GATE EE 2025 Set 1 — Question 26
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Electrical Machines → Three-Phase Induction Machines → Starting & Speed Control
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Question
The operating region of the developed torque () and speed () of an induction motor drive is given by the shaded region OQRE in the figure. The load torque () characteristic is also shown. The motor drive moves from the initial operating point O to the final operating point S. Which one of the following trajectories will take the shortest time?
Correct answer
(A) O - Q - R - S
Solution
The dynamic equation for a motor drive is given by:
To find the time taken to accelerate from speed to :
To minimize the time , we must maximize the accelerating torque at every speed. The maximum developed torque available in the operating region is along the boundary . Therefore, the trajectory provides the maximum possible accelerating torque throughout the speed range, resulting in the shortest acceleration time.
To find the time taken to accelerate from speed to :
To minimize the time , we must maximize the accelerating torque at every speed. The maximum developed torque available in the operating region is along the boundary . Therefore, the trajectory provides the maximum possible accelerating torque throughout the speed range, resulting in the shortest acceleration time.
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