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[
1
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,
[
2
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.
As
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4
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tr
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en
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p
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[
5
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[
6
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.
T
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allen
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T
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m
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m
p
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p
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(
MPPT)
tech
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I
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Dr
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Vo
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7
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Ma
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ca
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[
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[
8
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[
9
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[
1
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[
1
1
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[
1
2
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ex
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a
cc
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[
1
3
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I
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liter
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,
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ev
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[
6
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[
1
4
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[
1
5
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.
C
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s
.
Ho
wev
er
,
t
h
ey
o
f
ten
e
x
h
ib
it
o
s
cillatio
n
s
ar
o
u
n
d
th
e
MPP
an
d
f
ac
e
ch
allen
g
es
in
ad
ap
tin
g
to
s
wif
tly
ch
a
n
g
in
g
en
v
ir
o
n
m
en
tal
c
o
n
d
itio
n
s
[
1
6
]
,
[
1
7
]
.
I
n
th
e
r
ec
en
t
ad
v
an
ce
s
in
ar
tific
ial
in
tellig
en
ce
,
ANFI
Ss
f
o
r
MPPT
ap
p
licatio
n
s
h
av
e
b
ee
n
d
ev
elo
p
ed
,
wh
ic
h
e
x
h
ib
it
b
etter
tr
ac
k
in
g
ac
c
u
r
ac
y
an
d
f
aster
co
n
v
er
g
en
ce
t
h
an
tr
a
d
itio
n
al
m
eth
o
d
s
[
1
8
]
,
[
1
9
]
.
Mo
r
eo
v
er
,
ef
f
o
r
ts
to
war
d
s
p
o
wer
q
u
ality
en
h
an
c
em
en
t
v
ia
ac
tiv
e
f
ilter
in
g
tech
n
iq
u
es
ar
e
also
b
ein
g
m
a
d
e
[
2
0
]
,
[
2
1
]
,
m
o
d
if
ied
co
n
v
er
ter
to
p
o
lo
g
ies
[
2
2
]
,
[
2
3
]
,
an
d
ad
v
a
n
ce
d
c
o
n
tr
o
l
s
tr
ateg
ies
[
2
4
]
‒
[
2
6
]
h
av
e
b
ee
n
o
n
g
o
in
g
;
y
et,
a
co
m
p
r
eh
e
n
s
iv
e
co
m
p
ar
ativ
e
ass
es
s
m
en
t
o
f
h
o
w
v
a
r
io
u
s
MPPT
s
ch
em
es
s
p
ec
if
icall
y
af
f
ec
t
h
a
r
m
o
n
ic
d
is
to
r
tio
n
in
g
r
id
-
co
n
n
ec
ted
s
y
s
tem
s
is
lim
i
ted
in
th
e
liter
atu
r
e.
T
h
is
s
tu
d
y
p
r
o
p
o
s
es a
n
o
v
el
c
o
m
p
ar
ativ
e
a
p
p
r
o
ac
h
f
o
r
th
e
e
v
alu
atio
n
o
f
th
e
ef
f
ec
tiv
e
n
ess
o
f
ad
ap
tiv
e
n
eu
r
o
-
f
u
zz
y
in
f
e
r
en
ce
s
y
s
te
m
(
ANFI
S)
-
b
ased
a
n
d
in
cr
e
m
en
tal
co
n
d
u
ctan
ce
(
I
C
)
-
b
ased
MPPT
s
tr
ateg
ies
,
s
p
ec
if
ically
in
ter
m
s
o
f
to
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
(
T
HD)
m
itig
atio
n
in
g
r
id
-
tied
PV
s
y
s
te
m
s
.
T
h
e
d
ev
elo
p
ed
s
im
u
latio
n
m
o
d
els
th
at
p
r
ec
is
ely
r
ep
r
esen
t
th
e
co
m
p
le
x
in
ter
ac
tio
n
s
b
etwe
en
MPPT
alg
o
r
it
h
m
s
an
d
h
a
r
m
o
n
ic
g
en
er
atio
n
m
ec
h
an
is
m
s
u
n
d
e
r
v
ar
y
i
n
g
le
v
els
o
f
ir
r
a
d
ian
c
e.
T
h
e
a
n
aly
s
is
em
p
lo
y
s
M
AT
L
AB
s
o
f
twar
e's
h
ar
m
o
n
ic
a
n
aly
s
is
to
o
ls
to
r
ig
o
r
o
u
s
ly
ev
alu
ate
T
HD.
T
h
e
r
esu
lts
s
h
o
w
th
at
ANFI
S
-
MPPT
m
eth
o
d
s
co
n
s
is
ten
tly
m
ain
tain
a
lo
wer
T
HD
v
alu
e
an
d
d
em
o
n
s
tr
ate
t
h
e
p
o
ten
tial
f
o
r
a
d
u
al
s
tr
ateg
y
f
o
r
e
n
er
g
y
h
ar
v
est
an
d
p
o
wer
q
u
ality
.
T
h
e
s
t
u
d
y
p
r
o
v
i
d
e
s
b
a
s
i
c
k
n
o
w
l
e
d
g
e
f
o
r
e
n
e
r
g
y
s
y
s
t
e
m
e
n
g
i
n
e
e
r
s
a
n
d
n
e
t
w
o
r
k
o
p
e
r
a
t
o
r
s
a
n
d
p
r
o
v
i
d
e
s
p
r
o
m
i
s
i
n
g
s
o
l
u
t
i
o
n
s
to
l
a
r
g
e
-
s
c
a
le
s
o
l
a
r
p
o
we
r
p
l
a
n
t
d
e
p
l
o
y
m
e
n
t
s
u
n
d
e
r
s
t
r
ic
t
p
o
w
er
q
u
a
l
i
t
y
s
ta
n
d
a
r
d
s
.
2.
M
E
T
H
O
D
2
.
1
.
Sy
s
t
e
m
co
nfig
ura
t
io
n a
nd
ANF
I
S
-
M
P
P
T
i
nte
g
ra
t
io
n
I
llu
s
tr
ated
in
Fig
u
r
e
1
,
t
h
e
p
r
o
p
o
s
ed
g
r
id
-
tied
PV
s
y
s
tem
o
p
er
ates
in
a
th
r
ee
-
p
h
ase,
s
in
g
le
-
s
tag
e
co
n
f
ig
u
r
atio
n
an
d
in
clu
d
es
a
PV
ar
r
ay
,
a
DC
lin
k
ca
p
ac
ito
r
,
a
t
h
r
ee
-
p
h
ase
v
o
ltag
e
s
o
u
r
ce
in
v
er
ter
(
VSI
)
,
an
L
C
L
f
ilter
,
an
d
th
e
g
r
id
[
1
9
]
.
T
h
e
PV a
r
r
ay
g
en
er
ates D
C
p
o
wer
th
at
ch
ar
g
es a
DC
lin
k
ca
p
ac
ito
r
,
f
o
r
m
in
g
th
e
VSI
in
p
u
t,
wh
er
e
th
e
v
ar
ia
b
le
ir
r
ad
ian
ce
a
n
d
tem
p
e
r
atu
r
e
m
u
s
t
b
e
co
n
s
id
er
ed
,
an
d
it
ag
ai
n
s
tab
ilizes
th
e
D
C
b
u
s
v
o
ltag
e
wh
ile
atten
u
atin
g
a
h
ig
h
-
f
r
eq
u
en
cy
r
ip
p
le.
T
h
e
DC
p
o
wer
is
th
en
co
n
v
er
ted
in
to
AC
th
r
o
u
g
h
a
th
r
ee
-
p
h
ase
VSI
s
y
n
c
h
r
o
n
ize
d
to
th
e
g
r
i
d
th
r
o
u
g
h
a
p
h
ase
-
lo
ck
ed
lo
o
p
(
PLL
)
,
wh
er
e
b
y
t
h
e
L
C
L
f
ilter
f
ilter
s
o
u
t
th
e
s
witch
in
g
h
ar
m
o
n
ics
t
o
m
ee
t
th
e
g
r
id
s
tan
d
ar
d
s
.
