research article control of variable speed variable pitch...

Research ArticleControl of Variable Speed Variable Pitch Wind Turbineat Above and Below Rated Wind Speed

Saravanakumar Rajendran and Debashisha Jena

Department of Electrical Engineering National Institute of Technology Karnataka Surathkal 575025 India

Correspondence should be addressed to Debashisha Jena bapu4002gmailcom

Received 12 May 2014 Revised 1 October 2014 Accepted 3 October 2014 Published 22 October 2014

Academic Editor Adrian Ilinca

Copyright copy 2014 S Rajendran and D Jena This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

The paper presents a nonlinear approach to wind turbine (WT) using two-mass model The main aim of the controller in the WTis to maximize the energy output at varying wind speed In this work a combination of linear and nonlinear controllers is adaptedto variable speed variable pitch wind turbines (VSVPWT) systemThemajor operating regions of theWT are below (region 2) andabove rated (region 3) wind speed In these regions generator torque control (region 2) and pitch control (region 3) are used Thecontrollers in WT are tested for below and above rated wind speed for step and vertical wind speed profile The performances ofthe controllers are analyzed with nonlinear FAST (Fatigue Aerodynamics Structures and Turbulence) WT dynamic simulationIn this paper two nonlinear controllers that is sliding mode control (SMC) and integral sliding mode control (ISMC) have beenapplied for region 2 whereas for pitch control in region 3 conventional PI control is used In ISMC the sliding manifold makes useof an integral action to show effective qualities of control in terms of the control level reduction and sliding mode switching controlminimization

1 Introduction

In recent years wind energy is one of the major renewableenergy sources because of environmental social and eco-nomic benefits The major classification of wind turbines(WT) is fixed speed wind turbine (FSWT) and variable speedwind turbine (VSWT) Compared with FSWT VSWT havemany advantages such as improved energy capture reductionin transient load and better power conditioning [1] Forany kind of WT control strategies play a major role onWT characteristics and transient load to the network [2] InVSWT the operating regions are classified in to two majorcategories that is below and above rated wind speed Atbelow rated wind speed the main objective of the controller(ie torque control) is to optimize thewind energy capture byavoiding the transients in the turbine components especiallyin the drive train At above rated wind speed the majorobjective of the controller (ie pitch control) is to maintainthe rated power of the WT For extracting the maximumpower at below rated wind speed the WT rotor speed should

operate at reference rotor speed which is derived fromeffective wind speed In general wind speed is measured bythe anemometer which is varying along the rotor shift area soit is difficult to get themeanwind speed by thismeasurementSeveral literatures are addressing this issue by estimating theeffective wind speed But some other literatures assume thatthe effective wind speed is directly available [3 4] In [5] acombination of proportional integral (PI) and SMC is usedto adjust the turbine rotor speed for extracting maximumpower without estimating the wind speed In [6] a PI basedtorque control is used to control the WT where optimalgains are achieved by particle swarm optimization and fuzzylogic theory without estimating the wind speed Estimationof effective wind speed by an inversion of static aerodynamicmodel with known pitch angle is discussed in [7] Nonlinearstatic and dynamic state feedback linearization control isaddressed in [8 9] where both the single- and two-massmodel are taken into consideration and the wind speed isestimated by using Newton Raphson (NR) To accommodatethe parameter uncertainty and robustness a higher order

Hindawi Publishing CorporationJournal of Wind EnergyVolume 2014 Article ID 709128 14 pageshttpdxdoiorg1011552014709128

2 Journal of Wind Energy

Rotoraerodynamics

Drivetrains GeneratorWind

speed120592

120596r 120596g

Ta TgPe

Figure 1 Schematic of WT

slidingmode controller is proposed in [10] which ensures thestability of the controller in both the regions that is belowand above rated speed An extended Kalman Filter basedwind speed estimator is discussed in [11] which uses theconventional ATF and ISC for controlling the WT In [12]fuzzy logic control has been proposed and the effective windspeed is estimated using sequential Monte Carlo simulatorDiscrete time optimal LQRLTR based on optimal quadraticfunction is studied in [13] In [14] the effective wind speedis estimated by the frequency domain data fusion andthe observer is formulated based on the mixed sensitivityproblem with linear matrix Inequalities

For above rated wind speed authors in [15] discussed themultivariable control strategy by combining the nonlinearstate feedback control for region 2 with linear control forregion 3 Finally the results are compared with the existingcontrol strategy such as PID and LQG In [16] the WTcontroller is the combination of linear control for blade pitchangle with 119867

infinnonlinear torque control Nowadays fuzzy

and neural networks (NN) are the powerful soft computingmethods for controlling nonlinear systems Authors in [17]discussed a fuzzy 119875 + 119868 and neurofuzzy controller forcontrolling the WT at above rated wind speed PSO is usedto train the adaptive neurofuzzy controllerWT control usingadaptive radial basic NN used for both pitch and torquecontroller is addressed in [18] Active disturbance rejectionbased pitch control for variable speedWT is presented in [19]where the extended state observer is used to estimate the statevariable and disturbance In [20] the controller has two partsthat is nonlinear feed-forward path and linear feedbackpath The feed-forward path uses the information about thedesired power output wind velocity and the turbine speedto determine the pitch angle required In [21] NN based pitchangle control is implemented by usingmultilayer perceptronswith back propagation learning algorithm and radial basisfunction network for tuning the pitch controller

This paper uses a PI control for pitch control and twononlinear controllers such as SMC and ISMC for torquecontrolThe paper is organized as follows Section 2 discussesthe modeling of two-mass model Problem formulation andcontrol objectives are discussed in Section 3 The proposedcontrollers for all the regions are discussed in Section 4Section 5 discusses the validation of the results using FASTsimulator Finally in Section 6 a conclusion is drawn fromthe obtained results which concludes that the proposedcontrollers are working fine for controlling the WT at belowand above rated wind speed

2 WT Model

WT is a device which converts the kinetic energy of thewind in to electric energy Simulation complexity of the WT

purely depends on the type of control objectives In case ofWT modelling complex simulators are required to verify thedynamic response of multiple components and aerodynamicloading Generally dynamic loads and interaction of largecomponents are verified by the aeroelastic simulator Fordesigning a WT controller instead of going with complexsimulator the design objective can be achieved by usingsimplified mathematical model In this work WT modelis described by the set of nonlinear ordinary differentialequationwith limited degree of freedomThis paper describesthe control law for a simplified mathematical model with theobjective of optimal power capture at below and above ratedwind speed The proposed controllers are validated for FASTWTmodel in three different cases of wind speed profile suchas below rated wind speed (region 2) above rated wind speed(region 3) and a smooth transition between these two windspeeds (region 25) The parameter of the two-mass modelis given in Appendix A Generally VSWT system consists ofthe following components that is aerodynamics drive trainsand generator shown in Figure 1

Equation (1) gives the nonlinear expression for aerody-namic power capture by the rotor

119875119886=1

21205881205871198772

119862119875(120582 120573) 120592

3

(1)

From (1) it is clear that the aerodynamic power (119875119886) is directly

proportional to the cube of the wind speed The powercoefficient 119862

119875is the function of blade pitch angle (120573) and tip

speed ratio (120582)The tip speed ratio is defined as ratio betweenlinear tip speed and wind speed

120582 =120596119903119877

120592 (2)

Generally wind speed is stochastic nature with respect totime Because of this tip speed ratio gets affected which leadsto variation in power coefficient The relationship betweenaerodynamic torque (119879

119886) and the aerodynamic power is given

in (3)

119875119886= 119879119886120596119903 (3)

119879119886=1

21205881205871198773

119862119902(120582 120573) 120592

2

(4)

where 119862119902is the torque coefficient given as

119862119902(120582 120573) =

119862119875(120582 120573)

120582 (5)

Substituting (5) in (4) we get

119879119886=1

21205881205871198773119862119875(120582 120573)

1205821205922

(6)

Journal of Wind Energy 3

Table 1 Coefficients values

1198860= 01667 119886

3= minus001617

1198861= minus02558 119886

4= 000095

1198862= 0115 119886

5=minus205 times 10

minus5

0 2 4 6 8 10 12 140

01

02

03

04

05

120582

Cp

Figure 2 119862119901versus 120582 curve

In above equation the nonlinear term is 119862119901which can be

approximated by the 5th order polynomial given in (7)

119862119875(120582) =

5

sum

119899=0

119886119899120582119899

= 1198860+ 1205821198861+ 1205822

1198862+ 1205823

1198863+ 1205824

1198864+ 1205825

1198865

(7)

where 1198860to 1198865are the WT power coefficient

The values of approximated coefficients are given inTable 1 Figure 2 shows the 119862

119901versus 120582 curve

Figure 3 shows the two-mass model of the WT Equation(8) represents dynamics of the rotor speed 120596

119903with rotor

inertia 119869119903driven by the aerodynamic torque (119879

119886)

119869119903119903= 119879119886minus 119879ls minus 119870119903120596119903 (8)

Breaking torque acting on the rotor is low speed shaft torque(119879ls) which can be derived by using stiffness and dampingfactor of the low speed shaft given in (9)

119879ls = 119861ls (120579119903 minus 120579ls) + 119870ls (120596119903 minus 120596ls) (9)

Equation (10) represents dynamics of the generator speed 120596119892

with generator inertia 119869119892driven by the high speed shaft torque

(119879hs) and braking electromagnetic torque (119879em)

119869119892119892= 119879hs minus 119870119892120596119892 minus 119879em (10)

Gearbox ratio is defined as

119899119892=119879ls119879hs

=

120596119892

120596ls (11)

119879ls = 119899119892119879hs (12)

From (10) the high speed shaft torque 119879hs can be expressed as

119879hs = 119869119892119892 + 119870119892120596119892 + 119879em (13)

Putting the values of 119879hs from (13) in (12) we get

119879ls = 119899119892 (119869119892119892 + 119870119892120596119892 + 119879em) (14)

120596gTaJg

Kg

Jr

TemThs

TlsB ls

Kls

Kr

120596t

Gear box (ng)

Figure 3 Two-mass model of the aero turbine

Pow

er

Aerodynamic power

Region 1 Region 2 Region 3Wind speedWratedWcutin

Wcutout

Prated

Region 25

Figure 4 Power operating region of wind turbines

3 Problem Formulation

Figure 4 shows the various operating region in VSVPWTRegion 1 represents the wind speed below the cut in wind

speed Region 2 represents the wind speed between cut inand rated wind speed In this region the main objective isto maximize the energy capture from the wind with reducedoscillation on the drive train Region 25 represents the windspeed nearer to the rated wind speed that is transient periodRegion 3 describes the wind speed above the rated windspeed In this region pitch controller is used to maintain theWT at its rated power

31 Control Structure The time response of WT electricalsystem is much faster than the other parts of the WT Thismakes it possible to decouple the generator and the aero-turbine control designs and thus define a cascaded controlstructure around two control loops

(1) The inner control loop consists of electrical generatorwith power converters

(2) The outer loop has the aeroturbine control whichgives the reference to the inner loop

Figure 5 shows the WT control levels In this paper wemade an assumption that the inner loop is well controlled


Aero

turbine

control

Pitch anglereference

Generatortorque

Level 1Level 2

referenceDFIG flux andtorque control

Pitch actuatorangle control

Fast WTnonlinear

model

120573120573

Tem

Pe

∙120573

120596r

120573ref

Temref

Figure 5 WT control levels

32 Control Objective In this work we consider two objec-tives First objective is torque control for optimal powerextractionwith reduced oscillation on the drive train at belowrated wind speed To achieve the above objective (Region2) the blade pitch angle (120573opt) and tip speed ratio (120582opt) areset to be its optimal value In order to achieve the optimaltip speed ratio the rotor speed must be adjusted to thereferenceoptimal rotor speed (120596

119903opt) by adjusting the control

input that is generator torque (119879119892) Equation (15) defines the

referenceoptimal rotor speed

120596119903opt

= 120596ref =120582opt120592

119877 (15)

Second objective is the pitch control for above rated windspeed where torque control input is consider as maximumvalue In region 3 only the pitch angle is varying accordingto the difference between the nominal speed and outputgenerator speedThis work addresses both controller designsto achieve the control objectives for below and above windspeed

33 Classical Control Techniques In region 2 in order tocompare the results of proposed and existing conventionalcontrollers a brief description of the well-known controltechniques that is ISC (indirect speed control) and ATF(aerodynamic torque feed-forward) are discussed in thissection In ISC it is assumed that the WT is stable around itsoptimal aerodynamic efficiency curve The two-mass modelcontrol signal is given in (16)

119879em = 119870opths1205962

119892minus 119870119905hs120596119892 (16)

where

119870opths = 051205881205871198775

11989931198921205823

opt119862119875opt (17)

119870119905hs= (119870

119892+119870119903

1198992119892

) (18)

where119870119905hsis the low speed shaft damping coefficient brought

up to the high speed shaftIn ATF proportional control law is used to control the

WT The rotor speed and the aerodynamic torque (119879119886) are

estimated using Kalman filter which is used to control theWT [22] The control law is given in (19)

119879em =1

119899119892

119886minus (

119870119903

1198992119892

+ 119870119892) 119892minus119870119862

1198992119892

(120596119892ref

minus 120596119892) (19)

120596119892ref

= 119899119892119896119908

radic119886 (20)

119896119908=

1

radic119896opt

= radic21205823

opt

1205881205871198775119862119875opt

(21)

119896opt =1

2120588120587

1198775

1205823

opt119862119875opt (22)

The optimal value of proportional gain is found to be 119870119888=

3 times 104 The above existing control techniques have three

major drawbacks that is the ATF control havingmore steadystate error so an accurate value of 120596

119892refis needed and in


ISC the WT has to operate at its optimal efficiency curvewhich introduces more power loss for high varying windspeed Both the controllers are not robust with respect todisturbances To avoid the above drawbacks two nonlinearcontrollers that is ISMC and SMC are proposed in region 2For region 3 control conventional proportional Integral (PI)control is considered

34 Wind Speed Estimation The estimation of effective windspeed is related to aerodynamic torque and rotor speedprovided the pitch angle is at optimal value

119879119886=1

21205881205871198773119862119875(120582)

1205821205922

(23)

The aerodynamic power coefficient is approximated with 5thorder polynomial as given in (7)

