J. Electrical Systems 9-4 (2013): Regular paper

Transcription

1 D. Hamza Zergat, L. Benasla *, A. Belmadan, M. Rahl J. Electrcal Systems 9-4 (03): Regular paper Soluton of Combned Economc and Emsson Dspatch problems us Galaxy-based Search Algorthm. JES Journal of Electrcal Systems The Galaxy-based Search Algorthm (GbSA) s an optmzaton technque developed recently by Hamed Shah-Hossen at Shahd Behesht Unversty-Iran [, ]. GbSA s a meta-heurstc that uses a modfed Hll Clmb algorthm as a local search and resembles the spral arms of some galaxes to search the optmum. In ths paper, GbSA s proposed for solv the Combned Economc and Emsson Dspatch (CEED) problem under some equalty and nequalty constrants. The equalty constrants are the actve power flow balance equatons, whle the nequalty constrants are the mnmum and maxmum power output of each unt. The voltage levels and securty are assumed to be constant. The CEED problem s obtaned by consder both the economy and emsson obectves. Ths b-obectve problem s converted nto a sle obectve functon us a prce penalty factor. The valdty of GbSA s tested on two sample systems and the results are compared to those reported n the recent lterature. The study results are qute encourag show the good applcablty of GbSA for CEED problem. Keywords: Economc dspatch, emsson dspatch, Combned Economc and Emsson Dspatch, Galaxy-based Search Algorthm.. Introducton In recent years the economc dspatch problem has taken a sutable twst as the publc has become ncreasly concerned wth envronmental matters. The absolute mnmum cost s not anymore the only crteron to be met n the electrc power generaton and dspatch problems. The generaton of electrcty from the fossl fuel releases several contamnants such as sulfur oxdes (SO ) and oxdes of ntrogen (NO X ) nto the atmosphere. These gaseous pollutants cause harmful effects on human bes as well as on plants and anmals [3]. The economc dspatch problem n a power system s to determne the optmal combnaton of power outputs for all generat unts whch wll mnmze the total cost whle satsfy the constrants. When the envronmental concerns that arse from the emssons produced by fossl-fueled electrc power plants are combned wth the EDP then the problem becomes Combned Economc and Emsson Dspatch (CEED) problem. Ths problem consders two obectves such as mnmzaton of the cost and emsson from the thermal power plants wth both equalty and nequalty constrants. The economc load dspatch s one of the maor problems n power system operaton and plann. It s a large-scale hghly non-lnear constraned optmzaton problem. The tradtonal methods used to solve ths economc load dspatch problem are Lambda teraton method, Gradent, Newton, lnear programm and nteror pont method. Recently, meta- * Correspond author: L.Benasla Department of Electrcal Eneer, USTO, Oran, Algera, E-mal: benasla@yahoo.fr Department of Electrcal Eneer, USTO, Oran, Algera Department of Computer Scence, USTO, Oran, Algera Copyrght JES 03 on-lne : ournal/esrgroups.org/es

2 J. Electrcal Systems 9-4 (03): heurstc technques such as Smulated Anneal, Genetc Algorthm (GA), Partcle Swarm Optmzaton (PSO) and Tabu search algorthm are used to solve ths problem [4]. In ths paper, a new meta-heurstc technque called Galaxy-based Search Algorthm (GbSA) has been proposed to solve the CEED problem. The b-obectve CEED problem s converted nto a sle-obectve functon us a prce penalty factor. In order to show the effectveness of the proposed algorthm, t has been mplemented on two dfferent test systems. Satsfactory smulaton results are demonstrated and also compared wth the results obtaned by other algorthms n the lterature.. Problem formulaton.. Economc dspatch The optmal Economc dspatch s the mportant component of power system optmzaton. It s defned as the mnmzaton of the combnaton of the power generaton, whch mnmzes the total cost whle satsfy the power balance relaton. The problem of economc dspatch can be formulated as mnmzaton of the cost functon subected to the equalty and nequalty constrants [5]. In power statons, every generator has ts nput/output curve. It has the fuel nput as a functon of the power output. But f the ordnates are multpled by the cost of $/Btu, the result gves the fuel cost per hour as a functon of power output [6]. The fuel cost of generator may be represented as a polynomal functon of real power generaton: F( PG ) = ( a PG + b PG + c ) ( = =,,..., ) Where F s the total fuel cost of the system, s the number of generators, a, b and c are the cost coeffcents of the -th generat unt... Emsson dspatch The emsson functon can be defned as the sum of all types of emsson consdered, such as NO x, SO, CO, partcles and thermal emssons, ect, wth sutable prc of weght on each pollutant emtted [7]. In ths paper, only NO x emsson functon s taken nto account. Ths functon s llustrated by equaton () f the valve pont effect s not taken nto account. () E( P ) = ( α P + β P + γ () G G G ) = Where E s the total NO x emsson of the system, α, β and γ are the emsson coeffcents of the -th generat unt..3. Constrants Dur the mnmzaton process, some equalty and nequalty constrants must be satsfed. In ths process, an equalty constrant s called a power balance and an nequalty constrant s called a generaton capacty constrant. 469

