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25. ElmlClll'i of [1cctro.fl1C(hanlc;ll Encrg C~1on
_..865-886
1nltodut'- - »IiftIt 1IIf'CIar.c:~ RI _ to dr.Iw 0 c.c. at OIIT....,[ Sr«t .."31Ch>rx1.'Illon-----lnl.mal 01 ToIaICharxkru.1Ic-Scries""""",,,,,-CompoIOI Sprr:d (ootrol 010 St,1es DC. Motor-Nrr:CMlty of • Sla,t..--5"unt Motor St.r1..-- Th,..,·poInt St.r1('f-F"", · potnl Sta,I.. _ SlorUn& and Spttd (ontrol of Snit:> Motor...... Glldln& f SllIrlln£ Rrsl5t"""r---Shoot Moton--Strlcs Motor 5lor1err-T",I>lOr (""troll..- St.n....
or
or
31. Testing of D.C M.xhln~
.1091 -11 14
Brake TOSt-5wlnbUITlCl 101- -Advanl>£", or Swlnl>ulTlCl T.... --Maln Ol~t.£c.-l<e£""""liv_
32. Transformer ..
... 1115-1210
Working Principle of Tran,lormc:r- TfllrlSfnr ..... C"",lrue· Uon- (orn I~ I T..",lorm,,-[,M.f, EQIlRlon oIT .. n'I()fmlmum Em . dencr---V.,iation 01 Effkirnq wilh Pwo r"'lOy [[fl. leney_ Auto· t rln,fo, mer _ ( un"~" Ion of 1- Wind Ing T, .... 'lorm.' Into Auto-uan,lormer---l'.IlIlIcl ~IlIIIor> 01 5 i ngle·~ 1rill\Slormerr----QjJr,lloo, T",ns·
and""""",,,,"
I",,,,,,,,.
33. Tr~llSrOlmrr : Thr~ Phas~
... 1211-1242
Three·pilase T,.",forme's-Th'''''·prn..e T ra",lorm« Coo· I1«!Ioos-SW/S",' 0' YIY CooncCllon-Oel",.Oelta or Connt v-v
34. Inll uctlon Moto,
,1243- -13 12
CI""nGltion of AC Motors-Indu-"Fr--RoIIN r INQ!Ir .ne! Ilre>lOown TINQ!Ir- Reblion be: lwttn TINQ!Ir.nd Slip-- EfI/:0 In on Inducll"" 1.10'01'_ TOO'QII< O=1opN by :an Indueu"" Mo. IIN-TOO'QIIn>lrUCIIoo of lhr (1,,10 D,ag'......-M.. ,mum Q\f1Inllu,,- 513nlng of Ind,,,"ion MoIIN,--OI'ctlon MoIor Selr·.' ~r1I"~-EQlJ .....I...i O fculi 0I51nglophaI.c: Indur:U"" Motor Wilhoill (OI. l ou-EQII ..... I.nl (ulrull ~ \VI!h
pha;e MoIor-Rq>Ulsion T)'P" MoIors--Ropulsk'" Mol".. Rl ' ......utl..Control Olflco-cnllal ~civ'tr-SwlI(htd~. Mot,.C...-or-1>On bdwccoo VIl Slqop /noJlfy ,he. ~) ..~m ..·ilh lhe help of mCd IOf ....chi""_"".;.,.._,, SutOr sl-aryin, IO«jIlC Whne currnu-."'Ilrll,n, II donto for moIor--cootroi. a. In nlO0 mean leng,h .. f ' lIe I"'lh .• coil wiill N 'urn' clrr),ing' culTOn, o f 1 .mp has III mmf of F. esl.blishin. l nux of •• ~Ialed by
• ~ F. '. ".It.rn: : c
0
,,, ,, ,
0
,
f
r
•
,,=
...... / • ..... •
•
, M.\lF _ _
, ~ 2$.l
f1t.
t-t
RdcrtllCC po,nl 0 corr.,,;ponJ; to lhe u""""chc\l .pnna. En s + Jr For anal) .... II II &>.umed thaI .........11(' AU ..... ) .. bJthly ptrmC.hle and ,hal the cleanncc" poin. M H"" m,,,·cm.:dl or mcm""r) i, IIClli"blc. So thaI the mmf 0( lite coil is ""lui",d 10 dn •• lhe nU1 in lhe rtgi()n OARe only. The nu,·n,mf
"mpIc.
t""
25,2 (0)
Elements of Elec;:tromechanlcal Energy ConYer.1on
871
rel.'ioo,hil" are ploned f,,,. lheoe tWuil _motr OA (,,1) e"abllShes a nu OIJ ("~Il . In Ihi. I"',ilion, 'he mo,'a!:>!e mem"'" e~p"ricncu . f""" in .och a direction that the enOA ~
V..F.~
lie
_ Yt dW_
Oul of the energy &Ii\-ned by lhe SOU",.,. half is ' {red in lhe magnetic flCld. Whe", has !he: n:n'"-'nlng half boon u{ilized1 O bviously. Ihi' m",t hav'e boon transfo'med into tile moch,nittdinJ anicle. lbe .""'IY and fom: "" • .., ..,I.ted in , tf'II'IJ of magnetic_.yOl •
"""h ""11""""
' ... L .. ~ It .. L .. ~'" ("V) '.,." L .. sin 9 .. Lm .in l"'II"l.,. COlI ("'J _ 90"', 'Cfm
Since ',,'.ntI '1>' "";1, In: ahk~. the """"mum mulual intl ....·"""c is "'I'"",:mcd by ,he SlUIl W,_
(i.I W. _ in mUlual,,,,,,,,,,,,,,,,,,
i.) W, " W _ ToW
bo'' ' ' ' 'n 'h" and .,'
"
cnerzy lIOn:d in tbe ,y""m _ Sum 0( ~II tho " ...."y.[nm, ~iiod .bo.. ~
.. W,. 11',. W,. 11-'•• W,
T _ Torq". produced. fill' f IiO
.,,,,mcd
"·,,h
If i.. i•. i, an: '0 be ronMan! cum,,". for . implicity. "" Ihltheir deo,'a",C$ respecl!O e (and hence "'nh ""pectl" 'ime: II .n: lhe .""'sy·t"",,i whkb ind""" '. =0] If i. .. i." 1,.T _ I. .. ',i, (- .in9.ros9) r.".. """h a nO al 0 . .. 49. and the torque ;,. """"mum ., 0 ,,_ 45"_ If one of the SIatOr cun~nlS is ",''e1'>Cd. lhe "",ull diff.",. For lhi" leI i. __ i, ,"d '. ~ • I,
T
T~I...
j,j,(,in9 > ros01
And the ",a,,,mum ""'I"'" ceun.'" e _ 45"_ This is. pr»i,iOd for1'Olor. "'hrch i, crud,....y \Iet",,«:n the I .... " cools
,wot
-
87S 25.6.2.1. Different Categories From tillcm can be ;,""gined I" "" ,,-ith permanent magnetS in place of eoil-e~citcd elec{romagnets, All th< in{eq>re1alion. mad< abovt are
876 Y~Iid,
EIec1,al Technology eJOmo'lI')'
lines of rel."n, eMl'lY Inm< and Ihcir dcrivllivcs for iorqllCIII "I,.gap t'Ol~_ for 1M ~1I;nr sM>o'lI ;" Fig Z~4 I,("~ It> Iw CO/culilIN.
Ld "'" ",Iative I":r",,,ability oftl.e core material be 1000. If!be flux density i. B Wb / m'. and" i,!be permeability. !be eDergy-loreIilg~tlk ~hly Ms "n adting COIl "f 800 rums, ~ co'" h~." crosss~c'icnol area'" 5 em x 5 em. N~gkcI reillCla"u '" 1M ""'IM'ic ci,nir 'ode.
.00"'"'0
tUrk.,
,., tt.H. ~IIN C.... _ With thrse inpuli. the device coo...,ru "'" ........y inlo orocl Ile ... inducla&>ce whicb ....ne. ...ilb the .yllCm """ibon. and I moUon mu~ Ile Ihe«.. In odditioo. coil mUll carry I cunmt.. lI.vinl underilood Ille linc:ar. mot....,·ly.,em. il is euier 10 undtntand tile syslem .... 11 .. rotary ...... ion. ,,·ith duo modi'lClOlOO!IS. E........ 15.3. .... dow"'y fJlcl"d ro.ari~! ".adi~. "', .hr loll""·,,.! Mil aNI ",~ ..... I UJd""WMU .
r,
,, 400.
I., " 0./6/1
n.
r, " 2
L, " 0.04 .. 0.02 CO$ 26 M.. .. O.OIt COS 6 ..-Itnt 6 is Iitt S{lQUoQII!k (UU of _< 3 >< 1]20 -75) 10-1 .0,0675
Check : SIo.-ed ·enc'llY at 8 in 1m", of 1-, and W,.. _!n (25 .10"J>::c> ( R )'+IN'",)'
Force i. in .wch a din: tu",p~
15.7.
..... ,.~ .,If-
n.... co""le field·.y"em. Ihus, ",lease. an energy of 50 joule•. ") Calcula"""",, of Energy iopul from .Iectrical sources~, -
L" i l + L"i,
MW [1.(11.< c","",n' and fl", _linl gf ~ ""'" """<W'It
CoI-$pOO 01 COI-piIch PItch 01 a W'ndi"IQ Bock PItCh Front PIICfI R<e$l.jlQIlI PilCI'l
Commutolor PIlch
Two-Ioyef WInding Degree 01 R&-9r1troncy 01 on Almolure Wlndiog MoAlplex Winding Lop and Wove Wr.dIng
= """"''''' """'"
01 Col!; and 01 ~'s SlrrPeK WCN8 wrdng
ConvnuI
-
~OIdeColi lIse$ lop and Wf;NfJ.
Types 0 1 Genofolors
BrvsI1 Conlocl Drop Genelated E.M.F or EM.F fQlXllion 0 1 a ~alOf ion loss In Armoture ToIalloIIln 0 D.C
,,",-"'a
.,," ""'"' ""'"
--"""
ConslOllI 01
Sl~
Col \dI11oI , lor MaxiTun ElnclElncy
" ... Generator conv~rts mechanocol ~nergy into electrical VIU'9'I' USIng electromagnet ic inductIon
888
EJectrio;;aI Technology
26. 1. ClnMaIor
~
An .IO"I'< roil
,.,
....
~,
'"
"'" joiDCd to I"," alip-ring' 'a- and .// which ore in'ui.akd from orh other and from ..... ceotral shaft. TWo coIlttting brushes (of carbon or copper) ~ agai ... t ..... slip-ri",.. Their fuoctioo is 10 ooIleCC """,imum .,m.f. i. indbC"" in the roil "hen in tbis posi.ion (Fig. 263), In \he ... x' qu.utor t'Owlu.ion i. •. from 9ft' to 180'". the flux link"" " 'ith tbe coil gradually iAc.--- but til< rat. o f change of flu. linkag"" J«f'NUS. Hen«. the indoctd •. m.f. dcr... as,,, gradually till in position 5 of lhe coil. il i. reJuced .o Urn "al"". So, we fir. rw m..<arboo """i'Ion, ,he Indt>«:d •. mL in tho roil i, 7dt> Al>Iher irttplllUnl po,nt worth ","",mbe,;ng ;,. !ha, c,'cn "ow lhe CU""", indueed OIl !be coil ,iJeS i •• I'"maling '" before, It is only due '0 !he ",,",if)'ing ",,!iun of the .plil-rings (.]", called rommutalr,,-) that it unhl,,,,,",i,,,,,,r in the .~'mtal dn:uit 11,,..,.
26.3. Practlccl Generator
D.C. GeneralOf"S
891
underlying con,!rucUOII and wondng of an lC!ual genomor iIIu,!no<ed in Fig. 16.8 ""hioh """.iWl of the follo""ing essential ",,!"is : I. Magne!ic Fr.,"" or Yoke l.. Po1e Coil, or F".. WCoi], 4. Armature Core Commu tator ArmalUn: ....'lnJing. '" Conductors aru,n.-s and Ikanng • Of the"". the yok. 11>< pole .boes """" !wo I""P"""
.
.92
Electrical Technology
(I) Lbc:y ~1Id out the flux in tht air PI> and also. be;"'; of ~cm...-non. ~ thoo rel..untt of the magnetic palh (it) they '~pporIlh< uciting coil< (or flCld coils) ... $/x;>o.I'n in fi g. 26.14. 1b. 15). II i. keyed ill the Obcd "" lhe periphery of tbe dis.'e-lailed or 'ONge_,hapcd ,0 make tbe lamin.ali()ll, ",If_locking in 1"'>,lioa. The pu~ uf u,ing laminalion, is 10 reduce !he: loss d.... lOcddy""IWlII •. Thin ...... ,lie l.miJlalIons. g~~'e, i. "'" "";,,ancc offered '0 ,be iooueIoape in a cuil pull",", V'.ffiou, coooc~ of "'" .oil_ are '",,,I.'ed from each UI""" Th; oull(/uo,o<s "'" rloord in !he: omwu~ ,Iou whith "'" linrd """h lou~h 'mul."", """enal. ·l"I1i. ,101 insulalioo is fukled a!lc numberof ... M........ " is rquallO III< numhe, of III'In:lltl,~coil" I""'h con,unmntor "'~t""nl ;, coo~ 10 !he: armalUre condU':Ior by means of. coppel«l by (hangin~ I"," position of icver- in tilt ""'cbc:5. A flexible rower pigtail mounted "' &,;, I,,!, of &,;, bru or rond"""", ronstiluung I roil side .,.. a multi·l,,", coil ;. wrapped with a tape u • lUll' (fi JI. 26.23 ) and iJ placed in tho annalu", 0101. I, ""'Y be n
.ample 26.1). "Tho ,id< of a roil (I .lum '" m"hi,um) i. coiled a winding ele"",nl. Obviously. the number of "indi", elen .. n" is ,wice the number of coilCe between the bepllll;ngs of ' .... 0
lOr!; which !lie di"""ly con5CC\lli~ \WIlL
r .. Y. - YT ........for I"" ""Dd,nl
I,. __ .
- y...
_forwa~wiDd;nl
10 ~. cod-pir.:bes as low as cighHflJtttteOII " 5")( I.t ,f we.t.on from a ,iven poin, and move from """ coil to anothc-r. ,hen III cood!IC,or. dllluid be 1I.. ,..1Kd and "'" should roach lho .. me poin, ilEain ..."hoot I !:ftat or di"'"OOlinu"r in bel".ceO.
26.26.
~x
Lap.wIndIng'
II IS ihowrI in ~II· "l6.2!i ...hieh cmployuinSk>-rurn coi", In Lop ""IOdin.. tht flflUhu!& mel of "';1 .. o:onnccted 10 • rommuIaIOf lItpn rri.•. r. ~ r f ~ 2. thenwc g" • pmgre","'c or rig/It.handed w""linK I.•.• winding prog=ses In the clock .... ise din:cllOll as,\eOn from tbe rommul.igned 10 tbe lop conduclonl atld eVen "umbe", 'o.he low"", ,ide" lor. Iw--lo)'..winding_ 11>< rommuWor segmonts wi!! also be numbd consecutively. the number of lhe <eg' menlS will be the IIIUIIC ... Ib., of lhe uwe' ,ide con"""",d to il. E~mplc- 16_ 1. Drow a dt'-e/oped dWllrtJm 0[ a .impl. 2.la),,,r 1trp'"·indiog!vra4·poI,, gt""rtJ· ror ~'ilh 16ooit.. 11.",,-"" ~..".
~
11 11 :lOLl
t' \ Ie
\I I)
,,
I
IJl'l:U11Z619211I.lOlllJl~
1\
fj .
221. l'iI 6 31 I I
'J .'! 1) I'D~ ' I IJ
~ '
15
,
(
N
\
Tho proceC beeIo ,hen ew:a ....m.n 8$ 6ho"h posil""'" caD be 1oca1Cd by findln, the dim;1ion of cum:nlS flow"" ill the variousmnduc. KIn. If CUr=l1l in !he roOOUft as the numberof "ThtI is .'IIy auch. w'ndiDa; is _ ..... llple circwt" 01" ·patOIlc]" w,ndi"l- In gcoenI. n.".\ber of parIOIlcI pUlIs III......nR.,..p w~ 1ft ",the nn>lllplk,ly (plcx) of the lap "'IIIdi"l- For eumple. a 6-poIe dupIe.1lap w,!>du>1 has (6 " 2) _ 12 ~lcl paIlts in its annalure, .\, T1x: .,m.f. be1wecn the .'" and -ve bru>hes '" ""1111110 the • •m.f. ~ in any ..... of the pa ... I,"1 palllo. If Z '" the 10111 number of """"lUre condU l(' a ronductor ""S' I)",nt uf>ller \be oriainaJ pok 8«au>c the "'Indint l"''i'""'iIa in one difI'Ctio10110 !he itA "'''~'lM\UlI pooIl (alA'S' Ut Fi, 26.)5) tbem!bo W>DdlllJ is !laid 10 K ~,~ If. bow· e.'er." fall. one 0loi 10 !he righ~ Ibm il ii ~,~ Amln>Ul, .. 2-Loytt w,ndin, and JUppooin. that coodllClOr tlB h~ In !he uPJI"f half'" lhoIliot. !bon lOOn, DIIC ptllbibr..). Vah"" of Z .. \0 or 34 W<J\l1d be pc:rf ••
The number or "",I. i_~. HeCM lor. round from It.: ~Iation. PYo! ± 2 He" 2
"
Th" ~1IbOn has bttII f(JUDd by rurrangtng ~ ~Iauon si'"aI In (S) above. his obviuilablt. for llI's winding. TIle number f am .. lu~ puaJld palh.< .. 2m .. ~ '" i, It.: rnuillphc"y of !be ,,;ndinl.
7.
8. E.umplt 2U Dm", a dev.loprd dUll""" of .. 8""pia 2·/ayu ....' ......·jlldml/or /J -I-pok d.e.
of" .impk "vW rFJKl . ....'11.1. "'''IP''r l "h. 1"11
Ia)v,'n In the "lure luove bttn f",,1Id in ""$ man"", tn lbe lowt< pan of R,. 26.36 is shown the equivalent rin, or "1'i .... diagJVII which;,.ery helpful in IlJIderstaodinS the fDnrLllion o( v"';O\IS pMIllcl path.- in the .....1..... 11 ;u"en lhal the windin. iJclclI of FIg. 2-.37 dot indIIad ~"'(L is from left 10 ngbI wI>cmas in the scrond ponioa il i, from rigIM 10 left. H........ i............. ....,..,.., only 1_lMIflllcl pMh< through the ...,1Id,nliO thot 1_ bn.to/IQ ore noquiRd. on.. po6lli~ and ' - ""'I";"'" From the "'t",v"'n' rinl diqram. II i$...",!hat pDUII N is the ~pontin.. poinl of the c.mJ•. Induced in lhe IW{l ponions of lbe w,ndin •. H~ncc. !hi. fi~es lhe posilion of the negati~ bru .... 8uI at il ;1 &l lbe back and not al lhe con\JlIullUor end of the ormMuf'l/. the negativc brush has IWO "I.''''U'~ posuioru i.~. citllt< poinl P or Q. "These pointl on lbe "'tu;"alent diagram COI'TUpond torommUlator ..,,,,,,,nl> No. ) and II . N...... we will fond the pos,tion of lhe pDlili~ brush. 11 is (ound th.ll ~ arc two mtetinl ""'MI of the induced C.m.(L i.~. "",nb l. and AI but both these poanttn &l the _t 01" """..,.,...mu· \alOf ~ of the arrtWlItt_ "IlIQo: t_ poinu n ~ by on.. Iaop only. namely. the Iaop com· poIfd 01 condurun 2 ....:I 9. loot:rM;e middlc point R of tIIl$loop fius the position of the posiu"" bnM. ... bit .. ~ be pla.:ed ;., with commUlaKJr """"",ftl No. 7. We fmd that for OM poI,tiooaof the.~ bnM. ~ n 1_ .llC1IIliv~ positi<JN (ot the - ve brush. Tabn, the +vc bnM at poinl R ....:I IICRlt,VC bru ? &f>Iain tho "'aootI for ~_ ....""". (No. it "ouId .....1• ...., 4 Ii....
~ne.
,
\\ ound Ish
1, ,
,,
~ ,
~
•
...
FIg. lUI
In 1ltis C&>e. !be fieW windingo are joinod in .. rie. wilh the annalure conduclon (Fig. 26.43). A. they cany full )OIld CIUI1!nt. !hey cons;'l of relati .... ly few turns of thick wire or o!rips. Soch genemon are rarely used except for 'pecial PUIpOSCS I.~. as boostcn rI/;, (iii) Con'pound ",ound II is • combination of • few ~ and • few shunt ""ndinp and.an beeilher sIIM-shUllI ()f long_shun( as shown ;" Fig. 26.44 (,,) and
',)
](l •
J
-
... a~
~~
.' ~"
-,., , . -
•
I
I"
j,~
j
~ r-I~Od
J '
FIg. 211.44
·"1,,1 , 1"
- 912
E~ITechnology
\110) resptaa !he I\rr'Ie$ r... I"- When series roeld tWIs!he 011 ... , rleld, gencntor is uid La be commuwivcly.a>mpOUndcd. On the otherI>and r..1d _ !be shWlI rock!, the gmeralor is Wd La be difJcrt:oLi.lJly complllllI oontaCt ~_ .../lcQ = 1 ~ from commuUllor Rpnen13 10 bnn.hcs and rmally !O the: CJllc:rna1 kNod. [IS value dtng i~
.. SO+2.S2A \\;)111ge drop on oeriel; f,.ld wiooing .. 52,.0,Q3.1.56V Alma".", vo11l1ge drop 1/1• .. 52 X O.OS .. 2,6 V Drop at IlrusI'Iel .. 2 ,. ( .. 1 V
E, • V. Ill." ..rio drop .. boIs" drop
•
FIg. 26.47
.. SOD. 2.6+ LS6+2. S06. (6' £"""'P~ 26.5.
II. Uwrl-.l/tun/ rompounJ g.~Ttl1or :;'N ,.,,11
for a simplex wave-wound generalor No. of parallel paths " 2 No. of contlu:ON
IDg.""""IS.""""lede.m.f.E,,,
",here
x;
K
q,::: volt
q,::; X(~)VOll
A .. 2-forsirnplex
w.~-winding
_ P _for 'imple.. tap-"inding
E, ..
i,. .(2:' )(I;Z (~) .. ~Z (~) Voll - Ql in f3d1.
For • given d.c. """,tune, Z, P and A ...., ron:Ok 10 I>c 7.0",Wb ? (Ek!ct. 'loclli:oc:§· l. Allalo.bIod l' ni~. 199.' )
SoiUll1lCl.
E• ..
tI>:::(~)VOlts
He....
K
7 x IO- l Wb. Z K 51 )( 20 .. 1020. A" P K 4. N K I~ ,-p.m.
E,
K
7Xl0-J)(~oo.OXI500(~) .. I7Il5 V
E:umple l1i.9 . An /l.pole d.~. g.~mlar has .roo """,,'uu condI in panllcl
" ,.
"
Hence, with w",'e-,,;n< l000i(0) x (414)
. """
m
.
• .. 129. 1 mWb per panoIlel path .. 3114 .. 7.15 A.
Annatu,," C\I~t •:""m..... 26. n. tI uparu'~ly r.u:itrd srMmu>r, "'ltrn ""111'''8 'If /OQ() 'p,"'- supplied 2QQ It aI 12j V. What ..-ill M ,/tr 1.-1 ,...""", wMn lit. qH!M drop. If> 800 'p.m. if Il u ""e/'MSN , OJ,,,,,, 1M' ,lor """,,,Ii'" IYSUIWIU .. Q,{}l oIrm tlIId bfldlo dtop .. 2 V. !OIl.4
"~~~~~:::':;::: r-~ , ' ,-~~ Al 800 I.p.m. E,>" 135)C 8OYl000 .. 108 V Ifl isthe ....... ioadc"",,nl. tbmtemtinal volt_ II" V;, given by
SoIullon. Since the induced Voltage E is nlOtl: Illan the !emlinal vol1age v, the machine ;. work· ,nl ... I Benera1or.
E - V'O Ill.. or 240 - 220_I. "O..1;I. _I(IOA E. _ ZN (PItt) or 240 . \0" 10-J " l x (900'600)(412) ; Z 'O IItXIO Smce there an: & tll11\S in I coil, il ""'InS tbete on: L61C1ivc conductonkoil. Hence, the number 0( coil • • 8tXXY16 .. SOO. £"""P~ 26,14, In" 120 V c~ VfII:_ 1M ""I.J SoIaIIooL (i)
I. . . IlUIl25 . 4.8A ; I .. 1001. ; 1." 104.111.
\bt .... dfvp in.rna"iD< 0.04.4. 19 V ArmIIun: voItoF drop • 104.8 >< 0.06~ 6.29 V
..
E. " 120.).19.6.29 .. I)()-' V Short SlIun! (Fig. 26.33 (r)) \u1I1'" drop in ..rico ..,;'>< 0.04 .. 4 V \u1\I.&e _ ......,. ",;ooin, 0 120.4.124V 0 124/2j . SA ; .. 1. __ 100.3.I05A
(iI)
..
vol. '. '00' , 3
Armat\Ir< 0.1/(0.1 . 0.04).74.86 A. II melln.\ that the ""00 field cu< 0.03. 1.575 V
poIu is 261) 111m und 1M ~fd pok 4[n:tiW! """"ro~ i, ~ wlwlml frVt8i~g, If 1M ItaJ 96 roils """i~B J IlInII fH' coil and is -.....-rd dl4pla lap. mkwltu~ /. ) Jbu fHr pok fir) tjfn:riW! poI~ "rr/'''8,h aNI t~, ~ ~i'·gop flllX
""""tw,..
. \:.::~"'1'0.""-
!11m
I~
........"I!>.
"'.......
y
I--
tk,..iry.
SoIullon. (tI ) Z. (96)( 3)( 2.576. P. 6.JI. p)( pi ... .. 6" 2 .. 12. N .. 1200 r,p.m . ..
2jO.
"' ''S~'' I200 (~):
fig. 25060
.. ... .. 0.004Wb
!lr l Inner diamet ... of tho pole ~ c",,1e i. _ 350 • 6 _ 356 rum. S,nce tilt", an: 6 poIeI. tilt ...1 r..ld pole nux covuage i. 8O'lo of ooe-li.th of the pole shoe ciltlt. Hence, lbe .ffeni,.., pole an: Itngill io
_ 0.149)( 0.260 .. 0.03874 mm! Au. dm,;ly B .. 0.043410.03874 .. 1.12 T
t;...mple l6.21 1 " ~ A 4.pck d.~. ~r%' "'im 1200 rotIdw:t,,"g~"''''''~J 250 vaIu .... ..,-. d",..", 01 5f)() rpm. TI>t poI~-.""", haw ~ iI< (1()()Ut(j()" (414) whichgi-;e, . .. 30mWb When speed i. kepi consIanl at 1000 """ only. Or to F1220 V on O.C.,
,
-.
., .. (22('L/400) 10.10 mWb _ 16.5 mWb
D.C. o.n.r.lono
923
Th .... by ;ncrt~n& tbt Ih",,,-fI(Jd-i:in;uil res.i_ willllhe help of addinC e,uem.1 rhcoslaiic, !be ~/ll in IlIc flCld-i:iJaJil il dccrused so as 10 Ik. liil Keep .. rne nux per pole, chaDge IlIc .peed. is heldronslanl III 30 mWb. on D.C. c.m.f. of220 V is obtained Ill. speed of N r.p.m .. £ivtn
If.
220 _ lOxJ(1-'xSOOxNl6O. N _ 5~rpm AI 220 V, lhe nWl can be "",,,,W/ICd .. 30 mWb prt.. idcd!he fl(ld nlf"fttIl
4OOIR"
II; IIDdsaJ1~.
- 200IRn
or R/l - 0.~5 R" Thus. !he f .. ld ciJaJi, ~i'lIInce be m.l1lCed 10 the new value of 0..'i5 R" in otdtr 10 ""'a,n 30 mWboffl ... per pole (rom. YOI~c of 220 V.
mu.'
I;;" Ally DIller combllwKxI of proper speed and nWllpole can be c",*," and worked 001 on "l1li1 ... 1111($.
2'-2114,. A Jhort·J~II~1 d.c. t:""'fH1WId Iftllualor .upplitJ 200 A aI 100 V. "INc "'Ju, 0/""""1"",. uriu ji.ld and J~unt jitlJ wlnd/IlIf' ,,'" 0.04. o.OJ and 60 ohnu ""p«fi,·.Iy.
~'""",pk ImIU
Find 1M • .",P"Ufltu AIs" find 1M ~.", Ifmnated i l _ mochiM is ctHIIf«l~d lou and liil }:ddJ ClorTftlOl lot.s. (il 11).'...... '--111.1 11Ii. 00 ;1 due 10 ,he .-eve....1 of of the. '"""-'."'" 0,,", every portion 0( the ruwin. rot1'~. uoo.. N lind $ puk .hcma'ely, thereby .U""''''' $ II'" N poIorily respeotivcly The run: "'Kk'l""' one: romple.e c)dc of """""ire reversal aflCr pauil/a ~ ont pa;rof polu. If P is the nu,nbeJ of poin lind N. the a/lI\a1ute ,\jlttd io •.p.m .• II>Clic nux , Hence, an e.rn.f, i. induttd in !he body ofth( cort :ocrordinllo !be laws of ~l«tron"'8"dic induction, This ~,m, f, t.hough small, up large Cllm'nt in lhe bodyofth( "ore due tn it> .mall ""i'lane1.' hy"o",.i. coeffICient but which also JIOS*" IUgb eJecrrical resisli.i[y.
..,1,
N
N
~"
'-
IS
S
'0'
'"
I.,..
26.35. Totollo5s in a D.C. Generator
n.. vanons lusses occutring in. gencrtltor can be .ub-divided as foUo,,',: (.til
(;oppcrL.-
Ii) AmU01UreCOJl!l"rlos<m/.'R. ['01. E:/. .. lhepowcrootpuifrom......nu..1 ,,-here R• .. resistance of annalu,"" lind imetpOle. and .. ries rleld ...~ndins etc. Thi. I",. i. abool30 to 4Q'l. of full·luod los ....
92.
~
Iii) Field coppe.-Ioos. In ...... case of "'un, gencn.lon, i, is ~ally mn<WIl and fJ.R.. (or VI.. ). In ...... cue: of ...rit5 £flImIlor. il i ... I..l R......1Im: R" is ~i 8'_,'
--
-~-~~-
....
..... 1000.... _
26.36. Sh"ay Lones u .... Uy. rnagr>etlc: and medwticlllOUI ol,.,nemar. SOD" 40 X 10-1 .. 20 kW Tout ~ II$. - " " " .. 12!iO .. r..,1d copper.Ioa .......... ""1'1'"'"..... .. fl2S0.12S0~42-JJ"0.U)...-.us.2.77ltW
•
29.
20 .. 2.771
"'OOE87.83'10
no
h~mplt 26.!li .... s hllnl ,~n""'/r ",.. Q ,,1.. .... rtI'nl <Jf 196 ... 01 v. TIw. ~Im~ 100us ~'" 710 W """ 1m. .h..mji~lJ roll rrsiJl.lJOC. is 55 n 1/ il lit,. a 1-:1... < 200 .. O.IW1
Q
Fat lIIU,mumclflciency.
i'R• •
at 210 V
1!01elotu·I. Osmanla Ualy_ 19901 SoIuIlols.. T""".nai voI",¥ _ 20 x 10 _ 200 v
I.... 2OQI:50. 4 A;I. _W ." _204A I.R• .. 24 xO.5 .. 12 V • B~ dr-op~ 2 x I _ 2 V E, _ 200 . 12 . 2_ 214 \' . a, in l'ig.26.6.5. Si",,~ il'Oll and friction 1S5el .we not gi~ .... only ~kcoric~1
t
'"
efficiency of m. machiM can Ix: found OUL
ToW p(N/u gmmued in m. onnaIure .. 214xU ~~.IJ6 W UsefulOilIpul • 200 X 20 .. 4.000 W '1,. .. 4,CO:VS.IJ6 _ 0.n9
FIg. 26.65
or 71.9'K
f.umpk Z6.Z8. It I"",·,hwu ~-~'tJUNi 1'_lUlo' 81...,. Uf) ""lis lJI FL. _put of 100 It. 1M rt',islancu of .'tlritxa "'Intiinls of ,I" """,/ri_ am.all" " (Uorlwling brus" ('iJ,Uacf! 0.1 &s fi,,'d 0.02 n inul]l'Dle fir/d 0.025 n: .hunt fi.ld (i..clwlinl ",swialinl ",.illanul 100 n 1M j"", 10Sl Ql FI~ .. }OOO IV; "'Intingumd/nc,."" 10lSU lO,a} j()() W Cohill/< FL. rIrIe;'.u:y of ,I" mad,j_. ( .If,.-tr\c:;oJ M..:h i __ y.1. iQllon: \ ',,(,'. I~" )
a,.. _
n. ...
Outpul _ 240 x 100 _ 24.000 W
Total ...... lure circuli tt'l.0WI0t _ 0.1 + 0.02 . 0.025 .. 0.145 n
I", • 2ao.'100 .. 2~ A :. I. _ 100 . 2,"" Armature c;TCuit ~r 1000 _ 1 02.~1 X 0.143 .. 1.521 W Shun, field «>PPt' loss .. 2.4 x 240 ~ ~76 W lronlooo _ I(l()(IW ; FritIIl)l'Ilou .. :500W TOlItllou .. 1.521 ... 1.50(h 516 _ 3.591 W; " ..
102,~
A
,
2~.O::~597
.6.S7. 117 '
EDmjllr 26.29. In a d.c. """'hint 1M 'Qlal il'lHr IQU;r 8 kW 11I u, ",,,·,J.ptrd ~nd urj,all_ 1/ urilall"" "'''''''lIS Ih~ _ . hi 'pHd i. rt'/i"ad by n%. 1M IUlal,ron IruJ I. follnd 10 M 5 tW CalCWn,r ,"" "Jilt"";' and ~dJV CI< 05' ~ IJJlS kW F..xamp~ l6.JO. ~ lry'lu",i, aNi ~dJY ru...-~nllMu. in ad_c. maclri_ ""'!ling at WOO 'p.m. al'l' 250 W and 100 W 1'l'.~~'i,..,I), lj'''''fl''-T ",ma.,.. ''''"'''anl. ",ha • •'P"~ ..'illi:>e tatal 1_ lone. be halnd? IElcctrintl M""hiMS-l. Gujarat Unh. 1989)
o.
Solution . T",. 11oss
w .. w. ~
W. .. W,.AN .. BN'
250W
c.
Ax(I{l()(ll(i())~250;
W, z 100W
..
Bx(I Q(l(lI60)'ElOO;
A ~ 15
8~9f25
Lei N be the new speed in r.p .•. at which 100aiioss is one half ofllle loss at 1<XXl I.p,m. New loss zP.50.IOOVZ _ 17SW
~-;.W copper krsses .. 3". 1m, Sol"'.... A 4-pok bp-"',ndJ", Iw 4 panlkl pm.. in ...... un If i. iJ ~'O(Ir>d for """ve~ Ihe ..... woce at .... Ibc ,emmw I:w;:comeo (4 X O.IS)" 0,6 mm. a. il obviou. from R,. 2667
, " T.~"'7-'"
I
, 4 pull"'l poth> (Lap-wlf'ldn,,)
2 panillel p;lth$ (""Ye-" ind,nll:)
Power raltnll: " d ,,4 JIm""",,", fIeN,'ftII X and y" rl4
Jlmuance 1kI"'''"' ItI and N _ ,
(oj Lac>-"'indJ"II
(bl W."'-"inding
""""', ""'''II'' (u)" (21)" 4. lkI 934
EIectnc.ITechnology
r"" .
5. eu:u.... "'" Iltn per poIe ...... n:d 011 MI·~ 50 kW. .I(I) V. 8-poI1< Llrl>-wound dc. J'm' and lind thr vclUlte. noBk ,,.,.. ,
>ok: pu'J'O'< of. c"",muw"" in 0 d,c .
Go""""< taICd ain't_ of III" ."....... "
~
ill
(al qw 1'18.27.1 the hne JOinIng the ",ntn:' of NS poIrs, (b) 'flo: mag""'i" ocu,,".1 axis or pi""'" (MN.A,) .Qi""ide. with the g....... ""'a1 neutral lUi, or pi .... (C,NA) Magne11C neulral ni. may be defined as the .. is 01""8 "'hieh 110 e,m,f, i, prod""W in lhe &mI:l"tn: condOCld Rule. The c"rn"1 d"e",ion i. downward, in conducl through ,he arma'ure is no longer "nifonn and .ymmo'rical . bou,1h< pole .,is. "'ther it ha, been distortro. lbc nux i, Ott" to he cro ...'ded at tho tn,ili"g pole tip' but weakened or thmned oot 01 the leading pole tip' (the pole tip which i. r;~ ""'. during rotatioo by """",ure roodooors i, kIlO"," .. ,ho leading pole 'ip aoo ,he other a, trailing pol. 'ip). The strengthening.nd w~akenmg of nux is "'J'ill'l,dy >I>o,,'n for a foor-pole machi"" in Fig. 27..1. A; ,,:cn, air.~ap n u, denSIty under on< pole ""If is greater ,h.n tha, undenne other pole half. If Fig. 27.3 " ,hown the rc,ultanl m.m.f. OF ... hieh is fouoo by v«'orialiy (". Of'J par-~II~I to pular ax .. and Of'" """",ndicul .. to this ui•. We find lhat
,"'U"'-''''4'
s
. . .-
... ..", . ,....,,----"-'~1'
'flo) Iii:
Ag. 21.$ (il com""""nl Of'" i •• t ntht angle< to Ihe ,'ootor OF.. (of Fig, 27, I) "'I'R"'"U"g the ..... in m.m.f. I, prod"""" d' AOC and BOD i.
360 X Z
A. I..,u mod""",,", constitute OIIC tum.
!"..
Total number 01 tu"," m the«! angle. '" 360 xU De"",g ... ti.in, amp-mrm per pair uf poles .. [)emagntlising amp _ tntrWpole
~~
xZI
,.,
'" .!...xZl
27.4. Closs-mognellslng AI per pole "The cond\lC1on 'y;ng berween angles AOD and BOC constitute Wlul cros.-magncli,ing CO< ~oo z Z (~ .. ~ )
K
7.1
K
ZI
f!,-'"'
29.. )
-'2P-- ~) 360
(Remembering that twu cuoduc1on make """ tum)
AT~e. ZI(2~-:W) _ {lUI on
. (iI Fo o~~5 ira.~
jl~~; I~~i'r tJf~;;~ ,., ' t , q ,"5'!' ~[~
M ~ ' "-or
i ~~~~~rl ~, ~;_~=~ -hunl field lwru. 523110 _
~: I ~PP""'.J
Eumplt 21.5. A 4_~. 5Q.kW, Z50--V __ .~ ...'OWId sluml ptltrollJl' iJ .so
I _ 1OS12 A
Cunml in clcll """'pm"'"'
"V are under N-pole and in ,he "I'I""i'" dirf'(:lion when lhey "'" u!l'h SUWlio. holf lhe: ..... ,h 1ac' =a with ~gmc:n' 'I>' i. docttases from ,",gmc:m 'b' 10 the. brush, again gi,ing alotal of 40 A a, the bru!.h. Fig. 27.10 (~) doe-p,cts ~'" ",o"",nt when co.l B "al"""'l at the eOO of comm utat iofl or ohonei"",it period. For ideal commutation, current through i, should have ",ver;cd by now bu" as >hown, it i. carrying J~ A only (instead of 20 A). The difference of curren, bel ...".," co,l. C and B i.~. 2O.IS _ 5 A '" th;, case. Jumps di=tly fron, "'gment b 10 tho bru.h through all" th~, prod""i", spa"'. If the change. of rumnt through coil 8 am plotted on. time ba$c (os ,n I~,. 27.1 I) it will be repttsCntcd by a honzontal lill< AB i,~.• constant current of 20 A up to the time of beginninjl of commutatiofl. From the fiOl,h of commutatiofl. the current will be rel"""'nte<e) art used. ,hen thert is 1Xl 11kI..,,, ..... nt rOO" the rurnnll0 follow the oec-
8
A
, I·x
c
PI (\.,' '
1 + .< 21
I·,
Fill- V.1Z
950
Eh>etr~
Teo;hnoIogy
ond longer p.olh. i. ""auld I""(cnbly (01""" .he (,"'. paIh. Bu. ",hen carbon hru. h''''ing hIgh
res.stance 1m • .ed. IMn cu""nll rom.ng from C '" ,II prtfcr HJ P"" Ihrough 1M !ottOnd path bec.use (il the resistance 'I of lhe fi"" path "'ill inrn:"", d"" to lhe diminishin, ..... of conlae' of bar '/>' ""i", the bru>h ODd btnu" liil ~i""""'" "of sn-vnd (l"th will ~ dllC ", "",idly i"""""I0& rodlac1 ua ofba! 'a' ""th 1M brush H.""". carbon bruCC voltage by prodIIc18g a ,.>-ers18g •. m,r in lhe "","-eireulled COIl under romma"'''''''. nils re'-eninl e.mJ., as 1hc """'" an '.nI.'- In OppO$II"'" 10 the ",aelanek ,,,,dIM lllIlu4d,
'-"'*"
1.",,,-
bHt"d~
IMIh
IIU
Fig. 27.13
prnduud b ,'
.M",,"'.
tI," 111',.. tlrmmurr
n.. diI!ould be k.pI In mmd d"'l Ilt!d."