T
h
e
ANFI
S
-
b
ased
MPPT
co
n
tr
o
ll
er
was
in
co
r
p
o
r
ated
in
to
th
e
in
v
er
te
r
clo
s
ed
-
lo
o
p
s
tr
u
ctu
r
e
with
a
r
ec
o
n
f
ig
u
r
a
b
le
o
u
t
p
u
t,
wh
er
eb
y
th
e
m
o
d
u
latio
n
i
n
d
ex
an
d
s
witch
in
g
s
ig
n
als
wer
e
d
y
n
a
m
ically
ad
ju
s
ted
f
o
r
s
im
u
lta
n
eo
u
s
tr
ac
k
in
g
o
f
th
e
MPP
wh
ile
s
atis
f
ac
to
r
ily
r
eg
u
latin
g
th
e
h
ar
m
o
n
ic
d
is
to
r
tio
n
.
T
h
e
ANFI
S
alg
o
r
ith
m
u
s
es
r
ea
l
-
tim
e
f
ee
d
b
ac
k
f
r
o
m
th
e
PV
ar
r
a
y
(
v
o
ltag
e
an
d
cu
r
r
en
t)
a
n
d
g
r
id
c
u
r
r
e
n
t
h
ar
m
o
n
ics
to
o
p
tim
ize
th
e
in
v
er
ter
p
u
ls
e
-
wid
th
m
o
d
u
latio
n
(
PW
M)
to
k
ee
p
th
e
T
HD
as
lo
w
as
p
o
s
s
ib
le
wh
ile
m
ax
im
izin
g
t
h
e
MPPT
ef
f
i
cien
cy
.
T
h
e
p
r
o
p
o
s
ed
m
o
d
el
h
as
b
ee
n
s
im
u
lated
with
MA
T
L
AB
Simu
lin
k
s
o
f
twar
e,
wh
ich
allo
ws
f
o
r
a
c
o
m
p
r
eh
e
n
s
iv
e
an
aly
s
is
an
d
v
is
u
aliza
tio
n
o
f
th
e
b
eh
av
io
r
o
f
th
e
s
y
s
tem
.
Deta
iled
s
p
ec
if
icatio
n
s
an
d
p
a
r
am
et
er
s
o
f
th
e
co
m
p
o
n
e
n
ts
u
s
ed
in
th
e
s
im
u
latio
n
ar
e
g
iv
en
in
T
a
b
le
1
in
o
r
d
er
to
e
n
s
u
r
e
th
at
th
e
r
esu
lts
ar
e
clea
r
a
n
d
r
ep
r
o
d
u
cib
le.
2
.
2
.
P
V
a
rr
a
y
m
o
dellin
g
Mo
d
ellin
g
PV
ce
lls
is
ess
en
tial
f
o
r
u
n
d
er
s
tan
d
in
g
an
d
o
p
tim
izin
g
s
o
lar
e
n
er
g
y
s
y
s
tem
s
.
T
h
e
s
in
g
le
-
d
io
d
e
m
o
d
el
(
SDM)
is
th
e
d
o
m
in
an
t
ap
p
r
o
ac
h
f
o
r
s
im
u
latin
g
th
eir
elec
tr
ical
b
eh
av
io
r
[
2
7
]
.
I
n
Fig
u
r
e
2
,
th
e
SDM
tr
ea
ts
a
p
h
o
to
v
o
ltaic
ce
l
l
as
an
eq
u
iv
alen
t
cir
cu
it
co
n
s
is
tin
g
o
f
a
cu
r
r
en
t
s
o
u
r
ce
,
a
d
i
o
d
e,
an
d
r
esis
to
r
s
.
T
h
e
cu
r
r
en
t
s
o
u
r
ce
g
en
e
r
ates
p
h
o
to
c
u
r
r
en
t (
I
ph
)
d
ir
ec
tly
p
r
o
p
o
r
tio
n
al
t
o
th
e
in
te
n
s
ity
o
f
th
e
in
cid
en
t
s
o
lar
lig
h
t
an
d
th
e
ce
ll
ar
ea
.
T
h
e
d
io
d
e
i
s
m
o
d
eled
as
a
p
-
n
ju
n
ctio
n
,
wh
ich
ac
co
u
n
ts
f
o
r
th
e
ce
ll’s
n
o
n
lin
ea
r
cu
r
r
e
n
t
-
v
o
ltag
e
p
r
o
p
e
r
ties
.
T
h
e
cir
cu
i
t
in
clu
d
es
a
s
er
ies
r
esis
tan
ce
(
R
s
)
r
ep
r
esen
tin
g
m
ater
ial
an
d
co
n
tact
r
esis
tan
ce
,
an
d
a
s
h
u
n
t
r
esis
tan
ce
(
R
sh
)
ac
co
u
n
tin
g
f
o
r
lea
k
ag
e
c
u
r
r
e
n
ts
[
2
8
]
.
T
h
is
eq
u
iv
ale
n
t
cir
cu
it
s
im
p
lifie
s
th
e
an
aly
s
is
o
f
t
h
e
p
er
f
o
r
m
an
ce
o
f
PV
ce
lls
u
n
d
er
d
if
f
er
en
t
co
n
d
itio
n
s
an
d
th
u
s
en
ab
les
d
esig
n
o
p
tim
izatio
n
a
n
d
ef
f
icien
cy
im
p
r
o
v
e
m
en
ts
.
T
h
e
f
u
n
d
am
en
tal
e
q
u
atio
n
d
escr
ib
in
g
th
e
m
o
d
el
’
s
cu
r
r
en
t
-
v
o
ltag
e
(
I
-
V)
ch
ar
ac
ter
is
tic
is
g
iv
en
as
(
1
)
[
2
9
]
,
[
3
0
]
.
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
Mit
ig
a
tin
g
h
a
r
mo
n
ic
d
is
to
r
tio
n
in
g
r
id
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co
n
n
ec
ted
P
V
s
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:
a
co
mp
a
r
a
tive
…
(
B
o
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r
o
u
a
A
d
el
)
305
=
ℎ
−
−
(
+
)
ℎ
(
1
)
W
h
er
e
I
an
d
V
ar
e
th
e
o
u
tp
u
t
cu
r
r
en
t
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d
v
o
ltag
e,
r
esp
ec
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ely
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h
e
d
io
d
e
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r
r
e
n
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d
is
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lcu
lated
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s
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g
th
e
Sh
o
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d
i
o
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e
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2
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.
=
0
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(
+
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−
1
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(
2
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Her
e,
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0
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th
e
r
ev
er
s
e
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atu
r
atio
n
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r
r
e
n
t,
an
d
n
is
th
e
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ea
lity
f
ac
to
r
.
T
h
e
th
er
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al
v
o
ltag
e
V
T
is
d
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in
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(
3
)
.
=
(
3
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I
n
(
3
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k
is
th
e
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o
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t
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1
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3
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-
23
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,
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is
th
e
ab
s
o
lu
te
tem
p
er
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r
e,
an
d
q
i
s
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e
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o
f
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th
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e
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atu
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r
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T
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n
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,
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e
a
b
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e
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,
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d
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e
c
h
ar
g
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o
f
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tr
o
n
(
1
.
6
0
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0
-
19
C
)
.
Fig
u
r
e
1
.
Pro
p
o
s
ed
PV sy
s
tem
T
ab
le
1
.
Sp
ec
if
icatio
n
s
v
al
u
es f
o
r
th
e
p
r
o
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ed
m
o
d
el
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p
e
c
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f
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c
a
t
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V
a
l
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V
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r
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y
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r
a
t
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p
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r
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pv
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p
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c
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r
c
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i
t
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l
t
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g
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o
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t
h
e
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V
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r
r
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y
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0
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.
6
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t
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r
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i
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c
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p
a
c
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t
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r
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f
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L
f
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l
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r
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t
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LL
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F
r
e
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e
n
c
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t
h
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g
r
i
d
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g
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1
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z
5
0
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1
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0
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4
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V
5
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H
z
Fig
u
r
e
2
.
Sin
g
le
d
io
d
e
m
o
d
el
o
f
PV c
ell
Fig
u
r
e
3
s
h
o
ws
th
e
ch
a
r
ac
ter
is
tics
cu
r
v
es
o
f
cu
r
r
e
n
t
(
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-
V)
an
d
cu
r
r
en
t
(
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-
V)
v
o
ltag
es
i
n
p
h
o
to
v
o
ltaic
m
o
d
u
les
at
d
if
f
er
en
t
le
v
els
o
f
s
o
lar
r
ad
iatio
n
.
