individual blade pitch control of a floating oﬀshore wind ...€¦ · iii. individual blade...

Individual Blade Pitch Control of a Floating Offshore

Wind Turbine on a Tension Leg Platform

Hazim Namik∗

and Karl Stol†

Department of Mechanical Engineering, The University of Auckland, Auckland , New Zealand

A disturbance accommodating controller (DAC) to reject wind speed perturbations isapplied on a 5MW wind turbine mounted on a tension leg platform (TLP). Multi-bladecoordinate (MBC) transformation is used to address the periodicity of the floating windturbine system. A method to apply DAC after applying MBC transformation is developedand several implementation options are presented. Simulations were carried out to assessthe fatigue loads of the system in accordance with IEC61400-3 standard design load case 1.2;however simulations were restricted to region 3 analysis due to the lack of region transitionlogic currently implemented for the DAC. A gain scheduled PI (GSPI) controller is used asa baseline/reference controller to compare the performance of the DAC. Simulation resultsshow that the DAC significantly improves power and speed regulation, reduces tower fatigueloads, and maintains the fatigue loads of the blades and the shaft to a comparable level tothe baseline controller applied on the TLP. This improvement is due to the use of individualblade pitching and rejecting wind speed variations. Relative to an onshore wind turbinewith a GSPI controller, the DAC reduces tower side-side fatigue load and maintains theblade and shaft loads to a comparable level. Tower fore aft fatigue loads remain higher by27% (instead of 45% increase by the baseline controller on the TLP).

Nomenclature

A (ψ) = periodic state matrixA = augmented and azimuth averaged state matrixB (ψ) = periodic actuator gain matrixB = augmented and azimuth averaged actuator gain matrixBd (ψ) = periodic disturbance gain matrixC (ψ) = a periodic matrix that relates the measurements, y, to the states, x

C = augmented and azimuth averaged C matrixD (ψ) = a periodic matrix that relates the measurements, y, to the control inputs, uGd = disturbance minimization gain matrixH = wave heightK, Knr = state regulation gain matrix in the mixed and non-rotating (denoted by nr) frames of referenceKe = disturbance estimator gain matrixT = wave periodTc (ψ) = control input u transformation matrixTd (ψ) = augmented states vector, w, transformation matrixTGen = applied generator torqueTo (ψ) = output measurements y transformation matrixTs (ψ) = state x transformation matrixXnr = an entity X transformed to the non-rotating frame of referenceu = control inputs vector

∗PhD Candidate, Department of Mechanical Engineering, 20 Symonds Street, Auckland, Private Bag 92019, Auckland MailCentre, Auckland 1142, New Zealand, AIAA Member.

†Senior Lecturer, Department of Mechanical Engineering, 20 Symonds Street, Auckland, Private Bag 92019, Auckland MailCentre, Auckland 1142, New Zealand, Senior AIAA Member.

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American Institute of Aeronautics and Astronautics

48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition4 - 7 January 2010, Orlando, Florida

AIAA 2010-999

Copyright © 2010 by H. Namik and K. Stol. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

ud = disturbance input vectorw = augmented states vector with disturbance statesx = states vectory = measurements vectorz = disturbance waveform state vectorψ = rotor azimuth angleθ = commanded blade pitch angle

I. Introduction

Offshore wind resources are, in general, better than onshore wind;1–3 offshore wind is stronger and lessturbulent. However, most of the offshore wind energy potential lies in water deeper than 30m.4 Current

offshore wind farms have fixed foundations and therefore the deeper the water gets the more costly it becomesto construct wind farms further offshore. For water deeper than 60m, the most feasible option is to have afloating wind turbine.3,5

There are three main floating wind turbine concepts. Each concept uses a different principle to achievestability. The three floating concepts (shown in Figure 1) are: a ballast stabilized spar-buoy, a mooring linestabilized Tension Leg Platform (TLP), and a buoyancy stabilized barge platform. Of course, each concepthas its advantages and limitations. Early comparisons of all three platforms used simple static or dynamicmodels that usually excluded the effect of the control system.3,6–9

Figure 1. The three main floating concepts10

Control of floating wind turbines is a relatively new area of research. Nielsen et al.,3 working on aspar-buoy floating concept, developed an active control strategy to avoid structural resonance. That controlstrategy took into account the fact that as wind speed increases, the thrust force decreases which may causenegative damping of platform pitch motion in the above rated wind speed region. The controller introducedby Nielsen et al. achieved satisfactory results in reducing platform resonant motions in region 3 - above ratedwind speed - in simulation and scale model testing. Continuing on the work done by Nielsen et al.,3 Skaareet al.11 developed an estimator based controller to avoid resonant pitch motions of the turbine and improvefatigue life. This controller was compared to a standard onshore controller applied to an offshore floating

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system. Results showed improvements in tower and blade fatigue life but power output was reduced.Larsen and Hansen,12 using the same spar-buoy concept in refs. 3 and 11, used a Proportional-Integral

(PI) torque controller and a gain scheduled PI pitch controller. This controller was designed to limit theuse of the blade pitch due to the effect of negative damping in the platform pitch motion caused by the lownatural frequencies of the floating structure. This resulted in improved damping but increased rotor speedand power variations even when a constant torque algorithm was applied.

