(IJACSA) International Journal of Advanced Computer Science and Applications, Vol. 7, No. 7, 2016 Direct Control of Saturated Doubly-Fed Induction Generator using High Order Sliding Mode Controllers

Elhadj BOUNADJA Abdelkader DJAHBAR Department of Automatic Department of Electrical Engineering Ecole Nationale Polytechnique University HASSIBABENBOUALI Elharrach, Algiers, Algeria Chlef, Algeria

Mohand Oulhadj MAHMOUDI Mohamed MATALLAH Department of Automatic Department of Technology Ecole Nationale Polytechnique University DJILALI BOUNAAMA Elharrach, Algiers, Algeria Khemis Meliana, Ain defla, Algeria

Abstract—The present work examines a direct torque control mutual and leakage fluxes [11-17]. Because of this reason and strategy using a high order sliding mode controllers of a doubly- in order to realize an accurate representation of the DFIG, fed induction generator (DFIG) incorporated in a wind energy saturation must be taken into account in their mathematic conversion system and working in saturated state. This research modelling. Consequently, an accurate DFIG model taking into is carried out to reach two main objectives. Firstly, in order to account the saturation effect both in mutual flux and in leakage introduce some accuracy for the calculation of DFIG fluxes is used in this paper. performances, an accurate model considering magnetic saturation effect is developed. The second objective is to achieve After major advances in power electronics and material a robust control of DFIG based . For this purpose, a technologies, many works have presented the DFIG with Direct Torque Control (DTC) combined with a High Order different control algorithms. One of the conventional control Sliding Mode Control (HOSMC) is applied to the DFIG schemes used actually for the DFIG-based wind turbine is the side converter. Conventionally, the direct torque control having Direct Torque Control based on switching table and hysteresis hysteresis comparators possesses major flux and torque ripples comparators [18]. This strategy, however, has a few at steady-state and moreover the switching frequency varies on a disadvantages which limit its use, such as variable switching large range. The new DTC method gives a perfect decoupling frequency and torque ripple [19, 20]. In many research works between the flux and the torque. It also reduces ripples in these on DTC, these disadvantages are reduced by using SVM grandeurs. Finally, simulated results show, accurate dynamic scheme, but with the price of scarifying the robustness of the performances, faster transient responses and more robust control control [21]. are achieved. To incorporate a robust DTC without torque and flux Keywords—Doubly Fed Induction Generator (DFIG); ripples, we propose, in the present work, a direct torque control Magnetic saturation; Direct Torque Control (DTC); High Order based on high order sliding mode controllers (DTC-HOSMC) Sliding Mode Controller (HOSMC) for a DFIG in saturated state. Proposed by Levant in [22] the HOSMC strategy has many attractive features such as its I. INTRODUCTION robustness towards parametric uncertainties of the DFIG, and Recently, worldwide awareness for renewable energy moreover, it reduces the chattering effect. resources has been increasing. In particular, wind energy has been largely considered because of its economy and reliability. The present work provides the important features of the Wind turbines contribute a certain amount of the word DTC-HOSMC and presents simulation results for a DFIG electricity consumption [1]. They usually use a Doubly-Fed system. We compare the proposed strategy with a conventional Induction Generator (DFIG) for the electrical energy DTC. The present paper is organized as follows: we present the conversion process. As deduced from literature, many workers modelling of the wind turbine and the DFIG using the saturated investigate the DFIG from diverse aspects. However, in these model in section II. In section III, the proposed DTC-HOSMC, works, many simplifying hypotheses are considered in the is applied to control the saturated DFIG. The implementation modelling of the DFIG, with the neglect of magnetic saturation and the results obtained from the proposed controller are being the most important as in [1-10]. However, the shown in section IV. Finlay, it will be shown that using the phenomenon of saturation is present in all electrical machines. developed DFIG model and the proposed controller, the In addition, the exact calculation of the machine dynamic dynamic responses of the system can be determined accurately performances depends considerably on the saturation of the and more precise robust control is achieved.