119865 (120592) = 119879119886minus1

21205881205871198773119862119875(120582)

1205821205922

(24)

The estimated wind speed can be obtained by solving (24)usingMNRThe above equation has unique solution at belowrated region With known 120592 the optimal rotor speed 120596

119903optis

calculated by using (15) The above wind speed estimationis only considered for below rated wind speed conditionAppendix B gives the steps for MNR algorithm

4 Control Techniques for Below and AboveRated Wind Speed

41 Sliding Mode Control (SMC) for Optimal Power Extrac-tion The proposed control strategy combines MNR basedestimator with second order sliding mode controller SMC isone of the effective nonlinear robust approaches with respectto system dynamics and invariant to uncertainties Lyapunovstability approach is used in SMC to keep the nonlinearsystem under control The objective of the controller is tooptimize the energy capture from the wind by tracking thereference rotor speed In general designing SMC has twosteps First to find the sliding surface second is to develop thecontrol signal 119880

Time varying sliding surface is defined as

119878 = (120582 +119889

119889119905)

119899minus1

119890 (119905) (25)

where 119890(119905) is defined as the difference between rotor speedand reference rotor speed 119899 is the order of the system and 120582is positive constant Consider

119890 (119905) = 120596119903(119905) minus 120596ref (119905) (26)

Finally the sliding surface is defined as

119878 (119905) = 120582119890 (119905) + 119890 (119905) (27)

Generally three types of reaching law are proposed [23]Direct switching function method is applied in this workhaving the condition

119878 119878 le 0 (28)

The control should be chosen in such a way that thefollowing candidate Lyapunov function satisfies Lyapunovstability criteria Lyapunov candidate function is defined as

119881 =1

21198782

(29)

A sufficient condition is that the system output should stayon the sliding surface that is 119878(119905) By taking the derivate ofthe Lyapunov function 119889119881119889119905 le 0 only when 119878(119905) = 0 Fromthis it is clear that the defined control law is able to track thetime varying reference signal that is rotor speed reference If119881(0) = 0 then 119889119881119889119905 = 0 from this 119889119881119889119905 = 119878(119889119878119889119905) so119889119878119889119905 = 0

119889119881

119889119905= 119878

119889119878

119889119905= 119878 (120582 119890 (119905) + 119890 (119905)) (30)

The convergence condition is given by the Lyapunov equationwhich makes the sliding surface attractive and invariant Atsteady state the rotor should track the optimal rotor speedasymptotically that is 120596

119903(119905) rarr 120596ref(119905) as 119905 rarr infin Consider

= 119878 119878 = 119878 (120582 119890 (119905) + 119890 (119905))

= 119878 [120582 (119903(119905) minus ref (119905) + 119890 (119905))]

(31)

le 0meets the following condition

120582 (119903minus ref) + 119890 (119905)

lt 0 for 119878 gt 0= 0 for 119878 = 0gt 0 for 119878 lt 0

(32)

The values of the control variable are to be set in such a waythat the systemwill be stableThese control variables are givenas follows

119880

lt 119879em for 119878 gt 0= 119879em for 119878 = 0gt 119879em for 119878 lt 0

(33)

In order to derive the control input that is 119879em the followingconversion has been made By substituting the

119903(119905) in (31)

we get

120582(1

119869119903

119879119886minus119870119903

119869119903

120596119903minus1

119869119903

119879ls minus ref) + 119890 (119905) = 0 (34)

By using the relationship given in (14) finally we will get

120582(119879119886

119869119903

minus119870119903

119869119903

120596119903minus

119899119892119869119892119892

119869119903

minus

119899119892119870119892120596119892

119869119903

minus

119899119892

119869119903

119879em minus ref)

+ 119890 (119905) = 0

(35)

The control structure is defined as

119879em =119879119886

119899119892

minus119870119903

119899119892

minus 119869119892119892minus 119870119892120596119892minus119869119903

119899119892

ref +119869119903

120582119899119892

119890 (119905) (36)

Generally the SMC have two parts that is equivalentcontrol 119880eq and switching control 119880sw The switching is used


to avoid the parameter uncertainty and disturbances andthe equivalent control is used to control the overall systembehaviour that is tracking control

119880 (119905) = 119880eq (119905) + 119880sw (119905) (37)

The switching control is defined in two ways

119880sw (119905) = 119896 sign (119878) or 119896 tanh( 119878120593) (38)

Generally the SMC with signum function introducesthe chattering phenomenon in the system This chatteringintroduces high frequency dynamics in the WT systemthat is control action to the system in undesirable Toneglect this chattering a smooth control discontinuity isintroduced As the signum function varies between minus1 and+1 discontinuously it is replaced by a tangent hyperbolicfunction (tanh) Finally the torque control structure is givenin (39)

119879em =119879119886

119899119892

minus119870119903

119899119892


119899119892

ref

+119869119903

120582119899119892

119890 (119905) +119869119903

119899119892120582119896 tanh( 119878

120593)

(39)

where ldquo119896rdquo is the sliding gain which is chosen based onthe empirical results from the simulation In summary thecontroller performance depends on the sliding gain and theboundary layer thickness By using trial and errormethod thesliding gain is found to be 02 and boundary layer thicknessis 1 for simulation If the gain value increases more than02 it introduces more oscillation on the low speed shaftThe boundary layer is chosen arbitrarily that depends on thesystem performance

42 Integral Sliding Mode Control (ISMC) for Optimal PowerExtraction To improve the sliding surface and overcome thesteady state error the integral action is included in the slidingsurface

A sliding surface is defined as

119878 (119905) = (120582 +119889

119889119905)

119899minus1

119890 (119905) + 119870119894int

infin

0

119890 (119905) 119889119905 (40)

where119870119894is the integral gain

The order of the system 119899 = 2 then the sliding surfacemodified as

119878 (119905) = (120582 +119889

119889119905)

1

119890 (119905) + 119870119894int

infin

0

119890 (119905) 119889119905

= 120582119890 (119905) + 119890 (119905) + 119870119894int

infin

0

119890 (119905) 119889119905

(41)

By taking the same Lyapunov function as mentioned inSMC with the same condition

= 119878 119878 = 119878 (120582 119890 (119905) + 119890 (119905) + 119870119894119890 (119905))

= 119878 [120582 (119903(119905) minus ref (119905) + 119890 (119905)) + 119870

119894119890 (119905)]

(42)


120582 (119903minus ref) + 119890 (119905) + 119870

119894119890 (119905)


(43)


119903(119905) in (41)

we get

120582(1

119869119903

119879119886minus119870119903

119869119903

120596119903minus1

119869119903

119879ls minus ref) + 119890 (119905) + 119870119894119890 (119905) = 0 (44)

Finally the torque control structure is given in

119879em =119879119886

119899119892

minus119870119903

119899119892

120596119903minus 119869119892119892minus 119870119892120596119892minus119869119903

119899119892

ref

+119869119903

119899119892120582119890 (119905) +

119869119903

119899119892120582119870119894119890 (119905) +

119869119903

119899119892120582119896 tanh( 119878

120593)

(45)

The necessary condition of ISMC is to eliminate the steadystate error in conventional SMCThe linear sliding surface is

119878 (119905) = 119890 (119905) + 120582119890 (119905) (46)

By taking the Laplace transform of above equation

119878 (119878) = 119864 (119878) [119878 + 120582] (47)

The steady state error is calculated by applying the final valuetheorem (FVT) to conventional sliding surface

lim119905rarrinfin

119890 (119905) = lim119904rarr0

119878119864 (119878) = lim119904rarr0

119878

119878 + 120582sum(119878) =

1

120582119896120593 (48)

Equation (48) represents the conventional SMC havingsteady state error which is proportional to boundary layerthickness (120593) and inversely proportional to the coefficient 120582and sliding gain 119896

The steady state error is calculated by applying the finalvalue theorem (FVT) to integral sliding surface

119878 (119905) = 120582 119890 (119905) + 119896119894119890 (119905) + 119890 (119905) (49)


119878 lowast 119878 (119878) = 119864 (119878) [1198782

+ 120582119878 + 119896119894] (50)

lim119905rarrinfin

119890 (119905) = lim119904rarr0

119878119864 (119878) = lim119904rarr0

119878

1198782 + 120582119878 + 119896119894

lim119904rarr0

119878sum (119878) = 0

(51)

43 Pitch Controller For above rated wind speed the torquecontrol output is fixed to its rated value that is maximumvalue of the control input In this condition a linear pitchcontrol is introduced The gain scheduled pitch control isallowed to maintain the generator speed around its nominal


Table 2 CART 3 WT characteristics

Rotor diameter 433mGear ratio 43165Tower height 366mNominal power 600 kwMaximum generator torque 3753 kNm

value [24] To achieve the above objective proportional +integral (PI) control is introduced

Δ120573 = 119870119901119890 (119905) + 119870

119894int 119890 (119905) 119889119905

119890 (119905) = 120596119892norm

minus 120596119892

(52)

where 120596119892norm

is the nominal value of the generator speed thatis 1600 rpm and 120596

119892is the generator speed

5 Validation Results

The numerical simulations are performed on the CART(controls advanced research turbine) WT model and thecharacteristics are given in Table 2 The CART is located atthe NREL (National Renewable Energy Laboratory) NationalWind center near Golden Colorado The CART3 is a three-blade variable speed variable pitch WT with nominal powerrating of 600 kW It has mainly three parts that is rotortower and nacelle The rotor includes blade and their attach-ment points are called hub which is maintained by the lowspeed shaft The tower is a cantilever beam which supports ayaw bearing and nacelle The yaw bearing allows the turbineto rotate in the wind speed direction The nacelle housesthe complete drive train assembly It contains the gearboxgenerator and low speed shaft The gearbox is directlyconnected to the squirrel cage induction generator throughhigh speed shaft The generator is connected to the gridthrough power electronics that can directly control generatortorque [25] The power electronics consists of three-phasePWM (pulse width modulation) converters with a constantdc link voltage The main objective of the grid side converteris maintaining the dc link voltage constant [26 27]

51 Description for Simulator FAST is an aeroelastic WTsimulator which is developed by NREL It can able to modelboth two- and three-blade horizontal axis wind turbine(HAWT) This FAST code can predict both extreme andfatigue loads The tower and flexible blade are modeledby using the assumed mode method Other componentsare modeled as rigid bodies An advanced certified code isused in FAST to model the aerodynamic behavior of theWT WT loads are calculated by using BEM (blade elementmomentum) and multiple component of wind speed profile[28] FAST code is approved by the Germanischer Lloyd (GL)Windenergie GmbH for calculating onshore WT loads fordesign and certification [29] Due to the above advantagesand exact nonlinear modeling of the WT the proposedcontrollers are validated by using FAST In general three blade

0 100 200 300 400 500 6005

556

657

758

859

95

Time (s)

Win

d sp

eed

(ms

)

Mean wind speed 7ms

Figure 6 Test wind speed profile

turbine has 24 DOF (degree of freedom) to represent thewind turbine dynamics In this work 3 DOF is considered forWT that is variable generator rotor speed and blade teeterFAST codes are interface with 119878-function and implementedwith Simulink model FAST uses an AeroDyn file as an inputfor aerodynamic part AeroDyn file contains aerodynamicanalysis routine and it requires status of a WT from thedynamic analysis routine and returns the aerodynamic loadsfor each blade element to the dynamic routine [30] Windprofile acts as the input file forAeroDynThewind input file isgenerated by using TurbSimwhich is developed by theNREL

In order to analysis the performance of the WT threecases are chosen

52 Below RatedWind Speed (Region 2) The test wind profilewith full field turbulence is generated by using TurbSimdeveloped by NREL Figure 6 shows the hub height windspeed profile In general any wind speed consists of twocomponents that is mean wind speed and turbulence com-ponent The test wind speed consists of 10min dataset thatwas generated using Class AKaimal turbulence spectra It hasthemean value of 7ms at the hubheight turbulence intensityof 25 and normal IEC (International ElectrotechnicalCommission) turbulence type The above wind speed is usedas the excitation of WT

The proposed and conventional controllers are imple-mented using FAST interface with MATLAB SimulinkTable 3 shows the comparisons of proposed and conventionalcontrollers The main objectives of the controllers are tomaximize the energy capture with reduced stress on the drivetrain The efficiency of the controllers is compared by usingthe following terms that is aerodynamic (120578aero) and electrical(120578elec) efficiency given in (53)

120578aero () =int119905fin

119905ini119875119886119889119905

int119905fin

119905ini119875119886opt119889119905

120578elec () =int119905fin

119905ini119875119890119889119905

int119905fin

119905ini119875119886opt119889119905

(53)


Table 3 Comparison of different control strategy based on two-mass model using FAST simulator

Control strategy ISC ATF SMC ISMCStd (119879ls) (kNm) 9629 2303 2184 1359Max (119879ls) (kNm) 4562 1308 1314 734Std (119879em) (kNm) 0142 0369 0252 0198Max (119879em) (kNm) 1010 2500 1690 1260120578elec () 6973 7287 7689 7626120578aero () 8559 8506 9678 9656

0 100 200 300 400 500 6004

5

6

7

8

9

10

Time (s)

Win

d sp

eed

(ms

)

Effective wind speedEstimated wind speed

Figure 7 Wind speed estimate (MNR)

where 119875119886opt

= 051205881205871198772

119862119875opt

is the optimal aerodynamic powerfor the wind speed profile The following objectives are usedto measure the performance of the controllers

(1) Maximization of the power capture is evaluated by theaerodynamic and electrical efficiencywhich is definedin (53)

(2) The reduced oscillation on the drive train and controltorque smoothness are measured by the STD (Stan-dard Deviation) and maximum value

Figure 7 shows the estimation of effective wind speed byusing the Modified Newton Raphson (MNR) estimator TheMNR estimator gives the correct reference which ensures thedynamic aspect of wind

The rotor speed comparisons for FAST simulator areshown in Figures 8 and 9 The conventional controllers suchas ATF and ISC are not able to track the optimal referencespeed ATF has only single tuning parameter that is 119870

119888

which cannot minimize the steady state error In ISC duringfast transient wind speed it introduces more power lossMore over these controllers are not robust with respect tohigh turbulence wind speed profile To overcome the abovedrawbacks SMC and ISMC are proposed Figure 9 shows therotor speed comparisons for ISMC and SMC It is found thatISMC and SMC track the reference rotor speed better thanISC and ATF

