Question

Two generating units rated 300 MW and 400 MW have governor speed regulation of 6% and 4% respectively from no load to full load. Both the generating units are operating in parallel to share a load of 600 MW. Assuming free governor action the load shared by the larger unit is

• A. 400

Answer 1

The correct option is A 400
Given speed regulation of generating units is from no load to full load.

Hence the rated frequency (50 Hz) will be common for both units at no load and will droop to lower values as loaded to full load.

$Let,P_1=Loadsharedby400MWmachine$

$P_2=Loadsharedby300MWmachine$

$For400MWmachinedropinfrequencyfromnoloadtofullload=\frac{50\times 4}{100}=2Hz$

New frequency of operation of 400 MW machine $f_1=50-\frac{2}{400}{P}_1$.

For 300 MW machine drop in frequency from no load to full load = $\frac{50\times 6}{100}=3Hz$.

New frequency of operation of 300 MW machine $f_2=50-\frac{3}{300}{P}_2$.

We also know,

$P_1+P_2=600$

$Loadsharedbetweentwounits$

$P_2=600-P_1$

$f_1=f_2=f$

.....(Units operation is parallel)

$50-\frac{2}{400}{P}_1=50-\frac{3}{300}(600-P_1)$

$\frac{P_1}{200}=\frac{600-P_1}{100}$

$100P_1=200(600-P_1)$

$P_1=1200-2P_1$

3P${}_1$ = 1200

$P_1=400MW$