Emergingtrendsinvibration controlofwindturbines:a ...rsta.royalsocietypublishing.org/content/roypta/373/2035/20140069...active structural vibration control algorithms have ... of the

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ResearchCite this article: Staino A, Basu B. 2015Emerging trends in vibration control of windturbines: a focus on a dual control strategy.Phil. Trans. R. Soc. A 373: 20140069.http://dx.doi.org/10.1098/rsta.2014.0069

One contribution of 17 to a theme issue‘New perspectives in offshore wind energy’.

Subject Areas:structural engineering, energy, mechanicalengineering

Keywords:pitch control, active tendon control, windturbines

Author for correspondence:Biswajit Basue-mail: [email protected]

Emerging trends in vibrationcontrol of wind turbines: afocus on a dual control strategyAndrea Staino and Biswajit Basu

School of Engineering, Trinity College Dublin, Dublin 2, Ireland

The paper discusses some of the recent developmentsin vibration control strategies for wind turbines, andin this context proposes a new dual control strategybased on the combination and modification of tworecently proposed control schemes. Emerging trendsin the vibration control of both onshore and offshorewind turbines are presented. Passive, active and semi-active structural vibration control algorithms havebeen reviewed. Of the existing controllers, two controlschemes, active pitch control and active tendoncontrol, have been discussed in detail. The proposednew control scheme is a merger of active tendoncontrol with passive pitch control, and is designedusing a Pareto-optimal problem formulation. Thiscombination of controllers is the cornerstone of adual strategy with the feature of decoupling vibrationcontrol from optimal power control as one of its mainadvantages, in addition to reducing the burden onthe pitch demand. This dual control strategy willbring in major benefits to the design of modern windturbines and is expected to play a significant role in theadvancement of offshore wind turbine technologies.

1. IntroductionThe past decade has witnessed an unprecedenteddevelopment in the wind energy sector, and this growthis expected to continue over the next decade, particularlyin the offshore area. A hallmark of this development isthe design and deployment of multi-megawatt machineswith higher ratings and larger rotor diameters. Alongwith the larger machines come challenges such asincreased flexibility of blades/towers and associatedvibration issues, which can not only cause fatiguedamage with increased operating and maintenance costsbut also compromise the power output of the turbines [1].

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To curb the negative impacts of vibration and fatigue damage, researchers in recent years haveintroduced the concept of pitch control in wind turbines [2,3] as a means to control aerodynamicloads. The use of pitch control in general marks a major advancement towards control ofvibration, though it brings in associated difficulties related to careful design consideration toavoid interference with torque control [4]. As often unrecognized in the field of wind energy, loadcontrol and vibration control are two faces of the same coin. Hence, vibration control strategiescould be considered as an alternative effective means to achieve the identical aim of control ofstructural vibrations and fatigue-related damage in the same way that pitch control would doby load control. In fact, vibration control strategies would not have the drawback of interferencewith torque control or stresses generated by pitching the blades. Although structural vibrationcontrol has been an active area of research for the past two decades, developing structural controlstrategies and applying those to wind turbines is a relatively new field of research.

The primary modes of vibration of wind turbine blades are in-plane (primarily edgewise) andout-of-plane (primarily flapwise). These two modes of vibration are coupled, as the blades arestructurally pre-twisted in general. Besides, owing to the coupling of the aerodynamic loads inthe in-plane and out-of-plane directions, the responses (in-plane and out-of-plane) of the bladesare coupled too. This coupling gives rise to nonlinearity due to aero-elasticity, as the loads aredependent on the response of the flexible blades. Of the two modes, the edgewise mode has verylow or almost no aerodynamic damping, whereas the flapwise mode is aerodynamically dampedin nature. Thus, the edgewise modes are of concern, as they may induce instabilities, while theflapwise modes contribute to fatigue damage. In addition, the flexibility of the towers may couplethe motion of the tower to that of the blades in both the side-to-side and fore–aft directions, andis a source for generating undesirable blade/tower vibrations [5–7]. The importance of dynamiccoupling of the wind turbine tower and blades has been highlighted by Murtagh et al. [8] amongothers. They derived a model of a wind turbine including blade (flapwise)–tower interaction. Oncomparing the results from their model with the results from a model ignoring the coupling, anincrease in the blade tip displacement up to 256% was observed. The blade–tower interactionmay also become critical for the edgewise (or side-to-side) modes, which are inherently lightlydamped [9,10]. Recognizing the importance of controlling vibrations in wind turbines, severaltypes of vibration controllers have been proposed by researchers in recent years.

Passive control techniques have been investigated for structural control of both onshoreand offshore wind turbines [11–13]. One of the issues associated with the use of passivedevices for wind turbine structural control is that they may become ineffective as a resultof environmental/operational changes or in the presence of parametric variations. The use oftraditional passive tuned mass dampers (TMDs) in wind turbines also needs careful design. Infact, if the primary structure is very large (e.g. a wind turbine blade), the TMD will inevitablyhave a small mass ratio. As a consequence, accurate tuning of the natural frequency of the damperto the natural frequency of the primary structure may become difficult, and small deviationsfrom the optimal tuning may result in poor control performance. Further, tuning of the damper tothe rotational frequency of the turbine (which is generally associated with harmonic componentsthat mainly dominate the blade response) is not feasible, as it will lead to instabilities in theTMD–blade coupled system [14].

