重要的三个模型的比较.pdf

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1、 Fig.1.Collective and individual pitch control Identification of Wind Turbine Model for Individual Pitch Controller Design Vlaho Petrovi,Mate Jelavi,Student Member,IEEE,Nedjeljko Peri,Senior Member,IEEE University of Zagreb,Faculty of Electrical Engineering and Computing vlaho.petrovicfer.hr,mate.je

2、lavicfer.hr,nedjeljko.pericfer.hr Abstract-The use of wind power has been increasing rapidly over last few decades and according to all predictions this trend is likely to continue.At the same time need for better cost effectiveness of wind power plants has stimulated growth in wind turbines size an

3、d rated power.As wind turbines grow in size they are subject to extreme structural loads and fatigue.In order to reduce such loads advanced control methods are explored among which individual pitch control has demonstrated very promising results.To design an individual pitch controller suitable wind

4、 turbine model is required.Derivation of wind turbine model for individual pitch controller design is addressed in this paper.I.INTRODUCTION Modern wind turbines operate in a wide range of wind speeds,typically from 3 to 25 m/s.Power contained in wind is proportional to the third power of wind speed

5、 1 and therefore increases rapidly with increase of wind speed.To enable wind turbine operation in such a variety of operating conditions a sophisticated control system is needed that will optimize energy conversion during weak winds and constrain turbine power during strong winds.An efficient way t

6、o constrain wind energy capture is pitching the rotor blades around their longitudinal axis i.e.pitch control.To make wind turbines more cost effective and energy produced from wind less expensive wind turbines rated power is constantly increasing.The increase in wind turbine rated power is accompan

7、ied with extreme growth of wind turbines dimensions(tower height and rotor diameter of modern multimegawat wind turbines exceed 100 m).Because of that tower oscillations and structural loads get more emphasized.Therefore the control system,in addition to controlling the power output of the wind turb

8、ine,has to accomplish damping of the tower oscillations and reduction of structural loads.Tower oscillations are driven by aerodynamic thrust force and can be reduced by adequately changing blades collective pitch angle.Control methods for damping of the tower oscillations are not in the scope of th

9、is paper.Description of such methods can be found in e.g.2.Structural loads on the rotor blades are caused by gravity,inertia,wind shear and tower shadow.Wind shear and tower shadow introduce changes of wind speed depending on the vertical position.Therefore the blade is exposed to different wind sp

10、eeds as it rotates.This results in oscillations in blade structural loads where the most significant is the first harmonic on frequency equal to the wind turbine rotor frequency(1p once per revolution).As it has been shown in 3 loads caused by wind shear and tower shadow can be strongly influenced a

11、nd reduced by means of pitch control.Since each blade is influenced by different wind speed,oscillations in structural loads can be reduced only by individual pitching of each blade.Depending on measured local loads on rotor blade an additional pitch angle is added to the collective pitch angle c.Si

12、nce loads caused by wind shear and tower shadow are periodic additional pitch angle will be periodic too.The paper is organized as follows.In Section II the basis of individual pitch control are described.Mathematical model and experimentally identified model of wind turbine are given in Section III

13、 and Section IV respectively.II.INDIVIDUAL PITCH CONTROL The goal of the individual pitch control is to reduce the loads first harmonic at frequency 1p.In order to do so the individual pitch controller has to find adequate periodic pitch movement that will counteract periodic component of the loads.

14、Since the frequency of periodic pitch movement is known(1p)the controller needs only to calculate its amplitude based on loads measurements.Therefore it is convenient to use Parks d-q transformation:()33,1122cos,sin,33,cossin,dy iiqy iiiiidqcdiqiMMMMf MM=+(1)where My,i is measured blade load,i is bl

15、ade pitch angle and i is azimuth angle of the ith blade.Variables with indices d and q represent blade loads and pitch angles in d-q coordinate system.As it can be seen from(1),reliable blade loads measurements are necessary for individual pitch control.This poses no problem since reliable and preci

16、se equipment for blade loads measurements has recently become available 4.With Parks transformation(1)amplitude of the loads first harmonic is transformed into mean values of moments Md and Mq in d-q coordinate system.Therefore the control objective in d-q coordinate system is to reduce this mean va

17、lue to zero.Loads in d-q coordinate system also contain higher harmonics(3p,6p,9p)that originate from Parks transformation of higher harmonics of measured loads.These higher harmonics can not be influenced by 1p pitch actions so they have to be properly damped by the control algorithm.In Fig.1 a typ

18、ical performance of individual pitch control is shown and compared with the performance of collective pitch control(wind turbine responses on step change in wind speed are shown).It can be seen that periodic blade loads are reduced by introducing periodic component to blade pitch angle.Pitch activit

