---
title: "Droop for capacity sharing: 500 and 250 MW"
subject: "Power Plant Equipment"
chapter: 2
key: "semester_7/power_plant_equipment:droop-capacity-sharing-500-250"
source: https://www.bctengineer.com/q/semester_7/power_plant_equipment/droop-capacity-sharing-500-250
site: BCT Engineering
---

# Droop for capacity sharing: 500 and 250 MW

Power Plant Equipment · Chapter 2: Power/Frequency Control in Hydro Generator System

- Asked in: 2070 Asar, 8 marks
- Video: [Speed Load characteristics | Two Generators rated 200MW and 400MW | Solved Problem -1 | PSOC | droop](https://www.youtube.com/watch?v=MEGzoyxTT6w) — Simple n Easy Learning
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/power_plant_equipment/droop-capacity-sharing-500-250
- Whole chapter: https://www.bctengineer.com/md/semester_7/power_plant_equipment/chapter-2

## Question

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.

## 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.

## Answer

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).

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. For the same frequency change, units share in proportion to capacity only if:
   A. Their pu droops are equal
   B. The smaller unit has half the droop
   C. The smaller unit has double the droop
   D. Their MW/Hz droops are equal
   Answer: A. Equal fractional change in output requires dP/Pr = (df/f0)/R to be equal, so R1 = R2. (Key point: Sharing condition)

2. What droop must the 250 MW unit have if the 500 MW unit has 5%?
   A. 2.5%
   B. 10%
   C. 5%
   D. 7.5%
   Answer: C. R2 = R1 = 5% on its own rating. (Key point: Required droop)

3. Why is halving the droop for the half-size unit wrong?
   A. Droop is defined in pu on each unit's own rating, so the rating is already accounted for
   B. Droop does not depend on rating at all
   C. Smaller units must always have larger droop
   D. Droop must be set in MW/Hz
   Answer: A. In pu on own rating, the capacity is already included in K = Pr/(R f0), so equal R gives sharing by capacity. (Key point: Common mistake)

## Related in Power Plant Equipment

- [Load sharing: 500 MW and 250 MW, 5%/6% droop](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_plant_equipment%3Aload-sharing-500-250-5-6) — Power Plant Equipment, chapter 2, asked 2×
- [Load sharing: 250 MW and 500 MW, 4%/3% droop](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_plant_equipment%3Aload-sharing-250-500-4-3) — Power Plant Equipment, chapter 2
- [Droop for capacity sharing: 250 and 500 MW](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_plant_equipment%3Adroop-capacity-sharing-250-500) — Power Plant Equipment, chapter 2
- [Load sharing: 250 MW and 500 MW, 20%/10% droop](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_plant_equipment%3Aload-sharing-250-500-20-10) — Power Plant Equipment, chapter 2, asked 2×
- [Load sharing: 250/500 MW, frequency falls to 49.5 Hz](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_plant_equipment%3Aload-sharing-250-500-4-2) — Power Plant Equipment, chapter 2, asked 2×
- [Load sharing: 600 MW and 300 MW, 7%/8% droop](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_plant_equipment%3Aload-sharing-600-300-7-8) — Power Plant Equipment, chapter 2, asked 2×

## Related in other subjects

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