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Modeling Wind Speed Based on Fractional Ornstein-Uhlenbeck Process

Author

Listed:
  • Sergey Obukhov

    (Department of Electric Power Systems, National Research Tomsk Polytechnic University, 634050 Tomsk, Russia)

  • Emad M. Ahmed

    (Department of Electrical Engineering, College of Engineering, Jouf University, Sakaka 72388, Saudi Arabia)

  • Denis Y. Davydov

    (Department of Electric Power Systems, National Research Tomsk Polytechnic University, 634050 Tomsk, Russia)

  • Talal Alharbi

    (Department of Electrical Engineering, College of Engineering, Qassim University, Buraydah 52571, Saudi Arabia)

  • Ahmed Ibrahim

    (Department of Electric Power Systems, National Research Tomsk Polytechnic University, 634050 Tomsk, Russia
    Department of Electrical Power and Machines, Zagazig University, Zagazig 44511, Egypt)

  • Ziad M. Ali

    (College of Engineering at Wadi Addawaser, Prince Sattam Bin Abdulaziz University, Wadi Addawaser 11991, Saudi Arabia
    Electrical Engineering Department, Faculty of Engineering, Aswan University, Aswan 81542, Egypt)

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.

Suggested Citation

  • Sergey Obukhov & Emad M. Ahmed & Denis Y. Davydov & Talal Alharbi & Ahmed Ibrahim & Ziad M. Ali, 2021. "Modeling Wind Speed Based on Fractional Ornstein-Uhlenbeck Process," Energies, MDPI, vol. 14(17), pages 1-15, September.
    • Handle: RePEc:gam:jeners:v:14:y:2021:i:17:p:5561-:d:629768
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    References listed on IDEAS

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    1. Dinh Thanh Viet & Vo Van Phuong & Minh Quan Duong & Quoc Tuan Tran, 2020. "Models for Short-Term Wind Power Forecasting Based on Improved Artificial Neural Network Using Particle Swarm Optimization and Genetic Algorithms," Energies, MDPI, vol. 13(11), pages 1-22, June.
    2. Duan, Jikai & Zuo, Hongchao & Bai, Yulong & Duan, Jizheng & Chang, Mingheng & Chen, Bolong, 2021. "Short-term wind speed forecasting using recurrent neural networks with error correction," Energy, Elsevier, vol. 217(C).
    3. Arenas-López, J. Pablo & Badaoui, Mohamed, 2020. "The Ornstein-Uhlenbeck process for estimating wind power under a memoryless transformation," Energy, Elsevier, vol. 213(C).
    4. Wang, Jian Qi & Du, Yu & Wang, Jing, 2020. "LSTM based long-term energy consumption prediction with periodicity," Energy, Elsevier, vol. 197(C).
    5. Peter Alaton & Boualem Djehiche & David Stillberger, 2002. "On modelling and pricing weather derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 9(1), pages 1-20.
    6. Alhassan H. Alattar & S. I. Selem & Hamid M. B. Metwally & Ahmed Ibrahim & Raef Aboelsaud & Mohamed A. Tolba & Ali M. El-Rifaie, 2019. "Performance Enhancement of Micro Grid System with SMES Storage System Based on Mine Blast Optimization Algorithm," Energies, MDPI, vol. 12(16), pages 1-23, August.
    7. Tian, Linlin & Song, Yilei & Zhao, Ning & Shen, Wenzhong & Wang, Tongguang & Zhu, Chunling, 2020. "Numerical investigations into the idealized diurnal cycle of atmospheric boundary layer and its impact on wind turbine's power performance," Renewable Energy, Elsevier, vol. 145(C), pages 419-427.
    8. Zárate-Miñano, Rafael & Anghel, Marian & Milano, Federico, 2013. "Continuous wind speed models based on stochastic differential equations," Applied Energy, Elsevier, vol. 104(C), pages 42-49.
    9. Iversen, Emil B. & Morales, Juan M. & Møller, Jan K. & Madsen, Henrik, 2016. "Short-term probabilistic forecasting of wind speed using stochastic differential equations," International Journal of Forecasting, Elsevier, vol. 32(3), pages 981-990.
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