Active an Reactive Power Control of a DFIG with MPPT for Variable Spee Win Energy Conversion using Sliing Moe Control Youcef Bekakra, Djilani Ben attous International Science Inex, Electrical an Computer Engineering waset.org/publication/3431 Abstract This paper presents the stuy of a variable spee win energy conversion system base on a Doubly Fe Inuction Generator (DFIG) base on a sliing moe control applie to achieve control of active an reactive powers exchange between the stator of the DFIG an the gri to ensure a Maximum Power Point Tracking (MPPT) of a win energy conversion system. The propose control algorithm is applie to a DFIG whose stator is irectly connecte to the gri an the rotor is connecte to the PWM converter. To extract a maximum of power, the rotor sie converter is controlle by using a stator flux-oriente strategy. The create ecoupling control between active an reactive stator power allows keeping the power factor close to unity. Simulation results show that the win turbine can operate at its optimum energy for a wie range of win spee. Keywors Doubly fe inuction generator, win energy, win turbine, sliing moe control, maximum power point tracking (MPPT). I. INTRODUCTION THE most important avantages of the variable spee win turbines as compare with conventional constant spee system are the improve ynamic behavior, resulting in the reuction of the rive train mechanical stress an electrical power fluctuation, an also the increase of power capture. One of the generation systems commercially available in the win energy market currently is the oubly fe inuction generator (DFIG) with its stator wining irectly connecte to the gri an with its rotor wining connecte to the gri through a variable frequency converter as shown in Fig. 1. One of the most avantages of this system is that the rating of the power converter is one thir of that of the generator [1]. The oubly fe inuction generator is wiely use for variable-spee generation, an it is one of the most important generators for win energy conversion systems. Both gri connecte an stan-alone operation is feasible [2]. The variable spee constant frequency (VSCF) win power generation is mainly base on the research of optimal powerspee curve, namely the most mechanical power of turbine can be achieve by regulating the spee of generator, where the win spee may be etecte or not [1]. Through stuying the characteristics of win turbine, the paper use the maximum power point tracking (MPPT) control process. Firstly, accoring to the DFIG character, the paper aopts the vector transformation control metho of stator oriente magnetic fiel to realize the ecoupling control for Department of Electrical Engineering, El-Oue University Center, Algeria. e-mail: (youcef1984@gmail.com, benattous@yahoo.com). the active power an reactive power using sliing moe control (SMC). Sliing moe theory, stemme from the variable structure control family, has been use for the inuction motor rive for a long time. It has for long been known for its capabilities in accounting for moelling imprecision an boune isturbances. It achieves robust control by aing a iscontinuous control signal across the sliing surface, satisfying the sliing conition. Nevertheless, this type of control has an essential rawback, which is the chattering phenomenon cause from the iscontinuous control action. To alleviate the chattering phenomenon, the iea of bounary layer is use to improve it. It is calle a moifie controller. In this metho, the control action was smoothe such that the chattering phenomenon can be ecrease [3]. In this paper, we apply the SMC metho to the win energy conversion systems with MPPT control algorithm. Fig. 1. DFIG variable spee win energy conversion MPPT control II. MODEL OF TURBINE The win turbine input power usually is [4]: P v = 1 2 ρs ωv 3 (1) Where ρ is air ensity; S ω is win turbine blaes swept area in the win; v is win spee. The output mechanical power of win turbine is: P m = C p P v = 1 2 C pρs ω v 3 (2) 1607
