Transmission Line Theories for the Analysis of Electromagnetic Transients in Coil Windings

The chapter contains the basic theory of a distributed-parameter circuit for a single overhead conductor and for a multi-conductor system, which corresponds to a three-phase transmission line and a transformer winding. Starting from a partial differential equation of a single conductor, solutions of a voltage and a current on the conductor are derived as a function of the distance from the sending end. The characteristics of the voltage and the current are explained, and the propagation constant (attenuation and propagation velocity) and the characteristic impedance are described. For a multi-conductor system, a modal theory is introduced, and it is shown that the multi-conductor system is handled as a combination of independent single conductors. Finally, a modeling method of a coil is explained by applying the theories described in the chapter.