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[
1
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.
On
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-
[
5]
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alg
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d
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d
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all
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icien
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[
6
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.
Hen
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t
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[7
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[
1
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Ma
r
ch
20
25
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63
-
1
72
164
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y
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[
1
1
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B
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s
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y
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an
d
PV
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tem
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p
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[
1
3
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Ad
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th
e
p
o
ten
tial
to
co
n
tr
ib
u
te
s
ig
n
if
ican
tly
t
o
th
e
ad
v
an
ce
m
e
n
t
an
d
wid
esp
r
ea
d
ad
o
p
ti
o
n
o
f
s
o
lar
p
o
wer
tech
n
o
lo
g
ies.
2.
M
AXI
M
U
M
P
O
WE
R
P
O
I
N
T
T
RA
CK
I
NG
M
E
T
H
O
DS
Ma
x
im
u
m
p
o
wer
p
o
i
n
t
tr
ac
k
in
g
(
MPPT)
is
a
tech
n
iq
u
e
u
s
ed
to
ac
h
iev
e
m
ax
im
u
m
p
o
wer
f
r
o
m
p
h
o
to
v
o
ltaic
d
e
v
ices.
MPPT
wo
r
k
s
b
ased
o
n
v
ar
i
o
u
s
alg
o
r
ith
m
s
[
1
5
]
.
T
h
e
ab
ilit
y
o
f
t
h
is
alg
o
r
ith
m
to
d
etec
t
t
h
e
m
ax
im
u
m
p
o
we
r
o
u
tp
u
t
is
th
e
m
o
s
t
im
p
o
r
tan
t
f
ac
to
r
to
b
e
co
n
s
id
er
ed
in
ch
o
o
s
in
g
p
r
o
p
e
r
MPPT
tech
n
iq
u
e
[
1
6
]
.
At
d
if
f
er
en
t
p
o
in
ts
o
n
th
e
s
o
lar
p
an
els
ir
r
ad
ian
ce
lev
els
m
ay
v
ar
y
[
1
7
]
.
Du
e
to
th
is
v
ar
iatio
n
in
o
n
e
s
y
s
tem
,
th
er
e
m
ay
b
e
m
u
ltip
le
lo
ca
l
m
ax
im
u
m
p
o
wer
p
o
in
ts
[
1
8
]
.
T
h
er
e
ar
e
s
ev
er
al
p
u
b
licatio
n
s
th
at
d
ea
ls
with
MPPT,
b
u
t e
ac
h
tech
n
iq
u
e
h
as its
o
wn
lim
i
tatio
n
s
[
1
9
]
.
I
t
is
alwa
y
s
d
esira
b
le
to
ex
tr
ac
t
m
ax
im
u
m
p
o
s
s
ib
le
p
o
wer
f
r
o
m
th
e
s
o
lar
p
an
el
.
An
MPPT
co
n
tr
o
ller
en
ab
les
ex
tr
ac
tio
n
o
f
m
ax
im
u
m
p
o
wer
f
r
o
m
th
e
PV
ar
r
a
y
e
v
en
at
v
ar
y
in
g
lo
a
d
an
d
wea
t
h
er
co
n
d
itio
n
s
[
2
0
]
.
T
h
e
MPPT
co
n
tr
o
ller
is
a
s
em
ico
n
d
u
cto
r
d
ev
ice
wh
ich
is
co
n
n
ec
ted
b
etwe
en
th
e
PV
ar
r
ay
an
d
th
e
b
atter
y
o
r
in
v
er
ter
[
2
1
]
.
I
ts
wo
r
k
in
g
is
b
ased
o
n
a
n
alg
o
r
ith
m
d
e
v
elo
p
ed
to
ex
tr
ac
t
m
ax
i
m
u
m
p
o
wer
.
T
h
is
co
n
tr
o
ller
co
n
s
is
ts
o
f
two
im
p
o
r
tan
t
d
ev
ices
(
PV
s
y
s
tem
&
D
C
-
DC
co
n
v
er
ter
)
[
2
2
]
.
A
r
eg
u
lated
DC
-
DC
b
u
ck
-
b
o
o
s
t
co
n
v
er
ter
u
s
es
th
e
MPPT
tech
n
iq
c
u
e
to
ex
tr
ac
t
th
e
m
ax
im
u
m
p
o
wer
f
r
o
m
th
e
PV
ar
r
ay
th
er
eb
y
r
eq
u
ir
ed
p
o
wer
is
s
u
p
p
lied
to
th
e
lo
a
d
as sh
o
wn
in
Fig
u
r
e
1
.
Mu
ltip
le
alg
o
r
ith
m
s
ex
is
t
to
f
i
n
d
th
e
o
p
tim
al
o
p
er
atin
g
p
o
in
t.
Alg
o
r
ith
m
s
ca
n
b
e
class
if
ie
d
in
to
two
g
en
er
al
ca
teg
o
r
ies:
-
I
n
d
ir
ec
t
co
n
tr
o
l
(
q
u
asi
s
ee
k
in
g
)
:
T
h
ese
m
eth
o
d
s
r
ely
o
n
a
d
atab
ase
o
f
th
e
s
o
lar
-
PV
u
n
it'
s
p
ar
am
eter
s
.
T
h
e
ex
ten
s
iv
en
ess
o
f
th
e
d
atab
ase
v
ar
ies an
d
ca
n
in
clu
d
e
item
s
s
u
ch
as th
e
u
n
it'
s
p
o
wer
-
v
o
ltag
e
(
P
-
V)
cu
r
v
e
o
r
em
p
ir
ical
d
ata
[
2
3
]
.
T
h
u
s
a
d
r
a
wb
ac
k
to
th
ese
tech
n
iq
u
es
is
lo
n
g
er
tim
e
to
p
r
o
g
r
am
a
n
d
u
p
d
a
te
th
e
d
atab
ase
as th
e
u
n
it a
g
es.
-
Dir
ec
t
co
n
tr
o
l
(
tr
u
e
s
ee
k
in
g
)
:
T
h
ese
m
eth
o
d
s
s
h
ar
e
th
e
co
m
m
o
n
ality
o
f
r
el
y
in
g
s
o
lely
o
n
v
o
ltag
e
an
d
cu
r
r
en
t
m
ea
s
u
r
em
en
ts
an
d
th
e
r
ef
o
r
e
r
eq
u
ir
e
m
in
im
al
tim
e
as sp
ec
if
ic
u
n
it p
ar
am
eter
s
ar
e
n
o
t
r
eq
u
ir
ed
[
2
4
]
.
V
P
V
V
L
O
A
D
D
C
-
D
C
c
o
n
v
e
r
t
e
r
a
s
M
P
P
T
P
V
P
a
n
e
l
Fig
u
r
e
1
.
Fig
u
r
e
r
eg
u
lated
DC
-
DC
co
n
v
er
ter
as M
PP
T
co
n
tr
o
ller
2
.
1
.
I
ncre
m
ent
a
l
c
o
nd
uct
a
nce
(
I
C)
m
et
ho
d (
direct
co
ntr
o
l
)
T
h
e
I
C
m
eth
o
d
s
ee
k
s
to
r
ea
ch
th
e
p
ea
k
o
f
th
e
P
-
V
c
u
r
v
e
b
y
s
atis
f
y
in
g
,
as in
(
1
)
.
=
(
∗
)
=
+
=
0
(
1
)
W
h
er
e
P,
V,
an
d
I
ar
e
th
e
m
ea
s
u
r
ed
DC
p
o
wer
,
v
o
ltag
e,
an
d
c
u
r
r
en
t,
r
esp
ec
tiv
el
y
.
M
u
ltip
ly
i
n
g
(
1
)
b
y
1
/V
y
ield
s
.
1
=
+
=
+
(
2
)
W
h
er
e
G
is
co
n
d
u
ctan
ce
a
n
d
d
G
ar
e
in
cr
em
en
tal
c
o
n
d
u
ctan
c
e.
I
n
(
2
)
estab
lis
h
es
if
th
e
cu
r
r
e
n
t
o
p
er
atin
g
p
o
i
n
t
is
ab
o
v
e
o
r
b
elo
w
VM
PP
an
d
th
e
r
esu
lti
n
g
v
o
ltag
e
r
ef
er
en
ce
is
d
eter
m
in
ed
f
r
o
m
t
h
is
.
Fo
r
ex
am
p
le,
if
d
P/d
V>
0
,
th
en
G
+
d
G>
0
an
d
th
e
cu
r
r
en
t
o
p
er
atin
g
p
o
in
t
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
A
n
o
ve
l fa
s
t MP
P
T st
r
a
teg
y
w
i
th
h
ig
h
efficien
cy
fo
r
fa
s
t c
h
a
n
g
in
g
ir
r
a
d
ia
n
ce
i
n
…
(
P
u
j
a
r
i A
n
ja
p
p
a
)
165
is
o
n
th
e
lef
t
-
h
an
d
-
s
id
e
o
f
m
ax
im
u
m
p
o
we
r
p
o
i
n
t (
MPP)
[
2
5
]
.
Alter
n
ativ
ely
,
if
d
P/d
V<
0
,
th
en
G
+
d
G<
0
an
d
th
e
cu
r
r
e
n
t o
p
er
atin
g
p
o
in
t is o
n
th
e
r
i
g
h
t
-
h
a
n
d
-
s
id
e
o
f
MPP a
s
s
h
o
wn
in
Fig
u
r
e
2
.
Fig
u
r
e
2
.
P
-
V
cu
r
v
e
f
o
r
e
x
p
lan
atio
n
o
f
in
c
r
em
en
tal
co
n
d
u
cta
n
ce
m
eth
o
d
3.
P
RO
P
O
SE
D
M
O
D
I
F
I
E
D
I
N
CRE
M
E
N
T
A
L
CO
NDUC
T
ANCE
M
P
P
T
T
o
ex
tr
ac
t
th
e
m
ax
im
u
m
p
o
wer
f
r
o
m
s
o
lar
PV
s
y
s
tem
s
MPP
T
tech
n
iq
u
e
is
u
s
ed
.
B
etwe
en
PV
m
o
d
u
le
an
d
lo
ad
a
DC
-
DC
co
n
v
er
ter
i
s
co
n
n
ec
ted
a
n
d
d
u
ty
c
y
cle
o
f
th
e
DC
-
DC
co
n
v
er
ter
alwa
y
s
r
eg
u
lated
to
o
p
er
ate
th
e
PV
s
y
s
tem
a
t
m
ax
im
u
m
p
o
wer
p
o
in
t
(
MPP)
.
Fig
u
r
e
3
s
h
o
ws
th
e
co
n
v
en
tio
n
al
I
NC
m
eth
o
d
alg
o
r
ith
m
,
wh
ich
o
p
er
ates
with
h
ig
h
ef
f
icien
c
y
u
n
d
er
s
tead
y
ir
r
ad
ian
ce
.
I
n
th
i
s
m
eth
o
d
th
e
s
lo
p
e
o
f
t
h
e
P
-
V
cu
r
v
e
is
u
s
ed
t
o
v
a
r
y
th
e
d
u
ty
cy
cle
o
f
co
n
v
er
ter
to
g
et
th
e
v
o
ltag
e
co
r
r
esp
o
n
d
in
g
to
m
ax
im
u
m
p
o
wer
p
o
in
t,
.
MPP
is
r
ea
ch
ed
wh
en
=
0
,
as in
(
3
)
-
(
6
)
.
=
−
(
3
)
>
0
,
th
en
<
(
4
)
=
0
,
th
en
=
(
5
)
<
0
,
th
en
>
(
6
)
Fig
u
r
e
3
.
I
n
cr
em
e
n
tal
co
n
d
u
ct
an
ce
MPPT
alg
o
r
ith
m
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
14
,
No
.
1
,
Ma
r
ch
20
25
:
1
63
-
1
72
166
T
o
d
e
t
e
r
m
i
n
e
t
h
e
V
mp
p
,
k
n
o
w
l
ed
g
e
o
f
t
h
e
r
e
l
at
i
o
n
b
e
t
we
e
n
d
I
/d
V
a
n
d
–
I
/
V
.
I
f
t
h
e
s
l
o
p
e
i
s
n
e
g
a
t
i
v
e
,
t
h
e
n
M
PP
m
u
s
t
b
e
m
o
v
e
d
t
o
t
h
e
l
e
f
t
b
y
d
ec
r
e
a
s
i
n
g
t
h
e
m
o
d
u
l
e
v
o
l
t
a
g
e
.
I
f
t
h
e
s
l
o
p
e
is
p
o
s
i
t
i
v
e,
t
h
e
o
p
e
r
a
t
i
n
g
p
o
i
n
t
m
u
s
t
b
e
m
o
v
e
d
t
o
t
h
e
r
i
g
h
t
b
y
in
c
r
e
a
s
i
n
g
t
h
e
m
o
d
u
l
e
v
o
l
t
a
g
e
.
T
h
i
s
p
r
o
c
es
s
i
s
r
e
p
e
a
t
e
d
t
i
ll
t
h
e
s
l
o
p
e
is
ze
r
o
.
F
i
n
al
l
y
,
w
h
e
n
t
h
e
s
l
o
p
e
i
s
n
u
l
l
,
t
h
e
o
p
e
r
a
t
i
n
g
p
o
i
n
t
is
a
t
t
h
e
M
PP
a
n
d
th
e
a
l
g
o
r
i
t
h
m
s
t
o
p
s
t
h
e
v
o
l
t
a
g
e
a
d
j
u
s
t
m
e
n
t
.
Fo
r
v
ar
y
in
g
ir
r
ad
ian
ce
,
th
e
r
esp
o
n
s
e
o
f
f
ix
e
d
s
tep
s
ize
is
s
lo
w.
So
,
th
e
v
ar
iab
le
s
tep
s
ize
is
p
r
o
p
o
s
ed
wh
ich
d
ec
r
ea
s
es th
e
s
tep
s
ize
,
an
d
c
o
n
v
e
r
g
en
ce
o
f
MPP is sl
o
w
wh
en
it r
ea
c
h
es to
n
ea
r
th
e
p
ea
k
o
f
P
-
V
c
u
r
v
e.
A
m
o
d
if
ied
I
NC
alg
o
r
ith
m
is
p
r
o
p
o
s
ed
to
i
n
cr
ea
s
e
th
e
co
n
v
er
g
in
g
s
p
ee
d
with
f
ast
v
a
r
y
i
n
g
ir
r
a
d
ian
ce
.
