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.     

Simulating Feedback Linearization control of wind turbines using high‐order models

As wind turbines are becoming larger, wind turbine control must now encompass load control objectives as well as power and speed control to achieve a low cost of energy. Due to the inherent non‐linearities in a wind turbine system, the use of non‐linear model‐based controllers has the potential to increase control performance. A non‐linear feedback linearization controller with an Extended Kalman Filter is successfully used to control a FAST model of the controls advanced research turbine with active blade, tower and drive‐train dynamics in above rated wind conditions. The controller exhibits reductions in low speed shaft fatigue damage equivalent loads, power regulation and speed regulation when compared to a Gain Scheduled Proportional Integral controller, designed for speed regulation alone. The feedback linearization controller shows better rotor speed regulation than a Linear Quadratic Regulator (LQR) at close to rated wind speeds, but poorer rotor speed regulation at higher wind speeds. This is due to modeling inaccuracies and the addition of unmodeled dynamics during simulation. Similar performance between the feedback linearization controller and the LQR in reducing drive‐train fatigue damage and power regulation is observed. Improvements in control performance may be achieved through increasing the accuracy of the non‐linear model used for controller design. Copyright © 2009 John Wiley & Sons, Ltd.     

Modelling and control of synchronous generators for wide‐range variable‐speed wind turbines

The modelling and control of a wide‐range variable speed wind turbine based on a synchronous generator are presented. Two different methods to control the operation of the synchronous generator are investigated, i.e. load angle control and instantaneous vector control. The dynamic performance characteristics of these control strategies are evaluated and compared using three model representations of the generator: a non‐reduced order model including both stator and rotor transients, a reduced order model with stator transients neglected, and a steady‐state model that neglects generator electrical dynamics. Assessment on the performance of grid‐side controller is shown during network fault and frequency variation. A simplified wind turbine model representation is also developed and proposed for large‐scale power system studies. Simulation results in Matlab/Simulink are presented and discussed. Copyright © 2007 John Wiley & Sons, Ltd.     

Identification in closed‐loop operation of models for collective pitch robust controller design

To achieve load reduction and power optimization, wind turbine controllers design requires the availability of reliable control‐oriented linear models. These are needed for model‐based controller design. Model identification of wind turbine while operating in closed loop is an appropriate solution that has recently shown its capabilities when linear time‐invariant controllers and complicated control structures are present. However, the collective pitch control loop, one of the most important wind turbine loops, uses non‐linear controllers. Typically, this non‐linear controller is a combination of a linear controller and a gain scheduling. This paper presents a new algorithm for identification in closed‐loop operation that allows the use of this kind of non‐linear controllers. The algorithm is applied for identification the collective pitch demand to generator speed of a wind turbine at various operating points. The obtained models are presented and discussed from a control point of view. The validity of these models is illustrated by their use for the design of a linear fix robust controller. The performance based on simulation data of this linear controller is similar to that obtained with simulations based on a linear controller with gain scheduling, but its design and implementation is much simpler. Copyright © 2012 John Wiley & Sons, Ltd.     

Linear models‐based LPV modelling and control for wind turbines

The non‐linear behaviour of wind turbines demands control strategies that guarantee the robustness of the closed‐loop system. Linear parameter‐varying (LPV) controllers adapt their dynamics to the system operating points, and the robustness of the closed loop is guaranteed in the controller design process. An LPV collective pitch controller has been developed within this work to regulate the generator speed in the above rated power production control zone. The performance of this LPV controller has been compared with two baseline control strategies previously designed, on the basis of classical gain scheduling methods and linear time‐invariant robust H_∞ controllers. The synthesis of the LPV controller is based on the solution of a linear matrix inequalities system, proposed in a mixed‐sensitivity control scenario where not only weight functions are used but also an LPV model of the wind turbine is necessary. As a contribution, the LPV model used is derived from a family of linear models extracted from the linearization process of the wind turbine non‐linear model. The offshore wind turbine of 5 MW defined in the Upwind European project is the used reference non‐linear model, and it has been modelled using the GH Bladed 4.0 software package. The designed LPV controller has been validated in GH Bladed, and an exhaustive analysis has been carried out to calculate fatigue load reductions on wind turbine components, as well as to analyse the load mitigation in some extreme cases. Copyright © 2014 John Wiley & Sons, Ltd.     

Modelling–based approach for digital control design for nonlinear WECS in the power system

The case has been established that the wind power plant must be treated as an integral part of the electric system, thereby constituting the wind energy conversion system. Recent advancement in size and technology of wind turbines requires sophisticated control systems to effectively optimize energy conversion and enhance grid integration. As a first step toward controller design, modelling has become a prerequisite. This paper explores controller design based on modelling the wind speed as a stochastic process, and the wind turbine as a multi‐mass system with a soft shaft linking the turbine with the doubly fed induction generator. A control strategy incorporating a linear quadratic Gaussian (LQG) that relies on state estimation for full‐state feedback is proposed to augment a linear controller for generator torque control. The control objectives are to reduce stresses on the drivetrain and to ensure operation geared toward optimal power conversion. This study focuses on above‐rated wind speeds, and the LQG's main purpose is to add damping to the drivetrain, thereby minimizing cyclic fatigue, while a pitch control mechanism prevents rotor overspeed, thereby maintaining rated power. Simulations show the efficacy of the proposed paradigm in meeting the control objectives. Copyright © 2009 John Wiley & Sons, Ltd.     

