DEGL BASED OPTIMIZATION FOR PRACTICAL CONSTRAINED ECONOMIC POWER DISPATCH PROBLEM

Transcription

1 Journal of Electrcal Engneerng BASED OTIMIZATION FOR RACTICAL CONSTRAINED ECONOMIC OWER DISATCH ROBLEM B.ADMANABHAN (1) SIVAKUMAR R.S (2) (1) M.E (ower Sys Engg), Sardar Raja College of Engneerng, Alangulam, Trunelvel Dst. (2) M.E (ower Sys Engg), Anna Unversty of Technology, Combatore. (1) ; svakrs.88@gmal.com (2) J.JASER (3) Assocate rofessor, onjesly College of Engneerng, Nagercol. maltojasper@gmal.com Abstract - In ths paper a Dfferental Evoluton wth Global and Local Neghborhood () was appled to Non convex Economc Load Dspatch. Many nonlnear characterstcs of the generator such as ramp rate lmts, prohbted operatng zone, and non-smooth cost functons are consdered usng the above presented method n practcal generator operaton. The feasblty of the method s demonstrated for three dfferent systems, and t s compared wth other DE varants n terms of the soluton qualty and computaton effcency. The expermental results show that the above method was ndeed capable of obtanng hgher qualty solutons effcently n ED problems. Index Terms Economc dspatch problem, Dfferental Evoluton wth Global and Local Neghborhood, rohbted operatng zones, valve-pont loadng effect. S I. INTRODUCTION CARCITY of energy resources, ncreasng power generaton cost and ever-growng demand for electrc energy necesstates optmal economc dspatch n today s power systems. Economc Load Dspatch (ELD) s an mportant optmzaton task n power system operaton. The man objectve of Economc Load Dspatch s the allocaton of power generaton to dfferent generatng unts so as to mnmze the operatng cost whle satsfyng varous physcal constrants. Ths makes the ELD problem a large-scale non-lnear constraned optmzaton problem. Typcally, the cost functon of each generator has been approxmately represented by a sngle quadratc functon where the valve-pont effects and multple fuels are usually gnored. Ths would be often ntroducng naccuracy nto the dspatch result. Because of physcal lmtatons of the power generators, a generatng unt may have prohbted operatng zones between the mnmum and mum power outputs. Generators that operate n these zones may experence amplfcaton of vbratons n ther shaft bearngs, whch should be avoded n practcal applcaton. On the other hand, due to the fact that unt generaton output cannot be changed nstantaneously, the unt n the actual operatng processes s restrcted by ts ramp rate lmt [3, 5]. Moreover, the unts of real nput output characterstcs nclude hgher order nonlneartes and dscontnutes owng to the valve pont effect, whch has been modeled as a crculatng commutated snusodal functon n [6, 7]. The ED problem wth the above consderatons s usually a nonsmooth/non-convex optmzaton problem [3, 4]. Conventonal technques offer good results but when the search space s non-lnear and t has dscontnutes they become very complcated wth a slow convergence rato and not always seekng to the optmal soluton. The ncrease of the accuracy of the cost functon usually results n hgher nonlnear, non-smooth and non- convex functon where the classcal or gradent based methods cannot be appled [1].Therefore, the cost curve of a generator should not be too much smplfed for practcal power system operaton. Ths knd of optmzaton problem s very hard, f not mpossble, to solve usng tradtonally determnstc optmzaton algorthms. Many mathematcal assumptons-such as convex, quadratc, and dfferentable objectve and lnear or lnearzed objectve and constrants were requred to smplfy the problem. Hence the true global optmum of the problem could not be reached easly. New numercal methods are needed to cope wth these dffcultes, especally those wth hgh-speed search to the optmal and not beng trapped n local mnma. An mportant goal n the economc dspatch area s the utlzaton of mproved models for the generator producton cost 1

