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Journal of Ocean and Wind Energy (ISSN 2310-3604) http://www.isope.org/publications/publications.htmCopyright © by The International Society of Offshore and Polar EngineersVol. 2, No. 4, November 2015, pp. 223–230; http://dx.doi.org/10.17736/jowe.2015.arr04

Collective Pitch Feedforward Control of Floating Wind Turbines Using Lidar

David SchlipfStuttgart Wind Energy, Universität Stuttgart

Stuttgart, Germany

Eric SimleyDepartment of Electrical, Computer and Energy Engineering, University of Colorado

Boulder, Colorado, USA

Frank Lemmer (né Sandner)Stuttgart Wind Energy, Universität Stuttgart

Stuttgart, Germany

Lucy PaoDepartment of Electrical, Computer and Energy Engineering, University of Colorado

Boulder, Colorado, USA

Po Wen ChengStuttgart Wind Energy, Universität Stuttgart

Stuttgart, Germany

In this work a collective pitch feedforward controller for floating wind turbines is presented. The feedforward controllerprovides a pitch rate update to a conventional feedback controller based on a wind speed preview. The controller is designedsimilarly to the one for onshore turbines, which has proven its capability to improve wind turbine control performance in fieldtests. In a first design step, perfect wind preview and a calm sea is assumed. Under these assumptions, the feedforwardcontroller is able to compensate almost perfectly for the effect of changing wind speed on the rotor speed of a full nonlinearmodel over the entire full load region. In a second step, a nacelle-based lidar is simulated to scan the same wind field that isused also for the aero-hydro-servo-elastic simulation. With model-based wind field reconstruction methods, the rotor effectivewind speed is estimated from the raw lidar data and is used in the feedforward controller after filtering out the uncorrelatedfrequencies. Simulation results show that, even with a more realistic wind preview, the feedforward controller is able tosignificantly reduce rotor speed and power variations. Furthermore, structural loads on the tower, rotor shaft, and blades aredecreased. A comparison to a theoretical investigation shows that the reduction in rotor speed regulation is close to the optimum.

INTRODUCTION

Floating wind turbines offer a promising solution for harvestingthe immense potential of wind energy at deep water locations.New concepts have to be devised, particularly for collective bladepitch control to regulate the rotor speed because of the knownnegative damping of the platform pitch motion at low frequenciesintroduced by the wind variations at these frequencies (Fleminget al., 2014). Based on van der Veen et al. (2012), there are fourmain possibilities to address this problem by feedback control: Astraightforward approach is to lower the closed-loop bandwidthof the pitch controller under the platform pitch frequency, asdone by Jonkman (2007) and Larsen and Hanson (2007). Thesecond possibility is to use acceleration measurements to damp thepitch motion (Lackner and Rotea, 2011). Another option is to addadditional control inputs, such as the generator torque (Fischer,2012), individual blade pitch (Namik and Stol, 2010), or activemass dampers (Lackner and Rotea, 2011). Finally, using a blade

Received February 19, 2015; revised manuscript received by the editorsAugust 4, 2015. The original version was submitted directly to theJournal.

KEY WORDS: Floating wind turbine control, feedforward control, lidar-assisted control.

pitch to stall controller, as mentioned by Larsen and Hanson (2007),would avoid the negative damping. Alternative methods becomefeasible with lidar remote sensing technology, where informationabout incoming wind speed changes can be made available ahead oftime and thus can be used with model predictive (Schlipf, Sandner,et al., 2013; Raach et al., 2014) or feedforward control algorithms.

