单亲遗传算法对于在梯级水力发系统中多级电站的经济分配方法的改进作用毕业论文外文翻译.docx
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单亲遗传算法对于在梯级水力发系统中多级电站的经济分配方法的改进作用毕业论文外文翻译.docx
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单亲遗传算法对于在梯级水力发系统中多级电站的经济分配方法的改进作用毕业论文外文翻译
外文资料原文
Animprovedparthenogeneticalgorithmformulti-objectiveeconomicdispatchincascadedhydropowersystems
Abstract:
Themulti-objectiveeconomicdispatch(MOED)problemincascadedhydropowersystemsisacomplicatednonlinearoptimizationproblemwithagroupofcomplexconstraints.Inthispaper,animprovedparthenogeneticalgorithm(IPGA)forresolvingtheMOEDprobleminhydropowerenergysystemsbasedonthenon-uniformmutationoperatorisproposed.Inthenewalgorithm,thecrossoveroperatorisremovedandonlymutationoperationismade,whichmakesitsimplerthanGAinthegeneticoperationsandnotgenerateinvalidoffspringduringevolution.Withthehelpofincorporatinggreedyselectionideaintothenon-uniformmutationoperator,IPGAsearchesthesolutionspaceuniformlyattheearlystageandverylocallyatthelaterstage,whichmakesitavoidtherandomblindjumpingandstayatthepromisingsolutionareas.Finally,theproposedalgorithmisappliedtoarealistichydropowerenergysystemwithtwogiantscalecascadedhydropowerplantsinChina.Comparedwithotheralgorithms,theresultsobtainedusingIPGAverifyitssuperiorityinbothefficienc.
Keywords:
multi-objectiveoptimization;Improvedparthenogeneticalgorithm;Non-uniformmutationoperator.Cascadehydropowerstationgroupof.
Introduction
Optimizationofmulti-objectiveeconomicdispatch(MOED)incascadedhydropowersystemsisoneofthemostcomplicatedissuesinwaterresourcesmanagementasittypicallyinvolvestrade-offs.Forexample,asinglemultipurposereservoir,whichnotonlyserveshydropowerbutalsonavigation,itsdispatchermaywishtomaximizebenefitsfromhydropowergeneration,whilereleasingsufficientwaterfornavigationtosatisfythedemands.However,ahigherprofitfromhydropowergenerationwouldconflictwiththenavigationreleases,thatistosay,anyimprovementofoneobjectivecanbeachievedonlyattheexpenseofanother.Thecurveorsurface(formorethan2objectives),describingtheoptimaltrade-offsolutionsbetweentheobjectives,isknownastheParetofront.Inreallife,mostofreservoirsystemsservemultiplepurposesandtheyaremulti-objectiveinnature.Duetothedispatchrulesforajointoperationofcascadereservoirsenabletodevelopthecapacityofhydropowergeneration,theMOEDproblemincascadedhydropowersystemsbecomesanactiveresearchareainrecentyears.ThegoalofMOEDincascadedhydropowersystemsistodeterminethewaterdischargeprocessofallhydropowerstationsduringtheschedulingperiodinordertomaximizethetotalbenefitwhilefulfillingvariousactualwaterdemandsandothercomplicatedconstraintssimultaneously.Becauseofthecomplexpowerandhydraulicrelationsbetweencascadedhydropowersystems,themulti-objectiveoptimaloperationofcascadehydropowerstationsisalargescale,dynamic,andstrongcouplingnonlinearproblem,whichinvolvesmanyvariables,suchas,inflow,storage,discharge,waterlevel,waterhead,outputandgeneratedenergy.
Sofar,differentmethodstosolvetheMOEDproblemhavebeenproposedanddiscussedbymanyresearchers.Thetraditionalmethods,suchas,mixedintegerlinearprogramming(MILP),Lagrangerelaxation(LR),nonlinearprogramming(NLP),dynamicprogramming(DP)andprogressiveoptimalityalgorithm(POA),havebeenwidelyappliedinthepast.Andmanyachievementshavealsobeenobtained.Nevertheless,allofthemethodslistedaboveexistsomeshortcomingswhichmakethemlessefficientandevendifficultinsearchingfortheoptimalsolution.WhenMILPisemployedtosolvetheMOEDproblem,linearizationofthemulti-objectivefunctionsandconstraintscoulddeviatetheoriginalproblem,whichmakesthenon-inferiorsolutioninaccuracy.ForNLPmethodology,someapproximateapproachesareadoptedtodealwithdiscontinuous,non-differentiableandnon-convexmulti-objectivefunctions,andthesemethodsarecomputationalexpensive.LagrangemultipliersupdatingstrategyhasanunfavorableinfluenceontheefficiencyofLR,whichmakesthestabilityofsolutionpoor.ThoughDPmethodcanresolvetheoptimaloperationofasinglemultipurposereservoir,itsuffersfromthe‘‘curseofthedimensionality’’whichmakesthecomputationtimeincreasedramaticallywhenthedimensionofcascadedhydropowersystemsincreases.POAiswidelyusedinthemulti-objectiveoptimaloperationofcascadedhydropowerplants,butitissensitivewiththeinitialsolution,whichgenerallyshrinksthesearchingareaandtrapsitinthelocalParetooptimalfronteasily.