Fig
u
r
e
3
(
a)
s
h
o
ws
an
I
-
V
cu
r
v
e
co
r
r
esp
o
n
d
in
g
to
a
r
ad
iatio
n
lev
el
o
f
1
0
0
0
,
7
5
0
,
5
0
0
,
an
d
2
5
0
W
/m
2
,
in
d
icatin
g
th
at
as
th
e
r
ad
iatio
n
in
cr
ea
s
es,
th
e
s
h
o
r
t
cir
cu
it
cu
r
r
en
t
in
cr
ea
s
es
to
a
m
ax
im
u
m
v
alu
e
o
f
1
0
0
0
W
/m
2
.
T
h
e
d
ir
ec
t
co
n
n
ec
tio
n
b
etwe
en
s
o
lar
r
ad
iati
o
n
an
d
PV
m
o
d
u
le
o
u
tp
u
t
c
u
r
r
e
n
t
h
as
b
ee
n
o
b
s
er
v
ed
.
Fig
u
r
e
3
(
b
)
s
h
o
ws
th
e
P
-
V
cu
r
v
e
t
h
at
is
eq
u
iv
ale
n
t,
an
d
t
h
e
r
a
d
iatio
n
co
n
tr
o
ls
th
e
v
o
ltag
e
lev
el
o
f
th
e
p
ea
k
o
f
t
h
e
o
u
tp
u
t.
I
n
p
ar
ticu
lar
,
as
t
h
e
r
a
d
iatio
n
i
n
cr
ea
s
es,
th
e
p
o
we
r
p
r
o
d
u
ctio
n
in
cr
ea
s
es,
an
d
th
e
cu
r
v
e
o
f
1
0
0
0
W
/m
2
s
h
o
ws
th
e
h
ig
h
est
p
ea
k
p
o
wer
,
f
o
llo
wed
b
y
o
t
h
er
lev
els
in
th
e
d
ec
lin
in
g
o
r
d
er
.
T
h
ese
d
at
a
h
ig
h
lig
h
t
th
e
n
ee
d
f
o
r
ef
f
ici
en
t
MPPT
m
eth
o
d
s
to
m
ax
im
i
ze
en
er
g
y
r
ec
o
v
er
y
in
ch
an
g
in
g
en
v
ir
o
n
m
en
tal
co
n
d
itio
n
s
an
d
h
ig
h
lig
h
t
th
e
s
ig
n
if
ican
t
p
ar
t
o
f
s
o
lar
r
a
d
iatio
n
u
s
ed
to
s
elec
t
th
e
ef
f
icien
cy
a
n
d
p
er
f
o
r
m
a
n
ce
o
f
s
o
lar
s
y
s
tem
s
[
3
1
]
.
test
it
an
d
ass
ess
th
e
ef
f
ec
ts
o
f
r
ad
iatio
n
a
n
d
tem
p
er
atu
r
e
u
n
d
er
d
if
f
er
e
n
t e
n
v
ir
o
n
m
e
n
tal
co
n
d
itio
n
s
.
D
i
s
c
r
et
e
1e
-
0
6
s
1000
25
P
V
A
r
r
a
y
D
C
L
i
nk
3
ph2
L
I
n
ve
r
te
r
<
T
e
m
p
e
r
a
tu
r
e
(d
e
g
C
)
>
<
I
r
r
a
d
i
a
n
c
e
(W
/
m
2
)>
<
I
_
PV
>
<
V
_
PV
>
V
p
v
I
pv
An
f
i
s
B
as
ed
M
PP
T
in
out
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d
c
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e
f
L
C
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P
as
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em
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se
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a
b
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b
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o
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r
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Sco
p
es
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.
1
7
,
No
.
1
,
Ma
r
c
h
20
2
6
:
303
-
3
16
306
Fig
u
r
e
4
s
h
o
ws
th
e
im
p
ac
t
o
f
tem
p
er
atu
r
e
ch
an
g
es
o
n
th
e
I
-
V
an
d
P
-
V
ch
ar
ac
ter
is
tics
cu
r
v
es
o
f
PV
m
o
d
u
les.
Fig
u
r
e
4
(
a)
p
r
esen
ts
th
e
I
–
V
cu
r
v
es
at
f
o
u
r
d
if
f
er
e
n
t
tem
p
er
atu
r
es:
1
5
°C
,
2
5
°C
,
3
5
°C
,
an
d
4
5
°C
.
W
h
en
th
e
tem
p
er
atu
r
e
r
is
es,
s
h
o
r
t
cir
c
u
it
cu
r
r
en
t
r
em
ain
s
r
el
ativ
ely
s
tab
le,
o
p
en
cir
cu
it v
o
l
tag
e
d
ec
r
ea
s
es,
a
n
d
o
v
er
all
cu
r
v
es
ar
e
m
o
v
ed
to
lo
wer
v
o
ltag
es
at
h
ig
h
er
tem
p
er
atu
r
es.
T
h
is
b
eh
av
i
o
r
in
d
icate
s
th
at
h
ig
h
tem
p
er
atu
r
es
m
ay
h
av
e
a
n
eg
ativ
e
im
p
ac
t
o
n
th
e
v
o
lta
g
e
o
u
tp
u
t
o
f
PV
m
o
d
u
les.
Fig
u
r
e
4
(
b
)
is
th
e
co
r
r
esp
o
n
d
in
g
P
-
V
cu
r
v
e
an
d
h
ig
h
lig
h
ts
th
e
MPPs
o
f
ea
ch
tem
p
er
atu
r
e
c
o
n
d
itio
n
.
Op
tim
a
l
o
u
tp
u
t
is
attain
ed
at
th
e
m
in
im
u
m
v
o
ltag
e
an
d
a
tem
p
er
atu
r
e
o
f
2
5
°C
.
Op
tim
u
m
o
u
t
p
u
t
is
ac
h
iev
ed
with
a
m
in
im
u
m
v
o
ltag
e
an
d
a
tem
p
er
atu
r
e
o
f
2
5
°C
.
Ho
wev
er
,
as
tem
p
er
atu
r
es
r
is
e
ab
o
v
e
th
at
th
r
esh
o
ld
,
th
e
m
ax
im
u
m
p
o
wer
f
alls
s
ig
n
if
ican
tly
.
T
h
is
s
itu
atio
n
h
ig
h
lig
h
ts
th
e
cr
u
cial
r
o
le
o
f
tem
p
er
at
u
r
e
m
a
n
ag
em
e
n
t
i
n
PV
s
y
s
tem
s
,
as
ex
ce
s
s
iv
e
h
ea
t c
an
s
ig
n
if
ican
tly
r
ed
u
ce
e
f
f
icien
cy
a
n
d
o
v
er
al
l e
n
er
g
y
p
r
o
d
u
ctio
n
.
T
h
e
in
tr
o
d
u
ctio
n
o
f
ef
f
icien
t
co
o
lin
g
m
et
h
o
d
s
is
th
er
ef
o
r
e
e
s
s
en
tial to
in
cr
ea
s
e
p
er
f
o
r
m
a
n
ce
u
n
d
er
d
if
f
e
r
en
t te
m
p
er
atu
r
e
co
n
d
itio
n
s
[
3
2
]
.
T
h
is
s
tu
d
y
i
n
v
esti
g
ates
th
e
p
o
wer
o
u
tp
u
t
ca
p
a
b
ilit
ies
o
f
th
e
Su
n
Po
wer
SP
R
-
215
-
W
HT
-
U
PV
m
o
d
u
le,
co
n
f
ig
u
r
e
d
with
1
9
s
er
ies
-
co
n
n
ec
ted
m
o
d
u
les
p
er
s
tr
in
g
an
d
2
5
p
ar
allel
s
tr
in
g
s
,
r
esu
ltin
g
i
n
a
to
tal
p
o
wer
ca
p
ac
ity
o
f
u
p
to
1
0
2
k
W
.
