Understanding Synchronous Speed in AC Machines

Synchronous speed is a fundamental concept in understanding how AC electrical machines, like induction motors and synchronous motors, operate. It represents the speed at which the magnetic field produced by the stator windings rotates.

This rotating magnetic field is created by the alternating current flowing through the stator coils. The speed of this field depends directly on the frequency of the power supply and the number of magnetic poles in the stator winding.

Synchronous Speed Formula Explained

The speed of the rotating magnetic field, known as the synchronous speed (\(N_s\)), is determined by the following formula:

\(N_s = \frac{{120f}}{p}\)

Where:

• \(N_s\) is the synchronous speed in revolutions per minute (RPM).
• \(f\) is the frequency of the AC power supply in Hertz (Hz).
• \(p\) is the number of poles per phase in the stator winding.

The factor 120 comes from converting cycles per second (Hz) to revolutions per minute (RPM) and accounting for the fact that a magnetic field completes one revolution in two poles (a pole pair).

Components of the Synchronous Speed Formula

Let's look at the terms in the synchronous speed formula:

Understanding these components helps explain why a motor's synchronous speed changes if you change the frequency or the number of poles.

How Frequency and Poles Affect Synchronous Speed

From the formula \(N_s = \frac{{120f}}{p}\), we can see the relationships:

• Frequency (\(f\)): If the frequency increases, the synchronous speed increases proportionally, assuming the number of poles remains constant.
• Number of Poles (\(p\)): If the number of poles increases, the synchronous speed decreases, assuming the frequency remains constant. Motors can be designed with different numbers of poles (e.g., 2, 4, 6, 8 poles) to achieve different synchronous speeds for a given frequency.

Revision Table: Synchronous Speed Formula

Here is a quick summary of the key formula for synchronous speed:

Additional Information on Synchronous Speed

While synchronous speed is the speed of the rotating magnetic field, the actual speed of an AC induction motor rotor is always slightly less than the synchronous speed. This difference is called 'slip'. Synchronous motors, however, run exactly at synchronous speed under steady-state conditions.

The number of poles \(p\) is always an even integer (e.g., 2, 4, 6) because poles are created in pairs (North and South).