Physics-constrained large language model-assisted optimal scheduling approach for hydro-wind-solar systems considering multi-level backwater effects

Multi-level backwater effects couple downstream reservoir water levels with upstream tailwater levels and effective heads, which complicates the long-term coordinated scheduling of cascade hydro–wind–solar systems. This study addresses this scheduling problem by developing a physics-constrained Large Language Model (LLM)-assisted optimal scheduling approach. The approach combines POA decomposition, deterministic nonlinear physical evaluation, hard-feasibility screening, and LLM-assisted adaptive strategy design. The LLM operates at the strategy-design level, whereas hydraulic calculation, constraint verification, and schedule evaluation remain within the deterministic physical model. Case studies on a large-scale cascade hydro-wind-solar system show that the proposed approach can generate feasible and competitive scheduling strategies in representative wet, normal, and dry years, as well as Monte Carlo wind-solar scenarios. Compared with the expert-designed engineered algorithm (EDEA) baseline, it increases total power generation by up to 9 . 4 4 × 1 0 8 kWh and improves computational efficiency by up to 76.2 times in the tested cases. Compared to representative optimization methods, including metaheuristics, learning-based methods, and mathematical programming, the proposed approach achieves a favorable generation–computation trade-off. These results support the proposed scheduling approach within the tested cascade system. They also show that feedback-based LLM-assisted strategy design can improve the search process when coupled with POA decomposition, deterministic physical evaluation, and hard-feasibility screening.