Improvement of Transient Stability of VSC HVDC System with Particle Swarm Optimization Based PI Controller

Transcription

1 Improvemen of Transen Sably of SC HDC Sysem wh Parcle Swarm Opmzaon Based Conroller Improvemen of Transen Sably of SC HDC Sysem wh Parcle Swarm Opmzaon Based Conroller *N. Nayak, ** S.K Rou ray, *** P.K. Rou *S.O.A Unversy ** Hgh Tech Insue of Insue of Technology,*** S.O.A Unversy, Absracs : Ths paper proposes he mprovemen of power flow durng ransen condon of HDC lgh usng Conroller. The Opmal desgn of conroller for a HDC lgh s a challengng ask and me consumng usng he convenonal echnques. Ths work presens analyss of ransen sably of HDC lnk usng conroller, and he sably has been mproved by opmzed gans of conroller. The smulaon resuls are presened o show he effecveness of he proposed Parcle swarm Opmzaon Technque (PSO) based approach for he desgn of opmal convenonal conroller for a HDC lgh n a sngle machne decoupled power sysem. Index Terms: HDC lgh, PSO, Transen Sably, conroller.inroducon Hgh volage drec curren (HDC) ransmsson s an economc way for long dsance bulk power delvery and/or nerconnecon of asynchronous sysem wh dfferen frequency []. HDC sysem plays much more mporan role n power grds due o her huge capacy and capably of long dsance ransmsson. Convenonal HDC ransmsson sysem s based on lne commued hyrser recfers []. Insulaed gae bpolar ranssor, (IGBT) s recenly replaced by he convenonal hyrser based HDC lnk, due s fas conroller acon of GTO. Insulaedgae conrolled Thyrsers (IGCT) hgh power sold sae swches have symmercal urn on and urn off capables. They have gven a new nnovaon of HDC saons. HDC lgh s also called volage source conver HDC or SC HDC [3]. The convenonal HDC scheme employ lne commued curren source converer (CSC) based Thrsers. HDC lgh s a new echnology ulsng forced commued volage source converers [4]. HDC lgh can conrol boh acve and reacve power ndependenly whou commuaon falure n he nverer sde. I does no requre reacve power compensaor resulng much smaller equpmen sze. HDC lgh can be appled o he volage suppor n he recever sysem [5]. I provdes nerconnecon beween wo asynchronous power sysems [6], grd connecon of large wnd farm, [8] and undersea power ransmsson [9], Bdreconal power flow HDC lgh projecs for dfferen purposes already n operaon worldwde. For a sngle M/C power sysem conneced o nfne bus he nroducon of HDC lgh can enhance he volage suppor and mprove he sysem sably. In hs sudy problem of conroller desgn o formulaed as a mul objecve opmzaon problem. secon represens he nroducon par of hess work and secon descrbes he fundamenals of HDC sysem and SCHDC sysem. I ncludes he consrucon operang prncple and he ype of HDC lnks and her advanages and dsadvanages along wh s applcaons. secon3 descrbes he parcle swarm opmzaon echnque (PSO) descrbes he dfferen parameers of PSO lke velocy parameers, search echnque ec. Secon 4 descrbes he HDC sysem under our sudy. I descrbes he mahemacal modellng of synchronous generaor, volage sources converer (SC), volage source nverer (SI) and he DC lnk. secon 5 ncludes he smulaon resul and applcaon of PSO o opmze he gans of conroller used for HDC lgh. I descrbes he quck response of conroller wh PSO and s compared wh he resuls whou PSO. secon 6 conans concluson of hs work and a las secon gves he bblography and references of he presen work..mahemacal Modellng of Synchronous