ECONOMIC DISPATCH BY USING DIFFERENT CROSSOVER OPERATORS OF GENETIC ALGORITHM

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1 ISTABUL UIVERSITY JOURAL OF ELECTRICAL & ELECTROICS EIEERI YEAR VOLUME UMBER : 00 : 0 : (73-83) ECOOMIC DISATCH BY USI DIFFERET CROSSOVER OERATORS OF EETIC ALORITHM Serhat DUMA, Al ÖZTÜRK, M. Kenan DÖŞOĞLU and Salh TOSU Duzce Unversty, Techncal Educaton Faculty, Department of Electrcal Educaton 860, Duzce, Turkey serhatduman@duzce.edu.tr, alozturk@duzce.edu.tr, kenandosoglu@duzce.edu.tr salhtosun@duzce.edu.tr ABSTRACT The great advances n technology and ndustry have brought about an ncrease n the demand for energy n electrcal power systems. In order to meet ths ncreased demand, plannng the operaton of power systems and optmum operaton of those systems are requred. To obtan t, optmal power flow, reactve power optmzaton and solutons of the economc dspatch problem are requred. The problem of Economcal Dspatch (ED) s one of the lmted non-lnear optmzaton problems of electrcal power systems. Operaton of generators wth mnmum cost by beng held n certan lmt values s requred. Intutonal methods resultng n better conclusons have been used n solvng ths complcated non-lnear problem so far. In ths study, the conclusons obtaned on condtons wth lne loss and wthout lne loss of 3 and 6 swtchboards wth thermal fuel were compared wth each other by usng dfferent crossover operators of genetc algorthm (A). Keywords- Economc Dspatch, enetc Algorthm, Crossover Operators, ower Systems. ITRODUCTIO owadays, advances n technology cause more energy demand n power systems and make these systems more complcated. Operaton of power systems on optmal condtons and plannng of t are requred due to the ncreased energy demand and declne n energy sources. The ED problem, one of the non-lnear optmzaton problems n electrcal power systems, has an mportant place n the economcal operaton of the power system. Whle the energy capacty and relablty of the power system are boosted, the producton cost s decreased. In the process of mnmzng the producton costs of generators n order to meet the power demand n power systems, powers produced by generators are requred to be n the optmal value between maxmum and mnmum values. So far, too many optmzaton methods have been used n the soluton of ED problem. These methods can be classfed as classcal optmzaton, artfcal neural networks and heurstc algorthms. In the soluton of ED problem, lnear programmng and quadratc programmng are used as classcal optmzaton [,]. Such classcal optmzaton methods are hghly senstve to starng ponts and often converge to local optmum or dverge altogether. Lnear programmng methods are fast and relable, but have a Receved Date : Accepted Date:

2 74 Economıc Dıspatch By Usıng Dıfferent Crossover Operators Of enetıc Algorıthm drawback assocated wth the pecewse lnear cost approxmaton. on-lnear programmng methods have known problems of convergence and algorthmc complexty [3]. Methods based on artfcal ntellgent technques, such as artfcal neural network have been appled successfully [4,5]. The ark et al. presented the economc load dspatch for pecewse quadratc cost functons usng the Hopfeld neural network [6]. Yalcnoz et al. [7] was solved to constraned economc dspatch problem wth prohbted operatng zones usng Hopfeld neural network. Lee et al. [8] appled the adaptve Hopfeld neural network n the economc dspatchng of electrc power systems. Ln et al. [9] solved the nonconvex economc dspatch problem by usng ntegrated artfcal ntellgence. Besdes artfcal neural network approach, heurstc methods are also used n the soluton of economc dspatch problem [0-5]. Mantawy et al. [6] solved the problem of economc dspatch by usng genetc algorthm, smulated annealng and tabu search algorthms. Yalcnoz et al. [7] appled a genetc algorthm based on arthmetc crossover and He Da-kua et al. [8] hybrd genetc algorthm n the economc dspatch problem of power systems. Chen end Wang [9] utlzed Margnal Rate of Substtuton Decson Approach to solve ED problem. Song and Xuan [0] genetc algorthm based penalty functon method have been used to solve combned heat and power ED problem. Khamsawang and Jrwbhakorn [] utlzed dfferental evoluton algorthm and Younes et al. [] utlzed genetc algorthm and matpower to solve ED problem. In Turkey the soluton of ED problem was made by usng Lagrange functon n 380 kv, 4 bus, 6 thermal power plants [3]. In ths study, the ED problem, one of the optmzaton problems, was analyzed by usng dfferent crossover operators of A that s among the ntutonal methods. As an example, data of power systems n the studes conducted n ref. [3] and [4] was taken nto consderaton. The results obtaned by the appled method were compared to the results n ref. [3] and [4]. In ths study, t was seen that genetc algorthm, whch s among ntutonal methods, yelds more relable and better results n solvng the economc dspatch problem, one of the non-lnear problems n power systems, compared to the conventonal methods. It can be appled successfully n solvng the economc dspatch problem both n Turkey and the world.. ECOOMIC DISATCH enerators work between lmt values. These values vary dependng on the demand load n electrc power systems. ED tres to mnmum cost of fuel n the power systems. The economc dspatch determnes ts optmal sharng n accordance wth demanded load for each unt at ntervals of 3 and 5 mnutes [7]. Fgure shows thermal-generatng unts connected to a sngle bus-bar servng a receved electrcal load Load. The mathematcal terms when mnmzng the producton cost of the thermal power plants of the system n economc load dspatch are gven as follows: Mn F Mn a b c F F F () Fgure. thermal unts commtted to serve a load of Load Where a, b and c are the cost coeffcents of the -th generator and s the number of generators commtted to the operatng system. s the power output of the -th generator. The output power of generator must be hgher than the mnmum actve power value n the determned lmt values or equal to t or t must be lower than the maxmum actve power value or equal to t. Serhat DUMA, Al ÖZTÜRK,M. Kenan DÖŞOĞLU and Salh TOSU

