Lance Manuel

Comparing Estimates of Wind Turbine Fatigue Loads Using Time-Domain and Spectral Methods

Fatigue analysis for wind turbines is typically carried out in the time domain, using cycle counting techniques such as ASTMs Rainflow Cycle-Counting Algorithm. As an alternative, earlier workers investigated the feasibility of estimating wind turbine fatigue loads using spectral techniques such as Dirliks method to estimate stress range probability distributions that are based on spectral moments of the load in question. The present paper re-examines this approach with a particular view to assessing its limitations and advantages in the context of modern, large-scale wind turbines and design methods. These relative advantages are considered in terms of accuracy, statistical reliability, and efficiency of calculation. Field data on loads from a utility-scale 1.5 MW turbine near Lamar, Colorado in the Colorado Green Wind Farm are analyzed here as a representative example. The results show that valuable and reliable information about tower loads can be obtained very efficiently. By contrast, the limitations of the Dirlik method are highlighted by poor results for edgewise blade loads.

Statistical Extrapolation Methods for Estimating Wind Turbine Extreme Loads

*† rd 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, fifty-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.

Design Loads for Wind Turbines Using the Environmental Contour Method

When interest is in establishing ultimate design loads for wind turbines such that a service life of, say, 20 years is assured, alternative procedures are available. One class of methods works by employing statistical loads extrapolation techniques following development first of 10-minute load maxima distributions (conditional on inflow parameters such as mean wind speed and turbulence intensity). The parametric conditional load distributions require extensive turbine response simulations over the entire inflow parameter range. We will refer to this first class of methods as the “parametric method.” An alternative method is based on traditional structural reliability concepts and isolates only a subset of interesting inflow parameter combinations that are easily first found by working backward from the target return period of interest. This so-called inverse reliability method can take on various forms depending on the number of variables that are modeled as random. An especially attractive form that separates inflow (environmental) variables from turbine load∕response variables and further neglects variability in the load variables given inflow is referred to as the environmental contour (EC) method. We shall show that the EC method requires considerably smaller amounts of computation than the parametric method. We compare accuracy and efficiency of the two methods in 1- and 20-year design out-of-plane blade bending loads at the root of two 1.5 MW turbines. Simulation models for these two turbines with contrasting features, in that one is stall-regulated and the other pitch-regulated, are used here. Refinements to the EC method that account for the effects of the neglected response variability are proposed to improve the turbine design load estimates.

PARAMETRIC MODELS FOR ESTIMATING WIND TURBINE FATIGUE LOADS FOR DESIGN

International standards for wind turbine certification depend on finding long-term fatigue load distributions that are conservative with respect to the state of knowledge for a given system. Statistical models of loads for fatigue application are described and demonstrated using flap and edge blade-bending data from a commercial turbine in complex terrain. Distributions of rainflow-counted range data for each ten-minute segment are characterized by parameters related to their first three statistical moments (mean, coefficient of variation, and skewness). Quadratic Weibull distribution functions based on these three moments are shown to match the measured load distributions if the non-damaging low-amplitude ranges are first eliminated. The moments are mapped to the wind conditions with a two-dimensional regression over ten-minute average wind speed and turbulence intensity. With this mapping, the short-term distribution of ranges is known for any combination of average wind speed and turbulence intensity. The longterm distribution of ranges is determined by integrating over the annual distribution of input conditions. First, we study long-term loads derived by integration over wind speed distribution alone, using standard-specified turbulence levels. Next, we perform this integration over both wind speed and turbulence distribution for the example site. Results are compared between standarddriven and site-driven load estimates. Finally, using statistics based on the regression of the statistical moments over the input conditions, the uncertainty (due to the limited data set) in the long-term load distribution is represented by 95% confidence bounds on predicted loads.