.""",u...
and II> mag""'''' " .... un.
N,.,. I. ,. Z1,nl' .. 8, JjIt-., "lie", Nu ~ No, oflU"" "" lhe: compole . I... Arma'u", en"",,n' Z .. No. of :annaHu" condllClors ; J, ,. ('oil cUrTenl P .. No. "fple>; I," Air,pp k ngth undenlo.o cnmpok
Z .. S4Q; 1._ S\XlA; V"
~A;
P .. 6
Arm. m m.r ,. S40)< (S!XW>y.!)< 6,. 37.loO
952
Electrical Technology
'/110-
Coonp!< ."•• "" m.m.f. _ II, " 0.5 " 4 " 10"/41dt, one PO" of potts, If fluxc> from oil poIrs are .~ac;tl)' the >arne. then eom.f, induced in each panlk:l Jl"th i. the same and each path camtO< the....-.: CurttnL But despite bnt effon .. """'" 'ne i"""IIb1~ occur due e,tho>, to slogln "ana""". ,n ."_gap k:ngth or In the m.. g .... U'O propenio of .!ttl. ile""•. the ... i. ol" .. yo a 'light imbalance of • ,m.t, in the van"", parullel path.. The resull .. WI rot>ducr"", undt, ,1Il",¥a pole. ¥~ .... r.'" greater •. m.t. anoJ he"". carry larger current. Thc eUIn'"t diIDlbu!JOn at the bru>ht:s bo /0 II_nUl un. qUIII d"tri· / ~"fH'" III Ih . .....'h .. 'hrub., ~~Ipi"~ It; j,.,nk•• ~o,.·
,n
/>,,"""
"'U"""'". One £qu. li,,e, nng i, coo"",,1ed
u,.11 CorldLIC''''''
in ,he am",u", "'hieb "'" 'Wo rol", oJ>311 (Fig. n,17). Fo, example. 'f Ih. number of poIe:s i. 6, ,hen lhe numberof connccti"ru; f()l'e",--h equ3Hz.r nng" 3 i,~. equ31 '0 'he numbo, of pair of poles Maximum numberof equalizer ,ins, " equaJ ", lhe numbo, of condllClor.; under one pai, of poles. Hen«. npmbo, of ri ng, is
In pnoc1ice. 1>')1,,,,,·e•. tho numbe, of ring. i. limiled 10 20 "" 'mall,,- lIla, In Fog. !1. 16 is ,hown a de,.1oped arm.LUre ",OOtng. lIere. ooly 4 equalizing bus h... been used. It ..... ill be seen \h.1 111" numbo. of ""I0.lizing coonecliOllS to each t>ar is two i.e, Nllf,he number "f 1',,1e>. "-*'11 allcmalc 1 """'hi ..... and k>< 00
27. 14. Parallel Operation 01' Shunt Generalon Pow.r plams. wlltlher in d.c. or ,,"c . ".lIon" ...... ill lit g."e-rally found 10 ha,'e ..,,'eral smalle, generawn running in parallel mher than iarge , jnglo "nits capable of supplying lhe ma.imum peak 1000. llIe", smallcr units can be run ,mgl. or in ,·arll)U.' paml101 """,bin",,,", 10 ,uil 'll< "","01100d demand. SIKh pnoc1lce is con"dad 00 the eleclrical PO"'" planl OUCI""IC' bel""-."" ilS peak "31"" o;omcIimc. dUllng the day and its minimum >:,IL>< during the late nighl hourt which ""'an> """ then: mu" be: ",he.- 1"...."" ..... to ~ can: of "'" Load. MomlV....... ben "'" generalor does actually brt:akdown. il can be ,.,pairrd W1th """'" c ..... nd "'" in a ru'h. JI'"O"ded lbere are ther gO""r.llOn ",'ailable 10 malnllUn se",ice. 1M Addlliom 10 ' 'lanl Addili"", to """,~r plant. are frequently made in <Jf1Jcr 10 dinx1y IoIods. Prn,'",ion foo- funrn: ex",n.ion i .,
I
n
-,
'''"eb
27. 16. Load Shoring Bocau>c uf the,r .lighlly droupmg >"uI'"'-l!c chan>clcriMic-ICC. _!bod of COIIMclOnl in In 1'R'·~ntlnl any o.hoct or .uddcn o;b~ 10 ,"" and ","",>',n, I t.'. number of «Iual voll-ilg.: (beu""" gene"".,.. .... "'nOlng IR parallci\. From !hi> combined ChanoclcriStiC, the vol ...,. for any combined load can boe ~ off and ff1)tn 1lIrtt. Iho cun'tnl .supplies by oacb boe round (Fi •. 27.20). Ir me IcncnKn .... ve ol",icht II ... (~ ...... me abo'o'" fQtIl, ...... boe ot:u.ncd by .. mplr oakulauons . - ofl"'r/'Iically
....,."'Ior ......
leI ... d,ceu", !he Iood """"Ill of '''0 """""""" ...-!tidt ha .... lhouid b< ltpr ,n n..oo dw
ttl '1\I'Jhlly ,nCtU>OOd Iood.. In!hat~. lbe cw· , ___lL____lt=' ____ mM Ihroup its ~ "'indmg ,ncrea;o. ... hloCh -8 funhn" ~nl'locru. n, r..1d and '" ",,>e$ n, fI"'CIl'Icd FIg. 27.~ • m.f, th". ca" ..", II '0 tne ,"11 rnon: Iood. Since ,he 'Y"em load " as,umed '0 be COO".",. aencnlor No.2 "'ill drop son ... of II. load. the",by "'eakening its !iCn~1 r.eld ",h,eh ""II ""ull in iI, funh~r (In.>ppmg off its load, Since thl> dktl i. cumul.,i,'c Gc""""", ~". I ",II. ,heref"",. «Old 10 w.e ,he e",j", load and finally d,;,. ,encrator No, 2 Ii> a """or. "nut ""'''''.r of 01 leas! """ oIthe IIV aencraton" ill open. Ih .... >toppin, their panllel
r- "
,~
pow""
n... ..
",,",-
for n""-'III!he p::tnllel "I"'IlIUOfI of OVCfCd curTCill pa>Se> panly IlIroup the ~ r",1d rod of ~or No. I _ partly iI n"",... ~ .. ''''' njUJ-littr t--llIroup !be w.-or> r..1o.l .. mdinl of I"nnSiOl ,,"u. 2. Itt....,. the """",ron; an: ~fftatd In •• iml~ manna- "'Ith tht ......Ir the f!:'"DtRlor No. I c _ W~ the entJ", load. For ,...; ....;0;01 P"'I'"" di~;.;oo-, 01 load from..,.1oad 10 full-k..t."" ~nl
~""M;.oJ
1M
ill lhe ",gul.,;"" of each ICner.ru(XYIIXXl~ l17.JSk"
EXlOml'Ir n . l7. Two .h~1I1 8M"aI,," opUaimS ;~ pamlld dd;,'" a 1< above 'wu cq .... liun ....... e get I, _ 61..5 A ; I, .. 1873 A 161 \' .. 500-0 " 62.5110) .. J.81.lS \'
. 2nd J!Coc ... tor
"xarnple 27.18. Th'" ,hunt tenuolOrs, ~(U'h wil" a nt)·lo.aJ ,"Dltag' of 125 V art! '~""i"g Th~j, UI~mal cMrocICrUrk. can Dc l"un ee (i) aocwe becomes. ~ •
:.
l~~= 4V/] =~ 2 5P, 5V/, 51, 1,_3500_1,
.Ii)
411
1]. l.2ll.l Aandl, = 1.217A
~:nmpl~
27. " . Two ,hunt 8~~">1'O" A '" II Of''''''' in prall~1 and 'M;, lood-cllalYK'~ns tics nwy IH taken"" straight li~u Th~ voltag~ af g~n,ralO' A f,,11s fro", 240 Vat no 100,1 '0 220 V at 2QO A. M'hil~ tho, of B fall" from 245 V 11/ no [00" 10 220 V w 150lt. fN'~rmiM ,"" cur,-"uU '''f'pli",j b., ~"ch mach'M ta a co,"",,,,, /",,;1 of J()() A anJ 1M bu.-bor ""[Ia~ Soimion. TWQ graph. are plwed as .I>own 1beir equ"ion, "'" 240-{2{lI2OOjIA
Fulher. 1".1.
In
(Hhanllhlth • .." lni., Aprill"7 ) Rg. 27.26.
~ 245 - (25J1~)1"
~ JO(l
,~
'. ~
2lfJ
~,
0.0
~ - -,--.
~
~
'.
~ ,~
'W
C
----------
1 ~,
---~:.c"""' ;;";---------"O
I
Armature Reaction and Commutation
961
Thisgi.·., I" .. 168,75A.I._IJI.25A And
.
h IS rePITscn,cd by tlH: poin' C. in gmph. "' 00 i"' • .-sec';""...,;.fying lbe coodi,ion ,ha"wo currenlJ; (/A and 18 ) odd up '0 300 amp.
£ ...... p~ 27.20. I~ a co""i" $~b·slaliQl1. Iher~ a,., 5 d.c, 'hum g~n~ml"" in roroll~l> nxh """Iag an armal~'" ,."i'Umu of 0.1 n. nuuting ",,/o, sm,,, spud and acil~d Ia gi"" eqlHll induetd ~· m.f •. &xh ge"uator '""plin an oqlUJl of" ,oMlload of 150 kW '" n lumi""/I-oJI"~ of 500 V info a load of~d "";Slaaet. If I~ firld ~1I"rlll of QI1~ g'MrrJWriS ",1,",1 by 4%, 'h~ atll,,.' mtIOimag lI11cMn8 I,
~
curren! '''ppliOt'",,'ing (iiil from Iii ). "". I L-+ 4.1 I, u 510 From Ij,·) aoo (.I . ..-ege! I, ~ 3060{51 _ ~9/99 .. 60A(approx.) Frolll ll.) I, = 204.W=264A From (iii I V .. 26-1 -+ 24() .. 5il4 \01' ~ 504 x 264 waU .. III k\\ Ou'put of I" mach,ne Ou'pIl' of ,,,..h of -aluc in lin abovc. V _ 24ti vol1. Puning this value of V in (ir) . (I + ;~)" 0.12 ., 2
I., WJ-2_46 _ 14.2A From liii). we ha,'c 1• ., 40- (2 x 14 _2) ~ 11 .6 A lntcm:d volt"ll< drop in banery _ 11 .6" 0 . 172 ., 2 V :.
E._ 246 • 2 _ :us y
Armalure A.ac1Jon .00 Commutation
,
tl
'000,
"-
0.240
\,
,000fJo
963
I.
1
: uno
,
E,..nov
"'~.
'.
FIg. 27.29
EUnlpk 27-23. Th'" d.c. g'~''''IOTS.-l and 1/ art comtl'cl.d la a comrnGtI MaJ. .-I had a "-'lanl •• m./. of 400 V and i~ltrnai Tt!SUlanc. of 0.15 (hohiJ. I/ilas a ,.."..,lanl . .....f. of 410 Vand "" ulumtJl rt.iJ~ of 0.4 fI CukMial' IN currtlll and pat'>•. , OIJ.I"", from «< 0.25) .. 4l.1.8 V Ob,iou,ly. machine 1/ with • higb< l<m\;n.1 "61"KC 000 ,II< kilowatt 00[1"" of 'U"""",( .>!4{I V ond 245 V "'S-pe.p" """",'or deli,..ri", 200 ~W " 200 V .3"on number of i"l'-CQrIntd«l""""'= «>r-.J"" ....... ~: inl«pOie .i....... 1.0 em. flu>.de .."y in in"'rpoie 0 .3 Will ..'. I,,,,,,,, ,be effect or iron p.art. of ,ho oi"".. r , nd of leAhg'w.: "",,,. """ "" the IT"""' pole lIu, ill '0
(b) ~i"on It i, (d) bolh la).,.;j (b) (0) ""....., i' l . In. d«I d,c, ~Ior. """""" "",.. '0 be >h,11«I (a] ""'''''''
I") -...._1o.Iop-_II.< . ........,...... _ t.... of .... vt: ...... un: ~ pot" pol< iI '" "!be 110mb« < .. ~,k> ~ """"" _ .......1 .'hm .... y ..........
(d) _
......10= ~''''''''
of"'" -----w
,
volt
•
~
I
Shu",
Field
,.,
POle. I",,' .... ,
Flo;i.28.1 1I~"c".
if spc above rei . """ beoomes I:: _ 141 It i. 00'. io", Ihal "ocn I, i. intr-.::t«' initi.1 'mall value, ~'" nux 41 and hente go"Cr.llc-d e ,nJ. E. ''''''tea", d""'ll~ a, currenl so loog a, the polo. "'" "","Iumtoo This i. ","presented b)' !he straight portion o.l ;n Fig. 18 I (b). Bur as!he nux den,ity increa .... ,he poles become ",,'ur~kiI. so • gn:~lcr incn:a", in l i, ""luir-.:J to ",,"'OCC • gi"en intrca" QfI he ~ fron, lhe _l000i "'unt"", """'0 pro> iIIed In I .,,,,,Iar " ....y.
;obo.mt ufldcr..:t-Ioiod
'0
wi.
"*'
rond,"......
,how.
""ncnton.
I~ I
In'.. rruo.l and t:Irt...-nall:h.n~t~",rlQl U, Uj C(lrblnnoclro to an exld is dLfC 10 mognelic illeni • . 11 i ..""n thallhe Ii... pan of the CUm! is pnoWICC 08 ~I$ .""'tler,..,.... tana: and the ~"I ~ott.gc 0.'4 .. s1oght1y ~r than. OL If (,.Id rewo.W>Ce .. i ... , tllm slope ~ lilt IfilSWIte I...." i......'...t. _00 ... """ tht ~ to ... h",h the generator w,1I ooild up al a I"~ 'fttd. decn'lSCS, If R" i ........sed so moch!lw Ibt reo .i,tance 10"" dou not oul the O.CC. ... all (ilL £umpie 211. 1. 1M _n~/j",'i.,.. '-""''' of .. d.c, sh~IIlI._m"'r al 1m ~p.m. is;
,o
0.4
0.8
6f)
120
" J7H
,.,
1.0
1,4
202.5
211
23 J 217 2-10
1.8
J.O
"ar IhlS Ir~""IOT Ji/IJ (Il no I,,,,d r,"'1- fo' U 101a1 .hwu field ",-,.iJ/01IN' of 100 0 (ii) 1M ail,',:'u/ fidd ,...,.ra~ at 15()(hp.",. and liii) Ih~ maglltti::J]liItQS~ :
.0.5 60
" '"
" '"n.
" '"
H
N'
J.5A 152 V
1/ "'Ji<wrIN of fi~/d cir 974
Elec:trIuI Technology
PIo< 'M O.CCfor J7j "p."" ond d~'~""i,.,. the W)/I"p '" "'Mc~ ,lot ftIGC~ilW' will udre Iffi~ld ci",~i'
r/,.' 9.4 /15 16S 202.5 228.8 248.8265
n.. .... w o.c.e at 373 •. p.m. i. shown ,n I...... 0.1 represents 4O-Q Ii....
•
Fi,. 26.11 . ~ 160
-.
n.. voltage correspondin~ to point.1 is 260 V IIeDCC maclune will tlC,lC 10 260 ""It with 40 n ohun, fidd ~.
~
, .. ) From Fil . 28.11. n i. de."haI fOfe~dting the gcneral<J< 10 200 v. oxc;';ng cum:nt should be 3.8 A. F>ce. 2(ffi.' .. 32.6 n Additional ~ requtted .. 52.6 - 40
0
, ,, • ,, , -
ilxatJ01 ('unen,
I'Ig. 21.11
. 11.6.0 ,. ) In mi. case .• hunt field "",i.tance • 40 n ... (... abcwe) Terminal ""Itagc. 200 V :. Field CW'Ttnl. 2tXY40. 5 A Genented • •m.f. forudti"ll clltrent of5 A. 228.8 V
1::
E
V .. I. R, :.lfi• • F.-VorO.41• • 2Z8.8-20~28.8 A I..ood cum:nl/ _ 72 - 5 6 7 A
I , • 28.M.J.4 _
lOumplot lI.5.
n
E
n.e """,,-cil'Cllil cltamcl~rUlk of" Mp/ai1tM. IElecuic:aI l«h"""'cr. Bomblr Unk 1917) So/urion. Tho: O.e.e. ... plotted from tho ,i"~n d.", Ii " " '... n in Fi,. 28.13. Tho: )+,(11,,,,, (M is dnlwn u ",.w. I. ) Tho: ,'ill,"!!" to ""'/t,,,1t dlH U> ~'_UF~ ff'QCtu",.jind 1M load IWPP"~
&y IN
,.._m,or.
(~tronordlaonk.
AU...... bud I T..h·~ 1992 >
SoIutkm. When ,he 1<JOO'IOOO_ 21.6kW
f..nmplo l8. 11).
",/oun,
l~t""Qr ,,,.... the /QI/",,'/.I, ~-cI"'"I' elrll~ltrl,'lc
FitklcIITTt",: 0.5
/.0
1.5
1.0
O.C.
'"
m
'" "l1li"'''''
1M
t."""
$4
1.5
3.0
J.5"
2JO
U5 V
""""/WI,, and~/d ,..,II'''''~tI ",.. 0./ C and 8IJ C r'WMcril'tly.
wh~h 'M nwcMIIII
,,·iII tulll whm "'" (u" IhUIII (t l 1M ."DIu ltul dllt I" ,.trt/gn "'Mil 100 A .".. lit ,lit /t"",}1t/ZJ """. ",t of /75 V. (t l 1M (nfl'tnt"'t fl'd""lIolt lit ,p"d /"r lilt
PtJI'''"'
""""'l1l"I
_'l1l'i' '" "
:
C/JkIj/D" (_I ,hi ""',,,,, UJ
"'lilt IDmI Ipud.
,.,
nwcltlM III foil 10 ut:Ilt gn tJfMlt dl'C"liIl. ,J,:WtrkaI \1xIlinft.1, BunlbIor LII&. . 198111
'i6lulio IIM:......--..ill build up II ai"en by OM.
Ul \ .
It l With " ' V ICrmiNl p.d, 0Il1old
/.. _ I7YfiO _ 2.2 A
VoIu,., comllp)l>din. 10 lIIilllt-ld.:urrtnl " "Villi by OC _ Ill' V.
,
\'IlIp loot d"" to lImIIII~lllAClion and 1ImIIIlIn< drop_19, _ m_20V. Now. armalluedrop. 0. 1 1( 100. 10 V lei',' be IhI: "ollt 10.1 dullOlllIIIWn ~
e.ciling current of 3.6 A. I, ""'.,.. ,hal curren' throug/l ~o rn(JttO II"", for • 'till larger e.m.f, BOd SO 00. N",,·. lhe iener.tted e.m,f. in the arm;U"re h.. (_ ] to ,upply tho ohmic drop IfR .. in the '""inding BOd (b) 10 OV.ITO"'" Ihe ,,,,,,,,,ing ..,If·;ndoceJ •. m.f. in the field coil i.c, l. (d dl)be have a"""",iable self-ioouctance..
,"".-eased.
1/
~, a I/II.", + L. dlldl If (and .,-, long .. ). the gcneMed e.m.f. i. in eM'es, of tho ohmic drop R... energy wQUld conUnue be,ng .tored ,n the pole fields. For example. '" .nown in Fig 28 .17. """".ponding to field cUfrenl 0,0.. lhe ge"""ued e.nd. i. AB goc. I" >uJ>-ply obrruc drop IjR", and BC goe. toovercomo .. lf-induccde.m ,f. in the «>il. C. and !be: r",ld flu. 4>rtuT d,rectcr to ~ 4>. SO ,hat I"" vol"". bu,ld. do"'n fm/1l ilS oriS;"'" residual ,'01 ... . h g. 28 )8 (J) $bolo! "'" c_ "hen doc to MImI: "'ason "'" residuoJ "'"3DC\1sm gtU ",.,..,n.cd. He""". 1hc :uma",,,, volUte i. al.1 "',........ ,,'biF and 4>.. ,,", ",versed but an: din:cted 10 !he right .. $bolo'" Undo, condition. the ''''I",e "'''ldup is ,n!he rI;",,_ Obvioued polari.y ClI" be com:cled by u.. n¥ an CA"'1'1I31 1",,1 and independenl ",- lhe load. thIS cond,uon of oIlI.! not. lIovo-evcr. be forgoe .. n thai due 10 i""",ase in l ~ eu""n,. V i • • lso det ( ,ii) aivn ab, the .rr"", of dno",a.c In load RSISSance: pn:dofnlNltes the .rrtt' or tltetuSe In V ~ ... '" load i< n:1""""ly . mall
rtItQs,,,,
"".'ml. sit"",
,g""
da"'" tI", "" • •
.""ru momentarily. But due 10 (he lleVere. annalun: reaction f... 1Itis heavy L;llm'n,.oo i~ased 1. 11. d"",. the 'mninil yolLogc V i, dr.u1ically n:dUCft1 l1Ic .ffect of this ~ic rtduoctJon in V ......1.. in IcI$ load curn:nt ( • GA ). In ocItorr wonlJ ......... the ponioo INk of the curve. 111I"g< "'Iula .. on 01' • gcne" Uor i. me ...1 the change in il!i lenni!llli '0'011>8. ""ith the dunge in load """""' when it is ruruting ... ooruan, &prnd. If the c~ in ,.oI",K" be''ftoCn ..... 1oad and rullload i•• null. then the gC1LCr.. ..,.. is,aid 10 ho¥. good n:gololion but If the c hango in voltage i. large. Ibm i, 110. poor "'aula' ion. l1Ic wHup Nf.. I",'"n rJK SlDrian bILJ·bar flIIII ,"~ for md vll/wlwhr~n ~ur"'nl of(i) Zooll Wld/iI} SO A. . Q
./' SoIIUIon.
1.'
'"
IAL\tKSN. B Elftl. l\I..,bi"" Sum ..... 1991) (i!
VoItagc drop a 2(0)( 0.3 ., 60 II
BoosICen frum Fi ~. 28 . 2~. If the ..,Iies fi.1d amv-mnL< are ""'h thai the rated·1oad ,'oItage is grtare, Ihan thc oo.\oad \'ollag •. IMn ge"","'lur is ......... ","" p.",m/d. If ra~·luad mltage i, les, Illlin the no-load voltage. Ihen the genCd
..,ri.,
fXTice •• few una series amp-tums ore liken ,n order to .11"",· for the drop in arm.1.!""'. Any $UIpIU$ lmp-turn< ~ ~ changrd with the help ofa di,'MOI" rross the sn-it< ...irCt. divenor ... .liImpW ZS.I S, 8~nuQ'ar u ronYhun, grnc'll.lor constanL 11 440 V boll! •• """ load ond full-Iood, ","unt f",1d ampere-tums pcr pole ban '" be UICIU5Cd from 1600 x 5 ~ 8(QJ .0
Generator Characlerlatlca
987
(1600 x 6) ~ 9600 i.~. 1m iocre...., of (9600 _ 8(XX)) ~ 1600 >I T. n,. .. me i""",,,,,, in field AT can I>c brought abou! by add,ng a few <eries ,urn, [..." ~ be the number of ",rie, turns required per pole. Since [ocy ~arry 200 A. n X 200 .. [600; n .. Mturns/polo> J::~aanp[~ 18. 16. >I
I""g ,hun, c:omp<Jund g~M""I"r Ivu" ,h~nl fidd "';OOing of I()(x) lurns~, und sm'u fidd "'inJing of fM' I>OJ~ alld I"t.i."anc~ 0.05 n. In on1u 10 obUlla [/v ral~d roJlag~ bmh ", 00-1004 WId ",1I·1oad j,,' "/Mralion (1j shunl gM~ro/Qr. ;1 jJ nffU,«ll)' '0 incmJu fi~ld cum",' by 0.1 A. n." ",11·/004 arma'''I"t cu'rt,,1 ofllv cO< II
:. Strics an1l>-lUJ'1lll arc reduced
,,> 1~~:
>< 100 3
70 0:;,
£nmplt 28.18. II 150-kW, 14().V PNUa/(N" is 10 I>r COt11I)(J/JI1J.d ,lOch ,''',' iu ,'OII(lp riJ~,'
from no ,01" 0' _load '0 NO V or lull load Whnt ltri~sfi~ld f, CIl' "", oM ,hunt ficld i. ~.U'I'ro
,loa.
obI", ....
[rom "" ule"",1 JOu"'~. IIJn. [lfm, Ih. load ,~" i, "found ,h.. ,i" in ml"'8~ mil "" d by iMl't'Osing 1M .xcllmg ru,r.n'from 7 II 0' 110·1001/ In 12 II mfull-INUI. 0/,.,11 Shunilurns/poJ. .. 650. ltrin IOI"'s/poI' .. 4 tJ/ul ,niJUlnN' of ..riu "'IMmg, 0.000 O. If.IL.: ,,_hIlI' OJ ('QI1IItr",J I""!_sh",,,. finD ,/No 'nis'o"". of ,h~ ,m'cs amp"untS 01 ftO-lDati anD drop ill "",din, r.,i."JIll:< ar [ull.load. !'oIul"",FulJ-k.ad cllm:nl .. 2.'iO)( 10'1"240
'u,.,
_ 1()..\1 A
Iocn:a>,e in Ir"trQ'~ 125 V ai_bid and 1.75 A I" g,,,,mlr 15(J V Jl!umfi.1d ru'r.~lIf 1,25 A j, '" full I",,,/. Cn/rulol< til 'hr ",,,,imum number of "flU 'urnslpol~ lIud~ If> prod~~ 1M r.,,/tirrd ",,-load aNIf .. l1load l..x'alts a. Q sho,,·,hunr compo;uuJ pMrolor. Hi) i[llI< gm ..",,,, i, "q";ppM ...i,h J .. fLU lamyp"ir havi"g a "",'/J"U ",D.O] n C'Ok~IOI' dil't:rror ",im",« r.quirtd '" prrxiul'< Ih" dui",,/ '.'OfI,po~Mins_ !iiil '''''ag' ...gu/,,,,,,,, of ,h. rlJfllJ'l""''' 8m.rr"", Solution. Iii E:cries tumslpok n:qui..,.;i E J1Cn1400 ~ 2 II"""",. "un, mum numbcrof SC1>ti rum"'-jJOk n:qUlmJ for prod""inM tilt de,in:d .o"'p""nd g.... "'I.,.. lemunal ,·oll.gc il l. (Ii) Now. actual No_ uf "";0. lurrulpolc i< 3_ He""c. rum:nl pH""& IhruI!lh II can be found frum J)(/.. .. 8OO;lv .SOIY3A As shown in 1~1l. 28.) I . I... 400 - 18lXYJl .. 400Cl A Also (8lXYJ)( 0.02 .. (.I(J(W3)( IIJ ; H• .. 0.04 0 hill
"""'g""
(12S~ l :-O)( I()(){I50 .. ~ 16.1'"
f ig. 28.3 1
Eumplf' lL2O. 11 D,C. t~""r«l for mo,or dri"ing Ioads;>nd for be~vy p"""er ",,[Vice ., The dlffcrenlial--- (t) >hun, (iI) IIal e .... lIlIOn. G",,, n : _ f....... ~I. ohape UI .odI c. nO. o.c.c .. 100 •. p.nI. 0( • seric> "'............ 11> """""""ly..,.cilCd r)Co:! i ... (01 ....... : F",/d '''''"'(04) 10 40 5Q 60 75 ",,,,,,,,,,,. ,."." (V) 190..160 410 450 480
...... "';B010 " ~ 11. liOll ......... 01 ..... f ..1d _ _ .....,..... ..,...,. ........... t..t ..fta "'" bmw 01 Y and 130 V OIl "I"" < end of ,be: O,e.e. of ...)r~'",,04 de. i (e) ....... shun!
r"" ""na
(d) ""..... lbc: 'J' S (b) iD .........
(cl om••IL""
~
(d) ~ """""" (.1 rtduelion in f",1eI curn:n,
.1.
.-
If f",id lftiSWlc 1ina • ~ ....... '"""'" Jen<S r..1d «I '''''1 ... II>W of CO""nt 1hr<Jon ..,'n:tI,1I1hc annat"",. J _ UlICqUallUall th of mapcUC p.>Ics. ~, Optnuon obu,,,- ""od ""'\.lice IIId belo-' ~ opeed. , Q . .l6. '" bal;" tI... , lib_ pddo ...............c.. ....... lu, ... , • • 49 ...,mllto ..... bt..!, AIIL r. (49" Iy.z .. 24 or 2S Q. n. ,{mil n....f III) diff_...... Iflour fI&un: .... U ......wlod In ,...r~"", 10 III"'" MIL y"". of arrnaIu", .... lIion would be ""ersed.
of""'."".
n. '"
JlO'I'-
''''!
I),,,,,,,,,,,,
CHAPTER
learning Objectives
•
• • •
• • • • • •
• • • •
• • •
Motor Principle Compo,~
of Generator
D.C. MOTOR
and Motor Action Significance 01 the Back em,I-VoItoge Equotion of a Motor Conditions for Maximum Power
'cr_
Armature Torque of a Motor Shaft Torque Spa9d of a D,C. Motor
Speed RegulotlonTorque and Speed of a D,C. Molor Motor Cha _.-
,~ :;;;
- '~
"'" .... pp1lCdwilb=' fn)m tbc.upply""" .... !beyCXP"flCDC" J1'V~ ""j... " , • f""'" lending 10 rowe the ,,"",,'urn. Armarure ronduclOnl undd1JCU .. mech:uuc;li rorco on .... ~one poett. It .... ill be - " thaI,h.. ron:c;, if!. dirccciool OJIIIOI'iIC 10 thaI of.-mll," rotMion. 11enct'. il i. l"""", as .....,.,.,¥d fOftt or .....gnrtic q on !he ~ It"' "I;"&lW 1h,. Iha actlOll "" all umature rondooor IbM ,he poi.... """"'" has 10 ...'Orit.. n.e w()d """" in "'~, ... W' Of>!X:'O,IIOO i. convened.1lIO eJcctnc me'1Y. The~fon:, ".hould be ckarly uDdcnt<JOd 1\ only thn.>ll&h III< ,n""""",nwlIy of II". maa""'1C drag thaI conv.";",, " possible in • d,c.
tho,,,
."'''lY
,0,,"(;110e
'"
an l,duc kw",c direction (tlcmin.'. Let"! hand RuJel. 1100«:•. ,h. machine will
F.... D.3 (III
Stan rut~lml ;\/Iudocni... lhc:n:by dt'cloptng • IOrq1IoC ",'hieh ran
Tho
.....,"111. IS thof..., I•• ving this lopic. F.... n'" kt il be: """nled 001 thaJ in an ""'1 ....1 motOr .. jth >lOlled """IU~. torq ... b IlOl d ... In n>rpOloNln • manner shown II> F", 294 {/oj. ,.". pull .>.ZN )( (PIA) "01. ",11< .. N II ;n '.1'.5, [bel e.m.f. depends. among ",her (""'00, U(lVn < 20 .. l..lCI \ ob , .... MOI.,..[Fig29.7(b)J E• .. V-/. R. _2..'O_O-'l>!ribuliom during '''0 1C1ian.. an: indica!"" in '"'I 29.9 (o j and (b). A. a
gel>ll
(bl MOt(I....ctoan FIg. 2U
". _
2QO ..
13,,2 _ 226V
.--,"' ZN
P
"
D.C. Moto.
•
,
For. Lap-woond .",,.wee.
•
~
1001
'" "226>< 60 1000> lN (PIA)
E... 220 _ 220 .. ..
N~.
V·
... SO-40xO.7",_220\I
'.I~
2S~ 1O)~782 x NxO.7"'_220V
0. 1.19 ¢I 7.1, (PIA) 0. 1.19 ~ 25 X 10" X 782
~
40x I.v.!) _ 13 N.m
(n",pk It.... A tir. sJrMnI"-~'~ dn'~lops "" a.c ~ mJ. of llO V tJl 1500 r.pJII. "wi IlJ _ " tk'"r/opU fo' "" """"'Mtr of 50 A Ssalr'N siJllpiifnn. OJ.-pI .... ~ HI.... 1:.1«1. M..... ' ..... l",~ 1"3) Sol"."",. A l"'en d.c . .....ch,ne de'c~ Ibo umo e.m.f. in il5 annar ...... ~ ,,"'bel"" ""'DIna a-J I ~or '"' I rnotOI'". Only dilfcn;..,., i. lhallhi, ........ Ul'(: f.nI.f. i< knI ..", ~ 1arne th...,. ti .....IIn' tarq""-
T" -
N,,,,. .0.1>0.
0.I.19¢'7.A(PlA) .. 0 159" 25" 10"' ~ 800 x4.1 (412) _ 286.2 N-m t:. _ \' ,.II. _ 220_ 4.1xO,6 _193\1 1;-. .. 1N1 dot,.. i.r _ I ""'lap drop of2 V nuItts. nw rw/D ni. is JQ mWI>_ Cakll/tl" Ii, 1M spud and Iii , 1M ~J III _ ........ ' " (Electrinll..,h"""'w:1. r.;""""r l'nh-. 1"2)
Sohnioa. Annat= '''''I .... i. BJ,-rn by T. .. 9.sS ~ N-m E. .. V ~ I . fR. .. R,) .. 220 ~ 4() (0.2 .. 0.1) .. 2Oi! V
Now
T. " 9.55 X 208 X 4(V8OO .. ".J r< 45.9.000 W ; Cu lou . /. R•• 45' >< 0.8. 1.620 W
·.
4~8
TOIaJ inpu' • lmn + FnMlon Io«n~,
·.
"
-
m
..
>«1)
'·". '.."
Armllture input Armature Cu los! Po ...", < 1 .. 100 W 12,000 - 3.50. 11.(60 W; Oulput. I Ll 9 kW .. 11.190 W 11.(60 - I 1.1 90 .. .wiG \'t RowlONlllossc. TouJ IDOlOr input • VI x 240 > _ I.. lit""", ToO /,1 ..
•
T, - 40' andTI - 30 Pcrt~ n"g{4f)1t "'M" nwoin& atflJl-lood. 71'U,'O'MtrI of ;nulu",/,"" m/Qllnr ~.,~m i. 7.5 q.",', 1ft"" Slarl'''g CNrrrn' is 1.1 n"mu foll-1otJd raJcu/ot~
eostalS .,.. other .peed-con1rolUnl dev;"",. ",. speed "'gulalion i. dofiDCd as 'he ch""~ ill oputI .." •• Ih IHd /HI 1Ir~ _ _ U· ffd..< 100
29. 11. TOI'que and Speed of a D.C . Motor 11 will be J1I'O'"ed lhaI tbough
""'I"" of I
=1. Jtl il u; illMptUnl III.pm.
rnoIOr
i. odmllledly I funclion of Ilu~ and
lllttISllItt
In fu il U l/lI: spm:l which dqlcnds DO lorque and not 1';'-'"
"""" , JIIw betn pm",t\ earLet lhaI
,.. An.27.9 AIs.
T. . . 11>1. . .•An. 27.7 11 is secn from .",,-e Ibll incouse ill IlWl would de~ _ I A E", • V -I.. R• • 250 - (7 X 0.2) .. 24-8.6 V; E._ V -I. R. _ 250 - (49 X 0_2) _140.2 V
.. 1120. 130 - 0.51.,. a JJA • ~ E.. . 1200 !lS.75· 1. ,
•
I., + I", . JJ + (2WI15). J5 A • 230)( 35 .. 8.1I~ \\
1.,... cU'"'"t d"'''l1 by tooIor Pov.'C """,JoaduofA III 250 V Cak-wlau-JpN2JO· V. d.~.•hum moItJr III/II+'. C"I~wl"" '. ' 1MItmJIU' dn,,'oprd fbI W 4/krtlOrJ f~j 'M JPUd '" ,hi. IO<Mt 1M panicw"'rs of'M mol", a,.. a. fell",.,. . No>-Ioad eM'...,.' '" 5 A; Nf>.1oad 1/J.(hp.1fL A_ ,..IUla...... .. 0.5 fl.' 1/wIt'~kI ,..JOJ-" .. lio n l ilt«. T.........., ; s-booy l Di"U*Y 1_ 1 SoI..1ioL N.,.1oad Input .. 220)(' .. U OO W; t.. .. 2201'110 _ lA, I .. • 5 -2_)A No-load anrwu,", Do Iosl .. )1" 0.5 '" 4.5 W • COII'WIt Iosoe.s .. 1.100 - 4.5 .. U195.5 W Wb.... Inl,ul 10 II kW. Inpul curronl .. I UXJUI220 '" SOA. Atmiot urc current .. SO - 2 .. 411 \ Ann. Do loq "" 4S1 )(O.s .. l.ISl w : Total loq .. Ann. Cu loq .. ComtaDI "'--_ 1152 + 109S-S _ 224S W o..tp. .. 1l.000 - 2.248 .. 8,752 W F.iflciency _ 8.752 X 1001'11.000 _ 79.6 "Back un.f.aI_bod .. 220-()xO.5J . 1IS-SV Backe.nI.r. .l!~.-enload .. 220 -( .uxO.~1 I96V
"
"*'" .
'"'"
E
Speed N '" 1.150)( 1961218.5 .. I ,OJI r.p. m.
D.C. Molor
,.,
'..
1013
_ &'7 . 1 " ·m
Eumplt 19.29. 1M Qfm(JI~rr e,,,,.." ""i./lm= of a /8.65 J:W 25(). V "ri~.",Ol(}' is 0./ n 1M bnah ''ilflg~dmp is lie and IN unesfi~/d ".i"Qn~ isO.05. W"'~ 1M """or laMs 801\. spud IS 600 'p."'- Ca/c,.]tJ/~ 1M spe,d "'ne~ Ihe eu,,..nt i, 100 A
(F..kct. MIKilines. A~'LU'_ Sec. B. I99JI SoIUlimI..
60>P«d 'II'Iln> 1UfUllIIjIa., • . . 120 kW from _~,
ond_D,
u..
_Of .""",,n,.
... cloIe. d,c, ....... """'" lib. flu. pp«< """"'ne i, _ i n l from • 250-V ouppty ond talU", • ~ of 60 It. I,n •.p ..... l L A 3< "",otun: """''' ,,0.8 (1, A .... m< lh< fIw. rer pol< II 2JO V Lo hove d= ,'2.1 ....
400 V
_F {."',
1~.
=i".,.,.,
__ 1
I II, ....._ MO..,h,,,. COOIIIOCIed '0 ZlO-A !!Wn, tw on "",,'un: ","0.11 (1 and r .. k! ""i>l>il« of 100 n F..-.llilc ... 'o .... liIc 'PO>taDa: II 0 1 Il, vola&< drnfl rer brwIt b I vol! and .... r.. !d ~ .. ~ n
• UIIIpk It.Jl'l. A 220-.'DI, d.c-. un,s _'" is n,,,,,,,,, at a spud of IJOO tlIId d,.., ..'S 100 A. CakUWlt at ,,'I w spud 'N "'ill "'" ..,IIt~ tl.<w/opi~, halftilt '''''lW. TOIal,..si........,.. of tM """"'''''' tlIId /idd u 0./ ohm An _ lha, 'M mag ....'id 'akinr ]5 A "I 450 V. '/'llt """"'''" Is 1np ...CIUld ..-i,1o 500 c(HU/,."ro'.l and jlJIX ~, pol, I. t. ..
4>1. and .• T. " I: At hght loads. I. and 4> is small. But as I. tnrreasc •. T. increase> as the square of lhc current. Henre. T/I. curve i, a parabola •••hown in Fig. 29.14 . Afler ",tucat;"". 4> is ~Imo" independent of I. hence T... I, only. So !be characteristIC b al", inCt. ,pud vorie. invelKly as """,lUre lanl (Fill' 29 18).
~
/
! 0
"
Current
'"
•
,1
1.0 _
I
0
FIg. ZU7
FIg.
3 ."
-
o
BUI ""cIly .peat;n~. both E. ""d decrease ",i1b incre..ing load. H"",'"er. E. decrease! ,lightly more Ih.n • 50 ,halon ' k ",hok, Ih.,", i •• ome d'''rttit: in speed. The drol' ,·ane. from ~ 10 lj% of full·load ,peed. being depend.nl on saoural;"". armaou", ruclion and bru,h posilion Ite""e. th. aclual speed curve i, Ih,htly dn)Opinl .. by the: dotled line in Fig. 29,18 BUI. fDr all prac".al purposes. shunl mota.- is tat.. n .. a c"".tant-opeed molDr Becau", Ihere i. no appreciable cbange in Ihe .peed of. ,hunl moIor from n-load 10 full· load. i1 may be connected 10 load, which are lotally and suddenly Ihrown off ",ilhoul any fear of nee"i"" 'peed re.uhing, Due 10 the: corula""y of the:ir ,peed. ,hunl moIon are lunable for d';'inl ,ba[ling. macb".. lools. l.thc:.s. wood-working machi .... and for all OIh.r where on approximalely coo".ol .peed i. required .1. M. t:llancler;,,1 ie can be ded""cd from I II and (21 .b field oPJKI5CS 1M ihnn. field, Ihcn lb. mOIl>< is said 10 be d.tf..~nlia!ly compounded. The: characleristics of .""b motors he In between !bose of shunl and ",nc. moIors ••• bo"'n In RI, 29.21 , .. I (; unlDl. the-c"m puu nd Mot ....