3 Economıc Dıspatch By Usıng Dıfferent Crossover Operators Of enetıc Algorıthm 75 mn max for,..., Where () L Bj j j D D L B 0 0 B 00 (3) (4) Where D s power equlbrum and L represents the transmsson losses. B represents coeffcents of losses. j 3. EMLOYI THE EETIC ALORITHM enetc algorthms are search algorthms based on the process of bologcal evoluton. The flow dagram of A shows n Fgure. A s a wdely used method n the soluton of non-lnear optmzaton problems regarded as very hard among the conventonal optmzaton methods based on genetc logc [5]. A doesn t start the soluton wth a start pont as conventonal optmzaton methods do. A starts to operate wth more solutons compared to a startng populaton randomly created by takng determned ftness functon (FF) varables nto consderaton. Then t tres to turn the solutons nto an optmum soluton by usng genetc operators (eltsm, selecton, crossover, mutaton) [6]. Thanks to ths, better ones are selected among many solutons and worse ones are elmnated. The startng populaton s made haphazardly as a result of the varables codng. Form the ftness functon and the startng populaton The varables can be coded by dfferent ways such as dualty codng, permutaton codng, value codng, and tree codng. The structure of the problem dealt wth s crtcally mportant n choosng the codng type. In ths study, varables form the populaton by beng coded as the combnatons of 0 and genes. The FF values are computed for each lne of the populaton. Takng the FF values nto consderaton, a new populaton s created as a result of the usage of A s operators. The FF values are computed n every new populaton. The ones that gve the best results are taken nto account. These operatons contnue repeatedly as many as the numbers of generatons determned n A. Therefore, obtanng the desred result s tred by makng flourshng solutons wth A [7]. 3.. Formng the ftness functon Optmum operaton values of the generators wll be found by solvng the ED problem usng A n the system gven n Fgure. For ths, the goal functon (F) and constrant functons n ths problem are gven as follows: oal Functon F Mn F Mn Constrant Functons CF D L a b 0 mn max for,..., c (5) (6) (7) Compute the value of the ftness functon Has the desred result been acheved? YES Wrte the most convenent result Fnsh the Algorthm O Carry out Eltsm, Selecton, Crossover and Mutaton Create ew opulaton Fgure. The flow dagram of A Serhat DUMA, Al ÖZTÜRK,M. Kenan DÖŞOĞLU and Salh TOSU

