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.     

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.     

Effects of extreme wind shear on aeroelastic modal damping of wind turbines

Wind shear is an important contributor to fatigue loads on wind turbines. Because it causes an azimuthal variation in angle of attack, it can also affect aerodynamic damping. In this paper, a linearized model of a wind turbine, based on the non‐linear aeroelastic code BHawC, is used to investigate the effect of wind shear on the modal damping of the turbine. In isotropic conditions with a uniform wind field, the modal properties can be extracted from the system matrix transformed into the inertial frame using the Coleman transformation. In shear conditions, an implicit Floquet analysis, which reduces the computational burden associated with classical Floquet analysis, is used for modal analysis. The methods are applied to a 2.3 MW three‐bladed pitch‐regulated wind turbine showing a difference in damping between isotropic and extreme shear conditions at rated wind speed when the turbine is operating closest to stall. The first longitudinal tower mode decreases slightly in damping, whereas the first flapwise backward whirling and symmetric modes increase in damping. This change in damping is attributed to an interaction between the periodic blade mode shapes and the azimuth‐dependent local aerodynamic damping in the shear condition caused by a beginning separation of the flow. Copyright © 2012 John Wiley & Sons, Ltd.     

The application of passive air jet vortex‐generators to stall suppression on wind turbine blades

An experimental study was performed to assess the feasibility of passive air jet vortex‐generators to the performance enhancement of a domestic scale wind turbine. It has been demonstrated that these simple devices, properly designed and implemented, can provide worthwhile performance benefits for domestic wind turbines of the type investigated in this study. In particular, this study shows that they can increase the maximum output power coefficient, reduce the cut‐in wind speed and improve power output at lower wind speeds while reducing the sensitivity to wind speed unsteadiness. A theoretical performance analysis of a 500 kW stall‐regulated wind turbine, based on blade element momentum theory, indicates that passive air jet vortex‐generators would be capable of recovering some of the power loss because of blade stall, thereby allowing attainment of rated power output at slightly lower average wind speeds. Copyright © 2016 John Wiley & Sons, Ltd.     

A solution‐based stall delay model for horizontal‐axis wind turbines

This work proposes a new solution‐based stall delay model to predict rotational effects on horizontal‐axis wind turbines. In contrast to conventional stall delay models that correct sectional airfoil data prior to the solution to account for three‐dimensional and rotational effects, a novel approach is proposed that corrects sectional airfoil data during a blade element momentum solution algorithm by investigating solution‐dependent parameters such as the spanwise circulation distribution and the local flow velocity acting at a section of blade. An iterative process is employed that successively modifies sectional lift and drag data until the blade circulation distribution is converged. Results obtained with the solution‐based stall delay model show consistent good agreement with measured data along the National Renewable Energy Laboratory Phase VI and Model Experiments in Controlled Conditions rotor blades at low and high wind speeds. Copyright © 2014 John Wiley & Sons, Ltd.     

Harmonic balance Navier‐Stokes aerodynamic analysis of horizontal axis wind turbines in yawed wind

Multimegawatt horizontal axis wind turbines often operate in yawed wind transients, in which the resulting periodic loads acting on blades, drive‐train, tower, and foundation adversely impact on fatigue life. Accurately predicting yawed wind turbine aerodynamics and resulting structural loads can be challenging and would require the use of computationally expensive high‐fidelity unsteady Navier‐Stokes computational fluid dynamics. The high computational cost of this approach can be significantly reduced by using a frequency‐domain framework. The paper summarizes the main features of the COSA harmonic balance Navier‐Stokes solver for the analysis of open rotor periodic flows, presents initial validation results on the basis of the analysis of the NREL Phase VI experiment, and it also provides a sample application to the analysis of a multimegawatt turbine in yawed wind. The reported analyses indicate that the harmonic balance solver determines the considered periodic flows from 30 to 50 times faster than the conventional time‐domain approach with negligible accuracy penalty to the latter.     

