Research Article Variable Torque Control of …downloads.hindawi.com/journals/aaa/2014/903493.pdfResearch Article Variable Torque Control of Offshore Wind Turbine on Spar Floating

Research ArticleVariable Torque Control of Offshore Wind Turbine on SparFloating Platform Using Advanced RBF Neural Network

Lei Wang12 Shan Zuo2 Y D Song12 and Zheng Zhou3

1 Intelligent Systems and New Energy Technology Research Institute Chongqing University Chongqing 400044 China2 Institute of Intelligent System and Renewable Energy Technology University of Electronic Science and Technology of ChinaChengdu 611731 China

3Web Science Center University of Electronic Science and Technology of China Chengdu 611731 China

Correspondence should be addressed to Lei Wang leiwang08cqueducn

Received 2 January 2014 Revised 14 January 2014 Accepted 15 January 2014 Published 6 March 2014

Academic Editor Xiaojie Su

Copyright copy 2014 Lei Wang et alThis is an open access article distributed under theCreative CommonsAttribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Offshore floating wind turbine (OFWT) has been a challenging research spot because of the high-quality wind power and complexload environmentThis paper focuses on the research of variable torque control of offshore wind turbine on Spar floating platformThe control objective in below-rated wind speed region is to optimize the output power by tracking the optimal tip-speed ratioand ideal power curve Aiming at the external disturbances and nonlinear uncertain dynamic systems of OFWT because of theproximity to load centers and strong wave coupling this paper proposes an advanced radial basis function (RBF) neural networkapproach for torque control ofOFWTsystemat speeds lower than ratedwind speedThe robust RBFneural networkweight adaptiverules are acquired based on the Lyapunov stability analysis The proposed control approach is tested and compared with the NRELbaseline controller using the ldquoNREL offshore 5MW wind turbinerdquo model mounted on a Spar floating platform run on FAST andMatlabSimulink operating in the below-rated wind speed conditionThe simulation results show a better performance in trackingthe optimal output power curve therefore completing the maximum wind energy utilization

1 Introduction

Wind energy has been an important part of the renewableenergy It is significantly meaningful for optimizing theenergy system structure easing the energy crisis and pro-tecting the environment by actively developing wind energyWith the rapidly development of wind energy all over theworld promising and reliable wind turbine concepts havebeen developed Offshore wind turbine makes it possibleto go further into water deeper than 60m [1] thereforeit has become the key research in the field of renewableenergy

The floating offshore wind turbine (OFWT) conceptprovides a groundbreaking strategy to fully utilize the high-quality wind power in deep waters The design concept ofldquolarge floating offshore wind turbinerdquo was firstly proposedby Heronemus from Massachusetts Institute of Technol-ogy (MIT) in 1972 [2 3] American Renewable Energy

Laboratory (NREL) and MIT have completed the dynamicsystem modeling of OFWT and the three types of floatingplatform tension leg platform with suction pile anchorsSpar-buoy with catenary mooring drag-embedded anchorsand barge with catenary mooring lines through OC3 projects[4] Figure 1 shows the three primary types of floatingoffshore wind turbine concepts

Previous research results show that compared to onshorewind turbines OFWTs with six degrees of freedom areprone to pitching motion and to produce complex dynamicload because of proximity to load centers and strong wavecoupling [5] Meanwhile with the larger scale (the capacityof OFWTs reaches up to 10MW the diameter of bladesapproximates 200 meters) the blades of OFWT producehigher uneven loads due to the effect of turbulence windshear tower shadow and spindle tilt Accumulating of theabove two types of loads will result in devastating impact onthe fatigue life and output power quality of theOFWT system

Hindawi Publishing CorporationAbstract and Applied AnalysisVolume 2014 Article ID 903493 7 pageshttpdxdoiorg1011552014903493

2 Abstract and Applied Analysis

Mooring line stabilizedTension leg platform withsuction pile anchors

Ballast stabilizedSpar buoy with catenarymooring drag-embeddedanchors

Buoyancy stabilizedBarge with catenary

mooring lines

Figure 1 Floating offshore wind turbine concepts (image from Google)

Therefore it is urgently needed to reduce fatigue loads andimprove output power quality for OFWT system by utilizingadvanced control strategies

Control of OFWT is a relatively new yet challengingresearch area There have been a large number of recentachievements in the research of blade pitch control forOFWTin the above-rated wind speed region [6ndash13] In our previouswork [6] we propose a computationally inexpensive robustadaptive control approach with memory-based compensa-tion for blade pitch control However works on the variablespeed control for OFWT system in below-rated wind speedregion are relatively few

In this study to address the challenge that the systemparameters of OFWT are varying and uncertain due to thecomplex external wind and wave disturbances an adaptiveradial basis function (RBF) neural network approach isproposed for torque control of OFWT system at speedslower than rated wind speedThe robust RBF neural networkweight adaptive rules are acquired based on the Lyapunovstability analysis The proposed torque controller based onRBF neural network is presented and mounted on a Sparfloating platform for performance comparison with thebaseline torque controller in the below-rated wind speedregion

Section 2 briefly presents the wind turbine model andthe Spar floating platform utilized in this paper Section 3describes the two implemented controllers the baselinetorque controller and the proposed variable torque con-troller based on RBF neural network Section 4 shows thesimulation and results in which performances of the abovetwo controllers are compared with each other on Sparfloating platform Eventually conclusions are reported inSection 5

Cp

120582

minus10

05

04

03

02

01

020

15

105

00

1020

30

120573 (∘ )

Figure 2 Power coefficients for VSVP wind turbine

2 Wind Turbine and Platform Models

21 5MWOffshoreWindTurbineModel Thebasic propertiesof future offshore turbines can be estimated by consideringthe amount of kinetic energy density in the wind which canbe converted into kinetic energy of the turbine shaft Theexpression for power produced by the wind is simply given by

119875119878=1

2119862119901 (120582 120573) 120588119860V

3 (1)

where 120588 is air density and 119860 is the swept area of the turbinerotor with a radius 119877 giving 119860 = 120587119877