Machne A power sysem can be modeled by a se of nonlnear dfferenal equaons as dx/d = f( X, U) () Where X s he vecor of he sae varables and U s he vecor of npu varables. In hs sudy, he fourh order model as gven below s used for nonlnear me doman smulaon. dδ/d = ω ω () dω/d = (P m P e )/M (3) de q /d = (E fd (X d X dd ) I d E q )/ T do (4) de fd /d = (K a ( ref PSS ) E fd )/T a (5) Where δ = Roor angle ω = Roor speed P m = Mechancal Power P e = Elecrcal Power E fd = Equvalen excaon volage d and q = drec and quadraure axes respecvely E q = Inernal volages behnd he reacance X d X q Inernaonal Journal of Power Sysem Operaon and Energy Managemen (IJPSOEM) olumei, IssueI, 8

2 Improvemen of Transen Sably of SC HDC Sysem wh Parcle Swarm Opmzaon Based Conroller T a = Regulaor me consan T do = Tme consan of excaon crcu K a = Regulaor gan The dq axs converson of machne frame o nework frame s expressed as followng: q Q δ Q axs d δ D Daxs Fg..phasor dagram of nework o machne converson converers whch can realze he converson from AC o DC bdreconally. DC capacors are used as DC volage sources n HDC lgh whch need beng charged and recharged. Our analyss s based on a HDC lgh used n a sngle m/c power sysem whch s conneced o nfne bus. r R Syn. Gen. AC X / X / r r + jx r Conver er Load I Cd Cd R Inver er r + jx Load X / X / AC r Infne B Load Here d and f are he drec axs and quadraure axs volage across he ermnals n machne frame and D and Q are he ermnal volage n nework frame. D = f snδ+ d cosδ Q = f cosδ+ d snδ Fg..Model of decoupled SCHDC wh sngle machne conneced o nfne bus SCI or Recfer of HDC lgh apples he acve and reacve power conrol. Bu he SC II.e., nverer apples DC and AC volage conrol. The acve power s conrol by he phase angle of converer oupu volage, and he reacve power s conrolled by magnude of converer volage. In ha sense acve and reacve power conrolled ndependenly. In marx form can be wren as D cosδ sn δ d = Q sn cos δ δ f (6) The machne ermnal volages d = D cosδ+ Q snδ q = D snδ+ Q cosδ (7) Smlarly drec and quadraure axs curren njeced by he machne, s gven by Id = ID cosδ+ IQ snδ Iq = ID snδ+ IQ cosδ (8) Where, d, q represens machne frame 3. Modellng of vsc HDC HDC lgh s composed of ransformer flers, converers and D.C. capacors. Transformer s used o sep down he A.C. volage o he converer rang value, and he self commued sold sae devces such as seres and parallel of GTOS, IGBTs or IGCTs. Hgh frequency componens caused by he swches of he valves are solaed from power sysem, by flers. The hear of HDC lgh s The recfer conroller s shown n he fg.(4). The conroller consss of four pars. Power flow conrol loop, reacve power flow loop, phase locked loop (PLL) and PWM pulse frng. A ypcal SC HDC ransmsson lnk consss of wo converer saons one saon operaes as recfer and oher one operaes as nverer saon as shown n he fg.3.the mahemacal model developed n hs paper depends on a roang d.q frame. ransform RYB o D Q frame. Wh he ncreasng he applcaon of volage source converer., The dynamc equaons of recfer and nverer n he roang df frame can be wren as follows: 3..Recfer ( ) r.i ID= +ω + r D D rd IrQ Lr Lr Lr Inernaonal Journal of Power Sysem Operaon and Energy Managemen (IJPSOEM) olumei, IssueI, 8 r () l I = I Rsh () ( r.i ) IrQ = ω IrD + L L L (3) r rq Q rq r r r

