Power Control of Wind Turbine Based on Fuzzy Sliding-Mode Control

International Journal of Power Electronics and Drive System (IJPEDS)
Vol. 5, No. 4, April 2015, pp. 502~511
ISSN: 2088-8694  502
Journal homepage: http://iaesjournal.com/online/index.php/IJPEDS
Power Control of Wind Turbine Based on Fuzzy Sliding-Mode
Control
Tahir Khalfallah*, Belfedal Cheikh*, Allaoui Tayeb*, Gerard Champenois**
*Laboratoire de Génie Energitique et Génie Informatique LGEGI, Université Ibn Khaldoun de Tiaret, Algérie
**University of Poitiers, Laboratoire d’Informatique et d’Automatique pour les Systèmes, Bâtiment B25, 2, rue
Pierre Brousse, 86022 Poitiers, France
Article Info ABSTRACT
Article history:
Received Oct 1, 2014
Revised Dec 14, 2014
Accepted Jan 5, 2015
This paper presents the study of a variable speed wind energy conversion
system (WECS) using a Wound Field Synchronous Generator (WFSG) based
on a Fuzzy sliding mode control (FSMC) applied to achieve control of active
and reactive powers exchanged between the stator of the WFSG and the grid
to ensure a Maximum Power Point Tracking (MPPT) of a wind energy
conversion system. However the principal drawback of the sliding mode, is
the chattering effect which characterized by torque ripple, this phenomena is
undesirable and harmful for the machines, it generates noises and additional
forces of torsion on the machine shaft. A direct fuzzy logic controller is
designed and the sliding mode controller is added to compensate the fuzzy
approximation errors. The simulation results clearly indicate the
effectiveness and validity of the proposed method, in terms of convergence,
time and precision.
Keyword:
Fuzzy sliding mode control
Maximum power point tracking
Wind energy conversion system
Wound field synchronous
generator
Copyright © 2015 Institute of Advanced Engineering and Science.
All rights reserved.
Corresponding Author:
Tahir Khalfallah,
Departement of Electrical and Computer Engineering,
University Ibn Khaldun Tiaret, Algeria,
Email: tahir.commande@gmail.com
1. INTRODUCTION
Wind energy is becoming one of the most important renewable energy sources [1]. Recently, power
converter control has mostly been studied and developed for WECS integration in the electrical grid.
In recent years, variable speed WECSs have become the industry standard because of their
advantages over fixed speed ones such as improved energy capture, better power quality. They are capable of
extracting optimal energy capture in addition to having reduced mechanical stress and aerodynamic noise.
[2].
In terms of the generators for WECS, several types of electric generators are used such as Squired-
Cage Induction Generator (SCIG), Synchronous Generator with external field excitation, Doubly Fed
Induction Generator (DFIG) and Permanent Magnet Synchronous Generator (PMSG) with power electronic
converter system [3]. Therefore, the study of synchronous generator has regained importance. The primary
advantages of Wound Field Synchronous Generator are: The efficiency of this machine is usually high,
because it employs the whole stator current for the electromagnetic torque production. The main benefit of
the employment of wound field synchronous generator with salient pole is that it allows the direct control of
the power factor of the machine, consequently the stator current may be minimized any operation
circumstances [4].
The Sliding Mode Controller (SMC) is a particular type of variable structure control systems that is
designed as a robust control to drive and then constrain the system to lie within of the switching function.
However in the presence of large uncertainties or higher switching gain is required which produce higher
amplitude of chattering.

IJPEDS ISSN: 2088-8694 
Power Control of Wind Turbine Based on Fuzzy Sliding-Mode Control (Tahir Khalfallah)
503
Fuzzy logic has emerged as a powerful in control applications. It allows one to design a controller
using linguistic rules without knowing the mathematical model of the plant.
In this paper our objective is to apply a fuzzy controller combined with sliding mode to overcome
shattering of both sliding mode and fuzzy logic controllers and then to obtain a control system for a high
performance for power system [5]. Simulation results are provided to show the effectiveness of the proposed
overall WFSG control system.
2. WIND CONVERSION SYSTEM MODEL
The WECS described in this article includes the wind turbine, gearbox, WFSG, and back-to-back
converters. The rotor winding of the WFSG is connected to the grid by DC/AC converter, whereas the stator
winding is fed by back-to-back bidirectional PWM-VSC. In this system, the wind energy is transmitted
through the turbine to the three-phase WFSG and generated in electrical form. This energy is transmitted
directly through a bridge rectifier and inverter to the electrical network (Figure 1). We consider in this study
that the rectifier is perfect. So semiconductors are ideal [6]. In this paper our study is limited to the
generation of power in continuous form.
Figure 1 shows the equivalent diagram of the electrical portion of the string conversion of wind
energy.
Figure 1. WFSG based wind energy conversion system
2.1. Modeling of the Wind Turbine and Gearbox
The turbine power and torque developed are given by the following relation [7]:
  ,
2
1 32
pwa CVRP 
(1)
 