More recently, there has been a shift in vibration control strategies from passive to active andsemi-active. Use of active strut elements based on resonant controllers [15] inspired by the conceptof TMDs has been proposed for active control of vibrations in wind turbines. Investigations onthe use of synthetic jet actuators [16], microtabs and trailing edge flaps [17,18] have also beenconsidered by researchers. Active control strategies have been proposed by Staino et al. [19]and Fitzgerald et al. [14]. The control hardware takes advantage of the fact that the structureof the blade is hollow in nature. This allows controllers to be installed inside the blade withoutaffecting the external aerodynamic characteristic of the blades and hence does not interfere withaerodynamic performance. By exploiting the space available in the blade, Staino et al. [19] haveproposed an active tendon controller and Fitzgerald et al. [14] have proposed an active tuned massdamper (ATMD) for control of the vibration of blades. Control of vibration for variable-speed



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rotors has also been proposed by Staino & Basu [20]. A variant of the ATMD has been proposedby Fitzgerald & Basu [21] to reduce the requirement of the actuator control force in an ATMD. Thecontroller, termed a cable-connected active tuned mass damper (CCATMD), consists of a classicalATMD connected to the tip of the blade by a cable.

Semi-active control of wind turbines has been explored by Arrigan et al. [22,23] to suppressthe vibrations by using semi-active TMDs. The control algorithm is based on a short-time Fouriertransform and retuning the damper to track the dominant/natural frequencies of the structuralsystem. Control of both edgewise and flapwise vibrations has been investigated.

Recently, the issue of structural and mechanical vibrations in wind turbines due to theoccurrence of electrical grid faults has been analysed by Basu et al. [24] and Staino et al. [25].The study [24,25] indicated that the effect of electrical grid faults may propagate through themechanical subsystem of the turbine and cause major structural vibrations. The application ofcustom power devices to counteract the effect of grid fault-induced vibration is considered inthe study. Numerical results show that flexible alternating current transmission system (FACTS)devices and unified power quality conditioner (UPQC) in particular are successful in mitigatingvibrations due to electrical faults, and they can be conveniently applied to stabilize the generatorshaft speed, drive train oscillations, edgewise blade vibrations and tower responses.

Offshore wind energy has gained increasing attention owing to increased electricity generationof offshore power plants with respect to their onshore counterparts and also other advantagessuch as reduced visual impacts, less turbulence and lower noise constraints. For floating offshorewind turbines, it has been proposed to modify the blade pitch angle and the generator torque toimprove the damping of problematic motions and loads on floating platforms [26–28]. Recently,passive control of floating wind turbine nacelle and spar vibrations using multiple TMDs hasbeen investigated by Dinh & Basu [29]. In an overview of floating offshore wind turbines [30], thespar-type floating offshore wind turbine (S-FOWT) was shown to be the most suitable concept fordeep-water areas because of its lowered centre of mass, small water plane area and deep draft.The use of single and multiple TMDs for passive control of edgewise vibrations of nacelle/towerand spar of S-FOWTs was validated by Dinh et al. [31].

In this paper, first a multi-modal flexible wind turbine model based on an Euler–Lagrangeformulation is presented. Subsequently, a brief review of an active pitch controller is presented.A recently proposed active tendon controller for vibration control of wind turbine blades has alsobeen discussed and some results have been presented. Following the discussion on the pitch andactive tendon controllers, a new controller combining active tendon and passive pitch controlhas been proposed and investigated. This dual control strategy merges the benefits of the twocontrollers while eliminating some of the difficulties associated with active pitch control. Oneof the major benefits of the proposed improved control strategy (active tendon–passive pitch)is that it decouples vibration control from optimal power tracking. A Pareto-optimal problemis formulated for the design of the proposed controller, and the results show the encouragingpotential of the controller in the future, particularly for offshore deployments.

2. Euler–Lagrange wind turbine modelA flexible multi-body representation is adopted to describe the dynamic behaviour of a three-bladed horizontal-axis wind turbine (HAWT). The proposed structural model focuses on thevibrational response of the rotor blades and of the supporting tower. The model formulatedconsists of three rotating cantilever beams, representing the turbine blades, with variable bendingstiffness and variable mass along the length. The blades rotate at Ω(t) rad s−1 about the rotor hub’shorizontal axis. A schematic representation of the proposed wind turbine structural model isshown in figure 1. The formulation considers the blade in-plane and out-of-plane vibration modesand the tower side-to-side and fore–aft motions. The inclusion of the degrees of freedom (d.f.)associated with the tower into the Lagrangian formulation allows one to capture the dynamiccoupling between the blades and the tower [11]. The blade–tower interaction has been foundto have a significant impact on the dynamic response of the turbine [8], as it may lead to



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u31(Lb, t)

u21(Lb, t)

u11(Lb, t)u12(Lb, t)

Lb

LT

u11(x, t)u12(x, t)

n1(LT, t)

n2(LT, t)

n2(z, t)

n1(z, t)

X

X(a) (b)

X

X

ZZ

Z

x

Y

y

kŸ

W(t)

Y1(t)

jŸ

iŸ

Figure 1. Horizontal-axis wind turbine structural model. (a) Front view. (b) Side view. (Online version in colour.)

amplification of the oscillations associated with the blade response. The proposed vibration modelalso describes the centrifugal stiffening effect induced in the blades from the rotation and thecontribution arising from gravity. The coupling between the in-plane and out-of-plane modes dueto the structural pre-twist of the blades is also considered. Furthermore, the effects of variation inthe rotor speed are incorporated into the formulation.

