Two-stage stochastic robust optimization for the planning and operation of rural integrated energy systems considering source-load uncertainties

The transition to renewable energy in rural areas is hindered by the inherent unpredictability of renewable resources and load demand. This study proposes a two-stage stochastic robust optimization (TS-SRO) framework to address the integrated planning and operation of rural energy systems under source-load uncertainties. The optimal capacity allocation for renewable energy generation, storage, and conversion devices is determined in the first stage, while the second stage optimizes multi-energy dispatch under uncertainty. Renewable energy fluctuations are modeled through data-driven stochastic scenarios derived from historical data using a 0–1 programming clustering method. In contrast, load uncertainties are characterized via confidence interval-based box-type uncertainty sets. A Nested Column-and-Constraint Generation (NCCG) algorithm combined with dynamic weighting is introduced to resolve the computational complexity arising from multi-objective optimization and uncertainty coupling. A case study in northern China demonstrates the model’s efficacy: compared to the baseline scenario, the TS-SRO approach reduces total energy costs by 37.62% and carbon emissions by 85.33%. Sensitivity analyses reveal that economic performance deteriorates with increasing uncertainty budgets and confidence intervals while robustness improves. Notably, biogas combined heat and power unit pricing significantly influences system economics, whereas solar water heaters and heat pumps show minimal impact.