Load sharing: 250/500 MW, frequency falls to 49.5 Hz

Both generators move down their droop lines to the common frequency of 49.5 Hz; the load increase is the sum of what each picks up.

Method: with droop $R_i$ (pu, on its own rating $P_{ri}$) and rated frequency $f_0$, the droop line of each unit gives

$$\Delta P_i = -\frac{P_{ri}}{R_i\, f_0}\,\Delta f = -K_i\,\Delta f$$

where $K_i = P_{ri}/(R_i f_0)$ is the stiffness of the unit in MW/Hz. For the units together, $\Delta P_L = -\Delta f\,\sum K_i$.

Data: $P_{r1} = 250$ MW, $R_1 = 0.04$; $P_{r2} = 500$ MW, $R_2 = 0.02$; $f_0 = 50$ Hz. Initial loads: 125 MW and 250 MW (half load). $\Delta f = 49.5 - 50 = -0.5$ Hz.

Stiffness:

$$\begin{aligned} K_1 &= \frac{250}{0.04 \times 50} = 125\ \text{MW/Hz} \\ K_2 &= \frac{500}{0.02 \times 50} = 500\ \text{MW/Hz} \end{aligned}$$

Increase in load on each generator:

$$\begin{aligned} \Delta P_1 &= 125 \times 0.5 = 62.5\ \text{MW} \\ \Delta P_2 &= 500 \times 0.5 = 250\ \text{MW} \end{aligned}$$

Increase in system load:

$$\Delta P_L = 62.5 + 250 = 312.5\ \text{MW}$$

Answer: The system load increased by 312.5 MW. G1 shares 62.5 MW (now 187.5 MW) and G2 shares 250 MW (now 500 MW, i.e. fully loaded). Any further load increase would overload G2.