hinf controller design for a variable wind speed

8/4/2019 Hinf Controller Design for a Variable Wind Speed

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HinfController Design for a Variable Wind SpeedTurbineH. Gonzalez, H. R. Vargas

Abstract: This paper gives a description of a windgenerator system composed by a doubly fed inductiongenerator (DFIG), its dynamic model and each one of itssubsystems. Also, the control logic that regulates theactive and reactive power delivered by the DFIG isdescribed. The electrical control logic is based on statorflux oriented technique and the turbine speed is controlledvarying the blade pitch angle. The three regulators foundhad been designed using the frequency domain approachbased on genetic algorithms.Keywords: wind turbine, wind model, doubly fed inductiongenerator, stator flux oriented control, blade pitch anglecontrol.

I. INTRODUCTION

Given that certain wind turbine system parameters canchange over time, new approaches based in LQG [11],Hinf [12] and adaptive control [13], among others, hasbeen proposed. Those approaches seek to avoiddependence upon parameter variations and wind speedvariations.

II. DYNAMIC MODEL OF THE WINDThe wind speed distribution over the rotor sweptarea can be calculated as the sum of two components at

hub level: the first is the average speed and the second,called turbulence, related with the temporal variationsof the wind speed but defined in frequency domain withthe Kaimal spectrum [3]:

To simulate the fluctuations of the wind in the timedomain a white noise generator is used interconnectedto an analog filter [2] that shows a power spectraldensity (PSD) very approximate Kaimal model andgiven by equation (4).

H(s)=u O0182c i+l,3653cs+O,9846 (4)1,3463c 2S2 3,7593cs 1

o

The dramatic growth of wind power systems haspushed research and publications about thistopic around the world. South America is not anexception. The mathematic models of wind powersystems with their subsystems has been treated indifferent doctoral thesis, [1], [2], [3], [4], addressing inmore or less detail, the diverse phenomena whichappear dur ing the transformat ion process of windenergy in electric energy (aerodynamic, mechanic andelectromagnetic phenomena).The technology is changing the way electric poweris converted from wind power. Initial projectsemployed turbines of constant speed and squirrel cageinduction motor. Now, turbines of variable speed anddoubly fed induction generator (DFIG) are beingemployed. The stator winding of the DFIG isinterconnected to the electric network at constantfrequency and the rotor winding is interconnected to asystem of magnitude, phase and frequency variables.This system is composed by an AC/AC inverter thatregulates the active and reactive power delivered by theDFIG to the grid in spite of fluctuating wind.A control scheme used in DFIG is based in theoriented field control. The main advantage of thisscheme is the decoupling of the DFIG dynamic. Thisdecoupling permits to implement two independentregulators to the rotor current components: dr and qnallowing regulate the output power too [5], [6], [7], [8],[9]. Its control logic is backed up with a system thatregulates the mechanic speed of the rotor using a PIregulator which varies the blade pitch angle [10], [11],[12].

978-1-4244-2218-0/08/$25.00 (92008 IEEE.

={20Z to Z< m600 to > m

whereFrequencyTurbulence length scalez Tower heightStantadard deviation of the wind speedTurbulence strength

o Average wind speed

(1)

(2)

(3)

Authorized licensed use limited to: Universidad Industrial de Santander. Downloaded on August 06,2010 at 14:35:07 UTC from IEEE Xplore. Restrictions apply.


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Fig. 1 Block diagram representation of the equivalent wind speedmodel

In a turbine of three blades, spaced 120 degrees, hasbeen found that appearing fluctuations in theaerodynamic torque are produced by third orderharmonic components of the turbulence, with afundamental frequency of equal value to the speed ofthe rotor. This situation is known as "rotationalsampling of turbulence" (reported as the main cause offlicker from wind turbines). The block diagram shownin figure 1 models this situation. This system generatesa wind speed time series sequence located at hub level.

