Comparative analysis of methods for modelling the short‐term probability distribution of extreme wind turbine loads

We have tested the performance of statistical extrapolation methods in predicting the extreme response of a multi‐megawatt wind turbine generator. We have applied the peaks‐over‐threshold, block maxima and average conditional exceedance rates (ACER) methods for peaks extraction, combined with four extrapolation techniques: the Weibull, Gumbel and Pareto distributions and a double‐exponential asymptotic extreme value function based on the ACER method. For the successful implementation of a fully automated extrapolation process, we have developed a procedure for automatic identification of tail threshold levels, based on the assumption that the response tail is asymptotically Gumbel distributed. Example analyses were carried out, aimed at comparing the different methods, analysing the statistical uncertainties and identifying the factors, which are critical to the accuracy and reliability of the extrapolation. The present paper describes the modelling procedures and makes a comparison of extrapolation methods based on the results from the example calculations. Copyright © 2015 John Wiley & Sons, Ltd.     

Short‐term extreme response analysis of a jacket supporting an offshore wind turbine

Wind turbines must be designed in such a way that they can survive in extreme environmental conditions. Therefore, it is important to accurately estimate the extreme design loads. This paper deals with a recently proposed method for obtaining short‐term extreme values for the dynamic responses of offshore fixed wind turbines. The 5 MW NREL wind turbine is mounted on a jacket structure (92 m high) at a water depth of 70 m at a northern offshore site in the North Sea. The hub height is 67 m above tower base or top of the jacket, i.e. 89 m above mean water level. The turbine response is numerically obtained by using the aerodynamic software HAWC2 and the hydrodynamic software USFOS . Two critical responses are discussed, the base shear force and the bending moment at the bottom of the jacket. The extreme structural responses are considered for wave‐induced and wind‐induced loads for a 100 year return‐period harsh metocean condition with a 14.0 m significant wave height, a 16 s peak spectral period, a 50 m s ^{? 1} (10 min average) wind speed (at the hub) and a turbulence intensity of 0.1 for a parked wind turbine. After performing the 10 min nonlinear dynamic simulations, a recently proposed extrapolation method is used for obtaining the extreme values of those responses over a period of 3 h. The sensitivity of the extremes to sample size is also studied. The extreme value statistics are estimated from the empirical mean upcrossing rates. This method together with other frequently used methods (i.e. the Weibull tail method and the global maxima method) is compared with the 3 h extreme values obtained directly from the time‐domain simulations. Copyright © 2012 John Wiley & Sons, Ltd.     

Outlier robustness for wind turbine extrapolated extreme loads

Methods for extrapolating extreme loads to a 50 year probability of exceedance, which display robustness to the presence of outliers in simulated loads data set, are described. Case studies of isolated high extreme out‐of‐plane loads are discussed to emphasize their underlying physical reasons. Stochastic identification of numerical artifacts in simulated loads is demonstrated using the method of principal component analysis. The extrapolation methodology is made robust to outliers through a weighted loads approach, whereby the eigenvalues of the correlation matrix obtained using the loads with its dependencies is utilized to estimate a probability for the largest extreme load to occur at a specific mean wind speed. This inherently weights extreme loads that occur frequently within mean wind speed bins higher than isolated occurrences of extreme loads. Primarily, the results for the blade root out‐of‐plane loads are presented here as those extrapolated loads have shown wide variability in literature, but the method can be generalized to any other component load. The convergence of the 1 year extrapolated extreme blade root out‐of‐plane load with the number of turbulent wind samples used in the loads simulation is demonstrated and compared with published results. Further effects of varying wind inflow angles and shear exponent is brought out. Parametric fitting techniques that consider all extreme loads including ‘outliers’ are proposed, and the physical reasons that result in isolated high extreme loads are highlighted, including the effect of the wind turbine controls system. Copyright © 2011 John Wiley & Sons, Ltd.     

