Eco-Driving of Metro Trains Considering Variable Efficiency of Propulsion System

The main goal of energy-efficient train control (EETC) is to devise strategies and methods in order to consume the least amount of energy while respecting the system and the operational constraints. Typically, such problems are tackled by breaking the trajectory into various singular and regular phases. The main focus of this article is to provide a numerically efficient algorithm to solve this problem in a unified way instead of dealing with phases. In this research work, a convex nonlinear model for propulsion power is proposed. Using this model, the EETC problem is formulated as an optimal control problem (OCP) using Pontryagin’s maximum principle (PMP). Maximum effort limitation of the propulsion system, and acceleration and deceleration limits are considered as control constraints. Track speed limits are considered as state constraints. The optimality conditions allow formulating a boundary value problem (BVP). An initialization procedure is proposed, which enables to design continuation procedures (CPs) to solve the BVP. The results are compared with the dynamic programming (DP) solution. A tradeoff analysis between journey time and energy consumption is presented.