Joint Optimization of Speed and Voltage Trajectories for Hybrid Electric Trams

A tram with an on-board energy storage system is a promising candidate for urban traffic systems. The co-optimization of speed and voltage trajectories for a catenary-supercapacitors hybrid electric tram to minimize energy consumption from traction substations is presented in this article. A source-catenary-load-storage integrated optimization model is proposed to reflect the coupling performance between vehicle dynamics and power sources. Two different methods are designed to address this problem. First, a hierarchical method based on dynamic programming is proposed, and the optimal control problem is recast into two subproblems of speed trajectories optimization and supercapacitors voltage trajectories optimization. Efforts are made to reduce the computation burden. To further investigate the optimality of the hierarchical method, a coupling optimization method is designed using the three-dimensional dynamic programming. The performances of the two methods are evaluated by different track conditions and compared with the only optimizing speed profiles based method, which shows that the proposed methods can improve energy efficiency and reduce the fluctuation of catenary voltage. Meanwhile, the coupling method has lower energy consumption than the hierarchical method, but suffers from more considerable computation time. Finally, the influences of tram weight and dynamic traffic constraints are investigated.