An optimization method for train driving trajectory in urban rail systems

In urban rail systems, the kinetic energy of trains can be converted into electrical energy when the train applies regenerative braking. The converted energy is called recovery energy that can be transmitted backward to the power supply network for accelerating nearby trains. The previous studies in using recovery energy focus on optimizing timetable to synchronize the traction and braking times of trains. Instead of optimizing timetable, this paper develops a train trajectory optimization model to minimize the net energy consumption by improving the efficiency of recovery energy utilization. A genetic algorithm(GA) is used to find the optimal train trajectory. Finally, we present a numerical example based on Beijing Yizhuang subway line data to illustrate the effectiveness of the developed model on energy saving.