This work presents a collective pitch feedforward controller forfloating wind turbines. The approach is based on a controller thatwas developed for onshore wind turbines and successfully tested invarious field campaigns by Schlipf et al. (2014) and Scholbrocket al. (2013). The presented approach divides the lidar-assistedcontrol design into two steps: In the first step, the pure controlproblem is considered and perfect wind speed preview is assumed.The feedforward controller is designed based on the static, nonlinearpitch curve and is combined with the baseline feedback controller. Ina simulation with a fully aero-hydro-servo-elastic model assumingperfect wind preview, the feedforward controller is able to keepthe rotor speed nearly unaffected by an extreme operating gust.This demonstrates robustness against model uncertainties. In thesecond step, the problem is extended to accommodate the limitedpreview information obtained by a lidar system. Conventionallidar systems are only able to measure the line-of-sight velocity atlimited points in front of the turbine. Additionally, nacelle-basedsystems on floating wind turbines experience significant motions.

224 Collective Pitch Feedforward Control of Floating Wind Turbines Using Lidar

As a result, only the low frequencies of the wind speed previewcan be captured accurately. The controller is extended by addinglidar data processing and adaptive filtering stages. The extendedcontroller is tested under realistic conditions using a turbulent windfield and a detailed lidar simulator. The obtained spectrum of therotor speed is compared to the theoretical optimal spectrum thatcan be achieved with the utilized lidar setup. The optimal spectrumis calculated by using a linearized turbine model and an analyticmodel of the correlation between the lidar measurements and thereaction of the wind turbine (Simley and Pao, 2013).

SIMULATION ENVIRONMENT

For this study, a 5 MW turbine on a spar buoy is used (Jonkman,2007) and implemented in the coupled aero-hydro-servo-elasticsimulation tool FAST (Jonkman and Buhl, 2005). The controller isimplemented in MATLAB and coupled to FAST. The wind turbineexperiences the disturbance of a turbulent three-dimensional windfield generated with TurbSim (Jonkman, 2009). The wind fields areloaded into MATLAB and scanned during the simulations with arealistic lidar simulator. The wind turbine and the lidar simulatorare described in the following subsections.

Floating Wind Turbine

The coupled FAST model for the floating offshore wind turbine(FOWT) system consists of a flexible multibody system, whichexperiences external forces from aerodynamics, hydrodynamics, andthe mooring system. These are calculated in dedicated submodulesof the code. The following 21 degrees of freedom (DOFs) areenabled in the simulations: platform translational (surge, sway,heave) and rotational (roll, pitch, yaw) DOFs, first and secondflapwise and first edgewise blade modes, first and second fore-aftand side-to-side tower bending modes, rotor motion and drive trainrotational-flexibility. The vector of these modes is denoted by qand its derivatives as q. A second-order linear model is added forthe collective pitch actuator, resulting in a total of 22 DOFs. Thehydrodynamic model is based on linear potential flow theory withthe damping term of Morison’s equation to account for viscouseffects. The frequency-dependent solutions to the separated radiationand diffraction problem are achieved in a preprocessing step by ahydrodynamic panel code. During the simulation, the pre-calculatedfluid velocity and accelerations on several strips along the platformact as disturbance inputs to the hydrodynamic subsystem. In theaerodynamic subsystem, the disturbance inputs are the componentsof a turbulent three-dimensional wind field on several grid pointsover the rotor disk. With these inputs, aerodynamic forces arecalculated by applying BEM (Blade Element Momentum) theory.The floating spar buoy is anchored over three slack mooring linesattached at the fairleads below the center of buoyancy. Horizontaland vertical forces at the fairleads are calculated by iterativelysolving a quasi-static equation for a slack line, accounting forseabed friction.

The three translational platform DOFs are defined in the inertialcoordinate system, denoted by © . Its origin is the mean sea level ofthe nondeflected FOWT (q = q = 0). The turbulent wind fields aredefined in the TurbSim coordinate system, which has the sameorientation as the inertial coordinate system © and has its origin atthe hub of the nondeflected FOWT. Thus, the wind field can betransformed to the © coordinate system by a simple translation ofthe TurbSim coordinate system.

