Optimizing nuclear-renewable hybrid energy systems for cost efficiency based on energy security concerns in Puerto-Rico

This study develops an optimized scientific framework to identify least-cost energy mixes while enabling scale-invariant energy security assessment for Puerto Rico's clean-energy transition. A nonlinear programming model is formulated to minimize total energy cost, and a Gaussian Process Regression (GPR) surrogate with explainability is employed to identify key cost drivers and quantify techno-economic uncertainty. To address the complexity of hybrid energy systems, fifteen relevant Nuclear-Renewable Hybrid Energy System (N-RHES) features are systematically aggregated into six energy security variables representing system capacity, storage, renewable penetration, and demand characteristics. Using these variables, a dimensional-scaling framework based on the Buckingham π-theorem is developed to construct three dimensionless π-groups corresponding to Reliability, Resilience, and Renewability (3R). These metrics transform system-specific optimization outputs into transferable, scale-invariant engineering performance indicators suitable for comparing islanded energy systems of different sizes. The GPR surrogate provides posterior mean predictions [Formula: see text] and predictive variance [Formula: see text] to characterize uncertainty in Levelized Cost of Energy (LCOE) and energy security metrics. SHapley Additive exPlanations (SHAP) analysis indicates that nuclear capacity reduces LCOE by 1.4 ¢/kWh, whereas wind increases cost by 0.9 ¢/kWh in high-penetration scenarios. Under techno-economic uncertainty, the predicted LCOE is [Formula: see text] ¢/kWh, with the optimal nuclear-hybrid solution achieving 9.6 ¢/kWh while remaining below the 11.0 ¢/kWh policy constraint. Five hybrid configurations combining wind, solar PV, geothermal generation, battery storage, and hydrogen fuel-cell systems are analyzed, with selected cases integrating Small Modular Reactor (SMR) base-load supply. Optimization identifies three recommended configurations, with an SMR-renewables hybrid emerging as the least-cost solution. Configuration 5 achieves an LCOE of 10.0 ¢/kWh, delivers 70% renewable contribution, and reduces total energy cost by 18% relative to fossil-dominant mixes. By integrating techno-economic optimization with π-based dimensional scaling, the proposed framework provides physically interpretable and transferable energy security metrics applicable to heterogeneous hybrid energy systems and hurricane-exposed island grids.