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PDF models and synthetic model for the wind speed fluctuations based on the resolution of Langevin equation

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  • Calif, Rudy

Abstract

Wind energy production is very sensitive to turbulent wind speed. Thus rapid variation of wind speed due to changes in the local meteorological conditions can lead to electrical power variations of the order of the nominal power output, in particular when wind power variations on very short time scales, range at few seconds to 1h, are considered. In small grid as they exist on islands (Guadeloupean Archipelago: French West Indies) such fluctuations can cause instabilities in case of intermediate power shortages. The developed analysis in [14] reveals three main classes of time series for the wind speed fluctuations. In this work, Probability Density Functions (PDFs) are proposed to fit the wind speed fluctuations distributions in each class. After, to simulate wind speed fluctuations sequences, we use a stochastic differential equation, the Langevin equation considering Gaussian turbulence PDF (class I), Gram–Charlier PDF (class II) and a mixture of gaussian PDF (class III). The statistical and dynamical properties of simulated wind sequences are close to those of measured wind sequences, for each class.

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  • 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.
    • Handle: RePEc:eee:appene:v:99:y:2012:i:c:p:173-182
    DOI: 10.1016/j.apenergy.2012.05.007
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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.
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    5. Chang, Tian Pau, 2011. "Estimation of wind energy potential using different probability density functions," Applied Energy, Elsevier, vol. 88(5), pages 1848-1856, May.
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    2. Arenas-López, J. Pablo & Badaoui, Mohamed, 2020. "Stochastic modelling of wind speeds based on turbulence intensity," Renewable Energy, Elsevier, vol. 155(C), pages 10-22.
    3. Yang, Yuqi & Zhou, Jianzhong & Liu, Guangbiao & Mo, Li & Wang, Yongqiang & Jia, Benjun & He, Feifei, 2020. "Multi-plan formulation of hydropower generation considering uncertainty of wind power," Applied Energy, Elsevier, vol. 260(C).
    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 & Milano, Federico, 2016. "Construction of SDE-based wind speed models with exponentially decaying autocorrelation," Renewable Energy, Elsevier, vol. 94(C), pages 186-196.
    6. Liu, Guangbiao & Zhou, Jianzhong & Jia, Benjun & He, Feifei & Yang, Yuqi & Sun, Na, 2019. "Advance short-term wind energy quality assessment based on instantaneous standard deviation and variogram of wind speed by a hybrid method," Applied Energy, Elsevier, vol. 238(C), pages 643-667.
    7. Sudeesha Warunasinghe & Anatoliy Swishchuk, 2024. "Stochastic Modeling of Wind Derivatives with Application to the Alberta Energy Market," Risks, MDPI, vol. 12(2), pages 1-26, January.
    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. 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.
    10. Ma, Jinrui & Fouladirad, Mitra & Grall, Antoine, 2018. "Flexible wind speed generation model: Markov chain with an embedded diffusion process," Energy, Elsevier, vol. 164(C), pages 316-328.
    11. Burlibaşa, A. & Ceangă, E., 2013. "Rotationally sampled spectrum approach for simulation of wind speed turbulence in large wind turbines," Applied Energy, Elsevier, vol. 111(C), pages 624-635.
    12. 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.
    13. Guo, Peng & Chen, Si & Chu, Jingchun & Infield, David, 2020. "Wind direction fluctuation analysis for wind turbines," Renewable Energy, Elsevier, vol. 162(C), pages 1026-1035.
    14. Deep, Sneh & Sarkar, Arnab & Ghawat, Mayur & Rajak, Manoj Kumar, 2020. "Estimation of the wind energy potential for coastal locations in India using the Weibull model," Renewable Energy, Elsevier, vol. 161(C), pages 319-339.

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