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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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8
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6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
3
,
Sep
tem
b
er
20
25
:
201
7
-
20
29
2018
As
we
ar
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ex
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v
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1
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8
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6
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b
ased
alg
o
r
ith
m
.
Ullah
et
a
l.
[
1
7
]
h
av
e
s
h
o
wn
th
at
th
e
to
tal
h
ar
m
o
n
ic
d
is
to
r
t
io
n
(
T
HD
)
o
f
2
8
%
ca
n
b
e
r
ed
u
ce
d
to
b
elo
w
5
%
u
s
in
g
a
P
-
Q
-
b
ased
alg
o
r
ith
m
.
Oth
er
r
esear
ch
er
s
h
av
e
s
h
o
wn
s
im
ilar
r
esu
lts
[
1
8
]
-
[
2
1
]
.
Am
in
i
et
a
l.
[
2
2
]
h
av
e
d
em
o
n
s
tr
ated
th
at
th
e
s
o
u
r
ce
cu
r
r
en
t'
s
T
HD
ca
n
b
e
d
ec
r
ea
s
ed
f
r
o
m
2
0
.
2
%
to
4
.
2
%
f
o
r
an
R
-
L
lo
ad
.
R
u
d
i
an
d
Hash
em
n
ia
[
2
3
]
h
a
v
e
s
h
o
wn
th
at
T
HD
f
r
o
m
2
9
.
9
1
% is
r
ed
u
ce
d
b
el
o
w
5
%,
an
d
Ma
n
o
h
ar
a
et
a
l.
[
2
4
]
h
a
v
e
u
s
ed
th
e
s
y
n
ch
r
o
n
o
u
s
r
ef
er
en
ce
f
r
am
e
(
SR
F
)
m
eth
o
d
an
d
r
ed
u
ce
d
T
HD
f
r
o
m
2
6
.
2
3
%
to
5
.
9
7
%.
Gaic
ea
n
u
et
a
l.
[
2
5
]
h
av
e
r
e
d
u
ce
d
th
e
T
HD
o
f
t
h
e
cu
r
r
en
t f
r
o
m
2
7
.
7
% to
3
.
4
7
%.
B
ar
b
o
s
a
et
a
l
.
[
2
6
]
h
av
e
u
s
ed
a
P
-
Q
-
b
ased
co
n
tr
o
ller
f
o
r
g
r
id
in
teg
r
atio
n
as
well
as
an
a
c
ti
v
e
p
o
we
r
fil
ter
(
APF
)
f
u
n
ctio
n
ality
,
wh
ich
also
im
p
r
o
v
es
th
e
p
o
wer
f
ac
to
r
.
I
ov
et
al
.
[
2
7
]
h
av
e
s
u
g
g
ested
d
if
f
er
e
n
t
co
n
tr
o
l
cir
cu
its
f
o
r
s
in
g
le
-
p
h
a
s
e
an
d
th
r
ee
-
p
h
ase
in
teg
r
atio
n
,
an
d
th
e
co
n
tr
o
ller
h
as
b
ee
n
co
n
tr
o
lled
u
s
in
g
a
s
y
n
ch
r
o
n
o
u
s
r
ef
er
e
n
ce
f
r
am
e
co
n
tr
o
l
ap
p
r
o
ac
h
b
ased
o
n
p
h
ase
-
lo
ck
ed
lo
o
p
s
(
PLL
s
)
.
Sin
g
h
et
a
l
.
[
2
8
]
h
av
e
u
s
ed
an
in
v
er
ter
with
a
co
n
tr
o
ller
h
av
in
g
b
o
t
h
ac
tiv
e
p
o
wer
f
lo
w
to
th
e
g
r
id
f
r
o
m
r
e
n
ewa
b
le
en
er
g
y
s
o
u
r
ce
s
(
R
E
S
)
an
d
ac
tiv
e
p
o
wer
co
n
tr
o
l.
T
h
ey
u
s
ed
a
4
-
leg
i
n
v
er
ter
s
o
th
at
lo
ad
n
eu
tr
al
c
u
r
r
en
t
d
o
es
n
o
t
f
lo
w
t
o
th
e
s
o
u
r
ce
.
Azm
i
et
a
l
.
[
2
9
]
h
a
v
e
in
v
esti
g
ated
th
e
s
elec
tiv
e
h
ar
m
o
n
ic
elim
in
atio
n
tech
n
iq
u
e
f
o
r
im
p
r
o
v
in
g
T
HD
in
g
r
id
-
c
o
n
n
ec
ted
r
en
ewa
b
le
e
n
er
g
y
s
o
u
r
ce
s
y
s
tem
s
.
Y
a
ng
et
a
l
.
[
3
0
]
s
u
g
g
ested
c
o
n
tr
o
l
s
tr
a
teg
ies
f
o
r
ef
f
icien
t
p
o
wer
co
n
v
er
s
io
n
,
a
n
d
o
n
e
o
f
th
e
s
u
g
g
esti
o
n
s
is
a
PLL
-
b
ased
SR
F
co
n
tr
o
ller
.
Su
d
h
ak
ar
et
a
l
.
[
3
1
]
h
a
v
e
elab
o
r
ated
o
n
c
o
n
n
ec
tin
g
th
eir
PV
s
y
s
tem
to
th
e
g
r
id
.
th
ey
also
s
u
g
g
ested
th
e
u
s
e
o
f
PLL
f
o
r
g
r
id
s
y
n
ch
r
o
n
izatio
n
.
Sh
a
r
ew
et
a
l
.
[
3
2
]
h
a
v
e
d
o
n
e
a
d
etailed
an
a
ly
s
is
an
d
s
u
g
g
ested
th
at
to
k
ee
p
T
HD
b
el
o
w
5
%,
th
e
m
ax
im
u
m
PV
p
en
etr
atio
n
to
th
e
g
r
id
co
u
l
d
b
e
4
8
%.
Sh
af
iu
llah
et
a
l
.
[
3
3
]
h
av
e
d
is
cu
s
s
ed
m
an
y
co
n
tr
o
l
s
tr
ateg
ies an
d
h
ig
h
lig
h
te
d
ch
al
len
g
es f
ac
ed
b
y
in
teg
r
atin
g
R
E
S in
to
th
e
g
r
i
d
.
T
h
e
l
i
t
e
r
a
t
u
r
e
r
e
v
i
e
w
i
d
e
n
t
i
f
i
e
d
t
h
r
e
e
k
e
y
p
r
o
b
l
e
m
s
w
i
t
h
t
h
e
g
r
i
d
i
n
t
e
g
r
a
t
i
o
n
o
f
s
o
l
a
r
P
V
s
y
s
t
e
m
s
:
t
h
e
n
e
e
d
f
o
r
a
n
M
P
P
T
c
o
n
t
r
o
l
l
e
r
t
h
a
t
c
a
n
m
a
x
i
m
i
z
e
e
l
e
c
t
r
i
c
i
t
y
g
e
n
e
r
a
t
e
d
b
y
t
h
e
P
V
p
a
n
e
l
s
,
h
a
r
m
o
n
i
c
s
i
n
g
r
i
d
c
u
r
r
e
n
t
s
,
a
n
d
t
h
e
c
h
a
l
l
e
n
g
e
s
o
f
g
r
i
d
i
n
t
e
g
r
a
t
i
o
n
.
S
e
v
e
r
a
l
r
e
s
e
a
r
c
h
e
r
s
h
a
v
e
e
m
p
l
o
y
e
d
v
a
r
i
o
u
s
M
P
P
T
m
e
t
h
o
d
s
t
o
e
x
t
r
a
c
t
m
a
x
i
m
u
m
p
o
w
e
r
f
r
o
m
P
V
p
a
n
e
l
s
.
D
e
t
a
i
l
e
d
a
n
a
l
y
s
i
s
a
n
d
s
i
m
u
l
a
t
i
o
n
s
h
a
v
e
d
e
m
o
n
s
t
r
a
t
e
d
t
h
a
t
t
h
e
n
e
u
r
a
l
n
e
t
w
o
r
k
-
b
a
s
e
d
M
P
P
T
m
e
t
h
o
d
i
s
m
o
r
e
e
f
f
i
c
i
e
n
t
o
v
e
r
a
l
l
;
h
e
n
c
e
,
i
t
i
s
c
h
o
s
e
n
f
o
r
t
h
e
s
y
s
t
e
m
.
H
a
r
m
o
n
i
c
s
a
r
e
u
n
d
e
s
i
r
a
b
l
e
a
n
d
h
a
v
e
a
s
i
g
n
i
f
i
c
a
n
t
l
y
a
d
v
e
r
s
e
e
f
f
e
c
t
o
n
a
l
l
o
t
h
e
r
l
o
a
d
s
c
o
n
n
e
c
t
e
d
t
o
t
h
e
g
r
i
d
;
t
h
e
r
e
f
o
r
e
,
t
h
e
y
m
u
s
t
b
e
m
i
n
i
m
i
z
e
d
u
s
i
n
g
a
s
u
i
t
a
b
l
e
A
P
F
.
A
d
d
i
t
i
o
n
a
l
l
y
,
S
o
l
a
r
p
o
w
e
r
g
e
n
e
r
a
t
e
d
m
u
s
t
b
e
p
r
o
p
e
r
l
y
c
o
n
n
e
c
t
e
d
t
o
t
h
e
g
r
i
d
t
o
e
n
s
u
r
e
p
r
o
p
e
r
p
o
w
e
r
s
h
a
r
i
n
g
b
e
t
w
e
e
n
t
h
e
P
V
s
y
s
t
e
m
,
o
t
h
e
r
g
e
n
e
r
a
t
i
n
g
u
n
i
t
s
c
o
n
n
e
c
t
e
d
t
o
t
h
e
g
r
i
d
,
a
n
d
t
h
e
l
o
a
d
.
T
h
e
in
s
tan
tan
eo
u
s
r
ea
ctiv
e
p
o
wer
-
b
ased
ac
tiv
e
p
o
wer
f
ilter
was
d
esig
n
ed
an
d
d
e
v
elo
p
ed
.
I
ts
p
er
f
o
r
m
an
ce
was
v
er
if
ied
f
o
r
B
u
tter
wo
r
th
,
ellip
tic,
an
d
C
h
eb
y
s
h
ev
I
I
f
ilter
s
,
an
d
t
h
e
an
al
y
s
is
s
h
o
ws
th
at
th
e
C
h
eb
y
s
h
ev
I
I
f
ilter
p
er
f
o
r
m
s
m
u
ch
b
etter
[
3
4
]
.
I
t
h
as
b
ee
n
d
em
o
n
s
tr
ated
th
at
th
e
u
s
e
o
f
th
e
C
h
eb
y
s
h
ev
I
I
f
ilter
g
iv
es
m
u
ch
b
etter
p
er
f
o
r
m
an
ce
o
f
APF
.
So
f
ar
,
n
o
r
ese
ar
ch
er
h
as
u
s
ed
th
e
C
h
e
b
y
s
h
e
v
I
I
f
ilter
as
a
lo
w
-
p
ass
f
ilter
in
th
e
APF.
T
h
is
m
eth
o
d
also
p
r
o
v
id
es si
m
p
le
co
n
t
r
o
l f
o
r
g
r
id
i
n
teg
r
atio
n
.
A
s
y
s
tem
with
PV
co
n
n
ec
ted
to
th
e
g
r
i
d
is
d
esig
n
ed
an
d
a
n
aly
ze
d
to
e
n
h
an
ce
p
o
wer
q
u
ality
wh
ile
s
u
p
p
ly
in
g
PV
p
o
wer
to
th
e
g
r
id
.
A
n
eu
r
al
n
etwo
r
k
-
b
as
ed
MPPT
s
y
s
tem
is
d
esig
n
ed
an
d
d
ev
el
o
p
ed
.
I
n
s
tan
tan
eo
u
s
r
ea
ctiv
e
p
o
wer
th
eo
r
y
-
b
ased
ac
tiv
e
f
ilter
in
g
with
th
e
C
h
eb
y
s
h
ev
I
I
f
ilter
is
u
s
ed
f
o
r
f
ilter
in
g
an
d
is
s
y
n
ch
r
o
n
ized
with
th
e
g
r
id
.
Fig
u
r
e
1
d
ep
icts
th
e
s
u
g
g
e
s
ted
s
y
s
tem
.
I
n
th
e
m
eth
o
d
s
ec
tio
n
,
we
h
a
v
e
d
esig
n
ed
a
g
r
i
d
-
in
teg
r
ate
d
PV
s
y
s
tem
co
n
n
ec
ted
to
a
n
o
n
lin
ea
r
lo
ad
to
ev
alu
ate
an
ac
tiv
e
p
o
wer
f
ilter
's
p
er
f
o
r
m
an
ce
.
W
e
h
av
e
also
d
esig
n
ed
an
in
s
tan
tan
e
o
u
s
r
ea
ctiv
e
p
o
wer
-
b
ased
ac
tiv
e
p
o
wer
f
ilter
.
W
e
h
av
e
d
esig
n
ed
a
n
d
d
ev
elo
p
ed
a
n
eu
r
al
n
etwo
r
k
-
b
ased
MPPT
s
y
s
tem
,
wh
ich
is
s
im
u
lated
in
Simu
lin
k
.
Sectio
n
3
d
is
cu
s
s
es th
e
f
in
d
in
g
s
.
2.
M
E
T
H
O
D
I
n
th
is
s
ec
tio
n
,
th
er
e
ar
e
th
r
ee
s
u
b
s
ec
tio
n
s
.
Su
b
s
ec
tio
n
2
.
1
.
g
iv
es
d
etails
o
f
a
s
y
s
tem
d
esig
n
ed
,
in
clu
d
in
g
t
h
e
APF
d
esig
n
.
Su
b
s
ec
tio
n
2
.
2
.
d
ea
ls
with
PV
s
y
s
tem
d
esig
n
alo
n
g
with
b
o
o
s
t
co
n
tr
o
ller
(
B
C
)
,
s
u
b
s
ec
tio
n
2.
3
.
d
ea
ls
with
P
-
Q
th
eo
r
y
a
n
d
g
r
id
in
teg
r
atio
n
.
2
.
1
.
Sy
s
t
e
m
d
esig
n
T
h
e
s
y
s
tem
co
n
s
is
t
s
o
f
a
“
n
o
n
lin
ea
r
lo
ad
co
u
p
le
d
to
a
th
r
ee
-
p
h
ase
s
u
p
p
ly
v
ia
th
e
”
g
r
id
d
ep
icted
in
Fig
u
r
e
1
.
T
h
e
d
ec
is
io
n
was
m
ad
e
to
em
p
lo
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
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Dr
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I
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N:
2088
-
8
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2
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8
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4
I
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w
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lec
&
Dr
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,
Vo
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16
,
No
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3
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Sep
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25
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29
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2
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ased
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ased
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4
.
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asic A
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n
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s
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.
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y
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t
h
at
th
e
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ay
g
en
e
r
ates
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
E
n
h
a
n
ce
me
n
t o
f p
o
w
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u
a
lity o
f g
r
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r
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ted
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s
ystem
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s
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g
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ctive
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(
P
r
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ve
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K
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ma
t
)
2021
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ased
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
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9
4
I
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t J Po
w
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lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
3
,
Sep
tem
b
er
20
25
:
201
7
-
20
29
2022
T
h
e
f
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,
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d
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ated
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ter
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icted
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Fig
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.
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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t J Po
w
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lec
&
Dr
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s
t
I
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N:
2088
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8
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r
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3.
RE
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L
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S AN
D
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SS
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3
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1
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M
P
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ated
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n
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n
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t
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r
r
a
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s
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x
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u
m
p
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w
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n
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T
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e
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t
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o
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e
p
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f
r
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m
t
h
e
PV
a
r
r
a
y
c
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m
p
a
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d
t
o
P
&
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a
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C
m
e
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h
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s
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t
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h
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e
m
e
t
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d
s
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s
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t
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e
m
a
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n
s
cl
o
s
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t
o
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P
.
T
h
e
t
i
m
e
n
e
e
d
e
d
f
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h
e
N
N
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b
a
s
e
d
c
o
n
t
r
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l
l
e
r
t
o
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e
a
c
h
t
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e
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e
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t
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g
p
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n
t
i
s
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h
e
q
u
i
c
k
e
s
t
.
I
t
t
a
k
es
j
u
s
t
0
.
2
m
il
l
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e
c
o
n
d
s
,
as
s
h
o
w
n
i
n
F
i
g
u
r
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1
0
.
N
N
M
PP
T
c
o
n
t
r
o
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e
r
r
e
q
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e
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P
V
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r
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y
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t
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g
e
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o
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t
r
e
q
u
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e
s
o
n
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y
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e
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e
n
s
o
r
,
w
h
e
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e
as
b
o
t
h
P
&
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n
d
I
C
-
b
as
e
d
c
o
n
t
r
o
l
l
e
r
s
r
e
q
u
i
r
e
2
s
e
n
s
o
r
s
.
H
e
n
c
e
,
t
h
e
NN
-
b
a
s
e
d
MP
PT
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lg
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m
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s
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n
c
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p
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d
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o
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&
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n
d
I
C
.
3
.
2
.
I
ns
t
a
nta
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re
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ct
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po
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ba
s
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AP
F
T
h
e
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s
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tan
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s
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ased
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im
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lated
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lin
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e
r
f
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m
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d
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in
clu
d
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d
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to
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cu
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n
d
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ir
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u
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1
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r
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o
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r
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ted
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o
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s
er
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e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
3
,
Sep
tem
b
er
20
25
:
201
7
-
20
29
2024
th
at
th
e
cu
r
r
en
t
h
as
h
a
r
m
o
n
ics
.
T
h
e
s
h
ap
e
is
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o
n
-
s
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s
o
id
al
,
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d
f
r
o
m
Fig
u
r
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1
2
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er
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e
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at
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e
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HD
o
f
th
e
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o
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r
ce
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r
r
en
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4
.
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2
%,
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d
o
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ce
t
h
e
APF g
ets co
n
n
ec
ted
,
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e
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ef
o
r
m
b
ec
o
m
es si
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u
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o
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h
e
T
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is
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n
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e
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r
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m
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r
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1
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it
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3
4
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en
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o
th
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d
I
an
d
lo
ad
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I
a
r
e
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n
n
ec
ted
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f
r
o
m
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u
r
e
1
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.
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n
o
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er
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2
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ly
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ce
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ich
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