C P = 0 , 5 1 7 6 C ~ 6 - 0 , 4 P - 5 } - ~

The rotor aerodynamic power coefficient dependson the aerodynamic design of the turbine. Any designof wind turbine has a theoretical maximum value of0.593, called Betz limit. can be calculated usingequations (11) and (12)

(12)0.035+ 0,08/3 - /33 + 1IV. MECHANICAL MODEL

There are wind turbine mechanical parts such asblades, low speed shaft, gear box, high speed shaft andgenerator that form a mechanical system that cantransmit oscillations to the grid. Such dynamic systemis represented by a four mass equivalent model (Figure2.). This model may be described as follows:

1Kalmal - - - + ~ - - - + @ L~ __ EquivalentFilter SpeedJalmal SpeedFilter - - - + ~ x TSin (311)Stochastic

Whit. Nol.. ---+Generator

White Noi.eGenerator

White Nol.e ---+Generator

and

III. AERODYNAMIC ROTOR MODELThe conversion of the wind power to mechanical

power by the wind turbine rotor can be calculated by:

(A,P)T =-pAR P V2 (13)Aer 2 AdTAer - DRot (wRot - WI ) - QRot = J Rot dt wRot (14)dDRot (wRot -W I )+QRo t -1;. = JE n g I -W I (15)dtd1; - DGen (w 2 - wGen ) - Qcen = J Eng2 - w2 (16)dtdDGen (w 2 - wGen ) + QGen - TE1ec = J Gen dt wGen (17)

QRot =KRot f( wRot - WI ) dt (18)QGen =KGen f(w2 - wGen ) dt (19)

w2 (20)=-=nEngWIwhereTAer Aerodynamic torqueJ Rot Blades and rotor hub moment of inertiaKRot Low speed shaft tortional stiffnessDRot Low speed shaft damping coefficientwRot Turbine angular speedJ EngJ Gear boxes moment of inertiaJ Eng2WI Gear boxes angular speedsw2nEng Ratio gear boxKgen High speed shaft tortional stiffnessDgen High speed shaft damping coefficient

(10)where is the rotor mechanical power, p is the airdensity, A is the rotor surface, is the wind speed atthe center of the rotor (Fig. 1), Cp is the rotoraerodynamic power coefficient, p is the blade pitchangle and WROT is the turbine angular mechanicalspeed.

0 , 2 7 6 ~ ~ T F S + 0 , 0 3 0 70,3691dTF s + 1, 7722dTF S + 1

4 , 7 8 6 ; ~ T F S + 0 , 9 9 0 47,6823dTF s + 7,3518dTF s + 1

where is the turbine displacement angle. The boxesH(O,j) and H(3,j) that represent the effects of the dc andthird wind speed harmonic components on turbine shafttorque respectively, are given by

d ~ (8)where is the turbine blade radius.



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Fig. 2 Four mass mechanical equivalent

To rotor currents, the transformation equations to d-qcoordinates are given in equation (22):

(27)

(26)

(25)Rs RsR= R

Rr-w o

Wo-(wo -wr )

(wo -wr )

'Pds Lss Lm Ids'Pqs Lss Lm IqS'Pdr Lm Lrr Idr'Pqr Lm Lrr Iqr

The electromagnetic torque, the active and reactivepower on the stator side in the d-q coordinates are givenrespectively as:

wheres Stator winding resistancess Stator winding inductancer Rotor winding resistancerr Rotor windig inductancem Mutual inductancePI Even number ofpoles

Generador

Engrl

DFIGMODEL

Generator angular speedGenerator moment of inertiaGenerator electromagnetic torque

[ ~ : ] j[ CO.S(((Oot)) COS((Wi - 2[]J COs(wot+2[] ] [ ~ : ]-sm wot -sm wo t - ) -sm(wot+)J Ie(21)

Here, the doubly fed induction generator based onvariable speed use induction machine model in two axisd-q reference frame rotating at o synchronous speed.Beginning with stator currents, the transformationequations to d-q coordinates is given in equation (21):

~ d ' ] = ~ [ c O S ( O ) cos(O_2;J c o s ( O + 2 ; J ] [ ~ : ] (22)qr 3 . (8) . (8 277:J . ( 277:J+ Iewhere

3=2. PfLm (ldr1qs -lqJds)3

PACT =2. (Vdslds VqJqs)QREA %VqJds - Vdslqs )

(28)(29)(30)

