A new expression for the ground transient resistance matrix elements of multiconductor overhead transmission lines

摘要

The ground impedance matrix elements of a multiconductor overhead transmission line do not have analytical inverse Fourier transforms in the time domain. Thus, in general, the ground transient resistance matrix elements are to be determined numerically. Using the low-frequency approximation analytical expressions are available for the ground transient resistance. These expressions present however a singularity at t = 0 and require a careful treatment in a direct time domain analysis. In this paper, we show that the singularity in the ground transient resistance is due to the low frequency approximation. Also, we show that at early times, the ground transient resistance elements tend to an asymptotic value, which depend on the line geometrical parameters and ground relative permittivity. Finally, we propose new expressions which are analytical, non-singular, and which describe, within the limits of transmission line theory, both the early-time and late-time behavior of ground transient resistance in a more accurate way.