Prediction of the extreme wind speed in the mixed climate region by using Monte Carlo simulation and measure‐correlate‐predict method

The extreme wind speed at an offshore location was predicted using Monte Carlo simulation (MCS) and measure‐correlate‐predict (MCP) method. The Gumbel distribution could successfully express the annual maximum wind speed of extratropical cyclone. On the other hand, the estimated extreme wind speed of tropical cyclones by analytical probability distribution shows larger uncertainty. In the mixed climate like Japan, the extreme wind speed estimated from the combined probability distribution obtained by MCP and MCS methods agrees well with the observed data as compared with the combined probability distribution obtained by the MCP method only. The uncertainty of extreme wind speed due to limited observation period of wind speed and pressure was also evaluated by the Gumbel theory and Monte Carlo simulation. As a result, it was found that the uncertainty of 50 year recurrence wind speed obtained by MCS method is considerably smaller than that obtained by MCP method in the mixed climate. Copyright © 2014 John Wiley & Sons, Ltd.     

Environmental contours for circular‐linear variables based on the direct sampling method

Environmental contours are often used in the design of engineering structures to identify extreme environmental conditions that may give rise to extreme loads and responses. The perhaps most common application of environmental contours is for wave climate variables such as significant wave height and wave period. However, for the design of wind energy installations, the joint distribution of wind speed and wind direction may be equally important. In this case, joint modelling of linear (wind speed) and circular (wind direction) variables are needed, and methods for establishing environmental contours for circular‐linear variables will be required. In this paper, different ways of establishing environmental contours for circular‐linear variables will be presented and applied to a joint distribution model for wind speed and wind direction. In particular, the direct sampling approach to environmental contours will be modified to the case where one of the variables is cyclic. In addition, contours based on exceedance planes in polar coordinates will be established, and circular‐linear contours will also be calculated based on the inverse FORM (I‐FORM) approach.     

Trivariate maximum entropy distribution of significant wave height,wind speed and relative direction

A trivariate maximum entropy distribution of significant wave height, wind speed and the relative direction is proposed here. In this joint distribution, all the marginal variables follow modified maximum entropy distributions, and they are combined by a correlation coefficient matrix based on the Nataf transformation. The methods of single extreme factors and of conditional probability are presented for the joint design of trivariate random variables. The corresponding sampling data about significant wave heights, wind speeds and the relative directions from a location in the North Atlantic is applied for statistical analysis, and the results show that the trivariate maximum entropy distribution is sufficiently good to fit the data, and method of conditional probability can reduce the design values efficiently.     

Applied statistics for extreme wind estimate

The assessment of extreme wind speeds is a crucial issue for securing structural safety of wind turbines and inquiring largest loads to which turbines must be prepared to undergo. International standards suggest applying the Gumbel method of fitting the annual maxima to their theoretic probability distribution. Yet, often, wind databases are too short to apply such methods with statistical significance, and other procedures are commonly adopted [such as peaks over threshold (POT) and independent storms], which involve dependency on arbitrary thresholds for filtering data and issues of sub‐asymptocity, i.e. how well the selected dataset fits to density functions describing the distribution of peaks or extreme values. The present paper aims at contributing to such currently ongoing debate, providing a statistical analysis of the application of POT and independent storms methods on wind time series of various lengths from different geographical areas. The CERN data analysis framework ROOT has been employed for guaranteeing excellent standards of computational precision and wealth of statistical information. Analysis of uncertainties in the wind speeds estimates and tests of the goodness of fit of the datasets to the proper distributions have been carried on. An algorithm for choosing the optimum thresholds was developed, which encapsules and compromises the statistical complexity of the methods. A declustering procedure has been carried on for discriminating proper peaks in the POT method: it has been tested that such declustering provides a dramatic improvement of the statistical quality of the method. Copyright © 2014 John Wiley & Sons, Ltd.     

极端风况下双转子风力机降载复合控制策略

为降低双转子风力机在极端风况下的大波动载荷,基于双转子风力机气动与控制仿真系统,提出了基于独立变桨自抗扰控制器和偏航模糊控制器的降载复合控制策略,并分析了正常风况和极端风况下该策略的控制效果。结果表明：与传统PID独立变桨控制相比,在极端运行阵风和极端湍流模型下,独立变桨自抗扰控制方法使叶根挥舞弯矩标准差减小18%以上;与传统恒速偏航控制相比,在极端风向变化下,偏航模糊控制方法使偏航轴承滚动力矩标准差减小约27%。降载复合控制策略有效降低了极端风况下双转子风力机的大载荷,抑制了功率波动。     

Overcoming fundamental limitations of wind turbine individual blade pitch control with inflow sensors

