SLIDING MODE CONTROL OF A DOUBLY FED INDUCTION GENERATOR FOR WIND TURBINES

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1 SLIDING MODE CONTROL OF A DOUBLY FED INDUCTION GENERATOR FOR WIND TURBINES MOHAMED ADJOUDJ, MOHAMED ABID, ABDELGHANI AISSAOUI, YOUCEF. RAMDANI, HOURIA BOUNOUA Key word: Doubly fed induction generator, Sliding mode control, Vector control, Power control. Thi work preent a liding mode control (SMC) applied to a doubly fed induction generator (DFIG) ued in the wind energy converion ytem (WECS). Thi technique find it tronget jutification to the problem of ue of a robut non-linear control law for the model uncertaintie. The objective i to apply thi control to command independently the active and the reactive power generated by the aynchronou machine which i decoupled by the orientation of the flux. The obtained imulation reult how the increaing interet of a uch control in the electric ytem 1. INTRODUCTION The evolution of the wind electrical energy production doe not ceae increaing ince It i the ource which progree mot quickly and, it development i important conidering the diverity of the exploitable zone and the relatively intereting cot [1]. Moreover, thi energy world potential i etimated to be very important and repreent a very promiing energy ariing. In order to be able to tet control law of a wind ytem, it i eential to have a imulation tool able to model the whole energy tranformation chain and to tet it performance [2]. In thi paper, firt, a wind turbine ytem i preented and it characteritic are depicted to etimate it dynamic and performance in different operating condition. Then, a SMC of the DFIG ued to control independently the power i propoed and teted on a wind turbine equipped with a DFIG of 10 kw. 2. WIND TURBINE CHARACTERISTICS A total cheme of a wind energy converion ytem connected to the electrical power grid i decribed by Fig. 1. IRECOM Laboratory, Electrotecnical Department, Sidi Belabbe Univerity, Algeria, Moh, _adjoudj@yahoo.fr Rev. Roum. Sci. Techn. Électrotechn. et Énerg., 56, 1, p , Bucaret, 2011

2 16 Mohamed Adjoudj et al. 2 Fig. 1 Scheme of energy tranformation chain. The power available on the wind turbine i given by [3 4] 1 ρ 3 P= CpSv, (1) 2 where: ρ air denity, S turbine area, v wind peed, C p power coefficient. For the wind turbine, the power coefficient C P, depending at the ame time on the wind peed and the turbine rotating peed, i defined between 0.35 and 0.5. A wind turbine i dimenioned to develop on it haft a nominal power P n, obtained from the nominal wind peed v n. When the wind peed i higher than v n, the wind turbine mut modify it parameter in order to avoid the mechanic detroy [4 5]. Beide the nominal peed v n, it i alo pecified the tarting peed v d where the wind turbine tart producing energy and, the maximum wind peed v max where the turbine doe not convert any more the wind energy. The aerodynamic control principle that limit the power extracted from the turbine at nominal output power value of the generator i baed on pitch ytem [4 5] to adjut the blade lift force at the wind peed, to maintain the power appreciably contant. The interet of thi control appear by oberving the characteritic on the diagram in Fig. 2. Fig. 2 Turbine power veru it rotating peed, for variou wind peed.

3 3 Sliding mode control of a doubly fed induction generator GENERATOR MODELING The generator choen for the wind energy tranformation i the doubly fed induction generator (DFIG) [6 7]. Moreover, a DFIG controlled by the rotor i ued with a peed variation range limitation of ±50% of the nominal peed. Thi choice permit the ue of only one converter dimenioned for an output power of about 25 to 30% of the nominal output. It will be thu le bulky, le expenive and will require a le cumberome cooling ytem [8]. The modeling of the DFIG i decribed in the d-q Park reference frame. The following equation ytem decribe the total generator model. d ϕd Vd = R Id + θ& ϕq dt d ϕ ϕ d = LI d + MI q Vq = R Iq + +θ& ϕd dt ϕ q = LI q + MI (2) d ϕ V = Rr I + θ& ϕ = LI r + MId rϕ dt ϕ = LI r + MIq, d ϕ V = Rr I + +θ& rϕ dt where: /r are tator/rotor ubcript; V/I voltage/current; φ flux; R reitance; LM inductance mutual; σ leakage coefficient, (σ =1 M 2 /L L r ); θr / rotor/tator poition; θ& / θ& rotor/tator electrical peed. r 3. CONTROL STRATEGY OF THE DOUBLY FED INDUCTION GENERATOR θ For obviou reaon of implification, the d-q reference frame related to the tator pinning field pattern and a tator flux aligned on the d-axi were adopted [7 9]. Moreover, thetator reitance can be neglected ince it i a realitic aumption for the generator ued in the wind turbine. The DFIG i controlled by the rotor voltage via an inverter. It i an independent control of active and reactive power. In the d-q reference frame, in an aynchronou generator tator, the active power P and reactive power Q are: P = VdId + VqIq, (3) Q = V I + V I. (4) q The adaptation of thee equation to the implifying aumption give d d q

