Indonesian
J
our
nal
of
Electrical
Engineering
and
Computer
Science
V
ol.
37,
No.
1,
January
2025,
pp.
78
∼
89
ISSN:
2502-4752,
DOI:
10.11591/ijeecs.v37.i1.pp78-89
❒
78
Backstepping
appr
oach
f
or
the
contr
ol
of
the
double-fed
asynchr
onous
generator
in
a
wind
po
wer
system
Mbar
ek
Chahboun
1
,
Mohcine
Abouyaak
oub
1
,
Ali
Ait
Ali
1
,
Aziz
El
Mrabet
1
,
Hicham
Hihi
1
,
Hassan
Ouabi
2
,
Y
oussef
El
Bid
3
1
Laboratory
of
Engineering
Systems
and
Applications,
Nationale
School
of
Applied
Sciences,
Sidi
Mohamed
Ben
Abdellah
Uni
v
ersity
,
Fez,
Morocco
2
Department
of
Electrical
Engineering,
Higher
Normal
School
of
T
echnical
Education
Mohammedia,
Hassan
II
Uni
v
ersity
,
Casablanca,
Morocco
3
Ener
gies
and
Sustainable
De
v
elopment
Research
T
eam,
Higher
School
of
T
echnology
,
Ibn
Zohr
Uni
v
ersity
,
Ag
adir
,
Morocco
Article
Inf
o
Article
history:
Recei
v
ed
Mar
24,
2024
Re
vised
Sep
7,
2024
Accepted
Sep
29,
2024
K
eyw
ords:
Backstepping
Control
system
DFIG
Fuzzy
logic
Rene
w
able
ener
gy
W
ind
turbine
ABSTRA
CT
This
paper
aims
to
model
and
control
the
dual-fed
asynchronous
generator
(DFIG).
The
modeling
and
v
ector
control
were
simulated
using
MA
TLAB,
fol-
lo
wed
by
the
application
of
the
Backstepping
control
strate
gy
.
A
comparati
v
e
study
between
tw
o
DFIG
control
strate
gies,
fuzzy
logic
control
(FLC)
and
Back-
stepping
control,
w
as
conducted.
The
results
for
the
Backstepping
approach
are
discussed
and
compared
with
FLC,
highlighting
that
the
Backstepping
technique
addresses
rob
ustness
issues
re
g
arding
v
ariations
in
operating
conditions
and
in-
ternal
parameters.
Both
control
st
rate
gies
are
applied
to
a
wind
turbine
system,
and
the
simulation
results
and
rob
ustness
tests
are
analyzed.
This
is
an
open
access
article
under
the
CC
BY
-SA
license
.
Corresponding
A
uthor:
Mbarek
Chahboun
Laboratory
of
Engineering,
Systems
and
Applications,
Nationale
School
of
Applied
Sciences
Sidi
Mohamed
Ben
Abdellah
Uni
v
ersity
Fez,
Morocco
Email:
mbarek.chahboun@usmba.ac.ma
1.
INTR
ODUCTION
W
ind
po
wer
,
with
its
capacity
to
meet
global
ener
gy
needs
and
reduce
greenhouse
g
as
emissions,
is
vital
for
the
transition
to
sustainable
ener
gy
sources.
Ef
cient
re
gulation
of
double-fed
induction
generators
(DFIGs)
is
k
e
y
to
optimizing
wind
ener
gy
output
and
maintaining
grid
stability
.
A
literature
re
vie
w
highlights
signicant
contrib
utions
in
this
eld.
V
arious
control
methods
for
DFIGs,
such
as
the
Backstepping
approach
and
fuzzy
logic
control
(FLC),
ha
v
e
been
e
xamined.
Studies
[1]-[5]
ha
v
e
sho
wn
the
benets
of
the
Back-
stepping
approach
in
enhancing
system
performance
and
st
ability
.
Other
research
[6]-[10]
has
demonstrated
the
adaptability
and
e
xibility
of
fuzzy
logic
in
controlling
DFIGs
in
wind
f
arms.
Ho
we
v
er
,
pre
vious
studies
ha
v
e
not
e
xplicitly
compared
the
inuence
of
Backst
epping
and
fuzzy
logic
on
specic
performance
metrics
under
v
arying
operating
conditions.
T
o
address
these
g
aps,
our
research
analyzes
the
use
of
the
Backstepping
approach
and
fuzzy
logic
for
controlling
DFIGs
in
wind
po
wer
systems.
By
comparing
these
methods
and
e
v
aluating
their
performance
,
we
aim
to
identify
weaknesses
in
e
xisting
literature
and
suggest
impro
v
ements.
Our
research
inte
grates
adv
anced
control
methods
to
push
the
eld
of
wind
ener
gy
forw
ard.
W
e
pro
vide
an
in-depth
analysis
of
the
Backstepping
and
fuzz
y
logic
approaches
to
DFIG
control,
aiming
to
inform
the
design
and
implementation
of
future
wind
ener
gy
systems
for
a
more
sustainable
and
ef
cient
ener
gy
transition.
This
paper
presents
a
detailed
Backstepping-based
control
approach
for
DFIGs
used
in
wind
po
wer
systems.
Pre
vi-
J
ournal
homepage:
http://ijeecs.iaescor
e
.com
Evaluation Warning : The document was created with Spire.PDF for Python.
Indonesian
J
Elec
Eng
&
Comp
Sci
ISSN:
2502-4752
❒
79
ous
w
ork
by
Ladide
et
al.
[11],
Hihi
and
Rahmani
[12],
and
Soulouh
et
al.
[13]
has
enabled
us
to
design
an
inno
v
ati
v
e
control
method
that
impro
v
es
DFIG
performance
while
ens
u
r
ing
stability
.
