Power generator droop characterstics
What we know:


Droop is 5% at 100% load (15 MW)
Frequency is set at 50 Hz with a 12 MW load (so the No-Load frequency is higher than 50 Hz)


Note: This is what would be done practically with a generator. They are never run at 100% load, so typically would be used at some under rating. For example if the generator is running at 80% load, the speed would be set to provide 50 Hz at this load point. I've assumed here that this is what is meant by 12 MW @ 50 Hz ...not that 50 Hz is the no load speed. 

12/15 = 0.8 (12 MW is 80% of full load)

Therefore Droop at 12 MW is:     0.8 * 5 = 4% 

If the speed at 12 MW (50 Hz) has drooped 4 %, then the speed is 100 - 4 = 96% of full speed.

No-Load frequency:      (50/96) * 100 = 52.0833 Hz

Note: 50/96 = 0.520833r Hz  ...this represents the frequency drop for a 1% change in load. Since it's 6 decimals I chose to use 50/96 elsewhere in the calculations. 

We now need to decide if the under frequency trip will operate at 15.5 MW (The question was corrected for this to be 48 Hz)

15.5/15 = 1.03     (15.5 MW is 103% of full load)

Therefore Droop at 15.5 MW is: 1.03 * 5 = 5.17% 

Max frequency drop: (50/96) * 5.17 = 2.693 Hz  

Frequency at 15.5 MW:  52.0833 - 2.693 = 49.39 Hz     .....(this seems to indicate the under frequency trip of 48 Hz would not trip)

**** Speculation now. Let's assume that you have the number wrong in the question and that the frequency trip does trip.

The load on the generator is now as you specified:  2 * 4 + 3.5 = 11.5 MW.

11.5/15 = 0.767   (11.5 MW is 76.7% of full load)

Therefore Droop at 11.5 MW is 0.767 * 5 = 3.833%

Frequency drop at 11.5 MW: (50/96) * 3.833 = 1.997 Hz  (we can round this up to 2)

Frequency at 11.5 MW: 52.0833 - 2 = 50.0833 Hz

****This seems to give what you said was the correct answer.....however by my calculations the frequency trip would not actuate.

What is Droop?



Droop is a governor characteristic that reduces fuel/throttle as the load increases. It is fixed at only 1 point, it's defined point. It is a slope defined for the genset. For example a 1500 rpm genset may droop 5% at full load. So the speed will drop 75 rpm to 1425 at full load. Since the frequency of the generator is related to the number of poles and speed....the frequency drops by 5% at full load. At 50 percent load the frequency drop (droop) would be 2.5%. 

With the values calculated we can plot the droop for the question: