Application of RGA to Optimal choice and Allocation of UPFC for Voltage Security Enhancement in Deregulated Power System

Transcription

1 Applcaton of RGA to Optmal choce and Allocaton of UPFC for Voltage Securty Enhancement n Deregulated Power Sytem A.Karam,, M.Rahdnead,3, A.A.Gharave,3 Department of Electrcal Engneerng, Shahd Bahonar Unverty of Kerman, Kerman, IRAN Kerman Regonal Electrcty Company (K.R.E.C, Kerman, IRAN 3 Internatonal Reearch Center for Scence and Technology, Mahan, IRAN Abtract: Voltage tablty become a crucal ue n power ytem epecally under heavly loaded condton. The man purpoe of th paper to dentfy the optmal locaton of Unfed Power Flow Controller (UPFC to enhance power ytem voltage tablty by ung real genetc algorthm (RGA. The propoed method demontrate the mprovement of voltage tablty margn by mplementng to a modfed IEEE cae tudy. Key-Word: Voltage tablty, Voltage collape, UPFC, Real Genetc Algorthm (RGA, FACTS Devce Introducton Voltage collape phenomena n power ytem have become one of the mportant concern n the power ndutry over the lat two decade, a th ha been the maor reaon for everal maor blackout that have occurred throughout the world ncludng the recent Northeat Power outage n North Amerca n Augut 003. Pont of collape method and contnuaton method are ued for voltage collape tude [l]. Of thee two technque contnuaton power flow method ued for voltage tablty analy. Thee technque nvolve the dentfcaton of the ytem equlbrum pont or voltage collape pont where the related power flow Jacoban become ngular [, 3]. The voltage collape occur when a ytem loaded beyond t maxmum loadablty pont. Voltage collape tude are carred out wth the am to maxmze the loadng capablty of a partcular tranmon lne. Tradtonally hunt and ere compenaton ued to maxmze the tranfer capablty of a tranmon lne [4]. Recently the new concept of Flexble AC Tranmon Sytem (FACTS wa developed by Electrc Power Reearch Inttute (EPRI, whch nvolve a famly of fat actng, hgh power electronc devce. FACTS controller provde fat and relable control over the three man tranmon parameter,.e., voltage magntude, phae angle and lne mpedance. For th reaon, control of FACTS devce ha receved a lot of attenton n power ytem tablty enhancement [5]. Ung FACTS controller, lke Statc Var Compenator (SVC and Statc Phae Shfter (SPS, to mprove tranent tablty ha been explored n the pat year and hown to be effectve [6]. In th reearch voltage tablty enhancement modeled a an optmzaton problem and Unfed Power Flow Controller (UPFC appled to mprove voltage tablty margn. Th paper organzed a follow: n ecton the optmzaton problem defned and formulated. RGA algorthm decrbed n ecton3. Secton 4 preent Smulaton tool and Secton 5 preent the mulaton reult through a cae tudy whch followed by concludng remark a ecton 6. Problem Formulaton Nonlnear dynamcal ytem uch a power ytem can be generally decrbed a follow: x& = f (x, λ,p ( Where: n x R : Correpond to tate varable l λ R : Repreent a partcular et of noncontrollable parameter that drve the ytem to bfurcaton n a qua-tatc manner. λ caue the ytem teadly move from one equlbrum pont to another. K R p : Repreent a ere of controllable parameter aocated wth control ettng. In th reearch λ the dtance between operatng and voltage collape pont. The maxmum λ wll be determned through

