GATE 2023 EE – Question 48

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 · Numerical answer

A three phase 415 V, 50 Hz, 6-pole, 960 RPM, 4 HP squirrel cage induction motor drives a constant torque load at rated speed operating from rated supply and frequency delivering rated output. If the supply voltage and frequency are reduced by 20%, the resultant speed of the motor in RPM (neglecting the stator leakage impedance and rotational losses) is ___________ (Round off to the nearest integer).

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Correct answer: 760

Explanation

Rated slip is $s=\dfrac{1000-960}{1000}=0.04$, so the slip speed is 40 rpm. With $V/f$ constant (both reduced 20%), the flux is unchanged and in the linear region the torque is proportional to slip speed. For the same constant load torque the slip speed remains 40 rpm. The new synchronous speed is $0.8\times1000=800$ rpm, so $N=800-40=760$ rpm.