3 Improvemen of Transen Sably of SC HDC Sysem wh Parcle Swarm Opmzaon Based Conroller (4) 3..Inverer: P = ( C ) C ri ID = +ω I Q + L L L (5) ri Q Q Q IQ = ωid + L L L (6) I I = C C I = I Rsh (7) I D D D r r Where I r D, I r Q, D, Q are df axs currens of recfer sde, and I D, I Q, D and Q are he df axs curren and volages of nverer sde. r r + jx r and r + jx are he complex mpedance of recfer and nverer respecvely. L r and L are he nducance of smoohng reacs used n converer and nverer respecvely., and I are he d.c. lnk volage and curren. C s he cap ar of he d.c. lnk, R sh and R sh are he shun ressances of he HDC sysem. The swchng frequency of he recfer s 5 Hz where as he swchng frequency of he nverer saon s 46 Hz makng rd and rq are he conrol npu o he recfer D and Q o he nverer, Expandng he P n (3) he sysem equaon can be wren as ( r.i r rd) D u IrD = +ω IrQ + Lr Lr Lr (8) ( r.i r rq) Q u IrQ = ω IrD + Lr Lr Lr (9) {( ) ( )} ( ) = I + l I r I + I D rd Q rq r rd rq I ri I D D 3 D = +ω Q + Lr L L () ri u I = ω + Q () u Q Q 4 ID L L L R C 4. Parcle Swarm Opmzaon Parcle Swarm Opmzaon (PSO), one of he laes meaheursc algorhms, was frs nroduced by Kennedy and Eberhar 995. PSO s based on he meaphor of socal neracon and communcaon such as brd flockng and fsh schoolng. Snce PSO s populaon based and socally cognve n naure, he members n a swarm end o follow he leader of he group,.e., he one wh he bes performance. In a PSO algorhm, each member s called a parcle, and each parcle fles around n he muldmensonal search space wh a velocy, whch s updaed accordng o he parcle s curren velocy, he parcle s own experence and he experence of he neghbors. Dependng on he sze of neghbors, wo ypes of basc PSO algorhms were developed PSO wh a local neghborhood and PSO wh global neghborhood of Kennedy e al.. In he former model, called he lbes, each parcle moves owards s bes prevous poson and owards he bes parcle n s resrced neghborhood. Whle n he laer model, called he gbes, each parcle moves owards s bes prevous poson and owards he bes parcle n he enre swarm. PSO was frs developed o opmze connuous nonlnear funcons. Snce PSO s easy o mplemen and s effcen o oban qualy soluons, has araced much researchers' aenon n recen years. The applcaon of PSO consss of neural nework ranng, power and volage conrol, opmal power sysem desgn, feaure selecon, masssprng sysem, elecromagnec, cluserng, logc crcu desgn, lo szng problem, ask assgnmen problem, auomaed drllng, and schedulng problems. More leraure can be found n he reference of Kennedy e al.. Besdes he wde range of applcaons above, he nonlnear connuous funcon opmzaon s sll consdered he benchmark problem when explorng he properes and performance of PSO algorhms. Therefore, hs paper ams a employng PSO on opmzng 4 newly developed es problems n Congress on Evoluonary Compuaon PSO Algorhm The gbes model of Kennedy e al. s followed n hs sudy. Accordng o he gbes model, each parcle moves owards s bes prevous poson and owards he bes parcle n he whole swarm. In he PSO algorhm, parameers were nalzed and he nal populaon was generaed randomly. Each parcle wll hen be evaluaed o compue he fness funcon value. Afer evaluaon, he PSO algorhm repeas he followng seps eravely. Wh s poson, velocy and fness value, each parcle updaes s personal bes (bes value of each ndvdual so far) f an mproved fness value was found. Inernaonal Journal of Power Sysem Operaon and Energy Managemen (IJPSOEM) olumei, IssueI, 83