3 D. Hamza Zergat et al.: Soluton of CEED problems us GbSA A. Equalty constrant The total power generaton must supply the total power demand P d and the total power transmsson losses n the network P L. Hence, P P P = 0 G d L = A. Inequalty constrants Accord to those constrants, the power output of each generator s restrcted by mnmum P Gmn and maxmum PGmax power lmts. (3) P G mn P P (4) G G max.4. Combned economc and emsson dspatch (CEED) Optmzaton of Combned Economc and Emsson Dspatch (CEED) problem can be formulated as: Mn[ F( PG ),E( PG )] (5) CEED eages the concurrent optmzaton of fuel cost and emsson control that are contradctory ones. The b-obectve economc and emsson dspatch problem s converted nto sle optmsaton problem by ntroduc prce penalty factor P as follows: Mn T( PG ) = F( PG ) + Pf E( PG ) (6) Subect to the power constrants gven by (3) and (4). The prce penalty factor P f s the rato between the maxmum fuel cost and maxmum emsson of correspond generator [8]. F( P ) G max Pf = (7) E( P ) G max The steps to determne the prce penalty factor for a partcular load demand are:. Fnd the rato between maxmum fuel cost and maxmum emsson of each generator.. Arrae P f ( =,..., ) n ascend order. 3. Add the maxmum capacty of each unt ( PG max ) one at a tme, start from the smallest P f untl P Gmax P d. 4. In ths stage, P f assocated wth the last unt n the process s the prce penalty factor of the gven load P f. Once the value of P f s known, then (6) can be rewrtten n terms of known coeffcents and the unknown output of the generators. f Mn T( P ) = ( A P + B P + C (8) G G G ) = 470

4 J. Electrcal Systems 9-4 (03): Where: A = a + P fα, B = b + P f β, C = c + P fγ.5. Modfed CEED problem formulaton The modfed CEED problem formulaton s based on ts transformaton nto an unconstraned problem wth (-) varables [9]. In order to acheve the modfed CEED problem, we apply two elmnatons separately: Frstly, to elmnate the lnear nequalty constrants, new varable θ has to be ntroduced. The nequalty constrants gven by (4) can be formulated as P P G mn 0 G (9) P P G max G mn The functon lmted between 0 and s the functon sn ² θ : 0 sn² θ (0) Compar equatons (9) and (0) PG = PG mn + D sn² θ () Where D = PG max PG mn and θ s an unconstraned varable. Secondly, to elmnate the lnear equalty constrants, we express PG as a functon of PG. P = P + P ( P + D.sn² θ ) G ch L G mn () = P = L G D.sn² θ (3) Where = L = P + P P. ch L = Gmn Substtuton of the expressons () and (3) n (8) gves: Mn G( θ ) = = = [A ( P Gmn + D sn² θ )² + B ( P Gmn + D sn² θ ) + C ] + A ( L D sn² θ )² + B ( L D sn² θ ) + C (4) After development, equaton (4) can be represented n the follow general form: T T Mn G( θ ) = (sn² θ ) M(sn² θ ) + (sn² θ ) V K (5) + = M and V are (-)-by-(-) and (-)-by- array of total cost coeffcents and K s a constant total coeffcent scalar. The off-dagonal elements of matrx M are: M = D D A (6) and the dagonal elements of matrx M are: M = D ( A + A ) (7) The elements of vector V are: V = D ( A P + B LA B ) (8) G mn The constant K s: K = A L² + B L + C T ( P ) (9) + G mn For modfed economc dspatch A = a, B = b, C = c 47

