Inclusion of Frequency-Dependent Soil Parameters in Transmission-Line Modeling

This paper presents an analysis of transmission-line modeling when the soil conductivity and permittivity are treated as frequency dependent. It also presents a methodology to include this particular behavior on frequency-dependence realization of transmission lines and cables. The frequency-dependent soil parameters can be synthesized with a simple first-order model. It demands only three parameters statistically independent, one being associated with the low-frequency conductivity as obtained in conventional modeling and the other two are a function of the frequency dependence in soil conductivity and permittivity. The new formulas used for the ground return impedances for overhead lines and underground cables are presented. Instead of using an analytical approximation of the infinite integrals involved, a numerical approximation using a Gauss quadrature technique was implemented. These expressions can be understood as an extension of the well-known Carson and Pollaczek formulas. Three distinct cases are presented in order to asses the impact of frequency-dependent soil parameters with respect to the asymmetry of the circuit. The effect of frequency dependence in soil parameters is evaluated using frequency and time domain. In the frequency domain, modal analysis is applied to assess the overall impact in the ground mode propagation. To obtain the time-domain response, the line was modeled in the frequency domain using a phase-domain approach and a numerical Laplace transform was applied