2 optmzaton proce conderng employng UPFC. Optmzaton problem can be formulated a: Max F(u = ( λ λ0 F(x,λ,p0 ( S.t C(u = 0 T = DxF(x,λ,p0w u = ( x,λ,w,p Where: D x F * : Correpondng ytem Jacoban w: normalzed rght zero egenvector n R n of D x F *. Thu, the dea to maxmze the dtance between a gven operatng pont defned by λ 0 and the collape pont[7].. UPFC Bac Concept UPFC contructed from two power electronc converter, the ere converter and the hunt converter, whch are connected together by a common DC lnk a hown n Fg. [8]. The ere converter connected n ere wth the tranmon lne through a ere tranformer. It nect a voltage V B, n ere wth the lne, whoe phae angle can vary between 0 to π wth repect to the termnal voltage and whoe magntude can vary from 0 to a maxmum value determned by the devce ratng. The hunt converter connected parallel wth the lne through a hunt tranformer. It man functon to provde real power requred by the ere converter plu loe by regulatng the DC bu voltage at a dered value. It can alo operate a an ndependent reactve power compenator. The common DC capactor C dc provde a drect voltage upport for the converter operaton and alo functon a an energy tore. A can be een, there are three controllable parameter: the magntude and phae angle of the ere nected voltage and the hunt reactve power compenaton. They can be controlled n a varety of way to meet dfferent obectve. Th ha made UPFC very flexble to control for a pecfc applcaton. Fg.. Schematc tructure of UPFC.. UPFC Steady State Inecton Model The teady tate necton model of UPFC can ealy ncorporate the UPFC nto the power flow equaton [9].Fg. how the UPFC crcut arrangement. The ere converter repreented by an AC voltage ource n ere wth a reactance X. UPFC necton model derved a follow: I P conv Qconv V - + V X Fg.. UPFC crcut arrangement Frt t neceary to conder only the ere voltage ource. The voltage V, and the current I are defned a : V = V + V (3 V V I = (4 X The ere voltage ource V controllable n magntude and phae.e.: γ V = rve (5 Where 0 < r < rmax and 0 < γ < π In the next tep, the ere voltage ource tranformed to a current ource, I = bv, n parallel wth the lne, where b = a hown n X Fg.3. X = b I Fg.3. Tranformed ere voltage ource The current ource I correpond to the necton power at bue and a follow: S = V ( bv = rbv n γ rbv coγ (6 S = V ( bv (7 = rbvv n( θ + γ + rbvv co( θ + γ Where θ = θ θ The ere voltage ource necton model can be een a two dependent load a hown n Fg.4. V θ X I Fg.4 Inecton model of ere voltage ecure

3 = rbvv P = rb V n( γ (8 P n( θ + γ (9 = rbvv Q = rb V co( γ (0 Q co( θ + γ (... UPFC Model The apparent power uppled by the ere voltage ource converter calculated from γ V V * Sconv = VI = re ( ( X The actve power uppled by converter Pconv = Pconv = Re( Sconv (3 = rb V V n( θ + γ rb V n( γ The reactve power delvered or aborbed by the converter ndependently controllable by UPFC and can be modeled a a eparate controllable hunt reactve ource Q conv. The UPFC necton model contructed from the ere voltage ource (Fg. 4 wth the addton of a power equvalent to P conv + Qconv to node a hown n Fg.5.The model can be ncorporated to the power flow equaton by ncludng b nto the bu admttance matrx and addng the UPFC necton power at bue and [0]. X Fg.5. UPFC necton model P = rb VV n( θ + γ (4 P rb VV n( θ + γ (5 = rbv co( = rbvv Q = γ + Qconv (6 Q co( θ + γ (7. UPFC Cot Functon The captal cot functon of UPFC can be repreented a Equaton (8 repectvely []. C UPFC =0.0003S -0.69S+88.(US$/KVAr (8 Where: C UPFC n US$/KVAr and S the operatng range of the FACTS devce n MVAr. 3 Soluton Algorthm Heurtc method may be ued to olve complex optmzaton problem. They are able to gve a good oluton of a certan problem n a reaonable computaton tme, but they do not aure to reach the global optmum. GA a global evolutonary earch technque that can reult a feable a well a optmal oluton. GA tart wth a random ntal populaton n order to elect the bet ndvdual. Croover and mutaton and electon all together are the functon of aocated wth GA to handle the evolutonary earch reachng the bet oluton. Ordnary (bnary GA can be modfed ung real code a real-ga (RGA, n whch decodng not needed to be done, whle t may ncreae the peed and the accuracy of earch proce. The maor ue of RGA can be addreed n croover a well a mutaton and electon tage. In the followng thoe tage are explaned n detal []. 3. Croover Croover one of the man feature of RGA that make t dfferent from bnary GA. Three knd of convex croover technque are ued n th paper baed on the followng formula [3]: O = λ P + ( λ P (9 O = λ P + ( λ P λ {0,} O = λ P + ( λ P O = λ P + ( λ P λ,λ [0,] (0 O = λ P + ( λ P O = λ P + ( λ P λ [ 0.5,.5] Where: P, P are the two parent, O, O are two ther offprng and λ, λ are two random number. 3. Mutaton Mutaton for ntroducng artfcal dverfcaton n the populaton to avod premature convergence to a local optmum. An arthmetc mutaton operator that ha proved ucceful n a number of tude dynamc or non-unform mutaton. It degned for fne-tunng amed to acheve a hgh degree of precon and appled n th paper. For a gven parent P, f the gene P k elected for mutaton, then the reultng gene elected wth equal probablty from the two followng choce: t b O K = PK r(pk + a k ( T ( t b O = + K PK r(bk PK ( T