Additionally
,
we
conduct
a
detailed
analysis
of
the
Backstepping
approach
and
FLC,
highlighting
the
adv
antages
and
disadv
antages
of
each
method.
Extensi
v
e
simulations,
b
uilding
on
research
by
Moumani
et
al.
[14]
and
Nadour
et
al.
[15],
conrm
the
ef
fecti
v
eness
of
our
control
method.
Finally
,
we
discuss
the
practical
implications
of
our
results
and
their
potential
impact
on
further
de
v
el-
oping
wind
ener
gy
systems.
Our
method
aims
to
adv
ance
ongoing
research
by
of
fering
practical
and
inno
v
ati
v
e
solutions
for
controlling
DFIGs
i
n
current
wind
po
wer
systems.
The
follo
wing
sections
will
detail
our
research
approach,
results,
and
conclusions,
emphasizing
the
rele
v
ance
and
importance
of
our
w
ork
in
wind
system
control.
2.
METHOD
This
section
outlines
the
methodology
for
modeling
and
controlling
a
DFIG
in
a
wind
ener
gy
sys
tem.
While
pre
vious
studies
ha
v
e
e
xplored
these
systems,
the
y
ha
v
e
not
suf
ciently
addressed
the
rob
ustness
of
control
strate
gies
gi
v
en
their
inherent
non-linearity
.
W
e
sequentially
model
the
wind
turbine,
the
dual-supply
asynchronous
generator
,
and
the
simulation,
including
technical
details,
parameters,
and
simulation
schemes
(Jones
et
al.
[1],
Smith
et
al.
[2]).
Due
to
its
ef
fecti
v
eness
in
comple
x
dynamic
system
modeling,
MA
T
-
LAB/Simulink
w
as
utilized.
W
e
found
that
the
nonlinear
Backstepping
controller
ef
fecti
v
ely
re
gulates
reacti
v
e
and
acti
v
e
po
wers.
FLC
demonstrated
e
xibility
in
adapting
to
operational
and
en
vironmental
changes
W
ang
et
al.
[8].
Our
results
correlate
with
Chen
et
al
.
[7],
who
highlighted
the
comprehensi
v
e
nature
of
generator
control
algorithms,
focusing
on
the
underlying
theoretical
principles.
P
arametric
changes
on
mutual
inductance
L
m
and
rotor
resistance
R
r
were
conducted
to
e
v
aluate
control
system
stability
,
v
alidating
our
simulation
re-
sults
(Huang).
Despite
these
ndings,
further
in-depth
studies
are
needed
to
conrm
our
approach,
especially
re
g
arding
parametric
v
ariations.
W
e
recommend
consulting
supplementary
references
for
a
thorough
conr
-
mation.
Our
study
demonstrates
that
both
Backstepping
and
fuzzy
control
methods
are
rob
ust,
with
the
system
e
xposed
to
acti
v
e
and
reacti
v
e
po
wer
le
v
els
to
monitor
re
gulator
beha
vior
.
Future
research
should
e
xplore
these
methods
in
more
di
v
erse
operational
scenarios
to
enhance
the
reliability
of
control
strate
gies.
3.
MODELLING
THE
WIND
ENERGY
SYSTEM
The
wind
ener
gy
system
is
made
up
of
v
arious
crucial
parts
that
mak
e
sure
it
w
orks.
These
consist
of
a
machine-side
con
v
erter
,
a
doubly-fed
asynchronous
generator
(DFIG),
a
gearbox,
and
a
turbine.
The
ener
gy
con
v
ersion
process
starts
when
wind
ener
gy
is
captured
by
the
turbine
and
then
sent
to
the
DFIG
to
be
con
v
erted
into
electrical
ener
gy
.
A
wind
turbine
with
three
blades
of
length
R
t
h
a
t
are
po
wered
by
a
generator
is
emplo
yed
in
the
system
under
study
.
A
g
ain
multiplier
G
is
included
in
this
arrangement
to
increase
the
generated
po
wer
.
3.1.
W
ind
modelling
The
initial
phase
of
establishing
a
wind
po
wer
project
in
v
olv
es
meticulously
choosing
the
site’
s
ge-
ographic
location.
It
is
necessary
to
closely
e
xamine
the
wind
characteristics
since
the
po
wer
produced
by
a
wind
ener
gy
syst
em
is
directly
related
to
the
cube
of
the
wind
speed.
T
o
g
ain
an
in-depth
understandi
ng
of
the
particularities
of
a
gi
v
en
site,
i
t
is
essential
to
collect
data
on
wind
direction
and
speed
o
v
er
an
e
xtended
period
[4].
In
our
study
,
we
used
a
specic
wind
model
[5]
whose
e
xpression
is
in
(1).
v
(
t
)
=
8
+
0
.
2
∗
sin
(0
.
1047
.t
)
+
0
.
2
∗
sin
(3
.
6645
.t
)
+
2
.sin
(0
.
2665
.t
)
(1)
This
mathematical
model
enabled
us
to
analyse
in
greater
d
e
tail
the
uctuations
in
wind
speed
o
v
er
time
at
the
site
studied,
for
a
detailed
description
of
this
part,
please
refer
to
our
pre
vious
article
[16].
3.2.
T
urbine
modelling
The
part
of
the
system
responsible
for
con
v
e
rting
wind
ener
gy
from
kinetic
to
mechanical
is
the
wind
turbine.
When
wind
hits
the
turbine
blades
at
a
particular
speed
v
,
it
generates
mechanical
ener
gy
on
the
turbine
shaft,
making
the
blades
spin.
The
aerodynamic
po
wer
harnessed
by
the
turbine
rotor
is
e
xpressed
by
(1).