Recently,therehasbeenanincreasinginterestinadaptiveheuristicsearchalgorithmsmodeledfromthebiologicallymotivatedadaptivesystems,forsolvingtheMOEDproblem,becauseoftheirpowerfulglobalsearchingcapacity,suchasgeneticalgorithm(GA),antcolonyoptimization(ACO)algorithm,particleswarmoptimization(PSO)algorithm,andartificialbeecolony(ABC)algorithm.However,beingsamewiththeclassicalmethods,alltheseheuristicsstochasticsearchalgorithmsmentionedabovehavetheirdrawbackstoo.Forexample,sometimestheymaysufferfromprematureconvergence,andthesearchingabilityofthesealgorithmsissensitivetoparametersettings.GAisoneofthemostpromisingtechniquesinnaturaladaptivesystemfieldofevolutionaryalgorithmparadigmandhasreceivedgreatattention,becauseofitsflexibilityandeffectivenessforoptimizingcomplexsystems.Butsometimes,thetraditionalGAmayproduceaviolatingoffspringinthecross-overoperation,whichhasanegativeeffectontheefficiencyofGAbyreasonofhavingtorestoretheviolatingoffspringoradoptapenaltyfunctionintheobjectivefunctionstodiscardtheviolatingoffspring.Inordertoovercomethisdisadvantage,parthenogeneticalgorithm(PGA)isproposedasanimprovedGA.InGA,thecrossoverisalwaysseenasthemajoroperatorandthemutationoperatorjustplaysanassistantrole.ButinPGA,onlythemutationoperationismadeandnoinvalidoffspringisgenerated.
Accordingtotheparthenogeneticschematheoremsproposedinliterature,wefindthathighrankschemasinthesubsequentgenerationdecreaseexponentiallythoughtheirfitnessvaluesaremoreoptimalthantheaverageoneinthepopulation,whichmaycausethehighrankschemasthatmatchtheglobaloptimalindividualtobedesertedfastbeforetheglobaloptimalindividualisfound.ItseemsthatPGArunsawayfromtheareawheretheglobaloptimalindividualliesthoughsearchnearsthearea,whichreducesthesearchingefficiencyofPGA.Inordertoovercomethisshortcomingandavoidtheundesirabletendency,thispaperpresentsanimprovedparthenogeneticalgorithm(IPGA)basedonthenon-uniformmutationoperatortosolvetheMOEDproblemincascadedhydropowersystems.Meanwhile,thegreedyideaandtheideaofmutatingasinglecomponentoftheindividualvectorratherthanmodifyingallthecomponentsareincorporatedintoIPGAinordertoavoidpossiblerandomjumpsandtoensurethealgorithmtostayatthepromisingareajustfoundbythesearchengineforthebetteroptimalindividual.
Therestofthepaperisorganizedasfollows.Section‘Numericalmodel’describesthemodeloftheMOEDproblemincascadedhydropowersystems.Section‘Improvedparthenogeneticalgorithm’presentstheIPGAandintroducesitsrealizationprocessindetail.Section‘ImplementationofIPGAforeconomicdispatchincascadehydropowersystems’evaluatestheproposedalgorithmandcomparesitwithdifferentalgorithmsusingthedatafromahydropowerenergysystemwithtwocascadereservoirsinChina.Finally,weconcludethispaperinSection‘Conclusions’.
Numericalmodel
Theeconomicdispatchofcascadedhydropowerplantsisatypicalproblemintheoptimalfieldsofhydropowerenergysystem.Usually,theoperationpurposeistomaximizethetotalpowergenerationbenefitsortotalelectricityproductionofcascadedhydropowerplantsduringtheschedulingperiodbydeterminingtheoptimalprocessofwaterdischargevalueofhydropowerstations,undertheconditionofsatisfyingallconstraints.However,withthedevelopmentofsocialeconomyinChina,changeofpowerconsumptionstructurerequiresmostlarge-capacityunitstobeinvolvedinpeakloadregulationofelectricitygrid.Inordertoguideoptimaloperationofcascadereservoirsandgivefullplaytocapacitybenefitsofcascadehydropowerstations,amathematicalmodelisestablishedbasedontheprinciplesof
(1)maximumtotalelectricityproductionand
(2)maximumtotalleastoutputofthecascadedhydropowerplantsinthispaper.Thespatialcouplingofahydropowerenergysystemwithtwocascadereservoirsisshownin,andtheobjectivefunctionsandconstraintsofaforementionedmathematicalmodelareexpressedasfollows:
Obviously,thisisamulti-objectiveoptimizationproblem.Weightedapproachandconstraintmethodareusuallyemployedbymanyresearcherstohandleitinwaterresourcesmanagement.Fortheconstraintmethod,allobjectivesexceptthemajoroneareconstrainedtospecificvaluestoyieldaParetooptimalsolution.Withincrementofthespecificvalues,themodelisrunagaintofindanotherParetooptimalsolutionuntilthetrade-offrelationshipbetweentheobjectivesissufficientlyrepresented.Inweightedmethod,allobjectivesareincorporatedintooneobjectivefunctionsimultaneouslybydifferentweights,andadifferentsetofweightsisadoptedineachrunoftheoptimizationmodelfortheoptimaltrade-offsolution.However,theconstraintmethodhasbeenusedmorefortheMOEDprobleminasinglemultipurposereservoirorcascadedhydropowersystemsbyvariousresearchers.Becausewhenthenon-inferior
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