Section 2. Section 3 describes the Multi-Agent System-based Reference Governor (MAS-RG). Section 4 shows simulation results to demonstrate the feasibility of the proposed approach. The final section draws some conclusions. 2. POWER PLANT AND MULTI-AGENT SYSTEM

2. I

Description oJ'Power System (Usoro, 1977)

The power plant is a 600 MW oil-fired drum-type boiler-turbine-generator unit It is a balanced draft, controlled recirculation drum boiler capable of delivering 4 . 2 ~ 1 0Ib/hr ~ of steam at a pressure of 2600 psig and at 1005°F. Six recirculation pumps supply the required recirculation flow to provide sufficient flow for full load operation. Two forced draft fans supply the primary air, and two induced draft fans are controlled to maintain a furnace pressure at a desired pre-set value. Two condensate pumps, a combined booster and main boiler feedpumps handle the feedwater flow. The turbine is a tandem compound triple pressure steam turbine. It consists of three parts: a highpressure turbine, an intermediate pressure turbine, and low twin pressure turbines rotating on a common shaft at a ratcd spced of 3600 rpm and exhausting pressure at a 2 inch Hg absolute. The generator is coupled with the turbine and has a 685,600 kVA, 3 phase, 60 Hz, 22 kV, with a power factor of 0.90. In this paper, the model has twentythree state variables and twelve control valves ( u,,u2,...,u12) associated with physical processes. The control valves are named as following: u i : fuel flow, u2: gas recirculation, uj: induced draft fan, uq: forced draft fan, u5: combustor gun tilt, u6: superheater spray flow, u7: reheater spray flow, ux: governor control valve, u9: intercept valve, uI0: deaerator valve, u I I : feedwater valve, u/z: feedpump turbine flow. The model is reorganized into four main modules, which are boiler system, turbine-generator system, condenser system, and feedwater system. The proposed MAS-RG is one of the functional systems based on multi-agent sysieiri which is inlercoiinected with the distributed subsystems that are components of thc four main modules. Fig. 1 shows thc largcscale distributed thermal power plant model and MAS. The proposed scheme will be applicable to other types of plants, including nuclear and fuel cell plants.

408

2.2

Multi-Agent System

An agent is a computer software program that is autonomous and situated in some distributed environments to meet its design objective (,Padgham and Winikoff, 2004). Since the agents are faced with different environments, they are designed differently and properly for the given environment. Moreover, the agent is intelligent because it is reactive, proactive, social, flexible, and robust. In a large-scale distributed complex system, the agent's autonomous and intelligent properties can reduce the complexity by reducing the coupling problems between the subsystems (Gupta and Varma, 2004). Furthermore, the proactive, reactive, and robust properties can be well suited for applications in a dynamic and unreliable situation (Hossack, et al., 2003, McArthur and Davidson, 2004, Zhang, et al., 2004). In order to design the MAS-RG, design of architectures for a single agent system and an organization for multi-agent system are required in advance. First, the architecture of a single agent system is shown in Fig. 3. Since the agent is situated in an environment that is the power plant, it needs a perceptor and effecter to act and react (Junpu, et al., 2000). First, thc senscd raw data arc processed and mapped into a scenario, and then an objective, which is a sub-goal, is initialized under the situation to achieve the main goal that is the optimal operation. The initial objective is sent to other agents through the communicator for eliminating redundancy and conveying the mission of the agent to others. After confirming the objective, the best plan i s chosen for the objective (sub-goal) in decision-making. Depending on the plan, an algorithm module is selected to launch the plan. Finally, the action made by the algorithm module effects through the effecter into the environment. Most decisions are made in the decision-making process, which i s like in a human brain (Heo and Lee, 2005a). A Multi-Agent System (MAS) can be defined as a loosely coupled network (organization) of problem solvers (agents), which interact with each other to solve problems that are beyond the individual capabilities or knowledge of each problem solver (agent). In order to perform the cooperative works, it is presented to build multiple hierarchical structures for the multi-agent system organization as shown in Fig. 4. The organization has low level, middle level,

Fig. 3. Single agent architecture.

Fig. 4. Organization of MAS.

Fig. 5. Composition of MAS for the power plant. and high level, and agent iii each level has a specific role in the society so that the agents pursue their tasks by the proactive property. In this paper, the high level agent is the task delegation and interface agcnt, thc middlc lcvcl agcnts arc thc mcdiatc and monitoring agents, and the low level agents are intelligent agents. The hierarchical structure that has three levels gives advantages for dynamic organization and autonomous systems (Kosakaya, et ul., 2003, Velasco, et ul., 1996). Moreover, the idea of multiple hierarchical structures is well fitted for the large-scale distributed system. Although there are multiple hierarchical structures, each hierarchical structure has a different formation from the others becausc thc structurcs arc constructed to fit for operating each real physical subsystem so that the organization is better optimized for the given power plant.