Lidar Simulator

In this work, a nacelle-based scanning lidar system is simulated.The simulator is based on Schlipf et al. (2009) and is extended

by including the platform motion to realistically reproduce lidarmeasurements from a floating wind turbine. The platform andturbine motion highly influence the lidar measurement, since thecoordinates 6xi1¬ yi1¬ zi1¬7

T of the lidar measurements are designedin the lidar coordinate system ¬, but change their locations in theinertial coordinate system © because of the system’s motion.

In general, a lidar system is only able to measure the componentof the wind vector in the laser beam direction. Therefore, theline-of-sight wind speed vlosP1i measured by a stationary lidarsystem at point i with coordinates 6xi1© yi1© zi1© 7

T can be modeledby a projection of the wind vector 6ui1© vi1© wi1© 7

T at point i onthe normalized vector of the laser beam. This is mathematicallyequivalent to the scalar product of both vectors:

vlosP1i = xni1© ui1© + yni1© vi1© + zni1© wi1© (1)

where the normalized laser vector measuring at a distance ri fromthe lidar system is:

xni1©yni1©zni1©

=1rLi

xL1© − xi1©yL1© − yi1©zL1© − zi1©

with rLi =√

x2i1¬ + y2

i1¬ + z2i1¬0 (2)

The position of the lidar system within the inertial coordinatesystem is defined by 6xL1© yL1© zL1© 7

T . However, real lidar systemsmeasure within a probe volume. For pulsed lidar systems, this isdue to the length of the emitted pulse (Cariou, 2013). Additionally,if the lidar system is not fixed in the inertial frame, but moving withthe velocity 6xL1© yL1© zL1© 7

T , Eq. 1 can be adjusted as follows:

vlos1i =

�∫

−�

(

xni1© 4uai1© − xL1© 5+ yni1© 4vai1© − yL1© 5

+ zni1© 4wai1© − zL1© 5)

frw4a5da0 (3)

Fig. 1 Normalized range weighting function for the used pulsedlidar system

Fig. 2 Optimized lidar scan trajectory

Journal of Ocean and Wind Energy, Vol. 2, No. 4, November 2015, pp. 223–230 225

Fig. 3 Coherence (left) and transfer function (right) between the lidar estimate of the rotor-effective wind speed and the real rotor-effectivewind speed, based on the analytical model ( ) and from simulation ( ); fitted filter ( )

The volume measurement is modeled by the range weightingfunction frw , depending on the distance a to the measurement point.For the pulsed lidar system considered in this work, a normalizedGaussian shape weighting function is used (see Fig. 1), followingCariou (2013). The function is parameterized by a standard deviation�L, depending on the pulse width at half-maximum of WL = 30 m:

frw4a5=1

�L

√2�

exp(

−a2

2�2L

)

with �L =WL

2√

2 ln 20 (4)

The wind vector 6uai1© vai1© wai1© 7T is an evaluation of the wind

field along the laser beam at:

xai1©yai1©zai1©

=

xi1©yi1©zi1©

+ a

xni1©yni1©zni1©

0 (5)

During the aero-hydro-servo-elastic simulations, the lidar simulatorcalculates the lidar position, velocity, and inclination based on thecurrent values of all six platform modes and all four tower modesand their derivatives. The line-of-sight wind speeds vlos1i are thencalculated using Eqs. 2 to 5 and applying Taylor’s Hypothesis ofFrozen Turbulence (Taylor, 1938), which assumes that turbulentwind travels with the mean wind speed from the measurementlocation to the rotor.

For this work, the scan trajectory is optimized for the 5 MWonshore reference wind turbine by using the method presented inSchlipf, Cheng, and Mann (2013). The optimal trajectory is found bycalculating the coherence between the rotor-effective wind speed andits lidar estimate based on an analytic correlation model for severalcircular scan setups. The trajectory with the highest value of thecoherence bandwidth is the circle with nP = 8 measurement points,a normalized radius of r = 003 (corresponding to a half openingangle of 1607 deg), and the first and the last measurement distanceat x11¬ = 005D = 63 m and x51¬ = 105D = 189 m, respectively. Theoptimal scan trajectory is illustrated in Fig. 2. The coherenceand transfer function of the correlation model and from thesimulation below using simulated lidar measurements are plottedin Fig. 3.