_8M.
--
D.C. MOlor
1017
the load is li~ely 10 be removed totally ~ ,ueh a, in ,orne Iype' of coal CUlling Held moehine, or for driving he.vy machine 1001, ,,·hieh ha,. 10 lake sudden cUls Shu",--F.. ld ":. quile "flen. Due 10 .hunt winding., speed "'ill 001 beco"", . , ce"iwly high bUI due 10 ",n", "indms,. "will be able to lob bd~ncy loward, .peed in".bilily and motor running ..... y unless designed properly
=
,
Doff. Comp, Cum, C""",,,
..
~'--
,.,
• "",. D .Z1
'"
rump" 29JZ. The [oll,,~'ing 'l!S~I!. M',re ob/"int'd[rom a .Ial,e "'rquueJ1 011 a .~rin molO, :
20 30 4U 50 TarqlU(N . mJ 12S.S 230.5 349.8 46.2 OtdI;0"" MotOr input _ 460 x 20 _ 9.200 W
J --.,
Field and IUTTIIlun: eu loss
_ WxO.!i _ 200W Ignonng iron and friction l",~. OOtput _ 9.200 - 200 _ 9.000 W
!'peed f""" _ 10 full·lood" ,mall bencc: thIS moIor" ""ually n'femdlO'" ",,_.,.,N _ 1beopc. chill • cenain .-.1.... of cum:1l1 is n'quorw uu "i> ",ooJd bold ilpeed being kepi cooSiaN fiJr. n:1 ..;vcJy IonS period j.t. for indi, ,dtl:l! driv;nll of!IUCk In""h,ne. as llilles. The oI1"nl ,""ulatO< en.blr.$ the "",uim! spooJ cootrol t(> be obIainttl cas;l}' and oconomically.
Stomnlal')" of A pplkaliono T>fW
t>,..-"or
Shunl
('/lDnJl:un.&1
IpplU:fJIJo~s
Approxltnalcly connan, For drivin& cortSIanl opocd line >hafltng Lallie. speed Adjustable speed MedJurn staruJlg torqu< (Up Centrifugal purnp" Mochloe toolJ to 1.5 F.L '''''1'''') BIo"'Er$ and ite Sol"""".
When nmnina It",!. ",""hine ,npt." ,. used 10 mee! the following Ioues (il aIma!U", Cu k>S$ liil ~unt CII Imo lriil irun~. and I,., m«:ha/lical ktMes i.r. flieti.,.,.nd windage Ihan torq..c. we ""II tiod the: moo(>l' output" I>cll "dra",·,. current f 52 A .... ",II u~ the oo-Ioad data for tilldtn, lhe: """,tanl I~ of the mooor. N., load n>OIO< 'nput • 220 K J . 1100 W; Ann. Cu 10M _ 31 KO.! ~ 2 W :, ConIWlt or OIaAding " - oJ!hc: onotor .. 1100 -2 _ 1m Witt. ~ wm. Cu kIu _ sol I( 0.2 _ :500 W
Fi~'
Ilence.tOOllIllOlor"- • Im~.soo.lmW M.,.".- input on load _ 220" 52 .. 11.--140 W: ootpul .. 11..wo Im ~ 118-12 W T.. .. \1.55 lC ooll"'tlN .. 9 ..H lC 984211436 _ M , ~ I'o-m
£.on,,,,,, l1I.J<J. A d.l".•h"III """,hiM " 'h,/< running a!1 ~~MrtJf(}f thw/op< a .-alIa[;' of 2SO V at I(}()() ~p.,". OIl ,....100II. II "m nsiSfuna of 0.5 n and fI,ld r..i""",,~ of 250 U WMII fh~ mochiM "' ... "" -'0< 'IIP.Il It> is at ,."../ooJ i • ., A o. 250 V. Col€"IQ/~ Ih(" spud mill rf!il",r"'! of/hl" mochlll~ ,,·1Im /1 nuu ......,u"'.
N, ..
E., ..
E., ..
3')'"
""'m:tl,
D.C. MoIC . '_ _'C02 _ ' __
Ir"", _
"'" ...
EDmplt}'tAO. 1M anna'"", ~'".J,,,, poI" ZJI) V d.c•• i.1op crHlMClrti. 1M,.. aI', J2Q ,Iou, ~Ir .1", mn.U."'1ns 8 rond"",,,~. 1M flo.u. pu pok ;, 20 ",Wb and OOn-m1 UJoI .... b:!- 1M mol", IS II JI no,. ,uiJ"'nu of "mvu" ... <JNJ ji,/J "ur"';l ,,~ 0.1 and 125 a f'UIJ«'I;,-dy- /f'M """'i"",,llosHI )< 6:X lISO (t). oS> _
'",\\b
T. " 9.55x21564x1L8/IISO _ IlIIJll\.m
EJ. "
21 ~ .64 " 71.8 "' 15,483 W W; R"""k>nalloose. _ 15.483 - 14.920 .. S6J \\ ItH Malo< ,nl"'t .. VI .. 230 " 74. 8 .. 17.204 W; Toea! loss. 17.204 - 14.920. 2.284 W .......... ~.~ a. of po ..·c, inpul " !21W17.2Q4 - 0.131.,.- \J.J~
"iii Driving """'..... ,n arnoaturc..
0...'1""
-
1 ~ .920
""="'11"
I'.uomplt 29.41. A 7.46 HV, 151i-V ~"'" mOIar..,u, a lin< ell,"", af 5 A ~'h..., nutIt'''I IIIIu. CalclllDIr 1M rlflL:imcy us (J mol(" ..-h< 2 or ~ .. ! 2
Eumple 29.44. A 6-""'~. 5())..V ..·m~-e 'M .".,N and IOrq~ M'~/optd ", ,lot _ "·N~ ;. d"",·s 20 A from IN uq>pIy ....iIts! N~,I~ct a"""'...... """Ii"". 1/ ma,,,,,'i~ and m and frictoon lou .. 900 W ; Iou _ 162 • 1000.900 _ 1.062 W MOIOf inpul .. SOO x 20 .. 10.000 W
Ii) T.. _ (iii
9.5~X~
E ISUN - m
Oulpul .. 10.000 - 2062 .. 7.9311 k\\
~ 11" ~ x 100 .. 1.938 x 100 .. 0 .79-1 InPUI
10.000
. n .......
IOU."
t.::."",~ 29... 5. "jO.li.p. (J7.J k W~ 46f).V d.c. Jhwu moM, """,u., Uglu COl,""' of 4" and nuu oJ lupud of661hp_m. ~ "sisltll1C~ ofW armol",.. dtruil (u.e/lUlin g bnJS~J) uO.J 0 and lhill oflM .hwu fitld d",,,i/ 270 O. ikl,,,,,i_ M'~n 1M molo, is ntnning alfoll Wad
(i ) lhe Cw'"N u.p..1 (ii) 1M 'fH'ed. Dtl,,,,,illt: W < 1.1 .. 1113 W \\ hon running lipi I. _ " - 1.7 .. 2.3 A; AmIaIu", Cu Io«s .. 2.l' x 0.3 .. 1.5 W (negligible) No-load """"tim: inpul _ 460" 2.3. 1.0511 W As """"lure Cu "'"" i$ negligible. hence 1.000S W iron. fri.c,ion and windage los>cs SoI DI ......
"'I"=""
""bicb "'ill be ISStlmed 00 be oonsWU.
LeI full·1oad annal"",- inpul cu~1 be I•. "Then t\mWure inpul • 460 I. W; AnnanueCu loss .. Ou!put _ 31.3kW _ 37.300 W
J.' >< < onnomn: 0.1 U Dclcnninc!he: ""'I"" and .meoeD< """". < drop .. bei., «1""0 1.5 V pu bru ,,·,tIl the 1> "" indicOlion of
ThyrlslOf tnvarlars Thyristor Speed Control of $eparolely-excitoo D,C . Motor Thyristor Speed Control of D.C. Sen9s Motor
> Full-wove Speed Control of a Shoot Motor > Ttwnslor Control 01 a Shunl Motor ThyrisTor Speed Control of a Ser\e$ DC. Motor > NecessJty 01 a Starter > Shu1t !VIator Starter > 1lY~1 Sforter > Four-poinl Starter > Stort'ng and Speed Coone>! of SerIas Motors
speed of any common de motor rnt gc ego· troll. T1Iese method. as applied 10 .hunt, ""'",pound and sma mo«Jn ",ill \)., dil Ag.3O.1
"uia Df ltlUimum 10 minimum spt«l of 6: I '" f';,ly common. t u.~ _'0.1. A saJ V sluml "",ro, 'lUU : .. 0.8 4>,;N,_250rpm;N:_?
2(0)(
.!t. l!.t. _ 4&8 )( ....!L
N ~ )( or :.:1 ~ f.' 4> 250 H, .. 1
476
084>' N~ .. 310 r.p.m. . ,
Eu,npic .100.2. .4 2j() mit d.c. sh"", moIa, hll. dl"mtJIIII"t! I"t!si.w"" of0,25 "",,", "" 1001111 'atts II"""'.', ,,/tr"'nl uf 50.4 mlll rum til 75(J r.p.m. If ,h, flu., of mO/or is rNllt:~, 4»
.::u)(--I.
E..
fl.""" T., .. ¢I, I.. and T.," , I.,.
T., _To1
..
,1. ,-,101 , _ 0.9 ¢I, ., :5(1 ¢I , _ 0.9 . /. 1 - 55.6 A f.'. , .. 2:5(1-(:5(I)(O.2j) .. 237.~V; E:.,.2:5(1-(5S.6)liN 10 rotH ,Iv "'""'''''''' 6tJ() to 800 r.p...... """,,, ,tOO.Jd M _roN III ,,,, Uumt firld r,,.,,"" ! Au_ '''''''M IfWJgIITlir c1""'" is lUU ..
11±;I2I-60
•
coo.,am.
1", _ I."..::..l _ 40xw~x _ ~
..
220-{40 xO.5) .. 200 V;
, •
.oc
Since lorq"" ",mains
,
•
,
E., .. '220- (4Os)(0..5) _ (220 - 20- or
.unE, Ii« ii,
1991)
4>,I, -I.,",., _4011,.,
• UO-40xO..'i _ 200V; 1:.,_ 220_0.5 1..,
Now,
N,4>, '" 220- 0.5 Iol . I..'i N'x 40 N,4>, 200 N, I., 1.,- 401,.,+24.000 _ 0 or 1,., _ 63.8" E
.'!'.I. _ 4>,
-
40 63.S .. 0_627
_(]I" "'*'. ""
or 4>, - 0.627 4>,
K
1il..7'A. "'''',
crorrr,,'
Eumplll' 3O. I\l. 0'\ lie. JhwIt """"Iurr of 20 0'\ i- a 110 V "'I'f'Iy. o'\nnarurr rlrntil ""I.ume. i. 05 ohm. For "diKing 1M I/H~ t.y 50%. t:.. /cu/a .. 'M ",sis""",. ",quit>< 1000 • O.24g6
mv
,-,-
. ...
D.C. Supply I,
t
1 amp
~,
• M
".
Speed Control of D.C. Motors
1037
I. _ 49.mp E .. ..
N,
E
2~-49)(0,2
2402 0.2486
.. 24O.2
nU2 E
""".
r.p.rn.
Nola : II) 1'11< '''''"'poion of «>nSI>nt nUll h...implifO '"F..,
rii:i;
From la' .00 Ib I, 1;;1
,'. _.00 E"
M
..·1. ) ..·1&1
x23O _ 1!t4
•
184. H. 1.1Sohm 240 - 2(J (1.40)" 212 • N 212 x 230. 212. NJ .. 230 ~ IOOO ~ 922 r.p~n. •
Enmllfe 30.13. A 7.48 U~ 220 V. 990 rp."', .huIII me/or Iul$ a ful/load .!firit"", vf 88%. Ih. "'m",,,,,, ,,,,is/aIIN' is (J,0l! ohm "ltd shunl fidd cU'n'n1 is Z A. If ,h. 'p<ed ollhis molo, i. n!.laced '0 -150 'P.rn. by ilUating a "'JOIa"U in Ihe a"""lurr drewII. futd Iht molar aUlpus. Ih. """"I"n' CU,,,,"'. Ulu"al rt:.iJttJn< 5(XW(X) .. 127.11 voll ce 10 be oddcd ." .... 2m'Ial ..... cifled by Tto k, &lid t, in the equa!i""" below "'rnSl!ot machi"" constaol.'; appearing In the usual emf.eqttation and lOI'tj .... -equ.tion for the d.c. sitU"! hlOlor. 211.2 z *1 x i" X N, .. kl X 1.10 x 60CI or 211.1I61iO _0.32 T.. _ t, x i" ~ 1., x 1.1Ox n
1£., _
*, .
_t,
Sinrque. "'iII remain "onMan l 01 'XIO r.p.m. also. lbe eoou Id be appro~una"'ly K"cn by
i"
a 1"x(600r'900).0.7 llamp
G...... for I ,,: For .ppru~ima'" ron FL ArmalUre Current 117.65 - 2 _ 115.65 amp I.SOx 11~_6S .. l?3.5 .mp L,m" of ,toni1\3 JIC with the r.. 1eI "" ,Iia! the motor . \O ~ run al9:1O f.p.'1\- wllkin.OIl """".,. CWThunl·wouM motor Iwi • fiOm< onnatun: cum., and (/I) !lie spe¢d wi'" the rijI'oW r",1d pc, .. ¢I, 600
..
1000
.. (200- 1 7.~R,I. R _ 4.&0
193'
,
n.
.. Additional ,...i"anl(H" ha4 """aI~'" oNi fi~1J ""/JitInCt, of 1.2 0 onJ 5(lO n n'lp«Ii.",Iy. Wllt-n """,in, Oft no·I""'. lilt! CI"n'II' I~" i. 4 " oNilhe 'p',J is WOO ence.R .. 6.5 _ 0.5 E 6ll Since !he load i.< IW~. annature currenl i. 01"" hoJved because nux renlain. conslaJU. Hence. lOA . .!!.L 250-IOx6.5 ,'. HXXl .. 240 or NJ _ 771 ••p.m.
I" .
Example .10.21 . A ]50- V .hut" m%r with Orllla(U"" "",istance 0/0.5 ahm nm. ar 6IXl 'p.m. Oft foll ·1oad and I~S IU1 Omt(lW"" ~ur"'n1 0/20 A. If ""siJlanr:e of 1.0 ailm i. placrd i~ 1M arnttltu", drr:uil. find rM spud a/ (< 1.5 .2l5 V ,
. 1.
'.,
235. N .600x 2JS .. 587.sr,~
240"
NO
",
r..umplr JO.ll • ..t lW V .h~nl ,"",or Ml,1r a~ a"""'~,,, "".i,ranu 0/0.5 Irnr is ~U'jINlIO gi,'~ """"'anI main fi~ld. A. full load Jh~ mOl", ".,..- of 500 "", prr ",in~" and on flrmalu", CWT"'''' of JOA. 1/" ""jOlon("#! 0/ 1,0 ohm i, ploud ill 1M omlll'U" circuir. flM 1M 01 1.1 foll.load lo"l"< (6') doubU foll.load lorqu~. (EMI. MachI_I, NRGPur l in;" , 199JI
,aU,
'WIulion. SinWll. Ib< "fI I•. T .. I.
It is given Ih.1
'.
"-' N,
'" ,.<m.nee
"'"
A
s\""" nux "'main' ~on.t.,.,t. T. ," I. , and T., ~ loJ. or
• t.'., • ToO
38.~
T., : hence I" ~ I., J6.5 A 220 - (36.5 ,,0.(8) .. 217. 1 n • 220 - 36 .5 R, ; N , _ 900 '.p.m.: N, • 450 r.p. on, E
.. ~ • ~)(~ t.... in lhe second c"'!". 1993)
N, .. 8OOr,p.m .. E.. ~240 - I~"0,6 s 231 V Flux ,.",-"mini c~t.,., t , T .. I, . S"",,, lorqllC i.< the ..... ,.. in both c."". I., " ' " _ 1~ A. LeI R be the odJitinal ,."i.lance i"",,,«1 in series with tho annature, ~.. ,,, 240 - 1~ (R • 0.6): Nl Solution. He,.,.
.. 400 r.p.m.
. 00 .00 •
1046
Eleclrlcal Technology
11'' '.... AAaJ 1 ",u. M'il~ 1M """"fUr.. in 1M 1fltIi:hi~ ,1/ (a) if 1M juJl-
(6 ) Wilar rrJiJUJni mllJI M p/«,d in load .pud iJ I<J t... mlllUd /Jy 50 {NT Un' ",'ill!
,Ir, gro.. rorqlU' """"ini.., C"OOlI,,,,,/? As_ "" (DetlriU1 I",,, I .. IM.8 A ; PernHssibl1"""",..... Uoin.
"', ..
E., ..
!!.;..~
E.. 170 x (63&595) .. ISO V LeI It, be !be new value of armOlure dn:u1t resIStance f()l" ""§tng !he speed from S9S •. p.m. 10 630
we get
N,
E.,..
•. p.m. ISO .. 2OO-SOR, .. R . O.40 lie....,. Bmu.Hue .,noml resi' in the same direction. Despite the fOCI Ih .. C;lj>i131 oollay invol\'ell1 '" 309.3(11 - 5.040 .. ~.260 w Armatun: cUln'nl .. 5O.f,26Or.l.'iO .. 917 A Bock c.m.f.
E., "' 300 •.p.m . .. 550 - (917 " 0.0]) .. 540.83 V
Bock •. m.f. ! '., III 180 •. p.m. .. 540.83" 18W300 .. 324 .5 V
""'I""
5i""" i. the oame. lIIe annan".., currenl of the main moIOr is .Iso ,he same j~. 917 A because lIS excilaOOn .. independent of its speed. V ,", J24S + (91? xQ.Q I) _ 3)3.67 V v.:Der.1l< flux can be ckcrca""d a nd ~""ndy. the "Pffil of lhc TIIOIor incr.,.~ .
. -
FIg.30.1D
,.\ " ..... IU ... 1)I"~Mor
A di,-et\or ocross the- Innatun: can be oucd for g,v,ng sp<Ws I""u than the normal 5pced (Fig. N>1U",,,11iHId Wf'qur . if I, is t<dooal dlll: ." 3JmlIlurtO dI,-.:no.-. Ito: 4> mulIag< "PI'lied """". the ormal= lt1"minals can be Urote " 0.0312 _ 0.GI5 0 " BS-141.4(0.00I.0.0IS) .. n21V
'.
!'...
'"
77.22 100 .. '"1j" 141.4 /2
(.;
" , " 707 "'"1j 77.22" 141.4" 200 102'1 r.p.m.
,.) Let ,"" IOU) ... ,
5t..!u
H, /:'., • 240 - 40 x 0.3.228 V ; N, • lSOO "p.m. /:'.) " 240 - 40 (Ir + 0.3) V ; H) .. 1000 "p,m,
H,
N.....
Speed Control of D.C. Molor.
1053
228 .. 240_40(R+O')) ; R. I.9Q ISOO 1000 ~ :le..14. JI 4-pok urU!:~·_ftm moto, ......... """""II} Ql6(X) "p ..... """ 250 V d.r. • ~ppI)' UJJ:j"I W A. Tho/Wd coils arr N>/111",r~d or in HriU. Esrimau ,'''' 'P"rd WId c~rTrnl wb:n try 'he mol.". emu "" ~cOtlJt«ud in ""0 parol/ Mi"""
i,,,,,"
Sol ution. WMn coil. arc' connecled in 1'0'0 parallel groops. I
Hence.
Now
_ N"
••
,
I., _ Nt'
,I., _ N,'
and
(!!J. Y.. N,)
•.
: I., ,
I.,
... til
Sill ;V _ ~ J 3 .7 V
.:Kamplo 3CI.J6. A d.c. uri~s moIor ".,u at 1000 r.p.m. "'M~ tatin! 20 it at 200 V Jlrmtllu .... I.r O.S n. Mrinfidd ,..sWanct i$ 0.2 n. Find lhe '{H'rdfor '" rOl",1 n"~nt 0/20 it "'hen a di>~""'ofQ.2 n ,..siJIan« i. used Qaoss 1M urU!:sfi~/d. Filu/or" field nIT.,.,'" of 10 A is 70 ~r Cl'n1 of fo' lO JI. "'riJl"'M~
t"",
1054
Electric.) Technology
SoluCion. F... _ 200 -
(O.~.
0.2)( W .. 186 v; N, " IIXXI ' .p_m.
5,....., div~rllI< I'OsislanCe' equals ~ r...1d miWUl<e. ,1\0 nIOtO< """"nl of 20 A i. d"oded equally belWttn the two. H....,., • • """"nJ of 10 A now. lhrough oerie. f .. ld and produces flux which i. 70% of thal corns.ponoii"" to 20 A. In !her W1lI'ds. "', .. 0.7 01" ¢I,I¢I:, .. 111).7
30-". A 200 V. d.r. yriu mol", raur 40), "'~n ",,,,,j~, at 700 '-p,"'- Calc~lalol\, .pull 01 >4'hich I~ will nM ~nd 1M c,,,,..m rakft from ,"" Sl, .. I. p. Si""" 1rq"" remains the~.
Combi""d res;""""e of the lwo parallel pa'hl _ omn 0.025 0 Total ann. circuil ~ 0.1 ~ 0.02S .. 0.12S 0 _ 250-28.28xO.I2S _ Z46.SV K
,...i.,..""..
20 N, - "" •.p.m. .. 246 2465 X 28.2812' Eurnple JO.J9. A 4.pol~. 230 V "'iu moIr """ at I()()() ~p.", ....'~n the looJ cur,,"IIl is 12 .... The "riu Ji~/d ,,"siS/ana is O.S 0 and I~ '",,,alu"" ,~,i""""" 1.0 0. The" .~n·~" fi~/d cmls ,,'" /lOW ""S""'I"'d from all in ~rriu 10 two In urir. wilh two pa"'II~1 path. , '., .. ,
~ '"' .!.?1 • ..lL
~
!!.J...~. !J.. N,
E..
"
(.:
.·n
--
N, .. .'14 r.p.rn. 180 35.6 Eun'pl. JO.41. II uri,. mol", U "mning QIt ~ 44() V ci",~i' K'ith Q ~gula'I~J ~.j"~n~" ofR Ufor spud odju"m~n'. Th~ """",.'" andfidd roil. hn,'~" ,,*,I u, ...... g.,IN,.I • ....,X 434 08 • •.lSO •. p.IIl .
T .. 1. andp<Jw.rP .. TxN
P," 4>,xl200xW and
0 , .. 0.84>,>< 1350x15
!i...
l200xW4>1 . 1.48 l)50xI5xO.84>, lI.nee. powe, in tho frrsl C~ i, 1.48 Ii""" tho power in tho..-oond c.....
P,
Eumple 30.42. >I d.c. seri". "'irk an UJU(II~T(lIed/it1d OM ~.xlixible ,"",islanee. ...Mn running al u ctnuin '""cd on a Xi""" load .aUs 50 >I QI 46lJ V. If 1M 1,,{Jd.'o,q~ ...... riu as 1M elllw of!/",
."".d. colculate Iht ",.IJlan"" rrquind 10 nduu
1M ."".d by
(Nal',llur,
15%.
UIll~. l';u.·",,,botr
1m. '~h.d .... Unl.,. 19871
Solullon. let the ,peed bot (J) radian. wi'
From ele.:tro-mech side.
T .. /'
i' ..
(0.75 (0)'
,
, _ 0.75'
Coolrarinll SImilar relatioo.hip In pre,ioo, c.....
.
J, _ (0.75,W)
'" i' .. 50' ,•
x 0.422 .. 1055
,• ,,,"'"
32,48.mp
• • I X 0.75
'".""
• •
/Iich voTks as 1M "IWl1~ of spud. 1M molor rau. " Cit,,,,,,, of 15 11 M'MIf 1M >(N~d U 6lJIJ r.p.m. CakwlQI~ 1M 'p"~d and Cit",,'" wlltn 1M mofOr1i~IJ'''';Mjlfg i, ,hunr.d 11y" di'V!.ing through them. although the volt",e aeros> each mQlor i. ;.~., half the ,upply .oltagt. Wlltn joined in para1~!. "olrage ...".".. eado machi .... is V. !bough cU'""'t drawn by each
vn
""""'" is
In.
Who,. In
""noll~
Now .peed K t.', I ., _ E, I current (beinll"'ries motors) At.3U.lljol
,
1060
Electrical Technology
..... -- -V
2V
112
torq... .. Q) I ..
... 1.10.
T .. WMn In
I
i'
(1m) ..
(.o'
4> .. 1)
r'i-t
'. 'iil
Stne.
I:. v/2 v .peed .. .::!. .. - - - 4> I 21 T1tu .,wH iJ __J..tdI !if W ~ 1'/ Ilk _ _ ..II~~ in fHII'OJl~/. SlIfIIlwly T .. 4>, .. i'
~ (ii'l
I le~
nor
'0'....
j~
'0••
- . IINM ",NWH •.'
..... ~ ,.,..,..u..L
_
"-
Th. 1"'0 moton arc ~"Pjn~,...
'th...,.
M' JNNI- T.:'" 0
m
~'" ~
111" .yOle", of spud conlrlll II ..,wly combined with rbe ~.n.ble "" iSWlCe n",tbod of coowl doooibed in All. 30.3 (1).
V
AfoNVNffl.MN' L -rr;
~~
0
m--..r)--
n. V~::
L 'WoI.WW.VWMTff'
Now.
*
N.
( ... gleelmg I. R. drop) CI> .. I .. E• .. 1'1 or E... JdoJl . . . · 0.25
'lj() .. x 0000.pttd oI .... iI/WL SpMlofthclin.lmolWl' N, • 5N,.; SpccdoftheKOOlldmolOrN, . 4N.. let Ibt \be ....... Clll'l'tnidrawn by the ~~. thrn f:., _ U x ~ U x H,.U x:5 H.. .. U x I H.. Eo' •
m.
£., ..
1', ,,
9xUH",
.. II)
0.159 £.1 .. 0 IS9X U N",'tI.1 .0 lS9tr N N. SIWI ......... d ... IO&Cm of 1St _ .. S xO. l j9 V Shafl ""'I'" due 10 F .... of 2ftd moIor • A md II< lord rnay"" brooghI '" IO:SI qwckI)r by ...,n,ei!ha Ii) t'oicIoon Braking,. 1"1 I!Jcaric 8.v.ina The c:ommonly •....,d ma:lwucal brake h.u 0111" lInowbak =istaJ>Ce II as s/l(>v,'n in Fig. 30.21 (h). Thoe f",1d wincHn, i., how",....", ""'I'" .'MII 1M _ i~ ju11peed COIItrol Cirell''''.
"""""'ie
lui,.
vuI.
30. 10. Uncontrolled lI.ctlllers
l.I"""""n.
A. """'" c.-1 ..... mrurlCfJ are ,,!oed for I.., 10 d.c. con\"CQion I..... ,,"fIe-n "'" Mlpply is bu. Ihc """'" 10 be contmIled il I d.e, ",.ct"ne FII. 30.26 (/II ..now. • ""If-....e uncontrolled l>:IoIh r«tif> ond in""""
(10""'wcr g~'" (>Il1",- ()r.c., triuered (or fired) into conduc';"". the thyri.tor remain. in the rondoctin~ ,tate for the re" of til< h.oJf-cyck ; ,~" UplO 180". The firing angle a can be adjuMe< peak value of ' .c. in .... ! vollall". Ob'iOttSly. V. is "",UI voltage I'L or V• .. I've" by V~ .. 2 " half·.....'" _urIC!" ou'pIIl V V :!V '(I ••
V• ..
2"-tx{I+oo<W--:CI"COf(lt·.
~cos-2
(/» .o ..'n In !he r,gUrt dunn, Ih"
bOn
ON pmod. fOr ,w'tch in, T, OFF. _ond tlty .... lnt" T1 " trio"raJ into condUCt"'" _lIo ..·,ng C IIlICt- the med"",;'al ,,.'11 C."""
mown
30.14. Thyristor Speed Control of Separately-excited D.C . Motor In Fig, .lO,]2. ,he bndge """ir..". convon. a "ohage in,o d.c. voltqc I\'bich ;. then applied 10 the arma,"", of ,he scp'>r~lel~-e.cjled d.c. motor M, A, we bJuw. >pcc:d of a moIori, givt'n by
N _ V-~.R. ( ; )
oonsI"",
If ~ " kcp< and al>o if I. R. i. ncglecttd. ""'n. N_ V _ aac acl'l'" the annature. The ,'oJ..., or thIS vol,. rumisbed by the rect'· f"" oan t.. clwl~od by wryIng the fi,· "'I angle Iloftbe lhyrislOr T ... ,th !be help of it' contol drcuiL AI a i. in.;n-aSi.'d j.~.lhyri>tor fi,;ng iJ del.yed
""I,·
~
ro
~
, ,
M
Speed Control of D.C. Molor.
1071
more. ,IS conductioo pmod i. rWuced and. hence. annat""" voltage i. dom:asod whieh. in tum. d«:ruseJ the motor Sf'ttd. When a is ~ I.~ .. tIIynSlor i, rom! earlier. con.doaction period ,. ",crease M'
-
L.
"'""'"
'"""
L
1
-'
tI
rkl-{ I
tDB·
30.16. Full - wav. Sp•• d Control of a Shunt Motor Fig. 3034 _ . c; ..,ui. whiob ptO'Iides a wide of speed con· A.C trol for I fracciooal kW ,""unt dc. Supply motor. The ejmlil ~ I bridge cir· euit ror full·wave =tifocalion of the I.e .• upply. The . hunt f .. ld winding ;$ pmnanently coo_led acros. the d.c output of the bridgc circuit. The armature volta,ge "supplied tIItoogb lbyriSlOl'T. The magnitude of Ihi •
• ••
""'g'
•
,.•
,,.., " ""'=, , , •D, ~.
•
•
'0
,
...
\
~~
o;~
Trigger
" •T
Shunt Fiold
1072
Electrical Technology
vollJ.g¢ (and ho:nee. lhe II-.r o.peod) up VC 1IIIlR quicldy 1bereby decn:."IIR ... hkh lead •• 1> early .w,lChing ON 0( T in eac:h h.oJf-cycle, A. a ~ult. po ....er .upplied 10 tho annalUre ;. inr~ which increaors """"'" spud tbm:by C'OTIIpe"-'w.
30.17. ThVrlstor Speed Control of a Shunt Motor Tho .peed of. shun, d.c.rooIor (upl 5 kW) may be ",sul.1ed over • wide ""'ge "'ith \he hdp of the fuli·w."" "",Iif..,.. u.ing only ooe maiD thyri"or (or SCH) T .. shown ;11 ~'jS. 30.35, n.. r,rinj angl\ed by H, Ihefcl>jI controllins lhe mDlOI" ~ Tho Ihyri .. or and SUS ($II""", unilattn\ '''''ilCh) on: reset (i.e.. 5IOp conducuoo) "'hell ~"'h half·.....ve of V1IIi."8" drtJp\1O v;ro. Ikf"'" ,wiu:lunl OIl tbo "'pply. H, i. increased by luming il in tho coome.-dock"'i",, din:cti"". Ne~I. whe:n supply is .wild..d ON. C gtls charged "ia mDlor annature and diode D, (king forward ru~), It meall.> Ihal illllkes mIlCh [""ge, for Vr'o ~h tile breakdown ~ollage. of SUS - due 10 larSe limt cllllSllnl of H,- C "'twork. ()nrc: Vc ",,,,,he. thaI value. SUS rondllClil suddenly and IriU'''' T imo rondun;oa. Since thyri<mr .tanS rondllClinglale (i",,, 115 0: is loUiC). il furnishes k>w voltiiif (adl tuM cy ~ • larse d,Shllbuice in Ihe vottaae .. ,ulation oflhe .... pply Ii..... In Fie_ 30.37 !he nosi9l&llCe R u.sOO f.". Maninl' ,""un,1noIOr il.hown. II will be o.cen llui, ,he .larlInll ... ,i,tance R i. in sen.. with !he """""'N and II(~ wilh lhe a whol~. The licid ",indin, 01 eunneclod dirtttly ""'fOSS ,tie lines, he"" •• hu", field ",,,,,nl i. independent of 'he
_ "'Ii
1074
Elec:trleal Technology
resiO\:UlCe II. If ~nlJuduced in ~ """'" ci1'CUi~ .hen I .. will b¢ small .. \be OWl. he",,~ Marlin! ,.,.,..., 7 .. woold b..."",11 (... 7 , " mak .... i, unsui",bIe for w;c ,,;jlll v";ablc: ... pecd moIOrS. Thi. hal! ""ulled in "'idespn:;>d applica,joo of four·poin! .tarter discUS!lCd belo .....
FIg.30AI
30.22. FOUr-point Siorte,
0'
, ,
,
~,
•
,
, ,
"""
•
FIg. :10.42
r
,.,
'. 0.'
""
~$' --
,~
~-
"
•
Speed Control 01 D.C_ M= '= 'C ~' ,----, 1" O~ n ,-Such. mner wilh it< in!emlll wirinS is .oo..'n_ connected to. Ioo,-"'unl compotIIOi rrolUlf in 30.42. Wl>en compared to m. lII=-p,;nI SIan;'IlaI1ing arm through HOLD-ON cot! and finally to Al the end oftbe 0IatI:urn is ~t~ and
try lhr: HOLD-ON belw.,.n the 'lat!ing arm th ... forein, field cur~"al fII mil W paso through tho field meo.lal. 1l>c r",1d lev,", can be rno~ back W ineruoe the mol", spocd. II w,ll be leen thar POW tbe uppcn"'" of """~" i, ope""i..., beeau~ 'btl;n& lI'nI no longer I"""hc$ ~ btu< ..-c. W~n """'" is Slopped by ope""'& m. main swilch. the stanin& lI'nIlS released and Drl ,ts "'oy back II "rike< lhe field Ie,,,,. so th.t both lI'nI' on: "'tumed ,imultaneou,ly 10 O r F l""i6Drl.
30.24. Starting and Speed Control of s.r\es Motor For 0IatI'''3 and spocd ."",reI of ..,ne>. moIor .ither • race-plate Iypc or drum·t)"pe controller i. used "hich USU411y has the re,·.",ing karure also. A f"""-plate t)Pcept for. "'I'"r~te o'"rload C;"'''II, 00 inter-locking or ."'on,,,"c fe .. ure, callSIj :;rij21i!:
, . U' " !. ~ • :..
i
-
~
:r~ :!~,~
=-
~I:
ri'::
§.
•z
I!:I If:..!.. !!
• •
9
"
"
~
."~'a.
So,""""U"~"'''N-~_? _ It... 0-._ , :i •• • ~ I .' • i! ii .... ~....
~
if;j;P;:;:~-~
It;.. ,_
.
!..a;z-.,..,_-
I
.0 • !
,.=iiri~ ."
it
' • -,- --~~~u 'ii ' • .~N
11•
-9_:;;;.
~~ ~ Sif"B ~ if -g2"'C'iiI",,~
~!~i'
~~
i_
~!.-=,.,;!.
~~~
if
I'!!!-i"
;-~!I.
....
..
l [-- , -
:'!1i~":n [~ifl!f..o;l.1!
,ld If~ If~
s
:r~: 8"9:
;a
~~
I
~li~"'OIel;" f n s,~f!:" . . _, \' J; " .i . . i. i.
iii- ~ i. ,•, lu~ . ~ u"'r ' ' I-'''...I7L",,17~lu. -; i" u; ~~~~ u"'l-'" ..""l~ l:..-; ~l~ ~i ~iltl ~ .', i.~ ..:~"'r'" ~t">I~ ~1~·~~"')Z~u"'171. ~· !JC ~~ ~Ii!! ~I!. ~.~'~.,~ ~ 't" ~ i" i!"!! -t I '''''~''' · . -. --" , '.i -~l;li" Ii it mlnl. gi'en in (hJ. we ha .. c
"
,
.
K' .. 4(I(W7.9S xO.IU .. 32.68 K .. 32.6/1"' .. 1.645 "
.. muimum I"'rmi .. ibk annalu ... co""OI .. KI ). I,64~x97.94.16 1 A
J. A. rnotoo- ponionalCly incn:asrd bettd, the volLagc pm.ided by T(; b«uo'or:$ I»p: enough 10 bn:.tI«lo",-n Zener diode Z, aAd he""" triU"r T, ,nto condllClion. Con~ ... ndy. R, i •• honed OIIt and DOW I. flOWJ vi. motor T,• T,. R, and R, and back 10 the: nellli" •• """Iy leTlTlinal 5. N It, iocu' out. I, incn: ...... armaIlIIe torqut "..""'~. moror 'P""'I incn:ases which funbcr inc"'~ tho vllag" ""'1"" of the 'achogener.l'or. Al 5OITIO speed. Z, !nab down. 11>creby Inu"";n, T, int" CQrkluOtod thai ,he fUBClion of C i. 10 ...·;ICh T, • ON and OFF. Hence. it is
"""",un:.
r,. r,
usually
called ~_ ..
r.
IHl#UI. ~"P«;u".
n.. funclion of ,he diodes D, and 0, .. 10 allow \he decay ofinduc,ive ene'llY stored in tile motor arm.uun: and field w""n $ul'Ply i. dioconneclod. Supply failure will c ...... ,he thyric no ot,,"ing resistance a. all • •hereby making tile entire .ys.tenl quile errlCien, and optimiud" ",pro. Ilanin,h"",. 1l>«c an: blued on tile principle of 'voItage cboppi",' (An. 30.12). By varyillltlle chopping frequcnc). tile ratio of !he ti"", lIIe ~oIuge i. ON to lIIe time it i. OFF can be varied. By varying .hit r.uio. ,he. .V"~ vollas" "!'Plied to lIIe molorCIUI be changed. A low ave"'g. voltage is needed 10 hmilllle
h UI !.~ i '~i ~ " r d-IP, h,oAi ~~ ,?! o'lifb t !·o'~ ,!!: ii't 001 j.. " • i !fi> .~l-o ~ 'I'l!.~ ~ s[~_ l ! f~;;e: ~l ~[.3 ' ~ fa, ~~! 1 , > '! .... f '" 1 ~ i _ ~',o l'l ~ ll~ : ~h j.f .,' °il' ~ FI~!'
, . 'J' .. ~ ' I'; I!· '. ,H f "" - I· ." i! q .~oo~, ~ i p. ~~ , _~ ~ ~ll ~j !,I ~ ' f"Oh .Phi'Hi. : t , 6 !, 'j' H !- Jl, ~, q tJi: ~ h •• t .H ~ ih~~1
1 ,
EO
S2i1i,
8
[
:"I
!:l 15
, rt ...."= q • I J i i..i "' ·,, 0. · -c H . .. =c '. ~" i !!. ·,. . a!J•; I. .11: I! -1 eH " f " .t, ~~ IH ~ l' ~ ,! ~ I.§ C "'I"). :l"'· -
1I
'i
~
I f_
s"'~i,s.
iI
~. 1l: i~[ -i l!.Q,~ -U·",
;;-'i B
'Ii ,!",;': !..
SIS IE -l:t.i ~_d~t ! '!l> B
!.i. 1i lT"'; ~ .ii-!Fd
i:t ! .. h .! :tlE· ~~
H
Ii• •
~ ! •
l! •I, • g l, ~ • !
~
.
·
a [_ • Ii!
~
1088
Eleclrlcal TeIIm< Ihal th< ..«f" 1 no, i. pr-ofl(lrtionaI '" the [ .. kI. Anno' ........ i!W>ce _ 0.3' O. f .. ld ...,i.. 1m« _ I~ O. hil 7..1 C (II I 113 0 1Ir. ..... . I':ng. Gnod. 1.1'-T."- Jon< 19IU,
r""".
10. A tic. Kne> _or", operating no.v wpply_ It tom 50 A Ill!d "'... '" 1«pet Lo Ill< fldd ,""",,,nl1I1,1 " , 91 ~ ,.p.m.)
([ltd. ·r.dl""~.
(;WlIIIo. 11r.1lonce to be c"""""tftl In "im Iho umalw-.: for mlultJO.V serie • ....,..,.. t.a. . 1nIstanc< 0/'0.4 n and lakes. c,"",nl 0/' 1S A "'hen Ihe", i. no oddi. llooaJ con""I'" =i!Jantud , """" for!loe motor. 'The: muilllllm SIatIm, CII1Te1II ill no! 10 ",orm ;, ....:rv¢d f""" 11>0 Ii", 10 tho ~ ...>d. CoIrul ... tIr ....i .....,. bc1.....,n tho" if lh< .....; .. u .. """"nl in tIr ocoond .. ud i. 14 A. lb< ..........,.., ""is",""" or tIr moIof i. 0.4 0. 11..l.l.l 01 20. A totaIly..cnc1o>Ot(JO . . . Ihormal lim< ronSI.1n' 0(2 Iv. and r. ...llCm"...,.", rio ",.....
(b) ..ruf~ing the :LC. yo1~
( ,., !l. b
"
14. b
•., 15. b
(a) full
«> (a) in"~ly
(b) indirtttly
(~)
(4) panboIic.lIy
lineM1y
ANSWERS IO.b
II. a
CHAPTER
learning Objectives
•
• • •
Brake Test SwnbI,me', Test
,...