Jonkman13 implemented several control strategies involving a torque controller with constant poweralgorithm and gain scheduled PI blade pitch controller for a 5MW wind turbine on a barge platform. Two ofthese strategies (tower top feedback and pitch to stall regulation) were not capable of reducing the pitchingmotion of the barge platform. The third and final strategy of detuning the speed controller gains producedthe best reduction in platform pitching. Further reduction in platform pitching motion was deemed necessaryby Jonkman. However, there was a limit to the improvement in performance from detuning controller gainsas it approached open loop control.

Working on a TLP, Matha14 performed extensive loads analysis using the same gain-scheduled PI con-troller implemented on the barge by Jonkman.15 Matha found that motions of the TLP were not as significantas the barge and hence the turbine loads were closer to the onshore wind turbine subjected to the same windconditions using the same controller. However, the turbine loads such as the tower fore-aft bending loadsbecome more significant with increasing wind speed due to platform pitching motion and therefore has tobe reduced. Platform pitching also affects the tension in the mooring lines. Excessive pitching can lead toone of the mooring lines becoming slack which could then fail when it subjected to sudden tension.

In our previous work,16,17 we have shown, in our simulations, that a multi-objective controller thatutilizes individual blade pitching applied on the barge floating concept was able to achieve sizable reductionsin platform motions and tower loads while maintaining or improving power and rotor speed regulation.However, this reduction came with the cost of increased blade pitch actuation and hence blade flappingloads.

The objective of this paper is to investigate to what extent can a control system influence the motion andloads of the tension leg platform concept under normal operating conditions. Extreme events simulationsare outside the scope of this paper as the blade pitch controller is usually shutdown (blades are feathered).Individual blade pitch state space control, using multi-blade coordinate transformation, is implemented tofacilitate asymmetric loading on the turbine. The system performance is compared to an onshore system interms of fatigue loads, power, and speed regulation.

The 5MW wind turbine model and the properties of the TLP are discussed in section II. Benefitsand methods to achieve individual blade pitching with an emphasis on a particular method (multi-bladecoordinate transformation) are discussed in section III. Disturbance accommodating control and a methodto implement it after applying the multi-blade coordinate transformation are given in section IV. SectionV includes a brief descritpoin of the implemented controllers with results presented in section VI. Finallyconclusions are drawn in section VII.

II. The Wind Turbine and Floating Platform Model

In this study the same wind turbine developed by Jonkman13 and used by Matha14 is used. The windturbine is a fictitious 5MW machine with its properties based on a collection of existing wind turbines ofsimilar rating; the model is commonly known as the “NREL Offshore 5-MW Baseline Wind Turbine”. Thewind turbine has three blades that are 61.5m long. The TLP floating system is the same used by Matha.14

The TLP is a cylindrical platform with four 27m spokes for the mooring lines. Further model details arelisted in Table 1.

III. Individual Blade Pitching

There are many ways to achieve Individual Blade Pitch (IBP) control depending on the control objectives.Multi-blade coordinate (MBC) transformation can be used to facilitate individual blade pitching.18–20 MBCtransformation captures periodic properties of a system in a linear time-invariant (LTI) model – usefulfor control design. Although MBC transformation does not capture all the periodic effects, it has beenshown that the residual periodic effects are negligible for analysis and control design for three bladed windturbines.19 Bossanyi21 implemented IBP control using PI controllers to mitigate blade loads. He used a

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Table 1. NREL 5MW turbine model details

Wind Turbine

Power Rating 5MW

Rotor orientation Upwind

Control Variable speed, variable pitch, active yaw

Rotor, hub diameter 126m, 3m

Hub height 90m

Rated rotor, generator speed 12.1 rpm, 1173.7 rpm

Blade operation Pitch to feather

Maximum blade pith rate 8 deg/s

Rated generator torque 43,093 Nm

Maximum generator torque 47,402 Nm

Tension Leg Platform

Diameter 18m

Draft 47.89m

Water depth 200m

Platform mass 8,600,410kg

direct and quadrature (d-q) axis representation (a form of MBC) to be able to allow for MIMO control usingPI controllers. Wright22 achieved IBP control using disturbance accommodating control. He used an internalmodel for the wind disturbance and the effect of wind shear to drive the individual blade pitching. Thismethod uses IBP to only reject wind disturbance; states are regulated using collective blade pitch. Anotherform of IBP is to use direct periodic control. Periodic control allows the controller gains to change dependingon the rotor azimuth position and control objectives.23,24 Periodic control captures all the periodicity of thesystem. Stol et al.19 showed that there were no noticeable differences between the performance of controllersdesigned after MBC transformation and controllers with direct periodic control. Therefore, state spacecontrol designed after applying MBC transformation is used to achieve individual blade pitching without theextra complexity of implementing a direct periodic controller.

Individual blade pitching can be used to create asymmetric aerodynamic loads that mitigate platformmotions.17,25 The IBP controller can command each blade differently changing the thrust and torque createdby each blade such that a restoring moment is created by the rotor. For example, to restore platform pitchwhen the turbine is pitching forward, the blade(s) at the top half of the rotor will be commanded to increasethrust while blade(s) at the bottom half of the rotor will be commanded to reduce thrust. This creates abackwards pitch restoring moment thus allowing for reduction in platform pitching with minimal change thetotal rotor thrust.

