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Study on a feeding circuit model formulated to use multipurpose solvers for multi-train simulators

Reduction of energy consumption is one of the recent key topics in railway sector. There are many investigations such as SiC devices, permanent magnet motors, onboard and stationary energy storage and reversible substations to absorb regenerative braking, energy efficient driving and traffic management. Multi-train simulators play an important role in evaluating the effect of these countermeasures. In the simulator, power feeding circuit must be modeled to calculate the energy consumption with high accuracy. There are some literatures of modeling and solving feeding circuits, however most of them linearized some nonlinear but important characteristics of trains and substations. We have also proposed a methodology of precise modeling and solving power feeding circuits of railway systems implemented in the multi-train simulator. The methodology is flexible and characterized by the special node numbering and introduction of ‘tie nodes’ which is solvable by multipurpose solvers. In this paper, we analyze the solvability of the methodology and introduce the virtual ‘tie nodes’ to decrease errors of circuit equation if the distance of two nodes is very near. The criterion whether the virtual tie node should be used or not is finally analyzed.