SMALL SIGNAL ANALYSIS OF FLEXIBLE AC TRANSMISSION SYSTEM USING INTERLINE POWER FLOW CONTROLLER (IPFC)

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1 SALL SIGNAL ANALYSIS OF FLEIBLE AC RANSISSION SYSE USING INERLINE POWER FLOW CONROLLER (IPFC) CH. ENAA RISHNA REDDY,.RISHNA ENI, 3 G.ULASIRA DAS, 4 SIRAJ A. Prf., Dparm f EEE, CBI, Gaip, Hyraba, Iia Prf., Dparm f EEE, CBI, Gaip, Hyraba, Iia 3 Prf., Dparm f EEE, JNUH, Hyraba, Iia 4 E, Dparm f EEE, CBI, Hyraba, Iia c_h_v_k_r@yah.cm ABSRAC h Irli Pwr Flw Crllr (IPFC) i a vlag-urc-cvrr (SC)-ba flxibl ac ramii ym (FACS) crllr which ca ijc a vlag wih crllabl magiu a pha agl a h li-frqucy hrby prviig cmpai amg mulipl ramii li. I hi papr, h u f h IPFC ba crllr i ampig f lw frqucy cillai i iviga. A x Hffr-Phillip ml f a igl machi ifii bu (SIB) ym iall wih IPFC i ablih a u aalyz h ampig rqu cribui f h IPFC ampig crl h pwr ym. h pial f variu IPFC crl igal up h pwr ym cillai abiliy i iviga a uig crllabiliy ix. h ffc f hi ampig crllr h ym, ubjc wi variai i laig cii a ym paramr, i iviga. Rul f imulai ivigai i alab ar pr valia h prp apprach. y wr FACS, IPFC, Dampig, Small Sigal Sabiliy NOAIONS: P A : rafrr pwr f primary li, P B : rafrr pwr f cary li, P : al rafrr pwr f li, : rmial vlag f grar, I i : Dirc axi curr f li i, C : c lik capaciac H : iria ca ( = H) m i : ulai ix f ri cvrr δ i : Pha agl f ri cvrr vlag b : Ifii bu vlag c : lag a c lik : rmial vlag f h grar : Dirc axi rai ychru racac f grar A : AR Gai A : im ca f AR I iq : Quaraur axi curr f li i, : Dirc axi ay-a ychru racac f grar q : Quaraur axi ay-a ychru racac f grar, : Racac f ri cuplig rafrmr, 84

2 . INRODUCION Lw frqucy cillai wih frqucy i h rag f.. Hz ar f h rul f h ircci f larg pwr ym. m pwr ym ar abl if lcrmchaical cillai ccurrig i ach ara ca b amp a a pibl. icra pwr ym cillai abiliy, Pwr Sym Sabilizr (PSS) i a impl, ffciv, a cmical mh []. "Flxibl AC ramii Sym (FACS)" chlgy ha b prp urig h la hr ca a prvi br uilizai f xiig ym. Irig FACS capabilii uch a pwr flw crl, ampig f pwr ym cillai, vlag rgulai, a raciv pwr cmpai mak hm a g pi fr ffciv uilizai f pwr ym. I hi papr f h FACS capabilii i ampig ir-ara cillai ha will b accuraly iviga fr IPFC. Irli Pwr Flw Crllr, which i prp by Guygyi a al [] i l998, i a FACS crllr fr ri cmpai wih uiqu capabiliy f pwr flw maagm bw muli-li f a ubai. I h IPFC rucur a umbr f ivrr ar lik ghr a hir c rmial. Each ivrr ca prvi ri raciv cmpai, a a SSSC, fr i w li. Hwvr, h ivrr ca rafr ral pwr bw hm via hir cmm c rmial. hi capabiliy allw h IPFC prvi bh raciv a ral cmpai fr m f h li a hrby pimiz h uilizai f h vrall ramii ym. Lik hr FACS lm, IPFC ca b u fr icraig pwr ym abiliy agai larg a mall iurbac. I hi papr h vlag f cuplig capaciac bw w SC-ba cvrr i u a a a variabl. Oupu pwr f h grar i u a a ipu f PI crllr, which cra prpr ampliu mulai rai fr h cary cvrr.. DYNAIC ODEL OF HE SYSE WIH IPFC A igl-machi ifii-bu (SIB) ym wih IPFC, iall w li i cir. hi cfigurai which ci f w paralll ramii li, cc h grar G a ifii bu, i illura i figur. Figur Sigl achi Ifii Bu Sym Wih IPFC PSS i akig i accu i h pwr ym. Opraig cii a paramr ar rpr i h appix. Phillip-Hffr liar ml f a igl-machi ifii bu ym wih IPFC i riv frm h liar iffrial quai. Nglcig h riac f all h cmp f h ym lik grar, rafrmr, ramii li, a ri cvrr rafrmr, a liar yamic ml f h ym i riv a fllw: = ( ω ) δ ω () [ P P D( )] ω m ω = (). ( Eq E f )/ [ E f + A( rf )] A E q = + E f = / Whr, (3) (4) P = P + P (5) P = ( I + q E q = E q +( - I ) + ( I q + I q ) (6) )( I + I ) (7) = + j q (8) = q I q +j[ E q - ( I + I )] 84

