Stochastic Optimization Approach for Off-Grid Integrated Energy System Considering Renewable Energy Uncertainty

Off-grid integrated energy systems offer a practical solution for remote regions lacking access to the main power grid; however, their planning and design are challenged by the inherent uncertainty of renewable energy resources. To address this issue, this paper proposes a stochastic optimization framework for off-grid integrated energy systems that explicitly accounts for wind speed and solar irradiance variability. Continuous probability distributions combined with Monte Carlo sampling are employed to generate stochastic scenarios, which are embedded into a bi-objective optimization model minimizing total system cost and pollutant emissions under power balance and device operational constraints. Unlike existing studies that primarily focus on cost–reliability trade-offs, this work introduces the Renewable Energy Penetration Rate (REPR) as a quantitative, planning-oriented indicator and systematically investigates its interactions with economic performance, pollutant emissions, and renewable uncertainty. The REPR is not only used to characterize renewable utilization levels, but also to support investment decision-making and the comparative assessment of Pareto-optimal configurations. A real-world off-grid service area is adopted as a case study. The results show that increasing the REPR leads to a significant reduction in carbon emissions while exhibiting a nonlinear impact on total system cost. Specifically, the proposed framework identifies a Pareto-optimal solution set in which the total system cost varies within 40–92 million ¥, carbon emissions are reduced by 86% compared with diesel-dominated configurations, and the REPR increases from 70% to 96.4% as renewable capacity expands. In addition, the analysis reveals that higher renewable volatility requires a larger stochastic sample size to ensure solution stability. These findings demonstrate that the proposed framework provides a more comprehensive and decision-relevant assessment of off-grid integrated energy systems under renewable uncertainty, thereby offering practical insights for low-carbon and economically viable system planning.