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Research Papers

# Statistical Extrapolation Methods for Estimating Wind Turbine Extreme Loads

[+] Author and Article Information
Patrick Ragan, Lance Manuel

Department of Civil, Architectural, and Environmental Engineering, University of Texas, Austin, TX 78712

J. Sol. Energy Eng 130(3), 031011 (Jul 02, 2008) (15 pages) doi:10.1115/1.2931501 History: Received January 18, 2007; Revised September 07, 2007; Published July 02, 2008

## Abstract

With the introduction of the third edition of the International Electrotechnical Commission (IEC) Standard 61400-1, designers of wind turbines are now explicitly required, in one of the prescribed load cases, to use statistical extrapolation techniques to determine nominal design loads. In this study, we use field data from a utility-scale $1.5MW$ turbine sited in Lamar, Colorado to compare the performance of several alternative techniques for statistical extrapolation of rotor and tower loads—these include the method of global maxima, the peak-over-threshold method, and a four-moment process model approach. Using each of these three options, $50-year$ return loads are estimated for the selected wind turbine. We conclude that the peak-over-threshold method is the superior approach, and we examine important details intrinsic to this method, including selection of the level of the threshold to be employed, the parametric distribution used in fitting, and the assumption of statistical independence between successive peaks. While we are primarily interested in the prediction of extreme loads, we are also interested in assessing the uncertainty in our predictions as a function of the amount of data used. Towards this end, we first obtain estimates of extreme loads associated with target reliability levels by making use of all of the data available, and then we obtain similar estimates using only subsets of the data. From these separate estimates, conclusions are made regarding what constitutes a sufficient amount of data upon which to base a statistical extrapolation. While this study makes use of field data in addressing statistical load extrapolation issues, the findings should also be useful in simulation-based attempts at deriving wind turbine design load levels where similar questions regarding extrapolation techniques, distribution choices, and amount of data needed are just as relevant.

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## Figures

Figure 1

The instrumented 1.5MW wind turbine

Figure 2

Distribution of the available 10min data records, binned by hub-height mean wind speed

Figure 3

GEV short-term distribution fits to global maxima for different wind speed bins

Figure 4

Long-term distribution fits based on the method of global maxima

Figure 5

Sample POT data for FBM in the 9–11m∕s bin: three alternative threshold levels

Figure 6

Comparison of short-term distribution fits for various thresholds for FBM in the 9–11m∕s bin

Figure 7

Summary of short-term distribution results for various thresholds for FBM in the 9–11m∕s bin

Figure 8

W3P short-term distribution fits to POT data with optimal thresholds

Figure 9

Long-term distribution fits based on the POT method

Figure 10

Distribution function based on the four-moment process model (sample FBM time series in the 15–17m∕s bin)

Figure 11

POT short-term distribution fits based on an optimal threshold versus a μ+1.4σ threshold for the 9–11m∕s bin

Figure 12

POT short-term distribution fits based on an optimal threshold versus a μ+1.4σ threshold for the 19+m∕s bin

Figure 13

W3P versus Generalized Pareto short-term distribution fits for loads in the 13–15m∕s bin

Figure 14

POT data for FBM in the 9–11m∕s bin (circled peaks satisfy a minimum time separation of 10s—compare with Fig. 5)

Figure 15

Correlation between successive peaks over a threshold versus time separation and threshold level for FBM in the 17–19m∕s bin

Figure 16

Fifty-year return loads: range of predictions, mean and standard error bars resulting from subsets of various sizes, based on 100 repetitions. (The horizontal dashed line is the prediction based on the entire data set.)

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