Table 3 gives the performance analysis of all the conven-tional and proposed controllers From Table 3 it is clear that

222242628

332343638

4

Roto

r spe

ed (r

ads

)0 100 200 300 400 500 600

Time (s)

ISCATF

wref

Figure 8 Rotor speed comparison for ATF and ISC for FASTsimulator

0 100 200 300 400 500 6002

22242628

332343638

4

Time (s)

Roto

r spe

ed (r

ads

)

ISMCSMC

wref

Figure 9 Rotor speed comparison for SMC and ISMC for FASTsimulator

the STD of 119879em and 119879ls is less for ISMC compared to SMCand ATF This ensures the smoothness of the control inputand low speed shaft torque in ISMC compared SMC andATFTable data shows that ISC having lowest STD of 119879em and119879ls but its efficiency is very low (6973) compared to allother controllers So a trade-off should be made between theefficiency and the fatigue load on drive train


0

05

1

15

2

25

ISC ATF SMC ISMCControl strategy

Low

spee

d sh

aft to

rque

(Nm

)

minus05

times105

Figure 10 Boxplot for low speed shaft torque using FAST simulator

0100020003000


Gen

erat

or to

rque

(Nm

)

minus4000

minus3000

minus2000

minus1000

Figure 11 Boxplot for generator torque using FAST simulator

To analyze the controller performances in amore detailedfashion Figures 10 and 11 show the box plot for low speedshaft torque and generator torque with the mean medianplusmn25 quartiles (notch boundaries) plusmn75 quartiles (boxends) plusmn95 bounds and the outliers From the size of theboxes shown it is clear that the ISC experiences minimumvariation than others It ensures that ISC having the min-imum transient load on the drive train at the same timewe have seen from Table 3 that the efficiency of ISC is notcomparable with other controllers Comparing the box plotof ISMC and SMC ISMC has less variation in low speed shafttorque and generator torque this indicates smoothness of thecontroller and reduction in transient load

Figure 12 shows the boxplot for rotor speed for FASTsimulator From this figure it is observed that ISMC and SMChave almost same variation in the reference rotor speedApartfrom ISMC and SMC other controllers such as ATF and ISCare having more variations in reference speed

The frequency analysis is carried out by using the PSD onthe low speed shaft torque which is shown in Figure 13 Asthe SMC plot is completely above the ISMC plot it can beconcluded that low speed shaft torque variation is more forSMC than ISMC This indicates that ISMC gives minimumexcitation to the drive train compared to SMC

Figure 14 shows comparison of low speed shaft torque andcontrol torque for ATF SMC and ISMC by considering ISCas baseline control All the low speed shaft torques (LSSTq)and control torques (ControlTq) are having higher valuescompared to baseline controller

222242628

332343638


Roto

r spe

ed (r

ads

)

wref

Figure 12 Boxplot for rotor speed using FAST Simulator

Table 4 SMC performance for different wind speed profiles

Mean windspeed (msec)

Electricalefficiency ()

119879ls standarddeviation kNm

Max (119879em)kNm

7 (msec) 7689 2184 16908 (msec) 7451 2031 178385 (msec) 7422 2011 1922

Table 5 ISMC performance for different wind speed profiles




Max (119879em)kNm

7 (msec) 7626 1359 12608 (msec) 7449 1172 152685 (msec) 7468 1198 1762

As shown in Figure 15 the SMC controller has improvedpower capture by 075 compared to ISMC An intermediatetracking has been chosen and a compromise has been madebetween efficiency and load mitigation From the aboveanalysis and results given in Table 3 it is observed that eventhough SMC gives slightly more efficiency than ISMC byconsidering transient load on drive train and smooth controlinput ISMC found be optimal

In order to avoid the torsional resonance mode by choos-ing the proper tracking dynamics a trade-off is made betweenpower capture optimizationwith smooth control and reducedtransient load on low speed shaft torque A good dynamictracking that is similar to WT fast dynamics gives betterpower capture but it requires more turbulence in controltorque Conversely slow tracking gives smooth control actionwith less power capture The simulations are performed withdifferent mean wind speed at region 2 The results are givenin Tables 4 and 5 From these tables it observed that withan increase in mean wind speed the maximum value of thecontrol input (119879em) also increases In all the cases both SMCand ISMC controllers are having almost same efficiency butthe transient load reduction is better for ISMC As the meanwind speed increases the rate of increase of STD is morefor SMC than ISMC It observed that when the wind speedundergoes high variation the ISMC can produce better powercapture with reduced transient load on the drive train


05 1 15 2 2540

60

80

100

120

140

160

180

Frequency (Hz)

Pow

erfr

eque

ncy

(dB

Hz)

SMCISMC

0times10-3

Figure 13 PSD for low speed shaft torque using FAST simulator

0

20

40

60

80

LSSTq ControlTq

Abov

e bas

eline

()

Comparison for LSS and control torque

ATFSMCISMC

Figure 14 Comparison for baseline control with other controllersfor LSS and control torque

53 Transition between Below and Above Rated Wind Speed(Region 25) Figure 16(a) shows the test wind speed consistsof 10min dataset that was generated by the binary file formatIn this wind profile the wind speed changes in step of every50 sec starts from 6msec to 18msec This shows both theabove and below rated wind speed are included in the windprofile For below rated wind speed torque control comesinto action with constant pitch angle and above rated windspeed pitch control comes into action with rated torqueFigure 16(b) shows the generator speed for SMC and ISMCfor below and above rated wind speed Both controllersachieve the nominal value of the generator speed at 250 secThe corresponding wind speed is around 115msec whichcan be seen from Figure 16(a) As the wind speed approachestowards the rated speed the WT generator speed reachesthe nominal value that is 16755 radsec Figure 16(c) showsthe electrical power comparison for SMC and ISMC for

0

5

10

ATF SMC ISMCAbov

e bas

eline

()

Comparison of generated average power

Figure 15 Comparison for baseline control with other controllersfor generated average power

the transition period At region 25 ISMC can able to extractthe more power than SMC with almost same mechanicalstress on the drive train Figure 16(d) shows the generatortorque comparison in region 25 for SMC and ISMC It canbe observed that ISMC produces more generated torquecompared to SMC in region 25 that is 250 sec to 400 sec Asgenerator speed remains constant from 200 sec onwards it isobvious that ISMC captures more power compared to SMCThe STD of generated torque for SMC and ISMC is foundto be 1060 kNm and 107 kNm respectively which is almostsame Figure 16(e) shows the pitch angle comparison for SMCand ISMC at region 25 Pitch variation found to be more forSMC compared to ISMC So the pitch actuator needs morecontrol action for SMC + PI

Figure 17(a) shows the test wind speed consists of 10mindataset that was generated by the binary file format In thiswind profile the wind speed changes with vertical windprofile starts from 6msec to 18msec This shows boththe above and below rated wind speed are included in thewind profile Figure 17(b) shows the generator speed for SMCand ISMC for below and above rated wind speed Bothcontrollers achieve the nominal value of the generator speedat 280 secThe correspondingwind speed is around 115msecwhich can be seen from Figure 17(a) As the wind speedapproaches towards the rated speed the WT generator speedreaches the nominal value that is 16755 radsec Figure 17(c)shows the electrical power comparison for SMC and ISMCfor the transition period At region 25 ISMC can extractmore power than SMC with almost the same mechanicalstress on the drive train Figure 17(d) shows the generatortorque comparison in region 25 for SMC and ISMC It canbe observed that ISMC produces more generated torquecompared to SMC in region 25 that is 280 sec to 415 sec Asgenerator speed remains constant from 280 sec onwards it isobvious that ISMC captures more power compared to SMCFigure 16(e) shows the pitch angle comparison for SMC andISMC at region 25 Pitch variation was found to be more forSMC compared to ISMC So the pitch actuator needs morecontrol action for SMC + PI

Figure 18 shows the rotor speed comparison of SMC andISMC controller with the rotor inertia parameter uncertainty(+30) and disturbance of 5119899

119892kNm From this figure it

is concluded that with the disturbance and uncertaintyISMC can track the reference rotor speed which ensures therobustness with respect to uncertainty and disturbance


0 100 200 300 400 500 6006

8

10

12

14

16

18

Time (s)

Win

d sp

eed

(ms

)

(a)

20406080

100120140160180200

Gen

erat

or sp

eed

(rad

s)

SMCISMC

0 100 200 300 400 500 6000

Time (s)

(b)

0

1

2

3

4

5

6

7

Elec

tric

al p

ower

(W)

Rated power

times105

100 200 300 400 500 600Time (s)

SMCISMC

0

(c)

500

1000

1500

2000

2500

3000

3500

4000G

ener

ator

torq

ue (N

m)

100 200 300 400 500 600Time (s)

SMCISMC

0

(d)

05

10152025303540

Pitc

h an

gle (

deg)

minus5100 200 300 400 500 600

Time (s)

SMCISMC

0

(e)

Figure 16 Simulation results of 600 kW CART 3WT using SMC and ISMC in full range of operation (step change wind profile) (a) Windspeed profile (b) generator speed (c) electrical power (d) generator torque and (e) pitch angle


6

8

10

12

14

16

18W

ind

spee

d (m

s)

0 100 200 300 400 500 600Time (s)

(a)

020406080

100120140160180200

Gen

erat

or sp

eed

(rad

s)

100 200 300 400 500 600Time (s)

SMCISMC

0

(b)

0

1

2

3

4

5

6

7

Elec

tric

al p

ower

(W)

Rated power

times105

100 200 300 400 500 600Time (s)

SMCISMC

0

(c)

1000

1500

2000

2500

3000

3500

4000

Gen

erat

or to

rque

(Nm

)

500100 200 300 400 500 600

Time (s)

SMCISMC

0

(d)

05

10152025303540

Pitc

h an

gle (

deg)

minus5100 200 300 400 500 600

Time (s)

SMCISMC

0

(e)

Figure 17 Simulation results of 600 kW CART 3WT using SMC and ISMC in full range of operation (vertical wind profile) (a) Wind speedprofile (b) generator speed (c) electrical power (d) generator torque and (e) pitch angle

6 Conclusion

In this paper a combination of linear and nonlinear controlfor VSVPWT has been proposed The proposed nonlinearcontroller such as SMC and ISMC is designed for wide range

of below rated wind speed profiles The main aim of thecontroller is to capture the maximum power with reducedoscillation on the drive train at below rated speed Thesimulation of the controllers is performed by NREL CART3 600 kWWT From the analysis it is concluded that the


0 100 200 300 400 500 6002

22242628

332343638

4

Time (s)

Roto

r spe

ed (r

ads

)

ISMC

SMCwref

Figure 18 Rotor speed comparison of controllers with parameteruncertainty and disturbance of 5119899

119892kNm

proposed ISMC (region 2) with conventional PI controller(region 3) can achieve the maximum power in all the regionsof wind speed

Appendices

A Two-Mass Model Parameters

Rotor radius 119877 = 2165mair density 120588 = 129 kgm3rotor inertia 119869

119903= 325 sdot 10

5 kgsdotm2generator inertia 119869

119892= 344 kgsdotm2

shaft damping coefficient119870ls = 9500Nmradshaft stiffness coefficient 119861ls = 2691 sdot 10

5Nmradrotor friction coefficient 119870

119903= 2736Nmradsec

generator friction coefficient119870119892= 02Nmradsec

gear ratio 119899119892= 43165

cut in wind speed 6msecrated wind speed 13mseccut out wind speed 25msec

B Modified Newton Raphson Algorithm

The estimation of effective wind speed is done by using themodified Newton Raphson At instant 119905 the effective windspeed is obtained from rotor speed and aerodynamic torque

Step 1 1205920= 120592(119905 minus 119879

119904)

Step 2 120592119899+1

= 120592119899minus 119865(120592) ∙ 119865

1015840

(120592)((1198651015840

(120592))2

minus (119865(120592) ∙

11986510158401015840

(120592)))Step 3 119899 = 119899 + 1Step 4 Stop if 119899 gt 119899max or |120592

119899minus120592(119899minus 1)|120592

119899lt 120576min go

to Step 2Step 5 119899

119891= 119899

where 120592119899is the result of the first 119899 iterations and 119879

119904is the

sampled rate fixed here as 1 sec

Conflict of Interests

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

References

[1] T Burton D Sharpe N Jenkins and E BossanyiWind EnergyHandbook Wiley Publications New York NY USA 2001

[2] F D Bianchi F D Battista and R J MantzWind Turbine Con-trol Systems Principles Modelling and Gain Scheduling DesignSpringer 2nd edition 2006

[3] Y Lei AMullane G Lightbody and R Yacamini ldquoModeling ofthe wind turbine with a doubly fed induction generator for gridintegration studiesrdquo IEEE Transactions on Energy Conversionvol 21 no 1 pp 257ndash264 2006

[4] Y D Song B Dhinakaran and X Y Bao ldquoVariable speed con-trol of wind turbines using nonlinear and adaptive algorithmsrdquoJournal of Wind Engineering and Industrial Aerodynamics vol85 no 3 pp 293ndash308 2000

[5] M Liao LDong L Jin and SWang ldquoStudy on rotational speedfeedback torque control for wind turbine generator systemrdquoin Proceedings of the International Conference on Energy andEnvironment Technology (ICEET rsquo09) pp 853ndash856 October2009

[6] M Sheikhan R Shahnazi andANooshadYousefi ldquoAn optimalfuzzy PI controller to capture themaximum power for variable-speed wind turbinesrdquo Neural Computing and Applications vol23 no 5 pp 1359ndash1368 2013

[7] K Z Oslashstergaard P Brath and J Stoustrup ldquoEstimation ofeffective wind speedrdquo Journal of Physics Conference Series vol75 no 1 Article ID 012082 2007

[8] B Boukhezzar H Siguerdidjane and M Hand ldquoNonlinearcontrol of variable-speed wind turbines for generator torquelimiting and power optimizationrdquo Transactions of the ASMEJournal of Solar Energy Engineering vol 128 no 4 pp 516ndash5302006

[9] B Boukhezzar and H Siguerdidjane ldquoNonlinear control of avariable-speed wind turbine using a two-mass modelrdquo IEEETransactions on Energy Conversion vol 26 no 1 pp 149ndash1622011