3 . MULTI-AGENT SYSTEM-BASED REFERENCE GOVERNOR With the proposed architectures of single agent and multi-agent system, the MAS-RG is developed to obtain the optimal mapping between set-points and varying unit load demand. The composition of MAS for the power plant is shown in Fig. 5 , where the functionality of individual agents is explicitly defined. In this paper, the reference governor cluster system will be mainly discussed. However, the functionality of individual agents is introduced in other paper [Heo and Lee, 2005al. Although all agents are connected with network, the reference

409

governor cluster, which is made of set-point generation agent and steady-state model agent, performs mainly for the MAS-RG. However, the refercnce governor cluster will cooperatc with the monitoring system, knowledge processing system, and reinforcement system clusters to obtain better performances. An operator will command and monitor the preference and status through the interface agent toifrom the reference governor delegation agent who has all access for the MASRC. In order to realize the MAS-RC, first, all feasible operating points, which satisfy all imposed constraints, need to be found using the on-line performance monitoring agent and virtual simulation agent. The virtual simulation agent simulates the power output responses with various set-point conditions. Since system response is in steady-state, the constant control inputs and static power, pressure, and temperature outputs become a pair of operating points. However, the admissible power outputs can be obtained within an appropriate steam pressure and reheaterisuperheater temperature ranges. Fig. 6 shows the power output responses with different steam pressure and reheaterisuperheater temperature values for 450MW power set-point. This implies the same power output can be obtained with different steam pressure and reheatedsuperheater temperatures. During the simulation by the virtual simulation agent, the on-line performance agent evaluates the operating points in order to find the admissible power, steam pressure, and reheated superheater temperature operating points. The power-pressure operating window is obtained in Fig. 7. The reheaterisuperheater temperature operating range is 1359.67"R-1459.67"R (900°F-1000°F) for all power ranges. Since the design and operation of reheater are essentially the same as the superheater, we decide that the reheater and superheater temperature setpoints arc equal. Fig. 8 shows thc powcr-control input operating windows. When pressure and temperature are changed, control inputs ( ul,u*,..., uIZ ) are varied to produce the desired power output. The gap between the upper and lower limit is obtained by changing the pressure and temperature within the operating windows.

Power plant condition might change as the plant agcs, in which case, the updating o f MAS-ISSMs 500 480 460 440

5 420 400

4 0

100 200 300 400 500 600 700 800 900 1000 time (sec)

Fig. 6. Power output responses with various set-point conditions for 450MW set-point. 3000 -

-

2800 -

~

~

-

2600 -

p 2400v)

4 2200 -

5

g a

2000-

1800-

~

1600-

-

-

-

1400} 1200 I

1

upperlimit lower limit 150 260 2kO 300 350 400 i 5 0 500 550 600 Power (Id1W) ~

-

looo'

-

Fig. 7. Power-pressure operating window.

In order to find the set-points of power, pressure, and temperatures, the next step is the development of the steady-state model using the steady-state model agent. The main algorithm module of the steady-state agent is Neural-Network (NN), which is the best approximator for nonlinear systems. The steady-state models are called Multi-Agent System based Intelligent Steady-State Models (MAS-1SSMs) (He0 and Lee, 2005b) and expressed as follows: Powev: Ed =$, ( u , , u2,...,u12)

(1 ,a)

Steam pressure: pd = $2 ( u , ,u 2 ,...,u 1 2 )

(Ib)

Re heater / Superheater temperatures: ) RT, =STd = & ( U , , U ~ , . . . , U ~ ~ (1,c)

Fig. 8. Power-control input operating windows. 410

I

I

takes place after checking the difference between previously obtained operating data and current output data that are generated under the same condition. With the operating windows and MAS-ISSMs, the multiobjective Optimization problem can be tackled by the set-point generation agent and the cooperation of other agents. In this paper, the objective functions are accounting for the minimization of load-tracking error, fuel consumption, heat loss rate, pollutant emission, and extension of duty life on the equipment. Thus, the objective functions are J,(u)=lE,,,,

-EJ, J, =ul, J, =-u2, J , = u 3 ,

J, = - u ~ , J , = -us, J, = u,, J , = u,, J , = -u*, (2)

J9 =-u9, J 10 =-u 10'

Jll

=-%I,

J12 = -12

'

where, Euklis the unit load demand and the decision variables ( u ) are control variables as shown in Fig 1. When the unit load demand, Ezt,dis given from a central dispatch centre, the set-point generation agent creates the solution space, R,,R2,..., R,,, using the power-control input operating windows, Fig. 8. An operator commands the objectives and their preferences for the multiobjective optimization problem through the interface agent. The reference governor delegation agent adjusts the preference values by investigating the condition of power plant with historical data. After confirming the preference values, the multiobjective optimization problem i s solved by Particle Swarm Optimization (PSO), which is one of the algorithm modules in the setpoint generation agent. During the search for the solution, one of the MAS-ISSMs, Ed = 4, (u,,u, ,..., u,, ) , is utilized to evaluate the load-tracking error. The PSO algorithm is well suited for the reference governor because of the simple implementation, quality solutions, and the fast convergence. The performance monitoring agent evaluates the performances produced from the setpoint generation agents which utilize different optimization techniques. The detail comparison of the performances are shown in other references (Heo, et al., 2005).