CONTROLLER DESIGN

In this section, the baseline controller is briefly described. Thenthe lidar-assisted collective pitch feedforward controller is derived,first for perfect wind preview and then for realistic wind preview.

Fig. 4 Feedback control loops and collective pitch feedforwardcontroller assuming perfect wind preview

Baseline Feedback Controller

The baseline feedback controller is an adaptation of the onshorebaseline controller (Jonkman, 2007), which combines an indirectspeed controller (ISC) for the generator torque and a collectiveblade pitch controller (CPC) (see Fig. 4). The feedback controllerstogether adjust the turbine’s operation under changing rotor-effectivewind speed v0 and use measurements of the generator speed ìg .The generator speed signal is filtered by using a single-pole low-passfilter to mitigate high-frequency excitation of the control systems.

Below rated wind speed, the goal of the torque controller is tomaximize the energy yield. Thus, the generator torque Mg needs tobe adjusted to track the inflow conditions. The generator torque isheld constant above rated wind speed as long as the blade pitchangle remains above a threshold of �fine = 1 deg.

The CPC regulates the rotor speed when the turbine operatesat rated power. The collective blade pitch angle command �c iscomputed by using a gain-scheduled PI controller on the speederror between the filtered and the rated generator speed ìg1rated. Forthe FOWT, the gains of the PI pitch controller are reduced to avoidnegative damping of the platform pitch motion (Jonkman, 2007).

Collective Pitch Feedforward Controller Design for PerfectWind Preview

The basic idea of adding feedforward control to a feedbackcontroller is to complete the two main tasks for controllers (referencesignal tracking and disturbance compensation) independently byboth controllers such that they do not interfere with each other.

For the design of the collective pitch feedforward controller (FF),perfect knowledge of the rotor-effective wind speed v0 is assumedas a first step. The feedforward controller is designed such thatchanges from the wind speed v0 to the generator speed ìg are


Fig. 5 Steady pitch curve for the 5MW reference onshore ( ) andfloating ( ) wind turbine obtained from steady-state simulations

compensated for by an additional blade pitch angle �FF. In thiscase, the feedforward controller is not counteracting the controlaction of CPC and ISC.

For controller design purposes, the rotor speed ì is modeled bythe following equation of motion:

J ì=Ma4v01 �1 q1 q5−Mg/igb (6)

where igb is the gearbox ratio and J is the overall drive trainmoment of inertia about the rotation axis. Moreover, Ma is theaerodynamic torque depending on the rotor-effective wind v0, thecollective pitch angle �, the vector of modes q, and its derivative q.

The steady states for all turbine states and inputs in the closedloop depend on the steady wind speed v01ss . For above rated windspeed, the steady aerodynamic torque is constant:

Ma1ss4v01ss1 �ss1 qss1 qss5=Mg1rated/igb0 (7)

Thus, �, q, and q need to be simultaneously aligned along theirsteady functions �ss , qss , and qss to hold the rotor speed constantfor changing v0 in Eq. 6. These functions are obtained from steadystate simulations. Figure 5 displays the steady collective pitch angleof the onshore and floating wind turbine as a function of v0 withonly minor differences.

With the availability of a wind preview, an inversion of the pitchactuator dynamics is possible such that the collective blade pitch �counteracts variations in v0 based on a feedforward collective bladepitch command �FF. Here, the inverse pitch actuator dynamics areapproximated by a simple preview time � . Aligning the modes andtheir derivatives along their steady functions is more complicated.However, the results of the simulations with perfect wind previewbelow show that aligning only the collective pitch angle alreadyprovides very good results compared to the feedback-only case andthat the modes quickly approach their steady values.

