Reference Power Systems Protection Handbook

Reference Protection Handbook

CHAPTER 1 The Principles of Power-network Calculations By C. H. LACKEY. INTRODUCTION

point in the circuit to which the voltage is related. E ah therefore means the voltage of phase-a relative to phase-b; E an means the voltage of phase-a relative to neutral-no It is essential, if confusion is to be avoided, that the nomenclature decided upon shall be most rigorously applied. If this is done, interphase-voltagevectors, which sometimes give trouble, become quite simple. There are six for the three phases, namely E.ab and E ba , E bc and E cb , E ca and E ac ; and these are shown In fig. 2.

The use of calculator-boards for the evaluation of network currents and voltages is established practice, and results in a great saving of time as compared with direct calculation. The manipulation of a calculator-board may not demand great skill on the part of the operator, or require a full knowledge of the principles involved, but the interpretation of the results and a full realisation of the nature of the problem to be solved and its implications do require a sound knowledge of the basic principles of calculation. Apart from this, a calculator-board is often not available, or the problem may be simple enough for direct solution. Engineers associated with the design and performance of power-supply systems should so equip themselves as to be able to predict current and voltage values under both normal and abnormal conditions: a clear understanding of the basic principles of fault-calculations is of paramount importance in this connection. Attention is devoted here mainly to the principles of faultcalculation, but it should be understood that many of the principles, such as those of vector-algebra and networkreduction, are equally applicable to load-studies. Fault-calculations have come to be regarded as the prerogative of experts, and as operations requiring rather exceptional skill. Experience is without a doubt a necessary adjunct to speed, but no great skill or mathematical ability is necessary for the proper understanding and solution of most problems. The subject will be considered under the following four headings: Vector- Representation. Vector-Algebra and Impedance-Notations. Network-Reduction and the Calculation of Balanced Faults. Symmetrical-Component Methods. The approach will be practical rather than theoretical, and some elementary background knowledge will be assumed.

fen

\-----E""

Ebn

E'a

+

---


1\

-IeRg GENERATOR

" n

t

Ecn

X

l-l~

'I

I

b

~cn

-IcH

"' "'

\

"' "'

Veb

I

Ie

"'"'

_ _--;;;j,.:::::......:=-='""=-==-:="'=--::-:;~Eon Von

NEUTRl\l l:ARfHING

RESl5TOR

lb

(a)

Ebn

Vb.

Ebt.

10.

(not to scale)

(b)

I I

FIG. 5.

I

\(Ub ,

\

,

VECTOR-ALGEBRA AND IMPEDANCE NOTATIONS

\

Vector-Algebra All students are familiar with the elementary principles of vector-algebra, such as the expression of an inductive impedance in the form Z = R + jX, and the rationalization of expressions as in the following example:

FIG. 4.

12

GENERATOR Zg

z.e Ib

1\

The scalar value of this is IZI = YR2 + X 2, and X/R = tane Hence R = IZI cose, and X = Izi sine.

a. I.

F

----+ Ie

c.

tIe

~

(a)

Substituting these values in equation (1) gives Z = Izi (cose + j sine).

• Eeb (NOT TO SCALE)

It is proved in standard mathematical text-books that

cose + j sine = .i e .

II

Ee~

. --IrE'cb'T Eeb

Substituting .i 8 in the equation for Z gives Z = IZI .i e

I

Ie

len

(2)

This is known as the exponential method of specifying a vector. leI.

An impedance-vector has been taken by way of example, but the same principles hold good for current, voltage, or any other vectors. The physical significance of a vector expressed exponentially is perhaps not so obvious as when it is expressed in rectangular coordinates, but the exponential form is sometimes easier to manipulate in division and multiplication. The rules are the same as for ordinary algebra. Thus AXx AV = A(x + y) and AX/AY = A (x-y).

Ea.n

I

Ibe ' I

i

I

I I I

E'bc..E~C

: Ebn I

If we take a voltage-vector E = lEI .i e . and a current vector I = II cie" then EI lEI .i e , x III Je, EI III .j(e, + 8,), and E/I lEI Je./ III Je, = (I EI / III )J(e, - e,)

I

Ebc( NOT TO SCALE)

(b) FIG.

E

I Z

E I

I

6.

5 + JIO 2 + j3 5 + JIO 2 + j3 40 + j5 13

Consider also the following. Let Z = Z,Z2Z3/z..ZS. X

Expressing this exponentially, we have Z = Iz,1 .i e , x Iz21 .i e , x IZ3! .i e , Z.I .i e, x IZsl .i e ,

2 - j3 2 - j3

I

Iz.. Zsl , IZ 1 IZ./ IZ 31 x .j(ed ed ed - e, - e,) IZ·IIZs/ e 1 ZTI .i , (3)

It is not proposed to go into details of this part of the

work; we shall rather devote our attention to one or two important aspects that experience shows are not so well understood. where

These are: (a) the exponential method of specifying a vector; (b) vector-operator-a; and (c) the resolution of parallel impedances.

Algebraically, and in rectangular coordinates, an inductive impedance is expressed as

+ jX

T and e

I z,1 Iz21 Iz31 1z..IIZs! ' (e, + e2 + e3 - e. - es).

The evaluation of IZTI and e is merely arithmetrical, since all the components are plain numbers. If it is desired to give the final value of Z in rectangular coordinates, i.e. R and X, it is easy to do so, because R =IZTI cose, and X = IZTI sine.

The exponential method of specifying a vector

Z = R

1Z I

(1)

13

called operator j. Any vector-quantity multiplied by j is thereby rotated 90° anti-clockwise. If any vector, say a current vector, II Ea, is multiplied by vector I.i e , we get I.i(a e). The length of the vector II is unchanged, but its inclination to the reference-line is increased from a to (a + 8). Thus to multiply a vector by U 12 lJ" means simply that its angle to the reference-line is increased by 120°, i.e. the vector is turned through 120° counterclockwise; and multiplying by l. j240' turns the vector through 240°. The quantity l.i 120' is called a 120°-operator, and is usually denoted by the small letter a. Operator U240' is then a'.

A little reflection will show that equation (3) can be written down at once for any division of vector expressions, without the preliminary steps indicated above.

I

Take now a numerical example, and suppose that it is required to evaluate the following expression in terms of Rand X. Z = Z,Z./Z.Z.Zs, where Z, = 2 + j3, Z. = 4 - j2, Z. = 3 + j4, Z. = 2 + j2, Zs = 2 - j4.

In rectangular coordinates, a = I.i120'= cosl20° + jsinl20° = -0.5 + jO.866 a' = I.i240'= cos240° + jsin240° = -0.5 - jO.866

Writing the expression in exponential form gives Z =IZTI .ie, where IZTI =

\z,\z·1

IZ·I

IZ.I IZsl

Operators a and a' are used in symmetrical component work (as described later) as a simple means of rotating vectors through 120° and 240° respectively.

and 8 = 8, + 8. - 8. - 8. - 8s. Then

IZ,I = V2'

+

3' = 3.60 8, = tan- 1

3/2 = 56°

The resolution of parallel impedances

If a circuit comprises impedances in parallel, the total impedance is obtained from

IZ·I = V4' + (-~. = 4.471 • = tan- -2/4 = _27° /Z·I = V3'

+

4' = 5.00: 8. = tan- 1 4/3 = 53°

IZ.I = V2'

+

2' = 2.82 8. = tan- 1 2/2 = 45°

I

I

_1_ = ~1_ + _1_. + _1_ + Z Z, Z. Z.

..

Thus, for three impedances in parallel, 1 Z2Z. + Z.Z, + Z,Z. Z Z,Z.Z. Z = Z,Z.Z. Z.Z. + Z.Z, + Z,Z. In working out an expression of this kind, each impedance must be put in its vector from (R + JX) or Z I .i e . A simple alternative procedure, which is specially advantageous for more than two circuits, is as follows. Let R, + jX" and R. + jX•. 1 ~+~ Then z, Z. Z 1 + R. + jX.

/Zsl = V2'+(-4)' = 4.47 : 8s = tan- 1 -4/2 = _63° 3.6 x 4.47 = 0.25, 5 x 2.82 x 4.47 8 56 - 27 - 53 - 45 + 63 = _6°. Z IZTI .i e = 0.25.j(-6') R Izi cos8 = 0.25 cos (_6°) = 0.25 x 0.99 = 0.249. X IZ/ sin8 = 0.25 sin (_6°) = 0.25 x (-0.1) = - 0.026. Hence Z = 0.249 - jO.026. IZTI

I

The time saved by this method is well exemplified in star/delta transformations, where the expressions Z,Z,/Z" Z,Z,/Z" and Z,Z'/Z, require to be evaluated. Here the calculations of IZ,I ' Z.I, IZ.! ' 8" 8., and 8. for the first expression are equally applicable to the other two, whereas with rectangular coordinates there is nothing common to the three calculations.

Rationalise each term separately:

I

_1_ = 1 x R,-jX, + R, + jX, R,-jX, R. + jX. Z R, - jX, + R. - jX.

R,' + X,'

X

R.-jX. R.-jX.

R.' + X.'

R, + R. _j ( X, + X. ) R,'+ X,, R.'+ X.' R,~+ X,, R.'+ X.' The first two terms, consisting of resistance divided by the sum of the squares of resistance and reactance, are called the "conductance" of the circuit, and such terms are denoted by the small letter g. Similarly, quantities

Vector-operator-a

Two methods of expressing a vector have been mentioned, namely the rectangular-coordinate method, e'f' Z = R + jX, and the exponential me!h~ e.g. Z = ZI.-I e . In each of these the quantity j = V-I, and is

14

ohms to a voltage-base other than that to which they belong in practice. In this connection students are doubtless familiar with the concept of transformer equivalent impedance, referred to the primary or to the secondary winding. In the same way any impedance can be transferred from one voltage-base to another. The transferred impedance must of course have a value different from the natural impedance, in order that its effect in the circuit may be the same. The criterion so far as these calculations are concerned is that the same proportion of the driving-voltage shall be absorbed by the new value of the impedance. Expressed algebraically, I1Zl/El = hZ2/E2, where the suffix (1) indicates the initial or natural conditions, and suffix (2) the new-voltage-base conditions. From the above identity,

like the last two terms, involving reactance divided by the sum of the squares of resistance and reactance, are called the "susceptance" of the circuit, and are denoted by the small letter b. The last expression may thus be written as:

liZ = gl + g2 - j(bl + b2), and, generally, for any circuit involving a number of parallel impedances: liZ = gl + g2 + ga + -j(bl +b2 +ba + ) = G - jB, where G = gl + g2 + ga + . . and B = bl + b2 + ba + Thus Z

= _1_ , which, when rationalized, G -jB

gives, Z

+ jB G + B2 G

(4)

2

Zl Z2 Za Z.

= = = =

2 4 3 2

+ + -

X Zl El h E2 X ~ X Zl El El (because the current must be inversely proportional to the voltage)

j3, j2, j4, j2.

=

g2 = ga = g. =

2 22 + 4 42 + 3 32 + 2 22 +

32 22 42 22

=0.154 bl = =0.200 b2 = =0.120 ba = =0.250 b. =

3 22 + 32 -2 = 42 + 22 4 = 32 + 4 2 -2 = 22 + 22

(

~:

)

2

X

Zl

(5)

Taking transformer-impedance by way of example: Z, = Zp(E,/E p)2 and Zp = Zs (E p /E s )2, where ZIand Zp are the total equivalent impedances of a transformer referred to the secondary and primary sides respectively, and E s and E p are the secondary and primary voltages. Suppose that it is required to transfer the impedance of a 33-kV overhead line (say 8.6+ j 11.4 ohms) to a voltage-base of 6.6-kV. Z33-kY= 8.6 + j11A Zhh-kY =(8.6 + j11A) (6.6/33)2 = 0.344 + jOA56

Then gl =

~ x ~

Z2

The use of this equation for determining the impedance of parallel circuits can be a great time-saver, and reduces the problem to little more than simple arithmetic. Consider, for example, four parallel impedances as follows:

0.231 0.100 0.160 0.250

Per-cent-notation

G = gl+g2+ga+g. = 0.724 B = (bl+b2+ba+b. = 0.041 Z =

G + jB G 2 + B2

The percent impedance of a circuit, or of a piece of equipment, is the impedance-drop in the circuit, or in the equipment, when it is carrying a specified current, expressed as a percentage of the line-to-neutral voltage. Thus, % impedance ZI x 100, (6) line-to-neutral voltage where Z is the ohmic impedance of the circuit or equipment, and I is the specified current. In practice, MVA is invariably used instead of current in connection with per-cent impedance; this is permissable because MVA is proportional to current for a given voltage. Further, when specifying the per-cent impedance of. for example, a transformer or a generator, it is usual to give it for its rated current (MVA). Thus a 15-MVA transformer may have its impedance given as lOper-cent at 15 MVA or a

0.724 + jO.041 (0.724)" + (0.041)2

0.724 + jO.041 = 1.38 + jO.078 0.526 Impedance-Notations There are three ways of expressing the impedances of the various components of a network, namely (I) in ohms, (2) as a per-cent value, and (3) as a per-unit value, and in each case the expression may be in vector or in scalar form. Ohm-notation

The only matter to which attention need be drawn in connection with ohm-notation is that of relating the

15

30-MVA generator may have an impedance of 20 per-cent at 30 MVA. When using percent impedances, it is frequently necessary to transfer them from their natural MVA-base to some other MVA-base. Since the per-cent impedance-drop is directly proportional to current, and therefore to MVA, we have a very simple proportionality for such transfers, as follows: % impedance at MVA (A) = % impedance at MVA (B) x MVA (A) MVA (B)

approximate result is required, it is sufficient to treat the impedances as scalar quantities, and so make the additions, subtractions, and so on purely arithmetical. If however, such a simplifying assumption is not permissible, ohmic impedances must be expressed in their R + jX or IZI .j6 form, and per-cent and per-unit impedances in per-cent or per-unit resistance and reactance drops, as given above in equations (8) and (9). Relations between impedance-notations

It often happens that the impedances of networkcomponents are not all given on the same basis; for example, cable and line impedances are usually given in ohms, whereas transformer and machine impedances are usually given in per-cent or per-unit values. The same basis must obviously be used for all the components of the network, and so it becomes necessary to transfer some impedances from the given basis to the basis chosen for the calculations. We shall therefore derive expressions for the relations between the three notations, in order that such transfers from one basis to another may readily be made.

For example, if a generator has an impedance of 15 per-cent at 50 MVA, its impedance at 100 MVA is % impedance (100 MVA) = 15 x 100 = 30% 50 Per-unit-notation

The per-unit impedance of a circuit, or of a piece of equipment, is the impedance-drop in the circuit, or in the equipment, when it is carrying a specified current, expressed as a decimal fraction of the line-to-neutral voltage.

Let Z =impedance per phase of the circuit or of the equipment, in ohms, I =any given current per phase, in amperes, E =the rated line-to-line voltage, in kV, and M = 3-phase MVA based on E and I (M = V3EII1000). From equation (6), ZI % impedance x 100 = v'3ZI 1000E 10E

Thus, P.U. impedance ZI line-to-neutral voltage

.................(7)

Obviously the only difference between per-unit and per-cent impedance is that the former is the one-hundredth part of the latter. The 15-MVA transformer mentioned above has a per-cent impedance of lOper-cent and a per-unit impedance of 0.1. The rule for transferring a per-cent impedance from one MVA base to another, as given above, is clearly applicable also to per-unit impedances.

v'3 1000M v'3E '

Now I % impedance

and therefore, substituting for I

v'3z x 1000M 10E 100ZM -,

Vector-expression of per-cent and per-unit impedances

v'3E (10)

E2

If the ohmic impedance Z is written in its vector-form

R + jX in the expressions given above for per-cent and per-unit impedances, we have the concept of per-cent or per-unit resistance and reactance.

and Z

% imp. x E2 100M -ZM -,

Similarly, P.U. impedance =

E2

Thus, % impedance _ _ _--=Z=I x 100 line-to-neutral voltage

and Z

(11)

P.U. imp x EO

(12)

(13)

M

= (RI x 100) + jJSL x 100) ... (8) Ean Ean where Ean is the line-to-neutral voltage.

For example, a 20-MVA transformer with lOper-cent impedance (at 20 MVA), and a rated voltage of 33kV, has an ohmic impedance, from equation (11), of

Similarly, P.U. impedance= RI + jJSL (9) Ean Ean When all the impedances in a network are known to have, or may be assumed to have, the same, or approximately the same, power-factor, or when only an

2 Z33-kV = 10 X 33 - 5.44 ohms. 100 x 20 A 20-MVA generator with a per-unit impedance of 0.125 (at 20 MVA), and a rated voltage of 11 kVhas an ohmic impedance, from equation (13), of

16

NETWORK-REDUCTION AND THE CALCULATION OF BALANCED FAULTS

=

0.125 x 11" - 0.76 ohm 20 A 132-kV overhead line with an impedance of 12 ohms has a percentage impedance on a basis of 100 MVA, from equation (10), of ZIl-kV

An electrical power-network, from the point of view of fault-calculations, is merely an arrangement of series and parallel impedances between the source of supply and the fault. For the calculation of the total fault-current, the network is reduced to a single equivalent impedance between the source and the fault. For a radial network, the process of reduction is simply the addition of the various generator transformer, and line impedances. An example of this is given in fig. 7(a) and 7(b), the impedances in 7(b) being shown in ohms, per-cent, and per unit values. The value of the 3-phase fault-current is derived by dividing the line-to-neutral voltage by the equivalent impedance in ohms. If per-cent or P.U. impedances are used. Base MVA x 100 Fault MVA ----'------,------,--, or Total per-cent impedance Base MVA Fault MVA Total P.U. impedance In all these calculations the assumption is made that the impedance-values are identical for each phase, and so only one phase need be calculated.

100 x 12 x 100 - 6.9, 132 2 and the P.U. impedance is 0.069. % impedance =

rv V

GENEP~TOR

I IOMVA:IS.l'

GENERATOR 2 IOMVA:12'S!

- ....--T--....-

OVERHEAD LINE OF COPPER CONDUCTORS 0-1 SQ. IN. PER PHASE

LOADS ~T II kVAND 33kV OMITTED AS NOT RELEVANT TO THE PROBLEM

-..,..

T2

z" (0'43 +j 0-57).a PER MILE

...._

33kV

S1

S MVA:

2

IIkV

Example of radial system

From fig. 7(b), the impedance of the equivalent circuit is 0.774+j2.131 ohms at 6.6 kV.

6·6k'/

MI~ES

Hence the fault-current

0·2 SQ. IN. P. I. L C_ CABLE Z~(o·215+JO'122)1l.PER MILE

FAULT

IF =

6600/Y3 575 - j1590 0.774 + j2.131 If only the numerical value of the current is required,

(a)

j 68

0+jO'5S

O+jl00

a+J \-0

0+

= YR2 + X 2

Z

ZPU.

0.774 2 + 2.131" = 2.27 ohms, and

= Y

IF = 6600/Y3 - 1690 A. 2.27

0+jO·Z97

The current in the 33-kV line is

79+ j 105

TRANSFORMER

1

0+ j a-43b

IF33 = 1690

x

6600 =340 A. 33000

x

6600 11000

Similarly

0-79+ j 1-05

LINE

0-344+jO-456

IFll = 1690 --!--

33-kV BUSBAR

1020 A.

Current in generator 1 0+j160

O+jl'6

TRANSFORMER 2

OtjO'69B

II 99+jS6

0-99+)0-56

CABLE

=

_--=Z=2__ X IFI Z, + Z2

0.545 x 1020 = 463 A. 0.655 + 0.545

0·43+ jO'Z44

Similarly 178+j469 17S+j4'S9 TOTAL F TOTAL

(b)

0774+jZ-131

12 =

Zl Zl

FIG_ 7.

17

+ Z2

X IFll

_ _0_._65_5_ _ x 1020 = 557 A. 0.655 + 0.545 It is important, if the phase-angles of the generatorimpedances Zl and Z2 are not equal, that each shall be 6 form. expressed in its R + jX or The voltage at the 33-kV busbars is the line-to-neutral voltage plus the voltage-drop between the source and the 33-kV busbars. The impedance to the 33-kV busbars in ohms at 6.6 kV is Z =(0+jO.298) + (0+j0.436) + (0.334+j0.458) =0.334 + j1.l92 The current in amperes at 6.6 kV is IF6.6 = 575 - j1590. Hence the impedance-drop = - IZ = -(575 - j1590) (0.344 + j1.192) = -(2099 + j144).

IZI % = Y178 2 + 489 2 = 519% The 3-phase fault MVA = 100 x 100 519 = 19.3 MVA. The fault-current MVA x 1000 IF6.6 = V3 x 6.6 19.3 x 1000 1690 A, as before.

Izl.i

Y3 x

Expressing this as a vector quantity,

e

= tan- 1

100 x 100%= 17.2 MVA. 528% With vector-impedances, as above, the MVA is 19.3. The error resulting from the assumption of equal phase-angles is therefore

V6." = Y3X Y1716 2 + 1442 = 2980 V on a 6.6 kV basis. The actual line-to-Iine volts V33 = 2980 x 33/6.6 = 14,900 V.

Error % = 19.3 - 17.2 19.3 = 10.65%

Now, using the per-cent impedances figures of fig. 7(b), the total per-cent impedance on a 100-MVA basis = 178 + j489.

e

0·67+ i 6·\ 0·4 + j 3·62

o 24+jO·75 1·75+jO·9 0·Z4+jO·75 0-4+ j 3·62 ~.

