Progressive Linear Programming Optimality Method Based on Decomposing Nonlinear Functions for Short-Term Cascade Hydropower Scheduling

Short-term optimal scheduling of cascade hydropower stations enhances their flexible regulation and power generation capabilities. However, nonlinear function relationships and multistage and hydraulic interdependencies present significant challenges, resulting in considerable solution errors, premature convergence, and high computational demands. This study proposes a progressive linear programming method that decomposes nonlinear functions to address these challenges. First, to accurately represent nonlinear functions and mitigate computational complexity, the entire feasible domain is partitioned into multiple contiguous subdomains in which nonconvex nonlinear functions within each subdomain can be equivalently replaced by linear relationships. Second, a progressive linear programming optimization algorithm is devised to prevent premature convergence, utilizing continuous subdomains rather than discrete points as state variables and incorporating the progressive optimality principle. Finally, to increase the solution efficiency, a dimensionality reduction strategy via the feasible domain state dynamic acquisition method is presented and optimized after excluding the infeasible states in each stage. The simulation of three cascade hydropower stations in a river basin in southwest China shows that the proposed method can achieve a superior peak regulation effect compared to the conventional mixed integer linear programming and progressive optimality algorithm. During the dry and wet seasons, the residual load peak–valley differences at the three stations are reduced by 612 MW and 521 MW compared to the MILP and 1889 MW and 2439 MW compared to the POA, which underscores the effectiveness of the method in optimizing the short-term scheduling of cascade hydropower stations.