Multivariable Centralized Control with Decoupling and Feedforward Compensation for Residential Wind Turbine

Transcription

1 Milano (Italy) Auut - September, Multivariable Centralized Control with Decouplin and Feedforward Compenation for Reidential Wind Turbine Miuel E. González*. Juan Garrido**. Fernando Morilla***. Francico Vázquez** *Univeridad Autónoma de Zacateca, Ramón ópez Velarde, CP 9 Zacateca, México (Tel: ext. 55; mionzal49@yahoo.com.mx). **Computer Science and Numerical Analyi Department, Univerity of Córdoba) Córdoba, Spain ( juan.arrido@uco.e and fvazquez@uco.e) *** Computer Science and Automatic Control Department, UNED, Madrid, Spain ( fmorilla@dia.uned.e)} Abtract: The mall wind turbine for reidential ue are multivariable procee that work under turbulent wind condition and abrupt electrical load chane. In thee procee, it i neceary to apply a complex control ytem that allow a ood performance on the power production. For thi aim, in thi paper, a multivariable centralized control by decouplin i preented to control the wind turbine, in comparion with a decentralized control. The problem due to diturbance by wind turbulence and electrical load chane are reduced uin feedforward compenation.. INTRODUCTION The interet in the mall wind turbine for reidential ue ha rown recently, ince with a mall turbine ( to 5 kw) and ood wind condition, it i poible to produce neceary enery for a home or a mall buine workin the wind turbine on off-rid mode. In ome countrie of America and Europe, it i poible to ell enery or reduce the tariff of the conventional enery, workin the wind turbine in on-rid mode (Milivojevic et al., ). The mall wind turbine can baically provide electrical enery of two way: a) Storin it in a battery and tranform it into an AC inal uin an inverter; thi cheme i uually ued when the intallation i very far from the rid. b) Throuh a power converter that adapt the inal with manitude and fruency like the inal of rid; thi cheme i aduate for urban zone and can work on both mode: offrid and on-rid mode (Remu and Frede, 4). Generally, the power converter for option b) are: Rectifier Boot converter Inverter. Back to back voltae ource converter. Matrix converter. The converter baed on rectifier i imple and economic; however, it ruire that the wind turbine work with contant anular peed, wherea in the other two cae, the peed can be variable. Mot of commercial mall wind turbine reulate the anular peed of the rotor only with the variation of the electromanetic torque of the enerator, becaue they do not have a pitch control of blade anle. Thi produce vibration in the mechanical tructure, warmin up in the power converter, exceive noie and low power efficiency. In addition, it i neceary to conider the problem of the wind turbulence in urban zone and electrical load chane (Martínez et al., 7). In thi paper, a reidential wind turbine of kw workin in off-rid mode i conidered, that deliver directly enery to a home throuh a converter (Rectifier - Boot - Inverter), operatin with contant anular peed. Thi wind turbine (Naai et al., 9) can be een a a multivariable proce with two output to be controlled (the turbine anular peed and the enerated power), two manipulated input (the field current of the enerator and the pitch control of blade anle), and two not manipulated input conidered a diturbance (the variation of the wind peed and the electrical load). In order to improve the performance of the wind turbine and reduce the interaction effect, a multivariable centralized control by decouplin i preented. In addition, in order to reduce the problem due to diturbance caued by the wind turbulence and the electrical load chane, a feedforward compenator i included. Fi.. Wind turbine and control ytem diaram. Copyriht by the International Federation of Automatic Control (IFAC) 557