The wind turbine rotor blades are represented as rotating pre-twisted cantilever beams oflength Lb with variable mass, stiffness and thickness per unit length. The cross section of the bladeat distance x from the root has structural pre-twist ϑ(x), chord length c(x) and mass per unit lengthμb(x). The pre-twist is measured with respect to the free end of the beam, i.e. ϑ(Lb) = 0◦. Themotions of the blades are described by a modal approximation in the co-rotating frame (x, y, z),where the x-axis is the blade axis and the z-axis coincides with the Z-axis of the ground-fixedframe (X, Y, Z).

Each mode of vibration is associated with the corresponding mode shape, for which anappropriate function approximation can be computed from the eigen-analysis of the bladestructural data. The coupled mode shapes have been computed using a finite-element approach.Using the Rayleigh–Ritz method [32], the deformation variable uj1(x, t) associated with thein-plane displacement of blade j is approximated by N1 vibration modes as

uj1(x, t) =N1∑i=1

Φi1(x) qji1(t), j = 1, 2, 3, i = 1, . . . , N1, (2.1)

where qji1(t) are the generalized in-plane displacements and Φi1(x) the corresponding in-planemode shape functions such that Φi1(Lb) = 1 for all i. Similarly, the blade response in the out-of-plane direction uj2(x, t) is represented by N2 degrees of freedom

uj2(x, t) =N2∑

k=1

Φk2(x) qjk2(t), j = 1, 2, 3, k = 1, . . . , N2, (2.2)



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where qjk2(t) is the kth out-of-plane vibration mode of blade j and Φk2(x) is the kth out-of-planemode shape with Φk2(Lb) = 1 for all k.

The azimuthal angle Ψj(t) of blade j with respect to the Z-axis is given by

Ψj(t) = Ψ1(t) + (j − 1)2π

3, j = 1, 2, 3, (2.3)

where Ψ1(t) is the azimuthal angle of the first blade,

Ψ1(t) =∫ t

0Ω(τ ) dτ . (2.4)

The wind turbine nacelle is modelled as a rigid discrete mass Mnac located at the tower top.The supporting tower is modelled as a flexible Euler–Bernoulli beam of length LT and variablemass μT(z) along its length. The tower side-to-side and fore–aft motions, denoted by v1(z, t) andv2(z, t), respectively, are modelled as

v1(z, t) =M1∑h=1

Φh3(z)q4h1(t), h = 1, . . . , M1

and v2(z, t) =M2∑l=1

Φl4(z)q4l2(t), l = 1, . . . , M2,

⎫⎪⎪⎪⎪⎪⎪⎬⎪⎪⎪⎪⎪⎪⎭

(2.5)

where Φh3(z) and Φl4(z) are the side-to-side and fore–aft tower mode shape functions, respectively,and q4h1(t) and q4l2(t) the corresponding generalized coordinates. The tower mode shapefunctions are such that Φh3(LT) = Φl4(LT) = 1 for all h, l. The parameters M1 and M2 denote thenumber of assumed modes for v1(z, t) and v2(z, t), respectively.

The equations of motion for the considered wind turbine vibration model with N degrees offreedom can be written as

[M(t)] {q̈(t)} + [C(t, Ω)]{q̇(t)} + [K(t, Ω2, Ω̇)]{q(t)} = {Qext(t)}, (2.6)

where [M(t)] ∈ RN×N is the mass matrix of the system, [C(t, Ω)] ∈ R

N×N is the damping matrix(including structural damping), [K(t, Ω2, Ω̇)] ∈ R

N×N is the stiffness matrix and {Qext(t)} ∈R

N represents the vector of generalized non-conservative (i.e. dissipative or external) loads(forces/torques) transferred to the system. The aerodynamic loads associated with the windpassing through the rotor area and the load arising due to gravitational effects have beenconsidered as generalized loads. A detailed description of the formulation of the Lagrangian fora three-bladed HAWT system can be found in [19]. The time-dependent entries in the systemmatrices arise from the formulation of the blade dynamics in a rotating frame of reference andrepresent mass, damping and stiffness contributions. Details of the wind turbine system matricesobtained using the proposed Euler–Lagrange approach are provided in [33].

From the time-varying system matrices in [33], it can be seen that the formulation with theblade–tower interaction gives rise to negative damping terms for the edgewise dynamics. This isconsistent with the study carried out by Thomsen et al. [6], who reported that total damping ofthe blade vibrations in the edgewise direction may become negative, with a detrimental impacton the structural performance of the blade. It is important to note that the occurrence of negativedamping arises from the coupling between the tower and the blades. In fact, the side-to-sidemotion of the tower may result in coupling with the in-plane motion of the blade, leading toan amplification of the oscillations associated with the time-varying dynamics. This is reflectedin time-varying stiffness and time-varying damping, with the possibility of negative damping.The omission of the blade–tower interaction in the model would not allow one to capture thisphenomenon and therefore it could result in an underestimation of the blade response.