By applying the d-q transformation, using equations(21), (22) and (23), the stator and rotor voltagesequations result:Vds Ids 'Pds 'Pds~ Iqs d 'PqS 'Pqs (24)Vdr Idr dt 'Pdr 'PdrVqr Iqr 'Pqr 'Pqr

ddt 0 r (23) There are two operation modes ofDFIG, which dependon the magnitude and phase of rotor voltage respect toinduced voltage: In the sub-synchronous operationmode, magnitude rotor voltage is greater than inducedvoltage magnitude, and the rotor voltage is in phasewith the induced voltage. In the super-synchronousoperation mode, magnitude rotor voltage is less thaninduced voltage magnitude, and the rotor voltage is theanti-phase with the induced voltage. In order to avoidthe instability of the generation system is best to controlthe DIFG generated power applying rotor voltagebetween 0 Vdr 00 and -00 Vqr 0, using thesuper-synchronous operation mode.



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VI. STATOR FLUXORIENTED CONTROLThis approach seeks to emulate the control of a

direct current machine, having into account the nextconsiderations: Stator resistance Rs is neglected, mainly on powermachines greater than 10 kW.

Magnet izat ion current phasor ms is supposedconstant.

Grid frequency is supposed constant.Assuming that stator flux magnitude and direction arekept constant, the magnetic flux equations, equation(27), may be expressed as

The proposed stator flux oriented control uses tworobust and independent controllers based on direct andquadrature axis components of the rotor current, /d nand, /qr, respectively.Figure 3 depicts the block diagram representation of

the control st ructure developed, where dr ref andqr ref ' are obtained from equations (38) and (39),respectively. The anti-windup compensator constant isadjusted in order to the resulting system, with theintegral action given by the robust control regulator, iseffect ively not affected by saturation. The transferfunctions / dr and /q r are equals and are obtained/Vdr IVAfrom the space state DFIG representation, equation(36), taking into account that slip is constant.

\}Iill = L m = L ss / + L m/ dr\}IqS 0 L ss / qs L m/ qr

2 _\}Idr = ~ I / m s l oL rr / drss

\}Iqr (JLrr / qr2m _

LssLrr

(31)(32)(33)(34)(35) Fig. 3 Block diagram of a PI control

The above equations can be used to obtain the DFIGsimplified model, equations (36) and (37).

- sl 0[/@ ] aL rr [/@ aL rr [ ~ /q r -W sl - /q r 0aL rr aL rr

(36)

(37)

During the design stage the command hinfopt of theRobust Control Toolbox of Matlab was used.Previously, cost functions were defined to the nextvariables: a) error signal b) control actionand the output signal equation (40).The selection of k;, Gi Y hi was carried out us ing

genetic algorithms (GA), equation (41). The objectivefunction is based on the transient response of thesystem when is excited with a step input, minimizingthe ITSE and ISE performance indexes related with theerror signal, e(t), and the control action, u(t)respectively. N is the number of points, used to evaluatethe transient response, at which the system reach thesteady state. t(i) is the simulation time.

The active and reactive power in the coordinates systemare given by

(38)

(39)

k(s/ +1)w (s)- 2 /a 22 - ( ~

(N 2 N 2J=100- O,st;t(i) e(i) 6,st;U(i) (41)

VII. ROBUST HinfCONTROLThe stator flux or iented control is used in order to

decouple the control of the active and reactive power.

The fol lowing GA parameters were used: a)Crossover rate of 70%, b) Mutat ion rate of 0.5% c)Population size of 20. The algori thm is stopped if thestandard deviation of performance function of each



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individual is less than 0.01 or if maximum number ofiterations is exceeded; here 500.The speed control of the turbine is carried out using thepitch angle control technique. The control scheme isshown in figure 4. The plant model, =OJg;fp , isobtained linearizing the equation system via Taylorexpansion.

Pitch

Fig. 4 Anti-windup speed robust controlThe robust controller was designed again, followingthe steps given above, but the new objective function isdefined by equation (42). The new GA parameters

were: a) Crossover rate of 60% and b) Mutation rate of0.5%, while all other parameters were kept constant.

