Stability analysis of pitch‐regulated,variable‐speed wind turbines in closed loop operation using a linear eigenvalue approach

A multi‐body aeroelastic design code based on the implementation of the combined aeroelastic beam element is extended to cover closed loop operation conditions of wind turbines. The equations of a controller for variable generator speed and pitch‐controlled operation in high wind speeds are combined with the aeroelastic equations of motion for the complete wind turbine, in order to provide a compound aeroservoelastic system of equations. The control equations comprise linear differential equations for the pitch and generator torque actuators, the control feedback elements (proportional–integral control) and the various filters acting on the feedback signals. In its non‐linear form, the dynamic equations are integrated in time to provide the reference state, while upon linearization of the system and transformation in the non‐rotating frame, the linear stability equations are derived. Stability results for a multi‐MW wind turbine show that the coupling of the controller dynamics with the aeroelastic dynamics of the machine is important and must be taken into account in view of defining the controller parameters. Copyright © 2008 John Wiley & Sons, Ltd.     

A study on the prediction of aerofoil trailing‐edge noise for wind‐turbine applications

This paper presents a comparative study between the so‐called BPM and TNO models for the prediction of aerofoil trailing‐edge noise with particular emphasis on wind‐turbine applications (the BPM model is named after Brooks, Pope and Marcolini who first proposed the model, and the TNO model is named after the TNO institute of Applied Physics where it was first proposed). In this work, two enhanced versions of the BPM model are proposed, and their performances are compared against two recent anisotropic TNO models that require more detailed boundary‐layer information than the BPM‐based models. The two current enhanced models are denoted as BPMM‐PVII and BPMM‐BLkω, where the former uses a panel method with viscous‐inviscid interaction implemented (PVII) for boundary‐layer calculations, the latter estimates the boundary‐layer (BL) properties using a two‐dimensional k‐ω turbulence model (kω), and BPMM stands for BPM‐Modified. By comparing the predicted sound spectra with existing measurement data for seven different aerofoils tested in the current study, it is shown that the BPMM‐PVII model exhibits superior results to those by the other models for most cases despite the simplicity without considering anisotropy. The BPMM‐PVII model is then combined with Prandtl's nonlinear lifting‐line theory to calculate and investigate three‐dimensional rotor noise characteristics of an NREL UAE Phase‐VI wind turbine (NREL UAE stand for the National Renewable Energy Laboratory Unsteady Aerodynamic Experiment). It is demonstrated that the current approach may provide an efficient solution for the prediction of rotor aerodynamics and noise facilitating industrial design and development for low‐noise wind turbines. Copyright © 2016 John Wiley & Sons, Ltd.     

基于升力线理论的大型风力机气弹响应研究

针对风力机不断向大型化发展的趋势,导致结构柔度增加,气弹耦合特性和振动增强,研究了大型风力机高效精确的气弹响应分析方法。为了更准确模拟大型风力机气流沿叶片展向的三维流动现象,采用螺旋尾涡升力线模型代替传统叶素动量理论,建立了叶片气动载荷分析模型,进而结合风力机多体系统动力学模型,构建了机组的气弹耦合动力学方程和数值求解方法。以某10 MW风力机叶片为例,研究了稳态风况下不同风速的叶片气动性能,以及有效攻角、切向力等沿叶展方向的分布特点,并与采用修正叶素动量理论的气弹分析程序（HAWC）对比,结果表明,升力线理论无需引入经验修正模型即能获得叶素动量理论经修正后的分析精度。最后,通过非稳态风况下风力机的气弹响应分析,证明本文方法对大型风力机气弹耦合分析的有效性和准确性。     

