Seite - 168 - in Emerging Technologies for Electric and Hybrid Vehicles

Energies 2017,10, 5 Equation (15) shows that k and τi should be determined before calculating Δt. In the aforementionedsimulation, thevalueofk forτ2 andτ3 canbeobtaineddirectly fromEquation(13), asshowninTable2. This indicates thatwhenk is larger thanone, theestimatedτ’short andτ’long are closer toτ1 andτ2. This isbecause thevoltageacross theRCnetworkwithτ3 hasa lowerdegreeof variability, comparedto thosewithτ1 andτ2. It canbeobservedfromTable2 thatτ’short andτ’long are nearlystablewhenk is larger than10.Hence,k is selectedas10 throughout thepaper. Inorder to set aproperτi inEquation (15), thediscreteFourier analysis of the loadcurrent is employedtodetermine the lowerbandwidth limitationof theECM.ThecurrentspectrumsofUDDS andWLTPtestsareshowninFigure6. It canbeobservedinFigure6a,b that thereexistsa largeDC component (PointsAandC)due to thenonzeromeanvalueof the twocurrentprofiles. Since the characteristicsof theDCcomponentcannotbemodeledbytheRCcircuit, theyareneglectedwhen determiningthe lengthof thefitteddataset. Themajor lowfrequencycomponents for the twoprofiles arearound0.00146Hz(pointB)and0.00138Hz(themeanvalue frompointDtopointE), respectively. Hence, themeanvalueof the long-term timeconstant is selectedas 704 s. Inorder to exclude the voltagevariationcausedbythe larger timeconstants (larger than10τi), theprior1-hmeasuredbattery voltagedataset isemployedtoestimate theRCparameters. )UHTXHQF\ +] $ % )UHTXHQF\ +] & ' ( (a) (b) Figure 6. The spectral analysis of the load current: (a) the urbandynamometer driving schedule (UDDS) test; (b) theworldwideharmonizedlightvehicles testprocedure (WLTP) test. 3.2.3. ImprovedFittingFunction FromEquations (6)and(7), it canbeobservedthatonly the initialvaluesVRC,short(0),VRC,long(0) andtimeconstantsτshort,τlong canbeobtaineddirectly fromthefittingresults; thus,weshoulddothe furthercomputations toobtain theresistancesandcapacitancesofRCnetworks. In [37,39–41], twoinitialvoltagesacross theRCnetworksarepredeterminedas IRshort and IRlong respectively, fromwhichtheresistancesof theRCnetworkscanbederivedunder theknowledgeof the currentvalue. In [49], thecapacitancesof theRCnetworksarefirstlyobtainedfromthe initialvoltage values. Bothof theabove twomethodshaveanassumptionthat thecapacitorsof theRCnetworks havealreadyconvergedto thesteadystateat theendof thepulse-dischargingperiod. Usually, in theparameterextractiontest, inorder toobtainasmuchdataaspossibleatdifferent SoC intervals, the lengthof thepulse-charging/dischargingperiodisusuallysetasseveralminutes (resulting in2%SoCvariation in thispaper),while therest time isusuallysetasoneormorehours (suchas2h in thispaper) togetanaccurateOCVvalue. For theshort-termRCnetwork, thevoltage caneasilyconverge to theequilibriumstateduringthepulse-dischargingprocess,which isshownin Figure7. Inotherwords, there isnocurrentflowingthroughthecapacitorbranchof theshort-termRC networkduringthe last stageof thepulse-dischargingperiod; thus,VRC,short(0)at thebeginningof the restperiodcanbeexpressedas: VRC,short(0)= IRshort (16) 168