Inter
national
J
our
nal
of
P
o
wer
Electr
onics
and
Dri
v
e
System
(IJPEDS)
V
ol.
17,
No.
2,
June
2026,
pp.
933
∼
945
ISSN:
2088-8694,
DOI:
10.11591/ijpeds.v17.i2.pp933-945
❒
933
Impr
o
v
ed
contr
ol
strategy
f
or
harmonic
curr
ent
mitigation
in
DFIG-based
wind
turbines
supplying
linear
and
nonlinear
loads
Hind
Elaimani,
Nour
eddine
Elmouhi
Laboratory
of
Inno
v
ation
in
Management
and
Engineering,
Edv
antis
Higher
Education
Group,
ISGA,
Rabat,
Morocco
Article
Inf
o
Article
history:
Recei
v
ed
Sep
8,
2025
Re
vised
Mar
8,
2026
Accepted
Apr
23,
2026
K
eyw
ords:
Acti
v
e
lter
DFIG
Harmonic
mitig
ation
Sliding
mode
THD
ABSTRA
CT
Impro
ving
po
wer
quality
is
a
major
challenge
in
grid-connected
wind
ener
gy
systems,
especially
under
mix
ed
linear
and
nonlinear
load
conditions.
This
paper
proposes
an
enhanced
control
strate
gy
for
harmonic
current
mitig
ation
in
a
doubly
fed
induction
generator
(DFIG)-based
wind
turbine.
The
proposed
approach
inte
grates
ux-oriented
v
ector
control
with
an
acti
v
e
harmonic
compensation
algorithm
implemented
through
the
rotor
-side
con
v
erter
(RSC).
Unlik
e
con
v
entional
methods
that
tar
get
only
specic
harmonic
orders,
the
proposed
strate
gy
mitig
ates
all
current
harmonics
at
the
point
of
common
coupling
(PCC).
Simulation
studies
conducted
under
v
arious
load
conditions
demonstrate
that
the
method
signicantly
reduces
the
total
harmonic
distortion
(THD)
and
ensures
near
-sinusoidal
stator
currents.
The
results
conrm
the
ef
fecti
v
eness
and
rob
ustness
of
the
proposed
control
approach
in
impro
ving
the
po
wer
quality
of
DFIG-based
wind
ener
gy
con
v
ersion
systems.
This
is
an
open
access
article
under
the
CC
BY
-SA
license
.
Corresponding
A
uthor:
Hind
Elaimani
Laboratory
of
Inno
v
ation
in
Management
and
Engineering,
Edv
antis
Higher
Education
Group,
ISGA
27,
A
v
enue
Oqba,
27
A
v
.
Oqba
Ibn
Naa,
Rabat
10090,
Morocco
Email:
h.elaimani@gmail.com
1.
INTR
ODUCTION
In
recent
decades,
the
global
demand
for
electri
cal
ener
gy
has
increased
rapidly
due
to
industrializat
ion
and
the
widespread
use
of
electrical
appliances
[1],
[2].
T
o
meet
this
gro
wing
demand
while
reducing
en
vironmental
impact,
man
y
countries
are
inte
grating
rene
w
able
ener
gy
sources
into
their
po
wer
systems,
with
wind
ener
gy
emer
ging
as
a
prominent
option
due
to
its
high
potential
and
reliabilit
y
.
Se
v
eral
recent
studies
ha
v
e
in
v
estig
ated
harmonic
mitig
ation
in
rene
w
able
ener
gy
systems.
A
rst
w
ork
[3]
implemented
a
unied
po
wer
quality
conditioner
(UPQC)
combining
series
and
shunt
acti
v
e
lters
to
reduce
current
and
v
oltage
distortions,
achie
ving
a
decrease
in
total
harmonic
distortion
(THD)
from
o
v
er
55%
to
less
than
5%.
Another
study
[4]
e
xplored
reacti
v
e
po
wer
control
on
the
grid-side
con
v
erter
of
a
w
a
v
e
ener
gy
system
to
attenuate
v
oltage
harmonics.
A
comprehensi
v
e
re
vie
w
[5]
has
also
discussed
the
use
of
in
v
erter
-based
distrib
uted
generation
units
as
acti
v
e
po
wer
quality
conditioners
for
harmonic
compensation.
Moreo
v
er
,
research
in
v
olving
indirect
current
control
(ICC)
combined
with
fuzzy
logic
control
(FLC)
demonstrated
ef
fecti
v
e
harmonic
reduction
under
highly
nonlinear
loads,
maintaining
compliance
with
IEEE
519-1992
standards
[6].
Finally
,
studies
on
DFIG-based
wind
turbines
ha
v
e
critically
analyzed
harmonic
reduction
methods
to
enhance
the
quality
of
the
current
injected
into
the
grid
[7].
T
ogether
,
these
w
orks
highlight
the
need
for
more
inte
grated
and
adapti
v
e
strate
gies
capable
of
addressing
comple
x
harmonic
proles
in
rene
w
able
ener
gy
systems.
Among
J
ournal
homepage:
http://ijpeds.iaescor
e
.com
Evaluation Warning : The document was created with Spire.PDF for Python.
934
❒
ISSN:
2088-8694
v
arious
generator
congurations
for
wind
ener
gy
con
v
ersion,
doubly
fed
induction
generators
(DFIGs)
are
widely
emplo
yed
because
of
their
ef
cienc
y
and
controllability
.
Se
v
eral
control
strate
gies
ha
v
e
been
de
v
eloped,
including
sliding
mode
control,
which
of
fers
f
ast
response
and
high
precision
[8]–[10].
Modern
wind
ener
gy
systems
are
e
xpected
not
only
to
deli
v
er
acti
v
e
po
wer
b
ut
also
to
pro
vide
ancillary
services
such
as
reacti
v
e
po
wer
support
and
harmonic
current
mitig
ation.
V
oltage
uctuations
and
harmonic
distortions
can
disrupt
sensiti
v
e
equipment
and
de
grade
po
wer
quality
,
quant
ied
by
THD
[11].
Numerous
methods
ha
v
e
been
proposed
to
reduce
harmonics,
including
modied
rotor
-side
con
v
erter
(RSC)
control,
grid-side
con
v
erter
(GSC)
adjustments,
and
e
xternal
acti
v
e
lters
[2],
[12]–[17].
Despite
these
adv
ances,
a
comprehensi
v
e
strate
gy
capable
of
suppressing
all
harmonic
components
while
maintaining
the
main
objecti
v
es
of
the
wind
ener
gy
con
v
ersion
system
(acti
v
e
po
wer
generation
and
reacti
v
e
po
wer
compensation)
is
still
lacking.
T
o
address
this
g
ap,
this
study
proposes
a
harmonic
m
itig
ation
strate
gy
inte
grating
a
mult
i
v
ariable
lter
with
sliding
mode
control
of
both
RSC
and
GSC.
The
proposed
approach
ensures
near
-sinusoidal
stator
currents
at
the
point
of
common
coupling
(PCC)
under
dif
ferent
load
conditions
[18]–[22],
thereby
enhancing
o
v
erall
po
wer
quality
in
DFIG-based
wind
ener
gy
systems
connected
to
the
grid.
Compar
ed
to
e
xisting
RSC–GSC
harmonic
mitig
ation
schemes,
the
proposed
approach
inte
grates
a
multi
v
ariable
lter
with
sliding
mode
control
on
both
con
v
erters,
enabling
more
rob
ust
suppression
of
multiple
harmonic
components
under
highly
nonlinear
and
unbalanced
load
conditions.
Unlik
e
con
v
entional
PI-based
methods
or
standalone
APFs,
our
method
ensures
near
-sinusoidal
stator
currents
at
the
PCC
without
compromising
acti
v
e
and
reacti
v
e
po
wer
control.
The
remainder
of
this
paper
is
or
g
anized
as
follo
ws:
Section
2
presents
the
system
modeling,
including
the
DFIG
conguration
and
l
oad
representation
un
de
r
linear
,
nonlinear
,
balanced,
and
unbalanced
conditions.
Section
3
details
the
harmonic
current
identication
methods
and
introduces
the
proposed
mitig
ation
strate
gies.
Section
4
discusses
the
simulation
setup
and
results,
highlighting
performance
analysis
and
observ
ed
limitations.
Finally
,
section
5
concludes
the
paper
and
outlines
future
research
directions.
2.
SYSTEM
MODELING
AND
METHODOLOGY
2.1.
T
opology
of
the
studied
system
Currently
,
v
ariable-speed
wind
systems
based
on
the
DFIG
are
the
most
widely
used
technology
in
onshore
wind
f
arms.
Their
main
adv
antage
lies
in
the
f
act
that
the
static
con
v
erters
are
sized
for
only
a
fraction
of
the
nominal
po
wer
of
the
DFIG,
as
the
y
are
connected
to
the
grid
through
the
rotor
winding.
The
o
v
erall
conguration
of
the
studied
system
is
illustrated
in
Figure
1.
It
consists
of
the
wind
ener
gy
con
v
ersion
system
that
supplies
v
arious
types
of
loads,
including
linear
,
non-linear
,
balanced,
and
unbalanced
loads.
Figure
1.
Block
diagram
of
wind
ener
gie
con
v
ersion
system
Int
J
Po
w
Elec
&
Dri
Syst,
V
ol.
17,
No.
2,
June
2026:
933–945
Evaluation Warning : The document was created with Spire.PDF for Python.
Int
J
Po
w
Elec
&
Dri
Syst
ISSN:
2088-8694
❒
935
2.2.
DFIG
modeling
Starting
from
the
schematic
representation
of
a
DFIG
in
the
reference
frame
of
three
phases,
as
wi
d
e
ly
presented
in
[23]–[26],
and
adopting
the
assumptions
that
the
stator
resistance
R
s
is
ne
gligible
(which
is
reasonable
for
higher
po
wer
le
v
els)
and
that
the
stator
ux
φ
s
is
constant
(assuming
a
constant
st
ator
v
oltage
V
s
)
and
oriented
along
the
dq
axis,
the
machine
equations
can
be
e
xpressed
as
(1)–(4).
