A search algorithm that couples physical rules for balancing wind and solar output fluctuations via hydropower in ultra-short-term scheduling

Hydropower serves as a critical flexible resource in ultra-short-term scheduling due to its operational elasticity, while the output uncertainties from wind and solar energy frequently induce power fluctuations that compromise grid stability and prolong optimization processes under stringent temporal constraints. In this study, an ultra-short-term scheduling model based on the search algorithm of coupled physical rules that uses hydropower to balance the output fluctuations is proposed to address these problems. First, a three-layer scheduling objective that strategically coordinates hydroelectric flexibility is developed to suppress wind and solar power volatility and minimize the number of hydropower stations involved in regulation. Second, a universal method for linearizing piecewise interval constraints by employing binary variables is designed to ensure that the model meets feasibility specifications when running. Finally, a search algorithm based on the physical rules of cascade hydropower stations, such as hydraulic and electrical connections, is constructed to reduce the calculation time. A case study involving four hydropower plants and adjacent wind and solar units demonstrates the model's effectiveness in balancing wind and solar power fluctuations. Compared to traditional mixed-integer linear programming methods, the proposed search algorithm shortens solution time by 52.75 s, achieving a 77.7 % improvement in computational efficiency.