A. Multi-Blade Coordinate Transformation

Wind turbine systems are usually modeled with Degrees of Freedom (DOFs) in the fixed and rotating framesof reference. Therefore, the effects of the DOFs in the rotating frame of reference (e.g. blades) on those inthe fixed frame of reference (such as the tower) will be periodic. MBC transformation is used to transformthe DOFs that are in the rotating frame of reference to the fixed frame of reference.18 For a three bladedwind turbine, transforming any three DOFs in the rotating frame of reference will result in three DOFs inthe fixed frame of reference that describe the effect of the whole rotor on the turbine system. These threetransformed DOFs are often termed collective, cosine-cyclic, and sine-cyclic components.

For a linearized representation of a wind turbine about an operating point, the state space model is givenby Eq. 1‡ where x is the state vector, u is the control input vector, ud is the disturbance input vector, y is themeasurement vector, A (ψ) is the periodic state matrix, B (ψ) is the periodic actuator gain matrix, Bd (ψ)is the periodic disturbance gain matrix, C (ψ) relates the measurements to the states, and D (ψ) relates themeasurements to the control inputs. The state vector x in Eq. 1 contains states that are both in the fixed

‡The ∆ symbol that indicates perturbation about the operating point is omitted for brevity and clarity.

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and rotating frames of reference.

x=A (ψ)x+B (ψ)u+Bd (ψ)ud

y=C (ψ)x+D (ψ)u(1)

MBC transformation of Eq. 1 yields a state space model whose states are all in the non-rotating/fixedframe of reference as shown in Eq. 2 where the subscript nr indicates the transformed entity into the non-rotating frame of reference. This transformation is achieved by applying Eqs. 3 - 5. Note that the disturbancevector ud is assumed to have no inputs in the rotating frame of reference and hence the vector itself is nottransformed. The new transformed matrices Anr, Bnr, Bd,nr, Cnr, and Dnr and the transformation matricesTc (ψ), and To (ψ) are omitted for brevity and can be found in ref. 18. Ts (ψ) is defined by Eq. 6 where Ω isthe rotor speed. Matrices T1 (ψ) and T2 (ψ) are omitted for brevity and can be found in ref. 18.

xnr

=Anr xnr+Bnr unr

+Bd,nr ud

ynr

=Cnr xnr+Dnr unr

(2)

x = Ts (ψ) xnr

(3)

u = Tc (ψ) unr

(4)

y = To (ψ) ynr

(5)

Ts (ψ) =

[

T1 (ψ) 0

ΩT2 (ψ) T1 (ψ)

]

n×n

(6)

The transformed system in Eq. 2 is not time invariant; it is still slightly periodic.18 Strictly speaking,periodic analysis should follow the transformation but Stol et al.19 found that by averaging the transformedmatrices (Anr, Bnr, Bd,nr, Cnr, and Dnr), little information is lost and hence time invariant control designcan be used without performance loss. Therefore,with a controller designed by averaging the system matricesafter applying MBC transformation, the commanded actuator effort, u

nr, will be time invariant. However,

individual blade pitching is achieved when this command is transformed back to the rotating frame of refer-ence19 by expanding Eq. 4 into Eq. 7 where TGen is the applied generator torque, and θn is the commandedblade pitch angle for blade n. Equation 7 clearly shows that even if the controller commands are time invari-ant in the non-rotating frame of reference, the actual blade commands are periodic resulting in individualblade pitching.

u =

TGen

θ1

θ2

θ3

=

1 0 0 0

0 1 cos (ψ) sin (ψ)

0 1 cos(ψ + 2π

3

)sin

(ψ + 2π

3

)

0 1 cos(ψ + 4π

3

)sin

(ψ + 4π

3

)

u

nr= Tc (ψ) u

nr(7)

IV. Disturbance Accommodating Control

In this section, we explore implementing disturbance accommodating control (DAC) for periodic systemsafter applying MBC transformation. DAC theory is summarized below.

A. Disturbance Accommodating Control Summary

Disturbance accommodating control (DAC) is used to minimize or cancel the effects of persistent disturbancesud that affect a dynamic system given by Eq. 1. A realisable DAC, where direct measurement of thedisturbance is not possible, requires a disturbance estimator to estimate the applied disturbance to thesystem and correct for that.22,26 The disturbance estimator requires a disturbance waveform model given by

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equation Eq. 8 where z is the disturbance waveform states vector. The choice of matrices F , Θ, and initialconditions z (0) determines the nature of the assumed waveform (step, ramp, periodic, etc.).

z = Fz

ud = Θz(8)

Usually a disturbance estimator is required to obtain an estimate of the disturbance states using systemmeasurements y (based on the waveform model - Eq. 8). The disturbance estimator is given by Eq. 9 where

w =

[

x

z

]

and Ke is the estimator gain. The augmented matrices A, B, and C are defined by Eqs. 10, 11,

and 12 respectively.

