Transmission Line Parameters

An overhead line has series resistance and inductance, and shunt capacitance, spread along its length. These parameters set how much power it can carry and how its voltage behaves.

Resistance

R = ρl/A, increased by spiralling (stranding), temperature and skin effect (AC current crowds to the surface, more at high frequency and for large conductors).

Inductance

For a three-phase line with equilateral spacing D (or transposed, with D = GMD):

L = 2 × 10⁻⁷ ln(D/r′) H/m per phase, with r′ = 0.7788 r (the GMR of a solid round conductor).

• Unequal spacing: use the geometric mean distance D_m = (D_ab D_bc D_ca)^(1/3); transposition balances the phases.
• Single-phase two-wire line: loop inductance 4 × 10⁻⁷ ln(D/r′) H/m.
• Bundled conductors (two or more per phase) increase the effective GMR: for 2 conductors at spacing d, GMR = √(r′d). This lowers L, raises C, and reduces corona.

Capacitance

C = 2πε₀/ln(D/r) F/m to neutral (uses the actual radius r, not r′).

• Single-phase: line-to-line C = πε₀/ln(D/r).
• Charging current = V_ph ωC per unit length.
• Earth raises the capacitance slightly (method of images).

Corona

When the field at the conductor surface exceeds the breakdown strength of air (about 30 kV/cm peak, 21.2 kV/cm RMS), the air ionises: corona. It causes power loss, radio interference and a hissing sound. It is reduced by larger conductor diameter, bundling and greater spacing. Disruptive critical voltage V_c = m₀ g₀ δ r ln(D/r).

Sag

For a span L with conductor weight w per metre and tension T (supports at equal level):

Sag = w L²/(8T)

Ice and wind loading increase the effective weight: w_eff = √((w + w_ice)² + w_wind²).

Worked example

A three-phase line has conductors of radius 1 cm in an equilateral triangle of side 2 m.

• L = 2 × 10⁻⁷ ln(2/(0.7788 × 0.01)) = 1.11 mH/km per phase.
• C = 2π × 8.854 × 10⁻¹²/ln(2/0.01) = 10.5 nF/km to neutral.

Practice