Page - 89 - in Hybrid Electric Vehicles

3.2.Auxiliarypowerunit Normally,anauxiliarypowerunit isacombinationof theengineandthegenerator.Thediesel enginemodel accounts for the requested torqueTer according to the engine output torqueTe andtheenginespeedωe. Ter¼Teþ Je dωe dt (4) Subsequently, the fuel consumptionMe is calculatedusing thedensityofdiesel fuelρf for the diesel engine. Me¼ ðtc 0 medt ρf ðtc 0 vdt (5) where tc is the final time of the driving cycle. Themathematical model of the generator is similarwiththemotor.TherequestedtorqueTgr isdeterminedaccordingtothe inputtorqueof thegeneratorTgandthe inertia Jg.TheoutputpowerPg isa functionof thegeneratorspeedωg andtorqueTgrdefinedbya2Dlookuptable. Tgr¼Tgþ Jg dωg dt (6) Pg¼ fðωg,TgrÞ (7) 3.3.Hybridenergystoragesystem Themodel of lithium-ion batteries of the designedHESS is aRintmodel [24]. If the output powerof thebatterypack isPbat, theenergyequilibriumof this circuit canbeexpressedas Rbati2bat�UbatibatþPbat¼0 (8) Then, thecurrentof thebattery is calculatedby ibat¼ Ubat� ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi U2bat�4RbatPbat q 2Rbat (9) TheSOCof the lithium-ionbatteriesat timek isdefinedas SOCbat,k¼SOCbat,0þ ðk t¼0 ibatðtÞdt (10) The internal resistanceRbat and capacitanceCbat are calculated via lookingup two2Dmaps. The data of thesemaps are obtained according to the references [26, 27] for A123 system’s ANR26650M1-B lithium-ionbattery. A Hybrid Energy Storage System for a Coaxial Power-Split Hybrid Powertrain http://dx.doi.org/10.5772/67756 89