Line parameters and effect of configuration

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 $y = G + j\omega C$.

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 %.

 Larger spacing D  -> L up,   C down
 Larger radius r   -> L down, C up,  R down
 Bundling          -> L down, C up,  corona down