An investigation on wind turbine resonant vibrations

Wind turbine resonant vibrations are investigated based on aeroelastic simulations both in frequency and time domain. The investigation focuses on three different aspects: the need of a precise modeling when a wind turbine is operating close to resonant conditions; the importance of estimating wind turbine loads also at low turbulence intensity wind conditions to identify the presence of resonances; and the wind turbine response because of external excitations. In the first analysis, three different wind turbine models are analysed with respect to the frequency and damping of the aeroelastic modes. Fatigue loads on the same models are then investigated with two different turbulence intensities to analyse the wind turbine response. In the second analysis, a wind turbine model is excited with an external force. This analysis helps in identifying the modes that might be excited, and therefore, the frequencies at which minimal excitation should be present during operations. The study shows that significant edgewise blade vibrations can occur on modern wind turbines even if the aeroelastic damping of the edgewise modes is positive. When operating close to resonant conditions, small differences in the modeling can have a large influence on the vibration level. The edgewise vibrations are less visible in high turbulent conditions. Using simulations with low‐level turbulence intensity will ease this identification and could avoid a redesign. Furthermore, depending on the external excitation, different aeroelastic modes can be excited. The investigation is performed using aeroelastic models corresponding to a 1.5 MW class wind turbine with slight variations in blade properties. Copyright © 2015 John Wiley & Sons, Ltd.     

Development of an aeroelastic code based on three‐dimensional viscous–inviscid method for wind turbine computations

Aerodynamic and structural dynamic performance analysis of modern wind turbines are routinely estimated in the wind energy field using computational tools known as aeroelastic codes. Most aeroelastic codes use the blade element momentum (BEM) technique to model the rotor aerodynamics and a modal, multi‐body or the finite‐element approach to model the turbine structural dynamics. The present work describes the development of a novel aeroelastic code that combines a three‐dimensional viscous–inviscid interactive method, method for interactive rotor aerodynamic simulations (MIRAS), with the structural dynamics model used in the aeroelastic code FLEX5. The new code, called MIRAS‐FLEX, is an improvement on standard aeroelastic codes because it uses a more advanced aerodynamic model than BEM. With the new aeroelastic code, more physical aerodynamic predictions than BEM can be obtained as BEM uses empirical relations, such as tip loss corrections, to determine the flow around a rotor. Although more costly than BEM, a small cluster is sufficient to run MIRAS‐FLEX in a fast and easy way. MIRAS‐FLEX is compared against the widely used FLEX5 and FAST, as well as the participant codes from the Offshore Code Comparison Collaboration Project. Simulation tests consist of steady wind inflow conditions with different combinations of yaw error, wind shear, tower shadow and turbine‐elastic modeling. Turbulent inflow created by using a Mann box is also considered. MIRAS‐FLEX results, such as blade tip deflections and root‐bending moments, are generally in good agreement with the other codes. Copyright © 2017 John Wiley & Sons, Ltd.     

Open‐loop frequency response analysis of a wind turbine using a high‐order linear aeroelastic model

Wind turbine controllers are commonly designed on the basis of low‐order linear models to capture the aeroelastic wind turbine response due to control actions and disturbances. This paper characterizes the aeroelastic wind turbine dynamics that influence the open‐loop frequency response from generator torque and collective pitch control actions of a modern non‐floating wind turbine based on a high‐order linear model. The model is a linearization of a geometrically non‐linear finite beam element model coupled with an unsteady blade element momentum model of aerodynamic forces including effects of shed vorticity and dynamic stall. The main findings are that the lowest collective flap modes have limited influence on the response from generator torque to generator speed, due to large aerodynamic damping. The transfer function from collective pitch to generator speed is affected by two non‐minimum phase zeros below the frequency of the first drivetrain mode. To correctly predict the non‐minimum phase zeros, it is essential to include lateral tower and blade flap degrees of freedom. Copyright © 2013 John Wiley & Sons, Ltd.     

Design and validation of the high performance and low noise CQU‐DTU‐LN1 airfoils

This paper presents the design and validation of the high performance and low noise Chong Qing University and Technical University of Denmark LN1 (CQU‐DTU‐LN1) series of airfoils for wind turbine applications. The new design method uses target characteristics of wind turbine airfoils in the design objective, such as airfoil lift coefficient, drag coefficient and lift‐drag ratio, and minimizes trailing edge noise as a constraint. To express airfoil shape, an analytical expression is used. One of the main advantages of the present design method is that it produces a highly smooth airfoil shape that can avoid the problem of curvature discontinuity. An airfoil profile with discontinuous curvature can produce a discontinuous pressure gradient (i.e., local flow acceleration or deceleration), which enhances flow separation and thus decreases the airfoil performance. By combining the design method with the blade element momentum theory, the viscous‐inviscid xfoil code and an airfoil self‐noise prediction model, an optimization algorithm has been developed for designing the high performance and low noise CQU‐DTU‐LN1 series of airfoils with targets of maximum power coefficient and low noise emission. To validate the airfoil design, CQU‐DTU‐LN118 airfoil has been tested experimentally in the acoustic wind tunnel located at the Virginia Polytechnic Institute and State University (Virginia Tech), USA. To show the superiority of the CQU‐DTU‐LN1 airfoils, comparisons on aerodynamic performance and noise emission between the CQU‐DTU‐LN118 airfoil and the National Advisory Committee for Aeronautics (NACA) 64618 airfoil, which is used in modern wind turbine blades, are carried out. Copyright © 2013 John Wiley & Sons, Ltd.     

