For the same frequency change, units share in proportion to capacity only if:

The smaller unit has half the droop

The smaller unit has double the droop

Why is halving the droop for the half-size unit wrong?

Droop is defined in pu on each unit's own rating, so the rating is already accounted for

Droop does not depend on rating at all

Smaller units must always have larger droop

2070 Asar · 8 marks

Droop for capacity sharing: 500 and 250 MW

Short answer

For capacity-proportional sharing, both units must have the same per-unit droop. Therefore the 250 MW unit must have a droop of 5% on its own rating, same as the 500 MW unit.

Two generating units of 500MW and 250 MW capacities respectively are operating in parallel and supplying power to a common load. When each generator is half loaded, they operate at a common frequency of 50 Hz. If the droop regulation of 500MW generating set is 5% based on its rating, what must be the droop regulation of 250 MW generating unit based on its own rating so that they share the change in load according to their capacities.

For two units to share any change in load according to their capacities, each must change by the same fraction of its rating for the same frequency change.

From the droop definition, for a common $\Delta f$ :

\frac{\Delta P_1}{P_{r1}} = \frac{\Delta f/f_0}{R_1}, \qquad \frac{\Delta P_2}{P_{r2}} = \frac{\Delta f/f_0}{R_2}

Sharing by capacity requires

\frac{\Delta P_1}{P_{r1}} = \frac{\Delta P_2}{P_{r2}} \;\Rightarrow\; R_1 = R_2

So $R_2 = R_1 = 5\ \%$ .

Check with numbers: for, say, a 75 MW increase,

\begin{aligned} K_1 &= \frac{500}{0.05 \times 50} = 200\ \text{MW/Hz}, \quad K_2 = \frac{250}{0.05 \times 50} = 100\ \text{MW/Hz} \\ \Delta f &= -\frac{75}{300} = -0.25\ \text{Hz} \\ \Delta P_1 &= 50\ \text{MW}, \quad \Delta P_2 = 25\ \text{MW} \end{aligned}

Ratio $50:25 = 500:250$ , i.e. in proportion to capacity ✓.

Answer: The 250 MW unit must have a droop of 5 % on its own rating (the same per-unit droop as the 500 MW unit).

✓ Answer checked by Claude Opus 5.5 (high effort)

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