A Comparison of Standard Coherence Models for Inflow Turbulence With Estimates from Field Measurements

The Long-term Inflow and Structural Test (LIST) program, managed by Sandia National Laboratories, Albuquerque, NM, is gathering inflow and structural response data on a modified version of the Micon 65/13 wind turbine at a site near Bushland, Texas. With the objective of establishing correlations between structural response and inflow, previous studies have employed regression and other dependency analyses to attempt to relate loads to various inflow parameters. With these inflow parameters that may be thought of as single-point-in-space statistics that ignore the spatial nature of the inflow, no significant correlation was identified between load levels and any single inflow parameter or even any set of such parameters, beyond the mean and standard deviation of the hubheight horizontal wind speed. Accordingly, hence, we examine spatial statistics in the measured inflow of the LIST turbine by estimating the coherence for the three turbulence components (along-wind, across-wind, and vertical). We examine coherence spectra for both lateral and vertical separations and use the available ten-minute time series of the three components at several locations. The data obtained from spatial arrays on three main rowers located upwind from the test turbine as well as on two additional towers on either side of the main towers consist of 291 ten-minute records. Details regarding estimation of the coherence functions from limited data are discussed. Comparisons with standard coherence models available in the literature and provided in the International Electrotechnical Commission (IEC) guidelines are also discussed. It is found that the Davenport exponential coherence model may not be appropriate especially for modeling the coherence of the vertical turbulence component since it fails to account for reductions in coherence at low frequencies and over large separations. Results also show that the Mann uniform shear turbulence model predicts coherence spectra for all turbulence components and for different lateral separations better than the isotropic von Karman model. Finally, on studying the cross-coherence among pairs of turbulence components based on field data, it is found that the coherence observed between along-wind and vertical turbulence components is not predicted by the isotropic von Karman model while the Mann model appears to overestimate this cross-coherence.

Foundation models for offshore wind turbines

The objective of this study is to investigate what effect the use of alternative models for monopile pile foundations for shallow-water offshore wind turbines has on extreme loads associated with long return periods that are needed during design. We employ a utility-scale 5MW offshore wind turbine model with a 90-meter hub height in stochastic simulations; the turbine is assumed to be sited in 20 meters of water. Selected 20-year wind-wave combinations are employed as we study comparative time histories, power spectra, response statistics, and probability distributions of extreme loads for fixed-base and flexible foundation models. Two alternative flexible foundation models are considered and longterm loads are studied in comparison with the use of a fixed base model. A discussion on the varying dynamics, on short-term response statistics, and on extrapolated long-term loads from limited simulation is presented. It is shown that root-mean-square (RMS) tower loads are higher for the flexible foundation models than for the fixed-based one. This is due to the smaller stiffnesses of these models. Extreme loads are also higher for the flexible foundation models though not to the same degree as the RMS loads. Seastates involving wind speeds close to the rated wind speed control long-term 20-year loads which can be as much as 15% higher for the flexible foundation models compared to the fixed-base one.

Low-Dimensional Representations of Inflow Turbulence and Wind Turbine Response Using Proper Orthogonal Decomposition

A demonstration of the use of Proper Orthogonal Decomposition (POD) is presented for the identification of energetic modes that characterize the spatial random field describing the inflow turbulence experienced by a wind turbine. POD techniques are efficient because a limited number of such modes can often describe the preferred turbulence spatial patterns and they can be empirically developed using data from spatial arrays of sensed input/excitation. In this study, for demonstration purposes, rather than use field data, POD modes are derived by employing the covariance matrix estimated from simulations of the spatial inflow turbulence field based on standard spectral models. The efficiency of the method in deriving reduced-order representations of the along-wind turbulence field is investigated by studying the rate of convergence (to total energy in the turbulence field) that results from the use of different numbers of POD modes, and by comparing the frequency content of reconstructed fields derived from the modes. The National Wind Technology Center’s Advanced Research Turbine (ART) is employed in the examples presented, where both inflow turbulence and turbine response are studied with low-order representations based on a limited number of inflow POD modes. Results suggest that a small number of energetic modes can recover the low-frequency energy in the inflow turbulence field as well as in the turbine response measures studied. At higher frequencies, a larger number of modes are required to accurately describe the inflow turbulence. Blade turbine response variance and extremes, however, can be approximated by a comparably smaller number of modes due to diminished influence of higher frequencies.

