---
title: "Load sharing: 1000 MW and 500 MW units"
subject: "Power Plant Equipment"
chapter: 2
key: "semester_7/power_plant_equipment:load-sharing-1000-500"
source: https://www.bctengineer.com/q/semester_7/power_plant_equipment/load-sharing-1000-500
site: BCT Engineering
---

# Load sharing: 1000 MW and 500 MW units

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

- Asked in: 2079 Baisakh, 6 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/power_plant_equipment/load-sharing-1000-500
- Whole chapter: https://www.bctengineer.com/md/semester_7/power_plant_equipment/chapter-2

## Question

Two generators of 1000 MW, 2% and 500 MW, 4% are supplying to a common load. When each generator is fully loaded, they operate at common frequency of 49.5 Hz. Calculate the system load shared by each unit when frequency increased to 50 Hz.

## Short answer

Stiffness: G1 1000 MW/Hz, G2 250 MW/Hz. Frequency rise 0.5 Hz causes G1 to drop 500 MW to 500 MW, G2 to drop 125 MW to 375 MW. At 50 Hz, system load is 875 MW.

## Answer

When frequency rises, both units move up their droop lines and reduce output in proportion to $P_r/R$. Rated frequency is taken as $f_0 = 50$ Hz.

**Method:** a unit with droop $R$ (pu on its own rating $P_r$) and rated frequency $f_0$ changes its output by
$$
\Delta P = -\frac{P_r}{R\,f_0}\,\Delta f = -K\,\Delta f
$$
where $K = P_r/(R f_0)$ is its stiffness in MW/Hz. All units run at the same frequency, so $\Delta P_L = -\Delta f \sum K$.

**Data:** G1: 1000 MW, 2 %; G2: 500 MW, 4 %; fully loaded at 49.5 Hz; frequency rises to 50 Hz, so $\Delta f = +0.5$ Hz.

$$
\begin{aligned}
K_1 &= \frac{1000}{0.02 \times 50} = 1000\ \text{MW/Hz} \\
K_2 &= \frac{500}{0.04 \times 50} = 250\ \text{MW/Hz} \\
\Delta P_1 &= -1000 \times 0.5 = -500\ \text{MW} \\
\Delta P_2 &= -250 \times 0.5 = -125\ \text{MW}
\end{aligned}
$$

| Unit | At 49.5 Hz (MW) | Change (MW) | At 50 Hz (MW) |
|---|---|---|---|
| G1 | 1000 | −500 | 500 |
| G2 | 500 | −125 | 375 |
| Total | 1500 | −625 | 875 |

**Answer:** At 50 Hz, **G1 supplies 500 MW and G2 supplies 375 MW**; the system load is **875 MW** (a reduction of 625 MW).

## Check yourself

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

1. When frequency rises from 49.5 to 50 Hz, what do the units do?
   A. Reduce output along their droop lines
   B. Increase output
   C. Stay unchanged
   D. One rises, one falls
   Answer: A. Rising frequency means falling load on a droop characteristic. (Key point: Direction)

2. What are K1 and K2?
   A. 500 and 125 MW/Hz
   B. 1000 and 250 MW/Hz
   C. 1000 and 500 MW/Hz
   D. 2000 and 500 MW/Hz
   Answer: B. K1 = 1000/(0.02x50) = 1000; K2 = 500/(0.04x50) = 250. (Key point: Stiffness)

3. How much does each unit shed for df = 0.5 Hz?
   A. 1000 MW and 250 MW
   B. 250 MW and 62.5 MW
   C. 500 MW and 125 MW
   D. 500 MW and 250 MW
   Answer: C. dP = K x 0.5. (Key point: Reduction)

4. What are the loads at 50 Hz and the system load?
   A. G1 500, G2 125, total 625 MW
   B. G1 1000, G2 500, total 1500 MW
   C. G1 500, G2 375, total 1500 MW
   D. G1 500, G2 375, total 875 MW
   Answer: D. 1000 - 500 = 500; 500 - 125 = 375; total 875 MW. (Key point: Final result)

## Close variants set in other exams

- [Load sharing: 600 and 300 MW at 49 Hz](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_plant_equipment%3Aload-sharing-600-300-49hz) — Power Plant Equipment, chapter 2, asked 4×
- [Load sharing among three generators](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_plant_equipment%3Aload-sharing-three-generators) — Power Plant Equipment, chapter 2, asked 3×
- [Load reduction: 500 MW and 250 MW units](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_plant_equipment%3Aload-reduction-500-250) — Power Plant Equipment, chapter 2, asked 3×

## Related in Power Plant Equipment

- [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 decrease: 250 and 500 MW at 49 Hz](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_plant_equipment%3Aload-decrease-250-500-49hz) — Power Plant Equipment, chapter 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
- [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: 600 and 300 MW, 51 Hz no-load](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_plant_equipment%3Aload-sharing-600-300-51hz) — 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×

## Related in other subjects

- [Load sharing between two stations in parallel](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machines_ii%3Aload-sharing-two-stations) — Electric Machines II, chapter 1