4 76 Economıc Dıspatch By Usıng Dıfferent Crossover Operators Of enetıc Algorıthm A operates as an unrestrcted optmzaton method. Restrcted optmzaton problem, n case of the neglgence of the constrants, s turned nto an unrestrcted optmzaton by beng dscplned wth F. In ths way, AF values wll be held n certan lmts. Whle generators are beng held between mnmum and maxmum lmt values, f the power balance s not obtaned, the nconvenent values wll be elmnated n the soluton space by exposng the am functon to the penalty functon. The total constrant functon s squared n order not to prevent achevng the result by changng brand and n respect of the problems condton t s multpled by an approprate coeffcent. In ths study, the (a) coeffcent s taken as 5. enalty functon s gven as follows: CF F a (8) Ftness functon s gven as follows: FF Mn F F (9) In ftness functon, the producton values of generators are regarded as varables and must be held between certan lmt values. 3.. Varables codng The startng populaton represents a gene pool whose all elements are formed at random. There are dfferent codng methods n the formaton of ths gene pool and bnary number system s preferred n ths study. In ths system, the genes consst of the elements, 0 and. In ftness functon, no matter how many varables there are, the coded genes of those varables accordng to the varables bt numbers form ndvduals by standng sde by sde n the populaton. The bt numbers of the varables to be coded are gven n Table. The bt numbers of the varables [8] are computed as the followng: n max mn (0) Table. Bt numbers of varables to be coded Varables Lower lmt In ths study, each varable n A forms an ndvdual n the populaton by beng 90 bts n the aggregate from 5 bts. Also, t starts the soluton wth a startng populaton formed by a computer program randomly wth 90 bts, 00 lnes, and codes whose bt values are 0 and n the aggregate. After the startng populaton s formed, each ndvdual s wrtten n ts place n the FF by turnng the bnary number system t s coded wth to decmal system. The A operators: eltsm, selecton, crossover and mutaton degrees form a new populaton n each generaton A Operators Upper lmt ftness values are calculated by turnng every ndvdual of the populaton n bnary number system to decmal system. Two ndvduals from those that gve the lowest value are selected by eltsm and the other ndvduals are selected by tournament method among themselves and then crossover and mutaton operators are appled. The crossover operator s the process n whch prospectve new ndvduals are created by the gene exchange of selected ndvduals. In ths study, the ED problem has been solved by usng dfferent crossover operators One pont crossover (OX) A random number s produced n one pont crossover operator. If ths number s lower than the determned crossover rate, two ndvduals wll be selected from tournament method soluton space. Between the selected two ndvduals, new ndvduals are produced Bt numbers Serhat DUMA, Al ÖZTÜRK,M. Kenan DÖŞOĞLU and Salh TOSU

5 Economıc Dıspatch By Usıng Dıfferent Crossover Operators Of enetıc Algorıthm 77 by makng replacement between these ndvduals from the pont n the value of the random number [7, 9]. One pont crossover s shown n Table. Table. One pont crossover arent arent Canddate arent (Chld ) Canddate arent (Chld ) Two pont crossover (TX) Two random numbers are produced n ths crossover operator. If these numbers are lower than the determned crossover rate, two ndvduals that was selected by tournament method wll be selected. ew ndvduals are produced by makng replacements from two ponts correspondng to two randomly produced number values between these two ndvduals [9]. Two pont crossover s shown n Table 3. Table 3. Two pont crossover arent arent Canddate arent (Chld ) Canddate arent (Chld ) Mult pont crossover (MX) More than two random numbers are produced n ths crossover operator. If these numbers are lower than the determned crossover rate, two ndvduals that was selected by tournament method wll be selected. ew ndvduals are produced by makng replacements from ponts correspondng to randomly produced number values between these two ndvduals [9]. Mult pont crossover s shown n Table 4. Table 4. Mult pont crossover arent arent Canddate arent (Chld ) Canddate arent (Chld ) Order based crossover (OBX) A group of ponts s selected randomly n ths method. The characters correspondng to the ponts selected as the frst chromosome exactly save ther places. The characters belongng to the selected ponts of the second chromosome are placed behnd the characters placed n the same ponts of the frst chromosome. In the other empty postons, a new chromosome s created by placng the dsused genes of the frst chromosome (from left to rght) respectvely, also consderng the genes transferred by the second chromosome [30] Lnear ordered crossover (LOX) It was developed by Falkenauer and Bouffoux. Operaton degrees [30] are gven as follows:. Select two parents from the exstng populaton randomly,. Select two nferor consecutons n the two selected chromosomes, 3. Detach the nferor consecuton selected from consecuton from the chromosome and determne the empty places, lkewse carry out the same processes n the consecuton, 4. lace the frst nferor consecuton nto and the second nto Mutaton In many studes, the concluson that mutaton rate must be taken between %0.5 and %.5 has been obtaned, A has been operated many tmes and mutaton rate has been m Serhat DUMA, Al ÖZTÜRK,M. Kenan DÖŞOĞLU and Salh TOSU