V
sd
=
0
V
sq
=
V
s
=
ω
s
φ
s
V
r
d
=
R
r
I
r
d
+
dφ
r
d
dt
−
ω
r
φ
r
q
V
r
q
=
R
r
I
r
q
+
dφ
r
q
dt
+
ω
r
φ
r
d
(1)
and:
φ
sd
=
φ
s
=
L
s
I
sd
+
M
I
r
d
0
=
L
s
I
sq
+
M
I
r
q
φ
r
d
=
L
r
I
r
d
+
M
I
sd
φ
r
q
=
L
r
I
r
q
+
M
I
sq
(2)
The
stator
currents
are
gi
v
en
by
the
follo
wing
system,
as
(3).
I
sd
=
φ
s
L
s
−
M
L
s
I
r
d
I
sq
=
−
M
L
s
I
r
q
(3)
The
acti
v
e
and
reacti
v
e
po
wers
become
(4).
P
s
=
V
sq
I
sq
=
−
M
L
s
V
s
I
r
q
Q
s
=
V
sq
I
sd
=
V
s
φ
s
L
s
−
M
V
s
L
s
I
r
d
(4)
The
pre
vious
equations
describe
the
dynamic
beha
vior
of
the
DFIG
under
the
assumptions
of
ne
gligible
stator
resistance
and
constant
stator
ux
oriented
along
the
dq-axis.
This
mathematical
model
forms
the
foundation
for
analyzing
the
generator
performance
and
its
interaction
with
the
electrical
netw
ork.
In
practical
applications,
the
DFIG
supplies
v
arious
types
of
load,
which
can
be
linear
or
nonlinear
,
balanced,
or
unbalanced.
Accurate
modeling
of
these
loads
is
essential
to
e
v
aluate
their
impact
on
po
wer
quality
,
particularly
harmonic
distortions.
The
ne
xt
section
presents
the
modeling
approaches
for
the
loads
connected
to
the
system.
2.3.
Load
modelling
Since
wind
turbines
are
connected
to
the
distrib
ution
grid,
t
he
y
are
often
located
clos
e
t
o
poll
uting
loads
that
inject
harmonics
into
the
netw
ork.
The
load
is
connected
to
the
wind
ener
gy
con
v
ersion
system
via
the
point
of
common
coupling,
as
sho
wn
in
Figure
1.
T
w
o
types
of
loads
are
considered:
i)
Linear
loads:
which
may
be
inducti
v
e
and/or
resisti
v
e,
consuming
acti
v
e
and/or
reacti
v
e
po
wer;
ii)
Nonlinear
loads:
represented
here
by
a
three-phase
diode
bridge
rectier
supplying
a
direct
current
(DC)
load,
which
can
also
ha
v
e
inducti
v
e
and
resisti
v
e
components.
If
the
load
v
alues
are
identical
across
the
three
phases,
the
load
is
considered
balanced;
otherwise,
it
is
unbalanced.
A
preliminary
test
w
as
conducted
to
v
alidate
the
modeling
of
balanced
and
unbalanced
loads.
The
corresponding
current
w
a
v
eforms
are
sho
wn
in
Figure
2.
At
time
t
=
500
ms,
a
v
ariation
in
the
acti
v
e
and
reacti
v
e
po
wer
of
the
loads
is
imposed
in
order
to
increase
the
THD,
with
the
aim
of
highlighting
the
proposed
solution
for
the
con
v
erter
system’
s
contrib
ution
to
harmonic
mitig
ation.
T
o
a
v
oid
o
v
erloading
the
article
with
gures,
spectral
results
for
all
cases
are
summarized
in
T
able
1,
including
THD
and
the
percentage
of
the
main
harmonic
components.
The
high
v
alue
of
the
DC
component
is
mainly
due
to
the
nonlinear
nature
of
the
load.
As
observ
ed
in
Figure
2,
a
DC
component
appears
in
balanced
and
unbalanced
load
conditions,
e
xplains
the
asymmetry
of
the
w
a
v
eforms
with
respect
to
the
time
axis.
Impr
o
ved
contr
ol
str
ate
gy
for
harmonic
curr
ent
mitigation
in
DFIG-based
wind
turbines
...
(Hind
Elaimani)
Evaluation Warning : The document was created with Spire.PDF for Python.
936
❒
ISSN:
2088-8694
2.4.
Simulation
of
the
wind
ener
gy
system
in
the
pr
esence
of
harmonic-polluting
loads
T
o
highlight
the
performance
of
the
wind
ener
gy
system
in
the
presence
of
electrical
loads,
the
simulation
of
the
con
v
ersion
system
connected
to
the
grid
through
the
PCC
w
as
carried
out.
On
the
other
side,
the
PCC
is
connected
to
harmonic-polluting
loads,
as
illustrated
in
Figure
1.
The
simulations
produced
the
results
sho
wn
in
Figure
3.
The
results
of
the
spectra
of
the
currents
injected
into
the
grid
I
g
are
summarized
in
T
able
2.
Based
on
these
results,
it
is
observ
ed
that
the
presence
of
the
wind
ener
gy
system
w
orsens
the
situation:
in
f
act,
the
THD
increases
and
the
grid
current
becomes
more
distorted.
