Scenario-Based Stochastic Optimization for Long-Term Scheduling of Hydro–Wind–Solar Complementary Energy Systems

As the global energy transition accelerates, clean energy development has surged. However, accurately modeling correlations and uncertainties of hydro, wind, and photovoltaic energy remains challenging in long-term scheduling for energy complementarity. This study employs Latin hypercube sampling and Cholesky decomposition to capture the temporal correlations of water runoff, wind, and photovoltaic resources. It generates numerous scenarios for uncertainty simulation. The scenario set is reduced based on probability distance while maintaining a high-fidelity approximation. A stochastic dual-objective model is proposed for long-term multi-energy complementary system scheduling (LMCS), aiming to maximize expected revenue considering carbon emission costs while ensuring minimum power output guarantees. An evolutionary algorithm—namely, an orthogonal multi-population evolutionary (OMPE) algorithm based on orthogonal design and a multi-population search framework—is introduced, along with constraint-handling strategies. Three annual-regulation hydropower stations in the Hongshui River Basin serve as a case study. The experimental results indicate that generated scenarios capture temporal characteristics with high accuracy. The proposed algorithm efficiently solves the LMCS problem, achieving average increases of 5.46% and 3.89% in revenue and minimal output compared to benchmarks. The validation results demonstrate that orthogonalization-based initialization, recombination operators, and dominance rules significantly enhance OMPE performance. Sensitivity analysis indicates that economic efficiency and risk trade-offs can be adjusted by varying scenario numbers.