estimate of its value can be obtaine : Where C p represents the win turbine power conversion efficiency. It is a function of the tip spee ratio λ an the blae pitch angle β in a pitch-controlle win turbine. λis efine as the ratio of the tip spee of the turbine blaes to win spee: v est = R.Ω t λ optim (5) The aeroynamic power reference value must be set to the following value: λ = R.Ω t v (3) P aer ref = 1 2 C p maxρs ω v 3 est (6) International Science Inex, Electrical an Computer Engineering waset.org/publication/3431 Where R is blae raius, Ω t is angular spee of the turbine. C p can be escribe as [5]: C(β,λ) = (0.5 0.0167.(β 2)).sin( π.(λ+0.1) 18.5 0.3.(β 2) ) 0.00184.(λ 3)(β 2) (4) A figure showing the relation between C p, β an λ is shown in Fig. 2. The maximum value of C p (C p max = 0.5) is achieve for β = 2 egree an for λ optim = 9.2. Cp 0.5 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 X: 9.2 Y: 0.5 B = 4 B = 3 B = 2 0 0 2 4 6 8 10 12 14 16 18 Lama Fig. 2. Aeroynamic power coefficient variation C p against tip spee ratio λ an pitch angle β III. MAXIMUM POWER POINT TRACKING (MPPT) Maximum power variation with rotation spee Ω of DFIG is preefine for each win turbine. So for MPPT, the control system shoul follow the tracking characteristic curve (TCC) of the win turbine [6]. Each win turbine has TCC similar to the one shown in Fig. 3. The actual win turbine, Ω is measure an the corresponing mechanical power of the TCC is use as the reference power for the power control loop [6]. In orer to make full use of win energy, in low win spee β shoul be equal to 2 egree. Fig. 3 illustrates the win turbine power curve when β is equal to 2 egree. To extract the maximum power generate, we must fix the avance report λ optim is the maximum power coefficient C p max, the measurement of win spee is ifficult, an From figure 2 we can see there is one specific angular frequency at which the output power of win turbine is maximum occurs at the point where C p is maximize. Connecte all the maximum power point of each power curve, the optimal power curve (MPPT curve) is obtaine. Turbine mechanicale power (W) 4000 3500 3000 2500 2000 1500 1000 500 MPPT 4 m/s 5 m/s 6 m/s 7 m/s 0 0 100 200 300 400 500 600 700 800 Turbine rotational spee (rpm) Fig. 3. Turbine powers various spee characteristics for ifferent win spees, with inication of the maximum power tracking curve IV. MODELING OF THE DFIG The general electrical state moel of the inuction machine obtaine using Park transformation is given by the following equations [7]: Stator an rotor voltages: V s = R s i s + t φ s ω s φ sq V sq = R s i sq + t φ sq +ω s φ s V r = R r i r + t φ (7) r (ω s ω)φ rq V rq = R r i rq + t φ rq +(ω s ω)φ r Stator an rotor fluxes: φ s = L s i s +Mi r φ sq = L s i sq +Mi rq φ r = L r i r +Mi s φ rq = L r i rq +Mi sq (8) The electromagnetic torque is given as: C e = pm(i r i sq i rq i s ) (9) 1608
an its associate motion equation is: C e C r = J Ω t The state variable vector is then : X = [ i s i sq i r i rq ] T (10) We lea to an uncouple power control; where, the transversal component i rq of the rotor current controls the active power. The reactive power is impose by the irect component i r. P s = V s M L s i rq (13) International Science Inex, Electrical an Computer Engineering waset.org/publication/3431 B = The state moel can then be written as : With : Ẋ = [ t i s t i sq Ẋ = A.X +B.U (11) t i r U = [ V s V sq V r V rq ] T A = Where: t i rq a 1 aω +ω s a 3 a 5 ω aω ω s a 1 a 5 ω a 3 a 4 a 6 ω a 2 ω a 6 ω a 4 σ ω s ω σ +ω s b 1 0 b 3 0 0 b 1 0 b 3 b 3 0 b 2 0 0 b 3 0 b 2 a = 1 σ σ, a 1 = Rs σl s, a 2 = Rr, a 3 = RrM σl sl r, a 4 = RsM σl sl r, a 5 = M σl s, a 6 = M,b 1 = 1 σl s, b 2 = 1, b 3 = M σl sl r. ] T