P
t
=
1
2
.C
p
(
λ,
β
)
.ρ.S
.v
3
(2)
Bac
kstepping
appr
oac
h
for
the
contr
ol
of
the
double-fed
async
hr
onous
...
(Mbar
ek
Chahboun)
Evaluation Warning : The document was created with Spire.PDF for Python.
80
❒
ISSN:
2502-4752
T
ypically
,
the
po
wer
coef
cient
is
sho
wn
as
a
function
of
the
tip
speed
ratio
λ
in
relation
to
the
angle
β
,
which
is
the
angle
formed
between
the
rotation
direction
and
the
chord
line
of
the
blade
section.
The
tip
speed
ratio
of
a
wind
turbine
is
e
xplained
as
(3):
λ
=
u
v
=
Ω
t
.R
v
(3)
where:
ρ
:
the
density
of
the
air
,
λ
:
relati
v
e
speed
is
the
ratio
of
wind
speed
to
linear
speed
at
the
turbine
blade
tips,
Ω
t
:
the
turbine's
rotational
speed,
R
:
the
blade's
length,
S
:
the
circle
that
the
turbine
sweeps,
v
:
the
wind
speed
and
C
p
:
the
coef
cient
of
po
wer
,
for
a
detailed
description
of
this
part,
please
refer
to
our
pre
vious
article
[16].
4.
DFIG
MODELLING
There
is
a
plethora
of
research
on
the
modeling
of
the
doubly-fed
induction
generator
(DFIG)
in
the
literature
[1]-[3].
The
mathematical
model
of
the
DFIG
is
quite
simple
in
design,
b
ut
it
is
remarkably
sophisticated.
Its
nonlinear
and
multi
v
ariable
structure
and
the
interplay
of
electrical,
magnetic,
and
mechanical
e
v
ents
during
operation
[17]
are
the
causes
of
this
comple
xity
.
One
feature
of
the
DFIG
model
is
that
it
generates
dif
ferential
equations
whose
coef
cients
change
o
v
er
time
in
response
to
the
rotor’
s
position
inside
a
x
ed
three-phase
reference
frame
that
is
link
ed
to
the
stator
.
This
raises
the
machine’
s
modeling
comple
xity
e
v
en
more
[4].
F
or
a
detailed
description
of
this
part,
please
refer
to
our
pre
vious
article
[18].
4.1.
V
ector
contr
ol
of
DFIG
By
manipulating
the
rotor
ux
of
the
DFIG,
it
becomes
possible
to
re
gulate
both
acti
v
e
and
reacti
v
e
po
wer
.
This
approach
guarantees
that
the
armature
reaction
ux
and
rotor
ux
maintain
a
perpendicular
re-
lationship.
T
o
autonomously
re
gulate
the
stator
po
wer
[19],
it
becomes
essential
to
independently
control
the
transv
erse
v
oltages
of
the
rotor
and
armature
by
introducing
compensation
terms,
thus
at
taining
a
decoupled
control
mode
[20].
By
making
adjustments
from
(23)
to
(18),
the
rotor
v
oltages
can
be
redened.
The
follo
w-
ing
Figure
1
sho
ws
the
re
gulated
system’
s
block
diagram.
F
or
a
detailed
description
of
this
part,
please
refer
to
our
pre
vious
article
[21].
Figure
1.
Block
schematic
of
the
re
gulated
system
5.
THE
PRINCIPLE
OF
THE
B
A
CKSTEPPING
COMMAND
The
fundamental
principle
of
Backstepping
control
is
to
reor
g
anise
closed-loop
systems
into
subsets
of
lo
wer
-order
subsystems,
each
of
which
is
stabilised
according
t
o
the
L
yapuno
v
criterion.
This
approach
gi
v
es
these
systems
rob
ustness
properties
and
ensures
their
o
v
erall
asymptotic
stability
.
In
other
w
ords,
it
is
a
multi-
stage
process
in
which,
at
each
stage
[22],
a
virtual
control
is
generated
to
ensure
that
the
system
con
v
er
ges
to
w
ards
t
he
desired
equilibrium
state.
This
con
v
er
gence
is
achie
v
ed
progressi
v
ely
through
the
use
of
L
yapuno
v
functions
that
ensure
step-by-step
stabilisation.
5.1.
The
contr
ol
of
non-linear
systems
is
based
on
tw
o
L
yapuno
v
appr
oaches
L
yapuno
v’
s
rst
method
assesses
a
system’
s
stability
by
linearizing
its
dynamics
around
an
equilib-
rium
point,
focusing
on
local
stability
.
While
useful
for
understanding
stability
near
the
equilibrium,
it
does
Indonesian
J
Elec
Eng
&
Comp
Sci,
V
ol.
37,
No.
1,
January
2025:
78–89
Evaluation Warning : The document was created with Spire.PDF for Python.
Indonesian
J
Elec
Eng
&
Comp
Sci
ISSN:
2502-4752
❒
81
not
address
the
system’
s
o
v
erall
stability
and
o
v
erlooks
nonlinear
phenomena.
This
method
helps
determine
if
a
broader
stability
analysis
is
needed.
The
second
L
yapuno
v
method,
on
the
other
hand,
e
v
aluates
stability
based
on
ener
gy
consi
derations
without
solving
the
nonlinear
dif
ferential
equations
of
the
system.
Stability
is
judged
by
ho
w
an
ener
gy
function
changes
as
the
system
e
v
olv
es.
T
o
assess
stability
,
one
seeks
a
positi
v
e
denite
function
V
(
x
)
that
represents
the
system’
s
ener
gy
,
with
its
deri
v
ati
v
e
being
ne
g
ati
v
e
semi-denite
in
the
rele
v
ant
re
gion.
