Sliding mode control without reaching phase for multimachine power system combined with fuzzy PID based on PSS

Transcription

1 WSEAS RANSACIONS on SYSEMS and CONROL Faza Db, haddou Ben Mezane, Ismal Boumhd Sldng mode conrol whou reachng phase for mulmachne power sysem combned wh fuzzy PID based on PSS FAIZA DIB, HADDOUJ BEN MEZIANE, ISMAIL BOUMHIDI Deparmen of physcs, LESSI Laboraory Unversy of sd Mohammed ben Abdellah Faculy of scences Dhar Mehraz, Fez, Morocco Absrac: - he obecve of hs paper s o desgn a nonlnear robus conroller for he mulmachne power sysem. We presen n hs sudy a sldng mode conrol mehod whou he reachng phase by modfyng he erms of he oupu rackng error combned wh he fuzzy Proporonal Inegral Dervave based on Power Sysem Sablzer (FPID-PSS). he Mamdan fuzzy nference s used n hs sudy o fnd he opmal values of he hree parameers ( p,, d ) of (PID -PSS). he proposed approach s desgned o elmnae compleely he reachng phase and o enhance he sably and he dynamc response of he mulmachne power sysem. In order o es he effecveness of he proposed mehod, he smulaon resuls show he dampng of he oscllaons of he angle and angular speed wh reduced overshoos and quck selng me. ey-words: - Fuzzy Logc, Reachng Phase, Sldng Mode Conrol, Proporonal Inegral Dervave, Power Sysem Sablzer, Mulmachne Power Sysem. Inroducon he sably of power sysems s one of he mos mporan aspecs n elecrc sysem operaon. he sze and complexy of modern elecrc power sysems necessaes he consrucon of reducedorder dynamc models []. Deermnaon of ransen sably s one of he maor ems of power sysem operaon and plannng []. Mos conrollers PSSs used n elecrc power sysem employ he lnear conrol heory approach based on a lnear model of a fxed confguraon of he power sysem and hus uned a a ceran operang condon. he fxed parameer PSS, called convenonal PSS, s wdely used n power sysems, ofen does no provde sasfacory resuls over a wde range of operang condons [3]. o overcome hese drawbacks, a lo of dfferen echnques have been repored n he leraure peranng o coordnaed desgn problem of he PSS [4]. he proposed conroller n hs paper conss of he combnaon of he sldng mode conrol whou reachng phase wh he fuzzy proporonal negral dervave based on power sysem sablzer (FPID- PSS). he man obecve of he Mamdan fuzzy nference mehod s o adus he correcves gans for he opmal seng of conroller parameers PID- PSS whch provde a good performance and beer resuls. he Sldng Mode Conrol (SMC) s essenally a swchng feedback conrol where he gans n each feedback pah swch beween wo values accordng o some rule [9]. he swchng feedback law drves he conrolled sysem s sae raecory n o specfed surface called he sldng surface whch represens he desred dynamc behavor of he conrolled sysem [5]. he SMC s used n hs paper due o s dsurbance reecon, srong robusness subec o sysem parameer varaons, unceranes and exernal dsurbances. Durng he reachng phase, he rackng error canno be conrolled drecly and he sysem response s sensve o parameer unceranes [0]. Several mehods have been proposed o compleely elmnae he reachng phase [6], [], [8]. o accomplsh hs, he general exponenal form of rackng error s nroduced. A modfed sldng mode conrol s used o elmnae he reachng phase, and ensures opmal rackng subec o mnmal conrol effor. he obecve of he proposed approach s o compensae he flucuaons n mulple modes of oscllaons and elmnaes he reachng phase whch drecly nfluences he rackng errors n he mulmachne power sysem. hs mehod guaranees he robus performance for dampng low frequency oscllaons. E-ISSN: Volume 0, 05

