A single 50 Hz synchronous generator on droop control was delivering 100 MW power to a system. Due to increase in load, generator power had to be increased by 10 MW, as a result of which, system frequency dropped to 49.75 Hz. Further increase in load in the system resulted in a frequency of 49.25 Hz. At this condition, the power in MW supplied by the generator is_____ (rounded off to two decimal places).

The correct answer is 130.

Step 1: Understand the droop control characteristic of the synchronous generator.
Droop control relates the generator power output to the frequency deviation. The relation between power output ($P$) and frequency ($f$) is linear and can be written as:

$\Delta P=-R·\Delta f$

or equivalently,

$\frac{P_2-P_1}{f_2-f_1}=\text{constant slope}$

Step 2: Determine the droop slope using the first change in load condition.
Initially, the generator operates at a no-load/base condition delivering power $P_1=100\text{ MW}$ at a frequency of $f_1=50\text{ Hz}$.
When the load increases, the power output is increased by 10 MW, so the new power becomes:

$P_2=100+10=110\text{ MW}$

The corresponding frequency drops to $f_2=49.75\text{ Hz}$.
Calculating the slope (change in power per unit change in frequency):

$\text{Slope}=\frac{P_2-P_1}{f_1-f_2}=\frac{110-100}{50-49.75}=\frac{10}{0.25}=40\text{ MW/Hz}$

Step 3: Calculate the power supplied at a frequency of 49.25 Hz.
Let $P_3$ be the power supplied at frequency $f_3=49.25\text{ Hz}$.
Using the slope calculated in Step 2 with respect to the initial condition ($P_1=100\text{ MW}$ at $f_1=50\text{ Hz}$):

$\text{Slope}=\frac{P_3-P_1}{f_1-f_3}$

Substitute the known values:

$40=\frac{P_3-100}{50-49.25}$

$40=\frac{P_3-100}{0.75}$

$P_3-100=40·0.75$

$P_3-100=30$

$P_3=130\text{ MW}$

Thus, the power supplied by the generator at 49.25 Hz is 130 MW.