Overhead lines
Surge impedance and propagation velocity
- where
- surge impedance (Ω)
- series inductance per phase (mH/km)
- capacitance to neutral per phase (nF/km)
- propagation velocity (km/s; shown as m/µs)
Explain this equation
Gives the surge (characteristic) impedance of a lossless line and the speed at which voltage and current waves travel along it. These are the starting data for switching and lightning surge studies and for surge impedance loading.
L and C are the per-kilometre inductance and capacitance per phase. A travelling wave must magnetise the inductance and charge the capacitance as it moves, so the ratio of voltage to current in the wave is √(L/C), independent of length. The 10⁻³ and 10⁻⁹ convert mH and nF to H and F.
v = 1/√(LC) because the wave front advances as fast as each metre of line can be charged through the next metre of inductance. For an overhead line in air, LC is close to µ0ε0, so v is close to the speed of light.
Sense check: overhead lines give 300–450 Ω and about 290–300 m/µs; cables 20–60 Ω and about 150–200 m/µs. A velocity above 300 m/µs means the L or C entered is wrong.
Watch out: losses are neglected, which is right for fast surges but not for power-frequency long-line calculations.
Lossless characteristic (surge) impedance and travelling-wave velocity of a line or cable from its per-unit-length inductance and capacitance.
Enter your values to see the result.
Good to know
Overhead lines give roughly 300–450 Ω and close to the speed of light (≈ 290–300 m/µs). Cables give 20–60 Ω and about half that velocity. Use L and C from the line-inductance and line-capacitance calculators or from the cable data sheet.
Common mistake
Taking Zc from √(L/C) using total line values in one and per-km values in the other; both must be per unit length.
Limits
Lossless line (R and G neglected), so this is the surge impedance used for travelling waves and SIL, not the full characteristic impedance √(z/y) at power frequency.
Sources
- Grainger, J.J. & Stevenson, W.D. Power System Analysis (McGraw-Hill), chapters 4–6: inductance, capacitance and current-voltage relations of a transmission line
- Glover, J.D., Overbye, T.J. & Sarma, M.S. Power System Analysis and Design (Cengage), chapters 4–5: transmission line parameters and steady-state operation
- Naidu, M.S. & Kamaraju, V. High Voltage Engineering (McGraw-Hill Education)
For competent high-voltage engineers. Results are calculations from the published methods shown and depend entirely on the data you enter. They are not a substitute for a system study, manufacturer data, the applicable standards and Engineering Recommendations, or your organisation’s safety rules. Never use a result to justify working on or near live HV equipment.