External Equivalent. EE 521 Analysis of Power Systems. Chen-Ching Liu, Boeing Distinguished Professor Washington State University

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1 xtrnal quvalnt 5 Analyss of Powr Systms Chn-Chng Lu, ong Dstngushd Profssor Washngton Stat Unvrsty

2 XTRNAL UALNT ach powr systm (ara) s part of an ntrconnctd systm. Montorng dvcs ar nstalld and data ar avalal from on s own systm. Hor, scurty analyss dpnds on accurat and rlal load flow modls of th non-montord parts of th systm as wll. Approxmat rducd modls for load flow studs of th non-montord parts ar calld xtrnal quvalnts. ntrnal Systm (normal load flow modl) oundary uss xtrnal Systm (quvalnt modl) dl)

3 xtrnal oundary 3 0 ntrnal us Systm

4 . Ward quvalnt (=948) : ntrnal : oundary : xtrnal y nodal analyss. ( = ) () 0 0 = () (3) y ():

5 y (): ) ( ) ( ) ( ] [ q : Lt q = q q (4) = (4)

6 n loc dagram: ntrnal Systm () Ward quvalnt q Four asc Stps n th constructon of a ward quvalnt:. Dtrmnaton of th xtrnal ntwor data from avalal nformaton. Otanng th ward quvalnt ntwor q y Gaussan lmnaton.

7 3. Usng th valus for th complx voltags at th oundary uss from th ntrnal stat-stmaton stmaton to comput th flows n th Ward quvalnt ranchs. 4. oundary matchng,.., addng fcttous nctons at th oundary uss so that t q.(4) holds. as cas: rsults of th stat stmaton (load flow) for th ntrnal systm wthout contngncy.

8 Why ar th orgnal and rducd modls quvalnt? n th as cas, f on solvs th load flow (4), th soluton [, ] (systm stat) s xactly th sam as that of qs. ()-(3). ( ) Th xtrnal quvalnt modl can usd n th contngncy valuaton.

9 Ward quvalnt gvs rasonaly accurat rsults for ral powr flows, whras th accuracy for ractv powr flow s rlatvly poor. (Ths s du to th fact that th chang n ractv powr ncton to mantan constant voltag at xtrnal P uss s not accountd for.)

10 . Ward-P quvalnt Th Ward rducton procss s appld only to xtrnal P uss. Th xtrnal P uss ar rtand. Th Ward-P quvalnts gv xcllnt rsults for contngncy valuaton. Gvn th systm loc dagram: ntrnal systm ~ oundary xtrnal systm

11 (Nod (us) Admttanc Matrx )

12 To otan th ward-p quvalnt, on nds to do Gaussan lmnaton to lmnat part,.., 0 vv 0 v v 0 Th Ward-P quvalnt ntwor: ntrnal ~ systm ~ (+)

13 3. xtndd Ward To comn th smplcty of th Ward quvalnt wth th rspons of th Ward-P quvalnt. t s a Ward quvalnt wth addtonal ractv support at th oundary uss such that ts ractv rspons s clos to that t of th Ward-P quvalnt. Th ractv support n th xtndd Ward s drvd so that th ncrmntal rspons (lnarzd rspons from th as cas) for th ractv powr flows s almost th sam as that from th Ward-P quvalnt.

14 ncrmntal form of Dcoupld Load Flow: T P P P T P P P...,..., Consdr th dcoupld load flow: P t l f ncrmntal form: P : thn, St : or P flow) load (DC P

15 On th othr hand: : so whr As, F For shunts 0 : G 0

16 can otand from y dltng rows & columns corrspondng to P uss, doulng th shunts. * * * * * * * From q. (+), f th rows and columns corrspondng to th xtrnal P uss ar dltd, thn th dcoupld ractv powr flow s gvn y: W

17 Th ractv rspons of th Ward-P quvalnt to th changs n oundary us voltag s W 0 W 0 On th othr hand f on starts wth th orgnal ntwors and prforms th Ward quvalnt, th dcoupld ractv powr flow would W Th ractv rspons of th Ward quvalnt s gvn y: (*) W W

18 y quatons (*) &() (). f th Ward quvalnt s dsrd to hav th sam ractv rspons as th Ward-P quvalnt, ractv nctons should of th amount: ~ (#) W W * * * * * * * An approxmaton to (#) wll drvd that can mplmntd n a powr flow program. Th approach s to construct a ntwor th corrspondng matrx of whch s.

19 Consdr th -th componnt of,.., ~ Whr: m m m m m m m m...(a) n othr words, th corrspondng ntwor has a shunt gvn y.

20 Now suppos and w m w m : Thn and m m v m (shunt) : Thn m m m w (shunt) w : Thrfor v w m : so, and : y Practcall v

21 y th aov drvaton, an approxmat formula s otand: formula s otand: ~ ~ ~ Ward-P oundary xtrnal ~ oundary v ~ / / / ~ ~ ~ ~ ~

22 Th constructon of an xtndd Ward quvalnt s summarzd low:. Otan a Ward quvalnt of th xtrnal systm.. Start agan from th orgnal systm. Ground all xtrnal P uss. Apply Gaussan lmnaton on th us Admttanc Matrx to lmnat all xtrnal uss to otan th quvalnt shunts at th oundary uss, whch ar th admttancs

23 3. Augmnt th Ward quvalnt y nsrtng a shunt at ach oundary us. Th xtndd Ward quvalnt has n found to gv accurat rsults for contngncy valuaton.

24 Furthr nformaton F. F. Wu and A. Montcll, Crtcal rvw of xtrnal ntwor modlng for on-ln scurty analyss, nt. Journal of lctrcal l Powr and nrgy Systms, Oct. 983, pp. -35.