Sliding mode control of the DFIG used in wind energy system
This paper, presents the application of the direct vector control using the sliding mode control (SMC) on the doubly fed induction generators (DFIG). The synthesis of the control laws is based on the model obtained by the orientation of the stator flux. The active and reactive powers that are gene...
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Інститут технічних проблем магнетизму НАН України
2018
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| Цитувати: | Sliding mode control of the DFIG used in wind energy system / H. Glaoui, A. Harrouz // Електротехніка і електромеханіка. — 2018. — № 3. — С. 61-67. — Бібліогр.: 34 назв. — англ. |
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irk-123456789-1479352019-02-17T01:24:14Z Sliding mode control of the DFIG used in wind energy system Glaoui, H. Harrouz, A. Електричні станції, мережі і системи This paper, presents the application of the direct vector control using the sliding mode control (SMC) on the doubly fed induction generators (DFIG). The synthesis of the control laws is based on the model obtained by the orientation of the stator flux. The active and reactive powers that are generated by the doubly fed induction generators will be decoupled by the orientation of the stator flux and controlled by sliding mode controllers that have been developed. In order to rule on the validity as well as the performance of this type of adjustment, we will check its robustness by varying some parameters of the machine doubly fed induction Цель. В статье представлено применение прямого векторного управления с использованием управления режимом скольжения (SMC) на индукционных генераторах двойного питания (DFIG). Синтез законов управления основан на модели, полученной с помощью ориентации потока статора. Активные и реактивные мощности, генерируемые индукционными генераторами двойного питания, разделены ориентацией потока статора и управляются разработанными контроллерами режима скольжения. Чтобы определить достоверность и эффективность данного типа регулирования, проверяется его надежность путем варьирования ряда параметров машины двойного питания. 2018 Article Sliding mode control of the DFIG used in wind energy system / H. Glaoui, A. Harrouz // Електротехніка і електромеханіка. — 2018. — № 3. — С. 61-67. — Бібліогр.: 34 назв. — англ. 2074-272X DOI: https://doi.org/10.20998/2074-272X.2018.3.08 http://dspace.nbuv.gov.ua/handle/123456789/147935 621.31 en Електротехніка і електромеханіка Інститут технічних проблем магнетизму НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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Електричні станції, мережі і системи Електричні станції, мережі і системи |
| spellingShingle |
Електричні станції, мережі і системи Електричні станції, мережі і системи Glaoui, H. Harrouz, A. Sliding mode control of the DFIG used in wind energy system Електротехніка і електромеханіка |
| description |
This paper, presents the application of the direct vector control using the sliding mode control (SMC) on the doubly fed induction
generators (DFIG). The synthesis of the control laws is based on the model obtained by the orientation of the stator flux. The
active and reactive powers that are generated by the doubly fed induction generators will be decoupled by the orientation of the
stator flux and controlled by sliding mode controllers that have been developed. In order to rule on the validity as well as the
performance of this type of adjustment, we will check its robustness by varying some parameters of the machine doubly fed
induction |
| format |
Article |
| author |
Glaoui, H. Harrouz, A. |
| author_facet |
Glaoui, H. Harrouz, A. |
| author_sort |
Glaoui, H. |
| title |
Sliding mode control of the DFIG used in wind energy system |
| title_short |
Sliding mode control of the DFIG used in wind energy system |
| title_full |
Sliding mode control of the DFIG used in wind energy system |
| title_fullStr |
Sliding mode control of the DFIG used in wind energy system |
| title_full_unstemmed |
Sliding mode control of the DFIG used in wind energy system |
| title_sort |
sliding mode control of the dfig used in wind energy system |
| publisher |
Інститут технічних проблем магнетизму НАН України |
| publishDate |
2018 |
| topic_facet |
Електричні станції, мережі і системи |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147935 |
| citation_txt |
Sliding mode control of the DFIG used in wind energy system / H. Glaoui, A. Harrouz // Електротехніка і електромеханіка. — 2018. — № 3. — С. 61-67. — Бібліогр.: 34 назв. — англ. |