2 WSEAS RANSACIONS on SYSEMS and CONROL Faza Db, haddou Ben Mezane, Ismal Boumhd hs paper s organzed as follows: he nonlnear mahemacal model of he mulmachne power sysem represened by sae-space s proposed n secon. he PID based on PSS conroller s descrbed n Secon 3. he fuzzy PID-PSS s desgned n whch he gans of hs conroller are uned n secon 4. he proposed conrol mehod s appled n Secon 5. he performances of he proposed mehod accordng o robusness ess are shown hrough smulaons of he mulmachne power sysem n Secon 6. Fnally, concluson s gven n Secon 7. Mulmachne power sysem Under some sandard assumpons, he dynamcs of n nerconneced generaors hrough a ransmsson nework can be descrbed by he classcal model wh flux decay dynamcs. he nework has been reduced o nernal bus represenaon assumng loads o be consan mpedances and consderng he presence of ransfer conducance. he dynamcal model of he h machne s represened by he classcal hrd order model [7]: δ = ω ωs ωs ω = ω ω H E = E E X X I d ( P D ( ) E I ) m s q q ( ( ) ) q f q d d d () I q and Id represen currens n d q reference frame of he h generaor, E q s he ransen EMF n he quadraure axs, Ef ( ) s he equvalen EMF n he excaon col, X d and X d are drec axs reacance and drec axs ransen reacance, respecvely, where : ( δ δ ) ( δ δ ) ( δ δ ) ( δ δ ) n G cos Iq = GE q + E q =, B sn n G sn Id =BE q E q =, + B cos () Pm s he mechancal npu power assumed o be consan, D s he dampng facor; all parameers are n p.u. H, represens he nera consan, n seconds; d s he drec axs ransen shor crcu me consan, n seconds; δ s he roor angle, n radans; ω represens he relave speed, ωs = π f s he synchronous machne speed, n rad/s; G and B are he h row and h column elemen of he nodal conducance marx and nodal suscepance marx respecvely, whch are symmerc, a he nernal nodes afer elmnang all physcal buses n p.u.. We consder Ef () as he npu of he sysem [7]. he sae represenaon of he h machne of a mulmachne power sysem can be wren n he followng form: x = [ x, x, x3] = δ, ω, E q For =,... n, represens he sae vecor of h subsysem, and he conrol appled s gven by: u = Ef (3) d x = x x = f( X) (4) x = f ( X) + u 3 Where ( ) ( ) ( ) ( ) n G cos x x f( X) = A dx 3 x3 =, B sn x x n G sn x x f( X) = ex 3 + h x3 =, + B cos x x Wh A = a bx cx 3 And ωs ωs ωs a = P ; b = D ; c = G H H H m ( ( d d ) ) (5) ω X X B s Xd X d d = ; e = ; h = H d d 3 PID based on PSS desgn Power Sysem Sablzer (PSS) s desgned o mnmze he power sysem oscllaons afer a small or large dsurbance so as o mprove he power sysem sably. he ransfer funcon of he h PSS s gven by [8]: E-ISSN: Volume 0, 05

3 WSEAS RANSACIONS on SYSEMS and CONROL Faza Db, haddou Ben Mezane, Ismal Boumhd u ( + s )( + s3) ( )( ) = s ω W pss pss + s W + s + s (6) n order o mprove he performance of he conroller. he rules bases are n he followng form [4]: If e s A and e s B, hen α s C m m m Fg. : Block dagram of he Convenonal Power Sysem Sablzer. Where PSS s he PSS gan, w Washou me consan and {,, 3, 4} are he me consans. me Consans 3 = 3, = 4, Idencal Phase Compensaor Block. he block dagram of he convenonal PSS s shown n fg., n whch case he generaor roor speed devaon s used as he only sablzng sgnal. he Convenonal PSS consss of an amplfer, a washou fler and wo lead-lag compensaors [8]. In hs secon we presen he PID-PSS for dampng he oscllaons n mulmachne power sysem. A se of PSS parameers whch gve good sysem performance under a ceran operang condon may no gve equally good resul []. o have good performance of PSS under dfferen condons, Proporonal