AdYcrIlogeI at ~'I
Mt*l Dbodvanlogil$
• ---~ HopId!III0'''-' Test
• • • • • •
A/lamoIt\Ie COrw\ec'hOnIIOI Hopknson'1 TesT
TESTING OF D.C. MACHINES
MerIts of Hopk~ ' 5 1&$1 Reladotlon or RIn"W1O Down " for senes Moten AIIId', " Test Objacttve Ter! Qv9$tIons end Answers on D.C. Molors.
..
TUl ing is pufonnf.d lin D.C. rnochinu to dt.lumi~ dfi(icncy and powu losses
1092
Electrical Technology
31 .1 8fok. Test I. is I dim:1 metbod andcon.;ru:of Ipply.", IbnIk.'01 " 'IIOf-.
Then. shaft torq ... T.. developed by lhe moIor • (W, _ W,) R \:g·m .. 9,gl ( W, - W,) R N'm
--
MOI"'"""'pull"''''''' .. T.. x 111: N ",.n " !ll >dIs .. 118.6 .. 21t .. 12 .. &.",",5 II Now.motoron"". _ 49>fl'
i< r
,
"
,
-
.
"
~
l
• •
~ ., M
• ,
"
1I
N
~
f(, '>-lJ
Y~ J ~.
,-
[ fie. 31.2 (.,
At. 31.2 (I»
Kumple 31.2(.). TM /ol/""'ing milling' arr oomi/mJ "'h~n doing" load ,~" I}" a d.r.•hunl motor using a brakr drum: 10 kg olld 35 kg D;o"",'er of 1M dmm Spring /Jaw""" reading Spud of Ih~ molOr Lm~
9S0 r.p.>n.
cwr",m
Cakulm~
'"
,h, OWl'''' pm....' and 'h, 'ffic;,nry.
"'pl'li~d ,""II08~
(EloctrlclOl t:"gi~" .. M ........ Unlv. 1986)
,uri"""
SoIulion . .,.".,. on tb< drum F. (35 - 10) .. 2!i kp'l _ 2!i x 9.8 N Drumradm. R .. 2Ocm~0.2m:TorqueT~~FxR.2!ix9. 8xO .2 .. 49N N .. 95(I.l00 .. 9516 r.p,;. : ma 2K (95.1(i) _99.5.-.d1. Motor ""lpUI _ T .. xm",·all .. 49x99.5_4.876W Motor i~rul .. 2OO> I""
~
•
"""
"f'
"
"
"
tJ --,...,
fig. 31.3. D,C. Stu'O: MoO>< 8rake T. .
SoIutlon.. Net foooe on rullcy • 1 '11)-0.17 . 2.731nIli", WII is W< 100 .. 71.1 OJ I" lho ahove ,,,101l1'lions. ill .... """n ....v,""" llw , I, mechan~.d I,,",,, re ... ,. COtry. (1'.Ioc.1ricI1':"ICiMrrin.. t 'ni>. 1'l1li71 'wiul;' ..., N< 10,7a2 1.4W v..at>1< """ .. 2 14 .. 3.6_ 2S W•. COI'ISIatlil ~ W,_ 2915_25_ 2&90\1
'1"'.-
I".u:.
t •• .
#,1".
If " " the Full·load annaru... CUITrot. lhen full ·1oIod IOOIOr ;npul CUlJeftt "(/... 2.55) A. FL ...... or pow< (1.(132
-
Lme inpulc"rrem 1 _ ' . + I ... _ 223.5 ~ 2.55 _ U6 A F.L'I'"wcrinpllt . 226>cicncy _
44.76(W49 . 7W~0.9or 90%.
hnmpk' .11.6. A 200· V, .hum mOlor d~"el"ps dn oulpul "1/7.158 lW ...h~" I"lmg 20.2 kIY. n" firld ru;,IdNc~ is 50 a (lml amwlurt .-uiJwnc~ Q.06 1.1. WI,,",I is Ihr ,jJiei,"ey wui (Hm'," mpw ~'Mn II" OW!"', j, 7.46 kW ? ( EIK1.M~chl_1. Ali~~rlo Muslim U"h. 1\189)
SolullO". In the nr51 CIISC': ()ulplll _ 17.158 W
J~
_ 2(1.200 W
Total kJ,;..", _ W.lOO - 17 .158 ~ 3.1»2 W ; 10Jlllt current _ 2O.2(ltYl...oo _ 10 I A I.. _ 2W50 .. 4A;I._1lI1_4 .. 97A
Arm:lI=Culoos _ 91 l xO.06 _ 5M.5W Cl)n".m 1m..". -. 3.041 - S64.5 _ 2,477.5 _ 2478 W (al'P"'x.) In lho ........nd ..... '" : ..
Let.
I• •
Now.
"
Inl"'t currem-.(I.+4)A + coruUrnt I"""",
""'1iIllIrrturrcn\
in",t power .. output +
I;R.
200(1, .4) _ 7.460 + 0.06 I; + 2.478 (lJ)(jI.' - 2001, ~ 9. IJ8 _ (I I, ..
200±boo' - 4~(I.06)(9.138 2xO,06
..
200±194 (1.12 _ 3.283.3 A or46A
We "ill "'JCCllhe !argcrvlll"" I>oI,d by Ihe SK'jnbuI"rU! mdlwd g"'"' I'" 1~lIoM'ing ""ul .. : RUIIII!II8 ligh1 : annalurt cu,,,,m "'IU 6.5 II ami fi~IJ c~rll"nl 1.1 11.. With 'M a,,,,,,'u1"< '''chd, ,h~ C~m"m MU' 70 II whtn" pOl~nri,,1 diff"~It'" of J V M'II' appli~d fo 'h~ b"lShtJ. I:Jf;mal~ 'h~ ~jJieirncy
""""hines"", OOI1J><Xted in pantllel. 'Tky ""'.10 begin w;!lL.eratorcu~, I, e"" be adjuSled to any de,irnd value by in· emuing !he ...cilalion 01" Gorby mllioOing thenciwion 01" M and!he~ values 0( differenlamn........ arc read.
Sptn.I ~OIr: IS A """"nl for d.c. J upply il ",bled he", to lfmaIUfe-,apul for lWO nIKh'.... whicb are under bld"lO-back "'lIcnerti"c ICW. The", an: dilTcren1 von.IIO", in 1w>d1inl and I,v,al !he 1..1 dlu... II i,"lwayo desirable to dnw !he d",uil diaanm occonJ,nK 10 which tho calculalion. ore bo,n, ",1.led,
Testing 01 D.C. Machlnea
u..mpk 11.12.
1103
n.r Hopa1UQfl', u.s"" /It'0'11I1 ~ lui"" a pair of slum! ""'/orl,
In SUl:h a I,., Qlf 250-V mat:/tws. I~ lin~ rur",m "'". 5O.A. and 1M ",{)for cwrrrnl.lf)(j A "m IMeI""ing III< fi~ld cu,"'"" of 6 A. "nd J A. The """"'ure of roch machiM ",as 0.015 { l Co/culm. rlt, .Jfidmq of "1C1t (Ad." 1':1fct. M ""hines. A~\I .U':' S«. II. 1"11
,.,i"'''''''t
,,,,,,,M,,t.
Sol ution. The O'ill,l ".~llsJ'" J~II.
IOdd : I)n~ WJII~g~ .. Ij() V .. rurnm wkm/rom luppiy 1}'IUm ~.uIi«lin8fi~/J r"rr~nlJ .. 50 A .. nwW, tJl'miJlu" (:urnm .. )8() A ' fi~/J rl'rrenl' 5 A tmd 4.2 A. C"Ir"lm~ 1M ~ffl('i~1IQ of lh~ machin~ ......-ting QS ~ 8t:MrrlllJT. A"""'~", rF'UltlllC ~u.ioo. Tbo ronnc: .. 7.434/2 .. 3.7 L7 W
'10101" £lTklenry
I
Ann.Cuioss .. 2.8Sg W F"",IdCu Io&s .. 2SO)( 4,2 .. 1050 W 250Y Sln-y1oo>e5 .. 3.711 W Total..,.. .. 2.888huo11lljlsofb :. Imake of111e whole SCI _ VI, ; ootpul _ V,i,. TOIall",>ng f ,. ToW~
Arma,un:eu loss • 44 2 x 0.3 . ~81 W. Series f,.ld Cu 10M . 4{lx ~6_1.24(1 W
Stray los"" '" ~,837 W ; Total I" ..., .. 581 + 2.24(1 + 5.837 .. 8.MB W Output .. 400 X 44 .. 17.600 W 'I. .. 1?6OW(17.6OO+8.65B) .. O.67or67%
TutOfiol Problem No. 31.1 I. A j()().V. >hun, molo< ,oka . total cum:n' of S A ,,'1Im runnin, unloaded. 1lIe ... ,,,"""'" I)( ond ,he fldd n 125 Cokula1' the clfocirncy and "'hen the """""'" .. IoodoNI and of 100 A. ('!IO. ~ '1- ; 45.1 ~WI
""""'= c"run i. O.2S n
talon, a",m,,"
""i>tmc.
n.
'"'!Pu'
1. A de .hu", moo::.-.....:I., 12.S kW ""'PU' run ... T>O-k>a .unil", 2JO.V "",,,hi...,., 0ITIIatUI< ourrc"to)7 A antld cum"," 0.81 A :mel 0.8 A. C.IcuIOlc thc cff"ocicrKiimila.- oeries",..,.,... ,he fI1" .."". obtain«!. I'.Joch has _ " ' " an1 th< ah.. n load corMI,tioru The armatu", ""ii ...... 0,0'I1l.
OBJECTIVE TEST - 31 I. One of thc nwn advanug of S,,·inbume·. '051 i, """ I,
3. The mosI"""""",isseJ of • loti< d.e. ,),,,,""""",,," i......_ (a) H~ ·.
(a) is applicable both 10 sbun! ann
shu", molOf i ••!«l foo-
1112 ~.
Electrice. Technology
n.. ....," IlIina"""'''''''' be """'IOn
1. 'Illm&ll. pole:< pLaotd in between "'" main poles. Their filnctioo islO ossisI oonunu-lalioo by prodI.o;ing lhe ... xiliaryor~g flu .. Consoquenliy. brush "JWI"",y,",lnl~ IlI""",- fIcl Q..... e........ ......ru.... d L "'*j .... bnIsIt dwl,.r," -."' ..............., rr..m 1M -..r. What muld It .... .... MIld Ito..- rouJd It .... ..,"_cd ! ~ . IIiood,.
of the following (2USr·-...!! AIL I. WbenmotorUnver.looded. 2. Whr:fo il is insWled .. _place hmng.eoui =
J. Whr:fo ...... wiroding is shorted Q. III. Wlta! CIlIUfS .... rosponsIble ror o • .,.. . beo t ln~o( ....m m .. tator in a d .c. moIor! II .... It could be duc cilh type. are known as Ii) C'Un'-' ylI" and lul.mll· I)'pt. Another !'ettnl «lion "" shown in ~.'8. 32.8(,,~ lhec-irrularcylindrical coils are u....:l in mosl of the """'-type transfOl'Illtrs because of thei, mechanical mength. Such cy lirdical coils are wOlind in ho:lk:U La)":n willt the diff=ntlay",", insulated fro",,,,,,,hodlt1 by paper. cloth, mi.corto boatdorcoolina duets. Fig.32.8«(") sIIows !lie K"""nll _.mge"",,,, of the>e wil. wi Ilt respect 10 the core. ill>ulating cylinde-no Off"lI", boatd are t>Sed 10 "'parnte the cy\iDdricaI ....·indings from !lie""", and from eacb Iber. Since the low· voltage (LV) winding is USI:>d ahlo.. glI more 51"P' may ~ ~ for very 10l"Il' \.I'lJ\Sfc.-mtn os in Fia_ J2,9(~). From the~ of~i&. 32-9, il oan ~ shown tIw maximum gross""",..rnon fQrFig. 32.9 (b) .. O..'l'; .....t for RS. 32.9(c) il 1s0.616.1 ~ d" the
rR
~oftheC)'llidicaI roil.
'c .:::::;;,1'
,.,
... O.71 d ..
'"
_
,,'
O.9d -*j
FIg. 32.11
,,'
32.4. SheU-type Transformllf' In IM5e case 01"". the roil • .." fonn·",(••dd bul "'" multi.llyer disc lype IHually wound in the form of pancalLe$, n.. diff..."" loyus of $Ulh ""'k ....-fare does "'" provido sufflcien! cooling area. tile 5ido, of tho tank "'" corrugatci or ~ided witll ladi"""" moonled on the ,ido. . Good transformer oil «..,.. ;, _ _"'. runarbbIo stabtl"l' ... nJ. ~ ...d err """tOnIlary windings. Thc",fOl1', it ... 31oopo...., ... produce&odf·indu=l ... m.f. in the primary. ~-""" in· 30 . ... .....--. TtUss~
•
I
Maximumlhl>.in~inwcb:n
.. B"xA
f '"'
I'rcqllCfoC)'ofa.c.inpulinllz As .ItoVIn in Fig. 32.14, nux UIC~ f""01 its zero val ... 10 III&llltl&lIJ1 vllIIC4>"lIIone quarttrof!he cycle I.~. in lI4fsorond. ..
•
A"C"!O&eratcofchiUlgcofflux '" li1J
..
FIg.32.U
4f"Wbl~ orvoh
Nnw. raIe of """nzc 01" flux po:r !Urn """"" indUC"voll If fl"" ''""'" ~"u.roIdDIly. thon r.m ..... vol ... of induced ... m.f. is obtai oed t.,. mullipl ~ing the avcmgc val ... with form fa ~.\;!
T..nsfonMr
1123
Similarly, '.""- vaI""oflho • .m.f induo:od in ~ """"Y os,
G a 444/N,oP.. _ 4.44/N:1I,,11 ... iUI II is llmlliom (,1 ond(ir11M1 E,JN, • £,!N: .. 4.44/oP... I, _111M "-ltLfAum is Iho_ ia botII the prin.-y 1Ind ...... _.,. ..indinp. In on Ideal InR'former 011 V, _ E, Ind £,. V, ,.,~ V, is \he te<minat ~oIta&e
_1oId.
(fl&.12.I~).
32.7 Voltage Tronsformotlon Rallo (K) I'rom«jWlIionJ (,1 and (Ii), we &eI
,
EJ. • !:!.1. K , N,
-.
Tbi, con,WI' K i. t.......... At vol, ... IntruformltlJoa
iii If H,> N, i.~. x> I. then lJUlSformer .. caUcd ~ nnsformer, fii) If H) < H, ;.~. K '" I, ,hen lfll'lSfOtTl'l/!' i. knwn ., ~ .." tnlMformer.
f ~~~ ti:.
II,
_
E,
~
,
~
I1 1 !
I"
)
Apin. for on idth,all5fomoer. in"", VA • OU'PUI VA. f ig. :1:1.15
1 , ait, K
~
V,/,. V, I, or I
V
"""""'. CIlf'I'tfIIIItt ill tho, " ' _ roDo of the (voIttge)
rransr...........,.,
nil(>.
.:Umpltt ,11.1. n.. ............ j/IU IknsJry in dw t:tNr of" 2WJOOI).mllS. 5O-Hz ~o_r l 'ok". 1991[ ~a,1ooL
,i,
!iH W.mayu.. ••
10, • H,> _ thallfi 1"\o9o_,cb: " ' - - . n ... dn.-y will ~1IiIly "'"'JlR'Ily..t "''''iIllbocddycurmoc..t by~ laMes . •: ........Ill A ""'8"-pItos~ ,~ Itas 400 pfVitOry "'" 1000 T1w ""t ~rou·_'1oni>1 0.-... oflM cDff 1,60 ~'" . IJIM pn"""y ,,·,rIII,n, Iw rOM«ud 10 0 5IJ.H: .upply u/ 52Q V. ((,klllat~ (ij 1M {H~k \.,1.... of f/IH d~ 'mty in ,I>< 1I1lD'317.s. U)40 ThiI. hovo'ever. rMoca !be 0\l1 and MUlu ;nlO leN ..wntlon. Thll.;n f04 o. an den.. nwy lIIpO. Aprll",, 1
(liv~~
\lie numl)(r of lum, required 00 ,he IWO sides. We .holl fill! clkul'le the L V,-!um>, round the fiaure off!o the ~XI higher ~,.cn numw, .., thai &iv," rna.m,mn nu. do:n,i!y i. 1>01 exc=ltd. With ,be ~orrec!"" numbtr of L.V !um., cakul.!e H.V..!" ..... by Innlfonnalion ratio. I'unhI>d pri_? cw,,,,nl. ahw,-bs 400
Enmple 32. 12. It ~i"gl~·pJo.u. mmsfrmer ,,'ilh 8 milO of 44(J11/().. V laus Q no·load CU""nt of5A a! 0.1 pa",.", f""'or/agging. Iflhu~canda,,' '""plies a ,'urrtm of 1M A 81 a p.J. afO.8Iasging, ~Iimalr lh. cumnllat.n by 1M primary. (~:Itd. .:n~I"''lPb llnh . 1991) cos., _ 0.S .... ~cot-\0,8)r36·54' COlI+, _ 0.2 ~.toIl-'(0.2) . 78· 3O' K • V,IV,_ 11(}'44(} _ 114 I,' _ KI, .I20xIl4 ",30A 10 _ 5A.
Solution..
Angle between 10 and
"
I,'
.78·30'-36· 54' . 41 · 36' Using parallelogram law of vee"", (l'ig. )2, 19) We grl
I, "
J(5'+30'+2xSX30xcos41036')
• 34.4SA ~ ",sull2n' current
could also
I\a~.
been found by resolving
I,' and 10 into their X and Y-<X)mponcnlS, E~ am~ 32.B . A ,ratUfornu," ha.. a pn'mary .. w/;"g oJ lu",.. aNI a ucrmdary winding of 21J() ,,,,,,... When 1M load C""~"' 011 lM suOfldary I. 8f) A al 0.8 pmn iii","", II """""" in 1~1. 32.21
'.
MOftoI Problenu 32.2 t , 1bo pnm.y of. IJ !Ito omonduy U 1132
32.12. Equivalent Re.lstance In Pi,. 32.23 I cr.nIfonncr is IhmvJt wllllM primary and o«ancIary windinillul\'c mltwlcu ~ HI and Rl fftjI«Iively. The r H i _ have bfta Ihown ultMllllO 1M wlndln,..
1133
Tranatom.-
Ie
."OUl! X, and X2 ore known as primary and '.':tllldary IMJwp reacllnca
•
~pectlvely.
FoIlowin. few poinll ibould be Itcpt in mind : I . The luIer windi"li:oJI IfOf todo . hence il in DO way coouibutcl 10 tho ~a- or ~ Iiun tho plmary 10 the scmndary windi ..... Z. TheP""'l")' '101,. V, wiU I.."" lO5Upply oactive drop/,x, in MIdouonlO f ,R,. Similarly t; wiU lu.ve 10 supply I) R) and I) Xl' l. In .. KIUIIlnnSformer. the pnmlf}' and ICCOndary ""indinas are IlOI pboed 011 st~ 10," i... with V, 10 give E,.
", .. V, + I, (R, . jX,) .. V, . I, Z, l11e Y«IOr di.gmn for such Im, ... fonner for diff...,nl kinds of loads i• .oov.'n in Fig. n.:?9. In tho$< d.lgrfJDS. ve' .. 5.8 0
,
"''''acranee •
1 )< X OI 9.1 X X Ol 1 V, xlOOoc4~ ItlXXl xlOO.X OI _48.40
X,'" X,' • 48.40. Givon R/R,' - X/X,' or(R , .Rt)lH,' _ (X1 +Xl.')lX1'(7.!i+5.8)15.8.48.4JX,· .'. X1' - 21.1n X, • 48.4 - 21.l _ 2730.X, _ 1J 1"(3171111XXl)'.O.17S0 h.umplt 32.19. Thtjoll(M'ing datn nju "'" I·~~ lraMI"rmer : Tum ratio 19.5: I . R, _ 25 n ; X, _ f{)() 0 .. H, .. 0.06 0 .. 0.25 1.25 A le."Jing Ih. p= by 10'.
X,.
n. No·load cur"nl_
TIlt IUmukJry deliw,.. 200 A al " """inal voI/a8' oj 500 V and pf. a10.8 "'88"'8. Om""i,..
"38
EIectrlcIII Technology
by 1M aid of" '~Ior di"Irom. I~ pri"",ry applkd ""'UlI~. 1M primary p./. and Ihr rffKif'IIC'J.
(EIoI ,,~,
'
V,
...
'0'
(0' ~
1k ....,...,...imaie volule drop for klllRnl power flClOr becomes
(I:Ro:! a. t,. /,Xo,lint)
,.1,
ifll"neral appmIinwe voll.ll" drop is (I, ~ roo t Xo, .;n t) It may be noIed Ihai approIinwe ,·oll.lje drop .. ",ferred 10 prinwy ;. (f,~ «If t,. "
I,
lOOx I, R", ..
....
Xo, lin t)
Rm a. t ± I,
•
V
1
.',
Xg; lin t X 100 ... 100 I, Xg;: .
"""'t ..
•
v.,
. ,~
'''-
,
9 - .... 1'
....c
'Ult
,.'
,¥
32. 17. exact Voltage Ofop W'1Ih merma: IOF.,. 32.35. it;. 10 bo"'*f.-rring the exciting cimJil """""" the Iemlinal!: as in ~ig. 32.40 or in Fig. 32.41 (aj. h 'hoold be l\Oled lhal in Ihi.case Xo " V ,11"
I, R,
'.
I
X,
.
.~
1 "
,-
~L
Ro , x. ' "•
'-
I R,
f '~ 1 " " ""' ~ .
'r'
All. 32.3\1
E,
,,
< -
j
-'.
1"
I
•"
~
0.~ ~
"
"-
"-
"
0,
I l.
w,
Il, - E,
',
FIg. 32.40
"
l,, ~
1144
."
Electrical Tac:hnology
, " " "
>-:D "
"
.~
> c~r,.nl.
"'''f'''l
,tI no
I N"IIl'ur Iln;'·...,.;I). WiQler Iml
T.lln.forme.
=
1145
SuI",;.,•• Loads arU'O"nttted os oJIuwn in Fill. 32 ,42. 1'1 _
_7.41 at unily p.f.
10. - I(XnV720. 13.89 al zero lagging p.r. These "'" ",11ec1d rnagnctirinll cumm "'" ig!lbon -circuit tests of a !JlIrufCed e.m1. in!he...,...,.wy winding. TIl" bell'" 10 lind ltanSiOl'l1'l:llion ralio K.
Tbt no-load veclOr diagram is obown in Fi&. 32.]6. If Wis!he wallmetcr ~inl (in F'I. 32.43).
.." W.
V,/o"""~
J.,in..,.
:.
CQl~_WIV,/D
.. J., .. 1~ .. JDCQl~:· Xo-V,IJ. and H._V,J1~ Or oince!he curmlIls prac1icaIly alI-e:ey I\bould ho converted {o the panun ",{erred to L.V. ~ide by {r,IOsformiog lhem ",ilably. From S.c. Test reading.. Z . 36/5 " 100luns R .. 11005 . 4.4{)ohrru. X~( l tf~4.41"'~ 8.9ohrns The>.; OR ... ferred 10 H.V. side. For ",ferring ohesc '0 L Y. ~ide. ,,,,,,,form (hese using the nl1io of !Urns. as fo!!ow. : " .. 4.40x(2O)'I!XXI)~KO.176oh", '< L .. 8,98>«2OOI1!XXI) .. O.Jfio/un Equivalent circuil can be drawn wi'" RG and X.. cakul.l«l above ""d r, and.e", of the con: lamin.'ion, an: given. 'llIe core loss i, rnadt up OflWO pans (i) byslr""i~ lo!<s W. E P8'!./as given by Sleinnlct7:. e"'pirical ,dOlio. and (m eddy current Ion W• .. QB'-_ wh.", Q i•• ronSlanl. Tbe lOCal core·lns, is giv". by
f
L"'--'I'
W," WW .+ • " PB_f +Q,,---_ If "'.., carry out two . ' periments using two different f""l""oc;", bul the same ma.imum nu. density, ..." should be able 10 find the """,{ants P and Q and he""" cakul.1e hY'leresis and eddy (urn:n{ los ... Kp;iflOlely.
1148
u.n..... 32..29. ~ al same
/n a 1mru/mII!< In.,co:>,.,,/o.S ~foouuJlo~52 War 4(J Hz and 90 War60H" ploJ:jlu tktuily. CDIft{>f'le /Joe ~ys/e ..sis and Wdy ..,.,.... hnHs ar SO Hz. I£1«1. ~Iao:hu..s, N'«P"r l nh. 1993)
n'
ScIIuUon. SiDc:e!be flux densily is !be wno in bod> cases. ~c"" use!be ...1aIion Total rortloM W, • A/+Bf' or W,II.A.+BI :. 52140 .. A. + 408 and 9IW6O. '" + 60B ; . . A. .. 0.9 ODd B .. 0.01 At SO Hx.. !be IwO 10&50..... W• .. "', .. 0.9" SO . 45 w : W. " _ O.ol" so' _ 2S W
sf
EDmpk J!...JO. /n ",."..·u Wu U!$I .... " 10 J:, Lpn"wn of*~t SlHI lomi""'ioru. tltun.uimum jlux u.uily and "''''?form lacUJ' ",.,. mniroai~d ~ONUJn' tJNJ ,n., j"oIJqo..~ .-rsw/s. ....'e oh"'/ned: 15 40 50 60 80 F.-rqurory (Htl 18.5 Total lou (""") OJcvJale I~ eddy cu'",,,, lou fN' kg al a frtqUtnCJ of SO H::. Ihlort. 'I........ .C\l.I.£. See B. 19911
''''
Solution. When nllX de"."y ODd "'''"C fDml fK1n for iron lou can be "Tincn as W, _ A/+8/ 1 Of WII - "'+B/ The values 0( W/ Ifor dilf.",n, freq""ncl", "'" M under:
1254050
W,lf
0.74 lbe paph belweml """
B_o.o l ..
80 0.9 1.0 l.l D WII has been ploned in Fil. 32.44. As oecn from it. A. _ 0.5 and
Eddy """"uIIOJS 11 SO H>; .. BI' .. 0 .01 EddycurTellllosslka .. ~IO .. 2..'i W
EumpW J2.31 . In
60
leS! lor'~
"so',", 2.S W
IV,
+
I
d~Iu7l11I1Qli"" olllr~
10 .... of II lou .. _~ found to bot 2500 W '" no,mol volta:. and I ... quency. WIr~~ 11r~ oppli~d oolto:< and frrqW!1f("y ...., ... Vand 25 H" 1~;rGfJ IosHs ......... Iooutt! 10 ~ &SO W. CaJc..Ict. !nil.•"d ~1""'I'nDJ.b l Ill,. 19911 Solution. The nux density 111 boll! c ..... i. the wne because in KC<JOd case voltage '" weU as fmqueDC)' 2I"e hal ,«I. Flux &Mily ..,malning Ihe samt. !be eddy cum:ru Ioos is proponiooal to I' and hySlO""'I bs .. f Hys....... is loss ..f. A/and eddy cum:nlIOJS ~ I' .. BI' "'bm:A. and B .... coo.unu. Q
.uo. V, 'iO-1l: tronsj"lmfld W, _ Bf I - (7/SO) x loo'.I400W .. New....,.., 1"" _ 13<Xl. 1400 .. 2700 \ \ ~:nml'l< 32...lJ. A rraflS/l)rnwr M'i/n M"""} ,mlage impreJ.f~d has tI f/w: dtnn'" uf J.4 Wb/m' lliIII I) m" ID •
I!
V,- d nonmrs"" n......" t.::Mb 10 pnmll}' ond ~(.. indin, rtprt!iCnl the ful1·1oooJ L" 10 I.,.. of. traIlsformor ~nd5 01\ curren! anJ iron lou "" volr.oge. He"",". lOCal depends on voIl-ampcn: (VA) and 001 oa ~ angle bc:lweo:n voI\.Oge &nod L-!
"w
"" • Zw'K' ..
,odprimarycurmul, _
VA, _ 33OtO.9
"sc
m
330V
.. IOO,tJA
I, .. ',_ I(XY3A. Now.f,. XI, I, • (100I3)K6 .. 200 A Now. I'ovo-cr ;"pu, on sbon-clI"Cui, _ II.."J, coo ~ "Cu IOSI .. I; R,. .. (1(XY3)' K 1.'18 • 330 K (I(XY3J x CQf..sc; sc _ 0.2
AsI."negiigible.haIoe
',K _
F.L.~ al f MII-load "~"Y p.J. iHrmtlll10f f'l '''''' 10.. (ii) foil-load roppu IOJ< /HId fiii) .......imum ~J!ici~nry '" lUIilY p.f IEIod. t:nltll.- A \lItlESe aiven \lie following: Rot .. 0.1 Hl. x", . 0.31 n ;R,,- 600 n. ~_ :lO!H! USO"SIhe """""imote "'Iui'-alem dR:Uit of Fli. 32.4 I. " .., ha ..... I, .. VIx,,_20G'300_{2I3)A I~ ..
10 "
V"R,, " 200'600 .. {1m
A
J/~+I; . J(213)'+(11 3l' .. 0.145A
As .... n from"J. 32.49 ~,
,r,
,., 'r,. Hi)
'.x.
•
.!..s..113 .. ! .9.26.6. '.2132·
90" - 26.6· .. 63.4·; Angle beI",,,,,n 10 and 63.4" - 36.9".26..5"; K .40)'200. 2 • KI,.2x IO _ lOA • (0.14~' .. 2fl- + 2 >< 0.145 X 2O>' En","'" 32.41. The /0 .. ""Img' ..'i.wing "'a JOO·,tVA. 1I.an2SOO· V. 5O·H: Imnsl"''''''' hlu If}(} Ill"" WId a rr,is/aJlrf' ",O.(J(i. 1M. ~ig~-wlmg~ "',lIdln, lit,. 9/0 Illnu tJNi a nsis""," '" 1.6 D. WMn 'M I.>: ,,'ond'''Z is sNm-("'"","ed. 1M"'1/."-1 cp,"", is oblQi-J ...,11. 55()..V applied '" 1M ILl'. ..';IId"". Ca/cllla,. Ii) 1M "'Illi""I"" rr,ul<JlJt:~ """ /~~ rrtJt:ftJ""'" til rrlerrrd IV h. ... JitU will Iii} 1M I""u,~ ,.,.,."lQnu of f"lJCh ,,·,lIdlng. Soimion. A.sum,". I full-load efficiency afO.985. the full-load ptimuyturren,,5
FL I, a IOJOY20}}m~A Total Iran'fanner ,,"I!age drop.." ",(erred to ~muy i. I, (R", CO< 0.6) .. 67 V Hclltt. primary v"lt>.ge has to be r.tiscd from 2000 V to 2067 V ,nordrrtocornpcru.alc roo- the lCII.OJ wlltitgc drop in the lrn""f()f11>Or. In tllat c.... occondary voltage on load woold ",main the .ame.." on ..,.Ioad. Exampt. 32A7. ,\ 25£V5()(). V ImtUjormu ga,'~ ,it< lol/"",;ng I'." ff. wlts : Shon' (';rrwjl t... ,: " 'ilh lo",.",,/Iage "'indong .iwrr·c,rrujl"" : 20 V; 12 A 100 W OfH'~--
F.L scrondary cum,'"
z", _ 20112.1.6670;
100 .. O.()9.$O
12'
X",,_ Jr(,C""'",-_c,c.,,,,~,,) _1.5180
As Ro and X. ..,fer 10 primary. ~nce "'" will tr;tn,fer Ihr$ V", ..
203.5'.157.6'
:.
V,' .. 257.4\"
f..Dmplr ll.4lI. A. 2./01230 V. J tV,t I"",./mmu O.c. 130 V, 1 amp. I()() W
r,,,·
8l.~
.. IRoos. + IXsin._13[0..'lh:0.8 + 1.02'ilxO.6] _ 13{O.424+0.6JSI _ 13..'llvoll$ In Ie"",, Of".lhe VtIIl'ile "'Iulalion _ I ~~I )( 100% _ 5.1C7~ ~ Example 31 .... ' . A 10 WA 5aV250 V. ,mgk.piwJ. lronsfimn~r NIS IIJ ........ "'''''' ~ffic"Jlryof 94"" ,,'IlM IkJj"'ri~g 9!:.I'l> of ilS rot~J at u~il:" p./. UI."",U ,,. ~fficimry "'hr~ Ik/"",""g '" foil-load ""Ip'" at pJ. of 0.8 lagg,ng. INagpur llnh'ft'OlI~.I~.onmlwr 1998)
""'1""
SoIUtiOIl. ROI..! OUlpul al ~nily p.f... 1!XX)() W. H."ce. 90% of rared OIIIP'1'I • 9.<XKI W In",,1 ... ith 9-1% efficiency _ 9IXOO.9-I W Losses,", 9000(( IIO.9-I)-I) .. S74W Al muJmum effic,ency. vanable copper-loY _COIISlalll_ Core loss _ 574/2 _ 287 W Al rat.d curn;nL, Lei tile ropp v,' . v,.
lI'e .... rmu and _ eT are lOA and 7~ W n:J(>tt:I;.~t)". C,*u/o/r W fuJl ·1otId rfficirtoCY '" wn,Iy [1OI'>'U /<JcWr andfoll.1otId rrr"/olion al 0.(11) _,..factor /on;"g. IN"IIPUr I :"h en;lly Apm 19991 I~"";ltalt.
SolUTion . AI a load of 4 kVA . !he wod cum:nlS are : LV. side:: 4<Xn'2OO • 20amp And ltV. side:
From !he Ie;.( dati.. full_load "'PP"'.klp .. 15 W ADd comWII rore-1osI; .. 65 W
From S.c.IeSt.
Z _ 15110 .. I!!! ohms R • 7S1100 _ o.75011m .< ..
J I!!!' - 0.73'
. 1 .JO"t""~
Alilhese .mes.panme1..... ltIe",rerml IOT1>c H.V. side. since 11>c S.C. leSt has bocn condIIClCd frofll ll V. '-KIt .. 4(XXI! (4())) + 65+ 7S)
Full·load offici.,",y III u""Y p.r.
• O.966 .. ~ Full load ~ regul ..... "" III 0.80 lag'"1 p.r
..
Ir=.+I.lances iD ohm can be obtoined thus : %RxVI _ %CUlossxV, , . .. %Cu loss )( V,
Ho,o. Xo , ·
,
100 )( / -
,
100)(/
; SmularlyR", "
100)(/,
%Xxv, .. v , >eiency). C"",idcringprimarywinding, """
X~III )( 100 .. 357 V,
4)(3300 100 >ec. core loss as found from D<J-lQad ~Sl. is 1-111 W. (6) From S.C. les!. 360110,5' . J.l6 IJ «) R., _ K-Ro, " (2200200)) >< 3.26 _ 0.0326 0
If., •
•
Now. ?", _
VI x
~l
100x/, :.
!K. I)
-100 ~l
14'1
Z, • ..
~. 86 .. 8190: IK 10.5
XOI .. J(SI9 1 - l _U,' ) . 7.51 D It l ifl
X/n ..
K' Xoo .. (22(v.220(l)'
~ "ill""", Ibo ddiniticlnol n:au~ioo
"'.!11 .. 0.075 1 U
_ gi........ Alt. )2.24 (3).
We 'II ill find !he ri .. in prinwy vol. . neCIrIl from 00-10l0= 0.44876 ohm 051.5/ . 15U>(0,6 .1.648+5.87. 7.52'10 .:.u...p~ 32.57. A lra",jormtCr has CQp~r'/os'()f 1.5'f"vod rro \
11".
SupPOOII it i. ""luiml ' o lind IIw: VQltagc drop 011 rull·)OIId HI • Ilgging
1aI loiN -/, Xo:z and is drawn perpendicular 10 1M. Obviou,ly. ON iI IIload voI.oV,. Now, ON .. op,. oV,. Similarly. OL i. V,. TIle ""11aiC drop .. OP - OL .. 11'. Hm:e.pam1!agCll:gulatioo'do'ool1'j1"
J
OP-OL OP
lJ' )0; 100- OP i< 100
It IS....., \hal for fU>ding mltagedrop, triangle IMNnctd "'" be lIra"in. bIll .imply the lldius OU'. ll>< dia,T1m .how. cI • ...-ly how the _ondary 10:""'011 vol""" fall. os the angle Df la8 ;'1I"
(Eledrical Madtu- III. Gttiarall'nl •. 1986)
SoIulion. Total I"" .... for bo!h transformer< _ ~ + 7.~ F.L. 1= for carb traru.fort"D 0tIIJ-t .. a.- lost. .. iron Jo.s
IMtes
•
'''''
II may be IKlICd hen: !hat effICiency i. baocd 01\ pGWCfOUlpu. ,n walts and not ill voll-ompcmponding lO maximum efflcimry iI; I , ..
J(W,JIW. ) .
II is thll val"" of the OUlpul curren! "'rueh will make the a. Iou CQuallO the iron lou. By """"" design. j, is pouible 10 make the maximum effICiency DCCtII"" any de5imlload. ~ 1< ) II _..., 1P¥Ca utili 1000 and fulllood Cu - . Ihon Il1o ..... ",lucb Ioto<s ...,.kI beoqual (LL caonpondi",10 mui ....... .rrinmc:y) iI P- by
F.L 0"'1"''''' u.p.r... U x I _ U kW: " .. llIU.n _ O.97 or !n ~ (iI)
tbl"t~ I _ UnilypJ".
a. Iou _ 400 x ( 11"2/
_ 100 W. Iron 10M ~mai", CCJnSlanI I I 3~ W. Total lou _ 100 + 350
. ~.'iO W.
HlI(·1of,d 0UlpuI"
u.p.r. .
12.!i kW
" _
1 2 .~( 12.5
+ 0.4S) _ '16.52 '"
.... I . 32.". If 1', IUId 1', W IN iNlt OM ct1pfNr Wua ata Iro"'/cmtU'rotl {wll·laad.fi"" 1M "'Iio of 1', aM P2 .,..,h rJwu marirnJom ~flid,,1tC"f oa:urs al 75~ foll·/ood. (EINL M""h) IllS MilEs..:. B. Sumlll.r 1"2)
S I ;;.. If PI is thea. loss II full· load. ilt vaill«0.75)1 . 91'/ 16. Al muimum effocieDcy. ,1CQu.ols the ir<Jn loa 1', whlc:b""";'" ronsIaJIt throughout. Hmco..11 maximum cff",iency. P, _ 9P/16 or P,IP, _ WI6. I' 32.61. A 110001210 V. Ijli-i:VA. 1-p/raH. JO.H:.IrtJn.f/u,.,,,u MJ MI"I'/tm of 1.41:W F andF.L.Culouofl.6 1:W. lkunnJM /M .tVA It»d for mIU. ~flici~1tC"f aM ,-a1u~ of m1U. ~ffid~nry G' omity pJ. (;'1 1M tfflCklKJ til /tQJ/1-:L. 0. 8 pJ. kadu,g ISa FIoct. Machine, Nagpur UIliy. I'I9J)
m
1171
Transformer s.~utiM.
(f) Load kVA corresponding 10 """,imum dfocicn:;y is
.. FLkVA> < l00;4.142 .. !Hi.J..I "" M Co 1"'< (6_2515)' .. ns W
TTansformer ,-allase drop as .. ferred 10 soocondary _ 1,{R,,;,tOft .. X",J;n t l - 10(0.6xO.8 .. 1.9xO.6) _ 162 V .. V, _ 4OO-16.2_lS.UV Prmwy tum'n( _ 4CII»'2OO _ 20 A tVA rom,ponding to,\-.4 x J70lW .4.32 tVA . . lII as full-tODd and al'" as ""If-/cod. tHurm;"" its ~ffic;~..cy i, op.t:rntu a, ""ity pJ and 6IJ '!IIi of full. load. (~:IMr\c.. "~KN":w.lnh . 1987)
M""'..
SoIutlQa. 11>< fil;l that dr",,,,r>CY '" 1M wnc i.~. 92 'l. .. \>oIlI fuU _load and half·load w,ll Mlp us Jo lind the iron and
roppor """"'..
Al full-Mod o.'pul.600 kW • Input .. ((IMl.92 .. 6$2.2 kW : Total ..... ~(62.2 - 600 .. 52.2 kW I.L"I .. . Iron los< - II remain. conSlanl at 011 loads. -hi._(kVA)'. Y • PLeul....