19、y has a frequency of 1p(typically less than 0.5Hz in modern turbines)what doesnt impose great demands on pitch system.To be able to design an individual pitch controller a wind turbine model is required that can relate structural loads to changes in pitch angle.Such a model is described in the next

20、section.III.MATHEMATICAL MODEL OF WIND TURBINE For wind turbine modelling advanced methods like blade element and momentum theory 1 are used that can model wind turbine aerodynamics and mechanics in detail.However,such models result in implicit mathematical expressions that are not suitable for cont

21、roller design.So another approach,suggested in 5,will be used here.In this approach wind turbine is modelled based on performance coefficients(Cxy in the following expressions)that relate quasi-static loads(forces and moments)to wind speed,pitch angle and rotor speed.For defining forces and moments

22、on wind turbine,coordinate systems suggested by Germanischer Lloyd are used(Fig.2).The proposed model includes only tower flexibility while blades are considered as rigid.This approximation is allowable since wind turbine tower is far more flexible than its blades.The most important part of the mode

23、l is the proper modelling of blade loads.Loads on any other part of the turbine can be calculated by proper transformation of blade loads as it will be shown.Out-of-plane blade thrust force Fx,i can be expressed as:()22,1,2x iarFxw iiw iFRCvv=,(2)where a is air density,Rr is rotor radius and is roto

24、r speed.Relative wind speed for ith blade vw,i is a result of actual wind speed vw0,i and tower fore-aft oscillations 5:,0,33cos24rw iwifafaitRvvxxh=+?,(3)where ht is tower height and xfa is tower top displacement caused by tower bending.The blade azimuth angle i equals to zero when ith blade is in

25、top vertical position.The last part of equation(3)describes the influence of tilt rotation of the tower top.Tilt rotation has azimuth dependent effect which varies over rotor radius.The 3/4 blade radius location of the rotor blades is assumed to be the effective location for taking Fig.2.From left t

26、o right:rotational blade coordinate system with origin at blade root,fixed hub coordinate system with origin in hub centre and nacelle coordinate system with origin on the tower top tilt rotation into an account.The multiplier 3/(2ht)is the ratio between displacement and rotation if a prismatic beam

27、 of length ht is subjected to a bending force load 5.While the blade out-of-plane thrust force has mainly aerodynamic origins,forces in other two axes can be described as the sum of aerodynamic,gravitational and inertial components:,.y iy ae iy gr iy in iz iz ae iz gr iz in iFFFFFFFF=+=+(4)Aerodynam

28、ic components are defined similarly to the out-of-plane thrust force(2):()()22,22,1,21,.2y ae iarFyw iiw iz ae iarFzw iiw iFRCvvFRCvv =(5)It should be noted that in most cases aerodynamic force Fz,ae,i can be omitted due to its small values.Gravitational force is always directed towards the ground b

29、ut as blade rotates,gravitational influence is shifting between y and z axes in blade coordinate system:,sin,cos,y gr ibiz gr ibiFm gFm g=(6)where mb is blade mass and g is gravitational acceleration.Inertial forces manifest differently in y and z axes.While Fy,in,i is reaction to acceleration,Fz,in

30、,i represents centrifugal force:()(),2,y in ibhubcm bz in ibhubcm bFmRzFmRz=+=+?(7)where Rhub is hub radius and zcm,b is z-axis coordinate of blade center of mass.Besides blade forces,blade moments have to be defined as well.Moment Mx,i causes rotor rotation so it is not important for structural loa

31、ds considerations.Moments in other two axes have mainly aerodynamic character and they can be expressed similarly to the aerodynamic forces(2)and(5):()()32,32,1,21,.2y iarMyw iiw iz iarMzw iiw iMRCvvMRCvv =(8)As stated before,blade loads are the main source of loading for the rest of the turbine.In

32、order to find the loads on the nacelle,loads from rotational blade coordinate systems are transferred into fixed hub coordinate system:()()3,13,13,1,cossin,cossin,h hubx iiy huby iiz iiiz hubz iiy iihubiFFFFFFFFmg=+(9)where mhub is the hub mass.It can be noted that force in z axis besides blade load

33、s also contains the gravity of the hub.Moments on the hub can also be expressed using blade loads:()()3,13,13,13,1cossin,cossin,y huby ihubx iiiz iihubcm hubiz hubz iiiy ihubx iiiMMRFMmgxMMMRF=+=+(10)where xcm is x-axis coordinate of the hub centre of mass.Hub gravity appears in moment My,hub becaus

34、e hub centre of mass isnt located in the origin of the hub coordinate system.Forces on the nacelle are equivalent to the forces on hub,except for the gravity of generator and nacelle that appears in z-axis:(),.x nacx huby nacy hubz nacz hubgennacFFFFFFmmg=+(11)Moments on the nacelle in y and z axes