2 Milano (Italy) Auut - September, To evaluate the wind turbine performance with the propoed controller, the mathematical nonlinear model of the wind turbine a well a a model to enerate the inal of the wind are ued. Fiure how a block diaram of the proce and the control ytem. Thi paper i oranized a follow: the mathematical model of wind turbine i decribed in Section. The correpondin linearization i obtained in Section. In Section 4, the dein of the controller i explained. Finally, Section 5 how the reult, and concluion are dicued in Section.. WIND TURBINE MODE The mathematical model preented in thi ection decribe in detail the wind turbine behavior. It ha been obtained from an analyi baed on diaram of fiure, which conider the mechanim of rotation, the aerodynamic of the blade and the electric enerator. Alo, a model i preented to decribe wind peed inal, which allow to obtain more realitic reult. With thee model, it i poible to imulate the proce under different operation condition, applyin diturbance that conit on electrical load variation and wind turbulence. Thee model are very ueful to evaluate wind turbine performance with different controller.. Mechanim of rotation The chematic diaram of the rotation mechanim of the fiure, how how the wind force move the propeller to enerate the torque a and produce the anular peed ω r. The anular peed ω in the haft of the enerator, i produced after earbox bein two ection: low and hih peed. The moment of inertia in the ection of low anular peed i: Jr ω r a Brωr N h () where J r i the moment of inertia, B r i the vicou friction coefficient and h i the torque ruired in the part of hih peed to rotate the enerator haft. The earbox ratio i Nω /ω r (Boukhezzar et al., 7). The moment of inertia in the ection of hih anular peed i: J ω h Bω em () where J i the moment of inertia of enerator, B i the friction and em i the torque produced by the electromanetic field of the enerator. The dynamic of wind turbine i obtained from () and () coniderin only the anular peed ω r : J ω Bω t r a t r J J + N J ; B B + N B ; N t r t r em. Aerodynamic The torque a enerated by the wind force depend on the aerodynamic propertie of the turbine, apect like: form, ize and orientation of it blade, a well a peed, direction and wind denity (García-Sanz and Torre, 4). () The relation between wind peed v and anular peed of the turbine ω r, i decribed by the tip-peed-ratio where R i the rotor radiu: R ω v r λ (4) Fi.. Wind turbine rotation mechanim. The tudy of the aerodynamic of the turbine i realied uin the Blade Element Momentum (BEM) theory, that i baed on the Glauert Propeller theory applied in wind turbine. Thee theorie allow to know the efficiency of enerated power C p (λ,β) and produced torque C q (λ,β), uin the ratio λ and blade orientation anle β. The curve in the fiure decribe aerodynamic efficiency behavior of a enerator with three blade (model NACA44). Fi.. Power C p (λ,β) and torque C q (λ,β) efficiency. From the curve of C q (λ,β) and the followin expreion, torque a can be determined a follow: a.5 ρπ RvCq( λ, β ) (5) where ρ i the the wind denity.. Electric enerator In order to determine the enerated power P, it i neceary to conider the voltae E produced by the electric enerator, accordin to the anular peed ω and the filed current I f, a follow: 55

3 Milano (Italy) Auut - September, E KI fω () where K i a contant of the enerator. For a reitive load R, the power i iven by (7), where X αnω r i the enerator reactance. R P K I fω R + ( N r) α ω Finally, the produced electromanetic torque i: P () ηηω m where η i the electrical enerator efficiency and η m i the mechanical efficiency..4 Equation of the nonlinear model In ummary, the followin four uation decribe the nonlinear model of the wind turbine: J ω Bω (9) t r a t r a ρπ RvCq( λ, β ) () R P K I fn ωr R + ( αnωr) () P η η Nω () m r.5 Wind peed model The wind peed i a natural phenomenon decribed by a tationary tochatic proce compoed of a media peed v m, ut and turbulence v n. The model in (), and reported by (Maoud, ) to enerate the turbulence inal, capture the behavior of thi natural phenomenon in a proper way: M m n n i i i i i v v + v ; v A( ω )co( ωt+ φ ), A S S π 9,5 σ h/ vm S( ωi ) + ( ωih/ vm) ( ω ) ( ω ) + ( ω ) ( ω ω ) i i i i+ i+ i 5/, (7) () where h i the heiht of the point of wind meaurement, σ i the tandard deviation, φ a random inal with uniform ditribution from -π to π that reproduce the ut and turbulence, with a pectrum ditributed throuhout the fruencie defined by ω i with M 5.. INEAR MODE Uin a firt-order Taylor erie to obtain wind turbine linear model for the operation point, the partial derivative of the nonlinear uation (9 -) are evaluated a follow: v+ β + ω bv + b β + b ω, a a a a r 7 r v β ωr I + ω + R b I + b ω + b R, f r f 4 r I f ω R r P P P P I + ω + f r I f ω R r R b I + b ω + b R 5 f r 9 (4) By coniderin that the followin uation repreent the electromechanical ytem that control the blade anle: β() β () ref K β Tβ + + Kβ (5) and by applyin aplace tranform in (4), the followin repreentation of tranfer function matrix () can be obtained. The aplacian operator ha been omitted for clarity. W I R r f 4 V P + + ref β 4 The different tranfer function in () are iven by b b K β () () d () d () e () () () bd 5 () bb K bb β d () d () e () b b () d () 4 () d (), () bb 4 () bd 9 () bb d () d () d () J+ B+ b b, e () T + + K t t 4 7. Calculation of parameter β β () (7) The wind turbine contant of Table are ued to calculate the parameter from b to b 9 of the linear model in (7). Table. Wind turbine contant and contraint. J t 5 k m h 9 m B t,9 N m/rpm σ N v min - v max 4 - m/ η, P nom kw η m,4 P max 4 kw ρ,5 k/m ω rnom 5 rpm K, Ω /rad ω rmax 4 rpm α,7 Ω /rad R nom 4 Ω R m β min - β max 5-9 deree K β,5 I fmax 4 A T β Such contant and contraint correpond to a wind turbine with a ynchronou electric enerator (SG, Sawafuji Electric Co., td.), earbox (CNH-45-, Sumitomo Heavy Indutrie, td.) and fiber la blade (NACA44). 559

4 Milano (Italy) Auut - September, Beide the contant of Table, it i neceary to know the value of input and output for the operation point. In thi cae, it i ruired that the wind turbine work at contant anular peed and ood power efficiency condition. Accordin to the curve of fiure, the wind turbine work with ood power efficiency for value of C p (λ,β), and λ, for an anle β 7,. The efficiency can be increaed; however, there exit the rik of aturatin β to it minimum value. With thee data and uin (4) for a wind peed of m/, the turbine reache it nominal peed ω rnom of 5 rpm. From the nonlinear model uation (9-) in tationary tate for the operation point in quetion, it i poible to find the followin expreion to calculate the field current I f, beind.54 A. I f ( λβ, ) C ρπ Rv p Bω t rnom λ ηη m Rnom + ( αnωrnom ) KNωrnom Rnom () Finally, uin (), the enerated power i very near from it nominal value 9,5 W. With thi numerical value, the tranfer matrix of the proce i: -7,55 -,5 5 +, + 5, 47 +, 4 +, 5 G, ,5 5 +, + 5, 47 +, (9) 7, -9,95 5+, 4 5+,, , 5 +, 4. CONTRO SYSTEMS Before deinin the multivariable controller, the proce interaction i meaured by mean of the relative ain array (RGA) (Skoetad and Potlethwaite, 5). The RGA element λ of the proce in tationary tate i,77. Thi indicate a coniderable level of interaction and that the uitable pairin i to control the peed of the rotor ω r with the field current I f, and the enerated power P with the orientation anle of the blade β ref. 4. Decentralized control The olution for the control problem of the wind turbine can be approached uin a decentralized control. The control cheme i depicted in fiure 4. Uin a PI tructure, each controller i tuned for the correpondin tranfer function in (), that take into account the interaction of the other loop. + k + k k k q () There exit different method for the tunin of controller, like: heuritic, relay, Gerhorin band, amon other (Ho et al., 997) and (Morilla et al., ). For thi work, it ha been decided to ue the iterative proce propoed by (Vázquez et al., 999), that wa implemented in the computer tool TITO, available in Thi tool facilitate the tunin of the ain of the controller, uin ain marin, phae marin