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II. MODELING OF WIND ENERGY CONVERSION SYSTEM Where the rotor frequency ωr is given by: The wind energy conversion system adopted in this work is based on wind turbine driven a DFIG. In such configuration,  ωr  ωs ωm  the is directly connected to the network, whereas, the rotor is fed by the grid via two converters (AC/DC) and The flux linkages in (5) are obtained from the following (DC/AC). In addition, the rotor side converter (DC/AC) is used equation system: to control independently the DFIG active and reactive powers.  sd  Lsisd  Lmird A. Modeling of the wind turbine   sq  Lsisq  Lmirq The mechanical power captured from the wind turbine,  (7) used in this investigation, is expressed as below:  rd  Lrird  Lmisd   qr  Lriqr  Lmiqs P  0.5C λ,βR2 ρ v3  t P The equation system in (7) is used to calculate the d and q components of stator and rotor currents: With:  1 R: radius of turbine (m), ρ: density of air (kg/m3), v: speed isd  (Lr sd  Lm rd ) Ls Lr of wind (m/s) and CP: the power coefficient.   1 i  (L   L  ) According to [3], the power coefficient Cp is function of the  sq r sq m rq  Ls Lr (8) tip speed ratio λ and the blade pitch angle β (deg), as follows:   1 ird  (Ls rd  Lm sd )  Ls Lr 116 21  1 C p  0.5109(  0.4β  5)exp( )  0.0068 λ  i  (L   L  ) λ λ  rq s rq m sq i i  Ls Lr With: With: L2 1 1 0.035  1 m , L  L  L , L  L  L (9)    s s m r r m 3 LsLr λi λ  0.08β β  1 The magnetizing current im is given as follows [14, 15]: The tip speed ratio λ is given by:

2 2 Ω R im  imd imq (10) λ  t  v Where: In (4) Ωt represent the rotational speed of the wind turbine. i  i i , i  i  i (11) B. Modeling of the DFIG md sd rd mq sq rq Below, we develop the conventional model of the DFIG In steady state and by aligning the q-axis of synchronous without saturation. According to this model, both mutual flux rotating reference frame on stator flux vector, the following and leakage fluxes saturation are considered. In these models, equations can be written [2, 8]: the DFIG is considered as a generalized wound rotor induction machine taking the stator resistance into consideration. The Vs latter is neglected in many works e.g. in [1-19]. ψds  ψs  , ψqs  0 (12) s 1) Linear DFIG model L V   L i  m s (13) The d and q equivalents circuits for the DFIG are shown in r r rd L  Fig. 1 [15]. Based in these schemas, the equations of s s the DFIG in the d-q synchronous referential are given by:  dird vrd  Rrird  Lr  gωsLrirq  dt  di (14)  d  rq LmVs v  R i  ψ  ω ψ vrq  Rrirq  Lr  gωs Lrird  gωs  sd s sd dt sd s sq  dt L    s s  d vsq  Rsisq  ψsq  ωsψsd LmVs  dt  Tem   p iqr (15)  L  d s s v  R i  ψ  ω ψ  rd r rd dt rq r rq  d vrq  Rrirq  ψrq  ωrψrd  dt 

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2) DFIG model with saturation The saturation coefficient Ksϭ can be represented by the Using the linear model explained in the previous section, function [11]: we develop a DFIG model taking the mutual flux saturation 1 i

isd Rs Lsϭs Lrϭs Rr ird In this study, the errors between reference and measured of

i the electromagnetic torque and the rotor flux have been chosen md as sliding mode surfaces, so the following expression can be vsd Lms vdr written:

S     r r _ ref r  (21) (a) S  T  T  Tem em _ ref em isq Rs Lsϭs Lrϭs Rr irq By substituting the rotor flux and the electromagnetic i mq torque in (21) by their expressions given, respectively, by (13) Lms and (15), one obtains: vsq vrq

 L S  L i  m    r r réf r rd s (a)  Ls  (22) L V Fig. 1. Equivalent circuits of a DFIG: (a) on d-axis, (b) on q-axis S  T  p m s i  Tem em réf qr  Lss s

