## Example

The vehicle road load characteristic on a level road is Ttr=24.7+0.0051 wh2. The induction motor torque-speed relationship in the linear region is given by Te= KIM( 40- m), including the gear ratio of the transmission system. The rated torque of 40 Nm is available at a speed of 35 rad/s. Find the steady state operating point of the vehicle.

Solution

The induction motor torque constant is

The steady state operating point is obtained by solving the vehicle road load characteristic and the motor torque speed characteristic, which gives

The speed of an induction motor can be controlled in two ways, by varying stator terminal voltage and stator frequency.

Changing the terminal voltage changes the torque output of the machine, as is evident from Equation 5.30. Note that changing the applied voltage does not change the slip for maximum torque. The speed control through changing the applied frequency is based on the frequency and synchronous speed relation e=4pfP; changingf changes e. Figures 5.22 and 5.23 show variations in torque-speed characteristics with changes in voltage and frequency, respectively. What is needed to drive the induction motor is a power electronics converter that will convert the available constant voltage into a variable voltage, variable frequency output, according to the command torque and speed. The top-level block diagram of such a drive system is shown in Figure 5.24. First-generation controllers of induction motor drives used in EVs employed slip control (constant V/Hz control) using a table of slip vs. torque. The performance of such a drive for vehicle applications is poor, because the concept of V/Hz control is based on a steady state equivalent circuit of the machine. The dynamic performance of the machine improves significantly using vector control. The dq-axes transformation theory for induction motors will be presented as an introduction to vector control theory in the next section, after the discussion on regenerative braking. Induction motor drives will be discussed in Chapter 8.

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