Fuzzy sliding mode control of doubly-fed induction generator driven by wind turbine

International Journal of Power Electronics and Drive System (IJPEDS)
Vol. 10, No. 3, Sep 2019, pp. 1592~1602
ISSN: 2088-8694, DOI: 10.11591/ijpeds.v10.i3.pp1592-1602  1592
Journal homepage: http://iaescore.com/journals/index.php/IJPEDS
Fuzzy sliding mode control of doubly-fed induction generator
driven by wind turbine
M. Benmeziane1
, S. Zebirate1,2
, A. Chaker1
, Z. Boudjema3
1 SCAMRE Laboratory, Maurice Audin National Polytechnic School of Oran, ENPO, Oran, Algeria
2 IMSI, University of Oran 2 Mohamed BENAHMED, Oran, Algeria
3 Department of Electrical Engineering, University of Sidi Bel-Abbes, Algeria
Article Info ABSTRACT
Article history:
Received Jan 22, 2019
Revised Mar 1, 2019
Accepted Apr 8, 2019
This paper present a hybrid nonlinear control based on fuzzy sliding mode to
control wind energy conversion system using a doubly fed induction
generator (DFIG). Consiting of coupling fuzzy logic control and sliding
mode control this technique is introduced to avoid the major disadvantage of
variable structure systems, namely the chattering phenomenon. Effectiveness
and feasibility of the proposed control strategy are verified by simulation
results in Matlab Simulink.
Keywords:
Doubly fed induction generator
Fuzzy logic
Nonlinear controller
Power control
Sliding mode controller Copyright © 2019 Institute of Advanced Engineering and Science.
All rights reserved.
Corresponding Author:
Meriem Benmeziane,
Department of Electrical Engineering,
National Polytechnic School of Oran,
Maurice Audin, Algeria.
Email: m.benmeziane@yahoo.fr
1. INTRODUCTION
Wind power has become increasingly popular because of the increasing difficulty of the
environmental pollution and the greenhouse effect. Huge efforts have been made in promoting the wind
energy conversion system, to reduce costs, increase reliability and robustness [1]. Variable speed operation of
wind turbine is usually used to provide energy with best efficiency. Those based on doubly fed induction
generators are widely used especially in high power fields, thanks to different advantages it presents namely:
reducing the size of the converter, operating in a large game of speed, and the possibility of controlling
independently the generated active and reactive powers [2].
A Doubly Fed Induction Generator (DFIG) is an electrical asynchronous three-phase machine with
open rotor windings which can be fed by external voltages. The typical connection scheme of this machine is
reported in Figure 1. The stator windings are directly connected to the line grid, while the rotor windings are
controlled by means of an inverter [3].
Many control techniques are used to control doubly fed induction generator. Zerzouri et al. have
tried to improve the performance of a DFIG wind energy conversion system; they have proposed the vector
control with the PI controller to decouple the active and reactive power of the stator. They have used a single
PI in each control loop, but this control has oscillations, exceedances, and the decoupling is not fully
maintained [4]. Poitiers et al. have used the RST polynomial controller, they have found that the RST control
is more robust than the PI control compared to the rotor resistance variation, but the oscillations
remain apparent [5].