2 V is wind speedpassing the rotor 119862

119901denotes power coefficient of wind

turbine which is a nonlinear function of the tip-speed ratio120582 and the pitch angle 120573 [14] Figure 2 depicts the curve of

Abstract and Applied Analysis 3

power coefficients for variable speed and variable pitch windturbine It indicates that for a different 120573 there will be adifferent curve for the 119862

119901minus 120582 while for a fixed 120573 there will

be an optimal 120582 at which the power output is maximum Inaddition for any tip-speed ratio 120582 power coefficient 119862119901 isrelatively maximum when blade pitch angle 120573 = 0

∘ When 120573increases 119862

119901decreases simultaneously

Note that the tip-speed ratio is defined as

120582 =

VTipV

=119877120596119903

V (2)

where VTip is the tip speed and 120596119903is the rotor speed

For a constant value of 120573 = 0∘ the mathematical model

of 119862119901is expressed as

119862119901 (120582) = 1198881 (

1198882

1205821

minus 1198884) 119890minus11988851205821 + 1198886120582

1

1205821

= (1

120582minus 0035)

(3)

where the coefficients (1198881 1198882 1198884 1198885 1198886) depend on the aero-

dynamic design of the blade and operating conditions of thewind turbine In this paper the coefficients are 1198881 = 051761198882 = 116 1198884 = 5 1198885 = 21 and 1198886 = 00068 [15] For the ldquoNREL5MW reference offshore wind turbinerdquo model simulated inthis paper the peak power coefficient of 0482 occurred at atip-speed ratio of 755 and a rotor-collective blade-pitch angleof 00∘ [16]

In the case of the variable speed wind power generationsystem the maximum power point control from the windturbine can be adopted The maximum power of the windturbine is given by

119875max =1

2

1205881205871198775119862119901 max

120582lowast3120596lowast3

119903 (4)

The physical properties of the specified wind turbinemodel used for analysis the ldquoNREL 5MW reference offshorewind turbinerdquo are listed in Table 1 [16] This wind turbine ismounted on a Spar floating platform

22 Floating Platform The Spar-buoy platform is modeledfor the support structure The NREL 5 MW offshore floatingplatform input properties for the OC3-Hywind Spar-buoyused in this paper are briefly summarized in Table 2 [4]

3 Implemented Controllers

This section gives the detailed information about the twocontrollers simulated in the analysis

31 The Baseline Generator Torque Controller The baselinegenerator torque controller is built on the best performancepresented by Jonkman in his previous research on the Spar-buoy platform [17]

In the below rated wind speed region the purpose is tooptimize power captureThe generator torque is proportional

Table 1 NREL 5MW turbine model properties

Power rating 5MWRotor orientation Configuration Upwind 3 blades

Control Variable speed variablepitch active yaw

Rotor hub diameter 126m 3mHub height 90mCut-in rated cut-out wind speed 3ms 114ms 25msRated rotor generator speed 121 rpm 11737 rpmRotor mass 110000 kgOptimal tip-speed-ratio 755Blade operation Pitch to featherMaximum blade pitch rate 8∘sRated generator torque 43093NmMaximum generator torque 47402NmUsing the turbine model data from [16]

Table 2 Physical properties for the OC3-hywind spar-buoy

Diameter 65mDraft 1200mPlatform mass 7466330 kgWater depth 3200mNumber of mooring lines 3Using the barge platform data from [4]

to the square of the filtered generator speed to maintain aconstant optimal tip-speed ratio

The generator torque for this region is expressed as

119879120596119903

119892= 1198791

119892+

119879lowast

119892minus 1198791

119892

1205961199032 minus 1205961199031

(120596119903minus 1205961199031) (5)

where120596119903is rotor speed1198791

119892is the generator torque at the rotor

speed inwhich this region starts (1205961199031)119879lowast

119892is rated torque and

1205961199032

is the rotor speed in which the rated torque is reached

32 Advanced Generator Torque Controller Based on RBFNeural Network We propose a RBF neural network forvariable torque control of the OFWT system The totalnumber of input signals in the OFWT torque control systemis no more than 4 Consequently it is a computationallyinexpensive approach to utilize the RBF neural network forlinearization and approximation

In this paper the RBF neural network is a three-layerforward network including an input layer a hidden layerwith a Gaussian activation function and a linear output layerThe mapping from input to output is nonlinear while themapping from hidden layer to output layer is linear thereforespeeding up the process of study obviously and avoidinglocal minimum problem The topological structure of RBFnetwork is presented in Figure 3

The control block diagram of RBF neural network isillustrated in Figure 4


Input layerHidden layer

Output layerx1

x2

xn

h1

h2

hm

w1

w2

wm

F

i j

(x)sum

Figure 3 Topological graph of RBF neural network

Controlled

RBF NN

objectu(k)

y(k)

ym(k)

+

minus

Figure 4 Control block diagram of RBF neural network

In RBF network119883 = [1199091 1199091 119909119899]119879 is the input vector

ℎ119892 is a nonlinear RBF activation function which is given by

ℎ119892= Φ (

10038171003817100381710038171003817119883 minus 119862

119892

10038171003817100381710038171003817) = exp(minus

10038171003817100381710038171003817119883 minus 119862

119892

10038171003817100381710038171003817

2

21198872119892

)

119892 = 1 2 119898

(6)

where 119898 is the number of neurons in the hidden layer and119862119892 = [1198881119892 1198882119892 119888119894119892 119888119899119892]

119879 is the central vector of 119892thhidden neuron 119861 = [119887

1 1198872 119887119892 119887119898]119879 is the basis-width

vector 119887119892 gt 0 is the base width constant of 119892th modeand the weight vector of the linear output neurons is 119908 =

[1199081 1199082 119908119892 119908119898]119879

The output 119877119899 rarr 119877 of the neural network is defined as

119865 (119909) = 119908119867 =

119898

sum

119892=1

119908119892Φ(10038171003817100381710038171003817119909 minus 119862

119892

10038171003817100381710038171003817) (7)