T
h
e
p
r
o
p
o
s
ed
b
lo
ck
d
iag
r
a
m
is
s
h
o
wn
in
Fig
u
r
e
4
.
Fig
u
r
e
5
s
h
o
ws th
e
I
-
V
cu
r
v
e
o
f
th
e
PV m
o
d
u
le
u
n
d
er
d
if
f
e
r
en
t le
v
els o
f
s
o
lar
ir
r
ad
ian
ce
an
d
also
th
e
MPPs
wh
ich
ca
n
b
e
c
o
n
n
ec
te
d
ap
p
r
o
x
im
ately
b
y
a
s
tr
aig
h
t li
n
e
(
MPP lin
e)
.
A
lo
ad
lin
e
is
g
en
er
ated
a
n
d
it c
a
n
b
e
im
p
o
s
ed
o
n
th
e
I
–
V
cu
r
v
e
wh
en
th
e
PV
m
o
d
u
le
s
u
p
p
lies
p
o
wer
to
th
e
lo
ad
.
T
h
e
p
o
wer
g
en
er
ated
b
y
th
e
PV
m
o
d
u
le
is
th
e
p
r
o
d
u
ct
o
f
th
e
v
o
ltag
e
an
d
cu
r
r
e
n
t
o
f
PV
m
o
d
u
le
at
th
e
in
ter
s
ec
tio
n
p
o
in
t
b
e
twee
n
th
e
lo
ad
lin
e
an
d
th
e
I
–
V
cu
r
v
e.
T
h
er
ef
o
r
e,
th
e
o
u
tp
u
t
p
o
wer
o
f
PV
m
o
d
u
le
v
ar
ies
ac
co
r
d
in
g
to
th
e
s
o
lar
ir
r
ad
iatio
n
(
I
–
V
cu
r
v
e)
a
n
d
th
e
r
esis
tan
ce
o
f
th
e
lo
ad
(
lo
a
d
lin
e)
.
T
h
e
r
e
l
a
t
i
o
n
b
et
w
e
e
n
t
h
e
i
n
p
u
t
-
o
u
t
p
u
t
v
o
l
t
a
g
e
a
n
d
c
u
r
r
e
n
ts
f
o
r
a
DC
-
DC
c
o
n
v
e
r
t
e
r
is
r
e
p
r
es
e
n
te
d
b
y
(
7
)
.
=
1
−
(
7
)
=
1
−
(
8
)
Div
id
e
in
(
7
)
with
(
8
)
we
g
et
(
9
)
.
=
(
1
−
)
2
2
(
9
)
W
h
er
e
D
is
th
e
d
u
ty
cy
cle
o
r
d
u
ty
r
atio
,
V
input
is
th
e
in
p
u
t
v
o
ltag
e
o
f
th
e
co
n
v
er
ter
o
r
th
e
v
o
ltag
e
o
f
th
e
PV
m
o
d
u
le
V
pv
,
I
input
is
th
e
in
p
u
t
cu
r
r
en
t
o
f
th
e
co
n
v
er
ter
o
r
th
e
cu
r
r
en
t
o
f
th
e
PV
m
o
d
u
le
I
pv
,
R
input
is
th
e
in
p
u
t
r
esis
tan
ce
o
f
th
e
co
n
v
er
ter
o
r
th
e
r
esis
tan
ce
s
ee
n
b
y
th
e
PV
m
o
d
u
le,
an
d
R
output
is
th
e
o
u
tp
u
t
r
esis
tan
ce
o
f
th
e
co
n
v
er
ter
o
r
lo
a
d
r
esis
tan
ce
R
l
oad
.
Fro
m
(
9
)
it
is
n
o
t
i
c
e
d
th
at
d
u
ty
cy
cle
ca
n
b
e
r
eg
u
lated
to
f
o
r
c
e
th
e
in
p
u
t r
esis
tan
ce
o
f
th
e
co
n
v
er
ter
to
b
e
v
ar
ied
u
n
til
th
e
lo
a
d
lin
e
cu
ts
th
e
I
-
V
cu
r
v
e
at
MPP.
(
9
)
ca
n
b
e
wr
itten
as
(
1
0
)
.
L
o
ad
r
esis
tan
ce
ca
n
b
e
ca
lcu
lated
at
an
y
o
p
er
atin
g
M
PP
b
y
s
u
b
s
titu
tin
g
th
e
d
u
t
y
cy
cle,
PV v
o
ltag
e
,
an
d
PV c
u
r
r
e
n
t in
(
10
)
.
2
(
1
−
)
2
=
(
10
)
=
√
1
+
√
(
11
)
S
o
l
a
r
P
a
n
e
l
D
C
-
D
C
C
o
n
v
e
r
t
e
r
D
C
L
o
a
d
M
P
P
T
C
o
n
t
r
o
l
l
e
r
L
o
a
d
R
e
s
i
s
t
a
n
c
e
(
R
o
u
t
p
u
t
)
V
o
l
t
a
g
e
S
e
n
s
o
r
(
V
P
V
)
C
u
r
r
e
n
t
S
e
n
s
o
r
(
I
P
V
)
D
u
t
y
R
a
t
i
o
(
D
)
T
e
m
p
.
I
r
r
a
d
i
a
n
c
e
V
i
n
p
u
t
V
o
u
t
p
u
t
I
i
n
p
u
t
I
i
n
p
u
t
Fig
u
r
e
4
.
B
lo
ck
d
iag
r
am
o
f
p
r
o
p
o
s
ed
DC
/DC
co
n
v
er
ter
with
m
o
d
if
ied
I
NC
alg
o
r
ith
m
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
A
n
o
ve
l fa
s
t MP
P
T st
r
a
teg
y
w
i
th
h
ig
h
efficien
cy
fo
r
fa
s
t c
h
a
n
g
in
g
ir
r
a
d
ia
n
ce
i
n
…
(
P
u
j
a
r
i A
n
ja
p
p
a
)
167
V
m
p
p
L
o
a
d
L
i
n
e
1
L
o
a
d
L
i
n
e
2
L
o
a
d
L
i
n
e
3
L
o
a
d
L
i
n
e
4
L
o
a
d
L
i
n
e
5
Fig
u
r
e
5
.
I
-
V
C
u
r
v
es a
t d
if
f
e
r
e
n
t ir
r
ad
ian
ce
s
with
lo
ad
lin
e
a
n
d
MPP lin
e
I
n
in
cr
e
m
en
tal
co
n
d
u
cta
n
ce
m
eth
o
d
t
h
e
s
lo
p
e
o
f
p
o
wer
v
s
v
o
ltag
e
(
)
o
f
s
o
lar
p
an
el
is
ze
r
o
at
th
e
MPP.
Gettin
g
ze
r
o
s
lo
p
e
in
p
r
ac
tical
s
y
s
tem
s
r
eq
u
ir
es
s
ev
er
al
iter
atio
n
s
.
I
t
is
r
ea
s
o
n
ab
ly
a
cc
u
r
ate
to
allo
w
an
ac
ce
p
tab
le
er
r
o
r
wh
ile
f
in
d
in
g
th
e
MPP.
