In this paper, a virtually coupled train formation (VCTF) control method based on the model predictive control (MPC) framework is proposed. The train track spacing error, velocity error, and riding comfort are chosen as the optimization goals, and the constraints of line speed, collision avoidance of the train platoon, traction/braking performance, and string stability are considered. The virtual coupling operation control problem is converted into a quadratic programming problem with constraints. This paper also proposes a coasting control strategy to improve the output of the MPC controller. Simulation results show that compared with the proportional derivative controller, the proposed control method can simultaneously reduce the tracking error and output acceleration, reducing running energy consumption. A study of a metro line is chosen to analyze the VCTF operation performance, and the simulation results show that the VCTF operation mode can improve the peak capacity and quality of service of flat hours compared with the communication-based train control operation mode.

Optimizing the operating speed curve of trains without adding new energy storage facilities is essential in the energy-saving operation of railways. In this paper, we propose an optimal train speed curve planning method for driving trains more energy efficiently. A refined traction energy evaluation model for induction motor propulsion systems is first presented. The proposed model considers the efficiency of the traction motor at different operating points and the efficiency of the inverter and gearbox. Then, the optimal energy-efficient speed profile problem is transformed into a multistep decision problem and solved using dynamic programming (DP). To verify the effectiveness of the proposed method, a case study was conducted on an actual subway line. The results obtained indicate that the speed curve produced by the proposed method results in a 20% energy consumption saving compared with the speed curve for actual operations. Furthermore, the results of comparison with a genetic algorithm indicate that the DP algorithm is better able to satisfy the constraints of the train traction system. Solving the optimal speed curve using the proposed method and programming the onboard controller of the train according to the optimal speed curve enables the train to be driven with greater energy efficiency.