ˆw =(A−KeC

)w +Bu+Key (9)

A =

[

A BdΘ

0 F

]

(10)

B =

[

B

0

]

(11)

C =[

C 0]

(12)

The realizable disturbance rejection control law is given by Eq. 13 where K is the state regulation gainmatrix and Gd is the disturbance minimization gain matrix. Gd is calculated by evaluating Eq. 14 wherethe resulting gain will minimize or completely cancel the persistent disturbance. The + symbol indicates theapplication of the Moore-Penrose pseudoinverse.

u = −Kx+Gdz (13)

Gd = −B+BdΘ (14)

B. DAC After MBC Transformation

After applying MBC transformation on a periodic system, DAC design becomes time invariant. The DAClaw in the non-rotating frame becomes Eq. 15 and the DAC gain is found by solving Eq. 16.

unr

= −Knrxnr+Gd,nrz (15)

Gd,nr = −B+nrBd,nrΘ (16)

The DAC law is in the non-rotating frame and therefore blade pitch commands have to be transformedback to the mixed frame using Eq. 4. Equation 17 shows the DAC law transformed into the mixed frame ofreference which results in periodic gain matrices where Kmbc (ψ) and Gd,mbc (ψ) are the periodic state regu-lation and periodic disturbance minimization gain matrices respectively as a result of MBC transformation.

u = −Tc (ψ)KnrT−1s (ψ) x+ Tc (ψ)Gd,nr z

= −Kmbc (ψ) x+Gd,mbc (ψ) z (17)

As discussed earlier, a disturbance estimator is usually required since direct measurement of the distur-bance states is rarely possible. Similar to the time-invariant DAC design, we form the augmented states

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vector wnr

using Eq. 18. Equation 19 can then be used to transform between wnr

and w where nd is thenumber of disturbance states.

wnr

=

[

xnr

z

]

(18)

w =

[

Ts (ψ) 0

0 Ind×nd

]

wnr

= Td (ψ) wnr

(19)

Given the definition of wnr

by Eq. 18, we form a new disturbance estimator for the MBC transformedsystem (Eq. 2). The disturbance estimator in the non-rotating frame is given by Eq. 20 where matrices Anr,Bnr, and Cnr are defined by Eqs. 21 - 23. Equation 20 does not represent the MBC transformation of Eq. 9.

ˆwnr

=(Anr −Ke,nrCnr

)w

nr+Bnr unr

+Ke,nr ynr

(20)

Anr =

[

Anr Bd,nrΘ

0 F

]

(21)

Bnr =

[

Bnr

0

]

(22)

Cnr =[

Cnr 0]

(23)

Since the actuator commands and the measurements are in the mixed frame of reference, we transformthe input and measurement vectors into the non-rotating frame and combine the two vectors into one foreasier implementation. The result is given by Eq. 24.

ˆwnr

=(Anr −Ke,nrCnr

)w

nr+BnrT

−1c (ψ)u+Ke,nrT

−1o (ψ) y

︸︷︷︸

Inputs

=(Anr −Ke,nrCnr

)w

nr+

[

BnrT−1c (ψ) Ke,nrT

−1o (ψ)

][

u

y

]

=(Anr −Ke,nrCnr

)w

nr+ E (ψ) v (24)

C. Implementation

Usually, the actual system model is nonlinear and therefore the state space models used only describeperturbations about an operating point. The implementations described below account for the linearizationof the controller.

There are two implementation options for DAC after MBC. The first option, illustrated in Fig. 2, usesEq. 15 instead of Eq. 17 since the output of the disturbance estimator is already in the nonrotating frame.The controller commands are then transformed into the mixed frame by applying Eq. 4.

In the second option, Eq. 17 can still be applied. For this option to work, the disturbance estimatoroutput w

nrmust be transformed back into the mixed frame using Eq. 19 before the control law is applied.

This implementation is shown in Fig. 3. Implementation option 1 is preferred as it requires periodic gaincalculations only for two matrices (E (ψ) and Tc (ψ)) whereas option 2 requires periodic gain calculationsfor four matrices (E (ψ), Klqr (ψ), Gd,mbc (ψ) and Td (ψ)).

Another variant of implementation option 1 is to avoid the redundant transformation of ∆unr

to ∆uand then back to ∆u

nr. This is achieved by rewriting Eq. 20 into Eq. 25 where ∆u

nrcomes directly from

the controller output and ∆ynr

is the only input that is transformed to the non-rotating frame. In blockdiagram, this is shown in Fig. 4. Note that the disturbance estimator now includes matrix Enr instead of theidentity matrix in the previous two implementation options. This option does not require the computationof the T−1

c (ψ) matrix which was part of the E (ψ) matrix given by Eq. 24.

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Nonlinear Model++

+-y y∆u

NRu∆

v( )ψE

NRv

u∆

NRx∆

z

zGxKuNRNRNRNR dˆˆ

,+∆−=∆

( )ψcT

opu

Controller

NRw

opydu

( )NRNRNR

NRNR

NRvIwCKAw e +−= ˆˆ

,&

Disturbance Estimator

Figure 2. Implementation option 1: both controller and estimator are in the non-rotating frame

Nonlinear Model++

+-y y∆u

v( )ψE

NRv

u∆

x∆

z

( ) ( )zGxKuMBCLQR d

ˆˆ, ψψ +∆=∆

opu

Controller

NRw

( )ψdT

w

u∆

opydu

( )NRNRNR

NRNR

NRvIwCKAw e +−= ˆˆ

,&


Figure 3. Implementation option 2: only the estimator is in the non-rotating frame

ˆwnr

=(Anr −Ke,nrCnr

)w

nr+

[

Bnr Ke,nr

][

unr

ynr

]

=(Anr −Ke,nrCnr

)w

nr+ Enrvnr

(25)

Unfortunately, this option cannot be implemented if actuator saturation limits exist because the limitscannot be transformed to the non-rotating frame. Furthermore, this setup cannot be used if the actuatordynamics are sufficiently slow. Otherwise, if the controller output in the non-rotating frame is passed directlyto the disturbance estimator, it could lead to wrong estimates as the passed input does not match the actualinput to the plant.