Deta
iled
p
ar
am
eter
s
o
f
t
h
e
PV
m
o
d
u
le
ar
e
p
r
esen
ted
in
T
ab
le
2
,
wh
ich
s
u
p
p
o
r
ts
th
e
an
al
y
s
is
o
f
its
p
er
f
o
r
m
an
ce
ch
ar
ac
ter
is
tics
.
(
a)
(
b
)
Fig
u
r
e
3
.
E
f
f
ec
t o
f
s
o
lar
ir
r
ad
i
an
ce
o
n
(
a)
I
-
V
ch
ar
a
cter
is
tics
cu
r
v
e
a
n
d
(
b
)
P
-
V
ch
a
r
ac
ter
is
tics
cu
r
v
e
(
a)
(
b
)
Fig
u
r
e
4
.
E
f
f
ec
t
o
f
tem
p
er
atu
r
e
o
n
(
a
)
I
-
V
c
h
a
r
ac
ter
is
tics
cu
r
v
e
an
d
(
b
)
P
-
V
c
h
ar
ac
ter
is
tics
cu
r
v
e
T
ab
le
2
.
Su
n
Po
wer
SP
R
-
215
-
W
HT
-
U
PV m
o
d
u
le
s
p
ec
if
icatio
n
S
p
e
c
i
f
i
c
a
t
i
o
n
V
a
l
u
e
M
a
x
i
m
u
m
p
o
w
e
r
P
MP
(W)
2
1
4
.
9
2
O
p
e
n
c
i
r
c
u
i
t
v
o
l
t
a
g
e
V
oc
(V)
4
8
.
3
V
o
l
t
a
g
e
a
t
M
P
P
V
MP
(V)
3
9
.
8
S
h
o
r
t
-
c
i
r
c
u
i
t
c
u
r
r
e
n
t
I
sc
(A)
5
.
8
C
u
r
r
e
n
t
a
t
M
P
P
I
MP
(A)
5
.
4
Te
mp
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r
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c
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(
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mp
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%
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0
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5
8
9
7
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
Mit
ig
a
tin
g
h
a
r
mo
n
ic
d
is
to
r
tio
n
in
g
r
id
-
co
n
n
ec
ted
P
V
s
ystems
:
a
co
mp
a
r
a
tive
…
(
B
o
u
led
r
o
u
a
A
d
el
)
307
2
.
3
.
M
P
P
T
a
pp
ro
a
ches
MPPT
is
a
cr
itical
f
u
n
ctio
n
in
PV
s
y
s
tem
s
,
en
ab
lin
g
o
p
tim
al
en
er
g
y
ex
tr
ac
tio
n
u
n
d
er
d
y
n
am
ic
en
v
ir
o
n
m
en
tal
c
o
n
d
itio
n
s
s
u
ch
as
v
a
r
y
in
g
s
o
lar
ir
r
ad
ia
n
ce
an
d
tem
p
e
r
atu
r
e
[
3
3
]
.
I
t
m
ax
im
izes
e
n
er
g
y
g
ath
er
in
g
,
im
p
r
o
v
es
g
e
n
er
al
s
y
s
tem
ef
f
icien
cy
,
an
d
r
aises
PV
in
s
tallatio
n
r
etu
r
n
o
n
in
v
estme
n
t
.
MPPT
wo
r
k
s
b
y
co
n
s
tan
tly
tr
ac
k
i
n
g
t
h
e
s
o
lar
p
an
el
v
o
ltag
e
an
d
cu
r
r
en
t
an
d
ad
ju
s
tin
g
t
h
e
elec
tr
ical
o
p
er
atin
g
p
o
i
n
t
to
ex
tr
ac
t
m
o
s
t
o
f
th
e
p
o
wer
.
T
h
e
s
y
s
tem
id
en
tifie
s
an
d
m
ain
ta
in
s
th
e
m
ax
im
u
m
p
o
wer
p
o
in
t
(
MPP)
th
r
o
u
g
h
an
alg
o
r
ith
m
t
h
at
is
ab
le
to
a
d
ju
s
t
th
e
MPP
ac
co
r
d
i
n
g
t
o
s
o
lar
ir
r
ad
ian
ce
,
am
b
ien
t
te
m
p
er
atu
r
e,
an
d
th
e
ch
ar
ac
ter
is
tics
o
f
th
e
p
h
o
to
v
o
ltaic
p
an
els
[
3
4
]
.
MPPT
g
u
a
r
an
tees
in
cr
ea
s
ed
b
atter
y
life
i
n
o
f
f
-
g
r
i
d
s
y
s
tem
s
,
th
u
s
r
ed
u
cin
g
t
h
e
en
er
g
y
lo
s
s
f
r
o
m
p
h
o
t
o
v
o
ltaic
s
y
s
tem
s
an
d
en
s
u
r
in
g
th
at
s
o
lar
p
an
el
s
p
er
f
o
r
m
b
est
in
d
if
f
er
en
t w
ea
th
e
r
co
n
d
itio
n
s
[
3
5
]
.
2
.
3
.
1
.
I
C
M
P
P
T
t
ec
hn
i
qu
e
I
n
cr
em
en
tal
c
o
n
d
u
cta
n
ce
(
I
C
)
is
a
wid
ely
u
s
ed
MPPT
tech
n
iq
u
e
u
s
ed
in
PV
s
y
s
tem
s
to
ad
d
r
ess
th
e
non
-
lin
ea
r
p
o
wer
o
u
tp
u
t
an
d
o
p
er
atin
g
v
o
ltag
e
d
y
n
am
ics
o
f
s
o
lar
p
an
els
u
n
d
er
v
ar
y
in
g
en
v
ir
o
n
m
en
tal
co
n
d
itio
n
s
[
3
6
]
,
[
3
7
]
.
I
C
is
o
f
ten
f
av
o
r
e
d
o
v
e
r
h
eu
r
is
tic
m
eth
o
d
s
lik
e
p
er
tu
r
b
an
d
o
b
s
er
v
e
(
P&
O)
b
ec
au
s
e
it
u
s
es
an
aly
tical
cu
r
r
e
n
t
an
d
v
o
ltag
e
d
er
iv
ativ
es
to
ac
cu
r
ately
p
in
p
o
in
t
th
e
MPP,
wh
er
e
th
e
P
-
V
s
lo
p
e
(
d
P/d
V)
r
ea
ch
es
ze
r
o
[
3
6
]
.
T
h
r
o
u
g
h
t
h
is
tech
n
iq
u
e,
th
e
s
y
s
tem
r
ed
u
ce
s
s
tead
y
-
s
tate
p
o
wer
o
s
cillatio
n
s
ar
o
u
n
d
t
h
e
MPP wh
ile
ef
f
icien
tly
m
ain
tain
in
g
a
f
ast r
esp
o
n
s
e
to
s
wif
t c
h
an
g
es in
ir
r
a
d
ian
ce
an
d
tem
p
er
atu
r
e
[
3
8
]
.
T
h
e
I
C
MPPT
f
lo
wch
ar
t,
illu
s
tr
ated
in
Fig
u
r
e
5
,
o
u
tlin
e
s
a
s
tr
u
ctu
r
ed
p
r
o
ce
s
s
f
o
r
d
y
n
am
ically
ad
ju
s
tin
g
th
e
r
ef
e
r
en
ce
v
o
ltag
e
V
ref
to
ac
h
iev
e
o
p
tim
al
p
o
wer
ex
tr
ac
tio
n
.
T
h
e
co
n
tr
o
l
s
y
s
tem
b
eg
in
s
b
y
ac
q
u
ir
in
g
m
ea
s
u
r
em
e
n
ts
o
f
t
h
e
PV
s
y
s
tem
'
s
v
o
ltag
e
V(
k
)
an
d
cu
r
r
en
t
I
(
k
)
at
th
e
c
u
r
r
en
t
s
tep
an
d
th
e
n
ca
lcu
lates th
e
in
cr
em
en
tal
ch
a
n
g
es in
v
o
ltag
e
(
Δ
V)
an
d
c
u
r
r
en
t (
Δ
I
)
u
s
in
g
(
4
)
a
n
d
(
5
)
[
3
9
]
,
[
4
0
]
.
