EMISSION CONSTRAINED OPTIMAL POWER FLOW BY BIG-BANG AND BIG-CRUNCH OPTIMIZATION

Transcription

1 C.V.G.Krshna Rao 1 G.Yesuratnam 2 J. Electrcal Systems 9-2 (2013): Regular paper EMISSION CONSTRAINED OPTIMAL POWER FLOW BY BIG-BANG AND BIG-CRUNCH OPTIMIZATION JES Journal of Electrcal Systems Ths paper presents an Emsson Constraned Optmal Power Flow(ECOPF) usng a numercally smple heurstc Bg-Bang and Bg-Crunch(BB-BC) optmzaton. The proposed optmzaton technque s appled to solve ths hghly non-lnear, non-convex and mult objectve optmzaton problem for N-0( wthout Transmsson Lne contngency) and N-1 (one transmsson lne contngency) cases of Power system network. The BB-BC method s tested on Gangour -25 and Modfed IEEE-30 bus power transmsson systems and ts robustness s compared wth Partcle Swarm Optmzaton wth Constrcton Factor (PSOCF).The out come of comparason confrms the promsng nature of BB-BC n solvng Emsson Constraned Optmal power flow. Keywords: Bg-Bang and Bg-Crunch, Emsson Constraned Optmal power flow, Envronmental optmal power flow 1. Introducton Rapd growth n power system sze and Electrcal power demand, problem of reducng the operatng cost and constranng thermal (whch meet major power demand) emssons has ganed mportance due to publc awareness and strngent target levels lad down by polluton control boards. In general, major toxc emssons are Carbon doxde(co 2 ), Sulphur Doxde (SO 2 ), and Ntrc Oxdes (NO x ). Dfferent methods such as Goal programmng [1], weghtng factor and epslon constrant method [2] and Mathematcal programmng aproaches such as Newton Raphson Methods[3] are reported n lterature. Recently nature nspred, populaton based algorthms such as Genetc algorthms, Swarm ntellgence, Bactera foragng, ant-colony search technques are appled to obtan qualty solutons [4] to optmzaton problems and also to over come the lmtatons of mathematcal programmng approaches [5]. Economcal /Envronmental dspatch problems are conflctng objectves. Mnmzaton of fuel cost alone results n ncreased Emsson levels of thermal power plants. On the other hand, mnmzaton of Emsson alone leads to ncreased fuel cost [6,7]. ECOPF leads to achevng Emsson target levels along wth reduced fuel cost compared wth mnmum Emsson Optmal dspatch.in recent tmes new heurstc optmzaton algorthms such as FreFlay [ 8] s appled to solve mnmum Emsson dspatch neglectng transmsson losses and the conflctng objectves such as Emsson and Fuel cost pareto optmal solutons ncludng transmsson losses s solved by Fre Flay algorthm[9]. Real and Bnary coded Genetc approach s appled to solve ECOPF[10] wth quadratc cost and emsson fuctons. The Conflctng,Economcal/Envronmental dspatch wth voltage stablty s solved by applcaton of Partcle Swarm Optmzaton wth constrcton factor (PSOCF) and Fuzzy Correspondng author 1 C.V.G.Krshna Rao,Assocate Prof,EEE Dept,M.VS.R Engg college,hyderabad , Emal :vgkrao_ch@yahoo.com 2 Dr G.Yesuratnam,Assocate Prof,Department of Electrcal Engneerng,Osmana Unversty,Hyderabad Copyrght JES 2013 on-lne : journal/esrgroups.org/jes

