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PROCEEDINGSOFTHEASME2010INTERNATIONALDESIGNENGINEERINGTECHNICALCONFERENCESSEEHTTP/WWWASMEORG/TERMS/TERMS_USECFMMODIFIEDTHEBATTERYEQUATIONSTOSIMULATEABATTERYPACKCOMPOSEDOFSERIESANDPARALLELCOMBINATIONSOFSINGLECELLSINORDERTOCONNECTTHEBATTERYPACKTOAMOTORWEHADTODEVELOPAPOWERCONTROLLERMODELASPARTOFTHESYSTEMINTEGRATIONWEFURTHERINCORPORATEDASIMPLEONEDIMENSIONALVEHICLEMODELTHATDRIVESONANINCLINEDPLANE,ATERRAINMODELTHATCONTROLSTHEINCLINE,ANDADRIVECYCLEMODELTHATCONTROLSTHEVEHICLESDESIREDSPEEDBYVARYINGTHEDRIVECYCLEANDTERRAINMODEL,WETESTEDTHEBEVUNDERVARIOUSDRIVINGCONDITIONSFIGURE1BLOCKDIAGRAMOFOVERALLBEVMODEL2SYSTEMMODELINGANDSIMULATIONTHETECHNIQUEWEDECIDEDTOUSEWASMATHBASEDMODELINGUSINGMAPLESIMASTHESIMULATIONENVIRONMENT,WHICHHASAGRAPHICALINTERFACEFORINTERCONNECTINGSYSTEMCOMPONENTSTHESYSTEMMODELISTHENPROCESSEDBYTHEMAPLEMATHEMATICSENGINE,ANDFINALLYTHEDIFFERENTIALALGEBRAICEQUATIONSDAESDESCRIBINGTHESYSTEMARESIMULATEDNUMERICALLYTOPRODUCEOUTPUTDATAFOR3DMULTIBODYSIMULATIONITUSESTHEDYNAFLEXPROENGINE,WHICHUSESLINEARGRAPHTHEORYFORSYSTEMSIMULATION1,1121BATTERYONEOFTHEMOSTIMPORTANTCOMPONENTSOFANELECTRICVEHICLEEITHERBEVORHEVISTHEBATTERYTHEREAREMANYWAYSOFMODELINGDIFFERENTBATTERYCHEMISTRIESDEPENDINGONTHEFIDELITYNEEDEDANDTHEBATTERYPARAMETERSOFINTERESTSEETHEARTICLEBYRAOETAL13FORANOVERVIEWOFSOMEOFTHETECHNIQUESGENERALLY,WITHINCREASINGMODELACCURACYCOMESINCREASEDCOMPUTATIONALREQUIREMENTSSOMEMODELINGTECHNIQUESTHATWEREVIEWEDWERETHELEADACIDMODELOFSALAMEHETAL14THEMATHEMATICALLITHIUMIONMODELOFRONGANDPEDRAM15THATINCORPORATESSTATEOFHEALTHANDTEMPERATUREEFFECTSTHELUMPEDPARAMETERMODELINSECTION31OFTHEPARTNERSHIPFORANEWGENERATIONOFVEHICLESPNGVBATTERYTESTMANUAL16THEKALMANFILTERINGTECHNIQUESOFPILLERETAL17THEELECTRICALCIRCUITMODELOFCHENANDRINCONMORA12ANDTHEIMPEDANCEMODELOFNELSONETAL18THESEDIFFERENTTECHNIQUESHAVETHEIRSTRENGTHSANDWEAKNESSESANDLIMITEDRANGESOFAPPLICATIONTHEREISAGREATINTERESTINUSINGLITHIUMIONBATTERIESINELECTRICVEHICLES,ASTHEYARELIGHTANDHAVEAHIGHERPOWERTOWEIGHTANDPOWERTOSIZERATIOTHANLEADACIDORNICKELBASEDBATTERIESGREATDEMANDSAREPLACEDONVEHICLEBATTERIESASTHEDRIVERACCELERATESANDBRAKESREGENERATIVELY,PUTTINGTHEBATTERIESTHROUGHPERIODSOFHIGHCURRENTDRAWANDRECHARGEDEPENDINGONTHEDRIVINGENVIRONMENT,THEBATTERIESCANALSOBESUBJECTEDTOLARGETEMPERATUREVARIATIONS,WHICHCANHAVEASIGNIFICANTEFFECTONTHEBATTERYSPERFORMANCEANDLIFETIMETHUSWENEEDEDTOMODELALITHIUMIONBATTERYCHEMISTRYOVERAWIDESTATEOFCHARGESOCRANGE,UNDERWIDELYVARYINGCURRENTS,FORVARIOUSTEMPERATURESSINCEWEWOULDEVENTUALLYLIKETOMODELTHISVEHICLEINAHARDWAREINTHELOOPHILSYSTEM,WENEEDEDAMODELTHATWASNOTCOMPUTATIONALLYEXPENSIVE,ANDWEDIDNOTREQUIREAHIGHFIDELITYMODELTHESEREQUIREMENTSLEDUSTOTHEELECTRICALCIRCUITMODELOFCHENANDRINCONMORAWEIMPLEMENTEDTHEIRCOMPONENTSINMAPLESIMANDUSEDACUSTOMFUNCTIONBLOCKTOREPRESENTTHENONLINEARRELATIONSHIPBETWEENTHESTATEOFCHARGEANDTHEELECTRICALCOMPONENTSEQUATIONS2TO6INTHEIRPAPERSEEFIG2FORABLOCKDIAGRAMOFTHEBATTERYFIGURE2BLOCKDIAGRAMOFSINGLECELLBATTERYMODELSINCETHEIRMODELISOFASINGLECELL,WEMODIFIEDTHEIREQUATIONSTOSIMULATEABATTERYOFCELLSINPARALLELANDSERIESTHECHENANDRINCONMORABATTERYCANBEDIVIDEDINTOTWOLINEARCIRCUITSWITHANONLINEARCOUPLINGBETWEENTHEMSEEFIG2FORLABELSOFTHESEDIFFERENTCIRCUITSONECIRCUITISALARGECAPACITORINPARALLELWITHARESISTORTHATMODELSTHECHARGESTATEOFTHEBATTERYANDSELFDISCHARGETHISCANBECALLEDTHE“CAPACITYCIRCUIT”ANOTHERCIRCUITISAVOLTAGESOURCEINSERIESWITHARESISTOR2COPYRIGHTCNULL2010BYASMEDOWNLOADED25JUN2011TO1132043335REDISTRIBUTIONSUBJECTTOASMELICENSEORCOPYRIGHTSEEHTTP/WWWASMEORG/TERMS/TERMS_USECFMCAPACITORNETWORKTHATMODELSTHETIMERESPONSEOFTHEBATTERYTHISCANBECALLEDTHE“TIMERESPONSECIRCUIT”TOADAPTTHEIRSINGLECELLMODELTOSIMULATEANENTIREBATTERYPACK,LETNPARALLELBETHENUMBEROFCELLSINAPARALLELPACK,ANDLETNSERIESBETHENUMBEROFPARALLELPACKSPLACEDINSERIESTOMAKETHEWHOLEBATTERYTHEOPENCIRCUITVOLTAGEINTHETIMERESPONSECIRCUITISMULTIPLIEDBYNSERIESTHECURRENTFLOWINGINTHETIMERESPONSECIRCUITISDIVIDEDBYNPARALLELWHENITFLOWSINTHECAPACITYCIRCUITTHERESISTORSINTHETIMERESPONSECIRCUITAREMULTIPLIEDBYNSERIES/NPARALLELANDTHECAPACITORSAREMULTIPLIEDBYNPARALLEL/NSERIESASINGLECELLOFTHEBATTERYMODELHASANOPENCIRCUITVOLTAGEOF33VANDACAPACITYOF8375MAHATA1ADISCHARGERATESTARTINGAT100STATEOFCHARGEBYPLACING8CELLSINPARALLEL,AND74OFTHESEPARALLELPACKSINSERIES,A2442V,67AHBATTERYPACKWASCREATEDTHISPACKISCOMPARABLETOTHATINA2007TOYOTACAMRYHYBRID19THECHENANDRINCONMORABATTERYMODELISSIMPLEENOUGHTOSIMULATEINASHORTAMOUNTOFTIMEWHILEBEINGCOMPLEXENOUGHTOPROVIDETHEFOLLOWINGVARIATIONSINTHEOPENCIRCUITVOLTAGEWITHSOCTRANSIENTEFFECTSOFCHARGEDEPLETIONANDRECOVERYANDTHEIRDEPENDENCEONSOCANDTHEVARIATIONINBATTERYCAPACITYWITHDISCHARGECURRENTFURTHERMORE,SINCEITISANELECTRICALCIRCUITMODELITCANEASILYBEINCORPORATEDINTOTHEELECTRICALSYSTEMOFTHEBEVMODELANDISAMENABLETOBEINGREPRESENTEDUSINGMATHBASEDMODELINGTECHNIQUESONEOFTHEDOWNSIDESOFTHISMODELISTHATNOTEMPERATUREEFFECTSOFANYKINDAREMODELED,ALTHOUGHCHENANDRINCONMORASTATEITWOULDNOTBEDIFFICULTTOINCLUDETHEMINANELECTRICVEHICLETHETEMPERATUREWILLVARYWITHEXTERNALENVIRONMENTALCONDITIONS,WITHHEATINGOFTHEBATTERYDUETOINTERNALLOSSES,ANDWITHENDO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