Optimal sizing of variable renewable energy systems using two-stage stochastic programming: A comparative analysis with the deterministic approach

In feasibility studies for the optimal sizing of variable renewable energy source systems, it is essential to accurately assess economic performance and energy indicators to ensure project viability. However, such evaluation presents several challenges due to the inherent variability of renewable energy sources, which are strongly influenced by meteorological conditions, energy demand, which is driven by the behavior of end-users, and electricity prices, which are subject to the uncertainty and volatility of the energy markets. This work proposes a two-stage stochastic optimization framework for the optimal sizing of photovoltaic and battery energy storage systems, adaptable to various system configurations. Uncertainty is addressed using a probabilistic approach based on Monte Carlo simulations, with scenarios derived from historical data to capture realistic variability. The main contribution of this study is the development of a structured framework for the quantitative comparison between deterministic and stochastic optimization approaches. To assess the advantages of incorporating uncertainty, the framework introduces three evaluation metrics, namely consistency, stability, and effectiveness, the latter being based on the Value of the Stochastic Solution (VSS), which quantifies the benefit of stochastic optimization compared to a deterministic formulation. The framework is tested on four case studies, including both aggregate and Renewable Energy Community configurations for the years 2025 and 2030. Results show that deterministic solutions can lead to a decrease of the objective function of up to 28% of when tested under new uncertainty realizations, while stochastic solutions remain stable within 4%. The stochastic formulation also provides a VSS of up to +10%, corresponding to higher total annual savings compared to the deterministic approach. Results also show the installation of storage systems further enhances system robustness, reducing sensitivity to uncertainty and improving economic performance. Overall, the proposed framework demonstrates that explicitly incorporating uncertainty in early-stage energy system planning leads to more reliable, stable, and economically efficient designs.