2 Journal of Electrcal Engneerng curves, wth the ablty of capturng a better cost-power output relatonshp. As a result, cost functons that consder valve pont loadng effects [8]-[11], fuel swtchng [28], [29], [13], and prohbted operatng zones [14]-[17] have been proposed. These mproved models generally ncrease the level of complexty of the resultng optmzaton problem. The economc dspatch problem has been solved va many tradtonal optmzaton methods, ncludng: Gradent-based technques, Newton method, Lnear programmng, and Quadratc programmng. The Lagrangan multpler method [1], whch s generally used n the ED problem, s no longer drectly applcable. Such classcal optmzaton methods are hghly senstve to startng ponts and often converge to local optmum or dverge all together. Newton based algorthms have dffculty wth handlng a large number of nequalty constrants [29]. Other methods lke Lambda Iteraton Method (LIM), Gradent Search (GS), Lnear, Quadratc and Dynamc rogrammng (L, Q, D), and Newton Methods (NM), ganed a lot of popularty n the last four decades. Ln et al. [20] presented ntegrated evolutonary programmng, Tabu search (TS) and quadratc programmng (Q) methods to solve non-convex ED problems. Ths ntegrated artfcal ntellgence method also requres two-phase computatons. Ln et al. developed an mproved TS algorthm for ED wth noncontnuous and non-smooth cost functons, but the prohbted zones and system spnnng reserve are relaxed n ths work. Methods based on artfcal ntellgence technques, such as artfcal neural networks, have also been appled successfully and are reported for example n [17]. Smlarly, E has also successfully to solve for ED problems. However, ts long executon tme s ts man dsadvantage. Dfferental Evoluton developed by Storn and rce s one of the excellent evolutonary algorthms. Dfferental Evoluton (DE) s one of the most recent populaton-based technques. The DE algorthm has been appled to varous felds of power system optmzaton. DE s an extremely powerful yet smple evolutonary algorthm that mproves a populaton of ndvduals over several generatons through the operators of mutaton, crossover and selecton. Dfferental evoluton presents great convergence characterstcs and requres few control parameters [21], [30], [31], whch reman fxed throughout the optmzaton process and need mnmum tunng. The purpose of ths paper s to present a soluton methodology for the economc power dspatch problem usng the Dfferental Evoluton wth Global and Local Neghborhood when non-convex, non-contnuous and hghly non-lnear cost functons are used. Ths s the case when valve pont loadng effects, and prohbted operatng zones are consdered. II. ROBLEM FORMULATION The ELD problem s about mnmzng the fuel cost of generatng unts for a specfc perod of operaton so as to accomplsh optmal generaton dspatch among operatng unts and n return satsfyng the system load demand, generator operaton constrants wth ramp rate lmts and prohbted operatng zones. The objectve of the classcal economc dspatch s to mnmze the total system cost by adjustng the power output of each of the generators connected to the grd. The total system cost s modeled as the sum of the cost functon of each generator, whch also ntakes the generatng lmts. That s to operate each generator wthn the mnmum and mum values. The objectve of ED s to determne the generaton levels for all on-lne unts whch mnmze the total fuel cost, whle satsfyng a set of constrants A. ECONOMIC DISATCH (ED) ROBLEM FORMULATION The fuel cost functons of the generatng unts are usually descrbed by a quadratc functon of power output. Thus the objectve functon s gven as[23], F ( ) a b c $/hr (1) g 2 Where a, b, c - the fuel cost coeffcents of the th unt N- Number of generatng unts n the system F ( g ) - total fuel cost [1] ower balance constrant N 1 g D Where, D Total power demand L Total network losses loss MW (2) [2] Capacty lmts constrants The generaton outputs g are restrcted to be wthn the lower and upper operatng lmts g, mn and g, 2

3 Journal of Electrcal Engneerng mn For = 1..N (3) Where, mn mnmum generaton lmt mum generaton lmt B. VALVE OINT EFFECT Large steam turbne generators wll have a number of steam admsson valves that are opened n sequence to obtan ever ncreasng output of the unt. As the unt loadng ncreases the nput to the unt ncreases and the ncremental heat rate decreases between the openng ponts for any two valves. Ths valve pont effect whch leads to nonsmooth, non-convex nput-output characterstcs, to be solved usng the heurstc technques. The valve pont effect s ncorporated n ED problem by supermposng the sne component model on the quadratc cost curve whch s gven below [3], mn F *( ) F ( ) e sn ( f [ ]) $/hr (4) Where F *( ) fuel cost f th unt wth valve pont effect e, f the fuel cost coeffcents of the th unt wth valve pont effect C. RAM RATE LIMITS One of unpractcal assumpton that prevaled for smplfyng the problem n many of the earler research s that the adjustments of the power output are nstantaneous. However, under practcal crcumstances ramp rate lmt restrcts the operatng range of all the onlne unts for adjustng the generator operaton between two operatng perods. The generaton may ncrease or decrease wth correspondng upper and downward ramp rate lmts. The Ramp-Up and Ramp- Down rate lmts of th generator are gven by, As generaton ncreases, 0 UR (5) As generaton decreases, 0 DR (6) Otherwse we can wrtten as, mn (, 0 DR ) mn(, UR ) 0 (7) Where, s the current output power 0 s the output power n the prevous nterval of the th generator unt UR s the up-ramp rate lmt of the th generator and DR s the down-ramp rate lmt of the th generator D. ROHIBITED OERATING ZONES The generatng unts may have certan ranges where operaton s restrcted on the grounds of physcal lmtatons of machne components or nstablty e.g. due to steam valve or vbraton n shaft bearngs. Consequently, dscontnutes are produced n cost curves correspondng to the prohbted operatng zones. For unt wth OZs, the feasble operatng zones can be descrbed as follows: mn LB UB, j 1 UB, j,1 LB, j... j... j 2,3,..., N N III. DIFFERENTIAL EVOLUTION (8) The dfferental Evoluton algorthm (DE) s a populaton based algorthm lke genetc algorthm usng the smlar operators; crossover, mutaton and selecton. The man dfference n constructng better solutons s that genetc algorthms rely on crossover whle DE reles on mutaton operators. Ths man operaton s based on the dfferences of randomly sampled pars of solutons n the populaton. The algorthm uses mutaton operaton as a search mechansm and selecton operaton to drect the search toward the prospectve regons n the search space. The DE algorthm also uses a non unform crossover that can take chld vector parameters from one parent more often than t does from other [23, 27]. By usng the components of the exstng populaton members to construct tral vectors, the recombnaton (crossover) operator effcently shuffles nformaton about successful combnatons, enablng the search for a better soluton space. The hghlghts of Dfferental Evoluton (DE) are, No dervatves are used Very few parameters to set A smple and apparently very relable method. DE s reported [22]-[32] to be the only algorthm, whch consstently found the optmal soluton, and often wth fewer functon evaluatons than the other drect search methods on benchmark nonlnear functons Smple vector subtracton to generate random drecton More varaton n populaton (because soluton has not converged yet) leads to more vared search over soluton space Sze and drecton 3

4 Journal of Electrcal Engneerng The man steps of the DE algorthm are gven below, A. INITIALIZATION Intalzaton generates ntal populaton 0 whch contans N p ndvduals x 0,, 1 N p. o, L U L b ( b b ) j N (9) j j j j j 1 Where, [b j U,b j L ] s the search space of the j th optmzaton parameter; α j s a real random number but not necessarly unform n the range [0, 1] B. MUTATION The mutaton operator creates mutant vectors by perturbng a randomly selected vector x a wth the dfference of two other randomly selected vectors x b and x c, G F.( ), 1,... N (10) a b Where x a, x b and x c are randomly chosen vectors among the N populaton, and a b c. x a, x b and x c are selected a new for each parent vector. The scalng constant F s an algorthm control parameter used to adjust the perturbaton sze n the mutaton operator and mprove algorthm convergence. C. CROSSOVER The crossover operaton generates tral vectors x by mxng the parameters of the mutant vectors x wth the target vectors x accordng to a selected probablty dstrbuton, ' " j,, f j CR or j q (11) j,, otherwse j, where =1,, N and j=1,, D; q s a randomly chosen ndex 1,,N p that guarantees that the tral vector gets at least one parameter from the mutant vector; ρ j s a unformly dstrbuted random number wthn [0, 1] generated anew for each value of j. The crossover constant C R s an algorthm parameter that controls the dversty of the populaton and ads the algorthm to escape from