Electric vehicle’s energy consumption of car-following

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NonlinearDyn(2013)71:323329DOI10.1007/s11071-012-0663-0ORIGINALPAPERElectricvehicle’senergyconsumptionofcar-followingmodelsShichunYang·ChengDeng·TieqiaoTang·YongshengQianReceived:7October2012/Accepted:25October2012/Publishedonline:9November2012©SpringerScience+BusinessMediaDordrecht2012AbstractInthispaper,weusetheoptimalvelocitytionandexhaustemission.Thus,researchersdevel-model,fullvelocitydifferencemodel,fullvelocityandopedsomemodelstostudythevehiclesenergycon-accelerationdifferencemodel,andthecar-followingsumptionandexhaustemissionandfoundthattheve-modelwithconsiderationofthetrafficinterruptionhiclesenergyconsumptionandexhaustemissionareprobabilitytostudytheelectricvehicleselectricitybothrelatedtoitsspeedandacceleration[613],butenergyconsumption.Thenumericalresultsshowthatthesemodelscannotbeusedtostudytheelectricvehi-theelectricvehicleselectricityenergyconsumptioncleselectricityenergyconsumption.ismoststableinthefourthmodelandthatthefourthInthispaper,weusetheoptimalvelocity(OV)modelcanreducetheelectricvehicleselectricityen-model[14],fullvelocitydifference(FVD)modelergyconsumption.[15],fullvelocityandaccelerationdifference(FVAD)model[16],andthecar-followingmodel[17]tostudytheelectricvehicleselectricityenergyconsumption.KeywordsCar-followingmodel·Electricitypower·Electricityenergyconsumption·Numericaltest2Therelatedmodels1IntroductionTheOVmodel[14]canbewrittenasfollows:dvi(t)Sofar,researchershaveproposedmanytrafficflow=αVsi(t)−vi(t),(1)dtmodelstostudytheexistingtrafficproblems(e.g.,jam,accident,pollution,etc.)[15].Thesemodelscande-wherevi(t),si(t)=xi−1(t)−xi(t)are,respectively,scribemanycomplextrafficphenomena,buttheycan-theithvehiclesspeedandheadwayattimet(xi(t)isnotbeusedtostudythevehiclesenergyconsump-theithvehiclesposition),αisthereactiontime,V(·)istheoptimalvelocityfunctionanddefinedasfollows:V(s)=V1+V2tanh(C1s−C2),(2)S.Yang·C.Deng·T.Tang()SchoolofTransportationScienceandEngineering,whereV1,V2,C1,C2arefourparameters.TherelatedBeihangUniversity,Beijing100191,Chinae-mail:tieqiaotang@buaa.edu.cnparametersaredefinedasfollows[18]:α=0.85s−1,VY.Qian1=6.75m/s,V2=7.91m/s,SchoolofTrafficandTransportation,LanzhouJiaoTong(3)−1,CUniversity,Lanzhou,Gansu730070,ChinaC1=0.13m2=1.57. 324S.Yangetal.TheFVDmodelcanbeformulatedasfollows:wherePb-outistheoutputpoweroftheelectricve-hiclesbattery,δisafactorrelatedtotheelectricdvi(t)=αVsi(t)−vi(t)+λvi(t),(4)vehiclesmass,mistheelectricvehiclesmass,fdtistherollingresistancecoefficient,iisthegradewherevi(t)=vi−1(t)−vi(t)isthespeeddiffer-whichconsidersthegradingresistance,CDistheaero-encebetweentheithvehicleanditsprecedingvehicle.dynamicdragcoefficient,AistheelectricvehiclesHere,α=0.41s−1andλisdefinedasfollows:frontalarea,ρistheairdensity,ηteistheelectricve-hiclestransmissionefficiency,ηmisthemotoreffi-0.5s≤100mciency.λ=(5)Inrealtrafficsystem,thetraditionalvehiclesbrak-0otherwise.ingenergyisoftenwastedwhiletheelectricvehiclesTheFVADmodelcanbewrittenasfollows:brakingenergycanpartlyberecoveredandrestoredintothebattery.Thus,basedonEq.