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236Vol.23No.6Jun.200320036ProceedingsoftheCSEE©2003Chin.Soc.forElec.Eng.0258-8013200306-0071-06TM73F123.9A790·6325310027AUCTIONGAMESINPOOL-BASEDELECTRICITYMARKETS:SINGLE-PERIODCASEGANDe-qiang,WANGJian-quan,HUZhao-yangCollegeofElectricalEngineering,ZhejiangUniversity,Hangzhou310027,ChinaABSTRACT:Thesingle-periodauctiongamemodelforanalyzingstrategicbehaviorinpool-basedelectricitymarketsispresented.ThefocusofthestudyistheNashequilibriuminpurestrategysense.Theequilibriumexistenceunderaratherrestrictiveconditionisproved.Thecharacterizationofequilibriumsundertightcapacityconstraintsisprovided.ItisdemonstratedthattheauctiongamedoesnotpossessapurestrategyNashequilibriumunderawiderangeofmarketconditions.toenhancethepredictionpoweroftheauctiongamemodelequilibrium,thequasi-equilibrium,isintroduced.Aweakerformofthecharacterizationofthequasi-equilibriumunderweakcapacityconstraintsisprovided.KEYWORDS:Powersystem;Electricitymarket;Gametheory;OptimizationPool-basedelectricitymarketNash1[1,2][3,4][5~7]1hCournotBertrand[8]~[12][13,14]ISO2[15][16~18]27223NewEnglandPool,NEPOOL22.1sPPminPs⋅T(1)s.t.0LPe=-)(T,FLPT≤-)(,PP0≤≤(2)Pe1LF(2)W(2)T[19,20]Australia,California,NordicPool,NewEngland,NewZealandT011+--+-+⋅=])([)(TTTFLPTLPePsgGlPPPTT)(ba--(3)lgabPKuhn-Tucker0434Envelopeiri(2)iiiLglGr+=∂∂=(4)2LPPPPˆ2111+=,LPPPPˆ2122+=(5)Lˆ21PcL^1PcFig.1Residualloadwhentwogeneratorsbidthesameprice2.20LPe≥-)(TFLPT≤-)(s12673k),(kkk-sspkkkkkkkPcTePcssTTT)()(),(-+=-=-glrp(6)k*k-sks)(sA(5)kckksmaxkkkkkPcssT*)(),(-=-rp(7)s.t.kkkssc≤≤(8)⎪⎩⎪⎨⎧∈=)(}{minarg),(TsPPsPPAWr:or(9)Prs)(⋅P)(⋅rksmax),(]),([),(*T**kkkkkkkkk----=ssPcssssrp(10)s.t.kkkssc≤≤(11)kks*k-s)(⋅kr)(**kkk-∈srs(12)(12))(srs∈)(⋅kr(pliersNksup,...,2,1=)Nash)(sr)(⋅kp)(⋅kr12(10))(skp2,1=ksks)(skpks)(sr(10)[21])(sr)(srWKakutani)(sr0LPe=-)(T112)(skp322Fig.2Competitionunderstrongcapacityconstraints11ARcA{a}7423{a}AP′′AA′′{a}A∑∑∈′′∈-′′-AjjjRAjjjPccPcs)()((13){a}s=*rPcA{a}{a}APcRcsA∑∈-AjjjRPcc)((13)AAA{a}{a}cs14──222AB1BAccAAAcs=BABcs=′LccPPPBABABˆ)(-+=′pBBs′′AABcss=′′}.s.t,ˆ)({maxABBBssLcs′′-′′=′′p)(Bsp3cBcAs_sBp(sB)3Fig.3Payofffunctioninthe2-generatorexample,ˆ)(ˆ)(LccLcsBABAeep--=--=′′0,0→eepp′′′()0ˆ⎥⎦⎤⎢⎣⎡--+=′-′′LccPPPBABAAepp0→e4AsBsB45ºsBcAsAA4Fig.4Quasi-equilibriumintwo-generatorauctiongameeMk,...,2,1=,1≥M],[scskk∈),(),(*kkkkkkssss--≥pp(14)pliersup,...,2,1NMMk++=∈ks],[sck],[**kkkssse-∉),(),(*kkkkkkssss--≥-pep(15)6757623EnergyRegulatoryCommission,FERCISO121∑∑∈′′∈=′′AjjAjjPP(17)mi,....,2,1=20=′′∑′′∈iAjijP(18)[23]∑′′∈′′