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GATE 2025 EE – Question 45

Electrical Machines · Three-phase induction machines: principle of operation, types, performance, torque-speed characteristics, no-load and blocked-rotor tests, equivalent circuit, starting and speed control · 2 marks · Multiple choice

A 3-phase, 400 V, 4 pole, 50 Hz star connected induction motor has the following parameters referred to the stator:

$R_r'=1\ \Omega$, $X_s=X_r'=2\ \Omega$

Stator resistance, magnetizing reactance and core loss of the motor are neglected. The motor is run with constant $V/f$ control from a drive. For maximum starting torque, the voltage and frequency output, respectively, from the drive, is closest to,

  1. 400 V and 50 Hz
  2. 200 V and 25 Hz
  3. 100 V and 12.5 Hz
  4. 300 V and 37.5 Hz

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Correct answer: (C) 100 V and 12.5 Hz

Explanation

The maximum torque occurs at the slip $s_m=\dfrac{R_r'}{X_s+X_r'}$, where the reactances scale with frequency: $X(f)=4\times\dfrac f{50}$. Maximum torque at starting needs $s_m=1$, i.e. $R_r'=X(f)$: $1=\dfrac{4f}{50}$, so $f=12.5$ Hz. With constant V/f, $V=400\times\dfrac{12.5}{50}=100$ V.