Load Extrapolation Methods for Offshore Wind Turbines
Authors: Agarwal Puneet , Manuel Lance 
Published: July 2010

Abstract
Statistical load extrapolation is required to predict long-term extreme loads for offshore as well as onshore wind turbines, as per design standards from the International Electrotechnical Commission (IEC). Load extrapolation involves three major steps: first, extracting load extremes from simulated time series of turbine loads; then, fitting " short-term?? probability distributions to these extremes for a given environmental state; and finally, integrating short-term distributions over all environmental states to develop a " long-term?? distribution from which the long-term load associated with a desired return period is obtained. Several different techniques are available for each of the three steps. The IEC design standards do not provide any guidelines regarding which techniques are suitable for accurate prediction of long-term loads. We present a review of various extrapolation techniques for offshore wind turbines. We use a 5MW utility-scale offshore wind turbine model (developed at the National Renewable Energy Laboratory) with a monopile support structure for stochastic time-domain simulations. From ten-minute simulations, we extract extremes using the global maxima method, the peak-over-threshold method, and the block maxima method. Using a convergence criterion for short-term distributions, we show that it is more important to carry out an adequate number of simulations than to extract more extremes from each ten-minute simulation. We show that the inverse first-order reliability method can be as accurate but more efficient than the direct integration method to estimate long-term loads.

Introduction
Offshore wind energy is becoming an important part of the overall energy mix in Europe and has great potential within the United States and other parts of the world. In the design of offshore wind turbines according to the guidelines [1] from the International Electrotechical Commission (IEC), long-term extreme loads (such as loads on the tower and the blades) can be estimated using the method of statistical extrapolation. The load extremes data required for the extrapolation is obtained from stochastic time-domain simulations of the wind turbine response. Statistical extrapolation, using the direct integration method, involves integration of the " short-term?? distribution of turbine load extremes conditional on specified environmental states with the likelihood of occurrence of the different environmental states to establish the " long-term?? distribution of loads, from which long-term loads may be obtained for a desired return period. As the joint probability distribution of environmental random variables is usually known for a chosen site, the accuracy of long-term load predictions depends on the accuracy of short-term distributions of turbine loads.
The IEC design standards [1, 2] do not unambiguously provide a procedure for statistical load extrapolation of wind turbine loads. The guidelines that are provided are vague at best; for example, they require short-term distributions to be ‘reliable’ but they do not define what constitutes a reliable distribution and how many simulations are needed for each environmental state. The standard does not clearly identify which method-i.e., global maximum, block maximum or peak-over-threshold—should be used to extract load extremes from each simulated ten-minute time series. The global maximum method, which is the single largest value from a ten-minute time series, is the most common and the simplest method. In the peak-over-threshold (POT) method, the maximum value from each segment of a time series that lies between two successive upcrossings of a chosen threshold is retained as a load extreme. In the block maximum method, one partitions the time series into individual non-overlapping blocks of constant duration, and the largest values from each of these blocks constitute a set of block maxima. Furthermore, it is of interest to know how these different extreme methods are related and whether long-term loads predicted by the different methods for extremes are comparable or not.