一种改进PSO算法的电力系统无功优化方法

64200812()JournalofNanjingInstituteofTechnology(NaturalScienceEdition)Vol.6,No.4Dec.,2008:1672-2558(2008)04-0013-06PSO,,,(,,211167):(PSO),,PSO.,,.,.PSO,PSO,3.IEEE-6.:;;:TM744:AReactivePowerOptimizationUsingPSOAlgorithminPowerSystemCHENJian2hua,LIXian2yun,ZHAIYin2sheng,QILei(SchoolofElectricPowerEngineering,NanjingInstituteofTechnology,Nanjing211167,China)Abstract:Particleswarmoptimization(PSO)isanewtechnologyintermsofswarmintelligenceoptimizationoriginatingfromartificiallifeandevolutionarycomputation.Theoptimizationisrealizedbyarrivingattheoptimizationsofeachparticleandthatofalltheparticlesasawhole.Sincethisalgorithmiseasytouseandhasfewerparameters,ithasbeenwidelystudiedandapplied.ThispaperintroducesresearchinwhichthePSOalgorithmwasappliedtothestudyofreactivepoweroptimizationinpowersystem,alongwithaconcreteprocedure.ThePSOwasimprovedbypresentingathirdextremevaluefordirectingsearchforthepurposeofenhancingthesearchingcapabilitiesofPSO.SimulationresultsofIEEE-6-buspowersystemareindicativeoftheefficiencyofPSO.Keywords:particleswarmoptimization;reactivepoweroptimization;globaloptimization:2008-10-09;:2008-11-20:(NA200704004):(1976-),,,,.E2mail:[e-mail]2060(OPF),.OPF,[1-3].,,(LP)(NLP)(DP).,,,;,;..[4].,()200812,(RobuStness).(SA)(GA)[5-7](Tabu)[8](ACO)[9].,CPU,;;,;,..(ParticleSwarmOptimization,PSO),.,,.,,,.PSO,,[10-14].PSO,[15]PSO,.,,,PSO,.PSO,PSOPSO,PSO,,.1[16],KennedyEberhart2090.[3]:..,.,,,gbest;,pbest.n,xi=[xi1,xi2,,xin]i,i(i)pbesti=[pi1,pi2,,pin];()gbesti=[pbest1,pbest2,,pbestn];xik()ki=[ki1,ki2,,kin](1)kid=k-1id+c1rand1(pbesti-xk-1id)+c2rand2(gbesti-xk-1id)(2)xkid=xk-1id+kid(3):i=1,2,,m(m);d=1,2,,n(n);c1c20,;rand1rand2[0,1];,,PSO[4],,,,,,.4164,:PSO2211,,,:1);2);3);4).,:minF=Nci=1iQci+PL+1Ndj=1VjVjmax-Vjmin2+2Ngk=1QkQkmax-Qkmin2(4):Vj=Vj-VjmaxVjVjmax0VjminVjVjmaxVjmin-VjVjVjmin,Qk=Qk-QkmaxQkQkmax0QkminQkQkmaxQkmin-QkQkQkmin:ii;Nc;Nd;Ng;Qcii;PL;Vjj;Qkk;;1;2.,,,,.212,Pgi-Pli=Nj=1Vj(Gijcosij+Bijsinij)=0(5)Qgi+Qci-Qli=Nj=1Vj(Gijcosij-Bijsinij)=0(6):PgiQgi;PliQli;GijBijijij;N.213.:UgiminUgiUgimaxi=1,2,,NgQcjminQcjQcjmaxj=1,2,,NcTtkminTtkTtkmaxk=1,2,,Nt(7):Ugi;Qcj;Ttk.:QgiminQgiQgimaxi=1,2,,NgUdjminUdjUdjmaxj=1,2,,Nd(8):Qgi;Udj.3PSOminF,,maxF=51()2008121/minF.X=(Tt1,Tt2,Ug1,Ug2,Qc1,Qc2,Qg1,Qg2).311.,,,.Xi,j=Xmini,j+(Xmaxi,j-Xmini,j)rand(9):Xi,jij;rand01.3121):((5)(6));2):QgiUdj,.,,,.3131),,pbest,pbestgbest,;2),,,,;3),pbest,pbest,pbestgbest,gbest;4),,,2).314PSOPSO,,,,.,PSO:nn+1,pbestigbesti,pbestm,(2)kid=k-1id+c1rand1(pbesti-xk-1id)+c2rand2(gbesti-xk-1id)+c3rand3(pbestm-xk-1id)(10):c3;rand3[0,1],,rand300.5.pbestm,pbestigbestipbestm,,.pbestm,,,.PSO1.PSO,,:,,6164,:PSO.:,.4IEEE6411IEEE62,222(46),Sload=135+j36,100.412N=50,200,019014,PSOPSO,1.,,,,,,,,.PSOPSO,,.PSO.IEEE63.1[17]PSOPSOT34110000192170193536501942341T15110000195470199671611000342UG1110501110001102783311032356UG2111001115001107980611043468Qc1010000105000109402601095766Qc2010000105000109308801092848QG1014430142660145538401469871QG2012770113850145538401473452U3019231102401101295411023055U4019380199741102262711032457U5019071101891103512911036156U601922019776110038411101348001108010877010889000108730071()2008125PSO,,.PSO,3,.IEEE6,PSO.PSO,.:[1].[J].:,1985,8(4):1-11.[2]RAYMONDRS,SUNDT.OptimalpowerflowbaseduponP2Qdecompositon[J].IEEETransonPAS,1982,101(2):397-405.[3].[J].,1987,11(5):3-11.[4],,,.[J].:,2001,28(3):64-67.[5],,.[J].,1998,22(11):18-20.[6],,,.[J].,2000,28(2):45-48.[7],,,.[J].,2000,12(1):15-18.[8],.Tabu[J].,2000,24(2):61-64.[9]DORIGOM.Antsystem:Optimizationbyacolonyofcooperatingagents[J].IEEETransonSystems,Man,AndCybernetics2PartB:Cyber2netics,1996,26(1):29-41.[10]GALLADEI,HAWARYAE,SALLAMKME.Swarm2intelligentlytrainedneuralnetworkforpowertransferprotection[C]//Canada:CanadianConferenceonElectricalandComputerEngineering,TorontoOnt,2001.[11],,,.PSO[J].,2003,23(2):26-31.[12]ABIDOMA.Optimaldesignofpowersystemstabilizersusingparticleswarmoptimization[J].IEEETransactionsonEnergyConversion,2002,17(3):406-413.[13]GAINGZL.Particleswarmoptimizationtosolvingtheeconomicdispatchconsideringthegeneratorconstraints[J].IEEETransactionsonPowerSystems,2003,18(3):1187-1195.[14],,.[J].,2004,24(4):25-29.[15],.[J].,2004,23(1):18-21.[16]EBERHARTR,KENNEDYJ.ANewOptimizerUsingParticleSwarmTheory[C]//Nagoya:ProcoftheSixthInternationalSymposiumonMicroMachineandHumanScience,1995:39-43.[17],,.[J].,2005,29(7):53-57.81