AI baIf·1oood Ottlput .. 300 tW ; Input _ :lO(W.92
tm.scs_{JOOO.9~
...m
- 3(0) .. 26.1 kW
Since Cu ..... bcwil ... onc--founll of i"'I'.L \'lillie. hena: -,,+y/4 .. 26.1
EDmple 32.70. ~ ltkU;mum ~JJk;~n< 101100 .. 0.06 kW Now, fuU-loadeurrenl i. kepi corutanl 001 voltage i. inc ... ascd ITom ~ V 10 10,OOOV. lienee, ""lput will be doubled 10 20 kW. Due IOC< 100 _o.n % Now. eddy current 1"",_ / and bySle ... I"" ...f. Ne .... eddy "",,","1 los... 0.05 (5OI2.'i)' .. 0.2 kW. 'it eddy current 1""5 ~ (0.2120) >< 100 .. I % Now, W. 0,06 >< (.$OJ2,'i) .. 0.12 kW. 'it W, .. (0.12120) >< 100 .. 0.6 'it K
,i,
E
Il t
..
to
10 + 0.15+0.05+0.06
>< 100 _ 117.4 '1< 1 00 (300 >< 0.8) + 6 E .... n tp~ 31.1J. A Jingle pilau Iransfor",,,, if mltd a/ 100·kVA, 2300f.?JO-V, 50 H .. The mmeimwnjlu< ,unsi/y in lhe co,. i, J.2 WMn' ond .he ne. "",ss·~ctiOllOI ano oflhe core i, 0,04 m'. Dotle""i"" /_) T/u> n"mbtr af primary and ucondary /II"" nuded. (h ) I/Ihe.".= lengrh of rhe ""'gM';C eirr:,,;1 i. 2.5 m aM lhe ,..Ia/;"" permt!/Jl>i/i/Y is J200. ,u..."",·M .he mag"",i.ing nl, N' g/ecl th.. currenr df'{IK'n for 10.< •• rd On .Ioim·d",uil w;l~f~II·1oaJ cu,renl jlowlng ••he pow.., input if 1200 Wand an ~n c'rr:w;' ~'irh 'a/ed voI.ag~, ,,,,,, pow.. inp'" ~w 400 W. iNl.""iM lhe effid~m:y af ,,,,,, tran$jo,..".., as 75 % affoll.Wad wilh O.g p,j. lag. (II) f/I"'" so_ rroruja""", i, comuCl~d II) a '''PP1y of simila, voIlog.. bur'doable rh. fTeq~mcy (i.~. , 100 HI). Whal is lhe ../Ject 0fI;/J 'l!kiency! (£Ject. ~ Bon,bwylnl~. 1 !I!I8~ F.L.'1 alO ,&p.f. -
e,,,'.
r"'" "')(..
So-llltlOfL (_I A!'pIyin, c.m.f. equation of the uan,formcr to the primary. we have 2m ~ 4.44>«1.2 >< O.O.4~ :. N,_ 116 K .. 23QJ23OO./Il0 N, .. KN, ~2\61IQ .. 21,6Df n B 1.2>< 2.5 1989 1)1) AT _lJx/. _ _ > m/UiJrullfl tf!ici~>Jce and reactance paramelers of the C<juivalent circu't evoJua!cd. from Iho S.C . ..,.,.
_ ~ _ O.!iollm
_ ~ _ O..1JJoIun
"'''''
1La,.., to be
Transformer
1177
Seriesl'toctancIuHon. Let .... I'mclionallad at which lhe concerned efficiency occurs, al unity p .r. ,",
, .0.968 40 .• -+ 0.8.. + 0.40 This lives the folio" ing val""" of x :
X," 1.25
1178
Eleclricel Technology
Th .... 114() 'lII 11'W« flttObon..,,,,,,,
'"llo;ra.>",
li..p:-.............. forma ..... _ ,n ",,' wa)'. the dala wt:« I:u>n"JII&IQu/Io ...... abcn-cor..- __ W.... 300 V .oppblalt fwl--loood ~ ........... J«I.......,. \II""'"""",rm..
It i•• ,,,,,,.former "'ith otIC ",;l1li"'8 onLy. poIrt of thIS (OO'nlOll 1<Joo( lOa distribution uble IOCOJ'I'tt11he V< 3 .. 1.5 kYo ..
Exlltllple J1.88. '1M primnry and =andary """ages of "" auro-"ansfi"'~' are 5()() V and 400 V ,u~'il'dy. SIw~' ~'ilh Illt aid of diagrom, ,lIt ell'ront di,'ribuliOll illihe windillg ~'''''"1'''' .uotrd;;'Y CUT""II. 10011 and CQlcula'~ II>< UQftomy of eu in 'his panicul"r cas~ Solution. Tht! oi""';1 is obowo in Fig. 30.61. K .. V,IV, .. 4011500 _ 08
' , " Kl, .. 0.8 x lOO .. 80A is show... ilIl~g. 32.61 . Savin, _ KWo _0 ,8 Woo An 32.33 •. Percenloge ""illS" 0.8 >< 100 .. 110 ..
Core area .. 0,03604/1..1 .. O.02TI m-• .. ern Thrn$ ofh, v. ,ide .. 66OlI8 .. 825 ; Turns of L V. ,;-
1
~,
2UiOV
j
"'''
" "." J
• (,
(0'
>
•~
.-,
N
d:
•
~
(.,
• (,
. . . ~U
The IXImm Il.U'J
'"i) """",um' "" Ilk- reJuilS obtain.d, SoluliooL(i) I, ~ 20" lO'n-lOO ~ H..lJ A (ii) /".. I,IK .. 8.33" 10 ~ 83..1 A (iii) kVA rating of aul-Ir..... fonncr VI, ~ 2640 " K3.3 " 10- ) _ 220 kH. Ii.) Percen1inc .. ...,inkVA"'ting_l20"IOO3
"
1100~
(.) I , ,, 220" lO 'n.wo _ '1 .7,\. I, _ /,_1," 9( ,7 - g3.3 .. 8 ..\ A (,il Per bumple .\l.~ I. R,PfiI! EMlmpk JO.M far ,"",'me!i,,,, polan',>' as s/w.m in Fi8. J2.62/ ..
~
~.OOO 3.000 + ~ + Cu los •
CuJoss.2J2W
AII~"""""
CuJoss _ 21Y4 _ 33W;lronlou _ 30W :.'1-,
5.000 ~ O.9797or 97.'J7% .000 + 33+30
CUJ'tTn' of!hc h.v. ~ide _ ~ I031220 _ 2.1.2 ,\ 32.93. A '"",,/onMr hill Q pri""'r)' w.lrag" ""ing of 11500 I'{>/'$ tmJ .«ondQf)' vo/,· Th'o ",,,,Jing. "'" ronn«IM in ,~ri~~ DM ./u prrmnry ;, COOMi'cud 10 D ."PfJly 0/ 11j(}() .'OIIS, 10 oc/ DS d "~"'~J1 ""/0 IrillU/O"""T. o"l~ntf"'~ 'M YO/ld.'tf' ""/1'1" oj /"" lroru/ormt!r. Qor~Jt''''' UI~MrvJ .- If II~ ,,..., "'inJing 1rtJn5/onMr i$ rulH tJl liS kVA. "'Ntl ...,11"" Ih~ tVA "'''''8 of llot UUItHrtJn5/Of1'I-'ronsjO(mu and Ih~ inJ",,·
r
•
1i, ... I. and C<JfIducth.."y Iran. lfoe "'I~d ""'pUI '" unity power-/acla, lNllgpUr l'nive ... il). Whiter 1999)
Solution. "",th!\O kVA ... !he r-.ting. the raIed CIII'I"CIll.< on the Iwo .ideo am 20.8 A (2400-V .i a.. load bu ... t>ars. In COI1IloCCting twoor"",", thaD IWU InlIISfonneB in panoIlol it i> C>lSelIwoI that !heir tt:nninaIs of sirnil.u" poiorit""""pined to Ihe...-.e bus--bars .. in Fig. 32.68. Ifth .. is IlOl done. the !Woe.m.f•. induced inlbo ~ which arepwalleled willi inc:onttt polarilles. will act together in tho Iooal SttOmI3ry cin;uit~ ",hen supplying"" load and ",ill hence produce the equIvalent of a dead short-cinouil as ohown ill Fig. 32.69. Th==cntain dcfiDi~ coodition. ",hich Fig. 32.118 must be grj,fJed in onIer to avoid any local circulating m the common load in proponion m their kVA ratings. Therondioo..s """ I. Pruna.y windingS of the tr.lIlSfonners should be suilable for the supply sy'~m voltage and fre-
"'own
2.
J. """
""""
The tnwsformers ptt1y CCJnDead. 11Icrefore. in thi' case. the Iwo traruf""""'" w!ll t>04.1'11trn lhe Jo;od io proponion to lhei. kVA
-
j
•
Fig. 32.69
11 ,hook! be DOled th.(lhe impedance. of Iwo
flJlTTOfom><no an be .........1boned,,,",,,,,
1o .. -..oItao ' ,1.,- 1 ,,7. ~ . 17. ..... " Ii) ",. lim: Z ,.. i. Ihe comboned 'nlpee ph:i'" ongk and ""'ifll1udc 0( 1 .... ; II be """"n frum the _"""11;00. or Ioadi ",. -"" lhal ""iIc •
"96 bmo.-eaI V1and Iwill be k".,..lI. Inxn'''I1hi1o, ~ InnSlOnnercunmlJ IA lad I.btwmo known In """"'............ pIoQe ....... """"'" 10 Vr _ . (p, "'~(Urhb,~.~;' "'" "'--0' ",_thc: _ _ al.........,.. t.oc-oa/y ~i4K ' . . . . . - . . . ~ Tho< '''''' p«1 lo'~ ~".. /f,Irq_ml, In ptJfdll,t tktumwho.o·,~ ",,0 slID", a l()Iullllllil of 100 kW at pi 0.81 I 'oil I 9lr71
Z. '" 5OOL-36.9' >< 00130.8' .. 67.4" 0.8Y.1_ ~7.9 kW 200 L-2.5.S" >< 0.664 L 2.4' m 132.8 L-23.4 112.8 "cos 23.4" .. 132,8" 0.915 .. 121.5 kW
, .... Second nruform tuttll()'l, Tftl{"a~
B, SO tVA . /,(}1Dlved procedut< by It.. ..a-mr ooIuo-. amp. .,,11 ..,... be .aanp«d ..Ihmrti.--.lIy
"'1""-",0"C •• _ -.... 01400 V. Th< """. . . 00I_00""""",,*>, wirIdiI&>. we (1. j l ) " ('lj + l S)_
I . Two .....
~
~
~_
CoboIaot .... ...",.. "'Wtid by - . ................... (' _ Th< orud<mt is
lid.'........
11)'
br ori_ mfurm The primarycurmm may be wn«i by the dl,';wn of lr.Imformaiioo l1IIio i.e. K ond by add iljoo (i f IlOI neglisibk) of lbe ..... bId currenl. U.ually. F, and E. "'""e the " me plioSO' (ll .."umod aOO .. e) bu, the", may be """" ptwe diffemlce belween the ""odue 10"""", diff=nccof inIemaI ~ in p>raIJel of aSiarlsw and • .wI della }.ph>o$"""n. OM'" /00 iVA aNi WOIM,ufJOWA a... ronnt £ .. _ E , .. (405-415) .-23OL- 72.9" z.. + Z. 0.0436 L 72.9'
!rItt..,....,.
r"" ....r...........
n
!WppI,"".
1.
(I" ;!'M A (., 1577 """ .,.,. A( KiIy'" (;.iJdt. I _ I 8 on: 00II""",«1 on ,*"Uol '" 1wI"", ... "npopUt '"
..rn mn,f be Dlirilinised ?
Bybmirwiog ,i"""
p<x"'' .
decrrasc '" f=iucllCY.
,
1208
l*Irk:aI Technology
OBJECTIVE TESTS - 32 I.
,,~_,...
(·)~L
'.1 ......
(0) ..., .... ....... ~IO .... _DlIhat ..........
__ 1 I. _ \\'hid>oI'lbcfol..,..'UlIiI_ ....... m-of
( 0' ~·...... 0JIIII ... 1Dmap (h)
...
•
(/:0) ....... '"
(e, """'" (d) frequoB 2.1.
1209
(1)) 64Q
(d) 100 ...... form portion .. the frequrncy (~) boIh ond kVA IallIIJ on: n:du«d IJI lIM: ...,... 1" rupp 1-) "-'!be_1DI«fUaUY
..... f"""",,,,,,,-io k i""",_ voIu&< I, i""",O>«!
(b) ~
Irl """'IJ i......ff
Transformer: Three Phase
1213
in the thinl~. This impro,'Od ....ign i, shown in Fig. 33.2 (a) whert donod ~ iDdicale the three windings and numbers in the cores and yoles represent the dirt 33.2. Thlee -phose Tlonl/olmel Coonectlons lbere an: voriou. mclboch I"ailable for I/'an,formin, 3_pha!e voll.,~, 10 higller or 10",.." 3-pIwe voltages i.,. for hindi,,,, a ron.'I ~ - Y 1~1 pm-dcI'. or V-V Scaoe ongIooo. ",.
""'~ ""*" ~- .. •"" '....,. ............( . IO~)
""'Y
......... ",·ell .. primary '-ol"'g'Orlo. sdis/MI"';IJ 0111-, ifllt, I,..t is fN,1o"wL With ~ unboL.nc:ul
,
, -h:t"r-~ "
Ioo """u-al
_1Ibo\..,.
"node,
T."nlll ormer : Thr .... Phase
1215
pr;>C1icall}' reduced to zero ... boreas 1:.-,.,. ar.l Eo< w ill rISe 10 nearly full pri"''''y I,,,,, voltage. This dI ffIC'Ully of shining (or floating) I'IMnIl CllIl be obviaIal by COIII>OCIin,lOI"ne"""I, lhen this provide< II ""'" for lhe mple-freq ... ""y currents and o.m.f •. and Ihe diffkulty is'lCfCO/l1e, Another way of avoiding thi' trouble of oocillaling """trnl is 10 prov;dc each of the Inil\Sf<Jl"lTCl"S "ith a third or teniary winding of ",latively low kVA rmng, Th; , l TIM: Ih""" j>hose "oftag~ rem.in pr:>Cticafly constant regardle" of load imbal"""".
J. An added ad.anlage "f thi. mnncction i, that if one t"""forrt'lct bee"",.. d".bled. the 'ySlcm can con,in"" to operate in open .delt. or in V - V although with redLlttd availablo capac'ly. llIc redu,cd capacilY is 58% and "'" 66-1% of the n""",,1 "aioc, ... nplaiocd in An. 33.7.
1216
Electrical TechnolOllY
, •
+ •
•
" A.
•
•
,
•
•
• •
,
,
•
• --+
A
• •
•
,
.
•
A
•
1
A
•»• c
I
•
., • '
IT .......... ~ Ag.lU
FIg. 33.1
33.5. Wyej o.na or Y/ 6. Connection
",11= ....
The nwn_fAtIus.......roon;" 01 .... sul¥.wion end of!hc1l'arlSlniwon I;"" voltage;,,1e> be >Ieppcd down. The primarywindinl U Y-conncacd willi gn>WIIied neunl OS IIIown in Fig.. J}.6. The
vol.
...., beI"ftfI .... oecoodaryalKl primary I.... is If Ji urnes .... lnIISI'onnation nocioof each iranifomICf ~ ;.1 JO" IIuft beNo'Ufl .... pnmary and --wy line..oo.,cs ..'IIicII ......... tIw I Y- A ...... r.......",.bank, twuI<JI be poraJleled "-lIhtllher. Y- Y d.uyvoltagelplu>tJd k>u if I~ tW /t»s ",51) lW 11w /mpMmoce drop atfol/·/oatl i. 7'Jh. Calc,,/ale 1M pnm{uy W1ImJr ,.·lItn a load of 1.200 lW al 0.8 pJ. is drll>"tl'td al 1J tv.
tJNf a",II.1oad
~ullon .
"-
Full load
Inlrrcr (/ag)! Il:am. T~-II,~brpdbl·.n. 1991)
Ira.
~n
m,..'
ord.,
SoIulloa. """,,,nll,e "'gulalion
_v,,,.,.. +>'."ID.
-
1220
Eleclncal Technology
• 1 x 0.8 + 6 xO.6 . 4.4% Induced ~ •. m.f. (line "alut) .4.800+ U%of4.800 _ 5.0IOV. ~ in Fill. 33.9, ~ phase vollage
LI_ __
-S.01OIJj .. 2.890V TransfOf'll1llOOn raOO K .. 2.89G16.6OO _ 0.437.
Fig. 33.1
Eumpk 33.9. A 21XlO-!VII., 6,6001400-1'; J·pllas~ transfomu:, is deIlQ·c()llR~cl~d "" 'M ~igh aJtJ J/tIN:OI1NN:ted "" 1M low·,'oliage Jid•. lklefmi", it> % " ..'SkJnC~ aJtJ % "'Ui~ /anN' drop., % effici~fICJ and % "g~/lIIion ()f! foil lood 0.8 p,f. leading give" 1M follov.'tng data, S.c. len; H. V. daul : 400 V. 175 A and 17 kW O.c. I.,,; L V. kta __ 400 I'; 150 A and }5 !W valtag~ .id.
SIll"!!,,... From S.C.leSl < 0,8-6xO.6 _ ~2 . 92%
Full·load primary line currenl ean be found from ,/3>< L(O);/, . 175A It """". Ihal S.c. rest ha. been carried 001 wxIer fuJI-load condilions. ~ 17. 15~32 kW; F.l...oulpowninFig.33. 10
T. we
'.
O_OI~ ~ O.O I ~
L. 71,j1," ohm
0
0.01» • j
I..
0
0.012 .. j0.030.0.0323 L.68.2"ohm
Z. + l .
0
o.oI1 . j~5Ko.0481
I. I.
0
~
0
Jc< 1312 L.-3O"
Z. + Z. 88.1L. - 31.1 "
0
Z, +Z • .. 43. 1 L.-2:7.7~
.. 3><S81 x Ur'.671.J kVA
1222
Electrical Technology
PoW .... fOC10 ;nl • "''''''''''n«:tro devprnl 969.8 kW at • rower of 0.9 1'""'5.nd an .ffic;'n 11,fj .. 57.7% ( ... ocarty 58%) in""ador per <enl con be p"wed ., follow.:
,-
•
i.,.. -'"
661
1223 M Ottn fTOm Fig. 33.12 (0)
,., - "'c.pacily"
J3. V• . 1, .. J3. V, (.13 J$)" )VLls
In MI. 33. 12 (1)). il is otn·ious!hal when'" - ,., bank becomes V - Vbant.. the secondary lin< cu"",nl I. ~ oqu.oJ 10 the _ondary phase curren' I.. V-VCapai'ltya .J3.V,I... ,fjV•. I.
.... is ~7.7 pc.. in .... - ,., bank "'" dolivmng their mlW loat!' .00 one """"former is .. moved. the overload on «ri of tl..-Iwo """';";"g """"f""""'" is 13.2% ~ lot.olbod in V-V VAItran;formcr
..
.J3. V.IJ
..
.fj .. 1.732
V,I.
o.~r·load
l1\liy be Cltl1ied lemporarily hUI """'" pro'·;,ion m,1S! be m;,ok 10 reduce the load If ",·.theal"'1 and COrtSe<jt>Cnl brul:idcd. The disadvantage< of this "",,""'-"'.ion ..., : Thi .
,...·rr
Tht a...,.,. P'l""«' f....."."" "bidt the V·ban>; """""'" is """ than \hal de theload. lJtif AOOIher ,ignificanl ]XlinllO no\e ;. IhOl, .xcept for a balanced unlly]Xl""'" farlor load. lhc two InUlSformers in !he V - Vbanlr. operalo at iliff.....,nl PO""" fac1Or\ (An. 33.&). 1. Sttondary tnml ...... ""II.OIC' "'00 1(> kct>mo unboJonced lO a ""alo~"'n' ,.·hen lhe k>atl is in, IY. """,,'·cr. be noccd!hal ifl""O""""f"""",,..., operuing in V - V.oo lOIded to nuod ..-.paci\)"
I
IUlfiI"" fM:laaII. 86.6"'" "Iliu """'ocu I6DtI ptJ""T11Il:l·ee ..... nplc. !O !7.nVA). lhcaddilion of. third Iral\Sfonncr itrrcase:s lhc tol.al caradty by .J3 or 113.2'J. (I.~. !O)O kVA). It mean< !hal f.... an i .....~ in (oot of!i(l'l, f.... 1lx. third lr.lru.f.forrner .. n.J . H~" kVA tatinw'nal.formn20 ~by_h-"f""""",
Qb.ioosly. in tlw ase. eacb tnrufOfTllel";" overloaded \0 theutenl of 1~..5 perce ... • liii] kVA ruti"l of the V _ V burk _ (2 >< 20) w 0.866 • 3-4.6--1 k\\ V - V
4
•
IIII~1i '" 34 .64 ~ o.~n or S1.1'l1>
4 "'''nl
60
O>-..Ioodi.., _ _ _ 73.M- onl~ wtle. f\lll .-....J Iood .. ouppIiod b)' the 4 - III _ III
thd ....]tlekn
i I _ V _ V"""" .
a~.
3 " l!O . 60 l VA
Tranl /ormer: Thr":':"'::: "-= _ c'e2e2e', -__ M
lUll, tilt
nlin& is redua:I il ,lit ("I iVA Iupplkd by wch ,'"""",,""'" , (b) i W luppliu by wch 1""4/0,,",,' ~ (EftL \ 11dIinr;...1. {;waIier Lnh . 1'.1911
1226
Electrical Technology
Solutio... A, ,tared in An 33.7. the ratio of optraling capacity 10 .,.. H.ble capacilY in an optn-~ is 0.866. Hence. ~VA of each transformer is one-half of the total kVA load divided byO.866. -
(40012) 0.866 _ 2]\1;.\\
Ibl As slaled in An 33.8. lhe Iwo lramformers haye power faclors of res (30 0 -
+) and
C'aIeno. I 1M ....... I/'aII>fOflllCl"s roil< 1I'ori;ma _ 86.6 per a:nl of thoir kVA rum,.. Iknee the capacity 10 rallnl ratio in a T-T. connection i~ 86.611>the;ame15in V - V oonncd 10 ..........dablt _Id be 0.928 ",ilidt rnakt:s JIIg.31'S thl. S !be 0Iber half as ,I>oW" in Fig. 33.14 (/». HellCC. when a balanced load of 1'.1. _ cos i, .""Iied. the teaser eulTtnt will la, or leoo the v01toge by < 5.77 >< 10-' ..
TeaserkVA
• 0.866 >< main kVA.O.866>< 19 .. 1fi.4k'"'"
33. 10. Three-phose 10 Two -pOose Conversion and vlca -verso
'0
Thi. con ......;on i< rnq";rod .... uppiy two-pIwe fumaces. link lwo-~circuit wilb J-phase system or
"• ,
A
, ,"
- ,,
I,.
,~
• I,.
•
I•
•
)
. 11:
'
" ~
" ~
,
, •. ,
,
'~
".
t V"
A
,
~
•
r,"'• ,, , ,
(.,
PrillW)l
,
In
, ,
W
-
• '.•
I.
1"
above. "'" number of lurn. between A ond D should be .Is (.fj 12) H, for makin! vollliurn the ume in boIh primaries. If so, then for secondaries having equal tums, the seoondary lerminal voltages will be eqIUIl in magnitude aJthough in phase qullodtlltu..,.
1230
eleclr~1
Tec:hnology
"'at
II is to be noo:d poi"' 0 i. naI the netltral point 0( the prinwy ouppIY bei;ause itS voltage WIth resp«:I !O lilly linc i. "'" V l,fi LeI Nbc the .... .,traI poi"" fl. position can bedrtrnninod as follow""1 .... (i)
~.
I",
!he «as oM Jlry bas Jj 12 time, the turnS of main primary. Hut voItItum is tt.; same. 11>oirsecoodaries ba,'e the same 111m, whid resul" in oquaJ >ooondary taminaI voltage. . 1. If main primary has N, turns and moin secondary hasN, turru. then main trarulfOfTflalOon rntio i. NIN, . Ho""ver.the trnn,fOfTTl3lion ndinof,oaseris
N/(JjN,12) ~ I.I~N!N, _ Ll~K
J.
If the load i. balanced Oil """ sidJIC«I oollleoO....- .ide lIS well.
~.
Under baI~ load cooilition,. main trnl"former l1IIi ng is 1~% grt:Iterthan that of the te.... ,. 11>0 cum:nl>;n eitherofthe two halv,", of main primary are !he ,"OCtonum of K/lM and O..~8 XI"
3,
,
lorl'IT)' E~.,nplt 33.111. 71. 1f
secondary tum, primary lnmS
~
(,fj 12 ~ 44(1)
-
;~- 1..!o5
_ 38 1 V : Secondary volts ~ 200 V (aJsoteaser" lio ..
1.I5)(lfl.2~1I1.905)
b~m"'" J3.1~. Th"Q .• jnSk·pho.. junwcu wo'*ing 01 / 00 V aFt < 3.000 .. I ~I A ar>d O.~8 KI, -
NOW.
-i
I, r "
17~ .312 _ K7.1 A
I, .. _ J151'.lfIr .. INJ·\
.:uml* 33.:0.
I~ ~ SCOI/-CO""..Cf...... ca/cwlole t1w: ""I"", ofli"'l Cltn-e",", on lite J·p/l(lu .id~ loads on 1M l·pItau sid~ ~~ .IOOtW tutd 450 tW both.., 100 V tutdO.707 pJ (10,) «Ontr i •• fI~. <me
Ihl
_ 72.7 A (il)
In.l
1+
1"
lor _ 32.512 a26.25A
26.U' .. 77.1 A
3-phase ~DC carries 52.5 A whereas theO!her2cany n. 1 A each [Fig. 33.27 (all.
O _~p .r.
Wi'" ...f....nee to Fig. 33.27 (bj we have I,... SOO.(J(J(J,I8()" O..'l .. 12.500 A Tea>l!.. CDI\lIeClion! IJId veclor diagramnJ"e 5110,,·" in Fig. 33.28. X .. .w4,600 .. 1""2: 12T .. ~XO.8 .. 5'OOOA l, T" I.I ~XI,..t.lx{lm)xS.OOO _ 62.SA
,I
1,,-62.5 A
l.. _ :I(KX)A
~
..., I.... IOOA C~ ·
,
~l 0
\.:; .. 3100kW
,.,
T ----,
""
J
-
Oi
~
c ,id/: d"itr IS 60fMJ .,.j i, il ,he same 'or \he (I>, The voI,_""", 131inl of!he ICUer p",nary ,.. .....,U as SCO':IIIdaty iuhe oame i.~. 601'< 2SO"
"'......-lrlUISf""""'. la-'
.. 69.3 )< 216."', 10-) .. 15 k\" TIle nlain ~oI"'lIlpel't ratinB of IOCOIId4ry i, .. 250" 69.3" 10' J .. 1L l k\'" ("""ltnlally. if ,,..0> wnlical Ir.J.nsfonncrs art usro fo.- I" _ : 51.5 " , 11.2: 7I.l Al l n .... ritooI ~_L AI ..... ' L'lI;''OniI)'. l m l ~
33.11 . PorOllltl Operation 0' 3·phOM Transformer. All tho: roodilions wbicb oppIy 10 Lhe palallcl operation 0( ,inale.pNuo tran II>< paral"'ll\IlIJIini 0( 3..p.a...: mons'''''''"'' boll ,,;!h the follovoins addition, : I. "The ........ """" II"JIIU ...cO~~ O.7611ot;g1ng.
ElItmple 3.'.27. Stair (i) Ih~ <su"tial WId (il) 1M Mslrtlble conJ;'iOllS '0 /,., 'aI;sfi~ .0 thai two J.pIr.a .. I"",",/Cf"m(!'" ""'y cl,ume 'lICuss/ully In po",lIeL II 2.<XJQ·tVA ITGJU/oTm€r (AI I. c<mrlath orr a.r /01/"",. : Trans/orme, II re.i.I/1lK" 2% ."ac"'"« S % Trall./o,ma 8 re.isuma 1.6 %.,-,,='aIIU 3 % ([~ r--A«i,...,rilll/.· II, Bt>rnba) Unh. 1987\
"-''''''''1Il!
So/urlon. On the basis of 4.o:xl ~VA 'lo Z. a (4.C0Y2.o:xl)(2 . j8)m(4+)16) _ 16_5L76" ',. 7.. _ (1.6+ j3): %ZA + %Z._(5.6+jI6)E 19.8 L73.6" S ., S,oo) L - )6,9" ",(41XX1-)3,00)) S ZA "" 16.5 L76' Now S. · Z.. +Z. 75.o:xlL-3(i.~ "'19.8L73.6' E
Example li.n. T"", J·phan tNHUjom• mod B /Ia"" g I~ _ ftt>·/ood /,,.., VQ/t(Jg~ ""ie J,J()(jIJOIJ- V '",'ply n load of 7JO lVA '" 0.707 laggUlg w/",n o(H'rUling in pneot 10. wallIOClcr. Whik conrro'armooocs (b) p.... g< of unb.lo"".d Cu ...... ,. due '"
---
\e) provi>ioa of rlual .Ioctric ...... "'" (rTeCl i. (al t "'n> form~" must hove equol ,oll.ge OIling>
Cb) tr.>nsl'ornten
mwI]ul'< II1II>e
ratio of ...... _
,~
(el """"fcm>i08 the 'I"'no"" from • iccl flY poly phaS «nd.vy. _ mJ.
Ie) iocreueinltOll-. (d) 0110£0.:_ ...
w;1I roo
coo,......"" ?
ANSWERS I. e
2. " 3. a 4.c 5. < 6. b 7. b 8. b
' .J
'O. b 1I. J 12. c l3. lI '~. b 15. J
'''.J
CHAPTER
learning Objectives
INDUCTION MOTOR
.. Classification 01 AC Motors .. Induction Motor: General Principal .. Construction .. Phase-wound Rotc( ,... MOlhemol\cal Proof ,... Relation between Torque
Rolo< Power Foelor ,.. Condition lor Moxlrnum ",""'~ Torque
,.. Rot or E,M.f Clnd '~:~''''''''. under Running CondItIons
,..
Cond~1on
IOf Maximum
;o,"~
Under Running Conditions ,... Rotor Torque and Breakdown Torque ,.. Refollon between Torque Sj ip ,.. Fui-Iood Torque and Maximum Torque
,.. Starting To I.
!Ia,-.
c.
rc""',
...s FiEGAROS THEIR PII1NCIPlE OF OPt:RATlON (AI
~~hronous ",..h >n
(I) plain and (ii) &IIprr( II ) AS)' ...... n ....>USIIlOIon
I"
Indotellpo, mol"...
" 0., u,"" Q8C {'ingle double
I" ....
Slip-rin, (tx!mlal res1SlanCe) ,/.. 1.:_ _ __
(iii) shun'
{=,~ted
{~~~SOIl'd
1;'1 IqIUl,ion
I~) n:pulsioo'lJ\Ar\ ind.... ,""
A5 REGARDS THE TYPE OF CURRENT iii .'n~k: phase (ii) tJu« phase J. AS REGAROS THEIR SPEED 2.
ron.laln.peed
(l1
liil variable.peed
• . AS REGARDS THEIR STRUCTURAL FtAruIlES Iii open Ih'l ventilated
,..--
hi) enclosed I•• pipe-V~"'i1alffi
..;;;:-i
liii) ICmi-Cioo;ed (n)
riv'"M frame eye etc.
34.2. Induction Molol ; Genelot Principle A. I gcoenl rule. convernon of cl«:lrical po\"..-lou> mocban;"al IX"'"" lUes pl~ in the f'OWi_/t pat of an eltt!ric tnCIItO". In d.c. moIon.lhe cloctrio pawn is = an: redll""!. h has I reasonably good power faclor.
~.
II reqllires minimum of mainlenance. S. U ,tart.< "l' fl"Qrn ,.,,1 and ",,0l Slartini moIor and has OO1!O be ,ynchroni..:d. lIS ."mini amlllgemem i •• imple especially fr 5q1l;m:J..cage Iyp< motor. f:.;..J.,mboJles; I. lis speed cannot. be vBl"le..l without ...mlking some of ilS e{f,dellC}'.
1. 3.
JU'I lik ad.c. shunl mOlor. its speed deere.... wilh increase in load. lIS ,wring 10na "'" 01 1"IiGf1~ ~ """"'" _ . ICoun8sy GauIam EIecUic """""'"l
....
fig. :1< number Qf pole. P. pn>dIroced in 1h< rotaUni r",k) i. p _ 'bI wh. TIl< rotoo-" wound fa< '" mony poles as the number of ","",- pol~. and i. alway. woond 3-ph. se eyen . ·It." 'M SIa/'" iI .. o~"d r>r'o.p/tas. TIl< th== pru..c.lre stafmi inlemally. TIl< othtrth= winding Icnninal, an: broughl OIl' lind ""'''''''''led 10 three in,ulaled .Iip-rings ",oonted on the ,hafl wilh brushes ""'li"3 on \hem [Fig. 34.5 (b) [. The5e Ihree bru,h", ar~ furlher '~Iem.lly coonceled 10 a 3-phase 'Iarcaring ,1".1da (II) fon 1.1 venlil:uoon crill \1l l<mlinat bon {,fl .hp-rinp (III bnu/>o. and bnJsII Io.>Iden..
FIg. ".'
Ie!
34.6. PJoduetlon of Rotating Field II w,1I now be shown -pe, ~ 4>_',fi and i, pOSili"e, 4>, • 4>_',fi bm is still nego1iw_ 1l>cir ""ulllml, as sbown in FiB_ 34, 10 (i,1. is 4>,~
(r)
WlI,
E
H.""".
E
¢I./,fi and is posili-.. 4>,
~ ¢I_',fi and i. also posili,' •. TIle resullanl ¢I,. ¢I~ and "," ftuthe.shifl,' +,'
': .. (...io awl' .. 1...in (;' (";n '
(!)/ ..
COf' (III) ..
¢I!
34.7. Thr_-phose Supply II ...ill now be.". ""2
,
0f),"O.
.Ji of). ¢>'--T
c"" be .,am pm\'Ctllhal of). - "2 ¢I...
So. the .......1...11 i• 6O'WIJ. 34 14('iil].
.,atn of
the »In< val"". bu,lIas fWlller rowed clockwise 'hrough "" ""Sle of
1252
EIectTk:alTeclmology
- e resultant is and has roIaltd dockw;", 'hrough an additioo.1 ,ngle fiO" or through In IIlgJo of 180" from tbt stan. Hcn<e. we conclude that the ",.wI ..nt n"" i. of COO,""" value ~
't)
t"''' i.e. J.5 l;m~.II'r mnximultt I'QI~~ oflll~flux
du. Q":I plu..~. 2. ,lie ".~IIQIIl fI= rohlln W"OuNi th~ , fUll)#" fit SJ~c"rrm"u. spud 1/;"011 b, N, .. no pI'. Fig. J4.I~ (a) ,110"" the graph of ,he roIJIting nux ;n. ,Imrie w.y. As bef."..,.,be P ".,.. d,ff.",nce bt-tw~n the ,ynchrooous speed N, and the actual.peed N of the rotor is known as "ip. Thoogh it may be e'pre'J>I' I
'm: I ...qu~ttq of ,he '1)101' ~~"'nlJ ,,' s,,,ntlsllll. I FJoaricaJ Madlinrry U: D.onclt>n' UniT. 199 1I
""' .. lion. (i l Stator r,dd ",vol,'eo.' ,)nehrorx:..u speed. gtve" by N, _ 12Oj'I'_I20"30/~ _ 1500r.p.m.
(ul rotOf (Ill" motor) ,pee • _ 1.
r - s/-lx/-I .. 5Q II ..
EUJl1pie -"'.4. It J .. i""II('I;{}II IIIOIor tJ wo"nd JOT 4 po/~s and is "'I'f'/iedlrom 5O-Ih $),OO - 600){I.'iO{bO.6 "~(H'UIT€nt """,!lCTlptanl.
The effecl "frotor power foetor"" mln,- k~4"" is ill u,lratcd in Fig. 34, 17 and Fi~. j.j. 18 for values of .,. From the abov~ "pre,,",ion fn< torque. i, i, de." thai as ~, incre:""", (and Ir10< ronJLIh.se al ." ..,dtlill:
R, ..
1llIOf.w~
Xl .. rulQ.- tt3lill
£
;
C lhe culKm-ge V .... " "",,ve IIftn In Aft. 34.11 th.d T.. • ..
T. -
, , X', H'. , t,v II, kjVtl ,5..
R, + X,
""'here',i.yo,.",,,hcrcO/U.an.
. .!
Henee1 ,,~v
/.,
Ckar1Y"he 'ORI"" is very ",,,,i,ive 10 any eMn," in lhe supply voIllIge. A ch.n.. 0(5 pcr ""III in I~ ill tho: ..... """"'. This r.., iSoi
""" ....h.n«1ion. ""mary pIYM voIlaf:e os \I>O of J.8 , r
K_ IIl.B. Rocor phuc voIlage at OWIdslilioo 1100" III 8 • Z89_5V h i II""" impcdenc< 289~ • U.!III V; I... 11.5lW.oI S6. 7~l...' ~ pJ. .. O.orroOIS6 dL17 I, • IIIK .. 100 x 3.~ .. 380 ... ; E, a1 ~la11< 10 . 1.130;X, . (3.6) x 1.13 .. 1-4.70
Electrk:.aITechnology
1260
'.. (R,I' + (X,')' , Now.
N,
~
,
• _,_ •
30001 3 .. 117A A (1,3)' + (14.7)'
l2(lx5{V6 .. IIXX),pm_(5oW3)rps
V'R,'
..
211N, . (R,')' + IX ,')'
X {30CMJlJj)'XI J .. ~ I JN. n' (13' + 147')
) 1~(5013)
TUtorial Problem No. 34. \ I.
10 the c... of IU, Ij.-poIe j""",,,jon moo::.-. the: ""wiy f~ r·r m, W"t weIOC100 •
110.67 ~.
j\., '..l7~
l 1.95 ", IIJOJI
OI>.in .. .lIp ond ( .. , 10rque < of. 4.p!!be ....... "" ~ of the sutor ... ppI) freq",,"cy. , ..... ,." "" <J{ •. I1I.f. indUCN In lhe tOtor at ""," d.un is ",.~imuon because lIx: n:1 .. iH speed bel"""'" Ibe rol\lI" and lhe ,-e,ol\.-in, !Ullor nux Is maximum, In f..:t. Ibe nlOl()1' i.~u,,'alcnt 10 a 3.pha", lrarufootlCl" "'''h 0 dlOlt- • if R, i, con,lam.
Hene". for In .. value. o f .Iip. the
1rquo/,lip Cur", "appruxtmal"ly K "nigh' line 1\, .lip increas •• (fnr
~
!
",
,.
./
,
•,•
j
-~
.. ..,,
\
,
•
+ - Slip
,.
-,
tnct'tlO>ing load Ott the motor).the lorque , c oJ", Increase, at>r large "alues chlip
"
T
~
(,:,)'
"'
"'
•••
~~
Ilo""e. !lie 1""4""',lIp curve i. a n:clllngular hYl"'rbola. So. WP "'. thaI "y<md 10. poinl of m"",mum !Onj'IC. any further Ule.""", in moIor load results in &':."ase of lorque rIe""I"I""l by to. moIo'idaJ itS tt:m1inal volage i. rcdllCed .0 ~16 (i ~. 8O'lI.) of (ts name-pll,e
»H.t.
ope"".'
",,>«I
",,,n,.
34.25. Ful-Iood ~
T~
«Id Maximum Torque
'/ be Lbr ,lop COfl'C'pondinB 10 full-Ioood 1Orq.... 1he" _.Art14.l0
.!L
T· -
"'here,, ..
•
2' f R,IX, I
(R,/X:) ....
~-
~/j
i "+J,
R/X," ,,,,,i".. ncei.,,,,;dSlili "'IC'~
1266
ElectriealTechnology
..
.""
A J .. /IJdutIJtM _ f I II,M",fi;JJ,/INIJ WflIII' wIIJdt II ~ 11/
Eumpl~. 34.13(_).
Ipttd.
q lIN wHfIII'dtopl /(I m hi IN rtNIli WliIll, jINi "" f1Krt_ M/flOW","" flHl'f
SoIullon. M _
r_ Nt, '" n,_NIl THMJlI'' ''.'''\II,.Jj v/ -'I III
7, - (~r -hM _13'
.
",*(_MJ4..I4I,/J _ ,N /,
!i,.J4j . IJ III"hl,ll1 IJ Ij I
,.,.., C. ~",. ...wIt' PI .ps; 'iMMI III 1/
• ~, ."M.,.n
/, 'flHlu mll
~~lIf 1M
II:! IiMtlllWjlUftlttll::iIWM ~qpu Me.: ....,
Eumpk..M.1l "'). A IXM"(I'JNJlM-.JIUIt. /HW lI/IIik.,imlllHlOfllMll6U111H11111I1K'III' IIiIIIJ IN NII#II/~, '6111 f'fIIMp 11/1(/ flIII# W WI/IIII 11M 11M • JPIi I( filii I'J'IIf Willi 'Jllt/Nt'r/IJ}fj, fMElIIw (I) . _ . 0fN1'NINIf IPIi 1/iN" II IJ 1M 11m, III tollllfllillli JIIw /1/ /fI1jW/Iff MIl (U) INIW /NIfNIf INMf, AHliN IIIIIHHII 18 flffllWr rllNlllM,
addili(>lani", rorq_ of IM~, COni ami a mtLTi", ..m 10rqIU. 0/200 ~r ernl offoll.rood torq.... o.,,~",,_ (i) foil. rood spHd (,I) spud m mO!3)' 0. 12' +(0. 14xO.&5)' .
] 211N.
f..' 2 X,
.~
,
n'
b: (!>OIl) . 2 x 0.&5 .. \19.9 N-m Specd~mgromallimumtorque.N.
IIXXI(I - 0.14). 860 111'"
II001 WIItop. Ih'foll·load "'" is J'J>. EJlimattlM p"rrmIllS' rtJOCI;"" in slaW' wlragt 10 thvt/op foll·I""'" tarq~ . al half Ji "- T \100 4lO
h~
900 IlSOl8Ollll5021OO
~
• s,...I(r.p.m.)
,~
'" •
, " 450 Ii
'"~
" ""
,.)
.\100 nSOl80022S021OO Spocd (r,p.m."
