Power system analysis and design

Power system analysis and design

J DUNCAN GLOVER MULUKUTLA 5 SARMA

THOMAS J OVERBYE

ISBN-13: 978-0-405-20587-6 ISBN- 10: 0-495-29597-3 THOMSON THOMSON,

ENGINEERING

3?2ã0815”81351?k

be reproduced or used in any form or by any means—graphic, electronic, or mechanical, including photocopying, recording, taping, web distribution or information storage and retrieval systems-—without the written permission of the publisher.

Symmetrical Faults Symmetrical Components Unsymmetrical Faults

System Protection

Power-System Controls Transmission Lines: Transient Operation Transient Stability

% Aye -b-daa J aeig ¬ ( lau: TỆ “a 24 +5 (255V s $233.42"

Vena = G@THEV 5 1T went ụ Zoo A

Nes G79-8//2 2 AROV 4 © > 200/fP 214rad

ACey) = VA-68 đơa Cob each) A

+ WÍ2 : (tr 130°) [am La») 273-46 [~G0°A ÄLCC) + 76:46 I et Cab ¬ 667) z 103% an (wb 60°) A (49 Z:2 ~42% H

cor Ys Ceol ye 5 lane 2 70°F ¿z6 5 Go Bees tet APPEAR te THE Answer,

ch3 ASC LY a vee JR ce Cate 20’) 5 waste Gas BUT

yCe js lard œ@ ( tt tE 6” 5

eCede ake bir: Jz Ref de® ‘|

THE RESOLTAMT HAS WE SAVE FREGuUEnCyY GI,

(ay Ee (ioe Lo") /(e (534°) = 20 /-5a.0 &

THE CoRReey LAGS Te SeuRce veLTAGE BY E3 ?‹\

Power FaeteR 2 Get SEV =» a-G LAGQIng

gh Bast

«vk: 120 Zo s (G0 9") Corte jos d+ Veons

Cay pled = WCEVACEY = [67B-B ex Cat =te8" }Ï [ 200 en Cáb~ 8 31

= & (678-8) (200) [ane + cos 26a vo]

(b> Ps: va ca (5+ B) 2 A486 x aia Ga ô

= -LING xo” bị ABSesBED = <c 1⁄14 ri peLiveerp

% =—G.Cѧ6Š AT” VAR Agse Renn + + 66-65 kvae DBELWE ECO

(AD THE PuAsee cuReenT (-T) a jana /=stoine’ = tad ves? A

LEAVES ‘ThE Positive TERMWAL OF THIS GENERATER + THE Conteaseg Pewee FACTOR 1S Tas GC toS 185°) = @IIBG LAGEING

ail ”

cos (3+ CE) AC) x mu 219-58 et Cube acd

= @-†66®% ¬ Co [ve ee Cat NA“

x 5:5 RÍO + A.Sbáa.nioP đa (2+6) Vị

SauReé Povs6©& €ÐCY4E, s Sø CẾ- B3: Ge CB6.38) = 1.0

= Avot wie” CL) Lo Be? ae Cua Cack.2) |

c Bobs» to” Ge Crat-ed dD Ww

Pe Vian (8-8) 2 221% 73:46 Gn C2460) 20 Vị

PS 2 Ga C¥~BYs 9 LAGaing

Cod PCED = CE) ACEI= BAT» (SGV Cor Caste a0" Cos (eot-~ 20")

% Gas ate CL) (om C-ad) vom CzezÈ x 180°) 1

= B.064 wie? Cae C resk te } WwW

€): MĂX „3w Cá-e› 2 2s Wek Ady (4079

= <BoGikvag Agsoreed =< + 3.069 kvAR Dativerep

212

Co Peck): 6788 verse cnt Cabs 4s?)

2-204 x và

9 + 2Ö b5Á net On Come wae} W

oe

2.4% SaktO

a B43 elo” Ges Cote &B°) Gen Coal ~ tag")

(4> @e vi fx = (ans.8/da Ÿ 25 = 4.216 tố” VAR DeLivaned

(a) Be R-Ax = le-4252 2G0Q5 [68.2 R

ACky=s (678-2/26.93) an C tae A874 68-2)

n 2S21 Gn Cakeus-2) A

Packd= (26-2 cass Coat & 03.297) Lasart an Cea + ia.279]

G.eS5 xio? an” Cok + 3.2")