4 Improvemen of Transen Sably of SC HDC Sysem wh Parcle Swarm Opmzaon Based Conroller The basc elemens of PSO algorhm s summarzed as follows: Parcle X denoes he h parcle n he swarm a eraon and s represened by n numbers of dmensons as X [ x, x, =... xn ] where x j s he poson value of he h parcle wh respec o he j h dmenson (j =,,., n). Populaon X s he se of NP parcles n he swarm a eraon,.e., X = [ X, X,... X NP ]. () Parcle elocy s he velocy of parcle I a eraon. I can be defned as = [ v, v,... vn ], () where v s he velocy of parcle I a eraon j wh respec o he j h dmenson. Inera wegh and acceleraon coeffcens w s a parameer o conrol he mpac of he prevous veloces on he curren velocy. I has an mpac on he radeoff beween he global and local exploraon capables of he parcle. A he begnnng of he search, large nera wegh s used o enhance he global exploraon whle s reduced for beer local exploaon laer on n he search. c and c are consan parameers called acceleraon coeffcen whch conrol he maxmum sep sze ha he parcle can do. Personal bes P represens he bes poson of he parcle wh he bes fness value unl eraon, so he bes poson assocaed wh he bes fness value of he parcle obaned so far s called he personal bes. For each parcle n he swarm, P can be deermned and updaed a each eraon. In a mnmzaon problem wh he objecve funcon f ( X ), he personal bes P of he h parcle s obaned such ha f ( P ) f ( P ). To smplfy, he fness funcon of he personal bes s denoed as pb f = f ( P ). For each parcle, he personal bes s defned as P = [ p, p,......, pn ] where P j s he poson value of he h personal bes wh respec o he j h dmenson (j =,,., n). Global Bes G denoes he bes poson of he globally bes parcle acheved so far n he whole swarm. For hs reason, he global bes can be obaned such ha f ( G ) f ( P ) for I =,,.NP. To smplfy, he fness funcon of he global bes s denoed as gb f = f ( G ). The global bes s hen defned as [ g g g ] G =,,... n where g j s he poson value of he global bes wh respec o he j h dmenson (j =,,..n). Termnaon Creron I s a condon ha ermnaes he search process. I mgh be a maxmum number of funcon evaluaons or a maxmum CPU me ha ermnaes he search. 3.3 Inal Populaon A populaon of parcles s consruced randomly for he PSO algorhm. The connuous values of posons are esablshed randomly. The followng formula s used o consruc he nal connuous poson values of he parcle unformly: x j = xmn + ( xmax xmn )* r (3) Where x max and x mn are gven bounds of he connuous funcons and r s a unform random number beween and. Inal veloces are generaed by a smlar formula as follows: v j = v mn + ( v v )* r max mn (4) where vmax = ( xmax xmn) / and vmn = vmax, and r s a unform random number beween and. Connuous velocy values are resrced o some range, namely [ ] v j = v mn,v max Durng he reproducon of he PSO algorhm, s possble o exend he search ousde of he nal range of he search space. For hs reason, he poson values volang he nal range are resrced o he feasble range as follows: x j = x ( xmax xmn ) mn + *r (5) The only excepon was he problem 7 for whch he opmal was no nsde he search lms. The populaon sze s aken as. As he formulaon of 4 funcons suggess ha he objecve s o mnmze 4 connuous funcons, he fness funcon value s he objecve funcon value of he parcle X. Tha s f ( X ). For smplcy, f ( X ) wll be denoed as f. 4.. Compuaonal Procedure of PSO The complee compuaonal procedure of he PSO algorhm can be summarzed as follows: Inalzaon Se =, NP = Inernaonal Journal of Power Sysem Operaon and Energy Managemen (IJPSOEM) olumei, IssueI, 84