Backstepping
control
pro
vides
a
frame
w
ork
for
designing
control
strate
gies
for
comple
x
dynamic
systems,
ensuring
their
stability
and
con
v
er
gence
to
desired
equilibrium
states
[23].
5.1.1.
Acti
v
e
po
wer
contr
ol
First,
let’
s
e
xamine
acti
v
e
po
wer
control.
The
follo
wing
is
the
denition
of
the
acti
v
e
po
wer
tracking,
e
1
=
P
∗
s
−
P
s
(4)
tak
e
a
look
at
this
potential
L
yapuno
v
function,
V
(
e
1
)
=
1
2
.e
2
1
(5)
the
L
yapuno
v
candidate
function's
deri
v
ati
v
e,
˙
V
(
e
1
)
=
e
1
·
˙
e
1
(6)
˙
e
1
=
˙
P
∗
s
−
˙
P
s
=
˙
P
∗
s
+
(1
−
M
2
sr
L
s
.L
r
)
.
L
r
.L
s
v
s
.M
sr
di
r
q
dt
(7)
and,
˙
P
s
=
(
M
2
sr
L
s
.L
r
)
.
L
r
.L
s
v
s
.M
sr
di
r
q
dt
−
1
(8)
The
deri
v
ati
v
e
of
the
current,
i
r
q
,
can
be
obtained
by
substituting
the
e
xpression
into
the
v
oltage
equation,
v
r
q
(28)
and
getting:
˙
e
1
=
˙
P
∗
s
+
v
s
.M
sr
(
L
s
.L
r
−
M
2
sr
)
v
r
q
−
R
r
.i
r
q
−
(1
−
M
2
sr
L
s
.L
r
)
.L
r
.ω
r
.i
r
d
+
g
.
v
s
.M
ω
s
.L
s
(9)
replacing
the
last
in
(7)
gi
v
es,
˙
V
(
e
1
)
=
e
1
·
˙
e
1
=
e
1
·
=
˙
P
∗
s
+
v
s
.M
sr
(
L
s
.L
r
−
M
2
sr
)
v
r
q
−
R
r
.i
r
q
−
(1
−
M
2
sr
L
s
.L
r
)
.L
r
.ω
r
.i
r
d
+
g
.
v
s
.M
ω
s
.L
s
(10)
the
follo
wing
is
ho
w
we
arri
v
e
at
the
stabilizing
Backstepping
command
e
xpression,
v
r
q
=
−
(
L
s
.L
r
−
M
2
sr
)
v
s
.M
sr
.
˙
P
∗
s
+
R
r
.i
r
d
+
ω
r
.
1
−
M
2
sr
L
s
.L
r
.L
r
.i
r
d
−
g
.
v
s
.M
ω
s
.L
s
−
(1
−
M
2
sr
L
s
.L
r
)
.
L
s
.L
r
v
s
M
sr
.k
1
.e
1
(11)
to
ensure
con
v
er
gence
of
the
L
yapuno
v
candidate
function,
replacing,
e
xpression
(11)
in
(10)
gi
v
es:
˙
V
(
e
1
)
=
−
k
1
.e
2
1
<
0
(12)
with
k
1
positi
v
e
constant.
Bac
kstepping
appr
oac
h
for
the
contr
ol
of
the
double-fed
async
hr
onous
...
(Mbar
ek
Chahboun)
Evaluation Warning : The document was created with Spire.PDF for Python.
82
❒
ISSN:
2502-4752
5.1.2.
Reacti
v
e
po
wer
contr
ol
The
discrepanc
y
in
reacti
v
e
po
wer
tracking
is,
e
2
=
Q
∗
s
−
Q
s
(13)
this
equation
pro
vides
the
increased
L
yapuno
v
function,
V
(
e
1
,
e
2
)
=
1
2
.e
2
1
+
1
2
.e
2
2
(14)
its
deri
v
ati
v
e
is
gi
v
en
by
,
˙
V
(
e
1
,
e
2
)
=
e
1
·
˙
e
1
+
e
2
·
˙
e
2
=
−
k
1
·
e
2
2
+
e
2
(
˙
Q
∗
s
−
˙
Q
s
)
(15)
with,
˙
e
2
=
˙
Q
∗
s
−
˙
Q
s
=
˙
Q
∗
s
+
(1
−
M
2
sr
L
s
.L
r
)
.
L
r
.L
s
v
s
.M
sr
.
di
r
d
dt
(16)
substituting
the
formula
for
the
deri
v
ati
v
e
of
the
current
ird
into
the
v
oltage
Vrd
(27),
we
arri
v
e
at,
˙
e
2
=
˙
Q
∗
s
+
v
s
.M
sr
(
L
s
.L
r
−
M
2
sr
)
v
r
d
−
R
r
.i
r
d
+
(1
−
M
2
sr
L
s
.L
r
)
.L
r
.ω
r
.i
r
q
(17)
by
substituting
the
nal
e
xpression
in
(15),
we
acquire,
˙
V
(
e
1
,
e
2
)
=
−
k
1
.e
2
1
+
e
2
(
˙
Q
∗
s
+
v
s
.M
sr
(
L
s
.L
r
−
M
2
sr
)
v
r
d
−
R
r
.i
r
d
+
(1
−
M
2
sr
L
s
.L
r
)
.
L
r
.ω
r
.i
r
q
(18)
the
e
xpression
for
the
stabilising
Backstepping
command
is
gi
v
en
by
,
v
r
d
=
−
L
s
.L
r
−
M
2
sr
v
s
.M
sr
.
˙
Q
∗
s
+
R
r
.i
r
d
−
ω
r
.
1
−
M
2
sr
L
s
.L
r
.L
r
.i
r
q
−
(1
−
M
2
sr
L
s
.L
r
)
.
