Two-stage virtual coupling high-speed railway train operation control method considering train operation curve optimization

In order to maintain the train tracking accuracy of the virtual coupled train formation (VCTF) while reducing energy consumption during operation, in this paper, we propose a two-stage virtual coupling high-speed train operation control method that considers optimizing the train operation curve. Based on train dynamics, we take minimizing energy consumption and operation time deviation as the main objectives for the train operation curve optimization in Stage I, establish a dynamic programming model with time discretization, and design an algorithm to satisfy the requirements of precise parking and on-time operation of the train, in which a variable time step solving algorithm is considered to improve the solving efficiency. The optimal energy-saving train operation curve obtained in Stage I is used as the expected operation curve of the leader train in the VCTF. In Stage II, we adopt the Distributed Model Predictive Control (DMPC) to establish the virtual coupling high-speed railway train operation control model. With the goal of minimizing the position error and speed error of the VCTF, and the train safety interval, train speed, train control performance and passenger comfort constraints, the designed DMPC ensures the stability and safety of the operation of VCTF. Finally, simulation analysis is conducted on three different scenarios, the research results show that the methodology proposed in this paper can effectively reduce the energy consumption of trains during operation while improving the tracking accuracy of trains in VCTF. In terms of energy saving, the proposed method is superior to previous heuristic algorithms and reinforcement learning methods, with improvements of 16.12 % and 2.52 %, respectively. In terms of tracking accuracy, the peak distance and speed errors of the VC trains do not exceed 2 m and 0.24 m/s. In terms of solving efficiency, the variable time step dynamic programming method can improve the solving speed by nearly 30 % while ensuring the solving accuracy. Moreover, the energy consumption of Train 0 and Train 1 increased by 1.7 % and 0.66 % respectively compared to the expected operation curve. Simulation results with different expected intervals show that setting an appropriate expected tracking interval in actual operation requires a balance between train operation safety and energy efficiency.