4 Where: a k and b k are lower band and upper band of P k and r a unform random number choen from (0,. t the number of current generaton,t the maxmum number of generaton and b the parameter determnng the degree of non-unformty, that aumed to be 3. It can be ad that nonunformty decreae a the number of generaton ncreae [4]. 3.3 Selecton In general, electon baed upon a random choong proce, where one of the electon method known a roulette-wheel. Indvdual are mapped to the adacent egment of a lne a t hown n Fg.6. The length of each egment on th lne correpond to the ftne value of each ndvdual. A random number wll be generated and the ndvdual whoe egment pan the random number wll be elected (tral. Th technque analogou to a roulette wheel wth each lce proportonal n ze to the ftne value [4]. Fg.6. Roulette-Wheel electon operator Fg. 7 llutrate the flow chart of the propoed RGA technque n th tudy. Start Read the lne data, UPFC data Intalze frt generaton Calculate ftne tral Reproducton, croover and mutaton operator 4 Smulaton Tool In th paper, DIgSILENT commercal oftware ued a a mulaton tool. Th oftware ha developed n 976 n DIgSILENT Gmbh Company of Germany. Nowaday more than 80 countre ue th oftware to mulate and mplement neceary calculaton n power ytem. Some capablte of th oftware are: power flow calculaton, entvty analy, contngency analy, hort crcut analy, relablty modelng. Th oftware unable to determne optmal locaton of a well a the capacty of FACTS devce. In order to add th ablty, t modfed va DIgSILENT Programmng Language (DPL module. DIgSILENT Obectve Orented Programmng (OOP, however t could upport OOP faclte for uer. Th charactertc allow new developed oftware to be coded ung a language mlar to vual C. 5 Cae Study & Reult Analy Smulaton wa carred out on a modfed IEEE 4-Bu ytem, where t hown n Fg.8 page 6. Table,, 3 and 4 repreent; lne nformaton, tranformer data, ytem generaton and load data repectvely. Power flow tudy of th ytem how that the voltage collape frt occur at bu 4. Table. Lne Data Lne R (Ω X (Ω _ l3_ Calculate ftne Replacement of populaton No Convergence Table. Tranformer Data Tranformer Shc Volt. % u, Magntude HV-Sde n p.u. u, Magntude LV-Sde n p.u. trf_4_ trf_5_ trf_4_ Ye End Fg.7. Real Genetc Algorthm Flow Dagram

5 Load Actve Power MW Table 3. Load Data Reactve Power Mvar Power Factor ld_ ld_ ld_ ld_ ld_ ld_ ld_ ld_ ld_ ld_ ld_ Name Bu Type Table 4.Generaton Data Voltage [P.U.] Mn Reactve Power Lmt [Mvar] Max Reactve.Power Lmt[Mvar] ym_8 PV ym_6 PV ym_3 PV ym_ PV ym SL In th reearch one UPFC ued to enhance voltage tablty margn. UPFC modeled a Steady State Inecton wth capacty 60 MVAr. The bet locaton for UPFC ung RGA at lne 9-4 Voltage profle hown n Fg.9 where the voltage profle mproved gnfcantly. Voltage[p.u] bae optmal Bu Voltage Bu Number Fg.9. Voltage Profle After and Before Employng UPFC Voltage collape occur at Bu4 n bae cae. By ntallaton of the UPFC, voltage collape occur at Bu0.PV curve for the weaket bu (Bu4 n bae cae and at Bu0 n optmal cae are hown n Fg.0. From th fgure, t can be een that the dtance to noe pont of PV curve referred to the voltage collape pont, n the preence of UPFC ncreaed to 44. MW. Voltage[P.U] PV Curve X: 457. Y: MW P(MW Fg.0. PV Curve at Bu 4 n Bae Cae & at Bu0 n Optmal Cae Bae Cae(Bu 4 Optmal Cae(Bu 0 Voltage Securty Enhancement X: 49.3 Y: Cot Beneft Analy The beneft of ung UPFC nclude the mprovement of ytem dynamc behavor and thu enhancement of ytem relablty. However, ther man functon to control power flow, voltage control and reducng actve power loe. Gven that UPFC placed at optmal locaton, t capable of ncreang the ytem loadablty a well. However n deregulated envronment thee apect are playng a crucal role n the operatng horzon of electrcty market. A long a UPFC reduce ytem actve loe therefore the cot of uch loe hould be returned eventually. In th regard Table 6 repreent ytem actve loe for two cae (after and before UPFC employng where n the preence of UPFC devce ytem actve loe reduce to MW. Table 5.Modfed IEEE 4 bu Sytem Actve Loe Bae Cae Optmal Cae Loe (MW UPFC captal cot (ntallng and equpment equal to 3.7 mllon$ []. The reduced cot of loe that returned by ung UPFC devce calculated a 84 mllon$(the prce of actve power loe aumed 567 ($/kw [5]. Savng through th trade-of can be about 70.3 mllon $. 6 Concludng Remark In th paper, a propoed RGA methodology mplemented to determne the optmal locaton of UPFC. It for the am of ytem voltage tablty margn enhancement. Smulaton reult through a modfed IEEE 4-bu valdate the effcency of optmal placement of UPFC. Th algorthm alo effectve for the optmal locatng of the UPFC n the large cale power ytem. Future work can be conducted on the congeton management tude. Actve power loe n practcal power ytem can be reduced va the propoed technque. Acknowledgment The author of th paper acknowledged the fnancal upport of Kerman Regonal Electrc Company. Reference: []. R.Natean, G.radman, Effect of STATCOM,SSSC and UPFC on voltage tablty, IEEE Tranacton on Power Sytem, Vol 4,NO.,004,pp []. Dobon and H. D. Chang, "Toward a theory of voltage collape n electrc power ytem," Sytem& Control Letter, vol. 3, 989, pp

