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RESEARCH PAPERS

# Statistical Model of Extreme Shear

[+] Author and Article Information
Gunner Chr. Larsen

Risoe National Laboratories, Wind Energy Department, P.O. Box 49, DK-4000 Roskilde, Denmarkgunner.larsen@risoe.dkDepartment of Mechanical Engineering,  Technical University of Denmark, DK-2800 Lyngby, Denmarkgunner.larsen@risoe.dk

Kurt S. Hansen

Risoe National Laboratories, Wind Energy Department, P.O. Box 49, DK-4000 Roskilde, Denmarkksh@mek.dtu.dkDepartment of Mechanical Engineering,  Technical University of Denmark, DK-2800 Lyngby, Denmarkksh@mek.dtu.dk

J. Sol. Energy Eng 127(4), 444-455 (Feb 18, 2005) (12 pages) doi:10.1115/1.2035702 History: Received May 27, 2004; Revised February 15, 2005; Accepted February 18, 2005

## Abstract

In order to continue cost-optimization of modern large wind turbines, it is important to continuously increase the knowledge of wind field parameters relevant to design loads. This paper presents a general statistical model that offers site-specific prediction of the probability density function (PDF) of turbulence driven short-term extreme wind shear events, conditioned on the mean wind speed, for an arbitrary recurrence period. The model is based on an asymptotic expansion, and only a few and easily accessible parameters are needed as input. The model of the extreme PDF is supplemented by a model that, on a statistically consistent basis, describes the most likely spatial shape of an extreme wind shear event. Predictions from the model have been compared with results from an extreme value data analysis, based on a large number of full-scale measurements recorded with a high sampling rate. The measurements have been extracted from ”Database on Wind Characteristics” (http:∕∕www.winddata.com∕), and they refer to a site characterized by a flat homogeneous terrain. The comparison has been conducted for three different mean wind speeds in the range of $15–19m∕s$, and model predictions and experimental results are consistent, given the inevitable uncertainties associated with the model as well as with the extreme value data analysis.

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## Figures

Figure 7

PDF of normalized (horizontal) turbulence for U¯>15m∕s at the Oak Creek site

Figure 1

Bandwidth parameter as function of cut-off frequency (Cabauw site) for a difference-process based on synchronous measurements in altitudes 40 and 200 m, respectively

Figure 2

Bandwidth parameter as function of cut-off frequency (Näsudden site) for a difference-process based on synchronous measurements in altitudes 40 and 118 m, respectively

Figure 3

Most likely (stochastic) extreme shear profile

Figure 4

EV1 depiction of extreme shear events corresponding to mean wind speed bin [16m∕s; 18m∕s[

Figure 5

PDF of normalized (horizontal) turbulence for U¯>8m∕s at the Lammefjord site. Taken from (2).

Figure 6

PDF of normalized (horizontal) turbulence for U¯>15m∕s at the Oak Creek site. Taken from (2).

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