Computation of transient voltage and current profiles along illuminated multiconductor lines by means of the numerical Laplace transform

In this study, a transmission line model described in the q-s domain (spatial frequency-temporal frequency) is applied to obtain transient voltage and current profiles along field-excited multiconductor lines (also known as illuminated lines). The incident field excitation is incorporated into the model by means of Taylor´s formulation, in which such field is included by means of series voltage and shunt current sources distributed along the line. For the case of lines excited by an indirect lightning stroke, the corresponding field is computed according to the formulae proposed by Master and Uman. The inverse numerical Laplace transform is applied successively (twice) to obtain the results in the z-t domain, corresponding to the voltage and current profiles along the illuminated line. An initial validation of the model consists of two examples, in which simple analytical expressions are introduced for the voltage and current sources (separately) along the line in order to provide comparisons with alternative transients programme/electromagnetic transients programme. Then, three test cases corresponding to lightning strokes at different locations near the line are considered. Power system computer-aided design/electromagnetic transient design and control is used in this section for validation purposes.