Seite - 133 - in Emerging Technologies for Electric and Hybrid Vehicles

Energies 2016,9, 563 6.BatteryModelsValidation 6.1. Evaluating theOpenCircuitVoltageModels (VOC) Wijewardanaetal. [1]haveemployedacommonmodel forVOCthat iswidelyusedandfoundin literature. LamandBauer [20]haveredefinedthemodelequation tosuit theLiFeMgPO4 cathodetype batteries. Theyconcludedthat theOCVis temperature independent. They justifiedthisconclusion basedonsmall changesof theOCVmeasurementsdueto temperaturevariations,whichwere in the range2–8mV[20].Anabsoluteerrorof30mVforLiFeMgPO4batterycellwill leadtoanuncertaintyof 13%intheSOCestimationat1Cdischargeand25˝C,accordingtoBlanketal. [31]. Thebatteryofour vehicle isLiFeMgPO4-cathodetype. ItsOCVcurvesarepresentedearlier inFigure6.Accordingtoour measurements, theOCVtemperaturealterationisfrom15to90mV,whichisabout10timeshigherthan theresultpresented inReference [20]. Inourstudy,weuseabatterymodule thatcontains6cellblocks in series, with 50 cells in parallel for each. Moreover, the vehicle’s battery pack has 19modules. With thiscombinationofbatterycells, therangeofvoltagealterationbecomes1.71–10.26V,which is aconsiderablechange in thebatterypackoutputvoltage. WevalidatedbothVOCmodels inReferences [1,20]bycomparing thesimulationresultswithour ownmeasurements,asshowninFigure7.Weselectedthecharge-dischargecurvesatT=20˝Ctobe thereferencesforvalidation. TheVOCmodelutilizedinbatterymodel3doesnotfitourmeasurements. TheVOCofbatterymodel2betterfits theexperimentaldata. Thedeviation inanSOCrangespanning from10%to90%isabout0.03V.Thisdeviation increasesat lowtemperature. The influenceof the temperaturevariationontheOCVcurves isdefinedasdVOC{dT. Fromthe measurementsshowninFigure6, thevalueof this termwasfoundtobe1.25mVincaseofdischarge and0.69mVforcharging. TheVOCmodel2model ismodifiedforbetterfittingoftheOCVcurvealong theSOCrangeandthe temperature influence is considered. ThenewVOC ismodeledbyEquations (8) and(9)andtheconstantsvaluesof thenewVOCarepresentedinTable3. Thevalidationresultsare showninFigure8andinTable4. VOC,dischargepSOC,Tq“ a1 e´a2SOC`a3`a4 SOC`a5 e´ a6 1´SOC `TdVOC,d{dT (8) VOC,chargepSOC,Tq“ b1 e´b2SOC`b3`b4 SOC`b5 e´ b6 1´SOC `TdVOC,c{dT (9) Table3.VOCparametervalues. Constant Value Constant Value a1 ´1.166 b1 ´0.9135 a2 ´35 b2 ´35 a3 3.344 b3 3.484 a4 0.1102 b4 0.1102 a5 ´0.1718 b5 ´0.1718 a6 ´2ˆ10´3 b6 ´8ˆ10´3 dVOC,d/dT 0.00125 dVOC,c/dT 0.00069 6.2. Evaluating theBatteryModelsOutputVoltage Theaccuracyof eachmodel isyet tobeproved. Forobjective comparison, the thermalmodel elaborated inSection4 isemployedforallmodels. Thebatterycurrents inFigure6a,caredesignated as the inputs forallmodelsandtheoutputvoltageofeachmodel is investigatedagainst thevoltage response signal, shown inFigure6b,d. TheVOC ofmodel 3 [1] showeda largedeviation fromthe actualcurve,asshowninFigure7. Therefore, theVOCderivedfrommodel2 [20]willbealsoutilized inmodel 3. Figures 9 and10demonstrate the responses of the threemodels for bothdriving test. Thesimulationresultsgainedfrommodel1 reveal thehighestaccuracy for thefirst test. Themean 133