(N 2 N 2J100- o,ost;t(i)*e(i) +O,Olt;U(i) (42)

VIII. EVALUATION OF THE PROPOSEDCONTROL SYSTEMTo show the effectiveness of the proposed HinfRobust Controller, a comparison is made with thedesigned PI controller with GA method [16], using theturbine NM manufactured by Neg Micon. Thereference values correspond to the following: activepower -2 MW and mechanic speed 1515 rpm.Figure 5 shows the time response of the systemusing an average wind speed of 14.5 m/s and windturbulence of 40%. Comparing the variables, thecontrol action of the robust controller and the PIregulator are practically identical to the control loop ofthe mechanic speed of the shaft, but, the Hinf regulatorcan't follow the mechanic speed of the shaft around therated mechanic speed of the induction generator.Otherwise, the active power remains constant duringwind speed fluctuations, even though the control actionwas increased. If the average wind speed is near tothe rated speed of the turbine, 11 mis, the response ofthe two controllers is practically identical, see Figure 6.Therefore, it is recommended to use the robustcontroller when the wind speed is greater than the ratedspeed of the turbine.

a)

b)

c)Fig. 5 PI controller vs. Robust controller. a) Wind speed - 14 b)DFIG mechanic speed. c) DFIG active power.

In order to obtain the mechanical parameters of theactuator that regulates the mechanic speed of theturbine, the behaviour of the system during averagewind speed variations was analyzed, taking 11 m/s and24 m/s as the limits. Figure 7 shows that the maximumvariation of the pitch angle is about 22 degrees with anangular variation of 17 degrees per minute. Thesecharacteristics are fullfilled by commercial hydraulicactuators used to control the pitch angle.



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TABLA IDFIG PARAMETERSFrequency [Hz] 50Stator winding resistance [0] 0.001Stator winding inductance [mH] 0.07Rotor winding resistance [0] 0.0013Rotor winding inductance [mH] 0.08Mutual inductance [mHl 3Even number of polesMoment of inertia [Kgm 1 65

TABLA IIMECHANICAL PARAMETERS

Fig. 6 Active power - Wind Speed 11.....................

' ~ " ~ " " " " " ' - - ~ - ' - ' ~ v ~ " " ' ' ' ' _ ~ ''> :

Momento f inertia of the blades and the hub 49.5*105[Kg-m2]Lowspeed shaft tortional stiffness fKg-m /sg 114*10Low speed shaft damping coefficient [Kg- 105m2/sg2High speed shaft tortional stiffness 755.658*10High speed shaft damping coefficient [Kg- 1*103m2/sg]Gear box ratio 83.5

IX. CONCLUSIONILMa HRMNMJUT' _0., . . . . . .

Fig. 7 Pitch angle control. a) Wind profile. b) Pitch angleThe electrical specifications to the DFIG rotorinverter can be obtained from figure 8, taking asreference an average wind speed of24 rn/s:

X. BIBLIOGRAPHY

An effective way to control the active powerdelivered by a DIFG, during high wind speed, iscombining stator flux oriented control and pitch anglecontrol. The simulation shows that the Hinf controlleris more robust during variations of the wind speedcompared with a PI controller, though the mechanicspeed is greater than 40 rpm over the rated speed.The performance index ISE and ITSE are a goodalternative to obtain the performance function to designHinf controllers. This allows obtain an optimalcontroller for each one of the three decoupled variablesof the turbine dynamic model: rotor current Idr and Iqr,thus allowing to regulate the active and the reactivepower and the mechanic speed ofDFIG.o 35 V

130kWOt05Hz

Voltage phase (max.)PowerFrequency

[1] Carvalho Rosas, Pedro Andre. Dynamic InfluencesOf Wind Power On The Power System. PhD Thesis.Technical University of Denmark and Risoe NationalLaboratory. March 2003.

, - ~ - ~ ~ . ~ ' ~ " " - ' ' ' ~ . - ' ' ' ' ' ' ' ; ! ; , ' '

[2] W. Langreder. Models For Variable Speed WindTurbines ". MsC Theses, CREST LoughboroughUniversity and Risoe National Laboratory. 1996.[3] lov, Florin. Contributions to Modelling, Analysisand Simulation of Ac Drive Systems. Application toLarge Wind Turbines. Ph.D. Thesis. Dunarea de JosUniversity- Galati. 2003.

