Comparative Analysis of Five Numerical Methods and the Whale Optimization Algorithm for Wind Potential Assessment: A Case Study in Whittlesea, Eastern Cape, South Africa

Abstract

This study explores the potential of wind energy to address electricity shortages in South Africa, focusing on the Ekuphumleni community in Whittlesea. Given the challenges of expanding the national grid to these areas, wind energy is considered to be a feasible alternative to provide clean, renewable energy and reduce fossil fuel dependence in this community. This research evaluates wind potential utilizing the two-parameter Weibull distribution, with scale and shape parameters estimated by five traditional numerical methods and one metaheuristic optimization technique: whale optimization algorithm (WOA). Goodness-of-fit tests, such as the coefficient of determination (R2) and wind power density error (WPDE), were utilized to determine the best method for accurately estimating Weibull scale and shape parameters. Furthermore, net fitness, which combines R2 and WPDE, was employed to provide a holistic assessment of overall performance. Whittlesea showed moderate wind speeds, averaging 3.88 m/s at 10 m above ground level (AGL), with the highest speeds in winter (4.87 m/s) and optimum in July. The WOA method outperformed all five numerical methods in this study in accurately estimating Weibull distribution parameters. Interestingly, the openwind method (OWM), a numerical technique based on iterative methods, and the Brent method showed comparable performance to WOA. The wind power density was 67.29 W/m2, categorizing Whittlesea’s potential as poor and suitable for small-scale wind turbines. The east wind patterns favor efficient turbine placement. The study recommends using augmented wind turbines for the site to maximize energy capture at moderate speeds.