## Figure P82

The vehicle in Problem 8.1 is moving downwards so that it requires 250 N-m.

(a) What will be the input voltage for the motor from the inverter? Hence, determine the conversion ratio of the converter. Frequency is kept constant at rated value, and the motor is running at the rated speed.

(b) What should be the operating frequency of the inverter if the input voltage to the motor is kept constant at rated value, and the motor is running at rated speed?

Find the speed of the motor mentioned in Problem 8.1 for a braking torque of 350 N-m and the inverter frequency of 40 Hz when the motor is supplied at rated voltage.

A three-phase induction machine is operated from a variable voltage, fixed frequency source.

(a) Derive an expression for machine efficiency in terms of slip (not in terms of torque and speed). Include only stator and rotor copper losses and core loss in Ploss. Model core loss by a constant resistance in the equivalent circuit. To simplify the analysis, assume that core loss resistance and magnetizing reactance are large compared to the other parameters. Under this assumption, you can use an approximate equivalent circuit, where the core loss resistance and magnetizing reactance are directly across the stator terminals.

(b) Does motor efficiency depend on terminal voltage? Calculate the slip that maximizes motor efficiency.

An AC inverter is operated in a sinusoidal pulse mode. The transistor base current waveforms are shown in Figure P8.6. Sketch line-to-line voltages vAB, vBC, and vCA, and line to neutral voltage vANin the space provided. Briefly comment on the voltages. Are they balanced? (ici for i=1 to 6 are the base currents for transistors 1 to 6, respectively).

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