Optimal Control Strategies for Metro Trains to Use the Regenerative Braking Energy: A Speed Profile Adjustment Approach

The Regenerative Braking Energy (RBE) of metro trains plays an important role in metro energy saving. If the regenerative energy can be directly absorbed by the adjacent trains, the investment in other RBE usage equipments like super capacitors will be reduced. To increase the RBE usage, the overlaps of traction and braking processes of adjacent trains can be increased by timetable optimization or real-time train regulation. But if the overlaps cannot be realized, the RBE cannot be efficiently absorbed by the other trains. To solve this problem, this paper proposes an optimal train control method to absorb the RBE of the braking train by adjusting the speed profile of an adjacent train that runs at non-braking stage. A speed profile adjustment algorithm for the adjacent train is given considering the speed limits and gradients, in which a traction process is incorporated in the adjusted speed profile. Connected and unconnected DC power supply networks are both considered. In the connected DC power supply network, the RBE of the braking train can be absorbed by the adjacent adjusted train, which runs in the different power supply section. To test the robustness of the proposed algorithm, random train delays are considered in the simulations. The interstation running time will be regulated to reduce the train delay by a linear programming model, based on which, the speed profile of the cooperative train will be adjusted. Simulations are conducted based on a whole day data of Beijing Metro Line 4. The simulation results show that the proposed method improves the energy efficiency over 13% by improving RBE usage, and the proposed method also shows strong robustness in the train delay simulations, which makes it a promising method to be applied in real metro system.