(8),theelectricdvi(t)=αVsi(t)−vi(t)+λvi(t)vehiclesregenerativebrakingpowercanbedefineddtasfollows:+gai(t−1),ai−1(t)ai(t−1),dvρCDA2dvi−1(t)Pb-in=kvηteηmδm+mg(f+i)+v,ai(t)=ai−1(t)−ai(t)=dt2dt(6)(9)dvi(t)−,dtwherek(00ingenergythatcanberecoveredbythemotor(calledgai(t−1),ai−1(t)=andai−1(t)≤0,theregenerativebrakingfactor)andtheregenerative⎪⎩brakingfactorkisafunctionofthepropertiesofthe1,otherwise,electricvehiclesbraking,thebatterypropertiesandotherfactors.whereai(t)istheaccelerationdifferencebetweenHere,wedonotuseEqs.(8)and(9)toexploretheithvehicleanditsprecedingvehicle.Therelatedtheelectricvehicleselectricityenergyconsumptionparametersarethesameasthoseofthemodel[15].sincetheyconsidertoomanyfactors.Forsimplicity,Thecar-followingmodelwiththetrafficinterrup-weassumethattheroadhasnograding,i.e.,i=0.tionprobabilitycanbeformulatedasfollows:Equation(8)showsthattheelectricvehiclesbatterydvi(t)consumeselectricityenergyduetoitsresistance,so=αVsi(t)−vi(t)+λ1pi−1−vi(t)dtweshouldhereusetheparameterηetosubstitutetheparameterηmofEq.(8),wheretheparameterηeis+λ2(1−pi−1)vi(t),(7)thedrivingefficiencyoftheelectricvehiclesbatterywherepi−1istheprobabilitythattheprecedingvehi-andηe<ηm.Inaddition,Eq.(8)doesnotconsidercleoftheithvehicleisinterrupted,λ1,λ2aretwopa-theelectricityenergyconsumedbyotheraccessoriesrameters.Here,pi=0.2,λ1=0.5,λ2=0.2andother(e.g.,air-conditioner,electricpowersteering,etc.)andparametersarethesameasthoseofthemodel[15].theelectricityenergyconsumptionmayberelativelyHowever,theabovemodelscannotbeusedtostudyhighandaffecttheelectricvehiclesrunningdistance,theelectricvehicleselectricityenergyconsumption.soweshouldconsidertheeffectsoftheaccessoriesonToexploretheelectricvehicleselectricityenergycon-theelectricvehicleselectricityenergyconsumption.sumption,Mehrdad[19]proposedtheoutputpowerofThus,Eq.(8)canberewrittenasfollows:theelectricvehiclesbattery,i.e.,vdvρCDA2Ptotal=δm+mgf+vηteηedt2vdvρCDA2Pb-out=δm+mg(f+i)+v,+Paccessory,(10)ηteηmdt2(8)andEq.(9)canberewrittenasfollows: Electricvehiclesenergyconsumptionofcar-followingmodels325dvρCDA2Fig.1,weheredefinekasfollows[20]:Ptotal=kvηteηmδm+mgf+vdt20.5vv<5m/s+Paccessory,(11)k=5(12)(0.5+0.3v−5)v≥5m/s.20wherePtotalisthetotalpoweroftheelectricvehiclesOtherrelatedparametersvaluesareshowninTable1.battery.Infact,theparameterkisacomplexfunctionandrelatedtomanyfactors(e.g.,speed,acceleration,etc.),3SimulationsbutithasacloserelationshipwiththeregenerativebrakingforceasshowninFig.1[20].Thus,basedonBeforesimulation,wedefineEqs.(1),(4),(6),and(7),respectively,asModelA,ModelB,ModelCandModelD.First,weusethefourmodelstostudyeachTable1Thevaluesoftheelectricvehiclesrelatedparameterselectricvehicleselectricityenergyconsumptiondur-δ1.1ingthestartingandbrakingprocesses,wheretheini-m1500tialconditionsareasfollows:thereare11electricve-f0.015hiclesthatareuniformlydistributedonaroad,wherethefirstvehicleistheleadingoneandthe11thvehicleCD0.3liesattheoriginandtheother10vehiclesheadwaysA1.8are7.4m;thereisasignallightandabarrierontheρ1.2road,wherethesignallightislocatedat74mandtheηte0.85barrierislocatedat500m;allthevehiclesarestillηe0.85whent<0;thesignallightturnsgreenandalltheve-Paccessory1000hicleswillimmediatelystartatt=0;allthevehicleswilleventuallystopbecauseofthebarrier(seeFig.2).Basedontheabovediscussions,weobtaintheevo-lutionofthetotalelectricitypowerofeachvehiclesbatteryduringthestartingandbrakingprocesses(seeFig.3).Fromthisfigure,wehavethefollowing.