Slip of Three-Phase Induction Motor

Slip is an important parameter in the operation of a three-phase induction motor. It represents the difference between the synchronous speed of the rotating magnetic field and the actual speed of the rotor. Slip is essential for the operation of an induction motor because
electromagnetic torque is produced only when there is relative motion between the stator magnetic field and the rotor conductors.

Table of Contents

Definition of Slip

Slip is defined as the ratio of the difference between synchronous speed and rotor speed to the synchronous speed.

\[
s = \frac{N_s – N_r}{N_s}
\]

where

\(s\) = slip
\(N_s\) = synchronous speed (rpm)
\(N_r\) = rotor speed (rpm)

Slip is usually expressed as a percentage.

\[
\text{Slip (%)} = \frac{N_s – N_r}{N_s} \times 100
\]

Synchronous Speed

The synchronous speed of the rotating magnetic field is given by

\[
N_s = \frac{120f}{P}
\]

\(f\) = supply frequency (Hz)
\(P\) = number of poles

Rotor Speed

The rotor speed can be expressed in terms of slip:

\[
N_r = (1 – s)N_s
\]

This equation shows that the rotor speed is always slightly less than synchronous speed.

1. The slip of a 4-pole induction motor running on a 50 Hz supply at a rotor speed of 1440 rpm is:

(A) 0.02
(B) 0.04
(C) 0.06
(D) 0.08

Answer: B

Explanation: Synchronous speed, \( N_s = \frac{120f}{P} = \frac{120 \times 50}{4} = 1500 \, \text{rpm} \).
Slip, \( s = \frac{N_s – N}{N_s} = \frac{1500 – 1440}{1500} = \frac{60}{1500} = 0.04 \).

Slip at Different Operating Conditions

At Starting

At the moment of starting,

\[
N_r = 0
\]

Therefore,

\[
s = 1
\]

Thus, slip at starting is 100%.

2. At standstill condition, the slip of an induction motor is:

(A) 0
(B) 0.5
(C) 1
(D) Depends on load

Answer: C

Explanation: At standstill, rotor speed \( N = 0 \).
\( s = \frac{N_s – 0}{N_s} = 1 \).
Thus, slip is unity.

At Normal Operation

During normal operation, the rotor speed is very close to synchronous speed.

Typical slip values:

Small motors: 4% – 6%
Large motors: 1% – 3%

At Synchronous Speed

\[
N_r = N_s
\]

then

\[
s = 0
\]

In this condition, no relative motion exists, and therefore no torque is produced.

This is why an induction motor cannot run at synchronous speed.

Slip Frequency

The frequency of rotor current depends on slip.

\[
f_r = s f
\]

\(f_r\) = rotor frequency
\(f\) = supply frequency

Examples:

At starting: \(s = 1\), so \(f_r = f\)
During normal operation: rotor frequency is very small

3. If the slip of an induction motor is 0.03 and the supply frequency is 50 Hz, the rotor current frequency is:

(A) 1.5 Hz
(B) 3 Hz
(C) 15 Hz
(D) 50 Hz

Answer: A

Explanation: Rotor frequency is given by \( f_r = s \times f = 0.03 \times 50 = 1.5 \, \text{Hz} \).

Torque-Slip Characteristics

The torque developed by an induction motor varies with slip.

Key points:

At small slip, torque increases approximately linearly with slip.
At maximum torque, slip reaches a specific value called critical slip.
After this point, torque decreases rapidly.

4. An induction motor operates at a slip of 5%. If the synchronous speed is 1000 rpm, the rotor speed is:

(A) 950 rpm
(B) 975 rpm
(C) 900 rpm
(D) 1050 rpm

Answer: A

Explanation: \( s = \frac{N_s – N}{N_s} \Rightarrow N = N_s (1 – s) \).
\( N = 1000 \times (1 – 0.05) = 1000 \times 0.95 = 950 \, \text{rpm} \).
Hence, rotor speed is 950 rpm.

5. Which of the following statements about slip in an induction motor is correct?

(A) Slip is negative in motoring mode
(B) Slip is zero at starting
(C) Slip is always less than 1 in motoring mode
(D) Slip is independent of load