Modeling Wind Speed Based on Fractional Ornstein-Uhlenbeck Process

Sergey Obukhov,Ziad Ali,Denis Davydov,Talal Alharbi,Ahmed Ibrahim,Emad Ahmed

doi:10.3390/en14175561

Abstract

The primary task of the design and feasibility study for the use of wind power plants is to predict changes in wind speeds at the site of power system installation. The stochastic nature of the wind and spatio-temporal variability explains the high complexity of this problem, associated with finding the best mathematical modeling which satisfies the best solution for this problem. In the known discrete models based on Markov chains, the autoregressive-moving average does not allow variance in the time step, which does not allow their use for simulation of operating modes of wind turbines and wind energy systems. The article proposes and tests a SDE-based model for generating synthetic wind speed data using the stochastic differential equation of the fractional Ornstein-Uhlenbeck process with periodic function of long-run mean. The model allows generating wind speed trajectories with a given autocorrelation, required statistical distribution and provides the incorporation of daily and seasonal variations. Compared to the standard Ornstein-Uhlenbeck process driven by ordinary Brownian motion, the fractional model used in this study allows one to generate synthetic wind speed trajectories which autocorrelation function decays according to a power law that more closely matches the hourly autocorrelation of actual data. In order to demonstrate the capabilities of this model, a number of simulations were carried out using model parameters estimated from actual observation data of wind speed collected at 518 weather stations located throughout Russia.

Highlights

Most of the budget of the Russian Federation is provided by revenues from the sale of oil and gas, which determines the leading role of the oil and gas industry in the social-economic development of the country
Taking into account that the autocorrelation of real processes occurring in nature rarely correspond to an exponential function, in this work we investigated the possibility of using a model based on the fractional Ornstein-Uhlenbeck process, which allows for the generation of synthetic wind speed data with the property of long-range dependence and autocorrelation, a function that decreases according to a power law
The article presents a wind speed stochastic differential equations (SDE)-model based on a fractional Ornstein-Uhlenbeck process with a periodic long-run mean to capture the diurnal cycle and incorporate seasonal variations, and perform more accurate modeling operating modes of wind energy based power systems

Summary

Introduction

Most of the budget of the Russian Federation is provided by revenues from the sale of oil and gas, which determines the leading role of the oil and gas industry in the social-economic development of the country. The well-known standard designs of power supply systems do not always meet the established reliability requirements, which requires the use of new technical solutions. One of such solutions is the use of wind power plants in power supply systems. The results of the research carried out prove that the use of wind turbines in the power supply systems of technological facilities in the oil and gas industry provides a decrease in overall energy consumption and the cost of extracted geo resources, as well as increases environmental and energy security in areas of decentralized energy supply

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