From previous research results [13 18ndash25] we could learnthat a RBF neural network with enough hidden neuronscan approximate any nonlinear continuous functions witharbitrary precision In this paper in order to train the RBFneural network we utilize the Lyapunov stability to get theweights updating rules of the RBF neural network

In the first mode of operating at variable torque controlwhere the wind speed is less than the rated speed regionthe electrical torque of the wind turbine must be adjusted tomake the rotor speed track the desired speed that is specified

Rotor side

Generator sideGearbox

Tm

Jr

TLTH

Te

Jg

Kr Kg

120596r 120596g

Figure 5 Layout of drive train model

according to the optimal tip-speed ratio The drive traindynamics are depicted in Figure 5 The mechanical motionequations are given by

119869119903119903 + 119870119903120596119903 + 119861119903120579119903 = 119879119898 (120596 120573 V ) minus 119879119871

119869119892119892+ 119870119892120596119892+ 119861119892120579119892= 119879119867minus 119879119890

119899 =

120596119892

120596119903

=119879119871

119879119867

(8)

where 119869119903and 119869119892are themoment of inertia of the rotor and the

generator119870119903and119870

119892are the coefficient of viscous reaction of

rotor and generator respectively 119861119903and 119861

119892are the coefficient

and stiffness of rotor and generator respectively 119879119898 119879119890 119879119871

and 119879119867are the shaft torque at wind turbine end generator

end and before and after gear box respectively 119909 is the towerdisplacement and 119899 is the gearbox ratio 120579119903 and 120579119892 are themechanical angular position of the rotor and generator

We rewrite the above mechanical motion equations in acompact form as follows

119869119903+ 119870120596119903+ 119861120579119903= 119879119898(120596 120573 V ) minus 119899119879

119890 (9)

where 119861 are lumped parameters given by

119869 = 119869119903 + 1198992119869119892

119870 = 119870119903+ 1198992119870119892

119861 = 119861119903 + 1198992119861119892

(10)

119879119898is given by

119879119898 =

1205881205871198773119862119901 (120582 120573)

2120582(V minus )2 (11)

The affine form of the rotor speed equation can becharacterized by the following equation

119903= Γ (120596

119903 V) + 120574119879

119890 (12)

where 120574 is a constant negative value and 119879119890is the input signal

with

Γ (120596119903 V) =(1205881205871198773119862119901(120582 120573) 2120582) V2 minus 119870120596

119903minus 119861120579119903

119869

120574 =minus119899

119869

(13)


Construct a nonlinear approximation function throughRBF neural network given by

Γ (120596119903 V)120574

= Φ (120596119903 V) 119908 + 119871 (120596

119903 V) (14)

where |119871(120596119903 V)| le 119871max represents the lumped RBF neural

network approximation errorTo design the rotor speed tracking controller define the

rotor tracking error 119890 as follows

119890 = 120596119903minus 120596lowast

119903 (15)

where 120596lowast119903is the optimal rotor speed which is defined as

120596lowast

119903=120582lowastV119877 (16)

where the optimum tip speed ratio 120582lowast is given in Table 1The control system can be justified by considering the

Lyapunov function candidate as follows

119881 =1

minus21205741198902+

1

21205791

119908119879119908 (17)

where 1205791 gt 0 is the positive adaptation gain 119908 = 119908 minus 119908 isthe weight error 119908 and 119908 are the ideal weight and estimatedweight of the network respectively The Lyapunov functioncandidate 119881 is a positive definite function and le 0 is thesufficient condition for the robust stability of the nonlinearsystem We can get the following

= (120596119903minus 120596lowast

119903) (minus

Γ (120596119903 V)

120574minus 119879119890+120582lowastV119877120574

) minus1

1205791

119908119879 119908 (18)

Deriving the approximation through the neural networksΓ(120596119903 V)120574 = Φ(120596119903 V)119908+119871(120596119903 V) and Γ(120596119903 V)120574 = Φ(120596119903 V)119908

For the stability of the nonlinear system consider the follow-ing controller

= 119879119890= minusΦ (120596

119903 V) 119908 + 120581 (120596

119903minus 120596lowast

119903) + 120596119903 (19)

where 120581 gt 0 is the rotor speed tracking error feedback gain

Proof Based on (18) and (19) we can get

= (120596 minus 120596lowast) (minus119871 (120596

119903 V) minus 120581 (120596


119903) minus 120596119903+120582lowastV119877120574

)

+ 119908119879(minusΦ119879(120596119903 V) (120596


119903) minus

1

1205791

119908)

(20)

The weight updating rule of the network can be obtainedthrough the e-modification method given by

119908 = minus 1205791 (Φ119879(120596119903 V) (120596


119903) + 120592

1003816100381610038161003816120596119903 minus 120596lowast

119903

1003816100381610038161003816 119908) (21)

where 120592 is a constant positive value Combine (20) and (21) toget the following

= (120596119903minus 120596lowast

119903) (minus119871 (120596

119903 V) minus 120596

119903+120582lowastV119877120574

)

minus 120581(120596119903minus 120596lowast

119903)2+ 120592

1003816100381610038161003816120596119903 minus 120596lowast

119903

1003816100381610038161003816 119908119879119908

(22)

RBF NNcontroller

Onlineadaptation

Te

Te

Pm

120596r

120596r

120596r

f(middot)

Φ(120596r )w

120596lowastr

120596lowastr

Figure 6 Block diagram of the RBF NN variable speed controlscheme

It is assumed that 120596119903and lowast

119903are bounded so

10038161003816100381610038161205961199031003816100381610038161003816 le 1198711

1003816100381610038161003816lowast

119903

1003816100381610038161003816 =

10038161003816100381610038161003816100381610038161003816

120582lowastV119877120574

10038161003816100381610038161003816100381610038161003816

le 1198712

le1003816100381610038161003816120596119903 minus 120596

lowast

119903

1003816100381610038161003816

sdot ((119871max + 1198711 + 1198712) minus 1205811003816100381610038161003816120596119903 minus 120596

lowast

119903

1003816100381610038161003816 minus 120592119908119879119908 + 120592119908

119879119908)