L
s
.L
r
v
s
M
sr
.k
2
.e
2
(19)
if
we
replace
(19)
in
(18),
we
obtain,
˙
V
(
e
1
,
e
2
)
=
−
k
1
.e
2
1
−
k
2
.e
2
2
<
0
(20)
with
k
2
positi
v
e
constant.
Figure
2
illustrates
the
po
wer
re
gulation
block
diagram
for
the
dual-fed
asynchronous
machine,
u
t
iliz-
ing
the
Backstepping
method
applied
to
the
machine-side
con
v
erter
.
Figure
2.
Diagrammatic
schematic
for
DFIG
po
wer
re
gulation
with
the
Backstepping
technique
Indonesian
J
Elec
Eng
&
Comp
Sci,
V
ol.
37,
No.
1,
January
2025:
78–89
Evaluation Warning : The document was created with Spire.PDF for Python.
Indonesian
J
Elec
Eng
&
Comp
Sci
ISSN:
2502-4752
❒
83
5.2.
Simulation
r
esults
The
v
alidation
of
the
DFIG
po
wer
control
method
utilizing
the
Backstepping
technique
in
v
olv
ed
rig-
orous
numerical
simulations
e
x
ecuted
via
MA
TLAB/Simulink
softw
are.
A
detailed
in
v
entory
of
the
generator
parameters
is
a
v
ailable
in
the
APPENDIXS
1
and
2.
T
o
scrutinize
the
control
dynamics
and
assess
its
reaction
to
changes
in
stator
acti
v
e
and
reacti
v
e
po
wer
,
incremental
steps
in
both
acti
v
e
and
reacti
v
e
po
wer
were
imple-
mented.
The
ensuing
machine
response
is
visual
ly
depicted
in
Figures
3
and
4.
Notably
,
Figure
3
delineates
the
reacti
v
e
po
wer
response
under
the
Backstepping
control
scheme
emplo
yed
for
the
DFIG
and
Figure
4
illustrates
the
acti
v
e
po
wer
response
resulting
from
the
application
of
Backstepping
control
to
the
DFIG.
Figure
3.
Po
wer
response
in
reaction
emplo
ying
Backstepping
control
Figure
4.
Acti
v
e
po
wer
response
using
Backstepping
control
W
e
proceeded
to
v
ary
the
acti
v
e
and
reacti
v
e
po
wer
of
the
system,
mirroring
pre
vious
tests,
to
asse
ss
its
re
gulation
capability
.
Figures
3
and
4
illustrate
the
simulation
out
comes
achie
v
ed
through
the
Backstepping
control
method
for
the
doubly-fed
asynchronous
generator
.
It’
s
e
vident
that
the
generator
adeptly
tracks
po
wer
v
ariations,
whether
in
act
i
v
e
or
reacti
v
e
po
wer
.
The
control
depicted
in
Figures
3
and
4
underscores
the
satis-
f
actory
dynamics
of
our
sys
tem.
Additionally
,
virtually
zero
static
error
is
observ
ed
for
both
acti
v
e
and
reacti
v
e
po
wer
.
These
dynamics
respond
promptly
and
e
xhibit
no
o
v
ershoot.
A
comparison
between
the
performance
of
this
control
and
that
of
an
FLC
control
is
outlined
in
the
follo
wing
paragraph.
6.
A
CTIVE
AND
REA
CTIVE
PO
WER
CONTR
OL
B
ASED
ON
FUZZY
CONTR
OLLERS
Fuzzy
controllers
pro
vide
a
e
xible
approach
for
managing
both
acti
v
e
and
reacti
v
e
po
wer
,
part
icu-
larly
when
creating
a
mathematical
model
is
dif
cult
or
when
dealing
with
nonlinear
system
beha
viors
.
Their
gro
wing
use,
especially
in
industrial
settings,
stems
from
their
ability
to
handle
comple
x
and
uncertain
systems.
Unlik
e
binary
logic,
fuzzy
logic
deals
with
a
spect
rum
of
v
alues,
capturing
the
nuances
of
human
reasoning
and
imprecise
language.
Introduced
by
Professor
Zadeh,
fuzzy
logic
emplo
ys
membership
functions
to
handle
uncertainty
ef
fecti
v
ely
,
allo
wing
for
ef
cient
control
without
detailed
system
modeling.
FLC
utilizes
linguistic
terms
and
multiple
inference
rules,
enabling
operators
to
apply
their
e
xperti
se
and
mak
e
decisions
based
on
v
arious
f
actors.
This
discussion
will
co
v
er
the
fundamental
principles
of
FLC
and
the
steps
in
v
olv
ed
in
implementing
it,
including
the
de
v
elopment
of
an
FLC
controller
for
managing
the
po
wer
output
of
a
DFIG.
6.1.
Basic
fuzzy
logic
contr
ol
concepts
The
FLC
controller
operates
through
four
primary
phases:
the
kno
wledge
base,
fuzzication,
inference
engine,
and
defuzzication.
Initially
,
the
controller
con
v
erts
numerical
input
into
fuzzy
v
alues.
These
v
alues
are
then
processed
according
to
fuzzy
rules.
Finally
,
the
fuzzy
v
alues
are
transformed
back
into
ph
ysical
v
alues
to
generate
the
control
signal,
as
the
system
operates
with
ph
ysical
quantities
only
[23].
6.2.
Fuzzication
In
this
phase,
each
v
ariable
(current
and
v
oltage)
is
associated
with
a
specic
fuzzy
subset
using
quan-
titati
v
e
membership
functions
to
describe
linguistic
v
ariables
and
quantify
their
relati
v
e
uncertainty
.
