Effect of Compensation Factor on the Subsynchronous Resonance in Single Machine Infinite Bus System
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1 Effc f Cpnsain Fac h Sbsynchns Rsnanc in Sinl Machin Infini Bs Sys Mha S Al_S Elcical Eninin Dpan, Facly f Eninin, Tafila Tchnical Univsiy P..Bx 66, Tafila 66, Jan E-ail: _als@yah.c Absac - Sbsynchns snanc phnnn is s in sinl achin infini bs sys. Th sys is cps f synchns nas cnnc hh ansissins lin, cpnsa by a sis capaci an infini bs ba, Th cnl paa is h cpnsain fac which is h ai bwh acanc f h sis capaci ah incanc f h ansissin lin µ = c/ L. Th sabiliy f sys is s by valaih Einvals f h Jacbian aix f h sys. Th ffc f vayih cpnsain fac ah ffcs f AVR an PSS a als cnsi ihis sy. Ky Ws - sbsynchns snanc, pw sys sabiliz (PSS), aaic vla la (AVR), Einvals. I. INTRDUCTIN II. SYSTEM DESCRIPTIN A cpnsain sis capaci is wily s in pw syss ipv hi sabiliy an incas h pw capabiliy ansf vhiansissin lins. Alhh sis cpnsain capacichniq has hs avanas, i cass nsiabl inacin bwh lcical an chanical s, which ay la scin f h bin shaf lss f nas synchnizain. This phnnn is knwn in pw syss lia as sbsynchns snanc (SSR) phnnn. SSR can b fin as a ynaic phnnha xiss whn sis capaci cpnsain is s in a pw sys []. Th fis SSR pbl was xpinc in 97 slin in fail f a bin-na shaf f Mhav plan in Shn Califnia. I was nil h scn shaf fail which cc in 97 ha h al asn f h fail was knwn an i was call sbsynchns snanc. Whn a ansissin lin is cpnsa by a sis capaci, h sis capaci wih h incanc f h ansissin lin islf fs an (LC) cbinain wih naal fqncy f f C L, whh acanc is fin a a fqncy f. This fqncy will appa h f h na as a lain f h bas ( f ) fqncy, s h fqncy ( f ) will b f f f wh f f is call sp synchns fqncy an f f is call h sbsynchns fqncy []. Th invsia sys is a sinl achin infini bs (SIMB),which cnsiss f a synchns na wih ap winns (-q axis) cnnc hh a ansissin lin, cpnsa by a sis capaci infini bs ba as shwn in Fi.(-a), which psns h lcical l f h sys. Fi. -b shws h lcchanical ass-spin ap sys. I cnsiss f Exci (Ex), Gna (Gn), Lw Pss (LP) an Hih Pss (HP) bin scins. Evy scin has is wn anla n (M) an apin cfficin (D), an vy w sccssiv asss hav hi wn shaf siffnss cnsan (K). Th aa f lcical an chanical sys a pvi in fnc nb [] Fi.(): Elcical Ml an Mchanical Ml. IJSSST, Vl., N. ISSN: 7-8x nlin, 7-8 pin
2 III. MATHEMATICAL MDEL F THE SYSTEM Th ahaical l f h lcical an chanical sys is psn ihis scin Th ynaics f h na ap winns h q- an -axs a incl, whil h ffc f saain an ynaics f h bin vn a nlc. Usin c an qaa (-q) axs an Pak s ansfain, h cpl ahaical l scibih ynaics f h lcical an chanical syss can b win as shwn in scin, []: A. Synchns Gna ff f af ( f k f af fk E ff () af k ( ) ak V sin ( R a ) i () f fk ) i q q i v akq kq c k ak kk kk () ( ) i i ak k ( R a ) iq vcq q kq akq kkq kq ikq (5) q kq ( ) q akq V cs i af f () B. Tansissin Lin v v c cq i v (6) q c cq i v (7) C. Mchanical Sys Ih chanical sys h bin, na ah xci can b l by w fis ffnial qains as: Exci: ( ) (8) M D ( ) K ( ) (9) Gna: ( ) M T T D ( ) K ( ) K ( ) Lw Pss Tbin(LP): ( ) () M D ( ) K ( ) K( ) () Hih Pss Tbin(HP): ( ) () () () M D ( ) K( ) (5) IV. THE MDEL WITH PWER SYSTEM STABILIZER(PSS) AND AUTMATIC VLTAGE REGULATR(AVR) Th ain fncin f PSS an AVR a a api h na s scillains by cnllin is xciain sin axiliay sabilizin sinal. T cas a apin ffc, h sabiliz s pc an lcical q in phas wih sp viains. Fi. () shws h blck aa f h PSS an AVR,which cnsiss f h blcks [5]: I. Phas Cpnsain Blck. II. Sinal Wash Blck. III. Gain Blck Fi.( ).: AVR an PSS Blck Diaa Ml IJSSST, Vl., N. ISSN: 7-8x nlin, 7-8 pin