An
attem
p
t
h
as
b
ee
n
m
ad
e
in
th
is
th
esis
to
m
o
d
if
y
th
is
co
n
d
itio
n
o
f
ze
r
o
s
lo
p
e
to
f
in
d
MPP,
with
a
s
m
all
p
er
m
itted
er
r
o
r
.
I
n
p
r
o
p
o
s
ed
m
eth
o
d
,
p
e
r
m
itted
er
r
o
r
o
f
0
.
0
6
as sh
o
wn
i
n
(
1
2
)
is
u
s
ed
to
elim
in
ate
th
e
s
tead
y
-
s
tate
o
s
cillatio
n
in
th
e
s
y
s
tem
af
ter
th
e
MPP
is
r
ea
ch
e
d
.
T
h
e
p
er
m
itted
er
r
o
r
is
ch
o
s
en
to
b
e
m
o
r
e
th
a
n
MPPT
s
tep
s
ize
o
f
0
.
0
5
.
+
<
0
.
06
(
1
2
)
Fig
u
r
e
6
s
h
o
ws th
e
f
l
o
w
ch
ar
t
f
o
r
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
.
Fig
u
r
e
6
.
Pro
p
o
s
ed
m
o
d
if
ied
I
NC
MPPT
m
eth
o
d
u
n
d
er
f
ast v
ar
y
in
g
ir
r
ad
ian
ce
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
14
,
No
.
1
,
Ma
r
ch
20
25
:
1
63
-
1
72
168
3
.
1
.
Wo
r
k
ing
pro
ce
du
re
f
o
r
decr
ea
s
e
in s
o
la
r
irra
dia
nce
lev
el
Fig
u
r
e
7
s
h
o
w
s
th
e
lo
ad
lin
es o
n
th
e
I
-
V
cu
r
v
es
f
o
r
s
o
lar
ir
r
a
d
ian
ce
lev
el
at
0
.
4
an
d
1
.
0
k
W
/m
2
.
W
h
en
th
e
PV m
o
d
u
le
is
o
p
er
atin
g
at
1
0
0
0
W
/m
2
,
th
e
MPP o
p
er
ates a
t th
e
p
o
in
t A
(
V
MPP1
, I
MPP1
)
o
f
th
e
lo
ad
lin
e
1
as
s
h
o
wn
in
Fig
u
r
e
7
.
T
h
en
,
if
t
h
e
s
o
lar
ir
r
ad
ian
ce
is
d
ec
r
ea
s
ed
f
r
o
m
1
0
0
0
W
/m
2
to
4
0
0
W
/m
2
,
th
en
th
e
MP
P
im
m
ed
iately
co
m
es
to
p
o
in
t
B
(
V
B
,
I
B
)
alo
n
g
t
h
e
lo
ad
lin
e
1
,
wh
ich
is
f
ar
awa
y
f
r
o
m
th
e
MPP
o
f
4
0
0
W
/m
2
,
p
o
in
t
C
,
b
ec
au
s
e
th
e
d
u
ty
cy
c
l
e
o
f
th
e
DC
-
DC
co
n
v
er
ter
r
e
m
ain
s
u
n
alter
ed
.
I
n
o
r
d
er
to
tr
ac
k
th
e
n
ew
V
MPP
an
d
I
MPP
o
f
th
e
PV
m
o
d
u
le
eq
u
ati
o
n
(
11
)
is
u
s
ed
.
B
u
t
th
ese
two
v
alu
es
ar
e
u
n
k
n
o
wn
a
n
d
th
eir
a
p
p
r
o
x
im
ated
v
alu
es
ar
e
s
u
b
m
itted
in
(
11
)
to
tr
ac
k
t
h
e
n
ew
MPP.
As
s
h
o
wn
in
Fig
u
r
e
7
,
th
e
cu
r
r
e
n
t
at
p
o
in
t
B
,
I
B
is
v
er
y
clo
s
e
to
th
e
s
h
o
r
t
cir
cu
it
c
u
r
r
en
t
o
f
4
0
0
W
/m
2
an
d
th
e
I
MPP
is
ap
p
r
o
x
im
at
ely
eq
u
als
to
0
.
8
tim
es
o
f
th
e
s
h
o
r
t
cir
cu
it
c
u
r
r
en
t
(
0
.
8
*
I
SC
)
.
T
h
en
0
.
8
*
I
SC
is
ap
p
r
o
x
im
ated
as n
ew
I
MPP
.
T
h
e
V
MPP
at
all
th
e
s
o
lar
i
r
r
ad
ian
ce
lev
els
is
alm
o
s
t e
q
u
al
h
en
ce
th
e
p
r
ev
i
o
u
s
V
MPP
is
ap
p
r
o
x
im
ated
as
a
n
ew
V
MPP.
So
,
s
u
b
s
titu
tin
g
I
MPP
≈
I
B
an
d
I
B
=I
PV,
V
B
=
V
MPP
=
V
PV
in
(
1
1
)
to
tr
ac
k
th
e
n
ew
MPP to
th
e
lo
ad
lin
e
2
,
p
o
in
t C wh
ic
h
is
v
er
y
n
e
ar
to
n
ew
MPP.
V
m
p
p
L
o
a
d
L
i
n
e
1
(
V
M
P
P
1
,
I
M
P
P
1
)
L
o
a
d
L
i
n
e
2
A
B
C
(
V
M
P
P
0
.
4
,
I
M
P
P
0
.
4
)
(
V
B
,
I
B
)
Fig
u
r
e
7
.
MPP o
n
I
–
V
c
u
r
v
es
f
o
r
d
ec
r
ea
s
e
o
f
s
o
lar
ir
r
ad
iatio
n
lev
el
f
r
o
m
1
.
0
to
0
.
4
k
W
/m
2
4.
SI
M
UL
A
T
I
O
N
R
E
S
UL
T
S
I
n
th
e
p
r
esen
t
wo
r
k
STH
-
2
5
0
W
H
p
an
el
is
co
n
s
id
er
ed
an
d
,
as
s
h
o
wn
in
T
ab
le
1
,
th
e
s
p
ec
i
f
icatio
n
s
o
f
p
h
o
to
v
o
ltaic
p
an
e
ls
o
f
f
er
o
n
ly
a
f
ew
p
ar
am
eter
s
.
C
o
n
s
eq
u
en
tl
y
,
s
ev
er
al
m
an
d
ato
r
y
p
ar
am
ete
r
s
f
o
r
th
e
m
o
d
elin
g
o
f
th
e
p
h
o
t
o
v
o
ltaic
p
an
el
ar
e
o
m
itted
in
th
e
m
an
u
f
ac
tu
r
e
r
'
s
s
p
ec
if
icatio
n
s
,
n
am
ely
th
e
d
io
d
e
s
atu
r
atio
n
cu
r
r
en
t,
th
e
cu
r
r
e
n
t g
en
er
ate
d
b
y
th
e
li
g
h
t,
th
e
id
ea
lity
f
a
cto
r
o
f
th
e
d
io
d
e
,
an
d
th
e
s
er
ies an
d
s
h
u
n
t
r
esis
to
r
s
.