Fig. 8 AC inverter a) Power f low. b) Rotor voltage [4] P. Ledesma. Analisis dinamico de sistemaselectricos con generaci6n e6lica. Ph.D. Thesis.Universidad Carlos III de Madrid. 2001



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[5] Paul Etienne Vidal, Maria Pietrzak David, BernardDe ForneI. Stator flux oriented control ofa doubly fedInduction machine. Laboratoire d'Electrotechnique etd'Electronique Industrielle, Unite mixte de rechercheINPT-ENSEEIHT/CNRS. 2003[6] F. Poitiers, M. Machmoum, R. Le Doeuff, M.E.Zaim. Control of a doubly fed induction generator forwind energy conversion systems. Ecole Polytechniquede l'Universite de Nantes, SaintNazaire, France.[7] Jeong-Ik Jang, Young Sin Kim, Dong Choon Lee.Active and reactive power control ofDFIG for energyconversion under unbalanced grid voltage. Dept. OfElectrical, Eng. Yeungnam Univ. Daedong, Gyeongsan,Gyeongbuck, Korea. IEEE 2006.[8] S. Wang, Y. Ding. Stability analysis of fieldoriented doubly fed induction machine drive based oncomputer simulation. Electric Machines and powersystems, Vol. 21, 1993.[9] L. Morel, H. Godfroid, A. Mirzaian, J. Kauffmann.Double fed induction machine: converter optimisationandfiel oriented control without position sensor. IEEEProc. Electr. Power Appl. Vol. 145,julio de 1998.[10] Morten H. Hansen, Anca Hansen, TorbenLarsen, Paul Sorensen, Meter Fuglsang. Control designfor a pitch regulated, variable speedwind turbina. RisoNational Laboratory. Enero 2005.[11] Shashitanth Suryanarayanan, Amit Dixit. On thedynamics of th pitch control loop in horizontal axislarge wind turbines. American Control Conference,Junio 2005.[12] Hongwei Liu, Yonggang Lin, Wei Li. Study onControl Strategy of Individual Blade Pitch ControlledWind Turbine. Intelligent Control and Automation.WCICA 2006.[13] Lars Nielsen. Modelling and control of variablespeed HA WT utilizing hybrid Control. AalborgUniversity. Septiembre 2004.[14] Rocha, Ronilson. Martins Filho, Luis Siqueira. Amultivariable control for wind energyconversion system. Department of control andAutomation. Department of Computation CampusMorro do Cruzeiro. IEEE 2003.[15] Kathryn E. Johnson, Lucy Y. Pao, Mark Balas,Lee Fingersh. Control of variable speed windturbines, standard and adaptive techniques formaximizing energy capture. IEEE Control SystemsMagazine. 2006

[16] Gonzalez Acevedo, Hernando. Vargas Torres,Hermann Raul. Diseno de un controlador para unaturbina eolica de velocidad variable utilizandoalgoritmos geneticos. II Simposio Internacional enFuentes Alternativas de Energia y Calidad Energetica.2008

XI. BIOGRAPHIESHernando Gonzalez Acevedo. Received theB.Sc. degree in electronic engineering from theIndustrial University of Santander (UIS),Bucaramanga, Colombia, in 2000 and theM.Sc. degree in Electrical power from UIS in2007. Currently, he is a Professor with theElectronics Engineering School at Universityof Santo Tomas, Bucaramanga, Colombia. Hisareas of interest are control , robotics, windpower generation. Mr. Gonzalez-Acevedo is a member of AMSCP(Col) Research Group on automation, modeling, simulation andcontrol of industrial products and process. E- mail:hernando [email protected]

Hermann Raul Vargas Torres. Received theB.Sc. degree in electrical engineering from theUniversidad Industrial de Santander (UIS),Bucaramanga, Colombia, in 1985. The M.Sc.degree in Electrical power from UIS in 1990,and the Ph.D. degree in Electrical Engineeringfrom Universidad Pontiflcia Comillas (UPCG),Madrid, Spain, in 2002. Currently, he is aProfessor with the Elec tr ica l Engineer ingSchool at the Universidad Industrial de Santander (UIS),Bucaramanga, Colombia. His areas of interest are power systemsstability and control, transient analysis, power quality, protectiverelaying, wind power and policy analysis. Mr. Vargas-Torres is amember of GISEL (Col) Research Group on Electric Power Systems.

E-mail: hrvargasrWuis.edu.co

hinf controller design for a variable wind speed

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