Page - 162 - in Emerging Technologies for Electric and Hybrid Vehicles

Energies 2017,10, 5 This cycle is repeateduntil thebattery is fullydischarged. Datapoints (includingcurrent, voltage, charging capacity and discharging capacity) are collectedwith the sampling frequency of 1Hz. Therelevantvoltageandcurrentprofilesof thedischargingpulse-rest testduringthe66%–64%SoC interval areplotted in thebottomsubfigureof Figure 1. The chargingpulse-rest test is conducted similarly, that is it beginswitha fully-dischargedbattery, thenchargedat a2%SoC stepwithC/2 constant current and followedbya restperiod. Inorder to eliminate thepolarizationvoltage, the OCVvaluesareextractedat theendofeachrestperiod. Tooshort a rest time leads toa largeOCV estimationerror,whereas too longarest timemakes thewhole test timeconsuming. Ithasbeenshown previously that for the lithium-ionpolymerbatteries, electrochemical reactionsarenegligibleaftera 2-hrestperiod[47,48]. Therefore, therest time in thispaper ispredeterminedas2h. 2.2. ParameterEstimationAlgorithm Theelectricalbehaviorof theECMisexpressedas the followingstatespace formalism: [ dVRC,short/dt dVRC,long/dt ] = [ −1/RshortCshort 0 0 −1/RlongClong ][ VRC,short VRC,long ] + [ 1/Cshort 1/Clong ] I (1) Vt=OCV(SoC)+ IRin+VRC,short+VRC,long (2) whereEquation(1) is thestateequationandEquation(2) is theoutputequation,VRC,short andVRC,long represent thevoltagesacross theshort-termandthe long-termRCnetworks, respectively,OCV(SoC) is aneighth-orderpolynomialequationasa functionofSoC,Vt is thebattery terminalvoltageandthe positivecurrent I representscharging.Rin represents the internalresistance;Rshort andRlongdenote the diffusionresistances;andCshort andClong represent thediffusioncapacitances.Amongthem,Rin can bedirectlyobtainedfromeachpulse-rest cycle throughEquation(3); thecorrespondingfourvariables (V1,V2, I1 and I2)aremarkedinthebottomsubfigureofFigure1,andthevariationof identifiedRin withSoC is showninFigure2.SoCcanbecalculatedthroughEquation(4), inwhichCapdenotes the capacityof thebattery inAh. Rin= V2−V1 I2− I1 (3) SoC=SoC(0)+ 1 3600Cap ∫ t 0 I(τ)dτ (4) 6R& Figure2.Rin variationwithdifferentstateofcharge (SoC). For theCCoperatingscenario (I =0), theanalytical solutionsofEquation(1)arederivedas: ⎧⎨ ⎩ VRC,short(t)=VRC,short(0)e − tτshort + IRshort(1−e− t τshort) VRC,long(t)=VRC,long(0)e − tτlong + IRlong(1−e − tτlong) (5) 162