In a synchronous motor, the value of coupling angle depends on:

Synchronous Motor on Load:

• In DC motors and induction motors, when the load increased causes the motor speed decreases.
• The decrease in speed reduces the counter EMF which causes additional current is drawn from the source to carry the increased load at a reduced speed.
• This action cannot take place in a synchronous motor because it runs at a constant speed (i.e., synchronous speed) at all loads.
• When we apply mechanical load to a synchronous motor then the rotor poles fall slightly behind the stator poles while continuing to run at synchronous speed.
• The angular displacement between stator and rotor poles (called torque angle α ) causes the phase of back EMF Eb to change with respect to supply voltage V. This increases the resultant EMF Er in the stator winding.
• Consequently, stator current increases to carry the load.

The following points may be noted in synchronous motor operation:

• A Synchronous motor runs at the synchronous speed at all loads. It meets the increased load not by a decrease in speed but by the relative shift between stator and rotor poles i.e., by the adjustment of torque angle α.
• If the load on the motor increases, the torque angle α  also increases (i.e., rotor poles lag behind the stator poles by a greater angle) but the motor continues to run at synchronous speed.
• The increase in torque angle α  causes a greater phase shift of back EMF Eb with respect to supply voltage V.
• The greater phase shift of back EMF Eb with respect to supply voltage V cause increases the net voltage Er in the stator winding. Consequently, the armature current Ia increases to meet the load demand.
• If the load on the motor decreases, the torque angle also decreases. This causes a smaller phase shift of Eb with respect to V. Consequently, the net voltage Er in the stator winding decreases and so does the armature current Ia.
• Where Armature Current, \({I_a} = \frac{{V - {E_b}}}{{{Z_s}}} = \frac{{{E_r}}}{{{Z_s}}}\)

           And Zs is Synchronous Impedance

Here, α is torque angle or coupling angle