AjjP∑′′∈′′iAjijPMustRunRatio,MRR(19)MRR∑∑∈′′∈′′=AjjAjjRRPPM(19)HHINEPOOLHHI[22]12NEPOOL346Nash[1]SinghHHaoSPapalexopoulosATransmissioncongestionmanagementincompetitiveelectricitymarkets[J]IEEETrans.OnPowerSystems199813(2)672-680[2]WuFFVaraiyaPCoordinatedmultilateraltradesforelectricpowernetworks:theoryandimplementation[J]InternationalJournalofElectricPowerandEnergySystems199921(2)75-102[3]GanDChenQLocationalmarginalpricingnewenglandprospectivepresentationsummaryforpanelsessionflow-gateandlocationbasedpricingapproachesandtheirimpacts[C]ColumbusofOhioProceedingsofIEEEPESWinterMeeting2001[4]WangXifanBlockbiddingmodelbasedpowermarket[J]ProceedingsoftheCSEE200121(12)1-6[5]EthierRZimmermanRMountTetalAuniformpriceauctionwithlocationalpriceadjustmentsforcompetitiveelectricitymarkets[J]InternationalJournalofElectricalPower&EnergySystems199921(2)103-110[6]RichterCWShebleGGeneticalgorithmevolutionofutilitybiddingstrategiesforthecompetitivemarketplace[J]IEEETrans.OnPowerSystems199813(1)256-261[7]ZimmermanRThomasRGanDetalAweb-basedplatformforexperimentalinvestigationofelectricpowerauctions[J]DecisionSupportSystems199924(3-4)193-205[8]BaiXShahidehpourSMRameshVCetalTransmissionanalysisbynashgamemethod[J]IEEETrans.OnPowerSystems199712(3)1046-1052[9]GuanXHoY-CPepyneDLGamingandpricespikesinelectricpowermarkets[J]IEEETrans.OnPowerSystems200116(3)402-408[10]BialekJWGamingtheuniform-pricespotmarket-quantitativeanalysis[Z]submittedtoIEEETrans.OnPowerSystemsApril26,200186Continuedonpage8686231~4A5[1](DuanShanxu).Paralleloperationcontroltechniquesofthemodularinvertersystembasedonfullydigitizedcontrol[D].WuhanHuazhongUniversityofScienceandTechnology1999.[2]LinXinchun,ChenXikun,KangYong,etal.Researchonparalleloperationofthree-phaseUPSinverters[M].TelecommunicationsEnergyConference,2002.INTELEC.24thAnnualInternational,2002195-199.[3]ProdanovicM,GreenTC,MansirH.Asurveyofcontrolmethodsforthree-phaseinvertersinparallelconnection[J].PowerElectronicsandVariableSpeedDrives,2000.EighthInternationalConferenceon(IEEConf.Publ.No.475),2000472-477.[4]DuanShanxuMengYuXiongJianetal.ParalleloperationcontroltechniqueofvoltagesourceinvertersinUPS[M],PEDS'99.1999883-887.[5]LeeCS,KimS,KimCB,etal.ParallelUPSwithainstantaneouscurrentsharingcontrol[J].IndustrialElectronicsSociety,1998.IECON'98.Proceedingsofthe24thAnnualConferenceoftheIEEE,1998,(1)568-573.[6]MartinsAP,CarvalhoAS,AraujoAS,etal.AcontrolmethodforhighpowerUPSsinparalleloperation[M].Proceedingsofthe38thMidwestSymposiumonCircuitsandSystems,1995,(1)1996.[7]Jiann-FuhCh