Inegral Dervave (PID) based on PSS s presened. he supplemenary sgnal for each machne based on PID conrol law akes he followng form [3]: d ω u = k p ω + ω + k d k (7) d d 0 Where ω s he speed devaon of he machne and k p, k and kd are he PID conroller parameers, u s he supplemenary sablzng sgnal. m m m Where A, B and C are fuzzy ses. Supposng he wo npu sgnals of he Fuzzy-PID-PSS conroller are he error sgnal and he error devaon sgnal. Fg. : Srucure of he fuzzy-pid based on PSS conroller. he npu ranges of he wo sgnals (,) ee are from [-0.0, 0.0]. For he rule base, he fuzzy varables npu are defned by: ( e, e ) = { NB, NM, NS, Z, PS, PN, PB} and { k p, k, kd} = { VVS, VS, S, M, B, VB, VVB}, are he fuzzy oupus. he membershp funcons for he npus and he oupus varables are Gaussan. he oupus ranges of he gans { kp, k, } k for d =,, 3, of he hree generaors are from: kp = [ 0,70 ]; k [ ] [ ] = 0,7 ; k d = 0,0 kp = [ 0,50 ]; k [ 0,5 ]; [ 0,7] = k d = k = 0,50 ; k = 0,0 ; k = 0,5 [ ] [ ] [ ] p3 3 d3 he membershp funcons for he npus varables are gven n Fg. 3 and Fg Fuzzy PID based on PSS conrol he fuzzy conroller desgn ncludes he defnon he followng parameers: Number of parons of npu space and oupu membershp funcons, rule base, nference mehod, fuzzfcaon and defuzzfcaon [3]. In hs secon, he Fuzzy PID-PSS conroller s presened. More specfcally, a fuzzy nference sysem s used o adusng he gans of he conroller Fg. 3: Membershp funcons of error. E-ISSN: Volume 0, 05

4 WSEAS RANSACIONS on SYSEMS and CONROL Faza Db, haddou Ben Mezane, Ismal Boumhd Fg. 4: Membershp funcons of change of error he fuzzy rules are shown n able, able and able 3 respecvely [5]. able : he fuzzy rule marx of p de e NB NM NS Z PS PM PB NB PB PB PM PM PS Z Z NM PB PB PM PS PS Z NS NS PM PM PM PS Z NS NS Z PM PM PS Z NS NM NM PS PS PS Z NS NS NM NM PM PS Z NS NM NM NM NB PB Z Z NM NM NM NB NB able : he fuzzy rule marx of de e NB NM NS Z PS PM PB NB NB NB NM NM NS Z Z NM NB NB NM NS NS Z Z NS NM NM NS NS Z PS PS Z NM NM NS Z PS PM PM PS NM NS Z PS PS PM PB PM Z Z PS PM PM PB PB PB Z Z PS PM PM PB PB able 3: he fuzzy rule marx of d de e NB NM NS Z PS PM PB NB PS NS NB NB NB NM PS NM PS NS NB NM NM NS Z NS Z NS NM NM NS NS Z Z Z NS NS NS NS NS Z PS Z Z Z Z Z Z Z PM PB PS PS PS PS PS PB PB PB PM PM PM PS PS PB 5 Proposed conrol desgn 5. Sldng mode conrol whou reachng phase he sldng mode conroller wh dfferen posve characerscs ncludng he robusness agans he parameer changes, exernal dsurbances, and unceranes and quck dynamc response and smplcy of desgn s applcable n varous nonlnear sysems conrol [6]. I was successfully appled o elecrc moors, robo manpulaors, power sysems and power converers [9]. he response of a sysem conrolled by a SMC ncludes wo phases. he frs phase s called he reachng phase [6]. Durng hs phase, he conroller drves he sysem response owards 0. he second phase s he sldng phase, whch s reached a = s such ha s 0 s. In hs secon, we wll presen he prncple of he sldng mode conrol whou reachng phase. Le us consder he nonlnear sysem represened by he followng sae equaon: ( n) x = F( x) + Gxu ( ) (8) Where ( n x= xx,,... x ) = [ x, x,..., x n ] s a sae vecor, u R conrol npu. o avod hgh conrol npu gan, one nroduces he followng modfed oupu rackng error [0]. We presen he sldng mode conrol law ha elmnaes he reachng phase and acheves sldng a he onse of he moon. o realze hs obecve, we reformulae he oupu rackng error as follows [8]: E () = e () η () (9) Where he rackng error vecor s: ( n ) e = [ e, e,..., en ] = e, e,..., e and η () s desgned o sasfy he followng condons [6]: - o make E small enough a he onse of he moon =0. - Should rapdly vansh as he moon evolves a 0 A suggesed η () s gven n he followng exponenal form: η() = γ()exp( Z()) (0) Usng aylor seres: n ( ) γ( ) = γ ( 0)( 0) = 0! () ( ) d γ γ ( 0) = ( = 0) d () Z() = β (3) η ( ) = ( q + q q n )exp( β) (4) 0 n E-ISSN: Volume 0, 05