Aeroelastic design of large wind turbine blades considering damage tolerance

Modern offshore turbine blades can be designed for high fatigue life and damage tolerance to avoid excessive maintenance and therefore significantly reduce the overall cost of offshore wind power. An aeroelastic design strategy for large wind turbine blades is presented and demonstrated for a 100 m blade. High fidelity analysis techniques like 3D finite element modeling are used alongside beam models of wind turbine blades to characterize the resulting designs in terms of their aeroelastic performance as well as their ability to resist damage growth. This study considers a common damage type for wind turbine blades, the bond line failure, and explores the damage tolerance of the designs to gain insight into how to improve bond line failure through aeroelastic design. Flat‐back airfoils are also explored to improve the damage tolerance performance of trailing‐edge bond line failures. Copyright © 2016 John Wiley & Sons, Ltd.     

Wind turbine main‐bearing loading and wind field characteristics

This paper investigates the relationship between wind turbine main‐bearing loads and the characteristics of the incident wind field in which the wind turbine is operating. For a 2‐MW wind turbine model, fully aeroelastic multibody simulations are performed in 3D turbulent wind fields across the wind turbine's operational envelope. Hub loads are extracted and then injected into simplified drivetrain models of three types of main‐bearing configuration. The main‐bearing reaction loads and load ratios from the simplified model are presented and analysed. Results indicate that there is a strong link between wind field characteristics and the loading experienced by the main bearing(s), with the different bearing configurations displaying very different loading behaviours. Main‐bearing failure rates determined from operational data for two drivetrain configurations are also presented.     

Aeroelastic validation and Bayesian updating of a downwind wind turbine

Downwind wind turbine blades are subjected to tower wake forcing at every rotation, which can lead to structural fatigue. Accurate characterisation of the unsteady aeroelastic forces in the blade design phase requires detailed representation of the aerodynamics, leading to computationally expensive simulation codes, which lead to intractable uncertainty analysis and Bayesian updating. In this paper, a framework is developed to tackle this problem. Full, detailed aeroelastic model of an experimental wind turbine system based on 3‐D Reynolds‐averaged Navier‐Stokes is developed, considering all structural components including nacelle and tower. This model is validated against experimental measurements of rotating blades, and a detailed aeroelastic characterisation is presented. Aerodynamic forces from prescribed forced‐motion simulations are used to train a time‐domain autoregressive with exogenous input (ARX) model with a localised forcing term, which provides accurate and cheap aeroelastic forces. Employing ARX, prior uncertainties in the structural and rotational parameters of the wind turbine are introduced and propagated to obtain probabilistic estimates of the aeroelastic characteristics. Finally, the experimental validation data are used in a Bayesian framework to update the structural and rotational parameters of the system and thereby reduce uncertainty in the aeroelastic characteristics.     

Flap/lead–lag aeroelastic stability of wind turbine blade sections

The scope of this article is to investigate the aeroelastic stability of wind turbine blade sections subjected to combined flap/lead–lag motion. The work is motivated by recent concern about destructive ‘edgewise' vibrations of modern, half‐megawatt‐scale, blades. The aeroelastic governing equations derive from the combination of a spring–mass–damper equivalent of the structure and a ‘non‐stationary' aerodynamic model. The aerodynamic model used in the present context is the differential dynamic stall model developed at ONERA. The resulting equations of motion are linearized and their stability characteristics are investigated in terms of the system entries, expressed through suitable, non‐dimensional, structural and aerodynamic parameters. Copyright © 1999 John Wiley & Sons, Ltd.     