FIa. M .23
,
'"
del"'nW. 00 the .upply frequency. Now. Jet'" .... whot happen, "'hen bOlIt st.to< voltage alld freqllt...,y art changed. In J>'*1.i"'" IUpply --olt:g< and freq~' an'c varied in tbt: ........ proprfi"" in ordcrlO rrwnl:un • COft'itanl nux In Watt.,,,,,. For uarnpic. if volt:t.ge is dooblt of I ZOO '1"", If Ihr ,ralor supply /rrqurttq is rraur,d bJ ""If ClJlr~h",
la) ,'''' .rarar '""ply voimge rrqu;r~a for ""'i""';~i~K Ih, """" fl .... in the ;"""hi~r. (bJ .~,d m .. lorqld of 100 N·m.
I"" .....·
»(liutioa. ' 1 Syrn:hrooou. speed 01 50 Hz frNJ""""Y _ 120)( SlY4 a 1500 rpnt Hc ....·~, ,lip ~ for. 1<Jfq"""" 100 N·m _ 1.'iOO - 1200 _ ]((hprn. N"". syncbronou, '[>COd.., 25 H, z L5OlV2 z 7SO rpm. s,""" .1ip-.JIO!'d I1b to be lbe ... me f",. tbc \lin .. """"" Un:spe along lb •• pttJ a,t.. Suppose thaI "ollage and f""lt"'''''y are redl>Cc;r previoos value. i.~. to 110 V. 15 900 iiSO 1800 22j() 2700 Hz ",spee ro:mail"""" sarno in Eq. (.)
of An. 34.30 ex..-epllhe slip and voltage. henee
S, .. SI(V,/V,J' .. O.Oj X (~50J'.O.032
... Ar\.34.23
N, .. 12OO(1-O.032) _ 1I61.6rpnL ~'JW J..I.25. A 450. V. 6/J.lh 8-Pal~. i-pilau inJlI0 terminal ,ohage llICreIoSeS w,th capacilJ1J""'. If capacitance is in,uflieient. the generator ,ol'age will "'" build up. H.~. capacitor bank must be large ellOUgh to ,upply the ... active power DonnaJly drawn by the mol",.
loW''''
F..""mpie .J.l.26. A 44().1( 4_""'•. 1470 rpm. JO-kW, J -pMs, i'l1;''8 a j,.q_ncy 0/ 5() I/:Solu tion.
m
s
~ ,ffYI EI.73>(440)(40K30AkVA
1276 P. SCOf •• 30.4",O.83 Q • 1iliU""""'uoa. ~iDd the """'.......-,..... IlL< modu"",,, (,,11M ...-.",,11 ..',Il> Wj>-nnS' p ..... ((I • ~ ......,.. "'IIl> . .."......., oll[l pc< . - """ "",I " ,bIe ..> ., r.t:mduill wbe. ronn«."!NI to iu nonnaI "'Wi Y ,o""gll (d) _ "ondsllil WIth the """""" tn the o;m,,' (bl ... "". the . 1Ip-ring.< < (e) tho addiliooutl _ ~ "'luirul to Jivc muimum 1Orq"" ..... OO>Iill
CIIJU.' ..
=
"""co" ....
W.
[(~,
100
",.,ot""""
' ·m(tl 0.82 «I I .• 0111:'1",,-
MMItI~", ·II.
Y/t", .. t ·.....
LJiIIi~
19711
6 . A SO-IU. 8.pok 100ucti00 m0 . Iip-nl\jl' ~ It) • ""i"",",~ of 0 .2 n per phos< _ " " '10""80 botwooon 'Iip-ri,,&, i. 200 vlm. to tbe rotor eum:n' per pi\»< v.hm II>< .Iip i, 5~. II>< =i>wtcc bc"'a: "ill in cm:ui,. (1t.1 A I ,I. 3-"""",,, 50-11' i"-'oction mi<w>ce PO' p/mi< i. 8 0 ond oJ", .... fOIOf runn,". wi!.b .lip-"". """', ."""ilOd, .... rJ,p be,"Il ] PO' oxnC Ilo'.5 ,\ , •. 0 ,\ I 14, In . =wn s.p>Ie. SO-H" machi .., .... fOIOf ~ pe' phast i, 0.(1.1 n ond .... maximum I«'qU< oa:un at "1'«osc. SO-Ih induduction moeor whethe, squi""lermW>od. oome!ime employM. is .. follows , A I%g( fLu ..arch coil of many twru is pIacftl "",,","ily _gains! tho".... pbIC "" lhe oon-dri ving end of tho mowr, Quite oCtrn. il i. pos.'liblc 10 pick "psutliciefl! ,'ollage by induclion from lilt leakage fluxes!O DIuin. te3dingon!llt milhollme"". Obvion,ly .• large SO-IIz voltage will aI. ''''0 "0',-"& lIlRIlIO T. ",," to I/'OIS rotor ""1JlII11'.. (Fi& 3-1.38). lIS volueeon be c. pressed e"lter ,n terms of rotor i"p,n P, III rotor """'" 0011"" a 18 given below.
, ,
T .. !l. .. ...:..L.. • 01, 2!1:N,
r
___ in!rml.S of ""',.- input
Induction Motor
,
,
M""" inpo>< in SUtor, P,
,tatoo: Cu ond iroo """(Pa&P)
1281
,
_inp.IIP, ("i, oi,· p r )
, . , ..
_Cu ....
mec < ,'K'EfR: ,,1= 3s K'§'R, Ri +(.x ,)' S R; +(IX,l
'.
•
-1L _~,~ "
~
•
2lfN, _,_
2~Ns
27f.N, s
s
~
G R,
Ri+(sXi
K'E1' R:
" R,+(.X,J,
-
in lerm, m Il,
-intermsofl!',
Here. E,. E, . R, and X, "'JIf"'senl p~ val ..,,,_ In fact. 3 Ifn ft N,_ ki. ~"'Itd IheconSla/lI ofllle given machine. l ie""",. the above 1""l"" ..
Mor input
AI>o. rot'" ootput
«2 ~N T
rotor input
N"".
..
r"'or Cu los. rotor input
3
f/ RI_
• rotor OIltput x H, I H
-- '"' - ,
kNTxN, IN .. kN, T
3/' It. • or ~ .. MOl input
o
k N,Tor T« I ,'R}.
34.41 . Analogy with a Mechanlcol Clutch We ha,..,...,n above that. rotorCu loss ... ~p x ruIO.- input
Thi, (:or, c.... he further clarified by considering the working of. mechanical clutch (though it is
1286
EieclricalTechnology
001 n.... n' to!:>: a proof for ,'''' obo,'e) >lmilar 10
!he""" ...ru1ll""lOOlObik". A pi ... dUlCh "sOOIon in Fig. 34.39. II i, obvioo' Iball"" lOrtjoc on tile ed by (riClion !:>:,ween ,be discs and it i, true ,,'Ilelhcrm.dmch i, ,Iipptng 0<S9.S7,23kW
rfJo SoIull,. . li lN, ~ 120 "jG'6. l00)IpIlI., '" (]OO-'I1~)l1 000 .. 0.02j Ot2.1% (I/) MOiOt Inplll 1',.040 kW _' 1lI1", k... _ I kW; ro< .... input P • oW - I _ 39 kW l
"'I""
.', IUID< CU IOSS_J" "".... . 0.025 x 39 .. O.9?! ],;\, Illil P", '" 1', - rulOr C~ I""" .. 39 - 0.97' _ 38.025 kW ]'_ KI' .. - frictronand Wln." ... rulallonal I"", ~ 100. 1.2. 101.2 kW 0 .018 x!O!.2~ I.855kW 1- , ~ 1- 0.QI8 rolOr input, 1', .. l'~ + l"OIar Cu I",... 101.2 + I .85~ m 103.055 kW S!4lOl" inpo." .. P, + 'latur Cn and i ll)ll I""",,! rolOrCulos . . . - ' - X l ' .
I')
W)
•
103.055 + 2.44 . 3.5 .. 108.995 kW
108.995 .. Jj )( 3:>(0)( I()( 0.85; The en,i", power flow in the rootar ;. given below. M«:han;~al
Motor output
input
power
100.IU)W
O.\0!i5W
developed
Sla'or inpu'
100.,995 W T
•
in rQtOI" 100.200 W
Slator Cu & 1I"0Il
Ro'ati""al los, ..
'''''W
10"0'
""'W
liii) F.L df",jency
100kW
_
IOO.00l'108.995~0.917or 9 1 .7"
t;nmplr 34.36. Tk< powu inpUI 10 Ih~ roloroj ~ 44() V. 5(J.Hz. 6· pok J ·pIrou induct;"" ..wlo, is 100 tw. Tk< rowr ,1~1"lromo/ iv, fore. i. oou""d '" m(1k-t 120 eyel" per minuu. Calcuku, I i) lhe .lip (ii) ,I\, mlor sPffd (iii) mechanical PO'''''' ihvdQ{Kd (i.) 1M rotor cop~' wss pn phau and (Elecf. EnJ/X. A' llETE !itt. A JUM 19911 (0) .~rd if.1 ' '>;>e. {iii roIO< Cu \OS, (its il"Oll los. being negligibly .mall)
Now. no-load Io;.s of an il>doct;"" mot", CQIl,i.ts on ;) , talor iron los, and (m mechanical losses ,,",vided we neglecl lhe ,",all amounl or ""lor Cu 10&.< ulXle, no-load rondi,i"". M(.r",:,,"e r. these two Iosse, "'" iodcptDdcnt or the load 00 the motar. no-load 1$. _ W,_ WR _ 3W~ W~ • W,I2 where W, i. the sWar iron loss and W" i. the roIO From Ill< dala given
",
• 0.12.
r~O_18
Total stalorcopper Lo!;s • 3 X 43 .3' X 0.]8.1012
• FIg. 34.40
WatlS
ThIaI input lo,Ullor • 45.(0) Waru; SUllo< "opper 1m. • 1012 W"IS. ,ta'o, C of '~ Input ,,, ,II. mlOF, lIJId m~chtmirull"..,s "',. 1 % r>f IN: j"l'm of ,'''' M,,' Calc~"'.. (I) rl,1' ~",I ""or J/~.d, fiiJ 10"1'" d ••,~ I aT,.
I;~~ c~"'m'
.........
-_-........ .... lnpul''' _
• J3 l~'" /0 1M 1200 W ~'hil< 1M rolaliOlU1I/".~,~. are 600 W. Find (i! 1M rola' COPl'N /oJ •• til) 1M ,ro•.' lO'qu~ d"",loP 34.4.1. A 6 .po l~, 5O-Hl. 1.ph=~. induct;"" motor I"Itaterootput
StatorCu and iron :. St.tor input ",'O'aIl c/lx."ie'Ilill ~.m.f. il'\d""ed in rotor, K£, • 23114 .. 57. 7j V (al Slip f"," """,imum lot"tI""'. s.. ~ R,IX, ~ 0.0 1/0.1 g 0.1 or
'_ . , "
IO~
-- , ~ 21r.N, 2X ,
N , .. 120x';(VoI-l5(()r.p.n. . .. 25'.p.s,
'"
'L , •
2.m; N .. ( I - 0.(4) x l.soo ~ 1440 I_p.rn. Oro;. 'rq"" ~".loped, T, _ 9.sS I'.IN. 955 x612{){1440. 40.6 "'_m 16 I For mnimum lOrtjuc, ' .... R, / X) .. 0.1/0.9 .. 1/9:and f.', _d,': .. 77.4" 119 . 8.6 V
L," JO,I' .o-(0,9x Il9 ») _ 0.14140;
',4.61O.1414 .. 60'&A
,
'1.0154 E O.974
(Iii . N, ~ '20" 5W4 _ 1500 •. p.m,: N _ 1.500 - (0_04 x 1.500, = 1.440 ',p.m , f.', " .F-. .. O'!)4xIIO~4AV;Z,~O.0154Q ... found ab,we I, ~ 4.4~lOI54 = 286 A lbIai rotorCu!"", _ 31,' R, = 3 x 286' x 0,015 ~ 3,650 W Now,
rotor Cu 10""
E
•
rotor gros. OIllput 1- s RotorgruoiSOU'pulP.. _ 3.650 x O.96t1104_87.600W
1fT, j, tho g'''''' torq ... """eloped by the rotor. then
T,"
9,55P_IN_9.35 x R7.6Oil'144O~ 581N_ln
• -">:lim"'" 34.#. The ~lfollinmi 10"lur of 3-plwsr. 6-poIr. 5O-H: i/ulucliOf1 moIor I, 162.84 N·",_ Th. roto' t."'. J. is obJuwd /0 mutt 90 ,,",'dn p. ~ mj~u"_ Colculm. r,,) moto, OUlput (I» Cu 103. in roWr r~J "",lOr inpUl ~nd (tI) _!Jici"rrry If ",,,,hanirolwrq_ los/ in ,..inOOg€ am} /rkliOtO is 20.36 N-m and Sl%, losu. aIY !lJO W. ( Eltd. Mllddnrs-II, [,..,....., Unh·. (9811)
SoIuliooo. N,_ 120 X:lO'6x 1.0c0 •. p.m. FnqllCncy of rotor •. m.f. _9G'60 .. 1.5 H~" - /Af .. I ..sJ.I{ance of tillancc per pb:I~ as .. fe....ed 10 1lI10I". If r, IS Lhoo ""1Or",.OiW>CC pcr pIwc.lhen 1
Suppooo _"",!be_in balf ii. _ renIIIYe 1>Ilf1be_ ,.,ndin''''',1h Ibe ra.WIlhalooly twO~ Nand SJ>IlIoo .... Id 10 run al 01I00>I 1:100 rpm. In ordor 10 pn:"ftII I0Il_-' Ibo: -.". ~ ~Id bo rNoId 10 half ito bea",.. Ibe_ .... "'indiroi basonly hIlflbeori&lnal ... mbcrof llImII. h is found tbc:oe cooditions. dIis hIlf.tnm< fla, _ produca I flu.> tha, ""'.-c. in. ~ I"", from 'IS """end 10 the:0Ibcr .,. linear .ynchrooous
II. A:lOOJ. V. Z4--poIc. »I~' J.r"'-...... ~ lIIIIuctiooo """'"' boo. 0.016 n """ ~II tU d 001'\""
"*'"' _
c.. _
cff"""""
Il10_ I',MW.1lJ5"l\!JnaowwlF~I.-"l.oj., 1"'1 I~ , A J. '.»Hz..!iOO-V. 6-poIe -..on - - f i.............. ofJ7.J kW 'Tho,........ r_ .. 0_116. fnttlc>aaI ......'.....,. ...... _ 1..-n kW, ...,.. _ _ '" U ~W Dna-nlI"" (i) line .......... f~llhc c.. """ for 1hn 1004.
."S._p.nL
""Of
1111 5LS-I JI hil ...... 'ilil UI.!8 kWI (Eln-1ri I
1300
ElectricalTechnoiogy
"" ho.J Wllb. sllp<Jl4 pet ~ and ""''''0""",,0>1 <Jl ~A". _ h&lasc (d the m«1..."cal """",. .... veloped and (d the """'" ~ po< pIo&sr if_cum", is 6(l A, [ 1_l t.IJ 1619711r.p.JIL 1, 1_ " loi\ 5l.l kWlr l 0. 167 D 1 _
...... that the ""'" •. m.f. _
.y".._
IL An ioduclion """"" " ",noon, .. ~ of tilt Ij>O0 ,,,'0. }k""". on ir.d"",i"", n>QtOr is • ....,"'illly olJanlil1S. 10 and I;. ll;s the laller "'hich is lransfotTed to ,lie rotor. bee.u", I. is used ,n mttbll! the Cu and iron I",SCll in the .. alor ;,«If. QuI of the appl;ed primal)' vohage V,. some is absorbed in the prinlacy ,,,,,If (_ I,Z,) .nd the ",m,,;ning El j, tra",ferred 10 ,he rotor, If 11K: angle between E t .nd I ,' i, ~. then ROlorinp"tiphase = E,I,'c",,: TQllIlrotor;npul_ 3E, /,'c,,"~ The .~tric'al in!",l kHhc rotOr which is wasted in the form of heat is
(or~3f.'R,) I, .. f;IK
,,31,E,cmo I,'
KI, E, _' i.·,
Now
... or
z
E, .. KI;1
E, _ sKE, ..
elcctrkal input ""aSlOO '" heat K
J" (/,' I K)".K E,
Now. rotorou'J>Ut _ _ (1 -.)
3E,I,' cos" ..
rotor outpui
row.. i"J>U' -
"c,,"" _3E,I', cos . " s _ roIor 1nJ>U1".
I",,~
m
JE, I; cos. - 31:.",1,' cos •
(1 -.) X I"OIor input
..
""orCu)oss _sx roto.inpul
""{)fillJ>U' ...-.ffocoency _ I ~ s ~
f! ~ N"
actual .peed .ynchrolloo, 'JlCCd
In the: same: "'''y. otherrelalioo similar'o those dcri.td in Art. ]4,)7 can be found.
34 .49. Equivalent Clfcull of the Rotor When motof is loadod.lhe rotor cwn:nll, "given by
"s
1302
Elec:trical Tec: hnology
,
J
E
1,- • Hi +tsX,)'J
'"'l(R".;'
+
x:]
From !he """"~ ~1'hOO 11 "PI""l'" IhaJ. Ih< roooo equatins the fm.tdcrivati", ,o,.,m.lf i, is donc:. i, will be found that 1
"ta.
R.. ..
Ru, l +
,
20, ..
leabgeirnpedmL"or
Xg, .. 2",
,
the motor "" referred to primary
ilL ..
z",
H"""". the psl mrqoo)
P,. I;'
T,.
31,
" " "
" "
A
', "
'.
• "
FIg. M55
p. -. 9.5S!... N-m 27I.N 100 N N, .. l300r.p.m.. N . S300(I - O.<W) _ 144(h,p.m.
",
1308
Electrical Technology
'. •
(or T,
•
nu,l"" power- •
\l.5~"
391160'14-10. Z6A 1'o·m
9.55.!l.. 89.55> .. .J3 x44()x57.4xO.875
O'3U75W T\ .. 1 -(4323138.275) .. 0887 no 1IIt7""
EDmplo J.LSII.. II 400 V. J,to "a'-C()nM("IN ",duelhllt nlO/OT"'" D,'ollN' ~xri"ng ,1I1(I'ttk1JIC"~ of (0.06 .. j0.2/ Q rmd an ~q~;..,/orl row, ~ 0/(0.06 • jO.l1) n N~gl«l"'8 •.wllllg ........111. fowl 1M "",-",mum Bros. 1'0"'1" <JnJ 1M 'lip '" ..-Itkh i, hase.
V, _ 400r,fjv ..
1~2,'IOO
Fig. lA.56
w.
"urnpl . J..l.59. A 115V, (j().Hl. J_pl", ... Y·C{m"~r'NI. (i'IIUI~ jmluajo~ mutor hM an ,quimkm T-circuit con,uling "I'I
Prirruu)' P'>",=inpul
0
,fj V,
••
Gro.c,dro::icr< 16.17xO.08
C~.~02) a )$'15\\
"The rest of the solutioo i, the ."".,. as abo,'e. E ....mp"" ~.60. 7"/U> m,
"
...
•
~~
,
,
"'"
· wn
"
'"
R'
"'- • JR~+(X,.x;)'
'.
.
' •
,
R'
,
,
.
JR'+(X + X')'
•
0,6
JO.4' + 2'
.. 0.290< .29%
1309
InducUon Molor
(iii) llle ",,!ui>olenIClJ'Cuil r".. one phase r".. • .tJpof 0.05 is .hown ,n Fig. 32.59 (bl.
I,'
~
BlI\(20+0A)+j2J _ 11.2 _ jl.l
I , .. 231I{10 + j5()_0.89 _ j 4.4
I , _ I. + I,' _ 12,0< values ore R,' . 1.2 n. x,' .. 1.5 Il. 1bo exduDlllnnch Iwi on impedance of (4 + J 40) ( l If slip "' S% find (,) <WTCnt (it) cff!Cirnc)' (ii,) pow... ractor (iv) OIItput. A>Sum< frKt""" k>M [e be 2S(l W. { (I) Ill! II Iii! ~I '" (/ii! iU! Ii.) 5 I J . A 1O liP. 4-10 VoI~ l -pIwe, 1O Il. Induction """'"" .... itlt ,tar~l«d
(e)
nugnetisingCUl""l.i", cunt'Ilt dr.o ..... by Irllmfo. m ... and indueu"" mOl"", IS the c.u .. or tlld, •••• _"' po...c, factor. (Q) urn (b) unity
,. -.
( 1'0.... App-ll. lMhI Unl •. J ... 19811
5. In. J-phos< itlduJ row ....
.l·,
')'r.cIYunu. 'Cloptd""'l"" .....,. ... It!< ....... iI
(oil N"
,,- A (>.pol1'"1 N, _ 1.nJ rpm and ruMina -."h • _ n.OoI (~) ,..oIv'" opw,hlf ,lie ..
IQ) 11 - . )
-
U . n-"
,.
(~), 1(>0
(cI~
r_ional , lop of on
~
indoctiool motor ;, ,II <eupply .,,1"1' mn,u", .",,<WII
(M ""'"
i"P"l
IIIIRIba 01 poko (J) both (aJ and (bl (e)
ANSWERS I . b 1. ~ 3. e ~. c ~. e 6. r 1. r • . a ' .d 111. (1) 1~(")14-I()(;;I)60(i'·)UOO II . b 11. .. l3. h 1". (1 15. (1 16. . 17. b II. b 19. (I)"""""~(i.liDCn~(jji) i""",.-.(ivliDCnaiC:I (,.j (l'l)applil
, ,
V
I .. I'
Z .. J(R 1 + X ')
, ... "nt ..
J(R' " X')
-Fig. 35.2
,
I .. (V/X) sin.
ft g. 3 5. 1 II i, lire "'Iualion uf. circle in poilU" co· ordinales. ,,·ilh diameler «JuaitO V/X Such a circle i. dra .... n in Fig. 35.3. u,ing tlle magnilotk uf "'" C\UTe1I1 and """.... fOClor anal< t as polar co- it Cuts lite , .."tical a:< as referred 10 primary (iL ,ta,or) 4. tOlal resistance m ,Ite moIor a, referred 10 primary. In tlJi,
"'st. the mint' is locker ,iving point C. TlIe di"""'!tr o'D is dr.tWJI pcrpcn· diculru-IO the ,olUlle ,'eclor.
.wo
,
As • malter of pnlClical rontinge""y. it ., =ommcndcd tho, ,he .$Calc of current vecton .It.ould be SO cbosen thol the dilttnC.cr i. more than 25 cm. in order thai lile da.a of lile ~or may be ",ad "'ilb ",,,,,,,,. able act uraoy from .he d rc Ie diagram. With centre C and nId, ..... CO'. the ciR:1e can be dno.wlI.' n.c Ii"" 0'" is
perf"""."""
.,. ,
'\l'II' IiIlC 0''' lohwld ""'~,ure = 14.9OOn~ 10 _ 4.~ em. FI>'- Ioo;:.(;n& f"II·IiId poinl P. 8.\ j, eXlcnJeJ. AS i. ~ «)llltl (,,4.ll em and SP i5 drawn parallel [Q OU{PUt line O'A PL;. P"'l"'nWcul ... {" OX Line clll'Knl .. OJ> _ 6cm = 6 x ~ ~ Jt A.• _ 3O"(by n>easWl:1nt"IS short·circuil currenl with normal voltage i.~. 52 A and meas""" ~m = 26 em. AB "'1J'f=nls OIllpol lioc. Perpendicular biseclOl" of AB is drawn 10 loc.t< Ii"".
Now, mOlor OIllpul .. 3,7)0 watt, It will be represented by a line "' 3,13&700 '" 5.33 em 11>0 OIl1pul point P C~.ure' lOWS _ 20cm. IE i, drown a' an angl~ "r 66.4"
or.
with or
liii) 0'/)" dfllwn parallel to OX. Ne;. tilt righl angle bj""'1I" of 0'A. Ii..) \\,111 C os the cen"" ... > 0'11
1324
Electrical Tachnology
(~ )
1M line ~~TU~I and po~'a facl'" for raJcd OUI,,~I (h ) Ih~ mta,mum 1()"Iu~. As,umt sl,lIor ami rolQr Cu IQu~J .qual at stand3lUI. IA.Co Macl!i ..... ·I, Jadupur
SoI",;"n.
Power faclo(
()< 100 >< 4.'5
~ cc>s- I (0,3503) = 69"30' Tbt '"pul eum:nI I",on ,non"fireu;1 if nonnaJ ,,,({age we", appliro = 45 (41 511 (0) ~ 186,75 A aoo po"'" "'~en w""ld be ~ 2.7 30 (4151l00)' ~ 47.1XXl W. Lei the ",,,,n 15 2 1 A '" Ihat il n""'"lIre, 2.1 em and is laid al an angl~ of 84'44' willl OE ("'hich is ,'eroca! i. ~. alnng Y.a Vj,) (i~)
clr",lCOC)' .-
""'P'" _ PL • 3.JS .- 0.83
IIlfIUI
,. )
PH
or
IIJ~
4.05
I.E .O. I~ .-0.03 or 3"PE H
,.hps •
(101 Standsli1llOrq"" is ,....-.e>CnlCd hy RT
BT. 1.1 em. 3.1
,,3.0~
.-9,45 kW
E
' •• 9. ' ' '"
60.25 N· m
Ir) We 111,11 now locate point M on {he ",n,l-eirelt .... hlch rorTC:'lponds KI a OIanlnllOrqllC twIce tbc full ·1oAd IOrqIlC j.~. 20()'1, of P.L torque. l'ulJ-lotollOrqllCO .. PE. """""'"' 1;;1' 10 poiN S """h !hal N· .. PE. from poi'" S lin... Ii.... pantllcl kltooque Ii,.. liT CUllin, ,he ..emi-cu,,1c .. M. DnI .. "'N ptrptndiatl.. 10 "'" !!aK. II, wben rotor is .... oonary. ""Y ~ ,o< i' .. 0.93135' _ 0.07' 0 E
SIMorcu~
.. OM .. 19.6
MF
97S
>10.24 <Jhmlpho.~ TIu- 1<Jilot'IOrTilIg wrqw "nd lJo) Illcnlj .'. AH ~ 8.2" 0,24-10.62 .. 3.2 em ",I Starting torque .. AIf .. 3.2 em . ),2 x 1740 z 5,570 syncb.. ,,'alL (b) Line CM i, drawn perpendkular to til< '''''J'''' l ine 0' H. "The imercept MN represto" til< m.~imum t""J"" in 'ynduQnou, watlS. Mum,"m t""J"" _ Mil ~ 7.1~ em _ 7.15 X 1740 .. Il,+UI.yoch. "RU" (rl For findin8 the ",aximum POWCT, line OP i. drawn .. ngentia l to the scmi ·ci,dc . LPOE _ 28.5" .. ma.timum p.L ~ cos 28.5" .. 0..11'1 "The .Iip for maximum t""Jue is .. liN/Mil. 1.4n. 1S .. 0.195 (~) Line CL is drawn petpClIII.E.K t...1OdtM1 Z. Tho [011ad OUr=!< and pJ .. ,I>e (M'1i-{)U1 ...... "" and Ihe muimum ""tp<Jt POWCT """"loped , 149 A .1 1 .111 p.r. , 11U s"lIdo. kW or 2.515 Ibn.. ~·.L IDI"I)II< , 791.2 kW l lI.E.E. ~, ~ , A 4(1 h.p, (29,g., kW). j().Hz. 6-!",llxd tho: follow1"ll tcSl fi¥,,~ , N-load : 4W V, IS A. r .t. _ 0.1~ S.c. "", : 210 V. 140 A. r·t. • 0,25 'The "";oof.~ to rntoro, I".... on shon",ir rN """""
J-""""
I'WI,,,
to,.,.
hHttIG., '"!:
Rurullllj! lIght .. 60XI V, )4 Alphase CIl'i.e of tI>e f(II£I< ' " """'e it YIOod lorque . t ..... in!. {O.l.l8 1l 11 ~ (~ i •. ) 7. A ] .phMo induc""" lII0I.,.. t.t. flllJ·1oad ""tput <Jf I ~.6S kW .. 220 V. 720 ' .p,m, 'The full-k>ooJ p, 1. ,,0.83 .... dflClClICY i. 85% When fUIUlin, light. ,I> SA .. 0.2 p.f, Draw ,I>e oile Slanill,i """"". 1(01 1 261.7 N ... r6) (f ) 7.2 "'I'I""L) (u....IM L 'n i~) , . A 415· V, 4(1 h.p. 129.S( kWj. 3O.Hz. ~-<X>IIl>OCtcd motor S." foIlo"'in, trtion moIe lolm'lnl data (I"''' vol"",,) .
400- V. j().!l,•• _p/I= sw"""""""Icd
No load Ir'" 400 V. 9A. ""' • • 02 Shon ~ V, :;0 A. "'" • _ OA
",,,,uit _ :
From !be di~ find (a) !be I"", o"""nl and PO"10< lCrnlinah is ruloccd by 50%. " ""jog cUITCn' i, ruloccd by 50%, bu, 'OI'tjuc is mloc'Cd '0 25% of the fu1!.voltage value.
By u'in~ primary ro.i>IOf'S (Fig. 35.18), the applied voltage/ph",e can be reduced by a fraction 'x' (and It additionally impro"""' the po ....... fOClor of the line >ligMy l.
I" _ x l"" and T" . ;TK A,.een from Art 35.10. above,
t
~ (~
r ~(-'/:"" J Sj
8/
- x'(~1·, -;j·~f It i, ""viou. thaI the ratio of the ,;tartin! tOfquc 10 fuU-load 1""1"" is..' of thai obIained with direct '" ilching or acro",-the-line >larting. Thil; melhod i. useful for the smooth ,tarting of ""all machine, onl)'. (I»
Aut ... ' .......' ",.",....
Such 'taners, known variously as auln-.u.nm 01" 0 as to YOltage 10 110, 6~ oc 50 ]>C' cent of the line ,'oltagc. 10 onil the local conditions of supply, "Tho
red"""
1332
EIectnc.I Technology
V..;onne-lJ'aJlSfonnn-. if a I:Ippng oflfanSfDrmlll">O ra,io K is ~ ""'" """" '-011"11" ~ """or is ""VI Jj. as marl;C'd in Fi,. lS.ZO(b). """or cum:nt II starting I, ..
Tz " .K ~
,,,
-b.X I.,_X
.
...,
I
••
~
r-' :'" ~ } f, , '1, Ii ,
~.
,
1, 1'[
IlJ!l<Jf1'~nal
to tI>< "'Iu... of the voltage. we get
T , " (V I jj )',
With d,rccl-S"- ikhing.
With .ulo-tf1ln.focmer. T, .. (KV I
jj l'
T, . rT, 0< T~~ If . T", • If x lOnJu< witll dir..,l.,witd
in An. 34.11. (a) execpt th.l x has been
Exlorupl< full-Ioood C"""m or If .. 0.6 K _ 0.775 or 17.5% In ,he: case of an 0.10 staner.
K'(!..1X~1 "
..
!...
.0.6X(O'L)' X 0.05 .. 0,75 I, T. _ 0.75 ~ .. 75 '1. offull-Ioad '''''Iut.
!... • T,
T,
E.uunjJlf 35. ' ~ TM fulJ./OOI""g vn "n "u,q.,ron'I,)(n~' 'I) lu"il 'hc SI""i~8 " U'r-~f"rr"n rolio if "'" SUJIIIIy Ii .. ..."".. .. not to
<WT I" Star-d~lta Sr..n u This method " usN in the ca.. of motOf':S which art buil' to run normally with a dell.- ',ne "".,.,nI "
""'g"''''''''8
I~
Now.
_ 45x44W220 E OOA
J] x440 x I, " 0.8 _
11.!l(l(W.8~,
',_ 23.1 A
I• • i. / fj .fj(jl,fj .S2A .. /. 11, _52123.1_ 2.256 ~nlpl. 15 . I~ . II } -pl!m,. (,.pI•• 5(J·II, imll"";",, nom,,, luk .. 60 A 0/ full -/ood j/NM of940 r.p..... and d"vllJ('s a /If,,!'" of }5O N-m. n,r 'laning ,"nrM", "".d ",,/'ag' is J(J(),4, 1I'1oa, is 1M flarli.., wl'tju, ~ If a swr/dr/w SII"'~r is usrd. dn.m,iM ,"" Slam.., tQI'tjHr and "anin~ ~~"""t. n 1. Ktric101 MIICbh'ormal 'uitage were appliN. the line value of S.C. current would be. 40x (4OlV2OO) .. 80 A. I. ,'al",,) • 80 A : I. (pilase val",,) .. 800',fj A WIoe" COIlJ>eC1cd in .tar acroSs 400 V. the 'Iartlng of
Eumpk. Hol i. A /0 kp. (7,oM kW) ".0 10 ....·MII .fOnm ", notmiJl .'OJ"'Jd ~,,~ aM DII iltiliDJ ' ldnu., ......,.... of 15'1, offoJl· /ouJ I<mi/ ..... UpWu. I"(!/t.tgc """"'"' ...,..". is reduced l(I6O'J, of nonnal >-..1 ... _ In Iltlj """" _curreIM iJ !be oaIIIC . . It... ~nl but II doc",.....,. tn proponioo l"OIugt M .-oIlqc ...-mso lOOIOI _ 0 .6 of normal voIlage
'f - 3.06 /,
..
I"...W1Jngcurrrnl .. 0,6" 5.1
T....-q .... ~I
>tattmg "'vuld be,he .. "", II 1>d '" [.II·1oad .lip .. 4 p .. pp;ni. Ill""'" flUglO l-.
- S.,,,-h
• •
Ir
~
.
t
](J61
./
-
S\rrpIy
T
Slip R'RI'
Fit- 35.22
I,,",,"" ufthe I'OI()( cirt:un "', lho.1 fill(. _ond '(Cp ...• IC . respeellvdy. "Thr. JQ's"' ....."C, II, ._ .• elc. COII,i" of IllI'" ''''''''ance Jl, X,)' J - {!(Il, I s,)' + XiI "'hm: " _ sllp.' ,W1Jn, iL. unily "" ,
larily 111< _""nc_
Similarly
I,.. "
-r ..,!'.,...,,, , " (R,I.,) + X,
wllere '-. '" 'lip under normal running
•
~3.& • .& •.
"
s,
s,
~ R..-l =~~..!L
, ·(il
s,_, ." ._,
Similarly.
. .. (ii)
.:!ls.2 .. " ,, ______.•
!!J. ~!!L =!!!. _..... • ----'i...... .. K (.IallCa of various sect""" CUI he round .. Ii'·.... be""" PI • It, - R,. R, - KR, .(1 - K) It, : P:'" R, - H,. Kit, - /fR, • Kp, PI. R I- R.~K'p,clC e, e. lienee. ~ i. _" from above tIw if ,_, ;1 k"", .. 'n for ,he assumed "01 ... 1-. oftl>o ~"""ng ~Ulttnl, tJ-cn n con be cok"I.ICd.
"
F',..."plt J5.ll. Calc~lat~ 'he in a J.,,,p ro,,,, ,u/Jrona IMrU, "" u J pIttu~ uod","""" _ SI~p'
II , • uul ""iSla""" in ""or c,n;uillph:i.. on f,rsl Slud • ,./1_. 0.02/0.01 ~ I n K • (,_1""- '.. ((1.02)'" '" 0.4373
Now.
R,"
In; R) .. KR ,. 0.4573xl.O.-l~73Q
It , • 1(It, .0... 573 x 0."573.6,2091 n; R. '" KR, .. 6.4371" 0.2091 • O.O\IX> Q R, .. KR, _ 0.4H3 "O-O'JX>" 0,04)7 Q." '" Kit, '" 6 .4573" 0.~31.6,02 n{as ,i"en) n.e 1tSl".......,. of various Slane.- S«11OIlS .,.. .. round hck>w ;
p, '" 11,- IfJ • OAn) - 0.2091 ~ 0.2-4112 n p, '" It )- R• .. 0.2091 - 0.0956 . 0. 1135 n ; p. ~ R4 - R, . 0,09:16 - 0,0437 '" 0.0519 n
PI • R, - It, .. I - 0.4 513 '" 0.5417 n .
p, '" It j
-
'1- 0.0437 - 0.01 '" U.OlJ7 n
n.e t(S'>WW:C< of vorious oed""'l ore ihown in I~~. 35.24. lS.14. Clowling II "'" been (""nil dw. indunoon IIXIIOfS. ~Iarly W ~""'rocy 10 run.«ably al ~ .. 10...... Ofte.fC"Cnlh of
"IulfTCl-at" I)'PC••.,"'.... ...." eMi"'l a
w" ")'rochtonoul speed N.. Thi. plio""",.
enon Ii kn",,'n ~. en ...·lin' of an Indue ...,n """or Thi, ""' 000 'S due 10 tho f.o, lite •.c. "'i ndin, of tho o!ltor produces a nux "'a'·e. "'hich IS 1\(10 • ptI'" "'A'·c. Iii•• romple. "'"'C con,i"'"B or a fuJ>damcnl ~1 "'",'c. ,. hkh ~""hm """,I~ and oo.kl honnonic, like 3r0",'"",. "" lorque lienee. lOla! mocor wrq ... Ita> !It"", componenlS : (i ) W fundAmcnLll 00H:jUave. ~ d,ff"",,,,,. of 1" 120" .. 2 x 360" + 120" .. 120". lloey .." up 1 rorward """ii", r",ld . ..-,," • ly""hlOlOOU. opeed equal 10 Inlh .... 1M .y""hf()fK)uJ Jpced "r 'he fundalMn lal In
1
!
\'-fu- ,0.6
1.0
""'~IF "'e 1108101'".~, load ""'I~ il i. possible thallhc ""'I'" """d<Jped by !he nlOlOr may rill bel ... tru. \ood torque. Whet! IhiI happrn •. lhe _ .... ,11 001 """'" ..... tc IIf'IO i.. """""I . peed ..... "'ill remain ",""inl'" Sf>«d. "'hieh i. nearly Inill of; .. full-speed. ThOl .. ... ferml 10 Ij rno ...... ng of lhe motQO".
The Jorqoc.'pocd c~'m'lic of a double cap' n>OlOf may be appro>irn;ima'e JOfq"'" may be found by neglecting the ouler C"llt imptdanco a ltogether. I lo ..'e, ... il dues c;ony """'" current, which is ol"""t e n,irely dc1eml lned by ii ' .... i'III ......,.
35. 111. Speed Control 01 Induction Molors" A 3-pb""-,, i,\duct;"" ntotO< is pm,,,ic"'ly • """"ant_,peed machiD"01. 1Itap This 1I'ICIhod. Ihough llIe cheapesl and llIe easirst. is nn!ly ...... btc.u~ Iii alarp: changt III >'Oltqc.$ ' ran. 0'0'""
Thi. method .. MUlJ flW/icaM.,.. ....irrtI.c. ~ bocau"" \be "Iui""l-age rocor odopts ilJlC •• lip can be ,ne,u.ed i.r . • peed eln be dcit.
T, "T.. K.,IR1"/(',/(R,.r)or{Rl.rYH1".,ls, N, _ 120" ~ _ 100(lr B with ,uWly lffitu '. "
!!......~N N..
and
J.
•
,0bv~ dnOll' 'rocM "f lhe ..." i. N..... 1201/(P, - I'.) A.!he diff....,.,'i.Uy- be,,,,,,
One b,£ advantage of thIS rnelh<xl is Ibm any . p01131< IndI.o:cd in thc...coooJary ",ndin!. the""'"oN is ill«'mnCd bullnl is In ,he oPI''''inl own .. rJHnfWlUDlinr winding or un"", ,,;Dding. 1\ is al", housed in _ rlon (in the upper pari) and is connected 10 the conunutalor In. """',...,. ,imil..- to tbe annalUre of. d.c. moIor.
(iiif SHundary "indlng. It i. contained in the .w,,, """ , bot end of ~""b ~ winding i. roonected 10 """ of the pair of brushe!i arnnged on the cOInmutolor. 1ncsc bru>b~. are moon",d OIl two ..panIC brush mckc .... which ore de!iigtlO'd to mow in opposite di=tioo, relative to the cenlre lillt of lhe ,,,",,,ponding ,{alor phase (lLru>.I>o, are separated. In fact. magnilude of !be volug. in,itc1N inl !he ndinll depends 00 lilt ang~ of separa~on of tho 1>ru>.1>0, .... , and .... ,> R, >nd R, and C, .00 C,. How 'lip-frequency •. m.f. i. induced in seoondary winding i. deraildary winding, thereby indudnll volulle and so producing =nlS in il which ... ao:t with !he field to prod""" ~lt>ch'iJ, 1(."11') torque in .Ilt .UIlIH'. Si""" "o'or Cannl)< "".... IS a "",clion. il make. Ihe rotOr rollte in tho """,*""Ioe shit-ids. 1be moIor fan circulates ,uffiroUgh pipes which.,., of ampl. =tion. Sc","'I~ I)' Wor-oed) \-eotlLo!fd '1)1"" These mOl"", are similar 10 lhe ,d[·vemil.,ed tyl'"
(.iiil
• .tcrpl thai venhlauon" prm'idcd by I separa,ed
blow~r.