3 If h gral Pul Wih ulai (PW) i u fr SC, h vlag quai f h IPFC cvrr i q cria will b []: p q = I I q + c m m cδ cδ (9) p q whr, = I I pq = p + j q = pq q + c m iδ m iδ () j k δ () [ I cδ + I δ ] c 3m = q i 4C 3m + I cδ + Iq iδ 4C Frm figur, w hav: = j [ ] () I + pq + j L I (3) hi quai i -q cria i a fllw: + j q = j [( I + I )+j( I q + I q )]+ +j L ( I +j I q )+ p + b iδ + jb cδ (4) I h hr ha, accrig figur, w hav: = q ( I q + I q ) (5) q = E q -( - )( I + I ) (6) Figur.Phar iagram f iviga ym Frm (6) (), i ca b bai: L q L whr, a li. L L q L I I I I c Eq m = c q q q = q + L = + iδ cδ ( m ) iδ m iδ (7) c m cδ + b iδ = ( ) c m cδ m cδ (8) (9) L () Κ = - L () = + q q L Κ () = (3) i h ri racac f ach ramii 3. LINEAR DYNAIC ODEL Pwr ym cillai abiliy a crl ca b ui uig a liariz ml f h pwr ym. b A liar yamic ml f h ym illura i figurl, i bai by liariig h liar ml f h ym pr i abv ci, 84

4 aru a praig cii. h liariz ml i a fllw: δ ω 4 E = q E f c A 7 pm qm + A cm vm 5 ω D p δ qδ A cδ vδ 3 A 8 6 pm A cm A qm vm pv qv A 9 vv δ ω E + q E f c pδ m δ qδ m δ vδ A cδ (4) I h a-pac rprai, h pwr ym ca b ml a = A + BU Whr h a vcr a crl vcr ar a fllw: = δ ω Eq E f U = m m δ δ m i h viai i pul wih mulai ix m f vlag ri cvrr- i li-. By crllig m, h magiu f ri ijc vlag i li- ca b crll. m i h viai i pul wih mulai ix m f vlag ri cvrr- i li-.by crllig m, h magiu f ri ijc vlag i li- ca b crll. δ i h viai i pha agl f h ijc vlag pq. δ i h viai i pha agl f h ijc vlag pq. c i h viai f cuplig capaciac vlag bw cvrr, Uig h mahmaical ml f h SIB wih IPFC a a pac rprai i (4), h c Phillip-Hffr ml r liar ml f h SIB ym ca b bai icluig IPFC [3]. Whr U = m m δ δ p = pm p pm δ pδ q = qm q qm δ qδ v = vm vδ vm vδ hi ml ha 8 ca, pr blw a, ar fuci f h ym paramr a iiial praig cii a blw.h ym i icrpra wih IPFC. La flw aalyi i prfrm bai h praig pi which i giv a fllw: P =.9, Q =.958 =. b = pq = =. 43 =.944 I = I =. 785 q δ = q δ = δ = h ym i liariz abu hi praig pi. h -ca fr h ym iall wih IPFC, ar cmpu a fllw: =.55 =. 43 =. 4 = =.85 = = = = pv = =.87 =. 6 qv pm =.55 pm =. 53 pδ =.376 pδ =. 45 qm =.36 qδ =. qm =.56 qδ =. 33 vm =.36 vδ =. 9 vm =.38 =. vv vδ 843

