Page - 163 - in Emerging Technologies for Electric and Hybrid Vehicles

Energies 2017,10, 5 where VRC,short(0) and VRC,long(0) are the initial voltages of corresponding RC networks and τshort = RshortCshort, τlong = RlongClong, which represent the short-term and the long-term time constants, respectively. SubstitutingEquation(5) intoEquation(2), theoutputequation is rewrittenas: Vt(t)=OCV(SoC)+ IRin+VRC,short(0)e − tτshort +VRC,short(0)e − tτlong + IRshort(1−e− t τshort)+ IRlong(1−e − tτlong) (6) Duringtherestperiod,wherethereisnocurrentexcitation(I=0),Equation(6)canbesimplifiedto: Vt(t)=OCV(SoC)+VRC,short(0)e − tτshort +VRC,long(0)e − tτlong (7) With the knowledge of Rin and charging/discharging OCV-SoC relationships, RC network parameters (Rshort,Cshort,Rlong andClong) can be obtained through fitting the experimental data withrelevantexponential functions,as ⎧⎨ ⎩ y= IRshort(1−e − tτshort)+ IRlong(1−e − tτlong) I =0 y=VRC,short(0)e − tτshort +VRC,long(0)e − tτlong I=0 (8) where y = Vt − OCV(SoC) − IRin. Since there only exists 2% SoC variation during each pulse-charging/discharging period, it is reasonable tomake an assumption that theRCnetwork parameterskeepconstantduringthisperiod. Inaddition, consideringthat thebatteryhasconverged to thesteadystateaftera2-hrest,VRC,short(0)andVRC,long(0)aresetaszeroat thebeginningof the pulse-charging/dischargingperiod. Basedon theaboveanalysis, theRCnetworkparameters canbeestimated throughfitting the experimentaldatasetwithEquation(8). Thecost functionof thecurvefittingmethod J is tominimize the sumof squarederrors between the estimation results and themeasureddata, subjected to the followingconstraints: ⎧⎨ ⎩ J=minr,τ n ∑ k=1 [Vmt (tk)−Vet (r,τ,tk)]2 s.t. Rshort, τshort, Rlong, τlong >0 (9) where tk is the input timesequence,n is the lengthof thefittedexperimentaldataset, r=[Rshort,Rlong], τ= [τshort,τlong],Vet is themodel estimatedvoltageandV m t is thevoltagemeasurements fromthe pulse-rest test. 3.RCNetworkParametersEstimation BasedontheIntroduction inSection1, theRCnetworkparametersshowdiversevaluesunder differentoperatingscenarios. InHEV/EVapplications,batteriesusuallywork in twotypical scenarios: theCCchargingscenarioandthedynamicdrivingscenario. In theCCchargingscenario, continuous externalchargingcurrentsareappliedtothebatteries,andthetransportof ions ismainlydrivenbythe electricfield.While for thedynamicaldrivingscenario, especially for theurbandrivingcondition, the loadcurrenthas thecharacteristicsofdiscontinuousamplitudevaluesandawide-spreadfrequency spectrum. Inthiscase,besides theelectricfield, thegradient inconcentrationisalso largelyresponsible for the transport of ionswithinbatteries [45]. Therefore, theRCnetworkparameters employed in differentoperatingscenariosshouldbe identifiedthroughdifferent identificationapproaches. 3.1. RCNetworkParameters for theCCChargingScenario Thepolarizationvoltage(VP) isadoptedtoillustratethevariationofRCnetworkparametersunder theCCexcitation.Accordingto theaforementionedbatteryoutputequation,VP canbeobtainedas: VP=VRC,short+VRC,long=Vt−OCV(SoC)− IRin (10) 163