In this chapter, we give an overview of lightning discharges, which can cause electromagnetically induced effects in power and telecommunication systems. Then, we describe modeling of the lightning return stroke and explain “engineering” models, in which the spatial and temporal distribution of the current or the line charge density along the lightning channel is specified based on such observed lightning return-stroke characteristics as current at the channel base, the speed of the upward-propagating front, and the channel luminosity profile. Also, we discuss the equivalency between the lumped-source and distributed source representations, and the extension of engineering models to include a tall grounded strike object. Further, we describe two primary approaches to test lightning return-stroke models that are referred to as “typical-event” and “individual-event” approaches.

We introduce three different sets of telegrapher's equations with source terms and corresponding equivalent circuits that can be used for studying voltage and current surges induced on an overhead conductor by transient electromagnetic fields such as those produced by lightning. The source terms (forcing functions) incorporated into the classical telegrapher's equations are derived, using the electromagnetic theory, following works of Taylor etal. (1965), Agrawal etal. (1980), and Rachidi (1993), who arrived at different coupling model formulations. Since all three formulations are based on Maxwell's equations, they yield identical results, as demonstrated by Nucci and Rachidi (1995). As of today, the model of Agrawal etal. (1980) has been most widely used for the evaluation of lightning-induced effects on power and telecommunication lines.

The first peer-reviewed paper, in which the finite-difference time-domain (FDTD) method for solving discretized Maxwell's equations was used in a simulation of lightning-induced surges, was published in 2006. About 30 journal papers and a large number of conference papers, which use the FDTD method in simulations of lightning-induced surges, have been published during the last 15 years. FDTD procedures used in simulations of lightning-induced surges are classified into two types in terms of spatial dimension: two-dimensional (2D) and three-dimensional (3D). About 30% of the simulations as of today have employed the 2D-FDTD method in the cylindrical coordinate system, and about 70% of the simulations have used the 3D-FDTD method. In the 2D case, the FDTD method is employed to express the distributed sources in terms of incident electromagnetic fields illuminating overhead conductors, to be incorporated in the equivalent distributed-parameter circuits of those conductors. The equivalent circuit depends on the field-to-conductor coupling model. There are three major coupling models that yield the same results, the most popular of which is the model proposed by Agrawal et al. (1980). One of the reasons for using the two-step or hybrid approach is that horizontal closely spaced thin conductors can be represented easily by a distributed circuit. In some 3D-FDTD simulations, the subgridding technique has been used to represent horizontal closely spaced thin conductors. The subgridding technique employs locally fine grids for representing closely spaced thin wires or other small structures that exist in the working volume. In other 3D-FDTD simulations, a nonuniform gridding technique has been used. The transmission-line (TL) engineering model has been most frequently used for representing the lightning return stroke. The modified TL model with linear current decay with height (MTLL) and the modified TL model with exponential current decay with height (MTLE) have also been employed. Further, the TL model extended to include a tall strike object has been developed. As of today, about 70% of the FDTD simulations have been concerned with induced surges associated with lightning strikes to flat ground, and about 30% with lightning strikes to the top of mountain, building, or tall object. In this chapter, journal papers on the FDTD-based studies of lightning-induced surges are classified in terms of spatial dimension, lightning channel representation, and application. An overview of these works is given and six representative works are described in detail.