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The first derivative of (22), gives: Ksm used in the determination of the saturated value of the mutual inductance Lms is sketched in figure 3. Likewise, the S  L i consideration of the leakage flux saturation, I in (18)-(20)   r rréf r rd sat  L V (23) was assumed to be equal to 1.8×In =15.8 A, where the leakage S  T  p m s i  Tem em réf rq flux saturation coefficient Ksϭ is shown in figure 4.  Lss If we replace the d and q rotor currents derivatives in (23) by their expressions given from (14), one obtains:

S   v  R i  g L i    r r réf rd r rd s r rq Stator Side  Converter  V L  L  (24) S  T  p s m v  R i  g L i  gV m  Tem em réf  rq r rq s r rd s   Ls Lr  Ls   DC bus We define the functions G1 and G2 as follows: Rotor Side G1  Rrirq  gsLrirq r réf  Converter DFIG (25)  Vs Lm  Lm   G2  p  Rrirq  gsLrird  gs  s  Tem réf Grid  S  Ls Lr  Ls  a Sb Sc PWM After substituting (25) in (24), the derivative of (24) gives: vrd vrq S  v  G ψr_ref

 r rd 1 Sψr

+ c

- DTC- c  V L (26) s m ,ab   T STem r ST  p vrq  G2 em_ref HOSMC r,ab  I em L L + - V  s r Tem Flux and Torque Basing on the super -twisting algorithm establish ed by Levant ψr Estimation in [22,23], the high order sliding mode controller contains two parts: Fig. 2. Bloc diagram of HOSMC-DTC applied to the DFIG  0.5 v  α sign(S )dt β S sign(S )

 rd 1  r 1  r  r m 1.2   (27) s  0.5 V  α sign(S )dt β S sign(S )  rq 2  Tem 2 Tem Tem 1 In order to guarantee the convergence of the sliding manifolds to zero in set time, the constants α1, β1, α2 and β2 can be chosen as follows [2,6,28]: 0,8

 1  1  0,6  2 (1  1) 1  4i I (   ) msat  1 1 (28)

 K saturation Mutualcoefficient flux 0,4 1  G2 0 6 10 15 20 25 30 Magnetizing current i (A)  pV L m    s m  2 2 Fig. 3. Mutual flux saturation coefficient K  Ls Lr sm  2 (b)

   pV L (   ) s  2  s m  2 2 1.2 2  42    Ls Lr  (2  2 ) (29)  1 2  G2   0.8 IV. SIMULATION RESULTS In this section, simulations are realized with a 7.5 KW 0.6 DFIG coupled to a (311V, 50 Hz) network, utilizing the Matlab/Simulink environment. The parameters of the machine 0.4 I are shown in Table 2. sat

Leakage flux saturation coefficient K saturation Leakagecoefficient flux 0.2 The consideration of saturation into account for the mutual 0 15.8 40 60 80 Current i (A) flux of the investigated DFIG is realized by taking Imsat in (16)- (17) to be equal to 0.7× I = 6 A. In this equality, I is the rated n n Fig. 4. Leakage flux saturation Coefficient Ksϭ current given in Table 2. The mutual flux saturation coefficient

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The two DTC control strategies; classical DTC and DTC- 0 1.04 T HOSMC are simulated and compared in terms of reference em r -10 T * tracking and robustness against machine parameter variations. em * 1.02 r

A. Test of reference tracking -20 1 The goal of this test is to explore the behaviour of the two DTC control strategies while maintaining the DFIG’s speed at -30 0.98 its nominal value. The simulation results are shown in figures 5 -40 -49 and 6. From these figures we can see that for the DTC- -50 Rotorflux (Wb) 0.96 HOSMC control method, the torque and rotor flux track almost -50 perfectly their references values. In addition, and contrary to -51 0.3 0.4 0.5