| series |
Електротехніка і електромеханіка |
| work_keys_str_mv |
AT glaouih slidingmodecontrolofthedfigusedinwindenergysystem AT harrouza slidingmodecontrolofthedfigusedinwindenergysystem |
| first_indexed |
2025-07-11T03:09:01Z |
| last_indexed |
2025-07-11T03:09:01Z |
| _version_ |
1837318376313061376 |
| fulltext |
Електричні станції, мережі і системи
ISSN 2074-272X. Електротехніка і Електромеханіка. 2018. №3 61
© H. Glaoui, A. Harrouz
UDC 621.31 doi: 10.20998/2074-272X.2018.3.08
H. Glaoui, A. Harrouz
SLIDING MODE CONTROL OF THE DFIG USED IN WIND ENERGY SYSTEM
This paper, presents the application of the direct vector control using the sliding mode control (SMC) on the doubly fed induction
generators (DFIG). The synthesis of the control laws is based on the model obtained by the orientation of the stator flux. The
active and reactive powers that are generated by the doubly fed induction generators will be decoupled by the orientation of the
stator flux and controlled by sliding mode controllers that have been developed. In order to rule on the validity as well as the
performance of this type of adjustment, we will check its robustness by varying some parameters of the machine doubly fed
induction. References 34, figures 9.
Key words: doubly fed induction generators (DFIG), vector control, sliding mode control.
Цель. В статье представлено применение прямого векторного управления с использованием управления режимом
скольжения (SMC) на индукционных генераторах двойного питания (DFIG). Синтез законов управления основан на модели,
полученной с помощью ориентации потока статора. Активные и реактивные мощности, генерируемые индукционными
генераторами двойного питания, разделены ориентацией потока статора и управляются разработанными
контроллерами режима скольжения. Чтобы определить достоверность и эффективность данного типа регулирования,
проверяется его надежность путем варьирования ряда параметров машины двойного питания. Библ. 34, рис. 9.
Ключевые слова: индукционные генераторы двойного питания (DFIG), векторное управление, управление режимом
скольжения.
Introduction. The technique of sliding mode control
(SMC) was first developed for a linear system of the second
order, and since then, the spectrum of its use has been
extended to a larger case of linear, nonlinear, discrete and
multi-variable systems [1, 2]. Variable structure control has
gained some popularity because of its simplicity and
efficiency. In such a system, the command by switching
makes it possible to bring the figurative point of the
evolution of the system on the super sliding surface. When
this hyper-surface is reached, the sliding regime occurs [3-5].
Many strategies have been developed over the past
decade to optimize the power extracted from the wind
energy conversion system. Several authors have tackled the
control problem of electrical machines operating in the field-
weakening region. For example, Taraft and all [6], Saleh
Mobayen, Fairouz Tchier [7], Ansarifar, and all [8], Bartolini
and al. [9], Benbouzid and al. [10], Seibel and al. [11] which
used the sliding mode approach to achieve active and
reactive power control. Hongchang Sun and all [12] explored
the maximum wind power tracking of doubly fed wind
turbine system based on adaptive gain second-order sliding
mode. Kassem and all [13], Belmokhtar and all [14]
proposed a dynamic modeling and robust power control of
doubly fed induction generators (DFIG) driven by wind
turbine at infinite grid. Weng and al. [15] a sliding mode
regulator for maximum power tracking and copper loss
minimisation of a doubly fed induction generator.
Abdeddaim and all [16] Optimal tracking and robust power
control of the DFIG wind turbine.
With the planned strategy, the generated wind
energy can reach twice its nominal value thanks to a fast
and reliable electric control completely robust. Indeed, by
employing an appropriate control technique where the
power produced in DFIG mode is derived from both the
stator and the rotor. In addition, the power supplied by the
rotor increases in this case by 100 % with respect to the
nominal power of the stator. However, this solution
makes it possible to maintain the operation of the wind
energy conversion system in its stable zone.
The system considered consists of a dual-feed
induction generator whose stator is directly connected to
the gate and its rotor is powered by a matrix converter. In
this paper, the sliding-mode approach to performing
active and reactive power control is used.
