Impedances of a Single-Phase AC Railroad Electric Traction Network

Abstract

In calculating traction network impedances, the greatest difficulties arise due to the need to take into account mutual inductive couplings between different wires of the multiwire contact system, between the rails, between the wires and rails, and between the contact systems of different tracks. However, no matter how accurate the methods of accounting these couplings are, numerous assumptions and uncertainties result in impossibility to guarantee the calculation of these impedances with an error of less than 5-10%. In taking into account mutual inductive couplings, it is convenient to use a simplified method, in which, instead of considering each pair of conductors, an average dependence for each multiwire network as a whole or an average dependence between two networks are considered. This approach produces virtually no effect on the accuracy of determining the resulting traction network impedances, yet it dramatically simplifies the calculations. A multiwire network can be represented as a set of "conductor-ground" loops. Equations for determining the impedance of the resulting loops are given, in which multiwire contact or rail networks behave as a conductor. On the basis of such loops, it is possible to determine the inductively decoupled impedances of the contact and rail networks for single-track and double-track sections, which are used for drawing up a traction network equivalent circuit. In doing so, the current leak from rails to ground must be taken into account for a rail network, which can be performed by introducing a special coefficient for inductively decoupled rail network impedance. A methodology for calculating this coefficient is presented.