SIMULATION OF OFFSHORE WIND TURBINE RESPONSE FOR EXTREME LIMIT STATES

When interest is in estimating long-term design loads for an offshore wind turbine using simulation, statistical extrapolation is the method of choice. While the method itself is rather well-established, simulation effort can be intractable if uncertainty in predicted extreme loads and efficiency in the selected extrapolation procedure are not specifically addressed. Our aim in this study is to address these questions in predicting blade and tower extreme loads based on stochastic response simulations of a 5 MW offshore turbine. We illustrate the use of the peak-over-threshold method to predict long-term extreme loads. To derive these long-term loads, we employ an efficient inverse reliability approach which is shown to predict reasonably accurate long-term loads when compared to the more expensive direct integration of conditional load distributions for different environmental (wind and wave) conditions. Fundamental to the inverse reliability approach is the issue of whether turbine response variability conditional on environmental conditions is modeled in detail or whether only gross conditional statistics of this conditional response are included. We derive design loads for both these cases, and demonstrate that careful inclusion of response variability not only greatly influences long-term design load predictions but it also identifies different design environmental conditions that bring about these long-term loads compared to when response variability is only approximately modeled. As we shall see, for this turbine, a major source of response variability for both the blade and tower arises from blade pitch control actions due to which a large number of simulations is required to obtain stable distribution tails for the turbine loads studied.

A Comparison of Wind Turbine Design Loads in Different Environments Using Inverse Reliability Techniques

The influence of turbulence conditions on the design loads for wind turbines is investigated by using inverse reliability techniques. Alternative modeling assumptions for randomness in the gross wind environment and in the extreme response given wind conditions to establish nominal design loads are studied. Accuracy in design load predictions based on use of the inverse first-order reliability method (that assumes a linearized limit state surface) is also investigated. An example is presented where three alternative nominal load definitions are used to estimate extreme flapwise bending loads at a blade root for a 600 kW three-bladed, stall-regulated horizontal-axis wind turbine located at onshore and offshore sites that were assumed to experience the same mean wind speed but different turbulence intensities. It is found that second-order (curvature-type) corrections to the linearized limit state function assumption inherent in the inverse first-order reliability approach are insignificant. Thus, we suggest that the inverse first-order reliability method is an efficient and accurate technique of predicting extreme loads. Design loads derived from a full random characterization of wind conditions as well as short-term maximum response (given wind conditions) may be approximated reasonably well by simpler models that include only the randomness in the wind environment but account for response variability by employing appropriately derived ‘‘higher-than-median’’ fractiles of the extreme bending loads conditional on specified inflow parameters. In the various results discussed, it is found that the higher relative turbulence at the onshore site leads to larger blade bending design loads there than at the offshore site. Also, for both onshore and offshore environments accounting for response variability is found to be slightly more important at longer return periods (i.e., safer designs). @DOI: 10.1115/1.1796971#

Performance Indicators for Structural Systems and Infrastructure Networks

AbstractEstablishing consistent criteria for assessing the performance of structural systems and infrastructure networks is a critical component of communities’ efforts to optimize investment decisions for the upkeep and renewal of the built environment. Although member-level performance and reliability assessment procedures are currently well-established, it is widely recognized that a member-oriented approach does not necessarily lead to an efficient utilization of limited resources when making decisions related to the management of existing deteriorating structures or lifeline systems, especially those that may be exposed to extreme events. For this reason, researchers have renewed their interests in developing system-level assessment methods as a basis to modern structural and infrastructure performance evaluation and design processes. Specifically, system-level performance metrics and characteristics such as reliability, redundancy, robustness, resilience, and risk continue to be refined. The objecti...