Question

A 100 MVA, 50 Hz synchronous generator having inertia constant H = 5 kW-s/KVA on full load at unity power factor. The load is suddenly reduced to 60 MW. Due to time lag in governor system, the steam valve begins to close after 0.5 second. The change in frequency that occurs in this time is ______Hz.

• A. 1

Answer 1

The correct option is A 1
The rating of the machine G = 100 MVA

Intertia constant, H = 5 kW-s/KVA
= 5 KJ/KVA = 5 MJ/MVA

Kinetic energy stored in the rotating parts of generator and turbine at synchronous speed (f = 50 Hz)
$=HG=5\times 100=500MJ$

Excess power input to the generator shaft before the steam valve begins to close,

$=100-60=40$ MW

Excess energy transferred to rotating parts in 0.5 sec
$40\times 0.5=20$ MJ

Since, Kinetic energy, K.E $\propto f^2$
So, frequency at the end of 0.5 sec

$f_2=f_1\sqrt{\frac{Totalenergystoredin0.5sec}{Energystoredatsychronousspeed}}$

$f_2=50\sqrt{\frac{500+20}{500}}=50\times 1.02=51$ Hz

Change in frequency $=f_2-f_1$
=$51-50=1Hz$