or both a pecification. For a phae marin of º in both loop and the tranfer function in (9), thi tool obtain the followin PI parameter: k k,9 A/rpm; T 9,, 5.4 rado/w;.4. p i p Ti () Since the diturbance due to the wind turbulence a well a load electric chane affect coniderably the performance of the wind turbine, a feedforward () compenator have been deined to attenuate it effect. The feedforward element to compenate the wind turbulence are approximated to the followin tranfer function: v v q () The feedforward compenation for load electric chane i iven by: 4 R (), R () 49.. () q () 4. Centralized control by decouplin Fi 4. Decentralized PI control with feedforward. Multivariable centralized control by decouplin i another approach to reualte the wind turbine. A it i a more complex tratey, it can be expected to obtain a better control performance and interaction attenuation. The cheme i hown in fiure 5. A decoupler network D() i dein, in uch a way that the new apparent proce Q()G()D() i diaonlly dominant, where G() i the proce tranfer matrix in (9). Then, a decentralized control K() with two PI controller i tuned for thi apparent proce Q(). 5

5 Milano (Italy) Auut - September, Fi. 5. Centralized control by decouplin with feedforward. Two method for the decoupler dein exit: dynamic decouplin, when D() i calculated uin the tranfer function of proce G(), and tatic decouplin, when only teady tate information G() i ued. In thi work, tatic decouplin i elected, ince in previou publication it ha hown ood reult (González el al., ). The dein of tatic decoupler network i imple and it i baed only on the proce ain in tationary tate. If two element of the decoupler network are et to unity, for example d () and d (), the other two element are calculated a follow (Morilla et al., 5): d, d ( ) (4) Then, the tatic decouplin with d d for the proce iven in (9), i: d d.47 d d.55 (5) Uin a phae marin of º in both loop a performance pecification, the PI parameter of the decentralized control, obtained by TITO tool, are the followin: kp,5 A/rpm; Ti 75,75, () kp 5, rado/w; Ti 7, The control tratey i completed aain with a feedforward compenator; however, in thi cae, it i deined takin into account the apparent proce Q()G()D(). The approximated feedforward element are: () v (). +.5 () v () q () R () () () R () q () Gain chedulin for power reference (7) () In Section, it i mentioned that the wind turbine mut operate at contant anular peed in it nominal value. Neverthele, the power cannot operate alway in the nominal value, ince it depend on divere factor, like the wind peed and the enery demand of the electrical load. If the wind peed i hih, the wind turbine will work near it nominal power; however, for mall wind peed, the power will have to fall tryin to achieve a ood power efficiency, C p (λ,β)>.. With reard to the electrical load, a mall value of R implie a reat demand of power; however, when the value of R i bi, there i little power conumption and the enerated power mut decreae accordin to the demand. Therefore, the power reference mut depend on the wind peed, the electrical load and power efficiency. In thi work, a ain chedulin i ued to determine the power reference (9). Thi function i obtained ubtitutin the field current in teady tate () in the enerated power () with the value of the contant of Table. Thi enerate an expreion for the power reference P d that depend on the wind peed v and the electrical load R, for anular peed contant ω rnom. P d R 4,9,9 R + 4,74 Generated Power P Wind Speed v ( v ) 7 Fi.. Power baed on the wind peed v and load R. (9) 5. RESUTS Some imulation are performed to evaluate the wind turbine performance with the propoed controller. Fiure 7 how the repone to tep chane in the wind peed without turbulence, from to m/. The electric load R nom i 4 Ω Anular Speed ω r [rpm] I f [A] Fi. 7. Repone to tep chane in the media peed of wind Electric oad R Generated Power P [W] β ref [deree] Set Point Dece - Cent