1·36+j 1·36

'·75+jO·9 (a.)

o 55+j0224

l

~~~~el /·08 +jO·S5

0·55+1 C224

\

(d)

= 70°, and

= 1690 cos70 - j1690 sin70 = 578 - j1590, as before. The procedure for P.D. impedances is obviously exactly the same. It is frequently permissible, if vector-results are not required, to assume that the phase-angles of all the impedances are the same. If this is done in the preceding example, a total scalar impedance of 582% is obtained on an MVA basis of 100. The three-phase fault MVA is then

The scalar line-to-line volts.

145+ jO·8

489 178

IF6.6

The phase-to-neutral voltage at the 33-kV busbars, expressed on a 6.6 kV basis, = (E + jO) + IZ = (6600/V3 + jO) - (2099 + j144) = 1716-j144.

175+ j09

6.6

I (e)

FIG. 9.

18

x 100

An error of such an amount is often quite permissible, and because of the relative simplicity of scalar impedances they should be used wherever vector results are not required, and where great accuracy is not important.

equivalent star-group (say ZAB, ZBC' and ZCA) as follows: ZAB =

_ _Z_A_Z_B_ _ ZA + ZB + Zc

(14)

ZBC =

- -ZBZC ---

(15)

ZA An example of an interconnected network

ZCA =

Consider now a simple interconnected network, as shown in fig. 8. Let it be supposed that a three-phase fault occurs at sub-station C, and that it is required to determine the currents in all branches of the network. Fig. 9(a) is the impedance-diagram for the network of fig. 8. In fig. 9(b) the impedances of the two parallel cables, each 1.75 + jO.9, have been resolved into the single impedance Zl = 0.87 + j0.45, and the four series-impedances of the 66-kV line and transformers have been resolved into the single impedance Z2 = 1.28 + j8.74. Z2 is in ohms at 33 kV, i.e. the actual ohms at 66 kV of the line have been multiplied by (33/66)2, and the transformer-impedances have been calculated on a

+

ZB

+

Zc

(16)

_ _Z_cZ_A_ _ ZA + ZB + Zc

(o.)

20MVA

"_ ..........__..,..1.oooo-33kV

(b)

B

FIG.

Applying this to the delta-group ZA' ZB, Zc of fig. 9(b) gives the equivalent star-group ZAB, ZBC' ZCA of fig. 9(c). For example:

D

ZAZB

ZAB = ZA F

FIG.

10.

8.

=

+

ZB

+

Zc

(1.75 + jO.9) (1.45 + jO.8) (1.45+jO.8) + (1.36+j1.36) + (1.75+jO.9.) 0.55 + jO.224.

Similarly ZCA = 0.439 + jO.371, and

33-kV basis. Although these steps have simplified the impedance-network, the delta-group of impedances ZA, ZB, and Zc is not amenable to reduction by the laws of series and parallel impedances; but it can be replaced by an equivalent star-group. Any delta-group of impedances (say ZA, ZB, Zc in fig. 10) is related to the

ZBC = 0.53 + j0.416.

The network may now be reduced to fig. 9(d), and further, by combining the parallel impedances, to fig. 9(e), and finally to fig. 9(f) which shows it as a single equivalent impedance of 2.3 + j7.17 in ohms at 33 kV;

19

and the total three-phase fault-current may be determined thus: phase-to-neutral voltage IF = equivalent impedance 33,000

V3 X(2.3

leaving a junction must be equal. Refer to fig. 11, which is an enlarged diagram of this part of the network, and consider the junction between ZB' Zc, and Z2' First assume a direction for the current I c ; it is immaterial which direction is chosen so long as it is indicated clearly,

+ j7.17)

= 775 - j2420 amperes.

ASSUMED DIRECTION FOR Ie

To find the current in each branch of the network, we must now work back from the equivalent impedance to the original network, dividing up the total current IF between the various branches according to their respective impedances. From fig. 9(d) the currents in the branches Zx and Zy are obtained by the ordinary rule for parallel circuits thus: Ix =

z,

z,

-

Z X If, where Z is the impedance of Zxand Zy Zx in parallel = 1.08 + jO.~5 (fig. 9(e)),

= 1.08 + jO.85 = (775 _ j2420) =

Iy

1.31 + jO.82 917 - j2078.

_ -Z

-

Zy = =

X

FIG. 11.

IF since the result is related to the direction chosen. Suppose that Ie flows from left to right as shown in fig. 11. Then I B , or I c + 12 I B - 12 (12 = I y of fig. 9(d)) Ic (145 - j890) - (-142 - j342) 287 - j548.

1.08 + jO.85 x (775 - j2420) 1.81 + j9.15 - 142 - j342.

The distribution of current in fig. 9(d) is now determined. The next step is to find the currents in the delta ZA, ZB, Zc, of fig. 9(b), corresponding to those of the equivalent star ZAC' ZBC' ZCA of fig. 9(c). There are two steps in this, namely first finding I Aand I B, and then finding I c . To find I A and I B, equate the voltage-drops between equivalent star and delta terminals as follows: IBZ B = IABZ AB + IBcZBc (see fig. 9(c)), where lAB = If = 775 - j2420, and I Bc = ly = - 142 - j342. Hence I B (1.75+jO.09)

The result may be checked by considering the junction of Zj, ZA' and Zc. Thus (again referring to fig. 11). I, I A + I c , or Ic II - I A (I, = Ix of fig. 9(d)) (917 - j2078) - (630 - j 1530) 287-j548. The current in each of the two cables on the left-hand side of fig. 8 is one-half of the current in impedance ZI of fig. 9(b). Thus

(775 - j2420) (0.55+jO.224) + (-142-j342)(0.53+ j0.416), from which I B = 145 - j890. =

Icables

Similarly, IAZ A = IABZ AB + IcAZ cA (see fig. 9(c)) , where lAB = If = 775 - j2420 as before, and I CA = Ix = 917 - j2078.

=

~ 2

=

917 - j2078_ 458 - jl039. 2

Similarly, the current in each of the generators is one-half of the total fault-current, since in this example the generators have equal ratings and impedances. Thus

Hence I A (1.45+jO.8) = (775 - j2420) (0.55+jO.224) + (917 - j2078) (0.439 + jO.371), from which I A = 630 - j1530.

Im!e

=

l!:.2

= 775 - j2420_ 387 - j1210. 2

The total current and the current in each branch of the network have been calculated, and the results are summarized in fig. 12. The impedances ofthe 66-kV line and its associated transformers were reduced to ohms at

To find the current Ie in the branch Zc, remember that the sum of the currents flowing into any junction is zero, or, in other words, the total currents entering and

20

33-kY, and the actual current In the 66-k Y line therefore Ibh-kv I, x 33/66 (-142 - j342) x 33/66 -71-jI71.

method is usually more convenient than the per-cent. The per-unit method is usually preferred for synchronous-machine studies in general and for calculator-work. (iii) When vector-impedances are to be used, there is little to choose in fault-current and fault-voltage calculations between ohms, per-cent, and per-unit notations, unless most of the data happen to be in a particular notation. In this case, the student should, to begin with. use the notation thatcomes most naturally to him.

IS

This is the value given in fig. 12.

SYMMETRICAL-COMPONENTS METHOD Basic Relations

~-jI71

The basic principle of symmetrical-component theory is expressed in the following relations: I" = 1"0 + 1"1 + I,,:, (17) Ih = I ho + Ihl + Ih :, (18) Ie = Iell + lei + Ie:' (19) where I". I h , and Ie' are the phase-currents, and (i) components with suffix '0' have zero phasesequence. (ii) components with suffix '1' have positive phase-sequence, and (iii) components with suffix '2' have negative phase-sequence.

B

F

Using operator a, these relations can all be expressed in terms of phase-a as follows: (20) I a = laO + I al + I,,:, I h = laO + a 2 I ai + ala:' (21) Ie = 1"0 + alai + a 2 I"2 (22) Equations (21) and (22) for the phase-b and phase-c currents can be expressed in another way as follows:

TOTAL FAULT-CURRENT

775 -

j 2420

FIG. 12. Choice of impedance-notation

Having now referred in greater detail to the three notations in use, we may consider their relative spheres of application. (i) A decision must be made on whether or not it is permissible to use scalar values of ohms, per-cent, or per-unit. For phase-to-phase faults, or for phase-toearth faults in solidly-earthed systems, and where only the magnitudes of fault-currents and fault-voltages are required (i.e. not their phase-angles), scalar impedances are very often permissible, and negligible errors result from their use. The reason for this is either that the phase-angles are very similar (for example the impedances of generators and transformers are mostly reactive), or that one kind of impedance predominates. (ii) When scalar impedances are permissible, per-cent and per-unit values are usually preferred to ohms, unless most of the data are in ohms. The advantage of per-cent and per-unit values is that they can be added together irrespective of voltage, whereas ohmic values have to be brought to a common voltage-base. As between per-cent and per-unit there is nothing to choose for fault-current calculations. When voltages are involved, and when it is necessary to calculate voltage-drops, the per-unit

EQUATION (21): I b = laO + a 21al + ala:' = lao+ (-0.5 - jO.866)la1 + (-0.5 + jO.866) la2 = laO - 0.5 (Ial + la2) - jO.866(Ial - Id

..

...................... (23) (22): I c = laO + alaI + a 2 1a2 = laO + (-0.5 + jO.866) lal + (-0.5 - jO.866) la2 = laO -0.5 (Ial + Id + jO.866 (Ial - la2) · (24) EQUATION

Corresponding terms in equation (23) and (24) are identical, apart from the signs of the j terms, and this simplifies the calculations of phase-b and phase-c currents. These relations between phase-values and component values hold good for phase-to-neutral voltages as well as for currents. Calculation of the sequence-components

The utility of the basic principle expressed in equation (20), (21), and (22) above depends on knowing the

21

sequence-component currents lao, lab and la2' The first step in the calculation of these is to determine the impedance of the network to their flow. This is not necessarily the same for currents of each sequence. There are two reasons for this: first, that the impedance of the generators, transformers, and so on may not be the same for all sequence-currents, and, second, the path through the network, from the source to the fault, may not be the same for each. It is therefore necessary to have a network-impedance diagram for each phasesequence component. These diagrams are generally referred to as the sequence-impedance networks. A simple line-diagram of the network is prepared, showing the generators, transformers, lines, and so on with which the calculation is concerned, and the position of the fault. The positive-sequence impedance-diagram contains the impedances of all the parts of the network between the source of supply and the fault; and the values of the individual impedances (ohms, per-cent, or per-unit) for the generators, lines, and so on are the ordinary star-impedances as used in three-phase fault-calculations. The only voltages generated (by normal machines) are positive sequence (a, b. c), and therefore the generator voltages are placed in the positive-sequence network. Fig. l3(a) is a single-line diagram for a simple network comprising two generating-stations with interconnectors, and with a fault (of some kind) at F. Fig. 13(b) is the corresponding positive-sequence impedance-diagram. It is usually assumed that all generator internal voltages are equal in magnitude and phase. On this basis the four generator-terminals 1, 2, 3, and 4 are all at the same potential, and the diagram can be simplified by joining these points and using a single source of e.mJ. E, as in fig. 13(c). This impedance-diagram has two terminals, namely the neutral-terminal N I and the fault-terminal Fl' Consider now the impedance of the network to the flow of negative phase-sequence currents. The impedance-diagram is the same as for positivesequence. The impedances of transformers, lines, and so on to negative-sequence currents are the same as their positive-sequence impedances, but for generators the negative-sequence impedance is only about 70 per cent ofthe positive-sequence impedance. Further, there is no generated voltage in the negative-sequence network, because, as stated above, positive-sequence voltages only are generated. Fig. 13(d) is the negative-sequence impedance-diagram of the network of fig. 13(b). The two terminals of the diagram are N z and F 2 • In considering the impedance of the network to the flow of zero-sequence currents, it should be remembered that the three zero-sequence currents are by definition equal in magnitude and phase. They can only flow, therefore, when the fault provides an exit from the phases whereby they can return to the system-neutral. Such an exit is provided only when the fault is between one or more phases and earth, and the system-neutral must be earthed so that the return-circuit to the neutral is complete. Thus zero-sequence currents flow only in earth-faults, and they traverse only those

N. .---- - - - - - - - - - - - --:-----0- - - - - - - - - - - - - - - - - - - - I

e I

e,

I

3

2

Fl

e,

4

(b)

I

ej>--: :

e~--'

EoN,

r------ ----- - ---.- -- --8-------- - ----- - ---- - --,

:

:

F,

(ej POSITIVE-SEQUENCE NETWORK 2

~~ ~ ro

'---------'-:

Fz

(d) NEGATIVE-SEQUENCE

NETWORK

~ (e) ZERO-SEQUENCE NETWORK

FIG.

13.

parts of the network directly connected to earthed neutrals. The zero-sequence impedances of the generators, transformers, and lines are often quite different from the positive-sequence and negative-sequence impedances. Neglecting the values of the impedances, the zero-sequence impedance-diagram for the network of fig. 13(b) is as shown in fig. l3(e). The neutral-point of generator 4 is not earthed, and so the impedance of this N,

o e

Zz

Z,

FIG.

22

14.

Zo

Referring to the diagrams of fig. 15, we may now calculate the sequence-component currents as follows (E is the phase-to-neutral voltage): Earth fault: (see fig. 15(a)). E ......................(25) lao = I al = I az = Zo + Z, + Z2 Phase-to-phase-fault: (see fig. 15(b)). E ................................................(26) Z, + Z2 I az = -I al (27) lao = O. Two-phase-to-earth-fault: (see fig. 15(c)).

machine does not appear in the zero-sequence network. There is, further, no generated voltage in the zero-sequence network, because, as stated above, only positive-sequence voltages are generated. The two terminals of the zero-sequence diagram are No and F o. If the values of all the impedances in the positive, negative, and zero sequence diagrams are known, each may now be reduced to a single equivalent impedance. The positive-sequence diagram now becomes the single impedance Zj, the negative-sequence diagram Zz, and the zero-sequence diagram Zz, as shown in fig. 14. All that is now required to enable Iaj, I az , and lao to be calculated is a knowledge of the voltages impressed across the impedances Zj, Zz, and Zoo Since the only voltage in the three impedancediagrams is that in the positive-sequence diagram, the negative-sequence and zero-sequence impedance diagrams must be connected in some way with the positive-sequence diagram in order that negative-sequence and zero-sequence currents may flow. The question is how the diagrams should be connected, and it can be shown that the answer depends on the kind of fault, i.e. whether it is phase-to-earth, phase-to-phase, two-phase-to-earth, or three-phase, a different connection applying for each. The methods of connection for each kind of fault are shown in fig. 15(a) to 15(d). For an earth-fault all the three diagrams are connected in series; for a phase-to-phase-fault the positive-sequence and negative-sequence diagrams are connected in parallel; for a two-phase-to-earth-fault all the three diagrams are in parallel; and for a three-phase-fault there is only the positive-sequence diagram. The correctness of these connections is proved in books dealing with the theory of symmetrical components.

N,

N,

t,

r,

~

...

1.,

'2

F,

NZ

t

1.. F,

ca.) hnh·fUlt

1""I.-ee-pr,a.-:.e-falllt

~N E

t,

r

Z,

...

"

TWO-;l~./t5t·

'.

tc· euth-fa.vIC

FIG,

Z,

(30)

(31)

The six steps are: (i) Determine (by inspection) the sequenceimpedance diagrams (the zero-sequence diagram is required only for faults involving earth). (ii) Fill in the values of the sequence-impedances. (iii) Reduce the diagrams to their equivalent impedances ZI' Zc, and Zo. (iv) Connect the equivalent impedances together in accordance with figs. 15(a) to 15(d), according to the kind of fault.

N2

...

-E

(29)

I az = O. lao = O. Attention should again be drawn to the important convention that all vectors are for the positive direction; that is to say, they represent quantities acting away from the source towards the fault. This applies equally to the symmetrical-component vectors of the fault-current, and therefore the values of I al , and I az , and lao derived above are for the directions neutral-to-fault, as indicated by the arrows in figs. (15a) to 15(d). These relations are obviously very simple indeed, and therefore the symmetrical components of currents for any of the four kinds of faults mentioned above are easy to determine when the sequence-impedances are known. When the components of current are known, the actual phase-currents are obtained by addition, in accordance with equations (20), (21), and (22), or with equations (20), (23), and (24).

Z2

FZ

•

I al =

(28)

Z2 Zo Z2 + Zo

Zo Z2 + Zo Z2 lao = -Ial X Z2 + Zo Three-phase-fault: (see fig. 15(d)).

z,

Z2

Z, +

I az = -I al x

N,

NZ

E

I al =

15.

23

GENERATORS ~,

N,

1'4, 0

0

19kv

p

19kv

)2,6

)2'6

j 14

J 13

J IS

1'4, 0

0

19kv

19kv

1'4,

j 1·3

J14

1 15

pI

j 18

jl33

j 20 Q,

Q

R,

)24 Iw< 1·0 za:: - w -'z ::E w O\.:J a::::E ""0 V> a:: a:: .... 0·8 ela:: :) < ell ell

V>

I- :) < ell < ::E< > ::E II >-

0·6

0·4

0·2H--+-+-+-~1£_-~:....-_t-~~-_+----_::::l:_-~--_!

A = 0'\

o

0·4

0·2

X A

=

21.

0·8

MVA AT FAULT MVA AT BUSBARS

=-_,= + I

FiG.

0·6

~ Y

FRACTIONAL D.C. COMPONENT OF LINE TIME-CONSTANT (T)

FRACTIONAL D.C. COMPONENT OF LINE TIME-CONSTANT.

63

/·0

I ·8.----.----,-

I ·6 t------+----t-----+---+---+---+--t-----tc--+--t---

1·4 t - - - - - - - \ l - - - - -

W

u

1·2

'" uo

w::::>

::::>", "'''' 00 "'I-

W


..to

"c: 8., V> ~

"

v

50

'y

.,

c:

Stalloy Core: St" x 7~" dlams )( 3' deep

a.

0

Secondary VVlndlng' 300 turns (I) & (2) Average-reading Instruments (3) & (4) R.m.s.-reading instruments

o .\.L----------'-----------'----50 o 100

150 A.T

EXCiting Ampere-turns

FIG.

10.

OPEN-CIRCUIT EXCITATION CURVES USING VARIOUS TEST-METHODS.

72

These curves are widely used for protective currenttransformers as, for a low-reactance current transformer, they contain all the information necessary to assess the capabilities of a current-transformer and its consistency with others of the same nominal design. It is important to appreciate, therefore, that the form of this curve is affected by the methods of test, the instruments used, or the basic data curves from which it is derived. This is illustrated in fig. 10, which gives a series of excitation curves for the same current-transformer for different test-conditions. The first curve (1; is for average values of voltage and exciting current for applied sinusoidal voltage. The second curve (2) is similarly for average values but is for sinusoidal current. Considering curves (1) and (2), the average value of voltage, regardless of waveform, depends on the average flux-change, which depends on maximum flux and hence on peak magnetizing-current. Two points on these curves, (a-a') of equal average voltage, would have the same peak magnetizing-current. The current of curve (1), being peaky, will have a smaller average value than that of curve (2) and so will lie to the left. The Lm.S. value of a quantity is very dependent on wave-form, and this is noticeable in curves (3) and (4). Taking the sinusoidal-voltage case (3), the Lm.S. value of the peaky magnetizing current will be greater than its average value but will still be less than that of the sinusoidal current, and this curve will thus lie between (1) and (2). For similar values of sinusoidal current (b-b') the average voltage being the same, the Lm.S. value of the peaky voltage will be very much higher, raising the level of this curve as shown. This sinusoidal current/Lm.s. curve gives the impression of a higher saturation level. Curves of average values are shown because many average-reading instruments of the rectifier type are in general use, these being scaled in terms of 1· I times average value, which gives the true r.m.s. value only for a sine wave. It should be noted that all the curves coincide in the unsaturated region because both current and voltage are approximately sinusoidal. The curve normally used for protective gear is No. (3) i.e. sinusoidal voltage with r.m.s. reading instruments, and most design-data curves, e.g. those in fig. 7 and fig. 9, are given for this condition. This is valid in most applications of low-impedance schemes with linear burdens since the secondary current, and thus voltage, is nearly sinusoidal. For high-impedance schemes the voltage may become very peaky on internal faults and curve (4) is more applicable. However, this is not gen~ral1y used even for high-impedance systems, the addItional voltage obtained being considered .as an add~tional safety-factoL In any case, the validity of using a curve would depend upon whether the relay used is responsive to Lm.S. values or average values.

SO%i IO~.v

KNEE POINT

o

> u

a

Exciting Current

FiG.

11.

KNEE-POINT VOLTAGE.

materials except, perhaps, mumetal. It is difficult to define this transition, and use is made of the so-called 'knee-point' voltage for this purpose. It is generally defined as the voltage at which a further 10 per cent increase in volts requires a 50 per cent increase in excitation-current as shown in fig. 11. For most applications, it means that the current-transformer can be considered as approximately linear up to this voltage. This voltage does not necessarily correspond to that given by the saturation factor and its associated burden, but will be of the same order.

Special Requirements for Protective Current-transformers Instruments and meters are required to work accurately up to currents of the order of full load only. Accuracy is not rquired above this and saturation may, in fact, be advantageous in limiting the overload imposed on a secondary burden. Saturation could therefore take place at secondary currents above about 150 per cent of normal rating but, in many cases, it will be considerably in excess of this because of the iron section needed to obtain the required accuracy. This is not necessarily so when high-permeability core-materials are used. Protective gear, on the other hand, is concerned with a wide range of currents from fault-settings to maximum fault-currents which may be many times normal rating. While larger errors may be permitted in protective current-transformers it is extremely important that saturation should be avoided whenever possible in order to eliminate gross errors. The widely differing requirements of current-transformers for instruments and for protection usually mean that it is advisable to provide separate transformers for these two duties. In smaller classes of switchgear, however, economic limitations may require that instruments, such as ammeters, are energized from the protective current-transformers. An acknowledgement of the special requirements of protective current-transformers is given by B.S. 2046, which is concerned with the specification of currenttransformers for non-balance systems of protection. B.S. 81, for Instrument Transformers, is under-going revision and may in future utilize some of the methods of

Knee-point Voltage

The transition from the unsaturated region to the saturated region of the open-circuit exitation characteristic is a rather gradual process in most of the core

73

accuracy and to saturation-factor. As most currenttransformer specifications seem to favour the 5-ampere level and as the I-ampere level is often preferable from protection design considerations, it is worth while reviewing the significance of the secondary level in more detail. As previously pointed out, the main requirement associated with protective current-transformers is that they should maintain their ratio with a prescribed accuracy for primary currents greatly in excess of the rated current. This factor is important in both slow-speed and high-speed protective systems and in both balance and non-balance systems. For slow-speed balance systems the required saturation-factor is determined largely by the steady-state stability conditions, but a much higher saturation-factor will generally be required for highspeed balance-systems due to the transient fluxes occurring in the current-transformers under fault-conditions. In some high-speed non-balance systems, such as distance protection, transient effects may have to be taken into account and similarly high saturation-factors will thus be needed. This requirement of high saturation-factor has become an important aspect of modern protectivesystems. The level of performance required of protective-systems has increased and system conditions have become more severe. In order to achieve adequate protective-systems it has been necessary to reduce the VA requirements to as Iowa value as possible and, in some cases, to a value which is low compared with the internal burden of the current-transformer and the external lead burden. With these considerations in mind, for high-speed low-VA protective gear a I-ampere secondary level is very desirable except for those current-transformers having primary ratings sufficiently high to give the required saturation-factor with a 5-ampere secondary. At these higher primary ratings the physical problem of

specifying performance given in B.S. 2046. It should be noted that B.S. 2046 is concerned with currenttransformers for protective systems such as overcurrent, earth-fault, and distance. In the latter case, special consideration may be necessary for high-performance high-speed distance. The requirements associated with balance systems of protection are so various and so dependent upon the particular protective system that it has not yet been considered advisable to attempt to standardise this type of current-transformer. However, the methods of specifying and defining output used in B.S. 2046 are applicable to current-transformers for balance systems and are to be preferred to those used in B.S. 81. In addition to the current-transformer tests specified in B.S. 2046, balance systems of protection would require conjunctive testing of some form either as type-tests or individual proving-tests.