Model‐independent periodic stability analysis of wind turbines

In this work, a new method is proposed for the stability analysis of wind turbines. The method uses input–output time histories obtained by conducting virtual excitation experiments with a suitable wind turbine simulation model. Next, a single‐input/single‐output periodic reduced model is identified from the recorded response and used for a stability analysis conducted according to the Floquet theory. Since only input–output sequences are used, the approach is model independent in the sense that it is applicable to wind turbine simulation models of arbitrary complexity. The use of the Floquet theory reveals a much richer picture than the one obtained by widespread classical approaches based on the use of the multi‐blade coordinate transformation of Coleman. In fact, it is shown here that, for each principal mode computed by the classical approach, there are in reality infinite super‐harmonics of varying strength fanning out from the principal one at multiples of the rotor speed. The relative strength of each harmonic in a fan provides for a way of measuring how periodically one specific fan of modes behaves. The notion of super‐harmonics allows one to justify the presence of peaks in the response spectra, peaks that cannot be explained by the classical time‐invariant analysis. The Campbell diagram, i.e., the plot of system frequencies vs. rotor speed, is in this work enriched by the presence of the super‐harmonics, revealing a much more complex pattern of possible resonant conditions with the per‐rev excitations than normally assumed. Copyright © 2014 John Wiley & Sons, Ltd.     

Real‐time hybrid aeroelastic simulation of wind turbines with various types of full‐scale tuned liquid dampers

The present paper presents the real‐time hybrid simulation (RTHS) technique for multimegawatt wind turbine (WT) with various types of full‐scale tuned liquid dampers (TLDs). As an evolvement of the pseudodynamic testing technique, the RTHS is executed in real time, thus allowing accurate investigation of the interaction between the aeroelastic WT system and the rate‐dependent nonlinear TLD device. As the numerical substructure, the WT is simulated in the computer using a 13‐degree‐of‐freedom (13‐DOF) aeroelastic model. As the physical substructure, the full‐scale TLDs are manufactured and physically tested. They are synchronized with each other by real‐time controllers. Taking advantage of RTHS technique, 2‐ and 3‐MW WTs have both been simulated under various turbulent wind conditions. TLDs with different configurations have been extensively investigated, eg, various tuning ratios by varying the water level, TLD without and with damping screens (various mesh sizes of the screen considered), and TLD with flat and sloped bottoms. It is shown that a well‐designed TLD is very effective in damping lateral tower vibrations of WTs. Furthermore, RTHS results and results from a proposed theoretical model are compared. This study gives comprehensive guidelines for employing various types of TLDs in large WTs and indicates huge potentials of applying RTHS technique in the area of wind energy.     

A simple frequency‐domain method for stress analysis of stall‐regulated wind turbines

A simple method, based in the frequency domain, was developed for calculating the dynamic response of a stall‐regulated wind turbine. Emphasis is placed on two aspects of the method, which are necessary in order to obtain a reasonable linearization of behavior when the blades are stalled. First, the tangential (in‐plane) component of turbulence is included, in addition to the axial component. Second, the linearized relationship between lift coefficient and angle‐of‐attack is adjusted to account for the effects of dynamic stall: separate linearizations are used for excitation and damping of vibration. A thorough comparison is made between linear and non‐linear dynamic‐stall methods, with the conclusion that the accuracy of the linear method depends upon the frequency and amplitude of oscillation. The linear dynamic‐stall method is accurate at blade vibrational frequencies, but it can be inaccurate at frequencies in the vicinity of 1P or below, when the angle‐of‐attack oscillates with an amplitude of 3° or more. Load spectra of a Nordtank 500 turbine, calculated using the frequency‐domain method, are compared with measurements. The frequency‐domain method provides estimates of load spectra and aerodynamic damping (stability) that are useful for preliminary design and optimization, but the method lacks sufficient accuracy and generality to be used for certification. Copyright © 2011 John Wiley & Sons, Ltd.     

Bend‐bend‐twist vibrations of a wind turbine blade

Dynamics of a wind turbine blade under bend‐bend‐twist coupled vibrations is investigated. The potential and kinetic energy expressions for a straight nonuniform blade are written in terms of beam parameters. Then, the energies are expressed in terms of modal coordinates by using the assumed mode method, and the equations of motion are found by applying Lagrange's formula. The bend‐bend‐twist equations are coupled with each other and have stiffness variations due to centrifugal effects and gravitational parametric terms, which vary cyclicly with the hub angle. To determine the natural frequencies and mode shapes of the system, a modal analysis is applied on the linearized coupled equations of constant angle snapshots of a blade with effects of constant speed rotation. Lower modes of the coupled bend‐bend‐twist model are dominantly in‐plane or out‐of‐plane modes. To investigate the parametric effects, several blade models are analyzed at different angular positions. The stiffness terms involving centrifugal and gravitational effects can be significant for long blades. To further see the effect of blade length on relative parametric stiffness change, the blade models are scaled in size and analyzed at constant rotational speeds, at horizontal and vertical orientations. These studies show that the parametric stiffness effects should be taken into account when designing long blades.     