5 WSEAS RANSACIONS on SYSEMS and CONROL Faza Db, haddou Ben Mezane, Ismal Boumhd For = 0, n, where β a posve consan, q s seleced o sasfy condon -- and Z () s seleced o sasfy condon --. Expandng (9) by he aylor s seres leads o n ( ) ( ) n E( ) = (( e (0) η (0)) ) + o ( ) (5)! Where = n ( ) o n. ( ) ( ) e s an nfnesmal of hgher order of η (0) = (0) (6) n hen (3) becomes o ( ),.e., Condon -- s sasfed. he values of q can be obaned by resolvng he equaon se n (4). We defne a modfed sldng surface as: ( n) ( n) S() = E () + kn E ()... () + + k E (7) hs modfed surface exponenally converges o he orgnal one. Once he sysem sae reaches he sldng surface never leaves. In hs sudy, he relave degree s r=3 hen, he swchng funcon can be wren as: S() = E () + ke () + k E() (8) Where E() = e() η() (9) η( ) = ( q0 + q + q )exp( β) (0) e = δ δr = x x r e = e = x () e = e = a bx cx dx I q For =, n. Where k = [k,k, ] are he coeffcens of he Hurwz Polynomal: h( λ)= λ + kλ + k () S () = k E () + ke () + E () (3) = k E () + k E () η () + F( x) + G ( x) u x are known, we can easly consruc he modfed sldng mode conrol: u = ueq + u smc (4) ueq = ( k () () () ( )) E + k E η + F x (5) G ( x) he equaons represenng he sldng mode conrol have been reformulaed whch he reachng phase s elmnaed. he modfed sldng mode conrol erm s: If F ( x) and G ( ) usmc = sgn( ) S G ( x) α (6) he conrol npu u smc o ge he sae δ o rackδ r. 5. sldng mode conrol whou reachng phase combned wh Fuzzy PID-PSS he conrol law used n hs sudy s composed by hree erms, he equvalen conrol u eq, he robus erm represened by he sldng mode conroller whou reachng phase u smc, and he PID-PSS adaped by he mamdan fuzzy logc u FPID PSS. u = ueq + usmc + ufpidpss (7) Wh α s he gan of sldng mode conroller. k E () + ke () u = G ( x) η() F( x) αsgn( S) + + (8) d ω + k p ω+ k ω d + k d d 0 k p, k, k d are he opmal value of proporonal gan, negral gan and dervave gans, respecvely. he combnaon beween he hree conrollers, he equvalen conrol and he modfed sldng mode conroller wh he fuzzy PID based on PSS, enhances he dampng of he oscllaons and he sably of he nework and elmnae compleely he reachng phase. 6 Smulaon of mulmachne power sysem o evaluae he performance of he proposed conrol, we performed he smulaon n MALAB for he hree-machne nne-bus power sysem as n Fg. 5, wh he am o show he valdy and he performance of he proposed conroller. Deal of he sysem daa are gven n able 5 [7]. Fg. 5: hree-machne nne-bus power sysem. he followng equlbrum pon: Xr = ( x r,x r, x 3r ) = δ ω E q For =,, 3 of he hree-machne sysem s consdered: E-ISSN: Volume 0, 05

6 WSEAS RANSACIONS on SYSEMS and CONROL Faza Db, haddou Ben Mezane, Ismal Boumhd x = , x = 0, x =.0566 r r 3r x = , x = 0, x =.050 r r 3r x = 0.300, x = 0, x =.07 3r 3r 33r robus performance of he mulmachne power sysem. he conrol parameers of sldng mode conrol used areα = he specfed parameers of he PSS ha are used n hs sudy gven n able 6 n appendx and he parameers of he PID conroller are gven n able 7 n appendx. We presen he parameers of he modfed rackng error E (), we choose: β = 0.5 ; β = 3.35 ; β =.6 3 From he mehod n [], one can make: η (0) = q0 = x (0) x r (0) η (0) = q βq0 = x (0) x r (0) η (0) = q βq + β q0 = x (0) x r (0) (9) Fg.6: Roor angle δ o demonsrae he performance and he robusness of he proposed mehod, wo performance ndces: he Inegral of he me mulpled Absolue value of he Error (IAE) and he Inegral of me weghed Squared Error (ISE) based on he sysem performance characerscs are beng used as: ( ω ω ω3 ) (30) 0 ( ω ( ) ( ) ω ω3 ( )).. 