Therefore,
a
ltering
solution
is
essential.
Figure
2.
Three-phase
current
responses
for
balanced
and
unbalanced
load
cases
T
able
1.
Summary
table
of
the
THD
of
load
currents
Frequenc
y
(Hz)
I
cbalanced
I
cunbalanced
t
=
100
ms
t
=
500
ms
t
=
100
ms
t
=
500
ms
I
ca
I
cb
I
cc
I
ca
I
cb
I
cc
0
86
217
86.88
154
104
217
386
2622
50
100
100
100
100
100
100
100
100
300
5.05
12.63
5.05
8.99
6.10
12.63
22.46
15.24
600
1.4
3.5
1.40
2.49
1.69
3.5
6.23
4.23
900
0.64
1.59
0.64
1.13
0.77
1.59
2.83
1.92
THD
(%)
5.31
13.26
5.31
9.44
6.40
13.26
23.59
16
1
1.05
1.1
1.15
1.2
0
0.5
1
I
g
B
a
l
a
n
c
e
d
(PU)
Balanced Load
5
5.05
5.1
5.15
5.2
0.4
0.6
0.8
1
Balanced Load
1
1.05
1.1
1.15
1.2
Time(s)
0
0.5
1
I
g
U
n
b
a
l
a
n
c
e
d
(PU)
Unbalanced Load
5
5.05
5.1
5.15
5.2
Time(s)
0.4
0.6
0.8
1
Unbalanced Load
Figure
3.
The
currents
injected
into
the
grid
to
which
the
wind
turbine
and
the
loads
are
connected
Int
J
Po
w
Elec
&
Dri
Syst,
V
ol.
17,
No.
2,
June
2026:
933–945
Evaluation Warning : The document was created with Spire.PDF for Python.
Int
J
Po
w
Elec
&
Dri
Syst
ISSN:
2088-8694
❒
937
T
able
2.
Summary
table
of
the
THD
of
load
currents
Frequenc
y
(Hz)
I
g
balanced
I
g
unbalanced
t
=
100
ms
t
=
500
ms
t
=
100
ms
t
=
500
ms
I
g
a
I
g
b
I
g
c
I
g
a
I
g
b
I
g
c
0
146.48
366.18
146
73.61
152.12
366.19
350
380
50
100
100
100
100
100
100
100
100
300
8.52
21.3
8.52
45.54
8.85
21.3
13.85
22.12
600
2.36
5.91
2.36
12.36
2.45
5.9
11.57
6.13
900
1.07
2.69
1.07
5.75
1.12
2.69
4.37
2.79
THD
(%)
8.95
22.36
8.95
47.8
9.29
22.36
31.24
23.23
3.
HARMONIC
MITIGA
TION
When
the
wind
ener
gy
system
w
as
connected
to
a
distorted
grid,
the
line
current
I
g
abc
e
xhibited
harmonic
frequenc
y
components
of
v
arious
orders,
not
limited
to
the
6th
harmonic.
In
most
pre
vious
studies,
control
strate
gies
tar
geted
only
a
single
harmonic
order
,
which
w
as
then
used
to
modify
the
DFIG
con
v
erter
control.
In
contrast,
the
control
strate
gy
de
v
eloped
in
this
w
ork
c
on
s
iders
all
signicant
harmonic
components
present
in
the
load
current
I
cabc
.
This
comprehensi
v
e
approach
allo
ws
for
a
more
accurate
compensation
under
both
balanced
and
unbalanced
conditions.
3.1.
Harmonic
curr
ent
identication
Se
v
eral
harmonic
identication
techniques
ha
v
e
been
reported
in
the
literature.
The
m
ost
class
ical
one,
widely
used
in
acti
v
e
po
wer
lter
control,
i
s
the
instantaneous
po
wer
(PQ)
theory
,
originally
proposed
by
Akagi.
It
i
s
based
on
the
Concordia
transformation,
applie
d
to
phase-to-neutral
v
oltages
V
sabc
and
load
currents,
to
compute
instantaneous
acti
v
e
and
reacti
v
e
po
wers.
These
po
wers
can
be
decomposed
as
(5).
(
P
=
P
+
e
P
Q
=
Q
+
e
Q
(5)
The
DC
components
P
and
Q
correspond
to
the
fundamental
components
and
are
e
xtracted
using
lo
w-pass
lters.
The
A
C
parts
e
P
and
e
Q
are
then
obtained
by
subtracting
these
DC
components,
allo
wing
the
harmonic
currents
generated
by
nonlinear
loads
to
be
identied.
Another
widely
used
technique
is
based
on
the
synchronous
reference
frame
(SRF)
method,
introduced
by
Bhattacharya
and
illustrated
in
[27].
Lik
e
the
PQ
method,
it
be
gins
with
the
Concordia
transformation
applied
to
the
load
currents,
follo
wed
by
a
P
ark
transformation
that
projects
them
onto
the
rotating
dq
frame.
In
this
frame,
the
fundamental
component
appears
as
a
DC
term,
while
harmonic
components
manifest
as
A
C
terms.
