Synchronous speed is calculated by a formula
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:
| Symbol | Description | Units |
|---|---|---|
| \(N_s\) | Synchronous Speed (Speed of rotating magnetic field) | RPM (Revolutions Per Minute) |
| \(f\) | Frequency of AC Power Supply | Hz (Hertz) |
| \(p\) | Number of Poles in Stator Winding | (Unitless, number of poles) |
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:
| Concept | Formula | Variables |
|---|---|---|
| Synchronous Speed | \(N_s = \frac{{120f}}{p}\) | \(N_s\): Synchronous Speed (RPM) \(f\): Frequency (Hz) \(p\): Number of Poles |
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).
Important Questions from Alternator and Synchronous Motors
A certain application requires power at a frequency of 16.67 Hz, while the available grid frequency is 50 Hz. A 3-phase synchronous motor connected to the 50 Hz, 3-phase grid, driving a synchronous generator, is used for this application.
Which one of the following combinations is a suitable choice for the number of poles in the motor and generator, respectively?
- What happens when an alternator is said to be over excited?
For unity power factor loads, the effect of an armature reaction in an alternator is
Alternators are rated at-
In a large alternators, the field winding is placed on the -