Implicit Floquet analysis of wind turbines using tangent matrices of a non‐linear aeroelastic code

The aeroelastic code BHawC for calculation of the dynamic response of a wind turbine uses a non‐linear finite element formulation. Most wind turbine stability tools for calculation of the aeroelastic modes are, however, based on separate linearized models. This paper presents an approach to modal analysis where the linear structural model is extracted directly from BHawC using the tangent system matrices when the turbine is in a steady state. A purely structural modal analysis of the periodic system for an isotropic rotor operating at a stationary steady state was performed by eigenvalue analysis after describing the rotor degrees of freedom in the inertial frame with the Coleman transformation. For general anisotropic systems, implicit Floquet analysis, which is less computationally intensive than classical Floquet analysis, was used to extract the least damped modes. Both methods were applied to a model of a three‐bladed 2.3 MW Siemens wind turbine model. Frequencies matched individually and with a modal identification on time simulations with the non‐linear model. The implicit Floquet analysis performed for an anisotropic system in a periodic steady state showed that the response of a single mode contains multiple harmonic components differing in frequency by the rotor speed. Copyright © 2011 John Wiley & Sons, Ltd.     

风力机叶片动态气弹变形及其对整机性能的影响

基于风力机整机刚柔耦合模型,文章提出了一种叶片动态气弹扭转变形分析的新方法。该方法采用SIMPACK和AeroDyn软件联合数值仿真对风力机在几种恶劣风况下进行动力学分析,通过对分析结果的变换处理,进而得到叶片在复杂工况下的动态气弹变形数据。采用该方法,重点分析了叶片气弹扭转变形对风力机气动功率及气弹稳定性的影响。该方法为大型风电叶片的气弹特性评价以及气弹剪裁设计提供了一种新的技术手段。     

Aeroelastic analysis of a wind turbine blade using the harmonic balance method

An aeroelastic model for wind turbine blades derived from the unsteady Navier‐Stokes equations and a mode shape–based structural dynamics model are presented. For turbulent flows, the system is closed with the Spalart‐Allmaras turbulence model. The computation times for the aerodynamic solution are significantly reduced using the harmonic balance method compared to a time‐accurate solution. This model is significantly more robust than standard aeroelastic codes that rely on blade element momentum theory to determine the aerodynamic forces. Comparisons with published results for the Caradonna‐Tung rotor in hover and the classical AGARD 445.6 flutter case are provided to validate the aerodynamic model and aeroelastic model, respectively. For wind turbines, flutter of the 1.5 MW WindPACT blade is considered. The results predict that the first flapwise and edgewise modes dominate flutter at the rotor speeds considered.     

Assessment of dynamic substructuring of a wind turbine foundation applicable for aeroelastic simulations

Dynamic vibration response of a wind turbine structure is examined. Emphasis is put on the dynamic interaction between the foundation and the subsoil, since stiffness and energy dissipation of the substructure affect the dynamic response of the wind turbine. Based on a standard lumped‐parameter model fitted to the frequency response of the ground, a surface foundation is implemented into the aeroelastic code FLEX5. In case of a horizontal stratum overlaying a homogeneous half‐space and within the low frequency range, analyses show that a standard lumped‐parameter model provides an accurate prediction of the frequency‐dependent foundation stiffness. The generalized stiffness matrix of the substructure is found to be in a reasonable agreement with the corresponding values based on a Guyan reduction scheme. In addition, experimental findings based on traditional and operational modal techniques on a Vestas V112‐3.3 MW wind turbine installed on drained soil clearly indicate that the energy dissipation related to the lowest eigenmode is described accurately in the aeroelastic simulation. Copyright © 2014 John Wiley & Sons, Ltd.     