A
simple
band-pass
lter
can
then
isolate
the
fundamental
component.
The
SRF
method
presents
se
v
eral
adv
antages:
it
is
immune
to
v
oltage
harmonics
and
requires
only
tw
o
current
sensors
to
identify
all
harmonic
components
of
the
nonlinear
load.
Ho
we
v
er
,
in
its
classical
form,
it
does
not
permit
the
e
xtraction
of
a
specic
harmonic
order
.
In
this
w
ork,
a
multi-v
ari
able
lter
(MVF)
is
emplo
yed
for
harmonic
e
xtraction,
as
described
in
[14].
The
MVF
enables
the
isolation
of
either
the
complete
harmonic
spectrum
or
a
specic
harmonic
order
,
including
both
direct
and
in
v
erse
sequence
components.
Its
transfer
function
is
e
xpressed
as
(6).
H
(
s
)
=
Y
s
Y
e
=
k
s
+
k
2
+
j
ω
c
s
2
+
2
k
s
+
k
2
+
ω
2
c
(6)
Where:
ω
c
:
characteristic
pulsation
of
the
lter
(corresponding
to
the
tar
geted
frequenc
y);
k
:
positi
v
e
constant
controlling
bandwidth
and
selecti
vity;
Y
e
:
input
signal
to
be
ltered;
and
Y
s
:
output
signal
ltered
at
the
selected
frequenc
y
.
The
cutof
f
angular
frequenc
y
of
the
lter
,
denoted
ω
c
,
is
dened
as
(7).
ω
c
=
εnω
f
(7)
Where
n
represents
the
order
of
the
signal
component
to
be
ltered,
ε
characterizes
the
type
of
component
(direct
or
in
v
erse),
and
K
is
a
posi
ti
v
e
constant.
A
Bode
diagram
of
the
selecti
v
e
lter
w
as
generated
to
analyze
the
ef
fect
of
dif
ferent
v
alues
of
the
parameter
K
.
It
can
be
observ
ed
that
increasing
K
reduces
the
lter’
s
selecti
vity
,
resulting
in
a
wider
Impr
o
ved
contr
ol
str
ate
gy
for
harmonic
curr
ent
mitigation
in
DFIG-based
wind
turbines
...
(Hind
Elaimani)
Evaluation Warning : The document was created with Spire.PDF for Python.
938
❒
ISSN:
2088-8694
bandwidth.
In
this
case,
instead
of
obtaining
a
signal
containing
a
single
frequenc
y
,
the
ltered
signal
e
xhibits
additional
components,
introducing
noise.
Ho
we
v
er
,
the
dynamic
response
of
the
o
v
erall
system
must
also
be
considered,
particularly
re
g
arding
the
stability
of
the
system.
According
to
F
ourier’
s
theory
,
an
y
periodic
signal
can
be
e
xpressed
as
a
sum
of
sinusoidal
components
at
multiples
of
its
fundamental
frequenc
y
.
T
o
isolate
harmonics,
it
suf
ces
to
remo
v
e
the
fundamental
component.
Based
o
n
frequenc
y
analysis
of
the
current
from
balanced
loads
(see
T
able
1),
and
ne
glecting
harmonics
abo
v
e
1
kHz,
the
current
in
phase
a
can
be
e
xpressed
as
(8).
I
c
(
t
)
=
A
0
+
A
sin(2
ω
t
+
φ
1
)
+
A
1
sin(12
ω
t
+
φ
2
)
+
A
2
sin(24
ω
t
+
φ
3
)
+
A
3
sin(36
ω
t
+
φ
4
)
(8)
After
remo
ving
the
fundamental
component,
the
harmonic
current
becomes
(9).
I
c
har
(
t
)
=
A
′
0
+
A
′
1
sin(12
ω
t
+
φ
2
)
+
A
′
2
sin(24
ω
t
+
φ
3
)
+
A
′
3
sin(36
ω
t
+
φ
4
)
(9)
3.2.
Pr
oposed
harmonic
mitigation
strategies
T
w
o
complementary
harmonic
mitig
ation
strate
gies
ha
v
e
been
considere
d
for
DFIG-based
wind
ener
gy
systems
supplying
nonlinear
loads.
Both
approaches
ha
v
e
been
indi
vidually
tested
and
e
v
aluated
in
pre
vious
w
orks.
In
this
study
,
a
third
strate
gy
is
proposed
as
a
combination
of
the
tw
o,
aiming
to
enhance
o
v
erall
performance:
i)
RSC-based
compensation:
In
this
approach,
RSC
control
is
modied
by
injecting
specic
harmonic
components
into
rotor
current
reference,
thereby
reducing
their
propag
ation
into
stator
current
[14],
[15].
ii)
FSC-based
acti
v
e
ltering:
Here,
t
he
the
full-s
cale
con
v
erter
(FSC)
operates
as
an
act
i
v
e
lter
tha
t
e
xtracts
and
compensates
for
the
harmonic
components
present
in
the
measured
grid
currents
[13],
[16].
iii)
Combined
adapti
v
e
strate
gy:
This
enhanced
method
mer
ges
the
adv
antages
of
the
pre
vious
tw
o.
It
introduces
an
adapti
v
e
adjustment
block
that
ensures
the
DFIG
maintains
its
primary
objecti
v
es—acti
v
e
and
reacti
v
e
po
wer
control—while
achie
ving
impro
v
ed
harmonic
mitig
ation
[23],
[24].
3.2.1.
RSC
contr
ol
modication
f
or
harmonic
curr
ent
injection
Dif
ferent
control
techniques
can
be
applied
to
po
wer
con
v
erters.
Among
them,
PI-bas
ed
control
remains
the
most
commonly
used
due
to
its
simplicity
,
whereas
adv
anced
nonlinear
techniques
such
as
backstepping
or
sliding
mode
control
pro
vide
superior
performance
in
terms
of
dynamic
response
and
po
wer
quality
.
In
this
w
ork,
sliding
mode
control
is
applied
to
both
con
v
erters,
as
e
xtensi
v
ely
de
v
el
oped
in
[23],
[24].
Based
on
the
mathematical
models
of
the
generator
,
DC
b
us,
and
grid
lter
,
control
la
ws
ha
v
e
been
deri
v
ed
to
manage
both
the
RSC
and
the
GSC.
The
RSC
controller
is
mainly
responsible
for
ensuring
that
the
acti
v
e
and
reacti
v
e
po
wers
follo
w
their
respecti
v
e
references.
In
the
modied
v
ersion
of
the
RSC
control,
the
same
fundamental
control
structure
is
preserv
ed,
b
ut
an
additional
term
is
introduced
to
eliminate
the
6th-order
harmonic.
This
is
achie
v
ed
by
injecting
the
corresponding
harmonic
current
into
the
rotor
current
reference
used
within
the
control
loop.
According
to
the
DFIG
model
presented
in
the
modeli
ng
section,
under
stator
ux
orientation
(aligned
with
the
d-axis),
acti
v
e
and
reacti
v
e
po
wer
control
requires
computing
the
rotor
current,
see
in
(4),
from
which
the
v
oltage
references
are
deri
v
ed.
In
steady-state
operation,
the
DFIG
inherently
couples
the
stator
and
rotor
currents,
acting
as
a
current
amplier
.
Consequently
,
the
harmonic
components
present
in
the
load
are
not
onl
y
incorporated
into
the
control
strate
gy
b
ut
also
amplied
to
ef
fecti
v
ely
compensate
for
the
harmonic
distortion
observ
ed
at
the
point
of
rene
w
able
resources
(PRR).
The
harmonic
components
of
the
rotor
current
references
are
obtained
as
(10).
i
r
dh
=
L
s
M
·
L
m
i
cdh
i
r
q
h
=
L
s
M
·
L
m
i
cq
h
(10)
Thus,
the
full
e
xpressions
of
the
rotor
current
references
are
gi
v
en
by
(11).
I
ref
r
q
=
−
L
s
V
s
·
M
·
P
ref
s
L
s
M
·
L
m
+
i
cq
h
I
ref
r
d
=
V
s
ω
s
·
M
−
L
s
V
s
·
M
·
Q
ref
s
L
s
M
·
L
m
+
i
cdh
(11)
Int
J
Po
w
Elec
&
Dri
Syst,
V
ol.
17,
No.
2,
June
2026:
933–945
Evaluation Warning : The document was created with Spire.PDF for Python.
Int
J
Po
w
Elec
&
Dri
Syst
ISSN:
2088-8694
❒
939
Once
these
updated
rotor
current
references
are
computed,
the
corresponding
reference
v
oltages
are
obtained
using
(1),
as
in
the
standard
control
structure.
These
v
oltages
are
then
applied
to
the
RSC,
which
is
controlled
through
pulse
width
modulation
(PWM).
Through
this
modication,
the
RSC
act
i
v
ely
cancels
the
6th-order
harmonic
component
of
the
load
current,
as
illustrated
in
Figure
4.
The
presence
of
harmonic
components
in
the
rotor
v
oltage
can
signicantly
af
fect
the
DFIG’
s
int
ernal
beha
vior
.
According
to
(1),
these
harmonics
generate
corresponding
harmonic
currents
in
the
rotor
circuit,
which
can
then
propag
ate
to
the
stator
s
ide.
The
frequenc
y
and
sequence
of
these
harmonics
are
dened
by
(3).
Consequently
,
the
induced
imbalance
between
rotor
and
stator
currents
can
lead
to
nonuniform
magnetic
loading,
resulting
in
localized
magnetic
s
aturation,
e
xcessi
v
e
heating,
and
increased
copper
and
iron
losses.
These
ef
fects
ultimately
reduce
the
o
v
erall
ef
cienc
y
and
operational
lifetime
of
the
DFIG.
Furthermore,
according
to
(4),
the
mismatch
between
the
generated
and
reference
po
wer
components
may
indicate
a
loss
of
tracking
accurac
y
in
the
initial
control
structure.
T
o
mitig
ate
these
ef
fects
and
m
aintain
po
wer
control
precision,
a
renement
of
the
rotor
current
references
is
therefore
required.