Choice of Secondary Rating Though B.S. 81 and B. S. 2046 give a preferred value of rated secondary current of 5 amperes they permit a I-ampere or O· 5-ampere level to be used where (a) the number of secondary turns is so low on a 5-ampere winding that the ratio cannot be adjusted within the requisite limits by the addition or removal of one turn, and (b) the length of the secondary connecting-leads is such that the burden due to them, at the higher secondary current, would be excessive. Requirement (a) may be largely associated with metering applications, as the precise transformation-ratio of protective current-transformers is not particularly important so long as the current-transformers are all the same. It has already been pointed out that the number of secondary turns can have a marked effect on the capabilities of a current-transformer both in respect to Volts

150

'" ~ o

100

>

RCT=

300

FIG.

600A Primary Rating

12.

I-AMPERE SECONDARY.

74

In. (at 300A)

Winding drop

Volts

150

r--_.. .====~~==========

100 o

>

c o .;:;

Saturation Factor = 30

RL= I Jl

~

..

~

50

o·oaJ1.

Vl

Ro=0·04J1. (at 300A) Relay volts

o

600A

300

Pri mary Rat; ng

FIG. 13.

5-AMPERE SECONDARY.

5-ampere secondary level as shown below. Peak open-circuit voltage for I-ampere sec. VI = Kalp.n. Peak open-circuit voltage for 5-ampere sec. V s = K7alp.n/5 where K and ex are constants for given core-material, and n is the number of turns of a I-ampere secondary. VS/V I = 1·4.

winding I-ampere secondaries would, in any case, favour a 5-ampere secondary. The following analysis may help to bring out the particular problems involved in choosing the secondary level. Fig. 12 shows the saturation-voltages plotted against primary rating (and thus secondary turns) for a barprimary current-transformer of core-section 'a' and secondary rating of 1 ampere. Also plotted are the various voltage-drops, which would occur at a multiple of the primary rating, given by the saturation-factor. Typical values are given from which it is seen that, for a primary rating of 300 amperes and a saturation-factor of 30, a core-section of 3 square inches would be required. For a 600-ampere primary-rating the core-section required would be 2 square inches, since the required saturationvoltage is only 50 per cent greater and there are twice as many secondary turns. Fig. 13 shows the equivalent ca~e for a 5-ampere secondary rating, the VA in the winding and load being the same, but the lead burden being kept at the same ohmic value. It can be seen that, in order to give the same saturation-factor, a core-section of about 7 times that used in the I-ampere current-transformer would be required. Such a current-transformer would be difficnlt to accommodate and would often be impracticable. In many cases it would be necessary to accept a currenttransformer with a much smaller saturation-factor in order to permit accommodation. One of the points often quoted in favour of the 5-ampere secondary level is that it does not give rise to such high peak-voltages when the current-transformer is open-circuited. This is not always so if the lead burden is significant and if the same saturation-factor is provided in both cases. In fact, in the cases shown in figs 12 and 13, a higher open-circuit peak-voltage is possible with the

Some Steady-state Problems Fault Settings

In applying protective gear, it is important to be able to assess the primary fault-setting in relation to the minimum level of fault-current to be expected. This is relatively easy in relay-systems where the reflected relay-impedance is small compared with the effective value of ZM, the shunt exciting impedance, as it will be sufficiently accurate to refer the actual relay settingcurrent to the primary by the turns-ratio of the feeding current transformer. Such conditions will probably apply to overcurrent relays, some earth-fault relays, and some low-impedance differential relays. The value of relay-impedance may not be low compared with exciting impedance, however, in the case of low-set earth-fault relays, high-impedance differential relays, and lowimpedance differential relays in protective-systems where there are many current-transformers connected in parallel. Where this arises, the primary fault-setting must be obtained by referring the vector addition of total exciting-current and secondary relay-current to the primary by the turns-ratio as shown in fig. 14. The above general calculation will be sufficient for most cases, but it is applicable to a given ratio of current-transformer and a given relay-setting. It some-

75

Simple Case of Two Current-transformers in Balance

The simple case of two current-transformers and a differential relay is shown in fig. 18. The separate equivalent circuits of the two transformers are connected as shown for through-fault conditions where tQe primary currents 'in' and 'out' are equal. This equality will exist on the secondary level, provided the turns-ratio of the transformers is the same, and the return current-paths may be omitted, a simplified equivalent circuit being obtained as shown. It can be seen that the relay is connected across a bridge formed by the burdens and the exciting impedances. The condition for no unbalance current is given by R]/R z = ZMdZMZ' It is thus possible to obtain theoretical balance for differing current-transformer designs and loading by satisfying this requirement. This condition is only true when ZMl and ZMZ have similar phase-angles.

4~)'

Ip

N( 1/+

I'

Secondary output of feeding current-transformeJ,

-> ->\ ( IR + 3 IE . FIG.

14.

FAULT-SETTINGS.

times happens that the best choice of these parameters has to be made in the design stages to give a minimum primary fault-setting. In the first case, many relays such as overcurrent and earth-fault have a range of settings obtained by providing a tapped operating-coil. The VA burden at the relay-setting will remain constant, but the ohmic burden will vary and so will the accuracy of the currenttransformer if its design is fixed. The primary faultsetting will be given, as shown in fig. 15, by the vector sum of exciting current and relay current. Expressing primary setting as a function of relay-setting will give:

[piN

Is

I p = N«VA/ZMIs) + Is) The minimum value of Ip is given when VA/ZMI s = Is i.e. when the exciting current and relay current are equal. This is shown in fig. 16 for the case when the phaseangles of ZM and ZR are equal. When the phase-angles are unequal the same condition, i.e. ZM! = !ZRI ' gives a minimum primary-setting but the vector sum of the two currents must be taken. Another problem is the case where the turns-ratio of the current-transformer is variable and the relay-setting is fixed, as shown in fig. 17. A similar condition, = ZRI, is required for minimum primary-setting, the turns-ratio being chosen to satisfy this relationship.

Ip/N VA

Is + IE IS(ZMIE)

Ip/N

Is

FIG.

15.

+ .',1A . ZMIs

FAULT-SETTING:

FIXED CURRENT-TRANSFORMER RATIO. CONSTANT RELAY - VA.

I

I

IzMI

Steady-state Balance

The value of unbalance current in the relay-circuit of a balanced group of current-transformers carrying steady-state through-fault current is important in slowspeed systems of protection as it will determine the upper limit of stability. Even where care is taken to avoid saturation, some unbalance is to be expected where current-transformers of different design or loading are used. The equivalent circuit is particularly useful in obtaining an estimate of the unbalance which will result with a particular arrangement.

VA ZMIs

Is FIG.

76

16.

VARIATION OF FAULT-SE1TING WITH RELAY-SETTING.

Is

ZMcxNZ IpjN

kNZ

Is

+ IE

I + ISZR S

kNz

IS(N+;~)

Ip

For minimum Ip ZR

N

kN

i.e. ZR=kNz=ZM. FIG.

17.

MINIMUM FAULT-SETTING: FIXED RELAY-SETTING, VARIABLE CURRENT-TRANSFORMER RATIO.

When RdR z and ZMljZMZ are not equal, it is possible to calculate fairly easily the resulting unbalance current. Using Thevenin's theorem the voltage across the relay circuit, when this is open-circuited, is determined. The unbalance current is calculated by applying this voltage to the relay impedance and exciting impedances as shown in fig. 19. It should be noted that, for accuracy, ZMl and ZMZ are complex values, but some simplification is possible if they are of the same phase-angYe. In this type of calculation it is normally sufficiently accurate to assume that the impedances ZMl and ZMZ are linear, and some average values for these are obtained from the excitation curves in accordance with their respective approximate working levels.

ZMZ as shown in fig. 20. The approximate expression for out-of-balance current is also shown. For small unbalance ZMZ must be kept small with respect to 2Mb which is an advantage in tranformer protection where the high-voltage current-transformer is usually much inferior to the low-voltage one. This particular arrangement can be considered in terms of the ampere-turns on the inferior currenttransformer. The secondary current of the good current-transformer is sufficiently accurate to supply secondary ampere-turns to the inferior currenttransformer which almost balance the primary ampereturns. The small unbalance does not result in appreciable output, because of the low value of ZMZ' This approach leads to the name "Magnetic Balance."

Principle of Magnetic Balance Single-phase Balance of Multi-terminal Group

It can be seen from fig. 18 that, if the value of ZMZ is small compared with 2Mb the value of R z must be made small compared with R I . The limit of R! will be when there is no external lead burden and it be~omes equal to the winding resistance. This value of R z may be still too large for balance and to eliminate it from the relay connection an additional winding is provided on current-transformer 2 so that, in the equivalent circuit, the relay may be considered as being connected across

N

The use of equivalent circuits can be extended to the case of a number of current-transformers in a balance group under divided through-fault conditions as shown in fig. 21. When the exciting impedances and lead burdens are different the calculation is tedious although it involves simple circuit-calculations. In most cases, some simplification is possible. For example, if all the current-transformers are of the same

N

[p

[p

FIG.

18.

EQUIVALENT CIRCUIT FOR SIMPLE CURRENT-BALANCE.

77

Interposing Transformers

Vca-Vcb

v

Vca

FIG.

The transformers can be inserted into the equivalent circuit as shown in fig. 24, and calculations of unbalance are possible though more laborious than in the simple case. Generally speaking, their inclusion should be avoided unless essential to some feature of the protective system, wither as a summation-transformer or to change the level of current. There is usually some minimum required core-volume relative to the main current-transformer volume and this will depend on the particular duty. They have a special application in some modern systems of protection where the burden of the relay equipment is low compared with the lead burden. By reducing the current level and mounting the interposing transformers close to the main current-transformers the overall burden may be reduced and better performance obtained with a relatively small interposing transformer. In fig. 25 this condition would be given as follows: Voltage required from main current-transformer without interposing transformers =IpIN (R 1 +R 2) Voltage required from main current-transformer with interposing transformer = IplN (R 1 +R 2/n 2 +2r). Voltage required from secondary of interposing transformer = IplNn (R z+rn 2 ). The relative values of Rio R z, and r will determine whether any advantage is gained from fitting interposing transformers. It should be noted, however, that if it were practicable to obtain the overall ratio of Nn on the main current-transformer itself, this would be the better arrangement.

Ip

"- N'

Vcb

J'_

v

£"

Ip

Rl

(ZMl ) }Rl)

(Rl +R2)

Z

N' (ZMl +Z102)'

MI Ip RIZM2-R2ZMl -N'-'-ZMI + ZM2

19. SIMPLIFIED CALCULATION OF UNBALANCE CURRENT.

design and loading the equivalent circuit is reduced to that shown in fig. 22 and it can be seen that balance is obtained assuming the exciting impedances are linear. This would not be strictly correct and the calculation should be made taking the mean values of ZM from the exciting curve according to the respective working levels as shown in fig. 23. The divided fault condition, however, is normally capable of being reduced to the simple form of two current-transformers in balance, making the calculation of unbalance a simple matter.

FIG

20.

Steady-state Saturation

The Importance of A voiding Saturation When the primary current and secondary burden are such that the required secondary voltage is in excess of the knee-point voltage, a current-transformer will produce a secondary current of distorted waveform. This secondary current will contain a high proportion of odd

SlMPLE ARRANGEMENT OF MAGNETIC BALANCE.

78

[p/3

[p/3

R.

~-;;--J\NV'v-- ......----lp/3 N

[p/N

_·---,.----JV..,.,..--r-----,~--'ffl'--_--__+--

[p/3 N

---+---+-_ [p/3N

"'--"N\......

FIG.

21.

CURRENT-BALANCE WITH MORE THAN TWO CURRENT-TRANSFORMERS-DIVIDED FAULT.

---~

.r-"""R...,....

Ip/3N

... ·[p/3 N

·--r-"""'V---..,..----r:-""".,.....-~--__+-L-"\",.,~--__t---t_.

FIG.

22.

SIMPLIFIED EQUIVALENT CIRCUIT-DIVIDED FAULT.

R

FIG.

23.

\p/3 N

R/3

DIVIDED FAULT. ALLOWANCE FOR MEAN VALUE OF

79

ZM'

N

N

Ip_/N~n,--,.-~",R",'n"".--_-.._..J'I"'Rrv,"-_-.._.J\JR"l"'-_ _r--JvR."nv'\.-_-r_I;LN n

FIG.

24.

EQUIVALENT CIRCUIT INCLUDING INTERPOSING TRANSFORMERS.

harmonics, will have a larger ratio-error, and may have zero-points considerably displaced from those of the primary current. Such steady-state saturation must, in general, be avoided up to the maximum value of through-current in balanced and phase-comparison systems of protl~ction. In high-speed protective systems the requirements for transient conditions, discussed later, automatically cater for this. In non-balance systems the results of saturation, while not so serious, still require some consideration. The harmonic content and limitation of output may modify time/current characteristics of overcurrent relays, directional relay characteristics, and the accuracy of distance protection. As with any non-linear system, calculation of the effects of steady-state saturation is not simple. It is not often that exact computation is required or justified, and as the effects will depend on the type of circuits and relays connected to the secondary winding actual test and observation are generally necessary. However, an understanding of the mechanism of steady-state saturation is worth-while and the following sections describe the effects obtained with simple secondary loads of resistance, reactance, and capacitance.

that the violent distorti.on takes place at a current about half the value corresponding to saturation in the previous two cases. This is because the non-linearity in the open-circuit impedance of the current-transformer is such that the incremental inductance in gradually reducing at flux densities above half the saturation-level. Ferro-resonance causes the cyclic peak of currentdistortion at such levels, this current-peak being due to the flux level in the inductance being driven beyond its normal level, giving saturation and consequent discharge of the capacitor through this saturated inductance. In the oscillgrams shown, the distortion is of relatively short duration and the waveform recovers to normal. The results given by the graphical analysis are for conditions of high current for which saturation could be normally expected. Because of the risk of resonance and distortion, the use of a capacitive burden is not common. Where it is used, care must be taken to design to much lower values of maximum flux-density than would normally be acceptable. There are other problems associated with capacitive burdens in relation to transient response which make them undesirable. I:n

Saturation with Capacitive Burden The combination of capaCIty and non-Imear inductance is known to produce complex waveforms through the action of what is known as "ferro-resonance." The solution of these problems is difficult, even with the simplification of two-stage excitation characteristics. The general shape of the waveform is as shown in fig. 29 where it appears derived from graphical analysis and fig. 31(c) which reproduces the actual oscillograms, 9 and 10. Oscillogram 10 shows some general agreement with the graphical result but the interesting feature about it is

rn'

N

FIG.

25.

INTERPOSING TRANSFORMER AND LEAD BURDEN.

80

Ie with L, Ie with L,

Is

t =

-

I

-Is ~.-

TIME

01 I

I

L,

FIG.

26.

1

L,

L,

GRAPHICAL CONSTRUCTION SHOWING SATURATION WITH RESISTIVE BURDEN (FINITE SLOPE IN SATURATION).

high value and short duration will occur as the primary ampere-turns cross the zero, from the negative to positive saturation-levels and vice versa as shown in fig. 30. If the saturation-level of ampere-turns is small compared with the peak primary ampere-turns, the peak value of voltage will be directly proportional to the peak primary ampere-turns, since the primary current has an approximately constant slope in this region. Oscillogram 11 (fig. 32) shows this waveform for a low-loss mu-metal core but it will be noticed that the pulse of voltage is displaced from the primary current-zero and has dissimilar leading and trailing edges. This is due to the effect of the hysteresis loop. Fig. 32 shows a construction which takes this into account and which agrees closely with the flux and voltage waveforms shown in oscillogram 11. It can be seen that the hysteresis effect does not materially reduce the value of peak-voltage.

Peak-voltage on Open-circuit or High-resistive Burden

The peak-voltages developed in the secondary winding do not generally present any problem provided that saturation does not take place. In recent years, however, attention has been given to the risk of high peak-voltages in current-transformers which have been inadvertently open-circuited on load or, under fault-conditions, in current-transformers which feed high-impedance relays. In both cases, considerable saturation takes place with consequent high peak-voltages. These are usually more of a problem in modern high-performance currenttransformers, particularly those of the post-type, with multi-turn primaries. For the conditions referred to, the peak primary ampere-turns are greatly in excess of the ampere-turns required to saturate the core. In the simple case, neglecting secondary load and iron losses, a pulse of voltage of

81

Is

v

Js

FIG. 27.

I,

SATURATION WITH RESISTIVE BURDEN (ZERO SLOPE IN SATURATION).

IplN

JJ 'IB L

Ip/N

LB

Ip/N

t FIG. 28.

SATURATION WITH REACTIVE BURDEN (ZERO SLOPE IN SATURATION).

82

Saturation with Resistive Burden

A simplification is obtained if the slope of the excitation curve is assumed to be zero in the saturated region. The transient when changing into the daturated region then disappears. The resulting waveshape is shown in fig. 27. It can be seen from the analysis and the oscillograms of progressively increasing primary current that the distortion resulting from saturation is generally in the form of a loss of the trailing part of the half-cycles of secondary current. This gives rise to a general loss of output, considerable harmonic content, and a possible large shift in the zeroes of the secondary current. This latter effect is especially important with respect to phase-comparison systems of protection. It is sometimes wrongly assumed that such protection is more immune from the effects of saturation than differential protection. This, as can be seen, is not necessarily the case.

The effect of saturation when the burden is a pure resistance is shown by the graphical analysis of a simple case (see fig. 26) and by the oscillographic records 1-4 (see fig. 31). The waveforms of secondary current and exciting current in fig. 26 are obtained by assuming a two-stage excitation curve for the current-transformer with constant slopes in both the saturated and unsaturated regions. The analysis is started at any point in time and the circuit conditions are changed when the exciting current passes through the values corresponding to the onset of saturation. With this type of change, a connecting exponential transient involving the magnetizing inductance and the secondary resistance must be included at each change. The transient in the unsaturated region is assumed to be long and is approximately equivalent to a constant offset in the exciting current. In the saturated region, the transient is of short duration.

Prospective

Is

-Is-I--

,~o~

--

TIME -;+0

-I.,

Jp/N.

.-

~

181

,

t'

I FIG.

29.

SATURATION WITH CAPACITIVE BURDEN (ZERO SLOPE IN SATURATION).

83

.. Current, Ip=",It

ls......--+~~-

-

- - - - - - --'''''--_____

B-H Curve

TIME..-

'" V = -k",I -JIo._--J

FIG.

30.

OPEN-CIRCUIT PEAK-VOLTAGE, IGNORING LOSSES.

Saturation with Inductive Burden

tained with a slow decay by the inductance of the load. Successive oscillograms of increasing primary current are shown in the oscillograms 5-8 (see fig. 31) which line up with the graphical waveform. It can be seen that the effect of saturation, in this case, is to lose the peaks of the secondary-current waveform, leaving zeroes relatively unchanged. Phase-comparison systems would be less affected by saturation of this type than differential systems. This is useful in some phase-comparison systems where the main secondary burden may be largely reactive due to the use of sequence networks.

Similar analytical methods may be used in the case of an inductive burden, the exciting current having a different phase-relationship from that of the resisitive case. Again, connecting transients are required but in this case the time-constant in the saturated region will not be zero, but will be determined by the Z/R ratio of the burden and the current-transformer-winding resistance. The resulting contruction is shown in fig. 28 and it can be seen that the secondary current does not drop to zero when the current-transformer saturates, but is mainC.T. and Load Data

0

+-_~_

Jp = 125

Ip

~

250

1p

~

500

Ip = 1000

Ip

~

250

(p

~

500

jp = 1000

60

Ip

50.,

N = 300

(a) Resistive Burden. Ip

(] N

~

00

125

50,.,

300

(b)

Reactive Burden. Ip~

b

N

~

~

125

50,.,

300

(c) Capacitive Burden. FIG.

31. eRO records showing effects of steady-state saturation. (Primary and secondary current-traces superimposed).

84

-

TIME

B-H Loop

FIG.

32.

OPEN-CIRCUIT PEAK-VOLTAGE, ALLOWING FOR HYSTERESIS.

The effect of the eddy-current iron-loss is to give an expression for peak-voltage as follows:

In most practical cases, the effect of eddy-current iron-loss or secondary resistive-loading must be taken into account. As the eddy-current loss can be represented by a shunt resistance in the equivalent circuit, its effects will be the same as a secondary loading resistance. Fig. 33 gives the mathematical and graphical solution to this problem. It can be seen that the transient generated in the shunt reactance and loading resistor slows down the rate-of-change of flux, alters the waveform of the secondary voltage, and reduces it peak value. Analysis for various values of resistance shows the dependence of the time-constant, and thus the peak value of voltage, 'on the resistance; but the area of the secondary voltage-wave remains substantially constant, as one would expect. Oscillogram 12 (fig. 33) shows the practical results obtained by loading the secondary winding with various values of resistance, starting initally with the open-circuit condition of oscillogram 11 in fig. 32.

v=

Kl~

The value of K depends on the core dimensions, lamination thickness, type of material, etc. B also depends on some of these but it is 'generally a fractional index ranging from about 0·4 to 0·6. Design-data curves have been evolved to enable peak-voltages to be estimated with corrections for external resistive loading, but there is still some disagreement between the calculated figures and the test figures. Practical testing of transformers is difficult as it is necessary to preserve a sinusoidal waveform on the primary and this requires high-power test-supplies. Calculation methods are of considerable value, therefore, and work is going on to improve their accuracy.

Differential Equation: dimidt

Solution: 1m =

.

I w t-

iR

=

i-i m

=

---"'-.! [ rx

FIG.

33.

rx w It

ocI[ 1_ e -rx(t + to)] W

-rx(t I-e

PEAK-VOLTAGE WITH HIGH-RESISTANCE SHUNT.

85

+ rx i m =

+ to)]

CHAPTER 5 Effects of Transients in Instrument Transformers By F. L. HAMILTON. INTRODUCTION Curren~-transformers and voltage-transformers play an important part in the operation of modern powersystems. They provide the link over which information is derived from the main high-voltage system for the purpose of measurement, control, and protection. Measurement and control are generally concerned with the longer-term steady-state conditions and transients will not be of any great significance. Protective equipments, particularly the modern highspeed types, are concerned with instantaneous conditions. The performance of current-transformers and voltage-transformers is therefore of considerable importance to protective gear at all times and particularly under conditions of fault on the primary system. The subject of the transient response of instrumenttransformers is therefore dealt with in this article, with particular reference to its effect on protective gear. The transient response will be the same in relation to instruments and meters but its significance will be less.

long duration and impose onerous conditions on current-transformers and are thus of considerable importance. The emphasis in this article is therefore given to this type of current-transient. Voltage-transients

Transients in voltage wave-forms can occur due to primary faults or to switching operations. They are generally of the form of a step-function representing a sudden change in voltage and may be accompanied by highfrequency oscillations due to the reactance and capacitance of the primary circuit. Again, these oscillations are of relatively short duration and are not of great significance to secondary apparatus. In some cases, where the phase-angles of lines and power-system components are not equal, the flow of d.c. exponential fault-current can give rise to d.c. exponential voltages and these may have to be taken into consideration. Fig. 2 shows how those d.c. voltages may occur under fault-conditions.