D. Collective Blade Pitch Drift

One limitation of DAC applied to wind turbine systems exist; collective blade pitch drifting.27 Assuminga linear wind turbine system, the collective blade pitch commanded by the feed-forward action of the DACto reject wind disturbances and maintain steady state is a linear function of the wind speed described byEq. 26 where uop is the actuators’ collective operating point. However, the collective blade pitch requiredto keep the floating wind turbine in steady state as the wind speed varies is a nonlinear function of wind

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Nonlinear Model++

+-y

opy

y∆u

NRu∆

du

( )ψ1−oTNRv

u∆

NRx∆

z

( )ψcT

opu

Controller

NRw

NRu∆

NRy∆

( )NRNRNRNR

NRNR

NRvEwCKAw e +−= ˆˆ

,&


zGxKuNRNRNRNR dˆˆ

,+∆−=∆

Figure 4. Alternative implementation of option 1 (Fig. 2)

speed as shown in Fig. 5. With steady state conditions, the DAC will force the collective blade pitch awayfrom the optimum angle as the turbine operates away from the linearization point. This will force the stateregulation part of the controller to work harder and eventually reach this optimum blade angle.

u = G∆x+Gd∆z + uop (26)

0

5

10

15

20

25

8 10 12 14 16 18 20 22 24

Bla

de

Pit

ch

(d

eg

)

Wind Speed (m/s)

Optimum operating point

DAC collective pitch command

Operating point

Figure 5. Optimum and DAC commanded collective blade pitch

The solution to this problem is given in Ref. 27. The solution is to limit the DAC to only command theperiodic perturbations while having a nonlinear blade pitch operating point as a function of wind speed thatfollows the optimum trajectory. For MBC transformed systems, u

nris given by Eq. 27 where θo, θc, θs are

the collective, cosine-cyclic, and sine-cyclic blade pitch commands respectively. Therefore, the solution canbe easily implemented by just zeroing the gains in the disturbance minimization gain, Gd,nr, that correspondto θo.

unr

=

TGen

θo

θc

θs

(27)

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V. Implemented Controllers

In this study, we implemented two controllers on the TLP: a gain scheduled PI (GSPI) controller - orcommonly referred to as the Baseline controller - and a disturbance accommodating controller.

A. Gain Scheduled PI Controller

The GSPI controller in this study will be used as the baseline controller for comparison. The Baseline con-troller is the best controller developed by Jonkman in his preliminary study to reduce platform pitch motionfor the barge floating system;15 the detuned GSPI controller. It consists of two independent controllers; agenerator torque controller and a gains scheduled collective blade pitch controller. This controller is alsoused by Matha.14

The relationship between the generator torque and generator speed is region dependent. In region 3where the objective is to regulate power to the rated, the applied generator torque is inversely proportionalto the generator speed.28

The gain scheduled PI controller commands the collective blade pitch to regulate rotor speed to therated. The controller gains are scheduled as a function of blade pitch to account for the change in turbinesensitivity at different wind speeds.15 This is a form of nonlinear control.

B. The Disturbance Accommodating Controller

The DAC is designed to reject wind disturbances using the theory described in Section IV B; wave disturbancerejection is yet to be investigated. To reiterate, MBC transformation is applied to the linearized periodicstate space model and followed by disturbance accommodating control design techniques.

The DAC was designed based on a 6 DOFs linearized state space model around 18 m/s wind speed. TheseDOFs include: Platform roll, pitch, and yaw, first tower side-side bending mode, rotor DOF, and drive traintwist. These DOFs were chosen to improve turbine performance, maintain stability, and resolve coupling incertain directions caused by the individual blade pitching of the controller. An example of such coupling canbe found in Ref. 25 where the individual blade pitching mechanism for platform pitch regulation resultedin platform roll excitation. However, unlike the barge concept, platform roll remained stable for the TLPconcept.

The DAC is implemented using implementation option 1 (as shown in Fig. 2) since actuator saturationlimits exist. However, the state regulation part of the DAC is implemented with full state feedback (FSFB).That is, all the 12 design states are being directly measured and being directly fed to the state regulator.Therefore, the control law becomes Eq. 28.

∆unr

= −Knr∆xnr+Gd,nr∆z (28)

The state regulation part of the DAC is implemented in FSFB because the selected design states canbe easily measured by readily available sensors. Furthermore, improvement in sensor measurement qualitymeans that they can be used directly without significantly affecting the dynamic response of the system.This means that signal processing (e.g. filtering) dynamics are becoming faster and embedded within thesensor unit. Therefore, a state estimator is not necessary for state regulation. However, for disturbancerejection, an estimate of the wind speed is required. Therefore, the implemented disturbance estimator isonly used to obtain wind speed estimates ∆z.

VI. Simulation Results

In this section we present the simulation results for the implemented controllers. The results of the DACare compared to the TLP Baseline controller as well as on the Baseline controller on an onshore system.Simulation conditions and setup are described next.

