Approaches to Stochastic Modeling of Wind Turbines

TL;DR

This paper evaluates different statistical distributions to model wind speed data from Polish turbines, finding Weibull distribution most effective for extreme values, and aims to develop a time-dependent stochastic wind model.

Contribution

It compares four distributions for wind speed modeling and identifies Weibull as the most suitable for extreme values, contributing to improved stochastic wind modeling methods.

Findings

Weibull distribution best models extreme wind speeds.

All considered distributions adequately fit the data.

Future work includes larger datasets and time-evolution modeling.

Abstract

Background. This paper study statistical data gathered from wind turbines located on the territory of the Republic of Poland. The research is aimed to construct the stochastic model that predicts the change of wind speed with time. Purpose. The purpose of this work is to find the optimal distribution for the approximation of available statistical data on wind speed. Methods. We consider four distributions of a random variable: Log-Normal, Weibull, Gamma and Beta. In order to evaluate the parameters of distributions we use method of maximum likelihood. To assess the the results of approximation we use a quantile-quantile plot. Results. All the considered distributions properly approximate the available data. The Weibull distribution shows the best results for the extreme values of the wind speed. Conclusions. The results of the analysis are consistent with the common practice of using the Weibull distribution for wind speed modeling. In the future we plan to compare the results obtained with a much larger data set as well as to build a stochastic model of the evolution of the wind speed depending on time.