Equivalency of Lightning Return-Stroke Models Employing Lumped and Distributed Current Sources

Abstract

We show that any engineering return-stroke model can be expressed, using an appropriate continuity equation, in terms of either lumped or distributed current sources with the resultant longitudinal-current distribution along the channel being the same. This property can be viewed as the duality of engineering models. The conversion alters the actual-corona current (if any) of the model. For lumped-source (LS) models the actual-corona current is unipolar and directed radially out of the channel core, while for distributed-source (DS) models it is unipolar and directed into the channel core. For LS models converted to DS models and for the Diendorfer-Uman (DU) model converted to the equivalent LS model, the corona current is the sum of the negated actual-corona current (if any) and a fictitious-corona current, the latter being bipolar. For the transmission-line (TL) model (no longitudinal current attenuation with height) expressed in terms of DSs, there is only a fictitious bipolar corona current component. Conversion of the traveling-current source (TCS) and Bruce-Golde (BG) models to equivalent LS models involves replacement of the actual, unipolar corona current with a fictitious one, the latter current being bipolar near the channel base and unipolar at higher altitudes