(23)

If |120596119903minus120596lowast

119903| ge (119871max +119871119908)120581+ (120592119908

2)4120581 or 119908 ge (1199082)+

radic(119871max + 119871119908)120592 + 11990824 we could get

le 0 (24)

Therefore the overall dynamic system is uniformly ulti-mately bounded

From the above equations we can see that the estimatedwind speed input enables the generator to track the optimaloutput power curve by generating a reference rotor speedThere are many previous researches working on estimatingwind speed without directly measuring the wind speed Inthis paper we utilize the sensorless scheme presented in [26]to estimate wind speed based on neural network Then wecould get the reference rotor speed by the following equation

120596lowast

119903= 119891 (V) =

120582lowastV119877 (25)

The block diagram of the RBF neural network variablespeed control scheme of the OFWT system is depicted inFigure 6

4 Simulation and Results

In this section the ldquoNREL 5MW reference offshore windturbinerdquo installed on a OC3-Hywind Spar-buoy floatingplatform is tested and simulated with the FAST and MAT-LABSimulink under mean value of 8ms turbulence windspeed which is below the rated wind speed

To verify the robustness and self-adaptation of theproposed variable torque controller based on RBF neuralnetwork compared simulations of two types of controllers


1000 200 300 400 500 600 700

02468

101214

Time (s)

Win

d an

d w

ave

Wind speed (ms)Wave height (m)

minus6minus4minus2

Figure 7 Wind and wave conditions

100 200 300 400 500 600 7000

50010001500200025003000

Time (s)

Out

put p

ower

(MW

)

Optimal output powerRBF NN controllerBaseline controller

Figure 8 Comparison in generator output power

the baseline torque controller and the proposed torquecontroller have been performed on the same offshore windturbine system Two comparison performances are simulatedbased on power tracking generator output power and torqueregulations

Figure 7 shows the turbulence wind and wave conditionsFigure 8 compares the average generator output power

tracking for the proposed torque controller based on RBFneural network and the baseline torque controller with theoptimal output power trajectory It can be observed thatthe proposed adaptive torque controller is able to follow theoptimal output power curve with better tracking accuracythan the baseline torque controller therefore completing themaximum offshore wind energy utilization

Figure 9 presents the compared curve in generatortorque

5 Conclusions

This paper mainly focuses on the variable torque controlof OFWT system for power tracking in below-rated windspeed region on a Spar-buoy floating platform In allusion tothe external disturbances and uncertain system parametersof OFWT due to the much more complicated external loadenvironment and strong wave coupling compared to theonshore wind turbine a robust adaptive torque controllerbased on RBF neural network is proposed and tested Two

100 200 300 400 500 600 70005

1015202530

Time (s)

RBF NN controllerBaseline controller

Gen

erat

or to

rque

(KNmiddotm

)

Figure 9 Comparison in generator torque

types of controllers are implemented on the OC3-HywindSpar-buoy floating platform for performance comparison thebaseline torque controller and the proposed torque controller

According to the average simulation results the proposedtorque controller based on RBF neural network is not onlyrobust to complex wind andwave disturbances but also adap-tive to varying and uncertain system parameters as well As aresult the advanced controller shows a better performance intracking the optimal generator output power curve thereforecompleting the maximum wind energy utilization

Conflict of Interests

The authors declare that there is no conflict if interestsregarding the publication of this paper

Acknowledgments

This work was supported in part by the National HighTechnology Research and Development Program of China(SS2012AA052302) theNational Natural Science Foundationof China (no 51205046) and the Fundamental ResearchFunds for the Central Universities (no CDJZR170008)

References

[1] F G Nielsen T D Hanson and B Skaare ldquoIntegrated dynamicanalysis of floating offshore wind turbinesrdquo in Proceedingsof the 25TH International Conference on Offshore Mechanicsand Arctic Engineering (OMAE rsquo06) pp 671ndash679 HamburgGermany June 2006

[2] W E Heronemus ldquoPollution-free energy from offshore windrdquoin Proceedings of the 8th Annual Conference and ExpositionMarine Technology Society Washington DC USA 1972

[3] WMusial and S Butterfield ldquoFuture for offshorewind energy intheUnited Statesrdquo Tech Rep 36313National Renewable EnergyLaboratory Golden Colo USA 2004

[4] J M Jonkman ldquoDynamics modeling and loads analysis ofan offshore floating wind turbinerdquo Tech Rep 41958 NationalRenewable Energy Laboratory Golden Colo USA 2007

[5] J M Jonkman and D Matha ldquoDynamics of offshore floatingwind turbines-analysis of three conceptsrdquoWind Energy vol 14no 4 pp 557ndash569 2011


[6] S Zuo Y D Song L Wang and Q-W Song ldquoComputationallyinexpensive approach for pitch control of offshore wind turbineon barge floating platformrdquo The Scientific World Journal vol2013 Article ID 357849 9 pages 2013

[7] W Lei Y-L He X Jin J Du and S Ma ldquoDynamic simulationanalysis of floating wind turbinerdquo Journal of Central SouthUniversity Science and Technology vol 43 no 4 pp 1309ndash13142012

[8] L Wang B Wang Y Song et al ldquoFatigue loads alleviation offloating offshore wind turbine using individual pitch controlrdquoAdvances in Vibration Engineering vol 12 no 4 pp 377ndash3902013

[9] H Namik andK Stol ldquoIndividual blade pitch control of floatingoffshore wind turbinesrdquo Wind Energy vol 13 no 1 pp 74ndash852010

[10] M A Lackner ldquoAn investigation of variable power collectivepitch control for load mitigation of floating offshore windturbinesrdquoWind Energy vol 16 no 3 pp 435ndash444 2012

[11] Y D Song ldquoControl of wind turbines using memory-basedmethodrdquo Journal of Wind Engineering and Industrial Aerody-namics vol 85 no 3 pp 263ndash275 2000

