Page - 90 - in Hybrid Electric Vehicles

The supercapacitors of thedesignedHESSuse anRCmodel [24].Given the output power of thesupercapacitorsPsc, theenergyequationof thesupercapacitor circuit is expressedas Rsci2sc�UsciscþPsc¼0 (11) Then, thecurrentof thesupercapacitors isobtainedby isc¼ Usc� ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi U2sc�4RscPsc q 2Rsc (12) TheSOCof thesupercapacitorsat timek is calculatedas SOCscðkÞ¼ Uscðk�1Þ� iscðk�1ÞCscðk�1Þ Usc,max (13) Tomakesurethesupercapacitorscanrecovertheregenerativebrakingenergyefficiently,theSOC ofthesupercapacitors iscorrectedaccordingtothevehiclevelocityduringthedrivingprocess. SOC�scðkÞ¼SOCsc,max ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1� 1�U 2 sc,min U2sc,max ! vðkÞ vmax � �2vuut (14) whereSOC*sc is thecorrectedSOC,SOCsc,max is themaximumSOC,Usc,maxandUsc,minare the maximumandminimumvoltages of the supercapacitors, respectively, and vmax is themaxi- mumvehicle velocity. The designed supercapacitor pack consists ofMaxwell’s 48-Vmodule andthedetailedparametersareobtained fromalaboratory test. TheDC/DCmodelof theHESSusesa2Dmap todetermine theenergyefficiencybasedon the inputpowerandthevoltageratio,whichcanprovideagoodprecisionandafastcalculationspeed. 4.Energymanagementstrategydesign The control strategyof a coaxial power-split hybridpowertrainonlyusing supercapacitors as energystoragesystemwasdesignedbyOuyangetal.previously,which involvesserieshybrid mode, parallel hybridmode, and themode transition logic [28]. For the coaxial power-split hybridpowertrainwith anHESS, onemore taskmust bedesigned—the energymanagement strategy of theHESS. The thermostatic control, the power follower control, and the optimal control [29] are the threemain control strategies for the serieshybridmodewhile theparallel electric assist control, the adaptive control, and the fuzzy logic control are normally used for the parallel hybridmode. Currently, the rule-based control, the filter control, themodel pre- dictive control, and the fuzzy logic control are the fourmain control strategies of anHESS to distribute thepowerdemandbetweenthebatteriesand thesupercapacitors. Investigations indicate that theperformanceof rule-basedcontrol strategycanapproach to that of the optimal control after optimization of the parameters of the rule-based control [30]. Hybrid Electric Vehicles90