5 D. Hamza Zergat et al.: Soluton of CEED problems us GbSA For modfed emsson dspatch A = α, B = β, C = γ 3. Galaxy-based search algorthm Recently, Hamed Shah-Hossen developed a new Galaxy-based Search meta-heurstc Algorthm that s an optmzaton technque nspred from nature. He appled GbSA to solve the prncpal components analyss problem [] and multlevel mage threshold []. The GbSA mtates the spral arm of spral galaxes to search ts surround. Ths spral movement s enhanced by chaos to escape from local optmums. A local search algorthm s also utlsed to adust the soluton obtaned by the spral movement of the GbSA (SpralChaotcMove). The pseudo-codes of the GbSA s: Procedure GbSA SG GenerateIntalSoluton SG LocalSearc h(sg) Whle (termnaton condton s not met) do Flag false SpralChaotcMove (SG, Flag) If (Flag) then Endf Endwhle Return SG Endprocedure SG LocalSearch( SG ) At frst, the ntal soluton s created by the functon GenerateIntalSoluton(SG). Follow soluton ntalzaton, the local search component of the GbSA, LocalSearch(SG), s actvated wth the ntal soluton n varable SG. The local search s a modfed Hll-Clmb. Other components of the proposed GbSA are called n the whle loop of the pseudo-code. SpralChaotcMove s the frst component n the loop whch globally searches around the soluton SG 3. Local search: modfed Hll-Clmb Hll Clmb s a mathematcal optmzaton technque whch belos to the famly of local search. It s an teratve algorthm that can be used to solve problems that have many solutons, some of whch are better than others. It starts wth a random (potentally poor) soluton, and teratvely makes small chaes to the soluton, each tme mprov t a lttle [0, ]. When the algorthm cannot see any mprovement anymore, t termnates. Ideally, at that pont the current soluton s close to optmal, but t s not guaranteed that Hll Clmb wll ever come close to the optmal soluton []. The relatve smplcty of the algorthm makes t a popular frst choce amost optmz algorthms. It s used wdely n artfcal ntellgence, for reach a goal state from a start node. Choce of next node and start node can be vared to gve a lst of related algorthms. Although more advanced algorthms such as smulated anneal or Tabu search may gve better results, n some stuatons hll clmb works ust as well []. 47

6 J. Electrcal Systems 9-4 (03): Pseudo-code of modfed Hll-Clmb search algorthm s shown n table. Table : The pseudo-code of the local search used n the GbSA Procedure LocalSearch // Input L s the number of components of canddate solutons. S s the current soluton wth L components such that S denotes the component th of soluton S. //Output //Parameters 3. Spral movement SNext s the output of the local search. ΔS s the step sze whch s set by functon NextChaos(). α s a dynamc parameter. Δ α s 0.5 k Max denotes the maxmum teraton that the local Search has to search around a component to fnd a better soluton. Re peat For = to L α k 0 whle SL f f ( SL ) p Goto Endf f f Endwhle SL S Endrepeat SNext S k p k max S α. ΔS; SU S SU ; Endf S SL ; Endf f ( S ) and Endrepeat f ( SU ) f f ( S) f ( SL) f f ( S) then then α α + Δα. NextChaos(); Endprocedure S + α. ΔS f ( S ) p SL SU ; SU SL ; f ( S ) then α ; α ; k k + k 0 k 0 The SpralChaotcMove has the role of search around the current soluton denoted by SG. When the SpralChaotcMove fnds an mproved soluton better than the SG, t updates the SG wth the mproved soluton, and the varable Flag s set to true. When Flag s true, the LocalSearch component of the GbSA s actvated to search locally around the updated soluton SG. The SpralChaotcMove s terated maxmally for Maxrep number of tmes. However, whenever t fnds a soluton better than the current soluton, the SpralChaotcMove s termnated. If SpralChaotc Move fnds a better soluton, Flag s set to true and Local Search s called to search locally around the newly-updated soluton SG. The whole process above s repeated untl a stopp condton s satsfed [].The SpralChaotcMove searches the space around the current best soluton us a spral movement enhanced by a 473