35.22. Standard Type, aI SquI".I-cage Motors Differen! !~I"'-' "f 3-pha.. 5quirTCl·c~g~ mol ...... "."d".diz~d. ""r""ding lu thoi, .I""uic ehllr'llClm.hC •. in'o,IX types. ile>ign.ted as design II. B. C. £and Frespete squirrel cage giving Ihe moIOr a high starting lo.qUC with klw """"ing rum:nt. 1llI:ir loded· ....or C"""'nl< with full volta", applied are ofm. .. me order as for cia .. C motors. 'Their full·load .Iip varies from S% 10 20 per cenl depending on !he opplic ..;"". T1>oi,.101 ,lrUo locked rf $p«'d. Q. 7. \\ hnl modifkaU..... .....,Id M IICuscs.he bearings lO heal. 3. flih"" of shoot cpH"" ",,"leh. 4. single·phasing on !he running POSItion of !he Slaner. Q. 10. WIoido .. the ...",~I':I""'" of bIo,,'-ou ... ln ind uction mo'""" ~ \.... 1bc commo.... st ""u,," i. single·phasUlB Q. 11, b) •......... pbtiin' · and II ... _ ? ,1m. By single-phasing ,. mean. ,he opening of one ",i.., (or le&1 of a ,b=-ph"", cimu, whefnlpon.he remain,,,! ~g al once beoorneo .ingle-pha... When. 'h"",·ph.ol;o lcin:ui, fu ...."'Ii".." oonnally. ,here"", 1l1rc:e distinc, eu'Tnll. flowmg In ,he circui' A< is known. any 'wu of me... ~nl$ use ,he thin! wi ... "" .he return [>alh i,e, one <Jf ,he 'hree pI1a5<s al"IS as • ""um path for !he other 'Wu. Ob,·lou,ly• ." open cirwit ,n one leg kil l> '''"'' of!he phases :IIId there: will bt only ooe CUfTl'nI or ~ worl:;inB. even though two wi..,. aI" left intact. n.: ",maiRlng ph;ue .u.mpl.< to cany .11 the Iood. n.: ...".1 ca .... of .ing~.ph .. i"g i' to f,oo
(al ",,",,-.cireu,' """'"' WIth normal volt>.g ' (e) fi...-dloo"""
r"",Of
(tI) motor "ml>.J>re .. refern>.! '0 ...,IX,
J. In Ill< eire'" d;ag=n of on ,ocI"",i,", """Of. I"',nl of max;mum ;nf'l" lie . ..... ,t.: lO"g"n' dr.:.." par.U"'1 to (~) ""'IK'1!In< (b)
(.ll2 (.)2'] ,e) 2 I (C1un."f> of .~c "elud~ Ill"-Tllft>. bu.;""", mao ch,,,,,, and power 1001> elc. h..... t>«n I""'si~le due 10 ,ho: ad"......,." """'" in ,to;, de,,!" ur ("",11"",,1 kiluwalt "lUI",. SUItt Ihc ""lu,ren.,n,.' of !be 'ppI",a. "00< diffe' 50 ,,'.doly. Ihc ,noIor-nlllllwIO.1unng,oouM'Y has deHIJICU matly dilf"""" tH,,$ 0( """'"
P«'''''''"'''''''
Single-pha.. moIUfS ""y I> hot-n
l1li
e>pI.incd '" ''''U "0)' . ,i) b) ''''0 ,fi.ld Of dooble(,,!.! ",,'0>1, IRIl . a maximum \'.1,,,, of",. lIS component A arod IJ ""II e""h be "'lu,l (<J ¢>,,12 !'e"oj>jull in amiclod",i", and dod..-i", di=tion. re'I..":ti .... ly. nu~e.
,.
,.,
.
,.,
..
o
I
/
J
o
"
,., Fig. 36.1
After """''' tim.. ' After threc-<juortc" of a eyeie •• gain ,he "",uitant i.
" 12 .. -
r", e.um(>k • • nux li .... n by "' .. taning wi""ing J.gs behind the applied voIt.o.ge V by I small angle "he""" currelll I~ takn by the nUlin w,""ing lajl' behi"" Vby. v~ I"",e angle. Ph ... angle bet"""'n I, and I~ is made as I'lie .. possible because the "anlng 10Jq"" ofa ",Iil.ph... motor is proportiOllai to ,in "- A ccnlrifngul switch S is Cnlltttcd in ~e> wi'h t~e 'laning wi""ing and II located inside the motor. lis fuoction is to .utoma["'all~ d,~onnect l11e 'lanmg .... i""ing froln lhe ,upply when the IIIOIor has ",aciled 70 10 SO PO' cent of ito full·load speed In the C;e of .plll-phase motors lhat are ""rmetically ~ ""''''d in refrigoration units. inslead of inlornall)'.moonted centrifugal , wi«;h. an cie! 0(610 8 U..-..,; the full ·kMMl cu""", l~ ~"" ..,., ofte" uoed i" I""fCfCIICC 10 II.. """,lie. ""llKilOr"'''" ~on;, 'f)'pica, appllC'llll(lni"'" fan ...... blow"", ",,,,nfullal pump> and SCl"""'nlll, "lUhi"i nuochi..... ,m.1I """,hi"" ,001 •. duplo':,,'in, ,,,;.how. in Rg. 36.11, IIIe di""",ion of fl)l.lUOII of StICh moton c... , t.. ",.'om;cd by ",~e"""lIthe connn:lion. of .... of the ",.,Id."II loot both). !' hu been ""gk>;;ted. the oxciling bhown con,isling or "niting ",,,,,,ar.cr: (111)'. Eaeh roIo, h.. bNn ",signed half ,he m_gnelismg "'''''lance' (i.~ .... half the oc'Wll rcact""""'" 11le
"'JlfI"""'"
(;+ j,, )
5 ... j
( x R + ,t,)
and il "'0' with a slop of •. 11le impedance of 'baorkwatd' running rotor"
------• In f""t. full , .• an:-- --------------------by ""]>ital .. half .. I..,. by !IT..JI1ctlcn. 1uc>
shown
~
:u"od
1374
z.. j .... (2:.S +J~) 2 "-s+ j(.... +..,1 and il"'lIS "'!Ill .. hI' of (2 - s). Under >laM;lill OODdilion•. V, . V.' bulllnder "'MUll OODdition. VI IS lln>O$l9O 10 9~% of !he awlocd voIlJa~ .
The: (orward wrque in synchronous ""lUi is T,
T'. '/'1'(2
s)
l1Ic lOO1llOrque j,
36,6 _ EqutvCJlenl
T •
K
I; " I s. SimUarly. bll"kward torque i.
T,- T.. COf. loA
C~ull-Wlth
l1Ic oore bi eat! bo rq>rnenlCd by M equi...a.:o, ~ wbich rnIIY bt """""""" ~Ilher in paraJltl or 1ft ~nQI '" nil !he "laI".lu,nl n:actancc .. """",'n UI Fil. 36. ]~, S,nce undtr OJM,nll "",,,.blions VIiS very Ilia)! V. is CQfTl'Spondingly. low) most of!he iron loss ,,",01 1'1_ in !he 'f"",,·artl """",' .,....,"Un& of !he common .lJtor and forward-"'M,", "",or. Core· 1oss Cum:nt I"" ~ los, I VI Ilene •. half value of core-I ... , equivalenl ~;""""" is', ~ Vi '._ A•• too .... " in I~a. 36.I~ (Il). ' , h.. been connected in parallol wi'h ... in .... h "",or.
"",': R~'isl(Nt(t of 110.: .1IJIllIning Fig, 3e.1$ mpadl'" lhal K'j1/ pill« 1M main an,l auxiliary wl'mJing ruTTI!nIJ in quadmtUr< al SlaTting.
z.. ..
IU..,lriaJ MachJn .... lll. Soulh Gujro .... , U.II •. 1985) Sc:>i"IjtMl, Let Xc bas.uta" w' od'n., in ~ quadrolw< >nd,s ouppI;.,;[ ",ilb" oinJle-pha>< of 100 V .. ~ II ... lho «aMstlll impodaro:eof Ill< nuin ",i..run. i. (S.l + j 10.1) ODd of ib< "u"h¥), "',din, II (19 1 + j 14.2). Fiod Ill< . _ or pi.oo" ""'" Ill< [)U\j;alm. n,mf ofa ,ina""' phaoe indI>ctioo mo< M""y moI(Ir1 . ' " filted with a device callod tloerrnoow wbieb provides prot""lion against overload. OYerbea hng. anti short-circuits elc. lbe ihtnnoslal usually COIlSislS of • bimetallic ~lemen lllllil is """rte be""" ........
.... """'" UI\II
or be.ode, It.
1378
Electric. 1i Technology
4. Sillgle-.·oI~. bOo·~.~r'>ib'" wltt. ""'It"elk -"lilcb 1)'1'" Such Ill()(ors lIT commonly u>cd in ,drig_flUors .... he'" il i, IlOl possible 10 usc: a ttnlrifugaJ ' .... i"'h. n.e eireuil di.gram i, ,;milar 10 Ihal'hown in Fig. 36.6. Sin.ce lhei, "1'PIic'lioo reqUIres jusl one direclion of rotation. lhe>;en lhe motor is 10
FIg.liS.l~
• Fig. 311.20
opcrule from lo....er-vohag•.
lhe two m.," .... "'ding. lIT co'lTIec~d in parallel (Fig,)6, 19). Whereas fo< higher ,oltage. they"", cnd I.ad of "'" SIlUt,ng windtng and both Icads of\be runninl ""indin, ..., IIroughl """ide .. • iIoladtor !)pe A> ,n Fig. 36.27, tho> ,000or ha.\ two lUooing winding .. two '\ill1ing windings "lid two c~,ton. One ntp.>C,tOl" is =d (01" high-speeWt motor [An.)6 4 (11)1 Ugfun-naIIOCt ...io. For ur.mpk. if "", ... 1. value of C _ 4 J.l" and K _ 6, tbcn low-voha&e primary act. OS ,f It Ir:>d • 144 J.l" i _ 6' ~ 4) ""1""-·,1'" con,lOCIeaV( ""l",n' pole, on the .wor and a oqu"""Ico ..lIich arc ~ midWlY be' ...... n tho uwal RioncirculI.oJ bro,h ott. The COi11peIUlIin& winding and thi' oddcd ..,..., ronnected in Ioenci . .1. R,·"ubllllHlart 1nd" ~~~~"""n .
,)
tti~
E.M.I'
-••
Ifbfush",,;.
" rolmur w,tII ma&ne,,,, all .. of Ihduced cum:nIS ("""'n bydob and arruw.) will bc l< in ~i,. 36.37 (aJ· . a
,00..,.'..:1
M
~III become an N_poIe on il> "'P. dinaIf-VC main poIel.. ru ,110",,, ,n I-'g. 36.3& (u,. the annalure pole< lie alonl! M' mal.Jnlil an an~1c of n wi.h
n' N.pok w,ll be rq>ellcd by the nllJn N-pole aNi the ru!Or $.poIt will ... milarly. be rqlClled by the _ " S·poIe. Comcquently•• he roIOr ",ill """Ie In cLock .... ;;.. ojircc'ion W;g.J6.)8 (b)J. SIIJCe the f~,.,. ,hoI;c of rt,uw-. il i, "I'P"'P'ialc to .hes ore ""moo counter-ckockwi", fron' IT'. "'ill al.., be counter-ckockw,,,,,. Ob, 1(>tlS1)', d,rr:od. berominl d:angemw:ly high :II no load. 1. Low pow... fat:1Of. e~ccpl II h,gh opeeds. 1. tendency to .park ., bnosbes.
36.13. Compensated Repulsion Motor 11 i. I modiHed form of tbe """&hI repulsion moIor diSC\WCd above. 11 h.. on additiOdai SWot wiNiina. called compcMatin& windin& "'hole pt.tIlIOOC ,. H) 10 i..."..we p"".....·flClot and (iiI to pru>'ide "'""'" ~ "'guJllion. Thi~ windi~1 il m""h ,mailer \lI:uI the w,nding and il; lIually WOUt>tl in the inner oJots of e..,b main pok and is CeCessary wear ar.tute (UJ'tL'$ prop.cd. One method. "hid! i, oI\cn used for large moo.CIn • ....,...,w. oCu.unu", !he windin. of each C()fllmUllllinll pole with II noon·(I\(b.cti,·c .... i5rance. as >hwn In f'i •. 36.44 (~).
,.,nd,,,,
"',tagftoge indIIccd by 1n>1sf_ action.
.no.rn.
n...
""i_
nU. ""'y
36.17. Universal Motor ... unm:rs.oJ
motO 1)',....,
nWlufoc.ur"Od in",,, />/fH (low I"',,'or .,mn.)
..,.,...,..,_H
dlstriltwlH-fi~1d ~".1Itd IJ/H
(hi&h I"'"er raling)
n.. non·a.>mponS3led motlIr hII lwo ..llOnl poIes.oo "jIullikeo l·polue"", d.c.
u,
motOr e~cq!I!hat whoolc of InIptlK" palh i. laminatN (Fil. 36.45) The lami·
IWN IWOr ;. IIIOCeiAt)" btnIae 11M: AUI U ollemlWll ,",'''''n mooor;' oporutd f""" a. vol,.
'/
•
{!>c
'\ ~~J, t:' ,..
~
•
...
" ~
., ,
~
•
,
I,.:/;'
N
•
••
,-:-, .~
~
•
,. ) Optntloa. As e1jlwIIOd ,n An. 36. ]6, sud! motor5dc1oelop Wlid"..,tiooal torque. K~' len of" hcIher they open'" on d.c. or a.c. JUpply_ The production of unidirectional 'DIqIIhown in Fig. 36.SO.1he motor spced i< controlled by connecting • variable resistaIK:e R in Slng~._
nUl t ...lrtf..... \I«ha. . . . Unlv ...... drInk m .. tfl. ha.-e ~ nUnlwr of Jp""it StIe. Morro'·.... il prevon" !he pining of contacts. u.mp~ JIi.4.
A }5Q.w, $jn~I'.phos~. 5Q.H:. 220-V ",,1,...=1 ..wio, fIUL1 01 2000 '1"" wtJ 1.0 A .. ~n so.ppIjnJfmm a 2ZQ. V dr, loq>pIy. If dot /ftOf1N" is NNIIt«IM W ZZQ.-Vat: • ..""t} IUtd "'*"'.0,4 1'"m.J'~ ~lIvlpud. w,...OIIdpO...t!T/an<w. Au ....... N.... 200tJnJ I.•• «1411 IDU~
SoIoNt-. OC Opn"a, .... , £ ••• V -I. R. _ 220-20><X/
"
'..'.
.. -1) the mosl den", porIion of !he field. The force ,ends to aUI!JI the 'p«:imon of materi.l in soch • WIY Illat the reloc· 1aJICe o f !he mogne';" palh !hal l~, Ihroogh the rna,erial will be mmimum,
,b.,
1395
,
Wben !he "a,or w",d,,'g is energised. !he revolving rnagnc'ic field . ,en. reloclallCe l >uffieienllO de,,,I,,,, r.«;'C$$M)' torq ... 1cteri .. ic of a ",lOCI"""" moIai,
The rotor is a smoolh chrome-sleel cylinder·· having
-----------------------------!1y, '""'0.- .......... an indu • 'Y!IChronou. I1I01<J< by y,n"" of i", ..,ieDeY. Roton of cJd electric cloclu. The rowr iJ Ithin """",I cylinder and !be shaft drl.-cs • V"- tJain
EURlpk .\6.6. A S.H¥, -I.pak. 210--1( 50.11~ rrlu.:-Id,"-", moIor MJ a 10"1'" ""8" of j(J' ..,ht~ mrM load CMdiliQns. Calr~Il!le Iii load IQrq~' WI IOrqu. angl. if II~ voIlag. drops /() lOS V aM (iu) "'ill Ih. rotOT p"1I." 0'" oj .y"",h"",,.WI ? SG!uh,)Ct. Ii) N, " 120)( SIlI4 _ ISIX} rpm ~ T.. _ 9_~3 " ,,"npullN _ 9.~~ " 80000'1 ~ _ 5J N·", ~ml'ng ulldn
.• Dd IYP"', ..... """·Uod,,,,~.,· m",," Oy ""fhn8 the bnIsh """ilion. by abou, I ~' .1c ..... i.
(~)
,,:anin, ""oolnB
(~) i> .. Ir~ml (b) ;. _ ..If. ........,
i~)
oq ... ml-og< ........ ~ faaoe i~ """"" i. loll '" !he " .""'"~
«I
Ibl .......... <mfof _ _
(d) ...... of die obovc
Ir) "-ormo:rcmfof~ 1Otot is op!
-< ~- ,,0:.,,0 "'-!l s' eS· .. !;;
",.,~", ~ §!a~·~ ~ I;~_ •
H'~i ' i"!f' ~i ~ ;~[
~
" , ., Iead 01 using """tinw, f"""" ore IICocr.>Uy fabricated from mild 'letl plat ... "",IJed k>JI"thtt in Ole lype and IiI") """"Jth-CC driven) altern.!rs. It h;u a large numbo, of projttting (.alient) pole •. having their core. bolted or dovelailed omo" heavy magnclk wbetl of and an: '10.0.:e di,advantage i. tbot ,bort·P"Ched roils cannot
"
~
J
111
',
\
-.::')
""""'"8.
U
:~'
"
"
J It ~
~"",,
In F'II- 37.1 J i, sho",n. """"""Inc w;r.ding with two coils pcr group per pole. Diff.",nt shapes of eoi I, "'"
1\ ~
- .. FIg. :17. 10
•
':41hr II Rt "" '.
"
~
••
, Ie
., V-
requ,red for tici, B B II II All roil groups of ph... 'I II are t:onr>! and the other ~'ll>c: "'p. The roil' OVC1lap tach Oll>c:'.jUSllike . hinglel on • ,ooflOp, For the 4-poIe. 24-. 101 .... Wt..,.,h"te shown in I~g. 37.J 2.lhc ]>Ok.pitch i. 2414.6. For n.. ~i",un' >oi''''''' ,I>c: coil' oltookl be full·l"tcl>c:d. It mean. tha, if one side of ll>c: coil i. in .101 No. 1. the 0100 side lJ10uki be la ~ No.7. 1M lWOllo!s I and 7 bcillj one poIe,pltch or 180' fdcd.icall oparc. To make 1I'W1a$ .imp~. roils ha'e bcC1Ilabcllod as I. 2. J and 4 rIC. In the 1kw:1oprd diagram of ~l" 37.14. !be coil number is !be numbcrof!be WoI in .. lUctIthe Ieft·hand >ide o(!be coil i. placed Ead> 01 tbe lhr= phue> has 2413 _ 8 coih. Iheoe 00", to OC'1«1ed as to li,-e maJl"n.. m
""tap: ...·...n connt •
•
" " "
I
L-v J
,
,
1410
Eleclrlc& 1 Technology
FIg. 37.1'(..,
"'the
wi""'i",
A simplifiod iliagrJm above j, shovrll below Fig. 37.14. 1"he method of ronstruc1ioo ro< 'hi' can be undersrooJ by c 10001y inSj>«:1i n~ the dC1i"", ."hown in Fig. 37.15 (a)and(I».
So farw. I\a.. di.",u~""" full'pitched coil' i.t. ooi1, ha"ing 'pall which i, oqua] to on< pole. pilch i.t. • panning ,,"er 180° (eleclrkal).
(>, Fla. 37.1!
Altem ato.-.
1411
As .hown On I~g. )7, 16, iflho: ooil.i
ri.1 ",m i> "'" than lheirarithrrdic;tl sum. n.e pilch fapart. Eo 2 Es cos 30'12 .. 2Ef oo, 15" vector ,um E 2 l!'s cos IS· ,•• 0 ~ 0 --" - CO< " ~ ,,,,",, .rithmetic ,urn 2 E$ 2 Ef Ilhon b)I lVi) )( 180' _ 40"
:. k, _ c< 18O'.4~" :. t,_roo 45"n . cos22.S· . O.'U Irl Ikfe « . (5J16)>01 10 pita.. wilh each (lllIer hut differ by on .ngle equal 10 IUlgular d"ploc-enl ~ 1"-, K::'r" • which CQ,"lltute one polar group OR- IlOl buDCh«i '" one oJoc but ,n Ihree different .1(11,. Angular displacement bet ...·""n ~ "y \ [W " .... bwltribuliorl r..".,. (t.) '" dc:fintd.,.
_ c.,n.f. wilh winding in 3s1oWpo>klphasc .. . fIn ...j!12
hJmple 31.1. c"/cuf.,,. 1M djJl
_on&lemJV2;nradi ......
'"1112
art
,,""tim!/ac/"r for " J6..ltX., 4.poI~.•;~,I~./a•..,"hlW-phtu~
(llro! .... 'UIl ~<JU1. ,/wn iJ WI ,hoc/rical pIwM dispJ"",m,nl 0/)(1'. f7nJ ,rJpllirally '" '" c(J/c"lmiM. 1M ',m/. of/h. Ji:I: weber:!. d .. P and ,/, . I:IJIN «T \'OIl R.M$. ,-alt>T~4.+ lf ¢, Tvol{ • .
This would nave been tbc ",-",n.1 value of lhe induced vollage if all the wil. in a ph..., were (;) full. pitched aoo (ii) COllCCntrale.l or buntl>amlOllK; .. CO< 50/l ---for 5th harmonic ."'. Ihl SImilarly. thedi>tribll1ioo factor is a1sodifftttnl fu"jiITrn,ol harmon"", I" value beoomI:s pitch-factor.
.. CO :rf"'l .... n· cio~
IJ ...1 '" SO .. 1:50 Hl, Sih harmollic. I, .. S '" SO .. 150 II. clc.
lRI h:!m"",ie.
h"fI'rW J7.3. lin 011~""'1(J{" loa< IB ~louIpoI~ ",ul wfiru roilllt'J iulou 1 and 16. C'*"'''U IIw pi""'~~ for lil fontlt-olill (U! In/ 1'/"_«- 1_ / 511, ~ll"oN1 /j~1 7t1t ..... _ie. ~ Hcro.coil!f*\is. (16 - 1). ISIIOIs. ..tnchf.Uullonby l~ I!moe. 0. • 180" >< l/18 .. 30" ii i I., • .,.... 3O"1:! .. """ IS ' "' h,) "" .. COl ] >< 30"12 .. 0 .707 I/i/l k.... • 00!0 S >< 30"'12 _ cO. 7S' .. O.l59lip! .I:,., .. em 7 " 3O"1:! • COl I OS' -coo 75 ' .. I.l..~. ~..... ",ple 37.6. A j.pha< J >< 0.96 >< 50 >< 0.03 >< 240. 15..).( \ • .{j £,. .. .{j )( 1534 .. 2651 \ .
"
Uncvult:\&C.
E..1III.phI 31.7. rmd lilt'
'.,,
_In.'' ' ' ' ' ,
UN! /"", ..,jla~ ,I{ a ,,,,,",,oontCIr-ti J·phltu. (}.p<Jh II'!> JI"MJnidtJlly JiJ'ribltr~J. liS '"IJU UN! 1M roil is riIrIkJ I1y I
SoMIon. SI""" winding i. rlIonled by """ >lot. i, i. shorl'pilCM«W"I'2V1.in(W"f2).O.\l6 Z _ Soi>< 12(1)'120 .. 6011, E • 4.;14>< 0.911 >< 12 _ 1801 V E, _ ./i >< 180:5 .. 3lli \-. K
w_ro
•
E.um .... 37.8. "TN ...,1M of 0
J.p#Ios~.
16·poJ, alt~rnoro ..... 144 .Iou <mJ W". a" 4
...wJOCl< J .. J
Nu. ohiO!.< I pole,
t . . . . . n m P12 ...in)>< 2C1'n _0.96;1_ 16,. nSl120 .. SO liz ",.infll2 3';nW"/2
No uf.I""/~ _ 1-14I3 _ 48:NoofcondUCI"",lslot~~ No of oonJuctur.l ,n ",nb/pIus< _ 48 ,. 4 .. 192 IUms/phase _
E... -
condUCIorsperph~_19212_96
4
'1*, *.I4>T
_ 4>< U I >< 0.966 >< 5 >< 10·' >< 96 .. Yll8 \
£mmpIt 37.11. ot 100pl)I~. :HJ-Ih (j()(hp."," alUmtllO' hrujba thf\SifyJIs/rim./iotl g/'.,.n b}'/~ lallU> .. 1.1,. 2~ •• 1.I >< 14.93_5.97 V 5th Iwmonic vol. .. 0.2)( 14.93 .. 2.98 V I'kne•. cquat"",olthei~e.m.f~" " .. 14,'30in (l + 5.!n oi. J 9 + Uloia 58 tbl Obv_11 4,9l>" J .Iou. Ifl/o' p/oaJ. $pm>l1 i:t Mr. find I/o' Imt ""/I"S' Irw/uctd lor (I flJU Pcal by th< JnI. 9th md 15th Iwmolll" •• '" ..-c .linW>Ol'~ehfVtloU$ S'M'''''''' T~ ~wl"'-sm~rawr $~I is f~d from a 25 Ill. t"TH-pM" a,r. .uppl,. A (j-pol~. IhrapIw,~ l"d""IiM IMlOr is t lulricall)' conni'Cltrilo 1M lerm;nllis of 1M s}nChrono"-f genaal'" ami at" dip of 5%. IXI€"'''n~: I') the f"q"e~cy of Ihe g~"..,altd ''O/lagt of lhe $)'»chroM..s RenerolOr. (UJ>. T""hokal Un i"usily 200 1)
fl""
"""()I"~ (120 >< 25¥1 0= 300 rpm. Ii) At 300 rpm, frequcocy oflile voltage ge .... ratcd by 2-1-poJe 'Yr.chronou. genernror-
SoIutl ..... Speed "f syochr",>.
11>e elflcior>ey of an ai' = iro=! rosI or cooling e-"""plpha", "f IR. which i. in ph.se with the annalw,:e'tlm:nt I. However-, this voltage drop is rracti Ea,'+/(R+jX,.J
This foc, is illustrated in the ,'eclor diagram ,,( J~g. 37.13. ·\ml&tu..., Ractkln
(e)
As in d.c. ger.era1CJrS, armature reaclion is the eff""t f llrmatWlO flu, on the main field !lux. In Ih~ c.... n/.wunllUJn, Ihe pa.,.r /""Ior "flM 1_ h", a con.iJutl/>lr ifIul ""tho tlfWUUu" rucfW~ . We "'ill ",
V-+,, -A:-+~
, !.
,..-'-
, , !> I
,.,
(~)
UN!..
,~ • . . N I'll : . hi
.. .
I.S I'll..
S
,
I'll, :
,:,, .:. ,. FIg. 37.l!4
A. """n from Fig. 37.24 (d). !he: m.m.f. (_ NI_) pmju n .. 01>0 .... fact> ha .... been >u"lIlWized briefly in the fo\l"""ing ""ra""r/l' whore the malter is
dL""""...t in terms of' flu.' r.llln than muu. "'"3.""" I.
Unlty l'...,.. F_ r
In this ..se (F'g. 37.25 (~)I!he ..-malure flu< i, cl"OSII-magnelising. ~ i. thai the fill< al !he leadIng liP" "fthe pole.< i. reduced while it " increased >1 !be lrailing lip". H"wevCf,!he", IwO .ffec" nearly If"", each .1lhcr \cavmg the. ' =n from Fig. 37.2"i (b). llere 11> n::~ Xl' HeO>Ce X, - X," X.· 1'1\1. 37.211 ThorefQn:, 11>1,,1 ,,,IIlIgo drop in on oj""..,,,.,.. undo. IOIod i ... JR. ~ jlX, .. J(R • .. jX,J .. IZ$ where t;. .. known .. 'ynchronou, iml"'Ua""" of lhe annolUre, lhe word 'synchronou,' being u..ed merely •• ~n indican,," tho,,, ",f.,", 10 ,he ""'"''''1
--
Hmoo, we ~ Ilw the 'o'ffIQrdifTcmItt bc!.w..," ..... 1oad ",h:OY'e..and IO:I1tIiiW ">!lag< I'i' oqu:d 10 IZ.. a• .>how .. in Fil. 37.26.
37. 18. Vector Olagroms of 0 looded Alternator Befon: discussing Ih: diagr;um:. folkl"'iIIi symbols.should be clcorly kepi '" woo. Eo " No._ •. m.f. Thi. ""ing lhe voIl1~ io>e fonon di",~ In An. 37.16. H."" •• il rept'CSOnlS!he maximlUll value of lhe induced •. m.f. E.. l..oo.d induced •. m.f. It i. the induced c.m.f. aft ... allow in!; for arm:llu'" reaction. E i• • ectrially Ie» 1luuo e..by IX•. 50m""'nc5. i, i. "..,u..... ". (Ex. 37.16),
,.,
(0' FIg, 3127
V _ Temunal vol"'B •• It .. """lOriaU) J.c..1luuo F..,br r/'Jor i, is 'o'ttWI'iaIly bs 1luuo l;'by Il whM: Z _
J(R~ + X~) . It may II.., "" ,,'rill"" .. Z. '
I
amwurerurrentlpha.o;cand._loodp.f. Milt.
_
In Fig. 37.27 1. ' is shown !he....., for 11"'1)' p.r.. In Fog. 3727 (h ) for
"'"'"I! p.f. and in Fig. 31.27 (~J
r.... Iooding p, f. Allthcsc diagnuru; apply 10 one phase of • 3·pha",o' 'The .JtcrnalOr i. dn'~n ... ynchA)l'o{)lJS $p<Xd and IlIe lI:nnon.al YOILq bc round from
... "'en •
, -,
T"IOO
In tile c... of lar~c ",.dune" lIIe ct»t of find,nt the "'iu1at>0/l by d,""'1 load,nl be.:Omcl prolllbl""t. IlellC< oo--Ioad ."It>.ge F:. i. r"."", in each tMe.
1428
Electrlc:al Technology
I.
SYII'IoronolU /mprt/aM. or £M.f: Ifr,hod. It" dot to (khn £ Hermponent (,(Ealong perptndicuLu direction
(117~
x 0601 z 2SOO
.. CD .. -A8.in~ + IJC"",,cale 0< caiculO!e
Si""~ Iht. .hnnall)< i, "3TCl"'~.u. Ii". voil>.ile
Jl" 2925 .. :5066 ,'OIl>
Ch«k; While dolivering bu,ng p.f. cu""m. TOllll p;cly 10 the
I. O.C.C i. p",",cd f",m!ht' Ii""" ....'" as shown in Fi,. 37.33 (a). 2 Similarly. S,c.c. ;. dr.I"'n from Ihc data given by the sbon-"' """'" _-..w ....... ~.""" ............ )'"""'"" lII< ..... of rqula""" .. i. oJ~ _""" ...... ,,,..,... from OIl ""'......... n.>I" "hy " " ""Ikd pc>Iumsti" method. n..: .oJ.. <Jf Z, is .... romun! bu, ...... ",'" "''''''''''''' "" k>w PI ..... ""'. iu ...1.... 1...,.b;~Jnpk' .t7 .20. f'rom Ih< lal/""'ing Irsl "'./IS, d~/erm;ne Ih~ ",,/wg< "gu/arron "I a lOOJ· V. I.pha", alt~mtJ/or (1~Ii'wing a cu,,
for a cen .. n field exci .... i,,". Wi'" ,he """"'excita'ion. ,lie O.C. ,·oIIOSo ".... 9C() Y.
n.. ""i"a"". bel"·""n • pair of tad C iU"IIIiU"'"
=",,,,,,,e
1tIQ"
Now, fleW A.T. required toprodtltt a '-oltagc of
V,., full·]ood i, lho """lOr sum oflhe followinl! -'
(il Field A.T. ""lui,,,,lIu prod,','e V (or if R. i, 10 be takeft inloac1 by the fdd AT *AB, ~Ul'd 10 pro::!llon full-load C\II'1"ftIIoo "",-,.,,,,,,,,,, lfia· 31 -14 (b)J Up.f. i> willy. the ........"'" ICIICtIOn 1Im:w·...,l'ItIlSlJl8 i.~. i"dlca iHb>lOr1in:rl 001)·. ~. freld ".T. J U
o
.,
,",
or
n."
Ag. 31.47
ElII,np!e J7.JO. A J,j·M VA. Y-aJ 'M~"
,,'nl ,c/w"'IC"U" -. '"I ( F~W
I''''''' '" 1M foil",,·""1 "''''
ellrmtl (Antpr}
E.MF. (\bI1J1
"
1610
.
'00 JfjO
'" "" .,'"
""
,jQ
)00
jJjO
H70
'"
""
'00 j(jjO
'"
j7S0
""l1li
A fuM c" ..... m of ZOO ~ IS foYUIl"ry '" CJr(:w..I~ fulllootl (ll'rtnl DrI .norl--' 52') . 126'52'. V",,'or 08 rtpre"""" •• dulli"" ~ '0 pn:>duce a Irnninal p.d. of 4160 VII Il.S p.f. lagging Ilfoll./ooJ.
06
"[13O'+wo'~2xlSOx200"~UIO'_126'52)JIn .. 313.8A
The genenICd plwee.m.f.£".com:sponding IOtI11se:'Ollage i.
1':0 ..
jlIOO + S3.3cos(90 - .)!' + 153.3.in(\lO - .) r
•
13'-'
%"8 _
• ,~
The I"'" , .. I"" ofregul.lion, found by ,be' ''''0 method .. "'" found ... iliff..- ~Iy from ...:II 0Iher. The liN metInJ gi\'C'l 00fT"IeWhal Ie...,. ,'31 .... ,,11i1e the ochor me!hod gives a ),lIle hig/>er value "" compared 10 the >Ctual val ... , However. the fir"",h""""" !t ... ~roIO"'''''Fi~/J
A",,,. ;
"
Q,C. T~rnrlnol V
S.C
""
t,",tat~'"
~"rrntl
'" " "
"00
""
2000
j." .ltJ r.fiHIn«t~d. W 11$0
"'" '" ""
in A,
~
10000iVA.
'"
) ""
""""'UTI! ~1f«"'"e ",~isWnc~ i. 0.2 U phast a!
FIg. 37.$2
full·1oad at 0.3 p.f.
~
V. fR. co. . .. 1155 • (288.7 x 0.2 x 0.8)
E
1.!O(hol1
Form opIlaFor 1905 V (or line "DiIa8IOr-OeXL• we ~ /:.•. IflO E;s I'IntJ>« add00
SoIutioo lllc acc. and fult·toad ,.ero p.L curve for [>h.se volt.ge are d.. in Fig. 37.61. 'The rortt..'I"Jnd iog [>h= voltages .. e: O.c.c. pllase voltage 3J5O -»to nlfJ 7940 86((1 Ph ..", volt.ge zero p.f. 0 866 4'Xl} (frj) 1L'l1 _ I(X10 >< I«(ntJj >'! &<MfUIU,"
7h~ /oll"",;n& I~" ~JU[I$ K""~ hl"m~d 56I)J
fuiling ""'fH'TU
~""tion.
F"",,,,,,, 1IC1 ~O.C.
line volts imo phase volts by dividinl the liven termioal ""I"", by ./3. :. O.c. ,olts (ph...,) : 3233.
- -
381O. .tISO. 46n. O.c.c. is plotted ,n Pig, 3 7.63. For ploltiog S,C.C,. we need t,,·o poi" ... One i. (0. 0) and the other i. (50 A, 35 A) . 10 f",,~ we "an do "'itbout pIottittg the S.c.c. because it
381O)(8 _
'00
v
~
~ r , ,
/
,
.p
•
Normal pna.. 'oltage
, ,
V ,
' $- ,
/
"."
. J04 8V
,
V
V
C
Leakage reactance drop
-"
0'
_ina all btcn used foin F:C. HCD(:c. CDF: ", tbe I'I:tior tnangie. L"" EF" .l to DC _ lieldamp--tumsforbalan::ingor-
• 15.700 F:F _ Gil ~ 640 >'OIl. k Hage "'~ drop'pI1ase Sbon R. i, ncgligibl "'pply'"~
I'Oh~ .
Ex.,ung = n I :
""
Thc:"' .... 16 po>k$, 144 .Iot,. ~ " t '.,,',1
",."UI"',,
'urn,
Ii"'""... !he P"'«IIUH< "'1;" 1>1000 .. full -kt.t It _,." (I
" C1aJlCt on !be q-uis is hightr. nwi ng 10 the larger air.gap. lit""". X.. '" X.., or X. '" X. or X. " X.
37.27 _ Phosor Dlagrom lor 0 Salient Pole Synchronous MachIne TheequivaJc:nlcif NOfi. as S«II foam "'&-.J7 72(QI.I.X... V.in & .IJXJ -
tt..n.pt. l7..lO. A J.plwst, """COIontC"';}, :lO-1h. ,}'nrnrm"'''ll1rnnlllor Iw, d'N!:{,'·w./. SJ""f,rVfII>IIS mrlDMr of0.6 p. It. " " " qllllodrronlJ0-
1.
"7'..!t""'" ...,...__
J.
A ~kVA. ~V. »Hz. .....~ l1JI--oal.--poi' the """t .... of the 1i"1 ordtt. U... "'ly. the three lamps an: mounted "' the ,''''''' """"''' of & "':m,ie _ the
•
' c
•
.- .
~37.n
-,>"•
,
•
-"
-~ - y'
,
,
,"
,
•
•
,
•
......... dtrtctioonof rotaIiooofligb! 1'lg.31.n
-'
•
, ,
•
.J I'lg. 31..a<J
•
"
AlternatOtS
1459
,nd~, "bethcr the iOCOlJling allrmalO< is running tcofast .,.-~'" .low (Fig. 37 ,g I). S)'I'Cbrooi'''''ion i. done a' the momenl the ur.::ros .. d lamp L, i. in the m,ddle of the dark period. Whon the alternalor 'oIWlly stcp-!he >peed oflhc gmemoroi...,.,... n>adline. F--, fall< back ' by. pI'w£ ODX",or (l. cI (.(
(.(
,,
(.j
1 '• •
(~
FIg. :17.12
&in 9 " I. Tlus JIO"'CfOUlplrt from """,hinc No. I goes Josupply ( _
E, .ynch.impedaaceZ,
E.
,.~m
2X,
aE __ 2X,
-if R. of both mac/ti....... ""gligible Ilore, Xsouii rea<WlCeof ont mad""" IIId ootofboth as in An. 37.31 SytICbroni1Jng p""'"ef (SIlpJllicd by madllfle No. IJ is P>t z E,I>tCOI., - I:: 'STCOI (90' - &) 3 EI>t.in & ilI::ISI SuboIillili n& Ibe value of , sy from above. lloEflX, p.. - E.amz,._ oE -p:.~ (marc IIttnnllcly, p .. _ a ~ ~in enx.1 TOlai ,ynct.onizulg ]l case. In"ead of P,, " u E!/X,. ..... "ppn.l,i"",U: ",«.I:1tIX. where v;, bus·bar voltage and E" (he ..hem.uor + IZ. A< """" from Fig. )7.&), for" lagging pL. " .. (II cos ... IH./ .. (1/ SIn • + IXil'"
's Z. No ... lei. for "'"'" "'"""', ""ile II be clwlseJ 10 (0: % liJ. S"",,,
v ... bclJ rigidly con.... n'. UlIC 10 Irrz 2£.•1n(1/'l ,.,11 be prOduced. which ",'ill ~ \IJI on odJiu"",1 """"nll",!II'on by I". E,-/L 1, The ,nternal pow« will hecQn",
dL~"ltn"t ~ an adtli,>(IrI:l! ~.n1.f. nC di'~""ei_~.
1".
(1£"",,9- VCO!i(O. 0. i 1\)1
"
n.. doff""""", toon.~ P' and P &i _!be lyndIronizinj: """' ... " .... p' . p .. tv ,""" «(/. (I) -
CalcuIOlc the 'yncbrooti:t.ing torque fur """ nxdtmicol dopc di>piocclD",n in , 6.000-k VA. 5().Hz. oltc"nWor ....1m runru", .. l.soo ,.p.rn with • ~ rI ( -'.i"ft"!filJ, 1OrJ01 1m 55Jl1 kW.lli N..·m (iil6-U k" . .1(19
"'''·ml
31.39. Effect or UneQuol Voltages lei us consider 'woahema ur~1
Dl'CbangoP In I:.xclIY' 1oII
=0 upplie> flOC tu.lf of the load (kW).:u>iJ "",,·half of tho load (kVAR). the opl Spe«!>
(0'
(0'
FIg.
37.~
(e'
Allamatora
1471
"""" load that, No, 2. Th, .• Can be made f'O"sible only when roIOr No. ,,,,hances it, angu,,,,.!"";,i,,,, willl rt:Spcl>J1 pav,..,.-li"" passing 1hrough B, rep""enl< the maximum ou!pU' for ilia, cxcitalioo, If OB is funhc.- rota1end \lachl""
ExIImpie J7.!' Twa 3~ $)"chronoUJ rlrHMnicall)'.aJup/cd 8.ne""on opcYOU In p<m,/lel "" 1M same load. /Ji't:rmine the kW IOU/pur mod pj. of each noaY7lchrQltOlC .. 800(5 - h)l5
" "" ,~
Ag.37.1oo
.. 160(S - h) .'. cr + QC .. 1000 or 200 (4 - h) + 160 (5 - h) = 1000 or h. Sf3 CP. 200(4-5f3)~467kW.QC.I60(5 -5/3 ).5]3kW fleoc", alirrnator A ,ul'Pli", 467 k" .",1 B "ufJIllies ~ll kW. AItemaW< A will ce ... , upplying any lotod wOe" Ii"" PQ is .,hiftod to poinl /). n .. n.lood ,upplied by .lternalor B (" 8N) is soch that the.poed vari.t"'" i. from 105~ ro 104%. Knowing that wbe" its speed .aries from I U~% to 100%. al'em.ror 11 ,uI'P1ie. a load of 800 kW. be:t"", load supplied forspeed ,'m>!i,," from 105% 10 100'11> is (by ptoportioo) ~ 800>< If5 .. tliOkW( .. BNj H~""". when 13 "m
37,4 1. nme-peOOd of Osclllat[on
""""iI..