This last enjoys interesting strong properties such as
the insensitivity to the variations of the parameters of the
controlled part as well as to the disturbances, which can
act on this last one. Its behavior does not depend any
more than the parameters that define the hyperactive
surface of the slip. Despite having various advantages,
this control technique also has a disadvantage that limited
its use initially. Indeed, in practice, imperfections such as
switching delays and hysteresis generate oscillations
around the sliding surface. Several techniques have been
proposed to overcome this disadvantage [11, 17]. Some
consist in approximating the discontinuous function by a
continuous function in the vicinity of the switching
surface, the reduction of chattering taking place at the cost
of a loss of precision. Due to the many advantages of
variable structure control, such as robustness, speed, and
simplicity of implementation, this type of control seems
to us quite suitable for dual feed generators for which
performance can be required. Moreover, as some
parameters of the generator prove to vary during the
operation and that the load is often unknown; the control
will have to take into account these parametric
disturbances and variations to avoid a degradation of
performances [18]. The main objective of this paper is to
advance the understanding of the controlled SMC in the
wind system, by studying its behavior with wind energy
system. Taking into account many unresolved issues
associated with wind energy, the results of the analysis
and evaluation of discretization behaviors in the SMC
systems are essential for their applications in the control
of renewable energies [19].
However, the analysis and evaluation of
discretization behaviors in SMC systems has proved to be
a difficult task due to the lack of work done on this topic.
There is apparently a gap between the expected ideal
dynamic performance based on continuous-time system
models and the actual dynamic performance when the
62 ISSN 2074-272X. Електротехніка і Електромеханіка. 2018. №3
control system is discretized. Delay in delivery of control
signals due to discretization is the key factor affecting
control performance. This is especially true when the
control is of a discontinuous nature, such as SMC.
«Disruptive» switching may cause incorrect actions due
to the timely delivery of control signals. These behaviors
can cause serious damage to industrial control devices
such as actuators [19]. In addition, the deteriorated
invariance property can worsen the reliability of SMC
systems, making controlled industrial processes
vulnerable to unexpected environmental changes.
Issues of interest in studying discretization behaviors
in SCM systems include:
conditions to ensure stability;
steady state boundary conditions;
system trajectory models (periodicity);
sensitivity of trajectories to initial conditions;
relationship between trajectory models and their
symbolic sequences;
dynamic behavior change with respect to the
sampling period.
To our knowledge, this research is the first to
systematically study the discretization behaviors of SMC
systems, and to develop methods for controlling the wind
system based on the DFIG generator. The significance of
this work lies in the fact that it promotes the
understanding of discretization behaviors in SMC
systems, thus providing useful measures to prevent
potential behavior from occurring. It also results in new
methods useful not only for the analysis of the
discretization of the SMC systems, but also for the
synthesis of the laws of the controls as a function of the
model obtained by the orientation of the stator flux.
The characteristic feature of a continuous time SMC
systems is that a sliding mode occurs on a prescribed
manifold, or switching surface, where a switching control
is employed to maintain the state on that surface [20-23].
Since the theory has been originally developed from a
continuous time perspective, implementation of sliding
mode for sampled data systems encounters several
incompatibilities due to limited sampling rate,
sample/hold effect, and discretization errors. As a result, a
direct translation of continuous-time SMC design for
discrete implementation leads to the chattering
phenomenon in the vicinity of the switching surface.
In this paper, basic results obtained in the study of
continuous-time and discrete-time SMC systems theory
during its over twenty years history are reviewed. The
discretization issue of SMC systems is introduced.
Machine model. Flux-Oriented Vector Control
presents an attractive solution for achieving better
performance in variable speed applications for the doubly
fed induction machine in both generator and motor
operation. With this in mind, we have proposed a control
law for the DFIM (doubly fed induction machine) based
on the orientation of the stator flux, used to make it work
as a generator. The latter highlights the relationships
between the stator and rotor quantities [24-26]. These
relationships will allow to act on the rotor signals to
control the active power exchange and reactivate between
the stator of the machine and the power system.