If variations of the rotor speed are taken into account (i.e. Ω̇(t) �= 0), the stiffness matrix of thesystem can be decomposed as

[K(t, Ω , Ω̇)] = [K̄(t, Ω2)] + [KΩ̇ (t, Ω̇)], (2.7)



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HAWT

b b*

pitch actuationsystem

active pitchcontroller

measured power +–wind

rated power

Figure 2. Control scheme for a fixed-speed pitch-regulated wind turbine.

where [K̄(t, Ω2)] ∈ RN×N describes the contribution due to the elastic properties of the blades

and the tower, the contribution from centrifugal stiffening and the contribution arising fromgravitational effects. The entries in [KΩ̇ (t, Ω̇)] are proportional to −Ω̇(t) and they account for theimpact of rotor speed changes on the stiffness of the blades through the blade–tower interaction.

In this study, the aerodynamic load due to the wind and the effect of gravity are modelledas external loads on the wind turbine structure and are denoted by {QL(t)} and {QW(t)},respectively. Further, an additional generalized load term {QΩ̇ (t)} associated with the rotoracceleration is derived from the Lagrangian formulation due to the blade–tower interaction. Thetotal generalized external load vector ({Qext(t)}) on the right-hand side of (2.6) is expressed as

{Qext(t)} = {QL(t)} + {QW(t)} + {QΩ̇ (t)}. (2.8)

3. Combined active tendon and pitch control

(a) Conventional active pitch controlPitch control is the most widely used method to regulate the mechanical power generated in windturbines [34]. In fact, commercially available wind turbines are nowadays equipped with pitchcontrol systems to enhance the efficiency of wind energy conversion and to improve the safety ofthe plant in case of high wind speeds or emergency situations [35]. Active pitch control is achievedby rotating each blade about its axis by means of hydraulic or electric actuators appropriatelylocated inside the wind turbine structure, depending upon the configuration of the active pitchcontrol system (collective pitch control or individual pitch control). Below rated wind speed, thereis generally no need to vary the pitch angle, since the wind turbine should produce as muchpower as possible, though some optimization of energy capture below rated wind speed is alsopossible [36]. At high wind speeds, pitch control can be used to prevent excessive mechanicalpower production and to limit the power generated to the rated level. In classical designs, PI(proportional and integral) and PID (proportional, integral and derivative) controllers are used forwind turbine control applications [36]. The control strategy is designed to provide the demandedpitch angle β as a function of the power error, defined as the difference between the rated powerand the actual power being generated. The main control loop to limit the power in a fixed-speedpitch-regulated wind turbine is illustrated in figure 2. When the measured power is below therated value, the power error is negative and the demanded pitch is set at the fine pitch limit (e.g.β = 0), to maximize the aerodynamic efficiency of the rotor. For positive values of the powererror, β is appropriately controlled to meet the prescribed power requirements.

Power regulation is operated by pitching the blades in order to decrease the angle of attack(and hence the lift coefficient) along the length of the blade. As a consequence, pitch controlalso has an important effect on structural loads [4] and strongly affects the aerodynamic loadsgenerated by the rotor. By assuming local quasi-static two-dimensional flow conditions around



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aerofoil sections and ignoring three-dimensional phenomena at the blade tip, the instantaneouslocal angle of attack α(r, t) [19] at a distance r from the blade root can be expressed as

α(r, t) = φ(r, t) − β(t) − ϑ(r), (3.1)

where β is the pitch angle of the blade and φ(r, t) is the instantaneous local flow angle. From (3.1),it can be seen that the angle of attack can be reduced by pitching the leading edge of the blades upagainst the wind, i.e. by increasing β(t). This, in turn, has an effect on the aerodynamic loads onthe blades pN(r, t) and pT(r, t), in the normal and tangential directions, respectively (with respectto the rotor plane). The aerodynamic loads are modelled as

pN(r, t) = 12ρV2

rel(r, t)c(r)[Cl(α) cos(φ) + Cd(α) sin(φ)] (3.2a)

and

pT(r, t) = 12ρV2

rel(r, t)c(r)[Cl(α) sin(φ) − Cd(α) cos(φ)], (3.2b)

where ρ is the density of air, Vrel is the relative wind velocity, Cl(α) is the lift coefficient and Cd(α)is the drag coefficient associated with the blade aerofoil.