[12] Y D Song B Dhinakaran and X Bao ldquoControl of windturbines using nonlinear adaptive field excitation algorithmsrdquoin Proceedings of the IEEE American Control Conference vol 3pp 1551ndash1555 Chicago Ill USA 2000

[13] L Wu W X Zheng and H Gao ldquoDissipativity-based slidingmode control of switched stochastic systemsrdquo IEEE Transac-tions on Automatic Control vol 58 no 3 pp 785ndash793 2013

[14] J F Conroy and R Watson ldquoFrequency response capabilityof full converter wind turbine generators in comparison toconventional generationrdquo IEEE Transactions on Power Systemsvol 23 no 2 pp 649ndash656 2008

[15] J Zaragoza J Pou A Arias C Spiteri E Robles and SCeballos ldquoStudy and experimental verification of control tuningstrategies in a variable speed wind energy conversion systemrdquoRenewable Energy vol 36 no 5 pp 1421ndash1430 2011

[16] J Jonkman S Butterfield W Musial and G Scott ldquoDefinitionof a 5-MW reference wind turbine for offshore system develop-mentrdquo Tech Rep TP 500-38060 National Renewable EnergyLaboratory Golden Colo USA 2009

[17] J M Jonkman ldquoInfluence of control on the pitch dampingof a floating wind turbinerdquo in Proceedings of the 46th AIAAAerospace Sciences Meeting and Exhibit Reno Nev USAJanuary 2008

[18] R M Sanner and J-J E Slotine ldquoGaussian networks for directadaptive controlrdquo IEEE Transactions on Neural Networks vol 3no 6 pp 837ndash863 1992

[19] Y Kourd D Lefebvre and N Guersi ldquoFault diagnosisbased on neural networks and decision trees application toDAMADICSrdquo International Journal of Innovative ComputingInformation and Control vol 9 no 8 pp 3185ndash3196 2013

[20] C K Ahn andM K Song ldquoNew sets of criteria for exponential1198712minus119871infinstability of Takagi-Sugeno fuzzy systems combinedwith

Hopfield neural networksrdquo International Journal of InnovativeComputing Information and Control vol 9 no 7 pp 2979ndash2986 2013

[21] S Sefriti J Boumhidi M Benyakhlef and I Boumhidi ldquoAdap-tive decentralized slidingmodeneural network control of a classof nonlinear interconnected systemsrdquo International Journal ofInnovative Computing Information and Control vol 9 no 7 pp2941ndash2947 2013

[22] K S Narendra andK Parthasarathy ldquoIdentification and controlof dynamical systems using neural networksrdquo IEEE Transac-tions on Neural Networks vol 1 no 1 pp 4ndash27 1990

[23] L Wu X Su P Shi and J Qiu ldquoModel approximation fordiscrete-time state-delay systems in the T-S fuzzy frameworkrdquoIEEE Transactions on Fuzzy Systems vol 19 no 2 pp 366ndash3782011

[24] X Su Z Li Y Feng and L Wu ldquoNew global exponentialstability criteria for interval-delayed neural networksrdquo Journalof Systems and Control Engineering vol 225 Proceedings of theInstitution of Mechanical Engineers no 1 pp 125ndash136 2011

[25] X Su P Shi L Wu and Y-D Song ldquoA novel control design ondiscrete-time Takagi-Sugeno fuzzy systems with time-varyingdelaysrdquo IEEE Transactions on Fuzzy Systems vol 20 no 6 pp655ndash671 2013

[26] H Li K L Shi and P G McLaren ldquoNeural-network-basedsensorless maximum wind energy capture with compensatedpower coefficientrdquo IEEE Transactions on Industry Applicationsvol 41 no 6 pp 1548ndash1556 2005

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Mooring line stabilizedTension leg platform withsuction pile anchors

Ballast stabilizedSpar buoy with catenarymooring drag-embeddedanchors

Buoyancy stabilizedBarge with catenary

mooring lines

Figure 1 Floating offshore wind turbine concepts (image from Google)

Therefore it is urgently needed to reduce fatigue loads andimprove output power quality for OFWT system by utilizingadvanced control strategies

Control of OFWT is a relatively new yet challengingresearch area There have been a large number of recentachievements in the research of blade pitch control forOFWTin the above-rated wind speed region [6ndash13] In our previouswork [6] we propose a computationally inexpensive robustadaptive control approach with memory-based compensa-tion for blade pitch control However works on the variablespeed control for OFWT system in below-rated wind speedregion are relatively few

In this study to address the challenge that the systemparameters of OFWT are varying and uncertain due to thecomplex external wind and wave disturbances an adaptiveradial basis function (RBF) neural network approach isproposed for torque control of OFWT system at speedslower than rated wind speedThe robust RBF neural networkweight adaptive rules are acquired based on the Lyapunovstability analysis The proposed torque controller based onRBF neural network is presented and mounted on a Sparfloating platform for performance comparison with thebaseline torque controller in the below-rated wind speedregion

Section 2 briefly presents the wind turbine model andthe Spar floating platform utilized in this paper Section 3describes the two implemented controllers the baselinetorque controller and the proposed variable torque con-troller based on RBF neural network Section 4 shows thesimulation and results in which performances of the abovetwo controllers are compared with each other on Sparfloating platform Eventually conclusions are reported inSection 5

Cp

120582

minus10

05

04

03

02

01

020

15

105

00

1020

30

120573 (∘ )

Figure 2 Power coefficients for VSVP wind turbine

2 Wind Turbine and Platform Models

21 5MWOffshoreWindTurbineModel Thebasic propertiesof future offshore turbines can be estimated by consideringthe amount of kinetic energy density in the wind which canbe converted into kinetic energy of the turbine shaft Theexpression for power produced by the wind is simply given by

119875119878=1

2119862119901 (120582 120573) 120588119860V

3 (1)

where 120588 is air density and 119860 is the swept area of the turbinerotor with a radius 119877 giving 119860 = 120587119877