Primary and Secondary Transients

Secondary transients

Transient conditions are set up in the power-system whenever it is dlstu:cbed, either by the occurrence of a fault or by the re-arrangement of connections, for example, by switching operations. These transient conditions give rise to transient voltages and currents which, under idealised concitions, should be reproduced accurately in the secondary circuits of voltage and current transformers. Since practical voltage-transformers and currenttransformers are far from ideal, transients receive considerable modification in passing through them and it is the errors and imperfections so caused which are of interest to protective-gear engineers. In general, it is sufficient to consider the response of current-transformers with respect to current-transients on the system and of voltage-transformers with respect to voltage-transients.

Besides the secondary reproduction of the primary transient, secondary transients may be generated in the internal and external circuits of instrument transformers under rapidly changing conditions. These secondary transients may be extremely important and will depend upon the design parameters of the transformer and the nature of connected secondary burden.

Reproduction of Transients in Voltage-transformers Voltage-transformer devices at present in use are of two main types: (a) A conventional transformer having primary and secondary windings and a magnetic circuit of high permeability. (b) A capacitor-transformer device using a capacitor voltage-divider, a tuned circuit, and an auxiliary transformer of conventional type. The two types are widely different in their characteristics and respond to transients in different ways. The response of the capacitor voltage-transformer (CVT) is of considerable importance since this type of transformer is being applied almost universally at systemvoltages of 132kV and above.

Current·transients

The main forms of current-transient which may occur in a power-system are: (a) D.C. components of exponential form such as those which are produced at the start of fault conditions (see fig. 1.). Similar currents can be produced under load conditions by the switching of reactive circuits. (b) High-frequency oscillatory currents caused by switching operations or restriking conditions in circuit-breakers. The latter type of transient is generally of short duration and is not of major significance to the secondary equipment. D.C. components, however, are of relatively

Transient response of wound voltage-transformers

The transient response of wound voltagetransformers is generally good, and the secondary reproduction of the transient primary wave-form is substantially correct.

86

Ils Xs - COMPONENTS OF SOUIlCE IMPEDANCE UP TO IlELAY POINT

ilL XL-COMPONENTS OF IMPEDANCE BETWEEN IlELAY AND FAULT

I

t_ -1. ~'AXIMUM PRIMARY TRANSIENT CURRENT ~I. T T

co

EFiLCTIVE PR:MARY TIME CONSTANT •

INITIAL VALUE OF CURRENT

FIG

1.

~ (X~ + X~) w(

-R V

( S + RLl

S

+

L)

[J I ,w1 22 1 T •

PRIMARY D.C. EXPONENTIAL CURRENT TRANSIENT.

In general, the design requirements for normal steady-state accuracy are low winding resistance and leakage reactance compared with the connected burden. These, together with relatively low working fluxdensities tend to minimise the problems of transient reproduction. A detailed analysis is not often necessary, but some general consideration of the effects is of interest. The most common primary transients likely to be impressed up on a voltage-transformer are caused as follows: (a) Energisation or de-energisation of the transformer at normal voltages- equivalent to a circuit being switched in or out. (b) Sudden increase of voltage to a value above normal. This can occur on a system with insulated or resistance-earthed neutral with voltagetransformers connected between line and earth. (Increased voltage is V3 time normal). (c) Collapse of voltage from normal system-voltage to fault voltage. This happens when a fault occurs on the primary system, the fault voltage depending on the system constants and the type and position of the fault.

Recovery of voltage from the fault voltage to normal system-voltage- which occurs when the fault is cleared by operation of circuit-breakers. (e) A d.c. exponential voltage which may occur under (c) if the system impedances have different time-constants.

(d)

Transient voltage at R :;:. v

dt SolVIng, y

Ie

Ie

- t

T

[

RL -

XL (RS ' RL)] ----:-(XS ; XL)

-.1 [mRL m -.

For one important case RS

~

RS ]

T

V.

_m_ _ . (m

+ 1)2

~. XL

ThiS gives a maximum Initial value of v when m =

FIG.

87

where m

a

Vo SL

Ie. Xs

•

I

I,

XL [RL usually being small with respect to XL

2.

D.C.

l

EXPONENTIAL VOLTAGES.

Vs

R

SWITCH ON

SWITCH

OFF~

'm

rp

< > - /--/VV\N'--~---""'---

R - - ; . - Vs

L

- L_ _- - - J L - - - - - o

c;- /

[r Note

If voltage collapses due to fault, then T2

~


> ~).

Solution for maximum value of im, I

., I If ~ <


t

~ Eo

. I-

~

4-

Delta Connection -

~

0

0·2

FIG.

2a.

K-

0·4

0·"

0·8

FAULT CURRENT DISTRIBUTION & MAGNITUDE

FOR EARTH FAULT NEAR STAR POINT OF A 33KV 50MVA TRANSFORMER.

That ampere turns balance is maintained between the windings. The magnitude of earth fault current is dependent on the method of earthing, i.e. solid, resistance or transformer, and transformer connection, i.e. star or delta. Star Connection -

Earthing Transformer

Fault current in this case is determined by the impedance of the earthing transformer windings. The distribution is as shown in fig. 2c. The above earth fault currents, particularly in the case of solid earthing, flow through the transformer coils causing them to try to assume a circular shape and thus produce very high mechanical stresses which are proportional to the square of the current. In resistance earthing the fault current is much reduced but consideration must be given to the possibility of flashover particularly if the resistor is of the liquid type.

t. 0

Resistance Earthing

Phase Faults

Phase faults have a similar effect to that of an earth fault on a solidly earthed transformer since current is only limited by transformcr winding impedance.

Solid Earthing

Transformer Connections and Fault Current Flow

The distribution of fault current for this configuration is shown in fig. 2a. It is only dependent on transformer winding impedance and thus is not directly proportional to the position of fault. The reactance decreases very quickly so that fault current is actually highest for a fault near the neutral point.

Under fault conditions, currents are distributed in different ways according to the winding connections. An understanding of the various fault current distribution is essential for the design of balanced differential protection, the performance of directional relays and setting of

105

o 3I o

31

l'

o

SUPPLY

3I

Jr

o

FIG.

3a.

FLOW OF FAULT CURRENTS IN TRANSFORMER WINDINGS.

applying the rule that the ampere turns produced by the fault currents flowing in the transformers secondary windings are balanced by equivalent ampere turns in the primary windings.

overcurrent and earth fault relays. Figures 3a and 3b show some typical examples. The current values shown are for transformers with equal phase voltages on primary and secondary side. The currents are devised by

106

r---------------I I

I

I

1-

I

-

--~I""_~OCIO

o o

SOURc.E.

r-- - - - ----- - - - ---I I

o

I

I

I

SoU~ 100

I

I

v

100

200

300

~oo

'00

cuRRENT rnA (1'1 TIMES AVERAGE)

FIG. 4. MAGNETIZATION CURVES OF THE CURRENTTRANSFORMERS USED IN PRIMARY-INJECTION TESTS.

123

90"

NO-LOAD FAULT-SETTING

180

1--+--+-+~-+----3~:---+';--.--t,;-----iI+;;;-;-+---i

PHASE-ANGLE BETWEEN

0'

~:~8~~R~~~ i~:g)

270"

FIG_

5.

RED-PHASE-TO-EARTH FAULT-SETTING WITH

differing designs. Peak surges of up to 14 times the current-transformer rating, and time-constants of 105ms. were obtained on these tests.

100

PER CENT 3-PHASE LOAD.

ditions are independent of source-impedance and transformer size. Stability under conditions of magnetizing inrush current is, however, dependent upon both the magnitude and the time-constant of the inrush current. The laboratory tests demonstrated the stability of the protection with heavy inrush currents, but the timeconstants of these inrush currents were much shorter

Site Tests

The characteristics of duo-bias protection concerned with fault-settings and stability under through-fault con-

120

100

0

0

\

\

'-

0

0

10 OPERATING·CURRENT IN TERMS OF MULTIPLES OF FAULT-SETTING

FIG.

6.

OPERATING-TIME OF DUO-BIAS PROTECTION.

124

I.V· SIDE.

FIG.

7.

RELAY-OPERATING CURRENT AND PRIMARY CURRENT UNDER THROUGH-FAULT CONDITIONS.

cerned with the output of a particular currenttransformer (which will be higher the 'better' the current-transformer) and not with the balancing of the outputs of current-transformers. Across the output of each power-transformer was permanently connected a 150-kVA auxiliary transformer, the secondary winding of which was opencircuited. The magnetizing-current of this transformer would produce very little bias, and did not therefore affect the validity of the tests. Throughout the tests Dudell oscillograph records were taken of the primary-current and relay-current in each phase, and the harmonic-bias current was recorded

than those usually associated with large powertransformers. The site tests at Rayleigh were made, therefore, to prove stability with an inrush current of long time-constant. The tests were made on 30-MVA and 60-MVA 132/22-kV transformers (see Table 1 opposite) using the current-transformers available on site. The magnetization-curves of these current-transformers are shown in fig. 9. It should be noted that these currenttransformers have a much higher knee-point than those which would normally be supplied for duo-bias protection. The use of these current-transformers does not, however, ease the test-condition, since here we are con-

FIG.

8.

CURRENTS DURING MAGNETIZING SURGE.

125

Table I-Data of Rayleigh Transformers Reference

T3

T2B

Rating

30 MVA: ON/OFB-cooled (15 MVA ON-rating)

60 MVA: ON/OFB-cooled (30 MVA ON-rating)

Connection

Star-Delta

Star-Delta

Voltage

132/33 kV

132/33 kV

Impedance

10·3%

12·4%

Ratio of associated H.V. currenttransformers

150/0·5

250/0·5

J_

on a moving-film cathode-ray oscillograph. Fig. 8 is a typical record and shows that the relay-current is well within the operating-level of the relay. Whereas the laboratory tests were made with control of asymmetry, thus permitting testing always under the most severe conditions of primary-currents, such control was not possible on site, and a large number of switching operations were necessary. A total of 69 switching operations were made during these tests. In many tests the harmonic bias was deliberately reduced below its normal level by altering the primary turns on the harmonic-bias reactor, the bias produced being in direct ratio to the number of primary turns. Although the harmonic bias was reduced to ! of its normal value protection still remained stable. Some of the more significant results are given overleaf in Tables 3 and 4. Examination of the results given above (and of the oscillograms taken) show that: (a) The greater the inrush current the greater the harmonic bias produced. (b) The greater the harmonic bias the less the relay current for corresponding inrush currents. (c) The continuation of the asymmetrical wave due to the longer time-constant did not produce any adverse effect on the stability of the protection.

1100

/

1000

V

V

./~ C.T. RATIO

150/0-5 D.C. RESISTANCE S'O In

1/

)v 00

REF.T2B CT. RATIO 250,.'0'5

D.C. RESISTANCE 3-5n.

I

'J

I

CONCLUSION From the laboratory and site tests described it can be concluded that: (1) Duo-bias protection is stable with through-fault currents of at least fifteen times the rated current of the current-transformers with magnetizing inrush surges having maximum peak values exceeding any likely to be found in practice, and also that it is stable with magnetizing surges having time-constants of at least 6 seconds. (2) The fault-settings of the protection are less than 40 per cent of the current-transformer rating with

200.

'00

600

'00

1000

CURRENT mA (I-I TIMES AVERAGE)

FIG. 9.

MAGNETIZATION-CURVES OF THE CURRENTTRANSFORMERS USED IN SITE-TESTS.

no through-load, and less than 60 per cent of the current-transformer rating with 100 per cent three-phase through-load. The phase-angle between the load-currents and the fault-currents is unimportant.

126

Table 2-Site-testing Data Transformer No:-

T3

T2B

Steady-state Magnetization-current

3·4 A (approx.)

Time-constant Normal lead-burden Current-transformersRatio Secondary turns D.C. resistance Excitation curve

6 sees (approx.) 6 ohms/phase

Red and blue phases-II A (approx.) Yellow phase 6 A (approx.) 2 sees (approx.) 4·6 ohms/phase

150/75/0·5 (used as 150/0·5) 295 of 19 s.w.g. 5 ohms Fig. 9

250/0·5 495 of 19 s.w.g. 3·5 ohms Fig. 8

Table 3---Results of Tests on Transformer T3

Nominal turns on harmonic-bias reactor (per cent)

Leadburden (ohms/phase)

Peak primary current

(% of operating-

(A)

current)

Relay-current

Harmonicbias current (rnA)

Red

Yellow

Blue

Red

Yellow

Blue

100

8

340

195

115

38

30

39

12

100

6

15

15

15

Negligible

9

10

Very small

57

8

100

190

125

45

46

38

57

8

30

30

50

6

14

8

33

8

120

50

125

20

26

24

8 Very small 2

Table 4-Results of Tests on Transformer T2B Nominal turns on harmonic-bias reactor (per cent)

Leadburden (ohms/phase)

Peak primary current

(% of operating-

Relay-current

(A)

current)

Harmonicbias current (rnA)

Red

Yellow

Blue

Red

Yellow

Blue

100

4·6

490

330

220

25

30

18

35

100

4·6

230

320

140

21

18

34

28

57

4·6

570

410

230

31

38

32

29

57

6·6

340

180

160

30

25

28

9

33

6·6

570

320

220

36

56

No record

8

33

6·6

110

120

170

29

33

27

Very small

(3) The operating-time of the protection is less than 100 milliseconds at 3 times the setting under all conditions of load and fault-current asymmetry, and is less than 65 milliseconds at 3 times the setting for internal faults with no through-load. (4) The correct performance of the system is unaffected by the presence of harmonics higher than the second, and by departures from the nominal

frequency greatly exceeding anything likely to occur in practice. These additional tests and appreciable operating experience with duo-bias protection have provided valuable confirmation that this system of transformer protection is basically sound in principle, and that it can be applied with confidence to the largest and most important transformers in service.

127

CHAPTER 8 The Requirements for Directional Earth Fault Relays By F. L.

HAMILTON AND

N. S.

ELLIS.

SUMMARY

Impedance Values Generator/Transformers. Zj = Zz = 23%. Zo = 10%.

This report deals with the conditions under which directional earth fault relays may be required to operate in conjunction with distance protection relays. Variations in system conditions which might occur in practice are related to the current settings, relay characteristics and forms of polarising. The results are plotted graphically in order to assist in the application of this type of relay.

Primary values. (Total impedance of generator/ transformer portion of busbar MVA rating). 1500 MVA Busbars Z, = Zz = 18·15 ohms, Zo = 8·05 ohms 2500 MVA Busbars Z, = Zz = 11·1 ohms, Zo = 4·8 ohms 3500 MVA Busbars Z, = Zz = 7·93 ohms, Zo = 3·43 ohms

GENERAL The investigations on which this report is based were made in connection with Distance Protective Schemes using a single directional earth-fault relay to control the operation of plain impedance relays for earth faults. The results, however, are of general interest in respect to the application of Directional Earth Fault relays to solidly earthed systems where the polarising winding is energised from a residual voltage transformer, provided the appropriate range of system conditions and characteristics is taken into account. This report deals with the particular case of a typical 132 kV system.

Secondary values. (On basis kV/ll0 VT). 1500 MVA Busbars Zj = Zz = 7·7 ohms 2500 MVA Busbars Z, = Zz = 4·62 ohms 3500 MVA Busbars Z, = Zz = 3·3 ohms

of 500/1 CT and 132

Zo = 3·33 ohms Zo = 2·0 ohms Zo = 1·43 ohms

Grid-Infeed. This is taken as overhead line impedance where Z, Zz and Zo = 2·5 Zl·

SYSTEM IMPEDANCES In the typical 132 kV system chosen, the relaying point is associated with busbars having 3,500, 2,500, or 1,500 MVA rating, the voltage transformer ratio being 132-kV-II0-volts and the current transformer ratio being 500/1. The station is assumed to have a local generating capacity and a proportional grid infeed. For example, in the case of 2,500 MVA breaking capacity, the generators have a load capacity of 360 MVA and the grid in-feed a short-circuit capacity of 1,000 MVA. The lines are assumed to have Z, =Zz = 0·7 ohm/ mile and Zo = 2·5 Zj. For convenience, the calculations are made on the basis of equivalent secondary voltages, currents and impedances. The impedances obtained from the maximum fault MVA will represent the minimum source impedances. In practice, the actual source impedances will vary over a range of values, the maximum of which will correspond to the minimum plant condition. The impedance encountered between the relaying point and the fault will be directly proportional to the distance from the fault to the relaying point, provided there are no in-feeds of fault current between these two points. This condition has been assumed in this analysis.

Primary values. (Total impedance of grid infeed portion of busbar MVA rating). 1500 MVA Busbars Zj = Zz = 29·3 ohms Zo = 72·5 ohms 2500 MVA Busbars Z, = Zz = 17·4 ohms Zo = 43·5 ohms 3500 MVA Busbars Z, = Zz = 12·4 ohms Zo = 31·0 ohms Secondary values (On basis kV/ll0 VT). 1500 MVA Busbars Z, = Zz = 12·1 ohms 2500 MVA Busbars Zj = Zz = 7·25 ohms 3500 MVA Busbars Z, = Zz = 5·18 ohms

of 500/1 CT and 132

Zo = 30·2 ohms Zo = 18·2 ohms Zo = 12·9 ohms

BOUNDARY CONDITIONS FOR OPERATION Taking an earth fault relay, the current circuits of which are energised by the residual current of the line C.T.'s and the voltage circuits of which are energised from the open delta voltage of the V.T.'s, the

128

- - -

GRIO-IN-F=£to

/32 K.V.

~

63·5'1.

FIG. leA) EQUIVALENT CIRCUIT.

To ~

63·5v fbt.-ARISINC, VOLfAG-£

ON !<E1JJ,Y ~ Vp

FIG. 1(B) SEQUENCE NETWORK FOR EARTH FAULTS.

129

= 3ID Zso

two quantities on the relay are:Voltage = V p = 3IoZ so Current = IE! = 31 0 The circuit conditions being investigated are represented in equivalent form in figs. l(a) and l(b), the parameters which are varied being the impedances Zu, Zu, ZLO and ZSl' ZS2 and Zso. The boundary conditions may be explored by:(a) First considering terminal earth faults, i.e. Zu, Zu, ZLO = 0, and varying ZSb ZS2, Zso down to their minimum value, i.e. maximum MV A. (b) Secondly, keeping ZSb ZS2, Zso at their minimum value and varying Zu, Zu, ZLO up to the maximum value to be considered. (c) Lastly, keeping Zu, Zu, ZLO constant at the maximum value to be considered and varying ZSb ZS2, Zso up to the maximum value to be considered, i.e. minimum plant conditions.

the relay is required. This will normally be decided by the maximum stage 3 setting, which may be of the order of 100-200 miles. The lower limits of these boundary lines are marked off corresponding to various line lengths for the stage 3 setting. (c) Distant Faults with Increasing Source Impedance The voltages corresponding to the lower limit of the boundary lines in (b) above are the lowest at which the relays are called upon to operate. It is of interest to note that these low voltages also correspond to small currents, i.e. the relay is not called upon to operate at low voltages and heavy currents. The currents at this lower limit are not, however, the minimum at which the relay should operate. These will be obtained by keeping the fault at the maximum chosen distance from the relaying point and following the appropriate curve to the line MQ, or a line parallel to this if the maximum source impedance is less than that corresponding to 250 miles of line. Whilst the current will reduce during this process, the voltage will rise again because of the increasing zero sequence impedance of the source. The current corresponding to a fault at the limit of reach and with maximum source impedance will give the minimum pick-up current of the relay. It will be noted that this minimum current value of the relay occurs with reasonable voltage, i.e. tends towards the minimum operating current with full volts. The boundary lines for 200 mile and 100 mile reach are shown in fig. 2 scaled against equivalent line lengths of source impedance. The maximum length of 250 miles corresponds to a range of about 30 referred to a minimum stage 1 setting of 8 miles. The curves shown through 'm' and 'n' are typical and presume a proportional reduction of generating plant and grid infeed down to about 20% power, and then further reduction of input with no local generation. Other conditions will not produce much deviation from these curves.

(a) Terminal Earth Faults Whilst terminal earth faults at the relaying position do not produce low polarising voltages in the relay, they form one boundary line enclosing the zone of operation of the earth-fault relay. For terminal faults Zu = ZL2 = ZLO = 0, the variation in relay voltage and current will depend entirely on the source impedance. Referring to fig. 2 showing the relation between relay volts and current in log/log form, the points A, B, C, give the relay voltages and current for the three maximum MVA's. For the condition of a terminal earth fault with increasing source impedance, the boundary here will be A, B, or C towards Q. It should be noted that at small currents on this boundary, conditions are such that the predominating impedance is that of overhead line, where Zo = 2·5 Zj, i.e. no generators in, and the residual voltage will rise above 63·5 volts. These boundary lines are typical, but will vary slightly according to the proportionality of line impedance to machine impedance. The boundary lines thus formed represent the upper limit of the voltage/current zone experienced by the relay.

RELAY CHARACTERISTICS The voltage/current characteristics for particular phase angles may be superimposed on the boundary diagram of residual voltage and current shown in fig. 2. The characteristics of two such relays are shown.

(b) Earth Faults beyond the Relaying Point with Minimum Source Impedance (Maximum MVA) In this case, the effect on the relay voltage and current of moving the fault away from the relaying point is shown. It should be noted that the condition of minimum source impedance is taken. The boundary line for this will obviously go through the Point A, B or C according to the appropriate maximum MV A. The relationship for relay volts and current is V p = 3IoZ so = IEFZ SO, and as Zso is constant (at its minimum value) this boundary line will be a straight line through A, B or C at 45° to the axis. The lower limit of this boundary line will depend on the maximum distance of the fault for which operation of

Type USE Relay

As used in XZA protection, having a nominal maximum torque angle of 30° and which consumes 3 VA in the voltage circuit at 63·5 volts. The characteristics for this relay are shown with 30°, 60° and 90° between polarising voltage and current. The basic equation for volts and current are of the general form VI = const, so that on log/log scales, the characteristic is a straight line at 45° to the axes. Comparator Relay

Such as obtained with the use of a rectifier bridge polarised relay arrangement. The maximum torque angle for the relay is 60°, and the VA for the voltage

130

/00

~---_-.:Q~:;o=======::;;::::===:;Z:====:;;;;;:~--=::::=-----------

60

c

~

.30 ~

~

2D

u

~

V)

.J

~

~

10

~

0

'vP ~

~.

~

r

~ ~\O ~ (J'/'

(j"l

~O~ -t-Q Q't-q,.~~ \9

~

5'0 4-'0

cJ>~

.i'

,3-0

/"'0

-\0> -

CDMP R.ELAY

'66° -

UNCOMPE.N:jATE 0

·5 ~---=---:-----:-----:-----A-::----;:;-~""';"""7---:-~--""'7-:-----r:---.",..-.-.2. -3 -4 -6 /-0 2-0 3-0 ,"'0 S-o 10 () 30 /(ESIOUAL Sf{. wttENr

/32 KV - 50L-(0 EARTHEO SYSTE.M - cr.: LINE

Z, :::Z1. = Q-7.o.../mile

FIG.

2

Zo:: 2:5"z.,

VT

DIRECTIONAL ElF RELA YS FOR DISTANCE PROTECTION.

131

500/1

= 132KV/llo

circuit corresponding to the characteristic shown would be 30. The theoretical characteristic for such relays is formed by two straight lines parallel to the axes. In practice, the corner so formed is rounded off, as shown in the characteristics. The characteristic may be compensated to give the increased voltage at higher currents by the unbalancing of the current inputs in favour of the restraint side of the comparator.

(d) The comparator type of characteristic is more

amenable to application and can give reasonable coverage with reasonable VA in the voltage circuits. (e)

The particular property of the hyperbolic relay characteristic which gives operation at very low currents at high voltages, and at very low voltages for very high currents may be a definite disadvantage in relation to possible spurious operation. The possibility of such operation would be increased considerably if the characteristic were lowered by consuming more VA in the voltage circuit, and it must be borne in mind that the voltage can increase to about 105 volts. The present relay characteristic gives operation at 105 volts and 0·1 ampere.

(1)

Current polarising from neutral current transformers would overcome some of the weaknesses of the hyperbolic relay characteristic. The required degree of current polarisation may be obtained from the curves in fig. 2. For example, to obtain complete operation for the whole boundaries given by A, a, m, the required minimum operation is 2 volts, 0·7 amperes, but actual operation is 13 volts, 0·7 amperes. The additional polarising effect from 0·7 amperes must be eqivalent to 11 volts (assuming the fault current and polarising current to be equal). If no allowance is made for increasing VA on the polarising circuit due to the requirement of two polarising windings, the VA in the current polarising circuit would be