Unit load demand E,,

I

Objective and preference

Fig. 9. Configuration of MAS-RG Casc 2: minimize J,(u),J,(u),J 2 ( u ) Case 3: minimize J,,(u),J,(u),J 2 ( u ),..., J,,(u) The objective functions are given in (2) and a vector of preference values is given as p = [1, 0.25,0.25,0, 0,0,0.25,0.25,0.25,0,0.25,0.25,0.25]. The demand power ( E,, ) is almost the same as the unit load demand as shown in Fig 10; however, the conflicting requirements cause slight difference between the demand power and the unit load demand. The demand pressure set-points ( Pd ) mapped for different number of objective functions are quite different as shown in Fig. 11. This is because the power-pressure operating window is quite large and the same amount of power can be produced on a wide range of pressure as shown in Fig. 7. Similarly, the demand reheaterisuperheater temperatures are shown in Fig. 12. As additional objective functions are added in the optimization, the plant is operating more conservatively in lower pressure and temperatures. Thus, all simulation results show that the MAS-RG can perform well in the multiobjective optimization problem and also in the on-line implenieniaiion since the pressure, ieniperatures setpoints need to be updated only when the unit load demand i s changed during the load cycle. Unit load deman

580

~

1

After finding the optimal solution,

U;

u ; , . . ., u;*

0

using

the PSO, the MAS-ISSMs are applied to map the optimal solution into demand power ( Ed ), steam ), reheater temperature ( RT, ) and pressure ( superheater temperatures ( ST, ) using (1). The setpoint scheduler block processes the task under the observation of set-point generation agent. Fig. 9 shows the configuration of MAS-RG.

100

200

case? - Case3

300 400 500 time (sec)

600

700

Fig. 10. Demand power set-point trajectories.

Case1

case:

2600

- - Case3

- 2500 m

-$

~

0 m ~

2400:

m

2? a

4. SIMULATION RESULTS

2300

2200 -

In the following, thc results of the MAS-RG will be shown. Simulations deal with three different cases:

2100 0

I

100

200

300

400

t 500

600

700

time (sec)

Case 1 : minimize J,(u) only

Fig. 11. Demand pressure set-point trajectories.

41 1

13901

0

100

200

300

400

500

600

700

time (sec)

Fig. 12. Demand reheatedsuperheater temperature set-point trajectories. Morcovcr, distributcd computing, which is thc advantage of the MAS, rcduces the computing time for on-line implementation. 5. CONCULSION

The Multi-Agent System (MAS) reduces the coupling problems of subsystems by intelligent dnd dsynchronous computation The MAS-RC gcncratcs the optimal mapping by searching for the best solution to the multiobjective optimization problem. The optimal mapping? between the varying unit load demand and the power, steam pressure and reheatedsuperheater temperature set-points are realized in an on-line implementation with the help or MAS. As one or the algorithm modulca, PSO is well suited for finding optimal solution in the multiobjcctivc optimization problcm In thc largcscale distributed power plant, the MAS-RG methodology shows good performances REFERENCES Decker, K. S. and Sycara, K. (1997). Intelligent adaptive information agents. Journal of Intelligent Information Sys., 9, pp. 239-260. Garduno-Ramirez, R. and Lee, K. Y. (2001). Multiobjective optimal power plant operation through coordinate control with pressure set point scheduling. IEEE Trans. on Energy Conversion, 16, (2),pp. 115-122. Ghezelayagh, H. and Lee, K. Y. (2002). Intelligent predictive control of a power plant with evolutionary programming optimizer and neurofuzzy identifier. Proc. Congress on Evolutionary Computation, 2, pp. 1308-1313. Gupta, R. P. and Varma, R. K. (2004). Agent based software integration at distribution control center. IEEE PES General Meeting, PESCM2004000930.PDF. Heo, J. S., Lee, K. Y. and Garduno-Ramirez, R. (2005). Multiobjective optimal power plant operation using particle swarm optimization technique. Proc. IFAC Congress, paper code: 04833.pdf, Tu-M06-T0/4, Prague. Heo, J. S. and Lee, K. Y. (2005a). Multi-agent system-based intelligent control system for a

power plant. IEEE PES General Meeting, CD,PESGM2005-000858.~df. Heo, J. S. and Lee, K. Y. (200Sb). Multi-agent system-based intelligent steady-state model for a power plant. Pvoc. the 13'" International Conference on Intelligent System Application to Power Systems (ISAPOS), Washington D.C.. Hossack, J. A,, Menal, J., McArthur, S. D. J. and McDonald, J. R. (2003). A multiagent architecture for protection engineering diagnostic assistance. IEEE Trans. on Power Systems, 18, (2), pp. 639-647. Junpu, W., Hao, C., yang, X. and Shuhui, L. (2000). An architecture of agent-based intelligent control systems. Proc. the 3"' World Congress on htelligent Control and Automation, pp. 404-407. Kennedy, J. and Eberhart, R. (1995). Particle swarm optimization. Proc. of IEEE internutional Confkrence on Neurul Networks (ICNN'95), LV, pp. 1942-1948, Perth, Australia. Kosakaya, J. Kobayashi, A. and Yamaoka, K. (2003). Cooperative multi-agent-based control technology for supervisory control and dataacquisition systems. Proc. Emerging Technologies and Factory Automation Conf:, pp. 19-26. Lee, K. Y. and El-Sharkawi, M. A. (Editors). (2002). Tutorial on modern heuristic optimization techniques with applications to power systems, IEEE Powcr Engincering Socicty, IEEE Catalog Number 02TP160, Piscataway, NJ. McArthur, S. D. J. and Davidson, E. M. (2004). Multi-agent systeins for diagnostic and coiidition monitoring applications. IEEE PES General Meeting, PESGM2004-000972.pdf. Padgham, L. and Winikoff, M. (2004). Developing intelligent agent systems. John Wiley & Sons, New York. Park, J.-B., Lee, K.-S., Shin, J.-R. and Lee, K. Y. (2003). Economic load dispatch based on a hybrid particle swarm optimization. Proc. International Conference on Intelligent Systems Application to Power Systems, CD ISAP03070.pdf, Lemnos, Greece. Usoro, P. B. (1977). Modeling and simulation gf a drum-turbine po wer plant under emergency state control, M.S. Thesis, Massachusetts Institute of Technology. Velasco, J. R., Gonzalez, J. C., Magdalena, L. and Iglesias, C. A. (1996). Multiagent-based control systems: a hybrid approach to distributed process control. Control Engineering Pmctice, 4,(6), pp. 839-845. Wittig, T., Jennings, N.R. and Mamdani, E.H. (1994). ARCHON: framework for intelligent cooperation. IEEE Trans. on Intelligent Systems Engineering, 3, (3), pp. 168-179. Wooldridge, M. (2002). An introduction to MuEtiAgent systems. John Wiley & Sons, Chichester, UK. Zhang, Z., MaCalley, J. D., Vishwanathan, V. and Honavar, V. (2004). Multiagent system solutions for distributed computing, communications, and integration necds in thc power industry. IEEE His' General Meeting, 1, pp. 44-47. 412

