Optimal control strategy for trains in emergency self-propelled running conditions

High-speed trains require self-rescue capabilities in the event of power loss due to traction network failures or other reasons. In these emergencies, trains rely on on-board energy storage equipment to operate and reach safe rescue points, such as the nearest station, to prevent disruptions to the normal operation of the entire system. The duration of emergency self-propelled operation is limited only by the on-board energy storage capacity. Therefore, implementing energy-saving control strategies to reduce energy consumption during operation can ultimately improve the success rate of reaching a rescue point. This paper addresses energy savings for high-speed trains operating in emergency self-propelled conditions. Firstly, a model was established to represent emergency self-propelled train operation, taking auxiliary power into account. Based on this model, an analysis leveraging the maximum principle identified the optimal control conditions under the emergency train operation. The subsequent derivation led to an analytical formula for the optimal constant speeds under partial traction conditions, resulting in an optimal constant speed strategy curve that corresponds to the lowest total energy consumption for the trains. By utilizing the optimal constant speed curve, a coasting energy-saving optimization algorithm was proposed to further reduce energy consumption during emergency self-propelled train operation. Based on simulation cases designed to reflect real railway scenarios, the constant speed operation strategy curve was generated through a solving process for different constant speeds, which verified the correctness of the optimal constant speed analytical formula developed in this paper. Furthermore, the coasting curve was optimized based on the optimal constant speed curve. The proposed algorithm was verified as correct and effective through a comparison of energy consumption during operation. In conclusion, the designed coasting algorithm based on the optimal constant speed can effectively reduce the total energy consumption of emergency self-propelled train operation, thereby improving the self-rescue success rate of high-speed trains.