local mnma. x (G) j, and x (G) j, are the j th parameter of the th target vector, mutant vector, and tral vector at generaton G, respectvely. D. SELECTION The selecton operator forms the populaton by choosng between the tral vectors and ther predecessors (target vectors) those ndvduals that present a better ftness are more optmal. '' '' ( G 1), f f ( ) f ( ) (12), otherwse Where =1.., N. c p Ths optmzaton process s repeated for several generatons, allowng ndvduals to mprove ther ftness as they explore the soluton space n search of optmal values. DE has three essental control parameters: the scalng factor (F), the crossover constant (C R ) and the populaton sze (N ). The scalng factor s a value n the range [0, 2] that controls the amount of perturbaton n the mutaton process. The crossover constant s a value n the range [0, 1] that controls the dversty of the populaton. The populaton sze determnes the number of ndvduals n the populaton and provdes the algorthm enough dversty to search the soluton space. The most common method used to select control parameters s parameter tunng. arameter tunng adjusts the control parameters through testng untl the best settngs are determned. Typcally, the followng ranges are good ntal estmates: F = [0.5, 0.6], C R = [0.75, 0.90], and N = [3*D, 8*D] n [38]. In order to avod premature convergence, F or N should be ncreased, or C R should be decreased. Larger values of F result n larger perturbatons and better probabltes to escape from local optma, whle lower C R preserves more dversty n the populaton thus avodng local optma. E. DE STRATEGIES Dependng on the way the parent solutons are perturbed to generate a tral vector, there exst many tral vector generaton strateges and consequently many DE varants. best/1 best/2 rand/1/bn rand/2 F. Only n 2006, a new DE-varant, based on the neghborhood topology of the parameter vectors was developed to overcome some of the dsadvantages of the classcal DE versons. The authors n proposed a neghborhood-based local mutaton operator that draws nspraton from SO. For each member of the populaton a local mutaton s created by employng the fttest vector n the neghborhood of that member and two other vectors chosen from the same neghborhood [26]. 4

5 Journal of Electrcal Engneerng The model may be expressed as, L ( t) ( t) ' ( ' F ( nbest p ( t) ( t) ( t)) ( t)) q (13) where the subscrpt nbest ndcates the best vector n the neghborhood of and p th, q th ( k, + k). A vector s neghborhood s the set of other parameter vector s that connected and t consders ther experence when updatng ts poston. The graph of nterconnectons s called the neghborhood structure. In the local model, whenever a parameter vector ponts to a good regon of the search space, t only drectly nfluences ts mmedate neghbors, ts second degree neghbors wll only be nfluence after those drectly connected to them become hghly successful themselves. Thus, there s a delay n the nformaton spread through the populaton regardng the best poston of each neghborhood. Therefore, the attracton to specfc ponts s weaker, whch prevents the populaton from gettng trapped n local mnma. IV. SIMULATION RESULTS Ths secton presents the computaton results of ED problem solved by Dfferental Evoluton wth Global and Local Neghborhood for 10, 13and 15 unt power systems. The non-smooth economc load dspatch (ELD) problem has been solved by varants of DE algorthm and s mplemented by MATLAB program on entum IV, 3.00 GHz personal computer. In order to smulate the valve pont effects of the generatng unts, a recurrng snusod component s added wth the objectve functon of fuel cost. However, many practcal constrants of generators, such as ramp rate lmts, prohbted operatng zones, and power loss are also consdered n the optmzaton process. The populaton sze N =500, the scalng factor F = 0.9 and the crossover factor C = 0.9 are consdered for the study. These values were determned by parameter settng through tral and error method. Large number of populaton s used to allow the algorthm to search the soluton space thoroughly but at the expense of computatonal tme. A. CASE STUDY I Ths case study conssted of 10 thermal unts of generaton wth the effects of valve-pont loadng, Ramp rate lmts, rohbted operatng zones, equalty and