A New Static Var System Auxiliary Controller for Damping Torsional Oscillations in Series Compensated Power System

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1 Intrnational Journal of Elctrical Enginring. IN Volum, Numbr (00), pp Intrnational Rsarch Publication Hous A Nw tatic Var ystm Auxiliary ontrollr for Damping Torsional Oscillations in ris ompnsatd Powr ystm harma P.R. YA Univrsity of cinc and Tchnology, Faridabad, India prsharma966@gmail.com Abstract In this papr th application of an tatic Var ystm (V) auxiliary controllr for damping torsional oscillations in a sris compnsatd powr systm is prsntd. A nw auxiliary controllr, known as th combind drivativ of ractiv powr and drivativ of computd intrnal voltag auxiliary (DRPDIVA) controllr has bn dvlopd and incorporatd in th V control systm locatd at th middl of a sris compnsatd long transmission lin. Effctivnss of proposd controllr is tstd on a systm having a similar sprad of th torsional mods as th first IEEE bnchmark modl. Eign valu analysis study is conductd for various lvls of powr transfr and sris compnsation. Th rsults of ignvalu analysis ar validatd by carrying out tim domain analysis study basd on non linar modl. Th proposd V auxiliary controllr along with induction machin damping unit (IDU) stabilizs all th torsional mods for a wid oprating rang and thus nhancing th dynamic and transint prformanc of th systm. Kywords: tatic Var ystm, Induction machin damping unit (IDU), Auxiliary controllr, Torsional oscillations. Introduction ris compnsation is mployd in powr systms to rais th powr transfr capability. Howvr sris compnsation givs ris to dynamic instability and R problms. R occurs whn a natural frquncy of a sris compnsatd transmission systm matchs with th complmnt of on of th torsional mods of th turbingnrator shaft systm. Undr such conditions th turbin gnrator oscillats at a frquncy corrsponding to torsional mod frquncy of turbin gnrator shaft

2 5 harma P.R. During this condition th torsional oscillations can grow and may rsult in failur of turbin shaft. [-]. vral countrmasurs for damping of torsional oscillations such as Excitation control, [] tatic Var ompnsator( V), tatic ompnsator (TATO), tatic synchronous sris compnsator ( ) and unifid powr flow controllr(upf) hav bn rportd in litratur [-0]. Among ths th application of V controllr has gaind importanc in rcnt yars. In rcnt yars V has bn mployd to an incrasing xtnt in modrn powr systms [] du to its capability to work as Var gnration and absorption systms. Bsids, voltag control and improvmnt of transmission capability V in coordination with auxiliary controllrs [] can b usd for damping of torsional oscillations. Damping of powr systm oscillations plays an important rol not only in incrasing th transmission capability but also for stabilization of powr systm conditions aftr critical faults, particularly in wakly coupld ntworks. G. N. Pillai and A. Gosh t.al. [8] dsignd a powr flow controllr proposing an intgral stat fdback controllr that rducs th advrs ffct of powr flow controllr on torsional intractions and compard th torsional charactristics of compnsatd powr systm with that of fixd sris capacitor compnsatd systm. Ning Yang t.al. [9] dsignd a controllr that could modulat th impdanc of lin for nhancing th damping of torsional oscillations. But th rsults show that th controllr is not abl to damp out all th unstabl mods. In th rcnt yars thyristor controlld sris compnsators hav bn dvlopd to control powr flow on th ransmission lin and ar vry ffctiv for damping powr systm oscillations [0]. Noroozian, t. al. [6] proposd a robust control stratgy for thyristor controlld sris capacitor and static VAr systms to damp lctromchanical oscillations. haudhuri, B. Pal t al dsignd a multipl input ingl output (IO) controllr for T to improv damping of critical intr ara mods using global stabilizing signals[]. R.K.Vrma [5] t.al. hav dscribd th us of T for damping subsynchronous oscillations whn providd with clos loop currnt control. Albrto ota imos [6] t.al. hav proposd a powr oscillation damping controllr dsign implmntd in T to supprss low frquncy oscillations..k. Gupta, Narndra Kumar [] dvlopd a doubl ordr V auxiliary controllr in ombination with continuously controllabl sris compnsation and Induction machin damping unit (IDU) for damping torsional mods in a sris compnsatd powr systm. Th schm is abl to damp out th torsional mods at wid rang of sris compnsation. Howvr th control schm is complx and th difficult to implmnt. This papr xamins th ffctivnss of static var systm for damping torsional oscillations in sris compnsatd ac systm. Th V considrd is quippd with PI controllr that rgulats th gnrator trminal voltag. Auxiliary signals namly drivativ of computd intrnal voltag and drivativ of ractiv powr hav bn incorporatd in th V control loop.. Th proposd controllr along with IDU is abl to stabiliz all th torsional mods ovr a wid rang of sris compnsation lvls at various lvls of powr transfr and provids a cost ffctiv solution to R damping. Th proposd controllr is simpl and asy to implmnt bcaus th auxiliary signals ar drivd locally at th V bus.

