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In this paper, a new HVDC power supply system for light rail systems is presented and compared to classical distribution networks based on AC/DC controlled converters. A simulation tool has been developed to simulate such a complex system, taking into account vehicle motion and HVDC electrical distribution. Then, an optimization of HVDC structure and control will be presented using Lagrangian formulation. All the results are compared to classical distributions, and show the effectiveness of the proposed power supply distribution used for light rail systems.