6 Milano (Italy) Auut - September, In fiure and 9, the ytem i imulated under more realitic condition, applyin the ame tep chane in the wind but with turbulence, model iven in (). The electrical load ha random variation from 4 to Ω. The reult how better performance of the wind turbine with centralized controller, maintain the anular peed very near hi nominal value, alo the trackin of the power reference i very ood, adjutin to the chane of the wind and the electric load Anular Speed ω r [rpm] I f [A] Fi.. Repone with decentralized control and Feedforward Anular Speed ω r [rpm] I f [A] Fi. 9. Repone with centralized control and Feedforward.. CONCUSIONS In thi work, the model of a mall wind turbine and it control i preented. The control objective i to reulate the anular peed in it nominal value and to fit the power enerated baed on the chane of the wind peed and electrical load, to maintain ood efficiency of power. Two multivariable controller are propoed: a decentralized and a centralized by tatic decouplin. In both cae, a feedforward compenation ha been deined to attenuate the diturbance effect of the wind turbulence and the electrical load chane. The power reference chane accordin to a ain chedulin function. The imulation how that the effect of the interaction between the variable are attenuated (fiure 7), and that in particular the centralized controller i robut, ince the wind 4 Generated Power P [W] β ref [deree] Generated Power P [W] β ref [deree] 5 5 turbine till ha a ood performance for hih and low wind peed and inificant chane in the electrical load. The power reference i calculated with the media wind peed, and the diturbance caued by the turbulence are attenuated by mean of the feedforward compenator. ACKNOWEDGEMENTS Thi work ha been carried out with financin of Conejería de Economía, Innovación y Ciencia de la Junta de Andalucía in the call of Project of Excellence of. REFERENCES Boukhezzar, B.,. upu, H. Siuerdidjane and M. Hand (7). Multivariable control tratey for variable peed, variable pitch wind turbine. Renewable Enery, Science Direct Elevier, 7 7. García-Sanz, M. and E. Torre (4). Control y experimentación del aeroenerador íncrono multipolar de velocidad variable TWT5. Revita Iberoamericana de Automática e Informática Indutrial, No., 5. González, M., F. Vázquez and F. Morilla (). Control Multivariable con Deacoplo para Aeroeneradore de Velocidad Variable. Revita Iberoamericana de Automática e Informática Indutrial 7, No. 4, 5 4. Ho, W.K., T.H. ee y O.P. Gan (997). Tunin of multiloop PID controller baed on ain and phae marin pecification. th IFAC World Conre pp.. Martínez F., Herrero., Gómez S., and González J. (4). Analyi of the Efficiency Improvement in Small Wind Turbine when Speed i Controlled. Indutrial Electronic ISIE, EEE International Sympoium, Maoud, B. (). Modelin and controller dein of a wind enery converion ytem includin a matrix converter. Thei PhD in Electrical and Computer Enineerin, Univeritiy of Waterloo, Ontario, Canada. Milivojevic, N., Stamenkovic, I. and Schofield, N. (). Power Enery Analyi of Commercial Small Wind Turbine. Indutrial Technoloy (ICIT) IEEE International Conference Morilla, F., F. Vázquez and J. Garrido (). Centralized PID control by decouplin for TITO procee. th IEEE International Conference on Emerin Technoloie and Factory Automation. Naai, B., K. Ameku and J. Nath (9). Performance of a kw wind turbine enerator with variable pitch control ytem. Applied Enery, Elevier, Remu T., and Frede B. (4). Flexible Control of Small Wind Turbine with Grid Failure Detection Operation in Stand-Alone and Grid Connected. IEEE Tranaction on Power Electronic9,. Skoetad, S. and I. Potlethwaite (5). Multivariable feedback control analyi and dein, Second Edition. John Wiley and Son, td. Vázquez, F., F. Morilla and S. Dormido (999). An iterative method for tunin decentralized PID controller. 4th IFAC World Conre. Vázquez, F. and F. Morilla (). Tunin decentralized PID controller for MIMO ytem with decoupler. 5th IFAC World Conre, Barcelona, Spain. 5