On the correction of the transient ground resistance at early times in lightning surge propagation studies

The impact of the ground losses on transient surges that propagate along transmission lines is taken into consideration in the telegrapher’s equations through the so-called transient ground resistance function ξ’g(t), for which numerous ex-pressions exist. The transient ground resistance appears in a convolution integral in the time domain telegrapher’s equa-tions. The transient ground resistance features a very fast variation over the first nanosecond or so, requiring the selec-tion of a subnanosecond time discretization in a direct time-domain solution, which might result in prohibitive compu-tation times. A practical solution is introduced which allows to use typical discretization times Δt for the analysis of lightning transients, namely in the order of hundreds of nanoseconds. The proposed approach uses equivalent integrals of the original ξ’g(t) function and its trapezoidal approximation for the first time segment from t = 0 to t = Δt, to ap-propriately adjust the value of ξ’g(t) at t = 0. The efficiency of the proposed approach is demonstrated considering the case of a buried insulated cable illuminated by lightning. The field-to-transmission line equations are solved using FDTD. The proposed method can straightforwardly be applied to overhead lines and to other EMP sources of disturb-ances.