Page - 136 - in Emerging Technologies for Electric and Hybrid Vehicles

Energies 2016,9, 563 ȱ (e)ȱ (f)ȱ 0 50 100 150 200-10 -5 0 5 10 Time[s] MSE = 1.5176% Figure 10. Battery simulation models and reference voltage signal for rapid acceleration and decelerationdriving test: (a) Batterymodel 1 response; (b)Mean square error of batterymodel 1; (c)Batterymodel2response; (d)Meansquareerrorofbatterymodel2; (e)Batterymodel3response (f)Meansquareerror inbatterymodel3. 6.3. TheProposedSynthesizedBatteryModel It is explicable that eachmodel has some flaws, as determined in Table 2. The simulation results inFigures9and10provethateventhebestperformingmodelsneedtobefurther improved. Accordingly, a synthesizedmodel that holds thebest qualities of eachmodel hasbeendeveloped. First, thecharge-dischargecharacteristicsofmodel1areconsidered.Additionally, thedischargingpart ourproposedVOC(SOC,T) isemployedinsteadofconstant(E0)value. Then,thehighlydetailedinternal resistancemodelofbatterymodel2 incaseofdischarging,which is representedbyEquations (7)–(11), (17)–(19), (21), (27) in Referance [20], is taking the place of the constant internal resistance (R). Thecapacity fadingeffect is consideredbyaddingRcyc frombatterymodel3 to the internal resistance. Theempirical equations incaseofdischargingare implementedbecause thecharging-discharging hysteresis isproperlymodeledbymodel1. Thesynthesizedmodel is showninFigure11. Figure11.Theproposedsynthesizedbatterymodel. Incaseofdischarging, theoutputvoltagereads: Vbatt “VOC,dischargepSOC,Tq´ ` RO`Rcyc`VS`VL ˘ ¨ i´K Q Q´ it ¨ pit` i ˚q`Ae´B ¨ it (10) andforcharging, theequationexpressedas: Vbatt “VOC,dischargepSOC,Tq´ ` RO`Rcyc`VS`VL ˘ ¨ i´K Qit´0.1Q ¨ i˚´K QQ´it ¨ it`Ae´B ¨ it (11) where dVS dt “ i CS ´ VS RSCS (12) dVL dt “ i CL ´ VL RLCL (13) 136