On the Choice Between Transmission Line Equations and Full-Wave Maxwell's Equations for Transient Analysis of Buried Wires

In this paper, we evaluate the validity of transmission line (TL) solutions in the study of interaction of lightning transients with buried wires. The considered transients have frequencies between a few kilohertz to a few megahertz with risetimes 0.1-10 mus. Comparative simulations using TL equations and full- wave Maxwell´s equations are carried out in the paper, and the solutions to both the equations are based on the finite-difference time-domain method. It is found that TL solutions are sufficiently accurate for lightning transient analysis of buried wires. It is also claimed that the TL approach remains valid for all transients having frequencies lower than those of lightning. TL solutions are computationally efficient, particularly when dealing with distributed power and railway systems. The TL approach is valid as long as the transverse electromagnetic mode (TEM) is dominant. However, other modes of propagation, classified as antenna modes, might be present depending upon the type of excitation source, its location, frequency, and the associated media. A possible approximate formula for the frequency above which the validity of TL solutions for buried systems is questionable is proposed based on the concept of penetration depth of fields into the soil. Discussions presented in the paper could motivate the application of TL solutions for electromagnetic transient analyses of the buried conductors of power, railway, and telecommunication systems.