Lightning Surge Propagation on a Single Conductor in Free Space

This paper introduces an analysis of lightning surge propagation on a conductor without any returning current path. The conductor can be either a free-space or grounded conductor as long as the reflected surge from the ground has not arrived. Unlike a TEM transmission line, this conductor is characterized with time/position-variant surge impedance as surge current attenuates during its propagation. In this paper, a simplified formula was derived. Using the unique parameter - attenuation coefficient of current - an iterative method was developed to evaluate actual propagation characteristics. This method was verified numerically, and is much more efficient in calculation and easier in implementation. It is found that the surge impedance is affected by the waveform of an impulse current source, but is independent of the slope of a ramp current source. It increases quickly if the source current has a short rising time or failing time. The simplified formula generates overestimated results, but the difference decreases with increasing distance to the source. The proposed method can be used to address surge voltage on the tower upon the arrival of a reflected surge from the ground.