∆
=
(
)
−
(
−
1
)
(
4
)
∆
=
(
)
−
(
−
1
)
(
5
)
I
f
Δ
V
is
ze
r
o
,
in
d
icatin
g
n
o
v
o
ltag
e
ch
an
g
e,
th
e
alg
o
r
ith
m
ch
ec
k
s
if
:
+
(
∆
∆
)
=
0
(
6
)
T
h
is
co
n
d
itio
n
s
ig
n
if
ies
th
at
th
e
MPP
h
as
b
ee
n
r
ea
ch
ed
,
an
d
th
e
s
y
s
tem
m
ain
tain
s
th
e
cu
r
r
e
n
t
r
ef
e
r
en
ce
v
o
ltag
e.
I
f
th
e
MPP h
as n
o
t b
e
en
r
ea
ch
ed
,
th
e
f
l
o
wch
ar
t e
v
al
u
ates th
e
s
ig
n
o
f
th
e
d
er
iv
ativ
e
ter
m
:
+
(
∆
∆
)
>
0
(
7
)
T
h
e
o
p
e
r
atin
g
p
o
in
t
is
to
th
e
lef
t
o
f
th
e
MPP,
n
ec
ess
itatin
g
an
in
cr
ea
s
e
in
Vr
e
f
to
s
h
if
t
t
o
war
d
th
e
m
a
x
im
u
m
p
o
wer
p
o
in
t.
C
o
n
v
e
r
s
ely
,
if
:
+
(
∆
∆
)
<
0
(
8
)
T
h
e
s
y
s
tem
m
u
s
t
d
ec
r
ea
s
e
Vr
ef
to
m
o
v
e
d
ir
ec
tly
to
th
e
MP
P.
T
h
is
iter
ativ
e
p
r
o
ce
s
s
co
n
ti
n
u
es
u
n
til
th
e
o
p
tim
al
v
o
ltag
e
is
ac
h
iev
ed
,
m
ax
im
izin
g
e
n
er
g
y
y
ield
an
d
b
o
o
s
tin
g
th
e
PV
s
y
s
tem
's
ef
f
icien
cy
.
T
h
e
(
6
)
s
er
v
es
as
th
e
co
r
e
cr
iter
i
o
n
f
o
r
d
ete
r
m
in
in
g
th
e
n
ec
ess
ar
y
ad
ju
s
tm
en
ts
to
Vr
ef
b
ased
o
n
th
e
in
cr
e
m
en
tal
ch
an
g
es in
cu
r
r
en
t a
n
d
v
o
ltag
e
.
2
.
3
.
2
.
ANF
I
S
-
M
P
P
T
a
pp
ro
a
ch
ANFI
S
is
a
h
ig
h
-
le
v
el
co
m
p
u
t
atio
n
al
in
tellig
en
ce
tech
n
iq
u
e
th
at
s
y
n
er
g
izes
la
n
g
u
a
g
e
p
r
o
c
ess
in
g
an
d
f
u
zz
y
l
o
g
ic
ca
p
ab
ilit
ies
with
th
e
lear
n
in
g
a
n
d
a
d
ap
tatio
n
m
e
ch
an
is
m
s
o
f
a
r
tific
ial
n
eu
r
al
n
etwo
r
k
s
[
3
9
]
,
[
4
1
]
.
T
h
is
h
y
b
r
id
ar
ch
itectu
r
e
all
o
ws
ANFI
S
to
m
o
d
el
co
m
p
le
x
n
o
n
lin
ea
r
i
n
p
u
t
-
o
u
tp
u
t
r
elatio
n
s
h
ip
s
b
y
m
ea
n
s
o
f
a
s
y
s
tem
atic
lear
n
in
g
p
r
o
ce
s
s
,
wh
ich
m
ak
es
it
p
ar
ticu
lar
ly
s
u
ited
f
o
r
MPT
ap
p
licatio
n
s
wh
er
e
th
e
o
p
tim
al
o
p
er
atin
g
p
o
in
t
is
h
ig
h
ly
n
o
n
li
n
ea
r
in
r
elatio
n
to
a
n
u
m
b
er
o
f
en
v
ir
o
n
m
en
tal
v
ar
iab
les.
ANFI
S
u
s
es
h
is
to
r
ical
d
ata
to
lear
n
th
e
c
o
m
p
lex
m
a
p
p
in
g
b
etwe
en
en
v
ir
o
n
m
e
n
tal
co
n
d
itio
n
s
(
tem
p
er
atu
r
e
a
n
d
ir
r
ad
ian
ce
)
a
n
d
th
e
co
r
r
esp
o
n
d
in
g
o
p
tim
al
v
o
ltag
e
th
at
y
ield
s
m
ax
im
u
m
p
o
wer
ex
tr
ac
tio
n
,
in
co
n
tr
ast
to
tr
ad
itio
n
al
MPPT
alg
o
r
ith
m
s
th
at
r
ely
o
n
in
s
tan
t
an
eo
u
s
m
ea
s
u
r
em
e
n
ts
an
d
p
r
e
d
eter
m
in
ed
d
ec
is
io
n
r
u
les.
T
h
e
d
ev
elo
p
m
en
t
o
f
th
e
ANFI
S
-
b
ased
MPPT
co
n
tr
o
ller
n
ec
ess
itate
s
r
o
b
u
s
t
d
atasets
th
at
en
ca
p
s
u
late
th
e
n
o
n
lin
ea
r
r
elatio
n
s
h
ip
b
etwe
en
en
v
ir
o
n
m
e
n
tal
v
ar
iab
les an
d
th
e
p
h
o
to
v
o
ltaic
(
PV)
s
y
s
tem
’
s
MPP
[
4
2
]
.
T
o
ac
h
iev
e
th
is
,
s
im
u
latio
n
-
b
ased
d
ata
g
en
er
atio
n
was
em
p
lo
y
e
d
,
lev
er
ag
i
n
g
th
e
s
in
g
le
-
d
io
d
e
m
o
d
el
o
f
th
e
PV
m
o
d
u
le,
wh
ic
h
in
co
r
p
o
r
ates
tem
p
er
atu
r
e
-
d
ep
en
d
en
t
cu
r
r
en
t
an
d
v
o
ltag
e
c
o
ef
f
icien
ts
Ki
an
d
Kv
to
r
e
p
licate
r
ea
l
-
wo
r
ld
o
p
er
atio
n
al
d
y
n
am
ics.
T
h
e
p
h
o
to
cu
r
r
en
t
I
ph
an
d
o
p
en
-
cir
c
u
it
v
o
ltag
e
V
oc
wer
e
ad
ju
s
ted
u
s
in
g
Ki
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.
1
7
,
No
.
1
,
Ma
r
c
h
20
2
6
:
303
-
3
16
308
an
d
Kv
,
r
esp
ec
tiv
ely
,
to
ac
c
o
u
n
t
f
o
r
tem
p
e
r
atu
r
e
v
ar
iatio
n
s
T
,
wh
ile
ir
r
ad
ia
n
ce
G
s
ca
le
s
th
e
p
h
o
t
o
cu
r
r
e
n
t
p
r
o
p
o
r
tio
n
ally
.
B
y
s
y
s
tem
atica
lly
v
ar
y
in
g
G
(
0
–
1
0
0
0
W
/m
²)
an
d
T
(
1
5
–
4
5
°C
)
,
th
e
I
-
V
c
h
ar
ac
ter
is
tics
wer
e
n
u
m
er
ically
s
o
lv
e
d
to
ex
tr
ac
t
V
mpp
an
d
I
mpp
,
g
en
er
ati
n
g
a
co
m
p
r
eh
en
s
iv
e
d
ataset
th
at
r
e
f
lects
th
e
PV
ar
r
ay
’
s
r
esp
o
n
s
e
to
d
y
n
am
ic
co
n
d
itio
n
s
.
T
h
e
(
9
)
a
n
d
(
1
0
)
is
u
s
ed
to
c
alcu
late
V
mpp
an
d
I
mpp
[
4
2
]
.
=
(
,
+
(
−
)
)
.
(
9
)
=
,
+
(
−
)
(
1
0
)
T
h
e
s
tan
d
ar
d
test
co
n
d
itio
n
s
(
STC)
s
u
b
s
cr
ip
t
r
ep
r
esen
ts
th
e
s
tan
d
ar
d
test
co
n
d
itio
n
s
(
GSTC
=
1
0
0
0
W
/m
2
,
T
STC
=
2
5
°C
)
,
Ki
r
ep
r
esen
ts
th
e
cu
r
r
en
t
tem
p
er
atu
r
e
co
ef
f
icien
t
(
A/°C
)
,
Kv
r
e
p
r
esen
ts
th
e
v
o
ltag
e
tem
p
er
atu
r
e
c
o
ef
f
icien
t (
V/°C
)
.
T
h
e
ANFI
S
ar
ch
itectu
r
e,
illu
s
tr
ated
in
Fig
u
r
e
6
,
tak
es
th
i
s
s
im
u
lated
n
o
r
m
alize
d
d
ata
s
et
as
it
s
p
r
im
ar
y
in
p
u
t,
s
o
th
at
th
e
f
u
zz
y
in
f
er
en
ce
s
y
s
tem
ca
n
u
s
e
th
e
im
p
licit
co
r
r
elatio
n
s
b
etwe
en
en
v
ir
o
n
m
en
tal
in
p
u
ts
an
d
o
p
tim
al
v
o
ltag
e
as o
u
tp
u
t.
T
h
e
ap
p
r
o
ac
h
h
el
p
s
to
tr
ain
th
e
ANFI
S c
o
n
tr
o
ller
o
n
p
h
y
s
ically
ac
cu
r
at
e
wo
r
s
t
-
ca
s
e
s
ce
n
ar
io
s
s
u
ch
as
r
ap
id
ir
r
a
d
ian
ce
tr
an
s
ien
ts
an
d
th
er
m
al
g
r
ad
ien
ts
,
a
n
d
is
well
p
r
ep
ar
e
d
to
r
e
d
u
ce
h
ar
m
o
n
ic
d
is
to
r
tio
n
wh
ile
m
a
in
tain
in
g
MPPT
ef
f
icac
y
in
g
r
id
-
co
n
n
ec
ted
s
y
s
tem
s
.
T
h
e
A
NFI
S
-
b
ased
MPPT
in
th
is
wo
r
k
u
s
es
a
f
iv
e
-
lay
e
r
ar
ch
itectu
r
e
to
m
a
p
ir
r
ad
ia
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ce
G
an
d
tem
p
er
at
u
r
e
T
in
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u
ts
to
th
e
o
p
tim
al
v
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ltag
e
V
mpp
o
u
t
p
u
t.
L
a
y
er
1
(
f
u
zz
if
icatio
n
)
is
a
r
ep
r
esen
tat
io
n
o
f
lin
g
u
is
tic
v
ar
iab
les
in
wh
ich
m
em
b
e
r
s
h
ip
f
u
n
ctio
n
s
ar
e
u
s
ed
t
o
tr
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s
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o
r
m
cr
is
p
in
p
u
ts
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to
f
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zz
y
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et
s
.
L
ay
er
2
(
r
u
le)
u
s
es
f
u
zz
y
lo
g
ic
p
r
in
ci
p
les
to
d
eter
m
in
e
th
e
f
ir
in
g
f
o
r
ce
o
f
a
p
r
ed
ef
in
ed
I
F
-
T
HE
N
r
u
le.
L
a
y
er
3
(
n
o
r
m
aliza
tio
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s
ca
les
th
ese
f
ir
in
g
f
o
r
ce
s
to
en
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u
r
e
th
at
t
h
eir
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tal
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u
m
is
th
e
s
am
e
as
u
n
ity
,
th
e
r
eb
y
r
e
d
u
cin
g
th
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ig
u
ity
o
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th
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r
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le
weig
h
t.
L
a
y
er
4
(
d
ef
u
zz
in
g
)
u
s
es
lin
ea
r
f
u
n
cti
o
n
s
to
ca
lcu
late
th
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co
r
r
esp
o
n
d
in
g
p
ar
a
m
eter
s
o
f
ea
ch
r
u
le.
I
n
th
e
f
in
al
s
tag
e,
L
ay
er
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(
s
u
m
m
atio
n
)
c
o
m
b
i
n
es
th
e
weig
h
ted
r
esu
lts
f
r
o
m
L
ay
er
4
to
y
ield
a
p
r
ec
is
e
V
m
p
p
v
alu
e,
e
n
ab
lin
g
ac
cu
r
ate
r
eg
u
latio
n
in
ch
a
n
g
i
n
g
en
v
ir
o
n
m
en
tal
co
n
d
itio
n
s
.
T
h
is
h
y
b
r
id
s
tr
u
ctu
r
e
u
s
es
n
eu
r
al
n
etwo
r
k
s
to
ad
ap
tiv
ely
lear
n
m
em
b
er
s
h
ip
f
u
n
ctio
n
s
,
an
d
u
s
es
f
u
zz
y
lo
g
ic
to
in
ter
p
r
et
r
u
les
-
b
ased
d
ec
is
io
n
-
m
ak
in
g
,
t
h
u
s
ac
h
iev
in
g
h
ig
h
p
er
f
o
r
m
an
ce
o
f
MPPT
f
o
r
d
if
f
er
en
t
ir
r
a
d
iatio
n
s
.
T
h
e
s
tr
u
ctu
r
e
was
d
esig
n
ed
t
o
co
n
v
er
t
s
o
lar
ir
r
ad
iatio
n
an
d
tem
p
er
at
u
r
e
in
to
th
r
ee
ap
p
r
o
p
r
iate
m
em
b
er
s
h
ip
f
u
n
ctio
n
s
(
MFs),
as
illu
s
tr
ated
in
Fig
u
r
es
7
an
d
8
.
T
h
e
s
h
ap
e
o
f
th
ese
MFs
g
en
er
ated
b
y
th
e
ANFI
S
co
n
tr
o
ller
ev
o
lv
es
th
r
o
u
g
h
o
u
t
th
e
tr
ain
in
g
p
h
ase.
T
h
e
f
o
r
m
s
o
f
th
e
M
Fs
wer
e
o
b
tain
ed
d
u
r
in
g
an
d
at
th
e
co
n
clu
s
io
n
o
f
th
e
tr
ain
in
g
p
h
ase.
Fig
u
r
e
5
.
Flo
wch
ar
t
o
f
I
C
alg
o
r
ith
m
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
Mit
ig
a
tin
g
h
a
r
mo
n
ic
d
is
to
r
tio
n
in
g
r
id
-
co
n
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ec
ted
P
V
s
ystems
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a
co
mp
a
r
a
tive
…
(
B
o
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led
r
o
u
a
A
d
el
)
309
Fig
u
r
e
6
.
ANFI
S
-
b
ased
MPPT
s
tr
u
ctu
r
e
Fig
u
r
e
7
.
I
r
r
ad
ia
n
ce
in
p
u
t M
F
Fig
u
r
e
8
.
T
e
m
p
er
atu
r
e
in
p
u
t
MF
Fig
u
r
e
9
g
r
ap
h
ically
d
ep
icts
th
e
f
u
zz
y
r
u
les
f
o
r
a
tem
p
er
at
u
r
e
o
f
2
3
°C
an
d
s
o
lar
ir
r
ad
ia
tio
n
o
f
6
5
0
W
/m
²,
illu
s
tr
atin
g
th
e
r
elatio
n
s
h
ip
s
an
d
co
r
r
elatio
n
s
b
etwe
e
n
th
e
v
ar
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les.
All
co
n
d
itio
n
s
ca
n
b
e
ad
ju
s
ted
b
y
m
an
ip
u
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e
s
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o
n
th
e
g
r
ap
h
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As
in
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icate
d
in
th
e
f
in
al
co
lu
m
n
,
th
e
tem
p
er
at
u
r
e
r
a
n
g
es
f
r
o
m
1
5
°C
to
4
5
°C
,
s
o
lar
ir
r
ad
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n
v
ar
ies
b
etwe
en
0
an
d
1
0
0
0
W
/m
²,
an
d
th
e
MPP v
o
ltag
e
ch
a
n
g
es a
c
co
r
d
in
g
l
y
.
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.
1
7
,
No
.
1
,
Ma
r
c
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:
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3
16
310
Fig
u
r
e
9
.
