Comparative analysis and application of new generation parameter methods for Weibull distribution in wind energy systems

The wind speed characteristics of a region must be determined and analyzed before installing any wind energy conversion system. Many different methods have been developed to determine the parameters of the two-parameter Weibull distribution, which is one of the most important approaches used for the determination, analysis, modeling, and estimation of the wind speed characteristic, and it is still a subject of research today. By using parameter estimation methods, the shape (k) and scale (c) parameters of the two-parameter Weibull distribution can be determined, and the wind speed characteristics can be modeled in the most appropriate way for a studied region. In this study, some newly proposed methods have been used apart from the well-known parameter estimation methods to analyze and evaluate comparably for the data of 10 regions of Turkey with high wind energy profile. A total of 11 methods have been used in this study, namely, Graphical Method (GM), Maximum Likelihood Method (MLM), Modified Maximum Likelihood Method (MMLM), Energy Pattern Factor Method (EPFM), Wind Energy Intensification Method (WEIM), Justus Moment Method (JMM), Power Density Method (PD), Lysen Method (LM), Method of Moments (MOM), Mabchour's Method (MMab), and Alternative Maximum Likelihood Method (AML). Among these, while WEIM was proposed in 2020, the EPFM and PD methods are also proposed recently. And despite being proposed in 1999, MMab has not been compared in many studies in the literature. All the methods mentioned above have been compared to each other for performance and efficiency using the data for the 10 regions, and the results have been interpreted. The comparison has been held out in three steps; i) By inspecting the fit that has been provided by the probability density functions which have been created by using the parameters that have been estimated by the methods, ii)By comparing the wind energy density which has been estimated by these methods to the actual wind energy densities of the studied regions, and iii) By using a total of 4 error performance metrics three of which are used in Statistics namely, Root Mean Squared Error (RMSE), Coefficient of Determination (R2), Chi-Square Test (χ2), and one other method which is used in these type of studies, called Wind Energy Error (WEE). The analyzes were carried out in a Matlab software environment. The wind energy densities of the regions have also been calculated and added as graphs in this study. The inspection made have been carried out based on region. As a result of the analysis, the most appropriate method determined for each region was specified at the end of the study. On the other hand, when looking at the overall study, it was seen that the model performance success for JMM was high.