Electromagnetic torqueElectromagnetic (N.m) -60 0.94 the classical DTC strategy in which the coupling effect 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 between the two axes is quite apparent, we remark that, in the 0 1.04 Time (s) Time(s) present DTC-HOSMC strategyT , the decoupling between the em r -10 T * axes is guaranteed. em * 1.02 r 8 1.5 B. Test of robustness-20 61 1 In order to check-30 the robustness of the used DTC control strategies, the machine parameters namely the stator and the 4

(%) 0.98

(%) r rotor resistances R-40 and R have been intentionally-49 doubled. m 2

s r e 0.5  The DFIG is working at its nominal speed-50 and is in state of Rotorflux (Wb) 0.960 saturation. Figures-50 6 and 7 show the simulation results. From -51 -2 0 0.3 0.4 0.5

these Figures, wetorqueElectromagnetic (N.m) -60 see that the parameters variation of the 0.94 0 0.2 0.4 0.6 0.8 1 -4 0 0.2 0.4 0.6 0.8 1 machine increase the time-response of the classical DTC sur Ecart Time (s) surC Ecart Time(s) -0.5 strategy slightly. However the results show that these -6 variations cause a marked effect on the torque and flux Fig. 6. DTC-HOSMC strategy responses (test of reference tracking) -8 -1 variations and this effect8 is more marked for the classical DTC 1.50 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 1.03 strategy than that with6 DTC-HOSMC. 0 Time(s) Time(s) 1 With parmeters variation With parmeters variation 4 1.02

0 1.03 -10 Without parmeters variation Witout parmeters variation (%)

T (%)  r emm 2 r T * 1.01  * e 1.02 0.5 em r -10 T *  * em 0 -20r 1.01 1 0 -20 -2 1 -30 0.99

-4 Ecart sur Ecart -30 surC Ecart 0.99 -0.5 0.98 -6 -40 -49 0.98 0.97 -40 -8 -1 Rotorflux (Wb) 0 0.2-49 0.4 0.6 0.8 1 0 0.2 0.4 -500.6 0.8 1 0.97 -50

Rotorflux (Wb) 0.96 -50 Time(s) Time(s)-51 -50 0.3 0.4 0.5 0.96 -60 0.95 -51 torqueElectromagnetic (N.m) 0.3 0.4 0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 -60 0.95 Electromagnetic torqueElectromagnetic (N.m) 0 0.2 0 0.4 0.6 0.8 1 0 0.21.03 0.4 0.6 Time 0.8(s) 1 Time (s) 0 1.03 With parmeters variation With parmeters variation Time (s) 1.02 Time (s) T  -10 Without parmeters variation Witout parmeters variation em 1.02 r -10 T * * T * 1.01  * em r em 6 r 0.4 1.01 -20 6 0.4 1 -20 1 4 0.2 4 -30 0.2 0.99 -30 0.99 0

0 (%) 0.982 (%)

(%) -40 r

0.982 -49 m

(%)

e r -40 -49 m -0.2

0.97  e -0.2 Rotorflux (Wb) 0.97 -50 

Rotorflux (Wb) 0 -50 0 -50 -50 0.96 -0.4 0.96 -51 -0.4 -51 0.3 0.4 0.5 -60 0.95-2 0.3 0.4 0.5 torqueElectromagnetic (N.m) -60 0.95-2 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 -0.6

Electromagnetic torqueElectromagnetic (N.m) 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 -0.6

Ecart sur Ecart Ecart sur Ecart Time (s) surC Ecart Time (s) Time (s) surC Ecart Time (s) -4 -4 -0.8 -0.8 Fig. 7. Classical DTC strategy responses (test of robustness) Fig. 5. Classical DTC strategy responses (reference tracking test) -6 6 -1 -60.4 -1 6 0.40 0.2 0.4 0.6 0.8 1 0 0.2 0 0.40.2 0.60.4 0.80.6 10.8 1 0 0.2 0.4 0.6 0.8 1

0.2 Temps (s) 0.2 Temps (s)Temps (s) Temps (s) 4 4 0 0

(%) (%) 2

2 (%)

