---
title: "What transposition is and why it is needed"
subject: "Power System Analysis I"
chapter: 4
key: "semester_4/power_system_analysis_i:transposition-what-why"
source: https://www.bctengineer.com/q/semester_4/power_system_analysis_i/transposition-what-why
site: BCT Engineering
---

# What transposition is and why it is needed

Power System Analysis I · Chapter 4: Line Parameter Calculations

- Asked in: 2081 Chaitra (new course), 3+3 marks; 2068 Bhadra, 4 marks (asked 2 times)
- Video: [Transposition of Transmission Line | Why it's done & How it balances the system](https://www.youtube.com/watch?v=qcYC50ZyqTM) — Electrology
- 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/transposition-what-why
- Whole chapter: https://www.bctengineer.com/md/semester_4/power_system_analysis_i/chapter-4

## Question

What is transposition in a three phase transmission line? Why is it required for these lines?

## Short answer

Transposition is the periodic exchange of phase conductor positions so each phase occupies every position for one-third of the length. It equalizes per-phase inductance and capacitance using geometric mean distance, eliminates unbalanced voltage drops, and reduces interference with communication lines.

## Answer

#### What transposition is
**Transposition** is the regular exchange of the positions of the three phase conductors along a line. Each phase occupies each of the three positions for **one-third of the length** of a complete transposition cycle. The exchange is done at special transposition towers.

```text
   Section 1    Section 2    Section 3
 pos1  a ---------- c ---------- b
 pos2  b ---------- a ---------- c
 pos3  c ---------- b ---------- a
      |<- l/3 ->|<- l/3 ->|<- l/3 ->|
```

#### Why it is required
1. **Equal inductance and capacitance per phase.** With unsymmetrical spacing (for example horizontal or vertical arrangement), each phase sees different distances to the other two. So each phase has a different flux linkage, inductance and capacitance. Transposition gives every phase the same average spacing, $D_{eq} = \sqrt[3]{D_{ab}D_{bc}D_{ca}}$, and so equal parameters:
$$
L = 2\times10^{-7}\ln\frac{D_{eq}}{r'}\ \text{H/m per phase}
$$
2. **Balanced voltage drops.** With unequal reactances, a balanced load current produces unequal drops, and the receiving-end voltages become unbalanced. Transposition keeps the receiving end balanced.
3. **No complex (imaginary) inductance terms.** Without transposition the flux-linkage equations contain $a$-operator terms. These make power transfer between phases appear, and the per-phase model fails. Transposition removes them, so the line can be treated as balanced and analysed per phase.
4. **Reduced interference with communication lines.** The induced voltages from the three phases cancel over a cycle. This reduces electromagnetic and electrostatic interference with nearby telephone and communication circuits.
5. **Reduced unbalance in charging currents and neutral (ground) currents.**

In practice, lines are transposed at switching stations or every few tens of kilometres. Even when a line is not physically transposed, it is usually *calculated* as transposed, because the error is small.

## Check yourself

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

1. What does transposition of a three-phase line mean?
   A. Swapping the line voltage between phases
   B. Each phase conductor occupying each position for one-third of the cycle length
   C. Increasing spacing between phases along the line
   D. Grounding one phase periodically
   Answer: B. Conductors are rotated in position so each phase spends one-third of the length in each of the three positions. (Key point: Definition)

2. What does transposition achieve for unsymmetrically spaced lines?
   A. It reduces resistance of each phase
   B. It gives each phase the same average spacing D_eq, hence equal L and C
   C. It eliminates corona
   D. It increases the line voltage
   Answer: B. With D_eq = cube root of Dab Dbc Dca for all phases, inductance and capacitance become equal. (Key point: Equal parameters)

3. Without transposition, a balanced load current on an unsymmetrical line causes what?
   A. Equal drops in all phases
   B. Unequal voltage drops and unbalanced receiving-end voltages
   C. Zero voltage drop
   D. Only a change in frequency
   Answer: B. Unequal reactances give unequal drops, so receiving-end voltages become unbalanced. (Key point: Balanced voltage drop)

## Related in Power System Analysis I

- [Transposition; single-phase capacitance with earth](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Atransposition-single-phase-earth-capacitance) — Power System Analysis I, chapter 4
- [Transposition and inductance of transposed line](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Atransposition-inductance-derivation) — Power System Analysis I, chapter 4, asked 2×
- [SLD with voltage levels and why three-phase](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Asld-voltage-levels-three-phase) — Power System Analysis I, chapter 1
- [Skin effect in transmission lines](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Askin-effect-brief) — Power System Analysis I, chapter 4
- [Transposition and transposition cycle layouts](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Atransposition-cycle-layouts) — 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

## Related in other subjects

- [Distortionless line and telephone lines](https://www.bctengineer.com/question.md?key=semester_3%2Felectromagnetism%3Adistortionless-line-telephone) — Electromagnetism, chapter 5
- [Band applications and microwave transmission lines](https://www.bctengineer.com/question.md?key=semester_7%2Frf_and_microwave_engineering%3Aband-applications-transmission-lines) — RF and Microwave Engineering, chapter 1
- [Waveguide vs transmission line](https://www.bctengineer.com/question.md?key=semester_3%2Felectromagnetism%3Awaveguide-advantages-over-transmission-line) — Electromagnetism, chapter 6, asked 3×
- [Three-phase full converter at 50% of maximum output](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_electronics%3Athree-phase-full-converter-50-percent) — Power Electronics, chapter 3