Page - 88 - in Hybrid Electric Vehicles

groupisseriallyconnectedby189cellsof theA123nanophosphate lithium-ionANR26650M1- Bcell. Theenergycapacityof thebatterypack isdecidedby theall-electricdriving range, and its c-rate is defined by the average output power. In this design, the energy capacity of the battery pack is 14 kWh. Both the PMSG and the PMSM are low-speed high-power electric machinesdevelopedbyJing-JinElectricTechnologiesCo.,Ltd. 3.Mathematicalmodel Amathematicalmodelof thecoaxialpower-splithybridpowertrainwithanHESSisestablished to analyze the systemperformance.According to theworkingprinciple of the entire system, a lumped-parametermodel isused. 3.1.Vehicledynamics Since the rear axle is used todrive thehybrid transit bus, the tractive force of the rear axle is determinedaccording to the longitudinalvehicledynamics [23]. F¼FrþFaþFiþFj¼mgcosαðf1þ f2vÞþ 1 2 ρACDv2rþmgsinαþδm dv dt (1) Therefore, the tractive forceF canbecalculatedaccording to thepracticaldrivingconditions. The loadsof the front and rearaxles canbe calculatedbasedon thevehicleparameters. Then, the friction factor and the slipof the tires canbedetermineddue to the required tractive force and the axle load. Moreover, the rotating speed and the driving torque of the tires can be obtained. If thevehicle isbraking, thebrakingforce imposedontherearaxlecanbecomputed accordingtothebrakingforcedistributionequation.Then, thebrakingtorqueandspeedof the rear tirescanbedetermined.Subsequently, themodelof the finaldrivedetermines therotating speedωmandthe torqueTm taking intoaccount the friction lossTl0andthe rotating inertia J0. Tm¼Twi0 þTl0þ i0J0 dω dt (2) ωm¼ i0ω (3) ThePMSMmodelaccounts for therequestedtorqueTmrandthe inputpowerPmcalculatedby a two-dimensional (2D) lookuptablemeasured fromamotor testbench [24]. In the coaxial power-split hybrid powertrain, a clutch is used to control the operationmode that is either the seriesor theparallelmode.Themathematicalmodelof the clutch is a simple friction model [25], which is used to determine the clutch state among the engaged, the slipping, and thedisengaged states. The torqueand speed transmitted through the clutchare alsodetermined. Hybrid Electric Vehicles88