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.     

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.     

Assessment of a comprehensive aeroelastic tool for horizontal‐axis wind turbine rotor analysis

This paper presents the development of a computational aeroelastic tool for the analysis of performance, response and stability of horizontal‐axis wind turbines. A nonlinear beam model for blades structural dynamics is coupled with a state‐space model for unsteady sectional aerodynamic loads, including dynamic stall effects. Several computational fluid dynamics structural dynamics coupling approaches are investigated to take into account rotor wake inflow influence on downwash, all based on a Boundary Element Method for the solution of incompressible, potential, attached flows. Sectional steady aerodynamic coefficients are extended to high angles of attack in order to characterize wind turbine operations in deep stall regimes. The Galerkin method is applied to the resulting aeroelastic differential system. In this context, a novel approach for the spatial integration of additional aerodynamic states, related to wake vorticity and dynamic stall, is introduced and assessed. Steady‐periodic blade responses are evaluated by a harmonic balance approach, whilst a standard eigenproblem is solved for aeroelastic stability analyses. Drawbacks and potentialities of the proposed model are investigated through numerical and experimental comparisons, with particular attention to rotor blades unsteady aerodynamic modelling issues. Copyright © 2016 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.     

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.     

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.     

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.     

Assessment of passive instability suppression means on pitch‐regulated wind turbines

The significance of three types of design modifications in view of defining passive means to extend the stability bounds of modern wind turbines is assessed in this paper. The first concerns the use of optimized airfoil shapes on a fixed blade planform while the other two concern the increase of structural flexibility by either bringing closer the flap and lead‐lag mode frequencies or introducing a soft yaw connection. Such an exploration of the stability envelope aims at providing the necessary understanding of the mechanisms that control aeroelastic damping and therefore at identifying means for improving the stability behaviour of the lowest damped system modes. Stability calculations are performed in the context of linear eigenvalue analysis using a state‐of‐the‐art stability tool. The model accounts for the full wind turbine configuration and the eigenvalue problem is formulated with reference to the non‐rotating (ground‐fixed) frame of reference through the multi‐blade transformation of all the rotating degrees of freedom. Results are presented in reference to a commercial multi‐MW, pitch‐regulated, variable‐speed wind turbine. They indicate that the soft yaw concept offers more significant margins of improvement compared with the flap‐lag coincidence, while aerodynamic optimization could be a basis for improvement. Copyright © 2007 John Wiley & Sons, Ltd.     

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.     

Effect of steady deflections on the aeroelastic stability of a turbine blade

This paper deals with effects of geometric non‐linearities on the aeroelastic stability of a steady‐state deflected blade. Today, wind turbine blades are long and slender structures that can have a considerable steady‐state deflection which affects the dynamic behaviour of the blade. The flapwise blade deflection causes the edgewise blade motion to couple to torsional blade motion and thereby to the aerodynamics through the angle of attack. The analysis shows that in the worst case for this particular blade, the edgewise damping can be decreased by half. Copyright © 2010 John Wiley & Sons, Ltd.     

High‐fidelity linear time‐invariant model of a smart rotor with adaptive trailing edge flaps

A high‐fidelity linear time‐invariant model of the aero‐servo‐elastic response of a wind turbine with trailing‐edge flaps is presented and used for systematic tuning of an individual flap controller. The model includes the quasi‐steady aerodynamic effects of trailing‐edge flaps on wind turbine blades and is integrated in the linear aeroelastic code HAWCStab2. The dynamic response predicted by the linear model is validated against non‐linear simulations, and the quasi‐steady assumption does not cause any significant response bias for flap deflection with frequencies up to 2–3 Hz. The linear aero‐servo‐elastic model support the design, systematic tuning and model synthesis of smart rotor control systems. As an example application, the gains of an individual flap controller are tuned using the Ziegler–Nichols method for the full‐order poles. The flap controller is based on feedback of inverse Coleman transformed and low‐pass filtered flapwise blade root moments to the cyclic flap angles through two proportional‐integral controllers. The load alleviation potential of the active flap control, anticipated by the frequency response of the linear closed‐loop model, is also confirmed by non‐linear time simulations. The simulations report reductions of lifetime fatigue damage up to 17% at the blade root and up to 4% at the tower bottom. Copyright © 2016 John Wiley & Sons, Ltd.     

Emergency stop simulation using a finite element model developed for large blade deflections

Predicting the load in every possible situation is necessary in order to build safe and optimized structures. A highly dynamical case where large loads are developed is an emergency stop. Design simulation tools that can cope with the upcoming non‐linearities will be especially important as the turbines get bigger and more flexible. The model developed here uses the advanced commercial finite element system MSC.Marc, focused on non‐linear design and analysis, to predict the structural response. The aerodynamic model named AERFORCE, used to transform the wind to loads on the blades, is a blade element momentum model. A comparison is made between measured and calculated loads for the Tjæreborg wind turbine during emergency braking of the rotor. The simulation results correspond well with measured data. The conclusion is that the aeroelastic tool is likely to perform well when simulating more flexible turbines. Copyright © 2005 John Wiley & Sons, Ltd.     