6 78 Economıc Dıspatch By Usıng Dıfferent Crossover Operators Of enetıc Algorıthm determned as Mutaton process s shown n Table 5. Mutaton formula [9,3] s gven as follows: m l () L () The power system for the 3-unt system has been solved wth lne loss and wthout lne loss by the proposed method. The mnmum cost values of the system are gven n Table 7 and Table 8 respectvely, the cost curves are gven n Fgure 3. Tablo 5. Mutaton Canddate ndvdual before mutaton Canddate ndvdual after mutaton RESULTS cost($/hr) The proposed method has been appled to two test systems; a power system wth 3 and 6 unts system respectvely. The cost functon of each unt s chosen as a quadratc functon for the test systems. The proposed method s compared wth Lagrange functon [3] and Tabu Search, SA-II [4]. The frst test system has 3 unts and detals of ths test system are gven n Table 6. The system demand s 850 MW n all smulatons. Unt () Table 6. Fuel cost coeffcents a b c mn max The system transmsson losses are calculated usng smplfed loss expresson: eneratons (a) cost($/hr) eneratons (b) Table 7. 3-Unt System results n the status wth lne loss 850 MW for demand load Crossover methods of A 3 Loss OX OBX TX MX LOX Tabu Search [4] SA-II [4] Serhat DUMA, Al ÖZTÜRK,M. Kenan DÖŞOĞLU and Salh TOSU

7 Economıc Dıspatch By Usıng Dıfferent Crossover Operators Of enetıc Algorıthm cost($/hr) OX OBX TX MX LOX Cost(Ş/h) eneratons (c) cost($/hr) eneratons (d) eneraton (f) Fgure 3. The curves of the results obtaned by the proposed method n 3-unt system and n the status wth lne loss and wthout lne loss: a) OX b)obx c) TX d) MX e) LOX f) All curves of the results n the status wthout lne loss enerator data of a 4 buses 380 KV 6 unts [3] power system used n Turkey s gven n Table 9, the results wth lne loss and wthout lne loss obtaned by the proposed method are gven n Table 0 and Table and the cost curves are gven n Fgure cost($/hr) eneratons (e) Table 8. 3-Unts System results n the status wthout lne loss. 850 MW for demand load Crossover methods of A OX OBX TX MX LOX (a) Serhat DUMA, Al ÖZTÜRK,M. Kenan DÖŞOĞLU and Salh TOSU

8 80 Economıc Dıspatch By Usıng Dıfferent Crossover Operators Of enetıc Algorıthm Unt () a Table 9. Fuel cost coeffcents b c mn max (d) (b) (e) 5.05 x OX OBX TX MX LOX Cost(Ş/h) (c) eneraton (f) Fgure 4. The curves of the results obtaned by the proposed method n 6-unts system and n the status wth lne loss and wthout lne loss: a) OX b)obx c) TX d) MX e) LOX f) All curves of the results n the status wthout lne loss Serhat DUMA, Al ÖZTÜRK,M. Kenan DÖŞOĞLU and Salh TOSU

