Influence of the residual inductance of the impulse generator for the generation of the lightning impulse voltage

This paper describes the theoretical analysis of lightning impulse voltage waveform with an overshoot or oscillation caused by the residual inductance of the impulse generator. The oscillating lightning impulse waveform is expressed by the following formula;vout (t) = A {e-α1t - e-α2t sin(ωt+θ)/sinθ}where A, α1, α2, ω, θ are constants, respectively. The front time, time to half value, peak value, oscillation frequency, overshoot voltage k-factor and virtual origin are derived from this expression. Some simulation results show the following merits;(1) The discussion on the definition of front time and tail time is possible by comparing with the base curve and overshoot.(2) The formula can analyze the effect of the residual inductance of the test circuit and express the overshot (i.e. k-factor and overshoot).(3) The formula can express the relationship between the oscillation frequency and the decay time.(4) The discussion on the meaning of base curve and waveform parameters is possible based on the theoretical analysis.