5 Improvemen of Transen Sably of SC HDC Sysem wh Parcle Swarm Opmzaon Based Conroller Generae NP parcles randomly as explaned before, X, =,,... NP where { } X = [ x x..., x ], n Generae he nal veloces for each parcle, =,,... NP where randomly. { } = [ v v,... v ]., n Evaluae each parcle n he swarm usng he objecve funcon f for I =,, NP. For each parcle n he swarm, se where [ P = p = x p = x,..., p = x ], n n P =, X pb ogeher wh s bes fness value f for I =,,. NP. Frs he bes fness value among he whole swarm such ha f mn{ = f } for I =,,.. NP wh s correspondng posons X. Se global bes o G = X such ha G = [ g = x, g = x,..... gn = xn ] wh f gb = f. s fness value Updae eraon couner = + Updae nera wegh w = (max_ fes FES) / max_ fes *( w wn ) + w ( ) n where max_fes, FES, w, and w n are he maxmum number of funcon evaluaon, number of funcon evaluaons, nal nera wegh, and fnal nera wegh respecvely. Updae velocy v j = w v + c r ( p x ) + c r ( g x ) j j j j j where c and c are acceleraon coeffcens and r and r are unform random numbers beween (, ). Updae Poson x + v j = x j j Updae personal bes Each parcle s evaluaed by usng he permuaon o see f he personal bes wll mprove. Tha s, f pb f < f for I =,,..NP hen personal bes s pb updaed as P = X for f = f. Updae global bes Fnd he mnmum value of personal bes. Tha s, pb f = mn f, I =,,.. NP; { } { : =,, NP} l.... gb f If l < f, hen he global bes s updaed as gb G = X l f = f and l Soppng creron If he number of funcon evaluaons exceeds he maxmum number of funcon evaluaons, ha sop; oherwse go o sep. 5. Conroller The Sae varables of recfer saon are I rd, I rq and for connvance volage and reacve power of he recfer are aken as he oupu varables. Snce he reference bus daxs volage s aken as zero he reacve power drecly conrolled by I rd. The Sae varables of nverer saon are I d, I q and d and q. Snce he nverer saon s operang n he acve and reacve conrol mode he oupu saes are I d, I q. As he reference bus n he nverer sde s chosen as one he daxs curren represen reacve power whereas qaxs curren represens he acve power flow n he nverer saon, he whole conroller sraegy s descrbe by he followng dagram. In he fgure 4.3. Table5. Conveno nal Wh PSO u ref kr +_ k p + s + + u ref Fg.3. conroller for recfer saon IQref ref Ouer Loop Fg.4. conroller for nverer saon Converer Conroller gan Inverer gan Kp Kp Kp 3 Kp 4 K K K _ u kr p + I rqref k + _ s + + k I rq p + kr s 4..3 u u + + I Ouer IQ rqref kr3 k p + Loop +_ s + + I rq u 4.. u u u 3 u 3 u 4 u 4 K Inernaonal Journal of Power Sysem Operaon and Energy Managemen (IJPSOEM) olumei, IssueI, 85

6 Improvemen of Transen Sably of SC HDC Sysem wh Parcle Swarm Opmzaon Based Conroller Dela.95.9 Dela(pu) me(sec) 6.Smulaon Resul In hs paper he convenonal conroller has been smulaed n MATLAB. The performance of conroller s esed under varous condons wh normal gans. The resul s compared wh he performance wh opmzed gans of conroller used PSO. Case : Here durng a LLLG faul a bus from s o. sec. Due o he faul he a.c. volage, has decreased o a crcal value.in Fg(4) s shown he mprovemen of dampng of and he performance of he PSO based conroller resores he sysem han he earler convenonal conroller., n bus, recfer oupu and respecve reacve power wh normal conroller and he resul s compared wh performance wh opmzed conroller. Due o decouplng