Calculation of remote effects of stray currents on rail voltages in dc railways systems

This study focuses on the analysis of the remote effects of stray currents and rail potentials along the rail line in DC traction systems, although the results can be extrapolated to AC systems. This study is essential to ensure the equipment and passenger safety, as well as the maintenance of rail infrastructures, subjected to corrosion in DC railway traction systems. The mathematical model developed in this study allows to obtain stray current and rail voltage distributions at the point where the train or the short circuit is located, x, and what is more important, it lets also to calculate its remote effects at any other point along the rail, y. Most of the railway electric models published in the literature do not calculate the remote effects of stray currents and rail potentials. Calculations are often done just at the specific point where the current is injected into the rail. However, the train and short-circuit currents actually generate remote effects as a voltage wave-front that propagates along the rails. Another contribution of this article is that the problem is defined as a function of the power demanded by the vehicle at each point, P(x), so the consumed current, I(x), is obtained by means of a power flow algorithm. Nevertheless the vast majority of references assume an already known input current, which, may only be obtained by power flow methods. With the aim of simplifying the lecture of this document, Table 1 provides the list of symbols used in this study.