usedtosimulatethebiddingstrategyofsuppliersinapowerpoolFirstly,asupplyfunctionmodelwithforwardcontractsispresentedAccordingly,itisprovedthatonlyoneoftheparametersbetweentheslopeandinterceptofthebiddingcurvecanbestrategyvariableinordertoachievedefiniteequilibrium(theNashequilibriumisastrategyprofileinwhicheachplayer’spartisasgoodaresponsetowhattheothersaremeanttodoasanyotherstrategyavailabletothasuppliersGenerallyspeaking,therearebasicallythreewaysforasuppliertodevelopanoptimalbiddingstrategy[]Thefirstonereliesonestimationofthemarketclearingprice(MCP)inthenexttradingperiod,thesecondoneisbasedonestimationofthebiddingbehaviorofrivalparticipantsandthethirdoneisgametheorybasedThemodelsofbiddingstrategyofsuppliersbasedongametheoryusedinthepowermarketaremainlyCournot,Bertrandandthesupplyfunctionmodel[]Amongthesemodels,boththeCournotandsupplyfunctionmodelsarewidelystudiedProbabilitytheoryisemployedtostudythebiddingstrategyofsuppliersbasedonthesupplyfunctionmodelinRefs[,],wherethebiddingcoefficientsofrivalparticipantsareassumedtoobeyajointnormaldistributionInRef[],aconjecturedsupplyfunctionisutilizedtosimulatethebiddingstrategyofsuppliersInRef[],asupplyfunctionmodelwhoseslopeandinterceptofthebiddingcurvevarywiththesamescaleisemployedtoanalyzethebiddingstrategyofsuppliers,wheretheinfluenceofcontractsfordifferenceCFDs[](CFDsmeansthatifthespotpricerisesabovethestrikeprice,whichisthepricelevelatwhichthecontractcanbecalled,supplierspensateretailersforthedifference,butifthespotpricefallsbelowthestrikeprice,thentheretailerspensatesuppliersforthedifference)onmarketequilibriumisconsideredInRef[],theconceptofvirtualrivalandthemethodofparameterestimationareintroducedtostudythebiddingstrategyofsuppliersbasedongametheory,wheretheslopeandinterceptofthebiddingcurveisalsoassumedtovarywiththesamescaleForwardcontractsareoneoftheefficientmeansforriskmanagement,anditisappliedinthepowermarketofmanycountriesThepowerpoolwillplantheelectricityofsuppliersaccordingtothemarketrules,thebiddingpriceofsuppliersandforwardcontractswhilethereareforwardcontractsbetweensuppliersandbuyersThebiddingstrategyofsupplierswillvarywiththeforwardcontractstoachievemaximumprofitInthispaper,asupplyfunctionmodelisusedtosimulatethebiddingstrategyofsuppliersinapowerpoolFirstly,asupplyfunctionmodelwithforwardcontractsispresentedAccordingly,itisprovedthatonlyoneoftheparametersbetweentheslopeandinterceptofthebiddingcurvecanbestrategyvariableinordertoachievedefiniteequilibrium(theNashequilibriumisastrategyprofileinwhicheachplayer’spartisasgoodaresponsetowhattheothersaremeanttodoasanyotherstrategyavailabletotha上升到高于履约价格,这是价格总水平在该合同可被称为,供应商赔偿零售商差异,但如果现货价格低于履约价格,则零售商补偿供应商差异[])被认为真正敌手概念,并且介绍参量估计方法学习出价战略供应商根据博奕论,倾斜和出价曲线截距也以同样变化尺寸而假定。期货契约是其中一个风险管理高效率手段,并且它在许多国家电力市场被应用。该电力联营在有早供应商与买家合同同时,将根据市场规则,供应商投标报价及远期合约为电力供应商作计划。供应商出价战略是随期货契约变化达到最大赢利。在本文,供应功能模型是用来模拟在一个电力联营供应商投标策略。首先,提出与期货契约一个供应职能模型。相应地,这是证明只有一个在斜坡和拦截之间参数是为了达到一定平衡可变参数。