Numerical investigation of airflow through a Savonius rotor

The aim of this report is to present a model of a rigid‐rotor system based on computational fluid dynamics (CFD), which is applied on a vertical axis wind turbine (VAWT) research. Its originality results from the use of the average value of the variable rotational speed method taken in a periodic steady‐state (PSS) of the VAWT rotor instead of the classical fixed rotational speed method. This approach was chosen in order to determine the mechanical and aerodynamic parameters of the wind turbine. The modeling method uses an implicit Euler iterative solution strategy, which resolves the coupling between fixed and moving rotor domains. The main methods that were adopted are based on the three‐dimensional modeling of the interaction of the fluid flow with a rigid‐rotor. The strategy consists of using the Reynolds averaged Navier Stokes (RANS) equations with the standard k‐ ? and SST k‐ ω models to solve the fluid flow problem. To perform the rigid‐rotor motion in a fluid, the one degree of freedom (1‐DOF) method was applied. In the present study, the steady‐state and dynamic CFD simulations of the Savonius rotor are adopted to contribute to the validation elements of the VAWT models that are used. The dynamic study allows the investigation of the rotor behavior and the relation between velocity, pressure, and vorticity fields in and around the rotor blades. The flow fields generated by the rotation of the Savonius rotor were investigated in the half revolution period of the rotor angle θ from 0° to 180°. In this range of θ, the focus is on generating and dissipating vortices. Copyright © 2013 John Wiley & Sons, Ltd.     

基于模态叠加法的风电机组塔架实时状态研究

振动模态是机械结构在某一自振频率下的振动型态,是多自由度系统的固有属性。在模态分析的基础之上,提出一种基于模态叠加法的风电机组塔架振动状态与应力状态计算模型。该模型首先通过有限元法得到塔架的模态,然后通过模态叠加法根据塔架各监测点处的振动值计算得到整个塔架的振动状态及应力状态。以某风电场2.0 MW风电机组为例,通过有限元法数值模拟验证该模型计算结果的准确性。研究结果表明,该模型具有精度高和速度快的特点,能够满足实时在线计算要求。     

Development of a modified stochastic subspace identification method for rapid structural assessment of in‐service utility‐scale wind turbine towers

The strong drive to harness wind energy has recently led to rapid growth of wind farm construction. Wind turbine towers with increased sizes and flexibility experience large vibrations. Structural health monitoring of wind turbines is proposed in the wind energy industry to ensure their proper performance and save maintenance costs. This study proposes a system identification method for vibration‐based structural assessment of wind turbine towers. This method developed based on the stochastic subspace identification method can identify modal parameters of structures in operating conditions with harmonic components in excitations. It benefits wind turbine tower structural health assessment because classical operational modal analysis methods can fail as periodic rotation excitation from a turbine introduces harmonic disturbance to tower structure response data. The effectiveness, accuracy and robustness of the proposed method were numerically investigated and verified through a lumped‐mass system model. The method was then applied to an in‐service utility‐scale wind turbine tower. The field testing campaign and modal parameter identification as well as structural assessment results were presented. Copyright © 2017 John Wiley & Sons, Ltd.     

大型水平轴风轮转子／塔架耦合系统的气动弹性稳定性分析

建立了大型水平轴风轮转子／塔架耦合系统的气动弹性模型，推导了转子／塔架耦合系统周期系数运动方程，给出了气动弹性稳定性分析方法。对一风力机模型进行气动弹性稳定性计算，得到了与有关文献基本一致的结果。     

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.     

Evaluation of a wind speed estimator for effective hub‐height and shear components

Estimates of the effective wind speed disturbances acting on a wind turbine are useful in a variety of control applications. With some simplifications, it is shown that for zero yaw error, any wind field interacting with a turbine can be equivalently described using a hub‐height (uniform) component as well as linear horizontal and vertical shear components. A Kalman filter‐based wind speed estimator is presented for estimation of these effective hub‐height and shear components. The wind speed estimator is evaluated in the frequency domain using the FAST aeroelastic simulator with the National Renewable Energy Laboratory's 5 MW reference wind turbine model and realistic hub‐height and shear disturbances. In addition, the impact of the inflow model, used to simulate the rotor aerodynamics, on the Kalman filter performance is investigated. It is found that the estimator accuracy strongly depends on the inflow model used. In general, the estimator performs well up to a bandwidth of 1 Hz when the inflow model used for simulation matches the model used to create the linear Kalman filter model and blade pitch angle remains close to the linearization operating point. However, inaccuracies in the linear model of the turbine when dynamic inflow is used for simulation as well as nonlinearities in the turbine dynamics due to blade pitch actuation cause performance to degrade. Finally, the improvement gained by employing a non‐causal wind speed estimator is assessed, showing a minor increase in performance. Copyright © 2014 John Wiley & Sons, Ltd.