Lightning return stroke current radiation in presence of a conducting ground – Part I: theory and numerical evaluation of the electromagnetic fields

摘要

The general theory describing the electromagnetic field radiated by a lightning strokeover a conducting ground is presented in this paper. The derivation of the Green functionsnecessary to solve the problem is discussed in detail, and the determination of theexpressions for the electromagnetic field components is carried out in a form thatminimizes the final computational costs. A method for the numerical evaluation of theelectromagnetic field is then proposed, and it is shown that it can be used starting from any‘‘engineering model’’ representation for the lightning current distribution along thechannel. Such method is based on a new efficient evaluation of the so-called Sommerfeld’sintegrals appearing in the electromagnetic field expressions, without resorting to any kindof approximated formulas for them. The numerical treatment of the Sommerfeld’sintegrals is characterized by a proper subdivision of the integration domain, the use of theRomberg technique and the determination of a suitable upper bound for the error due tothe integral truncation. In the second part of this work it will be shown how the resultsprovided by the developed theory can be used in order to assess the validity of the mostcommon simplified approach for the calculation of the lightning radiation over a lossyground plane.