Copyright 0Power Plants and Power Systems Control, Kananaskis, Canada 2006

ADAPTIVE GOVERNOR CONTROL AND LOAD SHEDDING SCHEME FOR AN INCINERATOR PLANT

Y. D. Lee"", C. S. Chen"",C. T. Hsub3' aNationalSun Yat-Sen University, Kaohsiung, Taiwan bSouthern Taiwan University of Technology, Tainan, Taiwan

Abstract: This paper presents an adaptive control strategy for the governor system of an incinerator cogenerator to maintain the steam pressure and system power frequency. Due to the unstable steam generation in incinerator plants, the turbine valves have to be controlled adaptively to keep the boiler steam pressure constant for normal operation. After tie-line tripping caused by utility faults, the governor system must be operated with constant frequency control for the islanding system. By this way, the surplus steam supply to turbines will be bypassed effectively. For the islanding operation, the deficiency of steam generation is then supplemented by boilers. To maintain thc system stability after transient disturbance for the isolated system, the load shcdding scheme is designed by considering the under steam pressure protection. According to the transient stability analysis, the system frequency can be restored successhlly after tie-line tripping with the adaptive change of governor control system from the constant steam pressure mode to the constant frequency mode. Copyright 020061FAC Keywords: Governor control system; boiler; cogeneration system; load shedding; transient stability

1 . SYSTEM DISCRIPTION

T

o study the effectiveness of governor controller

for cogenerators with unstable steam system, an incinerator plant in Taiwan with three sets o f boilers and an extraction-condensing type of turbine gencrator as shown in Fig. 1 was selected for computer simulation using CYMSTAB sortware package. Different from conventional cogeneration systems of industrial customers, all steam generated from the incinerator boilers is exhausted by the turbine generator, and then condensed as the feed water for boilers. The power output of the incinerator cogenerator varies with the steam generation according to the amount o f refuse burned. Due to the variation of heat value in the trash, the steam flow generated by incinerator cogeneration will fluctuate very seriously. Therefore, the governor control system of the turbine has to be operated with

constant pressure control to maintain the boiler steam pressure for normal operation. For the severe fault contingencies of external Taipower system, cogeneration systems are normally isolated by opening the tie-line breakers, and the governor systems of cogenerators are adaptively changed to the constant frequency control to prevent the isolated power system from collapsing. With the unstable steam generation, it becomes very difficult to control the stearn pressure arid system frequency for the isolated cogeneration. In this paper, an adaptive governor control system for the turbine generator has been presented to maintain the stable operation of the incinerator cogeneration system.

"Corresponding author.

I l l

Tel: 886-7-5256436; fax: 886-7-5256436. E-mai 1 address : D93X 1001 3(as t uden t . n s y s u . edu . tiv

ydl ccl216@yahoo. corn. t n ' Member, IEEE.

Fig. I . Incinerator cogeneration system.

413

2. GOVERNOR SYSTEM MODEL WITH BOILER DYNAMICS

3. THE MATHEMATICAL MODEL OF THE INClNERATOR COGENERATlON SYSTEM

The governor system model with boiler dynamics for the incinerator cogeneration system is represented as shown in Fig. 2. The dynamic change of steam flows generated by boiler systems affects the power output of the cogenerator, which can be calculated as the product of the valve flow area x2 and the throttle pressure x4 of steam inlet. The valve flow area can be controlled by the governor system so that the turbine inlet pressure will be proportional to the integral of the net inflow passing through the tube of distributed superheater. Ksir is the friction coefficient of the tubes in the superheater, and KDis the overall storage volume coefficient of the boilers. Both parameters dominate the time response of incinerator boiler systems. The steam pressure drop from drum to inlet turbine is represented as the square of mechanical input power P,,,. The steam generation of boiler Qn is determined by the heat release in waterwalls depending on the amount of trash burned. Instead of considering the fuel dynamics and the boiler control systcm, thc stcam flow Qn directly controllcd by operators can be considered as the input variable of this model. The turbine power output can be derived according to the dynamic steam flows measured by the distributed control system (DCS). T I , T2, TCHare the time constants of the speed relay, servomotor and steam chest of the turbine, respectively. For constant pressure operation of the governor controller WOODWARD505, the PID frequency controller is cascaded by the PID pressure controller. By this way, the speed reference Q , ,can ~ be adjustcd to maintain the constant steam pressure of header according to the variation of steam flows, and the power output of cogenerator is independent of the system frequency fluctuation. For constant frequency operation, the PID pressure controller and the frequency droop controller R1 are deactivated as shown in Fig. 3. The speed reference is then set equal to the actual speed, and adjusted automatically to reach the synchronized speed with rate change of 2rpm per second.