Similar to the feedforward controller for onshore wind turbines,a feedforward pitch rate �FF is added to the input of the integratorincluded in the feedback controller instead of adding the pitch angle�FF to the output �FB of the feedback controller. This modificationsimplifies the integration of anti-windup algorithms and switchingthe feedforward controller on and off.

Collective Pitch Feedforward Controller Design for RealisticWind Preview

In reality, the rotor-effective wind speed v0 cannot be measuredperfectly. As depicted in Fig. 6, the lidar system (L) is attemptingto measure a three-dimensional wind field ¶ and is only able toprovide raw lidar data (RLD). In this investigation, the RLD arethe line-of-sight wind speeds vlos, the index of the measurementpoint i (1 to 8), and the time stamp of each measurement. The

Fig. 6 Feedback control loops and collective pitch feedforwardcontroller assuming realistic wind preview

velocity 6xL1· yL1· zL1· 7T , the pitch angle äL, and the roll angleêL of the lidar system are added to the RLD. These values can beprovided by an inertial measurement unit (IMU), which is alreadyinstalled on some commercial lidar systems.

The RLD are transferred to the model-based wind field recon-struction (WRC) during the simulation. Similar to the approachfor floating lidar systems (Schlipf et al., 2012), the pitch angleäL and the roll angle êL are used to transform the projectedcoordinates 6xi1¬ yi1¬ zi1¬7

T into the wind coordinate system · ,which is aligned with the mean wind direction and moves androtates with the FOWT. Thus, measurements of the platform’stranslational DOFs are not necessary for the WRC. Based on Eq. 3,all line-of-sight wind speeds vlos1i are translated into longitudinalwind speed components ui1· by assuming point measurements andperfect alignment (vi1· =wi1· = 0) by:

ui1· =vlos1i + xni1· xL1· + yni1· yL1· + zni1· zL1·

xni1·(8)

where 6xni1· yni1· zni1· 7T is the normalized laser vector calculatedfrom the transformed coordinates similar to Eq. 2. All ui1· arestored in a buffer and condensed to an estimated v0L of the rotor-effective wind speed. Here, Taylor’s Hypothesis is used for thewind evolution (EVO), and therefore measurements of the severaldistances can be combined by shifting them in time (Schlipf et al.,2014). The transfer function between v0L and v0 is known tobe the optimal prefilter (PF) for the lidar estimate to remove alluncorrelated frequencies (Simley and Pao, 2013; Schlipf, Cheng,and Mann, 2013). Here, a second-order low-pass filter (Butterworth)with a cut-off frequency of fcutoff = 00201 Hz is fitted to the transferfunction (see Fig. 3). Since the filtered estimated v0Lf is close tothe rotor-effective wind speed v0, the collective pitch feedforwardcontroller can also be applied using realistic wind preview.

SIMULATION RESULTS

In this section, the collective pitch feedforward controller isevaluated by simulations using perfect wind preview and simulatedlidar measurements.


Fig. 7 Reaction to an EOG at 25 m/s. Top: rotor-effective windspeed equal to perfect wind preview ( ); All others: feedbackcontroller only ( ) and with additional feedforward ( ).

Simulations Using Perfect Wind Preview

In the first simulation study, the collective pitch feedforwardcontroller is tested assuming perfect wind preview. For this purpose,the full aero-hydro-servo-elastic model is disturbed by an ExtremeOperating Gust (EOG) at 25 m/s, according to the International

FB FB+FF FB+FFFB [%]

ãì [rpm] 2060 0003 101ãäP [deg] 00345 00022 603MyT [MNm] 5509 3408 6202

Table 1 Maximum values of the simulation with an EOG at25 m/s with perfect wind preview using the 5 MW referencefloating wind turbine (see Fig. 7)

Electrotechnical Commission (2005). The proposed feedforwardcontroller can achieve almost perfect cancellation of the effect fromv0 to ì (see Fig. 7). The overshoot of the rotor speed (deviationfrom ìrated = 1201 rpm) can be reduced by 9809%, the maximumdeviation from the static platform pitch angle äP by 9307%, andthe maximum tower base fore-aft bending moment MyT by 3708%compared to the feedback controller (see Table 1).

