Using Approximate Dynamic Programming to Maximize Regenerative Energy Utilization for Metro

With the rapid development of Metro, it has aroused more attention to its energy efficiency. The regenerative energy is a kind of energy generated by a braking train, which can be used by other trains nearby. Due to the application of regenerative braking and automatic train operation function, more and more studies focus on using regenerative energy by optimal train control. To maximize the utilization of regenerative energy for a couple of trains, we formulate a model and design an algorithm for maximizing the utilization of regenerative energy (MURE) by using the proposed approximate dynamic programming (ADP) approach to adjust the speed curve of the accelerating train. Then, we discuss three approximation methods for the proposed ADP-based approach such as rollout method, interpolation method, and neural network. The rollout algorithm could improve the basic policy for train control with carefully designing. The function approximation method using interpolation could further decrease the energy consumption with assuring punctuality. The neural network approximation usually cannot realize the effect superior to the interpolation strategy due to its complex structure, and it needs more computation time. Finally, the analysis of regenerative energy utilization is given by implementing the numerical experiments with field data from the Yizhuang line, Beijing subway. The numerical results show its effectiveness and stability.