Question

A 3-phase, 400 V, 4 pole, 50 Hz star-connected induction motor has the following parameters referred to stator: \[ R'_1 = 1 \, \text{ohm}, \, X_s = X'_1 = 2 \, \text{ohm} \] Stator resistance, magnetizing reactance, and core loss of the motor are neglected. The motor is run with constant \( v/f \) control. The output frequency from the drive is closest to:

• A. 400 V and 50 Hz
• B. 300 V and 37.5 Hz
• C. 200 V and 25 Hz
• D. 100 V and 12.5 Hz

Hint:

In \( v/f \) control of induction motors:
- The voltage and frequency are proportional, so reducing the frequency also reduces the voltage proportionally.

Answer 1

The Correct Option is D

Step 1: For a constant \( v/f \) control, the voltage \( V \) and the frequency \( f \) are proportional. This means that the voltage to frequency ratio is constant, i.e., \[ \frac{V}{f} = \text{constant} \]
Step 2: The motor is initially operating at 400 V and 50 Hz. If the frequency is reduced to \( 12.5 \) Hz, the voltage must be scaled down proportionally. Using the relationship \( \frac{V_1}{f_1} = \frac{V_2}{f_2} \), we get: \[ \frac{400}{50} = \frac{V_2}{12.5} \] Solving for \( V_2 \): \[ V_2 = \frac{400 \times 12.5}{50} = 100 \, \text{V} \]
Thus, the output voltage is 100 V and the output frequency is 12.5 Hz.