Question

Two generators $G_1$ and $G_2$ rated as 200 MW and 400 MW respectively, are operating in parallel. The droop characteristics of their governors are 4% and 5% respectively from no load to full load. At no load, the generators are operating at a system frequency of 50 Hz. If total load of 600 MW is being shared by the generators, then generation in $G_1$ and $G_2$ are respectively

• A. 266.67 MW, 333.33 MW
• B. 300 MW, 300 MW
• C. 231 MW, 369 MW
• D. 150 MW, 450 MW

Answer 1

The correct option is C 231 MW, 369 MW

Since the generators are in parallel they will operate at the same frequency at steady load. Let load on generator $G_1$ is $P_{G1}$ and load on generator $G_2$ is $P_{G2}$.
If $\Delta f$ is the change in frequency,

then, $\frac{\Delta f}{P_{G1}}=\frac{0.04\times 50}{200}$ .....(i)

$\frac{\Delta f}{600-P_{G1}}=\frac{0.05\times 50}{400}$ ...(ii)

From equation (i),

$\frac{\Delta f}{P_{G1}}=0.01$

$\Delta f=0.01\times P_{G1}$ ....(iii)

From equation (ii), $\Delta f=\frac{1}{160}(600-P_{G1})$ ...(iv)

From equation (iii) and (iv), we get

$\frac{P_{G1}}{100}=\frac{600-P_{G1}}{160}$

$16P_{G1}=6000-10P_{G1}$

$26P_{G1}=6000$

$\therefore P_{G1}=230.76MW$

$P_{G2}=600-230.76=369.24MW$