(%)

m r

m r e e -0.2

-0.2   0 0 -0.4 -0.4 -2 -2

-0.6 -0.6

Ecart sur Ecart

Ecart sur Ecart Ecart surC Ecart -4 surC Ecart -0.8 -4 -0.8 59 | P a g e -6 -1 -6 -1 0 0.2 0.4 0.6 0.8 1 0 0.2 0 0.4 0.2 0.6 0.4 0.8 0.6 1 0.8www.ijacsa.thesai.org1 0 0.2 0.4 0.6 0.8 1 Temps (s) Temps (s) Temps (s) Temps (s) (IJACSA) International Journal of Advanced Computer Science and Applications, Vol. 7, No. 7, 2016

0 1.04 V. CONCLUSION With paremeter variation With paremeter variation Without parameter varaition InWithout this paper, parameter we varaitionhave investigated a Direct Torque Control -10 T * 1.02 * em using  ar high order sliding mode controllers. The goal of this -20 control strategy has been to improve the calculation of the 1 dynamic performances of saturated DFIG driven by a wind -30 turbine driven. In the first place, the modelling of the saturated DFIG-based wind turbine has been carried out. The saturation 0.98 -40 -49 of both the magnetizing flux and of the leakage fluxes have

Rotorflux (Wb) been taken into account in the proposed DFIG model. Then, -50 0.96 -50 the synthesis of a new DTC combined with HOSMC has been -51 performed and this DTC-HOSMC has been compared with the 0.3 0.4 0.5 Electromagnetic torqueElectromagnetic (N.m) -60 0.94 conventional DTC in term of reference tracking. The tacking of 0 0.2 0.4 0.6 0.8 1 0 their references0.2 0.4 was achieved0.6 almost0.8 perfectly1 by the two DTC 0 1.04 Time (s) Time(s) With paremeter variation With paremeter variation strategies, however there appeared a coupling effect in the Without parameter varaition Without parameter varaition -10 conventional DTC responses, whereas this coupling was T * 1.02  * em r eliminated in the DTC-HOSMC. An investigation of 8 1.5 -20 robustness test has also been realized in which the parameters 61 of the DFIG have been intentionally modified. Some -30 1 disturbances on the torque and flux responses have been 4

0.98 induced by these changes but with a major effect with the (%)

-40 -49 (%) r m 2

0.5 conventional DTC strategy than with the proposed DTC-

e Rotorflux (Wb) -50 0.96  -50 0 HOSMC. On the light of these results, we conclude that the -51 robust DTC-HOSMC control method is a very attractive 0.3 0.4 0.5 -2 0 Electromagnetic torqueElectromagnetic (N.m) -60 0.94 solution for those devices that use the saturated DFIG as 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1

-4 happens in wind energy conversion systems. Ecart sur Ecart Time (s) surC Ecart Time(s) -0.5 Fig. 8. -6DTC-SOSMC strategy responses (robustness test) APPENDIX -8 -1 8 1.50 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 8 1.5 TABLE I. LIST OF SYMBOLS 6 DTC Time(s) DTC Time(s) 6 Symbol Significance 1 DTC-HOSMC DTC-HOSMC 4 DFIG Doubly-fed induction generator 1

(%) 4 DTC Direct Torque Control

(%) r m 2 0.5 e HOSMC High Order Sliding Mode Control  2 0 0.5 vds, vqs, vdr, vqr d and q axis stator and rotor voltages, ψds, ψqs, ψdr, ψqr d and q axis stator and rotor fluxes, -2 0 0 ψr_ref Reference rotor flux i , i , i , i d and q axis stator and rotor currents,

-4 -2 0 ds qs dr qr Ecart sur Ecart Ecart surC Ecart -0.5 Rs, Rr Stator and rotor resistances, -6 -4 Ls, Lr Stator and rotor inductances,