[10] B Beltran T Ahmed-Ali andM E H Benbouzid ldquoHigh-ordersliding-mode control of variable-speed wind turbinesrdquo IEEETransactions on Industrial Electronics vol 56 no 9 pp 3314ndash3321 2009

[11] A Khamlichi B Ayyat R O B Zarouala and C V VenegasldquoAdvanced control based on extended kalman filter for variablespeed wind turbinerdquo Australian Journal of Basic and AppliedSciences vol 5 no 9 pp 636ndash644 2011

[12] I Ciric Z Cojbasic V Nikolic and E Petrovic ldquoHybrid fuzzycontrol strategies for variable speed wind turbinesrdquo FactaUniversitatis Series Automatic Control and Robotics vol 10 no2 pp 205ndash217 2011

[13] R Rocha ldquoA sensorless control for a variable speedwind turbineoperating at partial loadrdquo Renewable Energy vol 36 no 1 pp132ndash141 2011

[14] Z XuQHu andMEhsani ldquoEstimation of effectivewind speedfor fixed-speed wind turbines based on frequency domain datafusionrdquo IEEE Transactions on Sustainable Energy vol 3 no 2pp 57ndash64 2012


[15] B Boukhezzar L LupuH Siguerdidjane andMHand ldquoMulti-variable control strategy for variable speed variable pitch windturbinesrdquo Renewable Energy vol 32 no 8 pp 1273ndash1287 2007

[16] J O M Rubio and L T Aguilar ldquoMaximizing the performanceof variable speed wind turbine with nonlinear output feedbackcontrolrdquo Procedia Engineering vol 35 pp 31ndash40 2012

[17] M A Ayoubi and L-C Tai ldquoIntelligent control of a large Vari-able speed Wind turbinerdquo Journal of Solar Energy Engineeringvol 134 no 1 Article ID 011001 2012

[18] H Jafarnejadsani J Pieper and J Ehlers ldquoAdaptive control ofa variable-speed variable-pitch wind turbine using radial-basisfunction neural networkrdquo IEEE Transactions on Control SystemsTechnology vol 21 no 6 pp 2264ndash2272 2013

[19] W Zhang and H Xu ldquoActive disturbance rejection based pitchcontrol of variable speed wind turbinerdquo in Proceedings of the30th Chinese Control Conference pp 5094ndash5098 July 2011

[20] A Abdullah and A Fekih ldquoPitch control design for optimumenergy capture in variable-speed wind turbinesrdquo in Proceedingsof the 10th International Multi-Conference on Systems SignalsandDevices (SSD rsquo13) pp 1ndash6Hammamet TunisiaMarch 2013

[21] A S Yilmaz and Z Ozer ldquoPitch angle control in wind turbinesabove the rated wind speed by multi-layer perceptron andradial basis function neural networksrdquo Expert Systems withApplications vol 36 no 6 pp 9767ndash9775 2009

[22] H Vihriala R Perala P Makila and L Soderlund ldquoA gearlesswind power drive part 2 performance of control systemrdquo inProceedings of the European Wind Energy Conference vol 1 pp1090ndash1093 2001

[23] P Ben-Tzvi S Bai Q Zhou and X Huang ldquoFuzzy slidingmodecontrol of rigid-flexible multibody systems with boundedinputsrdquo Transactions of the ASME Journal of Dynamic SystemsMeasurement and Control vol 133 no 6 Article ID 061012 pp1ndash8 2011

[24] M H Hansen A Hansen T J Larsen S Oslashye P Soslashrensen andP Fuglsang Control Design for a Pitch Regulated Variable SpeedWind Turbine Riso National Laboratory 2005

[25] L J Fingersh and K Johnson ldquoControls advanced research tur-bine (CART) commissioning and baseline data collectionrdquoNREL Report TP-500-32879 National Renewable Energy Lab-oratory Golden Colo USA 2002

[26] R Ottersten On control of back-to-back converters and sensor-less inductionmachine drives [PhD thesis] ChalmersUniversityof Technology Goteborg Sweden 2003

[27] R Pena R Cardenas R Blasco G Asher and J Clare ldquoAcage induction generator using back to back PWM convertersfor variable speed grid connected wind energy systemrdquo inProceedings of the 27th Annual Conference of the IEEE IndustrialElectronics Society (IECON rsquo01) pp 1376ndash1381 December 2001

[28] M Hansen J Soslashrensen S Voutsinas N Soslashrensen and HMadsen ldquoState of the art in wind turbine aerodynamics andaeroelasticityrdquo Progress in Aerospace Sciences vol 42 no 4 pp285ndash330 2006

[29] A Manjock ldquoDesign codes FAST and ADAMS for load calcu-lations of onshore wind turbinesrdquo Tech Rep 72042 Germanis-cher Lloyd Windenergie GmbH Hamburg Germany 2005

[30] D J Laino and A C Hansen Userrsquos Guide to the Wind TurbineAerodynamics Computer Software Aerodyn National WindTechnology Center National Renewable Energy LaboratoryGolden Colo USA 1250 edition 2003

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Submit your manuscripts athttpwwwhindawicom


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Journal ofEngineeringVolume 2014

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International Journal ofPhotoenergy


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High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Rotoraerodynamics

Drivetrains GeneratorWind

speed120592

120596r 120596g

Ta TgPe

Figure 1 Schematic of WT

slidingmode controller is proposed in [10] which ensures thestability of the controller in both the regions that is belowand above rated speed An extended Kalman Filter basedwind speed estimator is discussed in [11] which uses theconventional ATF and ISC for controlling the WT In [12]fuzzy logic control has been proposed and the effective windspeed is estimated using sequential Monte Carlo simulatorDiscrete time optimal LQRLTR based on optimal quadraticfunction is studied in [13] In [14] the effective wind speedis estimated by the frequency domain data fusion andthe observer is formulated based on the mixed sensitivityproblem with linear matrix Inequalities

For above rated wind speed authors in [15] discussed themultivariable control strategy by combining the nonlinearstate feedback control for region 2 with linear control forregion 3 Finally the results are compared with the existingcontrol strategy such as PID and LQG In [16] the WTcontroller is the combination of linear control for blade pitchangle with 119867

infinnonlinear torque control Nowadays fuzzy

and neural networks (NN) are the powerful soft computingmethods for controlling nonlinear systems Authors in [17]discussed a fuzzy 119875 + 119868 and neurofuzzy controller forcontrolling the WT at above rated wind speed PSO is usedto train the adaptive neurofuzzy controllerWT control usingadaptive radial basic NN used for both pitch and torquecontroller is addressed in [18] Active disturbance rejectionbased pitch control for variable speedWT is presented in [19]where the extended state observer is used to estimate the statevariable and disturbance In [20] the controller has two partsthat is nonlinear feed-forward path and linear feedbackpath The feed-forward path uses the information about thedesired power output wind velocity and the turbine speedto determine the pitch angle required In [21] NN based pitchangle control is implemented by usingmultilayer perceptronswith back propagation learning algorithm and radial basisfunction network for tuning the pitch controller

This paper uses a PI control for pitch control and twononlinear controllers such as SMC and ISMC for torquecontrolThe paper is organized as follows Section 2 discussesthe modeling of two-mass model Problem formulation andcontrol objectives are discussed in Section 3 The proposedcontrollers for all the regions are discussed in Section 4Section 5 discusses the validation of the results using FASTsimulator Finally in Section 6 a conclusion is drawn fromthe obtained results which concludes that the proposedcontrollers are working fine for controlling the WT at belowand above rated wind speed

2 WT Model

WT is a device which converts the kinetic energy of thewind in to electric energy Simulation complexity of the WT

purely depends on the type of control objectives In case ofWT modelling complex simulators are required to verify thedynamic response of multiple components and aerodynamicloading Generally dynamic loads and interaction of largecomponents are verified by the aeroelastic simulator Fordesigning a WT controller instead of going with complexsimulator the design objective can be achieved by usingsimplified mathematical model In this work WT modelis described by the set of nonlinear ordinary differentialequationwith limited degree of freedomThis paper describesthe control law for a simplified mathematical model with theobjective of optimal power capture at below and above ratedwind speed The proposed controllers are validated for FASTWTmodel in three different cases of wind speed profile suchas below rated wind speed (region 2) above rated wind speed(region 3) and a smooth transition between these two windspeeds (region 25) The parameter of the two-mass modelis given in Appendix A Generally VSWT system consists ofthe following components that is aerodynamics drive trainsand generator shown in Figure 1

Equation (1) gives the nonlinear expression for aerody-namic power capture by the rotor

119875119886=1

21205881205871198772

119862119875(120582 120573) 120592

3

(1)

From (1) it is clear that the aerodynamic power (119875119886) is directly

proportional to the cube of the wind speed The powercoefficient 119862

119875is the function of blade pitch angle (120573) and tip

speed ratio (120582)The tip speed ratio is defined as ratio betweenlinear tip speed and wind speed

120582 =120596119903119877

120592 (2)

Generally wind speed is stochastic nature with respect totime Because of this tip speed ratio gets affected which leadsto variation in power coefficient The relationship betweenaerodynamic torque (119879

119886) and the aerodynamic power is given

in (3)

119875119886= 119879119886120596119903 (3)

119879119886=1

21205881205871198773

119862119902(120582 120573) 120592

2

(4)

where 119862119902is the torque coefficient given as

119862119902(120582 120573) =

119862119875(120582 120573)

120582 (5)

Substituting (5) in (4) we get

119879119886=1

21205881205871198773119862119875(120582 120573)

1205821205922

(6)



1198860= 01667 119886

3= minus001617

1198861= minus02558 119886

4= 000095

1198862= 0115 119886

5=minus205 times 10

minus5

0 2 4 6 8 10 12 140

01

02

03

04

05

120582

Cp




119862119875(120582) =

5

sum

119899=0

119886119899120582119899

= 1198860+ 1205821198861+ 1205822

1198862+ 1205823

1198863+ 1205824

1198864+ 1205825

1198865

(7)





119903with rotor


119886)

119869119903119903= 119879119886minus 119879ls minus 119870119903120596119903 (8)






119869119892119892= 119879hs minus 119870119892120596119892 minus 119879em (10)


119899119892=119879ls119879hs

=

120596119892

120596ls (11)

119879ls = 119899119892119879hs (12)


119879hs = 119869119892119892 + 119870119892120596119892 + 119879em (13)


119879ls = 119899119892 (119869119892119892 + 119870119892120596119892 + 119879em) (14)

120596gTaJg

Kg

Jr

TemThs

TlsB ls

Kls

Kr

120596t

Gear box (ng)


Pow

er

Aerodynamic power


Wcutout

Prated

Region 25










Aero

turbine

control


Generatortorque

Level 1Level 2



Fast WTnonlinear

model

120573120573

Tem

Pe

∙120573

120596r

120573ref

Temref






120596119903opt

= 120596ref =120582opt120592

119877 (15)



119879em = 119870opths1205962

119892minus 119870119905hs120596119892 (16)

where

119870opths = 051205881205871198775

11989931198921205823

opt119862119875opt (17)

119870119905hs= (119870

119892+119870119903

1198992119892

) (18)





119879em =1

119899119892

119886minus (

119870119903

1198992119892

+ 119870119892) 119892minus119870119862

1198992119892

(120596119892ref

minus 120596119892) (19)

120596119892ref

= 119899119892119896119908

radic119886 (20)

119896119908=

1

radic119896opt

= radic21205823

opt

1205881205871198775119862119875opt

(21)

119896opt =1

2120588120587

1198775

1205823

opt119862119875opt (22)








119879119886=1

21205881205871198773119862119875(120582)

1205821205922

(23)


119865 (120592) = 119879119886minus1

21205881205871198773119862119875(120582)

1205821205922

(24)


119903optis





119878 = (120582 +119889

119889119905)

119899minus1

119890 (119905) (25)


119890 (119905) = 120596119903(119905) minus 120596ref (119905) (26)


119878 (119905) = 120582119890 (119905) + 119890 (119905) (27)


119878 119878 le 0 (28)


119881 =1

21198782

(29)


119889119881

119889119905= 119878

119889119878

119889119905= 119878 (120582 119890 (119905) + 119890 (119905)) (30)



= 119878 119878 = 119878 (120582 119890 (119905) + 119890 (119905))

= 119878 [120582 (119903(119905) minus ref (119905) + 119890 (119905))]

(31)


120582 (119903minus ref) + 119890 (119905)


(32)


119880


(33)


119903(119905) in (31)

we get

120582(1

119869119903

119879119886minus119870119903

119869119903

120596119903minus1

119869119903

119879ls minus ref) + 119890 (119905) = 0 (34)


120582(119879119886

119869119903

minus119870119903

119869119903

120596119903minus

119899119892119869119892119892

119869119903

minus

119899119892119870119892120596119892

119869119903

minus

119899119892

119869119903

119879em minus ref)

+ 119890 (119905) = 0

(35)


119879em =119879119886

119899119892

minus119870119903

119899119892


119899119892

ref +119869119903

120582119899119892

119890 (119905) (36)




119880 (119905) = 119880eq (119905) + 119880sw (119905) (37)


119880sw (119905) = 119896 sign (119878) or 119896 tanh( 119878120593) (38)


119879em =119879119886

119899119892

minus119870119903

119899119892


119899119892

ref

+119869119903

120582119899119892

119890 (119905) +119869119903

119899119892120582119896 tanh( 119878

120593)

(39)




119878 (119905) = (120582 +119889

119889119905)

119899minus1

119890 (119905) + 119870119894int

infin

0

119890 (119905) 119889119905 (40)



119878 (119905) = (120582 +119889

119889119905)

1

119890 (119905) + 119870119894int

infin

0

119890 (119905) 119889119905

= 120582119890 (119905) + 119890 (119905) + 119870119894int

infin

0

119890 (119905) 119889119905

(41)


= 119878 119878 = 119878 (120582 119890 (119905) + 119890 (119905) + 119870119894119890 (119905))

= 119878 [120582 (119903(119905) minus ref (119905) + 119890 (119905)) + 119870

119894119890 (119905)]

(42)


120582 (119903minus ref) + 119890 (119905) + 119870

119894119890 (119905)


(43)