Equations (3.1) and (3.2a,b) show that the loads on the wind turbine structure can be alleviatedby appropriately modifying the pitch angle β. However, careful design of the control algorithmis required in order to avoid alleviation of loads using the pitch controller from interfering withpower generation. In fact, small changes in pitch angle can have a dramatic effect on the poweroutput [34]. The application of active pitch control for wind turbine load reduction is presentedin [2,4,36]. Active pitch control interacts strongly with the turbine dynamics, in particular withthe tower dynamics, and under certain circumstances can lead to instability of the active systemif the gains of the controller are not designed properly. For large wind turbines, a significantamount of force is required and intense mechanical stresses are experienced at the blade root inorder to operate fast and effective pitch control. Further, as mentioned above, major reductionof the structural loads using active pitch control only is not possible without compromisingon the mechanical power generated by the rotor. The approach suggested in this paper aimsat complementing the application of pitch control with active tendon control. In this way, itis possible to reduce the burden on active pitch control for load reduction by decoupling themitigation of structural loads from the power regulation issue.

(b) Offline pitch controlThe conventional active pitch control proposed by Bossanyi [2,4] now forms an integral part ofany variable-speed wind turbine machine. Though the primary action of the pitch controller isto track the optimum tip speed ratio for maximum power generation (in what is called region IIcontrol [37,38]) and regulating the speed of the turbine rotor at the rated speed (in the zone termedregion III control [37,38]), pitch control can also be used for load control. The aerodynamic loadcontrol of wind turbines is achieved by pitching the angle of the blades based on appropriatecontrol algorithms. This has the effect of ‘dampening’ (reducing) blade vibrations and canalso incorporate effective damping in towers by using an active state feedback using the pitchcontroller of the blades. Two types of pitch control are possible: collective and individual [2,36].In the case of collective pitch control, all the blades are pitched at the same angle using a feedbackcontrol algorithm, whereas for individual pitch controllers the algorithms are designed to controlthe pitch angle of each individual blade separately and can be more effective than collectivecontrol. It has been shown [2,4] that pitch controllers can effectively control fatigue and in thatway prolong the life of the wind turbine blades. Even though the advent of pitch controllers hasbeen a landmark in the advancement of wind turbine control, including the design of machineswith higher capacity, they suffer from certain inherent drawbacks, particularly for future offshoredevelopments, as discussed previously. Hence, it would be ideal if the pitch demand for a windturbine, located offshore in particular, could be significantly reduced or if at the least controllers



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could be designed such that the role of the controllers in load control (vibration control) andpower control could be decoupled from each other.

By taking advantage of the active tendon controller conceptualized and examined in [19,20],it is proposed to improve it further by combining it with a pitch controller, thereby achieving theobjective of decoupling vibration control from power control in a wind turbine. Active tendoncontrol can control vibrations with tendons deployed inside the hollow structure of the blades. Ithas the advantage of not interfering with the external aerodynamic surface and indeed having nomajor impact on the power generation capability of the turbine. When used with pitch controlof the blades, a reduction in the force demand of the actuator of the active tendon is alsopossible (owing to the inherent aerodynamic load reduction by virtue of pitch angle), which is anadded benefit. This arrangement will relieve the burden on the pitch controller, with the primaryresponsibility of the pitch controller being to track optimal power till saturation, and even inthose situations the level of vibration will be significantly diminished due to the use of activetendon control. Vibration reduction (fatigue load control) and mechanical stress alleviation canbe performed by active tendon control. The apparent conflict between load/fatigue control andgenerating maximum possible power when exclusively pitch control is used will be eliminatedby this dual (active tendon–pitch) control strategy.

As the actuator dynamics of the pitch controller is of additional concern, the pitch controlalgorithm in the proposed dual control strategy is designed to avoid a real-time active controlstrategy. By contrast, an offline approach is proposed. This is based on a pre-calculated designdecision table (based on, for example, wind speeds, blade–tower–drive train responses, powerproduction) rather than a state feedback/PID controller in real time. The use of an offline controlscheme avoids the requirement for fast changing actuator dynamics, which not only reducesthe actuator demand and problems of actuator dynamics but also eliminates dynamic stressesgenerated due to pitching. Essentially, the pitch will need to be changed only infrequently atrelatively long intervals of time (fast changing dynamics and stability will not be an issue) andthe rate of pitching can be slow (quasi-static) to avoid dynamic stresses . An illustration of suchdual schemes (active tendon–offline pitch) follows.

(c) Active tendon controlThe application of active devices as in [19] is now considered for suppression of rotor vibrations.The active tendon control strategy works by providing a cable anchorage to the structure, withthe cable force or the displacement of the cable support controlled by an actuator. Staino et al. [19]proposed the use of active tendon control for suppressing edgewise vibrations, but the controlsystem arrangement could be equally applicable for controlling flapwise displacements as well(by rotating the cable/tendon arrangement inside the blade by 90◦) as shown in the followingsections. In fact, two sets of orthogonal cable arrangements can be used to facilitate independentcontrol in two orthogonal directions. An appropriate control algorithm can then be used toactuate the tendon controller. Active tendon control to mitigate flapwise blade vibrations has beeninvestigated in [39,40]. The hollow nature of wind turbine blades makes them suitable for theinstallation of the control devices. The control devices can mitigate the dynamic response withoutaffecting the aerodynamic performance of the structure. In particular, for practical advantages(e.g. ease of installation inside the blades in comparison with other power devices), the use ofactive tendons is proposed as a part of the dual strategy and numerically analysed for vibrationcontrol. The tendons are mounted on a frame supported from the nacelle (figure 3). Vector analysisof the equilibrium of forces transmitted to the blade results in a net control force acting on theblade tip in the flapwise direction. For the jth blade, the net force from the actuators/tendonsis proportional to the force Tj(t) and the sine of the angle ϕ0, as illustrated in figure 3. In themathematical framework used in this study, the active control force is modelled as an externalforce acting on each blade tip and is given by fj(t) = 2Tj(t) sin(ϕ0).