Rotorflux -0.5(%)error Lsϭ, Lrϭ Stator and rotor leakage inductances, -8 -6-1 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Lsϭs, Lrϭs Stator and rotor saturated leakage inductances, ϭ Leakage coefficient Time(s) torque Electromagnetic (%)error -8 Time(s) -1 0 0.2 0.4 0.6 0.8 1 0 In 0.2 0.4 Rated0.6 current, 0.8 1 8 1.5 Time(s) Lm Time(s)Mutual inductance, DTC DTC Lms Saturated mutual inductance, 6 DTC-HOSMC DTC-HOSMC p Number of pole pairs, 1 s Generator slip, 4 ωs, ωr Stator and rotor current frequencies (rd/s), 2 ωm Mechanical rotor frequency (rd/s), 0.5 Tem, Tem_ref Electromagnetic, Reference electromagnetic torque. 0 TABLE II. MACHINE PARAMETERS -2 0 Parameters Rated Value Unit -4 Nominal power Pn 7.5 KW

Rotorflux -0.5(%)error -6 Stator voltage Vn 220 V Stator voltage amplitude Vs 311 V

Electromagnetic torque Electromagnetic (%)error -8 -1 Stator current In 8,6 A 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Stator frequency f 50 Hz Time(s) Time(s) Number of pairs poles p 2 Nominal speed 흎 144 rad/s Fig. 9. Error curves (robustness test) m Stator resistance Rs 1.2 Ω Rotor resistance Rr 1.8 Ω Mutual inductance Lm 0.15 H Leakage stator inductance Lϭs 0.0054 H Leakage rotor inductance Lϭr 0.0068 H