119903(119905) in (41)

we get

120582(1

119869119903

119879119886minus119870119903

119869119903

120596119903minus1

119869119903

119879ls minus ref) + 119890 (119905) + 119870119894119890 (119905) = 0 (44)


119879em =119879119886

119899119892

minus119870119903

119899119892


119899119892

ref

+119869119903

119899119892120582119890 (119905) +

119869119903

119899119892120582119870119894119890 (119905) +

119869119903

119899119892120582119896 tanh( 119878

120593)

(45)


119878 (119905) = 119890 (119905) + 120582119890 (119905) (46)


119878 (119878) = 119864 (119878) [119878 + 120582] (47)


lim119905rarrinfin

119890 (119905) = lim119904rarr0

119878119864 (119878) = lim119904rarr0

119878

119878 + 120582sum(119878) =

1

120582119896120593 (48)



119878 (119905) = 120582 119890 (119905) + 119896119894119890 (119905) + 119890 (119905) (49)


119878 lowast 119878 (119878) = 119864 (119878) [1198782

+ 120582119878 + 119896119894] (50)

lim119905rarrinfin

119890 (119905) = lim119904rarr0

119878119864 (119878) = lim119904rarr0

119878

1198782 + 120582119878 + 119896119894

lim119904rarr0

119878sum (119878) = 0

(51)






Δ120573 = 119870119901119890 (119905) + 119870

119894int 119890 (119905) 119889119905

119890 (119905) = 120596119892norm

minus 120596119892

(52)







0 100 200 300 400 500 6005

556

657

758

859

95

Time (s)

Win

d sp

eed

(ms

)

Mean wind speed 7ms






120578aero () =int119905fin

119905ini119875119886119889119905

int119905fin

119905ini119875119886opt119889119905

120578elec () =int119905fin

119905ini119875119890119889119905

int119905fin

119905ini119875119886opt119889119905

(53)




0 100 200 300 400 500 6004

5

6

7

8

9

10

Time (s)

Win

d sp

eed

(ms

)



where 119875119886opt

= 051205881205871198772

119862119875opt






119888



222242628

332343638

4

Roto

r spe

ed (r

ads

)0 100 200 300 400 500 600

Time (s)

ISCATF

wref


0 100 200 300 400 500 6002

22242628

332343638

4

Time (s)

Roto

r spe

ed (r

ads

)

ISMCSMC

wref




0

05

1

15

2

25


Low

spee

d sh

aft to

rque

(Nm

)

minus05

times105


0100020003000


Gen

erat

or to

rque

(Nm

)

minus4000

minus3000

minus2000

minus1000






222242628

332343638


Roto

r spe

ed (r

ads

)

wref






Max (119879em)kNm

7 (msec) 7689 2184 16908 (msec) 7451 2031 178385 (msec) 7422 2011 1922





Max (119879em)kNm

7 (msec) 7626 1359 12608 (msec) 7449 1172 152685 (msec) 7468 1198 1762




05 1 15 2 2540

60

80

100

120

140

160

180

Frequency (Hz)

Pow

erfr

eque

ncy

(dB

Hz)

SMCISMC

0times10-3


0

20

40

60

80

LSSTq ControlTq

Abov

e bas

eline

()


ATFSMCISMC



0

5

10

ATF SMC ISMCAbov

e bas

eline

()









0 100 200 300 400 500 6006

8

10

12

14

16

18

Time (s)

Win

d sp

eed

(ms

)

(a)

20406080

100120140160180200

Gen

erat

or sp

eed

(rad

s)

SMCISMC

0 100 200 300 400 500 6000

Time (s)

(b)

0

1

2

3

4

5

6

7

Elec

tric

al p

ower

(W)

Rated power

times105

100 200 300 400 500 600Time (s)

SMCISMC

0

(c)

500

1000

1500

2000

2500

3000

3500

4000G

ener

ator

torq

ue (N

m)

100 200 300 400 500 600Time (s)

SMCISMC

0

(d)

05

10152025303540

Pitc

h an

gle (

deg)

minus5100 200 300 400 500 600

Time (s)

SMCISMC

0

(e)



6

8

10

12

14

16

18W

ind

spee

d (m

s)

0 100 200 300 400 500 600Time (s)

(a)

020406080

100120140160180200

Gen

erat

or sp

eed

(rad

s)

100 200 300 400 500 600Time (s)

SMCISMC

0

(b)

0

1

2

3

4

5

6

7

Elec

tric

al p

ower

(W)

Rated power

times105

100 200 300 400 500 600Time (s)

SMCISMC

0

(c)

1000

1500

2000

2500

3000

3500

4000

Gen

erat

or to

rque

(Nm

)

500100 200 300 400 500 600

Time (s)

SMCISMC

0

(d)

05

10152025303540

Pitc

h an

gle (

deg)

minus5100 200 300 400 500 600

Time (s)

SMCISMC

0

(e)


6 Conclusion




0 100 200 300 400 500 6002

22242628

332343638

4

Time (s)

Roto

r spe

ed (r

ads

)

ISMC

SMCwref


119892kNm


Appendices



119903= 325 sdot 10


119892= 344 kgsdotm2





gear ratio 119899119892= 43165




Step 1 1205920= 120592(119905 minus 119879

119904)

Step 2 120592119899+1

= 120592119899minus 119865(120592) ∙ 119865

1015840

(120592)((1198651015840

(120592))2

minus (119865(120592) ∙

11986510158401015840


119899minus120592(119899minus 1)|120592

119899lt 120576min go


119891= 119899


119904is the




References




































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of



















1198860= 01667 119886

3= minus001617

1198861= minus02558 119886

4= 000095

1198862= 0115 119886

5=minus205 times 10

minus5

0 2 4 6 8 10 12 140

01

02

03

04

05

120582

Cp




119862119875(120582) =

5

sum

119899=0

119886119899120582119899

= 1198860+ 1205821198861+ 1205822

1198862+ 1205823

1198863+ 1205824

1198864+ 1205825

1198865

(7)





119903with rotor


119886)

119869119903119903= 119879119886minus 119879ls minus 119870119903120596119903 (8)






119869119892119892= 119879hs minus 119870119892120596119892 minus 119879em (10)


119899119892=119879ls119879hs

=

120596119892

120596ls (11)

119879ls = 119899119892119879hs (12)


119879hs = 119869119892119892 + 119870119892120596119892 + 119879em (13)


119879ls = 119899119892 (119869119892119892 + 119870119892120596119892 + 119879em) (14)

120596gTaJg

Kg

Jr

TemThs

TlsB ls

Kls

Kr

120596t

Gear box (ng)


Pow

er

Aerodynamic power


Wcutout

Prated

Region 25










Aero

turbine

control


Generatortorque

Level 1Level 2



Fast WTnonlinear

model

120573120573

Tem

Pe

∙120573

120596r

120573ref

Temref






120596119903opt

= 120596ref =120582opt120592

119877 (15)



119879em = 119870opths1205962

119892minus 119870119905hs120596119892 (16)

where

119870opths = 051205881205871198775

11989931198921205823

opt119862119875opt (17)

119870119905hs= (119870

119892+119870119903

1198992119892

) (18)





119879em =1

119899119892

119886minus (

119870119903

1198992119892

+ 119870119892) 119892minus119870119862

1198992119892

(120596119892ref

minus 120596119892) (19)

120596119892ref

= 119899119892119896119908

radic119886 (20)

119896119908=

1

radic119896opt

= radic21205823

opt

1205881205871198775119862119875opt

(21)

119896opt =1

2120588120587

1198775

1205823

opt119862119875opt (22)








119879119886=1

21205881205871198773119862119875(120582)

1205821205922

(23)


119865 (120592) = 119879119886minus1

21205881205871198773119862119875(120582)

1205821205922

(24)


119903optis





119878 = (120582 +119889

119889119905)

119899minus1

119890 (119905) (25)


119890 (119905) = 120596119903(119905) minus 120596ref (119905) (26)


119878 (119905) = 120582119890 (119905) + 119890 (119905) (27)


119878 119878 le 0 (28)


119881 =1

21198782

(29)


119889119881

119889119905= 119878

119889119878

119889119905= 119878 (120582 119890 (119905) + 119890 (119905)) (30)



= 119878 119878 = 119878 (120582 119890 (119905) + 119890 (119905))

= 119878 [120582 (119903(119905) minus ref (119905) + 119890 (119905))]

(31)


120582 (119903minus ref) + 119890 (119905)


(32)


119880


(33)


119903(119905) in (31)

we get

120582(1

119869119903

119879119886minus119870119903

119869119903

120596119903minus1

119869119903

119879ls minus ref) + 119890 (119905) = 0 (34)


120582(119879119886

119869119903

minus119870119903

119869119903

120596119903minus

119899119892119869119892119892

119869119903

minus

119899119892119870119892120596119892

119869119903

minus

119899119892

119869119903

119879em minus ref)

+ 119890 (119905) = 0

(35)


119879em =119879119886

119899119892

minus119870119903

119899119892


119899119892

ref +119869119903

120582119899119892

119890 (119905) (36)




119880 (119905) = 119880eq (119905) + 119880sw (119905) (37)


119880sw (119905) = 119896 sign (119878) or 119896 tanh( 119878120593) (38)


119879em =119879119886

119899119892

minus119870119903

119899119892


119899119892

ref

+119869119903

120582119899119892

119890 (119905) +119869119903

119899119892120582119896 tanh( 119878

120593)

(39)




119878 (119905) = (120582 +119889

119889119905)

119899minus1

119890 (119905) + 119870119894int

infin

0

119890 (119905) 119889119905 (40)



119878 (119905) = (120582 +119889

119889119905)

1

119890 (119905) + 119870119894int

infin

0

119890 (119905) 119889119905

= 120582119890 (119905) + 119890 (119905) + 119870119894int

infin

0

119890 (119905) 119889119905

(41)


= 119878 119878 = 119878 (120582 119890 (119905) + 119890 (119905) + 119870119894119890 (119905))

= 119878 [120582 (119903(119905) minus ref (119905) + 119890 (119905)) + 119870

119894119890 (119905)]

(42)


120582 (119903minus ref) + 119890 (119905) + 119870

119894119890 (119905)


(43)


119903(119905) in (41)

we get

120582(1

119869119903

119879119886minus119870119903

119869119903

120596119903minus1

119869119903

119879ls minus ref) + 119890 (119905) + 119870119894119890 (119905) = 0 (44)


119879em =119879119886

119899119892

minus119870119903

119899119892


119899119892

ref

+119869119903

119899119892120582119890 (119905) +

119869119903

119899119892120582119870119894119890 (119905) +

119869119903

119899119892120582119896 tanh( 119878

120593)

(45)


119878 (119905) = 119890 (119905) + 120582119890 (119905) (46)


119878 (119878) = 119864 (119878) [119878 + 120582] (47)


lim119905rarrinfin

119890 (119905) = lim119904rarr0

119878119864 (119878) = lim119904rarr0

119878

119878 + 120582sum(119878) =

1

120582119896120593 (48)



119878 (119905) = 120582 119890 (119905) + 119896119894119890 (119905) + 119890 (119905) (49)


119878 lowast 119878 (119878) = 119864 (119878) [1198782

+ 120582119878 + 119896119894] (50)

lim119905rarrinfin

119890 (119905) = lim119904rarr0

119878119864 (119878) = lim119904rarr0

119878

1198782 + 120582119878 + 119896119894

lim119904rarr0

119878sum (119878) = 0

(51)






Δ120573 = 119870119901119890 (119905) + 119870

119894int 119890 (119905) 119889119905

119890 (119905) = 120596119892norm

minus 120596119892

(52)







0 100 200 300 400 500 6005

556

657

758

859

95

Time (s)

Win

d sp

eed

(ms

)

Mean wind speed 7ms






120578aero () =int119905fin

119905ini119875119886119889119905

int119905fin

119905ini119875119886opt119889119905

120578elec () =int119905fin

119905ini119875119890119889119905

int119905fin

119905ini119875119886opt119889119905

(53)




0 100 200 300 400 500 6004

5

6

7

8

9

10

Time (s)

Win

d sp

eed

(ms

)



where 119875119886opt

= 051205881205871198772

119862119875opt






119888



222242628

332343638

4

Roto

r spe

ed (r

ads

)0 100 200 300 400 500 600

Time (s)

ISCATF

wref


0 100 200 300 400 500 6002

22242628

332343638

4

Time (s)

Roto

r spe

ed (r

ads

)

ISMCSMC

wref




0

05

1

15

2

25


Low

spee

d sh

aft to

rque

(Nm

)

minus05

times105


0100020003000


Gen

erat

or to

rque

(Nm

)

minus4000

minus3000

minus2000

minus1000






222242628

332343638


Roto

r spe

ed (r

ads

)

wref






Max (119879em)kNm

7 (msec) 7689 2184 16908 (msec) 7451 2031 178385 (msec) 7422 2011 1922





Max (119879em)kNm

7 (msec) 7626 1359 12608 (msec) 7449 1172 152685 (msec) 7468 1198 1762




05 1 15 2 2540

60

80

100

120

140

160

180

Frequency (Hz)

Pow

erfr

eque

ncy

(dB

Hz)

SMCISMC

0times10-3


0

20

40

60

80

LSSTq ControlTq

Abov

e bas

eline

()


ATFSMCISMC



0

5

10

ATF SMC ISMCAbov

e bas

eline

()









0 100 200 300 400 500 6006

8

10

12

14

16

18

Time (s)

Win

d sp

eed

(ms

)

(a)

20406080

100120140160180200

Gen

erat

or sp

eed

(rad

s)

SMCISMC

0 100 200 300 400 500 6000

Time (s)

(b)

0

1

2

3

4

5

6

7

Elec

tric

al p

ower

(W)

Rated power

times105

100 200 300 400 500 600Time (s)

SMCISMC

0

(c)

500

1000

1500

2000

2500

3000

3500

4000G

ener

ator

torq

ue (N

m)

100 200 300 400 500 600Time (s)

SMCISMC

0

(d)

05

10152025303540

Pitc

h an

gle (

deg)

minus5100 200 300 400 500 600

Time (s)

SMCISMC

0

(e)



6

8

10

12

14

16

18W

ind

spee

d (m

s)

0 100 200 300 400 500 600Time (s)