nequalty constrants as n [2], [30]. In ths case, the load demand expected to be determned was D =2000MW. The comparatve results of DE are shown n the Table I. Table I CONVERGENCE RESULTS FOR 10 GENERATOR SYSTEMS Load demand=2000mw Unt best rand MW /1 best/2 /1/bn rand/2 Unt Unt Unt Unt Unt Unt Unt Unt Unt Unt loss Fuel cost ($/hr) Total power output B. CASE STUDY II Ths case study conssted of 13 thermal unts of generaton wth the effects of valve-pont loadng, Ramp rate lmts, rohbted operatng zones, equalty and nequalty constrants as n [21]. In ths case, the load demand expected to be determned was D =1800MW. The comparatve results of DE are shown n the Table II. Unt MW Table II CONVERGENCE RESULTS FOR 13 GENERATOR SYSTEMS Load Demand=1800MW best/1 best/2 rand/ 1/bn rand/2 Unt Unt Unt Unt Unt Unt Unt Unt Unt Unt Unt Unt Unt Fuelcost ($/hr) Total power output

6 Journal of Electrcal Engneerng C. CASE STUDY III Ths case study conssted of 15 thermal unts of generaton wth the effects of valve-pont loadng, Ramp rate lmts, rohbted operatng zones, equalty and nequalty constrants as n [25]. In ths case, the load demand expected to be determned was D =2630MW. The comparatve results of DE wth dfferent strateges are shown n the Table III. Unt MW Table III CONVERGENCE RESULTS FOR 15 GENERATOR SYSTEMS Load Demand=2630MW best/1 best/2 rand/ 1/bn rand/2 Unt Unt Unt Unt Unt Unt Unt Unt Unt Unt Unt Unt Unt Unt Unt Fuel cost ($/hr) Total ower Output From the table I, II and III t s proved that the fuel cost obtaned by computaton of method for economc dspatch problem wth multple constrants were lesser than the fuel cost obtaned by other strateges of Dfferental Evoluton. V. CONCLUSION Ths paper reported and compares the performance of dfferent DE strateges to solve the ED problem wth the generator constrants. The DE algorthm wth Global and Local Neghborhood has been demonstrated to have superor features, ncludng hgh-qualty soluton, stable convergence characterstc, and good computaton effcency. Many nonlnear characterstcs of the generator such as ramp rate lmts, valve-pont effect, prohbted operatng zones and nonsmooth cost functons are consdered for practcal generator operaton n ths paper. The results show that the presented technque n DE was ndeed capable of obtanng hgher qualty soluton effcently n ED problem. (a) Books: VI. REFERENCES [1] A.J. Wood and B.F. Wollenberg, ower generaton, Operaton and Control. New York: Wley, [2] Chaturved, Soft Computng Technques and ts Applcatons n Electrcal Engneerng ISBN Sprnger-Verlag Berln Hedelberg (b) erodcals: [3] B.admanabhan, Sva Kumar R.S, J.Jasper : Optmzaton of pecewse non-lnear mult constraned Economc power dspatch problem usng an Improved Genetc Algorthm, JEE Trans. Indus elect pow syst., 2010, 10, (3), pp [4] Lee, F.N., and Brepohl, A.M.: Reserve constraned economc dspatch wth prohbted operatng zones, IEEE Trans. ower Syst., 1993, 8, (1), pp [5] Chen,.H., and Chang, H.C.: Large-scale economc dspatch by genetc algorthm, IEEE Trans. ower Syst., 1995, 10, (4), pp [6] T.Aruldoss Albert Vctore, A. Ebenezer Jeyakumar, Reserve constraned Dynamc Dspatch of unts wth valve pont effects, IEEE Trans. ower Syst., 2005, 20(3),pp [7] D. C. Walters, G. B. Sheble, "Genetc Algorthm Soluton Of Economc Dspatch Wth Valve ont Loadng," IEEE Trans. ower Systems, Vol. 8, No. 3, pp , August [8] K. Wong, Y. Wong, "Genetc and genetc/smulatedannealng approaches to economc dspatch," IEEE roceedngs Gener, Trans and Dstr, Vol. 141, No. 5, pp , Sep [9] H. Yang,. Yang, C Huang, "Evolutonary rogrammng Based Economc Dspatch for Unts wth Non-Smooth Fuel Cost Functons," IEEE Trans. ower Systems, Vol. 11, No. 1, pp , February [10] J. ark; K. Lee; J. Shn; K. Lee, "A partcle swarm optmzaton for economc dspatch wth nonsmooth cost functons," IEEE Trans. On ower Systems, Vol. 20, No. 1, pp. 3442, Feb [11] C. E. Ln, G. L. Vvan, "Herarchcal Economc Dspatch for ecewse Quadratc Cost Functons," IEEE Trans. ower Apparatus and Systems, Vol. AS-103, No. 6, pp. I , June [12] W. Ln, F. Cheng, M. Tsay, "Nonconvex Economc Dspatch by Integrated Artfcal Intellgence," IEEE Trans. on ower Systems, Vol. 16, No. 2, pp , May [13] K. Y. Lee, A. Sode Yone, J. Ho ark, "Adaptve Hopfeld Neural Networks for Economc Load Dspatch," IEEE Trans. on ower Systems, Vol. 13, No. 2, pp , May [14] F. N. Lee, A. M. Brepohl, "Reserve Constraned Economc Dspatch Wth rohbted Operatng Zones," 6

