On the Periodic Braking of Freight Trains on the Long Steep Downhill

Based on the Pontryagin's maximum principle, the minimization of the freight train operation energy consumption is chosen as the optimization goal, the operation strategy of the train on the steep downhill section is researched. Analysis has been made and the results show that the train operation states are decided by the adjoint variable, the periodic braking should be applied while the train operates on the steep downhill section. The highest release speed of the train has been defined, which is the threshold that makes the next braking safe and effective. The linkage between the steep downhill and the adjacent sections is analyzed. The off-line switching points of the optimal train operation states are calculated by utilizing the numerical methods. The simulation results show that when given 12.1% slack of journey time, up to 58.2% reduction of train operation energy consumption can be achieved compared with that of flat-out running. The algorithm considering the periodic braking of the freight train on the long steep downhill section in this paper can be used to generate the off-line mode profiles.