Fast and accurate evaluation of the underground lightning electromagnetic field

Underground cables and devices may be very sensible to underground lightning electromagnetic field, especially if connected to power electronic systems. The underground lightning electromagnetic field can be analytically expressed in terms of Sommerfeld integrals, whose rigorous calculation requires a valuable computational effort. Approximate expressions and numerical approaches have been proposed to quickly evaluate such integrals. In this paper, we present an efficient procedure for the numerical evaluation of these integrals. The proposed method, originally developed in a form suitable for the evaluation of the Green function for layered media, is here developed for underground lightning electromagnetic field calculation. The method is essentially based on the analytical extraction of asymptotic part of the integrals and on a rational fitting of the remaining part, using a total least square algorithm. The method allows a fast evaluation of the underground lightning electromagnetic field in time domain, since hundreds of frequency samples can be computed per second. Finally, since the distance can be factorized in the fitting procedure, the method is also highly effective in the evaluation of the coupling between the lightning electromagnetic field and buried cables.