Energy-efficient handling of electric multiple unit based on maximum principle

Optimizing train handling to achieve energy-efficient operation is a cost-effective means for energy saving. The minimization of traction energy consumption of Electric Multiple Unit (EMU) train is chosen as the optimization goal and the necessary conditions of energy-efficient handling are deduced on the basis of the maximum principle. By analyzing the continuity of co-state variable without consideration of the influence of speed limitations and the jump conditions of co-state variable with consideration of the influence of speed limitations, the switching rules of optimal train operation states are obtained. On this basis, a numerical algorithm for searching the optimal sequence of train operation states is proposed and the correctness and effectiveness of the algorithm are verified by simulation. The simulation results show that when given 2.1% and 11.4% slack of journey time, up to 22.2% and 44.2% reduction of train traction energy consumption compared with that of flat-out running can be achieved correspondingly. The proposed algorithm is applicable for on-line generation of mode profiles for EMU trains.