Simu
latio
n
f
o
r
co
n
v
en
tio
n
al
i
n
cr
em
en
tal
co
n
d
u
ctan
ce
alg
o
r
ith
m
an
d
p
r
o
p
o
s
ed
alg
o
r
ith
m
ar
e
ca
r
r
ied
o
u
t
f
o
r
c
o
n
s
tan
t,
v
ar
iab
le
ir
r
ad
ian
ce
an
d
th
e
r
esu
lts
ar
e
c
o
m
p
ar
ed
.
T
h
e
s
am
p
lin
g
tim
e
f
o
r
th
e
MPPT
co
n
tr
o
ller
is
0
.
0
5
s
.
Simu
latio
n
is
ca
r
r
ied
o
u
t
f
o
r
1
s
ec
f
o
r
c
o
n
s
tan
t
ir
r
a
d
ian
ce
an
d
tim
e
is
4
s
ec
f
o
r
s
o
lar
ir
r
ad
iatio
n
lev
el
wh
ich
v
ar
ies f
r
o
m
lo
w
(
0
.
4
kW
/
m
2
)
to
h
ig
h
(
1
.
0
kW
/
m
2
)
an
d
th
en
r
ed
u
ce
d
to
lo
w
ag
ain
in
o
r
d
er
to
in
v
esti
g
ate
th
e
p
er
f
o
r
m
an
ce
o
f
th
e
s
y
s
tem
u
n
d
er
f
ast
-
v
ar
y
i
n
g
s
o
lar
ir
r
ad
i
atio
n
lev
el.
4
.
1
.
Sim
ula
t
i
o
n r
esu
lt
s
wit
h
v
a
ria
ble so
la
r
irra
dia
nce
I
n
th
is
test
co
n
d
itio
n
,
s
o
lar
ir
r
ad
ian
ce
is
v
ar
ied
f
r
o
m
5
0
0
W
/m
2
to
1
0
0
0
W
/m
2
at
tim
e
p
er
i
o
d
o
f
1
s
ec
an
d
th
e
n
it
is
d
ec
r
ea
s
ed
f
r
o
m
1
0
0
0
W
/m
2
to
8
0
0
W
/m
2
a
2
s
ec
tim
e
p
e
r
io
d
.
Ag
ain
,
it d
ec
r
ea
s
ed
f
r
o
m
8
0
0
W
/m
2
to
6
0
0
W
/m
2
at
3
s
ec
tim
e
p
er
i
o
d
.
4
.
1
.
1
.
Wit
h
t
he
I
NC
M
P
P
T
m
et
ho
d
Ov
er
a
f
o
u
r
-
s
ec
o
n
d
tim
escale,
a
s
o
lar
p
h
o
to
v
o
ltaic
(
PV)
s
y
s
tem
s
h
o
ws
v
o
ltag
e
an
d
c
u
r
r
en
t
ch
an
g
es
u
n
d
er
v
ar
y
in
g
ir
r
a
d
ian
ce
cir
cu
m
s
tan
ce
s
as
s
h
o
wn
in
F
ig
u
r
e
8
.
Du
r
in
g
th
e
f
ir
s
t
an
d
last
in
ter
v
als
(
0
–
1
s
ec
an
d
3
–
4
s
ec
)
wi
th
ir
r
ad
ian
ce
lev
el
s
o
f
5
0
0
W
/m
2
an
d
6
0
0
W
/m
2
,
th
e
s
y
s
tem
s
h
o
ws
v
ar
iab
le
v
o
ltag
e
a
n
d
c
u
r
r
e
n
t
o
u
tp
u
ts
(
1
7
-
3
4
V
an
d
2
-
4
A
f
o
r
th
e
f
ir
s
t
in
ter
v
al,
2
0
-
3
2
V
a
n
d
3
-
5
A
f
o
r
th
e
last
)
,
n
ev
e
r
r
ea
ch
in
g
a
s
tead
y
s
tate.
T
h
e
s
y
s
te
m
'
s
r
esp
o
n
s
iv
en
ess
o
r
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r
p
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r
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with
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tiv
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r
o
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e
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e
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8
7
9
2
A
n
o
ve
l fa
s
t MP
P
T st
r
a
teg
y
w
i
th
h
ig
h
efficien
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fo
r
fa
s
t c
h
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ir
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d
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ce
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n
ja
p
p
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)
169
an
d
2
–
3
s
ec
in
te
r
v
als.
I
t
r
ea
ch
es
a
s
tead
y
s
tate
f
aster
in
th
es
e
in
ter
v
als,
0
.
0
2
s
ec
o
n
d
s
f
o
r
t
h
e
f
o
r
m
er
a
n
d
0
.
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5
s
ec
o
n
d
s
f
o
r
th
e
latter
,
ag
ain
g
o
o
d
p
er
f
o
r
m
an
ce
.
T
h
is
s
h
o
ws
th
at
th
e
PV
s
y
s
tem
ca
n
h
an
d
l
e
g
r
ea
ter
ir
r
ad
ian
ce
lev
els we
ll,
estab
lis
h
in
g
s
tab
ilit
y
q
u
ick
l
y
,
b
u
t a
t l
o
wer
o
r
m
o
r
e
f
lu
ctu
atin
g
lev
els,
it st
r
u
g
g
le
s
to
r
ea
ch
a
s
tead
y
s
tate
d
esp
ite
a
s
tr
o
n
g
p
er
f
o
r
m
a
n
ce
r
atin
g
.
Simu
latio
n
an
aly
s
es
f
o
r
I
NC
m
eth
o
d
,
it
f
ail
t
o
tr
ac
k
MPP
f
o
r
s
u
d
d
en
v
ar
iatio
n
a
t
d
if
f
er
en
t
ir
r
ad
ian
c
e
lev
els
at
lo
w
in
ten
s
ity
an
d
tr
ac
k
b
etter
MPP
at
h
ig
h
in
ten
s
ity
.
Stead
y
-
s
tate
an
aly
s
is
an
d
d
y
n
am
ic
p
er
f
o
r
m
an
ce
ar
e
s
h
o
wn
in
T
a
b
le
2
.
T
h
e
s
y
s
tem
r
ea
ch
es
a
s
tead
y
s
tate
co
n
d
i
tio
n
in
2
0
m
s
at
m
ax
im
u
m
ir
r
a
d
ian
ce
an
d
d
y
n
am
i
c
p
er
f
o
r
m
an
ce
is
also
g
o
o
d
.
T
ab
le
1
.
Sp
ec
if
icatio
n
s
o
f
So
lt
ec
h
1
STH
-
2
5
0
W
H
PV p
an
el
at
s
tan
d
ar
d
test
in
g
co
n
d
itio
n
s
(
STC)
o
f
1
0
0
0
W
/m
2
an
d
2
5
C
C
h
a
r
a
c
t
e
r
i
s
t
i
c
s
V
a
l
u
e
M
a
x
i
m
u
m
p
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r
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o
l
t
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g
e
a
t
P
ma
x
,
V
m
p
3
0
.
7
V
C
u
r
r
e
n
t
a
t
P
ma
x
,
I
mp
8
.
1
5
A
S
h
o
r
t
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i
r
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i
t
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r
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t
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sc
8
.
6
6
A
O
p
e
n
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c
i
r
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u
i
t
v
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l
t
a
g
e
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V
c
o
3
7
.
