A Fourth Order Differential-Integral Formulation Applied to the Simulation of the Subway Grounding Systems

A new methodology is presented to evaluate both the distribution of touch voltage along a DC electrified subway or railway track as well as the distribution of leakage current density. The main goals of this work are determining voltage level to which users and/or operation and maintenance crews are submitted to under normal operating and failure conditions and the degradation level evaluation for the installations due to electrolytic corrosion caused by currents present in soil in metallic parts. Differential equations originated from mathematical formulation developed alongside the supplying circuit equation subway/railway grounding systems. These differential equations were obtained by considering an elementary part of the grounding system, represented by distributed parameters, thus permitting the determination of an electrical equivalent circuit for any part of the track. This circuit, when associated to the supplying circuit, enables a global evaluation of the system, whose solution brought us to develop a software named PCAM (Calculation Program for Subway/Railway Grounding). This software has an efficient graphic interface, which allows us to model several alternatives with minimum changes in its input data, such as the simulations of low insulation in some parts of a track, and in switching machines as well as a short circuit between the supplying conductor (catenary or third rail) and the grounding system in the fault point. To validate this methodology, measurements of touch voltage and traction current measurements were carried out in lane 2-Green, São Paulo Metro. Obtained data was compared to software results.