7 Journal of Electrcal Engneerng IEEE Trans. ower Systems, Vol. 8, No. 1, pp , February [15] J. Y. Fan, J. D. McDonald, "A ractcal Approach to Real Tme Economc Dspatch Consderng Unt's rohbted Operatng Zones," IEEE Trans. ower Systems, Vol. 9, No. 4, pp , November [16]. Chen, H. Chang, "Large-Scale Economc Dspatch by Genetc Algorthm," IEEE Trans. on ower Systems, Vol. 10, No. 4, pp , November [17] T. Jayabarath. G. Sadasvam, V. Ramachandran, "Evolutonary rogrammng Based Economc Dspatch of Generators wth rohbted Operatng Zones," Electrc ower Systems Research, Vol. 52, No. 3, pp , December [18] Chen CL, Chen N., Drect search method for solvng economc dspatch problem consderng transmsson capacty constrants. IEEE Trans ower Syst 2001; [19] DosCoelho, Del de Almeda, Maran V.C: Cultural Dfferental Evoluton Approach to optmze the Economc dspatch of electrcal energy usng thermal generators, IEEE Internatonal Conference on EFTA 2008, pp [20] Ln, W.M., Cheng, F.S., and Tsay, M.T.: Nonconvex economc dspatch by ntegrated artfcal ntellgence, IEEE Trans. ower Syst., 2001, 16, (2), pp [21] Leandro dos Santos Coelho, Vvana Cocco Maran, Combnng of Chaotc Dfferental Evoluton and Quadratc rogrammng for Economc Dspatch Optmzaton wth Valve-ont Effect, IEEE Trans. ower Syst., 2006, 21(2), [22] Storn, R., System desgn by constrant adaptaton and dfferental evoluton, IEEE Trans. on Evolutonary Computaton, Vol. 3, No. 1, 1999, pp [23] F.Benhamda, Y.Ramdan, K.Madles : A Hopfeld Neural Network soluton to Economc Dspatch problem ncludng Transmsson Losses, JEE Trans. on ower electrcal crcuts., 2008, 8, (4), pp. 1-8 [24] Anruddha Bhattacharya, ranab Kumar Chattopadhyay, A Modfed artcle Swarm Optmzaton for solvng the Non-convex Economc Dspatch, IEEE [25] K.T. Chaturved, Manjareepandt, Laxm Srvastava, Self-Organzng Herarchcal artcle swarm optmzaton for non convex Economc Dspatch, IEEE Trans. ower Syst., 2008, 23(1), [26] Swagatam Das, Ajth Abraham, Uday K. Chakraborty & Amt Konar, Dfferental Evoluton usng a Neghbourhood based Mutaon operator IEEE Trans. On Evolutonary Computaton, Vol.13, No. 3, 2009, pp (c) Artcles from publshed conference proceedngs: [27] K. Wong, B. Lau, A. Fry, "Modellng Generator Input- Output Characterstcs wth Valve-ont Loadng Usng Neural Networks," IEE 2nd Internatonal Conference on Advances n ower System Control Operaton and Management, pp , 7-10 Dec [28] A. El-Gallad, M. El-Hawary, A. Sallam, A. Kalas, "Swarm Intellgence for Hybrd Cost Dspatch roblem," Canadan Conf. on Electrcal and Computer Engneerng, Vol. 2, pp , May [29] J. ark, S. Yang, K. Mun, H. Lee, J. Jung, "An applcaton of evolutonary computatons to economc load dspatch wth pecewse quadratc cost functons," The 1998 IEEE Internatonal Conference on Evolutonary Computaton, Vol. 8, No. 3, pp , 4-9 May [30] K. rce, "Dfferental Evoluton: A Fast and Smple NumercalOptmzer," Bennal Conference of the North Amercan FuzzyInformaton rocessng Socety. NAFIS Jun 1996, pp [31] R. Storn, "On the Usage of Dfferental Evoluton for Functon Optmzaton," Bennal Conference of the North Amercan Fuzzy Informaton rocessng Socety. NAFIS Jun 1996, pp [32] R. Storn, and K. rce, Mnmzng the real functons of the ICEC 96 contest by dfferental evoluton, Int. Conf. Evolutonary Computaton, IEEE, 1996, pp B.admanabhan was born on June 26, He s dong hs M.E. (ower Systems Engneerng) degree n Sardar Raja College of Engneerng, Trunelvel Dst, TamlNadu, Inda. Hs area of nterest ncludes power system operaton and control and Soft Computng Technques. Intellgence. Sva Kumar R.S was born on May 12, He s dong hs M.E. (ower Systems Engneerng) degree n Anna Unversty of Technology, Combatore, TamlNadu, Inda. Hs area of nterest ncludes power system optmzaton and Artfcal J.Jasper was born on February 28, He s currently workng toward the h.d. degree wth the Faculty of Electrcal Engneerng, Anna Unversty, Combatore, Inda. He s presently an Assocate rofessor n the Department of Electrcal Engneerng, onjesly College of Engneerng, Nagercol, TamlNadu, Inda. Hs major research nterest ncludes power system operaton, Dstrbuted Generaton, ntellgent control and Electrcal Machnes. 7