V. FIELD ORIENTED CONTROL OF DFIG, In this section, the DFIM moel can be escribe by the following state equations in the synchronous reference frame whose axis is aligne with the stator flux vector, (φ s = φ s an φ sq = 0). The control of the DFIG must allow a control inepenent of the active an reactive powers by the rotor voltages generate by an inverter. By choosing a reference frame linke to the stator flux an if the per phase stator resistance is neglecte, which is a realist approximation for meium an high power machines use in win energy conversion, the stator voltage vector is consequently in quarature avance in comparison with the stator flux vector [7]: Q s = V s 2 M V s i r (14) ω s L s L s The arrangement of the equations gives the expressions of the voltages accoring to the rotor currents: i r = 1 i r +gω s i rq + 1 V r (15) σt r i rq = ( 1 + M2 ) 1 T r L s T s L r σ i rq gω s i r + 1 V rq (16) With: T r = Lr R r, T s = Ls R s, g = ωs ω ω s, σ = 1 M2 L sl r. VI. SLIDING MODE CONTROL A Sliing Moe Controller (SMC) is a Variable Structure Controller (VSC). Basically, a VSC inclues several ifferent continuous functions that can map plant state to a control surface, whereas switching among ifferent functions is etermine by plant state represente by a switching function [8]. The esign of the control system will be emonstrate for a following nonlinear system [9]: ẋ = f(x,t)+b(x,t).u(x,t) (17) Where x R n is the state vector, f(x,t) R n, B(x,t) R n m, u R m is the control vector. From the system (17), it possible to efine a set S of the state trajectories x such as: Where: S = {x(t) σ(x,t) = 0} (18) σ(x,t) = [σ 1 (x,t),σ 2 (x,t),...,σ m (x,t)] T (19) an[.] T enotes the transpose vector,s is calle the sliing surface. To bring the state variable to the sliing surfaces, the following two conitions have to be satisfie: σ(x,t) = 0, σ(x,t) = 0 (20) The control law satisfies the preceent conitions is presente in the following form: V s = 0 an V sq = V s ω s.φ s (12) { u = u eq +u n u n = k f.sgn(σ(x,t)) (21) 1609
International Science Inex, Electrical an Computer Engineering waset.org/publication/3431 Where u is the control vector, u eq is the equivalent control vector, u n is the switching part of the control (the correction factor), k f is the controller gain. u eq can be obtaine by consiering the conition for the sliing regimen, σ(x, t). The equivalent control keeps the state variable on sliing surface, once they reach it. For a efine function [10], [11]: 1, if φ>0 sgn(φ) = 0, if φ = 0 1, if φ<0 (22) The controller escribe by the equation (21) presents high robustness, insensitive to parameter fluctuations an isturbances, but it will have high-frequency switching (chattering phenomena) near the sliing surface ue to sgn function involve. These rastic changes of input can be avoie by introucing a bounary layer with with ε [9]. Thus replacing sgn(σ(t)/ε) by sat(σ(t)/ε) (saturation function), in (21), we have: Where, ε > 0 sat(φ) = u = u eq k f.sat(σ(x,t)) (23) { sgn(φ), if φ 0 φ, if φ < 0 Consier a Lyapunov function [10]: (24) V = 1 2 σ2 (25) From Lyapunov theorem we know that if V is negative efinite, the system trajectory will be riven an attracte towar the sliing surface an remain sliing on it until the origin is reache asymptotically [9]: V = 1 2t σ2 = σ σ η σ (26) Where η is a strictly positive constant. In this paper, we use the sliing surface propose par J.J. Slotine: Where: σ(x,t) = ( t +τ)n 1.e (27) x = [x,ẋ,...,x n 1 ] T is the state vector, x = [x, x,...,x n 1 ] T is the esire state vector, e = [e,ė,...,e n 1 ] T is the error vector, an τ is a positive coefficient, an n is the system orer. Commonly, in DFIM control using sliing moe theory, the surfaces are chosen as functions of the error between the reference input signal an the measure signals [9]. VII. APPLICATION OF SLIDING MODE CONTROL TO DFIG