Seite - 128 - in Emerging Technologies for Electric and Hybrid Vehicles

Energies 2016,9, 563 2. ExistingBatteryModels Differentmodelingapproachesare foundin the literature. Themostprominentbatterymodeling techniques are: Electrochemical, analytical, and circuit-basedmodels [8]. Electrochemicalmodels employnon-lineardifferential equations tomodel thechemicalandelectricalbehaviorof thecell [4,9]. Detailedknowledgeof thebattery chemistry,material structure andotherphysical characteristics are essential to achieve high accuracy and cover a large number of different operating points. However, the producers of batteries will rarely reveal the full parameters set of their products. Anothershortcomingofelectrochemicalmodels is thehighcomputationaleffort requiredtosolve the non-linearpartialdifferentialequations [8]. Electrochemicalmodelsarebettersuitedforresearch in battery’scomponents fabrication, likeelectrodesandelectrolyte [4,10]. Theanalyticalmodeling,onthe otherhand, reduces the computational complexity for thebattery. However, thatwouldbeon the expenseofcapturingthecircuitphysical featuresof thebattery, suchasopencircuitvoltage,output voltage, internal resistance,andtransient response [8]. Lumped electrical circuit models offer low complexity combined with high accuracy and robustness insimulatingbatteriesdynamics [11–13].Modelswithsingleordoubleresistor-capacitor (RC) networks are the best candidates for simulating the batterymodule [12–14]. RCparameters employedtomodel thebatterycharacteristic showadependencyontemperature, charge/discharge ratesandtheSOC.Several techniqueshadbeendiscussedin literature [1,15–19] forSOCestimation. Lam and Bauer [20] proposed a circuit model for the Li-ion battery with variable open circuit voltages, resistances and capacitances. The equivalent circuit components were represented as empirical functions of the current direction, the SOC, the battery temperature and the C-rate. Tremblayetal. [5,21]proposedanimprovedversionShepherd’smodel [22]. Thismodelconsiders the influenceofSOContheOCVbyconsideringthepolarizationvoltage in thedischarge-chargemodel. Differentdynamicmodels forLi-ion, lead-acid,NiMHandNiCdbattery typedwerepresented in Reference [5]. However, neither the temperature effect nor thevariationof the internal resistance were considered. Sawet al. [23] investigated the thermalbehavior for aLiFePO4–graphitebattery by coupling the empirical equations of the modified Shephard’s battery model with a lumped thermalmodel for the battery cell. The temperature development of a complete vehicle battery packunderdifferentdrivingcycleswassimulated in[23]. Tanetal. [24]have incorporatedthe thermal losses to Shephard’smodel for Li-ion battery cells by adding temperature dependent correction terms to themodel. Wijewardana et al. [1] proposed a generic electro-thermalmodel for Li-ion batteries. Themodelconsiderspotential correctiontermsaccountingforelectrodefilmformationand electrolyte electron transfer chemistry. In addition, the constant values in the empirical equations that represent theequivalentcircuit componentsof thebatterywereadjusted. Theseequationswere employedtomodel theelectrical components independenceofSOCandtemperature.Wijewardana et al. consider theC-rate effect in the estimationof SOCbyemployinganextendedKalmanfilter technique.Computational thermalmodelsandtemperaturedistributionestimationswereproposed in References [25–28]. Additionally, finite element analysis models to estimate the temperature distribution inthebatterywerepresentedinReferences [25,27–29]. Thiskindofsimulationrequires knowledge of thermal properties of the battery cell materials, such as thermal capacity, density, mechanicalconstructionandcoolingof thebattery. Foranaccurateparameterization intensiveand precisemeasurementsarenecessary. 3.OverviewofSelectedDynamicBatteryModels Theequivalentcircuitbatterymodelprovidesageneric,dynamicwayofmodelingLi-ionbatteries withmoderatecomplexity. Themoderatemodelcomplexitysupports the integrationof themodel in amultiphysicalsimulation,allowingtoanalyzedynamiceffectsoftheelectricdrivetrain. Threemodels areselectedfromthe literatureas thebestcandidates forLi-ionbatterymodeling, since theyare the most thoroughamongthereviewedmodels. Thesemodelsare: 128