0 (3) IAE = + + d ISE = + + d More han he values of he performance ndces IAE and ISE are lower, he response of he sysem n me doman s beer. Numercal resuls of hese ndces for all cases are presened n able 4. Fg.7: Roor angle δ able 4: Performance ndces of he conrollers IAE ISE Proposed Conrol e-007 SMC&FPID-PSS e-006 SMC&PID-PSS e-005 PSS Conrol e-005 In order o revew he valdy and he robusness of proposed conrol, smulaon sudes are carred ou for hree machnes nne bus. he am n hs secon s o compare he performance of he proposed conrol (SMC whou reachng phase & FPID-PSS) wh (SMC & FPID-PSS), he (SMC & PID-PSS) and he PSS. he smulaon resuls demonsraed ha he proposed conrol s capable o guaranee he Fg.8: Roor angle δ 3 E-ISSN: Volume 0, 05

7 WSEAS RANSACIONS on SYSEMS and CONROL Faza Db, haddou Ben Mezane, Ismal Boumhd Fg. 6-7 and Fg For he hrd generaor (G3), he roor angle δ3 and he speed devaon ω3 are sablzed n 0.5 second; see Fg. 8 and Fg.. he convenonal PSS conroller requres more me and more oscllaons before he same varables are sablzed. Implemened resuls n hs secon have demonsraed a superor performance of he proposed conrol n erms of elmnang he reachng phase and dampng of oscllaon and enhancng he sably of he sysem as compared wh he wo ohers conrollers. Fg.9: Speed devaon ω 7 Concluson In hs paper, he proposed conrol provdes an effcen soluon o elmnae he reachng phase and damp he Low frequency oscllaons n he mulmachne power sysem. A modfed oupu rackng error s nroduced n sldng mode conrol o reduce he conrol gan and o elmnae he reachng phase. he desgn problem of he PSS s solved and replaced by he fuzzy PID based on PSS, whch enhances he sably of he power sysem. Also, he robusness and he performance of he proposed conroller desgn has been proved and evaluaed by he dynamc smulaon resuls of he mulmachne power sysem. Fg.0: Speed devaon ω Fg.: Speed devaon ω3 Wh he proposed conrol, he mechancal varables such as he roor angles ( δ, δ ) and he speed devaon ( ω, ω ) n he generaors (G & G) are sablzed n 0.5 and second respecvely; see 8 Nomenclaure δ Roor angle ω Roor speed (pu) ω Speed devaon Pm Mechancal npu power Pe Elecrcal oupu power (pu) M Sysem nera E q Inernal volage behnd x d (pu) E fd Equvalen excaon volage (pu) X d ransen reacance of d axs (pu) X q Seady sae reacance of q axs (pu) X d Seady sae reacance of d axs (pu) do me consan of excaon crcu (s) Smulaon me (s) s Selng me w Washou fler (s) me consans of lead lag dynamc 4 compensaor (s) Gan of he Sablzer PSS Power Sysem Sablzer SMC Sldng Mode Conroller PID Proporonal Inegral Dervave FPID PSS Fuzzy PID based on PSS E-ISSN: Volume 0, 05