9 Economıc Dıspatch By Usıng Dıfferent Crossover Operators Of enetıc Algorıthm 8 Crossover methods of A Table 0. 6-Unts System results n the status wth lne loss MW for demand load 3 6 Loss 4 5 OX OBX TX MX LOX LF[3] Crossover methods of A Table. 6-Unts system results n the status wthout lne loss MW for demand load OX OBX TX MX LOX Cost ($/h) 5. COCULUSIO Due to the ncreased demand for power n both our country and the world, optmzaton studes n electrcal power systems are carred out. The ED problem, one of the optmzaton problems n power systems, s becomng more mportant. Analyzng and plannng the exstng systems better s necessary n order to meet the ncreased power demand n the most approprate way. Ths paper ntroduces an approach based on dfferent crossover operators of A to study the power system economc dspatch, whch s formulated as a constraned optmzaton problem. The proposed method has been appled to two test system. Frstly n ths study, the 3-unt power system has been regarded as wth lne loss and wthout lne loss. The exstng operaton results of ED problem has been compared wth the results of TS and SA-II by usng dfferent crossover operators of the genetc algorthm. Secondly, the results obtaned by the proposed method have been compared wth the exstng study result LF by regardng the 6-unt system wth lne loss and wthout lne loss. Accordng to the smulaton results, t has been seen that the mnmum cost results, obtaned by the proposed method n two dfferent power systems, have gven better results. An advantage of usng the proposed method s that t gves better results than the solutons obtaned by mathematcal methods n the soluton of ED problem, one of the optmzaton problems n power systems, and can contrbute much to a country s economy by beng used n plannng and operatng the power systems n accordance wth the demanded power. 6. REFERECES. Alder, R., B., Securty consderaton economc dspatch wth partcpaton factors, IEEE Transactons on ower Appled Systems, Bu, R., T. and haderpanah, S., Real power reschedulng and securty assessment, IEEE Transactons on ower Appled Systems, vol. AS-0, no. 8, pp , Al-Sumat, J. S., Al-Othman, A. K. and Sykulsk, J. K., Applcaton of pattern search method to power system valvepont economc load dspatch, Electrcal ower and Energy Systems, vol. 9, pp , Yalcnoz, T. and Short, M. J., eural networks approach for solvng economc dspatch problem wth transmsson capacty constrants, IEEE Transactons on ower Systems, vol. 3, no., pp , 998. Serhat DUMA, Al ÖZTÜRK,M. Kenan DÖŞOĞLU and Salh TOSU

10 8 Economıc Dıspatch By Usıng Dıfferent Crossover Operators Of enetıc Algorıthm 5. Yalcnoz, T., and Short, M., J., Largescale economc dspatch usng an mproved Hopfeld neural network, IEE roceedngs-eneraton, Transmsson, Dstrbuton, vol. 44, no., pp. 8-85, ark, J. H., Km, Y., S., Eom, I., K., and Lee, K., Y., Economc load dspatch for pecewse quadratc cost functon usng neural network, IEEE Transactons on ower Systems, vol. 8, no. 3, pp , Yalcnoz, T., Altun, H. and Hasan, U., Constraned economc dspatch wth prohbted operatng zones: a Hopfeld neural network approach, 0 th Medterrenean Electrotechncal Conference, vol., pp , Lee, K., Y., Sode-Yome, A. and ark, J.,H., Adaptve Hopfeld neural networks for economc load dspatch, IEEE Transactons on ower Systems, vol. 3, no., pp , Ln, W.,M., Cheng, F., S., and Tsay, M.,T., onconvex economc dspatch by ntegrated artfcal ntellgence, IEEE Transactons on ower Systems, vol. 6, no., pp , ang, Z. L., artcle swarm optmzaton to solvng the economc dspatch consderng the generator constrants, IEEE Transactons on ower Systems, vol. 8, no. 3, pp , ark, J. B., Lee, K. S., Shn, J. R. and Lee, K. Y., A partcle swarm optmzaton for economc dspatch wth nonsmooth cost functons, IEEE Transactons on ower Systems, vol. 0, no., pp. 34-4, Chaturved, K. T., andt, M. and Srvastava, L., artcle swarm optmzaton wth crazy partcles for nonconvex economc dspatch, Appled Soft Computng, vol. 9, pp , Turkay, B., Economc dspatch at the ambarl power plant usng genetc algorthm, Istanbul Unversty-Journal of Electrcal & Electroncs Engneerng, vol., no., pp , Bakrtzs, A., etrds, V. and Kazarls, S., enetc algorthm soluton to the economc dspatch problem, IEE roceedngs-eneraton, Transmsson, Dstrbuton, vol. 4, no. 4, pp , Km, J. O., Shn, D. J., ark, J.. and Sngh, C., Atavstc genetc algorthm for economc dspatch wth valve pont effect, Electrc ower Systems Research, vol. 6, pp. 0-07, Mantawy, A., H., Abdel-Magd, Y. L. and Selm, S. Z., Integratng genetc algorthms, tabu search and smulated annealng for the unt commtment problem, IEEE Transactons on ower Systems, vol. 4, no. 3, pp , Yalcnoz, T., Altun, H. and Uzam, M., Economc Dspatch Soluton usng a genetc algorthm based on arthmetc crossover, IEEE orto ower Tech. Conference, vol., pp. 4, Da-kuo, H., Fu-l, W. and Zh-zhong, M., Hybrd genetc algorthm for economc dspatch wth valve-pont effect, Electrc ower Systems Research, vol. 78, pp , Chen, Y.,M., and Wang, W.,S., Economc dspatch wth envronmental consderatons usng margnal rate of substtuton decson approach, Journal of Qualty, vol. 6, no., pp. 09-8, Song, Y. H., and Xuan, Q., Y., Combned heat and power economc dspatch usng genetc algorthm based penalty functon method, Electrc ower Components and Systems, vol. 6, no. 4, pp , Khamsawang, S., and Jrwbhakorn, S., Solvng the economc dspatch problem by usng dfferental evoluton, Internatonal Journal of Electrcal ower and Energy Systems Engneerng, vol., pp. -5, Younes, M., Rahl, M. and Kordak, L., A., Economc ower Dspatch Usng Evolutonary Algorthm, Journal of Electrcal Engneerng, vol. 57, no. 4, pp. -7, Kurban, M. and Basaran, U., Economc dspatch analyss for 4 bus 380-kV power system n Turkey, Electrc-Electronc, Computer Engneerng. atonal Congress and Far, Istanbul, Ah Kng, R., T., F. and Rughooputh, H., C., S., Eltst multobjectve evolutonary algorthm for envronmental/economc dspatch, The 003 Congress on Evolutonary Computaton, vol., pp. 08-4, 003. Serhat DUMA, Al ÖZTÜRK,M. Kenan DÖŞOĞLU and Salh TOSU

