Energy-efficient multi-train scheduling considering dynamic passenger flows and station-side utilization of regenerative energy

In response to global carbon neutrality goals and the growing emphasis on sustainable urban development, enhancing the energy efficiency of urban rail systems has emerged as a critical focus in sustainable transportation planning. In this context, effective operation requires optimization that captures key operational factors. Passenger load varies over time, which changes train mass and traction demand. With reversible substations, part of regenerative braking energy can be absorbed on the AC side by station auxiliaries or returned to the grid. These mechanisms motivate an integrated formulation that accounts for both effects. To leverage these effects, this paper proposes an energy-efficient multi-train scheduling strategy that adjusts train dwell times and inter-train departure intervals. An integrated operation model captures the interaction between train mass dynamics and power flow on the traction network, and the resulting nonlinear problem is solved with the Adaptive Leader Salp Swarm Algorithm (ALSSA). On Xuzhou Metro Line 2, incorporating dynamic mass alone reduces external energy supply by 4.28 %, and the proposed co-optimization delivers a further 5.62 %, for a total saving of 9.67 %. The results indicate that jointly modelling passenger-mass dynamics and substation-side use of regenerative energy significantly improves energy efficiency.