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Construction of SDE-based wind speed models with exponentially decaying autocorrelation

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  • Zárate-Miñano, Rafael
  • Milano, Federico

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.

Suggested Citation

  • Zárate-Miñano, Rafael & Milano, Federico, 2016. "Construction of SDE-based wind speed models with exponentially decaying autocorrelation," Renewable Energy, Elsevier, vol. 94(C), pages 186-196.
    • Handle: RePEc:eee:renene:v:94:y:2016:i:c:p:186-196
    DOI: 10.1016/j.renene.2016.03.026
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    References listed on IDEAS

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    1. Carta, J.A. & Ramírez, P. & Velázquez, S., 2009. "A review of wind speed probability distributions used in wind energy analysis: Case studies in the Canary Islands," Renewable and Sustainable Energy Reviews, Elsevier, vol. 13(5), pages 933-955, June.
    2. Lo Brano, Valerio & Orioli, Aldo & Ciulla, Giuseppina & Culotta, Simona, 2011. "Quality of wind speed fitting distributions for the urban area of Palermo, Italy," Renewable Energy, Elsevier, vol. 36(3), pages 1026-1039.
    3. 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.
    4. Calif, Rudy & Emilion, Richard & Soubdhan, Ted, 2011. "Classification of wind speed distributions using a mixture of Dirichlet distributions," Renewable Energy, Elsevier, vol. 36(11), pages 3091-3097.
    5. Kavasseri, Rajesh G. & Nagarajan, Radhakrishnan, 2005. "A multifractal description of wind speed records," Chaos, Solitons & Fractals, Elsevier, vol. 24(1), pages 165-173.
    6. Calif, Rudy, 2012. "PDF models and synthetic model for the wind speed fluctuations based on the resolution of Langevin equation," Applied Energy, Elsevier, vol. 99(C), pages 173-182.
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    Cited by:

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    4. Jónsdóttir, Guðrún Margrét & Milano, Federico, 2019. "Data-based continuous wind speed models with arbitrary probability distribution and autocorrelation," Renewable Energy, Elsevier, vol. 143(C), pages 368-376.

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