Int
ern
at
i
onal
Journ
al of
P
ower E
le
ctr
on
i
cs a
n
d
Drive
S
ystem
(I
J
PE
D
S
)
Vo
l.
11
,
No.
3
,
Septem
be
r
2020
, pp.
1459
~
1467
IS
S
N:
20
88
-
8694
,
DOI:
10
.11
591/
ij
peds
.
v
1
1
.i
3
.
pp
1459
-
1
4
67
1459
Journ
al h
om
e
page
:
http
://i
jp
eds.
i
aescore.c
om
A new
appr
oach to
extra
ct ref
eren
ce cu
rrents fo
r multile
vel
shunt
active filt
er i
n three
phase systems
A
bdelk
ad
er
Y
ou
s
fi
1
,
T
ayeb
Allaoui
2
,
A
bd
el
ka
der
Chak
er
3
1
Depa
rt
m
ent
of Electrical E
ng
in
ee
ring
,
Dj
il
a
li
B
ounaa
m
a
Khe
mis
Mili
an
a
Univ
er
sity
,
Alg
eria
2
Depa
rt
m
ent
of Electrical E
ng
in
ee
ring
,
Ibn
Khal
doun
Univer
sity
of
Tiare
t
,
Alg
eria
3
Depa
rt
m
ent
of Electrical E
ng
in
ee
ring
,
Na
ti
ona
l P
olyt
ec
hni
c
Sch
ool
of
Or
an
,
Alg
eri
a
Art
ic
le
In
f
o
ABSTR
A
CT
Art
ic
le
history:
Re
cei
ved
Dec
21
, 201
9
Re
vised
F
eb
15
, 2
0
20
A
ccepte
d
M
ar
24
, 20
20
In
thi
s
article,
we
pre
sen
t
a
n
ew
study
of
t
echnique
to
ext
ra
ct
r
efe
r
ence
cur
ren
ts
for
thr
ee
-
l
eve
l
shunt
a
ct
iv
e
filter
controlli
ng
by
fuz
zy
logi
c
.
Th
e
AP
F
s
is
r
ea
l
ize
d
using
thr
ee
p
hase
vol
ta
ge
an
d
the
ca
rr
ie
r
-
b
a
sed
PWM
strat
egy
.
A
ne
w
te
chni
qu
e
f
or
ide
nt
ifyi
ng
ref
ere
n
ce
cur
re
nts
will
b
e
deve
lop
ed.
It
is
base
d
on
conc
or
dia
me
thod
usin
g
multi
-
var
ia
bl
e
filter
,
and
ma
kes
the
tot
a
l
or
select
iv
e
ext
r
ac
t
ion
har
moni
c
cu
rre
n
ts
of
r
eferenc
es,
and
by
conse
quence
ma
king
th
ei
r
co
mpe
nsati
ons
,
total
or
sel
ec
t
ive.
T
he
result
s
of
digi
tal
simu
latio
n
in
the
Ma
tlab
-
Simul
ink
envi
ro
nme
nt
of
a
sys
tem
of
power
to
thyr
istor
outp
uts
on
an
indu
ctive
loa
d
show
well
the
eff
ectiveness
of
thi
s
new
techniqu
e
o
f
ext
r
action
of
th
e
har
moni
cs
of
r
efe
ren
ce.
Ke
yw
or
d
s
:
Act
ive P
ower
Fil
te
r
(APFs
)
Fu
zz
y
lo
gic c
urre
nt contr
oller
Harmo
nic
M
ulti
le
vel
(N
P
C) in
ver
te
r
M
ulti
va
riable
f
il
te
r
This
is an
open
acc
ess arti
cl
e
un
der
the
CC
BY
-
SA
l
ic
ense
.
Corres
pond
in
g
Aut
h
or
:
Abdelka
de
r Yousfi,
Dep
a
rtme
nt of
Ele
ct
rical
En
gi
neer
i
ng,
Faculty
of Scie
nce a
nd Tec
hnology,
Un
i
ver
s
it
y
of
Djil
al
i Bo
unaama
Khe
mis Mili
ana
,
Rue T
hn
ie
t El
Had K
hemis
M
il
ia
na
-
Ain
Def
la
-
Alge
ria.
Emai
l:
y
ous
fi_
pg@
yaho
o.
f
r
1.
INTROD
U
CTION
The
use
of
the ele
ct
rical
app
li
ance
is
increa
sing
l
y
inten
se
since
a
certai
n
num
ber
o
f
years
.
H
ow
e
ver,
the
majo
rity of
the
a
pp
a
ratuse
s
abs
orb
nonli
ne
ar
c
urren
ts w
hich
ge
ner
at
e ha
rm
on
ic
d
ist
ort
ion
s
i
n
t
he
whole
of
the
el
ect
rical
s
upply
ne
tw
ork
.
T
he
prese
nc
e
of
the
se
harmo
nics
is
a
w
kwar
d
i
ns
ofar
a
s
the
y
ca
n
det
erior
at
e
the
pe
rformanc
es
of
t
he
a
pp
a
r
at
us
es,
a
nd
eve
n
to
dama
ge
th
em.
A
so
l
ution
then
c
onsist
s
in
co
mp
e
ns
at
in
g
f
or
the h
a
rm
onic
di
stortions
wh
il
e insertin
g fil
te
rs
in
the elect
ri
cal
supp
l
y network
s
[1
,
2
]
.
The
se
filt
ers
se
ek
t
o
i
den
ti
f
y
t
he
harm
on
ic
c
ompone
nts
i
n
order
to
ef
fecti
vely
rei
nject
ion
t
hem
in
th
e
el
ect
rical
su
pp
ly
net
work
i
n
opposit
ion
of
ph
a
se.
T
he
y
ar
e
al
so
able
t
o
com
pensat
e
re
act
ive
powe
r
a
nd
t
o
com
pensat
e
for
t
he
possible
imbala
nc
e
of
a
three
-
ph
ase
syst
em
[
3
,
4
].
More
ove
r,
the
s
hunt
act
ive
filt
ers
ca
n
be
i
ns
erte
d
eas
il
y
in
t
he
e
xisti
ng
i
ns
ta
ll
at
ions
of
el
ect
ric
di
stribu
ti
on
with
ou
t
re
qu
i
rin
g
gr
eat
modific
a
ti
on
s.
Re
cognized
for
their
sim
plici
ty
of
im
pleme
ntati
on
,
f
or
th
ei
r
rob
us
tnes
s
and
t
heir
rel
ia
bili
ty,
they
re
presen
t
t
od
a
y
the
tech
ni
qu
e
most
lar
ge
ly em
ploye
d
t
o
cl
ean
se the
elec
tric
sy
ste
m
s.
A
thr
ee
-
le
vel
sh
unt
act
ive
f
il
te
r
based
on
the
te
chn
i
qu
e
of
e
xtracti
on
mu
lt
i
-
va
riabl
e
filt
er
ca
n
com
pensat
e,
in
real
ti
me,
co
m
plete
ly
or
pa
rtia
ll
y
an
y
dist
ur
ban
ce
bein
g
a
bl
e
to
occu
r
on
t
he
el
ect
rical
s
uppl
y
netw
ork
[
5
, 6
].
In
this a
rtic
le
, w
e prese
nt a new study
of tec
hn
i
qu
e t
o
ext
ra
ct
r
efere
nce c
urre
nts for
th
ree
-
le
vel
sh
unt
act
ive
filt
er
co
ntr
olli
ng
by
f
uzzy
lo
gic.
The
AP
F
s
is
r
eal
iz
ed
us
i
ng
t
hr
ee
phase
v
olt
age
a
nd
t
he
ca
rr
ie
r
-
bas
e
d
PWM
st
rateg
y.
A
ne
w
te
chn
iq
ue
f
or
identif
ying
re
f
eren
ce
c
urre
nts
will
be
de
velop
e
d.
It
is
bas
ed
on
con
c
ordia
met
hod
us
i
ng
m
ulti
-
var
ia
ble
filt
er,
a
nd
ma
kes
th
e
total
or
sel
ec
ti
ve
ext
racti
on
harmo
nic
c
urre
nts
of
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8
694
In
t J
P
ow
Ele
c
&
Dr
i
S
ys
t
,
V
ol
.
1
1
, N
o.
3
,
Se
ptembe
r
2020
:
14
59
–
14
67
1460
ref
e
ren
ces
,
a
nd
b
y
c
onseq
ue
nce
ma
king
their
co
mp
e
nsa
ti
on
s,
t
otal
or
sel
ect
ive.
T
he
res
ults
of
dig
it
al
simulat
ion
i
n
the
M
at
la
b
-
Si
m
ulink
e
nvir
onment
of
a
s
ys
t
em
of
po
wer
t
o
th
yr
ist
or
ou
t
pu
ts
on
an
i
nductive
load sh
ow
well
the e
ff
ect
ive
ne
ss of t
his n
e
w
techn
i
qu
e
of e
xtracti
o
n of
t
he
h
a
rm
on
ic
s
of re
fe
re
nce.
2.
CIRC
UIT
CONFIG
U
RA
TI
ON
The
s
ys
te
m
co
nf
i
gurati
on
of
the
act
ive
pow
er
filt
er
co
nne
ct
ed
to
the
el
e
ct
rical
network
is
sh
own
i
n
Fig
ure
1.
It
give
s
the
pro
pose
d
s
ys
te
m
w
hic
h
is
co
mpose
d
of
a
t
hr
ee
-
phas
e
source,
a
rect
ifie
r
as
a
non
-
l
inear
loa
d
a
nd s
hunt
act
ive pow
e
r fi
lt
er
[
7
-
9]
.
Figure
1
.
O
verview
of the
sys
te
m conf
i
gurati
on of T
hree
-
le
vel s
hunt acti
ve
pow
e
r fil
te
r
3.
DEVELOP
M
ENT
OF
THE
I
DE
NTIFI
C
ATIO
N MET
HOD B
Y
A M
ULTI
V
ARIA
BL
E FIL
TE
R
3.1.
Pri
ncipl
e of m
eth
od
m
ulti
va
ri
ab
le
filter
(
MVF
)
A
ne
w
ty
pe
of
extr
act
io
n
filt
er
name
d
her
e
mu
lt
ivaria
ble
Fil
te
r
(
MV
F
)
ha
s
been
de
velo
ped,
Its
basic
pr
i
nciple
is
ba
sed
on
the
w
or
k
of
S
ong
H
ong
-
S
co
k
is
base
d
on
the
extra
c
ti
on
of
the
f
undame
ntal
co
m
pone
nt
of the si
gn
al
s
, direct
ly acc
ord
in
g
t
o
the
(
−
)
axes
.
[
5
]
3.2.
Mathem
ati
c
al
mode
l
of
th
e
multi
vari
ab
le
filter
(
M
VF
)
In
his
res
earc
h,
Hon
g
S
c
ok
S
ong
prese
nted
how
he
rec
ove
red
the
eq
uiv
al
ent
tra
ns
f
er
f
unct
ion
of
the
integrati
on i
n
t
he
s
ynch
ron
ous r
e
fer
e
nces
fr
a
me exp
resse
d by
(1
)
[
5
,
10
]
.
dt
t
i
e
e
t
i
t
j
t
j
c
c
).
(
)
(
ˆ
−
=
(1)
He
f
ound in
La
place t
ransf
ormat
ion
t
he
f
ollow
i
ng
eq
uatio
n
“T
he dem
on
s
trat
ion
is
giv
e
n i
n
the a
nnex
of h
is t
hesi
s”
[
9]
:
2
2
)
(
)
(
ˆ
)
(
c
c
s
j
s
s
i
s
i
s
H
+
+
=
=
(
2)
Now
s
uppose
that
we
a
dd
t
wo
ne
w
c
on
st
ants
1
and
2
in
the
tra
ns
fe
rs
functi
on
of
eq
ua
ti
on
(
2)
.
