简介：

简介：Inthispaper,wefocusonthereal-timeinteractionsamongmultipleutilitycompaniesandmultipleusersandformulatereal-timepricing(RTP)asatwo-stageoptimizationproblem.Atthefirststage,basedoncostfunction,weproposeacontinuoussupplyfunctionbiddingmechanismtomodeltheutilitycompanies’profitmaximizationproblem,bywhichtheanalyticexpressionofelectricitypriceisfurtherderived.Atthesecondstage,consideringthatindividuallyoptimalsolutionmaynotbesociallyoptimal,weemployconvexoptimizationwithlinearconstraintstomodelthepriceanticipatingusers’dailypayoffmaximum.Substitutetheanalyticexpressionofelectricitypriceobtainedatthefirststageintotheoptimizationproblematthesecondstage.Usingcustomizedproximalpointalgorithm(C-PPA),theoptimizationproblematthesecondstageissolvedandelectricitypriceisobtainedaccordingly.WealsoprovetheexistenceanduniquenessoftheNashequilibriuminthementionedtwostageoptimizationandtheconvergenceofC-PPA.Inaddition,inordertomakethealgorithmmorepractical,astatisticalapproachisusedtoobtainthefunctionofpriceonlythroughonlineinformationexchange,insteadofsolvingitdirectly.TheproposedapproachoffersRTP,powerproductionandloadschedulingformultipleutilitycompaniesandmultipleusersinsmartgrid.Statisticalapproachhelpstoprotectthecompany’sprivacyandavoidtheinterferenceofrandomfactors,andC-PPAhasanadvantageoverLagrangianalgorithmbecausetheformerneednotobtaintheobjectionfunctionofthedualoptimizationproblembysolvinganoptimizationproblemwithparameters.Simulationresultsshowthattheproposedframeworkcansignificantlyreducepeaktimeloadingandefficientlybalancesystemenergydistribution.