3
V
Te
mp
e
r
a
t
u
r
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c
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f
f
i
c
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e
n
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c
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r
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t
v
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l
t
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g
e
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o
c
,
k
V
-
3
6
9
.
0
mV
/
C
Te
mp
e
r
a
t
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mA
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C
Th
e
n
u
m
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e
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o
f
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e
l
l
s
60
T
ab
le
2
.
Vo
ltag
e
a
n
d
c
u
r
r
en
t
v
alu
es a
t d
if
f
er
en
t ir
r
ad
ian
ce
c
o
n
d
itio
n
s
with
I
NC
m
eth
o
d
Ti
me
p
e
r
i
o
d
(
i
n
se
c
)
I
r
r
a
d
i
a
n
c
e
(
i
n
W
/
m
2
)
V
(
v
o
l
t
s)
I
(
a
mp
s)
R
e
a
c
h
e
s
t
o
st
e
a
d
y
st
a
t
e
(
i
n
s
e
c
)
D
y
n
a
mi
c
p
e
r
f
o
r
m
a
n
c
e
0
–
1
5
0
0
17
-
3
4
V
2
-
4
A
N
e
v
e
r
r
e
a
c
h
e
s
G
o
o
d
1
–
2
1
0
0
0
3
0
.
7
V
8
.
1
5
A
0
.
0
2
G
o
o
d
2
–
3
8
0
0
3
2
V
6
-
7
A
0
.
0
5
G
o
o
d
3
–
4
6
0
0
20
-
3
2
V
3
-
5
A
N
e
v
e
r
r
e
a
c
h
e
s
G
o
o
d
4
.
1
.
2
.
Wit
h
t
he
pro
po
s
ed
M
P
P
T
m
et
ho
d
I
n
th
e
p
r
o
p
o
s
ed
MPPT
c
o
n
tr
o
ller
in
itially
d
u
ty
cy
cle
is
g
en
er
ated
ac
co
r
d
in
g
to
th
e
ch
a
r
ac
ter
is
tics
o
f
th
e
I
-
V
cu
r
v
e
a
n
d
DC
-
DC
co
n
v
er
ter
a
n
d
r
e
g
u
lates
th
e
d
u
ty
cy
cle
b
y
u
s
in
g
a
s
m
all
s
tep
s
ize.
T
h
is
s
m
all
s
tep
s
ize
ca
n
im
p
r
o
v
e
ef
f
icien
cy
b
y
en
s
u
r
in
g
th
at
th
e
o
p
er
a
tin
g
p
o
in
t
is
o
n
th
e
MPP.
F
ig
u
r
e
9
s
h
o
ws
th
e
d
y
n
am
ic
p
er
f
o
r
m
an
ce
o
f
a
s
o
lar
p
h
o
t
o
v
o
ltaic
(
PV)
s
y
s
tem
o
v
er
f
o
u
r
s
ec
o
n
d
s
u
n
d
er
d
if
f
e
r
en
t
ir
r
ad
iat
io
n
lev
els.
Star
tin
g
at
5
0
0
W
/m
2
,
th
e
s
y
s
tem
o
u
tp
u
ts
2
4
v
o
lts
an
d
4
am
p
s
,
r
ea
ch
i
n
g
a
s
tead
y
s
tate
in
0
.
0
0
5
5
s
ec
o
n
d
s
,
d
em
o
n
s
tr
atin
g
ex
ce
llen
t
d
y
n
am
ic
p
e
r
f
o
r
m
an
ce
.
W
h
en
ir
r
ad
ian
ce
r
ea
ch
es
1
0
0
0
W
/m
2
,
v
o
ltag
e
an
d
cu
r
r
en
t
in
cr
ea
s
e
to
3
0
.
7
v
o
lts
an
d
8
am
p
s
,
r
esp
ec
t
iv
ely
.
T
h
e
s
y
s
tem
r
ea
c
h
es
a
s
tead
y
s
tate
in
0
.
0
3
s
ec
o
n
d
s
,
m
a
in
tain
in
g
ex
ce
llen
t
p
er
f
o
r
m
an
ce
.
W
h
en
ir
r
a
d
ian
ce
d
r
o
p
s
to
8
0
0
W
/m
2
,
th
e
s
y
s
te
m
ad
ap
ts
to
p
r
o
v
i
d
e
3
2
v
o
lts
an
d
6
am
p
s
,
r
ea
c
h
in
g
a
s
tead
y
s
tate
in
0
.
0
3
s
ec
o
n
d
s
,
ex
h
ib
itin
g
co
n
s
is
ten
t
p
er
f
o
r
m
a
n
ce
.
Ultim
ately
,
r
ed
u
cin
g
ir
r
a
d
ian
ce
to
6
0
0
W
/m
2
y
ield
s
3
3
v
o
lts
an
d
5
am
p
s
,
r
ea
ch
in
g
a
s
tead
y
s
tate
in
0
.
0
3
s
ec
o
n
d
s
with
ex
ce
llen
t
d
y
n
a
m
ic
b
eh
av
io
r
.
T
h
e
s
o
lar
PV
s
y
s
tem
r
esp
o
n
d
s
well
t
o
i
r
r
ad
ian
ce
v
ar
iatio
n
s
an
d
s
tab
ilizes
r
ap
id
ly
,
w
h
ich
is
ess
en
ti
al
f
o
r
r
eliab
le
an
d
ef
f
icien
t so
lar
en
er
g
y
co
n
v
er
s
i
o
n
.
T
h
e
v
o
ltag
e
,
cu
r
r
e
n
t
v
alu
es
,
a
n
d
p
er
f
o
r
m
a
n
ce
o
f
th
e
PV
s
y
s
tem
with
th
e
p
r
o
p
o
s
ed
MPPT
ar
e
s
h
o
wn
in
T
ab
le
3
.
Fro
m
th
e
s
im
u
latio
n
r
esu
lt
a
n
aly
s
is
,
it
is
o
b
s
er
v
ed
p
r
o
p
o
s
ed
MPPT
tr
ac
k
s
MPP
with
in
m
illi
s
ec
o
n
d
s
at
lo
w
an
d
h
ig
h
in
ten
s
ity
.
T
h
e
s
y
s
tem
will
al
s
o
r
ea
ch
to
s
tead
y
s
tate
with
in
3
0
m
s
an
d
th
e
d
y
n
am
ic
p
er
f
o
r
m
an
ce
of
th
e
s
y
s
tem
is
v
er
y
g
o
o
d
.
T
ab
le
4
co
m
p
ar
es
th
e
p
er
f
o
r
m
an
ce
o
f
th
r
ee
d
if
f
er
e
n
t
m
et
h
o
d
s
f
o
r
m
ax
im
u
m
p
o
wer
p
o
in
t
tr
ac
k
in
g
(
MPPT)
in
s
o
lar
PV
(
p
h
o
to
v
o
l
taic)
s
y
s
tem
s
.
T
h
e
p
r
o
p
o
s
ed
m
eth
o
d
f
o
r
m
ax
im
u
m
p
o
wer
p
o
i
n
t
tr
ac
k
in
g
in
s
o
lar
s
y
s
tem
s
b
ea
ts
th
e
P&
O,
I
NC
,
a
n
d
P&
O
m
eth
o
d
s
ac
r
o
s
s
m
a
n
y
p
ar
am
eter
s
.
