---
title: "Load sharing among three generators"
subject: "Power Plant Equipment"
chapter: 2
key: "semester_7/power_plant_equipment:load-sharing-three-generators"
source: https://www.bctengineer.com/q/semester_7/power_plant_equipment/load-sharing-three-generators
site: BCT Engineering
---

# Load sharing among three generators

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

- Asked in: 2078 Bhadra, 5 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-three-generators
- Whole chapter: https://www.bctengineer.com/md/semester_7/power_plant_equipment/chapter-2

## Question

Three generators of 500MW, 2% drop, 250MW, 4% drop and 200MW, 3% drop are supplying to a common load. When each generator is fully loaded, they operate at common frequency of 49Hz. Calculate the system load shared by each unit when frequency increased to 50Hz.

## Short answer

Each unit's stiffness K = P_r/(R f0): G1 500, G2 125, G3 133.33 MW/Hz. With ∆f = +1 Hz, G1 loses 500 MW (to 0 MW), G2 loses 125 MW (to 125 MW), G3 loses 133.33 MW (to 66.67 MW). Total load = 191.67 MW.

## Answer

All three units are fully loaded at 49 Hz. As frequency rises to 50 Hz, each moves up its droop line and sheds load equal to its stiffness times the rise ($f_0 = 50$ Hz).

$$
K_i = \frac{P_{ri}}{R_i f_0}, \qquad \Delta P_i = -K_i\,\Delta f, \qquad \Delta f = +1\ \text{Hz}
$$

| Unit | Rating (MW) | Droop | $K_i$ (MW/Hz) | Reduction (MW) | Load at 50 Hz (MW) |
|---|---|---|---|---|---|
| G1 | 500 | 2 % | 500/(0.02×50) = 500 | 500 | 0 |
| G2 | 250 | 4 % | 250/(0.04×50) = 125 | 125 | 125 |
| G3 | 200 | 3 % | 200/(0.03×50) = 133.33 | 133.33 | 66.67 |
| Total | 950 | – | 758.33 | 758.33 | 191.67 |

**Answer:** At 50 Hz, **G1 = 0 MW** (it reaches its no-load point, $49 + 1 = 50$ Hz), **G2 = 125 MW**, **G3 = 66.67 MW**; total system load ≈ **191.67 MW**.

## Check yourself

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

1. How is each unit's load at 50 Hz found?
   A. Full load minus K x 1 Hz
   B. Full load plus K x 1 Hz
   C. Rating x droop
   D. Rating / 3
   Answer: A. Each sheds K x df with df = +1 Hz. (Key point: Method)

2. Why is G1's load 0 MW at 50 Hz?
   A. It trips
   B. Its no-load frequency is 49 + 0.02x50 = 50 Hz
   C. Its K is zero
   D. It has the highest droop
   Answer: B. Its droop line reaches zero output at exactly 50 Hz. (Key point: G1 result)

3. What are K2 and K3?
   A. 250 and 200 MW/Hz
   B. 62.5 and 66.7 MW/Hz
   C. 125 and 133.33 MW/Hz
   D. 125 and 200 MW/Hz
   Answer: C. K2 = 250/(0.04x50) = 125; K3 = 200/(0.03x50) = 133.33. (Key point: Stiffness values)

4. What is the total system load at 50 Hz?
   A. 950 MW
   B. 758.33 MW
   C. 125 MW
   D. 191.67 MW
   Answer: D. 0 + 125 + 66.67 = 191.67 MW. (Key point: Total load)

## Close variants set in other exams

- [Load sharing: 1000 MW and 500 MW units](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_plant_equipment%3Aload-sharing-1000-500) — Power Plant Equipment, chapter 2, asked 4×
- [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×

## 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: 250/500 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: 900 MW and 450 MW generators](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_plant_equipment%3Aload-sharing-900-450) — Power Plant Equipment, chapter 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: 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×
- [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

## Related in other subjects

- [Per unit circuit of three-generator system, 30 MVA base](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Apu-circuit-30mva-g1-g2-g3) — Power System Analysis I, chapter 3
- [Three-phase fully controlled bridge with R load](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_electronics%3A3ph-full-bridge-controlled-r-load) — Power Electronics, chapter 3
- [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
- [Impedance diagram: three generators, j100 and j130 Ω lines](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Aimpedance-diagram-three-gens-j100-j130) — Power System Analysis I, chapter 3