T
h
e
f
u
zz
y
r
u
les s
u
r
f
ac
e
o
f
ANFI
S c
o
n
tr
o
ller
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
h
e
d
y
n
am
ic
ir
r
a
d
ian
ce
p
r
o
f
il
e
u
s
ed
in
th
is
s
tu
d
y
,
as
s
h
o
wn
in
Fig
u
r
e
1
0
,
was
m
eticu
lo
u
s
ly
cr
af
ted
to
r
ep
licate
r
ea
l
-
w
o
r
ld
s
o
lar
v
ar
iab
ilit
y
an
d
r
ig
o
r
o
u
s
ly
ev
alu
ate
th
e
p
e
r
f
o
r
m
an
ce
o
f
th
e
p
r
o
p
o
s
ed
ANFI
S
-
b
ased
MPPT
co
n
tr
o
ller
.
T
h
e
p
r
o
f
ile
en
co
m
p
ass
es
a
1
.
3
5
-
s
ec
o
n
d
s
im
u
latio
n
in
ter
v
al,
ch
ar
ac
ter
ized
b
y
ab
r
u
p
t
f
lu
ctu
atio
n
s
an
d
tr
an
s
itio
n
s
b
etwe
en
4
5
0
W
/m
²
an
d
1
0
0
0
W
/m
²
ir
r
ad
iatio
n
lev
els.
T
h
e
s
e
v
ar
iatio
n
s
wer
e
d
elib
er
ately
s
tr
u
ctu
r
ed
to
s
im
u
late
tr
an
s
itio
n
al
en
v
ir
o
n
m
en
tal
co
n
d
itio
n
s
s
u
ch
as
s
u
d
d
en
clo
u
d
co
v
er
an
d
r
ap
id
s
o
lar
in
ten
s
ity
c
h
an
g
es,
ch
allen
g
in
g
th
e
s
tab
ilit
y
a
n
d
r
esp
o
n
s
iv
en
ess
o
f
g
r
id
tied
PV sy
s
tem
s
in
p
r
ac
tical
ap
p
licatio
n
s
.
T
h
e
g
r
ap
h
s
h
o
ws
a
s
h
ar
p
g
r
a
d
ien
t
o
f
0
.
3
5
,
0
.
7
,
a
n
d
1
.
0
5
s
ec
o
n
d
s
,
s
i
m
u
lated
in
ex
tr
e
m
e
s
ce
n
ar
io
s
,
an
d
v
alid
ates
th
e
co
n
tr
o
ller
'
s
ab
ilit
y
to
m
ain
tain
MPPT
ef
f
icien
cy
an
d
s
u
p
p
r
ess
h
ar
m
o
n
ic
d
is
to
r
tio
n
.
T
h
is
p
r
o
f
ile
en
s
u
r
e
s
co
m
p
r
eh
e
n
s
iv
e
test
in
g
o
f
th
e
ad
ap
tab
ilit
y
o
f
th
e
ANFI
S
m
o
d
el,
h
i
g
h
lig
h
tin
g
its
ab
ilit
y
to
r
ec
alib
r
ate
p
o
wer
ex
tr
ac
tio
n
s
tr
ateg
ies u
n
d
er
d
is
co
n
tin
u
o
u
s
s
o
lar
in
p
u
t swif
tly
.
T
h
is
ex
p
er
im
en
tal
s
etu
p
alig
n
s
with
th
e
s
tu
d
y
'
s
o
b
jectiv
e
o
f
e
v
alu
atin
g
T
HD
m
itig
atio
n
an
d
e
n
er
g
y
y
ield
o
p
tim
izatio
n
in
g
r
i
d
-
tied
s
y
s
tem
s
s
u
b
jecte
d
to
u
n
p
r
ed
ictab
le
ir
r
ad
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n
d
y
n
a
m
ics.
T
ab
le
1
s
u
m
m
ar
izes
th
e
k
e
y
p
ar
am
eter
s
o
f
th
e
m
o
d
el
p
r
o
p
o
s
ed
i
n
Fig
u
r
e
1
.
Fig
u
r
e
1
0
.
I
r
r
a
d
ian
ce
p
r
o
f
ile
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
Mit
ig
a
tin
g
h
a
r
mo
n
ic
d
is
to
r
tio
n
in
g
r
id
-
co
n
n
ec
ted
P
V
s
ystems
:
a
co
mp
a
r
a
tive
…
(
B
o
u
led
r
o
u
a
A
d
el
)
311
3
.
1
.
T
H
D
a
na
ly
s
is
3
.
1
.
1
.
T
H
D
a
na
ly
s
is
a
t
8
0
0
T
h
e
p
er
f
o
r
m
a
n
ce
o
f
MPPT
tech
n
iq
u
es
at
an
ir
r
ad
ian
c
e
lev
e
l
o
f
8
0
0
W
/m
2
is
d
etailed
in
Fig
u
r
e
1
1
,
wh
ich
p
r
esen
ts
th
e
h
ar
m
o
n
ic
s
p
ec
tr
u
m
p
lo
ts
f
o
r
b
o
th
c
o
n
tr
o
l
s
tr
ateg
ies
,
f
u
lf
illi
n
g
t
h
e
r
eq
u
ir
em
e
n
t
f
o
r
v
is
u
aliza
tio
n
o
f
th
e
h
ar
m
o
n
ic
co
n
ten
t.
Un
d
er
th
is
co
n
d
itio
n
,
th
e
ANFI
S
-
b
ased
M
PP
T
s
tr
at
eg
y
(
Fig
u
r
e
1
1
(
a)
)
ac
h
iev
ed
a
T
HD
v
alu
e
o
f
0
.
3
8
%.
On
th
e
o
th
er
h
an
d
,
th
e
c
o
n
v
en
tio
n
al
in
cr
em
e
n
tal
co
n
d
u
ctan
ce
(IC
-
MPPT)
tech
n
iq
u
e
(
Fig
u
r
e
1
1
(
b
)
)
p
r
o
d
u
ce
d
a
h
ig
h
er
T
HD
o
f
0
.
6
5
%.
T
h
is
v
ar
iatio
n
h
ig
h
lig
h
ts
th
e
ANFI
S
m
eth
o
d
'
s
ex
ce
p
tio
n
al
ca
p
ab
ilit
y
in
r
e
d
u
cin
g
h
ar
m
o
n
ic
d
is
to
r
tio
n
.
T
h
e
v
is
u
aliza
tio
n
o
f
th
e
h
ar
m
o
n
ic
s
p
ec
tr
u
m
d
em
o
n
s
tr
ates th
at
th
e
ad
ap
tiv
e
ANFI
S c
o
n
tr
o
ller
ef
f
ec
tiv
ely
d
im
in
is
h
es th
e
m
ag
n
itu
d
e
o
f
s
p
ec
if
ic
lo
wer
-
o
r
d
e
r
h
ar
m
o
n
ics r
esu
ltin
g
f
r
o
m
th
e
s
witch
in
g
b
eh
a
v
io
r
o
f
th
e
VSI
.
(
a)
(
b
)
Fig
u
r
e
1
1
.
T
HD
an
aly
s
is
at
8
0
0
W
/m
2
: (
a)
ANFI
S
-
MPPT
an
d
(
b
)
I
C
-
MPPT
3
.
1
.
2
.
T
H
D
a
na
ly
s
is
a
t
4
5
0
Fig
u
r
e
1
2
p
r
o
v
id
es
a
c
o
m
p
a
r
ativ
e
T
HD
an
aly
s
is
at
th
e
l
o
wer
ir
r
ad
ia
n
ce
lev
el
o
f
4
5
0
W
/m
²,
a
s
ce
n
ar
io
th
at
r
ig
o
r
o
u
s
ly
c
h
allen
g
es
th
e
ad
ap
ta
b
ilit
y
o
f
th
e
MPPT
co
n
tr
o
ller
s
u
n
d
er
less
-
th
an
-
o
p
tim
al
s
o
lar
co
n
d
itio
n
s
.
Fig
u
r
e
1
2
(
a)
s
h
o
ws
th
e
T
HD
p
r
o
f
ile
o
f
th
e
ANFI
S
-
MPPT
s
tr
ateg
y
,
wh
ich
r
eg
is
ter
s
a
T
HD
o
f
0
.