7 D. Hamza Zergat et al.: Soluton of CEED problems us GbSA chaotc varable generated by NextChaos(). The pseudo-code of SpralChaotcMove s shown n table. Table : The pseudo-code of the SpralChaotcMove used n the GbSA Procedure SpralChaotcMove // Input S s the current best soluton wth L components such that S denotes the th component of soluton S. // Output SNext s the output, whch s found frst that s better than the gven soluton S. Flag s set to true to ndcate that a better soluton has been found. // Parameters Each θ s ntalsed by ( + NextChaos()). Δθ s a parameter. Here, 0.0. r s Δr s set by the value NextChaos() n each procedure call. Maxre p s the maxmum teraton that the SpralChaotcMove searches. Repeat for = to L θ ( +. NextChaos()). π ; Endrepeat whle rep p Maxrep Repeat for = to L SNext S + NextChaos (). r.cos( θ ); Endrepeat f ( SNext ) f ( S ) then Flag true ; GotoEndpro cedure ; Endf Repeat for = to L SNext S NextChaos (). r.cos( θ ); Endrepeat f ( SNest ) f ( S ) then Flag true ; GotoEndpro cedure ; Endf r r + Δr; Repeat = to L θ θ + Δθ ; f ( θ f π ) then θ π ; Endf Endrepeat rep rep + ; Endwhle Endprocedure. The chaotc sequence s generated by the logstc map: xn + = λ.xn.( xn ) n = 0,,,... (0) The ntal value x 0 should be chosen from [0, ]. λ s the control parameter, and x n denotes the varable at dscrete tme n. The logstc map exhbts chaotc dynamcs when λ = 4 and x 0 [0,] {0, 0.5, 0.5, 0.75, }. 474

8 J. Electrcal Systems 9-4 (03): Smulaton results GbSA has been tested on IEEE 30-bus sx-generator and eleven generator sample systems. These test systems are wdely used as benchmarks n the power system feld for solv the CEED problem and have been used by many other research groups around the world for smlar purposes. The results obtaned from the GbSA are compared wth other populaton-based optmzaton technques, whch have already been tested and reported by earler authors. The GbSA parameters are taken as follows: λ = 4, x 0 = 0. 5, Δα = 0. 5, Δθ = 0. 0, r = 0. 00, Kmax = 00, Maxrep = 500. The smulatons were run for three dfferent cases: Case : Mnmze total fuel cost (Economc Dspatch). Case : Mnmze total emsson (Emsson Dspatch). Case 3: Mnmze fuel cost and emsson smultaneously (CEED). 4. Test System I The detaled data of ths system are gven n [6].Ths power system whch s consdered as lossless, s nterconnected by 4 transmsson lnes and the total system demand for the load buses s MW. Operat lmts, Fuel cost and emsson coeffcents for ths system are llustrated n table 3 [3]. Table 3: Generaton lmts, fuel cost and emsson coeffcents of sx-generator system F ( PG ) apg + b PG + c =.0 - (ton/h) Generator P P G mn G max a ($/MW²h) b ($/MWh) c ($/h) α (ton/mw²h) β (ton/mwh) γ (ton/h) = ($/h) E ( P ( G ) G ) α PG + β P + γ The prce penalty factor s evaluated to ton/h. The optmal values of the generated powers, fuel cost and NO x emsson for case, and 3 are reported n table 4. Table 4: GbSA soluton of Economc Dspatch, Emsson Dspatch and CEED for test system I. Generator Case Case Case 3 θ opt (rd) P Gopt (pu) θ opt (rd) P Gopt (pu) θ opt (rd) P Gopt (pu) P G6opt (pu) Fuel cost ($/h) Emsson (ton/h)

9 D. Hamza Zergat et al.: Soluton of CEED problems us GbSA Accord to table 4, the fuel cost n case s 5.4% and 3.8% lower than that found by consder cases and 3, respectvely. In addton, the emsson level n case s 0.4% and 9.65% hgher than that found n cases and 3, respectvely. We can see that the fuel cost and emssons are reduced by consder the CEED. Convergence characterstcs of fuel cost (case ), NO x emsson (case ) and total cost (case 3) are shown n fgures and respectvely. Fuel cost ($/h) Fuel cost Iteraton number NO x emsson 0,40 0,35 0,30 0,5 0,0 0,5 0,0 0,05 0,00 0,95 0,90 0,85 0,80 NO x emsson (ton/h) Total Cost ($/h) Fgure. Convergence of fuel cost (case) Fgure. Convergence of total cost (case 3) and NO x emsson (case ) Iteraton number These graphs ndcate that GbSA converges rapdly to the optmal soluton. In order to demonstrate the performance of the GbSA, ts results are compared to those obtaned us Non-domnated Sort Genetc Algorthm (NSGA) [3]. The comparson results are gven n table 5. Table 5: Comparson of fuel cost and emsson for test system I. Case Case Case Case3 Algorthm GbSA NSGA GbSA NSGA GbSA NSGA* P G (pu) P G (pu) P G3 (pu) P G4 (pu) P G5 (pu) P G6 (pu) Fuel cost ($/h) Emsson (ton/h) NSGA*: Best compromse solutons. From the above table, t s noted that the fuel cost (case ) obtaned by GbSA s comparable to that obtaned us NSGA. Moreover, the NO x emsson (case ) obtaned by GbSA s better than that obtaned us NSGA. The fuel cost obtaned by GbSA n case 3 s hgher than that obtaned by NSGA*. Moreover, NO x emsson obtaned n the same case by GbSA, s better than that obtaned us NSGA*. 476

