Question

A 50 Hz synchronous machine is supplying 50% of the maximum power that
it is capable of delivering through a transmission line to infinite bus. A sudden
fault occurs that increases the system reactance to such a value that it delivers
20% of the maximum power. When the fault line is isolated the power which
can be delivered is 75% of the maximum power. Determine the value of
critical clearing angle.

Answer 1

Answer:

your answer is 67.4°

Let Pm is maximum power that can be delivered.

∴ Pm sin δ0 = 0.5 Pm

or δ0 = 30°

During fault the resistance is 500% of the value

before the fault r1 = 0.2, r2 = 0.75

δc = cos-1

(Ps/Pm) + r2 cosδm - r1cos δ0

r2 - r1

But 0.5 Pm = 0.75 Pm sin δm

or δm = 41.8&deh;

= 180 – 41.8

= 138.2° = 2.412 radian

∴ δc = cos-1

0.5(2.412/0.5236) - 0.75 × 0.745 - 0.2 × 0.866

0.55

= cos-1 (0.383) = 67.4°