---
title: "Inductance of twin-bundle line, 16 mm radius"
subject: "Power System Analysis I"
chapter: 4
key: "semester_4/power_system_analysis_i:twin-bundle-150km-16mm"
source: https://www.bctengineer.com/q/semester_4/power_system_analysis_i/twin-bundle-150km-16mm
site: BCT Engineering
---

# Inductance of twin-bundle line, 16 mm radius

Power System Analysis I · Chapter 4: Line Parameter Calculations

- Asked in: 2070 Magh, 5 marks
- Video: [Power Systems | Lecture-11 | Bundled Conductors in Transmission Line](https://www.youtube.com/watch?v=uUjPXxHpJaI) — Engineering Devotion
- 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/twin-bundle-150km-16mm
- Whole chapter: https://www.bctengineer.com/md/semester_4/power_system_analysis_i/chapter-4

## Question

Compute the inductance per phase for a 150 km line using phase conductors of 16 mm radius and configured as given below. Assume complete transposition of the phases. [Figure: horizontal single-circuit line; each phase a, b, c is a two-conductor bundle with sub-conductor spacing d = 45 cm; centres of adjacent phases D = 7.5 m apart.]

## Short answer

Inductance per phase is 0.968 mH/km, giving 145.1 mH for 150 km.

## Answer

Each phase is a two-conductor bundle, so its self-GMD for inductance is $D_s = \sqrt{r'd}$. The line is transposed, so $D_m = \sqrt[3]{D_{ab}D_{bc}D_{ca}}$.

```text
   o--o         o--o         o--o
    a    7.5 m   b    7.5 m   c
   d = 45 cm, r = 16 mm
```

**Data:** $r = 0.016$ m, $r' = 0.7788 \times 0.016 = 0.012461$ m, $d = 0.45$ m, $D = 7.5, 7.5, 15$ m, 150 km.

#### Mutual GMD

$$
D_m = \sqrt[3]{7.5 \times 7.5 \times 15} = 9.4494\ \text{m}
$$

#### Self GMD of bundle

$$
D_s = \sqrt{0.012461 \times 0.45} = 0.074882\ \text{m}
$$

#### Inductance

$$
\begin{aligned}
L &= 2\times10^{-7}\ln\frac{9.4494}{0.074882} = 2\times10^{-7}\times4.8378 \\
&= 9.676\times10^{-7}\ \text{H/m} = 0.9676\ \text{mH/km} \\
L_{150} &= 0.9676 \times 150 = 145.13\ \text{mH}
\end{aligned}
$$

**Answer:** $L = 145.1$ mH per phase for 150 km (0.968 mH/km).

## Check yourself

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

1. For a two-conductor bundle, the self-GMD for inductance is:
   A. sqrt(r d)
   B. r' d
   C. sqrt(r' d)
   D. sqrt(r' d^2)
   Answer: C. Two sub-conductors give a 4th root of (r')^2 d^2, i.e. sqrt(r' d), with r' = 0.7788r for inductance. (Key point: Twin bundle GMR)

2. For a horizontal line with 7.5 m between adjacent phases, D_m is:
   A. cube root of (7.5 x 7.5 x 15) = 9.45 m
   B. 7.5 m
   C. 11.25 m
   D. 15 m
   Answer: A. Outer phases are 15 m apart; D_m is the geometric mean of 7.5, 7.5, 15. (Key point: Mutual GMD)

3. Compared with a single conductor of the same radius, bundling gives:
   A. A smaller GMR and higher inductance
   B. A larger GMR and hence lower inductance
   C. No change in inductance
   D. Higher inductance and lower capacitance
   Answer: B. Sub-conductors spaced apart raise the effective GMR, so ln(D_m/D_s) and L fall. (Key point: Effect of bundling)

## Close variants set in other exams

- [L and C of triple-bundle line, D=8 m](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Atriple-bundle-18mm-45cm-8m) — Power System Analysis I, chapter 4, asked 2×
- [Inductance of 4-conductor bundle line, 6 m spacing](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Aquad-bundle-200km-12mm-6m) — Power System Analysis I, chapter 4, asked 2×

## Related in Power System Analysis I

- [Inductance and capacitance of 4-conductor bundle line](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Aquad-bundle-220kv-l-c) — Power System Analysis I, chapter 4
- [Inductance of composite-conductor single-phase line](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Asingle-phase-composite-conductors) — Power System Analysis I, chapter 4
- [400 kV twin-bundle line: reactances and charging VAR](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Atwin-bundle-400kv-reactances) — Power System Analysis I, chapter 4, asked 2×
- [Capacitive reactance and charging of 2-conductor bundle line](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Abundle-capacitance-9mm-40cm-10m) — Power System Analysis I, chapter 4, asked 2×
- [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
- [Inductance of 3-conductor bundled line, 6.1 m spacing](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Ainductance-three-subconductor-bundle-6-1m) — Power System Analysis I, chapter 4

## Related in other subjects

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- [Conductor selection, 100 MW 70 km 132 kV](https://www.bctengineer.com/question.md?key=semester_8%2Ftransmission_and_distribution_system_design%3Aconductor-selection-100mw-70km-132kv) — Transmission and Distribution System Design, chapter 4