The rotor currents (which are linke to active an reactive powers by equations (13) an (14), quarature rotor currenti rq linke to stator active power P s an irect rotor current i r linke to stator reactive power Q s ) have to track appropriate current references, so, a sliing moe control base on the above Park reference frame is use. A. Quarature rotor current control with SMC The sliing surface representing the error between the measure an reference quarature rotor current is given by this relation: e = i rq i rq (28) For n = 1, the spee control manifol equation can be obtaine from equation (27) as follow: σ(i rq ) = e = i rq i rq (29) σ(i rq ) = i rq i rq (30) Substituting the expression of i rq equation (16) in equation (30), we obtain: σ(i rq ) = i rq ( 1 σ ( 1 T r + M2 L s T s L r )i rq gω s i r + 1 V rq ) We take: (31) V rq = V eq rq +V n rq (32) During the sliing moe an in permanent regime, we have: σ(i rq ) = 0, σ(i rq ) = 0, V n rq = 0 Where the equivalent control is: V eq rq = ( i rq + 1 σ ( 1 T r + M2 L s T s L r )i rq +gω s i r ) (33) Therefore, the correction factor is given by: k Vrq : positive constant. V n rq = k Vrq.sat(σ(i rq )) (34) B. Direct rotor current control with SMC: The sliing surface representing the error between the measure an reference irect rotor current is given by this relation: e = i r i r (35) For n = 1, the spee control manifol equation can be obtaine from equation (27) as follow: σ(i r ) = e = i r i r (36) 1610
σ(i r ) = i r i r (37) Substituting the expression of i r equation (15) in equation (37), we obtain: σ(i r ) = i r ( 1 σt r i r +gω s i rq + 1 +V r ) (38) We take: V r = V eq r +Vn r (39) During the sliing moe an in permanent regime, we have: International Science Inex, Electrical an Computer Engineering waset.org/publication/3431 σ(i r ) = 0, σ(i r ) = 0, V n r = 0 Where the equivalent control is: V eq r = ( i r + 1 i r gω s i rq ) (40) σt r Therefore, the correction factor is given by: k Vr : positive constant. V n r = k Vr.sat(σ(i r )) (41) VIII. SIMULATION RESULTS The DFIG use in this work is a 4 kw, whose nominal parameters are inicate in appenix. In orer to evaluate the MPPT control strategy propose in this paper, MATLAB is use to carry out the simulation. We propose a step change in win spee is simulate in Fig. 4, the win spee is start at 5 m per secon, at 3 secon, the win spee suenly become 6 m per secon, as 6 secon, the win spee is 7 m per secon. Fig. 5 illustrates the turbine spee curve. We observe after the Fig. 4 an Fig. 5 when win spee v is 5m/s the optimal turbine spee Ω t of DFIG is 98.02 ra/s, when v is 6m/s, Ω t is 111.6 ra/s an when v is 7m/s, Ω t is 124.3 ra/s, after each ajustment, the stable turbine spee totally with the theoretical value. During this ajusting process, realize the maximum win energy tracking control. As can be seen from the Fig. 6, the stator active power injecte into the gri is controlle accoring to the MPPT strategy, when the reactive power is maintaine to zero, to guarantee a unity power factor at the stator sie as shown in Fig. 7. Fig. 8 an Fig. 9 present respectively stator an rotor current of the DFIG these show that with the when the win spee increases the amplitue of stator an rotor current increase. Fig. 10 presents the power coefficient C p, it is kept aroun its optimum value (C p = 0.5) as shown in Fig. 10. Fig. 4. Fig. 5. Fig. 6. A step change win spee profiles Turbine spee accoring the MPPT Stator active power injecte in the gri accoring the MPPT 1611
