---
title: "Charging current of 132 kV line, 6 m equilateral"
subject: "Power System Analysis I"
chapter: 4
key: "semester_4/power_system_analysis_i:equilateral-132kv-6m-charging"
source: https://www.bctengineer.com/q/semester_4/power_system_analysis_i/equilateral-132kv-6m-charging
site: BCT Engineering
---

# Charging current of 132 kV line, 6 m equilateral

Power System Analysis I · Chapter 4: Line Parameter Calculations

- Asked in: 2070 Bhadra, 6 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/power_system_analysis_i/equilateral-132kv-6m-charging
- Whole chapter: https://www.bctengineer.com/md/semester_4/power_system_analysis_i/chapter-4

## Question

Determine the charging capacitance and charging current per phase in a 50 Hz, 132 kV, 3-phase overhead line spaced at 6 m from each other and using 18 mm radius conductors per phase.

## Short answer

Capacitance per phase is 9.577 nF/km. Charging current per phase is 0.229 A/km.

## Answer

For equilateral spacing, the capacitance per phase to neutral is $C_n = 2\pi\varepsilon_0/\ln(D/r)$.

**Data:** $D = 6$ m, $r = 18$ mm $= 0.018$ m, 132 kV, 50 Hz.

#### Capacitance per phase

$$
\begin{aligned}
C_n &= \frac{2\pi \times 8.854\times10^{-12}}{\ln(6/0.018)} = \frac{55.63\times10^{-12}}{5.8091} \\
&= 9.577\times10^{-12}\ \text{F/m} = 9.577\ \text{nF/km}
\end{aligned}
$$

#### Charging current per phase

$$
\begin{aligned}
X_C &= \frac{1}{2\pi f C_n} = \frac{1}{2\pi \times 50 \times 9.577\times10^{-9}} = 3.324\times10^5\ \Omega\text{-km} \\
V_p &= \frac{132\,000}{\sqrt3} = 76\,210\ \text{V} \\
I_c &= \frac{V_p}{X_C} = \frac{76\,210}{332\,386} = 0.2293\ \text{A/km}
\end{aligned}
$$

(The charging reactive power for all 3 phases is $V_L^2/X_C = 52.4$ kVAR/km.)

**Answer:** $C_n = 9.577$ nF/km (0.00958 µF/km) per phase; $I_c = 0.229$ A/km per phase.

## Check yourself

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

1. For equilateral spacing D, capacitance to neutral per phase is:
   A. 2*pi*eps0 / ln(D/r')
   B. 2*pi*eps0 / ln(D/r)
   C. pi*eps0 / ln(D/r)
   D. 2*pi*eps0 / ln(r/D)
   Answer: B. Equilateral spacing gives D_eq = D and the actual radius r is used. (Key point: Capacitance formula)

2. The phase voltage used for charging current in a 132 kV line is:
   A. 132 000/sqrt3 = 76.2 kV
   B. 132 kV
   C. 132 000 x sqrt3
   D. 132 000/3
   Answer: A. Charging current per phase to neutral uses line voltage divided by sqrt3. (Key point: Phase voltage)

3. How is the charging current per phase found?
   A. I_c = V_L / X_C
   B. I_c = V_p x X_C
   C. I_c = V_p / X_C = V_p x 2*pi*f*C_n
   D. I_c = V_p / (2*pi*f*C_n)
   Answer: C. Charging current flows through the capacitive reactance X_C = 1/(2 pi f C_n) at phase voltage. (Key point: Charging current)

## Related in Power System Analysis I

- [Charging current of 60 Hz horizontal 132 kV line](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Ahorizontal-60hz-132kv-charging) — Power System Analysis I, chapter 4
- [Charging VAR of 132 kV equilateral line](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Acharging-var-132kv-6m-1-1cm) — Power System Analysis I, chapter 4
- [132 kV triangular line: L, C, charging MVAR](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Atriangular-132kv-18mm-parameters) — Power System Analysis I, chapter 4
- [ACSR 132 kV line: parameters and charging MVA](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Aacsr-132kv-8m-parameters-charging) — Power System Analysis I, chapter 4
- [132 kV horizontal line: susceptance and charging](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Ahorizontal-132kv-4-5m-susceptance) — Power System Analysis I, chapter 4
- [Capacitance of double circuit line, 6 mm radius](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Adouble-circuit-capacitance-6mm) — Power System Analysis I, chapter 4

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