INTERPRETATION OF RESULTS In order that the relay should operate satisfactorily under all practical system conditions, its voltage/current characteristic should lie between the axes and the area enclosed by the boundary lines appropriate to the particular application. It should be appreciated that the phase angle between polarising voltage and current will vary between 90° and 50° for the various system conditions. For example it is nearly 90° when the source is predominantly machine and transformer impedance (i.e. along lines aA, bB, cC of fig. 2) and nearly 50° when the source is predominantly line impedance (i.e. along the other boundary lines).

CONCLUSIONS From a consideration of the relay characteristics and boundary conditions, the following conclusions may be drawn. (a) The directional earth fault relay is not called upon to operate with low voltage and heavy current. (b) With the hyperbolic characteristic such as is obtained with Beam relays, it is difficult to cover a range of system conditions at low voltage and low current. (c) Although the USE characteristic might be lowered, this would require considerable VA on the voltage circuit. For example, to give a coverage comparable with that of the comparator relay would require

)'x

_1_= approximately 3 [11 \63.5 0·72 0·2 VA at 1 ampere, which is a reasonably low figure. Current polarising is not, however, always practical as it requires a neutral point to be available and in use near to the relaying point. The use of current polarising will require some care in relation to the choice of phase angle for the relay as the residual capacity currents will cause phase shifts between the residual C.T. current and the neutral C.T. current.

Y

3VA x [ 15 = 300 VA. \ 1.5) Generally, it can be considered that the hyperbolic characteristic is basically not particularly suited to this type of application.

132

CHAPTER 9

The Performance of Distance-Relays

By F. L. HAMILTON and N. S. ELLIS. INTRODUCTION

x

x

A variety of relays are used in protective systems of the distance-measuring class, typical forms being plain impedance, mho, ohm, reactance, and directional relays. All these come under the general description of distance-relays and are characterised by having two input-quantities respectively proportional to the voltage and current at a particular point in the power-system, referred to as the relaying point. The ideal forms of such relays have characteristics which are independent of the actual values of voltage and current and depend only on the ratio of voltage to current and the phase angle between them. The ideal characteristics are thus completely specified by the complex impedance Z=V/I. The impedance Z can be shown on a complex diagram having principal axes of resistance and reactance. The form of this function for the commoner types of characteristics is illustrated in fig. 1. Operation of the relay occurs in the shaded areas and no operation takes place in the unshaded areas. The boundary curve represents marginal conditions and is referred to as the "cut-off impedance". Practical distance-relays depart from the ideal and have characteristics which depend on the actual values of the input voltage and current. An approximation to the ideal is obtained only over a specific range of input quantities. Inside this range the relay will have errors which are acceptable, and outside the range it will have excessive errors and may not even operate. The operating-time of the relay will be variable and dependent on the individual magnitudes of the input quantities, being, for example, long for small inputs near the cut-off impedance and short for large inputs well within the cut-off impedance. The complete performance specification of a practical relay should thus include information on these aspects in addition to the ideal polar-characteristic such as is illustrated in fig. 1. In the past, various methods of specifying performance have been adopted to meet these difficulties. None of these, however, en'lbles the performance of the relay to be related easily to the requirements of the power-system and most do not facilitate comparison of different relays. It is the purpose of this article to outline methods which have recently been developed to overcome these difficulties and to outline the principal factors affecting the performance. The testing of distance protection is also considered and test-procedures outlined which are directly related to the new methods of specifying performance.

~,

l(a) PLAIN IMPEDANCE

." l(e)

REACTANCE

FIG.

1.

~" I (d)

DIRECTIONAL

IDEAL POLAR CHARACTERISTICS OF DlSTANCE- RELAYS.

the simplified diagram of fig. 2. Zs represents the source impedance from the relaying point P back to the generators and ZF the fault impedance of the powersystem from the relaying point to the fault. Both are supplied from the open-circuit system-voltage E. The current and voltage at the junction of the two impedances are proportional to those applied to the relay via the current and voltage transformers at the relaying point. The source impedance Zs depends on the amount of generating plant available behind the relaying point and is directly related to the short-circuit MVA available at the relaying poing. This will vary according to system conditions but it will normally be possible to assign an upper and lower limit to the short-circuit MVA and hence to Zs. The fault impedance ZF is proportional to the distance of the fault from the relaying point. The ratio of the voltage and current applied to the relay is always equal to ZF, but the actual values are determined by both Zs and ZF. Consider a fault at the nominal cut-off impedance of

P.- -Relaying point. Zt-.- - Fault impedance. ZS.--Source impedance.

Performance Requirements as Dictated by the Power-system The requirements for a particular distance-relay can be assessed in relation to the power-system by reference to

FIG.

133

2.

E.-- Normal system voltage. l.--Current at relaying point. Y.-Voltage at relaying point.

BASIC CIRCUIT OF POWER-SYSTEM UNDER FAULT- CONDITIONS.

the relay. The impedance ZF is thus fixed and will normally correspond to 80 per cent of the line protected. The voltage at the relaying point is then determined only by Zs. For a very large MVA source, i.e. small Zs, this voltage will approach the normal system-voltage. For a small MVA source, i.e. large Zs, the voltage will only be a fraction of the normal voltage and will be determined by the ratio Zs/ZF' A practical relay is required to work correctly between these limits of voltage. Since the top limit is normally fixed by the system-voltage it is usually necessary only to specify that the relay will work down to some minimum voltage Vm' Apart from the magnitude of the impedances Zs and ZF it is necessary to consider their phase angle. This determines the time constant of the primary transients which will occur in the voltage and current waveforms when a sudden fault is applied. With high-speed relays this factor becomes of great importance as the relay is required to measure correctly during the transient period. Since relays are generally connected to a three-phase system the problem is more complicated than that shown in fig. 2, as different types of faults can occur. The problem can, however, always be reduced to the simple case for a particular fault though it may be necessary to use different values for the source impedance according to whether the fault is to earth or between phases.

tv=:j

I DISTANCEt: RELAY

4>.\DIRECT CONNECTION

I: N

I

C (b) TRANSFORMER CONNECTION

FIG.

3.

RELATION BETWEEN VOLTAGE-TRANSFORMER BURDEN AND PERFORMANCE.

setting and hence the minimum voltage-setting is proportional to ~, all other parameters being constant. The general expression relating the voltage range, the voltage-transformer burden, and the basic relay-setting is thus of the form a:.

v~

w.

Factors affecting Relay Performance

Compensation of relays

Voltage-transformer Burden and Relay Sensitivity

A simple distance-relay element which has linear characteristics will have a curve relating applied voltage and current oftheform shown in curve (a) of fig. 4. With zero applied-voltage a certain minimum current known as the pick-up current is required to cause operation. With increasing voltage the operating-current increases

The optimum performance that can be obtained from a given relay is directly related to factors such as the burden on the voltage-transformers at nomal systemvoltage and the minimum operating-current of the basic relay-element. The relation between performance and voltage-transformer burden is illustrated in fig. 3. A relay is represented in fig. 3a which has a voltagetransformer burden Wand operates correctly from the normal system-voltage down to a minimum voltage V m • If transformers of ratio N: 1 are inserted in the input circuit as shown in fig. 3b the normal setting of the relay is unaltered because the ratio VII is unaltered. The minimum voltage is reduced to VmiN but the voltagetransformer burden is increased to W.N". If the useful performance-range of the relay is expressed as the ratio of normal system-voltage to minimum voltage for correct operation, this is related to the voltage-transformer burden by E a:.

Vm

vw.

The burden of the current input circuit is related in a similar manner to the voltage range of the relay. Normally this is not so important as the voltage-circuit burden, the main difference being that the voltage circuit is energised continuously whereas the current circuit is only energised to any extent during fault-conditions. The voltage range of the relay is also closely bound up with the setting in milliwatts (w) of the basic relayelement. For a particular relay the minimum current-

Ip

1m CURRENT

Jp.-Minimum

FiG.

134

pick-up current. Im.-Minimum current for correct operation.

4.

SIMPLE RELAY CHARACTERISTIC.

voltages and currents. The extra voltage range has only been obtained, however, at the expense of using the relay in a very delicate state below the nominal minimum setting. This introduces problems of variation of setting with friction, of long operating-times, and of general mechanical instability. Voltage compensation is therefore to be preferred to current compensation.

linearly. If the nominal impedance-setting is as shown by the dashed curve (b), the cut-off impedance will always be less than the nominal impedance, the percentage error becoming progressively smaller as the inputs are increased. If limits of permissible error are assigned as indicated by the dotted curves (c) and (d), then the relay characteristic must lie in the shaded area to be of practical use. It can be seen that for the example illustrated the minimum current at which the relay can be used is appreciably larger than the minimum pick-up current.

Presentation of Accuracy General

In the previous section the errors in a relay have been assessed in relation to a graph of voltage against current plotted on linear scales (figs 4, 5, and 6). Such a graph does not enable the errors to be determined directly and also has limitations in that the lower end of the scales is very cramped. Alternative methods are briefly reviewed in this section and indication given of merits and demerits of each form.

..,w

CURRENT FIG.

6.

RELAY CHARACTERISTICS WITH CURRENT COMPENSATION.

f-

Z

::>

a: w

Cl.

Compensation can also be obtained by introducing a step in the current-input to the relay. The resulting curve is then of the form shown in fig. 6. At first sight this is attractive and enables the relay to operate down to lower

2

5

10

20

50

10C

CURRENT-AMPS FIG.

135

7.

ACCURACY OF CURRENT GRAPH.

It is again convenient to plot y on log. scales and x on linear scales as shown in fig. 10.

'"

U ZI'O

----

«

-----------

8a. ~

!: Z J

a: '"a.

f-

Z

2

5

10

20

J

50 100

a: a.

VOLTS

FIG.

8.

'"

ACCURACY OF VOLTAGE GRAPH.

H '5 1·0 2'0

convenient method for plotting the results of steady state tests and enable characteristics of relays to be compared and assessed quickly.

5

10

20

50

RANGE-y

FIG.

10.

ACCURACY OF RANGE GRAPH.

Per-Unit Impedance versus Range Presentation Polar Characteristics

The per-unit impedance versus current x nominalimpedance method, while enabling relays to be assessed as individual items, is not readily applicable to assessing the requirement or perfomance of a relay in relation to a power-system. On a power-system, conditions are normally such that at a particular time, the source MY A and the length of protected line are known, the variable factor being the position of fault. At other times the source MY A may have different values. Information on the performance of the relay is required in terms of the length of line at which cut-off takes place as a function of source MY A. Ideally this length is constant. These two variables may be generalised in terms of per-unit fault position (x) and "impedance range factor" 0') where x= ~

andy

=

Zrv

The accuracy-range curves referred to previously can be plotted for various values of phase angle between voltage and current. Normally only the curve at the nominal angle and either side of this angle is required. A general idea of the relay performance outside this region is best given by a series of polar characteristics taken for fixed values of current. It would be theoretically possible to take such curves at fixed values of range (y) but in practice such elaboration is unjustified.

Operating Time of Relays

~

The variation of cut-off impedance with system conditions is not in itself adequate for applying distanceprotection. It is necessary to know the operating-time of the relays as a function of both fault-position and system-source conditions. In the simplified theory of distance-protection, a constant low operating-time of say 60 ms is assumed for the zone-l relays which extend to 80 per cent of the protected line. A further constant time of say 300 ms is assumed for the zone-2 relays up to ISO per cent of the first feeder. In practice the operating-time of a relay may become very long for fault-positions near the cut-off impedance. If the effect is very marked the zone-2 relay may operate before the zone-I relay. thus reducing the effective zone-l cut-off impedance. It is therefore important to present information as regards operating-time which can be readily applied to the evaluation of such effects. Conventional methods of presenting operating-time are considered below. One common method is to plot operating-time as a function of current for specified values of voltage. a series of curves being obtained as in fig. I I. This is difficult to relate to system-conditions. An improved form is shown in fig. 12. Operating-time is here plotted as a function of fault-position. curves

Zrv

and the symbols have the significance shown in fig. 9. The impedance range factor is conveniently referred to a~ range.

FIG.

9.

BASIS FOR IMPEDANCE-RANGE FACTOR

The variables x and yare related to the voltage and current applied to the relay by x x +y

v or

x -

E Z,

. E V

x +y

y

IZrv

136

.

The per-unit impedance/range curves (see fig. 10) already described are a particular contour curve in which the operating-time is infinite, i.e. operation of the relay is marginal. Similar curves can be plotted for a given operating-time and will be of similar shape. By plotting a series of curves in this manner a contour graph is obtained as shown in fig. 13. The outside curve represents the boundary between operation and nonoperation and thus shows the cut-off impedance. Successive curves approaching the origin give decreasing operating-times as the inputs to the relay are increased. The time of operation for a particular set of systemconditions is obtained directly from the graphs by finding the fault position (x) and the range (y) corresponding to the available source MVA and interpolating between contours. The curves can be extended to cover resetimpedances and reset-times as shown in fig. 14, without any difficulty.

400

E w 300 ~

t-

~ 200

i= c(

a:

:t

100

o

o FIG.

2 3 CURRENT

11.

4

TIME v. CURRENT GRAPH.

being given for various values of current. The faultposition is expressed on a per-unit basis, a value of 1 corresponding to the nominal cut-off impedance. It is necessary to use great care in evaluating such curves since a judicious choice of current values can give the impression of good performance as regards operatingtime. Closer examination may show that curves are concentrated in the region corresponding to large inputs to the relay. By replacing the constant current by constant range a set of curves corresponding to a given set of systemconditions is obtained. These are more easily applied. The general form is very much as for the constantcurrent curves of fig. 12.

1·0

200ms )( I

Z

Q tlI)

oQ.

t-

..J ~

it '1 w

. 2'5

FIG.

~

13.

3 5 10 RANGE-y

20

50 100

CONTOUR TIMING CURVES.

t(,')

Z

~

a:

lOOms

w

Q.

o

200ms

21·0 ~:::::::::::;;:;:::;::;;::-=~=:;=:-:: ~

1·0 PER UNIT FAULT POSITION

FIG.

12.

lI)

r----_-'200ms

oQ. t-

TIME v. FAULT-POSITION GRAPH.

...J

~

c(

II.

RANGE-y

Contour Presentation FIG.

With the methods of presenting operating-time so far described it is necessary to provide a separate curve to show the per-unit impedance range characteristics. It is thus necessary to have two separate sets of curves describing the performance of a relay. With the contour method described below only one set of curves is used to give complete information on both accuracy and operating-time.

14.

EXTENSION OF CONTOUR METHOD TO RESET CURVES.

System Application Contours The contour method of presentation can be extended to cover a complete scheme of distance-protection com-

137

prising a number of relays with different nominalimpedance settings and extra time-lag relays. In this case the nominal impedance used in the assessment of range and cut-off point is taken as that corresponding to the complete length of the protected line. All relaycharacteristics are then plotted on this basis. Overall timing contours are assessed from the individual contours for each relay and only composite curves need to be drawn as shown in fig. 15. Since the performance of the overall protection may be quite different for different types of fault it will normally be necessary to have a series of diagrams covering the principal types of fault such as phase-to-earth, phase-to-phase, and three-phase. The three-phase-fault condition is of particular interest as in most forms of distance protection the direc-

CUT-OFF IMPEDANCE

l'OI====~=========::::::::::".....r-----__-"COOms

RANGE-y

FIG.

16.

THREE-PHASE CONTOUR CURVES.

2' 0 f - - - - - - - - - - - - - - - - -

Test Methods ~

Cl

A method of testing distance-protection has been developed in parallel with the method of presentation described which tests the protection under conditions closely approaching actual conditions. In essence the method consists of providing a mimic three-phase system with source impedances in which relays can be connected to the junction of source and line impedances. Contour curves are thus obtained directly in terms of calibrated impedances without recourse to measurements of voltage and current, thus eliminating one source of errors immediately. The phase angle of the source impedances can be altered, thus enabling desired transient conditions to be set up. The test-bench which enables such tests to be made is described in the following article.

ZONE 2 CUT-OFF

:t

r----_-J.1~200

m.

...

Z

, ,

..J

... ~

..J

~ I· 0 ~===='=='-="='==':::~"'"""I~.,___\_-_';_---

z

::>

a:

... Q.

RANG£-y COMPOSITE TIMING ZONE I RELAY TIMING ZONE 2 RELAY TIMING

FIG.

15.

Typical Characteristics

SYSTEM APPLICATION CHART.

Typical curves for a medium distance relay using the methods outlined are given in fig. 17. These were taken on a polarised mho zone-l earth-fault relay used in our type- H distance-protection. The two sets of curves relate to conditions of minimum and maximum transient. It is of interest to note the effect of the transient on the timing contours and also that with this particular relay the boundary curves are identical. The latter feature indicates that transient over-reach effects are negligible.

tional feature fails for faults at or near the relaying point. The forms of characteristic obtained is indicated in fig. 16. It will be noted that the fraction of the line which is unprotected for particular source conditions on the power-system is obtained directly from the curves. This information is very difficult to obtain from the existing methods of specifying performance.

138

1·1 f-.

I

1·0

·9

.& l'(

1

z

-7

2,6

-

- ---

1-1_

-.......... ,

t---.. "'",4

1"-,;t"

,

\;

~ '5

'J:=J
l:

I

I

oI

*

I

I

I

I I

I

I

I

I

~~----+-O-,\' K + f(Sr)1 (2) The function (f) is the same for both inputs and for most devices is either a linear or square function i.e. the signal is either of the form S or S'. Over the working range of the relay it is always necessary for the constant K to be negligible so that the simplified equation (1) may be used. This may be achieved in practice either by making the input quantities very large or by modifying one of the inputs so that a further constant which is equal and opposite to K is effectively added to the equation. It will be noted that the above expressions are independent of the angle between the complex inputs.

LOCUS OF FEEDER IMPEDANCE

x

Phase-angle Comparator The general case may again be conveniently represented by the 'black box' of fig. 7, the two inputs signals now being designated by Sl and S2' The conditions for operation in the ideal case may now be written as:

------'-,-O""""-',-+-'',,---,f-------- R

FIG.

6b.

~

2

< Y

K. In the simplest case, this function merely involves the product of the three quantities, i.e.

The general case may be conveniently represented as in fig. 7 by a 'black box' with two pairs of input terminal and an output which may take the form of an electrical or mechanical signal. The two alternating input quantities may be either voltage or current according to the particular device in question. If the two inputs are denoted by an operating signal (So) and a restraint signal (Sr), then the conditions necessary to obtain an output can be expressed as: soe.1 sri (1) With all practical comparators it is necessary for the operating signal to be in excess of the restraint signal by a

Isdls21 cos y > K.

Practical Amplitude Comparators Beam Relay

One of the earliest comparators used, which is being gradually superseded, is the balanced beam relay. In this relay, two magnetic circuits are arranged to act at opposite ends of a beam as illustrated in fig. 8. Assuming that

I

151

angle between inputs. So far as is known, it is not used in any modern scheme of distance protection. This type of comparator should not be confused with the induction disc or cup phase-angle comparators described later. In the former the driving torque is the sum of two separately derived torques, whereas in the latter the two compared quantities combine in the production of a single torque.

the turns are equal on the two coil systems and that the magnetic circuits are similar, operation is obtained when +K (5) 01

11 2>11,12

It is necessary to ensure that the operating and restraining forces are adequately smoothed as otherwise there is a tendency for the beam to follow the pulsating forces and violent chattering may be set up. This is

Moving-Coil Relay'3

CJ

A moving-coil relay (see fig. 10) with two operating coils, the general construction of which is similar to that

RESTRAINT FIG.

8.

OPERATE

BALANCED-BEAM AMPLITUDE COMPARATOR.

particularly the case when the two inputs are 90° out of phase. It is difficult to design this comparator to work safisfactorily over a large range of input quantities due to the rapid increase of force with input-currents. The beam must be designed to withstand the large forces corresponding to maximum input and yet must also be sufficiently light to enable a small control force K to be used. The comparator is also very susceptible to positional errors as the operating force increases rapidly with change in position of the beam. The main application of this type nowadays lies in the provision of cheap starting elements with limited range and accuracy requirements.

OPERATE AND RESTRAINT COILS FIG.

MOVING-COIL AMPLITUDE COMPARATOR.

of a loudspeaker movement, is currently used by one manufacturer. With this unit, operating and restraining forces are proportional to the input currents. This, together with the high basic sensitivity of the movingcoil relay, enables a reasonable range to be obtained before thermal overloading limits the maximum values of input currents. As the forces are independent of the position of the coil the unit does not suffer from positional errors and also has a reset value equal to the operating value. An alternative form of relay similar in principle to an ordinary ammeter movment can also be used. In practice this form is currently used only in . conjunction with the rectifier comparator.

Induction Disc

By providing two entirely separate driving mechanisms on an induction disc as shown in fig. 9, an amplitude comparator is obtained. This unit suffers from most of the disadvantages of the beam relay with regard to range of operation but has not the positional errors, as the forces are independent of the actual position of the disc. It is much less efficient however and is slow in operation. There is also interference between the two magnetic circuits, which produces errors dependent on the phase

RESTRAINT

10.

Rectifier Comparator'·

A comparator circuit consisting of two bridge rectifiers and a sensitive output relay is shown in fig. 11. A moving-coil relay is normally used as the sensitive element, both axial and rotary types being currently used. The unit is capable of operating over a large range as the sensitive relay never obtains large restraint or operating inputs, these being limited by the action of the rectifiers to a value in the region of 3 to 5 times the relay-setting.

OPERATE

Transductor 12

FIG.

9.

The transductor can be used as shown in fig. 12. The output winding of the transductor is directly coupled to an input winding to which is applied the operatingcurrent input. The restraint input is rectified and applied to the bias winding of the transductor. The unit is inher-

INDUCTION-DISC AMPLITUDE COMPARATOR.

152

~

OPeRATE INPUT

RESTRAINT INPUT FIG.

11.

LEAF SPRING

RECTIFIER-BRIDGE AMPLITUDE COMPARATOR.

ently sensitive but has certain disadvantages associated with the transient response. It is not currently used by any manufacturer. FIG.

