I'm really confused in solving the following question.
An isolated 50 Hz synchronous generator is rated at 15 MW which is also the maximum continuous power limit of its prime mover. It is equipped with a speed governor with 5% droop. Initially, the generator is feeding three loads of 4 MW each at 50 Hz. One of these loads is programmed to trip permanently if the frequency falls below 48 Hz. If an additional load of 3.5 MW is connected then the frequency will settle down to ?
Here, is my understanding of the question. At 15 MW load the frequency should drop by 50*0.05 = 2.5 Hz so the load would be working at 47.5 Hz. Now the new load is 4*3 + 3.5 MW = 15.5 MW which is above the maximum capacity and also the frequency would have fallen below 47.5 Hz, so one of the load has to trip. So the new load = 4*2 + 3.5 MW = 11.5 MW.
If we consider linear droop from the generator the linear equation relating frequency to power would be
$$ f = -0.05P + Constant(K) $$ To find the constant we put f = 50 Hz at P = 12 MW (given in the question). So we get K = 50.6. So at 11.5 MW the frequency would be $$ f = -0.05 * 11.5 + 50.6 = 50.025 Hz $$. But the actual answer is 50.083 Hz. I know I differ slightly from the actual answer, I was wondering if my understanding of the question was right or wrong.