10 J. Electrcal Systems 9-4 (03): Test System II Ths system conssts of eleven generat unts, hav quadratc cost and emsson functons. The nput data for the -generator system are taken from [4, 5, 6] and the total demand s set as 500 MW. For ths system, transmsson losses are neglected. Operat lmts, Fuel cost and emsson coeffcents are gven n table 6. For comparson of results wth recent reports, coeffcents for the modfed CEED are taken as follows: A = a + P fα, B = b + P f β, C = c + P fγ P f s the prce penalty factor of each generator. Table 6: Generaton lmts, fuel cost and emsson coeffcents of eleven-generator system Gene rator P G mn (MW) P Gmax (MW) PG F ( PG ) = a + b PG + c ($/h) E ( PG ) = ( α PG + β PG + γ ) (Kg/h) a ($/MW²h) b ($/MWh) c ($/h) α (Kg/MW²h) β (Kg/MWh) γ (Kg/h) The optmal values of the generated powers, fuel cost and NO x emsson for case, and 3 are gven n table 7. Table 7: GbSA soluton of Economc Dspatch, Emsson Dspatch and CEED for test system II. Bus Case Case Case 3 θ opt (rd) P Gopt (MW) θ opt (rd) P Gopt (MW) θ opt (rd) P Gopt (MW) P Gopt (MW) Fuel cost ($/h) Emsson (Kg/h)

11 D. Hamza Zergat et al.: Soluton of CEED problems us GbSA Convergence characterstcs of fuel cost (case ), NO x emsson (case ) and total cost (case 3) are shown n fgures 3 and 4 respectvely. Fuel cost ($/h) Fuel cost NO x emsson NO x emsson (kg/h) Cost total ($/h) Iteraton number Fgure 3. Convergence of fuel cost (case) Fgure 4. Convergence of total cost (case 3) and NO x emsson (case ) These graphs clearly ndcate that GbSA converges rapdly to the optmal soluton. From the results, t s nferred that, the fuel cost and emsson are conflct obectves. Emsson has maxmum value when cost s mnmzed. The fuel cost n case s found to be better than other cases. The maxmum dfference between cases and s 77 $/h. But the emsson level n ths case s not the best. The best emsson s found n case. In order to demonstrate the effcency of GbSA, the results obtaned for eleven-generator sample system us λ-teraton method, Recursve method, Partcle Swarm Optmzaton (PSO), Dfferental Evoluton (DE), Smplfed recursve method, Genetc Algorthm based on Smlarty Crossover (GAbSC), Gravtatonal Search Algorthm (GSA) and GbSA are shown n table 8 and fgure 5. Table 8: Comparson of fuel cost and emsson for test system II. Method λ teraton [4, 5, 6] Recursve [4, 5, 6] PSO [4, 5, 6] DE [4, 5, 6] Smplfed Recursve [4, 5, 6] GAbSC [4, 6] GSA [4] GbSA Iteraton number Fuel cost ($/h) Emsson (Kg/h) It appears n table 8 that GbSA has smlar performance when compar other populaton-based optmzaton algorthms n the lterature. The PSO produced the hghest cost and emsson. 478