A. Simulation Conditions

Simulations were carried out using FAST29 with all 22 DOFs enabled using turbulent wind and irregularwaves; turbine yaw DOF was locked since no active yaw control was implemented to account for change inwind direction. The simulations were set up in accordance with the IEC-61400-3 standard for offshore wind

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turbines.30 Although this standard is written for offshore wind turbines with fixed foundations, it is used asa guideline for floating wind turbines. Specifically, the simulations were set up for dynamic load case (DLC)1.2 for fatigue load evaluation. However, region transition logic is not yet implemented for the state spacecontrollers and therefore we restrict our simulations in region 3.

Table 2 lists all the simulation parameters that were used to obtain the results. Although not an extensiveset of simulations, these are used to get indicative results for the DAC performance. Three wind speeds andthree wave heights are used while three wave periods are used for each wave height. All the the wind andwave conditions have different random seed numbers. The wave conditions were chosen based on the samereference site used by Jonkman15 located northeast of Scotland. For that site, at any wind speed there existsone wave height and a range of wave periods. The wave periods in Table 2 correspond to the minimum,average, and the maximum range of periods for that site that do not violate the assumptions of linear wavetheory (used by FAST). According to the IEC-61400-3 standard, for the linear wave theory to be appliedin deep water, Eq. 29 must be satisfied where H is the wave height, T is the wave period, and g is theacceleration due to gravity.

Table 2. Wind and wave conditions

Wind Speed (m/s) Turbulence Class Wave Height (m) Wave Period (s)

13.16416.08219.00014.27817.53920.80015.80316.90218.000

21.0 B 4.90

Wind Conditions Wave Conditions

15.0 B 3.40

18.0 B 4.00

H

gT 2≤ 0.002 (29)

The simulation results for the nine 600 seconds simulations are averaged for every wind speed as wellas averaged overall and then compared to the selected reference controller. This method is used to lookfor any noticeable trends as the wind speed is increased. However, these are not shown here since only afew performance metrics showed some trends with increasing wind speed; more simulations per wind speedare required in addition to more variations in wind speeds are required to verify these trends. Instead, theoverall averaged results across all wind speeds are presented next.

B. Results Compared to Offshore Baseline Controller

In this section we compare the overall averaged performance of the DAC when compared to the TLP Baselinecontroller (GSPI). Figure 6 shows eleven normalized key performance metrics. These metrics are normalizedrelative to the Baseline controller on the TLP; a value of less than 1 is desired meaning an improvementrelative to the baseline controller. The performance metrics range from root mean square (RMS) of thepower and speed regulation errors, RMS of blade pitch rate, RMS of platform velocities, and fatigue damageequivalent loads (DELs) of key turbine components.

The figure clearly shows that the DAC noticeably improves power regulation (44% reduction in power er-ror) and significantly improves speed regulation by reducing the rotor speed error by 73%. This improvementis mainly due to the use of individual blade pitching and the wind disturbance minimization.

Blade pitch actuation has significantly increased due to individual blade pitching as well as more controlobjectives. This increase is not close to the saturation limit of the blades. Normally, an increase in bladeactuation usually results in increased blade loads. However, for the TLP system the increase in bladeactuation had no negative effect on blade flapwise and edgewise DELs.

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0.56

0.27

4.99

0.94

1.01

0.87

0.62

1.03

0.49

0.94

0.55

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

Power Error

Speed Error

Blade Pitch Rate

Blade Flap

Blade Edge

Tower FA

Tower SS

LSS Roll Rate

Pitch Rate

Yaw Rate

Normalized Perform

ance Metric

Fatigue DEL Platform MotionsRMS of Power, Speed, and Blade Usage

Figure 6. DAC performance relative to TLP baseline

Tower fore-aft fatigue loads were reduced by an average of 13% due to a reduction in platform pitching.Tower side-side fatigue DEL were reduced by an average of 38%. This desirable reduction in side-side loadingis due to the inclusion of tower side-side DOF as an explicit control objective. Coupled with the explicitcontrol objective to reduce roll motion, the result is a reduction in the sideways loads induced on the windturbine which reuced platform rolling and tower side-side loads.

Low speed shaft (LSS) fatigue DEL are similar to the baseline controller despite an increase in bladeactuation. This is mainly due to the inclusion of the generator torque as an additional actuator for theDAC. If it was not included, then power regulation will be as good as speed regulation but shaft DEL will behigher. Therefore, the controller is sacrificing power regulation in favor of reducing shaft loads. As a resultof including generator torque, its usage has decreased to reduce shaft loads.

Although not shown here for brevity, the performance of only the state regulation part of the DAC (i.e.a standard state space regulator) results in worse performance in terms of power and speed regulation aswell as tower loads. Therefore, unlike the barge system,16 the DAC is not dominated by the wave motionresulting in noticeable improvement in several performance metrics when compared to an individual bladepitch state space controller.

C. Results Compared to Onshore Baseline Controller

The results of the previous two controllers (Baseline and DAC) applied on the TLP concept are compared tothe performance of an onshore wind turbine with a GSPI controller (Baseline onshore) to assess, relatively,the fatigue loads of the floating system. The performance metrics that correspond to platform motions arenot included since the onshore system does not have these DOFs.