3 A Nw tatic Var ystm Auxiliary ontrollr 5 ystm odl Th study systm consists of a stam turbin drivn synchronous gnrator (a sixmass modl) supplying bulk powr to an infinit bus ovr a long transmission lin (IEEE first bnchmark modl). An V of switchd capacitor and thyristor controlld ractor typ is considrd locatd at th middl of th transmission lin which provids continuously controllabl ractiv powr at its trminals in rspons to bus voltag and of drivativ of computd intrnal voltag and drivativ of ractiv powr auxiliary control signals. Th sris compnsation is applid at th snding nd of th lin. Figur. tudy ystm. Gnrator In th dtaild machin modl [8] usd hr, th stator is rprsntd by a dpndnt currnt sourc paralll with th inductanc. Th gnrator modl includs th fild winding f and a dampr winding h along d-axis and two dampr windings g and k along q-axis. Th IEEE typ- xcitation systm is usd for th gnrator. In th mchanical modl dtaild shaft torqu dynamics [] has bn considrd for th analysis of torsional mods du to R. Th rotor flux linkags ψ associatd with diffrnt windings ar dfind by: ψ f a ψ f + a ψ h + bvf + b id ψ h a ψ f + a ψ h + bid ψ g a 5ψ g + a 6ψ k + b5i () q ψ k a 7ψ g + a 8ψ k + b6iq Whr v f is th fild xcitation voltag. onstants a to a 8 and b to b 6 ar dfind in []. i d, i q ar d, and q axis componnts of th machin trminal currnt rspctivly which ar dfind with rspct to machin rfrnc fram. To hav a common axis of rprsntation with th ntwork and V, ths flux linkags ar

4 5 harma P.R. transformd to th synchronously rotating D-Q fram of rfrnc using th following transformation: i d cosδ sin δ i D i () q sin δ cosδ i Q Whr i D, i Q ar th rspctiv machin currnt componnts along D and Q axis. δ is th angl by which d-axis lads th D-axis. urrnts I d and I q, which ar th componnts of th dpndnt currnt sourc along d and q axis rspctivly, ar xprssd as: I c ψ + c ψ I d q f g h c ψ + c ψ () k Whr constants c - c ar dfind in []. ubstituting qn. () in qn. () and linarizing givs th stat and output quation of th rotor circuit as: X R A RX R + BRU R + BR U R + BRU R YR RX R + DRU R () X + D U + D U + D U YR R R R R R R R R Whr X R [ Δψ Δψ Δψ ψ ], f [ Δδ Δω] U R, U R ΔVf U R Y [ ΔI ΔI ] R h, [ Δi Δi ] D Q D g k Q chanical ystm Th mchanical systm (fig.) is dscribd by th six spring mass modl. Th govrning quations and th stat and output quations ar givn as follows: Fig.. ix-pring mass modl of mchanical systm