2 V is wind speedpassing the rotor 119862

119901denotes power coefficient of wind

turbine which is a nonlinear function of the tip-speed ratio120582 and the pitch angle 120573 [14] Figure 2 depicts the curve of








120582 =

VTipV

=119877120596119903

V (2)




119862119901 (120582) = 1198881 (

1198882

1205821

minus 1198884) 119890minus11988851205821 + 1198886120582

1

1205821

= (1

120582minus 0035)

(3)




119875max =1

2

1205881205871198775119862119901 max


119903 (4)















119879120596119903

119892= 1198791

119892+

119879lowast

119892minus 1198791

119892

1205961199032 minus 1205961199031

(120596119903minus 1205961199031) (5)





1205961199032







Output layerx1

x2

xn

h1

h2

hm

w1

w2

wm

F

i j

(x)sum


Controlled

RBF NN

objectu(k)

y(k)

ym(k)

+

minus




ℎ119892= Φ (

10038171003817100381710038171003817119883 minus 119862

119892

10038171003817100381710038171003817) = exp(minus

10038171003817100381710038171003817119883 minus 119862

119892

10038171003817100381710038171003817

2

21198872119892

)

119892 = 1 2 119898

(6)





[1199081 1199082 119908119892 119908119898]119879


119865 (119909) = 119908119867 =

119898

sum

119892=1

119908119892Φ(10038171003817100381710038171003817119909 minus 119862

119892

10038171003817100381710038171003817) (7)



Rotor side


Tm

Jr

TLTH

Te

Jg

Kr Kg

120596r 120596g



119869119903119903 + 119870119903120596119903 + 119861119903120579119903 = 119879119898 (120596 120573 V ) minus 119879119871

119869119892119892+ 119870119892120596119892+ 119861119892120579119892= 119879119867minus 119879119890

119899 =

120596119892

120596119903

=119879119871

119879119867

(8)










119869119903+ 119870120596119903+ 119861120579119903= 119879119898(120596 120573 V ) minus 119899119879

119890 (9)


119869 = 119869119903 + 1198992119869119892

119870 = 119870119903+ 1198992119870119892

119861 = 119861119903 + 1198992119861119892

(10)

119879119898is given by

119879119898 =

1205881205871198773119862119901 (120582 120573)

2120582(V minus )2 (11)


119903= Γ (120596

119903 V) + 120574119879

119890 (12)


with

Γ (120596119903 V) =(1205881205871198773119862119901(120582 120573) 2120582) V2 minus 119870120596

119903minus 119861120579119903

119869

120574 =minus119899

119869

(13)



Γ (120596119903 V)120574

= Φ (120596119903 V) 119908 + 119871 (120596

119903 V) (14)




119890 = 120596119903minus 120596lowast

119903 (15)


120596lowast

119903=120582lowastV119877 (16)



119881 =1

minus21205741198902+

1

21205791

119908119879119908 (17)


= (120596119903minus 120596lowast

119903) (minus

Γ (120596119903 V)

120574minus 119879119890+120582lowastV119877120574

) minus1

1205791

119908119879 119908 (18)



= 119879119890= minusΦ (120596

119903 V) 119908 + 120581 (120596


119903) + 120596119903 (19)




119903 V) minus 120581 (120596


119903) minus 120596119903+120582lowastV119877120574

)

+ 119908119879(minusΦ119879(120596119903 V) (120596


119903) minus

1

1205791

119908)

(20)


119908 = minus 1205791 (Φ119879(120596119903 V) (120596


119903) + 120592

1003816100381610038161003816120596119903 minus 120596lowast

119903

1003816100381610038161003816 119908) (21)


= (120596119903minus 120596lowast

119903) (minus119871 (120596

119903 V) minus 120596

119903+120582lowastV119877120574

)


119903)2+ 120592

1003816100381610038161003816120596119903 minus 120596lowast

119903

1003816100381610038161003816 119908119879119908

(22)

RBF NNcontroller

Onlineadaptation

Te

Te

Pm

120596r

120596r

120596r

f(middot)

Φ(120596r )w

120596lowastr

120596lowastr




10038161003816100381610038161205961199031003816100381610038161003816 le 1198711

1003816100381610038161003816lowast

119903

1003816100381610038161003816 =

10038161003816100381610038161003816100381610038161003816

120582lowastV119877120574

10038161003816100381610038161003816100381610038161003816

le 1198712

le1003816100381610038161003816120596119903 minus 120596

lowast

119903

1003816100381610038161003816


lowast

119903

1003816100381610038161003816 minus 120592119908119879119908 + 120592119908

119879119908)

(23)

If |120596119903minus120596lowast

119903| ge (119871max +119871119908)120581+ (120592119908

2)4120581 or 119908 ge (1199082)+


le 0 (24)



120596lowast

119903= 119891 (V) =

120582lowastV119877 (25)






1000 200 300 400 500 600 700

02468

101214

Time (s)

Win

d an

d w

ave


minus6minus4minus2


100 200 300 400 500 600 7000

50010001500200025003000

Time (s)

Out

put p

ower

(MW

)







5 Conclusions


100 200 300 400 500 600 70005

1015202530

Time (s)


Gen

erat

or to

rque

(KNmiddotm

)






Acknowledgments


References




































Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















120582 =

VTipV

=119877120596119903

V (2)




119862119901 (120582) = 1198881 (

1198882

1205821

minus 1198884) 119890minus11988851205821 + 1198886120582

1

1205821

= (1

120582minus 0035)

(3)




119875max =1

2

1205881205871198775119862119901 max


119903 (4)















119879120596119903

119892= 1198791

119892+

119879lowast

119892minus 1198791

119892

1205961199032 minus 1205961199031

(120596119903minus 1205961199031) (5)





1205961199032







Output layerx1

x2

xn

h1

h2

hm

w1

w2

wm

F

i j

(x)sum


Controlled

RBF NN

objectu(k)

y(k)

ym(k)

+

minus




ℎ119892= Φ (

10038171003817100381710038171003817119883 minus 119862

119892

10038171003817100381710038171003817) = exp(minus

10038171003817100381710038171003817119883 minus 119862

119892

10038171003817100381710038171003817

2

21198872119892

)