Reduced models of doubly fed induction generator system for wind turbine simulations

This article compares three reduced models with a detailed model of a doubly fed induction generator system for wind turbine applications. The comparisons are based on simulations only. The main idea is to provide reduced generator models which are appropriate to simulate normal wind turbine operation in aeroelastic wind turbine models, e.g. for control system design or structural design of the wind turbine. The electrical behaviour such as grid influence will therefore not be considered. The work presented in this article shows that with an ideal, undisturbed grid the dynamics of the doubly fed induction generator system is very well represented by the dynamics due to the generator inertia and the generator control system, whereas the electromagnetic characteristics of the generator can be represented by the steady state relations. The parameters for the proposed models are derived from parameters typically available from the generator data sheet and from the controller settings. Thus the models are simple to apply in any case where the generator data sheet is available. Copyright © 2005 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.     

Modelling and control of variable‐speed multi‐pole permanent magnet synchronous generator wind turbine

Emphasis of this article is on variable‐speed pitch‐controlled wind turbines with multi‐pole permanent magnet synchronous generator (PMSG) and on their extremely soft drive‐train shafts. A model and a control strategy for a full back‐to‐back converter wind turbine with multi‐pole PMSG are described. The model comprises submodels of the aerodynamic rotor, the drive‐train by a two‐mass model, the permanent magnet generator and the full‐scale converter system. The control strategy, which embraces both the wind turbine control itself and the control of the full‐scale converter, has tasks to control independently the active and reactive powers, to assist the power system and to ensure a stable normal operation of the wind turbine itself. A multi‐pole PMSG connected to the grid through a full‐scale converter has no inherent damping, and therefore, such configuration can become practically unstable, if no damping by means of external measures is applied. In this work, the frequency converter is designed to damp actively the drive‐train oscillations, thus ensuring stable operation. The dynamic performance of the presented model and control strategy is assessed and emphasized in normal operation conditions by means of simulations in the power system simulation tool DIgSILENT. Copyright © 2008 John Wiley & Sons, Ltd.     

A low‐order model for analysing effects of blade fatigue load control

A new low‐order mathematical model is introduced to analyse blade dynamics and blade load‐reducing control strategies for wind turbines. The model consists of a typical wing section model combined with a rotor speed model, leading to four structural degrees of freedom (flapwise, edgewise and torsional blade oscillations and rotor speed). The aerodynamics is described by an unsteady aerodynamic model. The equations of motion are derived in non‐linear and linear form. The linear equations of motion are used for stability analysis and control design. The non‐linear equations of motion are used for time simulations to evaluate control performance. The stability analysis shows that the model is capable of predicting classical flutter and stall‐induced vibrations. The results from the stability analysis are compared with known results, showing good agreement. The model is used to compare the performance of one proportional–integral–derivative controller and two full‐state feedback controllers. Copyright © 2006 John Wiley & Sons, Ltd.     

Flap/lead–lag aeroelastic stability of wind turbine blades

A numerical tool for investigating the aeroelastic stability of a single wind turbine blade subjected to combined flap/lead–lag motion is presented. Its development is motivated by recent concern about destructive edgewise vibrations of modern stall‐controlled blades. The stability tool employs a finite element formulation to discretize in space the structural and aerodynamic governing equations. Unsteady aerodynamics is considered by means of the extended ONERA lift and drag models. The mathematical form of these models allows for a combined treatment of dynamics and aerodynamics through the introduction of a so‐called ‘aeroelastic beam element’. This is an extended two‐node beam element having both deformation and aerodynamic degrees of freedom. Several linear and non‐linear versions of the stability tool are available, differing in the way that instantaneous lift and/or drag is treated. In the linear case, stability is investigated through eigenvalue analysis. Time domain integration is employed for non‐linear stability analysis. Results are presented and discussed for a 17 m stall‐controlled blade. Copyright © 2001 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.     

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.     

An input‐output linearization–based control strategy for wind energy conversion system to enhance stability

This paper proposes a novel control strategy for doubly fed induction generator (DFIG)‐based wind energy conversion system to investigate the potential of enhancing the stability of wind energy transmission system, a synchronous generator weakly integrated to a power system with a DFIG‐based wind farm. The proposed approach uses state feedback to exactly linearize the nonlinear wind energy transmission system from control actions (active power and reactive power control order of DFIG) to selected outputs (power angle and voltage behind transient resistance of synchronous generator) at first. Then, on account of the linearized subsystem, the stability enhancement controller is designed based on linear quadratic regulator algorithm to contribute adequate damping characteristics to oscillations of the synchronous generator system under various operation points. The proposed control strategy successfully deals with the nonlinear behaviors exist from the inputs to outputs and improve the robustness with respect to the variation of system operation points. Furthermore, not only the rotor angle stability but also the voltage stability is enhanced by using the proposed control strategy. The simulation results carried on the studied system verify the effectiveness of the proposed control strategy of wind energy conversion system for system stability enhancement and the robustness against various system operation points.     

A decoupling control strategy for wind turbine blades equipped with active flow controllers

The use of active controls has shown to be of substantial help in supporting the increasing size of wind turbines by reducing peak stresses and fatigue loads. In this respect, this paper proposes the use of intuitive frequency‐based control strategies for reducing loads in wind turbine blades equipped with multi‐input multi‐output (MIMO) active flow controllers. For that purpose, a loop‐shaping approach is considered for analysing the dynamic of actively controlled wind turbine blades. Preliminary aeroelastic simulations are carried out to validate the results. It is shown that the MIMO vibration control problem can effectively be decomposed into a number of decoupled single‐input single‐output control problems because of the strong correlation between the dominant aeroelastic blade dynamics and actuator deployments. As a result, it is demonstrated that classical single‐input single‐output control systems can perform as efficiently as MIMO controllers for damping the aeroelastic dynamics of wind turbine blades. Copyright © 2016 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.     

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.     

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.