5 A Nw tatic Var ystm Auxiliary ontrollr 55 δ ω, i,,,,5,6 ω ω ω ω ω ω i 5 6 i [ ( D + D ) ω + D ω K ( δ δ ) + T ] [( D ω (D + D + D ) ω + D ω K ( δ δ ) K ( δ δ )) + T ] [( D ω (D + D + D ) ω + D ω K ( δ δ ) K ( δ δ )) + T ] [( D ω (D + D + D ) ω + D ω K ( δ δ ) K ( δ δ )) + T ] [( D ω (D + D + D ) ω + D ω K ( δ δ ) K ( δ δ )) + T ] [( D ω (D + D ) ω + D ω K ( δ δ )) + T ] m m m m as: Aftr linarzing th abov quations th stat and output quations can b writtn X A X + BU + BU (5) Y X (6) X Y U, [ Δδ ] t, Δδ, Δδ, Δδ, Δδ5, Δδ6, Δω, Δω, Δω, Δω, Δω5 Δω6 [ Δδ Δω ] t U ΔI, ΔI 5, [ ] t D Q [ Δi, Δi ] T 5, D Q Excitation ystm Th stat and output quations of th linarisd IEEE typ xcitation systm ar drivd asfollows: whr X A X + B U Y X E E E E E X E E E E [ ΔV f Vs Δ ΔV r ] t, YE [ ΔVf ], U E [ ΔVg ] (7) Ntwork Th transmission lin (fig.) is rprsntd by lumpd paramtr T- circuit. Th ntwork has bn rprsntd by its α axis quivalnt circuit, which is idntical with th positiv squnc ntwork. Th govrning quations of th α-axis, T-ntwork rprsntation ar drivd as follows:

6 56 harma P.R. Figur. α axis rprsntation of th ntwork whr di α ( L + L T ) Vα V α Ri α dt di α ( L + L ) A Vα (R + R A )i α L diα Vα dt dvα n i α i α i α dt dvα s i α (8) dt L L L + A T + d and n F imilarly, th quations can b drivd for th β- ntwork. Th α-β ntwork quations ar thn transformd to D-Q fram of rfrnc and subsquntly linarisd. Th stat and output quations for th ntwork modl ar finally obtaind as: X [A ]X + [B ]U + [B ]U + [B ] U (9) N N N N Y [ ]X + [D ]U + [D ]U + [D N N N N N N N N Y N [ N ] X N, Y N [ N] X N N N N N N ] U N Whr, X N [ i D U Δ Δ id Δ v D Δ v D Δ i Δ i Q Q Δ v Q Δ v Q N [ Δi D Δ i Q ] t, U N [ Δ İD Δ İQ ] t U N Y Y [ Δ I Δ I D Q ]t N [ ΔVgD VgQ N [ ΔVD Δ V Q ] t Δ ] t, YN [ Δi D Δ i ] t Q ] t

7 A Nw tatic Var ystm Auxiliary ontrollr 57 tatic Var ystm Fig. shows a small signal modl of a gnral V. Th trminal voltag prturbation V and th V incrmntal currnt wightd by th factor K D rprsnting currnt droop ar fd to th rfrnc junction. T rprsnts th masurmnt tim constant, which for simplicity is assumd to b qual for both voltag and currnt masurmnts. Th voltag rgulator is assumd to b a proportional- intgral (PI) controllr. Thyristor control action is rprsntd by an avrag dad tim T D and a firing dlay tim T s. B is th variation in TR suscptanc. V F rprsnts th incrmntal auxiliary control signal. Th α, β axis currnts ntring TR from th ntwork ar xprssd as: Fig.. V control systm with auxiliary fdback di α L V α R i α dt di β L Vβ R i β (0) dt Whr R, L rprsnt TR rsistanc and inductancs rspctivly. Th othr quations dscribing th V modl ar: z Vrf z + ΔVF ( ΔV K Δi ) z D z () T T z ( K (z ΔB I z D + K Pz z T ΔB) T s K ΔV P rf )

8 58 harma P.R. Whr ΔV, Δi ar incrmntal magnituds of V voltag and currnt, rspctivly, obtaind by linarising V (V V ), i (i i ) D + Q D + Th stat and output qns. of th V modl ar obtaind as: X [A ]X + [B ]U + [B ]U + [B ] U () Y [ ]X + [D ] U Q Whr X [ i D Q U U Y i Z Z Z [ ΔVD V Q ΔV F [ Δi D Δ i Q ] t Δ B] t, Δ ] t, U ΔVREF Dvlopmnt of V auxiliary controllr Th auxiliary signal U is implmntd through a first ordr auxiliary controllr transfr function G(s) as shown in fig.5, which is assumd to b: ΔVF K B ( + st ) G(s) U ( + st ) Figur 5. Gnral first-ordr auxiliary controllr G(s) B K BT T + () T K T ( + st )

