AC voltage control of a 3-phase induction motor using a 3-phase AC regulator For which load torque characteristic does stator-voltage control produce the largest speed variation?

Introduction / Context:
Three-phase AC regulators vary the RMS stator voltage of induction motors, thereby modifying breakdown and rated torque approximately with V^2. The resulting operating speed depends on the intersection of the motor torque–slip curve and the load torque characteristic.

Given Data / Assumptions:

• Standard squirrel-cage induction motor.
• Stator voltage control (not frequency control).
• Torque capability scales roughly as V^2 for a given slip region.

Concept / Approach:
When voltage is reduced, available motor torque drops quickly (∝ V^2). For a constant-torque load, maintaining the same torque requires substantially higher slip, which means a larger reduction in speed. For loads where torque rises with speed (e.g., positive viscous damping), the operating point tends to stabilize at a higher speed for a given voltage; for fan-type loads where torque decreases with speed, the required torque falls, so speed drop is smaller.

Step-by-Step Solution:
Reduce voltage → motor torque curve scales down with V^2.Constant-torque demand → intersection shifts to much higher slip → larger speed reduction.For torque ∝ speed or torque ∝ speed^2, the required torque reduces at lower speed → less shift needed → smaller variation.

Verification / Alternative check:
Plot approximate torque–slip curves under different voltages and superimpose constant versus speed-dependent load torques; the constant-torque case shows the greatest speed change.

Why Other Options Are Wrong:

• (b) and (c): speed-dependent torques moderate the drop in speed when voltage is reduced.
• (d): only (a) gives the largest variation.

Common Pitfalls:

• Assuming voltage control is an efficient speed control method for constant-torque loads—it is not.

Final Answer:
Load torque is constant (independent of speed)