Table 1 lists the parameters of the incinerator cogeneration unit, which were provided by the manufacturer, or obtained from performing the field test. The typical values were used for the time constants of the servomotor of govcmor systcm and the steam chest of turbine. The coefficient of steam pressure drop KSM was estimated based on the calculation of fluid dynamics for the incinerator boiler systems. The parameter KU was derived from the dynamic relationship between steam pressure of header and total steam generation. The parameters of PID frequency controller of the governor system were tuned for the possible maximum load rejection to maintain the stable operation of the incinerator cogenerator. To develop the better system analysis with the above parameters of the cogeneration unit, the governor system model with constant pressure control in Fig. 2 is linearlized as shown in Fig. 4. The output u of the controller is calculated in Eq. (1). The transfer function is expressed as Eq. (2), and the corresponding parameters H are solved by Eq. (3), (4), (5) and (6), respectively with constants A, B, C, D calculated as follows. By the same way, the mathematical model of the isolated-incinerator cogeneration system with constant frequency operation is linearlized as shown in Fig. 5. The corresponding state equation of the system can be represented as Eq. (7). Table 1 Parameters of the cogeneration unit

Gen

kV MW 1 1 9 54 X.' q

and Boller ~~~~~~~~~

ZdO

H Xd X, Xd 8 1 9 6 4 1 0 8 0257 &,I 0 z,o U, dU 1 5 0031 008 0 1 2 TCH Vnlax V,,, RI 02 10 0 005

X, 06 SGI 2

02

654

TI 005

Tz 005

Dl

R2

p2

I2

D2

KD

KSH

04

0

4

01

0

001

025

06 PI

4

X d

0 169 D 1 11 1

I

Fig. 4. Linearlized governor system model for constant pressure operation. mnom NIW

Fig. 2. Pressure control of governor system model.

., I'IIl1n !\

l r l l l l \I111

k, '

1,111

,,I,,,

111,1

rT,

1

Fig. 3. Frequency control of governor system model.

414

Fig. 5 . Linearlized governor system model for ation.

For an actual remote fault of external Taipower system without causing the tripping of tie-line, the dynamic rcsponse of systcm frcqucncy has bccn monitored as shown by line 1 in Fig. 6. To maintain a constant steam pressure, the speed reference of governor controller has been adjusted accordingly with the change of system frequency as shown by line 2. Figure 7 shows the steam flow of the header and power generation of the cogenerator. It is found that the power generation of the incinerator cogeneration system can be adaptively controlled by constant pressure operation o r the governor system with the variation of system frequency and steam flow.

[

I . System frequency 2.Speed reference setting

58.6Hz and 61.5Hz, the governor system is operated with constant pressure control to maintain the steam pressure for the unstable cogeneration system. The rotor speed of cogenerator is varied with the system frequency because of rather large inertia of the external Taipower system. To prevent the cogenerator from operating with undesired speed to cause the damage of the turbine, an over frequency relay 81H with setting at 62.5Hz and an under frequency relay 81L with setting at 58.6Hz are installed at the tie-line. The electrical signal for turbine tripping is also used with frequency setting at 63Hz to coordinate with the over frequency protcction for tic-linc tripping. Additionally, thc governor control strategy is designed to adaptively change to the frequency control when the incinerator plant exports the surplus power to Taipower with system frequency operation over 61.5Hz. After tie-line tripping, the power output of cogenerator has to be adjusted rapidly to accommodate the in-plant local load by frequency control of the governor system. At the same time, the fluctuated steam pressure of boiler header is controlled by bypassing the excessive steam, or activating the load-shedding scheme proposed in Table 2. The turbine bypass valve is controlled with setting at 1.08 times of the normal operating steam pressure for thc boilers. On the other hand, the loadshedding scheme is designed to maintain the boilcr steam pressure to be higher than 0.92p.u for the normal operation of the turbine. The total amount o f load to be disconnected is determined by the minimum generated steam flows and the maximum electrical load served by the incinerator plant.

Table 2 Load shedding schemc Steam pressure (PA) 0.98

0.96

1

0.95 0.94

Time delay (sec) 0. I 0.1

0. i For every 10 second

Load shedding 3M W

2MW 2MW 1MW

5. EFFECTIVENESS OF THE GOVERNOR CONTROL SYSTEM Time (mm )

Fig. 6. Actual system frequency and speed reference sctting. h

2

8k1xo

I

1 Steam flow

2 Power generation

v

3

2165

2

'150

Ti e mi )

Fig. 7 . Steam flows ,?the Reader and power generation.