9 A Nw tatic Var ystm Auxiliary ontrollr 59 Th stat and output quations ar givn by X A X + B U () [ ] [ ] [ ] X [ D ] U Y + Whr [ ] Z X, Y ΔVF B, [ A ], [ B ], [ ], [ ] T K T T T D K BT T ombind Drivativ of Ractiv Powr and Drivativ of omputd Intrnal Voltag (DRPDIV) Auxiliary ontrollr Th auxiliary controllr signal in this cas is th combination of drivativ of th lin ractiv powr and th drivativ of computd intrnal voltag with th objctiv of utilizing th bnficial contribution of both signals towards improving th dynamic prformanc of th systm. Th control schm for th composit controllr is illustratd in Fig.5. Th auxiliary control signals U and U corrspond, rspctivly, to th drivativ of lin ractiv powr and th drivativ of computd intrnal voltag dviations which ar drivd at th V bus. Fig. 5. ontrol schm for (DR.PDIV) auxiliary controllr Drivati of Ractiv Powr Auxiliary ignal Th auxiliary control signal in this cas is th dviation in th lin ractiv powr ntring th V bus. Th ractiv powr ntring th V bus can b xprssd as: Q V i V (5) D Q Q i D whr i D, i Q and V D, V Q ar th D-Q axis componnts of th lin currnt i and th V bus voltag V rspctivly. Linarizing qn. (5) givs th dviation in th ractiv powr as:

10 60 harma P.R. ΔQ V V Δi DO i Δi QO D DO Q [F6 ] X T Q + i ΔV QO Q ΔV D (6) Δ (7) whr F 6 (x) vctor having non zro lmnts as F 6 (,)V Qo, F 6 (,5)-V Do,F 6 (,)-i Qo,F 6 (,6)i Do Th drivativ of th ractiv powr is obtaind by diffrntiating q.(7) ΔQ F6 [AXT + BU ] [F7 ] X T (8) whr F 7 F 6 A and F 6 B0 Th quation (8) can b writtn as U [F R ]X R +[F ]X +[F E ]X E + [F N ]X N +[F ]X (9) whr U ΔQ c Drivativ of omputd Intrnal Voltag Auxiliary ignal Th drivativ of computd intrnal voltag signal has bn drivd by computation of intrnal voltag of th rmotly locatd gnrator utilizing locally masurabl V bus voltag and transmission lin currnts. Th DIV signal has a mor bnficial influnc on th high frquncy Torsional oscillations. As it is not fasibl to obtain this signal by masurmnt as th gnrating station and th V ar locatd far apart from ach othr, thrfor it is attmptd to driv th proposd signal in trms of paramtrs, which ar availabl at V bus. Th paramtrs utilizd for th signal ar bus voltag, transmission lin currnt at V bus and ractanc btwn th gnrator and V trminal. Th lin charging capacitanc and th rsistanc of th gnrator stator and th transmission lin ar nglctd. Th dpndnt currnt sourc rprsnt th gnrator and transformd to an quivalnt voltag sourc bhind th subtransint inductanc, From th quivalnt circuit, th total inductanc L E btwn th bus and quivalnt sourc is givn as: Fig 6: α-axis rprsntation of simplifid systm for DIV signal

11 A Nw tatic Var ystm Auxiliary ontrollr 6 L ( XL X ) ω0 " E Ld + LT + / Th αand β axis componnt of intrnal voltag ar xprssd as: diα α V α + LE V5 α dt (0) d iβ β Vβ + L E V5β dt () Th abov quations ar transformd to D-Q fram of rfrnc as: D VD + L E i D + ω0 L Ei Q V5D () V + L i + ω L i () Q Q E Q 0 E D V5Q whr D and Q ar D-Q axis componnt of th intrnal voltag rspctivly. Th computd intrnal voltag signal is obtaind as: + () q d Aftr linarising quation () Δ (5) D0Δ D + Q0 Δ Q 0 Putting th valu of Δ Q0 0 D0 0 Δ and Δ Q in quation (6): D [ ΔV + L Δi + ω L Δi ΔV ] [ ΔV + L Δi + ω L Δi ΔV ] Q D E E Q D 0 E 0 E D Q 5Q 5D + Whr [ F ] X T +.[ F ] T Δ (7) X X T [ X X X X X ] R E N F ( Χ5) Vctor having non-zro lmnt as follows: F Q0 D0 (,) ω0 E, F (,) F (,) L 0 F 0 D0 Q (,5) ω0 E, F (,6) 0, F (,7) L 0 D 0 Q F (,) E, F ( ) 0,5 L E L 0. X T AX T + BU in quation F [ X T ] + F [ AX T + BU ]. Δ [ F ] XT, whr F [ F + F A] 0 0 Δ (8) D0 0 Q 0 and (9) 0