(a)

020406080

100120140160180200

Gen

erat

or sp

eed

(rad

s)

100 200 300 400 500 600Time (s)

SMCISMC

0

(b)

0

1

2

3

4

5

6

7

Elec

tric

al p

ower

(W)

Rated power

times105

100 200 300 400 500 600Time (s)

SMCISMC

0

(c)

1000

1500

2000

2500

3000

3500

4000

Gen

erat

or to

rque

(Nm

)

500100 200 300 400 500 600

Time (s)

SMCISMC

0

(d)

05

10152025303540

Pitc

h an

gle (

deg)

minus5100 200 300 400 500 600

Time (s)

SMCISMC

0

(e)


6 Conclusion




0 100 200 300 400 500 6002

22242628

332343638

4

Time (s)

Roto

r spe

ed (r

ads

)

ISMC

SMCwref


119892kNm


Appendices



119903= 325 sdot 10


119892= 344 kgsdotm2





gear ratio 119899119892= 43165




Step 1 1205920= 120592(119905 minus 119879

119904)

Step 2 120592119899+1

= 120592119899minus 119865(120592) ∙ 119865

1015840

(120592)((1198651015840

(120592))2

minus (119865(120592) ∙

11986510158401015840


119899minus120592(119899minus 1)|120592

119899lt 120576min go


119891= 119899


119904is the




References




































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















Aero

turbine

control


Generatortorque

Level 1Level 2



Fast WTnonlinear

model

120573120573

Tem

Pe

∙120573

120596r

120573ref

Temref






120596119903opt

= 120596ref =120582opt120592

119877 (15)



119879em = 119870opths1205962

119892minus 119870119905hs120596119892 (16)

where

119870opths = 051205881205871198775

11989931198921205823

opt119862119875opt (17)

119870119905hs= (119870

119892+119870119903

1198992119892

) (18)





119879em =1

119899119892

119886minus (

119870119903

1198992119892

+ 119870119892) 119892minus119870119862

1198992119892

(120596119892ref

minus 120596119892) (19)

120596119892ref

= 119899119892119896119908

radic119886 (20)

119896119908=

1

radic119896opt

= radic21205823

opt

1205881205871198775119862119875opt

(21)

119896opt =1

2120588120587

1198775

1205823

opt119862119875opt (22)








119879119886=1

21205881205871198773119862119875(120582)

1205821205922

(23)


119865 (120592) = 119879119886minus1

21205881205871198773119862119875(120582)

1205821205922

(24)


119903optis





119878 = (120582 +119889

119889119905)

119899minus1

119890 (119905) (25)


119890 (119905) = 120596119903(119905) minus 120596ref (119905) (26)


119878 (119905) = 120582119890 (119905) + 119890 (119905) (27)


119878 119878 le 0 (28)


119881 =1

21198782

(29)


119889119881

119889119905= 119878

119889119878

119889119905= 119878 (120582 119890 (119905) + 119890 (119905)) (30)



= 119878 119878 = 119878 (120582 119890 (119905) + 119890 (119905))

= 119878 [120582 (119903(119905) minus ref (119905) + 119890 (119905))]

(31)


120582 (119903minus ref) + 119890 (119905)


(32)


119880


(33)


119903(119905) in (31)

we get

120582(1

119869119903

119879119886minus119870119903

119869119903

120596119903minus1

119869119903

119879ls minus ref) + 119890 (119905) = 0 (34)


120582(119879119886

119869119903

minus119870119903

119869119903

120596119903minus

119899119892119869119892119892

119869119903

minus

119899119892119870119892120596119892

119869119903

minus

119899119892

119869119903

119879em minus ref)

+ 119890 (119905) = 0

(35)


119879em =119879119886

119899119892

minus119870119903

119899119892


119899119892

ref +119869119903

120582119899119892

119890 (119905) (36)




119880 (119905) = 119880eq (119905) + 119880sw (119905) (37)


119880sw (119905) = 119896 sign (119878) or 119896 tanh( 119878120593) (38)


119879em =119879119886

119899119892

minus119870119903

119899119892


119899119892

ref

+119869119903

120582119899119892

119890 (119905) +119869119903

119899119892120582119896 tanh( 119878

120593)

(39)




119878 (119905) = (120582 +119889

119889119905)

119899minus1

119890 (119905) + 119870119894int

infin

0

119890 (119905) 119889119905 (40)



119878 (119905) = (120582 +119889

119889119905)

1

119890 (119905) + 119870119894int

infin

0

119890 (119905) 119889119905

= 120582119890 (119905) + 119890 (119905) + 119870119894int

infin

0

119890 (119905) 119889119905

(41)


= 119878 119878 = 119878 (120582 119890 (119905) + 119890 (119905) + 119870119894119890 (119905))

= 119878 [120582 (119903(119905) minus ref (119905) + 119890 (119905)) + 119870

119894119890 (119905)]

(42)


120582 (119903minus ref) + 119890 (119905) + 119870

119894119890 (119905)


(43)


119903(119905) in (41)

we get

120582(1

119869119903

119879119886minus119870119903

119869119903

120596119903minus1

119869119903

119879ls minus ref) + 119890 (119905) + 119870119894119890 (119905) = 0 (44)


119879em =119879119886

119899119892

minus119870119903

119899119892


119899119892

ref

+119869119903

119899119892120582119890 (119905) +

119869119903

119899119892120582119870119894119890 (119905) +

119869119903

119899119892120582119896 tanh( 119878

120593)

(45)


119878 (119905) = 119890 (119905) + 120582119890 (119905) (46)


119878 (119878) = 119864 (119878) [119878 + 120582] (47)


lim119905rarrinfin

119890 (119905) = lim119904rarr0

119878119864 (119878) = lim119904rarr0

119878

119878 + 120582sum(119878) =

1

120582119896120593 (48)



119878 (119905) = 120582 119890 (119905) + 119896119894119890 (119905) + 119890 (119905) (49)


119878 lowast 119878 (119878) = 119864 (119878) [1198782

+ 120582119878 + 119896119894] (50)

lim119905rarrinfin

119890 (119905) = lim119904rarr0

119878119864 (119878) = lim119904rarr0

119878

1198782 + 120582119878 + 119896119894

lim119904rarr0

119878sum (119878) = 0

(51)






Δ120573 = 119870119901119890 (119905) + 119870

119894int 119890 (119905) 119889119905

119890 (119905) = 120596119892norm

minus 120596119892

(52)







0 100 200 300 400 500 6005

556

657

758

859

95

Time (s)

Win

d sp

eed

(ms

)

Mean wind speed 7ms






120578aero () =int119905fin

119905ini119875119886119889119905

int119905fin

119905ini119875119886opt119889119905

120578elec () =int119905fin

119905ini119875119890119889119905

int119905fin

119905ini119875119886opt119889119905

(53)




0 100 200 300 400 500 6004

5

6

7

8

9

10

Time (s)

Win

d sp

eed

(ms

)



where 119875119886opt

= 051205881205871198772

119862119875opt






119888



222242628

332343638

4

Roto

r spe

ed (r

ads

)0 100 200 300 400 500 600

Time (s)

ISCATF

wref


0 100 200 300 400 500 6002

22242628

332343638

4

Time (s)

Roto

r spe

ed (r

ads

)

ISMCSMC

wref




0

05

1

15

2

25


Low

spee

d sh

aft to

rque

(Nm

)

minus05

times105


0100020003000


Gen

erat

or to

rque

(Nm

)

minus4000

minus3000

minus2000

minus1000






222242628

332343638


Roto

r spe

ed (r

ads

)

wref






Max (119879em)kNm

7 (msec) 7689 2184 16908 (msec) 7451 2031 178385 (msec) 7422 2011 1922





Max (119879em)kNm

7 (msec) 7626 1359 12608 (msec) 7449 1172 152685 (msec) 7468 1198 1762




05 1 15 2 2540

60

80

100

120

140

160

180

Frequency (Hz)

Pow

erfr

eque

ncy

(dB

Hz)

SMCISMC

0times10-3


0

20

40

60

80

LSSTq ControlTq

Abov

e bas

eline

()


ATFSMCISMC



0

5

10

ATF SMC ISMCAbov

e bas

eline

()









0 100 200 300 400 500 6006

8

10

12

14

16

18

Time (s)

Win

d sp

eed

(ms

)

(a)

20406080

100120140160180200

Gen

erat

or sp

eed

(rad

s)

SMCISMC

0 100 200 300 400 500 6000

Time (s)

(b)

0

1

2

3

4

5

6

7

Elec

tric

al p

ower

(W)

Rated power

times105

100 200 300 400 500 600Time (s)

SMCISMC

0

(c)

500

1000

1500

2000

2500

3000

3500

4000G

ener

ator

torq

ue (N

m)

100 200 300 400 500 600Time (s)

SMCISMC

0

(d)

05

10152025303540

Pitc

h an

gle (

deg)

minus5100 200 300 400 500 600

Time (s)

SMCISMC

0

(e)



6

8

10

12

14

16

18W

ind

spee

d (m

s)

0 100 200 300 400 500 600Time (s)

(a)

020406080

100120140160180200

Gen

erat

or sp

eed

(rad

s)

100 200 300 400 500 600Time (s)

SMCISMC

0

(b)

0

1

2

3

4

5

6

7

Elec

tric

al p

ower

(W)

Rated power

times105

100 200 300 400 500 600Time (s)

SMCISMC

0

(c)

1000

1500

2000

2500

3000

3500

4000

Gen

erat

or to

rque

(Nm

)

500100 200 300 400 500 600

Time (s)

SMCISMC

0

(d)

05

10152025303540

Pitc

h an

gle (

deg)

minus5100 200 300 400 500 600

Time (s)

SMCISMC

0

(e)


6 Conclusion




0 100 200 300 400 500 6002

22242628

332343638

4

Time (s)

Roto

r spe

ed (r

ads

)

ISMC

SMCwref


119892kNm


Appendices



119903= 325 sdot 10


119892= 344 kgsdotm2





gear ratio 119899119892= 43165




Step 1 1205920= 120592(119905 minus 119879

119904)

Step 2 120592119899+1

= 120592119899minus 119865(120592) ∙ 119865

1015840

(120592)((1198651015840

(120592))2

minus (119865(120592) ∙

11986510158401015840


119899minus120592(119899minus 1)|120592

119899lt 120576min go


119891= 119899


119904is the




References




































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of




















119879119886=1

21205881205871198773119862119875(120582)

1205821205922

(23)


119865 (120592) = 119879119886minus1

21205881205871198773119862119875(120582)

1205821205922

(24)


119903optis





119878 = (120582 +119889

119889119905)

119899minus1

119890 (119905) (25)


119890 (119905) = 120596119903(119905) minus 120596ref (119905) (26)


119878 (119905) = 120582119890 (119905) + 119890 (119905) (27)


119878 119878 le 0 (28)


119881 =1

21198782

(29)


119889119881

119889119905= 119878

119889119878

119889119905= 119878 (120582 119890 (119905) + 119890 (119905)) (30)



= 119878 119878 = 119878 (120582 119890 (119905) + 119890 (119905))

= 119878 [120582 (119903(119905) minus ref (119905) + 119890 (119905))]

(31)


120582 (119903minus ref) + 119890 (119905)


(32)


119880


(33)


119903(119905) in (31)

we get

120582(1

119869119903

119879119886minus119870119903

119869119903

120596119903minus1

119869119903

119879ls minus ref) + 119890 (119905) = 0 (34)


120582(119879119886

119869119903

minus119870119903

119869119903

120596119903minus

119899119892119869119892119892

119869119903

minus

119899119892119870119892120596119892

119869119903

minus

119899119892

119869119903

119879em minus ref)

+ 119890 (119905) = 0

(35)


119879em =119879119886

119899119892

minus119870119903

119899119892


119899119892

ref +119869119903

120582119899119892

119890 (119905) (36)




119880 (119905) = 119880eq (119905) + 119880sw (119905) (37)


119880sw (119905) = 119896 sign (119878) or 119896 tanh( 119878120593) (38)


119879em =119879119886

119899119892

minus119870119903

119899119892


119899119892

ref

+119869119903

120582119899119892

119890 (119905) +119869119903

119899119892120582119896 tanh( 119878

120593)

(39)




119878 (119905) = (120582 +119889

119889119905)

119899minus1

119890 (119905) + 119870119894int

infin

0

119890 (119905) 119889119905 (40)



119878 (119905) = (120582 +119889

119889119905)

1

119890 (119905) + 119870119894int

infin

0

119890 (119905) 119889119905

= 120582119890 (119905) + 119890 (119905) + 119870119894int

infin

0

119890 (119905) 119889119905

(41)


= 119878 119878 = 119878 (120582 119890 (119905) + 119890 (119905) + 119870119894119890 (119905))

= 119878 [120582 (119903(119905) minus ref (119905) + 119890 (119905)) + 119870

119894119890 (119905)]

(42)


120582 (119903minus ref) + 119890 (119905) + 119870

119894119890 (119905)


(43)


119903(119905) in (41)

we get

120582(1

119869119903

119879119886minus119870119903

119869119903

120596119903minus1

119869119903

119879ls minus ref) + 119890 (119905) + 119870119894119890 (119905) = 0 (44)


119879em =119879119886

119899119892

minus119870119903

119899119892


119899119892

ref

+119869119903

119899119892120582119890 (119905) +

119869119903

119899119892120582119870119894119890 (119905) +

119869119903

119899119892120582119896 tanh( 119878

120593)

(45)


119878 (119905) = 119890 (119905) + 120582119890 (119905) (46)


119878 (119878) = 119864 (119878) [119878 + 120582] (47)


lim119905rarrinfin

119890 (119905) = lim119904rarr0

119878119864 (119878) = lim119904rarr0

119878

119878 + 120582sum(119878) =

1

120582119896120593 (48)



119878 (119905) = 120582 119890 (119905) + 119896119894119890 (119905) + 119890 (119905) (49)


119878 lowast 119878 (119878) = 119864 (119878) [1198782

+ 120582119878 + 119896119894] (50)

lim119905rarrinfin

119890 (119905) = lim119904rarr0

119878119864 (119878) = lim119904rarr0

119878

1198782 + 120582119878 + 119896119894

lim119904rarr0

119878sum (119878) = 0

(51)