Individual pitch control (IPC) provides an important means of attenuating harmful fatigue and extreme loads upon the load bearing structures of a wind turbine. Conventional IPC architectures determine the additional pitch demand signals required for load mitigation in response to measurements of the flap‐wise blade‐root bending moments. However, the performance of such architectures is fundamentally limited by bandwidth constraints imposed by the blade dynamics. Seeking to overcome this problem, we present a simple solution based upon a local blade inflow measurement on each blade. Importantly, this extra measurement enables the implementation of an additional cascaded feedback controller that overcomes the existing IPC performance limitation and hence yields significantly improved load reductions. Numerical demonstration upon a high‐fidelity and nonlinear wind turbine model reveals (1) 60% reduction in the amplitude of the dominant 1P fatigue loads and (2) 59% reduction in the amplitude of extreme wind shear‐induced blade loads, compared with a conventional IPC controller with the same robust stability margin. This paper therefore represents a significant alternative to wind turbine IPC load mitigation as compared with light detection and ranging‐based feedforward control approaches.     

高效低载的三维风力机叶片外形优化设计方法

常规风力机叶片的优化设计都是从二维翼型开始的,且翼型总是以升阻比最大为优化目标。然而,二维翼型的升阻比最大和三维叶片的高风能利用率与低气动载荷有本质的不同,采用以往的叶片优化方法常常会在提高风能利用率的同时,使叶片所受的气动载荷也提高。针对这一问题,提出基于多岛遗传算法和动量叶素理论,在给定风况条件下,以加权风能利用率最高与气动载荷最小为目标函数,以叶片各个截面的翼型型线及扭角作为设计变量,对三维叶片开展多目标优化方法设计研究。并对某实际NREL Phase VI叶片进行优化设计,结果表明：在给定风况下相比原叶片,优化叶片在风能利用率提升了3.06%的基础上,叶根弯矩降低了11.68%。在变转速与变风况下,优化叶片的气动效率整体提升,叶根弯矩明显降低。     

Experimental assessment of a blended fatigue-extreme controller employing trailing edge flaps

This paper presents an experimental assessment of a blended fatigue-extreme controller for load control employing trailing edge flaps on a lab-scale wind turbine. The controller blends between a repetitive model predictive controller that targets fatigue loads and a dedicated extreme load controller, which consists of a simple on-off load control strategy. The Fatigue controller uses the flapwise blade root bending moments of the three blades as input sensors. The Extreme controller additionally uses on-blade angle of attack and velocity measurements as well as acceleration measurements to detect extreme events and to allow for a fast reaction. The experiments are conducted on the Berlin Research Turbine within the large wind tunnel of the TU Berlin. In order to reproduce test cases with deterministic extreme wind conditions that follow industry standards, the wind tunnel was redesigned. The analyzed test cases are extreme direction change, extreme coherent gust, extreme operating gust and extreme coherent gust with direction change. The test cases are analyzed by on-blade angle of attack and velocity measurements. The load control performance of the Blended controller is compared to the pure fatigue oriented and the pure extreme load controller. The Blended controller achieves a maximum flapwise blade root bending moment reduction of 23%, which is comparable to the reduction achieved by the Extreme controller.     

Analytic analysis of load alignment for coning extreme‐scale rotors

Extreme‐scale wind turbines (rated powers greater than 10 MW) with large rotor diameters and conventional upwind designs must resist extreme downwind and gravity loads. This can lead to significant structural design challenges and high blade masses that can impede the reduction of levelized cost of wind energy. Herein, the theoretical basis for downwind load alignment is developed. This alignment can be addressed with active downwind coning to reduce/eliminate flapwise bending loads by balancing the transverse components of thrust, centrifugal, and gravitational force. Equations are developed herein that estimates the optimal coning angle that reduces flapwise loads by a specified amount. This analysis is then applied to a 13.2‐MW scale with 100‐m‐level wind turbine blades, where it is found that a load alignment coning schedule can substantially reduce the root flapwise bending moments. This moment reduction in this example can allow the rotor mass to be decreased significantly when compared with a conventional upwind three‐bladed rotor while maintaining structural performance and annual energy output.     

