Page - 129 - in Emerging Technologies for Electric and Hybrid Vehicles

Energies 2016,9, 563 ‚ Tremblayetal. [5] (batterymodel1) ‚ LamandBauer [20] (batterymodel2) ‚ Wijewardanaetal. [1] (batterymodel3) 3.1. TremblayBatteryModel (BatteryModel1) TremblayandDessaint [5] improvedtheirownmodel inReference [21]. Thenewmodel is shown inFigure 2. Only threepoints on the steady statemanufacturer’s discharge curve are required to parametrize themodel,whichare the fullvoltage, theendpointofexponentialvoltageregion,andthe nominalvoltage. Thevariationof theOCVfromareferenceconstantvoltage (E0) is related toSOC changesby incorporatingapolarizationconstant (K). Figure2.TremblayandDessaintbatterydischargemodel. Incaseofdischargingtheoutputvoltagereads: Vbatt “E0´R ¨ i´K QQ´ it ¨ pit` i ˚q`Ae´B ¨ it (1) andforcharging, theequationbecomes: Vbatt “E0´R ¨ i´K Qit´0.1Q ¨ i ˚´K Q Q´ it ¨ it`Ae ´B ¨ it (2) thevariablesandconstants inEquations (1)and(2)aredefinedinTableA1in theAppendixA.1. Although, the charging anddischarging characteristics are extensivelymodeled, someother influential factors like the variations in internal resistance (R) and temperature influence are not considered. Thecapacity fadingeffect isnot taken intoaccount in thismodelaswell. 3.2. LamandBauerBatteryModel (BatteryModel2) TheLamandBauerbatteryequivalentcircuitmodelisshowninFigure3. Themodeldemonstrates theVOCasa functionofSOC,avariableohmicresistanceRo, andtwovariableRC-networks:RSCS andRlCl for theshortandthe longtimetransient responses, respectively. LamandBaueralsoshowed therelationbetweencapacity fadingduetoaginganddifferentstress influences,whichare thecell’s temperature,C-rate, SOCandintensityofdischarge. LamandBauerparametrized their equations throughcurvefittingofexperimentalmeasurements. Theyemployedin their tests theLiFePO4battery cell. Theequivalentcircuit resistorsandcapacitorsequations for temperatures from20˝Candabove aredetailedinEquations(7)–(28) inReference[20].WereferalsototheVOCequationwiththecorrected constantsasproposedinReference [20]: VOCpSOCq“´0.5863 e´21.9 SOC`3.414`0.1102SOC´0.1718 e´ 8ˆ10´3 1´SOC (3) 129