The
n we
hav
e
the
fo
ll
owin
g
e
xpressi
on
:
2
2
1
1
2
)
(
)
(
.
)
(
)
(
ˆ
)
(
c
c
K
s
j
K
s
K
s
i
s
i
s
H
+
+
+
+
=
=
(
3)
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
ow Elec
& Dri S
ys
t
IS
S
N:
20
88
-
8
694
A n
ew
appro
ac
h
to
extract
r
ef
erence c
ur
re
nt
s for m
ulti
le
vel
shun
t
a
ct
iv
e fi
lt
er
…
(
A
bd
el
k
ad
er Y
ousfi
)
1461
we
set
=
20
an
d
vary
1
.
We
can
tra
ce
the
Bo
de
diagr
a
m
i
n
3D
(
gain
a
nd
ph
ase
as
a
f
un
ct
io
n
of
and
),
as
sho
w
n
in
F
ig
ure
2.
Figure
2. (a
)
G
ai
n
cu
r
ve
of
(
)
as
a fu
nction o
f
and
1
(
b)
phase
curve
of
(
)
as a fun
ct
io
n o
f
and
1
Figure
2
s
how
us
t
hat:
1.
a
t
f
=
50
Hz,
the
ph
ase
a
ng
l
e
of
B
od
e
dia
gr
a
m
is
null
,
t
his
mea
ns
that
the
t
wo
in
pu
t
an
d
out
put
sign
al
s a
re i
n p
hase eit
he
r
1
=
20
.
2.
to obtai
n
|
(
)
|
=
0
is
nec
essar
y
to
ma
ke
1
=
2
=
=
20
Eq
uation
(
4)
will
beco
me
as
a
f
ollow
up
:
(
)
=
̂
(
)
(
)
=
(
+
)
+
(
+
)
2
+
2
(
4)
The
e
xpressi
ons
li
nkin
g
t
he
ou
t
pu
t
co
mpo
ne
nts
of
the
mul
ti
-
var
ia
ble
filt
er
to
the
in
pu
t
com
pone
nts
are as
f
ollow
s:
−
−
=
)
(
ˆ
.
)
(
ˆ
)
(
ˆ
s
i
s
s
i
s
i
s
k
i
c
(5)
−
−
=
)
(
ˆ
.
)
(
ˆ
)
(
ˆ
s
i
s
s
i
s
i
s
k
i
c
(
6)
Fig
ure
3
giv
es
the circ
uit diag
ram of
the
m
ulti
var
ia
ble
filt
er d
esc
ribe
d by
(
5) an
d (6).
Figure
3. Ci
rcui
t
of
t
he
m
ulti
va
riable filt
er
(
M
F
V)
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8
694
In
t J
P
ow
Ele
c
&
Dr
i
S
ys
t
,
V
ol
.
1
1
, N
o.
3
,
Se
ptembe
r
2020
:
14
59
–
14
67
1462
Th
us
,
the
sel
ect
ive
identific
a
ti
on
of
harmo
ni
c
ref
ere
nce
c
urre
nts
in
a
t
hr
e
e
-
phase
c
urre
nt
sy
ste
m
is
done
directl
y
on
the
Co
nc
ordi
a
axis,
it
is
suf
fici
ent
to
know
their
fr
e
quenc
y
a
nd
di
recti
on
of
direct
or
re
ver
se
pro
pag
at
io
n
[
3
].
I
n
our
stu
dy
,
we
ha
ve
ide
nt
ifie
d
tw
o
ha
rm
on
ic
s
,
5
th
a
nd
7
th
simult
ane
ously
.
Fig
ur
e
4
sh
ows
Bl
ock
dia
gr
am
of
sim
ultane
ous
i
den
ti
ficat
io
n
of
the
har
m
on
ic
cu
rr
e
nts
r
efere
nces
5
th
a
nd
7
th
based
mu
lt
i
-
var
ia
ble f
il
te
r
(
M
V
F)
, th
e
c
hoic
e o
f
the
pa
ra
mete
rs
K
5
=
18
and
K
7
=
16
is
done
at
b
ase
of
t
he
dia
gr
a
m of
Bod
i
n
3D
[
12
].
Figure
4. Bl
oc
k
diag
ram
of si
mu
lt
ane
ous ide
ntific
at
ion
of t
he har
monic c
urren
ts
re
fer
e
nc
es 5
th
a
nd
7
th
b
a
sed
m
ulti
-
va
riable
filt
er
(MVF)
3.3.
Ident
ific
at
i
on
of over
all ha
r
mon
ic
s
ba
s
ed
multi
-
va
ri
ab
le
f
il
ter
Tw
o
-
ph
a
se
axe
s
(α
-
β
)
def
i
ne
d
as
the
sum
of
a
f
unda
menta
l
com
pone
nt
and
a
ha
rm
on
ic
com
pone
nt
[
11
]:
+
=
+
=
h
h
i
i
i
i
i
i
1
1
(
7
)
Role
of
t
he
m
ulti
var
ia
ble
filt
er
is
to
extrac
t
the
fund
a
me
ntal
com
pone
nt
s
of
the
pulsa
ti
ng
cha
r
ge
cu
rr
e
nt,
directl
y
al
on
g
the
axes
(
−
)
.
The
n,
the
ha
rm
on
ic
com
pone
nts
of
th
e
cu
rr
e
nt
al
ong
the
a
xes
(
−
)
,
ℎ
and
ℎ
are
ob
ta
in
ed by s
ub
tract
i
ng them
on e
ac
h
a
xis
, t
he ou
t
put o
f
mu
lt
iva
riable
f
rom it
s in
pu
t
[1
3
,
1
4
].