The results are presented in Fig. 7 where TLP Baseline refers to the performance of the Baseline controlleron the floating TLP. It is worthy to note that the performance of the TLP Baseline controller relative tothe onshore system is almost unity across most metrics with the exception of RMS power error, RMS bladepitch rate, and tower FA fatigue DEL. As a result of this unity, the performance of the DAC relative to theonshore system almost mirrors that of the offshore case in the previous section with the exception of thetower FA fatigue DEL.

The almost unity performance of the Baseline TLP demonstrates the effectiveness of the TLP concept.That is, because platform motions and rotations are kept small due to the mooring lines, turbine fatigueloads were of a comparable level to an onshore wind turbine with the same controller. However, the only

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1.13

1.06

1.10

1.03

1.01

1.45

0.98

1.02

0.62

0.29

5.45

0.97

1.02

1.27

0.60

1.05

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

Power Error

Speed Error

Blade Pitch Rate

Blade Flap

Blade Edge

Tower FA

Tower SS LSS

Normalized Perform

ance Metric TLP Baseline DAC

Fatigue DELRMS of Power, Speed, and Blade Usage

Figure 7. DAC and TLP baseline performance relative to onshore baseline

exception to this is the tower FA loads. This is due to the wave interaction with the platform and thepitching motion. This pitching motion also affects the power and speed regulation as the turbine rocks inthe pitch axis.

Even with the 13% reduction in tower FA fatigue DEL of the DAC compared to the Baseline TLP, towerFA loads are still increased by 27% by going to a floating TLP concept from an onshore point of view.Further reductions are desirable to make the TLP concept more attractive for development and prototyping.Adding the tower FA DOF as an explicit control objective is expected to further reduce tower FA DEL.

VII. Conclusions

The tension leg platform (TLP) floating concept was simulated for fatigue loads evaluation accordingto the IEC61400-3 standard dynamic load case (DLC) 1.2; however, the simulations were only restricted toregion 3. Simulation results for a gain scheduled PI (GSPI) controller (also referred to as the Baseline con-troller) applied on the TLP show that turbine fatigue damage equivalent loads (DELs) were of a comparablelevel to an onshore wind turbine with the same controller except for tower fore-aft (FA) fatigue DEL. Thisincrease coupled with increased power and rotor speed regulation errors is due to the wave interaction withthe platform inducing a pitching motion.

A disturbance accommodating controller (DAC) was implemented to reject wind speed perturbation inaddition to regulating several turbine states to improve performance and maintain stability of the system.A limitation of DAC is present when applied on a nonlinear system such as the floating TLP system; bladepitch drift away from the linearization point. This was resolved by introducing a nonlinear operating pointand limiting the DAC to only command periodic perturbations of the commanded blade pitch.

To deal with the periodic nature of the wind turbine system, multi-blade coordinate (MBC) transforma-tion was used to transform the system states in the rotating frame of reference to a fixed/non-rotating frameof reference. The result is a time-invariant system described in the non-rotating coordinate system whichthen allows for time invariant control techniques to be applied.

The performance of the DAC show significant improvements in power and speed regulation. Tower FAand side-side fatigue DELs were reduced while other component loads (blades and shaft) were maintainedto a similar level to that of the Baseline controller on the floating TLP system. This improvement is due tothe use of individual blade pitch and wind disturbance rejection. However, tower FA DEL is still 27% higher

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than that of an onshore wind turbine.

Acknowledgments

H. Namik would like to thank the Tertiary Education Commission of New Zealand for student fundingthrough the Top Achiever Doctoral Scholarship. We are also grateful for the support of Dr. Jason Jonkmanat the National Renewable Energy Lab (NREL) for providing the simulation models and advice.

References

1Shikha, Bhatti, T. S., and Kothari, D. P., “Aspects of Technological Development of Wind Turbines,” Journal of Energy

Engineering, Vol. 129, No. 3, 2003, pp. 81–95.2Brennan, S., “Offshore Wind Energy Resources,” Workshop on Deep Water Offshore Wind Energy Systems, 15-16th

October 2003.3Nielsen, F. G., Hanson, T. D., and Skaare, B., “Integrated Dynamic Analysis of Floating Offshore Wind Turbines,”

Proceedings of the 25th International Conference on Offshore Mechanics and Arctic Engineering, Vol. 2006, Hamburg, 4 - 9June 2006, pp. 671–679.

4Jonkman, J. M. and Sclavounos, P. D., “Development of Fully Coupled Aeroelastic and Hydrodynamic Models for OffshoreWind Turbines,” Proceedings of the 44th AIAA Aerospace Sciences Meeting and Exhibit , Reno, NV, 9-12th January 2006, p.CDROM.

5Musial, W., Butterfield, S., and Ram, B., “Energy from Offshore Wind,” Offshore Technology Conference, Houston,Texas, USA, May 1-4 2006, pp. 1888–1898.

6Bulder, B., Peeringa, J., Pierik, J., Henderson, A. R., Huijsmans, R., Snijders, E., Hees, M. v., Wijnants, G., and Wolf,M., “Floating Offshore Wind Turbines for Shallow Waters,” European Wind Energy Conference, ECN Wind Energy, Madrid,Spain, 16-19th June 2003.