The proposed feedforward controller demonstrates a good robust-ness against model uncertainties. Although the controller is designedwith a nonlinear model with only one DOF (rotor speed), staticaerodynamics, and no hydrodynamics, it is able to almost perfectlycancel out the effect from the rotor-effective wind to the rotorspeed for a full aero-hydro-servo-elastic model with 22 DOFs overa large range of wind speeds. This also yields less oscillation in theturbine and platform structure, such as the tower top displacementxT and the platform displacement xP .

Simulations Using Simulated Lidar Measurements

In the second simulation study, the robustness against windmeasurement errors is examined. For this investigation, a turbulentwind field with turbulence class “A” according to the InternationalElectrotechnical Commission (2005), resulting in a turbulenceintensity of 17% and a length of over 1 h, is generated withTurbSim with a mean wind speed of u= 18 m/s. The width andheight of the wind field are each 150 m and the resolution is5 m, resulting in 31 × 31 grid points. The temporal resolutionis 0025 s. With this wind field, the full aero-hydro-servo-elasticmodel is simulated for 3630 s. All states are initialized with theirsteady values corresponding to the rotor-effective wind speed(average over the rotor disk) at the beginning of the simulation.The first 30 s are ignored to avoid falsification of the results due tominor initialization effects. Again, calm sea is assumed. Duringsimulations, the wind field is scanned by the lidar simulator, takinginto account the current position, velocity, and inclination of thelidar system. From the raw lidar data, the rotor-effective windspeed is reconstructed and filtered as described above.

Figure 8 illustrates a representative 5 min period of the simulation.In the top part of the figure, a good agreement can be observedbetween the rotor-effective wind speed from the wind field and itsfiltered and time-shifted estimate based on the raw lidar data. Withthis more realistic wind preview, the variation in the rotor speed ìis still reduced significantly. Additionally, the variation in platformdisplacement xP , platform pitch äP , the tower top displacement xT ,and the resulting tower base fore-aft bending moment MyT arereduced. The effect of the collective pitch feedforward controllercan be observed clearly in the Power Spectral Densities (PSDs) ofFig. 9. The lidar-assisted controller can significantly reduce theinfluence of the wind disturbance to rotor speed at low frequencies.Since the adaptive filter has a cut-off-frequency at fcutoff = 00201 Hz,there is minimal improvement above this frequency and no reductionis achieved at the damped eigenfrequency of the tower (005 Hz) andthe 3P (three-times-per-revolution) frequency (006 Hz). In addition,the tower base fore-aft bending moment is significantly reduced


Fig. 8 Reaction to a turbulent wind field with mean wind speedof 18 m/s (illustrative 5 min excerpt). Top: rotor-effective windspeed ( ) and its filtered, time-shifted lidar estimate ( ). Others:feedback controller only ( ) and with additional feedforward ( )using simulated lidar measurements.

for low frequencies, especially at the dominant platform pitcheigenfrequency of 0003 Hz. Since the steady-states of the tower andthe collective pitch angle are changing with the mean wind speed,no reduction is possible at frequencies close to 0 Hz. The reductionin rotor speed and power variation for low frequencies is achievedby a higher pitch activity, which is represented by the pitch rate �.

