68 Electric and Hybrid Vehicles Motor rated power 3 v cr 0 0 mi/h v cr 2 v cr Vehicle speed at which heat engine is added FIGURE 3.15 Electric power requirement as a function of vehicle speed at which IC engine is added. 10% margin for the battery-pack recharging [7]. The exact amount of margin needed is the subject of a more complicated analysis, involving vehicle driving cycles, battery capacity, battery charge/ discharge characteristics and generator characteristics. 3.5.2.2 Initial Acceleration The electric motor with its higher peak power capabilities is more heavily used during initial accel- eration.
The mechanical power available from the IC engine can be blended with the electric motor power for acceleration, thereby reducing the power requirement of the electric motor. The power required from the motor depends on the velocity at which torque blending from the two propul- sion units starts. Figure 3.15 shows the effect of torque blending on the electric motor-rated power requirement during initial acceleration with a single-gear transmission for the IC engine. The figure shows that there will be very little power contribution from the engine until a minimum critical velocity v cr mph of the vehicle is reached due to its poor low-speed torque capability.
Therefore, torque blending should start after the vehicle has attained the critical velocity with single-gear transmission avoiding the use of engine for initial acceleration as much as possible without signifi- cantly increasing the rating of the electric motor. The power requirement from the electric motor increases nonlinearly with speed if IC engine torque blending is delayed beyond v cr mph. The quali- tative figure shows two curves with the extent of the constant power region as a parameter, x being an integer number. The lower curve has much wider constant power region than the upper curve.
The curves emphasize once again the need for extended constant power region of operation of the electric motor to minimize its size. The power requirement of the IC engine determined from rated vehicle velocity condition would typically be enough to provide the initial acceleration in combina- tion with the electric motor. 3.5.2.3 Maximum Velocity The power requirement from the propulsion system at maximum velocity is F v TR ⋅ max , which is supplied by a combination of the engine and the electric motor.
This requirement is given by ρ 3 P F TR ,max = ⋅ TR v m max m = + gv ax sin β mgC A 1 + F D C v + mgv C max max 2 0 The electric motor power required to meet the maximum velocity conditions can be uniquely defined by subtracting the engine power determined for cruising at rated velocity from the maximum veloc- ity power requirement. The electric motor power requirement calculated in this step would, in gen- eral, be less than the power requirement for the initial acceleration, unless the maximum velocity requirements are very stringent, such as very high speed on a steep grade. 1:x constant power range 1:3x constant power range