T
h
e
b
est
ef
f
icien
c
y
at
9
4
.
2
5
%,
lo
west
tr
ac
k
in
g
p
o
wer
lo
s
s
at
5
.
7
6
%,
an
d
f
astes
t
tr
ac
k
in
g
tim
e
o
f
0
.
2
8
s
ec
o
n
d
s
in
d
icate
o
u
ts
tan
d
i
n
g
ad
ap
tiv
e
n
ess
to
ch
an
g
in
g
s
o
lar
cir
cu
m
s
tan
ce
s
.
I
ts
s
tead
y
-
s
tate
o
s
cillatio
n
s
a
r
e
r
elativ
el
y
n
eg
lig
i
b
le,
e
n
s
u
r
i
n
g
c
o
n
s
tan
t
p
o
wer
o
u
tp
u
t.
P&
O
h
as
th
e
lo
west
ef
f
icien
cy
(
8
3
.
4
7
%),
b
i
g
g
est
tr
ac
k
in
g
p
o
wer
lo
s
s
(
2
4
.
6
0
%
)
,
s
lo
west
tr
ac
k
in
g
r
esp
o
n
s
e
(
1
.
4
2
s
ec
o
n
d
s
)
,
a
n
d
l
ar
g
est
s
tead
y
-
s
tate
o
s
cillatio
n
s
,
m
ak
in
g
it
th
e
least
d
esira
b
le
o
p
tio
n
.
I
NC
h
as
a
m
id
d
le
g
r
o
u
n
d
ef
f
icien
cy
o
f
9
1
.
5
1
%,
m
o
d
e
r
ate
tr
ac
k
i
n
g
p
o
wer
lo
s
s
(
1
7
.
0
5
%),
f
a
s
ter
tr
ac
k
in
g
tim
e
(
1
.
1
6
s
ec
o
n
d
s
)
,
an
d
s
m
all
s
te
ad
y
-
s
tate
o
s
cillatio
n
s
th
an
P&
O.
T
h
e
p
r
o
p
o
s
ed
tech
n
o
lo
g
y
im
p
r
o
v
es
s
o
lar
PV
s
y
s
tem
p
er
f
o
r
m
a
n
ce
,
m
ak
i
n
g
i
t a
p
r
o
m
is
in
g
s
o
lar
en
er
g
y
h
a
r
v
esti
n
g
s
o
lu
tio
n
.
I
t
is
f
o
u
n
d
th
at,
u
n
d
er
t
h
e
v
ar
i
atio
n
o
f
s
o
lar
i
r
r
ad
ian
ce
,
th
e
t
r
ac
k
in
g
s
p
ee
d
o
f
t
h
e
p
r
o
p
o
s
ed
tech
n
iq
u
e
is
5
.
6
tim
es
an
d
3
.
8
tim
es
f
aster
th
an
th
e
P&
O
an
d
I
NC
m
eth
o
d
s
.
T
h
e
p
o
wer
lo
s
s
d
u
r
in
g
t
h
e
tr
ac
k
in
g
is
also
less
wh
en
co
m
p
ar
ed
with
o
th
er
tech
n
iq
u
es.
T
h
e
s
tead
y
-
s
tate
o
s
cillatio
n
s
o
f
P&
O
an
d
I
N
C
m
eth
o
d
s
ar
e
lar
g
e
d
u
e
to
th
e
o
s
cillatio
n
s
in
th
e
d
u
ty
cy
cle,
wh
e
r
ea
s
it is
n
eg
lig
ib
le
f
o
r
t
h
e
p
r
o
p
o
s
ed
m
eth
o
d
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
14
,
No
.
1
,
Ma
r
ch
20
25
:
1
63
-
1
72
170
Fig
u
r
e
8
.
I
NC
MPPT
s
y
s
tem
s
im
u
latio
n
r
esu
lts
with
v
ar
iab
le
ir
r
ad
ian
ce
o
f
1
0
0
0
W
/m
2
:
(
i)
ir
r
ad
ian
ce
,
(
ii)
PV v
o
ltag
e
,
(
iii)
PV c
u
r
r
en
t
,
a
n
d
(
iv
)
PV p
o
wer
Fig
u
r
e
9
.
Pro
p
o
s
ed
MPPT
s
y
s
tem
s
im
u
latio
n
r
esu
lts
with
v
ar
iab
le
ir
r
ad
ian
ce
o
f
1
0
0
0
W
/m
2
:
(
i)
ir
r
ad
ian
ce
,
(
ii)
PV v
o
ltag
e
,
(
iii)
PV c
u
r
r
en
t
,
a
n
d
(
iv
)
PV p
o
wer
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
A
n
o
ve
l fa
s
t MP
P
T st
r
a
teg
y
w
i
th
h
ig
h
efficien
cy
fo
r
fa
s
t c
h
a
n
g
in
g
ir
r
a
d
ia
n
ce
i
n
…
(
P
u
j
a
r
i A
n
ja
p
p
a
)
171
T
ab
le
3
.
Vo
ltag
e
a
n
d
c
u
r
r
en
t
v
alu
es a
t d
if
f
er
en
t ir
r
ad
ian
ce
c
o
n
d
itio
n
s
with
p
r
o
p
o
s
ed
m
et
h
o
d
Ti
me
p
e
r
i
o
d
(
i
n
se
c
)
I
r
r
a
d
i
a
n
c
e
(
i
n
W
/
m
2
)
V
(
v
o
l
t
s)
I
(
a
mp
s)
R
e
a
c
h
e
s
t
o
st
e
a
d
y
st
a
t
e
(
i
n
s
e
c
)
D
y
n
a
mi
c
p
e
r
f
o
r
m
a
n
c
e
0
–
1
5
0
0
2
4
V
4
A
0
.
0
0
5
5
V
e
r
y
g
o
o
d
1
–
2
1
0
0
0
3
0
.
7
V
8
A
0
.
0
3
V
e
r
y
g
o
o
d
2
–
3
8
0
0
3
2
V
6
A
0
.
0
3
V
e
r
y
g
o
o
d
3
–
4
6
0
0
3
3
V
5A
0
.
0
3
V
e
r
y
g
o
o
d
T
ab
le
4
.
C
o
m
p
a
r
is
o
n
o
f
p
r
o
p
o
s
ed
MPPT
with
o
th
er
tech
n
iq
u
es f
o
r
v
ar
iatio
n
in
s
o
lar
ir
r
ad
ia
n
ce
P
a
r
a
me
t
e
r
P
&O
met
h
o
d
I
N
C
met
h
o
d
P
r
o
p
o
se
d
m
e
t
h
o
d
Ef
f
i
c
i
e
n
c
y
(
%)
8
3
.
4
7
9
1
.
5
1
9
4
.
2
5
Tr
a
c
k
i
n
g
p
o
w
e
r
l
o
ss (%)
2
4
.
6
0
1
7
.
0
5
5
.
7
6
Tr
a
c
k
i
n
g
t
i
me
(
s)
1
.
4
2
1
.
1
6
0
.
2
8
S
t
e
a
d
y
st
a
t
e
o
sc
i
l
l
a
t
i
o
n
s
La
r
g
e
S
mal
l
N
e
g
l
i
g
i
b
l
e
5.