2 J. Electrcal Systems 9-2 (2013): satsfacton approach[11,12].though most of these optmzaton methods are powerful,norder to get near global optmum solutons,proper choce of tral/tunng parameters are requred. In practcal stuatons,an optmzaton algorthm wth very few tral parameters to obtan the optmum soluton along wth smplcty n updatng the control varables to arrve at optmum solutons s hghly desrable. In ths Paper a smple, heurstc optmzaton method, whose update Equaton does not nvolve tral parameters/tunng parameters and devolped from the concepts of unversal evoluton, known as, Bg-Bang and Bg-crunch (BB-BC), s appled to solve ECOPF wth contnuous and dscrete control varables. The contnuous control varables are generatng unt actve power outputs and generator bus voltage magntudes, whle the dscrete ones are transformer-tap settngs and swtchable shunt devces. The optmzaton method of ths paper s appled to solve ECOPF for N-0 contngency wth real and reactve power control varables and n case of sngle lne contngency (N-1), BB-BC optmzaton s appled to reschedule real power generatng unts for ECOPF,whle mantanng same reactve power varables as obtaned n N-0 contngency. 2. Notaton The followng notatons are used F : total operatng cost ; T :Total emsson from real power generatng unts ; NB: number of buses, NG: number of generator buses ; NT: number of Transformers ; NL: number of lnes (branches) ; NSH: number of swtchable shunts ; NPQ: number of load buses ; NTR: number of transformers ; : actve power njecton at bus ; :reactve power at bus ; NP: populaton sze ; NC: number of control varables ; ET:Emsson Target ; k:generaton/teratons of optmzaton. 3. Problem formulaton In general Optmal power flow ams at mnmzaton /maxmzaton of target objectve functon of Power system subjected to equalty and nequalty constrants. In Ths paper Target objectve functons are quadratc fuel cost functons of thermal unts and non-convex Emsson functons of thermal unts. Objectve functons and constrants are detaled as follows. 257

3 C.V.G. Krshna Rao & G. Yesuratnam: Emsson Constraned OPF by BB-BC optmzaton A1. Fuel cost functon Mnmzaton of total operatng cost of thermal power plant can be consdered as follows = Ng = 1 a + b P + c g P 2 g $/h (1) Equaton (1) s sum of quadratc cost functons of thermal generatng real power loadng unts wth usual a,b,c cost coeffcents. A2. Emsson functon Emssons from thermal power plants, such as harmful SO 2 and NO x wth α, β, γ,λ,and χ as emsson co-effcents can be expressed as non-convex functon follows. Ng 2 ( α + β Pg + γ Pg + χ sn( λ Pg )) = 1 (2) A3.Equalty and n equalty contrants are as folows. () Actve power balance - + = 0 (=1, 2, 3, NB) () reactve power balance n the network - =0 (=NG+1, NB) () actve power generaton of generator buses (=1, 2, NG) (v) lmts on voltage magntudes of generator buses (=1, 2,.. NG) (v) lmts on swtchable shunts Q Q Q (=1,..NSH) (v) lmts on tap settng of transformers (=1,..... NT) (v) lmts on reactve power generaton of generator buses (=1, 2, NG) (v) lmts on voltage magntudes of load buses (=NG+1,.NB) (x) thermal lmts of transmsson lnes (=1,...NL) Emsson constraned dspatch requres the followng nequalty (x) Emsson constrant wth Emsson target ET Optmal Power Flow goal s to mnmse equatons(1)/(2) subjected to contrants lsted n A3.The control varables [u] are real power generaton, voltage magntudes of generators, transformer tap settngs and swtchable shunt devces and ther lmts are mplctly handled whle generatng the parameters randomly. The functonal operatng constrants such as slack real power generaton, load bus bar voltage magntudes, thermal lmts of 258

