Periodic Braking of Freight Trains with HXD2 Locomotive on Long Heavy Down Grade

An optimal control model of freight train operation, with focus on the regenerative braking energy, was established, based on the fundamental principles of railway traction and energy consumption analysis. The model was specifically developed for the following conditions:(1) the train travels along the track in the long steep downhill section at a non-constant speed while the air brake is applied. (2) The air recharging time should be guaranteed between two successive braking operations. The model was developed based on a pressure reduction of 50 kPa, which is a typical condition during braking. The optimal control strategies were studied for the case where the train travels along the track in the long steep downhill section. The time allocation for each sub-section between two stations was also studied. The optimality of the periodic braking strategy (full electrical braking-full braking-full electrical braking) was analysed using Pontryagin's maximum principle. The necessary conditions were also analysed for the case where the train enters and then leaves the long steep downhill section. The numerical algorithm used for optimal control of the train travelling along the track in the long steep downhill section and its adjacent section was presented in detail. The proposed model and numerical algorithm were verified by performing simulations of an HXD2 locomotive with 100 fully loaded cars. The simulation results were compared with those of the fuzzy predictive control and field test data. Based on the condition that the train is punctual, it is found that the energy consumption during train operation can be reduced by up to 5.6% and 17.9% with respect to the fuzzy predictive control and field test data, respectively.