FDTD analysis of distribution line voltages induced by inclined lightning channel

This paper investigates lightning induced voltages on a distribution line, when the lightning channel is not vertical but angled to the line and the earth, based on the finite-difference time-domain (FDTD) method. The effect of the current flowing into the earth, after the lightning channel touches the earth, is also investigated. The induced voltages are quite dependent on the angle of the channel to the line as can be easily estimated. The lightning angle with the line is found to cause a significant effect on the induced voltage, and the effect of the earth resistivity is made clear when considering the inclined channel. The induced voltage is proportional to the amplitude and frequency components of the inducing current, i.e. proportional to the current derivative di/dt which is inversely proportional to rise time Tf at the wave-front. The relation for the inclined channel is far more complicated than that in the vertical case, because the channel becomes a function of space (x, y and z). This fact has to be taken into account when discussing the effect of Tf. The current flowing in the earth is also affected by the lightning inclination and the voltage drop along the earth surface due to the current becomes larger than that in the vertical lightning case.