Stochastic Optimization and Reliability Analysis of Hybrid Solar–Battery Systems Under Uncertainty

Hybrid solar–battery systems are increasingly deployed in off-grid and weak-grid regions to provide sustainable and reliable energy access. These systems combine photovoltaic (PV) generation with battery storage to ensure continuous supply despite intermittent solar conditions. Designing such systems is challenging due to variability and uncertainty in solar irradiance, load demand, and component performance. Deterministic sizing methods, relying on average conditions, often result in under-dimensioned systems prone to outages or over-dimensioned systems with high capital costs. This paper presents an integrated stochastic optimization framework for hybrid solar–battery system design under uncertainty. The approach models the probabilistic behavior of solar irradiance and load demand and uses Monte Carlo simulation to evaluate system performance across thousands of scenarios. Key reliability indices, including Loss of Power Supply Probability (LPSP) and Expected Energy Not Supplied (EENS), are computed to quantify the cost–reliability trade-off. Advanced metaheuristic algorithms, such as Particle Swarm Optimization (PSO) and Genetic Algorithms (GA), are employed to efficiently search the non-linear, non- convex design space, handling mixed discrete–continuous variables and probabilistic constraints. Sensitivity analyses assess the impact of battery degradation, discount rate variations, and load growth scenarios on the optimal system design. The results demonstrate that the stochastic approach substantially improves re- liability while controlling costs compared to deterministic methods. This framework offers a rigorous tool for uncertainty-aware hybrid system planning, applicable to remote electrification, weak-grid enhancement, and sustainable microgrid deployment.