12 6 harma P.R. F B 0 Th drivativ of computd intrnal voltag is givn as: Δ [ F ] T. X Aftr xpanding th quation (9) U [F R ]X R +[F ]X +[F E ]X E + [F N ]X N +[F ]X Whr U Δ ė Induction achin Damping Unit (IDU) Th proprty of induction machin to act as a gnrator or motor is utilizd to absorb th mchanical powr whn thr is xcss and to rlas it whn thr is a dficincy. inc th machin coms into opration during transints only, it is dsignd for vry high short- trm rating and vry small continuous rating. onsquntly th machin has low inrtia, low powr, and small siz and low cost. Bcaus of it small mass and tight coupling with th intrmdiat prssur turbin it has bn considrd as a singl mass unit with IP turbin. Elctrically it is connctd to th gnrator bus. Th pr unit torqu (T im ) is givn by: s T im (0) ( ) s.x ω + 0r. r and slip ( ω0 ω ) s ω 0 Hnc by considring qn. (0) th mchanical systm modl is modifid as blow: ( Dω (D + D + D ) ω + Dω K ( ) K ( )) δ δ δ δ + Tm + T im ω

13 A Nw tatic Var ystm Auxiliary ontrollr 6 s.x s.x + Δ s s r r ΔT im () ( ) s.x ω + 0r. r Δω As dviation in slip, Δ s ω0 At normal oprating point s 0, Δs Δω Hnc, Tim ω r ω r 0 D Δω (D + DΔω K Δω 0 + D + D + Δω ω0r ( δ δ ) K ( δ δ )) Th damping cofficint trm - (D + D + D ) of intrmdiat prssur turbin is thus modifid to -(D + D + D + /ω 0 r ) on application of IDU, similarly othr mchanical quations can b modifid to account th damping ffct of IDU for its diffrnt Locations on th TG shaft. Th stat and output quations of th diffrnt constitunt subsystms along with th auxiliary controllr stat and output quations ar combind to rsult in th linarisd stat quations of ovrall systm as: X T [A]X () Whr, X T [ X R X X E X N X X ] t Th dimnsion of th systm matrix is 5 A as tudy Th study systm consists of 0 VA synchronous gnrator supplying powr to an infinit bus ovr a 00 kv, 600 km. long sris compnsatd singl circuit transmission lin. Th systm data and torisonal spring mass systm data ar givn in Appndix. Th V rating for th lin has bn chosn to b 00 VAR inductiv to 00 VAR capacitiv. 5%,0% and 8% sris compnsation is usd at th snding nd of th transmission lin.

14 6 harma P.R. Torsional oscillations tudy Th ign valus hav bn computd for th systm with and without (DRPDIV) auxiliary controllr incorporatd in V control systm for wid rang of sris compnsation and powr transfr lvls. Tabl prsnts th ign valus for th systm at gnrator powr P G 800 W for compnsation lvls of 5%, 0% and 8% without any auxiliary controllr. Whn no auxiliary controllr is incorporatd. od and 5 ar unstabl for all lvls of sris compnsation usd. od is unstabl at 8% and mod is unstabl at 5%. od is unstabl at 5% and 8%. od is unstabl at 5%and od0 is unstabl at 5% and0% lvl of sris compnsation in th systm at P G 800 W. Tabl shows th systm ign valus whn combind drivativ of Ractiv powr and drivativ of omputd intrnal Voltag Auxiliary ontrollr is incorporatd in V control systm. It can b sn that all th mods ar stabl at P G 800 W for all lvls of sris compnsation. Tabl shows th systm ign valus without any auxiliary at P G 00,500and 800 W at 5% compnsation lvl. ods5,, and ar unstabl at all powr transfr lvls and ods and 0 ar unstabl at P G 800W. Tabl shows th systm ign valus whn combind drivativ of Ractiv powr and drivativ of omputd intrnal Voltag Auxiliary ontrollr is incorporatd in V control systm along with IDU. It can b sn that all th mods ar stabl at all lvls of powr transfr at 5% of sris compnsation Th auxiliary controllr paramtr ar slctd basd on an xtnsiv root locus study and ar listd in Tabl and. Tim domain simulation tudy A digital computr simulation study, using a nonlinar systm modl, has bn carrid out to dmonstrat th ffctivnss of th DRPDIV auxiliary controllr in coordination with IDU undr larg disturbanc conditions for damping torsional oscillations. Applying a pulsd torqu of 0% for 0.s simulats a disturbanc. Th simulation study has bn carrid out at P G 800W for 0% sris compnsation lvl. All th slf and mutual damping constants ar assumd to b zro. Fig. 6. and 6. show th rspons curvs of th trminal voltag, V bus voltag, V suscptanc, powr angl, variation in torsional torqus without and with th DRPDIV auxiliary controllr along with IDU aftr th disturbanc rspctivly. It can b sn that thr is tndncy towards instability as is xpctd from ignvalu study whn no auxiliary controllr is usd in th V control systm and th application of proposd DRPDIV auxiliary controllr in coordination with IDU damps out voltag,powr angl and torsional oscillations ffctivly and sttling tim is considrably rducd and a significant improvmnt in dynamic and transint prformanc is achivd. onclusion In this papr th ffctivnss of DRPDIV auxiliary controllr along with IDU