119892 = 1 2 119898

(6)





[1199081 1199082 119908119892 119908119898]119879


119865 (119909) = 119908119867 =

119898

sum

119892=1

119908119892Φ(10038171003817100381710038171003817119909 minus 119862

119892

10038171003817100381710038171003817) (7)



Rotor side


Tm

Jr

TLTH

Te

Jg

Kr Kg

120596r 120596g



119869119903119903 + 119870119903120596119903 + 119861119903120579119903 = 119879119898 (120596 120573 V ) minus 119879119871

119869119892119892+ 119870119892120596119892+ 119861119892120579119892= 119879119867minus 119879119890

119899 =

120596119892

120596119903

=119879119871

119879119867

(8)










119869119903+ 119870120596119903+ 119861120579119903= 119879119898(120596 120573 V ) minus 119899119879

119890 (9)


119869 = 119869119903 + 1198992119869119892

119870 = 119870119903+ 1198992119870119892

119861 = 119861119903 + 1198992119861119892

(10)

119879119898is given by

119879119898 =

1205881205871198773119862119901 (120582 120573)

2120582(V minus )2 (11)


119903= Γ (120596

119903 V) + 120574119879

119890 (12)


with

Γ (120596119903 V) =(1205881205871198773119862119901(120582 120573) 2120582) V2 minus 119870120596

119903minus 119861120579119903

119869

120574 =minus119899

119869

(13)



Γ (120596119903 V)120574

= Φ (120596119903 V) 119908 + 119871 (120596

119903 V) (14)




119890 = 120596119903minus 120596lowast

119903 (15)


120596lowast

119903=120582lowastV119877 (16)



119881 =1

minus21205741198902+

1

21205791

119908119879119908 (17)


= (120596119903minus 120596lowast

119903) (minus

Γ (120596119903 V)

120574minus 119879119890+120582lowastV119877120574

) minus1

1205791

119908119879 119908 (18)



= 119879119890= minusΦ (120596

119903 V) 119908 + 120581 (120596


119903) + 120596119903 (19)




119903 V) minus 120581 (120596


119903) minus 120596119903+120582lowastV119877120574

)

+ 119908119879(minusΦ119879(120596119903 V) (120596


119903) minus

1

1205791

119908)

(20)


119908 = minus 1205791 (Φ119879(120596119903 V) (120596


119903) + 120592

1003816100381610038161003816120596119903 minus 120596lowast

119903

1003816100381610038161003816 119908) (21)


= (120596119903minus 120596lowast

119903) (minus119871 (120596

119903 V) minus 120596

119903+120582lowastV119877120574

)


119903)2+ 120592

1003816100381610038161003816120596119903 minus 120596lowast

119903

1003816100381610038161003816 119908119879119908

(22)

RBF NNcontroller

Onlineadaptation

Te

Te

Pm

120596r

120596r

120596r

f(middot)

Φ(120596r )w

120596lowastr

120596lowastr




10038161003816100381610038161205961199031003816100381610038161003816 le 1198711

1003816100381610038161003816lowast

119903

1003816100381610038161003816 =

10038161003816100381610038161003816100381610038161003816

120582lowastV119877120574

10038161003816100381610038161003816100381610038161003816

le 1198712

le1003816100381610038161003816120596119903 minus 120596

lowast

119903

1003816100381610038161003816


lowast

119903

1003816100381610038161003816 minus 120592119908119879119908 + 120592119908

119879119908)

(23)

If |120596119903minus120596lowast

119903| ge (119871max +119871119908)120581+ (120592119908

2)4120581 or 119908 ge (1199082)+


le 0 (24)



120596lowast

119903= 119891 (V) =

120582lowastV119877 (25)






1000 200 300 400 500 600 700

02468

101214

Time (s)

Win

d an

d w

ave


minus6minus4minus2


100 200 300 400 500 600 7000

50010001500200025003000

Time (s)

Out

put p

ower

(MW

)







5 Conclusions


100 200 300 400 500 600 70005

1015202530

Time (s)


Gen

erat

or to

rque

(KNmiddotm

)






Acknowledgments


References




































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











Output layerx1

x2

xn

h1

h2

hm

w1

w2

wm

F

i j

(x)sum


Controlled

RBF NN

objectu(k)

y(k)

ym(k)

+

minus




ℎ119892= Φ (

10038171003817100381710038171003817119883 minus 119862

119892

10038171003817100381710038171003817) = exp(minus

10038171003817100381710038171003817119883 minus 119862

119892

10038171003817100381710038171003817

2

21198872119892

)

119892 = 1 2 119898

(6)





[1199081 1199082 119908119892 119908119898]119879


119865 (119909) = 119908119867 =

119898

sum

119892=1

119908119892Φ(10038171003817100381710038171003817119909 minus 119862

119892

10038171003817100381710038171003817) (7)



Rotor side


Tm

Jr

TLTH

Te

Jg

Kr Kg

120596r 120596g



119869119903119903 + 119870119903120596119903 + 119861119903120579119903 = 119879119898 (120596 120573 V ) minus 119879119871

119869119892119892+ 119870119892120596119892+ 119861119892120579119892= 119879119867minus 119879119890

119899 =

120596119892

120596119903

=119879119871

119879119867

(8)










119869119903+ 119870120596119903+ 119861120579119903= 119879119898(120596 120573 V ) minus 119899119879

119890 (9)


119869 = 119869119903 + 1198992119869119892

119870 = 119870119903+ 1198992119870119892

119861 = 119861119903 + 1198992119861119892

(10)

119879119898is given by

119879119898 =

1205881205871198773119862119901 (120582 120573)

2120582(V minus )2 (11)


119903= Γ (120596

119903 V) + 120574119879

119890 (12)


with

Γ (120596119903 V) =(1205881205871198773119862119901(120582 120573) 2120582) V2 minus 119870120596

119903minus 119861120579119903

119869

120574 =minus119899

119869

(13)