The
in
ver
se
C
on
c
ordia
tran
s
formati
on
t
he
n
al
lows
us
to
ob
ta
in
the
t
hr
e
e
-
phase
re
fer
e
nces
of
t
he
ha
r
monic c
urre
nts:
−
−
−
=
h
h
r
e
f
c
r
e
f
c
r
e
f
c
i
i
i
i
i
2
3
2
1
2
3
2
1
3
2
3
_
2
_
1
_
0
1
(
8
)
Figure
5
prese
nts
the
diag
ra
m
f
or
t
he
glob
al
identific
at
io
n
of
the
re
fe
re
nce
c
urre
nts
ba
sed
on
t
he
te
chn
iq
ue o
f
th
e mu
lt
iva
riable
f
il
te
r.
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
ow Elec
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ys
t
IS
S
N:
20
88
-
8
694
A n
ew
appro
ac
h
to
extract
r
ef
erence c
ur
re
nt
s for m
ulti
le
vel
shun
t
a
ct
iv
e fi
lt
er
…
(
A
bd
el
k
ad
er Y
ousfi
)
1463
Fig
ure
5. Deter
minati
on
of t
he
r
efe
re
nce c
urr
ents
of
t
he
act
i
ve fil
te
r
us
i
ng the mult
ivaria
ble f
il
te
r
4.
FUZZY L
OG
IC
CUR
REN
T CO
NTR
OL
LE
R
This
m
odulati
on
te
c
hn
i
qu
e
a
lso
co
ns
ist
s
in
reducin
g
the
di
ff
ere
nces
between
t
he
re
fere
nce
cu
rr
e
nt
s
and
the
cu
rr
e
nt
s
ge
ner
at
e
d
by
t
he
act
ive
fil
te
r
an
d
that
at
const
ant
fr
e
quency.
T
he
v
a
ri
ables
in
the
e
quat
ion
can
be
easi
ly
imple
mente
d
wi
th
fu
zz
y
log
ic
w
hile
i
mpro
ving
the
pe
rfo
rma
nce
of
the
act
iv
e
filt
er
[1
5
-
1
7
]
.
Fig
ur
e
6
sho
w
fu
zz
y
lo
gic
c
on
t
ro
ll
e
r
s
ynopti
c
diag
ram
,
w
hic
h
po
ssesses
t
wo
in
pu
ts:
t
he
er
ror
(e)
,
(
e
=
ire
f
–
if)
a
nd it
s
der
i
vative
(
de)
, a
nd one
outp
ut: t
he
c
omman
d
(cd
e
)
[1
8
-
20
].
Figure
6. F
uzz
y
lo
gic
c
on
t
ro
ll
er syno
ptic dia
gr
a
m
A
f
uzz
y
s
ys
te
m is ma
de u
p o
f
f
our
esse
ntial
p
a
rts
[1
5
]:
1)
The k
nowled
ge
b
ase
consist
ing o
f
a
d
at
a
bas
e an
d
a
r
ule b
a
se.
2)
The
i
nf
e
ren
ce
sy
ste
m.
3)
Th
e
fu
zzi
ficat
ion i
nter
face.
4)
The
defuzzifi
c
at
ion
inte
rf
ace
The
f
uzz
y
lo
gi
c
current
c
ontr
oller
has
tw
o
inputs,
In
t
his
c
ase.
Cha
ng
e
na
med
of
e
rro
r
de
and
er
ror
e
on
e
ou
t
pu
t
na
med
s
.
He
re
t
he
cha
nge
of
er
ror
de
an
d
e
rro
r
e
is
the
in
put
va
riable
f
or
th
e
syst
em.
The
fu
zz
y
log
ic
c
on
t
ro
ll
er
is
cha
racteri
ze
d
as
foll
ows
:
1)
Ther
e
are
t
hree
fuzzy
sets f
or
each
of the t
wo inputs
(e, de
)
with
Gaussi
an membe
rs
hip
f
unct
ions.
2)
And
t
her
e
are f
ive fuzz
y
set
s
f
or the
outp
ut wi
th trian
gu
la
r membe
rs
hip
f
unct
ions
3)
Thir
d
i
m
plica
ti
on
s
us
i
ng
the
‘mi
nimum’
operat
or
,
in
fer
e
nce
me
cha
nis
m
ba
sed
on
f
uzzy
im
plica
tio
n
con
ta
ini
ng f
i
ve
fuzzy
rules.
4)
At last
d
e
fu
zz
yfi
cat
ion
us
i
ng the
‘cen
tr
oïd’
method.
The
li
ng
uisti
c r
ules fo
r
the
fuz
zy
lo
gic
c
urre
nt
co
nt
ro
ll
er
are a
s foll
ows:
1)
If
(e)
is zer
o
(ZE),
t
hen
(c
de)
i
s zer
o
(
ZE
).
2)
If
(e)
is
po
sit
iv
e
(P
),
t
hen
(c
de
)
is
big
posit
ive
(BP).
3)
If
(e)
is
neg
at
iv
e (
N)
,
the
n
(cde)
is
big
ne
gative
(BN).
4)
If
(e)
is zer
o
(ZE)
a
nd
(
de)
is
po
sit
ive
(P
)
, t
he
n
(cd
e
)
is
ne
ga
ti
ve
(N)
.
5)
If
(e)
is zer
o
(ZE)
a
nd
(
de)
is
neg
at
ive
(N
),
t
hen
(c
de)
is
posit
ive
(P).
Evaluation Warning : The document was created with Spire.PDF for Python.
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S
N
:
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8
694
In
t J
P
ow
Ele
c
&
Dr
i
S
ys
t
,
V
ol
.
1
1
, N
o.
3
,
Se
ptembe
r
2020
:
14
59
–
14
67
1464
Figure
7
.
F
uzz
y
ru
le
s e
sta
blishme
nt
5.
RESU
LT
S
O
F THE SI
M
U
LATION
Fo
r
cl
arit
y,
a
nd
to
a
n
un
der
st
and
i
ng
w
e
c
onsidere
d
to p
res
ent
only
the r
e
su
lt
s
we
see
i
nteresti
ng
.
T
he
gen
e
ral str
uctu
re
of
t
he
st
ud
ie
d
s
ys
te
m is
d
es
cribe
d
in
Fig
ure
8
.