Polarised Moving Iron"

A large number of relays are in use which employ a magnetic circuit and an attracted armature. These are of two types, one of which is not sensitive to the direction of the d.c. flux in the magnetic core and is not suitable as a comparator. The other type has a permanent magnet somewhere in the magnetic circuit and will only operate for a given sense of the d.c. input to the coil system.

13.

POLARISED MOVING-IRON COMPARATOR.

direction, the armature releases under the action of a mechanical spring. The relay must be reset by hand or by an auxiliary set of relays which complicates the overall scheme of protection.

Practical Phase-Angle Comparators Induction Disc

A torque is obtained by the interaction of the fluxes from the two magnet circuits which act in close proximity on the copper disc as illustrated in fig. 14. The unit has a very low sensitivity and suffers from interaction between the two magnetic circuits. It is also difficult io balance and there is a tendency for spurious torques where only one input is applied. It is currently used in directional elements where high performance is not required.

OPERATE INPUT

RESTRAINT INPUT FIG.

12.

TRANSDUCTOR AMPLITUDE COMPARATOR.

Relays of this type can be used as comparators by having double coils, one being used for the restraint input and the other for the operating input. Since the coils are on a common magnetic circuit, there is a certain amount of mutual coupling between the two inputs, which must be considered in the design of a relay with such a comparator. One type which is in use is illustrated schematically in fig. 13. An armature is held in an operated position in a loop magnetic circuit due to remanent flux. When the flux in the magnetic circuit is in the correct

FIG.

153

14.

INDUCTION-DISC PHASE-ANGLE COMPARATOR.

x

Induction Cup'

The induction-cup comparator is illustrated in fig. 15. It is an improved version of the induction disc phaseangle comparator just described. It is more efficient, can work over a larger range of input quantities, and has very little interaction. The forces are proportional to the product of the input quantities. In order to limit the torque produced at high inputs, a clutch mechanism is sometimes inserted between the contacts and the cup.

FIG.

INPUT 2

Is]

15.

IMPEDANCE DIAGRAM FOR

I z I
IS]-S21·

If ~I = w where

w is complex quantity with

S2

INDUCTION-CUP PHASE-ANGLE COMPARATOR.

angle y, this equation can be written as

Iw 1/

+ >1w-ll. This can be seen to represent a straight line on the imaginary axis through the origin as shown by the graphical construction of fig. 17. This however, is the characteristic of the ideal phase-angle comparator and can be expressed alternatively as

Electronic Relays

Experimental comparators have been produced using valve circuits 1" 15. Many of these have been very crude and lacking in accuracy, while others, though accurate, have been exceptionally complicated. None of them has found practical application as yet apart from experimental insallations. Present indications are that the transistor 18. 19. 20 offers a lot more promise here and may well be applied in the not far distant future in applications where exceptional range is required and for very high speeds. It will be noted that electronic comparators have been described under the heading of phase-angle comparators. This is deliberate as they lend themselves far more readily to this than to the amplitude comparator.

DERIVATION OF IDEAL CHARACTERISTICS Relation between amplitude and phase-angle comparators The expression for marginal operation of the ideal amplitude comparator has been given previously as: ISol>lsrl This can be written as:

FIG.

IMPEDANCE DIAGRAM OF

I w + 1I> I w -

1I

The combination of an amplitude comparator and ideal transformers is thus exactly equivalent to a phaseangle comparator and is illustrated in fig. 18. It can be shown that the converse, as illustrated in fig. 19, is also true.

where z = -Sr'So The characteristic of z on a polar graph is a circle as indicated in fig. 16. 1..Iz~

17.

1

154

AMPLITUDE COMPARATOR

PHASE·ANGLE COMPARATOR

I I

FIG.

18.

EQUIVALENCE OF PHASE-ANGLE COMPARATOR TO AMPLITUDE COMPARATOR PLUS IDEAL TRANSFORMERS.

Plain Impedance Characteristics

In general, therefore, any characteristic which can be produced by one comparator can also be produced by the other comparator with a different combination of the input quantities. The required relations are given below: or So=Sj + Sz and Sr=Sj-SZ, or Sj

So + Sr and Sz= So

2

From what has already been done, it is fairly easily seen that a plain impedance characteristic can be produced by applying a quantity proportional to the system voltage as the restraint input, and a quantity proportional to the system current as the operating input in an amplitude comparator. The system voltage and current considered are those associated with the faulty phase or phases.

Sr'

2

Derivation of Characteristics General

Thus

Having shown the equivalent of the two types of comparators it is convenient to take each characteristic in turn and consider first in each case that comparator which most simply produces the desired results.

or

I

11l2: ~I Zr

where So = I and Sr =

I:£ I

PLAIN IMPEDANCE RELAY.

Compensation of Characteristics

It will be noted in the above example that the minimum current at which the relay can be used is appreciably greater than the minimum pick-up current. In order that the relay may be utilised to full advantage, compensation can be added to produce a curve of the form shown in fig. 33. This compensation may take the form of a non-linear impedance in the voltage circuit of the relay to prevent the voltage input being effective until a value is reached which corresponds to the product of the minimum pick-up current and the nominal impedance setting.

E

Factors affecting Relay Performance Characteristics of Simple Relay

(b)

The various factors affecting the performance of a relay are most easily explained by taking a simple example such as the plain impedance relay based on the amplitude comparator. Considering a linear comparator comparing current signals, a circuit of the form shown in fig. 31 could be used. The relevant equation for operation is

V

Vm

These characteristics are shown in fig. 32 (curve a). With zero applied voltage a certain minimum current known as the minimum pick-up current (ip) is required to cause operation. With increasing voltage the current required increases linearly. At large inputs the impedance setting of the relay approaches Zr which is taken as the nominal setting of the relay. If limits of permissible accuracy are assigned as indicated by the line (b) and (d), the relay characteristic must lie within the shaded area to be of practical use. The useful working range of the relay thus lies between the minimum voltage V m and the normal system voltage (E).

FIG.

32.

CHARACTERISTICS OF SIMPLE RELAY.

Compensation may also be obtained by introducing a step in the current input to the relay. The resulting curve is then of the form shown in fig. 34. At first sight this is attractive and enables the relay to operate down to lower voltages and currents. The extra voltage range can only be obtained, however, at the expense of using the relay

160

A relay is represented in fig. 35a which has a voltage transformer burden Wand operates correctly from the normal system voltage down to a minimum voltage Vm' If transformers of ratio N: 1 are inserted in the input circuits as shown in fig. 35b, the normal impedance setting of the relay is unaltered because the ratio VI is unaltered. The minimum voltage is reduced to VmN but the voltage transformer burden is increased to WN'. If the useful performance range of the relay is expressed as the ratio of normal system voltage to minimum voltage for correct operation, this is related to the voltage transformer burden by:

v

a:

Vm

VW.

---

FIG.

33.

W

VOLTAGE COMPENSATED.

DISTANCERELAY

in a very delicate state below the normal minimum setting. This introduces problems of variation of setting with friction, of long operating times, and of general mechanical instability. Voltage compensation is therefore to be preferred to current compensation.

(a)

WN

2

I: N

. - - - - - - - - - , NI

]IIINV

DISTANCERELAY

I: N

IIC

(b)

Direct Connection. Transformer Connection.

(a) (b)

v

FIG.

35.

RELATION BETWEEN VOLTAGE-TRANSFORMER BURDEN AND PERFORMANCE.

FIG.

34.

The burden of the current input is related in a similar manner to the voltage range of the relay. Normally this is not so important as the voltage circuit burden, the main difference being that the voltage circuit is energised continuously whereas the current circuit is only energised to any extent during fault conditions. The voltage range of the relay is also closely bound up with the sensitivity of the basic relay element. For a particular relay the minimum current setting and hence the minimum voltage setting is proportional to ~, when w is the sensitivity expressed in milliwatts, all other parameters being constant. The general expression relating the voltage transformer burden and the basic relay setting is thus of the form

CURRENT COMPENSATED.

V.T. Burden and Relay Sensitivity

The optimum performance that can be obtained from a given relay is directly related to factors such as the burden on the voltage transformers at normal system voltage and the minimum operating current of the basic relay element. The relationship between performance and voltage transformer burden is illustrated in fig. 35.

E VOl

161

a:

jlW

\ W

The maximum voltage that can be applied to a given relay is often limited by thermal effects. The designs may thus be chosen so that the voltage corresponds to the normal system voltage. This can be achieved by the use of voltage-matching transformers or in most cases by the suitable choice of turns level on the relay coils. With a given sensitivity of relay element, this places a fundamental restriction on the maximum obtainable range. Exactly similar limitations occur due to mechanical forces and saturation of magnet circuits.

design of the impedance element it is possible to minimise the effects of the transients and still maintain a fast operating time. Theoretically a relay can be made free from transient effects by the correct use of a 'replica impedance'. In essence the principle is to ensure that the transient inputs are identical on both sides of the comparator. This is achieved by deriving a restraint current from the voltage through an impedance which is equivalent to the impedance of the faulted line. The transient components of operating and restraint currents are then identical.

Distortion, Operating Time and Transients

PERFORMANCE SPECIFICATION OF IMPEDANCE MEASURING RELAYS Cut off Impedance

Distortion of Characteristics

Review of Methods of Presentation

!he operating torque of a relay is in general of a pulsatIng n~t~re due to the alternating nature of the input quantItIes. When the operating and restraint inputs are in phase in an amplitude comparator, this is not normally of great consequence as the restraint and operating torques pulsate together and there is only a small residual pulsating torque on the relay element. If the operating and re.straint inputs are not in phase, however, very large pulsatIng torques are set up. These may cause distortion of the characteristics. For example, with a balanced beam relay, violent chattering commences and the setting becomes indeterminate. The effects may be minimised by electrical or mechanical 'smoothing', but this tends to increase the operating time of the relay. Because of this, it is normal to arrange that measurement ~s made w~en the inputs are approximately in phase In any partIcular design of relay. Apart from the fact that greater accuracy and consistency is obtained the operating time is in general smallest along this axis.

Under the heading 'Factors Affecting Relay Performance' the errors in a relay were assessed in relation to a graph of voltage against current plotted on linear scales (figs 32, 33, and 34). Such a graph does not enable the errors to be determined directly and also has limitations in that the lower ends of the scales are very cramped. Alternative methods are reviewed briefly in this section and indication given of the merits and demerits of each form. The first modification to the basic graph of volts against amperes is to replace the linear scales by log scales. Constant distances on the graph now represent constant percentage errors and difficulties associated with the cramping of scales at lower values are removed. In order that errors may be measured directly, it is preferable to plot the per-unit impedance as a function of current or voltage. Per-unit impedance is the ratio of cut-off impedance to the nominal impedance setting of the relay, i.e. per-unit impedance of I is fully accurate. In this case, the per-unit impedance can be plotted on a linear scale and the current or voltage on a log. scale. A comparison of the different methods is given in figs. 36 and 37. The most useful of the two final methods considered is that using current, as the minimum pick-up

Thermal, Mechanical and Saturation Limitations

Operating-time

The operating-time of a distance relay is dependent on a number of factors and cannot be simply assessed. The factors involved are: magnitude of individual inputs, ratio of inputs, phase angle between inputs, and transient components of each input. In order that fast operating-times can be obtained it is necessary to use light movements with low mechanical inertia. This conflicts with the requirements for 'smoothing' and some compromise is always necessary.

'"0f------7'""""'======== I.>J

U

Z

«

a I.>J 0-

f Transients

'Z=

When a fault occurs on a power system a transient d.c. component exists in both current and voltage inputs to the relay. These transient components may cause 'overreach' of the impedance measuring elements, i.e. transient operation for impedance in excess of the steady state setting. The transient components may alternatively cause an increase in operating-time. By correct

::J

d: LlJ

O-l-r---L.,-----;--r--r---,--...;-2 5 10 20 50 100 CURRENT (AMPERES)

FIG. 36.

162

PER-UNIT IMPEDANCE/CURRENT GRAPH.

Ls

1'0 w U

Z

-


FIG.

38.

BASIS OF RANGE FACTOR.

d::.

""



~ w

1I-

'1 FIG.

Per-unit Impedance versus Range Presentation 17

The per-unit impedance versus current times nominal-impedance method, while enabling relays to be assessed as individual items, is not readily applicable to assessing the requirements or performance of a relay in relation to a power system. On a power sytem, conditions are normally such that at a particular time, the source MVA and the length of the protected line are known, the variable factor being the position of the fault. At other times, the source MVA may have different values. Information on the performance of the relay is required in terms of the length of line at which cut-off takes place as a function of source MVA. Ideally this length is constant. These two variables may be generalised in terms of per-unit fault position (x) and 'impedance range factor' (y) where

39.

·2

'5 "02"0 5 10 20 RANGE 7j

50

PER-UNIT IMPEDANCE/RANGE GRAPH.

Polar Characteristics

The accuracy range curves referred to previously can be plotted for various values of phase-angle between voltage and current. Normally only the curve at nominal angle and either side of this angle is required. A general idea of the relay performance outside this region is best given by a series of polar characteristics taken for fixed values of current. It would be theoretically possible to take such curves at fixed values of range (y) but in practice such elaboration is unjustified.

Operating-time of Relays General

x

=

ZF and y ZN

= ~,

The variation of cut-off impedance with system conditions is not in itself adequate for applying distance protection. It is necessary to know the operating-time of the relays as a function of both fault position and system source conditions. In the simplified theory of distance protection, a constant low operating-time of say 60 mS is assumed for the zone-1 relay which extends to 80% of the protected line. A further constant time of say 300 mS is assumed for the zone-2 relays up to 150% of the first feeder. In practice the operating time of a relay may become long for fault positions near the cut-off impedance. If the effect is very marked the zone-2 relay may operate before the zone-1 relay thus reducing the effective zone-1 cut-off impedance. It is thus important to present information as regards operating time which can be readily applied to the evaluation of such effects.

ZN

and the symbols have the si~I).ificance ~hown in fig. 38. The 'impedance range factor IS convemently referred to as 'range' and this sliortened form will be used from now on. The variables (x) and (y) are related to the voltage and current applied to the relay by

v

=

(~:

y)

E

V orx = IZN

It is again convenient to pilot y on log scales and x on linear scales as shown in fig. 39.

163

Review of Methods

Various methods of presenting operating-time characteristics are in current use by various manufacturers. One common method is to plot operating-time as a function of current for specified values of voltage, a series of curves being obtained as in fig. 40. This is difficult to relate to system conditions. An improved form is shown in fig. 41. Operating time is here plotted as a function of fault position, curves being given for various values of current. The fault position is expressed on a per-unit basis, a value of 1 corresponding to the nominal cut-off impedance. It is necessary to use care in the evaluation of such curves, it being possible for all the curves to represent large inputs to the relay. By replacing the constant current by constant range, a set of curves corresponding to a given set of system conditions is obtained. These are more easily applied and assessed. The general form is very much the same as the constant current curves of fig. 41.

w

I:

i=; o

z

~

«c K At a fixed value of the phase-angle between inputs this is the equation of a rectangular hyperbola. Thus if the characteristics are plotted on log.-log. scales the locus is a straight line as illustrated in fig. 44. Curves taken at other angles will also be straight lines parallel to the original line.

(a) (b) (e)

FIG.

165

2

5

10

20

50

Square-law comparator. Modified square-law comparator. Linear comparator.

44.

SQUARE.LAW DIRECTIONAL RELAY.

100

SOURCE IMPEDANCE

LINE IMPEDANCE

Zso

Z/o

Z"

Z/.

8-D------10~;

tva

D-----r-17 .J

SINGLE PHASE-TO-EARTH FAULT (a)

100 50

J----I------+---+_-r--I-----.''

,/ ~~~ V

iP

",>x,1

lA3~ -,/

'Y0~

/ /

V

/

/ / /

I

/ / / / / V

I '1

/V

/V

+~ 'l~ ~~/ / 0/~~"

:/

V/

I

/

/

?,O

/ /

/

~ It /

/

>'B

--

/ r(I-

,-/

V

/

/

",

/

~

[7

-/

2

·5

/

c:s~

V

--

10

/

'5

2

5

V~ l'

r(V)

/

/

LIMIT OFn= 1

>'A- 00 >'B- 0 10

20

~ SO

100

>'A FIG.

66.

CUT-OFF IMPEDANCE OF ZONE-l RELAY FOR VARIATION IN SOURCE IMPEDANCES.

setting the adjustments must be made on the current input circuits. This follows directly from the considerations of an earlier section headed "Characteristics of Simple Relay" in which it was shown that the range of a relay is dependent on the burden on the voltagetransformers. Any alteration to the voltage input affects the range of the relay. It is common practice therefore to make the main initial adjustments in the current circuit and to make only fine adjustments or zone-2 settings in the voltage circuit.

Transient Response of Current-transformers and Voltage-transformers Current-transformers With any form of distance protection it is necessary to ensure that steady-state saturation of the currenttransformers does not take place when system conditions are such that the relays are operating near the cut-off impedance. This normally does not present any

177

2f--------------------

ZONE- 2 CUT-OFF

:r:

I-----__~

-------1200 m$

f-

\

t,)

Z

U.J ..J

Z

::::; I

ZONE-I CUT-OFF

\

:. .:_

[,.::,-~-~-~_:...:_:-_=-=-_=-_=_.:::_~_ =-=-=...::-=-=-=-='-='-=--\--------~-'---------

t:

\

z

::> I

c>:: U.J

0..

-5

2

5

RANGE

10

20

so

100

Y

- - - COMPOSITE TIMING ------- ZONE-I RELAY TIMING - - - - ZONE-2 RELAY TIMING FIG.

67.

SYSTEM APPLICATION CHART.

difficult design problem. With high-speed protection it is also necessary to ensure that transient saturation does not occur under the same system conditions. This may present difficulties with units having a high burden in the current circuits.

System Application Charts The contour method of presentation of distance relay characteristics already discussed can be extended to cover the performance of a complete scheme of distance protection comprising a number of relays with different nominal impedance settings. In this application of the method it is convenient to take the impedance corresponding to the complete length of the protected line as the nominal impedance ZN' All relay characteristics are then expressed on this basis and composite contours drawn representing the performance of the complete schmem, as illustrated in fig. 67. As the performance of the protection may be quite different for different types of faults it will normally be necessary to have a series of diagrams covering the principal types of fault, e.g. phase-to-earth, phase-to-phase, and three-phase faults.

Voltage-transformers

Electromagnetic voltage-transformers do not present any problem as the primary voltage is reproduced faithfully in the secondary winding. With capacitor voltagetransformers, transient voltages occur in the secondary whenever a sudden change of primary voltage takes place. These transient components consist of two damped oscillations, one at a frequency higher than the normal mains frequency and one at a lower frequency. The order of these frequencies is 200 cis and 12 cis respectively. The effect of these transients will depend on the particular type of relay in use. Normally there is a slight reduction in operating-speed of the protection. Cases have occurred however in which mal-operations have occurred with half-cycle protection in which this cause has been suspected.

Special Applications Distance relays may be applied to the protection of transformer feeders and to tee'd feeders. In recent years protective schemes employing distance relays and a carrier link between feeder ends have been used to an increasing extent in order to provide high-speed clearance over the complete length of line.

178

BIBLIOGRAPHY The following bibliography is not intended to be exhaustive of the literature on distance protection. It has been chosen so that further study may be made of topics dealt with in this paper. To assist in this respect number references have been given throughout the text to relevant papers. Further references will be found in the bibliographies given in the various papers listed. 1. GUTTMAN, Behaviour of Reactance Relays with Short-Circuit fed from both Ends, Elektrotechnische Zeitung, 1940. p.514 (in German). 2. CLARKE, Impedances seen by Relays during power Swings with and without Faults, ALE.E., 1945, p.372. 3. HUTCHINSON, The Mho Distance Relay, ALE.E., 1946, p.353. 4. WARRINGTON, Application of the Ohm and Mho Principles to Distance Relays, ALE.E., 1946, p.278. 5. LEWIS & TIPPETT, Fundamental Basis for Relaying on a Three-Phase System, ALE.E., 1947, p.694. 6. DEWEY & MCGLYNN, A New Reactance Distance Relay, ALE.E., 1948, p.743. 7. GOLDSBROUGH, A New Distance Ground Relay, A.LE.E., 1948, p.1442. 8. WARRINGTON, Graphical Method for Estimating the Performance of Distance Relays during Faults and Power Swings. ALE.E., 1949, p.608 9. BRATEN & HOEL, A New High Speed Distance Relay, C.LG.R.E., 1950, Paper 307.

10. NEUGEBAUER, The use ofRotating Coil Relays and Rectifiers in Protection, Elketrotechnische Zeitschrift, 1950, August. (In German). 11. The Effect of Coupling Capacitor Potential Devices on Protective Relay Operation, A.LE.E., 1951, p.2089. 12. EDGELEY & HAMILTON, The Applications of Transductors as Relays to Protective Gear, Proc.LE.E., 1952, August. 13. RYDER, RUSHTON & PEARCE, A Moving Coil Relay Applied to Modern System of Protection, Pro.LE.E., 1950. 14. BERGSETH, An Electronic Distance Relay using Phase Discriminator Principles, ALE.E., 1954. 15. All Electronic One Cycle Carrier Relaying Scheme, Four papers, p.161-186, ALE.E., 1954. 16. GIBSON, Improvements in Electric Protective and/or Fault Locating Systems for Polyphase Alternating Current Power Transmission Network, British Patent 743,323, 1956. 17. HAMILTON & ELLIS, The performance of Distance Relays, Reyrolle Review, No. 166, 1956. 18. BERGSETH. A Transistorised Distance Relay, ALE.E., 1956. 19. ADAMSON & WEDERPOHL, Power System Protection with Particular Reference to the Application of Junction Transistors to Distance Relays, Proc.LE.E., Part A, October, 1956. 20. ADAMSON & WEDERPOHL, A Dual-Comparator Mho-Distance Relay using Transistors, Proc. LE.E., Part A, August, 1956.

179