Int J Pow Elec & Dri Syst ISSN: 2088-8694 
Fuzzy sliding mode control of doubly-fed induction generator driven by wind turbine (M. Benmeziane)
1593
The sliding mode control (SMC) achieves robust control by adding a discontinuous control signal
across the sliding surface, satisfying the sliding condition [6]. In [7], a dynamical sliding mode power control
structure is suggested for DFIG. In [8], the SMC technique is used to control the rotational speed in the rotor
side as well as the dc-link voltage in the grid side of a wind energy conversion system; a model predictive
control based SMC is proposed to control a three-phase grid-connected converter and the grid current total
harmonic distortion and the switching losses are largely mitigated in [9].
DFIG
T
GB – Gearbox
IG – Induction Generator
RSC – Rotor-Side Converter
GSC – Grid Side Converter
T – Transformer
RSC GSC
GB
Figure 1. Configuration of DFIG- Wind Turbine
The SMC has a major inconvenience which the chattering effect is created by the discontinuous part
of control. Chattering causes several damages to the mechanical components. To treat these difficulties and
improve the performances, different methods were proposed such as by replacing the sign function with
saturation [10] or using Quasi-SMC and fuzzy mathematics [11]. In [12] an optimized sliding mode controls
(SMC) strategy to maximize existence region for single-phase dynamic voltage restorers. It is shown
analytically that there exists an optimum sliding coefficient which enlarges the existence region of the sliding
mode to its maximum. Also, it is pointed out that the optimum sliding coefficient improves the dynamic
response. In [13] the author proposes a SMC control strategy which combines a switched policy with a time-
based adaptation of the control gain, thereby allowing to effectively dealing with a very conservative prior
knowledge of the upper bounds on the uncertainties, which usually leads to a large control authority, and
related performance degradation in [14].
The fuzzy logic controller is a powerful tool for controlling complex processes, without the need of
a detailed mathematical model of the system. In fact, this technique of control has been used to solve the
unknown parameters variations or to remove the effect of nonlinearity; it has been successfully applied to
electromagnetic motors control and the fuzzy model of a plant is very easy to apply [15].
In this paper the sliding mode controller is combined with Fuzzy Logic (FL) to form a fuzzy sliding
mode controller (FSMC) to reduce the chattering phenomenon and improve time of reponse [16]. Design,
implementation, analysis and comparison between the classical sliding mode control (SMC) and the hybrid
fuzzy sliding mode control (FSMC) is presented with simulation in Matlab Simulink.
2. RESEARCH METHOD
2.1. DFIG model
The Doubly Fed Induction Generator DFIG model using Park transformation is as (1) [17]:
ds s ds ds s qs
qs s qs qs s ds
dr r dr dr r qr
qr r qr qr r dr
d
V R I ω
dt
d
V R I ω
dt
d
V R I ω
dt
d
V R I ω
dt
 
 
 
 

  


   


   


   

   

The flux can be expressed as (2):

 ISSN: 2088-8694
Int J Pow Elec & Dri Syst, Vol. 10, No. 3, Sep 2019 : 1592 – 1602
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














qs
qr
r
qr
ds
dr
r
dr
qr
qs
s
qs
dr
ds
s
ds
MI
I
L
MI
I
L
MI
I
L
MI
I
L




    
The stator and rotor angular velocities are linked by the following relation: ωs = ω + ωr.
The mechanical equation is given by (3):




 f
dt
d
J
C
C r
em
     
(3)
Where the electromagnetic torque Cem can be written as a function of stator ﬂuxes and rotor currents (4):
( )
em qs dr ds qr
s
M
C p I I
L
 
  (4)
2.2. Active and reactive power control
To easily control the production of electricity from wind, we will achieve an independent control of
active and reactive power by the stator flux orientation as shown on Figure 2 [18].
Figure 2. Power control between the stator and network
To realize a stator active and reactive power vector control, we choose a d-q reference-frame synchronized
with the stator flux [19]. By setting null the quadratic component of the stator flux, we have (5):
and 0
ds s qs
  
  (5)
and the electromagnetic torque can be expressed (6):
em qr ds
s
M
C p I
L

  (6)
By substituting (6) in (3), the following rotor flux equations are obtained:

1595
0
s s ds dr
s qs qr
L I MI
L I MI
  
 





(7)
Moreover, the stator voltage equations are reduced t (8)o:
0
ds
qs s s
V
V  







      (8)
By supposing that the electrical supply network is stable, having for simple voltage Vs that led to a stator flux
 s constant. This consideration associated with (7) shows that the electromagnetic torque only depends on
the q-axis rotor current component.
Using (8), a relation between the stator and rotor currents can be established (9)[20]:
s
ds dr
s s
qs qr
s
M
I I
L L
M
I I
L


  



  


(9)
The stator active and reactive powers are written(10):









qs
ds
ds
qs
s
qs
qs
ds
ds
s
I
V
I
V
Q
I
V
I
V
P
(10)
By using (1), (2), (4) and (10), the statoric active and reactive power, the rotoric fluxes and voltages can be
written versus rotoric currents as:
2
s s
s qr
s
s s s s
s dr
s s
ω M
P I
L
ω M ω
Q I
L L

 





   




2
2
( )
( )
s
dr r dr
s s
qr r qr
s
M
M
L - I
L L
M
L - I
L




 



 



2 2
dr
dr r dr r s r qr
s s
2 2
qr s
qr r qr r s r dr s
s s s
dI
M M
V R I L - gω L - I
L dt L
dI M
M M
V R I L - gω L - I gω
L dt L L
( ) ( )
( ) ( )


  



    



In steady state, the second derivative terms of the two equations in (14) are nil. We can thus write:
2
2
( )
( )
dr r dr s r qr
s
s
qr r qr s r dr s
s s
M
V R I gω L - I
L
M
M
V R I gω L - I gω
L L


 



   



The third term, which constitutes cross-coupling terms, can be neglected because of their small influence.
These terms can be compensated by an adequate synthesis of the regulators in the control loops [20]. Figure 3
shows the Power Control of DFIG.