The wind turbine rotates at a speed that depends on
the wind speed (Fig. 1). This speed is matched to that of
the electric generator through a gearbox [27, 28].
Fig. 1. Wind turbine model
The output power of wind turbine is given as
3),(
2 windpm vC
A
p
, (1)
where, pm is mechanical output power of the turbine (W);
is air destiny (kg/m3); A is turbine swept area (m2); β is
blade pitch angle (deg); λ is tip speed ratio of the rotor
blade tip speed to wind speed; Cp is performance
coefficient of wind turbine, which is the function of β and
λ; vwind is wind speed (m/s).
The tip speed ratio λ is calculated as
wind
T
v
R
. (2)
From an engineering point of view, there are many
different representing methods of performance coefficient Cp.
But they all represent Cp as a nonlinear function of β
and λ. In this paper, Cp is denoted as
i
C
i
p CeCC
C
CC i
643
2
1
5
))5.2((()),(
, (3)
where C1 = 0.645, C2 = 116, C3 = 0.4, C4 = 5, C5 = 21,
C6 = 0.00912.
Variable λi can be calculated as
1)5.2(
035.0
)5.2(08.0
11
3
i
. (4)
Wind turbine dynamics simulations have been run
for wind step changes. The characteristic feature of the
dependence of the wind turbine power upon the wind
speed has been illustrated in Fig. 2 (the nominal power
being 2 MW) [29].
0 5 10 15 20 25
-500
0
500
1000
1500
2000
2500
v
w
[m/s]
P
t [k
W
]
Fig. 2. Static characteristic of wind turbine mechanical power
as a function of mean wind speed
For a given wind speed vm the wind turbine power pt
and the moment mt = pt / wt.
ISSN 2074-272X. Електротехніка і Електромеханіка. 2018. №3 63
Model of generator «DFIG». In order to implement
the decoupling control of active and reactive power, it is
essential to transform the voltage and current of induction
generator stator and rotor from 3-phase form to dq form
under synchronous rotation coordinates. In addition, the
voltage and flux equations of induction generator are seen
as (5) and (6) respectively
;
;
;
;
drrqrqrrqr
qrrdrdrrdr
dssqsqssqs
qssdsdssds
θ
dt
d
IRV
θ
dt
d
IRV
θ
dt
d
IRV
θ
dt
d
IRV
(5)
,
;
;
;
qsqrrqr
dsdrrdr
qrqssqs
drdsrds
MIIL
MIIL
MIIL
MIIL
(6)
where Vds, Vqs, Vdr and Vqr are respectively the dq
coordinates components of stator and rotor voltage; Ids,
Iqs, Idr and Iqr are respectively the dq coordinates
components of stator and rotor current; ds, qs, dr and
qr are respectively the dq coordinates components of
stator and rotor flux; Lr, Ls and M = Lm.
The electromagnetic torque is expressed as:
)(2/3 dsqsqsdsem IIC ; (7)
qsqsdsds IVIVP ; (8)
qsdsdsqs IVIVQ .
This strategy consists to turn the rotor flux towards d
axis, and the stator flux towards q axis. After orientation
the stator and rotor fluxes are presented in Fig. 3
Fig. 3. DFIG vector after orientation
Consequently, the two fluxes become orthogonal
and we can write:
.0;; dsqrrdrsqs (9)
If resistance Rs is neglected we have:
.;0 sdsqsqs VV
dt
d
V
The developed active power and reactive power can
be rewritten as follows:
,; qssdss IVQIVP
where
,; qr
r
qsdr
s
ds I
M
L
II
L
M
I
where
.; qr
r
sdr
s
s I
M
L
VQI
L
M
VP
Sliding Mode Control. The term «variable
structure systems» appears because of the particular
structure of the system or regulator used, where this
structural change in a discontinuous manner between two
or more structures.
In the formulation of any practical control problem,
there will always be a discrepancy between the actual plant
and its mathematical model used for the controller design.
