Page - 137 - in Emerging Technologies for Electric and Hybrid Vehicles

Energies 2016,9, 563 TheresistancesandcapacitorsvaluesaredeterminedthroughEquations (14)–(18): RspSOC,ϑq“ ´ c1epc2SOCq`c3`c4SOC ¯ `c5Δϑ`c6SOCΔϑ (14) CspSOC,ϑq“ ´ c7SOC3`c8SOC2`c9SOC`c10 ¯ `c11SOCΔϑ`c12Δϑ (15) Rl pSOC,ϑ, IC´rateq“ ´ pc13epc14SOCq`c15`c16SOCq`c17Δϑepc18SOCq`c19Δϑ ¯ ˆ`c20pIC´rateqc21 `c22˘ (16) Cl pSOC,ϑq“ ´ c23SOC6`c24SOC5`c25SOC4`c26SOC3`c27SOC2`c28SOC`c29 ¯ `c30 ec31{ϑ (17) Ro pSOC,ϑq“ ´ c32SOC4`c33SOC3`c34SOC2`c35SOC`c36 ¯ c37ec38{pϑ´c39q (18) whereϑ is thebatterycell temperature inKelvin (˝K)andc1–c39 areconstants,whichtheirvaluesare listed inTable5. Table5.ConstantsvaluesofEquations (14)–(18). Constant Value Constant Value Constant Value Constant Value c1 1.080ˆ10´2 c11 ´6.580 c21 ´6.919ˆ10´1 c31 ´2.398ˆ103 c2 ´11.03 c12 12.11 c22 2.902ˆ10´1 c32 1.298ˆ10´1 c3 1.827ˆ10´2 c13 2.950ˆ10´1 c23 2.130ˆ106 c33 ´2.892ˆ10´1 c4 ´6.462ˆ10´3 c14 ´20.00 c24 ´6.007ˆ106 c34 2.273ˆ10´1 c5 ´3.697ˆ10´4 c15 4.722ˆ10´2 c25 6.271ˆ106 c35 ´7.216ˆ10´2 c6 2.225ˆ10´4 c16 ´2.420ˆ10´2 c26 ´2.958ˆ106 c36 8.980ˆ10´2 c7 1.697ˆ102 c17 6.718ˆ10´3 c27 5.998ˆ105 c37 7.613ˆ10´1 c8 ´1.007ˆ103 c18 ´20.00 c28 ´3.102ˆ104 c38 10.14 c9 1.408ˆ103 c19 ´5.967ˆ10´4 c29 2.232ˆ103 c39 2.608ˆ102 c10 3.897ˆ102 c20 6.993ˆ10´1 c30 3.128ˆ103 Thenewmodelshowsasignificantimprovementinthesimulationresponse,asshowninFigure12. Themeansquareerrorwasreducedtoonly0.256%.Thenewmodelshowsalso thebest resultwhenit employedforsimulatingtherapidaccelerationanddecelerationdrivingtest, thoughithadasmall offseterrorat thebeginningof3.2V.Thiserroryieldedfromanabsolutevoltageerrorof0.028Vin proposedVOCmodel, representedbyEquation (8), at the specifiedSOCand temperature values. Thebatterymodelsaresimulated inMATLAB/Simulinkenvironment. Figure13showstheSimulink model for theproposedbatterymodel. (a)ȱ ȱ ȱ (b) ȱ (c)ȱ (d)ȱ 0 50 100 150 200 250 300 350-10 -5 0 5 10 Time[s] MSE = 0.2559% 0 50 100 150 200-10 -5 0 5 10 Time[s] MSE = 0.7862% Figure12.Theproposedsynthesizedbatterymodelandreferencevoltagesignal: (a)Proposedmodel response for the circulardriving test; (b) Error of proposedmodel voltage for the circulardriving test; (c)Proposedmodel response for therapidaccelerationanddecelerationdrivingtest; (d)Errorof proposedmodelvoltage for therapidaccelerationanddecelerationdrivingtest. 137