It i
nclu
des
:
1.
The
t
hr
ee
-
phas
e pow
e
r netw
ork
.
2.
N
on
li
nea
r
l
oa
d (Three
-
phase
r
ect
ifie
r
).
3.
The parall
el
ac
ti
ve
filt
er
with
vo
lt
age
str
uctu
re (
t
hr
ee
-
le
vel
inv
e
rter
with
N
PC struc
ture
)
.
M
odel
s
an
d
simulat
ions
a
re
i
mp
le
me
nted
in
the
MATL
AB
/
Sim
ulin
k.
T
he
obje
ct
ive
is
to
validat
e
and
s
how
the
eff
ect
ive
ness
of
t
he
act
ive
c
ompe
ns
at
io
n
(to
ta
l
or
sel
ect
ive
)
harmo
nics
ba
sed
MVF
sel
ect
ive
com
pensat
ion i
s d
e
vote
d
t
o
th
e first t
wo h
a
r
monics
5
th
, 7
th
and both
at the
same ti
me.
Figure
8
.
Sim
ul
at
ed
sy
ste
m
Th
e Ta
ble
1.
a
r
e summariz
e
d of t
he
s
ys
te
m
paramet
ers
v
al
ue
s
Table
1
.
S
ys
te
m sim
ulati
on
pa
rameters
Para
m
eters
Nu
m
eric
al valu
es
So
u
rce
v
o
ltag
e
&
f
requ
en
cy
220
(
)
,
50
Ind
u
ctan
ce
L
s
an
d
resistan
ce
R
s
o
f
th
e
line
0
.
0115
,
1
DC lin
k
’s ind
u
ctan
ce
L
dc
,
Res
istan
ce
R
dc
0
.
2
,
10
Ind
u
ctan
ce
Lc
,
Res
istan
ce
Rc
0
.
1
,
1
Sh
u
n
t active
p
o
wer
filte
r
:
DC su
p
p
ly
vo
ltag
e
800
Res
istan
ce
R
f
,
I
n
d
u
ctan
ce
L
f
1
,
1
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
ow Elec
& Dri S
ys
t
IS
S
N:
20
88
-
8
694
A n
ew
appro
ac
h
to
extract
r
ef
erence c
ur
re
nt
s for m
ulti
le
vel
shun
t
a
ct
iv
e fi
lt
er
…
(
A
bd
el
k
ad
er Y
ousfi
)
1465
5.1.
Total co
mpen
sa
ti
on
of curr
ent
h
arm
on
ic
s
ba
se
d
on
a
m
ultiv
ariab
le
filter (
M
VF)
The
res
ults
of
numerica
l
si
m
ulati
on
of
the
sy
ste
m
Fig
ure
8
,
are
obta
ine
d
by
the
P
WM
comma
nd
of
the
in
ver
te
r,
a
nd
with
the
id
entifi
cat
ion
al
gorith
m
base
d
on
the
m
ulti
var
i
able
filt
er
t
o
i
den
ti
f
y
t
he
refe
ren
ce
harmo
nic c
urre
nts.
The
wa
veform
of
t
he
l
oad
cu
rr
e
nt
befor
e
a
pplyin
g
act
ive
f
il
te
ring
is
sho
wn
in
Fig
ur
e
9
.
T
her
e
is
a
sy
m
metri
cal
di
stortio
n
of
the
cu
rr
e
nt
ic
h
re
la
ti
ve
to
th
e
ha
lf
-
pe
rio
d
poin
t,
w
hich
mea
ns
that
t
he
m
ul
ti
ple
harmo
nics
of
2
an
d
3
a
re
none
xistent
in
the
s
pectr
um
of
,
and
t
hat
onl
y
th
os
e
of
ra
nk
(
6h
±
1
)
are
pr
ese
nt,
t
his is
confir
me
d b
y
t
he
s
pectr
um
of
(
Fig
ur
e
10)
.
Af
te
r
a
pp
l
ying
the
pro
posed
act
ive
filt
er
pa
rall
el
,
there
is
a
mar
ke
d
im
prov
e
ment
in
t
he
sh
a
pe
of
as
s
how
n
in
Fi
gure
11.T
he
fa
ct
that
has
rec
ov
e
re
d
it
s
si
nuso
idal
sh
a
pe;
t
his
is
c
onfi
rme
d
b
y
th
e
s
pectr
um
of
(
Fig
ur
e
12)
.
Re
assur
e
s
us
that
the
act
ive
f
il
te
r
has
gen
e
r
at
ed
a
c
urren
t
wh
ic
h
f
ollo
ws
it
s
ref
ere
nce
w
el
l
as
sh
ow
n
i
n
Fig
ure
13
.
T
he
disto
rtion
rate
of
t
he
main
s
c
urre
nt
is
imp
r
ov
e
d
s
o
t
hat
the
T
H
D
goes
fro
m
30.
84%
befor
e
filt
erin
g
to
0.5
1%
a
fter
filt
erin
g.
T
he
harmo
nic
spe
c
tra
of
t
he
c
urre
nts
(
Fi
gure
12)
justi
fy
t
he
pos
it
ive
beh
a
vior
of
the
act
ive paral
le
l fil
te
ring
.
Figure
9. Loa
d
cu
rr
e
nt b
e
f
or
e
com
pensat
ion
i
ch
Figure
10.
Harmo
nic
S
pectr
um o
f
l
oad cu
rr
e
nt
i
ch
befor
e
compe
nsa
ti
on
Figure
11
.
S
up
ply
c
urre
nt w
a
veform
i
s
afte
r
com
pensat
ion
Figure
1
2
.
Harmo
nic s
pectr
um o
f
s
uppl
y
c
urre
nt
i
s
after c
ompe
ns
a
ti
on
Figure
13.
C
urren
t
i
nject
ed b
y APF
and its
r
efere
nce
with
f
uzzy lo
gic c
on
t
ro
ll
ers
0
0
.
0
2
0
.
0
4
0
.
0
6
0
.
0
8
0
.
