--- title: "Line parameters and effect of configuration" subject: "Power System Analysis I" chapter: 4 key: "semester_4/power_system_analysis_i:line-parameters-configuration" source: https://www.bctengineer.com/q/semester_4/power_system_analysis_i/line-parameters-configuration site: BCT Engineering --- # Line parameters and effect of configuration Power System Analysis I · Chapter 4: Line Parameter Calculations - Asked in: 2075 Bhadra, 6 marks; 2071 Bhadra, 6 marks (asked 2 times) - 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/line-parameters-configuration - Whole chapter: https://www.bctengineer.com/md/semester_4/power_system_analysis_i/chapter-4 ## Question What are the line parameters? Also show how these parameters are affected by the line configurations. ## Short answer Line parameters: series R, L and shunt C, G per unit length. Configuration effects: larger phase spacing increases L, decreases C; larger conductor radius reduces R and L, increases C; bundled conductors lower L, raise C, reduce corona; transposition balances per-phase parameters. ## Answer The **line parameters** are the four distributed constants that set the electrical behaviour of a transmission line: series **resistance R** and **inductance L**, and shunt **capacitance C** and **conductance G**. All are given per unit length. R and L form the series impedance $z = R + j\omega L$; G and C form the shunt admittance $y = G + j\omega C$. | Parameter | Cause | Typical formula (per phase) | |---|---|---| | R | Resistivity of conductor | $R = \rho l/A$ (higher for AC due to skin effect) | | L | Magnetic flux linkage | $L = 2\times10^{-7}\ln\frac{D_m}{D_s}$ H/m | | C | Electric field between conductors | $C = \frac{2\pi\varepsilon_0}{\ln(D_m/r)}$ F/m to neutral | | G | Leakage over insulators and corona | Usually neglected | #### Effect of line configuration 1. **Spacing between phases ($D_m$, GMD).** L and C depend on $\ln(D_m)$. A larger spacing increases L and decreases C. Higher-voltage lines need larger clearances, so they have more L and less C per km. 2. **Arrangement (equilateral, horizontal, vertical).** With unsymmetrical spacing, each phase has different L and C. Transposition is used, and the equivalent spacing $D_{eq} = \sqrt[3]{D_{ab}D_{bc}D_{ca}}$ replaces D. For example, horizontal spacing D gives $D_{eq} = 1.26D$. 3. **Conductor size and type ($D_s$, GMR).** A larger radius gives a larger GMR, so lower L and higher C. Stranded conductors use the GMR of the strands; for a solid conductor $D_s = r' = 0.7788r$. Larger cross-section also lowers R. 4. **Bundled conductors.** Using 2, 3 or 4 sub-conductors per phase raises the self-GMD: $D_s^b = \sqrt{D_sd}$, $\sqrt[3]{D_sd^2}$, $1.09\sqrt[4]{D_sd^3}$. This lowers L (and reactance) and raises C, which increases the surge-impedance loading. It also reduces corona loss. 5. **Double-circuit lines.** Parallel conductors of the same phase act like a bundle. Proper placement (for example the hexagonal arrangement a-b-c / c'-b'-a') gives a high $D_s$ and low L for each phase. 6. **Height above ground.** Earth acts like image conductors. It slightly increases C, and has a negligible effect on L for balanced operation. 7. **Stranding and spiralling.** Spiralled strands are slightly longer than the line, which raises R by about 1–2 %. ```text Larger spacing D -> L up, C down Larger radius r -> L down, C up, R down Bundling -> L down, C up, corona down ``` ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Which are the four line parameters? A. Resistance, inductance, capacitance, conductance B. Voltage, current, power, frequency C. Resistance, reactance, impedance, admittance D. Inductance, capacitance, corona, skin effect Answer: A. R and L are series; C and G are shunt, all per unit length. (Key point: Four parameters) 2. What happens to L and C when phase spacing is increased? A. L increases, C decreases B. L decreases, C increases C. Both increase D. Both decrease Answer: A. L depends on ln(Dm/Ds) and C on 1/ln(Dm/r), so larger spacing raises L and lowers C. (Key point: Effect of spacing) 3. How does a larger conductor radius affect parameters? A. Higher L, lower C, higher R B. Lower L, higher C, lower R C. Lower L, lower C, higher R D. No effect on any parameter Answer: B. Larger radius means larger GMR (lower L), higher C, and larger area (lower R). (Key point: Conductor size) 4. What does bundling conductors do? A. Raises L and lowers C B. Raises Ds, lowers L, raises C, and reduces corona C. Raises R only D. Has no effect on inductance Answer: B. Bundling increases the self-GMD, lowering L and raising C, and also reduces corona loss. 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