These discrepancies (or mismatches) arise from unknown
external disturbances, plant parameters, and
parasitic/modeled dynamics [30, 31]. Designing control laws
that provide the desired performance to the closed-loop
system in the presence of these disturbances/uncertainties is
a very challenging task for a control engineer. This has led to
intense interest in the development of the so-called robust
control methods, which are supposed to solve this problem.
One particular approach to robust controller design is the so-
called sliding mode control technique.
The behavior of nonlinear systems with
discontinuities can be formally described by the
generalized state equation:
UtXFtX ,, , (10)
where nX is the state vector, t time and is the
function describing the evolution of the system over time.
This class of system has a term which represents, at the
same time, the discontinuity and the control: U.
Historically, the first regulators built on this model
have been simple relays. Easy to implement. They have
led the automation engineers to develop a theory that can
describe such an operation. The bases of such a theory
have been laid: it suffices to say that the behavior of the
system is described by two distinct differential equations,
depending on whether the equation of evolution of the
system is greater or less than a surface called hyper-
surface (increased surface) switching where:
))(),....,(),(()( 21 XSXSXSXS m .
So we have
.0,if,,
;0,if,,
tXStXU
tXStXU
XU (11)
We consider a nonlinear system defined as
),(),(),()()( txutxbtxftx n , (12)
where x is the state vector and are nonlinear functions and
is the control input f(x, t), b(x, t)u.
To design a sliding mode control law, we must firstly,
choose the switching surface (Fig. 4).
Fig. 4. Sliding mode in a phase plane
64 ISSN 2074-272X. Електротехніка і Електромеханіка. 2018. №3
We take the general form proposed by Slotine [24]:
e
dt
d
S
n )1(
, (13)
where e = x – xd is the tracking error; is xd the desired
state, is n the system order and is a positive coefficient.
After choosing the sliding surface, we must choose
the control law where the reaching condition defined by
Lyapunov equation satisfied
tSS
0 . (14)
The control law has the following form.
Thus, the vector control to be applied to the system
is obtained by adding two control terms such as
neq UUU , (15)
where Ueq on the sliding mode; Un allows to influence the
approach mode.
In order that the condition (19) is verified at any
time, is chosen as follows [32] (a complete study of
sliding-mode with ERL can be found in [32]
S
e
k
S
p
S
sat
1 00
, (16)
where k is the discontinuous gain,
prd
kk
S
t
/1
0
0
)1()0(
,
is the desired reaching time, 0, 0<0<1 and p>0,
S
sat is the saturation function
.1if,1
;11if,
;1if,1
sat
S
SS
S
S
(17)
The use of saturation function instead of sign
function is justified to avoid chattering phenomenon.
The sliding mode applied to DFIG. We will use
this technique to control the rotor currents of DFIG with a
strongly coupled model [33, 34] (Fig. 5).
Fig. 5. Global scheme mode of the DFIG control
Recall the model of DFIG in Park's Den which is
given by the following equations:
;
;
dqrr
dqr
dqrsdqr
dqss
dqs
dqssdqs
dt
d
IRV
dt
d
IRV
(18)
.
;
dqsdqrsdqr
dqrdqssdqs
IMIL
IMIL
(19)
The vector of the state variables chosen for the
control of the machine is given by:
qr
dr
qs
ds
I
I
x .
The model of the machine with the consideration of
the state variables is given by the following equations:
.
;
;
;
dt
dI
LV
L
M
ILcRV
L
M
ILbR
dt
dI
LV
L
M
ILcRV
L
M
ILbR
dt
d
V
L
M
ILcRaR
dt
d
V
L
M
ILcRaR
V
V
V
V
qr
rqs
ss
drrrqsrds
ss
qrrr
dr
rds
ss
qrrrdsrqs
ss
drrr
qs
dssds
ss
qrrsqss
ds
qssqs
ss
drrsdss
qr
dr
qs
ds
sL
a
1
,
rL
b
1
,
rsLL
M
c
.