Localization of wind turbine noise using a microphone array in wind tunnel measurements

An experimental investigation on scaled wind turbine models in a wind tunnel with a microphone array is presented. Our study focuses on the localization and quantification of aerodynamic noise sources on rotating wind turbine blades with the aim of identifying the contributing factors that have an impact on the source spectra. Therefore, wind tunnel measurements were conducted for three different blade geometries (NACA 4412 shape, Clark-Y shape, and sickle shape), five pitch angles between ?2° and +8° and five wind velocities between 5 and 13 ms^??1. For the localization of rotating sound sources with a microphone array, a rotating beamforming method based on the acoustic ray method is used. The Clean-SC deconvolution method was used to improve the resolution of the acoustic sources, and integrated spectra were calculated for the individual blades. The sound sources were localized at the wind turbine blades and assigned to the leading edge and trailing edge subregions. The results show a high dependency on the sound source distribution and the source strength with regard to the observed one-third octave bands, wind velocity, and blade geometry. Hence, the localization of rotating sound sources with a microphone array is a suitable method for the development of wind turbine blades that emit less noise.     

Broadband noise radiation analysis for an HAWT rotor

The paper demonstrates a computational methodology for the noise prediction of an horizontal axis wind turbine (HAWT) rotor in time domain. The aeroacoustic modeling is based on the Ffowcs Williams and Hawkings equation considering only the surface monopole and dipole noise sources. The accurate solution of the noise problem is strongly influenced by the unsteadiness of the rotor flowfield, the nonuniform inflow effects and the blade aerodynamic parameters which are included in the numerical model. The aerodynamic analysis uses a three-dimensional low-order panel method combined with a boundary layer correction model for the calculation of the blade pressure distribution, obtaining satisfactory agreement with experimental data. Acoustic pressure predictions for the NREL downwind rotor are presented for several cases proving that broadband noise propagation dominates at low- and mid-frequency ranges. Sound pressure level contours occur via Fourier transformations, while the directivity for a single frequency source is also examined.     

Indoor simulation of amplitude modulated wind turbine noise

Wind energy is the world's fastest‐growing renewable energy source; as a result, the number of people exposed to wind farm noise is increasing. Because of its broadband amplitude‐modulated characteristic, wind turbine noise (WTN) is more annoying than noise produced by other common community/industrial sources. As higher frequencies are attenuated by air absorption and building transmission, the noise from modern large wind farms is mainly below 1000 and 500 Hz for outdoor and indoor conditions, respectively. Many WTN complaints relate to indoor, nighttime conditions when background noise levels are lower. As recently reported, indoor noise has the potential to cause sleeping disorders. Studies on human response to amplitude modulated WTN have been mainly focused on the outdoors, where a large amount of measured data exists. This is not the case for indoors, where it is much harder to gather data. Hence, there is a need to understand the transmission of WTN into dwellings and to develop indoor annoyance metrics. In this article, we investigate the transmission of WTN into residential‐type structures. Using an outdoor WTN recording and structures with different properties/configurations, we made a series of computer simulations for indoor noise predictions and assessed the results employing several widely used metrics for WTN, for example, spectral content, modulation depth and overall levels. In general, the indoor noise levels are higher, and the average modulation depth is similar to those of outdoor recordings. In addition, there is a significant change in the spectral shape. These results could potentially explain indoor WTN annoyance. Copyright © 2016 John Wiley & Sons, Ltd.     

Effect of winds in a mountain pass on turbine performance

Mountain passes are potentially advantageous sites for the deployment of wind turbines because of road links and electrical transmission infrastructure. However, relatively little is known about wind characteristics and turbine response in these environments. Using hub height wind data from a mountain pass in Switzerland, this paper discusses the causes of the observed pass winds and how a generic wind turbine might perform in those conditions. During 3 months of winter measurements, the winds in the pass showed signatures of forcing by regional pressure gradients rather than local cooling or heating. Turbulence intensity was often less than 10%, and the magnitude of the wind shear power law exponent was less than 0.1. To understand the impact of pass winds on a wind turbine, we simulated a Wind Partnership for Advanced Component Technologies 1.5 MW wind turbine using the Fatigue, Aerodynamics, Structures, and Turbulence (FAST) aeroelastic simulator , forced by artificial wind fields of varying turbulence intensity and shear generated by the turbulence simulator TurbSim. We used the turbine simulation data to train a regression model that is used to predict the turbine response to the pass wind time series. Results showed that depending on long‐term wind characteristics, wind turbines in the pass may perform differently than predicted using a power curve derived from test measurements at another location. This method of generating site‐specific energy capture predictions could be combined with long‐term wind resource data and specific turbine models to better predict the energy production and turbine loads at this, or any other site. Copyright © 2013 John Wiley & Sons, Ltd.