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Figure 3. Power control of DFIG
2.3. Sliding mode control
The sliding mode technique is developed from variable structure control to solve the disadvantages
of other designs of nonlinear control systems. The sliding mode is a technique to adjust feedback by
previously defining a surface. The system which is controlled will be forced to that surface, then the
behaviour of the system slides to the desired equilibrium point. The main feature of this control is that we
only need to drive the error to a “switching surface”. When the system is in “sliding mode”, the system
behaviour is not affected by any modelling uncertainties and/or disturbances. The design of the control
system will be demonstrated for a nonlinear system presented in the canonical form(15) [21]:
x
 = f(x,t)+B(x,t)U(x,t), xRn
, URm
, ran(B(x,t)) = m (15)
With control in the sliding mode, the goal is to keep the system motion on the manifold S, which is defined
as:
S = {x : e(x, t)=0} (16)
e = xd
- x (17)
Here e is the tracking error vector, xd
is the desired state, x is the state vector. The control input U has to
guarantee that the motion of the system described in (17) is restricted to belong to the manifold S in the state
space. The sliding mode control should be chosen such that the candidate Lyapunov function satisfies
the Lyapunov stability criteria [22]:
2
)
(
2
1
x
S

 (18)
)
(
)
( x
S
x
S 
 
 (19)
This can be assured for:
 
x
S

 

 (20)
Here η is strictly positive. Essentially, equation (18) states that the squared “distance” to the surface,
measured by e(x)2
, decreases along all system trajectories. Therefore (19), (20) satisfy the Lyapunov
condition. With selected Lyapunov function the stability of the whole control system is guaranteed.
The control function will satisfy reaching conditions in the following form [23]:

1597
Ucom
= Ueq
+ Un
(21)
Here Ucom
is the control vector, Ueq
is the equivalent control vector, Un
is the correction factor and must be
calculated so that the stability conditions for the selected control are satisfied.
Un
= K sat(S(x)) (22)
Where sat(S(x)) is the proposed saturation function, K is the controller gain.
In this paper we propose the Slotine method [24]:
  e
ξ
X
S
n 1
dt
d








 (23)
Here, e is the tracking error vector, ξ is a positive coefficient and n is the relative degree.
2.4. Application of SMC to the DFIG
In our study, we choose the error between the measured and references stator powers as sliding
mode surfaces, so we can write the following expression:











S
ref
S
q
S
ref
S
d
Q
Q
S
P
P
S
(24)
The first order derivate of (24), gives:











S
ref
S
q
S
ref
S
d
Q
Q
S
P
P
S






(25)
Replacing the powers in (25) by their expressions given in (11), one obtains:














s
2
s
s
dr
s
s
s
ref
S
2
qr
s
s
s
ref
S
1
L
ψ
ω
I
L
M
ψ
ω
Q
S
I
L
M
ψ
ω
P
S






(26)
Vdr and Vqr will be the two components of the control vector used to constraint the system to converge to
Sdq=0. The control vector Vdqeq is obtained by imposing 0

dq
S
 so the equivalent control components are
given by the following relation:




























































s
s
s
dr
s
s
2
r
qr
r
*
s
s
s
s
s
s
2
r
qr
s
s
2
r
dr
r
*
s
s
s
s
2
r
s
eqdq
L
M
ψ
gω
I
gω
L
M
L
I
R
P
M
ψ
ω
L
M
ψ
L
M
L
I
gω
L
M
L
I
R
Q
M
ψ
ω
L
M
L
L
V

 (27)
To obtain good performances, dynamic and commutations around the surfaces, the control vector is
imposed as follows:
)
(
K dq
eqdq
dq S
sat
V
V 

 (28)
The SM will exist only if the following condition is met:
0
S
S 
  (29)