,
2
1 23
pw
t
a
a CVR
P
T 


(2)
Which  presents the ratio between the turbine angular speed and the wind speed. This ratio called
the tip speed ration and is defined as:
w
t
V
R

(3)
Where  is the air density, R is the blade length, wV is the wind speed, pC is the power
coefficient, t is the turbine angular speed.
The power coefficient  pC presents the aerodynamic efficiency of the turbine and depends on the
specific speed  and the angle of the blades. It is different from a turbine to another, and is usually provided
by the manufacturer and can be used to define a mathematical approximation.
The wind turbine shaft is connected to the WFSG rotor through a gearbox which adapts the slow
speed of the turbine to the WFSG speed. This gearbox is modeled by the following equations [8]:

 ISSN: 2088-8694
IJPEDS Vol. 5, No. 4, April 2015 : 502 – 511
504
G
m
t

 ;
G
T
T a
m  (4)
From the dynamics fundamental relation, the turbine speed is determined as follows:
memm
m
fTT
dt
d
J 

(5)
J and f are the total moment of inertia and the viscous friction coefficient appearing at the
generator side, mT is the gearbox torque, emT is the generator torque, and m is the mechanical generator
speed.
Figure 2 represents the power coefficient pC as a function of  and  .
Figure 3 shows the mechanical power as a function of rotor speed of the turbine for different values
of wind speed [9].
Figure 2. Power coefficient versus tip speed ratio Figure 3. Rotor power versus rotational speed of
generator
2.2. Modeling of the WFSG
In the synchronous d-q coordinates, the voltage equation of the WFSG is expressed as follows [10]:
dt
di
m
dt
di
m
dt
di
LimiLirv D
sD
f
sf
ds
dQsQeqsqedssds   (6)
dt
di
m
dt
di
LimimiLirv
Q
sQ
qs
qDsDefsfedsdeqssqs   (7)















qssQQQQ
dssDffDDDD
QQQ
DDD
imiL
imimiL
dt
d
ir
dt
d
ir




.
0
0
(8)
Where:
DL , QL : inductances of the direct and quadrature damper windings.
fL : inductance of the main field winding.
dL , qL : inductances of the d-axis stator winding and q-axis stator winding.

505
sfm : mutual inductance between the field winding and the d-axis stator winding.
sDm : mutual inductance between the d-axis stator winding and the d-axis damper winding.
sQm : mutual inductance between the q-axis stator winding and the q-axis damper winding.
fDm : mutual inductance between the field winding and the d-axis damper winding.
e : is the electrical angular speed, me p
The electromagnetic torque is expressed by:
 dsqqsdem iipT   . (9)
3. SLIDING MODE CONTROL
To achieve the maximum power at below rated wind speed, sliding mode based torque control is
proposed in [11]. The main objective of this controller is to track the reference rotor speed refm _ for
maximum power extraction. In conventional sliding mode control, sliding surface generally depends on error,
and derivative of the error signal is given in (10).
   xx
dt
d
x ref
n
x 






1

(10)
Where  is the positive constant and n is the order of the uncontrolled system.
The speed error is defined by [12]:
mrefmm
e  _
. (11)
For 1n , the position control manifold equation can be obtained from Equation (10) as follow:
  mrefmm  _
. (12)
The derivative of this surface is given by the expression:
.)()( 3_12 qsDsDfsfrefmm iimimccc  
(13)
During the sliding mode and in permanent regime, we have:
0,0)(,0)(  n
qsmm i 
. (14)
The current control qsi is defined by:
n
qs
eq
qsqs iii 
. (15)
The control voltage refqsi _ is defined by:
))((
)(3
_12
_ m
DsDfsf
refmm
refqs satk
imimc
cc
i m



