Urban rail transit (URT) develops rapidly in modern cities, and its energy efficiency attracts extensive attention. The utilization of regenerative energy (URE) is an important method for energy-efficient operation of URT. Regenerative braking is an energy recovery mechanism that slows down a moving train by converting its kinetic energy into electric energy. The electric energy can be utilized for other trains to accelerate in a cooperative way. To take full advantage of the regenerative energy, an energy calculation method which considers regenerative braking power to optimize the timetable is proposed in this paper. First, four operating modes of URE are defined and an integer programming model is formulated. Second, a branch and bound algorithm is designed to solve the optimal timetable in different scenarios. Third, the model is evaluated based on the operation data from the Yanfang Line, Beijing Metro, China. For peak hours, the results illustrate that the proposed method can significantly improve URE by 73.7% compared with the original timetable. Also, URE can be improved by 46.3% for off-peak hours. Finally, the comparison between the proposed method and the method based on the kinetic energy theorem is given. The simulation results illustrate that the proposed method could increase URE by 29.7% and 9.9% for peak and off-peak hours scenarios, respectively, in comparison with the method based on the kinetic energy theorem.
Trade-offs between energy maximization and parental care in a central place forager, the sea otter
