The Ornstein-Uhlenbeck process for estimating wind power under a memoryless transformation

• Published in: Energy (Oxford) Vol. 213; p. 118842
• Main Authors: Arenas-López, J. Pablo, Badaoui, Mohamed
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 15-12-2020; Elsevier BV
• Subjects: Autocorrelation functions; Comparative analysis; Computer applications; Datasets; Differential equations; Memoryless transformation; Ornstein-Uhlenbeck process; Probability density function; Probability density functions; Statistical analysis; Statistics; Stochasticity; Transformations (mathematics); Turbines; Wind power; Wind speed; Wind turbines; Mexico; Probability density function; Ornstein-uhlenbeck process; Wind speed; Wind power; Memoryless transformation
• ISSN: 0360-5442; 1873-6785
• DOI: 10.1016/j.energy.2020.118842

The main purpose is to build a wind speed model to assess its impact on the power output estimate of a wind turbine. This modelling is based on stochastic differential equations and memoryless transformations, considering a stable numerical scheme capable to optimize the computational complexity. According to statistical characteristics of a wind speed dataset recorded at a given location in Mexico, the model is parameterized for six probability density functions (PDF), showing exponential decay of the autocorrelation function. The suitability of the model for wind speed modelling and power output estimate is evaluated through a comparative analysis between the real dataset and the simulations; moreover, the quality of the findings have been assessed employing statistical measures criteria. Finally, and contrary to what has been reported, that is, the Weibull PDF is the best one to characterize wind speed in many regions of the world including Mexico, it turns out that among the six PDFs considered in this work, the probability density functions Beta and Log-Pearson 3 represent the best fit to the real wind speed data as well as providing an estimate of less than 1% of the semiannual produced energy by a wind turbine.
•Analysis of a wind speed model based on the Ornstein-Uhlenbeck process.•The Beta and Log-Pearson 3 distributions present the best performance.•Computational complexity and stability analysis are developed.•A fixed initial condition can significantly affect the evaluation criteria.