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2.5. Fuzzy sliding mode control of the DFIG
The disadvantage of sliding mode controllers is that the discontinuous control signal produces
chattering. In order to eliminate the chattering phenomenon, we propose to use the fuzzy sliding mode
control. The fuzzy sliding mode controller (FSMC) is a modification of the sliding mode controller, where
the switching controller term sat(S(x)), has been replaced by a fuzzy control input as given below [25].
Ucom
= Ueq
+ UFuzzy
(30)
The proposed fuzzy sliding mode control, which is designed to control the active and reactive power
of the DFIG is shown in Figure 4. To synthesis the fuzzy controller of the two variables (active and reactive
powers) fuzzy control uses a set of rules to represent how to control the system; these are the steps of
fuzzification and defuzzification as shown in Table 1. The membership functions for input and output
variables are given by Figure 5.
Figure 4. Bloc diagram of the DFIG control with FSMC
Table 1. Matrix of Inference
ΔE
E
NB NM NS EZ PS PM PB
NB NB NB NB NB NM NS EZ
NM NB NB NB NM NS EZ PS
NS NB NB NM NS EZ PS PM
EZ NB NM NS EZ PS PM PB
PS NM NS EZ PS PM PB PB
PM NS EZ PS PM PB PB PB
PB EZ PS PM PB PB PB PB
- NB: Negative Big,
- NM: Negative Middle,
- NS: Negative Small,
- EZ: Equal Zero,
- PS: Positive Small,
- PM: Positive Middle,
- PB: Positive Big.
Figure 5. Fuzzy sets and its membership functions
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
x 10
4
0
0.5
1
"membership change rate of errors"
Deltaed(k)
, Deltaeq(k)
sNG sNM sNP sEZ sPP sPM sPG
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
x 10
4
0
0.5
1
"membership control signals"
ud(k)
,uq(k)
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
x 10
4
0
0.5
1
"membership errors"
ed(k)
, eq(k)
K
PS-mes
F L
Vqr
n
S(P) Vqr-ref
PS-ref
-
+
+
+
K
QS-mes F L
Vdr
n
S(Q) Vdr-ref
QS-ref
-
+
+
+
Vqr
eq
Vdr
eq

1599
3. RESULTS AND ANALYSIS
These simulations represent a comparison between the conventional sliding mode control and
the fuzzy sliding mode control.In the aim to evaluate the performances of these two controllers,
three categories of tests have been realized by the simulation in Matlab/Simulink. The parameters utilized are
listed in Tables 2 and 3.
Table 2. DFIG parameters
PN= 1.5MW Vs=398/690 V f=50 Hz J=1000 Kg.m2
P=2 Rs=0.012 Ω Rr=0.021Ω fv=0.0024 Nm/s
M=0.0135 H Ls=0.0137 H Lr=0.0136 H
Table 3. Turbine parameters
Diameter=35.25 m
Gearbox G=90
Number of blade=3
3.1. Pursuit test
Simulation results are presented in Figures 6 and 7. As it’s shown by Figure 6, for the two
controllers, the stator active and reactive powers track almost perfectly their references and ensure a perfect
decoupling between the two axes. Both controllers proved very good performance for this test. On the other
hand, Figure 7 shows the harmonic spectrum of one phase stator current of the DFIG obtained using Fast
Fourier Transform (FFT). It is observed that the FSMC is effective in eliminating chattering phenomenon.
3.2. Sensitivity to the speed variation
The aim of this test is to analyze the influence of a speed variation of the DFIG on active and
reactive powers for the two controllers. For this objective and at time = 0.04s, the speed was varied from 150
rad/s to 170 rad/s. The simulation results are shown in Figure 8. As it is shown in Figure 8, the speed
variation produced a slight effect on the powers curves of the system with SMC controller, while the effect is
almost negligible for the system with FSMC one. It can be noticed that this last has a nearly perfect speed
disturbance rejection, indeed; only very small power variations can be observed (fewer than 2%). This result
is attractive for wind energy applications to ensure stability and quality of the generated power when the
speed is varying.
3.3. Robusness
In order to test the robustness of the used controllers, the machine parameters have been modified:
the values of the stator and the rotor resistances Rs and Rr are doubled and the values of inductances Ls, Lr
and M are divided by 2. The machine is running at its nominal speed. The results presented in Figure 10
shows that the parameters variations of the DFIG increase slightly the time-response of the two controllers.
On the other hand this results show that parameter variations of the DFIG presents a clear effect on
the powers curves (their errors curves) and that the effect appears more significant for SMC controller than
that with FSMC one. Thus it can be concluded that this last is more robust than the classical SMC controller.
We can therefore say that for the FSMC, the response time is significantly reduced and the oscillations are
limited and damped more rapidly compared to SMC controller. Simulations with this type of controller
presented very interesting performances in terms of reference tracking (time response, overshoot), sensitivity
to perturbation.
Figure 6. References tracking test
0 0.02 0.04 0.06 0.08 0.1
-10
-8
-6
-4
-2
0
x 10
5
Time (s)
Active
power
P
s
(W
)
Ps-ref
Ps
(SMC)
Ps
(FSMC)
0 0.02 0.04 0.06 0.08 0.1
-4
-3
-2
-1
0
1
x 10
5
Time (s)
Reactive
power
Q
s
(Var)
Qs-ref
Qs
(SMC)
Qs
(FSMC)