4. GOVERNOR CONTROL STRATEGY WITH LOAD SHEDDING DESIGN When the cogeneration system is connected to Taipower with system frequency fluctuation between

To demonstrate the effectiveness of the proposed governor control strategy and load-shedding scheme, the tie- line was disconnected intentionally to test the islanding operation of the incinerator plant with different operation scenarios. Before tie-line tripping, three sets of incinerators arc operated with in-plant load of 8MW. The power output of cogenerator fluctuated between 2SMW and 32MW due to the unstable steam generation. By adding an extra heavy load of 27MW in the plant, the maximum power flow over the tie-line will be changed from exporting by 24MW to importing by IOMW. With the deficiency of power gcneration in the plant, the load shedding has to be cxecuted to maintain the steam prcssurc o f cogeneration system with constant frequency operation after tie-line tripping. Three different operation scenarios have been selected for computer simulation to solve the system response of the islanding incinerator cogeneration system.

415

C h e A. Small amount ofpower jlow,y over the tieline In this case, the power output of incinerator cogenerator is varied with the reduction of steam generation as shown in Fig. 8. The tie-line power flow is assumed to be changed by k3MW. Figure 9 shows the system frequency response of the incinerator cogeneration system with constant steam pressure operation after intentionally tie-line tripping. For the cogeneration system with exporting 3 MW to Taipowcr systcm beforc tic-linc tripping, thc isolated system frequency will be increased lo 61 H L , and then gradually decreased to 60.6Hz due to the governor control action. On the other hand, the frequency will be decayed to he less than 58Hz within a very short time for the operation condition of importing 3 MW from Taipower before tie-line tripping. It is found that the fluctuation of system frequency could result in the unnecessary load shedding or generator tripping if the constant pressure operation is implemented for the isolated incinerator cogeneration system. If the constant frequency control mode of the governor system is adaptively applied after tie-line tripping, the system frequency can be restored to 60Hz effectively as shown in Fig. 10 despitc of the dynamic fluctuations of power generation of cogenerator and steam pressure of boiler. Case 13 Steam generafionsurplus of the cogeneration system In this case, the power output of incinerator cogenerator is 32MW, and the total load demand for

the auxiliary boiler systems is 8MW, which implies that the imbalance of power generation and load demand will be 24MW. Figure 12 and 13 show the responses of system frequency and power output of cogenerator by applying the constant frequency control aftcr tie-line tripping for the islanding operation of incinerator plant. With such a large power generation surplus for the isolated system, the system frequency is increased to 62.8Hz during the reduction of power generation from 32MW to 8MW. The surplus steam is bypassed effectively to limit the steam pressure of boilers at 1.08p.u, and the system frequency was restored to 60Hz in 30 seconds. Case C. Steam generation dejiciency of the cogeneration system The power output of cogenerator and total in-plant load are 26MW and 35MW, respectively. Eigure 14, 15 and 16 show the system responses of the cogeneration system after tie-line tripping. Due to the dcficicncy of powcr generation in the plant, thc system frequency of the isolated system has dropped to the minimum value of 59.2Hz. The steam valve is opened to increase the power output of cogenerator to restore thc systcm frequency around 60112 by constant frequency operation. With proper control of the steam valve, the decay of steam pressure will result in the limitation of the turbine power output. By activating the load shedding scheme proposed in this paper, the steam pressure can be controlled to be stable at 0.94p.u, and the power output of cogenerator will be reduced to 25MW after one and half minutes.

20

40

T i ole( S

60

XO

I00

~ C )

Fig. 11. Frequency response of cogeneration system in Case B. -

-+3MW

GMW

-3h4W

35 + +

58

20

40

- --60

2 XO

25

2

--

20 15 1 0

5

-

0

100

I 1 mc ( 5 c < )

Fig 9 Frequency response for constant pressure operation in Case A 60.51

I-

SY.7

+3MW

- - GMW

-3MW

[

' , , ' ;,\

59.5

20

40




Fig. 17. Three different specd reference settings.

~~

0.921

20

80

40 60 Timc(scc)

i.i

100

Fig. 15. Steam pressure of cogcneration system in Case C.

6. TRANSIENT STABILITY ANALYSIS OF THE INCINERATOR COGENERATION SYSTEM To investigate the transient stability of the incinerator plant, the cogeneration system with the neighboring Taipower network in Fig. 17 has been used for computer simulation of transient stability analysis. The 161kV tie-line is connected to Taipower Nankung substation which also serves other large customers in the heavy industrial park. The Talin power plant of Taipower provides 420MW to serve the load of Linyuan substation which is connected to Kaokang EHV substation. The rest of Taipower system has been represented as the equivalent generator unit connected to Kaokang substation. The mathematical models with two damping coils along the p and q axes by taking into account thc magnctic flux saturation cffcct arc considered for all generators. The governor and exciter systems of Taipower generators are also included to simulate the transient response more accurately for the fault contingency of external Taipower system. I7t.iiliilv

ha, ~IwngIlil I\\

-1f

11111

7 -

I ItllC (\CCI

T I IIK( x c 1

l,i,lllf

Fig. 16. Onc linc diagram ofthc study powcr systcm.

