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This paper describes a new approach for creating an optimal running curve of a train with the aim of minimizing total energy consumption, given the constraints of running time, limited motive force and limited train acceleration. A novel parameterization method of the running curve is proposed for mathematically demonstrating the relationship between the speed of the train and the position of the train. Then, the total energy consumption and the above constraints are formulated as functions depending on the parameters of the running curve. From this scenario, a constrained optimization problem is considered for minimizing the total energy consumption. After that, an effective method to obtain the solution of this optimization problem is presented. The effectiveness of the proposed approach is verified by computer simulations.

The design of an optimal running curve for train operation based on a novel parameterization method aiming to minimize the total energy consumption