=e BAW MIS 4 Brig nw Com C ack + 2264?) Ww (by BCke) ® [25a Gar (cake WSR WL 620.2 Cn (Cob mia.e? nae 1

ae 3 (28-~t/ f8 3 Casy + UGA evar DEUVERED

@ bí ;s G^ [ tex (@/P3 Cas | tant C1444 | 3.82]

4.5 T4, LEaving

2

P3 ÂCE) {CC [8E đa Cát] [4Œ eaat]

2 G4 C&S [ cn Cae ds ee Camb-45*)|

& 22-63 + 2 as (aat—-as°> My

Pe VL os CE-B) = &* & est (45 0°) = 20-63 MW

DELIVELED G@Qa VLAN d-B): Bx 4 Aw (-48-0") 2

= — 22.63% MvVAR DEWERED = 4 22-64% MVAR ABSeRBED

VỆ r Gn Cd-B) = en C- 48°) 2 O-TO7 Leaping

Ee (Cla) Lol] (2lae) s ta

ACK) a 2Ger Cok wad) A wim Gis ATT ned(s,

pled = wiley Acky = Ay | Can ao" fe Ge C2esk + qo" >)

s BAG AG Cant a4) Và

WCED ACL omd pLt) are pleted below: (gee wext baged

The Imakavtomesus Peuter la om anenage value of BAG bà,

and bhe Snag wency e bustee Ảxak of Woe nsolkage dt Cuanenk ,

w/e

THE REAL PowEe ABSeRBED QT TRA LeAD 93 Givew ay

Pe teen G-6Rn Gas BE 5 AAG

2

TAG REACTIVE Co 6Œ AQ@sefø% GT THE Leap 1S

Qs WoxGEB% Am S64 2 GER VAR

2

fe > PEAK MAGMETIC SHÁSGY 2 bh) a LIT a oad Cz.es»Ÿ se ie FS

Gà „ €3» V © 3t 1G 2 G6B VAR 19 SANISTIED,

#

& S.y ik = ZTI% = BF = Jord

Q s 1.5] = cou XẾ -aÖ—=se=

Ce aisCkyde ob ae 2 +2 OUT Pon Cost + 9)

(2z zCk3-ACE3+ ~2caL x? Ÿs Có E+ ø) Gợi Cosk+Ø)

eH WL Ama ate) «—

= — Q/A*+23(aE+@8)

Co) AVERACE REAL PoweR Ê SUPELIEĐ T6 Tác (DUCToQ 2 Œ at

INSTANTANEOUS POWER SUPPLIED Cro SUSTAIN THE CUAMAING BNERG'T

IN TAs MAQNETE FURBD WAS A MAXIMUM VALUB GF G}, —

Whiew ARE THE RERCTWR Cou26ES [ATO LAND C ABR SPECTIVELY,

EF ca”L€s\, Q(c+@$c >Q xe

a

TS BC) z P Cle emeat )j

m1 we

Cay 6.4 #” 2 Gse fae) Cs /-s¢) 2 750 {ge

2 B75 +A 644-5

Pe Re C Sd 2 B15 W AesoeGen, + 1x C5: GA%.S VAR ASsesece

The Fou Sh TRIACGLE (6 Gives BELetat

©) @, = P kea 6, = B15 tao Cee 9:32 2 190.62 vaR

@ > @ - Ge = G4A,.5 -V\B\.62 = A67.88 VAR

PR, 2V'G, = Gee) 0433 2 ABB WL ASSORELD

P= V*G, a(oof 903 5 BOOM AOSa§BEĐ

8 a a ye Đố * Qae Ÿ 2.58 % Bea VAR Detiverep

Seava

fe

+ (eoe ew Cassa 5 94.94 VAR

Qạr: Q&- 8, * te2e-2 - 484:32 BSAS-A kvag

Rose VỀ (tas.a8Ÿ Co.e8%243x ABTGW

Py 2 VÀ 2 (od.08) Cen): 1062-6y

(by ¥ y 5:88 4 s.VAAI z ^:2 2093 /— AB.s\

eq = (lod-o8) (288%) 2 24.63 A

$%x Ñ kêu 3 Gas és) Cas [-30°) = Bece /-30

Ge@t:Pt.É6 x3 Powe ABBR BREE GY THÊ, To CAU Loá® Shean? Ser Ss 5 2 2060 [s30

PowkR TRiAW GLE ;

