**Subject :**Electrical Machines II (AC Machines)

**Unit :**Synchronous motor

## Synchronous-motor power equation

**Synchronous-motor power equation:**

*Fig: 1 Equivalent-circuit of a synchronous-motor, assuming armature resistance is negligible & Fig: 2 Phasor diagram model for a synchronous-motor, assuming armature resistance is negligible*

- Except for very small machines, the armature resistance of a synchronous motor is relatively insignificant compared to its synchronous reactance, so that equation to be approximated to

- The equivalent-circuit and phasor diagram corresponding to this relation are shown in Fig. 1 and Fig. 2. These are normally used for analyzing the behavior of a synchronous motor, due to changes in load and/or changes in field excitation.

From this phasor diagram, we have,

Multiplying through by VT and rearranging terms we have,

- Since the left side of Eqn. above is an expression for active power input and as the winding resistance is assumed to be negligible this power input will also represent the electromagnetic power developed, per phase, by the synchronous motor.

Thus,

Thus, for a three-phase synchronous motor,

- Eqn. above, called the synchronous-machine power equation, expresses the electro-magnetic power developed per phase by a cylindrical-rotor motor, in terms of its excitation voltage and power angle. Assuming a constant source voltage and constant supply frequency, the Eqn. above may be expressed as proportionalities that are very useful for analyzing the behavior of a synchronous-motor: