I
n
d
on
e
s
ian
Jou
r
n
al
of
E
lec
t
r
ical
E
n
gin
e
e
r
in
g
a
n
d
Com
p
u
t
e
r
S
c
ience
Vol.
25
,
No.
3
,
M
a
r
c
h
2022
,
pp.
1236
~
1245
I
S
S
N:
2502
-
4752,
DO
I
:
10
.
11591/i
jee
c
s
.
v
25
.i
3
.
pp
123
6
-
1245
1236
Jou
r
n
al
h
omepage
:
ht
tp:
//
ij
e
e
c
s
.
iaes
c
or
e
.
c
om
T
h
e
h
a
r
m
o
n
ic
r
e
d
u
c
t
io
n
t
e
c
h
n
iq
u
e
s i
n
sh
u
n
t
ac
t
iv
e
p
o
w
e
r
f
il
t
e
r
w
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e
n
i
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e
gr
a
t
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it
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c
o
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io
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gy so
u
r
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e
s
Kam
b
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p
a
t
i
Ve
n
k
a
t
a
Govard
h
an
Rao
1
,
M
all
i
gu
n
t
a
Ki
r
an
Ku
m
ar
2
1
D
e
pa
r
tm
e
nt
of
E
le
c
tr
ic
a
l
a
nd E
le
c
tr
oni
c
s
E
ngi
ne
e
r
in
g,
S
c
hol
a
r
in
E
le
c
tr
ic
a
l
a
nd E
le
c
tr
oni
c
s
E
ngi
ne
e
r
in
g
K
one
r
u L
a
ks
hma
ia
h E
duc
a
ti
on F
ounda
ti
on, Va
dd
e
s
w
a
r
a
m, Andhr
a
P
r
a
de
s
h, I
ndi
a
2
D
e
pa
r
tm
e
nt
of
E
le
c
tr
ic
a
l
a
nd E
le
c
tr
oni
c
s
E
ngi
ne
e
r
in
g,
F
a
c
ul
ty
in
E
le
c
tr
ic
a
l
a
nd E
le
c
tr
oni
c
s
E
ngi
ne
e
r
in
g
K
one
r
u L
a
ks
hma
ia
h E
duc
a
ti
on F
ounda
ti
on, Va
dde
s
w
a
r
a
m, Andhr
a
P
r
a
de
s
h, I
ndi
a
Ar
t
icle
I
n
f
o
AB
S
T
RA
CT
A
r
ti
c
le
h
is
tor
y
:
R
e
c
e
ived
S
e
p
27
,
2021
R
e
vis
e
d
De
c
9
,
2021
Ac
c
e
pted
J
a
n
11
,
202
2
T
h
e
ar
t
i
c
l
e
co
v
ers
t
h
e
c
o
n
t
ro
l
t
ec
h
n
i
q
u
es
o
f
s
h
u
n
t
act
i
v
e
fi
l
t
er
s
u
s
i
n
g
s
w
i
t
c
h
i
n
g
d
e
v
i
ce
s
u
s
i
n
g
art
i
f
i
ci
a
l
n
eu
ra
l
n
et
w
o
r
k
(A
N
N
)
T
h
e
o
ry
.
T
h
e
b
a
s
i
c
i
d
ea
i
s
t
o
ach
i
e
v
e
p
erfec
t
d
i
s
t
u
rb
a
n
ce
mi
n
i
mi
za
t
i
o
n
i
n
b
o
t
h
s
t
ead
y
an
d
t
ran
s
i
e
n
t
s
t
at
e
s
.
T
h
e
p
a
p
er
t
al
k
s
ab
o
u
t
a
fo
u
r
-
l
eg
g
ed
co
n
v
ert
er
w
i
t
h
a
v
o
l
t
ag
e
s
o
u
rce
t
h
at
can
ad
j
u
s
t
fo
r
b
i
as
e
d
cu
rren
t
s
an
d
h
armo
n
i
c
el
emen
t
s
cau
s
ed
b
y
non
-
l
i
n
ear
l
o
a
d
s
.
A
s
h
u
n
t
co
n
n
ect
e
d
act
i
v
e
fi
l
t
er
i
s
u
s
ed
t
o
mi
n
i
m
i
s
e
h
armo
n
i
c
c
u
rren
t
s
.
T
h
e
n
ew
p
ro
p
o
s
ed
A
N
N
c
o
n
t
ro
l
l
er
fo
r
t
h
e
i
m
p
ro
v
emen
t
o
f
p
ercen
t
t
o
t
a
l
h
armo
n
i
c
d
i
s
t
o
r
t
i
o
n
(
T
H
D
)
i
s
i
n
co
mp
ari
s
o
n
.
T
h
e
en
t
i
re
p
o
w
er
fi
l
t
er
c
o
n
ce
p
t
i
s
b
a
s
ed
o
n
a
M
A
T
L
A
B
-
m
o
d
e
l
ed
w
i
t
h
A
N
N
co
n
t
r
o
l
l
er.
T
h
e
p
r
o
p
o
s
e
d
ci
rcu
i
t
i
n
t
h
i
s
res
earc
h
i
s
s
t
u
d
i
ed
u
n
d
er
v
ari
o
u
s
o
p
erat
i
n
g
s
i
t
u
a
t
i
o
n
s
a
n
d
s
i
m
u
l
a
t
ed
,
d
em
o
n
s
t
ra
t
i
n
g
t
h
e
s
y
s
t
em's
p
o
t
en
t
i
al
.
K
e
y
w
o
r
d
s
:
Ac
ti
ve
powe
r
f
il
te
r
AN
N
c
ontr
oll
e
r
Ha
r
moni
c
c
ur
r
e
nt
r
e
duc
ti
on
M
a
xim
um
powe
r
point
tr
a
c
king
Voltage
s
our
c
e
c
onve
r
ter
with
f
our
leg
ope
r
a
ti
on
Th
i
s
i
s
a
n
o
p
en
a
c
ces
s
a
r
t
i
c
l
e
u
n
d
e
r
t
h
e
CC
B
Y
-
SA
l
i
ce
n
s
e.
C
or
r
e
s
pon
din
g
A
u
th
or
:
M
a
ll
igunt
a
Kir
a
n
Kuma
r
De
pa
r
tm
e
nt
of
E
lec
tr
ica
l
a
nd
E
lec
tr
onics
E
nginee
r
i
ng,
F
a
c
ult
y
in
E
lec
tr
i
c
a
l
a
nd
E
lec
tr
onics
E
ng
inee
r
i
ng
Kone
r
u
L
a
ks
hmaia
h
E
duc
a
ti
on
F
ounda
ti
on
Va
dde
s
wa
r
a
m,
Guntur
-
522502,
Andhr
a
P
r
a
de
s
h,
I
ndia
E
mail:
ki
r
a
n.
malli
gunta@
gmail
.
c
om
1.
I
NT
RODU
C
T
I
ON
A
lar
ge
numbe
r
o
f
domes
ti
c
a
nd
bus
ines
s
e
lec
tr
ica
l
loads
ha
ve
r
e
c
e
ntl
y
be
e
n
f
us
e
d
int
o
f
a
c
il
it
y
gr
ids
.
I
t
c
a
us
e
s
pr
oblems
with
powe
r
qua
li
ty
[
1
]
,
[
2]
.
T
hy
r
is
tor
r
e
c
ti
f
ier
s
,
whe
n
c
onne
c
ted
to
the
f
a
c
i
li
ty
gr
id,
c
r
e
a
te
many
ha
r
moni
c
s
f
or
the
gr
owing
number
of
loads
that
do
not
r
e
s
pe
c
t
ohm's
law
,
s
uc
h
a
s
diodes
.
Ha
r
moni
c
s
c
r
e
a
te
volt
a
ge
dis
tor
ti
ons
,
g
r
id
los
s
e
s
,
a
nd
poor
load
ope
r
a
ti
on
a
s
a
r
e
s
ult
of
thi
s
.
As
a
r
e
s
ult
,
I
E
E
E
519
s
tanda
r
ds
[
3
]
a
r
e
r
e
c
omm
e
nde
d
a
t
the
g
r
id
to
mana
ge
ha
r
moni
c
c
ur
r
e
nts
c
a
us
e
d
by
r
a
pid
load
v
a
r
iations
.
T
he
s
hunt
powe
r
f
il
te
r
(
S
P
F
)
is
made
up
of
s
pe
c
ially
tuned
L
C
a
nd
high
ba
nd
pa
s
s
f
il
ter
s
e
tt
ings
.
T
he
s
e
a
r
e
s
im
ple
to
us
e
a
nd
pr
ovide
a
c
os
t
-
e
f
f
e
c
ti
ve
s
olut
ion
f
or
ha
r
moni
c
s
.
F
u
r
ther
mo
r
e
,
the
e
f
f
e
c
ti
ve
ne
s
s
of
s
hunt
f
il
ter
s
is
mos
tl
y
de
ter
m
ined
by
g
r
id
im
pe
da
nc
e
,
whic
h
mi
ght
c
a
us
e
s
hu
nt
r
e
s
ona
nc
e
phe
nomena
with
the
gr
id,
whic
h
is
not
de
s
ir
a
ble.
Ha
r
moni
c
r
e
duc
ti
on
r
e
s
ult
s
in
higher
e
f
f
icie
nc
y
of
powe
r
s
e
mi
c
onduc
tor
de
vice
s
[
4]
,
[
5]
.
T
he
vo
lt
a
ge
s
our
c
e
inver
ter
is
made
up
of
the
s
hunt
a
c
ti
ve
powe
r
f
il
ter
(
S
APF
)
volt
a
g
e
s
our
c
e
inver
ter
(
VSI
)
.
Voltage
dis
tur
ba
nc
e
s
in
the
pow
e
r
s
ys
tem
a
r
e
c
a
us
e
d
by
ir
r
e
gular
powe
r
ge
ne
r
a
t
ion.
T
he
a
lgor
it
hmi
c
c
ont
r
ol
method
us
ing
a
r
ti
f
icia
l
ne
ur
a
l
ne
twor
k
(
AN
N)
a
nd
pr
opo
r
ti
ona
l
int
e
gr
a
l
(
P
I
)
c
ont
r
oll
e
r
s
is
e
xplaine
d
in
th
is
wor
k
.
A
P
F
s
,
li
ke
P
I
(
f
o
r
li
ne
a
r
a
na
lys
is
)
or
p
r
e
dictive
(
non
-
li
ne
a
r
)
c
ont
r
oll
e
r
s
,
a
r
e
ge
ne
r
a
ll
y
c
ontr
oll
e
d
a
nd
pa
r
t
icula
r
.
I
n
ge
ne
r
a
l,
p
r
e
dictive
c
o
ntr
oll
e
r
s
a
r
e
c
los
e
to
the
c
ur
r
e
nt
powe
r
s
ys
tem.
T
h
e
c
ur
r
e
nt
methods
de
mons
tr
a
te
how
to
incr
e
a
s
e
APF
pe
r
f
or
manc
e
unde
r
dyna
mi
c
s
e
tt
ings
.
I
t
will
be
c
a
pa
ble
of
pr
e
c
is
e
ly
e
xe
c
uti
ng
the
r
e
f
e
r
e
nc
e
s
ignal
f
or
the
c
ur
r
e
nt
pa
r
a
mete
r
whi
le
maintaining
di
r
e
c
t
c
ur
r
e
nt
(
DC
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
ndone
s
ian
J
E
lec
E
ng
&
C
omp
S
c
i
I
S
S
N:
2502
-
4752
T
he
har
monic
r
e
duc
ti
on
tec
hniques
in
s
hunt
ac
ti
v
e
pow
e
r
fi
lt
e
r
…
(
K
ambham
pati
V
e
nk
ata
Gov
ar
dh
an
R
ao)
1237
volt
a
ge
[
5]
,
[
6]
.
T
his
c
ont
r
ol
a
ppr
oa
c
h
il
lus
tr
a
t
e
s
how
to
ha
ndle
mul
t
ivar
iate
f
e
a
tur
e
s
in
e
lec
tr
ic
dr
ive
a
ppli
c
a
ti
ons
.
I
t
pr
ovides
a
s
tr
a
ight
f
o
r
wa
r
d
wa
y
to
c
ompens
a
te
f
or
de
a
d
ti
me
a
nd
r
e
plac
e
puls
e
width
modul
a
ti
on
(
P
W
M
)
.
T
he
a
dva
ntage
of
thi
s
a
ppr
oa
c
h
is
that
it
is
s
uit
a
ble
f
o
r
a
ll
AP
F
a
ppli
c
a
ti
ons
be
c
a
us
e
the
output
pa
r
a
mete
r
s
a
r
e
known
.
2.
M
ODE
L
OF
A
F
OUR
-
L
E
G
P
WM
-
VI
CO
NV
E
RT
E
R
T
he
non
-
tr
a
dit
ional
e
ne
r
gy
pr
oduc
ing
s
ys
tem
i
s
de
picte
d
in
F
ig
ur
e
1,
a
long
with
a
typi
c
a
l
dis
tr
ibut
ion
s
ys
tem.
I
t
c
ons
is
ts
of
s
e
ve
r
a
l
non
-
c
onve
nti
ona
l
e
ne
r
gy
p
r
oduc
ti
on
un
it
s
,
s
uc
h
a
s
wind
a
nd
s
olar
e
ne
r
gy,
a
nd
dis
tr
ibut
e
s
powe
r
c
r
e
a
ted
to
s
mall
bus
ines
s
e
s
a
nd
homes
[
6]
,
[
7]
.
B
a
tt
e
r
y
ba
nks
mus
t
be
e
mpl
oye
d
f
or
long
-
ter
m
e
ne
r
gy
s
tor
a
ge
.
Alte
r
na
ti
ng
c
ur
r
e
nt
AC
/AC
a
nd
DC
/AC
s
tatic
puls
e
width
modul
a
ti
on
c
onve
r
ter
s
a
r
e
us
e
d
in
thes
e
gr
ids
[
8]
.
T
he
s
e
c
onve
r
ter
s
e
mpl
oy
the
maximum
pow
e
r
point
tr
a
c
king
(
M
P
P
T
)
a
ppr
oa
c
h
to
ge
t
gr
e
a
t
e
f
f
icie
nc
y
f
r
om
s
olar
a
nd
wind
e
ne
r
gy
[
9]
.
S
AP
F
is
c
onne
c
ted
to
point
of
c
omm
on
c
oupli
ng
(
P
C
C
)
in
a
s
hunt
c
onf
igu
r
a
ti
on
to
r
e
duc
e
c
ur
r
e
nt
wa
ve
dis
tur
ba
nc
e
s
a
nd
im
ba
l
a
nc
e
.
F
or
the
ba
s
is
or
de
r
de
picte
d
in
F
ig
ur
e
2,
S
APF
c
ons
is
ts
of
a
P
W
M
c
onve
r
ter
a
nd
a
ha
r
moni
c
f
il
ter
[
10]
,
[
11]
.
I
t
ha
s
a
n
e
quivale
nt
im
pe
da
nc
e
of
Z
s
,
a
n
im
pe
da
nc
e
of
Z
f
a
t
the
output
r
ippl
e
f
il
ter
,
a
nd
a
n
i
mpeda
nc
e
of
Z
L
a
t
the
load
ter
mi
na
ls
.
F
igur
e
1.
P
a
r
a
ll
e
l
c
onne
c
ted
powe
r
f
il
ter
f
or
hybr
id
e
ne
r
gy
ge
ne
r
a
ti
on
O
e
s
a
e
s
b
e
s
c
i
s
a
i
s
b
i
s
c
i
L
a
i
L
b
i
L
c
L
L
L
R
R
R
i
F
a
i
F
b
i
F
c
U
a
U
b
U
c
S
a
S
b
S
c
S
a
S
b
S
c
*
*
*
u
d
c
+
-
N
o
n
l
i
n
e
a
r
L
o
a
d
P
N
S
h
u
n
t
A
c
t
i
v
e
P
o
w
e
r
F
i
l
t
e
r
F
igur
e
2.
F
or
two
3
-
S
APF
,
a
n
a
na
logous
c
ir
c
uit
h
a
s
be
e
n
pr
opos
e
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2502
-
4752
I
ndone
s
ian
J
E
lec
E
ng
&
C
omp
S
c
i
,
Vol.
25
,
No.
3
,
M
a
r
c
h
20
22
:
1236
-
1245
1238
T
he
s
tudy
of
the
P
W
M
c
onve
r
ter
[
12]
is
s
hown
in
F
ig
u
r
e
3
.
I
t's
c
ompar
a
ble
to
a
th
r
e
e
-
pha
s
e
c
onve
r
ter
with
the
f
ou
r
th
leg
c
onne
c
ted
to
a
ne
utr
a
l
bus
.
B
y
incr
e
a
s
ing
the
f
r
e
que
nc
y
a
t
whic
h
s
wit
c
he
s
a
r
e
tur
ne
d
on
a
nd
of
f
,
thi
s
a
r
c
hit
e
c
tur
e
e
nha
nc
e
s
the
c
ontr
ol
l
it
he
ne
s
s
a
nd
v
olt
a
ge
qua
li
ty
that
is
pr
odu
c
ti
ve
.
I
n
ter
ms
of
f
r
e
que
nc
y
of
s
witch
on
a
nd
of
f
s
tate
s
,
T
h
e
volt
a
ge
is
c
a
lcula
ted
in
x
volt
s
,
whic
h
is
de
ter
m
i
ne
d
f
r
om
the
ne
utr
a
l
point
n
.
=
−
,
=
,
,
,
(
1)
I
n
ter
ms
o
f
mathe
matica
l
a
na
lys
is
,
the
c
or
r
e
s
pondi
ng
c
ir
c
uit
is
s
hown
in
F
igu
r
e
2.
0
=
−
0
−
(
2)
W
he
r
e
R
eq
a
nd
L
eq
a
r
e
the
im
pe
da
nc
e
of
the
theve
nin
a
t
the
s
e
c
ond
por
t.
As
a
r
e
s
ult
,
uti
li
s
ing
T
he
ve
nin's
phe
nomena
,
e
quivale
nt
im
pe
da
nc
e
c
a
n
be
c
a
lcula
t
e
d
a
lgebr
a
ica
ll
y
a
s
(
3)
.
=
+
+
=
+
(
3)
T
he
im
pe
da
nc
e
e
quivale
nt
va
lue
is
omi
tt
e
d,
r
e
s
ult
ing
in
Z
L
>
>
Z
s
a
nd
a
r
e
a
c
tanc
e
li
nke
d
in
s
e
r
ie
s
va
lue
of
3
–
7%
p.
u
.
,
whic
h
is
a
pp
r
opr
iate
f
or
a
pr
a
c
ti
c
a
l
s
ys
tem.
As
a
r
e
s
ult
o
f
(
2
)
.
R
e
q
=
R
f
a
nd
L
e
q
=
Ls
+
L
f.
u
v
S
v
S
w
v
d
c
+
-
P
N
S
n
S
u
S
u
S
v
S
w
S
n
w
n
R
e
q
L
e
q
Z
e
q
V
O
V
z
n
C
d
c
F
o
u
r
-
L
e
g
I
n
v
e
r
t
e
r
i
o
F
igur
e
3.
P
uls
e
width
modul
a
ti
on
f
or
a
f
ou
r
-
leg
c
ir
c
uit
with
two
leve
ls
3.
CU
RR
E
NT
CONT
RO
L
DE
VE
L
OP
M
E
N
T
WI
T
H
DI
GI
T
AL
T
E
CHNOL
OG
Y
T
he
pr
opos
e
d
c
ur
r
e
nt
c
ont
r
ol
s
tr
a
tegy
us
ing
digi
ta
l
tec
hnology
is
de
picte
d
in
F
igur
e
4.
I
t
outl
ines
a
c
ontr
ol
a
lgor
it
hm
that
is
f
e
d
int
o
a
mi
c
r
op
r
oc
e
s
s
o
r
a
s
a
n
input
.
T
o
i
ll
us
tr
a
te
ti
me
de
lay
a
nd
it
s
a
s
s
u
mpt
ions
,
dis
c
r
e
te
mathe
matics
is
us
e
d.
I
t
us
e
s
the
mos
t
s
witching
s
tr
uc
tur
a
l
inf
or
mation
a
va
il
a
ble
to
a
ppl
y
to
the
c
onve
r
ter
.
P
r
e
d
i
c
t
i
v
e
M
o
d
e
l
C
u
r
r
e
n
t
R
e
f
e
r
e
n
c
e
G
e
n
e
r
a
t
o
r
C
o
s
t
F
u
n
c
t
i
o
n
O
p
t
i
m
i
z
a
t
i
o
n
g
k
+
1
F
o
u
r
L
e
g
I
n
v
e
r
t
e
r
v
s
3
i
s
3
v
d
c
I
o
*
4
S
u
i
o
k
+
1
S
v
S
w
S
n
i
o
3
i
o
F
igur
e
4.
Digit
a
l
tec
hnology
wa
s
pr
opos
e
d
f
o
r
c
ur
r
e
nt
c
ontr
ol
Evaluation Warning : The document was created with Spire.PDF for Python.
I
ndone
s
ian
J
E
lec
E
ng
&
C
omp
S
c
i
I
S
S
N:
2502
-
4752
T
he
har
monic
r
e
duc
ti
on
tec
hniques
in
s
hunt
ac
ti
v
e
pow
e
r
fi
lt
e
r
…
(
K
ambham
pati
V
e
nk
ata
Gov
ar
dh
an
R
ao)
1239
3.
1.
Gener
at
or
o
f
c
u
r
r
e
n
t
r
e
f
e
r
e
n
c
e
T
his
is
a
unit
that
will
not
be
c
a
pa
ble
of
r
e
f
lec
ti
ng
c
ur
r
e
nt
tec
hnology,
that
is
unde
r
a
s
a
tur
a
ted
load.
T
he
s
ys
tem
volt
a
ge
s
a
nd
load
c
ur
r
e
nts
a
r
e
mea
s
ur
e
d
us
ing
thi
s
method.
As
a
r
e
s
ult
,
the
outpu
t
c
ur
r
e
nt
pr
of
il
e
of
the
s
ignals
a
t
the
ne
utr
a
l
poin
t
ter
m
inal
a
nd
the
l
oa
d
ter
mi
na
l
is
de
ve
loped.
3.
2.
M
od
e
l
o
f
p
r
e
d
ic
t
ion
I
t
f
unc
ti
ons
in
a
dis
c
r
e
te
ti
me
f
r
a
me
.
I
t's
a
c
yc
li
c
v
e
c
tor
e
qua
ti
on
that
r
e
pr
e
s
e
nts
a
f
o
r
e
c
a
s
ti
ng
model.
I
t
c
a
n
c
ons
tr
uc
t
a
s
a
mpl
e
ti
me
T
s
a
nd
a
s
s
ume
f
oll
o
wing
s
tate
s
a
t
a
ny
ins
tant
[
k
+
1]
T
s
knowing
the
f
r
e
que
nc
y
of
the
c
onve
r
ter
's
on
a
nd
of
f
pha
s
e
s
a
t
s
im
ult
a
ne
ous
kT
s
.
All
a
ppr
oxim
a
ti
ons
a
r
e
in
f
i
r
s
t
or
de
r
be
c
a
us
e
the
e
qua
ti
ons
a
r
e
in
a
s
ingl
e
o
r
de
r
r
ippl
e
f
il
ter
.
=
[
+
1
]
−
[
]
(
4)
T
he
c
ur
r
e
nt
a
t
por
t
2
a
nd
it
s
a
lgor
it
hm
c
a
lcula
ted
1
6
pos
s
ibl
e
pr
e
dicte
d
da
ta
f
r
om
(
2
)
a
nd
(
4)
.
0
[
+
1
]
=
(
[
]
−
0
[
]
)
+
(
1
−
)
0
[
]
(
5)
T
he
volt
a
ge
a
t
the
input
po
r
t,
Vo,
a
nd
the
vo
lt
a
ge
a
t
the
c
onve
r
s
ion
por
t,
V
xn
,
a
r
e
r
e
quir
e
d
to
a
nti
c
ipate
c
ur
r
e
nt
a
t
the
ou
tput
por
t,
i
o
a
t
(
k
+
1)
,
a
s
s
hown
i
n
(
5)
.
T
h
is
a
lgor
it
hm
is
us
e
d
to
de
ter
mi
ne
a
ll
s
ixt
e
e
n
va
lues
invol
ve
d
in
va
r
ious
g
r
oups
.
3.
3.
Op
t
im
izat
io
n
o
f
t
h
e
c
os
t
f
u
n
c
t
ion
T
he
16
a
nti
c
ipate
d
r
e
a
dings
f
or
i
o
[
k
+
1]
a
r
e
c
ont
r
a
s
ted
to
the
pr
e
c
e
de
nt
us
ing
a
c
os
t
f
unc
ti
on
g:
to
de
ter
mi
ne
the
be
s
t
duty
c
yc
le
f
or
the
powe
r
c
onve
r
ter
.
(
+
1
)
=
[
∗
(
+
1
)
−
(
+
1
)
]
2
+
[
∗
(
+
1
)
−
(
+
1
)
]
2
+
[
∗
(
+
1
)
−
(
+
1
)
]
2
+
[
∗
(
+
1
)
−
(
+
1
)
]
2
(
6)
T
he
output
c
u
r
r
e
nt
(
io
)
matc
he
s
the
s
tanda
r
d
c
ur
r
e
nt
(
i
*o)
whe
n
g
=
0
.
As
a
r
e
s
ult
,
the
im
p
r
ove
ment
a
im
f
o
r
the
va
lue/pr
ice
c
ombi
na
ti
on
is
to
ge
t
the
g
va
lue
a
s
c
los
e
to
z
e
r
o
a
s
pos
s
ibl
e
.
At
the
ne
xt
s
a
mpl
e
s
tate
,
the
volt
a
ge
ve
c
tor
v
x
with
the
lowe
s
t
c
os
t
f
unc
ti
on
is
c
hos
e
n
a
nd
us
e
d.
F
r
om
the
16
a
lt
e
r
na
ti
ve
f
unc
ti
on
va
lues
a
t
e
a
c
h
s
a
mpl
e
s
tate
,
the
s
witching
s
tate
that
o
f
f
e
r
s
the
lowe
s
t
pr
ice
of
g
is
c
hos
e
n.
T
he
a
lgor
it
hm
s
e
lec
ts
the
s
malles
t
s
witching
s
tate
a
nd
a
ppli
e
s
it
to
the
c
onve
r
ter
th
r
oughout
the
k
+
1
s
tage
.
4.
P
RODU
CT
I
ON
OF
CU
RR
E
NT
RE
F
E
RE
NC
E
S
I
GNAL
Wi
th
the
dq
a
ppr
oa
c
h,
the
r
e
f
e
r
e
nc
e
s
ignals
f
or
the
c
ur
r
e
nt
pa
r
a
mete
r
a
r
e
pr
ovided
a
s
input
f
r
om
the
r
e
f
e
r
e
nc
e
ge
ne
r
a
tor
.
I
t
ha
s
a
f
a
s
t
a
nd
a
c
c
ur
a
te
s
i
gna
l
tr
a
c
king
c
a
pa
c
it
y.
I
t
e
li
mi
na
tes
volt
a
ge
f
luc
tuations
,
whic
h
ha
ve
a
ne
ga
ti
ve
im
pa
c
t
on
c
ompens
a
ti
ng
pe
r
f
or
manc
e
[
13]
,
[
14]
.
F
igu
r
e
5
s
hows
the
r
e
f
e
r
e
nc
e
s
ignals
f
or
e
quivale
nt
c
ur
r
e
nts
a
t
the
load
ter
m
inal.
T
h
e
c
ur
r
e
nt
r
e
f
e
r
e
nc
e
ge
ne
r
a
tor
c
r
e
a
tes
c
ur
r
e
nt
s
i
gna
ls
to
de
c
r
e
a
s
e
c
ur
r
e
nt
im
ba
lanc
e
,
dis
tur
ba
nc
e
s
in
c
ur
r
e
nt,
a
nd
r
e
a
c
ti
ve
powe
r
.
T
he
a
ppa
r
e
nt
powe
r
a
ppli
e
d
by
a
n
a
c
ti
ve
powe
r
f
il
te
r
to
a
load
te
r
mi
na
l
is
e
xp
r
e
s
s
e
d
in
ter
ms
of
s
in(
L
)
a
nd
(
T
HD
(
L
)
)
a
s
(
7
)
.
=
√
∅
(
)
+
(
)
2
√
1
+
(
)
2
(
7)
T
he
pe
a
k
c
ur
r
e
nt
due
to
ha
r
moni
c
s
,
given
a
s
the
s
qua
r
e
of
the
f
s
,
is
the
T
HD
o
f
a
load
,
a
c
c
or
ding
to
the
(
7)
.
T
he
c
ur
r
e
nt
due
to
the
dis
tor
ti
on
c
ompone
nt
will
be
r
e
duc
e
d
to
ha
lf
of
the
c
onve
r
ter
's
on
a
nd
of
f
c
yc
le
f
r
e
que
nc
y
[
14
]
,
[
15]
.
T
he
dq
-
ba
s
e
d
a
ppr
oa
c
h
e
mpl
oys
a
r
otating
r
e
f
e
r
e
nc
e
f
r
a
me.
T
he
r
e
f
e
r
e
nc
e
s
ignals
s
in(
wt)
a
nd
c
os
(
wt)
we
r
e
c
oor
dinate
d,
a
nd
the
pha
s
e
of
the
r
e
a
c
ti
ve
c
u
r
r
e
nt
e
leme
nts
wa
s
c
h
a
nge
d
b
y
90
0
.
a
ll
of
whic
h
we
r
e
a
c
quir
e
d
f
r
om
a
s
ync
hr
onous
c
oor
dinate
s
ys
tem.
W
he
n
the
pha
s
e
locke
d
loop
P
L
L
volt
a
ge
is
tot
a
ll
y
dis
r
upted,
pur
e
s
inus
oidal
wa
ve
f
or
ms
c
a
n
be
ge
ne
r
a
ted.
W
e
c
a
n
r
e
duc
e
tr
a
c
king
e
r
r
o
r
s
a
s
we
ll
a
s
pha
s
e
volt
a
ge
unba
lanc
ing,
ha
r
mon
ics
[
16]
,
[
17]
,
whic
h
c
a
n
a
r
is
e
dur
ing
mea
s
ur
e
ment.
T
he
li
nk
be
t
we
e
n
the
im
por
tant
c
ur
r
e
nts
iL
x(
t)
(
x
=
u,
v,
w)
a
nd
their
dq
c
omponents
is
s
e
e
n
in
(
8)
(
id
a
nd
iq)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2502
-
4752
I
ndone
s
ian
J
E
lec
E
ng
&
C
omp
S
c
i
,
Vol.
25
,
No.
3
,
M
a
r
c
h
20
22
:
1236
-
1245
1240
[
]
=
√
2
3
[
−
]
[
1
−
1
2
−
1
2
0
√
3
2
−
√
3
2
]
[
]
(
8)
u
v
w
/
α
β
0
d
q
/
α
β
α
β
0
/
u
v
w
α
β
/
d
q
L
o
w
P
a
s
s
F
i
l
t
e
r
+
+
+
L
o
w
P
a
s
s
F
i
l
t
e
r
P
I
C
o
n
t
r
o
l
l
e
r
-
1
S
R
F
P
L
L
S
i
n
(
w
t
)
C
o
s
(
w
t
)
i
c
V
d
c
*
V
d
c
i
0
*
i
L
v
s
i
0
i
d
i
β
i
d
+
+
+
i
a
-
i
q
-
-
i
d
i
d
*
i
β
*
i
0
*
i
0
i
q
*
F
igur
e
5.
Us
ing
a
dq
-
ba
s
e
d
a
ppr
oa
c
h
a
s
a
c
ur
r
e
nt
r
e
f
e
r
e
nc
e
ge
ne
r
a
tor
B
e
twe
e
n
c
ur
r
e
nts
a
t
pha
s
e
a
nd
the
e
quivale
nt
AC
a
nd
DC
c
omponents
of
I
q,
ther
e
is
a
n
180
0
pha
s
e
s
hif
t.
T
o
ke
e
p
the
DC
volt
a
ge
c
ons
tant,
the
c
onve
r
ter
's
r
e
f
e
r
e
nc
e
c
ur
r
e
nt
a
nd
a
mpl
it
ude
mus
t
be
c
ha
nge
d
by
s
umm
ing
a
li
ve
ly
powe
r
r
e
f
e
r
e
nc
e
s
ignal.
I
n
pa
r
t
4.
1
,
it
will
go
thr
ough
e
ve
r
ythi
ng
in
de
tail
.
T
he
r
e
ve
r
s
e
P
a
r
k
a
nd
C
lar
k
tr
a
ns
f
or
mation,
a
s
i
ll
us
tr
a
ted
in
,
a
ids
in
the
c
onve
r
s
ion
of
id
a
nd
iq
s
ignals
to
th
r
e
e
-
pha
s
e
s
y
s
tems
(
9)
.
[
∗
∗
∗
]
=
√
2
3
[
1
√
2
1
0
1
√
2
−
1
2
√
3
2
1
√
2
−
1
2
−
√
3
2
]
×
[
1
0
0
0
−
0
]
[
0
∗
∗
]
(
9)
T
he
c
ur
r
e
nt
f
low
thr
ough
the
ne
ut
r
a
l
o
f
the
load
will
be
ba
lanc
e
d
by
ke
e
ping
the
e
quivale
nt
a
br
upt
va
lue
c
omput
e
d
f
r
om
c
ur
r
e
nts
a
t
pha
s
e
,
pha
s
e
s
hif
t
e
d
by
180
0
a
s
s
e
e
n
in
the
f
oll
owing
diagr
a
m
.
∗
=
−
(
+
+
)
(
10)
T
he
main
mer
it
of
the
c
ur
r
e
nt
ge
ne
r
a
to
r
e
xplaine
d
us
ing
a
dq
-
ba
s
e
d
method
is
th
a
t
it
a
ll
ows
the
us
e
of
a
dir
e
c
t
c
ontr
oll
e
r
with
DC
volt
a
ge
c
ontr
ol
.
T
he
main
dis
a
dva
ntage
is
that
the
dq
-
ba
s
e
d
c
ur
r
e
nt
c
oor
dinate
s
ys
tem
a
lgor
it
hm
will
not
o
r
ga
nis
e
the
c
ur
r
e
nt
r
e
f
e
r
e
n
c
e
s
e
c
ond
or
de
r
ha
r
moni
c
c
omponent
unde
r
un
ba
lanc
e
d
ope
r
a
ti
on.
T
he
a
mp
l
it
ude
o
f
the
ha
r
moni
c
ge
ne
r
a
te
d
is
de
ter
mi
ne
d
by
the
im
ba
lanc
e
d
load
c
ur
r
e
nt.
I
t
c
a
n
a
ls
o
pr
oduc
e
s
e
c
ond
a
nd
thi
r
d
or
de
r
ha
r
moni
c
s
of
id
a
nd
iq,
a
s
we
ll
a
s
thi
r
d
or
de
r
ha
r
moni
c
c
ur
r
e
nt.
B
e
c
a
us
e
the
load
c
ur
r
e
nt
is
de
void
of
thi
r
d
-
or
de
r
ha
r
moni
c
c
u
r
r
e
nt,
it
pa
s
s
e
s
thr
ough
the
load.
4.
1.
DC
vol
t
age
c
on
t
r
ol
B
a
s
ic
P
I
c
ontr
oll
e
r
is
us
e
d
to
c
ontr
ol
DC
volt
a
ge
.
T
he
s
low
r
e
a
c
ti
on
of
e
lec
tr
olyt
ic
c
a
pa
c
it
or
s
ha
s
li
tt
le
e
f
f
e
c
t
on
c
ur
r
e
nt
t
r
a
ns
ient
r
e
s
pons
ivene
s
s
.
As
a
r
e
s
ult
,
the
P
I
c
ontr
oll
e
r
c
a
n
be
us
e
d
to
c
ontr
ol
DC
volt
a
ge
[
18]
,
[
19
]
.
T
he
vo
lt
a
ge
pr
o
f
il
e
is
c
or
r
e
c
ted
unti
l
no
los
s
e
s
a
r
e
incur
r
e
d
a
nd
it
is
ke
pt
c
ons
tant.
C
(
s
)
G
(
s
)
V
d
c
i
e
e
+
-
F
igur
e
6.
M
a
int
a
ini
ng
the
Vol
tage
P
r
o
f
il
e
f
o
r
DC
d
iagr
a
m
Evaluation Warning : The document was created with Spire.PDF for Python.
I
ndone
s
ian
J
E
lec
E
ng
&
C
omp
S
c
i
I
S
S
N:
2502
-
4752
T
he
har
monic
r
e
duc
ti
on
tec
hniques
in
s
hunt
ac
ti
v
e
pow
e
r
fi
lt
e
r
…
(
K
ambham
pati
V
e
nk
ata
Gov
ar
dh
an
R
ao)
1241
T
he
a
mpl
it
ude
o
f
APF
in
the
pha
s
e
volt
a
ge
dir
e
c
ti
on
is
s
tabili
s
e
d
[
20]
a
nd
a
bs
or
bs
a
c
ti
ve
powe
r
.
As
s
hown
in
F
igur
e
6,
the
a
ppli
e
d
DC
volt
a
ge
is
c
om
pa
r
e
d
to
a
c
ons
tant
r
e
f
e
r
e
nc
e
va
lue.
W
it
h
ga
ins
K
p
a
nd
T
i,
the
e
r
r
o
r
c
r
e
a
ted
is
s
e
nt
to
the
P
I
C
ontr
ol
ler
.
W
it
h
DC
volt
a
ge
,
the
s
ingl
e
o
r
de
r
c
ontr
oll
e
r
with
P
I
is
f
e
d
to
the
tr
a
ns
f
e
r
f
unc
ti
on
.
(
)
=
=
3
2
√
2
∗
(
11)
T
he
c
ontr
oll
e
r
with
P
I
is
done
in
the
s
a
me
wa
y
a
s
a
c
los
e
d
loop
T
F
a
nd
is
s
hown
in
(
12
)
,
(
13)
.
(
)
=
(
1
+
1
.
)
(
12)
=
2
.
(
+
)
2
+
2
.
+
2
(
13)
with
ζ
=
1
a
c
r
it
ica
ll
y
da
mped
r
e
s
pons
e
s
ys
tem
is
c
r
e
a
ted,
Angula
r
s
pe
e
d
with
na
tur
a
l
f
r
e
que
nc
y,
ωn=
2π
•
100
r
a
d/s
,
I
ntegr
a
l
ti
me,
T
i
=
1/a
a
nd
pr
opo
r
ti
ona
l
ga
in
Kp
c
a
n
be
mea
s
ur
e
d
us
ing
AN
N.
=
√
3
8
√
2
∗
(
14)
=
√
3
2
√
2
∗
(
15)
4.
2.
T
r
ain
in
g
of
AN
N
W
he
n
c
ompar
e
d
to
f
uz
z
y
c
ontr
o
ll
e
r
s
,
AN
N
is
m
or
e
us
e
f
ul
be
c
a
us
e
it
is
mor
e
e
f
f
icie
nt
a
nd
f
a
ult
tol
e
r
a
nt.
T
o
i
mpr
ove
c
ont
r
ol
qua
li
ty
,
da
ta
f
r
om
ha
r
d
c
ont
r
oll
e
r
s
c
a
n
be
c
omm
un
ica
ted
with
in
tell
igent
c
ontr
oll
e
r
s
uti
li
s
ing
AN
N
[
21
]
,
[
22
]
.
F
e
e
d
f
or
wa
r
d
ne
ur
a
l
ne
two
r
ks
pe
r
f
o
r
m
the
f
unc
ti
on
of
the
c
omp
e
ns
a
ti
on
s
ignal
ge
ne
r
a
tor
[
23]
.
I
t
ha
s
thr
e
e
laye
r
s
,
with
s
e
ve
n
ne
ur
ons
in
the
inpu
t
laye
r
a
nd
twe
nty
-
one
ne
ur
ons
in
the
hidden
laye
r
(
s
e
e
F
igu
r
e
7)
.
∑
∑
∑
∑
∑
∑
∑
∑
/
/
/
I
s
a
I
s
b
I
s
c
V
s
a
Δ
I
d
c
V
s
b
V
s
c
I
s
a
*
I
s
b
*
I
s
c
*
2
1
T
a
n
s
i
g
F
igur
e
7.
AN
N
ne
twor
k
s
tr
uc
tur
e
p
r
opos
e
d
T
he
output
is
in
f
luenc
e
d
by
the
s
or
t
of
input
a
nd
h
ow
it
e
volves
.
As
pr
e
vious
ly
s
tate
d,
the
pr
opos
e
d
c
onc
e
pt
c
ons
is
ts
of
s
e
ve
n
input
ne
ur
ons
.
T
he
r
e
f
e
r
e
nc
e
,
load
volt
a
ge
,
s
our
c
e
c
ur
r
e
nt,
a
nd
output
f
o
r
e
r
r
or
(
P
I
)
c
ontr
oll
e
r
s
a
r
e
a
mong
them.
T
he
output
of
the
AN
N
is
ba
s
e
d
on
f
unda
menta
l
r
e
f
e
r
e
nc
e
c
ur
r
e
nts
.
T
he
hys
ter
e
s
is
load
c
ur
r
e
nt
c
ontr
oll
e
r
c
ons
is
ts
of
s
witching
s
ignals
a
s
output
.
5.
HARM
ONI
C
RE
DU
C
T
I
ON
USI
NG
M
P
P
T
M
P
P
T
tec
hniques
c
a
n
a
ls
o
be
us
e
d
to
s
olve
the
main
ha
r
moni
c
pr
oblem.
T
he
M
P
P
T
s
ys
tem
s
tands
f
or
maximum
powe
r
point
tr
a
c
king
[
24
]
.
M
P
P
T
a
ppr
oa
c
he
s
include
pe
r
tur
ba
ti
on
a
nd
obs
e
r
va
ti
on
[
P
&O]
,
hil
l
c
li
mbi
ng
(
HC
)
,
f
r
a
c
ti
ona
l
voc
,
a
nd
f
r
a
c
ti
ona
l
I
s
c
,
a
s
we
ll
a
s
ne
we
r
tec
hniques
li
ke
f
uz
z
y
logi
c
,
met
he
ur
is
ti
c
a
lgor
it
hms
,
a
nd
AN
N
.
T
he
s
e
tec
hniques
a
id
in
mai
ntaining
c
ons
is
tent
pr
e
c
is
ion,
doubli
ng
t
r
a
c
king
s
pe
e
d,
a
nd
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2502
-
4752
I
ndone
s
ian
J
E
lec
E
ng
&
C
omp
S
c
i
,
Vol.
25
,
No.
3
,
M
a
r
c
h
20
22
:
1236
-
1245
1242
c
onve
r
ti
ng
s
igni
f
ica
nt
a
mount
s
of
e
ne
r
gy
a
nd
po
we
r
.
T
he
P
&O
a
ppr
oa
c
h
is
the
mos
t
of
ten
ut
il
is
e
d
M
P
P
T
tec
hnique
in
s
olar
s
ys
tems
[
25]
,
[
26]
a
mong
a
l
l
a
va
il
a
ble
methods
.
T
he
P
&O
a
pp
r
oa
c
h
a
ids
in
m
a
xim
um
powe
r
tr
a
c
king,
a
s
we
ll
a
s
ba
lanc
ing
volt
a
ge
,
c
ur
r
e
nt,
a
nd
powe
r
a
mong
s
olar
P
V
modul
e
s
a
nd
a
s
s
is
ti
ng
in
powe
r
r
is
e
or
de
c
r
e
a
s
e
.
T
he
T
a
ble
1
pr
ovides
a
de
t
a
il
e
d
e
xa
mi
na
ti
on
of
s
e
ve
r
a
l
M
P
P
T
s
tr
a
tegie
s
[
27]
,
[
28]
f
o
r
r
e
duc
ing
T
HD
.
T
a
ble
1
.
S
umm
a
r
y
of
methods
in
M
P
P
T
M
P
P
T
T
e
c
hni
que
s
me
th
odol
ogy
B
e
ne
f
it
s
L
im
it
a
ti
ons
P
&O (
P
e
r
tu
r
b a
nd O
bs
e
r
ve
)
I
mpl
e
me
nt
a
ti
on
is
s
im
pl
e
a
nd
lo
w
-
c
os
t,
w
it
h
mi
ni
ma
l
s
e
ns
or
ne
e
ds
.
P
&O
f
a
il
s
to
de
te
r
mi
ne
th
e
g
e
nui
ne
M
P
P
a
nd
os
c
il
la
te
s
a
r
ound
it
a
s
e
f
f
ic
ie
nc
y
dr
ops
due
to
r
a
pi
d e
nvi
r
onme
nt
a
l
c
ha
nge
;
c
ons
e
que
nt
ly
, i
ts
pe
r
f
or
ma
nc
e
mus
t
be
e
nha
nc
e
d.
H
C
(
H
il
l
C
li
mbi
ng)
S
tr
uc
tu
r
e
is
s
im
pl
e
a
nd
s
tr
a
ig
ht
f
or
w
a
r
d
to
im
pl
e
me
nt
.
U
nde
r
va
r
yi
ng
s
ol
a
r
ir
r
a
di
a
nc
e
le
v
e
ls
,
H
C
f
a
ll
s
to
tr
a
c
k
th
e
M
P
P
a
nd
os
c
il
la
te
s
a
bout
it
;
th
e
t
r
a
c
ki
ng t
e
c
hni
que
mus
t
be
e
nh
a
nc
e
d.
I
nc
r
e
me
nt
a
l
c
onduc
ta
nc
e
I
mpr
ove
d
pe
r
f
o
r
ma
nc
e
in
s
e
tt
in
gs
w
it
h
qui
c
k
c
ha
nge
s
in
te
mpe
r
a
tu
r
e
a
nd
lo
w
os
c
il
la
ti
on
a
r
ound the
M
P
P
M
P
P
is
im
pos
s
ib
le
to
tr
a
c
k
in
pa
r
ti
a
l
s
ha
de
,
a
nd
th
e
c
ompl
e
xi
ty
of
it
s
c
ont
r
ol
c
ir
c
ui
tr
y
r
e
s
ul
ts
i
n a
hi
gh s
ys
t
e
m c
os
t.
R
C
C
(
R
ip
pl
e
C
or
r
e
la
ti
on
C
ont
r
ol
)
M
P
P
tr
a
c
ki
ng
a
t
hi
gh
s
un
i
r
r
a
di
a
ti
on
us
in
g
s
im
pl
e
,
le
s
s
e
xpe
n
s
iv
e
a
n
a
lo
gue
c
ir
c
ui
tr
y
a
nd
qui
c
k t
r
a
c
ki
ng
A
t
lo
w
s
ol
a
r
ir
r
a
di
a
ti
on,
R
C
C
ha
s
li
mi
te
d
tr
a
c
ki
ng
c
a
pa
bi
li
ty
;
s
ig
ni
f
ic
a
nt
tr
a
c
ki
ng
s
te
ps
a
r
e
ne
c
e
s
s
a
r
y ne
a
r
t
he
M
P
P
.
V
oc
A
s
im
pl
if
ie
d
te
c
hni
que
w
a
s
ut
il
is
e
d
to
a
ppl
y
a
li
ne
a
r
r
e
la
ti
ons
hi
p
be
twe
e
n
V
oc
a
nd
th
e
ma
xi
mum
out
put
vol
ta
ge
of
a
P
V
a
r
r
a
y
in
a
n
of
f
li
ne
(
s
ta
nd
-
a
lo
ne
)
a
ppl
ic
a
ti
on.
T
he
M
P
P
tr
a
c
ki
ng
pr
oc
e
dur
e
ha
s
a
poor
le
v
e
l
of
a
c
c
ur
a
c
y,
a
nd
c
ir
c
ui
t
ope
r
a
ti
on
c
a
n
be
di
s
r
upt
e
d by int
e
r
mi
tt
e
nt
l
oa
d s
he
ddi
ng.
I
sc
S
im
pl
if
ie
d
o
f
f
li
ne
a
ppr
oa
c
h
th
a
t
is
m
or
e
a
c
c
ur
a
te
th
a
n
th
e
V
oc
me
th
odol
ogy,
w
it
h
a
li
ne
a
r
r
e
la
ti
ons
hi
p
be
twe
e
n
th
e
I
s
c
a
nd
th
e
c
ur
r
e
nt
a
t
th
e
M
P
P
.
T
hi
s
me
th
od
ha
s
a
s
ig
ni
f
ic
a
nt
im
pl
e
me
nt
a
ti
on
c
os
t.
C
ur
r
e
nt
s
w
e
e
p
T
he
P
V
a
r
r
a
y
c
ur
r
e
nt
s
w
e
e
p
w
a
ve
f
or
m
is
us
e
d
to
obt
a
in
P
V
a
r
r
a
y
I
-
V
c
ha
r
a
c
te
r
is
ti
c
s
by
upda
ti
ng i
t
to
t
r
a
c
k t
he
M
P
P
a
t
a
de
f
in
e
d t
im
e
.
O
nl
y
pos
s
ib
le
if
th
e
tr
a
c
ki
ng
uni
t'
s
po
w
e
r
c
ons
umpt
io
n
is
le
s
s
th
a
n
th
e
P
V
s
ys
te
m'
s
pow
e
r
i
nc
r
e
a
s
e
.
C
ont
r
ol
li
ng t
he
dr
oop of
a
D
C
li
nk c
a
pa
c
it
or
W
he
n
th
e
A
C
s
y
s
te
m
li
ne
c
ur
r
e
nt
is
f
e
d
ba
c
k
to
c
ur
r
e
nt
s
a
ggi
ng
c
r
e
a
te
d
by
th
e
D
C
li
nk
vol
ta
ge
, t
he
M
P
P
T
f
unc
ti
ons
w
e
ll
.
D
e
s
ig
ne
d
a
nd
de
v
e
lo
pe
d
s
pe
c
if
ic
a
ll
y
f
or
us
e
w
he
n
th
e
P
V
s
ys
te
m
is
li
nke
d
to
th
e
A
C
s
ys
te
m l
in
e
i
n a
c
a
s
c
a
d
e
.
M
a
xi
mi
z
a
ti
on of
l
oa
d
c
ur
r
e
nt
/v
ol
ta
ge
W
he
n
th
e
P
V
a
r
r
a
y
is
li
nke
d
to
a
lo
s
s
le
s
s
pow
e
r
c
onve
r
te
r
,
in
c
r
e
a
s
in
g
th
e
lo
a
d
c
ur
r
e
nt
or
lo
a
d
vol
ta
ge
ma
xi
mi
s
e
s
th
e
P
V
a
r
r
a
y'
s
out
put
pow
e
r
ne
a
r
t
he
M
P
P
.
T
he
a
s
s
umpt
io
n
th
a
t
th
e
pow
e
r
c
onve
r
te
r
is
lo
s
s
le
s
s
c
r
e
a
te
s
unc
e
r
ta
in
ty
i
n de
te
r
mi
ni
ng t
he
pr
e
c
is
e
M
P
P
.
dP
/d
V
or
dP
/d
I
f
e
e
d ba
c
k
c
ont
r
ol
C
ompl
e
x
c
omput
a
ti
ons
c
a
n
b
e
ha
ndl
e
d,
a
nd
th
e
M
P
P
T
a
lg
or
it
hm pe
r
f
or
ms
w
e
ll
.
B
e
c
a
us
e
of
th
e
non
-
li
ne
a
r
r
e
la
ti
ons
hi
p
of
dP
/d
V
vs
V
,
it
is
c
ha
r
a
c
te
r
is
e
d
by
in
s
ta
bi
li
ty
a
nd non s
moot
hi
ng.
P
S
O
(
P
a
r
ti
c
le
S
w
a
r
m
O
pt
im
iz
a
ti
on)
Z
e
r
o
s
te
a
dy
s
ta
te
o
s
c
il
la
ti
on
a
nd
a
f
a
s
t
a
nd
s
ta
bl
e
t
r
a
c
ki
ng s
pe
e
d
I
t'
s
c
ha
ll
e
ngi
ng
to
de
te
r
mi
ne
th
e
be
s
t
de
s
ig
n
pa
r
a
me
te
r
s
.
F
L
C
(
F
uz
z
y L
ogi
c
C
ont
r
ol
le
r
)
F
L
C
doe
s
not
ne
c
e
s
s
it
a
te
te
c
hnol
ogi
c
a
l
e
xpe
r
ti
s
e
,
a
nd
th
e
d
e
s
ig
n
is
s
tr
a
ig
ht
f
or
w
a
r
d.
M
P
P
c
a
n
be
moni
to
r
e
d
in
di
f
f
e
r
e
nt
w
e
a
th
e
r
c
ondi
ti
ons
.
F
L
C
ma
y
or
ma
y
not
be
e
f
f
e
c
ti
ve
,
de
p
e
ndi
ng
on w
ha
te
ve
r
c
omput
a
ti
on e
r
r
or
i
s
us
e
d.
A
N
N
(
A
r
ti
f
ic
ia
l
N
e
ur
a
l
N
e
twor
k)
B
e
c
a
us
e
A
N
N
i
s
good
a
t
nonl
in
e
a
r
ta
s
k
s
a
nd
ha
s
a
hi
gh
tr
a
c
ki
ng
e
f
f
ic
ie
nc
y,
no
le
a
r
ni
ng
-
ba
s
e
d r
e
pr
ogr
a
mm
in
g i
s
r
e
qui
r
e
d.
B
e
c
a
us
e
th
e
P
V
a
r
r
a
y
pr
ope
r
ti
e
s
c
ha
ng
e
ove
r
ti
me
,
pe
r
io
di
c
tr
a
in
in
g
is
r
e
qui
r
e
d
to
e
n
s
ur
e
a
c
c
ur
a
te
M
P
P
.
D
E
(
D
if
f
e
r
e
nt
ia
l
E
va
lu
a
ti
on)
U
nde
r
pa
r
ti
a
l
s
ha
dow
in
g,
it
c
onve
r
ge
s
qui
c
kl
y
a
nd
f
in
ds
th
e
M
P
P
w
it
hout
os
c
il
la
ti
on,
a
nd
it
c
a
n
f
ol
lo
w
th
e
M
P
P
i
n
r
a
pi
dl
y
c
ha
ngi
ng
e
nvi
r
onme
nt
a
l
c
ondi
ti
ons
.
U
nde
r
c
ont
in
ua
l
pa
r
ti
a
l
s
ha
de
,
D
E
ta
ke
s
a
lo
ng t
im
e
t
o a
c
hi
e
ve
t
he
M
P
P
.
G
A
(
G
e
ne
ti
c
A
lg
or
it
hm)
G
ood
M
P
P
tr
a
c
ki
ng
pe
r
f
or
ma
nc
e
,
qui
c
k
tr
a
c
ki
ng
pr
oc
e
s
s
,
a
nd
a
bi
li
ty
to
a
c
hi
e
v
e
th
e
gl
oba
l
pe
a
k w
it
hout
os
c
il
la
ti
on.
B
e
c
a
us
e
G
A
is
a
non
-
de
te
r
mi
ni
s
ti
c
me
th
od,
th
e
out
c
ome
ma
y
di
f
f
e
r
e
a
c
h
ti
me
th
e
a
lg
or
it
hm i
s
e
xe
c
ut
e
d.
6.
S
I
M
UL
AT
I
ON
RE
S
UL
T
S
T
he
s
im
ulation
r
e
s
ult
s
of
pr
opos
e
d
c
ir
c
uit
s
a
r
e
d
i
s
playe
d
in
F
igur
e
8.
F
r
o
m
the
F
igur
e
8(
a
)
s
hows
the
ter
mi
na
l
volt
a
ge
,
F
igur
e
8(
b
)
e
xplain
a
bout
l
oa
d
a
t
the
ter
mi
na
l
of
c
u
r
r
e
nt
pr
o
f
il
e
,
F
igur
e
8
(
c
)
e
xplain
a
bout
C
ur
r
e
nt
pr
of
il
e
a
t
Ac
ti
ve
f
il
ter
ter
mi
na
l
,
F
igur
e
8(
d
)
d
is
plays
a
bout
Ne
utr
a
l
c
ur
r
e
nt
pr
o
f
il
e
a
t
load
ter
mi
na
l,
F
igu
r
e
8(
e
)
s
hows
the
C
ur
r
e
nt
a
t
ne
utr
a
l
ter
mi
na
l,
F
igu
r
e
8(
f
)
dis
plays
C
ur
r
e
nt
in
the
s
ys
te
m
F
igur
e
8(
g)
gives
a
bout
Voltage
p
r
of
il
e
a
t
DC
c
onve
r
ter
,
a
nd
F
igu
r
e
8
(
h)
C
ur
r
e
nt
a
t
the
gr
id
.
T
he
s
im
ulati
on
T
HD
va
lues
f
or
the
pr
opos
e
d
c
ir
c
uit
with
P
I
a
nd
AN
N
c
ontr
oll
e
r
f
or
r
e
duc
ti
on
of
ha
r
moni
c
dis
tr
o
r
ti
on
a
r
e
s
hown
in
Evaluation Warning : The document was created with Spire.PDF for Python.
I
ndone
s
ian
J
E
lec
E
ng
&
C
omp
S
c
i
I
S
S
N:
2502
-
4752
T
he
har
monic
r
e
duc
ti
on
tec
hniques
in
s
hunt
ac
ti
v
e
pow
e
r
fi
lt
e
r
…
(
K
ambham
pati
V
e
nk
ata
Gov
ar
dh
an
R
ao)
1243
F
igur
e
9
.
F
igur
e
9(
a
)
will
gives
the
va
lues
of
T
HD
in
c
a
s
e
of
P
I
c
ont
r
oll
e
r
a
nd
F
igur
e
9
(
b)
will
gives
the
va
lues
of
T
HD
in
c
a
s
e
of
AN
N
c
ont
r
oll
e
r
,
s
a
me
wi
ll
dis
playe
d
in
the
T
a
ble
2
.
F
igur
e
8.
C
ir
c
uit
output
s
that
ha
ve
be
e
n
pr
opos
e
d
;
(
a
)
volt
a
ge
a
t
the
s
our
c
e
ter
mi
na
l
;
(
b)
a
t
the
load
te
r
mi
na
l,
the
c
ur
r
e
nt
p
r
of
il
e
;
(
c
)
a
t
the
a
c
ti
ve
f
il
ter
ter
mi
na
l
,
the
c
ur
r
e
nt
p
r
of
il
e
is
dis
playe
d
;
(
d)
a
t
the
load
ter
m
inal
,
the
c
ur
r
e
nt
pr
o
f
il
e
is
ne
ut
r
a
l
;
(
e
)
c
ur
r
e
nt
f
lowing
via
th
e
ne
utr
a
l
ter
mi
na
l
;
(
f
)
c
ur
r
e
ntl
y
a
va
il
a
ble
in
the
s
ys
tem
;
(
g)
DC
c
onve
r
ter
volt
a
ge
pr
o
f
il
e
;
(
h)
the
c
ur
r
e
nt
s
tate
of
the
g
r
id
(
a
)
(
b
)
F
igur
e
9
.
Va
lues
of
T
HD
,
(
a
)
with
a
P
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I
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ian
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omp
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c
i
,
Vol.
25
,
No.
3
,
M
a
r
c
h
20
22
:
1236
-
1245
1244
7.
CONC
L
USI
ON
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he
s
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opos
e
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ing
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I
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L
I
NK
to
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pleme
nt
S
APF
with
AN
N.
T
he
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AP
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c
ompens
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tes
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or
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c
s
by
us
ing
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li
ne
a
r
load.
T
he
r
e
f
or
e
,
it
wa
s
de
ter
mi
ne
d
that
us
ing
P
I
,
the
ove
r
a
ll
ha
r
moni
c
dis
tor
ti
on
of
the
c
ur
r
e
nt
pr
o
f
il
e
a
t
s
our
c
e
ter
m
inals
is
4.
18
pe
r
c
e
nt,
but
us
ing
a
n
AN
N
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ler
,
i
t
is
2
.
97
pe
r
c
e
nt.
I
t's
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ls
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e
n
put
thr
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s
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c
e
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und
e
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va
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ious
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c
ums
tanc
e
s
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e
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ult
s
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ted.
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r
e
s
ult
o
f
the
r
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s
ult
s
obtaine
d,
it
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c
onc
luded
that
P
I
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les
s
e
f
f
e
c
ti
ve
than
AN
N.
R
E
F
E
RE
NC
E
S
[
1]
J
.
R
oc
a
be
r
t,
A
.
L
una
,
F
.
B
la
a
bj
e
r
g,
a
nd
P
.
R
odr
íg
ue
z
,
“
C
ont
r
ol
of
pow
e
r
c
onve
r
te
r
s
in
A
C
mi
c
r
ogr
id
s
,”
I
E
E
E
T
r
ans
ac
ti
ons
on
P
ow
e
r
E
le
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tr
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c
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L
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K
.
B
a
ig
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K
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P
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R
a
j,
G
.
G
.
R
a
ja
S
e
kha
r
,
T
.
V
ij
a
y
M
uni
,
a
nd
M
.
K
ir
a
n
K
uma
r
,
“
P
ow
e
r
qua
li
ty
e
n
c
ha
nc
e
m
e
nt
w
it
h
a
c
ti
ve
pow
e
r
c
ont
r
ol
,”
J
our
nal
of
C
r
it
ic
al
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e
v
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, vol
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.07.09.143.
[
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I
E
E
E
S
td
.
519
-
2014,
“
I
E
E
E
R
e
c
omm
e
nde
d
P
r
a
c
ti
c
e
a
nd
R
e
qu
ir
e
me
nt
s
f
or
H
a
r
moni
c
C
ont
r
ol
in
E
le
c
tr
ic
P
ow
e
r
S
ys
te
ms
,”
I
E
E
E
St
d. 519
-
2014
, vol
. 2014. I
E
E
E
, 2014, doi:
10.1109
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e
e
e
s
td
.2014.6826459.
[
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A
.
G
.
P
e
te
r
a
nd
K
.
A
.
S
a
ha
,
“
C
ompa
r
a
ti
ve
s
tu
dy
of
ha
r
moni
c
s
r
e
duc
ti
on
a
nd
pow
e
r
f
a
c
to
r
e
nha
nc
e
me
nt
of
s
ix
a
nd
12
-
pu
ls
e
s
H
V
D
C
s
ys
te
m us
in
g pa
s
s
iv
e
a
nd s
hunt
A
P
F
s
ha
r
moni
c
f
il
te
r
s
,”
i
n
2018 I
nt
e
r
nat
io
nal
C
onf
e
r
e
nc
e
on t
he
D
om
e
s
ti
c
U
s
e
of
E
ne
r
gy
,
D
U
E
2018
, A
p
r
. 2018, pp. 1
–
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.2018.8384
395.
[
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V
.
T
.
R
a
ma
R
e
ddy,
T
.
S
.
S
a
i,
M
.
K
.
K
uma
r
,
N
.
R
a
je
s
h,
a
nd
B
.
N
a
gi
R
e
ddy,
“
H
a
r
moni
c
mi
ti
ga
ti
on
a
nd
pow
e
r
qua
l
it
y
e
nha
nc
e
me
nt
us
in
g P
V
f
e
d s
e
r
ie
s
a
c
ti
ve
f
il
te
r
f
or
gr
id
s
ys
te
ms
,”
I
nt
e
r
nat
io
nal
J
our
nal
of
S
c
ie
nt
if
ic
and T
e
c
hnol
ogy
R
e
s
e
ar
c
h
, v
ol
.
9, no. 1, pp. 3004
–
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c
e
s
s
e
d:
J
a
n. 17, 2022. [
O
nl
in
e
]
. A
va
il
a
bl
e
:
w
w
w
.i
js
tr
.or
g.