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REFERENCES [14] H.M. Jabr , N.C. Kar, “Effects of main and leakage flux saturation on [1] D. Kairous and B. Belmadani, “Robust Fuzzy-Second Order Sliding the transient performances of doubly-fed wind driven induction Mode based Direct Power Control for Voltage Source Converter”, generator”, Electric Power Systems Research, Vol. No.8, 2007, pp International Journal of Advanced Computer Science and Applications 1019–1027. (IJACSA), vol. 6, no. 8, 2015, pp. 167-175. [15] H.M. Jabr, N.C. Kar, “Leakage flux saturation effects on the transient [2] S. Abddaim, A. Betka, “Optimal tracking and robust power control of performance of wound rotor induction motors”, Electric Power Systems the DFIG wind turbine”, Electrical Power and Energy Systems, vol. 49, Research, vol. 78, 2008, PP.1280-1289. 2013, pp. 234–242. [16] M. Iordache, L. Dumitriu, “Voiculescu, R. Nicolae, D., Galan, N.: [3] A. Davigny, “ Participation in the system services of wind Saturated Induction Machine Steady-state Performance assessment farms variable speed integrated storage inertial energy”; PhD thesis, through simulations”, IEEE transactions on energy conversion, 2014, pp. University of Lille, France, 2007. 368-374. [4] M. Edrah, K. L. Lo, O. Anaya-Lara, “Impacts of high penetration of [17] H.M. Jabr, N.C. Kar, “Starting performances of saturated induction DFIG wind turbines on rotor angle stability of power systems”, IEEE motors”, In: Proc. IEEE. Conf, Power Engineering Society General Trans. Sustain Energ, vol. 6, 2015, pp. 759-766. Meeting, Tampa Florida, USA, 24-28 June, 2007, pp. 1-7. [5] N. Bounar, A. Boulkroune, F. Boudjema, M. M’Saad, M. Farza, [18] S. Mefoued, “A second order sliding mode control and a neural network “Adaptive fuzzy for a doubly-fed ”, In: to drive a knee joint actuated orthosis”, Neurocomputing 2015, vol. 155, Neurocomputing, vol. 151, no. 2, 2015, pp. 756-769. pp. 71-79. [6] B. Beltran, M.E.H. Benbouzid, T. Ahmed-Ali, “Second order sliding [19] X. Yao, Y. Jing, Z. Xing. “Direct torque control of a doubly-fed wind mode control of a doubly fed induction generator driven wind turbine, generator based on grey-fuzzy logic”, In: International Conference on IEEE Trans., Energy Convers., Vol. 27, No 2, 2012, pp. 261–269. Mechatronics and Automation, 2007, Harbin, China. pp. 3587-3592. [7] M. Benkahla, R. Taleb and Z. Boudjema, “Comparative Study of Robust [20] G.S. Buja, M.P. Kazmierkowski, “Direct torque control of PWM Control Strategies for a DFIG-Based Wind Turbine”, International inverter-fed AC motors - a survey”, IEEE T Ind Electron 2004, vol. 51, Journal of Advanced Computer Science and Applications (IJACSA), pp. 744-757. vol. 7, no. 2, 2016, pp. 455-462. [21] S.Z. Chen, N.C. Cheung, K.C. Wong, J. Wu, “Integral sliding-mode [8] F. Poitiers, T. Bouaouiche, M. Machmoum, “Advanced Control of a direct torque control of doubly-fed induction generators under Doubly-Fed Induction Generator for Wind Energy Conversion”, Electric unbalanced grid voltage”, IEEE Trans. Energy Conver. 2010, vol. 25, Power Systems Research, vol. 79, no 7, 2009, pp.1085–1096. pp. 356-368. [9] X. Zhu, S. Liu, Y. Wang, “Second-order sliding-mode control of DFIG- [22] A. Levant, L. Alelishvili, “Integral high-order sliding modes”, IEEE T based wind turbines”, In: IEEE 3rd Renewable Power Generation Automat Contr, vol. 52, 2007, pp. 1278-1282. Conference, 24-25 September 2014; Naples, Italy, pp. 1-6. [23] A. Levant, “Higher-order sliding modes, differentiation and output [10] S. Z. Chen, N. C. Cheung, K. C. Wong, J. Wu, “Integral sliding-mode feedback control”, Int J Control, 2003; vol. 76, pp. 924-941. direct torque control of doubly-fed induction generators under [24] X. Zhu, S. Liu, Y. Wang, “Second-order sliding-mode control of DFIG- unbalanced grid voltage”, IEEE T Energy Conver, vol. 25, 2010, pp. based wind turbines”, In: IEEE 2014 3rd Renewable Power Generation 356-368. Conference; 24-25 September 2014, Naples, Italy, pp. 1-6. [11] L. Monjo, F. C´orcoles, J. Pedra, “Saturation Effects on Torque and [25] N. C. Kar, H. M. Jabr, “A novel PI gain scheduler for a vector controlled Current Slip Curves of Squirrel Cage Induction Motors”, IEEE doubly-fed wind driven induction generator”, in: Proceedings of 8th transactions on energy conversion, vol.28, No1, 2013, pp. 243-254. IEEE Int. Conf. Electrical Machines and Systems, vol. 2, 2005, pp.948– [12] N.C. Kar, H. M. Jabr, “A novel PI gain scheduler for a vector controlled 953. doubly-fed wind driven induction generator, in: Proceedings of 8th IEEE [26] P. Kundur, “Power Systems Stability and Control”, New York, Int. Conf. Electrical Machines and Systems, vol. 2, 2005, pp.948–953. McGraw-Hill, USA, 1994, pp. 296–297. [13] J. Zhao, W. Zhang, Y. He, J. Hu, “Modeling and Control of a Wind- [27] G. J. Rogers, D. S. Benaragama, An induction motor model with deep- Turbine-Driven DFIG Incorporating Core Saturation during Grid bar effect and leakage inductance saturation”, Arch Elektrotech, vol. 60, Voltage Dips”, Electronic Machines and Systems (ICEMS), 2008, 1978, pp. 193–201. pp.2438-2442. [28] B. Beltran, M.E.H. Benbouzid, T. Ahmed-Ali, “High-order sliding mode control of a DFIG-based wind turbine for power maximization and grid fault tolerance”, In: IEEE International Electric Machines and Drives Conference, May 2009; Miami, Florida, USA, pp. 183-189.

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