1
-
3
0
-
2
0
-
1
0
0
10
20
30
t
(
s
)
i
c
h
(
A
)
0
0
.
0
2
0
.
0
4
0
.
0
6
0
.
0
8
0
.
1
-
4
0
-
3
0
-
2
0
-
1
0
0
10
20
30
40
t
(
s
)
i
s
(
A
)
0
0
.
0
2
0
.
0
4
0
.
0
6
0
.
0
8
0
.
1
-
2
0
-
1
5
-
1
0
-5
0
5
10
15
20
25
t
(
s
)
i
f
-
i
r
e
f
(
A
)
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8
694
In
t J
P
ow
Ele
c
&
Dr
i
S
ys
t
,
V
ol
.
1
1
, N
o.
3
,
Se
ptembe
r
2020
:
14
59
–
14
67
1466
5.2.
Ha
rm
on
ic
c
om
pens
at
i
on
5
th
, 7
th
of
th
e l
oad c
urren
t
b
ase
d on
a
m
ulti
va
ri
ab
le
filter
(MVF
)
The
wa
veform
of
the
loa
d
c
urre
nt
befor
e
ap
ply
in
g
act
ive
f
il
te
ring
is
sho
wn
in
Fig
ur
e
14
.
The
re
is
a
sy
m
metri
cal
di
stortio
n
of
the
cu
rr
e
nt
ic
h
re
la
ti
ve
to
th
e
ha
lf
-
pe
rio
d
poin
t,
w
hich
mea
ns
that
t
he
m
ul
ti
ple
harmo
nics
of
2
a
nd
3
are
none
xistent
i
n
t
he
s
pectr
um
of
,
an
d
that
only
th
os
e
of
ra
nk
(
6
ℎ
±
1
)
are
pr
ese
nt,
t
his is
confirme
d b
y
t
he
s
pectr
um
of
(
Fig
ur
e
1
5
).
The
res
ults
of
simulat
ion
s
ob
ta
ined
by
the
mu
lt
i
-
va
riable
filt
er
met
hod
c
le
arly
sho
w
t
he
ef
fici
enc
y
of
sel
ect
ive
act
iv
e
pa
rall
el
filt
e
r
ing
,
this
a
pp
ea
red
on
the
im
pro
veme
nt
of
t
he
wa
ve
form
of
the
net
w
ork
c
urren
t
after
th
e
filt
ering
of
the
desir
ed
ha
rm
onic
s
(
5,
7)
see
Fig
ur
e
17.
Ta
b
le
2.
Gives
t
he
dist
ort
ion
rate
of
i
s
as
a
functi
on
of
t
he har
monics el
i
minate
d
We
ha
ve
set
up
t
he
pri
ncip
le
of
ext
racti
ng
the
har
m
onic
currents
to
be
co
mp
e
ns
at
ed
by
the
mu
lt
ivaria
ble
filt
er
method.
The
res
ults
of
sim
ulati
ons
ob
ta
ine
d
cl
ea
rly
assess
t
he
eff
ect
ive
ness
of
this
te
chn
iq
ue.
T
he
a
bili
ty
of
this
te
c
hn
i
qu
e
com
pen
sat
e
for
t
he
ha
rm
on
i
cs
desire
d
f
or
the
c
urren
t
l
oad
i
s
dem
onstrat
ed
by
rate
of
dist
or
ti
on
a
fter
filt
ering
of
the
s
ource
c
urre
nt,
the
maj
or
ad
van
ta
ge
this
typ
e
of
filt
ering
is
to minimize
the
e
nerg
y
sup
plied
by
t
he
act
ive paral
le
l
f
il
te
r
on
the
one h
an
d
a
nd
t
o
co
m
pen
s
at
e
fo
r
the m
os
t
harmf
ul h
a
rm
onic
s i
nd
i
viduall
y
a
nd sim
ultan
e
ou
s
ly on
t
he othe
r han
d
Table
2.
T
he
harm
on
ic
di
sto
rtion
rate
of
t
he source c
urre
nt
i
s
by the
mu
lt
iva
r
ia
ble f
il
te
r
The h
ar
m
o
n
ics to
compen
sa
te
0
(before
filter
in
g
)
Total h
ar
m
o
n
ic (
a
f
ter
filt
ering
)
C
o
m
p
en
satio
n
of harm
o
n
ics
(5, 7)
Cu
rr
en
t dis
to
rtion
r
ate
(T
HD
%)
3
0
.84
0
.51
1
5
.75
Figure
14
.
L
oa
d
c
urren
t
be
for
e compe
ns
at
io
n
i
ch
Figure
15.
Harmo
nic S
pectr
um o
f
l
oad cu
rr
e
nt
i
ch
befor
e
compe
nsa
ti
on
Figure
16.
Sup
ply
c
urre
nt w
a
veform
i
s
a
fter
el
imi
nation of
5
th
a
nd
7
th
ha
r
monic
Figure
1
7.
Harmo
nic s
pectr
um o
f
s
uppl
y
c
urre
nt
i
s
afte
r
com
pensat
ion
Figure
18.
C
urren
t i
nject
ed b
y APF
and its
r
efere
nce
with
f
uzzy lo
gic c
on
t
ro
ll
ers
0
0
.
0
2
0
.
0
4
0
.
0
6
0
.
0
8
0
.
1
-
3
0
-
2
0
-
1
0
0
10
20
30
t
(
s
)
i
c
h
(
A
)
0
0
.
0
1
0
.
0
2
0
.
0
3
0
.
0
4
0
.
0
5
0
.
0
6
0
.
0
7
0
.
0
8
0
.
0
9
0
.
1
-
3
0
-
2
0
-
1
0
0
10
20
30
t
(
s
)
i
s
(
A
)
0
0
.
0
1
0
.
0
2
0
.
0
3
0
.
0
4
0
.
0
5
0
.
0
6
0
.
0
7
0
.
0
8
0
.
0
9
0
.
