---
title: "Current chopping overvoltage in 132 kV breaker"
subject: "High Voltage Engineering"
chapter: 3
key: "semester_8/high_voltage_engineering:chopping-overvoltage-10a"
source: https://www.bctengineer.com/q/semester_8/high_voltage_engineering/chopping-overvoltage-10a
site: BCT Engineering
---

# Current chopping overvoltage in 132 kV breaker

High Voltage Engineering · Chapter 3: Overvoltages in Power System

- Asked in: 2068 Bhadra (old course), 6 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_8/high_voltage_engineering/chopping-overvoltage-10a
- Whole chapter: https://www.bctengineer.com/md/semester_8/high_voltage_engineering/chapter-3

## Question

In a 132 kV circuit breaker the bushing to ground capacitance is 0.01 μF and the transformer inductance succeeding the circuit breaker is 5 H. Calculate the voltage appearing across the poles of the circuit breaker if it breaks magnetizing current of 10 A flowing in the transformer.

## Short answer

The surge impedance of the transformer-bushing circuit is sqrt(L/C) = sqrt(5/10⁻⁸) = 22.36 kΩ. Chopping 10 A gives V = 10 × 22.36 kΩ = 223.6 kV across the breaker poles. The oscillation frequency is 1/(2π√(LC)) ≈ 712 Hz.

## Answer

When the breaker chops the magnetising current $i$, the energy in the transformer inductance moves to the bushing capacitance:

$$
\frac12 CV^2 = \frac12 Li^2 \;\Rightarrow\; V = i\sqrt{\frac{L}{C}}
$$

**Data:** $L = 5$ H, $C = 0.01\ \mu\text{F} = 1\times10^{-8}$ F. The current is chopped at an instantaneous value of $i = 10$ A.

#### Surge impedance of the transformer–bushing circuit

$$
\sqrt{\frac{L}{C}} = \sqrt{\frac{5}{1\times10^{-8}}} = \sqrt{5\times10^{8}} = 22\,360.7\ \Omega
$$

#### Voltage across the breaker poles

$$
\begin{aligned}
V &= 10 \times 22\,360.7 \\
&= 223\,607\ \text{V} \approx 223.6\ \text{kV}
\end{aligned}
$$

#### Frequency of oscillation

$$
f = \frac{1}{2\pi\sqrt{LC}} = \frac{1}{2\pi\sqrt{5 \times 10^{-8}}} = 711.8\ \text{Hz}
$$

For comparison, the normal peak phase voltage of a 132 kV system is $132\sqrt2/\sqrt3 = 107.8$ kV. The chopping overvoltage is therefore about 2.07 times the normal peak. This voltage appears across the open contacts and can cause restriking.

**Answer:** voltage across the breaker poles ≈ **223.6 kV** (oscillating at about 712 Hz).

## Check yourself

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

1. Chopping overvoltage is found by equating
   A. Energy in the inductance (1/2 L i^2) to energy in the bushing capacitance (1/2 C V^2)
   B. Charge in C to flux in L
   C. Power in L to power in the source
   D. Energy in the arc to V^2/Z
   Answer: A. The trapped magnetic energy moves into the capacitance. (Key point: Energy balance)

2. The voltage across the breaker poles is
   A. V = i sqrt(C/L)
   B. V = i sqrt(L/C)
   C. V = i L/C
   D. V = i/(sqrt(LC))
   Answer: B. Setting 1/2 CV^2 = 1/2 L i^2 gives V = i sqrt(L/C). (Key point: Formula)

3. For L = 5 H, C = 0.01 μF and i = 10 A, the voltage is about
   A. 22.4 kV
   B. 107.8 kV
   C. 223.6 kV
   D. 2236 kV
   Answer: C. sqrt(5/1e-8) = 22 360 Ω, times 10 A = 223.6 kV. (Key point: Numerical result)

## Related in High Voltage Engineering

- [Current chopping overvoltage at zero and peak](https://www.bctengineer.com/question.md?key=semester_8%2Fhigh_voltage_engineering%3Achopping-overvoltage-7a) — High Voltage Engineering, chapter 3
- [Overvoltage due to chopping of magnetising current](https://www.bctengineer.com/question.md?key=semester_8%2Fhigh_voltage_engineering%3Amagnetising-current-chopping) — High Voltage Engineering, chapter 3
- [Surge voltage at transformer with capacitance](https://www.bctengineer.com/question.md?key=semester_8%2Fhigh_voltage_engineering%3Atransformer-capacitance-surge-voltage) — High Voltage Engineering, chapter 3
- [Arrester current, resistance and rating on 132 kV line](https://www.bctengineer.com/question.md?key=semester_8%2Fhigh_voltage_engineering%3Aarrester-132kv-line-3000kv) — High Voltage Engineering, chapter 4

## Related in other subjects

- [Specifying breaker on 132/66 kV transformer](https://www.bctengineer.com/question.md?key=semester_6%2Fswitchgear_and_protection%3Abreaker-x-specification) — Switchgear and Protection, chapter 6
- [IDMT relays across 132/33 kV transformer (2000 A)](https://www.bctengineer.com/question.md?key=semester_6%2Fswitchgear_and_protection%3Aidmt-132-33kv-2000a) — Switchgear and Protection, chapter 7
- [IDMT relays across 132/11 kV transformer (3500 A)](https://www.bctengineer.com/question.md?key=semester_6%2Fswitchgear_and_protection%3Aidmt-132-11kv-3500a) — Switchgear and Protection, chapter 7
- [IDMT relays across 132/33 kV transformer (2700 A)](https://www.bctengineer.com/question.md?key=semester_6%2Fswitchgear_and_protection%3Aidmt-132-33kv-2700a-graph) — Switchgear and Protection, chapter 7