Abstract: Due to China's "high in the west and low in the east" topography, heavy-haul railways present the transportation characteristic of "heavy-haul downward and light-haul upward". This leads to poor traction-braking power matching during operation, resulting in low regenerative braking energy utilization and high electricity costs. Constructing a flexible power supply system with energy storage for heavy-haul railways helps promote high-proportion absorption of regenerative braking energy and achieve energy conservation and cost reduction. However, uncertainties in train load processes challenge efficient energy regulation. Accordingly, this study builds a probabilistic model for train load processes to characterize uncertainties, then develops a stochastic optimal operation model. Taking probabilistic loads as input, it solves matching power regulation strategies, providing references for engineering optimization of such systems.