Impedance of Conductor-earth Circuits in Electric Railway Tunnel

In power systems, especially in electric railways, sometimes conductors are suspended in tunnels. Carson formulas have been used to compute the impedance of conductors in a tunnel in the past. However, there exists an inherent modeling error when using Carson formulas to calculate the impedance of conductor-earth circuits in a tunnel. Based on model comparison between the semi-infinite earth and the circular tunnel with peripheral infinite earth, the conception of long and large tunnel in the electrical meaning is put forward. Taking a practical electrified railway tunnel as an example, impedances calculated from different formulas are compared and the relative errors of Carson’s formulas are presented. The results demonstrate that the impedance error become larger with the increase of frequency and become smaller with the increase of earth resistivity, and has a value of above 5% even under the fundamental frequency. Physical interpretations are given to explain the results, and the suitability of Tylavsky formulas for conductors in long and large tunnel is discussed.