The active elements are drawn in thin lines, while the support structure (e.g. a truss or aframe) is shown in bold. The introduction of active elements in the support structure allows



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DT0(t) sin(j0) = DT1(t) sin(j1)

wind

B A

2DT0(t) sin(j0)

T0 –

DT

0 (t)T 0+

DT0(t)

T 1+

DT1(t

)

T 1–

DT1(

t)T 1

–DT

1(t)

T 1+

DT1(t

)

j1

j0

Figure 3. Implementation of active vibration blade control based on active tendons. (Online version in colour.)

transfer of the control force to the hub without the generation of a reaction force in the flapwisedirection of the blade. In fact, the active elements produce forces that are external to the supportstructure and hence nullify the forces in the flapwise direction (e.g. the net flapwise load atjoints A or B is identically zero). Hence, mechanistically, this eliminates any flapwise reactionforces for the support structure if the algebraic condition �T0(t) sin(ϕ0) = �T1(t) sin(ϕ1) shownin figure 3 is met. The forces T0, T1, . . . are static prestressing forces in the cable. The controlforce determines the value of �T0(t) and the other active tendon forces (such as �T1(t)) can becalculated subsequently based on geometry and force equilibrium. The net control force acting onthe blade tip in the flapwise direction for the jth blade is given by

fj(t) = 2�T0,j(t) sin(ϕ0). (3.3)

In the mathematical framework adopted in this study, the active control forces have beenmodelled as external modal loads applied to each blade. The principle of virtual work is usedagain in order to include the effect of the controller into the Lagrangian formulation.

A numerical simulation is carried out to illustrate the capabilities of the active tendoncontroller described above. The numerical model presented in §2 has been simulated using thespecifications of the NREL 5 MW baseline reference wind turbine [41]. It should be noted that,although offshore dynamics are not included in this study, the control principles illustrated inwhat follows are equally valid for both onshore and offshore systems. In fact, the numericalresults presented in the paper can readily be extended to offshore wind turbines. A linear



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0

1

2

3

4

5

6(a) (b)

(c) (d)

time (s)

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1.0

1.2

time (s)

u 11(L

b, t)

(m)

0 5 10 15 20 25 30 35 40 45 500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 5 10 15 20 25 30 35 40 45 50−5

−4

−3

−2

−1

0

1

2

3

4

5

v 1(L

T, t

)(×

10–3

m)

u 12(L

b, t)

(m)

v 2(L

T, t

)(m

)

active tendon controluncontrolled

Figure 4. Active tendon control. (a) Out-of-plane blade response. (b) In-plane blade response. (c) Fore–aft nacelle motion.(d) Side-to-side nacelle motion. (Online version in colour.)

quadratic (LQ) controller with design parameter γ = 10−9 as in [19] has been synthesized basedon a reduced-order 4 d.f. model of the wind turbine. The parameter γ is associated with theweight R assigned to the control input {u(t)} in the LQ cost function

JLQ = 12

∫+∞

0[{x}T{x} + {u}T[R]{u}] dt, (3.4)

where {x} is the reduced state of the wind turbine and R = γ [I], with [I] the 3 × 3 identity matrix.The controller that minimizes the cost functional (3.4) is obtained by solving the LQ controlproblem as in [19]. It will be shown later that, as the value of γ is decreased, allowing larger valuesin the control effort, better vibration control performances are achieved. Of course, a smallervalue for γ entails a higher force requirement from the active tendons. The fundamental modesof vibration of the blades (in-plane and out-of-plane) and of the tower (side-to-side and fore–aft)have been considered for validation of the controller, leading to an 8 d.f. system. The mode shapesand frequencies have been computed by using ‘Modes’ [42]. Aerodynamic loads on the bladesand on the nacelle have been simulated using the modified blade element momentum (BEM)theory as described in [19,33]. The wind exciting the structure is represented as a steady windflow, including vertical wind shear effects due to the rotation of the blades. The wind loadingscenario therefore corresponds to a steady wind at the rated speed of 11.4 m s−1, with a maximumchange of 1 m s−1 in the vertical direction from the hub to the blade tip to simulate the wind sheareffect. The rotor speed has been set to the rated value of 12.1 r.p.m. The time history of the bladedisplacements (in-plane and out-of-plane) and of the tower top displacements (side-to-side andfore–aft) in the controlled (solid line, blue) and in the uncontrolled (dashed line, red) case areshown in figure 4.



11


.........................................................