8 WSEAS RANSACIONS on SYSEMS and CONROL Faza Db, haddou Ben Mezane, Ismal Boumhd 9 Appendx able 5: Nomnal parameers values Parameers Gen Gen Gen3 H X d X d D P m do able 6: Convenonal PSS parameers Parameers pss w PSS PSS PSS able 7: Convenonal PID parameers Parameers p d PID PID PID References []. Amn, R. Hemma, Robus decenralzed mul-machne power sysem sablzer desgn usng quanave feedback heory, Elecrcal Power and Energy Sysems, Vol. 4, 0, pp. -9. [] J.. Mendraa, R. Jayapal, H Loop Shapng Based Robus Power Sysem Sablzer for hree Machne Power Sysem, Inernaonal Journal of Compuer Applcaons, Vol., 00, pp [3]. B. Mezane, F. Db and I. Boumhd, Fuzzy sldng mode conroller for power sysyem SMIB, Journal of heorecal and Appled Informaon echnolog, Vol.54, 03 pp [4] M. A. Abdo, Robus Desgn of Power Sysem Sablzers for Mulmachne Power Sysems Usng Dfferenal Evoluon, Compuaonal Inellgence n Power Engneerng, Sprnger- Verlag Berln Hedelberg, Vol.30, 00, pp [5] H. N. Al-Duwash, M. Z. Al-Hamouz, A neural nework based adapve sldng mode conroller: Applcaon o a power sysem sablzer, Energy Converson and Managemen, Vol. 5, 0, pp [6] C. Ylmaz and Y. Hurmuzlu, Elmnang he reachng phase from varable srucure conrol, Journal of Dynamc Sysems, Measuremen, and Conrol: ransacons usng he ASME, Vol., No.4, 000, pp [7] A. Colba-Vegaa, J. Leon-Morales, L. Frdman, O. Salas-Pena and M.. Maa-Jmenez, Robus excaon conrol desgn usng sldng-mode echnque for mulmachne power sysems, Elecrc Power Sysems Research, Vol.78, 008, pp [8] H. Namul, Ibraheem, S. Farooq, Real me Smulaon of Auomac Generaon Conrol for Inerconneced Power Sysem, Inernaonal Journal on Elecrcal Engneerng and Informacs, Vol.4, 0, pp [9] A. G. E. Abera, B. Bandyopadhyay, Dgal Redesgn of Sldng Mode Conrol wh Applcaon o Power Sysem Sablzer, 34h Annual Conference of IEEE Indusral Elecroncs, IECON, 008, pp [0] E. Melloul, J. Boumhd and I. Boumhd. Usng fuzzy logc for elmnang he reachng phase on he fuzzy H rackng conrol, Inernaonal Journal of Modellng, Idenfcaon and Conrol, Vol.0, No.4, 03, pp [] Y. Pan, J. E. Meng, D. Huang, and. Sun, Praccal Adapve Fuzzy H rackng Conrol of Unceran Nonlnear Sysems, Inernaonal Journal of Fuzzy Sysems, Vol.4, No.4, 0, pp [] H. R. Jarwala, A. Chowdhury, Desgn of PID- PSS and SVC n a Mul-machne Sysem for Dampng of Power Sysem Oscllaons Usng Genec Algorhm, Power Elecroncs (IICPE), 0 IEEE 5h Inda Inernaonal Conference on, 0, pp. -6. [3] M. Solman, A.L. Elshafe, F. Bendary and W. Mansour, Robus decenralzed PID-based power sysem sablzer desgn usng an ILMI approach, Elecrc Power Sysems Research, Vol.80, 00, pp [4] A. F. Amer, E. A. Sallam and W. M. Elawady, Adapve fuzzy sldng mode conrol usng supervsory fuzzy conrol for 3 DOF planar robo manpulaors, Appled Sof Compung, Vol., 0, pp [5] Z. Hu, Y. Lang, Y. Chen and C. Zhang, A Novel Power Sysem Sablzer Based on Neural Nework Inverse Sysem, Proceedngs of 004 Inernaonal Conference on Informaon Acquson, 004, pp E-ISSN: Volume 0, 05

9 WSEAS RANSACIONS on SYSEMS and CONROL Faza Db, haddou Ben Mezane, Ismal Boumhd [6] M. Aae, R. A. Hooshmand and S. G. Saman, A coordnaed MIMO conrol desgn for a power plan usng mproved sldng mode conroller, ISA ransacons, Vol.53, 04, pp [7] Anderson P.M, A.A.Fouad, Power Sysem Conrol and Sably, nd Edon - A John Wly & Sons INC. Publcaon, 00. [8]. Chang and Y. Hurmuzlu, Sldng Conrol whou Reachng Phase and s Applcaon o Bpedal Locomoon, Journal of Dynamc Sysems, Measuremen, and Conrol, Vol.5, 998, pp. -7. [9] A. Jalvand, R. Aghmasheh, E. halkhal, Robus desgn of PID power sysem sablzer n mul-machne power sysem usng arfcal nellgence echnques, 4h nernaonal Power Engneerng and Opmzaon Conf, Shah Alam, Sclangor, Malasa, 00, pp [0] N. Yang, Q. Lu and J. D. McCalley, CSC conroller desgn for dampng nerarea oscllaons, IEEE rans on Power Sysems, Vol.3, No. 4, 998, pp , [] A. hodabakhan, R. Hooshmand, R. Sharfan, Power sysem sably enhancemen by desgnng PSS and SVC parameers coordnaely usng RCGA, Canadan Conf. on Elecrcal and Compuer Engneerng, 009, pp E-ISSN: Volume 0, 05