  
. (16)

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The stator currents qsi and dsi are the images, respectively, of the sP and the sQ , which must
follow their references.
3.1. Quadratic Rotor Current Control with SMC
The sliding surface representing the error between the measured and reference quadratic rotor
current is given by:
qsrefqsiqs iiei qs
 _)(
(17)
qsrefqsqs iii   _)(
(18)
Substituting the expression of qsi Equation (7) in Equation (18), Equation (19) and Equation (20)
can be obtained.
 qsQsQDfdsqss
q
refqsqs vimiaiaiair
L
ii   321_
1
)(
(19)
And,
n
qs
eq
qsqs vvv 
. (20)
During the sliding mode and in permanent regime, there is:
0,0)(,0)(  n
qqsqs vii  
(21)
Where the equivalent control is:
QsQDfdsqssrefqsq
eq
qs imiaiaiairiLv   321_
(22)
Therefore, the correction factor is given by:
 )( qsv
n
qs isatKv q

(23)
Where qvK is positive constant.
3.2. Direct Rotor Current Control with SMC
The sliding surface representing the error between the measured and reference direct rotor current is
given by:
dsrefdsids iiei ds
 _)(
(24)
dsrefdsds iii   _)(
(25)
Substituting the expression of dsi Equation (6) in Equation (25), there is:

507
 dsDsDfsfQqsdss
d
refdsds vimimibibir
L
ii   21_
1
)(
(26)
And,
n
ds
eq
dsds vvv 
. (27)
During the sliding mode and in permanent regime, Equation (28) can be obtained.
0,0)(,0)(  n
dsdsds vii  
(28)
Where the equivalent control is:
DsDfsfQqsdssrefdsd
eq
ds imimibibiriLv   21_
(29)
Therefore, the correction factor is given by:
 )( dsv
n
ds isatKv d

(30)
Where dvK is positive constant.
esfma 2 ; esQmb 2 ;
J
f
c 2 ;
J
p
c 3 ; edLa 1 ; eqLb 1 ; esDma 3 ;
J
T
c m
1
4. FUZZY LOGIC CONTROLLER
Fuzzy-logic control has the capability to control nonlinear, uncertain and adaptive systems with
parameter variation. Fuzzy control does not strictly need any mathematical model of the plant. Its control rule
can be qualitatively expressed on the basis of logic-language variation and the fuzzy model of a plant is very
easy to apply. In fact, fuzzy control is good adaptive control among the techniques discussed so far. In this
paper, fuzzy-logic control is associated with sliding-mode control to generate the switching controller term
 )( dqsiKsat  , which ensures the precision and robustness of the control [12].
The general structure of a fuzzy-control system is shown in Figure 4. There are two input signals to
the fuzzy controller, the error E and the change in errorCE , which is related to the derivative dtDE / of
error. The closed-loop error E and change in error CE signals are converted to the respective scale factors,
GEEe / and GCCEce / . The output plant control signal DU is derived by multiplying by the
scale factorGU , that is GUduDU * , and then integrated to generate the U signal [13].
The scale factors can change the sensitivity of the controller without changing its structure. The
fuzzy controller is composed of three blocks: fuzzification, rule bases, and defuzzification. The membership
functions for inputs output variables are shown in Figure 5. The fuzzy subsets are as follows: GN (Grand
negative), N (Negative), ZR (Zero), P (Positive), and GP (Grand positive). There are seven fuzzy subsets for
each variable, which gives 5 × 5 = 25 possible rules. The fuzzy rules that produce these control actions are
reported in Table 1.
The Defuzzification of the output control is accomplished using the method of center of gravity.
When the error is below zero, the universe of the control value should be expanded by a contraction-
expansion factor  xF . When the error is above zero, the universe should be contracted. Therefore  xF is
defined as   M
xMxF /1
. (M gain positive).

