Energy-efficient control of a train considering multi-trains power flow

For a selected train journey with multiple trains in the same traction power system, the given driving strategies of other trains can be abstracted as available external power flow. Aims at reducing the energy consumption of the multi-train system, this paper presents an analytical solution for optimising the selected train trajectory to maximise the utilisation of the external power flow. Specifically, a spatial-temporal area which combine the track grade along space and the external power over time is constructed and the problem is converted into the energy-efficient control of a train travels in the spatial-temporal area. Classical methods of constrained optimisation is used to show that the set of the optimal control modes and the optimal driving speed for the proposed problem are in a state of change. In order to obtain the optimal driving strategy, the spatial-temporal area is divided into grids, and the evolution of a key adjoint variable when the external power changes is discussed. The authors illustrate our results by finding optimal control sequences and associated speed profile for the freight train in some elementary but realistic examples.