CHAPTER 12 An Introduction to Distance Protection By D. ROBERTSON. BASIC PRINCIPLES It is as well to remind ourselves at the beginning that distance protection does not measure distance but actually the impedance between the relay and the fault. However, the impedance of a feeder is related to its length so that if the impedance per unit length of a feeder is known the protection can in effect measure the distance to the fault. H is fundamental to the requirements of discrimination that distance protection measuring characteristics for direct tripping need to be directional. Also because tripping is determined by measurement of the impedance to the fault, fundamental accuracy is necessary rather than comparative accuracy as required by differential protection. Thus a concept of zones of protection naturally develops where the first zone of measurement is that part of the protected feeder impedance to which the distance really can be set without any possibility that relay errors, instrument transformer errors or errors in estimation of the power system impedances will cause mal-operation. Typically a figure of 80% of the protected feeder length is chosen as first zone and many installations are operating successfully using this zone 1 setting criteria. The advent of more accurate relays both basically (i.e. better steady state accuracy) and dynamically (i.e. little or no transient over-reach) has encouraged use of 90% of protected feeder impedance for zone 1 settings by some users, but most authorities prefer to accept the better performance as increasing the safety factors, considering that 80% of feeder impedance gives adequate coverage. There is some justification for increasing the percentage coverage for phase fault relays but for earth fault relays the uncertainty of determining the zero sequence impedance makes it undesirable to change from the well established 80% value. The remainder of the feeder is protected by zone 2 which is set typically at 120% of the protected feeder impedance. This means that zone 2 will operate for busbar faults and faults at the busbar end of adjacent feeders. This allows the zone 2 to provide busbar protection in its own right or to act as back up to a busbar unit protection. Also the zone 2 acts as back up protection in the important area at the busbar end of adjacent feeders where, in general, a relatively high fault incidence may be expected. Discrimination between zone 1 and zone 2 is traditionally provided by a definite time lag relay which can be made to be very precise and relatively unaffected by climatic and electrical environmental conditions. Thus the grading of zone 1 and zone 2 is simple becausc it is only one step and only the circuit breaker operating time has significant variation.

A third zone of protection is traditionally provided which is not directional, this has special duties which depend on the type of scheme and facilities required. Because it is available for these duties it can also be used as a second stage of back-up protection covering typically the next feeder in the forward direction and the busbars and a small percentage of the feeder in the reverse direction. Impedance settings of this zone 3 are sometimes dictated by the zone 3 other duties and may also be limited by load impedance. Time settings of the zone 3 back-up have to take account of any I.D.M.T.L. relays which may be providing back-up for other equipment. This leads to the difficulty of grading inverse characteristics with definite time lag characteristics. However, the zone 3 time lag may always be set long enough to provide a back-up to the I.D.M.T.L. back-up if co-ordination ofthe two is a problem. Individual relays may be used for each zone and the six basic types of fault may each have an associated relay. With this arrangement a three zone distance protection requires 18 relays. There are two ways of reducing the number of relays; first, common relays may be used for zone 1 and zone 2; this is referred to as a zone switched relay. Secondly, a common measuring relay may be switched to the appropriate current and voltage signals by fault detecting relays; this is referred to as a phase switched relay. This concept of zones with increasing settings and time lags to give discrimination gives a very comprehensive protection scheme when viewed from the total power system aspect. In addition when the various zones are programmed with other equipment to provide the full facilities of which a modern distance protection is capable, the fact that it is all provided from one set of C.T. cores makes distance protection very attractive. Schemes of distance protection were originally built up from discrete relays of various characteristics with interconnection being done at the panel building stage. The need for faster and more sensitive distance relays has been met by using semi-condl'~tor designs which allows greater sophistication in the interconnection of the various relays. However the inclusion of the relay interconnection within the composite relay case can be a disadvantage if the overall relay design is not flexible enough to cater for the varieties and options within the various types of scheme. The inter-face between supplier and user is especially important in this respect because communication of the complexities and their possible options is not easy and changes introduced late in manufacture or on site while although unavoidable in some circumstances are not to be recommended.

180

x 10

30

20

]j

FIG.

......=!:::=o_",------

--~

2.

CIRCULAR POLARISED CHARACTERISTICFAULT CONDITIONS. W is ratio of minor to major axis

--+_R

=

ZN : NZN

x FIG. 1. CIRCULAR POLARISED CHARACTERISTICBALANCED CONDITIONS APPLICATION - ZONE I AND ZONE 2.

W~----,---

w ~ 0.354

1-+-\--'\---- w

x

I--f---\---- w

1----+--

~

0.5

~ 0.6

w

~

0.75

w

~

1.0

------'......",.-\-\-+---f----''--+-h'---f---,f----- R

___.......

+-_...1.-

----,(-

R

FIG. 3. CIRCULAR OFFSET CHARACTERISTIC BALANCED CONDITIONS AND FAULT CONDITIONS APPPLICATION - ZONE 3 POWER SWING BLOCKING.

FIG 4. CIRCULAR/ SHAPED OFFSET CHARACTERISTIC BALANCED CONDITIONS AND FAULT CONDITIONS APPLICATION - ZONE 3 POWER SWING BLOCKING.

TYPE OF RELAY

Further development produced a relay with a basic characteristic of a circle whose diameter is the relay setting and whose circumference passes through the origin of the R and X axes as illustrated in fig. 1. This was termed Mho relay because of the fact that the Mho characteristic when plotted on an admittance instead of an impedance polar diagram gives a straight line. The Mho relay is clearly directional and the characteristic angle is at the diameter of the circle which originates at the origin of the R and X axes. This characteristic is

Distance relays are generally classified by their characteristic as defined by a polar characteristic using resistance and reactance axes. Thus a plain impedance relay will operate when the ratio between the voltage applied to it and the current applied to it is a set value (setting) irrespective of the angle between the current and voltage. This characteristic is a circle with radius equal to the relay setting and centre at the origin of the R and X axes.

181

generally designed with a polarising signal derived in part from the sound phase voltage (conventionally referred to as Polarised Mho relay). With this type of polarising signal, during unbalanced fault conditions, when the faulted phase voltage can have significant phase difference from its reference but the sound phase voltages will not have changed their phase angle, the characteristic will change to that shown in fig. 2. The extent to which the characteristic is changed is dependent upon the relationship (magnitude and phase angle) between the faulted phase voltage and the sound phase voltage. This, in turn, is dictated by the magnitude of the source impedance in relation to the nominal measured impedance. Hence the various curves for different values of SIR (system impedance ratio). For balanced faults (i.e. 3-phase) the relay characteristic is the circle as in fig. 1 because all voltages are affected equally and remain in balanced phase relationship. Fig. 3 shows a modified impedance characteristic which is called the offset Mho characteristic and is used to supplement polarised Mho relays to provide definite operation for close up balanced faults where the polarised Mho relay is not sure to operate. The offset Mho characteristic develops from the requirements to have a large reach in the forward direction to use as a starter and overall back-up without encroaching too much on the load transfer of the feeder. The load impedance generally will be centred around the resistive axes and thus the offset Mho relay gives better discrimination with load whilst providing sufficient reverse coverage to ensure operation for close up faults in the forward direction (line earth bars left on) or reverse direction (busbar faults). Where very long starter or back-up reach is required, shaped characteristics need to be applied and these are x

represented typically by the characteristic in fig. 4. This off-set element can be set to a variety of characteristics from the conventional off-set Mho circle to a narrow waisted characteristic by choice of simple links within its printed circuit. It is particularly useful when used as shown in fig. 5 where the links for the top half of the characteristic are chosen to give a reasonably broad coverage to allow for errors in the power system data, fault resistance etc. and the lower half of the characteristic is chosen as the narrowest to give very good discrimination with load impedance.

R

X

1,0

FIG.

1.5

6.

DIRECTIONAL SHAPED CHARACTERISTIC BALANCED CONDITIONS TYPICAL APPLICATION - ZONE 1 AND ZONE 2 SHORT AND MEDIUM LENGTH LINES

One of the problems encountered by distance protection is the possibility of relatively large values of fault resistance in earth faults. This is obviously related to the length of line or magnitude of impedance being protected because the fault resistance is determined by the voltage, current and physical make-up of the fault. To eliminate resistance from the distance relay measurement on short lines, reactance relays may be used. This type of relay characteristic is effectively a straight horizontal line at the relay setting value above the R axes. Theoretically a reactance relay will operate when a certain reactance is reached without any limitation as to the resistance involved. However, all reactance relays will have limits and generally they are controlled by other characteristics such as an off-set Mho starter to keep their reach within reasonable limits. The use of two relays to provide a composite characteristic has always produced problems of contact racing, (if not in the operate mode quite often in the reset mode) and fig. 6 shows a reactance form of characteristic developed from a shaped Mho characteristic thus giving a directional reactance characteristic produced by one element.

1----W~O.6

---+---+_--L~f------

R

X

R

FIG. 5. CIRCULAR/SHAPED ASYMMETRICAL OFFSET CHARACTERISTIC BALANCED CONDITIONS AND FAULT CONDITIONS APPLICATION - ZONE 3 POWER SWING BLOCKING.

182

x

factor to compensate for the mutual effect. Obviously with this arrangement if the current returns via the sound phases there is no residual current and hence no compensation. Thus, in this case, the earth fault relays basic setting is the same as the phase fault relays. Under three-phase fault conditions there will be no residual current and no mutual effect so the earth fault relays will measure correctly. The phase fault relays will be energised with phase to phase voltage which is equal to phase to neutral vol+age times V3 and the currents will be the difference of the two phase currents which in the case of a three phase fault are displaced 120° in phase and will therefore give a V3 times factor on the current per phase. Hence both earth fault and phase fault relays will measure three-phase fault conditions correctly.

ZN SIR = 1.3

12

16

-+-.L-_....,I.O,.--~'-----:--"---+---~---:----

R

FIG. 7. DIRECTIONAL SHAPED REACTANCE CHARACTERISTIC FAULT CONDITIONS.

Because this characteristic is derived from the polarised Mho characteristic it retains the change in characteristic during unbalanced conditions as shown in fig. 7.

FAULT TYPES AND QUANTITIES APPLIED TO RELAYS

SCHEME ARRANGEMENT From the previous section, it is obvious that different types of fault require different input quantities fed to the relay and in full distance protection schemes it is conventional to provide relays for each main type of fault. Thus in each zone of protection six relays would be provided, red-yellow, yellow-blue and blue-red for phase faults and red, yellow and blue for earth faults. These would be connected directly to the appropriate current and voltage signals to measure their designated faults To obtain individual measurement in each zone for each type of fault a three zone full distance protection would therefore use eighteen relays (or more correctly eighteen measuring elements because with semiconductor design, the inputs and output tripping and logic circuits are often commoned and the dedicated element for each fault type resolves to a simple printed card). The use of eighteen elements is regarded as unjusitified economically for distribution systems and schemes with less elements are readily arranged by, in the first stage, using common relays for the first two zones by switching settings on completion of the zone 2 time lag. This results in using 12 relays in a full scheme, 6 relays for zone 1/zone 2 and 6 relays for zone 3. This is possible because the zone 1 and zone 2 relays are of the same type (i.e. directional distance) and the zone 3 relays are non-directional. Where schemes use the same type of relay for all zones, the setting can be switched twice or more, however, there is a requirement always for an independent set of relays to start the timing sequence. These detect that a fault exists and therefore have to be set to cover the complete range of all zones. The above schemes are referred to as zone switched schemes and a further reduction in number of relays (or elements) can be achieved by employing the technique of phase switching. Phase switched distance relays generally use only one master measuring relay and three starting relays and are referred to loosely as switched distance schemes. A typical switched distance arrangement is shown in fig. 8. Because this relay is a semi-conductor design all currents and voltages are fed to the elements via isolating transformers. The current transformers perform the additional duty of providing the replica impedance so

Because the power system has three phases which are carried on conductors in relative close proximity, the effective fault impedance of the conductors is made up from self and mutual impedance. Thus the fault currents in each conductor inter-act with the other two conductors and incorrect measurement would occur if compensation was not included to allow for this. With phase to phase faults the fault driving voltage is clearly the phase to phase voltage and the fault impedance does not include mutual effects because equal and opposite currents are flowing in the two conductors which cancel out any induced voltages. It is conventional therefore with phase to phase distance measurement to apply to the relay phase to phase voltage and the difference of the two phase currents, (because these are in phase opposition the difference results in twice the value of one phase current) which results in a measurement of one conductor impedance without any mutual effect. (Self impedance minus mutual impecance which is equal to the positive sequence impedance.) With phase to earth faults the driving voltage is clearly phase to neutral voltage and considering that the earth fault current could all return to the sending end via the earth path, considerable mutual effects can be present. This results in an earth fault impedance 1· 5 - 2 times the impedance measured by the phase fault relays. This can be compensated for simply by an increase in setting of the earth fault relays but for the fact that in some cases the earth fault current may return on the unfaulted phases (i.e. the sound phases). Thus if the earth fault relays are arranged to measure the increase in earth fault impedance caused by mutual effects by a simple increase in fault setting, this must be cancelled if the earth fault current returns via the sound phases. This can be achieved by feeding a signal to the earth fault relays derived from the sound phase current, and is referred to as sound phase compensation. An alternative compensation for earth fault relays is to feed an additional current signal to the relay which is derived from the residual current in the C.T.'s so that the current which is flowing back to source via earth is identified and can be fed to the relay with an appropriate

183

V,o---,..,

[ [ [

R STARTER

STAR DELTA SWITCHING

y

6

I;

1

1

f---f---- ,

T,

)

ZONE

PHASE SELECTION LOGIC

I,

lL lL lL lL lL

I

Z)

B ISTARTfR

~ ~ 1'0---,..,

)

ST ARTER

TRIPPING AND SIGNALLING

TIMERS AND SWITCHING

LOGIC INDICATION

r--

PHASE SELECTION CIRCUITS

T,

)

5S

SR

0

\'I0

FIG.

II.

185

~C

IA

rX"""J------------rrX!~-7r--------!'l-t>-1

II

- - - ..I

I

I

I

-{7

IT]- -: - ~ ~ +

,. - - - - - -

TRANSFER BLOCKING SCHEME

~

.L.. - - - - -

_I

Z,Z,Z. llK STl T;,

WITH DIRECTIONAL BLOCK INITIATE.

T:, I

- -

-

--4

ZONE'NSTANTANEOUSELEMENT BLOCK INITIATE ELEMENT SHORT TIME LAG ELEMENT ZONE 2 TIMER ZONE 3 TIMER INVERSION FUNCTION

x

ANCILLARY FEATURES Line Check

Polarised Mho relays require a voltage signal to ensure operation and the severe condition of a bolted 3-phase fault can cause failure to trip because the voltage at the primary of the V.T. is too low to give relay operation. The bolted 3-phase fault is caused by earth bars being left on a circuit when it is closed. A special feature can be provided for the special problem of the bolted 3-phase fault. The zone 3 or starting relays are invariably not dependent on voltage for operation and can thus be relied on to detect the bolted 3-phase fault. Because this type of fault can only occur when closing-in, the zone 3 or starting relay can be made to trip directly for a certain time after closing-in and this feature is referred to as line check. The switching of the time lag to give direct trip from zone 3 or starting relays may be achieved by an additional contact on the closing control (d.c.line check) or by an undervoltage relay which detects that the line has been de-energised (a.c. line check.)

fORWARD POLARISED MHO

---:::".....-====~"""=:::!==-.....c;'--

R

RFVERSE POLARISED MHO

Voltage Transformer Supervision

The distance relay is dependent on being provided with the correct voltages for operation and also to maintain stability. Operation due to load current is likely if the voltage signal is lost due to fuses blowing or being removed. Supervision of the voltage signals to the distance protection is therefore very important because the whole operation of the distance protection is dependent

DUAL CIRCULAR POLARISED MEASURING ELEMENT BALANCED CONDITIONS TYPICAL APPLICATIONS FORWARD - ZONE I AND ZONE 2 REVERSE- START FOR PROTECTION SIGNALLING OR REVERSE DIRECTIONAL FIG. BACK·UP (ZONE 4)

17.

189

x

with the attendant difficulties in ensuring stability, considering that it has to detect the difference between loss of voltage due to a primary fault and loss of voltage due to voltage transformer supply failure. Power Swing Blocking

Any sudden power system disturbance results in transient changes in the generator angles caused by changes in the power demand and the inertia of the generators. With substantial power system disturbance the generators can swing in this way until their apparent impedance is contained within the distance relay characteristic thus causing tripping. On transmission systems where power swing is a likely condition, distance protection can be fitted with power swing blocking which detects the power swing and blocks all the distance measuring relays. A typical power swing blocking arrangement is shown in fig. 18. A relay which matches the zone 3 characteristic is used with a time lag to detect the difference between a power swing and a fault. A power swing changes the impedance slowly from operation of the power swing element to operation of the zone 3 element, so that the power swing timing element can time out and block all the distance measuring relays. On the other hand a fault will effectively operate both the power swing element and the zone 3 element simultaneously resulting in blocking of the power swing element and thus resetting of the power swing timing element.

LOCUS OF APPARENT IMPEDANCE DURING TYPICAL POWER SWING

~=6"-£----,f--f-- R

POLAR CHARACTERISTICS OF OFFSET MHO POWER SWING BWCKING RELA Y & ZONE DISTANCE RELAYS -12v

R Y

B RY VB

-PSTR

RYB PS PST PSTR

-

PHASES POWER SWING ELEMENT POWER SWING TIMING CiRCUIT POWER SWING TIMER REPEAT RELAY

PSTR

...-

Directional Earth Fault

Certain power systems have a problem of high resistance earth faults and, although the distance relay has much better fault resistance coverage than is apparent from consideration of the simple characteristics, the use of sensitive directional earth fault relays is the only solution when very high earth fault resistance is present. The directional earth fault relay is essentially an overreach element and therefore if it is required for high speed tripping it must be used in one of the overreach types of scheme i.e. permissive over-reach or blocking. In a classical blocking scheme dual elements similar to the dual Mho elements would typically be used.

D.C. CIRCUIT - POWER SWING BLOCKING RELAY

FIG.

18.

upon the reliability of the voltage transformer output. Two basic forms of voltage transformer supervision are used, one which give an alarm only and therefore has no special high speed requirement and the other which is made fast enough to prevent the distance relays operating when a voltage is lost. With the high speed of distance protection measurement (typically 15 milliseconds) the voltage supervision scheme to prevent distance protection operation must be extremely fast

190

CHAPTER 13 Polarised mho distance relay New approach to the analysis of practical characteristics By L. M.

WEDEPOHL.

SYNOPSIS

INTRODUCTION

The use of the polarised mho distance relay for the protection of high-voltage lines has become widespread. Up to the present time, the relay has been thought to be of limited use in the protection of short lines, owing to its relatively small reach for arcing faults. However, recent practical tests have shown that the actual performance is considerably better than that predicted by theory. A new analysis is therefore developed in this paper which shows that the polarised mho relay has an offset characteristic, in the case of unbalanced faults, which encloses the origin and hence enhances the relay reach in the direction of the resistive axis. The degree of offset is a function of the source/line impedance ratio of the system to which the relay is connected. It is shown that the theory developed is in good agreement with results obtained in practice. It is shown in an Appendix that the theory also covers the cases of crosspolarised directional relays and polyphase impedance relays, both classes of relay having an offset characteristic. The paper concludes by discussing the implication of the results. It is noted that the polarised mho relay has most of the benefits of the reacatance relay, while retaining the advantages of being inherently directional and insensitive to load currents and power swings. It is also noted that, by using this method of analysis, the reach for lines with series capacitance may be predicted.

In the past two decades, the use of polarised mho distance relays for the protection of high-voltage transmission lines has become widespread, because of their inherent property of being simultaneously an impedance and a directional measuring element. This type of relay is associated with a number of advantages and drawbacks, and these have in the past been used as a basis for assessing its merits relative to other schemes of feeder protection. It is inherently directional and has the virtue that of all distance relays it is least sensitive to power swings. 1 On the other hand, by virtue of its constrained characteritic, it is rather insensitive to resistive components in the fault impedance and is, for this reason, of limited use in the protection of short lines, when resistance due to fault arcs may be appreciable compared with the line impedance. In these applications it is customary to specify reactance relays' or differential schemes of protection. The fault-arc problem is further aggravated by the fact that the polarising voltage, derived from an unfaulted phase or a tuned circuit, may be out of phase with the fault voltage. Recent measurements have been made to investigate the sensitivity of polarised mho relays to faults with simulated arc resistance, and it has been found that the results are not consistent with the present theory. The relays are found to be capable of operating in the presence of fault-arc resistances which considerably exceed the values predicted by simple theory; the situation improves as the source/line impedance ratio increases. As a result of these measurements, a new analysis of the polarised mho relay was developed, and it is the purpose of the paper to describe this, together with presentation of results and consideration of their practical implication.

List of symbols V R , V y , V B = phase-neutral voltages of red, yellow and blue phases, respectively, at relaying point I R , I y , I B = phase currents E= phase-neutral generated voltage on red phase II = positive-sequence current 12= negative-sequence current 10 = zero-sequence current K, KJ, K 2= relay constants Zn, ZnJ, Zn2= relay impedance constants 8= angle of Zn ZL = positive-sequence line impedance ZLO= zero-sequence line impedance Zs= positive-sequence source impedance Zso= zero-sequence source impedance p= Zso/Zs q= ZLO/ZL a= - i + ij\13 or /120

SIMPLIFIED THEORY OF POLARISED MHO RELAY It is well known that the characteristics of all distancerelay functions may be obtained by using either an amplitude or phase-comparing measuring element. The relationships in the polarised mho relay are more readily understood by considering the operation of the phase comparator. Identical characterisitcs may be obtained from both comparators if the following transformations are observed:

Sx = i(SI + S2) Sy = !(SI - S2)

0

191

Sl = Sx + Sy Sz = Sx - Sy where Sx and Sy are the operate and restraint input signals to the amplitude comparator, and Sj and Sz are the two inputs to the phase comparator. The criterion for operation of the two relays is Sx ,:;; Sy and -tr/2 ~ cP ~ Tr/2 where cP is the phase angle between Sl and Sz. The basic phase-comparator input quantities for a polarised mho relay are Sl = V p Sz = IZ n - V where V p is the polarising voltage and V and I are voltage and current at the relaying point. The corresponding inputs to the amplitude comparator to give identical characteristics are Sx = !(Vp + IZ n - V) Sy = HVp - (IZ n - V)] Fig. 1 shows the basic input arrangement for a mhoconnected phase-angle comparator. The two quantitites which are compared in phase are Sl = V Sz = IZ n - V or

where

V Zs

The relative phase angle between Sl and Sz is not disturbed if they are multiplied by the same quantity, i.e. (Zs + Zd/E. The two vectors to be compared in phase are therefore

Sf = S2 =

ZL Zn - ZL