3 A. PSS an AVR Mahaical qains: Th PSS an AVR ahaical qain a v Tw Tw v v v T Tk s v ksv (7) Ef TR Ef KR( vf E ) (8) (6) F Tabl (), i s claha h sys is sabl, wh all Einvals hav naiv sin. As incass, h sys will ls is sabiliy in a. 7. Tabl () ivs a cla pic a b h insabiliy a.7. V. SIMULATIN RESULTS: A. Silain Rsls fh Sys wih AVR an PSS Th pw sys scib ali was pa wih fifn fis- ffnial qains, na by vayih val f chanical q. This cass vaiain ih sys sabiliy which can b scls by valaih Einvals. By slcih cpnsain fac, h q chanical () =.9 p ni, ah infini bs ba vla (V)=. p ni whil h xciain vla f synchns na () =.7 p ni, h Einvals f Jacban aix (5 5) aix) f h sys a shwn in Tabl(). Tabl ( ): Einvals a. 7 Fi. () shws h spns f h sys a.68, whil Fi. () shws h spns a.7, whh sys is nsabl an Fi. (5), claly shws ha h sys is nsabl a c.6.5. Tabl (), Einvals a. 68 p c c 6 x - - a l Fi. (): Th Rspns f h Sys a. 68 IJSSST, Vl., N. ISSN: 7-8x nlin, 7-8 pin
4 a p c D a x Fi. (): Th Rspns f h Sys a. 68 F il p c c c a l p c D a a Fi (5): Th Rspns f h Sys a. 75 p c c a l p c D a B. Silain Rsls f h Sys wih AVR an PSS Ihis scin, h cas f an Pw Sys Sabiliz (PSS) an Aaic Vla Rla (AVR) h sys was invsia scib ali. Th sys wih an AVR an PSS has ls is sabiliy a. 7. Af insih AVR an PSS, i was fha h sys is nsabl a. 76. Tabl shws h Einvals a. 7, whh sys is sabl, b h sys wih AVR an PSS is nsabl a h sa val f. 8 as shwn in (Tabl )... a Fi. (), Th Rspns f h Sys a. 7 Tabl (): Einvals a. 7 IJSSST, Vl., N. ISSN: 7-8x nlin, 7-8 pin
5 Fi. (6) shws h spns f h sys a.7, whil Fi.(7) shws h spns whn.75, whh sys is ciically sabl an Fi.(8), claly ha h sys is nsabl a. 8 p c c F il a c a l.8.7 p c.6 D a a l v Fi. (6): Th Rspns f h Sys a. 7 p c c a a l Fi. (7) : Th Rspns f h Sys a p c.5 D a.5 a l v p c.6 D a F il a a l v F il Fi. (7) : Th Rspns f h Sys a. 75 p c c a l.5.5 Fi. 8: Th Rspns f h Sys a. 8 IJSSST, Vl., N. 5 ISSN: 7-8x nlin, 7-8 pin
6 VI. CNCLUSINS Sb-synchns snanc phnnn is s by valaih Einvals f h Jacbian aix a sinl achin infini bs sys..th ffc f vayih cpnsain fac ah ffc f AVR an PSS a als cnsi ihis sy. A cpl ynaic l f sinl achin infini bs wih AVR an PSS cnll a psn. Inclh -q axs ap winns f synchns na wih AVR an PSS, h Einavals f h (5x5) Jacbian aix is vala an i is bsv ha h sys lss sabiliy a pin. 7. Whn sin h AVR an PSS cnll, h Jacbian aix f (8x8) is analyz an i appas ha h ain f h sys sabiliy is incas ah sys bc nsabl a pin. 76. REFERENCES [] A.H. Nayfh, A.M. Hab, Chin. Cha-Min, A.M. Haan an Mili Lain, Applicain f Bifcain Thy Sbsynchns Rsnanc in Pw Sys, Innainal Jnal f Bifcain an Chas, Vl.8, N., 998, PP [] Kn, P. 99, Pw Sys Sabiliy an Cnl, Elcic Pw Rsach Insi, McGaw-Hill, Nw Yk. [] IEEE SSR Wkin Gp, Scn Bnchak Ml f C Silain f Sbsynchns Rsnanc, IEEE Tans. n Pw Appaas an Syss. Vl. PAS-, N.5, 57-6, May 985. [] Y. Y, Elcic Pw Sys Dynaics, Acac Pss, Nw Yk. 98. [5] Maj M. Alai an Bnyk S. Ranski, Th Effcs f Machin Cpnns n Bifcain an Chas as Appli Mliachin Sys, CHAS8, Chaic Mlin an Silain Innainal Cnfnc, Chania, C, Gc, -6 Jn 8. [6] J.W. Balanc an S. Gl, Sbsynchns Rsnanc in Sis Cpnsa Tansissin Lins, IEEE Tans. n PAS, Sp./c. 97, pp [7] L.A. Kil, D.G. Ray an M.C.Hall, Siplifi Tansissin an Gnain Analysis Pcs f SSR, IEEE Tans. n PAS, Nv./Dc. 977, pp [8] R.. Fa, E. Kaz an A.L. Schwalb, Navaj Pjc n Sbsynchns Rsnanc Analysis an Slins, IEEE Tans. n PAS, 985, pp [9] A. Eis, Sis Cpnsain Schs Rcih Pnial f Rsnanc, IEEE Tans. n PAS, Fb.99, pp.9-6. [] A.A.Fa an K.T. Kh, Sbsynchns Rsnanc Zns ih IEEE Bnch-Mak Pw Sys, IEEE Tans Pw Appaas Sys. PAS-97, PP. 7-75, IJSSST, Vl., N. 6 ISSN: 7-8x nlin, 7-8 pin
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