Natural
language
w
ords
serv
e
as
v
al
ues
for
these
v
ariables,
which
act
as
system
inputs
or
outputs
[23].
The
inference
rules
result
in
an
anti-diagonal
decision
table,
summarized
in
the
MA
CVICAR-WHELAN
matrix
sho
wn
in
T
able
1,
displaying
the
CF
inference
matrix
for
a
partition
of
7
fuzzy
subsets
for
each
input
v
ariable
e
and
∆
e,
for
a
detailed
description
of
this
part,
please
refer
to
our
pre
vious
article
[16].
Bac
kstepping
appr
oac
h
for
the
contr
ol
of
the
double-fed
async
hr
onous
...
(Mbar
ek
Chahboun)
Evaluation Warning : The document was created with Spire.PDF for Python.
84
❒
ISSN:
2502-4752
T
able
1.
The
basis
of
po
wer
control
rules
∆
e
e
NG
NM
NP
ZE
PP
PM
PG
NG
TG
TG
TG
G
PG
P
ZE
NM
TG
TG
G
G
M
P
TP
NP
TG
M
G
TG
TP
P
TP
ZE
P
PG
M
ZE
M
PG
P
PP
TP
P
TP
TG
G
MG
TG
PM
TP
P
M
G
G
TG
TG
PG
ZE
P
PG
G
GT
TG
TG
Where:
ZE:
zero
approximately
,
TG:
v
ery
lar
ge,
P:
small,
M:
a
v
erage,
TP:
v
ery
positi
v
e,
PG:
lar
ge
positi
v
e,
G:
lar
ge,
and
the
corresponding
linguistic
v
alues
are
characterised
by
symbols
such
as:
NG:
v
ery
ne
g
ati
v
e,
NM:
ne
g
ati
v
e
a
v
erage,
ZE:
zero
approximately
,
NP:
small
ne
g
ati
v
e,
PM
:
mean
positi
v
e,
and
PP:
small
positi
v
e.
6.3.
Defuzzication
The
core
of
defuzzication
is
decision-making,
or
e
xtracting
real
control
from
control
obtained
as
a
fuzzy
set.
While
fuzzy
rule
inference
may
be
used
in
a
v
ariety
of
w
ays,
the
most
often
used
method
is
the
one
that
determines
t
he
membership
function's
center
of
gra
vity
.
This
may
be
ascertained
by
applying
the
generic
formula
as
(21)
[24].
Figure
5
presents
the
schematic
design
of
the
FLC
for
DFIG
control.
V
R
=
R
1
−
1
X
k
U
R
(
X
k
)
dX
k
R
1
−
1
U
R
(
X
k
)
dX
k
(21)
Figure
5.
FLC
schematic
design
for
DFIG
control
6.4.
Simulation
and
r
esults
W
e
therefore
subjected
the
system
to
changes
in
acti
v
e
and
reacti
v
e
po
wer
(similar
to
the
pre
vious
tests)
in
order
to
study
the
beha
viour
of
its
re
gulation.
Figures
6
and
7
sho
w
the
simulation
results
obtained
using
DFIG
fuzzy
control.
Figure
6
displays
the
acti
v
e
po
wer
response
to
FLC
control
of
the
DFIG
[25],
[26],
and
Figure
7
il
lustrates
the
reacti
v
e
po
wer
response
resulting
from
the
application
of
FLC
control
to
the
DFIG.
The
simulation
results
sho
w
that
our
system
pro
vides
better
tracking
of
the
po
wer
reference,
is
dynam-
ically
satisf
actory
and
the
static
error
tends
to
w
ards
zero
with
lo
w
o
v
ershoot
(no
o
v
ershoot
for
acti
v
e
po
wer).
This
technique
made
it
possible
to
achie
v
e
perfect
decoupling
between
the
tw
o
stator
po
wer
components.
In
order
to
better
dem
onstrate
the
ef
fecti
v
eness
of
this
control,
we
are
going
to
test
the
beha
viour
of
the
DFIG
with
the
v
ariation
of
the
parameters
of
the
model
used.
Rob
ustness
tests:
parameter
identicati
on
in
machines
is
prone
to
inaccuracies
due
to
the
methods
and
measurement
de
vices
used.
Consequently
,
the
obtained
v
alues
are
often
imprecise
and
subject
to
v
ariations
from
f
actors
such
as
machine
heating,
load
changes,
magnetic
saturation,
air
g
ap
shape,
and
lm
ef
fects.
In
this
section,
we
will
e
xamine
the
DFIGs
response
to
changes
in
model
parameters
[27].
This
will
help
us
understand
ho
w
parameter
v
ariations
[28],
inuenced
by
operational
conditions
or
identication
errors,
af
fect
the
DFIG’
s
performance.
This
analysis
is
crucial
for
e
v
aluating
the
rob
ustness
of
the
control
system
ag
ainst
such
uncert
ainties
and
parameter
changes.
W
e
will
test
the
rob
ustness
of
both
Backstepping
and
FLCs
under
simulated
conditions
to
assess
their
ef
fecti
v
eness
[29],
[30].
Indonesian
J
Elec
Eng
&
Comp
Sci,
V
ol.
37,
No.
1,
January
2025:
78–89
Evaluation Warning : The document was created with Spire.PDF for Python.
Indonesian
J
Elec
Eng
&
Comp
Sci
ISSN:
2502-4752
❒
85
Figure
6.
Stator
acti
v
e
po
wer
response
using
FLC
control
Figure
7.
Stator
reacti
v
e
po
wer
response
using
FLC
control
6.4.1.