4 18 Mohamed Adjoudj et al. 4 M P = V I, (5) L 2 M V Q = V Ir +. (6) L L ω Lω i the tator reactance. Equation howing the relationhip between the rotor current and voltage are etablihed and will be applied to control the generator 2 2 M d I M V = Rr I + Lr g ( Lr ) ωi, (7) L dt L V R I L M d I g L M I MV g 2 2 = r + r + r ω + L dt L L. (8) Since the power grid frequency i impoed, θ & r = gω, g i the DFIG lip. From equation (5), (6), (7) and (8), a block diagram containing the rotorique voltage a input and active and reactive tatorique power a output, i etablihed in Fig. 3. Fig. 3 Block diagram of the generator. The power and the voltage are linked by a firt order tranfer function. Since the lip value i weak, it i poible to etablih a vectoriel control, becaue

5 5 Sliding mode control of a doubly fed induction generator 19 the influence of the coupling will remain weak and the d and q axe can be controlled eparately with their own regulator. The method ued in power control conit to neglect the coupling term and to inert an independent controller on each axe in order to control the active and reactive power independently; thi method i called direct becaue the rotorique voltage are contolled directly by the power controller. 4. SLIDING MODE CONTROL OF THE DFIG The liding mode control know a big ucce thee lat year. It i due to the implementation implicity and the robutne with regard to the ytem uncertaintie and the external diturbance. The SMC conit to return the tate trajectory toward the liding urface and to develop it above, with a certain dynamic up to the equilibrium [10 11]. It deign conit mainly to determine three tage THE SWITCHING SURFACE CHOICE For a non-linear ytem repreented by the following equation: &X = f( X, t) + g( X, t) u( X, t) ; Χ R n, u R, (9) where: f (, t), g (, t) X X are two continuou and uncertain non-linear function, uppoed limited. We take the general equation to determine the liding urface, propoed by J.J. Slotine [10], given by: e = X d X ; n 1 d S( X) = +λ e ; (10) dt T X = x, x&,..., x n 1 ; T X d = x d x,, x & d, && d,... (11) where: e error on the ignal to be adjuted, λ poitive coefficient, n ytem order, X d deired ignal, X tate variable of the control ignal CONVERGENCE CONDITION The convergence condition i defined by the Lyapunov equation [11], it make the urface attractive and invariant S( X) S& ( X) 0. (12)

6 20 Mohamed Adjoudj et al CONTROL CALCULATION The control algorithm i defined by the relation eq n =, (13) u u + u eq where: u control ignal, u equivalent control ignal, n u witching control term, at (S(X)/ ϕ ) aturation function, ϕ threhold width of the aturation function. n u = u max at (S( X )/ ϕ), (14) ign( S) if S at ( S( )/ ) X ϕ >ϕ =. (15) S ϕ if S <ϕ 5. ACTIVE POWER CONTROL To control the power we et n = 1, the expreion of the active power control urface become: get : ref ( ) SP ( ) = P P. (16) Taking it derivative and replacing it in the active power expreion (5) we ref S& M ( P) = P & + V I&. (17) L Taking the current expreion I & from the voltage V equation (8) and neglecting the coupling term, ince the lip g i weak, we have ref S& M ( P) = P & + V ( V RrI). (18) LLσ r eq n Replacing V by V + V, the control appear clearly in the following equation: (( + ) ) ref M eq n SP & ( ) = P & + V V V RI r, (19) LLσ r