Δ120573 = 119870119901119890 (119905) + 119870

119894int 119890 (119905) 119889119905

119890 (119905) = 120596119892norm

minus 120596119892

(52)







0 100 200 300 400 500 6005

556

657

758

859

95

Time (s)

Win

d sp

eed

(ms

)

Mean wind speed 7ms






120578aero () =int119905fin

119905ini119875119886119889119905

int119905fin

119905ini119875119886opt119889119905

120578elec () =int119905fin

119905ini119875119890119889119905

int119905fin

119905ini119875119886opt119889119905

(53)




0 100 200 300 400 500 6004

5

6

7

8

9

10

Time (s)

Win

d sp

eed

(ms

)



where 119875119886opt

= 051205881205871198772

119862119875opt






119888



222242628

332343638

4

Roto

r spe

ed (r

ads

)0 100 200 300 400 500 600

Time (s)

ISCATF

wref


0 100 200 300 400 500 6002

22242628

332343638

4

Time (s)

Roto

r spe

ed (r

ads

)

ISMCSMC

wref




0

05

1

15

2

25


Low

spee

d sh

aft to

rque

(Nm

)

minus05

times105


0100020003000


Gen

erat

or to

rque

(Nm

)

minus4000

minus3000

minus2000

minus1000






222242628

332343638


Roto

r spe

ed (r

ads

)

wref






Max (119879em)kNm

7 (msec) 7689 2184 16908 (msec) 7451 2031 178385 (msec) 7422 2011 1922





Max (119879em)kNm

7 (msec) 7626 1359 12608 (msec) 7449 1172 152685 (msec) 7468 1198 1762




05 1 15 2 2540

60

80

100

120

140

160

180

Frequency (Hz)

Pow

erfr

eque

ncy

(dB

Hz)

SMCISMC

0times10-3


0

20

40

60

80

LSSTq ControlTq

Abov

e bas

eline

()


ATFSMCISMC



0

5

10

ATF SMC ISMCAbov

e bas

eline

()









0 100 200 300 400 500 6006

8

10

12

14

16

18

Time (s)

Win

d sp

eed

(ms

)

(a)

20406080

100120140160180200

Gen

erat

or sp

eed

(rad

s)

SMCISMC

0 100 200 300 400 500 6000

Time (s)

(b)

0

1

2

3

4

5

6

7

Elec

tric

al p

ower

(W)

Rated power

times105

100 200 300 400 500 600Time (s)

SMCISMC

0

(c)

500

1000

1500

2000

2500

3000

3500

4000G

ener

ator

torq

ue (N

m)

100 200 300 400 500 600Time (s)

SMCISMC

0

(d)

05

10152025303540

Pitc

h an

gle (

deg)

minus5100 200 300 400 500 600

Time (s)

SMCISMC

0

(e)



6

8

10

12

14

16

18W

ind

spee

d (m

s)

0 100 200 300 400 500 600Time (s)

(a)

020406080

100120140160180200

Gen

erat

or sp

eed

(rad

s)

100 200 300 400 500 600Time (s)

SMCISMC

0

(b)

0

1

2

3

4

5

6

7

Elec

tric

al p

ower

(W)

Rated power

times105

100 200 300 400 500 600Time (s)

SMCISMC

0

(c)

1000

1500

2000

2500

3000

3500

4000

Gen

erat

or to

rque

(Nm

)

500100 200 300 400 500 600

Time (s)

SMCISMC

0

(d)

05

10152025303540

Pitc

h an

gle (

deg)

minus5100 200 300 400 500 600

Time (s)

SMCISMC

0

(e)


6 Conclusion




0 100 200 300 400 500 6002

22242628

332343638

4

Time (s)

Roto

r spe

ed (r

ads

)

ISMC

SMCwref


119892kNm


Appendices



119903= 325 sdot 10


119892= 344 kgsdotm2





gear ratio 119899119892= 43165




Step 1 1205920= 120592(119905 minus 119879

119904)

Step 2 120592119899+1

= 120592119899minus 119865(120592) ∙ 119865

1015840

(120592)((1198651015840

(120592))2

minus (119865(120592) ∙

11986510158401015840


119899minus120592(119899minus 1)|120592

119899lt 120576min go


119891= 119899


119904is the




References




































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of



















119880 (119905) = 119880eq (119905) + 119880sw (119905) (37)


119880sw (119905) = 119896 sign (119878) or 119896 tanh( 119878120593) (38)


119879em =119879119886

119899119892

minus119870119903

119899119892


119899119892

ref

+119869119903

120582119899119892

119890 (119905) +119869119903

119899119892120582119896 tanh( 119878

120593)

(39)




119878 (119905) = (120582 +119889

119889119905)

119899minus1

119890 (119905) + 119870119894int

infin

0

119890 (119905) 119889119905 (40)



119878 (119905) = (120582 +119889

119889119905)

1

119890 (119905) + 119870119894int

infin

0

119890 (119905) 119889119905

= 120582119890 (119905) + 119890 (119905) + 119870119894int

infin

0

119890 (119905) 119889119905

(41)


= 119878 119878 = 119878 (120582 119890 (119905) + 119890 (119905) + 119870119894119890 (119905))

= 119878 [120582 (119903(119905) minus ref (119905) + 119890 (119905)) + 119870

119894119890 (119905)]

(42)


120582 (119903minus ref) + 119890 (119905) + 119870

119894119890 (119905)


(43)


119903(119905) in (41)

we get

120582(1

119869119903

119879119886minus119870119903

119869119903

120596119903minus1

119869119903

119879ls minus ref) + 119890 (119905) + 119870119894119890 (119905) = 0 (44)


119879em =119879119886

119899119892

minus119870119903

119899119892


119899119892

ref

+119869119903

119899119892120582119890 (119905) +

119869119903

119899119892120582119870119894119890 (119905) +

119869119903

119899119892120582119896 tanh( 119878

120593)

(45)


119878 (119905) = 119890 (119905) + 120582119890 (119905) (46)


119878 (119878) = 119864 (119878) [119878 + 120582] (47)


lim119905rarrinfin

119890 (119905) = lim119904rarr0

119878119864 (119878) = lim119904rarr0

119878

119878 + 120582sum(119878) =

1

120582119896120593 (48)



119878 (119905) = 120582 119890 (119905) + 119896119894119890 (119905) + 119890 (119905) (49)


119878 lowast 119878 (119878) = 119864 (119878) [1198782

+ 120582119878 + 119896119894] (50)

lim119905rarrinfin

119890 (119905) = lim119904rarr0

119878119864 (119878) = lim119904rarr0

119878

1198782 + 120582119878 + 119896119894

lim119904rarr0

119878sum (119878) = 0

(51)






Δ120573 = 119870119901119890 (119905) + 119870

119894int 119890 (119905) 119889119905

119890 (119905) = 120596119892norm

minus 120596119892

(52)







0 100 200 300 400 500 6005

556

657

758

859

95

Time (s)

Win

d sp

eed

(ms

)

Mean wind speed 7ms






120578aero () =int119905fin

119905ini119875119886119889119905

int119905fin

119905ini119875119886opt119889119905

120578elec () =int119905fin

119905ini119875119890119889119905

int119905fin

119905ini119875119886opt119889119905

(53)




0 100 200 300 400 500 6004

5

6

7

8

9

10

Time (s)

Win

d sp

eed

(ms

)



where 119875119886opt

= 051205881205871198772

119862119875opt






119888



222242628

332343638

4

Roto

r spe

ed (r

ads

)0 100 200 300 400 500 600

Time (s)

ISCATF

wref


0 100 200 300 400 500 6002

22242628

332343638

4

Time (s)

Roto

r spe

ed (r

ads

)

ISMCSMC

wref




0

05

1

15

2

25


Low

spee

d sh

aft to

rque

(Nm

)

minus05

times105


0100020003000


Gen

erat

or to

rque

(Nm

)

minus4000

minus3000

minus2000

minus1000






222242628

332343638


Roto

r spe

ed (r

ads

)

wref






Max (119879em)kNm

7 (msec) 7689 2184 16908 (msec) 7451 2031 178385 (msec) 7422 2011 1922





Max (119879em)kNm

7 (msec) 7626 1359 12608 (msec) 7449 1172 152685 (msec) 7468 1198 1762




05 1 15 2 2540

60

80

100

120

140

160

180

Frequency (Hz)

Pow

erfr

eque

ncy

(dB

Hz)

SMCISMC

0times10-3


0

20

40

60

80

LSSTq ControlTq

Abov

e bas

eline

()


ATFSMCISMC



0

5

10

ATF SMC ISMCAbov

e bas

eline

()









0 100 200 300 400 500 6006

8

10

12

14

16

18

Time (s)

Win

d sp

eed

(ms

)

(a)

20406080

100120140160180200

Gen

erat

or sp

eed

(rad

s)

SMCISMC

0 100 200 300 400 500 6000

Time (s)

(b)

0

1

2

3

4

5

6

7

Elec

tric

al p

ower

(W)

Rated power

times105

100 200 300 400 500 600Time (s)

SMCISMC

0

(c)

500

1000

1500

2000

2500

3000

3500

4000G

ener

ator

torq

ue (N

m)

100 200 300 400 500 600Time (s)

SMCISMC

0

(d)

05

10152025303540

Pitc

h an

gle (

deg)

minus5100 200 300 400 500 600

Time (s)

SMCISMC

0

(e)



6

8

10

12

14

16

18W

ind

spee

d (m

s)

0 100 200 300 400 500 600Time (s)

(a)

020406080

100120140160180200

Gen

erat

or sp

eed

(rad

s)

100 200 300 400 500 600Time (s)

SMCISMC

0

(b)

0

1

2

3

4

5

6

7

Elec

tric

al p

ower

(W)

Rated power

times105

100 200 300 400 500 600Time (s)

SMCISMC

0

(c)

1000

1500

2000

2500

3000

3500

4000

Gen

erat

or to

rque

(Nm

)

500100 200 300 400 500 600

Time (s)

SMCISMC

0

(d)

05

10152025303540

Pitc

h an

gle (

deg)

minus5100 200 300 400 500 600

Time (s)

SMCISMC

0

(e)


6 Conclusion




0 100 200 300 400 500 6002

22242628

332343638

4

Time (s)

Roto

r spe

ed (r

ads

)

ISMC

SMCwref


119892kNm


Appendices



119903= 325 sdot 10


119892= 344 kgsdotm2





gear ratio 119899119892= 43165




Step 1 1205920= 120592(119905 minus 119879

119904)

Step 2 120592119899+1

= 120592119899minus 119865(120592) ∙ 119865

1015840

(120592)((1198651015840

(120592))2

minus (119865(120592) ∙

11986510158401015840


119899minus120592(119899minus 1)|120592

119899lt 120576min go


119891= 119899


119904is the




References




































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of





















Δ120573 = 119870119901119890 (119905) + 119870

119894int 119890 (119905) 119889119905

119890 (119905) = 120596119892norm

minus 120596119892

(52)







0 100 200 300 400 500 6005

556

657

758

859

95

Time (s)

Win

d sp

eed

(ms

)

Mean wind speed 7ms






120578aero () =int119905fin

119905ini119875119886119889119905

int119905fin

119905ini119875119886opt119889119905

120578elec () =int119905fin

119905ini119875119890119889119905

int119905fin

119905ini119875119886opt119889119905

(53)




0 100 200 300 400 500 6004

5

6

7

8

9

10

Time (s)

Win

d sp

eed

(ms

)



where 119875119886opt

= 051205881205871198772

119862119875opt






119888



222242628

332343638

4

Roto

r spe

ed (r

ads

)0 100 200 300 400 500 600

Time (s)

ISCATF

wref


0 100 200 300 400 500 6002

22242628

332343638

4

Time (s)

Roto

r spe

ed (r

ads

)

ISMCSMC

wref




0

05

1

15

2

25


Low

spee

d sh

aft to

rque

(Nm

)

minus05

times105


0100020003000


Gen

erat

or to

rque

(Nm

)

minus4000

minus3000

minus2000

minus1000






222242628

332343638


Roto

r spe

ed (r

ads

)

wref






Max (119879em)kNm

7 (msec) 7689 2184 16908 (msec) 7451 2031 178385 (msec) 7422 2011 1922





Max (119879em)kNm

7 (msec) 7626 1359 12608 (msec) 7449 1172 152685 (msec) 7468 1198 1762




05 1 15 2 2540

60

80

100

120

140

160

180

Frequency (Hz)

Pow

erfr

eque

ncy

(dB

Hz)

SMCISMC

0times10-3


0

20

40

60

80

LSSTq ControlTq

Abov

e bas

eline

()


ATFSMCISMC



0

5

10

ATF SMC ISMCAbov

e bas

eline

()









0 100 200 300 400 500 6006

8

10

12

14

16

18

Time (s)

Win

d sp

eed

(ms

)

(a)

20406080

100120140160180200

Gen

erat

or sp

eed

(rad

s)

SMCISMC

0 100 200 300 400 500 6000

Time (s)

(b)

0

1

2

3

4

5

6

7

Elec

tric

al p

ower

(W)

Rated power

times105

100 200 300 400 500 600Time (s)

SMCISMC

0

(c)

500

1000

1500

2000

2500

3000

3500

4000G

ener

ator

torq

ue (N

m)

100 200 300 400 500 600Time (s)

SMCISMC

0

(d)

05

10152025303540

Pitc

h an

gle (

deg)

minus5100 200 300 400 500 600

Time (s)

SMCISMC

0

(e)



6

8

10

12

14

16

18W

ind

spee

d (m

s)

0 100 200 300 400 500 600Time (s)

(a)

020406080

100120140160180200

Gen

erat

or sp

eed

(rad

s)

100 200 300 400 500 600Time (s)

SMCISMC

0

(b)

0

1

2

3

4

5

6

7

Elec

tric

al p

ower

(W)

Rated power

times105

100 200 300 400 500 600Time (s)

SMCISMC

0

(c)

1000

1500

2000

2500

3000

3500

4000

Gen

erat

or to

rque

(Nm

)

500100 200 300 400 500 600

Time (s)

SMCISMC

0

(d)

05

10152025303540

Pitc

h an

gle (

deg)

minus5100 200 300 400 500 600

Time (s)

SMCISMC

0

(e)


