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Research Papers

[+] Author and Article Information
Anand Natarajan

GE India Technology Center, 122 Whitefield Road, Hoodi, Bangalore 560066, Indiaanand.natarajan@ge.com

William E. Holley

GE Energy-Wind, 300 Garlington Road, Greenville, SC 29615

J. Sol. Energy Eng 130(3), 031017 (Jul 16, 2008) (7 pages) doi:10.1115/1.2931513 History: Received May 29, 2007; Revised February 13, 2008; Published July 16, 2008

## Abstract

Extrapolation of extreme loads using turbulent wind samples of various mean speeds and random starting points is addressed using probability distribution functions that are suitably distorted to fit the peak extremes. The tail of the extreme value distribution of the simulated loads is required to fit accurately and this tail is extrapolated to a $50‐year$ exceedance probability to determine the characteristic load. The Gumbel distribution with a quadratic distortion is especially addressed due to its asymptotic theoretical validity for Gaussian loads. The blade root moments and the hub moments are studied here with respect to their behavior under extrapolation using a quadratic Gumbel distribution. Verification with a large number of random seeds at various mean wind speeds is done, so as to assess the accuracy of the extrapolation and the convergence of the extrapolated load. Methods of accounting for the variance in the extrapolated load with changes in the random wind seeds are proposed.

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## Figures

Figure 1

Variation of the number of up-crossings of the specified level with change in the sinusoidal amplitude (B) and frequency (ω) plotted versus the normalized barrier level (A)

Figure 2

Quadratic Gumbel distribution fit to the extremes of a Gaussian input

Figure 3

Quadratic Gumbel distribution fit to the extremes of a non-Gaussian input

Figure 4

Stochastic behavior of the quadratic Gumbel fit showing a good fit to the extreme load data and appropriate extrapolation

Figure 5

Comparison of a load extrapolation using a Gumbel distribution with that of a Gumbel with a quadratic distortion

Figure 6

Normalized maxima of out-of-plane bending moment

Figure 7

Extrapolated normalized blade root out-of-plane bending moment and extrapolated normalized hub resultant moment

Figure 8

Variation of the extrapolated hub resultant moment with random seeds

Figure 9

Stochastic fit of the normalized extrapolated hub resultant load, showing that it is distributed as an extreme value distribution

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