What is the formula for estimating the power needed to start a synchronous motor with a full load running torque?

The formula for calculating the power necessary to start a synchronous motor with full load running torque is as follows:

Formula

P = 3VEbsin/Xs

Where

P - Power developed by the motor (in watts).

V - Line voltage (V)

Eb - Back EMF generated/phase (V)

 - The load angle (in degrees) is the angle formed between the back EMF & the terminal voltage.

Xs - Synchronous reactance (in Ω).

Important Points

Starting Condition: At starting, the load angle (δ) is normally minimal, but increases with motor acceleration.

Full Load Torque: The torque at full load influences the load angle and, consequently, the power calculation.

Maximum Power: Maximum Power is achieved when δ = 90 resulting in:

P = 3VEb/Xs

This formula estimates the electrical power input required to start a synchronous motor at full load conditions, taking into consideration its electrical characteristics & operational factors.