Extended Traveling Wave Theory for the Multistage Tower under a Direct Lightning Strike

This article presents a theoretical time-domain analysis of lightning surge propagation on a multistage and multi-conductor tower. An extended traveling wave theory using electric scalar potential is introduced. The non-TEM wave propagation in the tower is characterized by time/position-variant transient impedance. The analytical formulas of the transient impedance are presented for any position/time in the tower, as well as those of the reflection coefficient at a discontinuity. The concept of primary and secondary waves is introduced to depict the multiple reflections in the tower. It is found that the primary current wave attenuates during its propagation in the tower, and is corrected by a factor when crossing over the discontinuity. A pair of secondary waves is generated at the discontinuity, similar to a center-fed dipole. The proposed method is applied to evaluate the lightning current in a two-stage tower. The result of the proposed method is of high consistency with the FDTD result. It is also observed that the secondary waves could be neglected if the reflection coefficient is small. The traditional transmission line theory could lead to a significant error of the current in the tower.