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278Vol.27No.820038PowerSystemTechnologyAug.20031000-3673200308-0010-06TM470.61A1,2122212002402COMPARISONOFMARKETPOWERINTHREEOLIGOPOLYMODELSOFELECETRICITYMARKETSONGYi-qun1,2,HOUZhi-jian1,WENFu-shuan2,NIYi-xin2,WUFu-li21.ElectricalEngineeringDept.,ShanghaiJiaoTongUniversity,Shanghai200240,China;2.TheUniversityofHongKong,theHongKongSpecialAdministrativeRegion,ChinaABSTRACT:Ineconomics,marketpowerindicatestheabilityofafirmtoraisemarketprice.Intheoligopolisticelectricitymarket,marketpowermeasurestheabilityofagenerationfirmtoraisetheclearingpriceofelectricitymarket.Basedongametheory,marketpowerintheoligopolisticelectricitymarketisanalyzed.Afterthemarketclearingpriceofperfectcompetitioniscalculatedasbaseprice,thepercentagemark-upsofmarketpricesw.r.t.perfectcompetitioninCournot,Stackelberg(i.e.Leader-Follower)orForchheimer(i.e.Leader-priceTaker)modelsareevaluatedanalytically,whichactsasanindexofthemarketpowerinthecorrespondingelectricitymarket.Theimpactsofcostfunctioncoefficients,elasticityofdemand,thenumberofgenerationfirmsasleadersandcapacityconstraintsonmarketpowerarealsodiscussed.TheresultsofthisresearchshowthatamongthethreemodelstheCournotmodelpossessesthehighestmarketpower,theForchheimermodelhastheleast.KEYWORDS:Oligopolisticelectricitymarket;Electricitymarket;Marketpower;Cournotmodel;Stackelbergmodel;Gametheory;Powersystem.CournotStackelberg─Forchheimer─3CournotStackelbergForehheimerCournotStackelberg1MarketPowerfirm[1]LernerIndexLIPriceCostMarginIndexPCMIConcentrationRatioCRHHIHirschman-HerfindallIndexHHI[2][3]3[4~6]HHI27811HHIBialekHHI[5]HHIAlvaradoHHI[6][7][8-12]CournotSupplyFunctionEquilibria[8,9,11]3CournotBertrandSFECournotStackelbergForchheimer2Ni),1,2,(21)(2NiqcqbaqCiiiiiiiL=++=(1)aibiciqii∑=-=-=NiiqfefDep1(2)pDefipi),1,()(maxNiqCpqiiiiqiL=-=p(3)0dd=iiqpqi(2)pc*pcp*∑pcq)1/()(11pc∑∑==*++=NiiNiiicfcfbep(4))1/()(11pc∑∑==*∑+-=NiiNiiicfcbeq(5)33CournotStackelbergForchheimer[13]Cournotleaderfollowerprice-takerStackelbergForchheimer1StackelbergForchhei-mer2Cournot1CournotCournot12PowerSystemTechnologyVol.27No.8),,1()()(ðmaxNiqCqQpiiiiqiL=-=(6)∑==NiiqQ1(3)(6)i)(ijqj≠),1,(2,1**NicfqfbeqiNijjjiiL=+--=∑≠=(7)CournotccNash*ccp*cc∑q∑∑==++++=NiiNiiicffcffbep11*cc)1/()((8)∑∑==∑+++-=NiNiiiicffcfbeq11*cc)1/()((9)2StackelbergMN-Mk),,1()()(ðmaxNMkqcqQpkkkkqiL+=-=(10)p∑∑+==+=NMjkMjjqqQ11(10)k),,1(,11*NMkqfqfbeqNklMllMjjkkL+=---=∑∑≠+==(11)∑∑∑∑∑∑=+=+=+=+=+=+++-+++-=MjjNMkkNMkkNMkkNMkkkNMkkqcffcffcffcfbeq111111*(12)])1/()[()1/()(M(12)(2)∑∑+===--=