Transients and insulation
Lightning-induced overvoltage on a line (Rusck, simplified)
- where
- maximum induced voltage (kV)
- Rusck impedance constant, (1/4π)√(µ0/ε0) = 30 Ω
- peak return-stroke current (kA)
- conductor height (m)
- distance from strike to line (m)
- return-stroke velocity / speed of light
Explain this equation
Gives the peak voltage induced on an overhead line by lightning striking the ground nearby, using Rusck’s simplified formula. Use it to judge whether nearby strikes can flash over 11–33 kV insulation.
I_0 is the peak return-stroke current, h the conductor height and y the closest distance from the strike to the line. Z_0 = 30 Ω is a constant from free-space impedance, (1/4π)√(µ0/ε0). β is the return-stroke speed as a fraction of light speed; the bracket corrects for it.
The rising return-stroke current creates a changing electromagnetic field that couples to the line; the induced voltage scales with the current and the height of the line, and falls off with distance. The β term comes from integrating that field along an infinite line.
Sense check: with β = 0.4 the coefficient is about 38.8 Ω. A 30 kA strike 100 m from a 10 m high line induces about 116 kV, enough to flash an 11 kV pin insulator but not a 132 kV string.
Watch out: strikes closer than the attractive distance hit the line directly; this formula then does not apply.
Peak voltage induced on an overhead line by a nearby lightning strike to ground, using Rusck’s simplified formula as adopted in IEEE Std 1410.
Enter your values to see the result.
Good to know
Z0 = 30 Ω is Rusck’s constant (μ0c/4π). With β = 0.4 (return stroke at 1.2 × 10⁸ m/s) the coefficient is about 38.8 Ω, so Vmax ≈ 38.8 I0 h / y. Induced surges usually stay below about 300 kV, so they mainly threaten 11–33 kV lines with CFO below that; transmission lines are not usually at risk from induced voltages. Earth wires and nearby neutral conductors reduce the induced voltage.
Common mistake
Applying the formula to strikes that would attach to the line itself; within the electrogeometric attractive distance the stroke is direct, not induced.
Limits
Rusck’s simplified expression: step current wave, infinitely long single conductor, perfectly conducting ground, no shielding by nearby objects. Lossy ground (Darveniza correction), current front time, line terminations and flashover rate (IEEE 1410 method) are not included. Backflashover is not covered.
Sources
- Rusck, S. Induced lightning over-voltages on power-transmission lines with special reference to the over-voltage protection of low-voltage networks. Trans. Royal Inst. Technology, Stockholm, No. 120 (1958)
- IEEE Std 1410-2010 Guide for Improving the Lightning Performance of Electric Power Overhead Distribution Lines
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.