Statistical modelling and optimization for designing renewable energy systems

We explore the optimal allocation of solar, wind, and battery resources for large-scale renewable energy production and transmission. Using a combination of statistical modelling and optimization techniques, we analyze historical and synthetic power generation data to identify cost-effective investment strategies. To generate synthetic long-term scenarios, we extract seasonal trends from historical data and apply bootstrapping techniques to preserve statistical properties while simulating future variability. We employ a two-step optimization approach, first using a global method to identify the most promising region, followed by a local method for refinement. We compare single-year solutions and analyze their generalizability. 15-year and 100-year forecasts indicate that solutions incorporating long-term variability lead to more resilient planning. We find that the optimal mix of solar and wind remains stable across different time horizons, while battery storage varies to account for intermittency.