The vector diagram is shown in Fig. 2, and it is clear that the locus of ZL is a circle with Zn as diameter. In practise, the mho relay is not suitable as a directional element, since a finite value of Sl is required in order to effect operation, so that the origin is outside the relay characteristic, and there is no protection against terminal faults. The problem is solved in the polarised mho relay by making Sl = V p , where Vp is in phase with V but not proportional to it so that for terminal faults,

x

EZ L + ZL • R

E FIG.

Zs

Sz =

+

ZL

MHO-RELAY CHARACTERISTIC.

when V = 0, phase comparison can be effected. In this case,

E(Zn - Zd Zs + ZL

Sf

The criterion for operation is that

- TrI2 ~ ~ /So

2.

=

Zp

S2 = Zn - ZL

.:S Tr/2

where Zp is a vector of constant magnitude but in phase with ZL' The vector diagram is shown in Fig. 3, from which it is clear that phase comparison of Zn - ZL with Zp is the same as ZL, because these latter two impe-

~-

x

ts'--",_v_ _

----1

Phas~1-------s:Iz

comocr~_~

-v

I

n

R

FIG. FIG

1.

BASIC CONNECTION FOR MHO RELAY.

192

3.

BASIC POLARISED-MHO-RELAY CHARACTERISTIC.

dances are in phase: consequently, the 'polarised mho' characteristic is identical with the 'mho' characteristic, except that the origin in this case is a well defined point. The problem is in selecting a suitable polarising voltage V p' and three basic solutions are adopted in practice. V p is either derived from the fault voltage V through a resonant circuit tuned to system frequency (memory) or from an unfaulted phase through a suitable phase-shifting circuit (sound-phase polarising): alternatively, a combination of part sound-phase and part faulted-phase polarising is used. The last two methods do not solve the problem in the case of 3-phase faults, when an unpolarised mho characteristic is obtained, and operation for close faults once more becomes indeterminate. In practice V p and V are not in phase for terminal faults, because of the characteristics of the system, prinicipally unequal source-impedance/line-impedance angles. By considering a number of boundary conditions, Ellis3 has shown that, in most cases, a suitable choice of sound-phase polarising voltage gives rise to errors in phase of less than 1 SO between V p and V. The effect of phase shifts between these two voltages modifies the relay-imput equations to the following:

mho relays to systems are interested in the maximum negative value which ex: can attain, since this corresponds to a minimum value of R. Typically, () = 75°, and, if a = - 15°, R = O. This case is illustrated in Fig. 5, together with a typical range of system impedances superimposed on the diagram, including the effect of fault-arc resistance. It may be seen that the relay coverage under

= Zn -

R

4.

CHARACTERISTIC OF POLARISED MHO RELAY WITH PHASE SHIFT BETWEEN Zp AND ZL.

tic, and the diameter D lags Zn by a and has a magnitude sec a. For a = 15. sec a IS 1·035, which is a negligible increase. The polar equation of the mho circle is

IDI = IZnl

IZI

SI = Zne

IZnl

cos (cjJ - () + a) sec a where cjJ and () are the angles of ZL and Zn, respectively. The value of Z when cjJ = 0, i.e. the relay reach in the resistive axis for terminal faults, is R = Znl cos (() - a) sec a Engineers concerned with the application of polarised =

a

= - 15

arc-resistance conditions is rather poor. The effect shown in Fig. 5 is most severe in the case of short lines and low fault currents, corresponding to high source/line impedance ratios, and has detracted considerably from the appeal of these relays in this case. Warrington' has shown that, in these circumstances, a reactance relay is more suitable as a distance-relay element, despite the added complexity of the arrangement, since separate directional elements must be provided. In order to verify these conditions in practice, a series of measurements was made on a practical polarised mho distance relay, and marked disparities between theory and practice were noted. The reach in the resistive axis for terminal faults was found to be greater than expected, and it increased as the source/line impedance ratio increased. These results are presented and discussed in Section 7. The reason for the disparity between theory and practice is in assuming that V p and V are in phase or separated by a fixed angle a. In practice, this only applies when ZL and Zn are in phase. Deviations become progressively more severe as ZL moves around the polar diagram, and it is possible under certain conditions for a to equal 180°. In the Sections to follow, a more rigorous analysis of the operation of the polarised mho relay is presented, in order to take this effect into account. In Section 3 it will be seen that, in the case of the polarised mho relay, the input quantities to the relay take the most general form, i.e.

ZL

Zp and ZL have the same phase, and the angle between V p and V is accounted for by the additional rotation a. From the relationship in the vector diagram shown in Fig. 4, it is seen that Zn is achord of the mho characteris-

FIG.

POLARSED MHO CHARACTERISTIC

() = 75

S{ = Zp ~

S;;

5.

FIG.

S2

=

+

KZ L

Znl - ZL

It is shown in Appendix 12.1 that the locus of ZL at the boundary of operation of the relay is a circle, and a simple construction is developed which relates the position of the circle in the complex plane to the three constants Znh Zne and K.

I

193

ANALYSIS OF POLARISED-MHO-RELAY CHARACTERISTIC FOR PHASE-TO-PHASE FAULTS

VBR is not used in practice, because the vector position is such that inductive phase shift is required to achieve the correct phase relation with V yB , and this raises practical problems. There are no further advantages to be gained by this choice, and it will not be considered.

The system is shown schematically in Fig. 6, together with the sequence impedance diagram. The operation of a relay connected between yellow and blue phases is E_

Derivation of polarising voltage for phase-fault relay element

O---l\.Jv~ Zs ZL

R

The three practical cases are considered below for the derivation of the polarising signal SI' (a) SI = KIV YB + KZV R This is a case of mixed polarising, where K z is complex with an angle of approximately -90°. For later simplification, we write K z = -jY3K2. K I is generally real and approximately equals 1. Subsituting for VYB and VR and simplifying, SI = E(a 2 - a)[KIZ L + K2(Zs + ZL)]/(Zs + Zd

a2E _ r--~\,I\/'\I"------'\/\JVe---,y

oE_

SI = KIV YB + KzV YR K 1 is as before. For convenience in this case we write K z = K2 /60°. Substituting for the voltages and simplifying, SI becomes (b)

E(a 2

-

a)[KIZ L + K2Z L + (Y3/2)K2 /30 Z s]/(Zs + Zd 0

FIG.

6.

EQUIVALENT CIRCUITS FOR SYSTEM WITH PHASE FAULT

This is the case of a memory relay, where KIVYB is initially the interphase voltage prior to the fault, which then decays exponentially to the fault voltage. K I may have a small angle, owing to the resonant frequency of the tuned circuit not coinciding with the system frequency. In this case,

considered. The voltages and currents in each phase are VR

E

E (2a 2 ZL - Zs) 2(Zs + Zd

Vy VB V YR V YB IR Iy IB

E (2aZL - Zs) 2(Zs + ZL) E[(a 2 - I)ZL- I'SZs]/(Zs + Zd E(a 2 - a)ZJ(Zs + ZL) 0 E(a 2 - a)/2(Zs + Zd -

which is the signal just prior to fault occurrence. These three cases cover those generally used in practice. The general characteristics for the three types of mho relay may be obtained in the manner detailed in Appendix 12.1. The signal Sz in each is the same; SI takes the three alternative forms described in (a), (b) and (c) above. In order to obtain the general form of input signal Si and Sl, all input signals will be multiplied by the vector

Iy

Iy - I B E(a2 - a)/(Zs + ZL) The measuring signal for a polarised mho phase-fault relay is Sz = (Iy - IB)Zn - V YB which, in this case, is Sz = E(a 2 - a)(Zn - Zd/(Zs + Zd There are three possible practical alternative choices for polarising voltage: (c) combination of V YB and V R (b) combination of V YB and V YR (c)

(Zs + Zd/E(a2 - a) The input signals for the three cases then become (a) Si = K2Z s + (K I + K2)ZL Sl = Zn - ZL (b) Si = (Y3/2) /30° K2Z s + (K I + K2)ZL Sl = Zn - ZL (c) Si = KIZ s + KIZ L Sl = Zn - ZL

memory circuit associated with V YB'

194

Characteristic of polarised mho phase-fault relay The relay characteristics for the forward direction of power flow in the three cases are shown in Fig. 7. In all cases, the origin is enclosed by the relay characteristic, the degree of offset of the relay in the third quadrant being principally a function of the source-impedance

Polarised K j V YB +K z V R

Q

x

R R Q

K2 'Z n

b

1

Polarised K j V YB + K z V YR

x

--R

~IJ--

0=00

c

FiG. 7.

Polarised K j E YB (memory)

b

POLARISED MHO PHASE-FAULT-RELAY CHARACTERISTICS FIG.

8.

CHARACTERISTICS OF POLARISED MHO RELAY FOR CASE (a) OF SECTION 3.1

a Zs = 0

The relationship between the three general constants Znb ZnZ and K is given in Table 1.

bZs=oo

vector Zs and the constant K z. When Zs = 0, the characteristic always passes through the origin. The construction for this special condition for case (a) is shown in Fig. 8. By virtue of the construction for the relay characteristic, the diameter subtends an angle of 90 at the origin, which must therefore lie on the relay characteristic. Also shown in Fig. 8 for the same case is the construction for the special condition Zs = <Xl in case (a). It is evident that the characteristic is a straight line through Zn perpendicular to KzZs. From the foregoing, it would appear that the directional feature of the relay has been lost, since the origin is enclosed by the relay characteristic. This interpreta-

Table 1 Relationship between vectors

0

Case

Znj

Zn2

K

(a)

Zn

KzZ s

K j + Kz

(b)

Zn

(Y3/2)Kz /30 Zs

K j + Kz

(c)

Zn

KjZ s

Kj

0

195

ongm lies outside the relay characteristic, which is almost entirely in the third or negative-impedance quandrant. Only in the special case of Zs = 0 is it permissible to identify negative impedance and reverse power, since the characteristics for both directions of power flow are then identical.

R

ANALYSIS OF POLARISED MHO RELAY FOR EARTH FAULTS In this case, operation of a relay connected beween the red phase and earth is considered. The sequence diagram is shown in Fig. 10. I)

E/[(2 + p)Zs + (2 + q)Zd

11

I z = 10

Where Zso

FIG. 9. POLARISED-RELAY CHARACTERISTICS. CASE (a) OF SECTION 3.1; REVERSE-POWER-FLOW CONDITIONS

VR

= pZs and ZLO = qZL E - Zsl\ - Z,l z - pZ,lo E[(2 + q)Zd/[(2 + p)Zs + (2 + q)Zd E[(2 + P)a 2 Z s + (2 + q)a 2 ZL + (1 -p)Z,]I[(2 + p)Zs + (2 + q)Zd

tion follows from the fact that negative impedance in the forward sense and positive impedance with reverse power flow are normally identified. This assumption is not valid. In the case of reverse power flow, the relayinput equations change, owing to the new vector relationship between voltage and current. Typically, in case

E((2 + P)aZ, + (2 + q)aZL + (1- p)Zs]/[2 + p)Zs + (2 + q)Zd E(a 2

-

a)

3E/[(2 + p)Zs + (2 + q)Zd

(a), the equations become

Sl S2

=

K2Z s + (K I + K2)ZL Zn - ZL

= -

In the case of an earth-fault relay, the measuring current is a combination of phase and zero sequence to give correct measurement impedance, i.e.

The vector construction for this case is shown in Fig. 9. It may be seen that the characteristic is totally different from that for forward power flow. In particular, the

1m

IR + [(Zul/Zd - 1]1 0 E(2 + q)/[(2 + p)Zs + (2 + q)Zd

[1

The measuring signal in the case of an earth-fault relay is

E(2 + q)(Zn - Zd/[(2 + p)Z, + (2 + q)ZLJ

FIG.

10.

In this case, there are four practical cases of polarisingvoltage signal Sl to be considered: K1V R + KeV B, K1V R + KeV yB . K1V R (memory) and K1V R + KeV RB •

SEQUENCE DIAGRAM FOR PHASE-EARTH FAULT

196

Derivation of polarising voltage for earth-fault relays 5/ = KIV R + K 2 V B Writing for convenience K 2

(a)

K IVR

+

K 2V B

= K~

-

/-120°,

E[KI(2 + q)ZL + K~(2 + p)Zs + K~(2 + q)ZL + ~(1 - p)Zs~] ...

-

(2 + p)Zs + (2 + q)ZL E(2 + q){K2[(Y3 ~

+ Y3p ~)Zs/(2 + q)] + (K[ + K2)ZL} (2 + p) Zs + (2 + q)ZL

Writing K 2 = -

jK~,

E(2 + q){[Y3K~(2 + p)Zs/(2 + q)] + (K I + Y3K2)Zd (2 + p)Zs + (2 + q)ZL KjE =

E(2 + q){[K I(2 + p)Zs/(2 + q)] + KIZ L} (2 + p)Zs + (2 + q)ZL

E(2 + q){[Y3K~(cl!E + p)Zs/(2 + q)] + (K j + Y3K2)ZL} (2 + p)Zs + (2 + q)ZL

reason. The same arguments regarding extrerr,e limits of Zs apply, i.e. zero and infinity. In the former case, simple mho-relay characteristics are obtained and, in the latter case, reactance-relay characteristics.

Characteristic of polarised mho earth-fault relay element The input quantities S{ and S2 for the four cases are obtained by multiplying 51 and 52 by [(2 + p)Zs + (2 + q)Zd/(2 + q)E I.e. (a)

S{

52

RELA Y CHARACTERISTICS UNDER 2-PHASE-TO-EARTH FAULT CONDITIONS

Y3K2[( j- 30° + p LlQ~ )ZsJ(2 + q)] + (K[ + K2)ZL = Zn - ZL

=

(b) S{ = Y3K2[(2

Owing to the complexity of the voltage and current relationships, it is not possible to describe the characteristics in terms of the simple basic quantities as has been done in other cases. However, the following general observations may be made: (i) When Zs = 0, all characteristics are simple 'mho' circles through the origin. (ii) When Zs = 00 , the characteristics are straight lines whose angles of inclination are functions of Zs, as before. The choice of the type of sound-phase polarising is of some importance, since the vectors are subject to severe phase shifts. A danger exists when Zs is large that, if K2Z S is too far in the fourth quadrant, overreach for arcing faults will be experienced. The basis for selection of sound-phase polarising described by Ellis" is valid in this case, since the phase shifts described in his paper are in fact related to the effective position of K2Z S on the mho characteristic. In general, the preferred choice of 'sound phase' for a phase-fault element is VB for a RY relay while the preferred phase for a RE relay is also VB' It is important to note that the RE relay measures correctly

+ p)ZsJ(2 + q)] + (K[ + Y3K~)ZL

(c)

S{ = K j [(2 + p)ZJ(2 + q)] + K1Z L 52 = Zn - ZL

(d)

S{ = Y3K~Zs[( /- 60°

+ p)/(2 + q)] + (K[ + Y3KDZL

It may be seen that cases (a) and (d) are almost identical if K2 in the second case has a leading angle of 30°, while cases (b) and (c) are similar. The characteristics for cases (a) and (b) are shown in Fig. 11. The general appearance is similar to that for the phase-fault relays. The condition for reverse power is similar to that previously described for the phase-fault elements, and the characteristics are not plotted for this

197

x

(iii)

Sj

KjE

S2

S{

E(Zn - Zd/(Zs KjZ s + KjZ L

S2

Zn - ZL

+ Zd

The two characteristics are shown in Fig. 12. The angle of K~ has purposely been exaggerated to show the lack of coincidence between Zn and the diameter in this case.

1J:s~'---+---~-R

a

x

I

/.--- -~+i /

i.

!

/ /

I/!

!

Y

I

I!.

/ . I

il// / ! ~/ Yi",f,;:c- / ! /1JIi1 ~ ~/ 1/ /Cz~/

~ it /

rt:f----+---R

1

1.

/

i

.1\.,1::/

o /

ti

~/

b

FIG.

11.

*,~,0

G

x

!

POLARISED MHO EARTH·FAULT·RELAY CHARACTERISTICS a POLARISED S,

b POLARISED S,

= K1VR + K2VIl = K,V R + K2VYB --_R

for both RYE and RB E faults. In the former case, the characteristic encloses the origin as in the case of the simple earth fault, while in the latter case the origin is indeterminate, because VB falls to zero with VB, and a simple mho characteristic is obtained.

FIG 12. POLARISED MHO EARTH·FAULT-RELAY CHARACTERISTICS DURING '·PHASE FAULTS a POLARISED K,VR + K2V B b POLARISED K[ER (MEMORY)

RELAY CHARACTERISTIC UNDER BALANCED-FAULT CONDITIONS With the exception of the memory relay, the characteristics will be simple 'mho' circles, the origin being indeterminate. The diameter may not coincide with Zn if K2is not real. The behaviour of a RE relay polarised from VB and the same relay with memory are considered below:

PRACTICAL RESULTS Tests were carried out on a polarised mho phase-fault relay using the rectifier-bridge moving-coil principle. Polarising was as for case (0) of Section 4.1. and the constants of the relay were () (angle of Zn) = 60°, K 1 = 1.42 and K2 = 0'14/-15". A set of polar curves is presented in Fig. 13. These were obtained by connecting a relay to a 3-phase test bench and varing the line impedance together with simulated fault resistance. The curves are normalised. in that all vectors are divided by Zn. It follows that Z,/Zn = Y is the system-impedance range factor. The curves are presented for a number of such factors. The curves are not circles about the major diameter, since in this particular type of relay the criterion for operation is that the angle between the two signals S[ and S, is 75° rather than SlO°, so that the relay characteristic consists of the arcs of two

EZ,/(Z, - Z,) aEZ,/(Z, - Zd E/(Z, - Z,)

o (ii)

I

S, S2

S; S2

E[K,Z, - K2Ztl/(Z, + Z[) E(Zn - Zd/(Z, + Zd K,Z, - K2Z r Zn - Z,

198

characteristic which is independent of system conditions, i.e. ZL = Zw In the past, in certain cases, the setting of a polarised mho relay for line angles other than that of Zn has been specified in terms of the simple trigonometrical equation Zs = Zn cos (0 - ¢), where Zs is the setting for a line angle 0 - ¢ displaced from that of Zn. It may be seen from the analysis in this paper that the equation is not valid and that errors in setting may arise if this approach is used. If an accurate knowledge of the setting is required, the angle 0 - ¢ should not exceed 10°. In the case of lines with series capacitors, this condition cannot be met and the setting becomes indeterminate.

circles with the major diameter becoming a chord. If the reach in the resistive axis is critical, this effect could be taken into account. The theoretical curves are also given, and, apart from the disparity in reach in the resitive direction for the reason stated, the agreement between theory and practice is good.

ASSESSMENT OF THE CAPABILITIES OF THE POLARISED MHO RELAY In the past, it has been customary to use polarised mho relays for relatively long feeders, while reactance relays have been preferred for short lines where arc resistance x

CONCLUSIONS

nominal angle 60·

1·0

Owing to disparities between theory and practice in predicting the performance of polarised mho relays, a new theoretical analysis was undertaken, the treatment being presented in Section 1 of this paper. The charactenstics of the polarised mho relay for a number of well known connections are shown to have an offset in the negative-impedance quadrant in the case of unbalanced faults, thus providing added reach in the direction of the resistive axis. In particular, the reach for arcing-terminal faults is far greater than would be expected from a simplified analysis. Negative impedance and reverse power flow should not, in general, be identified, since the characteristic for reverse power flow is different from that for forward flow. It is shown that, for unbalanced faults, the polarised mho characteristic for reverse power flow is a circle lying almost entirely in the negative-impedance quadrant and not enclosing the origin, so that die relays are directional. The characteristics of crosspolarised directional relays are in accord with the general theory as shown in Appendix 12.2. For unbalanced faults, the origin is included within the relay characteristic for faults in the forward direction and lies outside it for faults in the reverse direction. In this case, the relay characteristic is a straight line. The polar characteristics of polyphase directional impedance relays may be obtained by the same general method (Appendix 12.3) and are in accordance with the results for single elements. The advantages of the reactance relay for short lines are not as great as may be expected from a simplified analysis, and the polarised mho relay may be favoured, because of its ability to adapt itself to the system conditions; i.e. increasing its reach in the resistive axis for arcing faults on short lines, whilst retaining the virtue of insensitivity to impedances due to load currents and power swings. If an accurate knowledge of the settings of a polarised mho relay is required, the angles of the nominal impedance Zn and the line impedance ZL should not differ by more than 10°. The setting in the case of lines with series capacitance may be determined for certain specific plant conditions but cannot be specified in the general case,

~-----d;::l::---tl.:""-_~-O-...L..:-'::'~.L----1:L5=--R

Zn

FIG.

13.

COMPARISON BETWEEN THEORETICAL AND EXPERIMENTAL RESULTS Y = Zs/Zn - 0 - experimental - - - - theoretical

has been a problem. This latter solution has not been ideal, because of the need for a directional-control element and an impedance element for preventing undesired operation on load current. From the analysis presented in this paper, it may be seen that, when the source impedance is large compared with the relay setting, the polarised mho characteristic is similar to that of a reactance relay, and the advantage of the latter becomes marginal. The condition of a very short line with arc resistance usually implies that the sourceimpedance/line-impedance ratio is high, and it follows that the polarised mho relay has the virture of automatically adapting itself to system conditions. Load current is not a problem, since in this case of balanced current flow, the characteristic is the classical mho circle. Generally the likelihood of a 3-phase arcing fault is small, and the lack of reach in this case would not be a serious drawback. The analysis also enables an assessment of reach to be made for faults which lie in the fourth quadrant. This may be necessary in lines which have series-capacitor compensation, and in the past it has been difficult to predict the relay behaviour in this case. A further important point which should be noted is that there is only one point on the polarised-mho-relay

199

since it is a function of the system sourceimpedance/line-impedance ratio. Finally, it should be noted that the analysis in this paper is based on the assumption that the faulted line is energised from one end of the system only. The analysis in the more general case does not lend itself readily to a simple geometrical interpretation. In this case, it would be more appropriate to study specific cases with the aid of a digital computer backed by practical results obtained from a test bench. This does not detract from the analysis in the paper, however, since the main effect of an interconnected system would be to alter slightly the amplitude and phase of the voltage derived from the unfaulted phases and to include reactive effects in the arc-resistance voltage, which is purely resistive in the simple case. The general form of the characteristic would remain unchanged. The comparison with earlier analysis is in any event valid, because this was invariably based on the assumption of a power feed from one end of the system only.

K

=

D/B

ZL = V/I

and A, B, C, D and K are, in general, complex. The boundary of relay operation is defined by the condition that S; and S2 should be displaced in phase by 90°. The vector diagram is shown in Fig. 14, the vectors Sf and S2 being represented by AB and DC, which are at

ACKNOWLEDGEMENTS The author wishes to thank A. Reyrolle and Co. Ltd. for permission to publish this paper. Thanks are expressed to Mr. F. L. Hamilton (Engineer-in-charge of research), and Mr. J. B. Patrickson (Deputy Engineer-in-charge of research) for helpful discussions during the preparation of this paper, and to Mr. T. H. Potts for carrying out the practical tests.

FIG. 14.

GENERAL VECTOR DIAGRAM FOR PHASE COMPARATOR OE = ZnZ/K

REFERENCES 1. WARRINGTON, A. R. VAN C.: 'Application of the ohm and mho principles to protective relays', Trans. Amer. Inst. Elect. Engrs., 1946,65, p.378 2. WARRINGTON, A. R. V AN c.: 'Reactance relays negligibly affected by arc impedance', Elect. World, 1931,98, p.502. 3. ELLIS, N. S.: 'Distance protection of feeders', Reyrolle Rev., 1957, (168), p.16 (which is chapter 11) 4. WARRINGTON, A. R. VAN c.: 'Protective relays, their theory and practice' (Chapman and Hall, (1962) p.285

right angles on the relay boundary. Since it is the locus of point B which is of interest, a point E is described, so that triangle OCD is similar to triangle aBE. The ratio between sides is OC/OB = K, so that corresponding sides of the two triangles are in the magnitude ratio K and separated in phase by 8, the angle of K. The corresponding sides EB and CD intersect at X, and the angle BXC is 8. By definition, AB and DC are at right angles; angle XBY is therefore 90° - 8 and angle ABE is 90° + 8. Since A and E are points fixed by Zn I, ZnZ and K and are not functions of ZL, AE must be a chord of the relaycharacteristic circle. A diameter of the circle must be AF, such that ABF is a right angle, and therefore angle FBE is 8. Since A is also on the characteristic circle, FE must subtend the same angle at B as at A, so that angle FAE is 8. Finally, FEA is a right angle, since it is subtended by the diameter. This diagram provides the basis for a simple construction for the general circle. It is noted that ZL = Znl is a point on the circle; the vector diagram is drawn for this special case in Fig. 15. Here B and A are coincident, since Znl = ZL and OC = KZ L =KZn1 . E is the same as before. The phase of the zero vector AB must be at right angles to DC (= ZnZ + KZ n1 ). The triangles OCD and OAE are similar, as before. A diameter is obtained by describing F so that angle FAE is8 and angle FEA is a right angle as before. A new point M is fixed so that MA is equal and parallel to OC (= KZ n1 ), and G is fixed so that MG is

APPENDIXES 12.1 General distance-relay characteristic The most general input to a 2-terminal phase-angle comparator is Sl = AI - BV Sz = CI + DV The relative phase angles are not disturbed if both signals are divided by BI to give S; Znl - ZL

S2

ZnZ - KZ L

where Znl

AlB

ZnZ

C/B

200

equal and parallel to DO (= zd. OH is drawn perpendicular to OA (= Znl), and it remains only to show that HF is parallel to MG and GFA lies on a straight line. This is done by noting that triangles OAH and EAF are similar (equal angles 8 and one right angle), and consequently triangles AHF and AOE are similar, since there is an equivalence in translation from H to 0 and F to E. However, triangles OAE and MAG are similar, and therefore MAG and HAF are similar, so that F lies on AG. The final construction of the general characteristic is shown in Fig. 16. Vector K is also shown for clarification.

K