Stochastic Modeling of Wind Turbines

In this paper we study statistical data collected from wind turbines located on the territory of the Republic of Poland. Sensors, mounted at three points of the wind power plant, took the readings of speed and wind direction. The readings were taken for 9 months with an interval of 10 minutes. The general direction of research aimed at the construction of the stochastic model that predicts the change in wind speed depending on time. The aim of this work is to find the optimal distribution for the approximation of available statistical data on wind speed. We examine four distributions with heavy tails, namely, the log-normal, gamma,Weibull and beta distribution. Each distribution is parameterized by three parameters (the beta distribution has four). For data processing, we used Python with NumPy, SciPy and Matplotlib. From the SciPy library we used statistics module that contains the function to search the parameters of the distribution provided by method of maximum likelihood. After finding the parameters of the distributions were drawn the graphs of the density distributions, which were verified with the histogram of the frequency distribution. The obtained results allow to assert that all distributions with good accuracy can be used for the purposes of approximation. However, the study quantile-quantile graphs revealed that the Weibull distribution better approximate extreme values. The obtained results are consistent with the data presented in the literature, whereWeibull distribution is often used to approximate the distribution of the wind speed. Our future work will focus on the problem of constructing a stochastic differential equation.