6 [3]. C.A Canzare, F. L. Alvarado, C. L. DeMarco, I.Dobon, and W. F. Long, "Pont of collape method appled to ac/dc power ytem," IEEE Tranacton on. Power Sytem, vol. 7, no., May 99, pp [4]. R.Bergen. Power Sytem Analy. Prentce-Hall, New Jerey,986 [5]. H,Chen,Y.Wang,R.Zohn, Analy of Voltage Stablty Enhancement va Unfed Power Flow Controller., IEEE Tranacton on Power Sytem, Vol.,NO.8,000, pp [6]. K.R.Padyar and?s.krhna, Tranent Stablty Enhancement Wth FACTS Controller, AC and DC power Tranmon,9 aprl 996,conference publcaton NO.43,996,pp [7]. C.A.Canzare, Applcaton of Optmzaton to Voltage Collape Analy IEEE/PES Summer Meetng,July 4,998,pp.-8 [8]. S.Lmyngcharoen,U.D.Annakkage,N.C.P ahalawaththa, Fuzzy logc baed unfed power flow controller for tranent tablty mprovement, IEE Proceedng Generaton,Tranmon Dtrbuton, vol.45,no.3, March998, pp.5-3 ld_ ym_ ln 3 [9]. M.Noroozan,L.Angqut,M.Ghandhar,a nd G.Andreon, Ue of UPFC for Optmal Power Flow Control IEEE Tran on power Delvery,Vol.,NO.4,pp [0]. H.A.Abdelalam,G.E.M.Aly,M.Abdelkr m,k.m.shebl, Optmal Locaton Of The Unfed Power Flow Controller In Electrcal Power Sytem, IEEE, Vol.9, NO.3, 004, pp.4-46 []. J.Bakaran,V.Palanamy, Genetc Algorthm to Optmal Locaton of FACTS Devce n a power Sytem Network conderng economc avng cot, academc ournal,vol.5,005,pp.-0 []. L.Erlch,G.Stamt,Y.Luo, Optmal Choce and Allocaton of FACTS Devce n Deregulated Electrcty Market ung Genetc Algorthm, Bulk Power Sytem Dynamc and control VI Augut -7, 004. [3]. H. Pohlhem, Geatbx: Genetc and Evolutonary Toolbox for Ue wth Matlab, www. Geatbx.com, [4]. Goldberg, D. E., Genetc Algorthm n Search, Optmzaton and Machne Learnng, Addon Weley Longman, 989. [5]. Tavanr, A report from Energy Mntry of Iran ym_3 3 ym_ ln ld_3 ln 4 ln 5 ln_3_4 ln_4_ ym_6 trf_5_6 ld_5 8 ym_8 ld_4 trf_4_7 7 ln_6_3 ln_6_ ld_6 ln_6_ 0 ln_7_8 9 ld_9 ln_7_9 ln 3 ld_ ld_ ln_0_ ld_0 ln_9_0 hnt_9 3 4 Voltage Collape occur at th bu ld_3 ln_3_4 ln_9_4 Fg8. Modfed IEEE 4-Bu