4 J. Electrcal Systems 9-2 (2013): lnes and Emsson target are handled by a quadratc penalty functon approach [13]. Due to ncluson of penalty terms, transformed objectve functon (FF) for ECOPF s as follows mn here,,, and PE are penalty terms for the slack bus generator MW lmt volaton, Load bus voltage lmt volatons, generator reactve power lmt volatons and volatons for thermal lmts of lnes and emsson level (target) volaton respectvely. Three types of smulatons can be carred out wth the equaton (3), they are OPF (Fuel cost mnmzaton) alone, and mnmzaton of Emsson alone (EOPF) and Emsson Constraned Optmal Power Flows (ECOPF). Equaton (3) ams at ECOPF. In case of OPF, PE term n equaton (3) s to be deactvated. For smulaton of EOPF, n place of F T (Pg) n equaton (3), E(Pg) has to be consdered wth deactvated PE term. Though,the paper s about ECOPF,OPF and EOPF s also smulated to reflect the contradctory nature of two objectve functons.e fuel cost functon and Emsson functon. 3.1 BIG-BANG AND BIG-CRUNCH (BB-BC) The BB BC algorthm s an evolutonary algorthm whch s based on the theory of unversal evoluton[14]. Accordng to ths theory, n the Bg Bang phase energy dsspaton produces dsorder and randomness s the man feature of ths phase; whereas, n the Bg Crunch phase, randomly dstrbuted partcles are drawn nto an order. In fact, BB BC generates random ponts n the Bg Bang phase and shrnks these ponts nto a sngle representatve pont va a center of mass n the Bg Crunch phase. After a number of sequental Bg Bangs and Bg Crunches, the dstrbuton of randomness wthn the search space durng the Bg Bang becomes smaller and smaller about the average pont computed durng the Bg Crunch, and the algorthm converges to a soluton. The BB BC method conssts of two phases a Bg Bang phase, and a Bg Crunch phase. In the Bg Bang phase, canddate solutons are randomly dstrbuted over the search space. Smlar to other evolutonary algorthms, ntal solutons are spread all over the search space n a unform manner n the frst Bg Bang. The Bg Bang phase s followed by the Bg Crunch phase. The Bg Crunch s a convergence operator that has many nputs but only one output, whch s named as the center of mass. Here, the term mass refers to the nverse of the objectve functon value. The pont representng the center of mass u CM, can be found by usng the followng equaton, 3 =1, 2.NC (4) where, s the th component of the j th soluton generated n the k th teraton; NP s the populaton sze n the Bg-Bang Phase. and f j s the amount of the objectve functon. After the Bg Crunch phase, the algorthm creates the new solutons to be used as the Bg- Bang of the next teraton step, by utlzng the prevous knowledge (center of mass). Ths s accomplshed by spreadng new off-sprngs around the center of mass usng a normal dstrbuton operaton n every drecton, where the standard devaton of ths 259

5 C.V.G. Krshna Rao & G. Yesuratnam: Emsson Constraned OPF by BB-BC optmzaton normal dstrbuton functon decreases, as the number of teratons of the algorthm ncreases., = =1, 2.NC (5) Where s a random number from a standard normal dstrbuton whch changes for each canddate.these successve exploson and contracton steps are to be carred out repeatedly untl the stoppng crtera. Update equaton (5) s free from choce of tral parameters. In general dfferent populaton search methods need proper choce of tral and tunng parameters n update equaton as optmzaton proceeds towards global optmum value. In case of genetc algorthm[10],update of control varables depends on choce of mutaton and cross over probabltes.pso[11] updates control varables depends on self confdence factor c 1, swarm confdence factor c 2 and nertal weght w. FreFly Optmzaton(FFO) also a heurstc algorthm that smulates the flashng behavour of frefles(lghtng bugs) developed by Dr.Xn-she yang[15],whose update equaton depends on tral parameters such as (ntal attractveness) and γ (absorpton co-effcent) and α (tunng parameter). Mean varance Mappng optmzaton(mvmo) [16 ] update equaton depends selecton strateges of off-sprngs and scalng factor f s to control the optmal search. Compared wth update equaton of all these popular and powerful methods BB-BC updates the control varables n a smple way. As the algorthm proceeds number of teratons optmum values falls n the neghbourhood of Center of mass. Next secton explans the mplementaton of BB-BC to ECOPF. 