Figure
4.
Modied
RSC
control
via
sliding
mode
for
harmonic
mitig
ation
3.2.2.
FSC-based
acti
v
e
ltering
f
or
harmonic
compensation
The
second
harmonic
mitig
ation
strate
gy
relies
on
a
dedicated
acti
v
e
lter
(AF)
implemented
through
a
shunt
con
v
erter
,
the
full-scale
con
v
erter
(FSC),
which
has
a
structure
similar
to
the
RSC
and
GSC
used
in
the
DFIG-based
wind
ener
gy
con
v
ersion
system
as
illustrated
in
Figure
1.
The
main
di
stinction
lies
in
the
control
technique.
While
the
RSC
and
GSC
are
dri
v
en
by
PWM
,
the
FSC
is
controlled
using
a
h
ysteresis
current
control
method.
This
enables
rapid
and
precise
tracking
of
the
harmonic
components
e
xtracted
from
the
load
current.
The
FSC
is
connected
in
parallel
with
the
load
and
is
e
xclusi
v
ely
responsible
for
compensating
the
isolated
harmonic
components
obtained
using
the
harmonic
e
xtract
ion
method
described
earlier
.
By
injecting
the
appropriate
compensating
currents
into
the
grid,
this
approach
ef
fecti
v
ely
reduces
the
THD
at
the
PCC.
The
FSC-based
acti
v
e
ltering
is
particularly
ef
cient
in
mitig
ating
multiple
harm
o
ni
c
orders
simultaneously
and
dynamically
adapts
to
v
ariations
in
load
conditions.
It
ensures
harmonic
compensation
without
af
fecting
the
primary
acti
v
e
and
reacti
v
e
po
wer
deli
v
ered
by
the
DFIG.
Impr
o
ved
contr
ol
str
ate
gy
for
harmonic
curr
ent
mitigation
in
DFIG-based
wind
turbines
...
(Hind
Elaimani)
Evaluation Warning : The document was created with Spire.PDF for Python.
940
❒
ISSN:
2088-8694
3.2.3.
Combined
generator
-and
grid-side
harmonic
mitigation
The
combi
ned
strate
gy
mer
ges
the
tw
o
pre
viously
discussed
approaches.
The
RSC
is
modied
to
inject
harmonic
components
directly
into
the
rotor
current
reference,
while
a
parallel
FSC-based
acti
v
e
lter
simultaneously
injects
compensating
currents
into
the
grid
(Figure
5).
This
dual-action
strate
gy
allo
ws
harmonics
to
be
mitig
ated
at
tw
o
le
v
els:
internally
through
the
generator
control
and
e
xternally
via
the
acti
v
e
lter
.
Such
an
approach
enhances
o
v
erall
harmonic
suppression
and
ensures
that
the
DFIG’
s
primary
objecti
v
es—acti
v
e
and
reacti
v
e
po
wer
re
gulation—are
maintained.
3.2.4.
Enhanced
method
of
the
RSC
modication
The
adapted
control
strate
gy
must
ensure
harmonic
current
mitig
ation
while
maintaining
the
acti
v
e
po
wer
control
of
the
DFIG.
It
is
essential
to
emphasize
that
harmonic
compensation
should
ne
v
er
compromise
the
acti
v
e
po
wer
output
of
the
wind
turbine,
especially
under
f
a
v
orable
wind
conditions
that
allo
w
for
nominal
po
wer
generation.
Therefore,
a
modication
of
the
rotor
current
references
is
implemented
at
the
RSC
le
v
el,
prioritizing
the
re
gulation
of
acti
v
e
po
wer
production.
The
core
idea
lies
in
limiting
the
reference
currents
according
to
the
o
wchart
illustrated
in
Figure
6,
which
ensures
that
harmonic
compensation
remains
ef
fecti
v
e
without
de
grading
the
primary
function
of
the
wind
ener
gy
con
v
ersion
system.
The
rotor
currents
are
rst
calculated
at
their
maximum
v
alues.
The
harmonic
currents
of
the
rotor
are
then
analyzed
to
determine
the
reference
currents,
which
are
used
to
calculate
the
reference
v
oltages
of
the
modulator’
s
pulse
width.
The
adjustment
mechanism
is
illustrated
in
Figure
7.
Blocks
1
and
2
illustrated
in
Figure
7
are
composed
as
(12)–(14).
V
C
C
Gq
-
E
q
ui
=
−
L
s
L
r
σ
M
V
s
˙
P
ref
s
+
R
r
I
r
q
+
g
ω
s
L
r
σ
I
r
d
+
g
M
V
s
L
s
(12)
V
C
C
Gd
-
E
q
ui
=
L
r
σ
V
s
ω
s
M
−
L
s
V
s
M
˙
Q
ref
s
+
R
r
I
r
d
−
g
ω
s
L
r
σ
I
r
q
(13)
V
C
C
Gq
=
−
L
s
L
r
σ
M
V
s
˙
P
ref
s
+
R
r
I
r
q
+
g
ω
s
L
r
σ
I
r
d
+
g
M
V
s
L
s
+
L
r
σ
v
1
sgn(
s
(
P
))
(14)
Figure
5.