£.~ ~)'rodll'OllOll' 11&, • tIlIlW1II lime I"'oiod off...e oso:iIlatiM. MSnycau>cs. ,oICJ w..·bo~. If IIw Mtwrol ~rit>d of oKil/ol;o., ...I"k op"""'" '" fo/I-lood and ""'/)' ,......•, ftrltN is 10 ~ /j""'N Ii>
•..u.... .J7.6S. A I()"MVA. 100tV, JpIoaH. 5fJ.H::. IS()Q r.p ..... "hma'tN' is ptJrWl~I~J ...·;'h Ofhur of ...... ~ ,_'u ~;ry. TIot- _ I l l of i""rna '" 'ht tOlar I. 2 '" /0' q.",2 """ 'M 'J>JI"hli"Jt\{Jld "(l(:'anc~ '" 'M machiM 1J 40%. C,.u~Io'r 1M ftYqu,nry '" o"",llolion "'1M {Ekd. Ma,·hlMry.l ll , "~nW'lon: llnl ... 19921
rot,,,
~
•
•
I~. o.llh.
1482
Electrical Technology
Tutorial Problem No. 37.8 I.
oj"""",,,
Sho", that on ruonin,," 1'lnI1if. SQ.!!,. 1O.OOO-kVA. 11.kV all "Tht !"'W~' r~'!: - ~~~I ~ il~ ~S..!"i! 6~ ,jgS~~(~ a8 !l~; lf~ ~ ~ i til ~~ ~~ H ~ • t i H 1 ~ P i ,~.; [
1.
[I
p,.. j!~
"
6'.
11"
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.
"III 141. ~· 5
~~
II
iO,
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5' &
H~
~
l!~
H
!
i "
.Ii .....
I.; I t H l
~I
•
': " '; 1'1 tl l
~ m
H ~
Ii
I.n
I
~ .h
':"" e _ e . :l. :. _ I:\.
il'!l
..
!'
ifUPdH , .• a
t~ ~
,. II
... 0
'·i1 ~ a Hi1 =
,-
!
H
,>-9 ... 9
:-
_gK
n
~ ~e~_ i
"" '-I ~"
~
'nH., '~ ii,hi l h. E.]
!I
!
-l~
. H I
';;o§ ~;-!",.
t.i
.. h.~J:.'
II
I iii
rt II
2,i!
s-a."
'! ! l'< ~~~ ~'[ '~I! f~ . ! t I· .-i !-....,,~ " {e!giii,~;t i ! r s t~g& ~ ~~ ~_-~~ ,~"d !*d •' { .'; •< t [i ,-. ri H. P " , -=q: , II 2. !C. ~! ~'" ~It H, ' 1 " ' 1 ' ' I . ~'fil [~ 1. .... ;- ; . !j J, '",..
I rli- [" , . I'a iI~~.;;
.'1 -- ,(--
~6Za~Z_5Z
§
,i .1 , I~"~
!
i
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-
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ii
.
I, _.
or ~H1 , Ii, 1f6
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...
,
ElKtricaI Technology
,.) p.l.ohbdCl"d (~) (~
u.
"*
.. hrtbor"io'\auia& ... ~pJa,,".
(iii - 16 7 lit. If. In • J ... _ . " lield ow.- of ~ produca I flllI·1ood _ _ <JUdfCd U>lly (b) it ... oo s.IIarpiHIor
"""'*"
Ibouih
Il>o>-
(i) wdl dalU/tl CC"r:IICd .. m.f•. of ",I.". .. I·
InDO"'" .i looUS Motor ,... Equivalent
at a
Circuit
SYNCHRONOUS MOTOR
Synctyonous Molor ,... Power Developed by $ynchfonous Motor ,... Synchronous Molor with Ditleraol Excitations ,... Effect ollncreaood Load I'Jith Constant ExC~oflon >- Eflect 01 Changing Excltatloo of Conslonllood 0 dn,'""
run., .peed.
l'lI"g'ng from 150 to 180) •. p.m. Some c~Ie0 only """Y to chanE" il' speed is to vary the supply frt<Jlltncy (because Ni. 120[1 PI. 2. It is no! i"""",olly II(NS i-ptt.d, 5&y. in d"",kwise
dirffiion. With llie rotOr po.,uon as .hown, suppooe the ,1.010' pole. III thai i.......1 .iwalN alpoiotoA andB. TbcIWO .imil.,. poles. N (of rotOr) and N. (of otalor) as "'ell .. SandS. will "'pcl ca.ch other. with tht ",,,,,II thol
=
lIM: roIO< lend> \0
roI~l.
Ihe Inlidoc);wlSe dirc-ction.
In
Ag.3II.1
1491
1\1"",.
Su. IWf. pcnud Iatu. >WOI poles. rot""" .."..nd. inlrn'hant< Ihri. Pl"'Iions"t' Ns is tt II Md S." puinI A, Under1llese Cl dirccuoo). Henu. "'" find that due 100000"nUOU. and npod rowion or _or poIe>;. "'" _ iJ wI>jocted 10 a .orqut .... hICh .$ ~Iy ""'nsml I_~" In ptJI'"
.""""".ioo.
_ ,ben
quo:k IlIe nIIor is "'bjeclcd 1(1 'orque .... h;c,h ~n& 10 mo"" i, firs( in onr d.rtttioo Ln !he du...,{i",,_ 0..',", to il> large ineni.>, Ihc rotor canllOl i!lS1anhlnrou,ly mlpond ." .uo:h quickly·n:ven,", Wfqu'' '
.-
•
,.,
.,...
~
Now. ~!he.,.,.,ruuon ohovo'n in Fil, 38.) fa)_ The fblor..,.J relor poItl are aIlnOCtJna each nthef, SuppoK ".. the rotor is nnI ""'ioIw'y, 1M i< .....ing clocl"';sc • .... ,Ib ""'" a,.,....t".. i, tluuu&h
,tan OWr depends on Ill" ~Ie, s,o). (l. 11ow~,'e\'.
~ot IUHJ/uo/Mle/, ririd o~ • . Auhe
,
'.
Q
: J 1
;1
~ 11
'o!"" I
....
J ,,:" -"~ 111 u,pl
'4
~
(a s-LI)
Fig. :JU
FIg. ,..5
'n.. worki"a 0( a synnOlJ. mocor i •. in many .... y~ .• imilar to lhc tr.uISm,ui.,., of mtthanj"aI PO"'e\' by a !ollar!. In Mg. 38.5 on: oIIown 1""0 pulley. P and Q ItWIsmininl po".... from lhe drj'·"10 tile load. lbc lwo pulley. on: .... urnod to be kynllogcthet (juO! as stalor and rotor poles "'" ,ole/lod...! ) hI:""" they fUn ~I u-"Ctly the """'" (","e"'8e) 5JICed V'hen Q i. loaded. il IliJhdy fan. behind OVo',ng In the Iwi" in !he ,h.ft (l",i" angle ","""pond. 10 C """hed "'~tag~ V. This back c.m,f dq>end$ on ",,,,,"excitation only (and ""'" on spt"Cd.1IS i~ d.c. rnoLOnI). n.. ""I vnlt"ie i~ """am", ( ... LOr) i. the vrt1""iIi/lrr-t~« (""'" lrithmc:lical. a. in d.e, 1lloouo moIDr angle II (Fig. 3S.7). so that a "'SUllanl voltage E. and her.ce cu",,"t I, i, broughl into exi''''nce. w hich '''J>Illie> losses." If. now. !he "lOIor i, Ioade..t. 1M" its rotOf will further fall back ill phal. by. gJ1:3lc. value of ",,~l' II - caJkd It.. load angk Of coupling angle (con-esponding to the [wilt in lhe shaft or 1M pulley.). Tho ""ultant voltage f:. i. ioc",ascd .nd moIor draw. an illo'" lion i. changro i.~ .. ..-hen mqn< 5wrl of"""rxtl back c.m.r. ,.~" -E. and !be 'mreOanrud (ii) ormolu,. cun.m Hill bad on/- Ii.) po_' <mgt. umJ (•• "",-lh lhe help of _ _ dia.llJ1UIU for ,'lIriQUS JXn''ttf.... ~ obow" In Fig. 38.14
,•
•
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", .. -"
o
_"'-
L
1,,, ... "'-'"
o,~
V
,..
-~ III 'AU'II.(II p.r. A,1iCCrI froon Fil_38. 14 (a)
Ac' ..
As' ...i!......1~
/'.~ ' 1..
o ' ,"
,.,
-~
o
",
'"
B
r.
,.,
FIg . • .••
38.9. Ellect of Incutased load with Constant Exc itation We WllL Slooy the effoct of increased \oad 01\ a I)nchronous motor under condi.ions of 1Ic$ to "",. '0 that power factor d«ruu •• from """~' 10 tt.< new ,at"" cos 'h. Since incrra", in I. i. much grea .... than the ./igm decrease in power f""lOr. tile to Ih), "',," a small I..... and benet. onuIl anglc lap brluoo V by o /Dqr p/Iase angle., ""~ich mut 10 inc",tiC both in I. and p,f.• power !l.r:d as under' I. A. load on the mo«Ir incfU$Cs. I , ;" rrnun rqtUrIln. QI urilatiD. 2. !'or under-and uver ...x~iled moIors. p.f. lend, 10 "PJ"lI'O'l"h unily ",ith ,ncrease in load, J. Both "'th undeHU"od ,,",'er-cxoit:t.tion, ohange in p.f. i. gre.tor than lI\ I. with increaso in load. 4. "",th normal cx~itation. wlltn load i. increased change in I. is great .. tlw1 ,n p.r. which ,ends tn bn:""", incn:""'ngly lagging_ F........ ple ~ A ](}.poI~. 69J· V. J(J·H:.. J." d-comr"",d ...",,/rrootolls mt K V, I• • os, = 4HO x 33.8 cOS 2.'!.1 · ~ 12.244 W TOIaI powe< 3 x 12.2-14 36,732 W ~ 36.732 kW It is;cen from above thaI as motor I.W i. incn::l!iOd I. rotor di'placcmen( incre","", from S" (olect) )0 SO" (elect) i.~. E. fall' hac'. in pha>t co",; i. tlJc, !"t< go""",,'o I, lap C. by 9f1' and ;,; in pha>< "'ilb V"""alUC p.r. il unilY. ",. 1Ifl1\:I1"'" .. dnt,,;ng a P"" laf bdl.,1000
o..: ..&6ed
As sIKno.'n in Pig, 38.20 (b). 5Uppooe due 10 do:c"rusc ;n eldu«< mough I""""" ( I"., COS ~) 10 meeI the cOllSWll IoIod "" the moe.".
Synchronous Motor
,
Ib I IM
'llIe effeboy,,, aI doe origmal load anz;k ", _ The ",sultanl v"ltalle E", ca ..... a Itadilo~ currenl/. , whose tn.pIta", cornp"""nl i. l..-go< Ihan I•. Hence, annalu,.., Ik"clop. ,nort pow .. than ,he load "" the motor. Accordingly, load angle dUff"'" from 0, to cr., "'hich dccrendy, annature OUJ'J'Cnl deere"c, from 1, 1 10 I., wbose in- ph ..e componenl/OJ. "'" . , E 1. _ In Ihal c',,, annaluft: Ikvelopl' 1""" .... >ufficiullO clU"J)' the c"On,lanl (ad "" the molOr. Henc •. we find Ihal varialio"s in Ihe excitali"" of •• ynchrooous motor nlnning "'ilh a gi ... ~ load (JItId""" v>riali"", in il> WaJ ""'ll~ OIIly,
1501
'"
0,
,, ,, ,
'" '., '.,
38. 11 . Differenl Torques of a Synchronous Motor Various I< ma:oimum hich 11M: IlIOIOr can develop ,,·,llIoot pullinl "'" of otq> Of ")'IKhroni.m i. called !he pull·...u1""I"'" Normally. wilt. 1O&d OIl {he mo"'r i. i""""osffi, "-' """,.. pmgn: .. ivc!y lend, to fall bad I,. pMU by some .ngle (callod load angle) behmd ~ p. T, ~ alN./tIJ
~60 . .!'...~9.55!.a. lit Ns
N.
Condilion (or mu,mum """'.... deve~ can be rotOr> .::...:..III.
..
do.
•
S"""
R."
",t II . 90".
. "n(O - a) .. O
HOAB: VI,iny ~ £R/sina . . •iny x V,ina/£.
From l> OBC: £RCO& y. V COS a_ £.
.. """ y_ (E. _ VC05 0.)1£. COIlO _ R./Z,and'inO_XsIZ.
Abo
Sub.lilu';ng tile .. val""" in Eq, (,) above. we B'"
P .. _ EI. ER[~_E~-Vroo"), .. -:;r - ---ex")__ - E,V,o Z, z, Z, z, Z~
£I'(R'+X'] • • _ E'R
.
~
..
Z'
,
~
Z.
Zl
Zs
EI' _!:.L'.:&. /i' R .. .::t:.. Zs Zl
,
__ .(11
Thi. gi'-e. the \-.1". of po"'.r at "hich the molOr falls out of ""p. Sol,-jng for from 1:4. Ii) abc",c, we gel
I..
E.
y
~Zs [V±jV'-4R•. (P"J_.J ".
'The (wo values of 1::, r=nt the ...itati"" lim; .. for any load. (iiI Find \ . It. and X., _ In llti. case, p .. vane, ",jIlt Ucitali(lOl or E.. I.e! us fil>d the value of the exc1t8l,on or indu.:(d em.
d(1'.. )_ .. L_ 2R, E• • 0. E. .. VZs· dE. Zs Z.' 2R, Pulling Ihis value of E. in Eq . (i) abo,· •. maxin,"," power tability "'" 10 be h.ar.dlro.
""or< .:::t.:....in(l+
•
l .in2(l
V'(Xd-X)
2X . X.
In
... pcr pb;Lsc
1
' .. n2«
til .... ... per ""'" ........
"•
• 9.55P~INs A•• o ScII...wl Junt 1990)
Solution. (il Motor p"""'" ,nput. ,fj " 11000" 60)1 0.8.913 kW (ii i >laIOrCU 1oWphasc.6O' >( I .3600 W; Cu lou for lhn:e pIrti<s .. 3)13600 .. 10.8 kW 1'.... 1')- l"OIorCu lou .. 91~ - 10.8 .. 904.2 kW
11K • .... I V. then m"",, ""' . \eadioa 1'0""" fllCh"""",~ motor with lonni",,1 vollage. , upply ""urrcnl and it' pOl..'er. factor kepi unaltert:d. lind the tlCitahOll emf anJ the load angle.
,
,,, • d-..i.
Dim;I;OO of
All. 38.31 11»
CUrro.' wilh "2i"I' Lag
~
AI'. - I,X. _ _ 65V.AB_I36.8V. FD .7I.SV OB x 40(1 coo 20' ~ 376 V
lie""". - I. (X. - X,) will be from F toward. 0 i..,,, along '-q' direction. Thu,.
E:tolles quite closely to lhe prt'viou, vain" calCl'la'oo by other fonnul•. ]
1513
". . _OIl""Tn",
bluapIe JLl4. A l-t"/unwlrNNu"rmtlru,, ;~ .. so' - 2xWIb.S000l2fO:
E. _ IS4\ .
In r l' 38.12 (III. L 8OA.oO fq' + 39". 'JI1' IIIJ .. " ._ JC(200 CCC,-.C","")-_-'C.-C"" CC.-", CC,-~-C .,. = : E. .. l1~ V. • :..mpl. 31. 15. II
22()()-~
J-t. y •..oll~uud. 50·l/z. a·pol, .ynrhronous "'oto' hus
"'II,
Z• .. (0_4 • j 6J~. Wlltn tlot mof"r al II(J-load. ,lor /u/J '.JCcu"liOll ~ aJjUJ"d so .1ItJI1;; I. IOtIIM ~I '" V. W/w" ~ _ u k>otkd. 1M r%r ~ "''''nltd by J" -o.allirol. Dra", 1M pItnsor dUl8""" _ 1M "moat"", n'''II'. p"""." 1«- DNI ech) .. 3" X (1If2) • I r (elect). A' o«n from Fig 38.33 (")' E• • (Ino' + 1270' - 2 X 1270 X 1270 X cos I'Z")'" • 266 V;
z".oO
JO_.' .. 6'
. 6.013 {}
~.
I, _ /:. I z"E266 16.013 .. oI.U \ FTnmAO.tB. 1210 • .... (S - .)
.. Nuw.
, ••
sm«(I-.)
••
rouJ rnoIOJ I"""er in"", •
266
sin I? 1270 X 0.20791266 .. 09926 WI ' (Xsi R.l ;' WI' (610.4) .116.11:1" 86.1S·- 83· .. 3.11I" :. p.f.• cosJ.I8"_ O.9'JSIIa., 3 VI. cos. ~ 3 x 1270)( 44.2 >< 0.998 .. 168 kW
• (5OII.2 .. 0.29-+(II54+46.2~2.21,) Solving IIIe .txw. quadra!ic equali"n, we &,,1 I, .. 71 A or
1443
•
I .. J,,'.,;=jz31'+71' .. 14ZA p.f.
~
',".2311242 . 0.9S (..... d)
[,ump!o 38.21 , A J pJun~, 440-1; 5(J Hz. JUJr~(Hm,"'ed !rJ=hlfJl1l)lJJ =/0' r,.us 7046 kW lrom r~ three p/oaJe _in>. The ""iJlanu "..r phmt aflhe '1f""" ~T' winding i. 0..5 ohn-~ The 'lU)t,,, OfH!T'(Iln 01" p./. 010.7.5 log. I"", OM m«iI<miraJ 10llt'. "",,,,,nllo 500 TI,. r.«"I,,,/iOll loss is 65(J wau.. A ....""... the 'oulTe lOT ad'aI;OII ro M a MpI:>.i"", ,hal moto.- is running
WIth
nonnal ~xcil"iQn bee,use E. E V
1518
Eleclrle;ol Technolo9v
When 1M """or load i. iJl •
•
.1''-"", ,. o
~ ])~ lJIV"
'.
Fig.3UO
Fig. 311'"
Since the l1eld current remain' ron'llrn~ the "alue of E. remai", 1M same. 231' .. 231' + 240' - 2 >< 231 x 240 coo (SI·4S' -.) (81·48' - .) _ 0,4325 or 81 · 48' - ... 64"24'
.. 0/0.5 n. When running Of! 2.{)o() vol". 15.H~ ."pply ""'''I.on Io.uc:o _ IlS.690-1000 .. 134.690W. 1J..Ut1l.\\ TocalCuIos< _ ]xISS'xO..s_36.080W Tocal nlOltt mpul ~ 135.6'10. 36.0lI0 .. 111:770 W ~
Ji
QIJIpdI •
X41' x 268.05 "COS, " 171.170; COl •• • .IIt (Itowi l ur",,,,,,,,y _ IJ.4.69()'111.7W .. 0.7845 or 7tl.4.5 'I.
Tutorial Problems 38.1 I. A l-plla ... .oo.v.• )'IIlcuJ ... "'" ..".U- OUf'I'lloed and tho: induced cn E. E V. The armature ""ITent 11.11" behind Vby. ,mall angle I). Its ""gle 0 with I':.i, r,Xffl by . tatorron,lants i.~. Ian e .. X,I II• . In Pig. 38.47 (b) ' exdtalion i, It" th"" 11m iL.. E. < V. Hem. E. i, > V. Here. tht resultant "ollage vec!or £~ is polled anliclocl<wise and so is /. It i. seen that oow JtlOlor is drawing a leading currenL it may also happen r"....""'" "01"" of e xcitation. that / may be in phaoe with V I,~ .. p.'- i~ unity IFig. 38.41 (dJl, At that timo. the """"ot drawn by tho tl>Olor would be m;',i';'~," . l'wo imporWlt points stand out clearly from tht above dis<ms;""': Iii The magn itude of armature ""rrent varies with ncit.tion. The CUtTen! h.. large value both for low and high ",d""s of excitation (though il i. lagging for low u~itation and looo;ng for higher tIll, a8 "'Umg, TM ind..ud 0"./ i. ;"""asM by JQ%, ,,,, ,."..y , 1aU~ ",,,,,,[,,Ur, 1M _ ~·uttllloe ~W''''''' mtd IN pJ TM """""M Iwu" .1)...-11..- ",...."'''''' of2 W ~, pMu mtd
Mt/jgib/, .....o on • ditT.rrnl ""ale. "'ferred to !he curmtl boUt ill magniloo. and phase
or.
"'pre"'"IS.
cos. .
He""". 08 I cos • • BL 'The po,.-er inpoll phase of Ihe motor
.. 1'/oos •• VxIJL
~
t
, '.
I .
, '. ,"" '
•
,
,
FIsI·3U4
ii ' .
'.
~
,
0
>.
-. - ",
'-.
,
,
Synchronous MOlor
con"..".
1527
con"""
A. Vi, powe. input i5 depend"n. on Ill., If mo.or i5 woding ",i.h • intak~. ,hen l""us of B is a .!migh. line 11.0 OX and.l.o j.~. line EF fOO' which 8/. i, ."",lanL Hence. EF. "'I'"",,,nl< a ron"""._pow.""" orod pumps ""'.J. iii rocor f:ol.l< Mol.. in pba>C by the cou~ing ulle n. A. load" progrt.. ively inett"""'" !hi, angle abo increaoa "" .. II> product """" lorque for roping wi,h lhe inc",ased l();j(j. If oow.lhe",;'..udden Joe",...., in tbc mol", Joad. lhe moIor i. ,mmediat of the field poleo of the moIo< (Fig. 38.57) 11>0 tor) Itmlinal, lIId "'" field .i,mit i, ldt u~u· ~uN. Motor stans a< an induction "..,tor and w~ik it reach .. ""my 9S'" of its ,ynduooow ,peed. lhe d,c. field is e.cited. At that "..,""'", the ,tator- and toIor- poles Bel engoged Of interlocked wilh each other and hc"c~ pull the ",otor into ugh tbe v.loe of thIS e.m.f goes on dec .... i'" as the toIor gathers speed.
Norm.lly. the field winding.< are "",ant for 110--V (or 250 V for large machine,) but during 'tarting ptriod there on: many thoo,ands of voll> tndoced 10 the"'. He"" • . lhe rotor w,nding' have '0 be highly i",ulaltd fOf with_ ,taridmg .uch ,'oltages.
Flu. 3UII
E\eclrieal Technology
'530
L When full hoo ,,,I. i•• ,..jlcl!N 00 to theannatu,," at~ •• vcry large cu""nl. usually ~ to 7 lime. lhe full-load armalUre culTOn, i. drawn by lhe moIor. In oome tlSeO. thi~ may nf 5O'l. 10 80% of the full· lin.. voltage i5 ,alisfa.otory. AUIO-transfon".r ronnec1;OOS 1m sbow" in Fig. J g.58. For red",,;ng thc SlIj>p!Y voltage. lbc ....,i«boo 5, an: d-.llIld Sl "",!:cpt op=. When !he motO< hat """n Spsed and $, """no: 38.22. Procedur. for Starting a Synchronous Motor \'''hike is adopIed.
""'"'III •modem •)'llChlonous
moIOI' provided
with damper ..'indiJljS. follow;"8 procedu",
I. Fi .." m.tlll field winding i, oOOn-Chon moIor depen'" On the >quare "f this vollage. ~.
A d.c. ncitaliDII i. n:quirul by .yoc"""""", moIor bu, not by indoctiDII moIor.
6. Syochmnul nllf$ are ",,""lIy """" C06dy and CQrnplie.. tctl!lan ,ndOClIOll motorS. i>u' tlw:) are p"flicularly "'11"::1;'. for IQ .... ·.peed dri... (below 300 •. p.....) """"USC WI( JlO"'",r (""'ore"" al,,·ay. be adju .. ed '" 1,0.nd lheir efflcieliey i. high, However. Ind"",iDII moIltage regul.!ion lal Po ..u r",,!o, cOfTKtioo (h· ..uci](:d synchronous """on having \cading power factor are widely used for improving pow.. factorof ~ powor 'ystem. which employ a la'lle numberofin(lU> 0' Indllction mol",? ,\.... Synehronou, """0,-, Q.6. \lmlion ....... '!'Klne applkalio .... oI'l'neh""",.., mutor! \.... I, consIant.peed I""", ..",ice l. reciproc'ling compressor dri,',," J. pow« f"",or cOITection 4. vollase "'gllla!ion of U'alt5mi"ion lines.
1532 Q. 7. \\Ml" ••,.Kbntnous no....,ilor ~ \.... An O'YaUci~ synchronous moror ill cal led ~ynchrooous capacitor. because. like. """,",ilOr. i. tal< .. a leadin, c"""nL Q. " \\MI." 1M ...... orfatall) .uort.in, or. S)1IdI..-.. ...... or! ~ II could be due 10 the folloa';ns cause.. I valli", m:oy be too low - al leaS! half ,DlII,e i. ~U;~ f.... Slan;ns 1. the", may be open-CircuIt in one pit...., - due to ,,'biclIIOOlOl" may up J. stalic f!"klion may be large _ ciIM' duc. to bigh belllcn,ion or too tighl hearln"
he.,
Q. t .
4. ullOf windin", m:oy be i~y ~ ~. f>eld I'J(ci wion l1UIy be 100 Stror1C\\ 1ut1 ....1d ... 1... . - - If •• ~""b .........
_or
r..u. 10llCaf1 !
,\ ... II t. lUually due '" thc fDlkrA"Ul.g rusons : I. voltage may be 100 )""" l. some faulty con"ection in auxiliary apparallU J. 100 m""h SWI"'8 load 4. op OBJECTIVE TESTS - 38 1_ In •• y.>el" .........
lII0I00".
damP"'
"",I\d)n~
(~).~
i.
fO'O .. iliOll ""Iy.
Ib) ""'I""-.aJ< (eJ bod: •. mJ.
l!
Cof) _ _ .....,.
(.I) " " " " - ..
I') I"""«
(dl ......
(.Io) i
In) 'yn
19. d
10. />
10. d 21. d
II . .. H.d
CHAPTER
Learning Objectives
• •
• • • • • •
Introduction
Stepper Motors Types 01 Stappeo' Motors
VorIobIe Raluctonce Stepper Motors Mutt~slack VR Stepper Motor PeIn'lOnenl-MOijnel Slepphg
Mo'cr H\'t>IId Stepper Motor Surnrnoo:y of StEIppel' Motors
• • •
Permoroenl-Mognel DC Molo< Low-lnertla DC Motors Shel-Iype Low-~tertlo DC MOo
•
P!lnlad-dcult (DIsc) DC Motor Perrnoroenl-Mogoel Synchro-
• • • • •
Synchros
•
• • •
• • •
SPECIAL MACHINES
I
: •• i"" control of IpCccir power oU'pIl' raJI8C' from about t woo. max,munl of BOO W The ""Iy """,inll iX'rI in U'CPI" "a moIor i. ilS rotor which !las "" ... ,nd,n, .. ronunul:ltoror ~ ThIS fcatu", makeslhe ,noIot'luI10 roIJuM and n:1,abok.
Slep "ngItI 'The qle Ihn:>ehrooism with the command pulse •. "''lien !he pul~ mlo i, hillh. the shaft rotation..,.,trIS cootiouoos, Openttion at high is called ·,lewinS·. When in lhc ,lewing range. lilt n""or get>r held in a f,~od "",ition and with rated current flowing in tile sLator willdings. It means that Slalling is 00 problem for'tlCh moIors whoe .... , for most of the other moIor., >Lalling ,..,."Its in lhc coUap .. of back emf (EI> and ~ vny high current which can lead to a quick bum-tlt. \ppllcltio"", .
r""
Su10' 11m 50 lurk. c~lru"'u rht JUpping (ltIgl~.
loa,.., J lulh ~lUh. SoIutl .....
ro"l~m~,J
10
N, . 8xS.40; N,.SO ~ • (SO - 40) x 3601 SO x 40. 1.8".
EnlnpW .l'~ ""~PP'"' mQ/or 10m ~ s,~p angle of 2.5", o",rumiM (a) "",Iulio" I.) """'her of "'p' requiredfor 1M 51oa/! 10 ma/c, 25 tn-oiutiOtlJ aloJ (~) 'haft ,.pud. if Ih~ $I~ppi"g f"'q"""CJ is 36(}() pp.
1538
Electrical Tectmology
SoIOI"'n. [" I R,,,,,[ulI"" .. 360' 1 ~ ~ 360' I 2.5" K 144 ""'" 1 revolution (.1 Now. slep; I ",·olullon .. 144. lienee. "'Guirt'tl for """'ing 25 r dittttioo of roIati"" depend, on tbe polarity of lbe ,Ialor co""nl. liiil Il )'boid St'PP'" Mol.,..
It has wound slat"'" poles and pe"""""mJy·mag""li:t.ed rotor pole. as ,"""wn in f~g.39_ 1 ("). It is bIor combines the fealures of VR sk"pper II>otor and PM Wor cod... the roror is compl.c:loJy frrlC. ~ng one or tI'>CJtt >Wor cool. ullStJllhc rotor to .lCp forward (or backward) to a position IhaI fomtS" pa!lt of k .... t rc]UC1aI>CC .... ith Ihc magnetiutJ WIlor leeth. ~ >lOp angk of thi' thrcc.-ph • ..,. four rotor ""'th motor is po .. !HJI 4 " 3 .. 30".
-.
Oo."
,
•
,
I \
••
,0
-
• •,
,
< '
,
,
",
< '
N
.,
...
• •,
•• • < '
,
-
."•
"
,
• • , , , "
, 1
0 '
\ \
",•
-~
IDQUlf
,r-
,0
II '.,
••
,
0'
•
"
; rutOl move! 30 12 = 15" in ,he CCW direc1ioo.
II ...-ill be"""" 'hal in half-slepping mode, ItISleppinl
II is al.., koown as mini-.tq>p,ng. It u,iliI.e, lwo J>hascs $i rnultancoUJily a, in ! ·pha",,·ON mode 001 with the Iwo currents deliber.lIely made "ntqual (unlike in half~"'ppinll, where the lwO phase currenlS have 10 be ""pt equal). TIlh= A i. beld co"Slant while that in phaoe B io i!>Creased in very ,mall i"",",""'nl< unlil maximum Cumnl is ,",,,,,hell. The Curren' in ""'..., A is ,ben <educed to zero ",ing the san~ very 'mall inc",menl,. In this wa y. tho ",.ulunt ''''P """ome. vcry ,mall and i. called 8 mirrostep. For e:uunple, a VR steppe< n>ol",- with a """,Iu,ion IIf 2(K) "ep> I,.,. (~ .. 1.8") can with mi.""''''pping have a rewluliOfl ofW.OOO steps I ,",v (~ ,.. 0.018"). S,epper moIor.; employing microO"ON modes are uSffi aJloMaldy. In thi, C""", the ".p ,;7", becomes h.lf of the 1IQ'lJl.1 .!l:p Of onefounh of tht pol~.p'~h (iL 90" / 2 ~ 4 ~" or 180" /4 r 45"), Mi"""lel'Pin& can .1 ... be employed '" hich ""II gi,'r fur1hO'l1i. aJ> Ita,'.
F_,'''n p~ ]9.3.
A single-",,,,/:'
rol", wuJ JU/I<Jr {I<J~s.
)-p"'lS~
VII moW, Iuz. a Sl~p an&/~ of 15"_Find 1M nw.wu of iI,
SoIutlon. Now. 11 -
xn I mN, or 15" _ 360" I 3 >< H,:
Fo< fiJ> II .. (H,
:.H,_8. - H,l >< 360" I H, . N,
Iii .... ltrn~, > N, H=.II_IH,_H,}>< 360"1 8 H,: or
~pIt
0'1,_ 12
H,_ I'>.
39.... """'''''M! VR supper moIor lias a s'~p ""gl~ of I.S'. HNI'M ttumbu of irs
""",_, sllJ,or ufIIlL
SoIulio.... A four.. stack moIor h.u four pha .... Hence .. m .. " :. H, _ S().. 1.8" _ 360" 14 >< H,:
I/." \\orUJ'II. In Fig.39.8 (a). pb=" IS sllown cxcittd """h tha, the "'" SUIO< pole i. a S .. pok so that i, attlllClS ,he "'I' H .. poIe of the rotor and brings il in Ii"" with theA ..'" axis. To turn the rotor.
154.
,
Electrical Technology phase A IS donccgiud "nd ph ..... h ;, •• ciled po.ili.ely. T1><mtorw;lltum in the CCW di=lion by a lull ",op of 18",
Truth T.bIe
,
-
•
0
0
• ,,"
-
•
0
-
"
0
0"
-'-
." ,"
Next, ph_ A and B "'" energized ncgali.dy One
,
.fler Ihe OIher 10 produce further ,,""'iom of 1!l"each in the .. ON
,.,
Full-Sl.J)lel .tru<wre .... bcr~8S a purely PM mOtor ""lui",. a multiple permar.e"t-lIlapt1. As compared to VII' motor. hybrid motor requires 1c" e>eit."oo to ochi~ve a gi,'en torq"", Ho .... ever. like a PM moIor. this motor ats.:. ! in full SlOps allhough il CO/,,,,, to resl at a point midw.y bc!wcen the ''''0 adjocenl full-'Iep positionIC'p I>f l.r ""..... numba- """'kl be "-"' ,,".If 500 >kJI '" lnlCtry IiI"" radio
and 1V interference.
(/) l>i5ad " onla ll"" Ii. Since lheir magnelic field i, aclive al an limes even when I1"IO\IJ< is no! being w-.ed. Ih",,,, mol"", an: made totally enclosed t" pROvenl their magoct< from coUttting magnclie junk from neighbourhood. tlence. as compared 10 woond-fleld liw:ir1eTion lUi) Beln, of 10... · vo1~
0011",
~ minImum
of radIO
Ind TV interfOfalCe.
Irl l>Nodunll!tl'l Iii Rorb ucess heat I_I liable to burn oot If ltalled or ope11Ited ",ilh the Wt'Oftt
Dru.hcs
,fry....,.,
supply ¥OIta&; li_) layer winde ... I_f poinl-t-poinl 1001 position"" j.~. os positioning se"""motors •• ,) with in· buill optical position ~r>tO .tart,
N
(.j Fig.3i.14
5lf3
0
3
1.50 per ~ "t of the rated torq"". If loaded beyood Ihi' point. the motor ]""" .ynduooism and ",ill run either a, on indUClion motor or stall. 1lIese motors art ",ually designed for direcH>n -Ii"" (DOL) slaning. 1lIe err",iency and P""''' (""lor of d,. permanenl -magnet tlciled syoch"'""", I1>OIOn .re each 5 10 10 point. better than lI>eir reluctrutee motor eou"' c<pam. (6, Ad'·an .... ges Since tbere arc no brushes or sliprinjl$. tbe", i. no .parking . Alw. bnr,h main",nance .. eliminated. Such moIor:< kt b). 120". In 'ynch"". thc$c "ollaaes are in ~ bu, differ In m.gnlludc boc~u"" of lhlcaJ coriO.lotion.
1'0l0I".
""""Ina
1554
Electrical Technology
' co l( s, o
\
(/, ~~ )
\ItaJ~
.,d
0'
llda!;'....
C"".idrr 1~ CQIItmilJaIlsmiu..- sbo ..-n in Fig_ 39.17. SUPf'O"I' Ih>t ;1$ ""or winding i. excited by •• ingle-pIwe .inuooodal K ~oItag. of nns value E, and lILal roIOr is held fOS! in ;IS displaced posilioo from !be electrical zero. If K .. Slalor !Urn. I roIOr IUrn •• !be ",.. v 1611' m- 18.MV
.fj "2(),,cO:I (3CI"- 150') .. - 17.3 V En • .fj E, cos (a - 30") .. ~Ij E, cos (3CI"- 30') .. 14.6 V E" •
E"
• .fj E,cO:I (0.+ 9ff) .. ..fj
x 20 )( ceo; (3CI" . 9ff )" - 11.3 \
39.16. AppIlcotioru of Synchros 1l>e .ynch"'" are e'ten.iwly used in ""yomcthani'm r()f lOnjue trans",i"i"". error dcle01,,">00
SYDCh"" ""' abo u5I:d for am< dctec\i"" in a """" conlrOL'Y ...m. In Ihi, ClI>C •• oonll....00 in the form 0( .. mechanical di.placcmcru of \be ex roIOr is con"cned 10 an eleccrical voll.lge which "PP'"'" " the cr rotor ... ,,>din, lemIinal. "'hich can be funher ampliflCd by an amplifIer. For thi, purpose. "'0 1'«Iuire .. ex ,ync:hro and • CToyochro a. sbo"'n in l'iJ. 39.19. DIlly tho ex i, .""lJIi7.N from ,II ~ingle·phase lie vollage "'W1Y which prod".", an I Il ""0.-
• e £_ is !be muinwm voltage indo.ad b~ !be cr lit_gap nu. w,,",n rouplillJ ",i.b Ibo row.- windingS i. m... imum lind (l .. !be "'SflI"w,.",nl an,1e or lilt. cr row.-.
ex
Specllli M.Chl'~ C' ,--, lC 5C 5, 7 -_
In go"""",,. the val"" of the rIDS voltage in-
t
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39.19. Switched Reluctanc. Motof 'The .,,-itchod rel",W\<e (SR) rnotOfopMl"" on !he: ~ basi< prtJICiple as. ,ariabie ",1",WIOe sttpper motor (An. 39.4). lor) Cu""'nldiun
Unlike a coo"emional .yr.chronou' nOOlOr. boIh lhe rolOr and SUlior of. SR fllOlo< have ... Iient poles as iOO .." in Fig. 39.22. Thi. PIicd 0011 Volla,q. The ;taU .. pIIa..:s are ,w,tched by .i,'~,I. derivNl from I ,haft·mounted ...... '" position l(~ 10 t"e.ltmhl< ,hal of. oo' drJut differs (ron. il in !he: foll"""ng respect< : \ the ,tala< be 9 V P''' 100 m, Th.c "'luivalent volt.g. is 9" 2101100 .. 1&.9 V. TIti. vohage i. applied to ,tator temu""l. i. 5, 5, of the re,.,lv..-. Suppo~ the .ngle e read from tbe resolver scale i. 61.3· . Th.c heigh' uf lhe building i. given in the form of voh.1; the rotor terminal. R, R" Assuming stator I rotor 'urn "'lio as unity ar lhe ooilding i$ round by • range finder.
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39.22. s.tvomotors llIey ore al'" ""II~ rontro! """"" and ru.ve higb.,,,,,!,,,, capal:>il";"', Unl;~e large industrial
pitt''''
""""". lhoy Ofe n'1011 i. the >arne .. !hat of OIlIer ekctron..,.nctk nlOle and J..phuc) ten-omolon are.....J 01 pmenl. S."'omoIOnl differ in application capabililie. from !AI!" ind""ri.] motors in !he (ol"""i",
""'"" ' I.
1. .\
They produce hIgh torque al all 'peNs indudin, zero speed. """Y "'" o::<pabk of holding. j;. They ar~ Ible 'I) re,um tD I given I""i,ion ,;me .f'.r tu". wi' ....... , ""y drifl
n.c", m'"DrS loo~ lile 'he u,uII rlec,ric m",,,,,,. n.cir mlin difference from ,ndUSlrial moIOr.i is 1Iw """" cI«m. wire$ COme Out I)r Lhrm for """,cr l& wdl "" for cl)",ml, The .e"l)m"'", ..-' ... i" ,,, a conlroller and nO! 10 Ihe elcel n ea l line through con'ac1DrS. Usually. I tlCho........ (speed indie ..;n, devi«) ;s mechanicilly con_ltd '" ,he rD;,...... p anp: <Jl <S
""f>P'"
,,'
tn ,Ih«e_ouck t 2m-(>OIe VR _ . the ""'" pol< pitch IS
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VRSlcwcrTTlOlort... .... pong!c
<Jl to'. Whot i. the I\llillbpeed <Jl • Ii.. n w:wer ."""" •• 111< i< .... ccmiD1< rotor of. "<J>P< ......... ,ui<wI ""..- ...... ~ 4i ....... wi'" !he help or.1octrk:ol wi"", only. wh;,;h 0( !he (olio"';.. fWO I~ .... uood 1 (a) ex or>d cr (b) CXandeR
ex ond CD
(d)
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11. The arr.n,.",.,n, '"'I""NI fo< produ,'"1 0 roucioOl «(11.01 \0 Ihc ...,.. or 4ifJamcc 0( tho oNfu ........... of 11M: fdlowul,
_
of,."
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conI
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~,..,.
diff....... tal 1rMS/lUn..
oIlof1llI ....,. ikIa:tJoa (rJ' _ _
.,.,.,hroo...,
1_' _ A IUl'J' (b)
& """"'"
di"" 0D0t0r
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moto
increase ,to rotOf ",>isuoce
(b) cootrol ,to torqu< (c) dccru>< i ..
;.,ert;.
(d! Jclance. ,hen i, i,. hybrid motor,
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El&clrlCilI Technology
0 .6. II... do Y"'I .,...... It 1 ,,_ S,no:c: VIl mowr bas macnclically IOeUInII roIor, ;, .. ,11Il0l induce."y ••m.f in 1IIeohon· ""Ctu...t W1ndJllIlL_ 1IIe "",,,u... ... ill JII)I on .. a gtncnto.-:and ~ .~prnc