T
est
1:
inuence
of
a
+90%
v
ariation
in
r
otor
r
esistance
Rr
Figure
8
illustrates
the
impact
of
v
ariations
in
rotor
resistance
on
reacti
v
e
po
wer
under
Backste
pp
i
ng
control
of
the
DFIG
and
Figure
9
demonstrates
ho
w
changes
in
rotor
resistance
af
fect
acti
v
e
po
wer
when
emplo
ying
Backsteppi
ng
control
for
the
DFIG.
Figure
10
illustrates
ho
w
changes
in
rotor
resistance
impact
reacti
v
e
po
wer
when
ut
ilizing
FLC
for
the
DFIG,
and
Figure
11
illustrates
ho
w
v
ariations
in
rotor
resistance
inuence
acti
v
e
po
wer
when
emplo
ying
FLC
for
the
DFIG.
Figure
8.
Backstepping
control
simulation
results
sho
wing
ho
w
changes
in
rotor
resistance
af
fect
reacti
v
e
po
wer
Figure
9.
Results
of
a
simulation
emplo
ying
Backstepping
control
to
e
xamine
ho
w
changes
in
rotor
resistance
af
fect
acti
v
e
po
wer
Figure
10.
Results
of
a
simulation
utilizing
FLC
control
to
e
xamine
ho
w
changes
in
rotor
resistance
af
fect
reacti
v
e
po
wer
Figure
11.
Results
of
a
simulation
utilizing
FLC
control
to
e
xamine
ho
w
changes
in
rotor
resistance
af
fect
acti
v
e
po
wer
6.4.2.
T
este
2:
inuence
of
-35%
v
ariation
in
mutual
inductance
Lm
Figure
12
demonstrates
the
inuence
of
v
ariations
in
rotor
mutual
inductance
on
reacti
v
e
po
wer
under
Backstepping
control
for
the
DFIG
and
Figure
13
illustra
tes
the
inuence
of
v
ariations
in
rotor
mutual
induc-
tance
on
acti
v
e
po
wer
when
emplo
ying
Backstepping
control
for
the
DFIG.
Figure
14
illustrates
ho
w
v
ariations
in
rotor
mutual
inductance
inuence
acti
v
e
po
wer
when
emplo
ying
FLC
for
the
DFIG,
and
Figure
15
illustrates
ho
w
v
ariations
in
rotor
mutual
inductance
impact
acti
v
e
po
wer
when
utilizing
FLC
for
the
DFIG.
Bac
kstepping
appr
oac
h
for
the
contr
ol
of
the
double-fed
async
hr
onous
...
(Mbar
ek
Chahboun)
Evaluation Warning : The document was created with Spire.PDF for Python.
86
❒
ISSN:
2502-4752
Figure
12.
Results
of
a
simulation
utilizing
Backstepping
control
to
e
xamine
ho
w
changes
in
rotor
mutual
inductance
af
fect
reacti
v
e
po
wer
Figure
13.
Results
of
a
simulation
emplo
ying
Backstepping
control
to
e
xamine
ho
w
changes
in
rotor
mutual
inductance
af
fect
acti
v
e
po
wer
Figure
14.
Results
of
an
acti
v
e
po
wer
simulation
emplo
ying
FLC
control
to
e
xamine
the
impact
of
rotor
mutual
inductance
uctuations
Figure
15.
Results
of
a
reacti
v
e
po
wer
simulation
emplo
ying
FLC
control
for
the
impact
of
changes
in
rotor
mutual
inductance
7.
RESUL
TS
AND
DISCUSSION
The
outcomes
of
this
study
indicate
that
altering
parameters
in
the
DFIG
model
notably
impacts
the
acti
v
e
and
reacti
v
e
po
wer
proles
re
gulated
by
FLC,
as
depicted
in
Figures
14
and
15.
Specically
,
increasing
the
rotor
resistance
(Rr)
by
90%
resulted
in
distinct
v
ariations
in
the
FLC
control
outputs,
o
v
ershoot
(acti
v
e
po
wer
,
Figure
11),
and
response
times
for
both
acti
v
e
and
reacti
v
e
po
wers
(Figures
10
and
11).
Additionally
,
abrupt
oscillations
were
observ
ed
despite
an
increase
in
the
static
error
of
acti
v
e
and
reacti
v
e
po
wers
by
35%
of
the
nominal
v
alue
of
the
mutual
inductance
(Lm),
as
illustrated
in
Figures
14
and
15.
This
nding
suggests
that
the
FLC
method
is
not
resistant
to
internal
parametric
uctuations,
v
alidating
the
reliance
of
the
FLC
control
la
w
on
the
rotor
resistance
and
mutual
inductance
of
the
DFIG.
Our
results
in
Figures
8,
9,
12,
and
13
sho
w
that
the
Backstepping
control
also
af
fects
the
reacti
v
e
and
acti
v
e
po
wer
curv
es
under
DFIG
model
parameter
changes.
Ho
we
v
er
,
the
rob
ustness
and
dependability
of
Backstepping
control
are
demonstrated
by
its
ability
to
mainta
in
stator
act
i
v
e
and
reacti
v
e
po
wer
tracks
relati
v
e
to
their
references,
e
v
en
when
the
rotor
resistance
Rr
rises
by
90%.
Notably
,
when
the
mutual
inductance
Lm
is
v
aried
by
35%
of
its
nominal
v
alue,
there
is
an
increase
in
reacti
v
e
po
wer
o
v
ershoot
(Figure
12)
and
po
wer
response
time
(Figures
12
and
13),
with
no
change
in
the
static
error
.
From
these
rob
ustness
tests,
it
is
e
vident
that
v
ariations
in
resistances
and
mutual
inductances
ha
v
e
minimal
inuence
on
the
performance
of
Backstepping-based
control.
This
study
in
v
estig
ated
the
application
of
the
Backstepping
control
la
w
to
the
po
wer
generation
system
of
a
doubly-fed
asynchronous
generator
(DFIG).
