Collaborative optimization of train timetable and speed trajectory considering stochastic photovoltaic power: A two-step approach

Abstract

Faced with the integrated system composed of the train power system, the photovoltaic (PV) power system, and the energy storage system (ESS), this research studies the energy-efficient operation and energy management strategy from the perspective of both train optimal control and timetable optimization, aiming at achieving a long-term energy consumption reduction. A two-step approach for collaboratively optimizing the train timetable, speed trajectory, and energy management strategy considering the stochastic characteristics of PV power generation is proposed to solve this large-scale complex problem. Before the two-step approach, a mixed-integer linear programming (MILP) model is established to optimize the energy consumption of the inter-station operation. On this basis, explicit energy consumption expressions for all inter-stations of the entire line are obtained by the proposed data fitting method. The historical PV power data is clustered to generate scenarios with different probabilities to characterize the stochastic PV power. The first step of this two-step approach is to minimize the total energy consumption expectations of all inter-stations determined by the obtained explicit energy consumption expressions to optimize the timetable while ensuring the total time and time window constraints are met. The second step is to minimize the weighted sum of energy consumption under all possible scenarios to obtain the optimal speed trajectory and energy management strategy based on the optimized timetable obtained in the first step. The validity of the model is verified by case studies using the real data of Qingdao Metro Line 11 under both scenarios with and without PV power. This study provides a novel method for energy-efficient operation and energy management of the integrated system and demonstrates the prospect of the proposed two-step stochastic optimization in reducing the net grid-supplied energy for the long-term operation of urban rail transportation systems.