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Stochastic wind speed modelling for estimation of expected wind power output

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  • Loukatou, Angeliki
  • Howell, Sydney
  • Johnson, Paul
  • Duck, Peter

Abstract

Increased wind energy penetration causes problems to the operation and system balancing of electric power systems. This in turn leads to the need for more detailed wind power modelling. The modelling and management of wind power involves two stages, neither of which is analytically tractable. In particular, the first stage involves stochastic variations in wind speed; wind speed typically presents noisy short-term variations, plus cyclicality over periods of 24 h and longer. The second stage refers to stochastic variations of the resulting wind power output, a non-linear function of wind speed. This paper proposes and tests an Ornstein-Uhlenbeck Geometric Brownian Motion model in continuous time to represent the wind speed, while including its longer-term daily cycle. It also illustrates a partial differential equation model of the wind speed and of the resulting wind power output, aiming at computing both their statistics. The proposed stochastic model has the potential to be used for various applications where wind speed or wind power are stochastic inputs, such as the optimal valuation of energy storage or system balancing. We verify by statistical tests that the results from the proposed model for the wind speed and the wind power match those from the empirical data of a wind farm located in Spain.

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  • Loukatou, Angeliki & Howell, Sydney & Johnson, Paul & Duck, Peter, 2018. "Stochastic wind speed modelling for estimation of expected wind power output," Applied Energy, Elsevier, vol. 228(C), pages 1328-1340.
    • Handle: RePEc:eee:appene:v:228:y:2018:i:c:p:1328-1340
    DOI: 10.1016/j.apenergy.2018.06.117
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    1. Xydas, Erotokritos & Qadrdan, Meysam & Marmaras, Charalampos & Cipcigan, Liana & Jenkins, Nick & Ameli, Hossein, 2017. "Probabilistic wind power forecasting and its application in the scheduling of gas-fired generators," Applied Energy, Elsevier, vol. 192(C), pages 382-394.
    2. Morales, J.M. & Mínguez, R. & Conejo, A.J., 2010. "A methodology to generate statistically dependent wind speed scenarios," Applied Energy, Elsevier, vol. 87(3), pages 843-855, March.
    3. Jan Kloppenborg Møller & Marco Zugno & Henrik Madsen, 2016. "Probabilistic Forecasts of Wind Power Generation by Stochastic Differential Equation Models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 35(3), pages 189-205, April.
    4. Verdejo, Humberto & Awerkin, Almendra & Saavedra, Eugenio & Kliemann, Wolfgang & Vargas, Luis, 2016. "Stochastic modeling to represent wind power generation and demand in electric power system based on real data," Applied Energy, Elsevier, vol. 173(C), pages 283-295.
    5. 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.
    6. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
    7. Sinden, Graham, 2007. "Characteristics of the UK wind resource: Long-term patterns and relationship to electricity demand," Energy Policy, Elsevier, vol. 35(1), pages 112-127, January.
    8. Li, Hongmin & Wang, Jianzhou & Lu, Haiyan & Guo, Zhenhai, 2018. "Research and application of a combined model based on variable weight for short term wind speed forecasting," Renewable Energy, Elsevier, vol. 116(PA), pages 669-684.
    9. Altunkaynak, Abdüsselam & Erdik, Tarkan & Dabanlı, İsmail & Şen, Zekai, 2012. "Theoretical derivation of wind power probability distribution function and applications," Applied Energy, Elsevier, vol. 92(C), pages 809-814.
    10. Suomalainen, K. & Silva, C. & Ferrão, P. & Connors, S., 2013. "Wind power design in isolated energy systems: Impacts of daily wind patterns," Applied Energy, Elsevier, vol. 101(C), pages 533-540.
    11. Villanueva, D. & Feijóo, A., 2010. "Wind power distributions: A review of their applications," Renewable and Sustainable Energy Reviews, Elsevier, vol. 14(5), pages 1490-1495, June.
    12. Scott D. Goddard & Marc G. Genton & Amanda S. Hering & Stephan R. Sain, 2015. "Evaluating the impacts of climate change on diurnal wind power cycles using multiple regional climate models," Environmetrics, John Wiley & Sons, Ltd., vol. 26(3), pages 192-201, May.
    13. Draxl, Caroline & Clifton, Andrew & Hodge, Bri-Mathias & McCaa, Jim, 2015. "The Wind Integration National Dataset (WIND) Toolkit," Applied Energy, Elsevier, vol. 151(C), pages 355-366.
    14. Carapellucci, Roberto & Giordano, Lorena, 2013. "The effect of diurnal profile and seasonal wind regime on sizing grid-connected and off-grid wind power plants," Applied Energy, Elsevier, vol. 107(C), pages 364-376.
    15. 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.
    16. Wang, Jianzhou & Niu, Tong & Lu, Haiyan & Guo, Zhenhai & Yang, Wendong & Du, Pei, 2018. "An analysis-forecast system for uncertainty modeling of wind speed: A case study of large-scale wind farms," Applied Energy, Elsevier, vol. 211(C), pages 492-512.
    17. 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.
    18. Früh, Wolf-Gerrit, 2013. "Long-term wind resource and uncertainty estimation using wind records from Scotland as example," Renewable Energy, Elsevier, vol. 50(C), pages 1014-1026.
    19. Erdem, Ergin & Shi, Jing, 2011. "ARMA based approaches for forecasting the tuple of wind speed and direction," Applied Energy, Elsevier, vol. 88(4), pages 1405-1414, April.
    20. Wang, Jianzhou & Hu, Jianming & Ma, Kailiang, 2016. "Wind speed probability distribution estimation and wind energy assessment," Renewable and Sustainable Energy Reviews, Elsevier, vol. 60(C), pages 881-899.
    21. 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.
    22. 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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