7Musial, W., Butterfield, S., and Boone, A., “Feasibility of Floating Platform Systems for Wind Turbines,” 23rd ASME

Wind Energy Symposium, NREL, Reno, NV, 5-8th January 2004.8Ushiyama, I., Seki, K., and Miura, H., “A Feasibility Study for Floating Offshore Windfarms in Japanese Waters,” Wind

Engineering, Vol. 28, No. 4, 2004, pp. 383–397.9Butterfield, S., Musial, W., Jonkman, J., Sclavounos, P., and Wayman, L., “Engineering Challenges for Floating Offshore

Wind Turbines,” Copenhagen Offshore Wind 2005 Conference and Expedition Proceedings, Danish Wind Energy Association,Copenhagen, Denmark, 25-28 October 2005.

10Jonkman, J. M. and Buhl Jr., M. L., “Development and Verification of a Fully Coupled Simulator for Offshore WindTurbines,” 45th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, 2007, pp. 28–53.

11Skaare, B., Hanson, T. D., and Nielsen, F. G., “Importance of Control Strategies on Fatigue Life of Floating WindTurbines,” Proceedings of the 26th International Conference on Offshore Mechanics and Arctic Engineering, San Diego, CA,10 - 15 June 2007, pp. 493–500.

12Larsen, T. J. and Hanson, T. D., “A Method to Avoid Negative Damped Low Frequency Tower Vibrations for a FloatingPitch Controlled Wind Turbine,” Journal of Physics: Conference Series, Vol. 75, 2007.

13Jonkman, J. M., “Influence of Control on the Pitch Damping of a Floating Wind Turbine,” 46th AIAA Aerospace Sciences

Meeting and Exhibit , Reno, Nevada, 7-10 January 2008, p. CDROM.14Matha, D., Modelling and Loads & Stability Analysis of a Floating Offshore Tension Leg Platform Wind Turbine,

Master’s thesis, National Renewable Energy Lab’s National Wind Turbine Center and University of Stuttgart, 2009.15Jonkman, J. M., Dynamics Modeling and Loads Analysis of an Offshore Floating Wind Turbine, Ph.D. thesis, University

of Colorado, 2007.16Namik, H. and Stol, K., “Disturbance Accommodating Control of Floating Offshore Wind Turbines,” 47th AIAA

Aerospace Sciences Meeting and Exhibit , Orlando, FL, 5-8th January 2009, p. CDROM.17Namik, H. and Stol, K., “Individual Blade Pitch Control of Floating Offshore Wind Turbines,” Wind Energy, 2009.18Bir, G., “Multi-Blade Coordinate Transformation and Its Application to Wind Turbine Analysis,” 46th AIAA Aerospace

Sciences Meeting and Exhibit , Reno, NV, 7-10th January 2008, p. CD ROM.19Stol, K., Moll, H.-G., Bir, G., and Namik, H., “A Comparison of Multi-Blade Coordinate Transformation and Direct

Periodic Techniques for Wind Turbine Control Design,” 47th AIAA Aerospace Sciences Meeting and Exhibit, Orlando, FL, 5 -8th January 2009, p. CD ROM.

20Engelen, T. v., “Control design based on aero-hydro-servo-elastic linear models from TURBU (ECN),” Proceedings of

the European Wind Energy Conference, Milan, 7-10th May 2007, pp. 68–81.21Bossanyi, E. A., “Individual Blade Pitch Control for Load Reduction,” Wind Energy, Vol. 6, No. 2, 2003, pp. 119–128.22Wright, A. D., “Modern Control Design for Flexible Wind Turbines,” Tech. Rep. NREL/TP-500-35816, National Renew-

able Energy Lab, 2004.23Stol, K., Dynamics Modeling and Periodic Control of Horizontal-Axis Wind Turbines, Ph.D. thesis, University of Col-

orado, 2001.24Stol, K., Zhao, W., and Wright, A. D., “Individual blade pitch control for the Controls Advanced Research Turbine

(CART),” Journal of Solar Energy Engineering, Transactions of the ASME , Vol. 22, 2006, pp. 16478–16488.25Namik, H., Stol, K., and Jonkman, J., “State-Space Control of Tower Motion for Deepwater Floating Offshore Wind

Turbines,” 46th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, 7-10 January 2008, p. CDROM.

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26Balas, M. J., Lee, Y. J., and Kendall, L., “Disturbance Tracking Control Theory with Application to Horizontal AxisWind Turbines,” Proceedings of the 1998 ASME Wind Energy Symposium, Reno, Nevada, 12-15 January 1998, pp. 95–99.

27Namik, H. and Stol, K., “Control Methods for Reducing Platform Pitching Motion of Floating Wind Turbines,” European

Offshore Wind 2009 , Stockholm, 14-16th September 2009, p. CD ROM.28Bossanyi, E. A., “The Design of Closed Loop Controllers for Wind Turbines,” Wind Energy, Vol. 3, No. 3, 2000, pp. 149–

163.29Jonkman, J. and Buhl Jr, M. L., “FAST User’s Guide,” Tech. Rep. NREL/EL-500-38230, National Renewable Energy

Laboratory, August 2005 2005.30“Wind Turbines Part 3: Design Requirements for Offshore Wind Turbines,” International Electrotechnical Commission

(IEC), Standard 61400-3 Ed. 1, 2009.

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individual blade pitch control of a floating oﬀshore wind ...€¦ · iii. individual blade...

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