Gererex 2x66 206Li406G6 2 ý Thể, 0666 19 (Goa VAR

Seounce, =.V x* os ¿a ›C^a — > = 2606 [ase

FRE GOMPLES Powee DELIVERED Gy Tue SevAce 1G EQUAL TO TRE TeTAL Comftay

Fowl AGSoRGED OM THE Leo hi,

“(B=

REACTIVE POWER LOSS ts THE Ling 16 Gi = Ft

ch Ss; = PgeA@, = tre +4 C4 Ai B6 de BG B12) = 200-7 [5328 \eva

TWE INPUT VOLTAGE 1S Given BY Vat ĐC [3 2 682-4 (RÀO

Tue Powe EACTER AT ME INeET 1S đơa 53228 = O-G LAGGING

+ GB88+9586 = Gana fas’ Vo Cramay

CPS), = Go Cars’ ata) = 0G LaAgane

mtd.

THE CARCUIC fØlÁOG(&@APA (4 SWobeMW BELows

{B=

Some = Di tS, + Sy = (Bo 84445-5417) kva

CL) LET 2 BE THE TMTEDAWCE CEA SERIES ComBinAtion bf Rawn X

" a

= mon — » Since Sa GT* = (S) = ¬ > tT Foltows TAAT

Daye _— 3+ = O44 ANB ae

PAWILARLY a (aS+4o5) we AAV mH CO eG O22 MON MAO tem

Sao = o0 Sax = OHA A—~

Av Bus 4, a3 = Say & 33, = (o gargvR)+ Ga-jon)= 4:54 Á*\ i

~

a TA 2 GOkW Ò Qorat aokvaR „KV 9x2 100 VA

Surrey ef 2 Cos (C9348) = OG LAGaING ae

Qe) T › EM Loox io? £25393"

Cos Coa) 2 BEB7’

Nove: TEV Lenos Va, XS TẾ We Positwe Aud THE REAL PER Blows FRom Neve A te MeDE 2

REY LAGS UY, , ENS WEGADVE Aud PewER Foews FROM Neds 2 Tr NOE A,

Preblem 2.32

Qeap = 5 Mvar minimizes the real power line losses (0.25 MW)

if Qeap has a value of 5.5 Mvar, the MVA power flow is minimized with a value of 10.25 'MVA

(Admittance valves are Shaton) RẺ

sees ona = (4956 - 34450) -386t,4ep) kh(b-t8ax-@3 | Vio] ~ (4980 tease) ][%] faci vier? [1-461 LIL

OoB17Tb +3109 | - 0.49604) 4980 ¥e| _ | veel [E4e67©

2.36

METE THAT THERE ARE Two BUSES FLUS THE REC ERENCE Bus

Awpy ONG LINE Fe@ THIS PReBLEm AFTER ConpvEeRTIVNG THE

VOLTAGE SGuRceS in FIG.2.23% Te CỤ RR€MT SGUÉC£6, THỂ,

EQuivALEMT Sougee impenances ARE:

Sẽ = Ben = (04 + $0.8) ff (-io.s) = O-1480-8) (seri)

Agter Converting impedance valves mm Figure 2:32

to aAÀwxitlasee Valves tue bus adumltiaue muctrin ioe

“! (so-il (co.sswstii) =0,x§ Vag -| o

O (-o.38334)1) (0.33¢3-Jo.as) - $0.28 Vie ©

Far Yan Xá» Nea

aot bia * đa 7 Nee? Gra tag © doy

WHERE Yu * Bro «Sie, “` # Ÿa»#

44° Yaa 5 Tat? Vase Sa 5 Vine Want Figs Yon t Vent "3%

ano Ya, 2 Yan > 7 Fee

Fae = đề Mew Ey La“ Ces) = fe 208 x26 [Sse

+ *1:aeS xiet //26:872 = Fog = Re C324) 2 S164 ku Pewee , 7 6Œ ,> 1.5, sẻ C s4) \; 4.323 kar PEuweeeS

BGA RIS 44 A B23 wie”

Pa n G322 VY ý Quà 6\42 VÀR ý Ben AGSRSED BY THE LoAD

PS = CnC BEaT?) zeBiacana, Sa,~ | Saale sesava

2.4.5 ane

(Hi) - ThuaSfeBliiG THE Ax Gammeeted Lea tte AN EQUINELENT N,

TAL IMPEDANCE PER PUASE of Tue EQuivaLauT Yo ig

Pa i€@goW awk G2 O VAR DeuvERED Bt WE SéniBintc-EmD SeuRcE

Co) PHASE VeLTAGE AT Loan TeRmmeats V2 t2ofo"—(24ja) Ca le")