35、are also called tilt and yaw moments.They can be expressed using hub loads and the gravity of generator and nacelle:()(),tilty hubx hubhubtz hubovnaccm nacgencm genyawz huby hubovMMFhhFxmxmxgMMFx=+=(12)where hhub is hub centre height,ht is tower height and xov is the distance between the tower top a

36、nd the rotor centre.Combining(12)with the wind turbine rotor dynamics and tower oscillations model described in 5 nonlinear mathematical model can be obtained.Since wind turbine is highly nonlinear,it is not possible to use a linear controller for wide variations of wind speed.As shown in 6 gain sch

37、eduling is good method for dealing with wind turbine nonlinearity.Therefore wind turbine model has to be Fig.4.Servo drive model in d-q coordinate system linearised in several operating points for which linear controllers will be designed.Blade out-of-plane thrust force can be linearised as follows:

38、,x ix vw ixixFFvFF=+,(13)where Fx,v,Fx,and Fx,are partial derivates.Other blade loads can be linearised in the same way as the thrust force(13).By combining linearised blade loads with Parks transformation(1)we obtain linear expressions for tilt and yaw moments:()()()()()()()(),3332233,223322tilthub

39、tx vw cxcxy vhubx vovz vw dz vovy vw qyhubxovzdzovyqyawz vovy vw dy vhubx vovz vwMhhFvFFMRFx FvMx FvMRFx FMx FMMx FvMRFx Fv=+=+()(),33,22qzovydyhubxovzqMx FMRFx F+(14)where vw,c,vw,d and vw,q are wind speed mean(collective)value,and wind speed in d-q coordinate system respectively.The above expressi

40、ons present needed model that relates loads with wind speed and pitch actions in d-q coordinate system.Such a model can be used for individual pitch controller design.For our model to be complete and suitable for controller design it has to include adequate model of servo drive used for positioning

41、of the blades.The servo drive has to be modeled in d-q axes as well.The principle of deriving servo drive model in d-q axes is shown in Fig.4.Electric servo drives of common modern wind turbine can be fairly well described by a mathematical model of second order.Since we are considering digital impl

42、ementation of controller we express servo drive by a discrete transfer function:()()()*121212121isizb zb zGzza za z+=,(15)where i is reference blade pitch angle demanded by the controller,and i*is actual blade pitch angle.From(15)we can write recursive equation describing servo behavior in time doma

43、in:()()()()()*122121212.iiiikakakbkbk=+(16)In Parks transformation(1)discrete time has to be used:tkT=,(17)where T is sampling time.By combining(16)with Parks transformation(1)servo drive model in d-q coordinate system is obtained as:()()()()()()()()()()()()()()*,.dDdCqCqqDqCdCdzGzzGzzGzzzGzzGzzGzz=

44、+(18)In(18)the transfer functions are defined as:()()()()()()()()()()()()()()()12121212121212121212*1212coscos 2,1coscos 2sinsin 2,1coscos 2sinsin 2.1coscos 2DCCbT zbT zGzaT zaT zbT zbT zGzaT zaT zaT zaT zGzaT zaT z+=+=+=(19)From(18)and(19)it is obvious that servo drive introduces coupling in the d-

45、q coordinate system and that coupling gets more emphasized with increase of rotor speed and sampling time.Coupling in d-q coordinate system is a consequence of lag between actual and desired pitch angle introduced by servo drive.As an example consider reference pitch angle to be pure sine function.D

46、ue to the servo drive dynamics,the actual pitch angle is lagged sine function which can be interpreted as the sum of sine and cosine functions.This coupling has to be accounted for when designing controller.The use of multivariable controller techniques for process decomposition often yields high or

47、der controllers that are not practical for implementation.Therefore another method for variable decoupling proposed in 3 is used here.Namely,when performing inverse Parks transformation(1)phase lag introduced by servo drive at the rotational frequency is added to the rotor azimuth angle.Therefore th

48、e argument of sine and cosine functions in relation for pitch angle in(1)transforms in the following way:()iiservo +.(20)Mathematical model given in this chapter is very useful for gaining insight into wind turbines operation.However it is derived using several simplifications what makes it less rel

49、iable.So another possibility to obtain needed process model is explored here.It is based on experimental identification of process model.Fig.5.Response of blade root bending moment in d-q coordinate system Md to step change in demanded pitch angle in d axis(left)and q axis(right)IV.EXPERIMENTAL IDEN

50、TIFICATION OF LOAD MODELS Process models were identified using recorded input-output data.Instead of experimenting on a real wind turbine professional software for wind turbine simulation and load calculation GH Bladed was used.GH Bladed uses complex aerodynamic and structural model of wind turbines