Worl Acaemy of Science, Engineering an Technology International Science Inex, Electrical an Computer Engineering waset.org/publication/3431 Fig. 7. Fig. 8. Stator reactive power Phase stator current Fig. 10. Power Coefficient C p variation IX. CONCLUSION In this paper a variable structure control base on a sliing moe control (SMC) of a oubly fe inuction generator (DFIG) gri-connecte win energy conversion system, incorporating a maximum power point tracker (MPPT) for ynamic power control has been presente. This structure has been use for reference tracking of active an reactive powers exchange between the stator an the gri by controlling the rotor converter. Simulation results show goo ecoupling between stator active an reactive power an goo performance obtaine in the presence of the variations of win spee. The obtaine results emonstrate that the propose DFIG system control operating at the variable spee may be consiere as an interesting way for problems solution in renewable energy area. APPENDIX A SYSTEM PARAMETERS Rate ata of the simulate oubly fe inuction generator: Rate values: 4 kw, 220/380 V, 15/8.6 A. Rate parameters: R s = 1.2(Ω) R r = 1.8(Ω) L s = 0.1554(H) L r = 0.1568(H) M = 0.15(H) p = 2 J = 0.2(Kg.m 2 ) Win turbine parameters: R = 3(m),G = 5.4. Air ensity : ρ = 1.22(kg/m 3 ). Fig. 9. Phase rotor current v ρ R P m APPENDIX B NOMENCLATURE win spee air ensity blae raius mechanical power of win turbine 1612
International Science Inex, Electrical an Computer Engineering waset.org/publication/3431 C p S ω λ Ω t C e C r J β V s,q V r,q i s,q i r,q φ s,q φ r,q R s R r L s L r M σ p T s,t r ω s ω g power coefficient swept area tip spee ratio angular spee of the turbine electromagnetic torque loa torque moment of inertia pitch angle stator q frame voltage rotor q frame voltage stator q frame current rotor q frame current stator q frame flux rotor q frame flux stator resistance rotor resistance stator inuctance rotor inuctance mutual inuctance leakage factor number of pole pairs statoric an rotoric time-constant stator q reference axes spee rotor q reference axes spee slip coefficient. REFERENCES [1] M. Verij Kazemi, A. S. Yazankhah, H. M. Kojabai, Direct power control of DFIG base on iscrete space vector moulation, Renewable Energy, Vol. 35, pp. 1033-1042, 2010. [2] R. Penaa, R. Carenasb, E. Escobarb, J. Clarec, P. Wheelerc, Control strategy for a oubly-fe inuction generator feeing an unbalance gri or stan-alone loa, Electric Power Systems Research, Vol. 79, pp. 355-364, 2009. [3] A. Hazzab, I. K. Bousserhane, M. Kamli, M. Rahli, Aaptive fuzzy PIsliing moe controller for inuction motor spee control, International Journal of Emerging Electric Power Systems, Vol. 4, No 1, pp. 1-13, 2005. [4] X. Zheng, L. Li, D. Xu, J. Platts, Sliing moe MPPT control of variable spee win power system, Power an Energy Engineering Conference, pp. 1-4, APPEEC 2009. [5] E. S. Abin, W. Xu, Control esign an ynamic performance analysis of win turbine-inuction generator unit, IEEE Trans. On Energy Convers., Vol 15, No 1, pp. 91-96, 2000. [6] A. M. Eltamaly, A. I. Alolah, M. H. Abel-Rahman, Moifie DFIG control strategy for win energy applications, SPEEDAM 2010, International Symposium on Power Electronics, Electrical Drives, Automation an Motion, 2010 IEEE, pp. 659-653, 2010. [7] M. Machmoum, F. Poitiers, Sliing moe control of a variable spee win energy conversion system with DFIG, International Conference an Exhibition on Ecologic Vehicles an Renewable Energies, MONACO, March 26-29 (2009). [8] A. Nasri, A. Hazzab, I. K. Bousserhane, S. Hajiri, P. Sicar, Two wheel spee robust sliing moe control for electrical vehicle rive, Serbian Journal of Electrical Engineering, Vol. 5, No. 2, pp. 199-216, November 2008. [9] Y. Bekakra, D. Ben attous, A sliing moe spee an flux control of a oubly fe inuction machine, Electrical an Electronics Engineering, 2009, IEEE Conference, pp. I-174 - I-178, 2009. [10] M. Abi, A. Mansouri, A. Aissaoui, B. Belabbes, Sliing moe application in position control of an inuction machine, Journal of electrical engineering, Vol. 59, N 6, pp. 322-327, 2008. [11] J. Lo, Y. Kuo, Decouple fuzzy sliing moe control, IEEE Trans. Fuzzy Syst., Vol. 6, No. 3, pp. 426-435, Aug. 1998. 1613