T i

-.I

511 Timr (sc‘c k

~

r-,

1111)

Fig. 18. Frequency response in Case D. Case D. Nearby,fault of external power system For the nearby power contingency, a bolted ground fault on the 161kV transmission line in Fig. 17 has been assumed for computer simulation. By the operation of circuit breaker to clear the fault, the Nankung substation becomes an isolated system. With large industrial loads to be served, the cogeneration system frequency has been dropped to be below 58.6Hz to activate the tie-line tripping by under frequency relay to result in the islanding operation of the incinerator plant. At the same time, the governor system was changed from constant pressure operation to constant frequency operation by the governor controller. With three different speed rcfercnce settings as shown in Fig. 18, the corresponding system frequency of the islanding system during the transient period has been illustrated in Fig. 19. It is found that the over shooting of system frequency has been reduced to 62Hz by setting the initial speed reference as the actual speed with ramping rate of 2rpmisec after tieline tripping. Case E. Severejuult of external power system For the severe fault, such as the tripping of EHV 345kV transmission line, the whole Taipower system is separated to form the southern and northern subsystcms. Bccausc of thc largc amount of powcr flows carried from the south to the north, the tripping of transmission lines will introduce serious unbalance between power generation and load demand in each subsystem. With such large amount of power generation surplus in southern Taiwan, the system frequency increases dramatically in a short time period. To test the over frequency protection of the cogeneration system, the load tripping at Linyuan bus and the constant power generation of Talin power plant have been assumed in the study system for computer simulation by transient stability analysis. Figure 20 and 21 show the system responses of cogeneration system with different timing to change the governor control strategy.

417

When the fault occurs, the system frequency is increased to activate the tie-line tripping of the incinerator cogeneration system. The change of governor system from the constant steam pressure to the constant frequency control has to be made at the system frequency of 61.5Hz to reduce the power output o f cogcnerator in timc as shown by line 1 . On the other hand, the isolated cogeneration system will collapse if the constant frequency control of governor system is applied at the system frequency of 62.5Hz due to the turbine over speeding.

I

581

2

Preq c m t d at 61 5 H z

2

-Freq

. 60 TIIIIC(SLC)

ccmbol at 62 S H z

I

46

I00

80

Fig. 19. Frequency response with different models of governor system in Case E 1

&Prea oanhol at 61 5 H z

-7-

FPO o m h o l

st

62 5Hzl

I 20

40

60

RO

100

T I inlei w c )

Fig. 20. Turbine power output with different models of govcrnor systcm in Case B

concluded that the proper load shedding and the adaptive governor control by changing from constant steam pressure to constant frequency are very critical for the incinerator plant to maintain power system stability after tie-line tripping. REFERENCES C. S. Chen, Y. L. Ke, and C. T. Hsu (2000). Protcctive rclay setting of the tie line tripping and load shedding for the industrial power systcm. IEEE Trans. on Indmtrial Applirutions, Vol. 36, No. 5, Sep. /Oct., pp. 1226-1234. CYME International Inc. (199 1). CYMESTAB/UDM User’s Guide and Reference Manual. Canada. F. P. de Mello (1991). Boiler models for system dynamic performance studies. IEEE Tvcms. on Power Systems, Vol. 6, No. 1, pp. 66-74. M. E. Flynn, M. J. 0’ Malley (1 999). A drum boiler model for long term power system dynamic simulation. IEEE Trans. on Power Systems, Vol. 14, NO. I , pp. 209-217. Woodward Governor Company (1997). 505 Digitul governors j’br steam tuvbines with single of splitiwnge uctzratovs Munzral85017Vl.

Y. D. Lee received the B.S. and M.S. degrees in electrical engineering from National Taiwan University of Science and Technology, Taipei, Taiwan in 1997 and 1999. He has been an electrical engineer at the Southern Incinerator Plant, Kaohsiung, Taiwan since 1998. He is currently pursuing the Ph.D. degree in electrical engineering at National Sun Yat-Sen University, Kaohsiung, Taiwan.

7. CONCLUSION The adaptivc control stratcgy of govcrnor system for the incinerator cogeneration has been demonstrated by transient stability analysis. The design of load shedding scheme based on the under steam pressure protection has been proposed to maintain the system frequency and boiler steam pressure for the incinerator cogeneration system after tie-line tripping. For the external system disturbance, the fluctuation of steam pressure, the governor control system and the boiler control system or the cogenerator will affect the system response. To maintain the boiler steam pressure by considering the unstable heat value of trash bum in the incinerator plant, the PID controllers of the governor system for the constant frequency operation and constant pressure operation are coordinated with each other. The power output of the turbine generator fluctuates with trash heat value by applying the constant steam pressure control for normal operation. After tie-line tripping to isolate the fault contingency of external system, the constant frequency control will override the constant pressure control loop so that the system frequency of the islanding system can be maintained. The frequency response and power output of cogenerator for different case studies have been simulated. The transient stability analysis of incinerator cogeneration system by considering the unstable steam generation due to dynamic change of heat value of trash has been performed. It is

C. S. Chen received the B.S. degree from National Taiwan University, Taiwan in 1976 and the M.S. and Ph.D. degrees from the University of Texas, at Arlington in 1981 and 1984 respectively, all in electrical engineering. From 1984 to 1994, he was with National Sun YatSen University as a professor. From 1993 to 1997, he was with the Kaohsiung Mass Rapid Transit Department as the Deputy Director to be in charge of electrical and mechanical system planning. From 1997 to 1998, He was a professor at the National Taiwan University of Science and Technology. He is currently a full professor of Electrical Enginecring Department at the National Sun Yat-Sen University. His research interests include thc distribution automation, cogeneration systems, electrical and mechanical system of mass rapid transit networks. He is a member of IEEE and a registered professional engineer at Taiwan.