15 A Nw tatic Var ystm Auxiliary ontrollr 65 has bn valuatd for damping torsional mods for wid rang of sris compnsation at various lvls of powr transfr. Th following conclusions can b drawn from th ignvalu and tim domain simulation study prformd Th proposd auxiliary controllr is abl to stabiliz all th systm torsional mods for wid rang of oprating conditions and systm mod (mod0) is stabilizd with a good stability margin. DRPDIV auxiliary controllr dvlopd for V rapidly damps out th voltag, powr angl and torsional oscillations thus nhancing th dynamic transint prformanc of systm. Thus th proposd damping controllr provids an fficint and robust control of torsional oscillations damping ovr a wid oprating rang and undr larg disturbanc conditions Rfrncs [] Narndra Kumar,.P. Dav, Application of auxiliary controlld static var systm for damping sub synchronous rsonanc in powr systms. Elctric Powr ystm Rsarch 7 (996) [] A.Yan and Y.N.Yu, ulty mod stabilization of torsional oscillation using output fdback xcitation control, IEEE Trans. On PA, Vol.0, No.6,98, pp []. K. Gupta, Narndra Kumar t. al, ontrolld ris ompnsation in coordination with doubl Ordr V Auxiliary ontrollr and Inductiopn achin for rprssing th Torsional Oscillations in Powr systm. Elctric Powr ystm Rsarch 6(00) 9-0. [] O.Wasynczuk, Damping sub-synchronous rsonanc using ractiv powr control, IEEE Trans., PA, Vol.00, No., pp.096-0,98. [5] N.G.Hingorani, " nw schm for R damping of torsional oscillations and transint torqus-part, IEEE Trans., PA, Vol.00, No., pp ,08. [6] Noroozian,. Ghandhari,. Andrsson,G. Gronquist J. Hiskns, A robust control stratgy for shunt and sris ractiv compnsators to damp lctromchanical oscillations IEEE Trans. On Powr Dlivry, Vol.6, Oct (00) [7]. K. Gupta, N. Kumar, Damping ubsynchronous Rsonanc in Powr ystms, IEE Proc. Gnr. Trans. Distrib.Vol.9, No.6, 00, pp [8] G. N. Pillai, Arindam Gosh, A. Joshi, Torsional Oscillation tudis in an ompnsatd Powr ystm, Elctric Powr ystm rsarch 55(000) [9] Ning, Yang, Q. Liu, J. D. cally, T controllr Dsign for Damping Intr Ara Oscillations, IEEE Trans. On Powr ystm, () (998) 0-0. [0] R.. Ramshaw, K.R. Padiyar, Gnralizd systm odl for lip Ring achins, IEEE Proc.0 (6) 97.

