Seite - 131 - in Emerging Technologies for Electric and Hybrid Vehicles

Energies 2016,9, 563 Table2.Comparisonbetweenthebatterymodels. Feature BatteryModel1 BatteryModel2 BatteryModel3 Charge-Discharge hysteresis ++ Considered in the outputvoltage + Considered in the internal resistance (R) equations - Charge-discharge Opencircuitvoltage - Constantvalue forE0 + VOC(SOC) + VOC(SOC) Internal resistance (R) - Constantvalue ++ R(SOC,T,C-rate) + R(SOC,T) Temperature influence - Notconsidered + Considered in the internal resistancemodel + Consideredaspotential correctionterms Capacity fading - Notconsidered + Considered in thebattery’susedcapacityestimation + Considered in the battery’s internal resistance (R) estimation TotalAssessment 2 6 4 4.BatteryThermalModel Ageneralenergybalance isappliedtoestimate thebatterycell temperature. It isassumedthat the thermaldistribution inside thecell isuniformandthat theconductionresistance inside thebattery cell isnegligiblecomparedwith theconvectionandradiationheat transfer [1,23,27,28]. Thechange in temperaturedependssignificantlyonthebattery thermalcapacity (Cp) andthedifferencebetween thegeneratedheat and thedissipatedheat. Thedissipationof theheat to thebattery surrounding isperformedbyconvectionandradiation.Generatedheatcomprises twosources, irreversibleheat generationbymeansof theeffectiveohmicresistanceof thecell’smaterial, andreversiblegenerated heatdueto theentropychange inbothcathodeandanode. Thetotalentropychanges in thebattery cell canbeconsideredaszeroaccordingtoReferences [1,29,30]. The temperaturedevelopment inside thebatterycell isdescribedas: mCp dTcell dt “ ipVOC´Vbattq´hAcellΔT´ σAcell ´ T4cell´T4amp ¯ (7a) whereΔT is thedifferencebetweenthebatterycellandtheambienttemperatures(Tcell´Tamp),h is the natural convectioncoefficient,m is the cellmass, i is the cell current,Acell is the surfaceareaof the singlebatterycell,σ isStefan-Boltzmannconstant,andε is theemissivityofheat.Assumingthat the temperaturedifferencesbetweenthecells in thesinglebatterymodulearesmall,Equation(7a)canbe generalizedfor thewholebatterymoduleas: MCp dTcell dt “ IpVOC´Vbattq´hAΔT´ σA ´ T4cell´T4amp ¯ (7b) whereM is the total cellsmass, I is thebatterycurrent,A is thesurfaceareaof thecellsblocks in the singlebatterymodule. Sawet al. [23]haspointedout to the contributionof the contact resistance inheatgeneration. Thecontact resistancecanbeneglected inthe investigatedbatteries, since thecellsarerealizing low ohmicoverwidecell connectorsbymeansofweldedconnections. Fifty individualcellsareconnected inparallel andwehaveanominal currentabout1.4Apercell. The resistanceof thesingle contact is0.2mΩ.Withfourweldingpointspercell connectors, thecontact resistance for thesinglebattery cell became 50μΩ. The power loss in the single cell due to contact resistance is determined as: Ploss = Icell2Rcontact =0.098mW/cell,which isanegligibleamount, thermally,aswellaselectrically. 5. ExperimentalCharacterizationof theBatteryandtheVehicleunder theTest 5.1. BatteryMeasurements Inorder tocharacterize theLiFeMgPO4-battery, severalexperimental testswere implementedon thebatteryatdifferentconditions.OCVvs. SOCmeasurementswereperformedat10,20and40˝C. Thebatterywasdischargeduntil thecut-offvoltageof2Vwasreachedandthenrechargedupto the nominal capacity. ALowC-rateofC/10wasused tominimize thedynamiceffectsand toachieve agoodapproximationtoanopencircuit. Figure5demonstrates thechargeanddischargeOCVcurves 131