3.2 Steps to mplement BB-BC to Power system optmzaton: 1Read OPF data (cost coeffcents of objectve functon, Emsson coeffcents, Lne, bus data and locaton of control varables) n power system network. 2. Generate ntal control varable matrx U of sze (NP*NC) wthn the lower and upper lmt of control varables.e th row of U can be generated as u = U lower *(U upper U lower )*rand (1, NC). 3 Set generaton(teraton) count k=1. 4. Intalze FFcount to 1. Row select of U to Fetch the row correspondng to Row select from U, modfy lne and bus data of power. system network. Solve for power balance equaton by usng Newton Raphson (NR)/Fast decoupled load Flow (FDLF). 6. Check for functonal operatng constrants, for any volaton of these constrants, actvate penaltes and Evaluate FF. set Row select=row select +1, FF=FF+1, return to 5, tll FFcount=NP. 7. obtan ucm usng equaton (4).check for stoppng crtera, f met dsplay current best soluton, else go to step Update control varables n accordance wth update Equaton (5). Ths step may result n volaton of control varable lmts. Those volated control varables should be made equal to ther respectve volated lmt. 9. Set k=k+1.return to step 3 tll k= Maxgeneratons. 260

6 J. Electrcal Systems 9-2 (2013): In ths paper, to satsfy power balance equatons (step 5), FDLF s used[17]. Durng ntal generatons of optmzaton algorthm, FDLF may not converge even though control varables are wthn the range. For such cases, an addtonal large penalty term proportonal to maxmum real and reactve power msmatch s added to FF.FDLF maxmum teratons and power balance msmatch tolerance are set to 10 and 0.001pu respectvely. Convergence crtera may be number of generatons or dfference between best functon value of k th and (k+1) th generaton less than a specfed tolerance. The above steps are mplemented for the two test systems mentoned n ths paper. The requred code s wrtten n MATLAB-7.0, as m-fles usng lbrary routnes of MATLAB 7.0 soft ware. Code s executed on a 2.1 GHz, Pentum IV PC. 4. Smulaton Results 4.1 N-O contngency. Test System 1: Gangour -25bus system wth 35 transmsson lnes,5 generators.ths system data s avalable at ref [1]. Cost and Emsson coeffcents are provded n Appendx. Total base case load of the system (7.30pu+j2.23pu) on 100MVA base. Total control varables are nne real valued contnuous varables pertanng to fve generatng unts. Generatng unt 1 s consdered as slack bus.termnal voltage of slack bus s consdered as control varable but ts real power generaton s constraned by penalty approach as ndcated n equaton(3). Lower and upper lmts of termnal voltages of generators are 0.9pu and 1.05 pu respectvely. Load bus voltage lmts are 0.95pu lower lmt and 1.05 upper lmt.populaton sze n each teraton of optmzaton s set to 15.The smulatons carred out for OPF resulted n mnmum cost of fuel as $/hr, but wth maxmum Emsson of lb/hr.where as EOPF resulted n maxmum fuel cost of $/hr, wth mnmum Emsson of lb/hr.However, ECOPF resulted n fuel cost $/hr wth a target Emsson of 1200 lb/hr. Generatng unt control varables