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1、HistoryofOptimalPowerFlowandFormulations•December2012Page1HistoryofOptimalPowerFlowandFormulations•December2012HistoryofOptimalPowerFlowandFormulationsOptimalPowerFlowPaper1MaryB.Cain,RichardP.O’Neill,AnyaCastillomary.cain@ferc.gov;richard.oneill@ferc.gov;anya.castillo@ferc.govDecember,2012
2、Abstract:ThepurposeofthispaperistopresentaliteraturereviewoftheACOptimalPowerFlow(ACOPF)problemandproposeareaswheretheACOPFcouldbeimproved.TheACOPFisattheheartofIndependentSystemOperator(ISO)powermarkets,andissolvedinsomeformeveryyearforsystemplanning,everydayforday‐aheadmarkets,everyhour,a
3、ndevenevery5minutes.Itwasfirstformulatedin1962,andformulationshavechangedlittleovertheyears.Withadvancesincomputingpowerandsolutionalgorithms,wecanmodelmoreoftheconstraintsandremoveunnecessarylimitsandapproximationsthatwerepreviouslyrequiredtofindasolutioninreasonabletime.Oneexampleisnonlin
4、earvoltagemagnitudeconstraintsthataremodeledaslinearthermalproxyconstraints.Inthispaper,werefertothefullACOPFasanACOPFthatsimultaneouslyoptimizesrealandreactivepower.Today,50yearsaftertheproblemwasformulated,westilldonothaveafast,robustsolutiontechniqueforthefullACOPF.Findingagoodsolutionte
5、chniqueforthefullACOPFcouldpotentiallysavetensofbillionsofdollarsannually.Basedonourliteraturereview,wefindthattheACOPFresearchcommunitylacksacommonunderstandingoftheproblem,itsformulation,andobjectivefunctions.However,wedonotclaimthatthisliteraturereviewisacompletereview—ourintentwassimply
6、tocapturethemajorformulationsoftheACOPF.Instead,inthispaper,weseektoclearlypresenttheACOPFproblemthroughclearformulationsoftheproblemanditsparameters.Thispaperdefinesanddiscussesthepolarpower‐voltage,rectangularpower‐voltage,andrectangularcurrent‐voltageformulationsoftheACOPF.Additionally,i
7、tdiscussesthedifferenttypesofconstraintsandobjectivefunctions.ThispaperlaysthegroundworkforfurtherresearchontheconvexapproximationoftheACOPFsolutionspace,asurveyofsolutiontechniques,andcomputationalperformanceofdifferentformulations.Disclaimer:Theviewspr