(1)Theevolutionofthetotalelectricitypowerofeachvehiclesbatterycanbedividedintothreepromi-nentstagesduringthestartingprocess.Inthefirststage,theevolutionofthetotalelectricitypowerofeachvehiclesbatterysharplyincreases.Inthesecondstage,eachvehiclesspeedstillincreasesbutitstotalelectricitypowerbeginstodecrease.Inthethirdstage,theevolutionofthetotalelectricityFig.1ThedistributionofthebrakingforceinADVISOR[20]powerofeachvehiclesbatterydoesnotchange.Fig.2Thecar-followingschemeduringthestartingandbrakingprocesses 326S.Yangetal.Fig.4Thetotalelectricitypowerduringthestartingandbrak-ingprocessesthreemodels,thetotalelectricitypowerofeachvehiclesbatteryofModelBislargerthantheoneofModelCandthetotalelectricitypowerofeachvehiclesbatteryofModelCislargerthantheoneofModelD.Tofurtherdisplaythedifferencesoftheelectricvehicleselectricityenergyconsumptionsofthefourmodels,wecalculatethetotalelectricitypowerofthe11vehiclesduringthestartingandbrakingprocesses(seeFig.4).Fromthisfigure,weconcludetothefol-lowingresults.(1)ThetotalelectricitypowerofModelAquicklychanges,i.e.,itquicklyincreasesanddecreases,whichproducestheimpracticaltotalelectricityenergyconsumption.(2)ThetotalelectricitypowersofModelBandModelChaveatransientchange,butthereisnopromi-nentdifferencebetweenthetwomodels.(3)ThetotalelectricitypowerofModelDislessthanthatoftheotherthreemodelsatfirstbuthigherthantheotherthreemodelsatlast.Fig.3Theevolutionofeachelectricvehicleselectricitypower,where(a)(d)are,respectively,thatofModelATovalidatewhichmodelconsumesleastelectricityModelDenergyduringthestartingandbrakingprocesses,wecalculatethe11electricvehiclestotalelectricityen-(2)Duringthebrakingprocess,theevolutionoftheergyconsumptionofthefourmodelsfrom0to70stotalelectricitypowerofeachvehiclesbattery(seeTable2).Fromthistable,thetotalelectricityen-maybeirregularandverycomplex,theregener-ergyconsumptionofModelDislessthantheotherationmodeissimple.threemodels.(3)Inallcar-followingmodels,thetotalelectricityFinally,weexploreeachelectricvehicleselectric-powerofeachvehiclesbatteryduringthestartingitypowerwhenasmallperturbationoccursinatraf-processislargerthantheoneduringthebrakingficsystemwithperiodicboundarycondition.Here,theprocess.initialconditionsaresetasfollows:(4)Duringthestartingandbrakingprocesses,theto-x1(0)=1m;xi(0)=(i−1)L/i,talelectricitypowerofeachvehiclesbatteryofModelAismuchlargerthantheonesoftheotherifi=1;vi(0)=V(L/i),(13) Electricvehiclesenergyconsumptionofcar-followingmodels327Fig.5Theevolutionofeachelectricvehicleselectricitypowerafter3×105timestepsandtheprofileattimestep3×105,where(a)(d)are,respectively,thatofModelAModelDwhereN=100isthetotalnumberofvehicles,L=time(seeFig.5).Fromthisfigure,weobtainthefol-1500mistheroadslength.Here,therelatedparam-lowingresults.etersare,respectively,definedasthoseintheabovefourmodels.Thus,weobtaineachelectricvehicles(1)EachelectricvehicleselectricitypowerofModelelectricitypoweroftheabovefourmodelsafteralongDwillbeaconstantandeachelectricvehicles 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