Spatio-Temporal Cooperative Optimization of Regenerative Braking Energy in Urban Rail Transit Based on Energy Flow Operator Decoupling and Phase Plane Dynamics

As urban rail transit systems evolve within the Industrial Internet of Things (IIoT), the intelligent recovery of regenerative braking energy becomes critical for energy efficiency. However, the existing train operation optimizations primarily focus on time-domain synchronization, frequently neglecting the spatial impedance constraints of the DC traction network. This oversight creates a discrepancy between theoretical energy matching and actual absorption. To address this, this paper proposes a spatiotemporal synergistic optimization framework integrating the analysis of electrical energy transmission factors and train relative motion. First, a dynamic multi-node circuit model based on Kirchhoff’s laws is established to characterize train fleet operations. By evaluating electrical energy transmission factors, the current distribution ratio and line impedance loss are identified as primary determinants of absorption efficiency. This physically quantifies the coupling among instantaneous energy distribution, transmission loss, and source-load relative distance. Second, a time-domain integration-based gradient analysis framework is formulated to deconstruct the energy gradient into amplitude and directional components. By mapping the relative position and speed of interacting trains, their relative motion states are systematically categorized. Subsequently, an adaptive gradient optimization strategy based on these motion states is introduced, which fine-tunes dwell times to precisely guide train trajectories into a low-impedance “optimal window” for energy absorption. Finally, a case study using operational data from Luoyang Metro Line 1 validates the proposed framework. Results demonstrate that the framework achieves dual spatiotemporal matching of braking and traction trains, outperforming the traditional fixed timetable and improving the regenerative braking energy absorption rate by approximately 13%.