5 4 cm = =. cδ 67 cm =.87 =. 6 cδ 4. DESIGN OF IPFC DAPING CONROLLERS imprv h ampig f lw frqucy cillai h ampig crllr ar prvi pruc h aiial ampig rqu. h p viai ω i cir a h ipu h ampig crllr which rflc h wig h machi a li f ir. A uch, h upu f h crllr i i pha wih h p viai. Fig. 3 Srucur f IPFC ba ampig crllr h rucur f IPFC ba ampig crllr i hw i Fig.3. I ci f gai, igal wahu a pha cmpai blck. h pimum paramr f h ampig crllr ar bai uig h pha cmpai chiqu [4]. h ig i pr a blw. h im ca f h pha cmpar ar ch uch ha h pha agl f h ym i fully cmpa. Fr h mial praig cii, h magiu a pha agl f rafr fuci, P / U, will b cmpu fr jω =. h gai ig f h ampig crllr i ch achiv h rquir ampig rai f.. A brv frm (4) hr ar fur chic f ipu igal ( m, δ, m aδ ) f h IPFC mula. h igal which ca achiv ffciv ampig crl a miimum crl c will b h m ffici. hi lci i ma a p lp cii bfr iallai f ampig crllr. h ccp f crllabiliy ix i u lc h m uiabl IPFC crl paramr frm h ampig crllr fr mulai [5]. (). Cmpu h aural frqucy f cillai ω frm h mchaical lp a ω = ω (). L γ b h agl f h rafr fuci G ( ) P =,(pha lag f bw u a P u u = m, δ m a δ a, whr [ ] hw i Fig.4.5, a, jω =. (3). h crllr ig i ma up f wahu filr a la-lag blck, wih h fllwig rafr fuci: w + G ( ) = + + w w i h wahu filr im ca a i valu ca b ak a a umbr bw a c. Aum fr h la-lag wrk, = a, whr a = (+ iγ ) /( iγ ) a ( a ) ω =. h rquir gai ig fr h ir rai ξ i bai a, ξω =, whr c ( ) G c ( ) G ( ) ar valua a jω =. G a G ( ) h ig valu crrpig cillary m f h ym ar cmpu a giv i abl. Frm h abl, w brv ha h ym ci f bh lcal m a ir ara m. h ir ara m ar ufficily amp, whra, h lcal m ar lighly amp. abl : Eig alu Of h Sym Eig valu Dampig rai f Ocillary Naural frqucy f Ocillai(Hz) m.3 ± 9.84 j ± 4.5 j Fr h mial praig pi, h aural frqucy f cillai ω i qual 9.84j ra/c. hi m i rpibl fr h lw frqucy cillai f aru.5 Hz wih vry l ampig f.3. h ampig crllr ar ig prvi h aiial ampig. h paramr f h crllr ar cmpu aumig a ampig rai (ξ ) f.. h gai a 844

6 pha agl f ( ) cmpu a giv i abl. G fr h variu ipu ar c all h crl igal a a im. abl 4 giv h cmpu valu f h iic. abl : agiu A Pha Agl Of h rafr Fuci G c ( ) G ( ) ( ) c G c P m P δ P m P δ I ca b ha h pha agl f h ym fr h crl paramr δ i ar 8 hrfr h ym bcm uabl wh h crllr ( δ ) i u. hi crllr i cir i furhr ivigai. abl 3 hw paramr f h rmaiig hr alraiv ampig crllr cmpu a h mial praig pi. abl 3: Paramr Of h Ipfc Dampig Crllr Dampig crllr Dampig crllr m Dampig crllr δ Dampig crllr m abl 4: Crllabiliy Iic Wih Diffr Ipfc Crllabl Paramr IPFC crl paramr Crllabiliy Ix m.7974 m.8 δ.94 δ.455 abl 4 rval ha h crllabiliy ix m, i crrpig IPFC crl paramr high a ha f δ, i iigifica cmpar m h hr crl paramr. Hc, u = i h b lci fr h ig f h IPFC ampig crllr ic h miimum crl c (h lw gai) i prvi w, h ampig crllr ba m hall b a ampig crllr m. I h x chapr h yamic rp f h ym wih a wihu h ampig crllr m i ui. h yamic prfrmac f h ym i furhr xami cirig a ca i which w m, m ampig crllr pra imulauly (ual crllr). I h x chapr rp f ω wih h hr alraiv ampig crllr i imula. h rp f ω i bai wih a p prurbai f P =.. Simulai rul hw ha h m rp ar iical which iica ha ay f h IPFC ampig crllr, prvi aifacry prfrmac a h mial praig pi. Hwvr, i rr lc h m ffciv IPFC crl igal fr ampig, h crllabiliy ix i cmpu. h ix i cmpu fr h lcrmchaical m ( 9.84jra/c) b amp akig i accu Fig. 4 rafr fuci f h ym rlaig cmp f lcrical pwr P pruc by ampig crllr u 845