FB FB+FF FB+FFFB [%]

DEL(MyT ) [MNm] 13909 11109 8000DEL(MLSS) [MNm] 2086 2065 9207DEL(Moop1) [MNm] 12075 11055 9006STD(ì) [rpm] 00952 00180 1809STD(�) [deg/s] 00253 00368 14508STD(xP ) [m] 20599 20150 8207STD(�P ) [deg] 10114 00550 4904STD(Pel) [MW] 004018 000752 1807EP [MWh] 500213 500020 990615

Table 2 Comparison of the results for the 1 h simulation at 18 m/susing feedback (FB) and using feedback and feedforward control(FB+FF)

Table 2 summarizes the results of the 1 h simulation at 18 m/s. Forthe calculation of the Damage Equivalent Loads (DELs), a referencenumber of cycles nref = 2 × 106 is used. Furthermore, a Wöhlerexponent of m= 4 is assumed for the fatigue load calculation of thetower base fore-aft bending moment MyT and the low-speed shafttorque MLSS. For Moop1, the out-of-plane blade root bending momentof blade 1, a Wöhler exponent of m= 10 is applied. Besides theabove-mentioned load reduction on the tower base (20%), additionalload reduction on shaft and blade root (7% and 9%, respectively)is achieved. This is mainly because the standard deviation (STD)of the platform pitch angle äP can be reduced by 50%. Over 80%reduction in the standard deviation of the rotor speed can be achieved.Since the generator torque is held constant for both controllers, thisresults in similar reduction in the standard deviation of the electricalpower Pel. When the feedforward controller is enabled, the ratedpower of 5 MW is better tracked and the energy production (EP) ofthe 1 h simulation is closer to 5 MW×1 h. The relative increase of46% in the standard deviation of the pitch rate is significant, but theabsolute value (00368 deg/s) is still below the value (00800 deg/s)of the onshore reference wind turbine controlled by the onshorefeedback controller with the same wind field.

These results confirm that collective pitch feedforward controlis very promising for FOWTs, even considering wind previewmeasurement uncertainties. The next subsection will rank theimprovements in rotor speed regulation.

Evaluation of the Results

The PSD of the rotor speed is compared to the theoreticalminimum PSD that can be achieved by a perfect feedforwardcontroller assuming linear turbine dynamics.

The linear model around the mean wind speed of 18 m/s isobtained from the FAST model and the tools provided by Jonkmanand Buhl (2005), enabling only the following four DOFs: platformsurge xP , platform pitch äP , tower top displacement xT , androtor/generator speed ì, as suggested by Sandner et al. (2014).

Using the linearized turbine model for the specific operatingpoint, the rotor speed can be written as a function of v0 and thereconstructed lidar measurement v0L:

ì=Gìv0v0 +Gì�GFFv0L (9)

where Gìv0and Gì� are the closed-loop transfer functions from

v0 to ì and � to ì, respectively, and GFF is the transfer functionof the feedforward controller. The closed-loop transfer functionsinclude the linearized FAST model, the pitch actuator, the generatorspeed filter, and the gain-scheduled PI controller.

Under the assumption that the closed-loop dynamics of theturbine/controller pair are linear and that v0 and v0L are jointly


Fig. 9 PSD for the 1 h simulation at 18 m/s: feedback controller only ( ) and with additional feedforward ( ); theoretical rotor speedspectrum for the feedback controller only ( ) and with additional feedforward ( )

wide-sense stationary random processes, the feedforward controllerthat minimizes the PSD of ì is defined by the frequency response:

GFF = −G−1ì�Gìv0

SRLSLL

(10)

where SRL is the cross-power spectral density between the rotor-effective wind speed v0 and the lidar measurement v0L, and SLL isthe PSD of the lidar measurement (Simley and Pao, 2013). Thetransfer function in Eq. 10 is comprised of two stages: First, thetransfer function −G−1

ì�Gìv0is the ideal feedforward controller

that reduces the rotor speed error to zero if v0L = v0. Second,because the lidar does not provide a perfect measurement of v0,the filter SRL/SLL yields the minimum mean square error (MMSE)linear estimate of v0 based on v0L (Kailath et al., 2000). Note thatSRL/SLL is equivalent to the transfer function GRL plotted in Fig. 3.However, since the wind speed signals v0 and v0L are modeledas jointly Gaussian random processes, the filter SRL/SLL is notonly the MMSE linear estimator of v0, but the optimal MMSEestimator of v0 among all possible estimators (Kailath et al., 2000).By using a MMSE filter to estimate v0 from v0L prior to the idealfeedforward controller stage, the controller (Eq. 10) also minimizesthe PSD of ì (Simley and Pao, 2013).

