Telegrapher's equations for field-to-transmission line interaction

In this chapter, we discuss the transmission line theory and its application to the problem of external electromagnetic field coupling to transmission lines, with particular reference to lightning-induced overvoltages on overhead power lines. After a short discussion on the underlying assumptions of the transmission line theory, we provide the derivation of field-to-transmission line coupling equations for the case of a single-wire line above a perfectly conducting ground. We also describe three seemingly different but completely equivalent approaches that have been proposed in the literature to describe the coupling of electromagnetic fields to transmission lines. The derived equations are extended to deal with the presence of losses and multiple conductors. The time-domain representation of the field-to-transmission line coupling equations, which allows for a straightforward treatment of non-linear phenomena as well as the variation in the line topology, is also described. Solution methods in the time domain are presented. The description of the main modelling features of an advanced computer code for the calculation of lightning originated voltages, i.e., the LIOV-EMTP-RV code, is given. The application of the illustrated theory and relevant computer codes to the case of a typical medium-voltage multi-conductor distribution feeder, which includes transformers and surge protection devices, is presented. The lightning performance assessment of traditional and compact overhead lines is dealt with as well