Droop calculation: 800 MW and 300 MW units

The droop line of each unit passes through its no-load point (51 Hz, 0 MW) and its present operating point (50 Hz, given MW). Extending the line to rated output gives the droop.

Frequency drop from no load to present load: $\Delta f = 51 - 50 = 1$ Hz.

Stiffness of each unit:

$$K_1 = \frac{600}{1} = 600\ \text{MW/Hz}, \qquad K_2 = \frac{200}{1} = 200\ \text{MW/Hz}$$

Droop on own ratings

Frequency drop at rated output: G1: $800/600 = 1.333$ Hz; G2: $300/200 = 1.5$ Hz.

$$\begin{aligned} R_1 &= \frac{1.333/50}{1} = 0.02667 = 2.67\ \% \\ R_2 &= \frac{1.5/50}{1} = 0.03 = 3\ \% \end{aligned}$$

Droop on the common base of 1000 MW

$$R_{new} = R_{own} \times \frac{S_{base}}{S_{rated}}$$ $$\begin{aligned} R_1 &= 0.02667 \times \frac{1000}{800} = 0.0333 = 3.33\ \% \\ R_2 &= 0.03 \times \frac{1000}{300} = 0.10 = 10\ \% \end{aligned}$$

Check: $\Delta P_i = (\Delta f/f_0)\,S_{base}/R_i$: G1 $= 0.02 \times 1000/0.0333 = 600$ MW ✓, G2 $= 0.02 \times 1000/0.1 = 200$ MW ✓.

Load sharing at 50.2 Hz

Frequency drop from no load $= 51 - 50.2 = 0.8$ Hz.

$$\begin{aligned} P_1 &= 600 \times 0.8 = 480\ \text{MW} \\ P_2 &= 200 \times 0.8 = 160\ \text{MW} \end{aligned}$$

Total load $= 640$ MW, i.e. the load has decreased by 160 MW (G1 sheds 120 MW, G2 sheds 40 MW).

Answer: $R_1 = 2.67\ \%$ and $R_2 = 3\ \%$ on own ratings (3.33 % and 10 % on 1000 MW base). At 50.2 Hz, G1 = 480 MW, G2 = 160 MW (total 640 MW).