An Investigation of Earth-Return Impedance Between Overhead and Underground Conductors and Its Approximation

This paper investigates numerical instability issues in the mutual impedance formula between an overhead conductor and a buried conductor proposed by Pollaczek with special reference to the integrand of Pollaczek's infinite integral. The integrand shows a negative real part and positive imaginary part at a high frequency, which result in negative resistance and inductance. The reason for this is the assumption of TEM-mode propagation in Pollaczek's formula as is well known. The fact suggests that numerical instability of the infinite integral is caused by incorrect integrand in a high-frequency region. Based on the observations, the applicable limit of Pollacezk's formula is analytically derived. Finally, a simple closed-form formula is developed, which approximates Pollaczek's formula with satisfactory accuracy.