1
-
2
0
-
1
5
-
1
0
-5
0
5
10
15
20
t
(
s
)
i
f
-
i
r
e
f
(
A
)
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
ow Elec
& Dri S
ys
t
IS
S
N:
20
88
-
8
694
A n
ew
appro
ac
h
to
extract
r
ef
erence c
ur
re
nt
s for m
ulti
le
vel
shun
t
a
ct
iv
e fi
lt
er
…
(
A
bd
el
k
ad
er Y
ousfi
)
1467
6.
CONCL
US
I
O
N
We
can
c
on
cl
ude
that;
t
he
pa
rall
el
act
ive
filt
er
ca
n
be
c
ompen
sat
ed
ha
rm
on
ic
s
gr
i
d
c
omplet
el
y
a
n
d
ind
ivi
du
al
l
y.
T
he
M
VF
i
d
e
ntific
at
ion
met
hod
is
ve
ry
e
ff
e
c
ti
ve
to
extract
the
ha
rm
on
ic
r
efere
nces
a
nd
easy
impleme
ntati
on
.
The
i
de
ntific
at
ion
of
harmo
nics
does
not
re
qu
i
re
a
c
on
t
rary
PL
L
c
ircuit
pq
a
nd
dq
.In
a
mu
lt
ivaria
ble
f
il
te
r,
we
ca
n
re
du
ce
the
num
be
r
of
e
xtracti
on
filt
ers
t
o
ob
t
ai
n
sel
ect
ive
c
ompen
sat
ion,
c
on
t
rary
to
the
e
xtracti
on
meth
ods
pq
and
dq
.
T
he
MVF
te
ch
nique
al
lows
us
to
se
le
ct
ively
or
c
omplet
el
y
c
omp
ensate
harmo
nics
i
n
t
he
netw
ork
.
T
he
MVF
te
ch
ni
qu
e
al
lo
ws
us
t
o
c
ompe
ns
at
e
harmo
nics
dist
or
te
d
a
nd
unba
la
nced
netw
o
r
k v
oltag
e re
gime.
REFERE
NCE
S
[1]
D.Ould
Abdesla
m,
P
.
W
ira,
D.
F
li
eller
,
J.
Merc
k
l
é,
“
Une
nouvelle
appr
oc
he
n
eur
o
mi
métique pour l'ide
nt
ifica
t
ion
et
la
com
p
ensa
ti
o
n
des
h
arm
on
i
ques
dans
le
s
sys
tè
me
s
é
lectr
i
ques
”
,
Inte
rnat
i
onal
Conf
ere
nc
e
on
Elec
tric
al
Engi
ne
ering
and
it
s
Appl
i
cat
ions
,
Sidi
B
el
-
Abbes,
Alger
i
a, 2006.
[2]
Y
P
Obulesu
,
“Cont
rol
Stra
te
gy
for
Three
Phase
Shunt
Acti
ve
Pow
er
Filt
er
with
Minim
um
Curr
en
t
Mea
sure
me
n
ts”,
Inte
rnational
Jo
urnal
of
Elec
tri
c
al
and
Computer
Engi
n
ee
ring
(IJ
ECE
)
,
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1
,
No
1,
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es
31
-
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,
2011.
[3]
N.
Bruy
ant
,
“
Etude
et
co
mman
de
g
éné
r
al
isé
es
de
f
il
tr
es
actif
s
par
allèles,
co
mp
ensa
ti
on
glob
al
ou
sél
ective
d
es
har
moni
qu
es,
r
é
gim
e
équilibré o
u
désé
qui
li
bré
”
.
Doctoral
th
es
i
s
,
l'uni
ver
sit
é
d
e
N
ant
es,
Franc
e, 19
99.
[4]
Abdus
al
am
,
M.
,
Poure,
P.
and
Saada
t
e,
S.
“
Ha
rdware
im
p
le
m
e
nta
ti
on
o
f
a
thr
ee
-
phase
a
ctive
fi
lt
er
sys
tem
with
har
monic
isola
t
i
on
base
d
on
sel
f
-
tuni
ng
filter
”
,
39th
I
EE
E
Pow
er
E
le
c
tronic
s
S
pec
ia
li
sts
Conf
e
renc
e
,
Isl
and
of
Rhodes,
Gre
ec
e
,
2008.
[5]
Mesbahi,
N
.
,
Ou
ari
,
A.,
Ould
Ab
desla
m
,
D.
,
Dj
a
ma
h,
T
.
and
Om
ei
ri
,
A.
“Dir
ec
t
p
ower
co
ntro
l
of
shunt
active
filte
r
using
high
s
el
e
c
ti
vit
y
fi
lt
er
(HS
F)
under
d
istorted
or
unbalanc
e
d
conditions”
,
E
le
c
tric
Powe
r
S
yste
ms
R
ese
arch
,
Vol.
108
,
pp
.
113
–
123,
2014.
[6]
N.
Bruy
ant
,
“
Etude
et
co
mman
de
g
éné
r
al
isé
es
de
f
il
tr
es
actif
s
par
allèles,
co
mp
ensa
t
ion
glob
al
ou
sél
ective
d
es
har
moni
qu
es,
r
é
gim
e
équilibré o
u
désé
qui
li
bré
”,
Doctoral
th
es
i
s
,
l'uni
ver
sit
é
d
e
N
ant
es,
Franc
e, 19
99.
[7]
M.
C.
B
enha
bi
b
and
S.
Sa
adate
,
“A
New
To
pology
for
a
Modular
Ac
ti
ve
Pow
er
Filt
er
”,
IE
EE
ISI
,
20
-
23
,
Dubrovnik,
Cro
a
t
ia,
2005
.
[8]
S.
Chenna
i
,
M
-
T
.
Ben
chouia
,
A
.
Goléa,
“H
arm
o
nic
Curre
n
t
Com
pensa
ti
on
b
ase
d
on
Thre
e
-
phase
Thre
e
-
le
v
el
Shu
nt
Acti
ve
Fil
te
r
usi
ng
Fuzzy
Log
ic
Curre
nt
Controll
er”
Journal
of
E
le
c
tric
al
Eng
ineering
&
Te
chnology
,
Vol.