漂浮式风力机平台结构设计与模态分析

风力机发展趋势使深海漂浮式风力机有着广阔发展前景.分析了漂浮式多浮柱平台的稳定机理,根据美国可再生能源实验室5 MW风力机模型,提出了平面对称结构浮柱平台设计思路,同时初步建立了深海多浮柱平台三维有限元模型.结合机械振动理论,采用有限元计算软件对三浮柱、四浮柱以及六浮柱平台模型进行模态分析,为进一步开展漂浮式平台的优化设计提供了一定参考依据.     

Leading edge erosion of wind turbines: Effect of solid airborne particles and rain on operational wind farms

Leading edge erosion (LEE) affects almost all wind turbines, reducing their annual energy production and lifetime profitability. This study presents results of an investigation into 18 operational wind farms to assess the validity of the current literature consensus surrounding LEE. Much of the historical research focuses on rain erosion, implying that this is the predominant causal factor. However, this study showed that the impact of excessive airborne particles from seawater aerosols or from adverse local environments such as nearby quarries greatly increases the levels of LEE. Current testing of leading edge protection coatings or tapes is based on a rain erosion resistivity test, which does little to prove its ability to withstand solid particle erosion and may drive coating design in the wrong direction. Furthermore, it was shown that there is little correlation between test results and actual field performance. A method of monitoring the expected level of erosion on an operational wind turbine due to rain erosion is also presented. Finally, the energy losses associated with LEE on an operational wind farm are examined, with the average annual energy production dropping by 1.8% due to medium levels of erosion, with the worst affected turbine experiencing losses of 4.9%.     

Digital tuft analysis of stall on operational wind turbines

Operational wind turbines are exposed to dynamic inflow conditions because of, for instance, atmospheric turbulence and wind shear. In order to understand the resulting three‐dimensional and transient aerodynamics effects at a site, a 10m stall‐regulated upwind two‐bladed wind turbine was instrumented for a novel digital tuft flow visualization study. High definition video of a tufted blade was acquired during wind turbine operation in the field, and a novel digital image processing algorithm calculated the blade stall directly from the video. After processing O(10⁵) sequential images, the algorithm achieved a ?5% bias error compared with previous manual analysis methods. With increasing wind speed (5m/s to 20m/s) the fraction of tufts exhibiting stalled flow increased from 5% to 40% on the outboard 40% of the blade. The independently measured instantaneous turbine power production correlates highly with the stall fraction. Some azimuthal variation in the stall fraction associated with dynamic stall induced by vertical wind shear was seen with a maximum in the 45–90° azimuthal location. The high detail, quantitative image processing method demonstrated good agreement with the expected behaviour for a stall‐regulated wind turbine and revealed azimuthal variation because of shear‐induced dynamic stall. The amount of reliable blade stall data to be obtained from digital tuft visualization has hereby been vastly increased. Copyright © 2015 John Wiley & Sons, Ltd.     

An improved BEM model for the power curve prediction of stall‐regulated wind turbines

Blade element momentum (BEM) theory is the standard computational technique for the prediction of power curves of wind turbines; it is based on the two‐dimensional aerodynamic properties of aerofoil blade elements and some corrections accounting for three‐dimensional wing aerodynamics. Although most BEM models yield acceptable results for low‐wind and pitch‐controlled regimes where the local angles of attack are small, no generally accepted model exists up to date that consistently predicts the power curve in the stall regime for a variety of blade properties and operating conditions. In this article we present a modified BEM model which satisfactorily reproduces the power curves of four experimental wind turbines reported in the literature, using no free fit parameters. Since these four experimental cases comprehend a great variety of conditions (wind tunnel vs field experiments, different air densities) and blade parameters (no twist and no taper, no taper but twist, both twist and taper, different aerofoil families), it is believed that our model represents a useful working tool for the aerodynamic design of stall‐regulated wind turbines. Copyright © 2004 John Wiley & Sons, Ltd.     