7 7 Sliding mode control of a doubly fed induction generator 21 During the liding mode and in teady tate, we have: S( P ) = 0, S& ( P ) = 0,V n = 0. (20) eq The equivalent control amount V i found from the previou equation and written a: σl L V = P& + R I, (21) eq ref r r VM During the convergence mode, o that the condition SPSP ( )&( ) 0 i verified, we et: M n SP &( ) = V V, σll (22) r and conequently, the witching term i given by V n = KV ign( SP ( )), (23) To verify the ytem tability condition, the parameter poitive. To reduce any poible overhoot of the reference voltage ueful to add a voltage limiter KV mut be V, it i often 6. REACTIVE POWER CONTROL The ame procedure a the active power i followed replacing P by Q and taking into account the reactive power expreion (6) to get ref M SQ & ( ) = Q& V I&. (24) L The expreion of the current I & i taken from the voltage V equation (7) ref M SQ & ( ) = Q & + V ( V RI r ), (25) LL rσ eq n Replacing V by V + V, the control appear clearly in the following equation:

8 22 Mohamed Adjoudj et al. 8 (( ) ) ref M eq n SQ &( ) = ( Q& + V V + V RI r, (26) LLσ r eq After conputation, the equivalent control amount V i found to be a follow: eq ref σll r V = Q& + Rr I, (27) VM and, the witching term i given by n V = KV ign ( S( Q)). (28) To verify the ytem tability condition, the parameter poitive. To reduce any poible overhoot of the reference voltage ueful to add a voltage limiter. KV mut be V, it i often 7. SIMULATION RESULTS Simulation i done to illutrate the performance of the liding mode control applied to the DFIG. A bloc diagram i propoed in Fig. 4 to control the whole ytem Fig. 4 Block diagram of the whole ytem.

9 9 Sliding mode control of a doubly fed induction generator 23 The reult plotted in the following figure how the power generated when reference ignal are applied. Fig. 5 how the anwer of the ytem with conventional PI controller, wherea Fig. 6 how the anwer with liding mode controller. 0 Active Power [W] P P ref Reactive Power [VAR] Q Q ref Time [] Fig. 5 Sytem repone with claical PI controller. 0 Active Power [W] P P ref Reactive Power [VAR] Q Q ref Time [] Fig. 6 Sytem repone with liding mode controller. The parameter of the DFIG are R = Ω, L = 0.07 H, R r = 0.19 Ω, L r = H, M = H.

10 24 Mohamed Adjoudj et al. 10 With PI controller the active and reactive power follow the deired variable but, it i oberved a mall coupling effect between the two control axe. In liding mode control, the anwer are without overhoot, no coupling effect, the tatic error goe to zero, rapid in tranient tate. 8. CONCLUSION In thi article, it i preented the control of a wind energy converion ytem baed on a doubly fed induction generator. Firt, a model of the generator i propoed; then, a control trategy by liding mode of the aynchronou generator allowing an independent control of the power i alo propoed. The liding mode controller of the active and reactive power are teted. The imulation reult how the ameliorated quality of the control baed on the controller by liding mode. Through the repone characteritic, we oberve good performance even with variation in the reference ignal. The output power follow the reference ignal without overhoot. The decoupling, the tability and the convergence toward the equilibrium are aured. Furthermore, thi regulation preent an algorithm of a very imple robut control and which ha the advantage to be eaily implantable in a computer control. Received on June 8, 2010 REFERENCES 1. P.W.Carlin, The Hitory and State of Art of Variable-Speed Wind Turbine Technology, NREL/TP , Février * * *, Aociation Danoie de l Indutrie éolinne. 3. E. Boanyi, Wind Energy Handbook, New York, Wiley, Meny Ivan, Modéliation et réaliation d'une chaîne de converion éolienne petite puiance, Laboratoire d'électrotechnique de Montpellier (LEM). 5. B. Multon, Etat de l art de aérogénérateur électrique, Rapport ECRIN, May A. Tapia, Modeling and control of a wind turbine iven doubly fed induction generator, IEEE Tran. Energy Converion, 18, 2, pp (2003). 7. Md. Arifujjaman, Vector control of a DFIG baed wind turbine, Journal of Electrical & Electronic Engineering, Itambul, 9, 2, pp (2009). 8. J.M. Carraco et al., Power-electronic ytem for the grid integration of renewable energy ource, IEEE Tran. Indutrial Electronic, 53, 4, pp (2006). 9. A. Boyette, Controle-commande d une GADA avec ytème de tockage pour la production éolienne,thèe de Doctorat,Univerité Henry Poincaré, Nancy I, Slotine, J.J.E. Li, Applied nonlinear control, Prence Hall, USA, H. Buhler, Réglage par mode de gliement, Pree polytechnique romande, Lauanne, 1986.