The state model of the machine is put in the
following form:
dqUtxgtxfX ,, ; (20)
r
r
qr
dr
qs
ds
L
L
txg
dt
dI
dt
dI
dt
d
dt
d
X
1
000
0
1
00
0010
0001
, ;
;qrdrqsdsdq VVVVU
.,
1
1
txf
V
L
M
ILcRV
L
M
ILbR
L
V
L
M
ILcRV
L
M
ILbR
L
V
L
M
ILcRaR
V
L
M
ILcRaR
qs
ss
drrrdsrds
ss
qrrr
r
ds
ss
qrrrdsrqs
ss
drrr
r
dssds
ss
qrrsqss
qssqs
ss
drrsdss
Sliding surfaces in the Park marker are defined to
control the rotor currents. They are given by the following
equations:
ISSN 2074-272X. Електротехніка і Електромеханіка. 2018. №3 65
,
;
qrqrrefq
drdrrefd
IIS
IIS
where Vdr and Vqr are the two control vectors, to force the
system path to converge to surfaces Sdq = 0.
The control vector Udqeq is obtained by imposing Sdq = 0
0,, dqUtxgtxf ; (21)
.
qs
ss
drrrqsrds
ss
qrrr
ds
ss
qrrrdsrqs
ss
drrr
eqdq
V
L
M
ILcRV
L
M
ILbR
V
L
M
ILcRV
L
M
ILbR
U
To have good performance, good dynamics and
good switching around surfaces the control vector is
imposed as follows:
)( dqdqeqdq SKsignUU . (22)
Simulation results. The figures below (Fig. 6)
represent the different curves by the simulation of the
DFIG with sliding mode controllers.
Fig. 6. Simulation results of the system GADA and voltage
inverter
Its characteristics have allowed us to cite the
performance of regulators in sliding mode, such as:
good continues stator currents compared to
references;
perfect decoupling between the two components of
the stator current.
Therefore, the control of the active power of the
stator is by the direct component of the current, while the
reactive power of the stator of the quadratic component of
the stator current.
In order to test the robustness of this control
structure by sliding mode, we studied the influence of
parametric variations on the performance of the
adjustment. We consider variations on all parameters that
can undergo changes (stator and rotor resistors, stator,
rotor and mutual inductors, and moment of inertia).
The results of the test of robustness to variations of
the reference power simulation obtained show that
decoupling is ensured at all times of the active and
reactive powers, despite the presence of slight oscillations
which are due to the Chattering phenomenon (Fig. 7).
Fig. 7 Results of the system with the function sign
The results obtained in Fig. 8, 9 show that
decoupling is ensured at all times of the active and
reactive powers, despite the presence of slight oscillations
that are due to the Chattering phenomenon.
Fig. 8. Robustness test for a variation of Rs
Fig. 9. Robustness test for a variation of Rr
Conclusion. In this paper, a complete system for
electrical energy production has been done via wind
66 ISSN 2074-272X. Електротехніка і Електромеханіка. 2018. №3
turbine by use of the doubly fed induction generator
(DFIG). The studied system has been formed of a DFIG
with stator and rotor, which in that stator has connected to
the grid directly, machine converter and grid converter.
With the consideration of turbine variable velocity state
and design controller for DFIG in form of using of the
sliding mode.
Firstly, we have introduced the simplicity of the
control variable structure by sliding mode non-linear
switching surface. Then, we are interested more closely in
the application of this type of control on the asynchronous
machine with double feeding. The setting of the active
and reactive powers by the sliding mode brings a
remarkable improvement and good system performance
with DFIG.
The results of the simulations obtained are evaluated
and carried out using the Matlab / Simulink software and
show the performance and the effectiveness of the
proposed control.
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Received 06.03.2018
Hachemi Glaoui1, Ph.D.,
Abdelkader Harrouz2, Ph.D.,
1 Department of Electrical Engineering,
Tahri Mohamed Bechar University,
Bechar, Algeria,
e-mail: glaouih@yahoo.fr
2 Department of Hydrocarbon and Renewable Energy,
Ahmed Draia University,
Adrar, Algeria,
e-mail: harrouz@univ-adrar.dz
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