风波耦合作用下风载荷对两种漂浮式风力机平台动态响应影响

为分析风载荷对漂浮式平台的重要影响,建立了基于单桩式及张力腿平台的漂浮式风力机整机模型,基于叶素-动量理论与辐射/绕射理论,运用水动力软件AQWA并结合有限元方法验证了风载荷及风波耦合的重要性,研究了波浪单独及风波耦合作用下漂浮式平台的时频域动态响应。结果表明：风载荷使平台产生了较大纵荡与垂荡漂移,其产生的倾覆力矩改变了纵摇平衡位置,风载荷使纵荡响应偏离平衡位置较垂荡与纵摇响应明显;对于纵荡响应,风载荷使两平台低频固有频率处的响应峰值增加;对于垂荡响应,风载荷使单桩式平台固有频率处的响应峰值减小,使张力腿平台纵荡-垂荡耦合响应及波浪频率处的响应峰值大幅增加;对于纵摇响应,风载荷使单桩式平台及张力腿平台低频固有频率处的响应峰值大幅增加;风载荷是引起单桩式平台纵荡-垂荡耦合运动的关键因素;波浪载荷是引起张力腿平台纵荡响应幅值较大的关键因素。     

台风-浪-流耦合作用下海上风力机基础结构水动力特性分析

为揭示台风-浪-流耦合作用下风力机基础结构的水动力特性,以广东外罗10 MW级海上风力机为研究对象,基于模式耦合器（MCT）建立中尺度台风-浪-流（W-S-F）实时耦合模拟平台,分析超强台风“威马逊”过境全过程海上风电场台风-浪-流的时空演变特性;再结合中/小尺度嵌套方法分析风力机单桩基础水动力荷载分布特性;提出不同波浪相位下基础柱极值荷载模型。结果表明：建立的W-S-F平台对台风路径的模拟精度较单WRF模式提高42.51%;台风-浪-流耦合作用下基础柱水平波浪力正峰值增大约20%,负峰值减小约18%,并沿水深方向呈指数型变化规律,周向沿180°波向角呈对称分布;T4相位为风力机基础强度设计的最不利相位,基底剪力最大达7.68×10⁶量级,基底弯矩最大达5.2×10⁸量级。     

Long‐term loads for a monopile‐supported offshore wind turbine

Accurate prediction of long‐term ‘characteristic’ loads associated with an ultimate limit state for design of a 5‐MW bottom‐supported offshore wind turbine is the focus of this study. Specifically, we focus on predicting the long‐term fore–aft tower bending moment at the mudline and the out‐of‐plane bending moment at the blade root of a monopile‐supported shallow‐water offshore wind turbine. We employ alternative probabilistic predictions of long‐term loads using inverse reliability procedures in establishing the characteristic loads for design. Because load variability depends on the environmental conditions (defining the wind speed and wave height), we show that long‐term predictions that explicitly account for such load variability are more accurate, especially for environmental states associated with above‐rated wind speeds and associated wave heights. Copyright © 2012 John Wiley & Sons, Ltd.     

输电线路设计覆冰厚度统计模型取用

根据捷克斯洛伐克Studnice覆冰观测站1940--1999年的覆冰观测数据,分别采用正态分布、极值Ⅰ型Gumbel分布、极值Ⅱ型Frechet分布、极值Ⅲ型Weibull分布对该数据进行了统计分析。由科尔莫戈罗夫一斯米尔诺夫入拟合度检验结果表明,极值Ⅱ型Frechet分布能较好地拟合该地区的年最大覆冰荷载。由于微地形等因素的影响,线路覆冰厚度的统计分布随地区而异。覆冰厚度是影响冰区输电线路安全、经济的一个重要因素。可根据覆冰观测数据选择概率模型确定设计冰厚。     

大型风力机地震动力响应研究

为研究地震载荷与风载荷联合作用下的大型风力机结构动力学响应,本文研究分别以Wind PACT 1.5 MW和NREL 5 MW风力机为研究对象,采用EI Centro 6.9级地震为输入激励,通过改进版的开源软件FAST(风电载荷仿真软件)计算风力机在正常运行、紧急停机和一直停机3种运行方式下的塔顶振动和塔架结构荷载情况,结果表明:地震载荷极大加剧了塔顶振动,机舱加速度峰值增大2倍以上。紧急停机操作可减小塔尖位移,一定程度上可以保护风力机结构安全。地震载荷主要增大了塔架一阶固有频率及其二倍频的振动。6.9级地震与额定风载荷联合作用下,NREL 5MW风力机塔基弯矩设计需求为159 MN·m,略大于极限风载荷作用。说明地震常发地区,塔架结构强度设计必须考虑地震载荷作用。     

