Closed-Form Earth-Return Impedance Formulas for Overhead and Underground Cables Considering Displacement Currents

摘要

This paper proposes closed-form formulas of earth-return impedances for overhead lines and underground cables, which can deal with high frequency displacement currents. Calculated results by the proposed approximate formulas are compared with those calculated by accurate formulas. It is confirmed that the approximate formula considering the displacement currents for the overhead lines as well as underground cables shows good accuracy in comparison with the accurate formula. The approximate formulas are applied to investigate the influence of the relative earth permittivity on the earth-return impedance. The effect of the displacement currents appears in a high frequency region above 1 MHz in the overhead lines, and in high frequencies higher than 500 kHz in the underground cables. Since the formulas are given in a closed form, those can be easily implemented in existing EMTPs as a numerically stable formula of the earth-return impedances of overhead lines and underground cables to avoid any numerical divergence in frequency domain and instability in time domain.