---
title: "Load sharing: 600 MVA and 500 MVA, 4%/6% droop"
subject: "Power Plant Equipment"
chapter: 2
key: "semester_7/power_plant_equipment:load-sharing-600-500mva-4-6"
source: https://www.bctengineer.com/q/semester_7/power_plant_equipment/load-sharing-600-500mva-4-6
site: BCT Engineering
---

# Load sharing: 600 MVA and 500 MVA, 4%/6% droop

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

- Asked in: 2080 Bhadra, 10 marks; 2076 Chaitra, 5 marks (asked 2 times)
- 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-600-500mva-4-6
- Whole chapter: https://www.bctengineer.com/md/semester_7/power_plant_equipment/chapter-2

## Question

Two generating units has following rating and droop characteristics: Unit – 1: 600 MVA, R1 = 4%; Unit – 2: 500 MVA, R2 = 6%. These two units are operating in parallel and sharing a total load of 900 MW at nominal frequency of 60 Hz. Unit – 1 supplies 500 MW and unit – 2 supplies 400 MW. If the load increases by 90 MW, calculate the new frequency and new generation of each generator.

## Short answer

Compute stiffness: K1 = 250 MW/Hz, K2 = 138.89 MW/Hz. Frequency drops by 90/388.89 = 0.231 Hz to 59.77 Hz. Unit 1 output rises to 557.86 MW, Unit 2 to 432.14 MW.

## Answer

Both units share the load increase in proportion to $P_r/R$, and the frequency falls to a common new value.

**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:** Unit 1: 600 MVA, $R_1 = 0.04$; Unit 2: 500 MVA, $R_2 = 0.06$; $f_0 = 60$ Hz. Initial: $P_1 = 500$ MW, $P_2 = 400$ MW. $\Delta P_L = 90$ MW. (MVA ratings are used as the MW base, i.e. unity power factor rating.)

**Stiffness:**
$$
\begin{aligned}
K_1 &= \frac{600}{0.04 \times 60} = 250\ \text{MW/Hz} \\
K_2 &= \frac{500}{0.06 \times 60} = 138.89\ \text{MW/Hz} \\
K_1 + K_2 &= 388.89\ \text{MW/Hz}
\end{aligned}
$$

**New frequency:**
$$
\begin{aligned}
\Delta f &= -\frac{90}{388.89} = -0.2314\ \text{Hz} \\
f_{new} &= 60 - 0.2314 = 59.769\ \text{Hz}
\end{aligned}
$$
(In per unit, $\Delta f = -0.003857$ pu.)

**New generation:**
$$
\begin{aligned}
\Delta P_1 &= 250 \times 0.2314 = 57.86\ \text{MW} \\
\Delta P_2 &= 138.89 \times 0.2314 = 32.14\ \text{MW}
\end{aligned}
$$

| Unit | Rating | Droop | Initial (MW) | Increase (MW) | New (MW) |
|---|---|---|---|---|---|
| 1 | 600 MVA | 4 % | 500 | 57.86 | 557.86 |
| 2 | 500 MVA | 6 % | 400 | 32.14 | 432.14 |

Check: $57.86 + 32.14 = 90$ MW.

**Answer:** New frequency ≈ **59.77 Hz** (drop of 0.231 Hz); unit 1 generates **557.86 MW** and unit 2 generates **432.14 MW**.

## Check yourself

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

1. What are K1 and K2 (MW/Hz) for 600 MVA at 4% and 500 MVA at 6% on a 60 Hz system?
   A. 250 and 138.89
   B. 150 and 83.33
   C. 250 and 83.33
   D. 15 and 8.33
   Answer: A. K1 = 600/(0.04x60) = 250; K2 = 500/(0.06x60) = 138.89 MW/Hz. (Key point: Stiffness)

2. What is the new frequency after a 90 MW load increase?
   A. 59.38 Hz
   B. 59.77 Hz
   C. 60.23 Hz
   D. 59.50 Hz
   Answer: B. df = -90/388.89 = -0.2314 Hz, so f = 59.769 Hz. (Key point: New frequency)

3. Are the initial loads (500 MW and 400 MW) needed to find the load increase on each unit?
   A. Yes, the shares depend on initial loading
   B. Yes, the larger initial load takes a larger share
   C. No, dP depends only on stiffness and df; initial loads just get added
   D. No, because the units share equally
   Answer: C. dPi = Ki x |df|, independent of initial load; the new output is initial plus dPi. (Key point: Initial loading use)

4. What are the new generations of unit 1 and unit 2?
   A. 550 MW and 440 MW
   B. 545 MW and 445 MW
   C. 590 MW and 400 MW
   D. 557.86 MW and 432.14 MW
   Answer: D. dP1 = 250x0.2314 = 57.86, dP2 = 32.14; so 557.86 and 432.14 MW. (Key point: New generation)

## Related in Power Plant Equipment

- [Load sharing: 600 MVA (6%) and 500 MVA (4%)](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_plant_equipment%3Aload-sharing-600-500mva-6-4) — 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: 600 and 500 MVA, 900 MVA load](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_plant_equipment%3Aload-sharing-600-500mva-to-100) — 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: 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×
- [Droop for capacity sharing: 500 and 250 MW](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_plant_equipment%3Adroop-capacity-sharing-500-250) — Power Plant Equipment, chapter 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
- [Parallel transformers and per-unit impedance load sharing](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Aparallel-operation-per-unit-impedance) — Electrical Machines I, chapter 2
- [Load sharing of two transformers in parallel](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Aparallel-transformers-load-sharing) — Electrical Machines, chapter 2
- [IDMT grading: R1, R2 with 1000/5 CTs](https://www.bctengineer.com/question.md?key=semester_6%2Fswitchgear_and_protection%3Aidmt-r1-r2-1000-5) — Switchgear and Protection, chapter 7, asked 2×