Transmission line models of the lightning return stroke

Abstract

This chapter discusses the modeling of the return stroke channel as a transmission line. A brief review of the pertinent literature indicates that the transmission line models of the return stroke can be roughly classified as either discharge-type models, which assume the return stroke to correspond to the discharge of a previously charged transmission line to ground through a closing switch, lumped-excitation models, which assume the return stroke to correspond to an initially neutral transmission line that is fed by a lumped voltage or current source at one of its terminations, or finally as models that use transmission-line or distributed-circuit theory to infer relevant lightning properties.A discussion is presented on the calculation of the per-unit-length parameters necessary for simulating the return stroke channel as a transmission line. It is shown that if a transmission line is intended to represent the lightning channel, it must be nonuniform (in order to accommodate the variation of the channel parameters with position) and nonlinear (in order to accommodate the temporal variation of the channel resistance as a function of the channel current and the gradual neutralization of the corona sheath surrounding the channel core). Engineering equations are presented for estimating the per-unit-length parameters associated with a vertical transmission line in the presence of nonlinear losses and corona. The proposed equations are suitable to computer simulation and can be easily implemented using a first-order FDTD scheme.Computed results show that the modeling of the lightning channel as a lossy nonuniform transmission line in the presence of corona is able to reproduce the most important characteristics of subsequent return strokes of negative lightning, including the reduction in amplitude and increase in front time of the lightning current with increasing height, realistic return stroke speeds, realistic speed profiles, and, if a suitable set of parameters is selected, most signatures typically observed in measured electromagnetic fields. Besides confirming the consistency of modeling the return stroke channel using transmission line theory, the obtained results suggest that the consideration of relevant lightning properties let model predictions closer to measured data. It can be expected, therefore, that model predictions are likely to consistently improve if better models become available for representing the various physical processes in the lightning discharge. A transmission line model of the return stroke is flexible enough to accommodate virtually any model improvement provided it can be written, analytically or numerically, in the form of per-unit-length parameters.