8
0
%.
T
h
is
r
elativ
ely
lo
w
d
is
to
r
tio
n
in
d
icate
s
th
e
ab
ilit
y
o
f
th
e
ANFI
S
co
n
tr
o
ller
to
ef
f
ec
tiv
ely
m
itig
ate
h
ar
m
o
n
ic
d
is
to
r
tio
n
an
d
th
u
s
im
p
r
o
v
e
th
e
q
u
ality
o
f
th
e
p
o
wer
o
u
tp
u
t
ev
en
u
n
d
er
lo
wer
s
o
lar
ir
r
a
d
ian
ce
co
n
d
itio
n
s
.
C
o
n
v
er
s
ely
,
Fig
u
r
e
1
2
(
b
)
illu
s
tr
ates
th
e
I
C
-
M
PP
T
ap
p
r
o
ac
h
,
wh
ich
ex
h
ib
i
ted
a
s
u
b
s
tan
tially
h
ig
h
er
T
HD
o
f
1
.
1
2
%.
T
h
e
v
i
s
u
aliza
tio
n
o
f
th
e
h
ar
m
o
n
ic
s
p
ec
tr
u
m
p
lo
ts
(
Fig
u
r
e
1
2
)
c
o
n
f
i
r
m
s
th
at
th
e
ANFI
S
m
eth
o
d
s
ig
n
if
ica
n
tly
s
u
p
p
r
ess
es th
e
p
r
o
p
a
g
atio
n
o
f
h
a
r
m
o
n
i
cs in
to
th
e
g
r
id
co
m
p
a
r
ed
to
t
h
e
I
C
m
eth
o
d
.
(
a)
(
b
)
Fig
u
r
e
1
2
.
T
HD
an
aly
s
is
at
4
5
0
W
/m
2
: (
a)
ANFI
S
-
MPPT
an
d
(
b
)
I
C
-
MPPT
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.
1
7
,
No
.
1
,
Ma
r
c
h
20
2
6
:
303
-
3
16
312
3
.
1
.
3
.
T
H
D
a
na
ly
s
is
a
t
6
0
0
Fig
u
r
e
1
3
s
h
o
ws
th
e
h
ar
m
o
n
ic
s
p
ec
tr
u
m
an
aly
s
is
ca
r
r
ied
o
u
t
at
a
6
0
0
W
/m
2
r
ad
iatio
n
lev
el
an
d
p
r
o
v
id
es
im
p
o
r
tan
t
d
etails
o
n
th
e
co
n
tr
o
l
ca
p
ab
ilit
ies
o
f
th
e
two
MPPT
s
tr
ateg
ies.
F
ig
u
r
e
1
3
(
a)
s
p
ec
if
ically
f
o
cu
s
es
o
n
th
e
T
HD
p
r
o
f
ile
o
f
th
e
MPPT
m
eth
o
d
b
ased
o
n
ANFI
S,
wh
ich
r
ec
o
r
d
e
d
a
T
HD
o
f
0
.
5
6
%.
T
h
is
v
alu
e
d
e
m
o
n
s
tr
ates
th
e
c
o
n
s
is
ten
t
ef
f
ec
tiv
en
ess
o
f
ANFI
S
i
n
m
ain
tain
in
g
a
lo
w
d
is
to
r
tio
n
r
ate,
ev
en
as
th
e
ir
r
ad
ian
ce
d
r
o
p
s
f
r
o
m
STC.
C
o
n
v
er
s
ely
,
Fig
u
r
e
1
3
(
b
)
s
h
o
ws th
at
th
e
I
C
-
MPPT
m
eth
o
d
y
ield
ed
a
s
ig
n
if
ican
tly
h
ig
h
er
T
HD
o
f
0
.
8
6
%.
T
h
e
in
cr
ea
s
ed
h
a
r
m
o
n
ic
d
is
to
r
tio
n
ass
o
ciate
d
with
t
h
e
I
C
ap
p
r
o
ac
h
in
d
icate
s
its
d
im
in
is
h
ed
ef
f
ec
tiv
e
n
ess
in
h
ar
m
o
n
ic
m
an
a
g
em
en
t
c
o
m
p
ar
e
d
to
ANFI
S
u
n
d
er
th
is
co
n
d
itio
n
.
B
y
m
ain
tain
in
g
a
T
HD
3
5
% lo
wer
th
an
th
at
o
b
tain
ed
b
y
th
e
I
C
m
eth
o
d
at
6
0
0
W
/m
2
.
(
a)
(
b
)
Fig
u
r
e
1
3
.
T
HD
an
aly
s
is
at
6
0
0
W
/m
2
:
(
a)
ANFI
S
-
MPPT
an
d
(
b
)
I
C
-
MPPT
3
.
1
.
4
.
T
H
D
a
na
ly
s
is
a
t
1
0
0
0
T
h
e
r
esu
lts
d
ep
icted
in
Fig
u
r
e
1
4
p
r
o
v
id
e
a
co
m
p
ar
ati
v
e
T
HD
an
aly
s
is
u
n
d
er
s
ta
n
d
ar
d
test
co
n
d
itio
n
s
(
STC),
s
p
ec
if
ically
at
an
ir
r
ad
ian
ce
lev
el
o
f
1
0
0
0
W
/m
²
an
d
a
tem
p
er
atu
r
e
o
f
2
5
°C
.
Fig
u
r
e
1
4
(
a)
s
h
o
ws
th
e
h
ar
m
o
n
ic
s
p
ec
tr
u
m
v
is
u
aliza
tio
n
f
o
r
th
e
ANFI
S
-
b
ased
MPPT
m
eth
o
d
with
a
T
HD
o
f
0
.
2
6
%.
T
h
is
o
u
tco
m
e
is
cr
u
cial,
as
attain
i
n
g
T
HD
b
elo
w
0
.
3
%
u
n
d
e
r
STC
in
d
icate
s
ex
ce
llen
t
p
o
wer
q
u
ality
,
s
tr
o
n
g
ly
s
u
p
p
o
r
tin
g
th
e
ca
p
ab
ilit
y
o
f
th
e
ANFI
S
s
tr
ateg
y
f
o
r
h
a
r
m
o
n
ic
s
u
p
p
r
ess
io
n
.
I
n
co
n
tr
ast,
Fig
u
r
e
1
4
(
b
)
r
ep
r
esen
ts
th
e
in
cr
em
en
tal
co
n
d
u
ctan
ce
(IC
-
MPPT)
tech
n
iq
u
e,
wh
ich
s
h
o
ws
T
HD
o
f
0
.
4
4
%.
T
h
is
in
cr
ea
s
e
in
T
HD
s
u
g
g
ests
th
at
th
e
co
n
v
e
n
tio
n
al
I
C
m
eth
o
d
is
s
ig
n
if
ic
an
tly
less
ad
ep
t
at
h
a
r
m
o
n
ic
r
ed
u
ctio
n
th
an
t
h
e
in
tellig
en
t
ANFI
S
m
o
d
el,
ev
en
u
n
d
er
o
p
tim
al
e
n
v
ir
o
n
m
e
n
tal
co
n
d
itio
n
s
.
T
h
e
ANFI
S
ap
p
r
o
ac
h
d
eliv
e
r
s
a
T
HD
th
at
is
ap
p
r
o
x
im
ately
4
1
%
lo
wer
th
an
th
e
I
C
m
eth
o
d
a
t
1
0
0
0
W
/m
².
T
h
e
s
u
p
e
r
io
r
p
er
f
o
r
m
an
ce
p
o
s
itio
n
s
th
e
ANFI
S
-
MPPT
as a
p
r
o
m
is
in
g
s
o
lu
tio
n
f
o
r
th
e
in
teg
r
atio
n
o
f
p
h
o
to
v
o
ltaic
s
y
s
tem
s
in
to
p
o
wer
g
r
i
d
s
.
(
a)
(
b
)
Fig
u
r
e
1
4
.
T
HD
an
aly
s
is
at
1
0
0
0
W
/m
2
: (
a)
ANFI
S
-
MPPT
an
d
(
b
)
I
C
-
MPPT
Evaluation Warning : The document was created with Spire.PDF for Python.