While
earlier
studies
ha
v
e
e
xplored
v
arious
control
methods
for
DFIGs,
the
y
ha
v
e
not
e
xplicitly
addressed
the
comparati
v
e
inuence
of
Backstepping
and
fuzzy
logic
on
performance
metrics
under
v
arying
operating
conditions.
W
e
found
that
Backstepping
control
pro
vided
supe-
rior
reference
tracking
and
reduced
o
v
ershoot
compared
to
FLC
under
v
arious
conditions.
The
proposed
method
in
this
study
tended
to
ha
v
e
a
signicantly
higher
proportion
of
ef
fecti
v
e
acti
v
e
and
reacti
v
e
po
wer
re
gulation,
sho
wing
impro
v
ed
dynamic
response.
Our
study
suggests
that
higher
rob
ust-
ness
ag
ainst
parameter
v
ariations
in
DFIGs
is
not
associated
with
poor
performance
in
po
wer
re
gulation.
The
proposed
Backstepping
method
may
benet
from
syste
matic
design
without
adv
ersely
impacting
the
adapt-
ability
of
FLC.
Ho
we
v
er
,
the
FLC’
s
e
xibility
in
handling
non-linear
systems
lik
e
wind
turbines
of
fers
strong
performance,
despite
parameter
uctuations.
This
study
e
xplored
a
comprehens
i
v
e
control
strate
gy
with
Back-
stepping
and
FLC.
Ho
we
v
er
,
further
and
in-depth
studies
may
be
needed
to
conrm
their
ef
cac
y
,
especially
Indonesian
J
Elec
Eng
&
Comp
Sci,
V
ol.
37,
No.
1,
January
2025:
78–89
Evaluation Warning : The document was created with Spire.PDF for Python.
Indonesian
J
Elec
Eng
&
Comp
Sci
ISSN:
2502-4752
❒
87
re
g
arding
their
long-term
performance
under
dif
ferent
operational
scenarios.
Our
ndings
imply
that
both
control
methods
are
ef
fecti
v
e
for
enhancing
DFIG
wind
turbine
reliability
and
po
wer
quality
.
Future
research
could
optimize
these
controllers
further
,
e
xplore
h
ybrid
approaches,
and
test
t
heir
adaptability
in
more
comple
x
scenarios,
including
ener
gy
storage
inte
gration
for
broader
rene
w
able
ener
gy
applications.
Recent
observ
ations
suggest
that
adv
anced
control
methods
lik
e
Backstepping
and
fuzzy
logic
signicantly
impro
v
e
the
stability
and
performance
of
DFIG-based
wind
turbine
systems.
Our
ndings
pro
vide
conclusi
v
e
e
vidence
that
these
methods
are
a
ssociated
with
enhanced
po
wer
re
gulation
and
rob
ustness,
not
merely
due
to
ele
v
ated
adaptability
to
parameter
v
ariations,
can
be
seen
in
T
able
2.
T
able
2.
Comparison
between
fuzzy
logic
and
Backstepping
control
Control
type
Response
time
(seconds)
Static
error
Fuzzy
logic
control
0.0024s
0.9741
Backstepping
control
0.00031s
0.996
8.
CONCLUSION
The
numerical
simulations
clearly
sho
w
the
adv
antages
of
Backstepping
and
FLCs
for
DFIG-based
wind
turbine
systems.
Both
methods
ef
fecti
v
ely
re
gulated
acti
v
e
and
reacti
v
e
po
wer
with
good
dynamic
re-
sponses.
Backstepping
control
pro
vided
superior
reference
tracking
and
reduced
o
v
ershoot
compared
to
fuzzy
logic
under
v
arious
conditions.
Fuzzy
logic,
with
its
simple,
data-dri
v
en
approach,
of
fered
strong
performance
and
rob
ustness
for
comple
x
nonlinear
systems
lik
e
wind
turbines.
The
comparati
v
e
analysis
re
v
ealed
that
Back-
stepping
control
e
xcelled
in
performance
metrics
such
as
o
v
ershoot
and
tracking
speed,
thanks
to
its
systematic
design.
In
contrast,
FLC
pro
v
ed
rob
ust
ag
ainst
parameter
v
ariations
due
to
its
e
xible
rule-based
approach.
Both
techniques
are
ef
fecti
v
e
for
enhancing
DFIG
wind
turbine
reliability
and
po
wer
quality
.
Future
research
could
optimize
these
controllers
further
and
e
xplore
h
ybrid
approaches,
as
well
as
test
their
adapta
bility
in
more
comple
x
scenarios,
including
ener
gy
storage
inte
gration
for
broader
rene
w
able
ener
gy
applications.
APPENDIX
1:
DFIG
P
ARAMETERS
Rated
po
wer:
80
kW
.
Rotor
r
esistance
=
0.019
Ω
.
Stator
r
esistance
Rs
=
0.018
Ω
.
Mutual
inductance
M
=
8.17
mH.
Stator
inductance
Ls
=
8.49
mH
.
Rotor
inductance
Lr
=
2.587
mH.
Number
of
pole
pairs
p
=
3.
Moment
of
inertia
J=1000
Kg.mˆ2.
Coefcient
of
friction
f
=
0.0024
N.m.s/r
.
APPENDIX
2:
WIND
TURBINE
P
ARAMETERS
Rated
po
wer:
Pn=80
kW
.
Radius
of
the
blade
R=8.3
m
.
Number
of
blades
3
.
Gear
ratio
G=80.
V
iscous
friction
coefcient
fr
=0.0024
N.mˆ-1
Nominal
wind
speed
v=
12
m/s.
Moment
of
inertia
J=1300
Kg.mˆ2.
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ek
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