effec he acve and reacve power, he recfer saon does no change a nverer saon faul as shown p(pu) p(pu) me(sec) me(sec) r(pu)..4.8 Pr(pu) me(sec) me(sec) Fg.5. Performance comparson of he conroller under ressance faul a bus Qr(pu) me(sec) Case : Here a cycle LLLG faul a bus wh same earhng operang condon s smulaed on he nverer sde, Fg. 5shows he sasfacory mprovemen of dampng n, acve and reacve power, power angle, roor angular velocy n boh recfers and nverer sde, Wh deferenal evoluon based conroller. Due o decouplng effec he acve and reacve power of recfer saon does no change a nverer saon faul Inernaonal Journal of Power Sysem Operaon and Energy Managemen (IJPSOEM) olumei, IssueI, 86

7 Improvemen of Transen Sably of SC HDC Sysem wh Parcle Swarm Opmzaon Based Conroller Pr Pr(pu). (pu) me(sec).5.8 Pr Fg.5. Performance comparson of he conroller under ressance faul bus Case 3: me(sec) Qr(pu) me(sec) Here a cycle faul a bus s creaed by ncreasng he load n he nverer sde( percen of he orgnal value) wh same earhlng operang condon s smulaed on he nverer sde, Fg. 6 shows he sasfacory mprovemen of dampng n, acve and reacve power, power angle, roor angular velocy n boh recfers and nverer sde, Wh PSO based conroller P Dela Dela.86 P me me(sec) Q Qr(PU) Q(pu) me..3 s me(sec).5 r(pu) me(sec) Inernaonal Journal of Power Sysem Operaon and Energy Managemen (IJPSOEM) olumei, IssueI, 87

8 Improvemen of Transen Sably of SC HDC Sysem wh Parcle Swarm Opmzaon Based Conroller Pb xr =.9Ω, x =.9Ω D.c. lnk capacor C = 5μ F a.c. fler capacor = μ F. P(PU).8 Q(PU) Fg.6. Performance comparson of he conroller under load faul a bus 7. Concluson In hs paper ransen sably performance of SC HDC s mprovemen by a conroller s nvesgaed. The gans of conrollers for recfer and nverer are opmsed by use of Parcle swarm opmzaonechnque. The effecveness of he proposed HDC conroller for mprovng ransen sably are demonsraed by a decoupled power sysem wh SCHDC subjeced o dfferen severe dsurbances. In all he cases s realsed ha he PSO based conroller sablze he sysem qucker han he convenonal conroller. 8.Appendx me(sec) me(sec) Base volage = 3 K(a.c.) 5 Pass power = MA Inal Operang Pon 6 MW and MAR Load : (Converer sde) 3 MW and MAR R.H Load : (Inverer sde) 3 MW and MAR R =,Ω L =.H Transmsson Lne Parameer x = x =.5 Ω / km (5 Km d.c. ransmsson lne ressance R =. Ω /km (5 Km) Shun ressance Rsh = R sh = Ω Converer Saon rr =.45Ω, r =.45Ω Qb 9.References. B.R. Andersen, L. Xu, P.J. Horon, P. Carwrgh. Topologes for HDC SC Transmsson. IEEE Power Engneerng Journal, June, 6: 45.. Mao Xaomng; Zhang Hao; Guan Ln; Wu Xaochen. Coordnaed conrol of ner area oscllaon n he Chna Souhern power grd (J). IEEE Trans. On Power Sysems, 6, (): P. Kundur. Power Sysem Sably and Conrol. McGrawHll, Companes, Inc, New York, Z Zhao, M.R. Iravan. Applcaon of GTO olage Source Inverer n a Hybrd HDC Lnk. IEEE Trans. On Power Delvery, 994, 9(): D.N. Koserev. Modelng Synchronous olage Source Converers n Transmsson Sysem Plannng Sudes. IEEE Trans. On Power Delvery. 