12 J. Electrcal Systems 9-4 (03): , , ,4 Fuel cost ($/h) λ-teraton Recursve PSO Fuel cost DE Smplfed Recursve GAbSC NO x emsson GSA GbSA 003, 003,0 00,8 00,6 00,4 00, 00,0 NO x emsson (Kg/h) Fgure 5. Comparson of the results. 5. Concluson In ths paper, economc and emsson dspatch problems are combned and converted nto a sle obectve functon. The converted obectve functon s solved by a newly ntroduced metaheurstc GbSA to mnmze the fuel cost and NO x emsson for a gven load. The GbSA mtates the arms of spral galaxes to look for optmal solutons and also utlzes a local search algorthm for fne-tun of the solutons obtaned by the spral arm. Test results have shown that GbSA can provde dentcal solutons to others methods. The comput tme of GbSA s nsgnfcant snce the number of teratons needed by the process to stop s very low. As a result, GbSA s acceptable and applcable for CEED problem soluton. Further extensons of GbSA should be explored to nclude more obectve functons or constrants wth regard to more realstc problems, as well as other data sets and standard test problems. References [] H. Shah-Hossen, Prncpal components analyss by the galaxy-based search algorthm: a novel metaheurstc forcontnuous optmzaton, Int. J. Computatonal Scence and Eneer, Vol. 6, Nos. /, 0. [] H. Shah-Hossen, Otsu s Crteron-based Multlevel Threshold by a Nature-nspred Metaheurstc called Galaxy-based Search Algorthm, Thrd World Coress on Nature and Bologcally Inspred Comput, 0. [3] A. Lakshm Dev, and O. Vams Krshna, Combned economc and emsson dspatch us evolutonary algorthms-a case STUDY ARPN, Journal of Eneer and Appled Scences Vol. 3, N O. 6, December 008. [4] S. Dhanalakshm, S. Kannan, K. Mahadevan, and S. Baskar, Applcaton of modfed NSGA-II algorthm to Combned Economc and Emsson Dspatch problem, Electrcal Power and Energy Systems, 33, 99 00, 0. [5] L. Benasla, A. Belmadan, and M. Rahl, Applcaton of SUMT Method to Combne Economc and Emsson Dspatch, Leonardo Journal of Scences, Issue 3, -3, July-December 008 [6] Y. Wallach, Calculatons and programs for power system networks, Prentce-Hall, Elewood Clffs, 986. [7] C.M.Hua, Ya H.T., and Hua C.L., (997). B-obectve power dspatch us fuzzy satsfacton maxmz decson approach, IEEE Transactons on Power Systems, Vol., N 4, pp.75-7, 997. [8] P. Venkatesh, R. Gnanadass, and P.P.Narayana, Comparson and applcaton of evolutonary programm technques to combned economc emsson dspatch wth lne flow constrants, IEEE Transactons on Power Systems, vol. 8, n, pp , 003,. 479

13 D. Hamza Zergat et al.: Soluton of CEED problems us GbSA [9] L. Benasla, A. Belmadan, M. Rahl, Hooke-Jeeves method appled to a new economc dspatch problem formulaton. Journal of Informaton Scence and Eneer (JISE), Vol.4 No. 3 May 008. [0] M.S. Geetha Devasena and M.L.Valarmath, Optmzed test sute generaton us tabu search technque? Internatonal Journal of Computatonal Intellgence Technques, Vol., Issue, 0-4, 00. [] A. Motaghed-laran, K. Sabr-laghae and M. Heydar, Solv Flexble Job Shop Schedul wth Mult Obectve Approach, Internattonal Journal of Industral Eneer and Producton Research, 97-09, Volume, N 4, 00 [] M.Twar, V.Bansal, and A.Baa, Ant Colony Optmzaton : Algorthms of Mutaton Test, Internatonal Journal of Eneer Research & Technology (IJERT), Vol. Issue 9, November- 0. [3] M.A. Abdo, A novel multobectve evolutonary algorthm for envronmental/economc power dspatch, Electrc Power Systems Research, 65, 7-8, 003. [4] U. Güvenç, Y. Sönmez, S. Duman, and N. Yörükeren, Combned economc and emsson dspatch soluton us gravtatonal search algorthm, Scenta Iranca Transactons D: Computer Scence & Eneer and Electrcal Eneer, 9 (6), pp , 0. [5] R. Balamurugan, and S. Subramanan, A Smplfed Recursve Approach to Combned Economc Emsson Dspatch, Electrc Power Components and Systems, 36 (), pp. 7 7, 008. [6] U. Güvenç, Combned economc emsson dspatch soluton us genetc algorthm based on smlarty crossover, Scentfc Research and Essays, Vol. 5(7), pp ,