NMkMjjkqfqfep11-++++∑∑+=+=NMkiNMkkicffcffbe11)1/()((13)))]1/([111∑∑∑+====′-′Δ++NMkMiMjjiiqfeqcfffM–N-MLF*LFp*LFΣq∑∑==+′′++′+′=MjMjjjjcffcffbep11*LF)1/()((14)(15)])1()1[(/)(1111*LF∑∑∑∑+===+=∑+++′′++-++′-=MMkkMjjMjNMkkkjjcffcffcfbecfbeq),1,(*LF*MjcfbpqjjjL=+′-=(16)),,1(*LF*NMkcfbpqkkkL+=+′-=(17)3ForchheimerMN-Mpk),,1(*NMkcbpqkkkL+=-=(18)M(19)1/()1/()(1111111∑∑∑∑∑∑∑==+==+=+=+==′′-+′′Δ-++++=--=MjjMjNMkkjNMkkNMkkkNMkMjjkqfcfeqfcffcffbeqfqfep(6)M),,1()2/(),1*MjcfqfbeqjMjiiijjL=+′′′′--′′=∑≠=(20)M–N-MForchheimerLT*LTp*LT∑q∑∑==∑+′′′′++′′′′+′′=MjMjjjjcffqcfbfep11*LT*LF)1/()((21)/)(11*LF∑∑=+=Σ-++′′-=MjNMkkkjjcbecfbeq(22)])1()1[(11∑∑+==++′′′′+MMkkMjjcfcff27813),1,(*LT*MjcfbpqjjjL=+′′-=(23)),,1(*LT*NMkcbpqkkkL+=-=(24)4MarketPowerMP31Cournot)]1/()/[()]1/()()1/()[(/)(111111*pc*pc*cccc∑∑∑∑∑∑======++++-++++=-=NiiNiiiNiNiiiiNiiNiiicfcfbecfcfbecffcffbepppMP(25)2Stackelberg)]1/()/[()]1/()()1/()[(/)(111111*pc*pc*LFLF∑∑∑∑∑∑======++++-+′′++′′+′=-=NiiNiiiNiNiiiiNiiNiiicfcfbecfcfbecffcfbfepppMP(26)3Forchheimer)]1/()/[()]1/()()1/()[(/)(111111*pc*pc*LTLT∑∑∑∑∑∑======++++-+′′′′++′′′′+′′=-=NiiNiiiNiNiiiiNiiNiiicfcfbecfcfbecffcfbfepppMP(27)abc(1)(25)~(27))]()1[()(2ccecNfbcfNbeNfMP+++-=(28)(29)]})2()1[()]()1{[(/}]2)(1[){(222222LFcfcNfMecNfbcfMNcfcMNNfbeNfMP++++⋅+++-++-+-=(30))}]()1[(]]/{[)(2LTecNfbcfNcfMNbecMfMP+++⋅+--=5IEEE6301p=e-fD=50-0.0152D($/MWh)323CournotStackelbergForchheimer1Tab.1Costcoefficientsoffirmsabc102.000.020000500201.750.017500500303.000.025000500403.000.025000500501.000.062500500603.250.0083405002Tab.2ResultsofequilibriaindifferentmarketstructuresCournotStackelbergForchheimerCournotStackelbergForchheimerMCP/($/MWh)10.63516.09514.82611.04012.64316.33915.19813.194/MW2590.842230.582314.112563.152457.702214.542289.59242144/%051.3439.413.81029.2320.214.36/MW431.74400.43496.13383.87500.00407.36500.00427.561*/$/h1864.004040.703901.801996.702821.504181.704099.002958.00/MW507.70438.69559.95441.34500.00446.15500.00483.262*/$/h2255.404609.204578.202395.803259.004767.104536.503486.90/MW305.39325.75294.17321.61385.71331.81303.43407.763/$/h1165.802939.402397.101292.901859.703049.802550.402078.40/MW305.39325.75294.17321.61385.71331.81303.43407.764/$/h1165.802939.402397.101292.901859.703049.802550.402078.40/MW154.16194.28177.94160.64186.28197.41182.73195.105/$/h742.621753.201470.70806.441084.401810.201551.001189.50/MW885.46545.68491.75934.08500.00500.00500.00500.006/$/h3269.405767.704683.903638.303654.005502.004931.503929.50*StackelbergForchheimer14PowerSystemTechnologyVol.27No.811Cournotefbcfcfcc02468100501001