Γ (120596119903 V)120574

= Φ (120596119903 V) 119908 + 119871 (120596

119903 V) (14)




119890 = 120596119903minus 120596lowast

119903 (15)


120596lowast

119903=120582lowastV119877 (16)



119881 =1

minus21205741198902+

1

21205791

119908119879119908 (17)


= (120596119903minus 120596lowast

119903) (minus

Γ (120596119903 V)

120574minus 119879119890+120582lowastV119877120574

) minus1

1205791

119908119879 119908 (18)



= 119879119890= minusΦ (120596

119903 V) 119908 + 120581 (120596


119903) + 120596119903 (19)




119903 V) minus 120581 (120596


119903) minus 120596119903+120582lowastV119877120574

)

+ 119908119879(minusΦ119879(120596119903 V) (120596


119903) minus

1

1205791

119908)

(20)


119908 = minus 1205791 (Φ119879(120596119903 V) (120596


119903) + 120592

1003816100381610038161003816120596119903 minus 120596lowast

119903

1003816100381610038161003816 119908) (21)


= (120596119903minus 120596lowast

119903) (minus119871 (120596

119903 V) minus 120596

119903+120582lowastV119877120574

)


119903)2+ 120592

1003816100381610038161003816120596119903 minus 120596lowast

119903

1003816100381610038161003816 119908119879119908

(22)

RBF NNcontroller

Onlineadaptation

Te

Te

Pm

120596r

120596r

120596r

f(middot)

Φ(120596r )w

120596lowastr

120596lowastr




10038161003816100381610038161205961199031003816100381610038161003816 le 1198711

1003816100381610038161003816lowast

119903

1003816100381610038161003816 =

10038161003816100381610038161003816100381610038161003816

120582lowastV119877120574

10038161003816100381610038161003816100381610038161003816

le 1198712

le1003816100381610038161003816120596119903 minus 120596

lowast

119903

1003816100381610038161003816


lowast

119903

1003816100381610038161003816 minus 120592119908119879119908 + 120592119908

119879119908)

(23)

If |120596119903minus120596lowast

119903| ge (119871max +119871119908)120581+ (120592119908

2)4120581 or 119908 ge (1199082)+


le 0 (24)



120596lowast

119903= 119891 (V) =

120582lowastV119877 (25)






1000 200 300 400 500 600 700

02468

101214

Time (s)

Win

d an

d w

ave


minus6minus4minus2


100 200 300 400 500 600 7000

50010001500200025003000

Time (s)

Out

put p

ower

(MW

)







5 Conclusions


100 200 300 400 500 600 70005

1015202530

Time (s)


Gen

erat

or to

rque

(KNmiddotm

)






Acknowledgments


References




































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











Γ (120596119903 V)120574

= Φ (120596119903 V) 119908 + 119871 (120596

119903 V) (14)




119890 = 120596119903minus 120596lowast

119903 (15)


120596lowast

119903=120582lowastV119877 (16)



119881 =1

minus21205741198902+

1

21205791

119908119879119908 (17)


= (120596119903minus 120596lowast

119903) (minus

Γ (120596119903 V)

120574minus 119879119890+120582lowastV119877120574

) minus1

1205791

119908119879 119908 (18)



= 119879119890= minusΦ (120596

119903 V) 119908 + 120581 (120596


119903) + 120596119903 (19)




119903 V) minus 120581 (120596


119903) minus 120596119903+120582lowastV119877120574

)

+ 119908119879(minusΦ119879(120596119903 V) (120596


119903) minus

1

1205791

119908)

(20)


119908 = minus 1205791 (Φ119879(120596119903 V) (120596


119903) + 120592

1003816100381610038161003816120596119903 minus 120596lowast

119903

1003816100381610038161003816 119908) (21)


= (120596119903minus 120596lowast

119903) (minus119871 (120596

119903 V) minus 120596

119903+120582lowastV119877120574

)


119903)2+ 120592

1003816100381610038161003816120596119903 minus 120596lowast

119903

1003816100381610038161003816 119908119879119908

(22)

RBF NNcontroller

Onlineadaptation

Te

Te

Pm

120596r

120596r

120596r

f(middot)

Φ(120596r )w

120596lowastr

120596lowastr




10038161003816100381610038161205961199031003816100381610038161003816 le 1198711

1003816100381610038161003816lowast

119903

1003816100381610038161003816 =

10038161003816100381610038161003816100381610038161003816

120582lowastV119877120574

10038161003816100381610038161003816100381610038161003816

le 1198712

le1003816100381610038161003816120596119903 minus 120596

lowast

119903

1003816100381610038161003816


lowast

119903

1003816100381610038161003816 minus 120592119908119879119908 + 120592119908

119879119908)

(23)

If |120596119903minus120596lowast

119903| ge (119871max +119871119908)120581+ (120592119908

2)4120581 or 119908 ge (1199082)+


le 0 (24)



120596lowast

119903= 119891 (V) =

120582lowastV119877 (25)






1000 200 300 400 500 600 700

02468

101214

Time (s)

Win

d an

d w

ave


minus6minus4minus2


100 200 300 400 500 600 7000

50010001500200025003000

Time (s)

Out

put p

ower

(MW

)







5 Conclusions


100 200 300 400 500 600 70005

1015202530

Time (s)


Gen

erat

or to

rque

(KNmiddotm

)






Acknowledgments


References




































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










1000 200 300 400 500 600 700

02468

101214

Time (s)

Win

d an

d w

ave


minus6minus4minus2


100 200 300 400 500 600 7000

50010001500200025003000

Time (s)

Out

put p

ower

(MW

)







5 Conclusions


100 200 300 400 500 600 70005

1015202530

Time (s)


Gen

erat

or to

rque

(KNmiddotm

)






Acknowledgments


References




































Volume 2014




Journal of











Journal of


Function Spaces






Algebra







































Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









Documents

Research Article Variable Torque Control of …downloads.hindawi.com/journals/aaa/2014/903493.pdfResearch Article Variable Torque Control of Offshore Wind Turbine on Spar Floating