 ISSN: 2088-8694
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Figure 4. Structure of the fuzzy controller Figure 5. Membership functions of e, ceand DU
Table 1. Rules base
GN N ZR P GP
GN GN GN GN N ZR
N GN N N ZR P
ZR N N ZR P P
P N ZR P P GP
GP ZR P GP GP GP
5. SIMULATION RESULTS AND DISCUSSION
To demonstrate the pertinence of the proposed WFSG Fuzzy-sliding-control approach (Figure 6),
simulation has been performed for 7.5KW WFSG wind power system using Matlab/Simulink™. The wind
profile used in our simulations is shown in Figure 7(a).
In addition, aerodynamic power is optimized with MPPT strategy and keeps at his nominal value
when the wind speed exceeds the nominal value as shows in Figure 7(b), and the power coefficient pC is the
maximum around 0.48 as shown in Figure 7(c).
By applying the proposed control scheme, the optimal speed command is accurately tracked to
extract the maximum power from the wind energy at any moment. In Figure 7(d) the generated torque
reference follows the optimum mechanical torque of the turbine quite well. Figure 7(e) shows the speed
tracking results of the WFSG. In terms of the actual wind speed, the optimal WFSG speed command is
obtained by Eq. (3).
The decoupling effect of the between the direct and quadratic stator current of the WFSG is
illustrated in Figure 7(f).
The stator current and voltage waveforms and these zoom of the WFSG are presented in Figire 7(g).
As shown in this Figures, the stator currents are proportional to the wind speed. This is due to the reason that
when the wind speed increases (not larger than 9.1 m/s), there is more power generated, thus yield more
currents in the stator windings of the WFSG.
Figure 6. Global diagram of simulation and control of WFSG with Fuzzy-SMC

509
Figure 7. System performance under wind speed variation. (a) Wind speed [m/s]. (b) Aerodynamic power
[W]. (c) Power coefficient. (d) Generated torque [N.m]. (e) Generator speed [rad/s]. (f) Direct and quadratic
stator current [A]. (g) Stator current and voltage with zoom [A, V]
6. CONCLUSION
In this paper, a fuzzy sliding mode controller is applied to control the power generated By the
WECS based on wound field synchronous generator and to realize nonlinear control. We have established a
model of the wind conversion chain, and design a control strategy based on vector control. This structure has
been used for reference tracking of active and reactive powers exchanged between the stator and the grid by
controlling the stator converter. A series of simulations are performed to test the effectiveness of this
controller. The simulation results show that the proposed fuzzy-SMC is very good in dealing with the time-
varying, nonlinear nature of WECS. The fuzzy-SMC was also proven more effective than the FLC and SM
controller regarding the control performance and power capture.

 ISSN: 2088-8694
510
ACKNOWLEDGEMENTS
The authors gratefully appreciate the support of Tiaret University, Algeria.
REFERENCES
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des aérogénérateurs à vitesse variable). PhD thesis; ENSAM; Bordeaux; 2003.
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BIOGRAPHIES OF AUTHORS
Tahir Khalfallah is PhD student in the Department of Electrical Engineering in at the Dr
Moulay Tahar University of Saida, ALGERIA. He received a MASTER degree in Actuator and
industrial control from the UDMT of Saida. His research activities include the Renewable
Energies and the Control of Electrical Systems. He is a member in Energetic Engineering and
Computer Engineering Laboratory (L2GEGI).
Belfedal Cheikh received the Magister degree in electrical engineering from Tiaret University,
Algeria, in 1996. Currently he is with the Department of Electrical Engineering, Tiaret
University. His fields of interest are control of electrical machines, power converters, modelling
and control of wind turbines. He is a member in Energetic Engineering and Computer
Engineering Laboratory (L2GEGI)
Allaoui Tayeb received his engineer degree in electrical engineering from the Ibn Khaldoun
University of Tiaret in 1996 and his master degree from the University of Science and
Technology of Oran in 2002.His research interests includes intelligent control of power systems
and FACTS, Active filter and renewable energies. He is a Director of Energetic Engineering and
Computer Engineering Laboratory (L2GEGI).

511
Gerard Champenois (M’09) was born in France in 1957. He received the Ph.D. and
“Habilitation” degrees from the Institut National Polytechnique de Grenoble, Grenoble, France,
in 1984 and 1992, respectively. He is currently a Professor with the Automatic Control and
Industrial Data Processing Laboratory (LAII), Poitiers National School of Engineering (ESIP),
University of Poitiers, Poitiers, France. His major fields of interest in research are renewable
energy systems, energy storage systems, electrical machines associated with static converter,
control, modeling, and diagnosis.

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