Question

A 100 MVA synchronous generator operates at full load at a frequency of 50 Hz. The load is suddenly reduced to 50 MW. Due to time lag in governor system, the steam valve begins to close after 0.4 sec. The frequency at t = 0.4 sec is ______ Hz (Given H = 4 MJ/MVA)

• A. 51.23

Answer 1

The correct option is A 51.23
G = 100 MVA
and H = 4 MJ/MVA
KE = GH = 400 MJ

Excess power input to the generator shaft before the steam valve begins to close
= 100 - 50 = 50 MW

Excess energy transferred to rotating parts in 0.4 sec
= 50 $\times$ 0.4 = 20 MJ

$KE\propto (speed{)}^2\propto (frequency{)}^2$

$f_2=f_1\times \sqrt{\frac{\text{Total energy stored in 0.4 sec}}{\text{Energy stored at synchronous speed}}}$

$f_2=50\times \sqrt{\frac{420}{400}}=51.23Hz$