are shown n Table 1. Wth these control varables total real power generaton to meet the load demand s pu, real power losses pu and mnmum load bus voltage pu occurred at bus no 15 and maxmum load bus voltage pu occurred at bus no 17.Smulatons are also carred to meet Emsson Targets of 1250lb/hr and 1300 lb/hr. The cost of fuel for these Emsson Targets are $/hr and $/hr respectvely. Table 1 : Control varables ECOPF wth target Emsson 1200 lb /hr BUS NO P g (pu) E g (pu) Test System 2:Modfed IEEE-30 bus system s consdered from ref [18].Base case load of ths Test system s (2.834pu+j1.2620pu).The fuel Cost and Emsson coeffcents are avalable n ref [11]. Generator real and reactve power varables are real values where as 261

7 C.V.G. Krshna Rao & G. Yesuratnam: Emsson Constraned OPF by BB-BC optmzaton transformer and capactve shunts are dscrete nteger postons. Ths system conssts of sx generatng unts Wth frst generatng unt as slack bus, four tap changng transformers and nne swtchable shunt devces, that amounts to total control varables 24,wth slack real genearaton dealt wth penalty approach.the transformer tap settng s consdered as (0.9+tap_ poston*0.005), where tap_ poston can take 41 dscrete steps n the range 0 to 40 nteger values. The tap_ poston 0 ndcates mnmum tap 0.9 and tap_ poston 40 ndcates maxmum tap of 1.1. Swtchable shunt consdered as (step _val*0.01), where step_ val can take 6 dscrete steps n the range of 0 to 5 nteger values, a step_ val 0 ndcates 0.00pu capactve shunt and 5 ndcates capactve shunt of 0.05pu(on 100MVA base). Populaton sze n each teraton of optmzaton s set to 20.The smulatons carred out for OPF resulted n mnmum cost of fuel generaton as $/hr,but wth maxmum Emsson of ton/hr. EOPF resulted n maxmum fuel cost of $/hr, but wth mnmum Emsson of ton/hr. Smulaton of ECOPF wth a Emsson target of 0.19 ton/hr resulted n Fuel cost $/hr. Contnuvous control varables of Generatng unts are shown n table 2, whle the transformer taps at lne number [11,12,15,16] are [1.09, 1.02,1.05,1.04], and shunts [at buses10,12,15,17,20,23,24,29] are [0.04,0.05,0.03,0.05,0.04,0.04,0.03,0.02,0.01] n pu.these control varables results n total real power generaton as pu,real losses as pu, mnmum load bus voltage pu at bus no 30 and maxmum load bus voltage pu at bus no 27.ECOPF s further tested to meet Emsson Targets of ton/hr and ton/hr. The cost of fuel for these Emsson Targets are 606.6$/hr and 611.7$/hr respectvely. Table 2 : Control varables Eectrcal power generatng unts by ECOPF wth Emsson target 0.19 ton /hr. BUS NO P g (pu) E g (pu) N-1 contngency Wth control varables as obtaned n N-0 contngency, the contngency analyss s carred out by Fast decoupled load flow method. Severty of contngency rankng lst s prepared based on real power loss crtera [19] for credble lne outages.from the severty lst,outage of lne number 16 n test system -1 wth real power loss of p.u and outage of lne number 5 wth real power loss of pu n test system -2 are pcked up for N- 1 contngency case. Table 3 ndcates the results of OPF,EOPF and ECOPF.For ECOPF smulaton s set to 1200lb/hr(test system-1) and 0.2ton/hr n test system-2,wth real power generatng unts as control varables,whle reactve power varables are same as that obtaned n N-0 case. It can be obesrved from table 3 that for N-1 contngency also ECOPF results n reduced fuel cost compared to OPF wth reduced Emsson. 262

8 J. Electrcal Systems 9-2 (2013): Table 3: comparason OPF,EOPF and ECOPF N-1 contngency. Test system-1 Test system-2 Type of Fuel Emsson Fuel Emsson dspatch cost($/hr) (lb/hr) cost($/hr) (ton/hr) OPF EOPF ECOPF Rescheduled real power generatons are ndcated n the table IV for ECOPF. Wth these control Varables n test system-1,the real power loss s pu,Mn and Max voltage are pu(at bus 18),1.0145pu( at bus 13) respectvely. In case of test system-2, the real loss s pu,mn voltage (at bus 30) and max voltage (at bus 28). Table 4 : Rescheduled real power generatons N-1 contngency. Bus no Test system -1 Test system -2 Bus no P g (pu) P g (pu) comparson wth PSOCF. 5.1 N-0 contngency Mean performance, convergence of BB-BC optmzaton, s compared wth well tested, wdely accepted Partcles Swarm optmzaton (PSO). Basc PSO wth constrcton factor (PSOCF) approach ensures fast convergence of algorthm [11].The populaton sze s set to 15 and 20 for Test System 1and Test System 2 respectvely for both optmzaton methods. Inerta weght (w) of PSOCF s ntally set to 1.2 and gradually reduced to w/1.5 wth constrcton factor 4.1.Self confdence factor c 1 and swarm confdence factor are 2.8 and 1.2 respectvely. It s to be mentoned agan here that BB-BC optmzaton does not requre any parameters except populaton sze. Comparson s done on bass of 30 ndependent runs wth dfferent ntal values for both optmzaton methods. Table 5 ndcates mean, best and worst performances of ECOPF for two Test Systems of ths paper wth target emsson of 1200 lb/hr for Test System-1 and emsson target of 0.19 ton/hr for Test System

9 C.V.G. Krshna Rao & G. Yesuratnam: Emsson Constraned OPF by BB-BC optmzaton Table 5: Mean, Worst and Best cost n $/hr N-0 contngency Method Test system -1 Test system-2 Mean worst best Mean worst best BB-BC PS0CF From the Table 5, t s clear that mean cost wth emsson targets by BB-BC s same as PSO-CF. Occurrence of Worst cost observed n BB-BC whch s nearly 4$/hr more than PSO-CF n Test System 2 s only one tme out of 30 runs. Table 6, convergence characterstcs at ntervals of 10 teratons of search process for the emsson targets mentoned n ths paper. Iteratons (k) took by each method to arrve at mean performance n each Test System s shown wth *. 10 teratons ndcates 150 functon computatons and 200 functon computatons for Test System-1 and Test System -2 respectvely. Table 6: Convergence Characterstcs N-0 contngency Iteratons(k) BB-BC PS0-CF Test case-1 $/hr Test case-2 $/hr Test Case-1 $/hr Test case-2 $/hr ** * ** ** BB-BC and PS0CF converged to mnmum and mean functon values for same number of teratons for test system-1 but n Test System -2 PS0CF arrved at mean cost for 30 teratons. For test system-1 BB-BC arrved at mean cost for same number of teratons,hower for test system-2 PSOCF converged for earler teratons. 5.2 N-1 contngency In order to test relablty of BB-BC optmzaton durng severe contngency case such as lne outage of Lne number -16 (test system-1) and lne number -5(test system-2), a 30 run smulaton smlar to that explaned above s carred out and results of such smulaton are ndcated n Table 7 for the Emsson targets as mentoned n