0 2 4 6 8 10 12

10

20

30

40

50

60

70

80

90

100(a) (b)

(c)

pitch angle (deg)

out-

of-p

lane

bla

de r

espo

nse

redu

ctio

n (%

)

0 2 4 6 8 10 12

10

20

30

40

50

60

pitch angle (deg)

in-p

lane

bla

de r

espo

nse

redu

ctio

n (%

)

0 2 4 6 8 10 12−20

0

20

40

60

80

100

pitch angle (deg)

pow

er lo

ss (

%)

no active tendonsactive tendons g = 10−7

active tendons g = 10−8



Figure5. Wind turbineperformancewith combinedactive tendon–pitch control. (a) Reductionof bladeout-of-plane response.(b) Reduction of blade in-plane response. (c) Mechanical power output reduction. (Online version in colour.)

It should be noted that the blade oscillations (figure 4) are mainly caused by the load arisingfrom gravitational effects at the rotational speed Ω = 12.1 r.p.m. It can be observed that by usingactive tendon control a substantial improvement of the out-of-plane blade response is achieved.The maximum blade tip out-of-plane displacement in steady operation is reduced from 5.2 to2.8 m, and a reduction of the peak-to-peak oscillation is also attained. Because of the structuralcoupling induced by the pre-twist of the blade, a reduction of the in-plane blade response isalso obtained. As no active control is operated on the nacelle, no significant improvement of thenacelle fore–aft motion is observed, although the side-to-side motion exhibits some reduction inthe controlled case.

(d) Dual strategy with active tendon and offline pitch controlA numerical study to assess the performance of the combined active tendons–pitch controllerhas been carried out. The proposed wind turbine model subjected to a steady wind flow atthe rated speed of 11.4 m s−1 has been considered. For the offline pitch controller, the desiredcollective blade pitch demand is sent as a command to the pitch actuator model. The blade pitchactuator allows a minimum blade pitch setting of 0◦, a maximum blade pitch setting of 90◦ anda maximum blade pitch rate of blade pitch setting of 8◦ s−1. For the active tendon controller,four different LQ configurations have been synthesized, corresponding to different values of thedesign parameter γ . In solving the LQ control problem for the active tendons, by appropriately



12


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1.8

2.0

2.2

2.4

2.6

2.8

3.0

3.2(a) (b)

(c) (d)

u 12(L

b, t)

(m)

−0.2

0

0.2

0.4

0.6

0.8

1.0

1.2

u 11(L

b, t)

(m)

0 20 40 60 80 100 120 140 1604.5

5.0

5.5

6.0

6.5

7.0

7.5

time (s)

Pm

ec(M

W)

0 20 40 60 80 100 120 140 160

−80

−70

−60

−50

−40

time (s)

blad

e co

ntro

l for

ce (

kN)

Figure 6. Combined active tendon–pitch controlwith variablewind speed. (a) Out-of-plane blade response. (b) In-plane bladeresponse. (c) Mechanical power output. (d) Active tendon control force. (Online version in colour.)

assigning the design parameter γ , it is possible to relatively prioritize the suppression of theout-of-plane blade response and the force usage to implement the control.

The results of the application of the combined active tendons–offline pitch controller areillustrated in figure 5.

Figure 5c shows that the active tendon controller has no impact on the power production,whereas the pitch control has the effect of reducing vibrations (figures 5a and 6) and has asignificant impact on reducing the power production.

(i) Wind speed variation

The results shown in figure 5 correspond to the application of the combined controller in the caseof constant wind speed. A scenario with increased wind speed excitation has been simulatedto test the performance of the proposed controller in the presence of wind speed variations.This analysis is of particular interest because power regulation using pitch control is requiredwhen the wind turbine is operating above the rated wind speed conditions. The simulation of theapplication of the combined control under varying wind speed is illustrated in figure 6. Initially,the turbine is operating at rated wind speed and the active tendon controller with γ = 10−9

is employed to reduce the blade displacement. Pitch control is disabled in the initial phase ofthe simulation, as active tendon control is effective in controlling vibrations and reduction inaerodynamic loads is not necessary. If the tendon controller had not been effective, the blade out-of-plane displacements could have gone up to about 5 m. At an instant of time t = 35 s, the windspeed is linearly increased to 12.5 m s−1 over a 15 s period. It can be observed that, while theblade tip response does not experience a significant increase due to the active tendon controller,the mechanical power generated by the turbine exhibits a strong increase up to more than 7 MW.At t = 90 s, pitch control with β = 4.5◦ is activated and correspondingly the power is restored toits rated value after a short transient. The activation of the blade pitch also leads to a reduced loadon the blade, and as a consequence the vibration of the blade is further reduced. This also impliesa smaller control force requirement for the active tendon controller as shown in figure 6d.



13


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Figure 6 also shows that active tendon and collective pitch control are almost uncoupled interms of impact on the dynamic response of the blade.

