Construction of SDE-based wind speed models with exponentially decaying autocorrelation. (August 2016)

• Record Type: Journal Article
• Authors: Zárate-Miñano, Rafael; Milano, Federico
• Is Part Of: Renewable energy. Volume 94(2016)
• Page Start: 186
• Page End: 196
• Publication Date: 2016-08
• Subjects: Stochastic differential equations -- Wind speed modeling -- Stationary process -- Regression theorem -- Exponential autocorrelation -- Non-gaussian processes; Renewable energy sources -- Periodicals; Power resources -- Periodicals; Énergies renouvelables -- Périodiques; Ressources énergétiques -- Périodiques; 333.794
• DOI: 10.1016/j.renene.2016.03.026
• Languages: English
• ISSNs: 0960-1481

Abstract

Abstract: This paper provides a systematic method to build wind speed models based on stochastic differential equations (SDEs). The resulting models produce stochastic processes with a given probability distribution and exponentially decaying autocorrelation function. The only information needed to build the models is the probability density function of the wind speed and its autocorrelation coefficient. Unlike other methods previously proposed in the literature, the proposed method leads to models able to reproduce an exact exponential autocorrelation even if the probability distribution is not Gaussian. A sufficient condition for the property above is provided. The paper includes the explicit formulation of SDE-based wind speed models obtained from several probability distributions used in the literature to describe different wind speed behaviors. All models are validated through numerical simulations. Finally, the proposed procedure is applied to model the wind speed observed at a meteorological station in New Zealand. A comparison of the statistical properties of the wind speed measurements and of the stochastic process generated by the SDE model is also provided. Highlights: The paper proposes a method based on the regression theorem and the Fokker–Planck equation, to construct wind speed models. The information required is the probability distribution and the autocorrelation function of the wind speed. The proposed models accurately reproduce both the probability distribution and the autocorrelation of the wind speed. The paper provides a collection of SDE-based models ready to be used in different studies related to wind power.