---
title: "Charging current of 60 Hz horizontal 132 kV line"
subject: "Power System Analysis I"
chapter: 4
key: "semester_4/power_system_analysis_i:horizontal-60hz-132kv-charging"
source: https://www.bctengineer.com/q/semester_4/power_system_analysis_i/horizontal-60hz-132kv-charging
site: BCT Engineering
---

# Charging current of 60 Hz horizontal 132 kV line

Power System Analysis I · Chapter 4: Line Parameter Calculations

- Asked in: 2069 Poush, 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/horizontal-60hz-132kv-charging
- Whole chapter: https://www.bctengineer.com/md/semester_4/power_system_analysis_i/chapter-4

## Question

A 60 Hz, 132 kV, 3-phase overhead line has horizontal configuration and uses conductors with radii 12 mm. The spacing between adjacent phases is 5 m. Assuming complete transposition, compute the charging current per phase and charging VAR for the line.

## Short answer

With Deq = 6.2996 m, per-phase capacitance is 8.882 nF/km. Per-phase charging current = 0.255 A/km; three-phase reactive power = 58.3 kVAR/km (19.45 kVAR/km per phase).

## Answer

For a transposed horizontal line, $D_{eq} = \sqrt[3]{D_{ab}D_{bc}D_{ca}}$ and $C_n = 2\pi\varepsilon_0/\ln(D_{eq}/r)$. Since no length is given, the results are per km.

```text
   a o-----5 m-----o b-----5 m-----o c
     |<----------- 10 m ---------->|
```

**Data:** $r = 0.012$ m, $D = 5, 5, 10$ m, 132 kV, $f = 60$ Hz.

#### Capacitance

$$
\begin{aligned}
D_{eq} &= \sqrt[3]{5 \times 5 \times 10} = 6.2996\ \text{m} \\
C_n &= \frac{55.63\times10^{-12}}{\ln(6.2996/0.012)} = \frac{55.63\times10^{-12}}{6.2633} \\
&= 8.882\times10^{-12}\ \text{F/m} = 8.882\ \text{nF/km}
\end{aligned}
$$

#### Capacitive reactance at 60 Hz

$$
X_C = \frac{1}{2\pi \times 60 \times 8.882\times10^{-9}} = 2.986\times10^5\ \Omega\text{-km}
$$

#### Charging current per phase

$$
I_c = \frac{V_p}{X_C} = \frac{132\,000/\sqrt3}{298\,645} = \frac{76\,210}{298\,645} = 0.2552\ \text{A/km}
$$

#### Charging VAR

$$
\begin{aligned}
Q_{3\phi} &= \frac{V_L^2}{X_C} = \frac{(132\times10^3)^2}{298\,645} = 58.34\ \text{kVAR/km} \\
Q_{ph} &= 58.34/3 = 19.45\ \text{kVAR/km}
\end{aligned}
$$

**Answer:** $I_c = 0.255$ A/km per phase; charging $= 58.3$ kVAR/km for the three-phase line (19.45 kVAR/km per phase).

## Check yourself

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

1. Compared with 50 Hz, the charging current at 60 Hz is:
   A. Larger by 60/50
   B. Smaller by 50/60
   C. Unchanged
   D. Larger by (60/50)^2
   Answer: A. I_c = V_p * 2 pi f C is proportional to frequency. (Key point: Frequency effect)

2. Capacitive reactance at 60 Hz is:
   A. X_C = 2*pi*60*C_n
   B. X_C = 1/(2*pi*60*C_n)
   C. X_C = 1/(2*pi*50*C_n)
   D. X_C = 60/C_n
   Answer: B. Use the given frequency in X_C = 1/(omega C). (Key point: Reactance)

3. No length is given, so results are:
   A. For 100 km
   B. For 1 m
   C. Per km
   D. For the whole line
   Answer: C. Per-km values of C, X_C and I_c are quoted. (Key point: Per unit length)

4. Three-phase charging VAR is:
   A. V_p^2 / X_C
   B. V_L / X_C
   C. V_L^2 x X_C
   D. V_L^2 / X_C
   Answer: D. Equivalent to 3 V_p I_c; 58.3 kVAR/km here. (Key point: 3-phase VAR)

## Related in Power System Analysis I

- [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
- [Inductive reactance of vertical 132 kV line](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Avertical-132kv-12mm-5m) — Power System Analysis I, chapter 4
- [330 kV quad-bundle line: inductance and charging](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Aquad-bundle-330kv-6m) — Power System Analysis I, chapter 4
- [Charging current of 132 kV line, 6 m equilateral](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Aequilateral-132kv-6m-charging) — 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
- [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

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