Combined
RSC
and
FSC-based
harmonic
mitig
ation
for
a
DFIG
system
Int
J
Po
w
Elec
&
Dri
Syst,
V
ol.
17,
No.
2,
June
2026:
933–945
Evaluation Warning : The document was created with Spire.PDF for Python.
Int
J
Po
w
Elec
&
Dri
Syst
ISSN:
2088-8694
❒
941
Figure
6.
Flo
wchart
of
the
reference
current
adjustment
Figure
7.
Block
diagram
of
the
modied
RSC
for
harmonic
mitig
ation
inte
grating
the
current
reference
recalculation
block
4.
EV
ALU
A
TION
OF
THE
CONTR
OL
STRA
TEGY
4.1.
Simulation
r
esults
The
simulations
were
conducted
to
e
v
aluate
the
v
alidity
and
ef
fecti
v
eness
of
the
proposed
control
strate
gy
.
A
1.5
MW
DFIG
model
w
as
de
v
eloped
in
MA
TLAB/Simulink.
Re
g
arding
the
load
conditions,
both
balanced
and
unbalanced
loads
are
considered.
Before
500
ms,
the
linear
load
consumes
500
kW
of
acti
v
e
po
wer
and
800
kV
AR
of
reacti
v
e
po
wer
,
while
the
nonlinear
load
absorbs
90
kW
and
1.2
MV
AR.
After
500
ms,
the
linear
load
remains
unchanged
with
500
kW
and
800
kV
AR,
whereas
the
nonlinear
load
increases
to
500
kW
and
3
MV
AR.
T
o
isolate
the
inuence
of
harmonic
mitig
ation
and
clearly
observ
e
the
control
dynamics,
the
system
w
as
simulated
under
x
ed
wind
speed
conditions.
This
approach
eliminates
additional
harmonics
that
could
arise
from
wind
speed
uctuations.
The
simulation
duration
w
as
set
to
600
ms
and
included
both
balanced
and
unbalanced
load
scenarios.
In
each
case,
linear
and
nonlinear
loads
were
applied.
A
step
change
in
acti
v
e
and
reacti
v
e
po
wer
w
as
also
introduced
to
increase
the
THD
and
e
v
aluate
the
control
system’
s
rob
ustness.
Impr
o
ved
contr
ol
str
ate
gy
for
harmonic
curr
ent
mitigation
in
DFIG-based
wind
turbines
...
(Hind
Elaimani)
Evaluation Warning : The document was created with Spire.PDF for Python.
942
❒
ISSN:
2088-8694
4.2.
Discussion
of
r
esults
T
o
streamline
the
analysis
and
emphasize
the
performance
of
the
proposed
strate
gy
,
the
discussion
focuses
on
the
THD
of
k
e
y
currents
(
I
r
,
I
s
,
I
c
,
and
I
g
)
under
the
most
se
v
ere
condition—unbalanced
loading.
The
simulation
results
yielded
the
current
w
a
v
eforms
sho
wn
in
Figure
8,
while
the
acti
v
e
and
reacti
v
e
po
wer
proles
are
presented
in
Figures
9
and
10.
Figure
11
illustrates
the
DC-link
v
oltage,
which
remains
stable
throughout
the
simulation,
conrming
the
proper
ener
gy
balance
and
rob
ustness
of
the
propo
s
ed
control
scheme.
T
able
3
summarize
the
spectral
analysis
THD
of
the
three-phase
currents.
1
1.05
1.1
1.15
1.2
-1
0
1
I
s
(PU)
1
1.05
1.1
1.15
1.2
-1
0
1
I
r
(PU)
1
1.05
1.1
1.15
1.2
Time(s)
-1
0
1
I
g
(PU)
5
5.05
5.1
5.15
5.2
-1
0
1
5
5.05
5.1
5.15
5.2
-1
0
1
5
5.05
5.1
5.15
5.2
Time(s)
-1
0
1
Figure
8.
The
currents
of
WECS
under
unbalanced
load
with
adjustment
block
Similar
to
the
pre
viously
proposed
method,
harmonic
compensation
is
successful
ly
achie
v
ed.
Ho
we
v
er
,
the
major
impro
v
ement
introduced
by
the
adjustment
block
lies
in
preserving
the
primary
ener
gy
con
v
ersion
function
of
the
wind
system.
Figures
9
and
10
sho
w
that
the
acti
v
e
po
wer
accurately
follo
ws
its
reference
deri
v
ed
from
the
mechanical
subsystem.
Moreo
v
er
,
the
rotor
currents
remain
undistorted
e
v
en
under
unbalanced
load
conditions,
thus
pre
v
enting
potential
operational
issues
in
the
DFIG.
0
1
2
3
4
5
6
Time(s)
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
P(PU)
Active Power
P
r
e
f
P
Figure
9.
The
acti
v
e
po
wer
of
WECS
under
unbalanced
load
with
adjustment
block
Int
J
Po
w
Elec
&
Dri
Syst,
V
ol.
17,
No.
2,
June
2026:
933–945
Evaluation Warning : The document was created with Spire.PDF for Python.