7 abl 5: Phillip-Hffr l Ca Fr Sym Wihu Ipfc i i DIGIAL SIULAION I rr ura h ffc f IPFC ampig lw frqucy cillai, igial imulai uig alab Simulik lbx i i w ca, wih a wihu IPFC.h blck iagram f fig 7 i u i mall igal abiliy ivigai f h pwr ym. h ALAB Simulik lbx i u uy h ym prfrmac ur iffr ampig crllr. Fllwig figur hw h rul f SIB wih iffr ampig crllr. h rr p viai a rr agl viai, rpcivly fr iffr ampig crllr ar ui. h ampig crllr ar ig by w mh. ) h p viai ( ω) i u a ipu igal fr ig f ampig crllr uig pha cmpai chiqu [4]. ) h lcrical pwr i ak a ipu fr h ig f PI-Dampig crllr [3,8]. 6. SIULAION RESULS R r a g l v ia i (ra ) im (c) Fig 6. Rr agl viai fr wihu IPFC R r p v i a i ( r a / c ).5 x =., im (c) =., wihu Fig 7 Rr Sp viai fr R r a g l v i a i ( r a ) ( m )IPFC crllr im (c) Fig 8. Rr agl viai fr wihu ( m ) IPFC crllr =., Rr p viai (ra/c ).5 x im (c) Fig 5. Rr p viai fr wihu IPFC =., R r p v a i ( r a / c ).5 x im (c) Fig 9. Rr p viai fr wih ( m =., ) yp ampig crllr 846

8 R r a g l v i a i ( r a ) im (c) Fig Rr agl viai fr R r p v i a i ( r a / c ) R r a g l v i a i ( r a ).5 x ( m ) yp ampig crllr =., wih im (c) R r p v i a i ( r a / c ) Fig Rr p viai fr =., wih ( m ) yp ampig crllr im (c).5 x Fig Rr agl viai fr =., wih ( m ) yp ampig crllr im (c) Fig 3. Rr p viai fr δ =., wih ( ) yp ampig crllr R r a g l v ia i ( ra ) R r p v i a i ( r a / c ) R r p v i a i ( r a / c ) im (c) x -5 5 Fig 4. Rr agl viai fr δ =., wih ( ) yp ampig crllr im (c) R r a g l v i a i ( r a ) 6 4 =., wih ual ampig crllr Fig 5. Rr p viai fr 8 x im (c).5 x =., wih ual ampig crllr Fig 6. Rr agl viai fr im (c) Fig 7. Rr p viai a P =., wih ( m ) yp ampig crllr 847

9 Fig 8. Rr p viai a ( m ) yp ampig crllr P =, wih Fig Rr Sp viai fr ( m ) PI yp ampig crllr =., wih =., wih ( m ) yp PI-ampig crllr Fig 9 Rr p viai fr Fig. Rr agl viai fr wih ( m =., ) PI yp ampig crllr =., wih ( m ) yp PI- ampig crllr Fig. Rr agl viai fr Fig 3 Rr p viai fr δ wih( ) PI yp ampig crllr =., 848