10 J. Electrcal Systems 9-2 (2013): Table 7 Mean, Worst and Best cost($/hr) for N-1 contngency. Method Test system -1 Test system-2 From the above table,t s clear that for N-1 contngency also the propsed BB-BC for ECOPF can relably perform on par wth PSOCF. 6. Concluson Bg-Bang and Bg-Crunch optmzaton method s appled to solve Envronmental Constraned Optmal Power flow wth contnuous and dscrete control varables. The results showed capablty of BB-BC Optmzaton method n arrvng at better fuel cost wth requred Emsson targets for two Test Systems for N-0 and N-1 contngency.the man advantage of BB-BC s that t s numercally smple algorthm and can relably solve nonlnear,non-convex mult-objectve optmzaton problems such as Emsson Constraned Optmal power flow. Ths s proved by Comparng BB-BC wth PSOCF ntellgent search optmzaton. References: Mean worst best Mean worst best BB-BC PS0CF [1] P. H. Hota, R. Chakrabart, P. K. Chattopadhya Multobjectve Dspatch Usng Goal- Attanment Method.J.Insttuton of Engneers (Inda), vol 82, September 2001, pp [2] D.P Kothar, J.S Dhlon, Power System optmzaton PHI,2006,Chapter-5. [3] chen S.D, Chen J, A drect Newton-Raphson economc Emsson load Dspatch Electrcal Power and Energy systems, vol-25,2003,pp [4] N.P.Padhy, Artfcal Intellgence and Intellgent Systems Oxford Unversty Press. [5] Bansal R.CDr(2005) optmzaton methods for Electrcal power systems an overvew Internatonal journal of Emergng Electrcal Power Systems vol 2,Iss 1,Artcle [6] Jacob Zahav, Lawrence Esenberg, An Applcaton of power dspatch Economcal /Envronmental dspatch IEEE Trans. On systems, Man, and Cybernetcs, July- 1977, pp [7] Tawfk Guesm,Hsan Hadj Abdallah, Ahmed Toum New Approach to Solve Multobjectve Envronmental /Economc Dspatch J. Electrcal Systems 2-2 (2006): [8] M.vnod Kumar G.Lakshm Phan Combned Economc Dspatch Pareto optmal fonts approach usng FreFly optmzaton Internatonal Journal of computer Applcatons Vol 30 no 12 sep [9] APostopoulous T,Valchos A(2011) Applcaton of FreFly algorthm for solvng Economc Dspatch,Internatonal Journal of Combnatroncs 2011.Artcle ID ,do. [10] K.S.Lnga Murthy, K.M. Rao, K.Srkanth, Emsson Constraned Optmal power flow Usng Bnary and real coded genetc algorthms Journal of the Insttuton of Engneers (Inda), vol 92, Sep 2011, pp

11 C.V.G. Krshna Rao & G. Yesuratnam: Emsson Constraned OPF by BB-BC optmzaton [11] P.Dutta and A.K.Snha Voltage Stablty Constraned Multple Objectve Optmal Power Flow usng Partcle Swarm Optmzaton I st Internatonal Conference on Industral and Informaton systems,pp ,8-11,august [12] J. Hazra and and A. K. Snha A mult-objectve optmal power flow usng partcle swarm optmzaton European Transactons on Electrcal Power Euro. Trans. Electr. Power (2010) Publshed onlne n Wley Onlne Lbrary wleyonlnelbrary.com).doi:.1002/etep.494. [13] L. Slman,T. Bouktr Iteratve Non-determnstc Algorthms n Optmal Power Flow: a Comparatve Study J. Electrcal Systems 7-4 (2011): [14] K. Erol Osman, Ibrahm Eksn, New optmzaton method: Bg Bang-Bg Crunch, Elsever, Advances n Engneerng Software 37 (2006), pp [15] X. S. Yang, Frefly algorthm, Levy flghts and global optmzaton, n Research and Development n Intellgent Systems XXVI, pp , Sprnger, London, UK, [16] István Erlch, Ganesh K. Venayagamoorthy A Mean-Varance optmzaton Algorthm WCCI 2010 IEEE World Congress on Computatonal Intellgence July, 18-23, CCIB, Barcelona, Span.www. [17] Anatass G.Balrtzs, N.Bskas, Chrstoforos E.Zoumas and Vaslos Petrds Optmal Power flow by Enhanced Genetc Algorthms IEEE Trans vol 17 no 2,May 2002, pp [18] k.y.lee,y.m Park and J L Ortz A unfed approach to optmal real and reactve power Dspatch, System Research, IEEE transacton on PAS,vol PAS-104,no 5, May 1985, pp [19] Abhjt Chakrabart,D.P.Kothar An Intoducton to Reactve Power Control And Voltage Stablty In Power Transmsson system text book,phi,pvt ltd,edton 1,2010. Appendx a $/hr b $/Mwh Generator cost and Emsson coeffcents Test System -1. c $/(Mw) 2 h α lb/h β lb/mwh γ lb/(mw) 2 h χ lb/hr λ 1/MW Unt no P mn MW P max MW 266