16 66 harma P.R. [] K. R. Padiayar, R.K. Varma, Damping Torqu Analysis of tatic Var ontrollrs, IEEE Trans. on Powr ystms, 6() (99) [] Januszwski,. achowski, J Bialk J.W., Application of dirct Lyapunov mthod to improv damping of powr swings by control of UPF, IEE Proc. Gnr. Trans. Distrib. vol 5, (00), [] haudhuri, B. Pal, B.. Robust damping of multipl swing mods mploying global stabilizing signals with T, IEEE Trans. On Powr yst., Vol.9, pp , Fb.00. [] assimo Bongiorno, Jan vnsson, Lnnart Angquist, ingl Phas V Basd for ub synchronous Rsonanc Damping, IEEE Trans. On Powr Dlivry, Vol., July 008, [5] Rajiv K.Varma, oubhik Auddy and Ysni msdini, itigation of sub synchronous rsonanc in a sris-compnsatd wind farm using FAT controllrs, IEEE transactions on powr dlivry, vol., no., pp , 008. [6] Albrto ota imõs, Digo havs avlli, Paulo ésar Pllanda, Nlson artin and Pirr Apkarian, Robust Dsign of a T Oscillation Damping ontrollr in a Wak 500-kV Intrconnction onsidring ultipl Powr Flow cnarios and Extrnal Disturbancs, IEEE transactions on powr systms, vol., no., pp.6-6, 009 Appndix Gnrator Data: 0 VA, KV, R a 0.006, X L 0., Xo0.95 T do 6.66, Tqo 0., Tdo 0.0, Tqo 0.057s X d.9, X q.7, X d 0.67, Xq., Xd 0., Xq 0. p.u.. I Typ Excitation ystm T R 0, T A 0.0, T E.0, T F.0s, K A 00, K E.0; K F 0.06 put. V Fmax.9, V Fmin 0, V Rmax 7., V R min -7. Transformr Data R T 0, XT 0.5 p.u. (Gnrator Bas) Transmission Lin Data Voltag 00 KV, Lngth 600 km, Rsistanc R 0.0Ω / km, Ractanc X 0.5 Ω / km uscptanc B.7μ mho / km V Data ix-puls Opration

17 A Nw tatic Var ystm Auxiliary ontrollr 67 T.ms, T 5ms, T D.667ms, K 00, K P 0.5, K D 0.0 Torsional spring-mass systm data All slf and mutual damping constants ar assumd to zro Tabl. ystm Eign Valus Without Auxilliary ontrollr od P G 00 W P G 500 W P G 800 W od ±j ±j ±j od.059±j ±j ±j0.76 od.0±j ±j ±j60.5 od ±j ±j ±j6.969 od -.067±j ±j ±j98.77 od ±j ±j ±j.987 Elctrical od -9.56±j ±j ±j9.665 Tabl. ystm Eign Valus With ombind Drivativ Of omputd Intrnal Voltag& Drivativ Of Ractiv Powr With Imdu At 5 % ompnsation Lvl od PG00W K B , T 0.0, T K B , T 0.00 T 0.05 PG500W K B , T 0.0, T K B , T 0.00, T 0.07 PG800W K B -.006, T 0.0, T K B , T 0.00, T od ±j ±j ±j98.00 od -.060±j ±j ±j0.566 od -.075±j ±j ±j od -.005±j ±j ±j od -.05±j ±j ±j od ±j ±j ±j7.88

18 68 harma P.R. Elctrical mod -.86± j ± j ±j9.56 Tabl. ystm Eign Valus Without Auxilliary ontrollr PG800W od 5% 0% 8% od ±j ±j ±j od.±j ±j ±j0.709 od ±j ±j ±j60.66 od.00±j ±j ±j6.999 od.000±j ±j ±j98.69 od 0.05±j ±j ±j7.86 Elctrical od -0.68±j ± ± Tabl. ystm Eign Valus with Drivativ of Ractiv Powr and Drivativ of omputd Intrnal Voltag Auxiliary ontrollr at P G 800W od 5% K B T T 0.5 K B T 0.00T 0. 0% K B -.0, T 0.0, T K B , T 0.00, T0. 8% K B -.00, T.0, T 0. K B -.009, T 0.00, T 0. od ±j ±j ±j98.00 od -.65±j ±j ±j od -.069±j ±j ±j60.67 od -.087±j ±j ±j od -.00±j ±j ±j od ± ±j ±j Elctrical od ± ± ±7.9

19 A Nw tatic Var ystm Auxiliary ontrollr 69 Fig.6. (a-g) Rspons curvs without any auxiliary controllr at Pg 800 W du to 0% incras in T mch for 0. scs (T-circuit odl) Fig.6. (a-g) Rspons curvs with DRPDIV auxiliary controllr and IDU at Pg 800 W du to 0% incras in T mch for 0. sc (T-circuit odl)

20 70 harma P.R.