Renewable Energy Supply Mode-Based Multi-Objective Daily Optimal Control of Cascade Pumping Stations with High-Frequency Data

This study proposes a multi-objective optimal control model for cascade pumping station (CPS) systems under renewable energy (RE) supply scenarios, aiming to enhance operational flexibility and promote low-carbon operation. The model integrates a segmented electricity pricing strategy, a one-dimensional unsteady flow simulation, and high-frequency data-based unit performance curves. A novel three-phase particle initialization strategy is developed to improve the feasibility and convergence of the optimization process. The optimization framework leverages multi-objective particle swarm optimization (MOPSO) to jointly minimize operational costs, maximize RE utilization, and reduce unit adjustment frequency. The proposed model is applied to two real-world CPSs in the Jiaodong Area Yellow River Water Diversion Project. The results demonstrate that, across different RE supply windows ([10:00–16:00], [11:00–15:00], and [12:00–14:00]), the optimized schemes achieve reductions in operational costs of 0.20%–9.44%, and improvements in RE utilization of 10.35%–56.25% compared to actual schemes. Furthermore, the optimization contributes significantly to carbon emission reductions. Given the presence of numerous similar CPS systems in the region, the proposed scheduling strategy offers substantial potential for promoting flexible load management and advancing renewable energy integration in large-scale water transfer projects.