Vibration suppression for monopile and spar‐buoy offshore wind turbines using the structure‐immittance approach

Offshore wind turbines have the potential to capture the high‐quality wind resource. However, the significant wind and wave excitations may result in excessive vibrations and decreased reliability. To reduce vibrations, passive structural control devices, such as the tuned mass damper (TMD), have been used. To further enhance the vibration suppression capability, inerter‐based absorbers (IBAs) have been studied using the structure‐based approach, that is, proposing specific stiffness‐damping‐inertance elements layouts for investigation. Such an approach has a critical limitation of being only able to cover specific IBA layouts, leaving numerous beneficial configurations not identified. This paper adopts the newly introduced structure‐immittance approach, which is able to cover all network layout possibilities with a predetermined number of elements. Linear monopile and spar‐buoy turbine models are first established for optimisation. Results show that the performance improvements can be up to 6.5% and 7.3% with four and six elements, respectively, compared with the TMD. Moreover, a complete set of beneficial IBA layouts with explicit element types and numbers have been obtained, which is essential for next‐step real‐life applications. In order to verify the effectiveness of the identified absorbers with OpenFAST, an approach has been established to integrate any IBA transfer functions. It has been shown that the performance benefits preserve under both the fatigue limit state (FLS) and the ultimate limit state (ULS). Furthermore, results show that the mass component of the optimum IBAs can be reduced by up to 25.1% (7,486 kg) to achieve the same performance as the TMD.     

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.     

A new seismic‐based monitoring approach for wind turbines

Wind turbine performance and condition monitoring play vital roles in detecting and diagnosing suboptimal performance and guiding operations and maintenance. Here, a new seismic‐based approach to monitoring the health of individual wind turbine components is presented. Transfer functions are developed linking key condition monitoring properties (drivetrain and tower acceleration) to unique, robust, and repeatable seismic signatures. Predictive models for extreme (greater than 99th percentile) drivetrain and tower acceleration based on independent seismic data exhibit higher skill than reference models based on hub‐height wind speed. The seismic models detect extreme drivetrain and tower acceleration with proportions correct of 96% and 93%, hit rates of 91% and 82%, and low false alarm rates of 4% and 6%, respectively. Although new wind turbines incorporate many diagnostic sensors, seismic‐based condition/performance monitoring may be particularly useful in extending the productive lifetime of previous generation wind turbines.     

Wave‐current interaction effects on structural responses of floating offshore wind turbines

This paper proposes a model considering the wave‐current interactions in dynamic analyses of floating offshore wind turbines (FOWTs) and investigates the interaction effects on the FOWT responses. Waves when traveling on current are affected by the current, leading to frequency shift and shape modification. To include such interactions in FOWT analysis, which has not been considered by the researchers till date, a nonlinear hydrodynamic model for multicable mooring systems is presented that is able to consider the cable geometric nonlinearity, seabed contact, and the current effect. The mooring model is then coupled with a spar‐type FOWT model that handles the structural dynamics of turbine blades and tower, aerodynamics of the wind‐blade interaction, and wave‐current effects on the spar. The analytical wave‐current interaction model based on Airy theory considering the current effect is used in the computation of flow velocity and acceleration. Numerical studies are then carried out based on the NREL offshore 5‐MW baseline wind turbine supported on top of the OC3‐Hywind spar buoy. Two cases, (1) when the currents are favorable and (2) when the currents are adverse, are examined. Differences of up to 15% have been observed by comparing the cable fairlead tension obtained excluding and including the wave‐current interactions. In particular, when irregular waves interact with adverse current, a simple superposition treatment of the wave and the current effects seems to underestimate the spar motion and the cable fairlead tension. This indicates that the wave‐current interaction is an important aspect and is needed to be considered in FOWT analysis.     

Experimental identification of modal parameters of an industrial 2‐MW wind turbine

This contribution presents modal testing of a 2‐MW wind turbine on a 100‐m tubular tower with a 93‐m rotor developed by W2E Wind to Energy GmbH. This research is part of the DYNAWIND project of the University of Rostock and W2E. Beside classical modal analysis schemes, this contribution mainly focusses on the application of operational modal analysis techniques to a wind turbine. Specific problems are addressed, and hints for modal testing on wind turbines are given. Furthermore, an effective measurement setup is proposed for identification of the modal parameters of a wind turbine. The measurement campaign is divided in two parts. First, a measurement campaign using 8 sensor positions on a rotor blade was done while the rotor is lying on ground. Second, a detailed measurement campaign was done on the entire wind turbine with the rotor locked in Y position using 61 sensor positions on the tower, the mainframe, the gearbox, the generator, and the low‐voltage unit. While the rotor blade was tested by classical and operational modal analysis techniques, the entire wind turbine was tested by operational modal analysis techniques only. The mode shapes and eigenfrequencies of the wind turbine identified within the measurement campaigns are within the expected range of the design values of the wind turbine. But in contrast, the damping ratios differ strongly from those given in guidelines and literature. Furthermore, a strong influence of aerodynamic damping compared to structural damping is observed for the first tower mode even for a parked wind turbine.