Real-time trajectory planning for rail transit train considering regenerative energy

This paper proposes an energy efficient driving strategy considering regenerative braking energy, arbitrary speed limits, variable grade profiles and curve radius. In actual operation, the reference speed curve of the Automatic Train Operation (ATO) system needs on-line recalculation when the operation circumstances change, such as delay or a temporary speed limit. An energy-efficient operation optimization model with arbitrary feasible initial and final velocities is built, and the optimal operation modes are obtained by means of the maximum principle. When the braking energy is fully recovered, the speed-holding operation mode is proved to be the most energy-saving regime. Then a numerical algorithm is presented to construct the energy saving speed curve for a given time with the consideration of speed limits. The feasibility of the algorithm is verified through the case study of Shenzhen Metro Line 1. With the flexibility of arbitrary initial and final speed values, the presented algorithm can be applied to ATO system for real-time calculation.