2 Wo-Aze = Wig ¿>ta.a° Vv

THE LING VOLTAGE MAGI TUDE AT Tue Leap TERMINAL 15

(Viens Ju = Jš WES 2 \S%.6A V

Ce) Tee cuggent Fee PuASE IN THE Y—COmMECTED LeAD Awp in THE Baan y

or me A-neap; Fiz Me = yee 2206/-63.8 A

243 GontD,

eer

C3 THe TUREL- PHASE GewPiix Yew e@ AGSCRRED GX dace LoAD |

Se BY, EP 2 AsOW ~ Ả 666 VÀ

B.5 av, 3) m (266K — 4 Goo VaR

Tah TAREE -CUASE Came.ean PawER ABGORGELD BY Te Lind 1S

Sit SBCRL+aRLD 22 BC 2444) GY = (5694 + 2560 VaR

ThE GU GF LEAD Gawhes AMD Line LESGES 18 Bua TÔ WE Cawee

DEL ve ROD VÑOWA THẺ Se Phey + $

¬

> \feøVA « jo VAR

~L6°

(QD THR PER-CBASE E@CIVALEMT Gigewt Goh TRE PROBLEM 1S Strown Below

Tota ComFLan Pewbh AT The LoaS Eu o@ BECELVING BaD (6

Seed + 56&o0.t6-1e+4e.7et «22 + 688 #4 B96 2 Geo [36.81

VarTs PBASE VOLTAGE VV, AG QEFERENCE ,

= % 3x Se cae) _ G60,0ce £23681" = lee [= B¢87° A

ay @ Cazes fo") :

/PHASE VeLTAGE AT SEanming EMD 6S Givan BY

UW, = 220e fore Co-aadad Cioo (236-87) = 24011/4.58 y

THE MAGHITUDE of Tet Lint Vo LisG VeLIaag AT THE GEa Bina EWD OF tha Line 1g

Que «BV, 2/2 (#24010) = 4160 V

(o> THE THRRE- PHASE CoMPLEeN— Powe LoSS IN THE Lind 19 Gwen BY

(G> - TUE THREE- PHASE SEMDING Powe 19

= BY, E*« B Caacin £4.58") Clo 26 ©8192)

S40kn «+ 4477 kvar

Sscags

NOTE MAT Se cney * Sacaey # Sicaey

f7

car Vax ® & ie áo 2 6.661 (60° ou

, UsinG VeLTAGE Distant » 2 YY Vans = Nay “ Bala | 3

Vv AN = 2a8 TE 6-667 £60" Gecrfers (oer jee) SL ET Ce 1b) 1o8- 4 / 2.46 * * 2n, ˆ * %

LOAD vacTaa® Vag = 2 16-4 = 162-6 Cr-cd

~ Buea tar > fe ig? - Cu +32) (3 s»(=® ì

216-4 fa BIS NÓ tông to MEV TRAL

(> 8g, = Ve, Eqh = B Casad L-0-63°) (Gave [Arar )

e Ze-t2 we” + 4 ide to”

Par * gonna 5 Qa, zt \evaR 5 Bets DALIVERED

(o> Lex 2, = 24 rầp * 2e z 5 FoR A BALANCED YO LOAD

2, 2 2 Bap FOR ABALANCED A-LOAD

USING EQvationsS wi FIG 2-2

-=5Q@«-` 7 2Á 2

: aye 4g PER PHASE EB@UIVALENT GtiReult 1S Blown Bets ý

REPLACE DEutTA BY WE EBUWALENT ME

ON A&A PER-PHASE BASIS Sys S564 te) 2 Gor44o) kva

AT THR SENDING ED

-32~

ND 1 &eiGo

CA LET Mà BE THE REFERENCE ¢ Vat

[oe #2400 /o’y TOTAL (MRE DANCE PER CUAS E Zz % (4 <1<5 43+ (6= Á 133 Gxátø3)~

? LANE cu@&eAt „ 249049 ` “ -

BeAto

Wim PoeSitwe A=GB-C PHRASE SEQUENCE |

¬- ^^ nh 2vA c1 T 3e 4 ~a\Ar (S66 Ä x—

b Ñ = 2ac0 fo” ~\@ 1 /~63-& Joa e4i Ì

Ce? Sy) cons ace Le Gras lo )€ a")