Hybrid PSO–L-BFGS-B Optimization of Small-Scale HAWTs for Low-Wind Tropical Sites: Blades Length and Hub Height Tuning with Multi-Site Indonesian Data

Abstract

Wind energy, offers strong potential for tropical regions, yet low and variable wind speeds limit the efficiency of conventional turbines. Therefore, this study proposes a hybrid optimization technique integrating particle swarm optimization (PSO) with the Limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS-B) algorithm to determine the optimal blade length and hub height of small-scale horizontal axis wind turbines (HAWTs). Multi-year wind datasets (2017–2020) from five Indonesian sites Jambi, South Sulawesi, NTB, NTT, and Maluku were statistically characterized using Weibull and Bi-Weibull distribution and incorporated into annual energy production (AEP) modelling. The hybrid PSO–L-BFGS-B method achieved 5–15% higher AEP than standard PSO, and 11–25% higher AEP compared to the baseline TSD-500 turbine, while also exhibiting smoother convergence and reduced interquartile variability across 30 independent runs. Sensitivity analysis showed that hub height exerts a stronger influence on AEP than blade length, reflecting the aerodynamic advantage of elevated rotors under low-wind tropical conditions. The results demonstrate that hybrid meta-heuristic optimization effectively tailors small-scale wind turbines for reliable and sustainable energy generation in tropical developing regions.