[
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A
.
K
.
R
oy,
G
.
R
.
B
is
w
a
l,
a
nd
P
.
B
a
s
a
k,
“
A
S
tu
dy
on
P
ow
e
r
Q
ua
li
ty
I
mpr
ove
me
nt
by
A
c
ti
ve
P
ow
e
r
F
il
te
r
in
H
ybr
id
S
us
ta
in
a
bl
e
E
ne
r
gy
S
ys
te
ms
,”
in
2019
I
nt
e
r
nat
io
nal
C
onf
e
r
e
nc
e
on
P
ow
e
r
E
le
c
tr
oni
c
s
,
C
ont
r
ol
and
A
ut
om
at
io
n,
I
C
P
E
C
A
2019
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r
oc
e
e
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ngs
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ove
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r
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G
.
V
.
S
.
B
a
bu
a
nd V
.
G
a
ne
s
h,
“
P
ow
e
r
qua
li
ty
e
nha
n
c
e
me
nt
i
n di
s
tr
ib
ut
e
d
e
ne
r
gy
r
e
s
our
c
e
s
by
f
our
le
g
vol
ta
g
e
s
our
c
e
c
onve
r
t
e
r
,”
in
I
E
E
E
I
n
te
r
nat
io
nal
C
onf
e
r
e
nc
e
on
I
nnov
at
iv
e
M
e
c
hani
s
m
s
f
or
I
ndus
tr
y
A
ppl
ic
at
io
ns
,
I
C
I
M
I
A
2017
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P
r
oc
e
e
di
ngs
,
F
e
b.
2017,
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10.1109/I
C
I
M
I
A
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K
.
D
e
ka
,
S
.
M
a
ha
pa
tr
a
,
P
.
K
.
B
or
dol
oi
,
a
nd
B
.
M
e
dhi
,
“
D
e
s
i
gn
a
nd
te
s
ti
ng
of
a
c
ont
r
o
l
s
ys
te
m
f
or
s
uppl
y
s
id
e
e
le
c
tr
ic
a
l
l
oa
d
ma
na
ge
me
nt
,”
in
P
r
o
c
e
e
di
ngs
of
2014
1
s
t
I
nt
e
r
nat
io
nal
C
onf
e
r
e
nc
e
on
N
on
C
onv
e
nt
io
nal
E
ne
r
gy
:
Se
a
r
c
h
fo
r
C
le
an
and
S
af
e
E
ne
r
gy
, I
C
O
N
C
E
2014
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a
n
. 2014, pp. 277
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C
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N
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E
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[
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T
.
K
omr
s
ka
,
T
.
G
la
s
be
r
ge
r
,
a
nd
Z
.
P
e
r
out
ka
,
“
M
in
im
um
I
nf
in
it
y
N
or
m
-
B
a
s
e
d
P
W
M
f
or
T
hr
e
e
-
P
ha
s
e
F
our
-
L
e
g
C
onve
r
te
r
s
,”
in
I
E
E
E
I
nt
e
r
nat
io
nal
Sy
m
pos
iu
m
on
I
ndus
tr
ia
l
E
le
c
t
r
oni
c
s
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J
un.
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.
N
our
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ld
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e
n
a
nd
A
.
M
.
A
.
I
br
a
hi
m,
“
M
ode
li
ng,
im
pl
e
me
nt
a
ti
on
a
nd
p
e
r
f
or
ma
nc
e
a
na
ly
s
is
of
a
gr
id
-
c
onne
c
te
d
phot
ovol
ta
ic
/wi
nd
hybr
id
pow
e
r
s
ys
te
m,”
in
P
r
oc
e
e
di
ngs
of
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I
nt
e
r
nat
io
nal
C
onf
e
r
e
nc
e
on
I
nnov
at
iv
e
T
r
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nds
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om
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r
E
ngi
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E
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r
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A
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H
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F
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ha
d
a
nd
M
.
S
.
R
e
z
a
,
“
S
in
gl
e
-
P
ha
s
e
S
hunt
A
c
ti
ve
P
ow
e
r
F
il
te
r
U
s
in
g
P
a
r
a
bol
ic
P
W
M
f
or
C
ur
r
e
nt
C
ont
r
ol
,”
in
P
r
oc
e
e
di
ngs
of
2019
th
e
7t
h
I
nt
e
r
nat
io
nal
C
onf
e
r
e
nc
e
on
Sm
ar
t
E
ne
r
gy
G
r
id
E
ngi
ne
e
r
in
g,
SE
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E
2019
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S
.
A
gr
a
w
a
l,
S
.
K
.
V
a
is
hna
v,
A
ji
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a
nd
R
.
K
.
S
oma
ni
,
“
A
c
ti
ve
pow
e
r
f
il
te
r
f
o
r
ha
r
moni
c
mi
t
ig
a
ti
on
of
pow
e
r
qua
li
ty
is
s
ue
s
in
gr
id
in
te
gr
a
te
d
phot
ovol
ta
ic
ge
ne
r
a
ti
on
s
y
s
te
m,”
in
2020
7t
h
I
nt
e
r
na
ti
onal
C
onf
e
r
e
nc
e
on
Si
gnal
P
r
oc
e
s
s
in
g
and
I
nt
e
g
r
at
e
d
N
e
t
w
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k
s
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N
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D
.
A
.
F
e
r
na
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s
a
nd
S
.
R
.
N
a
id
u,
“
A
nove
l
P
W
M
s
c
he
me
f
or
th
e
4
-
le
g
vol
ta
ge
s
our
c
e
c
onve
r
te
r
a
nd
it
s
us
e
in
dyna
mi
c
vol
t
a
ge
r
e
s
to
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a
ti
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E
S
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A
.
M
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I
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a
s
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S
.
I
.
S
a
lc
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C
.
G
.
R
us
u,
C
.
M
a
r
gi
ne
a
n,
a
nd
P
.
D
.
T
e
odos
e
s
c
u,
“
P
ow
e
r
f
a
c
to
r
c
ompe
ns
a
ti
on
f
or
a
s
in
gl
e
-
pha
s
e
A
C
-
D
C
H
ybr
id
M
ic
r
o
-
G
r
id
,”
in
2020
I
E
E
E
11t
h
I
nt
e
r
nat
io
nal
Sy
m
pos
iu
m
on
P
ow
e
r
E
le
c
tr
oni
c
s
fo
r
D
is
tr
ib
ut
e
d
G
e
n
e
r
at
io
n
Sy
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t
e
m
s
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E
D
G
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G
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W
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ng,
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L
.
D
ua
r
te
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nd
M
.
A
.
M
.
H
e
ndr
ix
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G
r
id
-
in
te
r
f
a
c
i
ng
c
onve
r
te
r
s
ys
t
e
ms
w
it
h
e
nha
nc
e
d
vol
ta
ge
qu
a
li
ty
f
or
mi
c
r
ogr
id
a
ppl
ic
a
ti
onc
onc
e
pt
a
nd
im
pl
e
me
nt
a
ti
on,”
I
E
E
E
T
r
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ti
ons
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ow
e
r
E
le
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oni
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s
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L
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A
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T
a
le
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h,
M
.
S
.
S
ha
dl
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a
nd
S
.
M
a
ji
d
F
a
te
mi
,
“
C
ont
r
ol
S
t
r
a
te
gy
of
a
S
in
gl
e
P
ha
s
e
A
c
ti
ve
P
ow
e
r
F
il
te
r
w
i
th
A
dj
us
ta
bl
e
D
C
L
in
k
C
a
pa
c
it
or
V
ol
ta
ge
f
or
T
H
D
R
e
duc
ti
on
in
N
on
-
li
ne
a
r
L
oa
ds
,”
in
2019
10t
h
I
nt
e
r
nat
io
nal
P
ow
e
r
E
le
c
tr
oni
c
s
,
D
r
iv
e
Sy
s
t
e
m
s
and
T
e
c
hnol
ogi
e
s
C
onf
e
r
e
nc
e
, P
E
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ST
C
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, F
e
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E
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K
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me
l,
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.
L
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id
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nd
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.
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ll
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h,
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ov. 2019, doi:
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P
r
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bha
ka
r
a
nd
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.
K
.
M
is
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E
T
r
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e
r
E
le
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N
ir
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r
opor
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ona
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s
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gl
e
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g
e
G
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te
d
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r
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e
r
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e
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r
ol
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r
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C
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c
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A
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A
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mun,
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odi
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P
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nt
e
r
nat
io
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C
onf
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nc
e
on
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nnov
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, E
ngi
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g and T
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.
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ya
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. M
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h, “
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N
N
B
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s
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ir
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r
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ont
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n
2018
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nv
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nt
and
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nt
e
ll
ig
e
nt
C
ont
r
ol
,
P
E
E
I
C
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A
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B
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li
ya
n,
M
.
J
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mi
l,
M
.
R
iz
w
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n,
I
.
A
ls
a
id
a
n,
a
nd
M
.
A
la
r
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j,
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nt
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ll
ig
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nt
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ont
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mp
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at
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obl
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ngi
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23]
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.
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ug.
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C
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A
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25]
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.
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, O
c
t.
2
019, vol. 2018
-
O
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, doi
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N
T
L
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C
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.
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. 2018, pp. 1
–
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. 44, no. 4, pp. 24
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10.1002/er
.5075.
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