Licchavi Lyceum

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Licchavi Lyceum

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.

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.

Slip at Different Operating Conditions

At Starting

At the moment of starting,

\[
N_r = 0
\]

Therefore,

\[
s = 1
\]

Thus, slip at starting is 100%.

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

If

\[
N_r = N_s
\]

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

Importance of Slip

Slip plays a crucial role in the operation of an induction motor because it:

  • Determines rotor speed
  • Controls torque production
  • Affects rotor current frequency
  • Helps analyze motor performance

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.

Applications of Slip Concept

Slip is important in analyzing:

  • Speed control of induction motors
  • Motor efficiency
  • Rotor current frequency
  • Torque characteristics