--- title: "Transposition and transposition cycle layouts" subject: "Power System Analysis I" chapter: 4 key: "semester_4/power_system_analysis_i:transposition-cycle-layouts" source: https://www.bctengineer.com/q/semester_4/power_system_analysis_i/transposition-cycle-layouts site: BCT Engineering --- # Transposition and transposition cycle layouts Power System Analysis I · Chapter 4: Line Parameter Calculations - Asked in: 2071 Magh, 6 marks - 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-cycle-layouts - Whole chapter: https://www.bctengineer.com/md/semester_4/power_system_analysis_i/chapter-4 ## Question Why is transposition carried out in overhead transmission lines? Draw the schematic layout for a complete transposition cycle for 3-φ single circuit and 3-φ double circuit transmission lines. ## Short answer Transposition balances phase inductances and capacitances in unsymmetrical spacing, reducing voltage unbalance and interference. A single-circuit cycle uses three sections, each conductor rotating through all positions. A double-circuit cycle transposes both circuits similarly while maintaining phase symmetry. ## Answer **Transposition** is the exchange of the positions of the phase conductors at regular intervals along the line, so that each conductor occupies each position for an equal length. #### Why transposition is done - With unsymmetrical spacing, each phase has different flux linkages and charges, so the **inductance and capacitance of the phases are unequal**. - This causes unequal voltage drops and **unbalanced receiving-end voltages** even for a balanced load. - Transposition makes the average $L$ and $C$ of every phase equal, so the line is **balanced** and can be analysed per phase with $D_{eq} = \sqrt[3]{D_{12}D_{23}D_{31}}$. - It reduces **interference with nearby communication (telephone) lines**, because the induced voltages from the three sections cancel. - In practice transposition is done at switching stations or every few tens of km. #### Complete transposition cycle: 3-φ single circuit The line length is divided into three equal sections; each phase takes positions 1, 2 and 3 in turn. ```text Pos Sec I Sec II Sec III 1 a ------\ c ------\ b ------ 2 b ------\ a ------\ c ------ 3 c ------ b ------ a ------ |<-l/3->| |<-l/3->| |<-l/3->| ``` | Position | Section I | Section II | Section III | |---|---|---|---| | 1 | a | c | b | | 2 | b | a | c | | 3 | c | b | a | #### Complete transposition cycle: 3-φ double circuit Both circuits are transposed together, and the same pattern is kept in every section: the two middle conductors belong to the same phase, and the top conductor of each circuit is the same phase as the bottom conductor of the other (in Section I, a is opposite c', b opposite b', and c opposite a'). ```text Sec I Sec II Sec III a o o c' c o o b' b o o a' b o o b' a o o a' c o o c' c o o a' b o o c' a o o b' |<--l/3-->| |<--l/3-->| |<--l/3-->| ``` | Row | Section I | Section II | Section III | |---|---|---|---| | Top | a, c' | c, b' | b, a' | | Middle | b, b' | a, a' | c, c' | | Bottom | c, a' | b, c' | a, b' | In each section the phases shift by one position, and over the full cycle every phase of each circuit occupies every position once. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What is the main reason for transposing a line? A. To reduce corona loss B. To equalise the average L and C of all three phases C. To raise the line's voltage rating D. To reduce line resistance Answer: B. Unsymmetrical spacing gives unequal L and C; transposition makes the average equal so the line is balanced. (Key point: Purpose) 2. If an unsymmetrical line is not transposed, a balanced load produces: A. Perfectly balanced voltages B. Zero voltage drop C. Unbalanced voltage drops and unequal receiving-end voltages D. Higher frequency Answer: C. Unequal phase impedances give unbalanced drops even for a balanced load. (Key point: Effect of not transposing) 3. A complete transposition cycle for a single circuit divides the line into: A. Three equal sections, each phase taking each position once B. Two equal sections C. Three sections where phase a always stays in the top position D. Four equal sections Answer: A. Each phase occupies positions 1, 2 and 3 for l/3 each. (Key point: Cycle structure) 4. How does transposition help nearby telephone lines? A. It shields the telephone line with earth wire B. It reduces current in the line C. It increases the spacing D. Induced voltages from the three sections cancel Answer: D. Because each phase takes all positions, induced voltages in the communication line average out. 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