Question

If we consider a Power-Angle Curve, we know that the synchronous generator becomes unstable beyond power angle of 90 degrees. Can you physically explain why is this region considered to be unstable region? If you can use explain using equations I would be grateful.

Answer 1

The active power output of synchronous machine is given by the equation  

E = Excited voltage

V= Voltage of infinite bus

X = Synchronous reactance

δ = Power angle ( angle between stator mmf and rotor mmf field )

Power angle gives the relation of electrical power output and mechanical input. When power angle starts increasing form 0° towards 90° the output increases sinusoidally reaches maximum when at 90° but further increase in the power angle beyond 90° decreases the output. Which Signifies that generator output power is less than the mechanical input. As in synchronous machine both stator mmf speed and rotor speed is equal and get locked with each other and thus rotor rotates at synchronous speed . The stator mmf speed is dependent upon the number of poles more the number of poles more will be the stator mmf speed and vice a versa.

When generated power is less than the mechanical input the poles of the electrical machine will lag behind thus will slip thus stator speed will decrease and machine will lose synchronism thus the generator become unstable. i.e as input available is more than the output required the rotor and stator speed will be different.