C. T. Hsu was born in Taiwan, 1963. He received the B.S., M.S., and Ph.D. degrees in electrical engineering from National Sun Yat-Sen University, Kaohsiung, Taiwan in 1986, 1988, and 1995, respectively. From 1990 to 1992, he was with Phoenixtec Power Company Limited as a Power Electronics Engineer, developing USP equipment. He is currently a Professor of Electrical Engineering at Southcm Taiwan IJnivcrsity of Tcehnology, Tainan, Taiwan.

41 8

Author Index Abu-Ayyad, M. Amracc, T. Andersen, P. Ansarimehr , P. Arakawa. h1. Bai. X. Balate, J. Barboza, L.V. Bathaee, S.M. Befekadu. G.K. Bendtsen, J.D. Boiko, I. Casolino, G.M. Caux, S. Cha, .J.S. Chawla, G. Chen. C.S. Cho, S.K. Choe, C.Y. Choi, M.S. Choi, S.Y. Chrarncov, B. Crainic, E.D. Cregan, hf. Ding, J . Duhay, R. Ebina, H. Ebrahimi, S. Erlich, I. Fadel, MI. Faille, D. Fang, Z. Fa rsangi , hl .i\f . Fernandes. C.E.M. Fernando, I.T. Flynn, D. Folly, K.A. Fusco, G. Givehchi, A.H. Golc, A.M. Gommlich, A. Giidat, R. Haake, D.

17, 35

Haase, T.

65

Haniachcr, T.

171 279 189 195 395 371 83 23 171 29, 237 213 95 219 125 413 231 143 207 219 395 101, 333 243, 401 195 17, 35 153 377 23 95 389 195 377 371 147 243, 401 41, 261, 291 107 71 147 249 183 183

Han, S.S. Hankache. W. Hashiguchi, T. Henckes, L. Heo, J.S. Hikiliara, T. Hiskens. I.A. Hissel. D. Hojo, M. Holbert, K.E. Hong, H.S. Hsu. C T. Hur, D. Jackisch, H. Jang. B.T. Jenik, P. Jeong, Y.W. Joergeriseri, C. Jokic, A. Jung, G. Kaberere, K. Karady, G.G. Karrari, 1c1. Kawai, K. Keller, H.B. Kezunovic, hl. Kim, B.H. Kim, H.H. Kirn, S.J. Kuri-Morales. A. F Kurth, M. Kwatny, H.G. Lee, C.J. Lee, H.J. Lee. J.G. Lee, J.I. Lee, J.W. Lec, K.W. Lee, K.Y. Lee, S.J. Lee, Y.D.

419

59 59 207 95 77 389 407 153 383 95 77 255 365 413 113 327 143 395 47 20 1 339 143 29 1 255 71, 83 189 249 137 309 131 365 315 7, 183, 345 353 131 113 365 231 47 119 309, 377, 407 207 413

Li, Z.

171 Pedersen, T.S. Petroianu, A.I. 101, 159, 291.333 Qahrarnan, B. 147 131 Radoj wic , Z . Rarnakrishna, G. 125, 273 Raiijbar, A. M. 65 Rasouli. W'. 2 79 Rawlisigs. J.B. 383 Rosehart, W. 71, 83 107, 213 Russo, hll. Sachdev, A!LS. 125 Saeki, 0 . 77 Saied, S.A. 83 Salgado, R .S. 371 Scisdcdos, L.V. 315 Shin. J . H . 231 Shin. J.R. 47, 131 Shin. M.C. 219 Shirakawa, M. 189 So&-Yome, A. 119 Song, J.I. 231 Susiiki. Y. 153 Teolis, C. 353 Torrisclii, U . 327 Toyosaki, G. 285 Trangbaek, K. 297, 303 Ukai, H. 77, 285 van den Bosch, P.P.,J. 339 309 Velas, J.P 383 Venkat. A.N. Verrna, S.C. 285 59 Wpher, H. Wcissbach. T. 183 Welfonder, E. 7. 183, 345 Wright. S.J. 383 Yariagihara, J . I. 165 Yang, K.M. 47 Yi, B.J. 231 Yoon, C.D. 219 2 79 Zafarahadi. G. 137 Zhang, Y. 195 Zhao, W. Zhou, J . 359 249 Zipser, S. Zoby, M.R.G. 165

195 159 207 255 213 267 hlajanne,Y . 32 1 Malik, O.P. 71, 83 273 Maruo. T. 53 hlataji, B. 89 Mataji, B. 177 hlatsurnoto, I(. 53 Matthes, J. 249 Mensah, E. 353 Miii, K.I. 365 hlritani, Y. 77 hlithulananthan, N 119 iliIkr t tcliiari, M. 237 Mocwane. K. 26 1 Moelbak, T. 201 Alondon. C. 389 Moon, Y.H. 365 Mori, N. 53 hlort ensen, J .H . 171, 201 Mozafari, A. 65 hlozafari, B. 65 Nakachi, Y. 285 Nakayama, H. 189 Navratil, P. 395 Newald. R . 327 Nezamabadi-Pour, H. 377 Nichur, D. 353 Niclscii. E.O. 201 Nielsen, R.J. 171 Odgaard. P.F. 177 Odgaard. P.F. 89, 297 Ohsawa, Y . 359 Ota, Y. 77 Pan. L. 243 Pandey, R.K. 1 Park, D.H. 207 47,131 Park, J.B. Park, J.K. 225 Park, J.Y. 225 Pariiiani, M. 2 79 Lilje, P. Lirn, S.I. Lin, I(. Losi, A. Llshosny, Z.

420