As explained in Simley and Pao (2013), the PSD of the regulatedoutput ì described by Eq. 9 when using the optimal feedforwardcontroller defined in Eq. 10 is given by:

Sìì = �Gìv0�2SRR

(

1 −�2RL

)

(11)

with �2RL representing the coherence between the reconstructed

lidar measurement and the rotor-effective wind speed. The optimalachievable rotor speed spectra calculated using Eq. 11 with feedbackonly (equivalent to setting �2

RL = 0 (Simley and Pao, 2013)) and withoptimal feedforward control are compared with the correspondingspectra from simulation in Fig. 9. The coherence �2

RL, shown inFig. 3, and the PSD SRR are calculated using the analytic modelpresented in Schlipf, Cheng, and Mann (2013).

As can be seen in Fig. 9, the theoretical rotor speed spectrumwith feedback only and the theoretically optimal spectrum with

feedforward control do not perfectly match the results from simula-tion. For example, the dynamics of the linearized model at the towereigenfrequency near 0.5 Hz do not match the simulated dynamics,and the linearized turbine model does not include dynamics associ-ated with the 3P frequency (0.6 Hz) caused by three rotating blades.Furthermore, as exhibited in Fig. 8, the turbine deviates significantlyfrom the linearization operating point of 18 m/s, and thus the linearmodel could be inaccurate for significant portions of the simulation.Nevertheless, the implemented feedforward control strategy achievesclose to the minimum possible rotor speed spectrum obtained usingthe simple linear model, up to the adaptive filter cut-off-frequency.

CONCLUSIONS AND OUTLOOK

In this work, a collective pitch feedforward controller for areference floating wind turbine is designed and evaluated. Thefeedforward controller is derived from a reduced nonlinear modelof the wind turbine and can be combined with a baseline feedbackcontroller and adequate lidar data processing.

In the first simulation study, the proposed controller shows itsrobustness against model uncertainties: Assuming perfect windpreview, the combined feedforward-feedback controller is able toalmost perfectly cancel out the effect from the rotor-effective windto the rotor speed in a full aero-hydro-servo-elastic simulation.

In the second simulation study, the controller performance in thepresence of wind measurement uncertainties is investigated. Thewind preview is based on a detailed simulation of a nacelle-basedlidar system moving with the floating wind turbine. The raw lidardata are condensed during the simulation with a turbulent windfield to an estimate of the rotor-effective wind speed by model-based wind field reconstruction and filtered by an adaptive filterdepending on the mean wind speed. Under these more realisticconditions, the performance of the combined feedforward-feedbackcontroller, when compared to the feedback controller alone, shows:

• 80% reductions in rotor speed and power variations• improvements in rotor speed regulation that are close to the

theoretical optimum• 20%, 7%, and 9% reductions in tower, rotor shaft, and blade

loads, respectively, primarily at low frequencies


In future work, a more detailed fatigue analysis based onthe design load case 1.2 from the International ElectrotechnicalCommission (2005) with irregular waves will be performed toestimate the benefit of the proposed controller over the lifetime of afloating offshore wind turbine. Additional investigations are plannedto transform the large reduction in rotor speed and power variationsinto further reduction of structural loads and increase in energyproduction. Furthermore, a comparison to feedback controllers withdisturbance estimation, such as the Disturbance AccommodationControl (DAC), without the need of preview wind measurementswill be carried out.

ACKNOWLEDGEMENTS

The research leading to these results has received funding fromthe foundation Karl Schlecht Stiftung (KSG). Partial funding supportfrom National Renewable Energy Laboratory is also gratefullyacknowledged.

REFERENCES

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