Seite - 159 - in Emerging Technologies for Electric and Hybrid Vehicles

Energies 2017,10, 5 modelexpresses the fundamentalelectrochemical reactionsbycomplexnonlinearpartialdifferential algebraicequations(PDAEs) [8]. It canaccuratelycapturethecharacteristicsof thebattery,butrequires extensive computational power to obtain the solutions of the equations. Hence, suchmodels are suitable for thebatterydesignrather thanthesystemlevel simulation. Incontrast, theECMabstracts awaythedetailed internalelectrochemical reactionsandcharacterizes themsolelybysimpleelectrical components; thus, it is ideal for circuit simulation software and implementation in embedded microcontrollers. Theaccuracyof theECMishighlydependenton themodel structureandmodel parameters. Theoretically, a higher order ECM can represent awider bandwidth of the battery application and can generatemore accurate voltage estimation results. However, the high order ECMcannot only increase the computational burden, but also reduce the numerical stability for the furtherbatterystates’estimation[9,10].Hence, consideringatradeoffamongthemodelfidelity, the computational burden and thenumerical stability, the secondorderECMis employed in this paper [11–18]. Thecommonstructureof thesecondorderECMis illustrated inthetopsubfigureof Figure1,where theopencircuitvoltage (OCV),which isa functionof stateof charge (SoC), stands for theopencircuitvoltage,Rin is the internal resistance,whichrepresents theconductionandcharge transfer processes [19–21], and two resistor-capacitor (RC) networks approximately describe the diffusion process. Among them, the short-termRCnetworkmodels the fast dynamics diffusion process (PartA in thebottomsubfigureofFigure1), and the long-termRCnetworkrepresents the slowdynamics diffusion process (Part B in the bottom subfigure of Figure 1). The abovemodel parameters canbe identified either through the time-domainor the frequency-domainparameter extractionexperiments. For the time-domainparameterestimationmethods,modelparametersare usually identified throughfitting the voltage response from theparameter extraction experiment withtheexponential-basedfunctions. Theelectrochemical impedancespectroscopy(EIS) test is the commonly-usedfrequency-domainparameterextractionexperiment.Comparedto the time-domain testprocess,one limitationof theEIS test is that theamplitudeof thecurrentexcitation isso lowthat the battery canbe consideredas equalizedduring thewhole test process,which seldomhappens inHEV/EV applications. In order to overcome the above drawback, references [22–24] propose superimposingthedirect current (DC)offsetover theEISsignals todetermine thecurrentdependency of impedanceparameters. However, since significant time is required for theEIS test, the battery SoC changes significantlyduring the test procedure if the amplitudeof the superimposed current is improper. This can reduce theparameter estimationaccuracyandmake thismethodpractically notapplicableatmoderateandhighcurrent rates [25,26]. Basedontheaforementionedanalysis, the secondorderECMwithparametersestimatedbythe time-domainanalysis isdiscussed in thispaper. 159