 ISSN: 2088-8694
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Figure 7. Spectrum harmonic of one phase stator current for SMC and FSMC controllers
Figure 8. Sensitivity to the speed variation
Figure 10. Robustness test
4. CONCLUSION
This paper presents Hybrid Fuzzy Sliding Mode Control of active and reactive power in a DFIG and
performance evaluations. After presenting a description of a doubly fed induction generator, a decoupling
control method of active and reactive powers for DFIG has been developed. After modeling the system,
the description of the classical sliding mode controller (SMC) is presented in detail, this controller has been
applied due to its excellent properties, such as insensitivity to certain external disturbances, however in
standard sliding mode there is larger chattering. A hybrid fuzzy sliding mode approach using vector control
strategy was established and presented. Responses of our system with this type of controller have shown that
the last gives very interesting performances toward reference tracking, sensitivity to perturbation and
robustness under parameters variation.
0 500 1000 1500 2000
0
500
1000
1500
2000
Frequency (Hz)
Stator current (SMC Controller) , THD= 3.05%
M
ag
0 500 1000 1500 2000
0
500
1000
1500
2000
Frequency (Hz)
Stator current (FSMC Controller) , THD= 2.85%
M
ag
0 0.02 0.04 0.06 0.08 0.1
-60
-40
-20
0
20
40
60
80
Time (s)
Active
power
Error
(%)
SMC
FSMC
0 0.02 0.04 0.06 0.08 0.1
-150
-100
-50
0
50
100
150
200
Time (s)
Reactive
power
Error
(%)
SMC
FSMC

