Torque–Speed Characteristics of Induction Motors

i Learning Objectives

By the end of this chapter you should be able to:

Read the torque–speed curve of an induction motor and identify the starting, full-load and breakdown torques.
Explain how the operating point is set by the balance of motor torque and load torque.
Describe how the curve shifts when the voltage and frequency are varied together, and why this makes frequency control attractive.
Use the linear low-slip relation to predict the slip under changed load, rotor resistance or voltage.

Demonstrative Video

Section 1

The Torque–Speed Curve

The torque of an induction motor depends on its speed, but no simple formula describes the whole range conveniently. It is easier to show the relationship as a curve.

Torque-speed curve of an induction motor — Typical torque–speed curve. Torques are shown as multiples of full-load torque T.

For a typical design, the starting (locked-rotor) torque is about 1.5 times full-load torque, and the breakdown (maximum) torque is about 2.5 times.
Motor torque is electromagnetic, the product of flux and rotor current. Load torque is mechanical, force times radius.

Condition	Torque relation	Result
Steady running	\(T_{motor} = T_{load}\)	Constant speed, slightly below \(N_s\)
Accelerating	\(T_{motor} > T_{load}\)	Speed rises
Decelerating	\(T_{motor} < T_{load}\)	Speed falls

Self-regulation. When the load increases, the speed falls until the motor torque again equals the load torque. If the load torque exceeds the breakdown torque (≈ 2.5T), the motor stalls abruptly.

Section 2

Varying Voltage and Frequency

For a squirrel-cage motor the curve depends on the stator voltage and frequency. At fixed frequency, torque is proportional to \(V^2\), and \(N_s\) is set by \(f\). In practice \(V\) and \(f\) are varied in the same proportion, which keeps the air-gap flux constant.

Family of torque-speed curves at different frequencies — Torque–speed curves at constant V/f: the same shape, shifted along the speed axis.

The shape of the curve stays the same, but its position shifts along the speed axis.
The torque depends on the slip speed \(N_s - N_r\). At constant flux, the same slip speed gives the same torque at any frequency.

Data for the example squirrel-cage motor — Example motor data.

The current–speed curve is V-shaped, with its minimum at \(N_s\). That minimum is the magnetising current that creates the flux. Since the flux is held constant, the magnetising current is the same at every synchronous speed.

Torque and current against speed at reduced V and f — Torque and current against speed at reduced voltage and frequency.

For the example motor, at 440 V/60 Hz the locked-rotor current is 100 A and the locked-rotor torque is 75 N·m. At 110 V/15 Hz (the same V/f) the locked-rotor current falls to 75 A, while the locked-rotor torque doubles to 150 N·m. At low frequency the rotor current at standstill is closer in phase to the air-gap flux, so it produces more torque per ampere.

Why Frequency Control Is Popular

It gives high torque from zero to full speed at modest current, and it permits economical regenerative braking.

Section 3

The Linear Low-Slip Region

Stable operation lies on the nearly straight part of the torque–slip curve between no load and breakdown. Here \(T \propto sV^2/R_2\), so the slope depends mainly on the rotor resistance: the higher \(R_2\), the larger the slip for a given torque. For two operating conditions:

Slip Under Changed Conditions

\(s_2 = s_1\cdot\dfrac{T_2}{T_1}\cdot\dfrac{R_2}{R_1}\cdot\left(\dfrac{V_1}{V_2}\right)^2\)

Here \(R_1\) and \(R_2\) denote the rotor resistance in the two conditions.

1 Worked Example — Combined changes

Problem. A motor runs at 3 % slip at full load. Find the slip if the load torque falls to 80 %, the rotor resistance is doubled and the voltage falls to 90 %.

\[s_2 = 0.03\times0.8\times2\times\left(\frac{1}{0.9}\right)^2 = 0.0593\]

Section 4

Summary

The torque–speed curve shows starting (≈1.5T), full-load and breakdown (≈2.5T) torques.
The operating point is where the motor torque equals the load torque.
At constant \(V/f\) the curve keeps its shape and shifts with \(N_s\).
At low slip, \(s \propto TR_2/V^2\).

Section 5

Chapter Review

Multiple-Choice Questions

MCQ 1. If the load torque exceeds the breakdown torque, the motor
(a) speeds up (b) stalls (c) runs at \(N_s\) (d) becomes a generator

Show answer
(b) stalls.
MCQ 2. At constant V/f, reducing the frequency
(a) changes the curve shape (b) shifts the curve to lower speeds (c) reduces the breakdown torque to zero (d) increases \(N_s\)

Show answer
(b).
MCQ 3. In the linear region, doubling the rotor resistance at the same torque
(a) halves the slip (b) doubles the slip (c) leaves the slip unchanged (d) quadruples the slip

Show answer
(b) doubles the slip.

Conceptual Questions

Why is the operating region right of the breakdown point stable and the region to its left unstable?
Why is the no-load current of an induction motor mainly magnetising current?