11 Economıc Dıspatch By Usıng Dıfferent Crossover Operators Of enetıc Algorıthm Mazumder,. and Runck, E.,M., enetc Algorthm For VLSI Desgn Layout Test Otomaton, rentce Hall TR, oldberg, E., D., enetc Algorthms n Search Optmzaton and Machne Learnng, Addson Wesley Longman, Ozturk, A. and Duman, S., Determnaton of the condtons of optmal operaton n power systems usng genetc algorthm, Journal of the Faculty of Engneerng and Archtecture of az Unversty, vol. 4, no. 3, pp , Saruhan, H., Optmum desgn of rotorbearng system stablty performance comparng an evolutonary algorthm versus a conventonal method, Internatonal Journal of Mechancal Scences, vol. 48, pp , Ozturk, A., Investgaton of voltage stablty n power systems usng genetc algorthm, hd. Thess, Sakarya Unversty, Cheng, R., en, M. and Tsujmura, Y., A Tutoral Survey of Job Shop Schedulng roblems Usng enetc Algorthms: art II. Hybrd enetc Search Strateges, Computers and Industral Engneerng, vol. 37, pp. 5-55, Saruhan, H., enetc Algorthms: An Optmzaton Technque, Technology, vol. 7, pp. 05-4, 004. S. Duman was born n Bandırma, Turkey, n 98. He receved the B.Sc. degree n electrcal educaton from Abant Izzet Baysal Unversty, Bolu, Turkey, n 008 and M.Sc. degree from the Department of Electrcal Educaton, Duzce Unversty, Duzce, Turkey n 00. He s currently student of h.d. n the Department of Electrcal Engneerng, Kocael Unversty, Turkey. Hs areas of research nclude power system transent stablty, power system dynamc stablty, FACTS, optmzaton technques, voltage stablty, optmzaton problems n power systems and artfcal ntellgent. A.Öztürk receved hs B.S. n Electrcal Engneerng Yldz Techncal Unversty, Turkey, n 996, hs M.Sc. n Electrcal Engneerng from Sakarya Unversty, Sakarya, Turkey, n 00 and hs h.d. n 007 from the same unversty. Hs research nterests nclude voltage stablty and optmzaton n electrc power systems M. Kenan DOSOLU was born n azantep Turkey, n 983. He receved the B.Sc. degree n electrcal educaton from A..B.Ü. Bolu, Turkey, n 006 and M.Sc. Degree from the department of Electrcal Educaton, Duzce Unversty, Duzce, Turkey n 00. He s currently student of h.d. n the Department of Electrcal Engneerng, Kocael Unversty, Turkey. Hs areas of research ncludepowersystem transent stablty, power system voltage stablty, FACTS, optmzaton technques, voltage stablty and wnd farm S. Tosun receved hs B.S. n Electrcal Educaton Marmara Unversty, Turkey, n 986, hs M.Sc. n Electrcal Engneerng from Marmara Unversty, Istanbul, Turkey, n 99. Hs research nterests nclude voltage stablty and optmzaton n electrc power systems. Serhat DUMA, Al ÖZTÜRK,M. Kenan DÖŞOĞLU and Salh TOSU