04 Jan 2022
04 Jan 2022
Status: a revised version of this preprint is currently under review for the journal WES.

Gaussian mixture model for extreme wind turbulence estimation

Xiaodong Zhang and Anand Natarajan Xiaodong Zhang and Anand Natarajan
  • Technical University of Denmark, Department of Wind Energy, Frederiksborgvej 399, 4000 Roskilde, Denmark

Abstract. Uncertainty quantification is a necessary step in wind turbine design due to the random nature of the environmental loads, through which the uncertainty of structural loads and responses under specific situations can be quantified. Specifically, wind turbulence has a significant impact on the extreme and fatigue design envelope of the wind turbine. The wind parameters (mean and standard deviation of 10-minute wind speed) are usually not independent, and it will lead to biased results for structural reliability or uncertainty quantification assuming the wind parameters are independent. A proper probabilistic model should be established to model the correlation among wind parameters. Compared to univariate distributions, theoretical multivariate distributions are limited and not flexible enough to model the wind parameters from different sites or direction sectors. Copula-based models are used often for correlation description, but existing parametric copulas may not model the correlation among wind parameters well due to limitations of the copula structures. The Gaussian mixture model is widely applied for density estimation and clustering in many domains, but limited studies were conducted in wind energy and few used it for density estimation of wind parameters. In this paper, the Gaussian mixture model is used to model the joint distribution of mean and standard deviation of 10-minute wind speed, which is calculated from 15 years of wind measurement time series data. As a comparison, the Nataf transformation (Gaussian copula) and Gumbel copula are compared with the Gaussian mixture model in terms of the estimated marginal distributions and conditional distributions. The Gaussian mixture model is then adopted to estimate the extreme wind turbulence, which could be taken as an input to design loads used in the ultimate design limit state of turbine structures. The wind turbulence associated with a 50-year return period computed from the Gaussian mixture model is compared with what is utilized in the design of wind turbines as given in the IEC 61400-1.

Xiaodong Zhang and Anand Natarajan

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Xiaodong Zhang and Anand Natarajan

Xiaodong Zhang and Anand Natarajan


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Short summary
Joint probability distribution of 10-minute mean wind speed and the standard deviation is proposed using Gaussian mixtures, and shown to agree well with 15-years of measurements. The results from the model could be taken as inputs for structural reliability analysis and uncertainty quantification of wind turbine design loads, especially towards the effects of extreme wind turbulence.