# Synchronous Motor

Synchronous Motor states that ” An AC Motor in which at steady state, rotation of the shaft is in sync with the frequency of applied current”. The synchronous motor works as AC motor but here the total number of rotations made by the shaft is equal to the integer multiple of the frequency of the applied current.

The synchronous motor doesn’t rely on induction current for working. In these motors, unlike induction motor, multiphase AC electromagnets are present on the stator, which produces a rotating magnetic- field. Here rotor is of a permanent magnet that gets synced with the rotating magnetic- field and rotates in synchronous to the frequency of current applied to it.

## Principle Operation of Synchronous Motor

To understand the principle of operation of a synchronous motor, let us consider what happens if we connect the armature winding of a 3-phase synchronous machine to a suitable balanced 3-phase source and the field winding to a D.C source of appropriate voltage. The current flowing through the field coils will set up stationary magnetic poles of alternate North and South.

On the other hand, the 3-phase currents flowing in the armature winding produce a rotating magnetic field rotating at synchronous speed. In other words, there will be moving North and South poles established in the stator due to the 3-phase currents i.e at any location in the stator there will be a North pole at some instant of time and it will become a South pole after a time period corresponding to half a cycle.

Let us assume that the stationary South pole in the rotor is aligned with the North pole in the stator moving in a clockwise direction at a particular instant of time, as shown in the above Fig. These two poles get attracted and force of attraction between stator poles and rotor poles – resulting in the production of torque in a clockwise direction try to maintain this alignment as per lenz’s law and hence the rotor pole tries to follow the stator pole as the conditions are suitable for the production of torque in the clockwise direction.

However the rotor cannot move instantaneously due to its mechanical inertia, and so it needs some time to move. In the meantime, the stator pole would quickly change its polarity and becomes a South pole. So the force of attraction will no longer be present and instead the like poles experience a force of repulsion as shown in the below given Fig.

If the rotor is brought to near synchronous speed by some external means say a small motor (known as pony motor-which could be a D.C or AC induction rotor) mounted on the same shaft as that of the rotor, the rotor poles get locked to the unlike poles in the stator and the rotor continues to run at the synchronous speed even if the supply to the pony motor is disconnected.

## Equivalent Circuit of Synchronous Motor

The equivalent-circuit for one armature phase of a cylindrical rotor three-phase synchronous motor is shown in the below fig. Exactly similar to that of a synchronous generator except
that the current flows into the armature from the supply.

All values are given per phase. Applying Kirchhoff’s voltage law in the given circuit

VT = IaRa + jIaXl + JiaXas + EF

Combining reactances, we have XS = Xl + Xas

VT = Ia (Ra +Xas) + EF

or VT =  EF + IaZs

where:
Ra = armature resistance (per phase)
Xl = armature leakage reactance (per phase)
XS = synchronous reactance (per phase)
Zs = synchronous impedance (per phase)
VT = applied voltage/phase (V)
Ia = armature current/phase(A)

## Phasor Diagram of Synchronous Motor

A phasor diagram is shown in the above Fig. illustrates the method of determining the counter EMF which is obtained from the phasor equation;

EF = VT – IaZs

The phase angle \delta between the terminal voltage VT and the excitation voltage EF in Fig. is usually termed the torque angle. The torque angle is also called the load angle or power angle.