997, (); Z. Huang. B.T. Oo, L.A Dessan, F.D. Galana. Explong olage Suppor of olagesource HDC. IEE Proc. Gener. Transm. Dsrb., 3, 5(): B.M. Han, S.T. Baek, B.Y. Bae, J.Y. Cho. Backoback HDC sysem usng a 36sep volage source converer. IEE Proc.Gener. Transm. Dsrb., 6, 53(6): Le Xu, Langzhong Yao, Chrsan Sasse. Grd Inegraon of Large DFIG Based Wnd Farms usng SC Transmsson. IEEE Trans. On Power Sysems, 7,(3): Paola Breses, Wl L. Klng, Ralph L. Hendrks, Rccardo ala. HDC Connecon of Offshore Wnd Farms o he Transmsson Sysem. IEEE Trans. On Energy Converson, 7, (): Chang Hsn Chen, Rchard W.G. Bucknall. Analyss of Harmoncs n Subsea Power Transmsson Cables Used n SCHDC Transmsson Sysems Operang Under SeadySae Condons. IEEE Trans. On Power Delvery, 7, (4): A. Tuson, and P. Ross, Adapng operaor sengs n genec algorhms, Evolu. Compu., vol. No., pp. 6 84, J. Gomez, D. Dasgupa, and F. Gonzalez, Usng adapve operaors n genec search, n Proc. Genec Evolu. Compu. Conf., Chcago, IL, jul. 3, pp B.R. Julsrom, Wha have you done for me laely? Adapng operaor probables n a seadysae genec Algorhms, Psburgh, PA, Jul. 59, 995, pp P.J. Anglne, Adapve and selfadapve evoluonary compuaon, n Compuaonal Inellgence: Adynamc Sysem Perspecve, M. Palanswam, Y. Akouzel, R.J. Marks, D. Fogel, and T. Fukuda, Eds. New York, IEEE Press, 995, pp J.E. Smh and T.C. Fogary, Operaor and parameer adapaon n genec algorhms, Sof Compu, vol. I, no..pp. 887, Jun A.E. Eben. R.Hnerdng, and Z. Mchalewcz, Parameer conrol n evoluonary algorhms IEEE Trans. Evolu. Compu. ol. 3. No., pp, 44, Jul R.Sorn and K.. Prce, Dfferenal evoluon A smple and effcen heursc for global opmzaon over connuous Space, J. Global Opm, vol., pp K. Prce, R. Sorn adn j. Lampnen, Dfferenal evoluona Pracval Approach o Global Opmzaon. Berln, Germany. Sprnger erlag, 5. Inernaonal Journal of Power Sysem Operaon and Energy Managemen (IJPSOEM) olumei, IssueI, 88

9 Improvemen of Transen Sably of SC HDC Sysem wh Parcle Swarm Opmzaon Based Conroller 9.. Feoksov, Dfferenal Evoluon: In Search of Soluons. Berln, Germnay : Sprngererlag, 6.. J. Ilonen, JK. Kamaranen, and J. Lampnen, Dfferenal evoluon ranng algorhm for feedforward neural neworks, Neural Process le., vol. 7, no., pp. 935,3.. B.R. Andersen. P.J. Horon and P. Carwrgh, Topologes for SC ransmsson, Power Eng. J.., vol. 6 pp. 45, jun... F. A.R Al Jowder and B. T. Oo, HDC LIGHT saon wh SSSC characerscs, IEEE Trans. Power Elecron. ol. 9 no.4 pp. 5359, Jun G. Asplund, Applcaon of HDC lgh o power sysem enhancemen, n Proc. IEEE Power Eng. Sac. Wner Meeng, jan. vol. 4, pp G. Zhang and Z. Xu, Seadysae model for SC based HDC sysem and s conroller desgn, n Proc. IEEE Power Eng. Sac. Wner Meeng. Jan/Feb., vol 3, pp G.B. Zhang, Zecel and G.Z. Wang, Seady sae model and s non lnear conrol of SC HDC sysem Proc. CSEE, vol., p.. Pp. 7,. 6. M. Durran. H. Werner, and K. Abbo, Synheses of mulobjece conrollers for a SC HDC ermnal usng LMIs, n Proc. IEEE Conf. Decson and Conrol, Dec. 4, pp S.Y. Ruan, G.J.L, X.H. Jao, Y.Z. Sun and T.T. Le, Adapve conrol desgn for SCHDC sysem based on backseppng approach, Elec. Power Sys. Res., vol. 77, no. 56, pp , Apr D. Aravndan, G.S. Ilango, C. Nagaman and A.. S.S.R. Sa., Power oscllaon dampng usng UPFC n auomac power flow conrol mode wh consan power reference, n Proc. In. Conf. Power and Energy sysem, Balmore, MD, Apr. 68, 8, pp H. Ebrahmrad, S. aezzadesh, and M. Jall Kharaajoo, Robus sldng mode conrol appled o speed conrol of PM synchronous moors, n Proc. In. Symop. Crcus and sysems. Jul., 3.vol., pp Q.Zhou, F. Wang adn L. L, Robu sldng made conrol of 4 WS vehcles for auomac pah rackng, n Proc. IEEE nellgen echcles Symp. Jun. 68, 5, pp Inernaonal Journal of Power Sysem Operaon and Energy Managemen (IJPSOEM) olumei, IssueI, 89