1601
NOMENCLATURE
DFIG Doubly Fed Induction Generator
Vs, f, ws, w stator voltage , frequency grid and electrical speed, respectively
Vds, Vqs ,Vdr, Vqr stator and rotor voltages in d-q reference frame, respectively
ids ,iqs , idr ,iqr stator and rotor currents in d-q reference frame, respectively
Φds, Φqs, Φdr, Φqr stator and rotor flux linkages in d-q reference-frame, respectively
Rs ,Rr stator and rotor resistors of machine per phase, respectively
Ls, Lr cyclic inductances of stator and rotor windings, respectively
M the magnetizing inductance
Te,Tr electromagnetic and resistant torque
Ps, Qs stator active and reactive powers, respectively
SMC, FLC sliding Mode Control and Fuzzy Logic respectively
PN, J, fv and P Nominal Power, inertia, viscous friction and the number of pole pairs, respectively
REFERENCES
[1] A. Rahab, F. Senani, H. Benalla, "Direct Power Control of Brushless Doubly-Fed Induction Generator Used in
Wind Energy Conversion System," International Journal of Power Electronics and Drive System, Vol. 8, No. 1, pp.
417-433, March 2017.
[2] K. Boulâam and A. Boukhelifa, "Fuzzy sliding mode control of DFIG power for a wind conversion system," 16th
International Power Electronics and Motion Control Conference and Exposition, Antalya, pp. 353-358, 2014.
[3] Kheira Belgacem, Abdelkader Mezouar, Najib Essounbouli, "Design and Analysis of Adaptive Sliding Mode with
Exponential Reaching Law Control for Double-Fed Induction Generator Based Wind Turbine," International
Journal of Power Electronics and Drive System, Vol. 9, No. 4, pp. 1534-1544, December 2018.
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of Power Electronics and Drive System, vol. 5, pp. 244-251, October 2014.
[5] Arama Fatima Zohra, Bousserhane Ismail Khalil, Laribi Slimane, Sahli Youcef, Mazari Benyounes, "Artificial
Intelligence Control Applied in Wind Energy Conversion System," International Journal of Power Electronics and
Drive System, Vol. 9, No. 2, pp. 571-578, June 2018
[6] Benkahla M., Taleb R., Boudjema Z, "A new robust control using adaptive fuzzy sliding mode control for a DFIG
supplied by a 19-level inverter with less number of switches," Electrical engineering & electromechanics journal,
no.4, pp. 11-19, 2018.
[7] B. Hamane, M. L. Doumbia, M. Bouhamida, M. Benghanem, “Control of Wind Turbine Based on DFIG Using
Fuzzy-PI and Sliding Mode Controllers,” IEEE Proceedings Ninth International Conference on Ecological
Vehicles and Renewable Energies (EVER), Monte-Carlo (Monaco), French, pp. 440-448, 2014.
[8] Z. Boudjema, A. Meroufel and Y. Djeriri, "Nonlinear Control of a Doubly Fed Induction Generator for Wind
EnergyConversion," Carpathian Journal of Electronic and Computer Engineering, Vol. 6, N°1, pp. 28 - 35, 2013.
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International Journal of Energy Engineering, vol/issue: 30(01), pp 30-36, 2013.
[10] O. Boughazi, “Sliding Mode Backstepping Control of Induction Motor,” International Journal of Power
Electronics and Drive System, vol/issue: 4(4), pp. 481-488, 2014.
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energy conversion system,” IEEE Trans Sustain Energy, vol/issue: 7(3), pp. 1327–35, 2016.
[12] Liao K., et al., “A sliding mode based damping control of DFIG for interarea power oscillations,” IEEE Trans
Sustain Energy, vol/issue: 8(1), pp. 258–67, 2017.
[13] H. Aschemann and D. Schindele, “Sliding-mode control of a highspeed linear axis driven by pneumatic muscle
actuators,” IEEE Trans. On Industrial Electronics, vol/issue: 55(11), pp. 3855-3864, 2008.
[14] B. Belkacem, “Hybrid Fuzzy Sliding Mode Control of a DFIG Integrated into the Network,” International Journal
of Power Electronics and Drive System, vol/issue: 3(4), pp. 351-364, 2013.
[15] S. Biricik, “Optimized Sliding mode control to maximize existence region for single-phase dynamic voltage
restorers,” IEEE Transactions on Industrial Informatics, vol/issue: 12(4), pp. 1486-1497, 2016.
[16] Ouassila Belounis, Hocine Labar, "Fuzzy Sliding Mode Controller of DFIG for Wind Energy Conversion,"
International Journal of Intelligent Engineering and Systems, Vol.10, No.2, 2017, pp.163-174, 2017.
[17] T .Mesbahi, T. Ghennam, E.M. Berkouk, “A doubly fed induction generator for wind stand¬alone power
applications (simulation and experimental validation),” IEEE XXth International Conference on Electrical
Machines (ICEM), Marseille, France, pp. 2028-2033, 2012.
[18] T. Ghennam, E.M. Berkouk, B. François, “Modeling and control of doubly fed induction generator (DFIG) based
wind conversion system,” IEEE, Second International Conference on Power Engineering, Energy and Electrical
Drives (Powereng), Lisbon, Portugal, pp. 507-512, 2009.
[19] Smail Mansouri, Ali Benatillah, “Indirect Control of a Doubly-Fed Induction Machine for Wind Energy
Conversion,” International Journal of Power Electronics and Drive System, Vol. 4, No. 3, pp. 400-405, September
2014.

 ISSN: 2088-8694
1602
[20] Zinelaabidine BOUDJEMA, Abdelkader MEROUFEL, Ahmed AMARI, “Robust Control of a Doubly Fed
Induction Generator (DFIG) Fed by a Direct AC-AC Converter,” PRZEGLĄD ELEKTROTECHNICZNY,
No/VOL: 12a/2012, pp. 213-221, 2012.
[21] S. EL-Aimani, B. Françoi, F. Minne, B. Robyns, “Modeling and simulation of doubly fed induction generators for
variable speed wind turbines integrated in a distribution network,” 10th European conference on power electronics
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machine,’’ Journal of Electrical Engineering, Vol. 57, No. 1, pp. 47–51, 2006.
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generators,” IEEE Transactions on Energy Conversion, pp. 896–905, 20 December 2005.
[24] Zinelaabidine Boudjema, Rachid Taleb, A. Yahdou, H. Kahal, “High order sliding mode control of a DFIM
supplied by two power inverters,” Carpathian Journal of Electronic and Computer Engineering 8/1, pp. 23-30,
2015.
[25] Sid Ahmed El Mahdi ARDJOUN, Mohamed ABID, Abdel Ghani AISSAOUI, Abedelatif NACERI,
”A robust fuzzy sliding mode control applied to the double fed induction machine,” International Journal Of
Circuits, Systems And Signal Processing, Issue 4, Volume 5, pp. 315-321, 2011.

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