新型变桨风力机关键部件载荷特性试验研究

以新型变桨距风力机为研究对象,针对其独特的变桨调节机构,通过风洞试验的方法,采用IMC载荷测试系统,对其关键部件进行载荷测试。试验结果显示：随着桨距角增大,叶根所受弯矩降低,但叶根挥舞弯矩较摆振弯矩减小更明显;塔筒俯仰方向的受力大于侧弯方向,当风轮转速约为243.5 r/min时,塔筒侧弯受力出现突增;不同桨距角下,变桨调节机构的齿条与齿条同步盘测点载荷大小随风速变化趋势一致,但随着桨距角的增加,表现为先增加后减小再增加的趋势。     

Large‐eddy simulation of stable boundary layer turbulence and estimation of associated wind turbine loads

Stochastic simulation of turbulent inflow fields commonly used in wind turbine load computations is unable to account for contrasting states of atmospheric stability. Flow fields in the stable boundary layer, for instance, have characteristics such as enhanced wind speed and directional shear; these effects can influence loads on utility‐scale wind turbines. To investigate these influences, we use large‐eddy simulation (LES) to generate an extensive database of high‐resolution ( ～ 10 m), four‐dimensional turbulent flow fields. Key atmospheric conditions (e.g., geostrophic wind) and surface conditions (e.g., aerodynamic roughness length) are systematically varied to generate a diverse range of physically realizable atmospheric stabilities. We show that turbine‐scale variables (e.g., hub height wind speed, standard deviation of the longitudinal wind speed, wind speed shear, wind directional shear and Richardson number) are strongly interrelated. Thus, we strongly advocate that these variables should not be prescribed as independent degrees of freedom in any synthetic turbulent inflow generator but rather that any turbulence generation procedure should be able to bring about realistic sets of such physically realizable sets of turbine‐scale flow variables. We demonstrate the utility of our LES‐generated database in estimation of loads on a 5‐MW wind turbine model. More importantly, we identify specific turbine‐scale flow variables that are responsible for large turbine loads—e.g., wind speed shear is found to have a greater influence on out‐of‐plane blade bending moments for the turbine studied compared with its influence on other loads such as the tower‐top yaw moment and the fore‐aft tower base moment. Overall, our study suggests that LES may be effectively used to model inflow fields, to study characteristics of flow fields under various atmospheric stability conditions and to assess turbine loads for conditions that are not typically examined in design standards. Copyright © 2013 John Wiley & Sons, Ltd.     

On wind turbine loads during the evening transition period

The late afternoon hours in the diurnal cycle precede the development of the nocturnal stable boundary layer. This “evening transition” (ET) period is often when energy demand peaks. This period also corresponds to the time of day that is a precursor to late‐afternoon downbursts, a subject of separate interest. To capture physical characteristics of wind fields in the atmospheric boundary layer (ABL) during this ET period, particularly the interplay of shear and turbulence, stochastic simulation approaches, although more tractable, are not suitable. Large‐eddy simulation (LES), on the other hand, may be used to generate high‐resolution ABL turbulent flow fields. We present a suite of idealized LES four‐dimensional flow fields that define a database representing different combinations of large‐scale atmospheric conditions (characterized by associated geostrophic winds) and surface boundary conditions (characterized by surface heat fluxes). Our objective is to evaluate the performance of wind turbines during the ET period. Accordingly, we conduct a statistical analysis of turbine‐scale wind field variables. We then employ the database of these LES‐based inflow wind fields in aeroelastic simulations of a 5‐MW wind turbine. We discuss how turbine loads change as the ET period evolves. We also discuss maximum and fatigue loads on the rotor and tower resulting from different ABL conditions. Results of this study suggest that, during the ET period, the prevailing geostrophic wind speed affects the mean and variance of longitudinal winds greatly and thus has significant influence on all loads except the yaw moment which is less sensitive to uniform and symmetric incoming flow. On the other hand, surface heat flux levels affect vertical turbulence and wind shear more and, as a result, only affect maximum blade flapwise bending and tower fore‐aft bending loads.