Abstract
The two-parameter Weibull probability density function (PDF) is widely utilized by different researchers and engineers to fit wind speed data for statistical analysis and modeling. The characterization of wind resources in the frequency and probability domain is necessary to estimate the power output potential of new wind energy projects. Considering that exist a variety of Weibull equations evidenced in the literature review, this article evaluates 11 different methods to calculate the shape and scale parameters of the Weibull PDF. In this sense, it was written an algorithm within a Matlab function that solves the 11 methods for calculating the Weibull PDF parameters. Wind speed data extracted from the ERA5 database was used as input data for applying the proposed algorithm, and statistical parameters such as the Root Mean Square Error (RMSE), the Relative Root Mean Square Error (RRMSE), and chi-square test (X2) we utilized for assessing the performance of each one of the 11 methods for modeling the wind distribution. The statistical results pointed that the numerical iteration methods (e.g. maximum likelihood method) showed better results than parameterized equations such as the Graphical Method, hence, this research recommends the implicit methods for determining Weibull PDF parameters of wind speed data.
Highlights
The growing energy demand around the world requires the generation of clean and renewable energy [1]
E −(vc )k cc where, v is the wind speed measured in m/s, k is the shape parameter, and c the scale parameter measured in m/s
According to the results of Graphical Methods (GM), it was observed that this method could not simulate the natural distribution of the wind speed (Figure 1), the statistical results showed the highest values of root mean squared error (RMSE), Relative root mean square error (RRMSE), and χ2
Summary
The growing energy demand around the world requires the generation of clean and renewable energy [1]. Wind energy allows the generation of electricity with low Greenhouse Gas emissions (GHG) compared to fossil fuels. Wind energy is an accessible, renewable, and at the same time a profitable source that is growing rapidly [3], it can be used to satisfy a large part of the planet's energy demand reducing the GHG [4]. The use of statistical tools allows a sound estimation of wind energy through in situ data from specific locations [5], generally, which eases the identification of potential areas for the construction of new wind farms [6]. The most common probability functions for characterizing the wind speed measured at a given location with monthly or yearly time horizons, are the Weibull, Rayleigh, and lognormal distributions. Among the most common distribution models, the Weibull function is considered the best [7]
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