10 h pwr ym wihu IPFC, wih IPFC ar bai a cmpar. Fig 4 Rr agl viai fr δ wih( ) PI yp ampig crllr Fig 5 Rr p viai fr ual ampig crllr =., =., wih PI- IPFC a a muliak crllr, ha a ffciv rl i ampig lw frqucy cillai. I hi hi, hi fuci f IPFC ha b iviga a umrical rul mphaiz i igifica ffc. I fac, v hr i ay ampig cffici i pwr ym, IPFC ca amp lw frqucy cillai. h ffc ar craig h ampliu a frqucy f pwr ym cillai. rvr i amp cillai far i cmpari wh hr i IPFC i h ym. h crllabiliy ix crrpig IPFC crl paramr m, i high a ha f δ, i iigifica cmpar h hr crl paramr. Hc, u = m i h b lci fr h ig f h IPFC ampig crllr ic h miimum crl c (h lw gai) i prvi, h ampig crllr ba m. Dyamic imulai rul hav mphaiz ha h ampig crllr which mula h crl igal m prvi aifacry yamic Prfrmac ur wi variai i laig cii a ym paramr. h rp f h SIB iall wih IPFC ba Dual cvrr i imprv wh cmpar wihu IPFC a iiviual ( m, δ,a m ) yp ampig crllr. Rp f SIB wih IPFC fr p prurbai i =.,a rf =. i g wih Dual crllr. Fig 6 Rr agl viai fr =., wih PIual ampig crllr 7. CONCLUSIONS h IPFC ba ampig crllr i ig fr w iffr ca. h upu f h lig im fr PI- ampig crllr i mr a cmpar Phacmpai ba ampig crllr. Pha-cmpai ba ampig crllr amp cillai far i cmpari wih PI-crllr. 849

11 abl 6: Cmpari f Slig im fr w ca IPFC ampig crllr PI Crllr Pha Cmpai m c 4.5 c -yp crllr δ -yp crllr c 5 c m 9 c 4 c -yp crllr Dual cvrr 8 c 3 c APPENDI h ym aa a iiial praig cii f h ym ar a fllw: Grar: = H = 8. J/A D = ; = 5.44; =.pu; =.3pu; q =.6pu ; P =.9; Q =.958 ; =.; b = [3] H.F.Hag, "DESIGN OF SSSC DAPING CONROLLER O IPROE POWER SYSE OSCILLAION SABILIY", 999EEE. [4] N.amby a.l.hari, "DAPING OF POWER SYSE OSCILLAION WIH UNIFIED POWER FLOW CONROLLER", IEE Prc.-Gr. ram. Dirib. l.5, N., arch 3. [5] "FLEIBLE AC RANSISSION SYSES (FACS)", IEE Pr, L 999. [6].. Pail, J. Shil, J. Jiag a R.. ahur, Applicai f SACO fr Dampig rial Ocillai i Sri Cmpa AC Sym, IEEE raaci Ergy Cvri, vl. 3, N. 3, Spmbr 998, pp [7] H.F.Wag a F.J.Swif, A Uifi l fr h Aalyi f FACS Dvic i Dampig Pwr Sym Ocillai Par I: Sigl- achi Ifii-bu Pwr Sym, IEEE raaci Pwr Dlivry, vl., N., April 997, pp [8] L. Fa a A. Fliachi, Rbu CSC Crl Dig fr Dampig Ir-Ara Ocillai, Prcig f IEEE PES Summr ig, acuvr, Briih Clumbia, Caaa, July 5-9,. Exciai ym: Cvrr rafrmr: A = 5; =.l pu A =.5 Cvrr paramr: m =.5; m =.; ramii li rafrmr: =.5 pu; =.5 pu L DC lik paramr: REFERENCES c =. pu; C = pu [] Ya-a Yu, "ELECRIC POWER SYSE DYNAICS", Nw Yrk, Acamic Pr, Ic., 983 [] Guygyi & al " HE INERLINE POWER FLOW CONROLLER CONCEP: A NEW APPROACH O POWER FLOW ANAGEEN IN RANSISSION SYSES", IEEE raaci Pwr Dlivry, l. 4, N. 3, July

12 Fig 7. Phillip-Hffr l (Liari l) Of A Sigl-achi Ifii-Bu (SIB) Sym Wih IPFC 85