6 Conclusion




0 100 200 300 400 500 6002

22242628

332343638

4

Time (s)

Roto

r spe

ed (r

ads

)

ISMC

SMCwref


119892kNm


Appendices



119903= 325 sdot 10


119892= 344 kgsdotm2





gear ratio 119899119892= 43165




Step 1 1205920= 120592(119905 minus 119879

119904)

Step 2 120592119899+1

= 120592119899minus 119865(120592) ∙ 119865

1015840

(120592)((1198651015840

(120592))2

minus (119865(120592) ∙

11986510158401015840


119899minus120592(119899minus 1)|120592

119899lt 120576min go


119891= 119899


119904is the




References




































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of




















0 100 200 300 400 500 6004

5

6

7

8

9

10

Time (s)

Win

d sp

eed

(ms

)



where 119875119886opt

= 051205881205871198772

119862119875opt






119888



222242628

332343638

4

Roto

r spe

ed (r

ads

)0 100 200 300 400 500 600

Time (s)

ISCATF

wref


0 100 200 300 400 500 6002

22242628

332343638

4

Time (s)

Roto

r spe

ed (r

ads

)

ISMCSMC

wref




0

05

1

15

2

25


Low

spee

d sh

aft to

rque

(Nm

)

minus05

times105


0100020003000


Gen

erat

or to

rque

(Nm

)

minus4000

minus3000

minus2000

minus1000






222242628

332343638


Roto

r spe

ed (r

ads

)

wref






Max (119879em)kNm

7 (msec) 7689 2184 16908 (msec) 7451 2031 178385 (msec) 7422 2011 1922





Max (119879em)kNm

7 (msec) 7626 1359 12608 (msec) 7449 1172 152685 (msec) 7468 1198 1762




05 1 15 2 2540

60

80

100

120

140

160

180

Frequency (Hz)

Pow

erfr

eque

ncy

(dB

Hz)

SMCISMC

0times10-3


0

20

40

60

80

LSSTq ControlTq

Abov

e bas

eline

()


ATFSMCISMC



0

5

10

ATF SMC ISMCAbov

e bas

eline

()









0 100 200 300 400 500 6006

8

10

12

14

16

18

Time (s)

Win

d sp

eed

(ms

)

(a)

20406080

100120140160180200

Gen

erat

or sp

eed

(rad

s)

SMCISMC

0 100 200 300 400 500 6000

Time (s)

(b)

0

1

2

3

4

5

6

7

Elec

tric

al p

ower

(W)

Rated power

times105

100 200 300 400 500 600Time (s)

SMCISMC

0

(c)

500

1000

1500

2000

2500

3000

3500

4000G

ener

ator

torq

ue (N

m)

100 200 300 400 500 600Time (s)

SMCISMC

0

(d)

05

10152025303540

Pitc

h an

gle (

deg)

minus5100 200 300 400 500 600

Time (s)

SMCISMC

0

(e)



6

8

10

12

14

16

18W

ind

spee

d (m

s)

0 100 200 300 400 500 600Time (s)

(a)

020406080

100120140160180200

Gen

erat

or sp

eed

(rad

s)

100 200 300 400 500 600Time (s)

SMCISMC

0

(b)

0

1

2

3

4

5

6

7

Elec

tric

al p

ower

(W)

Rated power

times105

100 200 300 400 500 600Time (s)

SMCISMC

0

(c)

1000

1500

2000

2500

3000

3500

4000

Gen

erat

or to

rque

(Nm

)

500100 200 300 400 500 600

Time (s)

SMCISMC

0

(d)

05

10152025303540

Pitc

h an

gle (

deg)

minus5100 200 300 400 500 600

Time (s)

SMCISMC

0

(e)


6 Conclusion




0 100 200 300 400 500 6002

22242628

332343638

4

Time (s)

Roto

r spe

ed (r

ads

)

ISMC

SMCwref


119892kNm


Appendices



119903= 325 sdot 10


119892= 344 kgsdotm2





gear ratio 119899119892= 43165




Step 1 1205920= 120592(119905 minus 119879

119904)

Step 2 120592119899+1

= 120592119899minus 119865(120592) ∙ 119865

1015840

(120592)((1198651015840

(120592))2

minus (119865(120592) ∙

11986510158401015840


119899minus120592(119899minus 1)|120592

119899lt 120576min go


119891= 119899


119904is the




References




































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















0

05

1

15

2

25


Low

spee

d sh

aft to

rque

(Nm

)

minus05

times105


0100020003000


Gen

erat

or to

rque

(Nm

)

minus4000

minus3000

minus2000

minus1000






222242628

332343638


Roto

r spe

ed (r

ads

)

wref






Max (119879em)kNm

7 (msec) 7689 2184 16908 (msec) 7451 2031 178385 (msec) 7422 2011 1922





Max (119879em)kNm

7 (msec) 7626 1359 12608 (msec) 7449 1172 152685 (msec) 7468 1198 1762




05 1 15 2 2540

60

80

100

120

140

160

180

Frequency (Hz)

Pow

erfr

eque

ncy

(dB

Hz)

SMCISMC

0times10-3


0

20

40

60

80

LSSTq ControlTq

Abov

e bas

eline

()


ATFSMCISMC



0

5

10

ATF SMC ISMCAbov

e bas

eline

()









0 100 200 300 400 500 6006

8

10

12

14

16

18

Time (s)

Win

d sp

eed

(ms

)

(a)

20406080

100120140160180200

Gen

erat

or sp

eed

(rad

s)

SMCISMC

0 100 200 300 400 500 6000

Time (s)

(b)

0

1

2

3

4

5

6

7

Elec

tric

al p

ower

(W)

Rated power

times105

100 200 300 400 500 600Time (s)

SMCISMC

0

(c)

500

1000

1500

2000

2500

3000

3500

4000G

ener

ator

torq

ue (N

m)

100 200 300 400 500 600Time (s)

SMCISMC

0

(d)

05

10152025303540

Pitc

h an

gle (

deg)

minus5100 200 300 400 500 600

Time (s)

SMCISMC

0

(e)



6

8

10

12

14

16

18W

ind

spee

d (m

s)

0 100 200 300 400 500 600Time (s)

(a)

020406080

100120140160180200

Gen

erat

or sp

eed

(rad

s)

100 200 300 400 500 600Time (s)

SMCISMC

0

(b)

0

1

2

3

4

5

6

7

Elec

tric

al p

ower

(W)

Rated power

times105

100 200 300 400 500 600Time (s)

SMCISMC

0

(c)

1000

1500

2000

2500

3000

3500

4000

Gen

erat

or to

rque

(Nm

)

500100 200 300 400 500 600

Time (s)

SMCISMC

0

(d)

05

10152025303540

Pitc

h an

gle (

deg)

minus5100 200 300 400 500 600

Time (s)

SMCISMC

0

(e)


6 Conclusion




0 100 200 300 400 500 6002

22242628

332343638

4

Time (s)

Roto

r spe

ed (r

ads

)

ISMC

SMCwref


119892kNm


Appendices



119903= 325 sdot 10


119892= 344 kgsdotm2





gear ratio 119899119892= 43165




Step 1 1205920= 120592(119905 minus 119879

119904)

Step 2 120592119899+1

= 120592119899minus 119865(120592) ∙ 119865

1015840

(120592)((1198651015840

(120592))2

minus (119865(120592) ∙

11986510158401015840


119899minus120592(119899minus 1)|120592

119899lt 120576min go


119891= 119899


119904is the




References




































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















05 1 15 2 2540

60

80

100

120

140

160

180

Frequency (Hz)

Pow

erfr

eque

ncy

(dB

Hz)

SMCISMC

0times10-3


0

20

40

60

80

LSSTq ControlTq

Abov

e bas

eline

()


ATFSMCISMC



0

5

10

ATF SMC ISMCAbov

e bas

eline

()









0 100 200 300 400 500 6006

8

10

12

14

16

18

Time (s)

Win

d sp

eed

(ms

)

(a)

20406080

100120140160180200

Gen

erat

or sp

eed

(rad

s)

SMCISMC

0 100 200 300 400 500 6000

Time (s)

(b)

0

1

2

3

4

5

6

7

Elec

tric

al p

ower

(W)

Rated power

times105

100 200 300 400 500 600Time (s)

SMCISMC

0

(c)

500

1000

1500

2000

2500

3000

3500

4000G

ener

ator

torq

ue (N

m)

100 200 300 400 500 600Time (s)

SMCISMC

0

(d)

05

10152025303540

Pitc

h an

gle (

deg)

minus5100 200 300 400 500 600

Time (s)

SMCISMC

0

(e)



6

8

10

12

14

16

18W

ind

spee

d (m

s)

0 100 200 300 400 500 600Time (s)

(a)

020406080

100120140160180200

Gen

erat

or sp

eed

(rad

s)

100 200 300 400 500 600Time (s)

SMCISMC

0

(b)

0

1

2

3

4

5

6

7

Elec

tric

al p

ower

(W)

Rated power

times105

100 200 300 400 500 600Time (s)

SMCISMC

0

(c)

1000

1500

2000

2500

3000

3500

4000

Gen

erat

or to

rque

(Nm

)

500100 200 300 400 500 600

Time (s)

SMCISMC

0

(d)

05

10152025303540

Pitc

h an

gle (

deg)

minus5100 200 300 400 500 600

Time (s)

SMCISMC

0

(e)


6 Conclusion




0 100 200 300 400 500 6002

22242628

332343638

4

Time (s)

Roto

r spe

ed (r

ads

)

ISMC

SMCwref


119892kNm


Appendices



119903= 325 sdot 10


119892= 344 kgsdotm2





gear ratio 119899119892= 43165




Step 1 1205920= 120592(119905 minus 119879

119904)

Step 2 120592119899+1

= 120592119899minus 119865(120592) ∙ 119865

1015840

(120592)((1198651015840

(120592))2

minus (119865(120592) ∙

11986510158401015840


119899minus120592(119899minus 1)|120592

119899lt 120576min go


119891= 119899


119904is the




References




































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















0 100 200 300 400 500 6006

8

10

12

14

16

18

Time (s)

Win

d sp

eed

(ms

)

(a)

20406080

100120140160180200

Gen

erat

or sp

eed

(rad

s)

SMCISMC

0 100 200 300 400 500 6000

Time (s)

(b)

0

1

2

3

4

5

6

7

Elec

tric

al p

ower

(W)

Rated power

times105

100 200 300 400 500 600Time (s)

SMCISMC

0

(c)

500

1000

1500

2000

2500

3000

3500

4000G

ener

ator

torq

ue (N

m)

100 200 300 400 500 600Time (s)

SMCISMC

0

(d)

05

10152025303540

Pitc

h an

gle (

deg)

minus5100 200 300 400 500 600

Time (s)

SMCISMC

0

(e)



6

8

10

12

14

16

18W

ind

spee

d (m

s)

0 100 200 300 400 500 600Time (s)

(a)

020406080

100120140160180200

Gen

erat

or sp

eed

(rad

s)

100 200 300 400 500 600Time (s)

SMCISMC

0

(b)

0

1

2

3

4

5

6

7

Elec

tric

al p

ower

(W)

Rated power

times105

100 200 300 400 500 600Time (s)

SMCISMC

0

(c)

1000

1500

2000

2500

3000

3500

4000

Gen

erat

or to

rque

(Nm

)

500100 200 300 400 500 600

Time (s)

SMCISMC

0

(d)

05

10152025303540

Pitc

h an

gle (

deg)

minus5100 200 300 400 500 600

Time (s)

SMCISMC

0

(e)


6 Conclusion




0 100 200 300 400 500 6002

22242628

332343638

4

Time (s)

Roto

r spe

ed (r

ads

)

ISMC

SMCwref


119892kNm


Appendices



119903= 325 sdot 10


119892= 344 kgsdotm2





gear ratio 119899119892= 43165




Step 1 1205920= 120592(119905 minus 119879

119904)

Step 2 120592119899+1

= 120592119899minus 119865(120592) ∙ 119865

1015840

(120592)((1198651015840

(120592))2

minus (119865(120592) ∙

11986510158401015840


119899minus120592(119899minus 1)|120592

119899lt 120576min go


119891= 119899


119904is the




References




































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















6

8

10

12

14

16

18W

ind

spee

d (m

s)

0 100 200 300 400 500 600Time (s)

(a)

020406080

100120140160180200

Gen

erat

or sp

eed

(rad

s)

100 200 300 400 500 600Time (s)

SMCISMC

0

(b)

0

1

2

3

4

5

6

7

Elec

tric

al p

ower

(W)

Rated power

times105

100 200 300 400 500 600Time (s)

SMCISMC

0

(c)

1000

1500

2000

2500

3000

3500

4000

Gen

erat

or to

rque

(Nm

)

500100 200 300 400 500 600

Time (s)

SMCISMC

0

(d)

05

10152025303540

Pitc

h an

gle (

deg)

minus5100 200 300 400 500 600

Time (s)

SMCISMC

0

(e)


6 Conclusion




0 100 200 300 400 500 6002

22242628

332343638

4

Time (s)

Roto

r spe

ed (r

ads

)

ISMC

SMCwref


119892kNm


Appendices



119903= 325 sdot 10


119892= 344 kgsdotm2





gear ratio 119899119892= 43165




Step 1 1205920= 120592(119905 minus 119879

119904)

Step 2 120592119899+1

= 120592119899minus 119865(120592) ∙ 119865

1015840

(120592)((1198651015840

(120592))2

minus (119865(120592) ∙

11986510158401015840


119899minus120592(119899minus 1)|120592

119899lt 120576min go


119891= 119899


119904is the




References




































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















0 100 200 300 400 500 6002

22242628

332343638

4

Time (s)

Roto

r spe

ed (r

ads

)

ISMC

SMCwref


119892kNm


Appendices



119903= 325 sdot 10


119892= 344 kgsdotm2





gear ratio 119899119892= 43165




Step 1 1205920= 120592(119905 minus 119879

119904)

Step 2 120592119899+1

= 120592119899minus 119865(120592) ∙ 119865

1015840

(120592)((1198651015840

(120592))2

minus (119865(120592) ∙

11986510158401015840


119899minus120592(119899minus 1)|120592

119899lt 120576min go


119891= 119899


119904is the




References




































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of






































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of

















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