Multi-Train Eco-Driving and Safety-Tracking Cooperative Optimization by Nonlinear Programming

Eco-driving and safety-tracking are two main topics in multi-train operations. Both are discussed separately in existing works, but have not truly been considered simultaneously. This paper integrates the two topics and proposes a general cooperation method for multi-train operation in urban rail transit system. The cooperative operation problem is formulated as an optimal control problem and then solved as a nonlinear program (NLP). By treating catenary voltages as control variables, we show that the dynamic electric power flow for the typical double-track DC railway system can be considered within the NLP, with no need to develop a complex power flow calculation for the coupled circuits. Compared to existing works, the proposed method achieves true cooperation among trains by minimizing the global substation energy usage, while ensuring dynamic safety-tracking distances among adjacent trains.