Transmission Lines: Parameters and Performance For students.

A transmission line is far more than a pair of wires: electrically it is described by four distributed parameters — resistance R, inductance L, capacitance C and conductance G per kilometre. Resistance comes from the conductor metal and grows with temperature and skin effect; inductance comes from the magnetic field around the conductors; capacitance comes from the electric field between conductors and earth; conductance represents tiny leakage currents through insulators and corona discharge into the air.

These parameters decide the line's performance: how much the voltage drops from sending to receiving end, how much power is lost as heat, and how much reactive power the line itself absorbs or generates. Engineers model the line with ABCD constants that relate sending-end voltage and current to receiving-end quantities, and they classify lines as short (below ~80 km), medium (80–250 km) or long (above 250 km), using a simpler model for each.

Key Concepts

• Skin effect: alternating current crowds toward the conductor surface, raising AC resistance above the DC value, especially in large conductors.
• GMD and GMR: geometric mean distance (spacing between phases) sets inductance; geometric mean radius (conductor self-geometry) refines it. Wider spacing means more inductance.
• Ferranti effect: on long, lightly loaded lines the shunt capacitance charges the line and the receiving-end voltage rises above the sending-end voltage.
• Corona: when the electric field at the conductor surface exceeds air's breakdown strength (~21.2 kV/cm), the air ionizes with a hissing glow, wasting power and creating radio noise. Bundled conductors reduce it.
• ABCD parameters: four constants with Vs = A·Vr + B·Ir and Is = C·Vr + D·Ir. For a short line, A = D = 1, B = Z, C = 0.
• Surge impedance loading (SIL): the power at which the line's inductance and capacitance exactly balance (SIL = V²/Zc); loading above SIL makes the line absorb reactive power, below it the line generates reactive power.

Formulas

• Voltage regulation: (|Vs| − |Vr|) / |Vr| × 100% for a given load, the percentage rise in receiving voltage when full load is thrown off.
• Transmission efficiency: η = Pout / Pin × 100%, where the difference is the I²R loss in the conductors.
• Series impedance per phase: Z = R + jX ohms, with X = 2πfL at 50 Hz.
• Surge impedance loading: SIL = V² / Zc megawatts, where Zc = √(L/C) is the surge impedance in ohms.

Worked Example

A 132 kV three-phase line has series impedance 5 + j15 Ω per phase and delivers 100 A at 0.9 power factor lagging. Receiving-end phase voltage is 132,000/√3 = 76,210 V. The impedance drop is I×Z = 100 × √(5² + 15²) = 1,581 V, angled so that the sending-end phase voltage works out to about 77,322 V, i.e. 133.9 kV line-to-line. Voltage regulation = (133.9 − 132)/132 × 100% ≈ 1.46%. Delivered power is √3 × 132 kV × 100 A × 0.9 ≈ 20.58 MW, losses are 3 × 100² × 5 = 0.15 MW, so efficiency is 20.58/20.73 ≈ 99.3% — typical of a short, well-loaded EHV line.

Common Misconceptions

• "Higher voltage is always better." Higher voltage cuts current and losses, but insulation, towers and switchgear get dramatically costlier — 132 kV is chosen where it fits economically, not everywhere.
• "DC resistance is enough for AC calculations." Skin effect, proximity effect and temperature all raise AC resistance, and ignoring them underestimates losses.
• "Line capacitance can be ignored." On short lines yes, but on long EHV lines the charging current and Ferranti effect dominate voltage behaviour at light load.

Real-World Applications

• Line designers choose conductor size and bundle configuration from R, L, C calculations to balance losses against corona and cost.
• System operators place shunt reactors on long lightly-loaded lines to absorb the capacitive reactive power and control the Ferranti rise.
• Relay engineers set distance-protection zones directly from the line's ohms-per-kilometre impedance.
• Utilities rate a line's thermal and stability limits from its parameters before approving new power transfers.

R, L, C and G are the DNA of every transmission line: they fix its voltage drop, its losses, its charging behaviour and its protection settings. Master the short-line model first, then add shunt capacitance for medium lines and distributed effects for long ones, and you can predict any line's performance before a single tower is built.