The speed of a three-phase synchronous motor is one of its most important characteristics. Unlike many other electric motors, a synchronous motor runs at a constant speed called synchronous speed, which is determined only by the supply frequency and the number of poles of the motor. Because of this property, synchronous motors are widely used in applications where constant speed operation is required.
Table of Contents
Synchronous Speed
The speed of the rotating magnetic field produced by the stator is called the synchronous speed.
The synchronous speed is given by
\[
N_s = \frac{120f}{P}
\]
- \(N_s\) = synchronous speed (rpm)
- \(f\) = supply frequency (Hz)
- \(P\) = number of poles
This equation shows that the speed depends only on supply frequency and number of poles.
Example
For a motor supplied with 50 Hz frequency:
2-pole motor
\[
N_s = \frac{120 \times 50}{2} = 3000 \text{ rpm}
\]
4-pole motor
\[
N_s = \frac{120 \times 50}{4} = 1500 \text{ rpm}
\]
6-pole motor
\[
N_s = \frac{120 \times 50}{6} = 1000 \text{ rpm}
\]
Thus, increasing the number of poles decreases the synchronous speed.
Rotor Speed of Synchronous Motor
In a synchronous motor, the rotor rotates exactly at synchronous speed once synchronization is achieved.
\[
N_r = N_s
\]
- \(N_r\) = rotor speed
- \(N_s\) = synchronous speed
This means the rotor locks with the rotating magnetic field.
Slip in Synchronous Motor
Slip is defined as
\[
s = \frac{N_s – N_r}{N_s}
\]
For synchronous motors:
\[
N_r = N_s
\]
Therefore,
\[
s = 0
\]
Thus, synchronous motors operate with zero slip during steady-state operation.
Effect of Load on Speed
One of the important characteristics of synchronous motors is that speed remains constant even when load changes.
When load increases:
- Rotor tends to slow down momentarily
- The torque angle increases
- Electromagnetic torque increases to balance the load
However, the speed remains equal to synchronous speed.
Torque Angle and Speed
The torque developed by a synchronous motor depends on the power angle (torque angle) \(\delta\).
\[
P = \frac{3VE_f}{X_s} \sin \delta
\]
- \(V\) = terminal voltage
- \(E_f\) = excitation voltage
- \(X_s\) = synchronous reactance
- \(\delta\) = torque angle
As load increases, the torque angle increases, but the speed remains constant.
Methods to Control Speed
Since synchronous motor speed depends on frequency and number of poles, speed control can be achieved by:
Changing Supply Frequency
Using Variable Frequency Drives (VFDs).
Changing Number of Poles
By modifying stator winding configuration (less common).
Advantages of Constant Speed
The constant speed characteristic of synchronous motors makes them ideal for:
- Industrial drives
- Pumps
- Compressors
- Conveyors
- Rolling mills