6
,
No.
5,
pp
.
595
-
604
,
2011.
[9]
Cheng
-
I
Chen
a
nd
Yeong
-
Chin
Chen,
“Com
par
a
ti
ve
Study
of
H
arm
oni
c
and
Int
er
har
moni
c
Est
i
ma
ti
on
Methods
for
Stationery
an
d
Time
-
Vary
ing
Signal
s,”
IE
EE
Tr
ansacti
ons
on
Industrial
E
le
c
tronic
s
,
Vol
.
61,
No.
1,
pp.
397
–
404,
2014
.
[10]
S.
Hong
-
Seok,
P
.
Hyun
-
Gyu,
N
.
Kw
anghe
e,
“
An
insta
nta
n
eous
ph
ase
ang
le
detec
tion
al
gor
it
hm
un
der
unba
la
n
ce
d
li
ne
voltage
con
dit
ion
”
,
in
:
I
EE
E
30th Annual
Po
wer
Elec
troni
cs
Spec
ia
li
st Con
fer
enc
e PE
SC’99
,
vol.
1
,
Au
,
1999
.
[11]
Scok,
S.H.
,
“
C
ontrol
Sch
em
e
for
PWM
Con
ver
te
r
and
Pha
se
Angle
Estim
at
ion
Algorit
h
m
under
Volta
g
e
Unbala
nc
ed
and
/or
Sag
Cond
it
i
on
”
,
PhD
in
E
le
c
tronic
and
E
le
c
tric
al
Engi
n
e
ering
,
Univ
ersity
of
Pos
te
c
ch,
Republ
ic of
Korea
,
South,
2001.
[12]
La
scu,
C
.
,
As
iminoaei,
L
.
,
Bl
aa
b
je
rg,
F.
,
Bo
ldea,
I.,
“
High
per
for
ma
nc
e
cur
ren
t
c
ontrol
ler
for
se
l
ec
t
ive
har
moni
c
com
pensa
ti
on
in
active
power
filt
ers
”,
Proc. of OPTIM’06
,
Vol
.
1
,
pp
.
205
-
212T
,
2006.
[13]
P.
Thi
rumoor
thi,
Rahe
n
i
T
.
D.
“Ada
pti
v
e
Met
hod
f
or
Pow
er
Quali
ty
I
mprov
em
en
t
through
Minim
izati
on
of
Harm
onic
s
Us
ing
Artif
ic
i
al
Int
el
l
ige
nc
e”
,
In
te
rnat
ional
Journal
of
Powe
r E
lectroni
cs
and
Dr
iv
e
Sys
te
ms
(IJ
PE
DS
)
,
Vol.
8
,
No.
1
,
p
p.
470
-
482
,
2017
.
[14]
K.
Kubo,
K.
Sakai
,
“
Fe
edf
or
ward
vol
ta
ge
c
ompe
nsa
ti
on
fo
r
digita
l
ac
t
ive
filter
using
fr
eque
ncy
dom
ain
dec
omposition
”
,
EPE’97
,
Trond
hei
m
,
Vol
.
4,
pp.
786
-
791.
1997.
[15]
N.
Gounden,
S.
Pete
r,
H.
Nal
la
n
dula
,
and
S.
Krit
higa
,
“Fuzz
y
log
ic
con
trol
l
er
wi
t
h
MP
PT
using
line
-
commutated
inve
rt
er
for
thr
ee
-
phase
grid
-
con
nec
t
ed
photovo
ltaic sys
te
ms
”
,
R
e
newabl
e
Ene
r
gy
,
Vol.
34,
pp.
909
–
915,
2009
.
[16]
M.
Ham
ee
d
,
B
.
Das,
and
V.
Pan
t,
“A
sel
f
-
tuni
ng
fuz
zy
PI
cont
rol
le
r
for
TCSC
to
im
prove
power
s
ystem
st
abi
l
it
y
”
,
El
e
ct
ric
Pow
er
S
yste
ms
Re
sear
ch
,
78
,
pp
.
1726
–
17
35,
2008
.
[17]
G.
K.
Singh
,
A
.
k.
Singh
and
R.
Mitr
a,
“A
si
mpl
e
fuz
zy
log
i
c
base
d
robust
ac
t
ive
pow
er
f
ilter
for
har
monics
mi
nimization
un
der
ran
do
m loa
d
var
iation,”
El
e
ctr
ic
Pow
er
Syst
e
ms
Re
search
,
Vol.
77
,
pp
.
1101
–
1
111,
2007
.
[18]
Mridul
Jha.
S.P.
Dubey,
“N
eur
o
Fuzzy
base
d
Co
ntrol
ler
for
a
Th
ree
Phase
Four
Wi
re
Shunt
Active
Pow
er
Filt
er”
,
Inte
rnational
Jo
urnal
of Powe
r
El
e
ct
ronics
and
Dr
iv
e
Syst
ems (I
JP
EDS)
,
Vol
1
No 2,
pp
.
148
-
15
5,
2011
.
[19]
B.
-
R.
Li
n,
T
.
-
Y.
Yang,
“T
hr
ee
-
l
eve
l
voltage
-
source
inv
ert
er
for
shunt
a
ct
i
ve
filter
”,
I
EE,
El
e
ct
ri
c
Pow
e
r
Appl
ic
a
ti
ons
,
pp.
744
–
751,
Nov.2
004.
[20]
K.
Selv
akum
ar1
,
et
al.,
“Hyste
r
e
sis
Control
3
-
L
eve
l
SI
-
NP
C
Inve
rte
r
with
W
in
d
Energy
Sys
tem,
”
Int
ernati
on
al
Journal
of
Power
El
e
ct
ronics
an
d
Dr
iv
e
S
yste
m
(
IJP
EDS)
,
Vol.
8,
No.
4
,
pp
.
1764
-
1770,
2017
.
Evaluation Warning : The document was created with Spire.PDF for Python.