(纳什均衡是一个策略配置文件,其中每个参与者部分是作为良好回应给其他人意思所做任何其他有用策略以便提供给参与者[])第二,当不同招标曲线拦截被选中时,研究该市场平衡。最后,今后合同不同效果在各个竞标策略模式供应商平衡策略中被分析。此外,当世代限制是活跃时候,出价战略也被研究。供应函数均衡模型与远期合约假定逆需求函数是一个线性函数p=r-sNiiq()即其中p是市场价格,r和S是拦截和边坡逆需求函数,iq是供应厂商i产生,N是供应厂商数目。iiiq+ipmaxNiiqqlp()maxrqs,ls供应厂商投标曲线假设作为一个线性函数iiiq+ip()如果i和i分别是拦截和边坡招标曲线,因此两者都是大于零i=………N电力价格被假设为明确统一电力联营价格,根据方程()和()计算供应商世代。如果期货契约是if,当成交价格是ik时,供应商平衡状态可以通过每个供应商最大限度个别利润函数而得到。iiiiiimax=pq-ff-Cqminmaxiiiqqq(i=……N)()没有一般性损失,假设供应厂商价值函数是一个二次函数,那么:然后,产生供应厂商一代i是相应地,系统边际价格是如果出家曲线截距和斜率供应商选择独立策略变量,当满足下面微分方程时,供应商利润最大。方程()和()表明,该拦截和斜坡报价曲线不是独立。为N变量,i和i,需要通过N方程加以计算,因此,存在着无限多平衡状态。这意味着只有一个参数之间拦截和斜坡报价曲线是独立,达到一定平衡。如果价格曲线倾斜是供应商选择策略变量i,方程()-()得出最理想供应厂商i函数则和(,i)是投标曲线经过一个点。如果投标曲线截断是由供应商选择策略可变量i,方程(),()和()得出最理想供应厂商i函数通过求解方程()()能够得出均衡投标策略。当价格曲线倾斜是供应商选择策略变量i,如果出价曲线穿过点,iiiifafb,这意味着供应商i是竞标边际成本在一代远期合约,投标曲线是然后,投标商一代i是相应地,这个系统临界价格是根据微分方程如同方程()得到供应商最理想发生函数i方程()表明,如果报价曲线通过点,iiiifafb策略变量i是独立远期合约。均衡供应函数模型与一代制约因素在上文所述最佳反应函数模型中,上一代尚未考虑制约因素。这一代通过方程(),()或()计算出来供应商i,被认为是当这一代限制。则这一代将会被设为价格界限值。如果从供应商那里通过最理想函数计算出来市场价格较低,并且低于这一阶段供应商极限价格,供应厂商利益有可能是负。结果供应商将要买电从从事现金交易市场以满足远期合约并尽量提高自身利润。供应商发电必要条件是其中ipq是供应商之外市场价格,()不等式可得使iq=miniq要不然使iq=如果存在其发电限制因素是主动供应商,那么这一代供应商所面对被动限制是以下剩余需求函数其中M–L和N–M分别是有多少供应商是超过这一带最高值和低于这一代最低值。maxiq和minkq分别是最高和最低几代供应商。几代供应商约束条件是没有积极预先利用方程(),(),()或()。如果仍然存在供应商一代超过他们这一代供应商限制,将计算一次剩余需求函ib数。计算过程重复,直至不存在供应商一代超过他们这一代人限制,然后,这一代供应商投标策略临界价格制约因素是limiq是此代最高和最低供应商。供应商临界投标策略。如果此代存在最高临界价格,则供应商通过投标策略选出临界价格应少于最高价格。如果此代价格存在最低限制,则供应商价格以高于此次最低限制价格。例如,在国内市场计划用六个生产者来分析不同投标策略。suppliersGenerallyspeaking,therearebasicallythreewaysforasuppliertodevelopanoptimalbiddingstrategy[]Thefirstonereliesonestimationofthemarketclearingprice(MCP)inthenexttradingperiod,thesecondoneisbasedonestimationofthebiddingbehaviorofrivalparticipantsandthethirdoneisgametheorybasedThemodelsofbiddingstrategyofsuppliersbasedongametheoryusedinthepowermarketaremainlyCournot,BertrandandthesupplyfuncAnalysisofequilibriumaboutbiddingstrategyofsupplierswithfuturecontractsZhiqiangYuan*,DongLiu,ChuanwenJiangElectricPowerSchool,ShanghaiJiaoTongUniversity,Shanghai,PRChinaReceivedMay;acceptedAugustAvailableonlineOctoberAbstractInthispaper,thesupplyfunctionmodelisemployedtosimulatethebiddingstrategyofsuppliersinthepowerpool,andmodelsofthesupplyfunctionwithfuturecontractsarepresentedItisprovedthatonlyoneoftheparametersbetweenslopeandinterceptofthebiddingcurveisanindependentvariableinordertoachievedefiniteequilibriumInthemeantime,theequilibriaofthebiddingstrategyaboutsuppliersarestudiedwhendifferentinterceptsofthebiddingcurvearechosenSomeexamplesareemployedtostudytheNashequilibriumstrategiesofsupplierswithdifferentfuturecontractsinvariousbiddingstrategymodelsTheresultsshowthattheequilibriaaredifferentindifferentbiddingstrategymodels,butthefuturecontractscaneffectivelymakespotpricesdecreaseinallthemodelsIntroductionTheelectricpowerindustryworldwideisexperiencingunprecedentedrestructuringfromthetraditionalintegratedregulationmonopolytoapetitivepowermarketTheobjectofderegulationistointroduceapetitionmechanismintothepowermarketandprovideincentivesforefficientoperationofthepowerindustry,eventuallyreducingthemarketpriceTheidealmarketisaperfectpetitivemarketinwhichparticipantsbidtheirmarginalcostintothemarketConsequently,themarketpriceislowinthiskindofmarketHowever,theelectricitymarketisdifferentfromothermerchandisemarketsInthepowermarket,onlyafewsupplierscanprovidepowerservicesinsomegeographicregionThisisduetotherestrictionofsomefactors,suchaslargeinvestmentscale,smalldemandelasticity,transmissionconstraintsandnolargelystorableelectricityConsequently,theactualpowermarketismoreclosetoanoligopolisticmarketinwhichthesupplierscanachievemaximumprofitthroughstrategicbiddingThatmeansthatthegenerationpaniespossessmarketpower,whichisharmfultotheoperationofthepowersystemandwillmakeelectricitypricefarhigherthanthemarginalcostofthepowermarketOnefamousexampleistheelectricitycrisisofCaliforniaofAmericainthesummer,whichmadetheelectricitypricefarabovepetitivelevelsSo,itismeaningfultostudythebiddingstrategyofsuppliersGenerallyspeaking,therearebasicallythreewaysforasuppliertodevelopanoptimalbiddingstrategy[]Thefirstonereliesonestimationofthemarketclearingprice(MCP)inthenexttradingperiod,thesecondoneisbasedonestimationofthebiddingbehaviorofrivalparticipantsandthethirdoneisgametheorybasedThemodelsofbiddingstrategyofsuppliersbasedongametheoryusedinthepowermarketaremainlyCournot,Bertrandandthesupplyfunctionmodel[]Amongthesemodels,boththeCournotandsupplyfunctionmodelsarewidelystudiedProbabilitytheoryisemployedtostudythebiddingstrategyofsuppliersbasedonthesupplyfunctionmodelinRefs[,],wherethebiddingcoefficientsofrivalparticipantsareassumedtoobeyajointnormaldistributionInRef[],aconjecturedsupplyfunctionisutilizedtosimulatethebiddingstrategyofsuppliersInRef[],asupplyfunctionmodelwhoseslopeandinterceptofthebiddingcurvevarywiththesamescaleisemployedtoanalyzethebiddingstrategyofsuppliers,wheretheinfluenceofcontractsfordifferenceCFDs[](CFDsmeansthatifthespotpricerisesabovethestrikeprice,whichisthepricelevelatwhichthecontractcanbecalled,supplierspensateretailersforthedifference,butifthespotpricefallsbelowthestrikeprice,thentheretailerspensatesuppliersforthedifference)onmarketequilibriumisconsideredInRef[],theconceptofvirtualrivalandthemethodofparameterestimationareintroducedtostudythebiddingstrategyofsuppliersbasedongametheory,wheretheslopeandinterceptofthebiddingcurveisalsoassumedtovarywiththesamescaleForwardcontractsareoneoftheefficientmeansforriskmanagement,anditisappliedinthepowermarketofmanycountriesThepowerpoolwillplantheelectricityofsup AnalysisofequilibriumaboutbiddingstrategyofsupplierswithfuturecontractsZhiqiangYuan*,DongLiu,ChuanwenJiangElectricPowerSchool,ShanghaiJiaoTongUniversity,Shanghai200030,PRChinaReceived6May2005;accepted9August2006Availableonline2October2006AbstractInthispaper,thesupplyfunctionmodelisemployedtosimulatethebiddingstrategyofsuppliersinthepowerpool,andmodel