Partial speed trajectory optimization for urban rail vehicles with considerations on motor efficiency

Among different efficiency-enhancing techniques on railway traction energy, speed trajectory optimization is regarded as a promising and feasible method as it requires no further upgrade on the railway infrastructures. This paper focuses on a special speed trajectory optimization problem for urban railway transportation, in which the train is required to alter its speed from one to another either by traction or regenerative braking within the time and distance constraints. Previous papers in this area propose a comprehensive Mixed Integer Linear Programming (MILP) model to solve this problem considering route gradients and speed limits etc. Further to the previous work, this paper tries to contribute in two aspects. First, this paper explicitly proves the rationality of the assumption of monotonicity of the speeds during the speed-changing process using Pontriyagin's Maximum Principle with some basic assumptions for engineering applications. Second, this paper proposes an improved optimization model which takes into account the motor efficiency during traction and braking. Optimization results verify and demonstrate the significant impact of the motor efficiency on energy saving.