(ii) Pareto-optimal formulation for dual control strategy

As discussed previously, the objectives of reduction in vibration in wind turbines and maximizingthe power generated are conflicting in nature. This, as expected, has also been confirmed byfigure 5, where one can observe the price of reduced power generation (figure 5c), to be paidfor reducing vibration (figure 5a,b) using pitch control. The use of an active tendon controller candecouple the two objectives to some extent but may be constrained by limits on the actuationcapacity as well. Also, there are constraints or limits on feasible pitch angles. Based on theseconsiderations, it is possible to cast a Pareto-optimal optimization problem to solve for the designvariables, i.e. control force F and pitch angle β, in the dual active tendon–pitch control strategy.The objective function is formulated by assigning weights to the two conflicting objectives ofvibration reduction and power generation maximization as

minβ,F

r = λrfmax (β, F) + (1 − λ)rP(β)

with the constraints βmin ≤ β ≤ βmax

F ≤ Fmax,

⎫⎪⎪⎪⎬⎪⎪⎪⎭

(3.5)

such that (2.6) is satisfied. The term rfmax (β, F) denotes the relative reduction of the controlled out-of-plane blade peak displacement with respect to the uncontrolled blade peak displacement andis defined as

rfmax (β, F) = 1 − max u12ctr (t)max u12unctr (t)

, (3.6)

where max u12ctr (t) and max u12unctr (t) are the blade out-of-plane peak response in the controlledand uncontrolled cases, respectively. The term rP(β) represents the relative power loss and it iscomputed as

rP(β) = 1 − Punctr

Pctr, (3.7)

where Pctr and Punctr denote the mechanical power generated by the turbine in the controlledand uncontrolled cases, respectively. The term λ is a scalar, and λ and 1−λ are the weights usedfor the vibration reduction ratio and power loss ratio, respectively. To solve this Pareto-optimaloptimization problem with only two variables, it is possible to carry out a numerical analysis witha discrete search technique by sampling the values over the possible ranges of F and β. However,even in that case, the total computation time may be significant. To avoid the computationallyintensive approach, a simpler technique is followed by exploiting the fact that the power loss isindependent of the tendon tension F (figure 5c) and hence rP(β) is a function only of β. Further,it can be observed from figure 5 that, to achieve the maximum possible vibration reduction or tominimize the vibrational response, the maximum value of F = Fmax should be used (since F hasno impact on power production). Hence, the first term in (3.5) is a function of β as F is known.Thus, the first and second terms in the objective function in (3.5) can be expressed as

g1 = 1 − rfmax (β) and g2 = rP(β), (3.8)

where g1 and g2 are functions of β. Using figure 5a,c, the functions g1 and g2 can be regressed bypolynomial functions for ease of representation and subsequent optimization calculations. Hence,the minimal value of the objective function is obtained by satisfying the condition

drdβ

= 0, (3.9)

which leads to the following equation:

λ

(dg1

dβ− dg2

dβ

)+ dg2

dβ= 0. (3.10)



14


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0 0.2 0.4 0.6l

b*

0.8 1.0−5

0

5

10

15

20

Figure 7. Optimal pitch angle. (Online version in colour.)

Table 1. Performance of the controller with optimal pitch angle.

β = β β = 1◦ β = 5◦

out-of-plane blade response reduction (%) 62.74 53.78 69.41. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

in-plane blade response reduction (%) 21.54 19.7 29.7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

mechanical power loss (%) 14.81 2.72 26.73. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

For a given value of λ, the solution of (3.10) gives the optimal value of β. The optimal value of thetendon force is given as Fmax. Using these two values, the desired minimization of the objectivefunction is attained with a specified weight λ. For the purpose of numerical illustration, weconsider the variation of β as a function of λ with constraints βmin = 0◦ and βmax = 15◦ (figure 7).

The simulated scenario corresponds to rated wind speed conditions. By selecting λ = 0.6, thecorresponding optimal pitch angle is β = 3.2◦ and the corresponding force requirement is Fmax =52 kN. Using the proposed optimal controller, 62.74% reduction of the out-of-plane blade peakresponse is achieved and the power loss with respect to the uncontrolled case is about 14.81%. Ifa different tuning of the pitch control is selected, either an increased power loss or an increasedblade vibration is obtained, as illustrated in table 1.

4. ConclusionA review of different structural vibration control strategies has been carried out in this paper. Ofthe different controllers proposed recently, specific attention has been focused on two promisingcontrol strategies: active pitch control and the recently proposed active tendon control. Details onthese controllers, including some key results, have been presented. A new dual control strategy bycombining active tendon control with passive pitch control has been formulated and presented.This new controller, which is an improved version of the active tendon controller, merges thebenefits of the two different control schemes while eliminating some of the drawbacks of eachof the individual control schemes. The dual control strategy avoids the actuator dynamics of theactive pitch control and the generation of dynamic stresses due to pitching, as it uses a passivepitch algorithm. Also, the force demand on the active tendon is reduced, as the pitch controlhas the effect of reducing the aerodynamic loads. Further, the proposed controller decouplesthe vibration control from the control for optimal power tracking, as the active tendon controldoes not interfere with the power production. A Pareto-optimal optimization formulation hasbeen cast and solved for the design of the proposed dual controller. The results indicate that,



15


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for example, using weights of 0.6 and 0.4 for the vibration reduction and power productioncriteria, respectively, achieves a vibration reduction of about 63% with a power productionloss of approximately 15%. If the pitch controller alone was used to achieve the same level ofvibration reduction, a power loss of over 50% would have occurred, or if the active tendoncontrol was solely used instead an increase in approximately 40% of the tendon force would havebeen required (though without any power loss). The proposed dual strategy shows encouragingprospects of applications in future with the significant positive impact it may have on the growthof offshore wind energy.

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