CO
NCLU
SI
O
N
I
n
th
e
p
r
o
p
o
s
ed
wo
r
k
a
n
o
v
el
an
d
f
ast
-
ac
tin
g
MPPT
f
o
r
f
ast
v
ar
y
in
g
s
o
lar
ir
r
ad
ia
n
ce
is
im
p
lem
en
ted
.
Sin
ce
th
e
p
r
o
p
o
s
ed
MPPT
is
n
o
t a
n
iter
ativ
e
m
eth
o
d
,
d
ir
ec
tly
it tr
ac
k
s
th
e
MPP wh
e
n
t
h
er
e
is
a
s
u
d
d
e
n
c
h
an
g
e
in
ir
r
ad
ia
n
ce
o
r
i
n
lo
a
d
.
Simu
l
atio
n
o
f
th
e
p
r
o
p
o
s
ed
MPPT
m
eth
o
d
is
im
p
lem
en
ted
f
o
r
v
ar
io
u
s
ir
r
ad
ian
ce
lev
els
an
d
co
m
p
a
r
ed
with
P&
O,
I
NC
alg
o
r
ith
m
s
.
I
n
th
e
c
o
n
v
e
n
tio
n
al
m
eth
o
d
b
y
tr
ial
an
d
er
r
o
r
,
th
e
p
ea
k
p
o
wer
p
o
in
t
is
r
ea
ch
ed
.
T
h
e
tim
e
tak
en
to
tr
ac
k
MPP
is
m
o
r
e.
So
,
th
e
p
o
wer
lo
s
s
in
th
o
s
e
m
eth
o
d
s
wil
l
b
e
g
r
ea
ter
.
T
h
ese
m
eth
o
d
s
co
n
tin
u
o
u
s
ly
t
r
ac
k
th
e
v
o
ltag
e
an
d
/o
r
c
u
r
r
en
t,
with
o
u
t
u
s
in
g
em
p
ir
ical
d
ata.
T
h
e
m
ain
ad
v
an
tag
e
o
f
s
u
ch
m
eth
o
d
s
is
th
at
th
ey
d
o
n
o
t
r
eq
u
ir
e
p
r
i
o
r
k
n
o
wled
g
e
o
f
t
h
e
PV
ar
r
ay
ch
ar
ac
ter
is
tics
.
T
h
e
d
r
awb
ac
k
s
o
f
th
e
co
n
v
en
tio
n
al
alg
o
r
ith
m
s
ar
e
s
lo
w
tr
ac
k
in
g
s
p
ee
d
,
a
n
d
s
te
ad
y
-
s
tate
o
s
cillatio
n
at
th
e
tr
an
s
ien
t
s
tag
es.
T
o
o
v
er
co
m
e
th
is
d
r
awb
ac
k
a
n
o
v
el
an
d
f
ast
-
ac
tin
g
m
o
d
i
f
ied
I
N
C
alg
o
r
ith
m
is
p
r
o
p
o
s
ed
t
o
in
cr
ea
s
e
th
e
co
n
v
e
r
g
in
g
s
p
ee
d
u
n
d
er
f
ast
v
ar
y
in
g
ir
r
a
d
ian
ce
.
I
n
t
h
e
in
c
r
em
en
tal
c
o
n
d
u
ctan
ce
m
eth
o
d
,
t
h
e
s
lo
p
e
o
f
p
o
wer
v
s
v
o
l
ta
g
e
ch
ar
ac
ter
is
tic
o
f
s
o
lar
p
a
n
els
is
ze
r
o
at
th
e
MPP.
B
u
t
it
ca
n
n
ev
er
b
e
m
et
p
r
ac
tically
;
s
o
,
a
p
er
m
itted
er
r
o
r
o
f
0
.
0
6
is
ac
ce
p
ta
b
le
to
d
etec
t
M
PP
.
T
h
e
p
r
o
p
o
s
ed
m
eth
o
d
d
ir
ec
tly
ca
lcu
lates
th
e
r
eq
u
ir
e
d
d
u
ty
cy
cle
to
o
b
tain
th
e
n
ew
MPP
b
y
co
n
s
id
er
in
g
th
e
lo
ad
lin
e.
T
h
is
r
ed
u
ce
s
th
e
n
o
r
m
al
iter
ativ
e
p
r
o
ce
s
s
an
d
r
ea
ch
es
th
e
r
eq
u
ir
ed
MPP
p
o
in
t
in
a
f
ast
way
.
T
h
e
r
esu
lts
s
h
o
w
th
at
th
e
o
v
er
all
tr
ac
k
in
g
s
p
ee
d
o
f
t
h
e
p
r
o
p
o
s
ed
MPPT
is
5
.
6
tim
es,
3
.
8
tim
es
f
aster
th
an
t
h
e
P&
O
m
eth
o
d
a
n
d
I
NC
m
eth
o
d
r
es
p
ec
tiv
ely
.
Du
r
in
g
th
e
v
ar
iatio
n
o
f
ir
r
ad
ian
ce
,
th
e
p
o
wer
lo
s
s
is
r
ed
u
ce
d
b
y
1
8
.
8
4
%
an
d
1
1
.
2
9
%
in
co
m
p
ar
is
o
n
with
th
e
P&
O
an
d
I
NC
m
et
h
o
d
s
.
T
h
e
p
r
o
p
o
s
ed
m
eth
o
d
also
m
in
im
izes th
e
s
te
ad
y
-
s
tate
o
s
cillatio
n
s
.
RE
F
E
R
E
NC
E
S
[
1
]
J
.
A
h
m
e
d
a
n
d
Z
.
S
a
l
a
m
,
“
A
m
o
d
i
f
i
e
d
P
&
O
m
a
x
i
m
u
m
p
o
w
e
r
p
o
i
n
t
t
r
a
c
k
i
n
g
m
e
t
h
o
d
w
i
t
h
r
e
d
u
c
e
d
s
t
e
a
d
y
-
s
t
a
t
e
o
s
c
i
l
l
a
t
i
o
n
a
n
d
i
m
p
r
o
v
e
d
t
r
a
c
k
i
n
g
e
f
f
i
c
i
e
n
c
y
,
”
I
E
E
E
T
r
a
n
s
a
c
t
i
o
n
s
o
n
S
u
s
t
a
i
n
a
b
l
e
E
n
e
r
g
y
,
v
o
l
.
7
,
n
o
.
4
,
p
p
.
1506
–
1
5
1
5
,
O
c
t
.
2
0
1
6
,
d
o
i
:
1
0
.
1
1
0
9
/
T
S
T
E
.
2
0
1
6
.
2
5
6
8
0
4
3
.
[
2
]
H
.
A
.
S
h
e
r
,
A
.
A
.
R
i
z
v
i
,
K
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rsity
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d
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P
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.
fro
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Ja
wa
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rlal
Ne
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ru
Un
iv
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rsity
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k
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d
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In
d
ia.
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tere
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sy
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ty
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n
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m
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m
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o
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IEE
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a
n
d
IAENG
.
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c
a
n
b
e
c
o
n
tac
ted
a
t
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m
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il
:
i
n
d
ra
ji
th
u
@
g
m
a
il
.
c
o
m
.
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