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n
i
n
p
u
t
r
esis
tan
ce
(
R
in
)
o
f
t
h
e
c
o
n
v
er
ter
m
atc
h
es
w
it
h
t
h
e
i
n
t
er
n
al
r
esi
s
ta
n
ce
o
f
P
V
ar
r
a
y
at
(
R
MPP
)
b
a
s
ed
o
n
Ma
x
i
m
u
m
P
o
w
er
T
r
an
s
f
er
T
h
eo
r
em
.
T
o
d
o
s
o
,
M
PP
T
r
eg
u
l
ates
th
e
i
n
p
u
t
v
o
lta
g
e
o
f
t
h
e
P
V
ar
r
ay
at
MP
P
b
y
ad
j
u
s
tin
g
th
e
d
u
t
y
c
y
cle
(
D)
o
f
th
e
co
n
v
er
ter
.
T
h
e
m
o
s
t
p
o
p
u
lar
MP
PT
alg
o
r
ith
m
s
in
p
r
ac
tice
ar
e
p
er
tu
r
b
an
d
o
b
s
er
v
e
(
P
&
O)
,
h
ill
cli
m
b
in
g
(
HC
)
,
an
d
th
e
i
n
cr
e
m
e
n
tal
co
n
d
u
cta
n
ce
m
e
th
o
d
(
I
NC
)
.
T
h
ese
co
n
v
e
n
tio
n
al
al
g
o
r
ith
m
s
ar
e
w
i
d
ely
ap
p
lied
d
u
e
to
th
eir
s
i
m
p
licit
y
,
ea
s
e
o
f
i
m
p
le
m
en
tatio
n
a
n
d
lo
w
co
s
t
[
4
]
.
T
h
e
o
th
er
co
n
v
e
n
tio
n
al
MP
P
T
alg
o
r
ith
m
s
u
s
ed
in
P
V
s
y
s
te
m
ar
e
p
r
esen
ted
in
[5
-
12]
.
I
n
liter
atu
r
e
[
1
3
-
17]
,
m
a
n
y
n
e
w
i
m
p
r
o
v
ed
p
er
f
o
r
m
a
n
ce
o
f
MP
P
T
alg
o
r
ith
m
s
h
av
e
b
ee
n
p
r
o
p
o
s
ed
.
Ho
w
e
v
er
,
t
h
e
co
m
p
o
n
en
t
s
s
izin
g
o
f
th
e
d
if
f
er
en
t
to
p
o
lo
g
ies
o
f
D
C
-
D
C
co
n
v
er
ter
s
h
av
e
n
o
t
b
ee
n
s
t
u
d
ied
w
id
el
y
al
th
o
u
g
h
t
h
is
s
izin
g
af
f
ec
t
s
s
i
g
n
i
f
ica
n
tl
y
t
h
e
o
p
tim
u
m
o
p
er
atio
n
o
f
th
e
MP
P
T
alg
o
r
ith
m
s
.
Fo
r
e
x
a
m
p
le,
t
h
e
p
o
o
r
l
y
s
el
ec
tio
n
o
f
th
e
co
n
v
er
ter
co
m
p
o
n
en
t
s
izi
n
g
,
e
s
p
ec
iall
y
ca
p
ac
ito
r
an
d
in
d
u
cto
r
ac
co
r
d
in
g
to
t
h
e
lo
ad
co
u
ld
m
ak
e
MP
PT
o
p
er
ate
less
o
p
tim
all
y
.
Un
d
er
s
u
d
d
en
s
tep
ch
an
g
es
i
n
ir
r
ad
ian
ce
,
th
e
s
elec
tio
n
o
f
th
e
MP
PT
s
am
p
l
in
g
ti
m
e
(
T
S
_MPPT
)
m
u
s
t
co
n
s
id
er
th
e
tr
an
s
ie
n
t
r
esp
o
n
s
e
o
f
t
h
e
MP
P
T
in
p
u
ts
s
u
c
h
as
P
V
’
s
v
o
lta
g
e
an
d
c
u
r
r
en
t,
in
o
r
d
er
to
av
o
id
th
e
d
ela
y
a
n
d
f
ail
u
r
e
i
n
tr
ac
k
in
g
o
f
m
ax
i
m
u
m
p
o
w
er
.
T
h
e
th
r
ee
m
o
s
t
co
m
m
o
n
l
y
u
s
ed
DC
-
D
C
co
n
v
er
ter
s
i
n
P
V
s
y
s
te
m
ar
e:
b
u
c
k
,
b
o
o
s
t
an
d
b
u
ck
-
b
o
o
s
t
co
n
v
er
t
er
s
.
T
h
e
cir
cu
it
p
ar
a
m
ete
r
s
an
d
m
o
d
e
o
f
o
p
er
atio
n
o
f
ea
c
h
t
o
p
o
lo
g
y
h
a
v
e
b
ee
n
d
is
cu
s
s
ed
i
n
[
1
8
,
1
9
]
.
B
o
o
s
t
co
n
v
er
ter
h
as
s
o
m
e
ad
v
a
n
ta
g
es
o
v
er
t
h
e
o
t
h
er
co
n
v
er
ter
s
a
s
i
t
is
m
o
r
e
s
tab
le
a
n
d
ef
f
icien
t
[
2
0
]
,
an
d
h
en
ce
ch
o
s
en
in
t
h
i
s
w
o
r
k
.
T
h
is
w
o
r
k
f
o
c
u
s
es
o
n
t
h
e
s
izi
n
g
e
f
f
ec
t
o
f
t
w
o
DC
-
DC
b
o
o
s
t
co
n
v
er
ter
co
m
p
o
n
e
n
t
s
i.e
ca
p
ac
ito
r
an
d
in
d
u
cto
r
,
o
n
tr
an
s
ien
t
r
esp
o
n
s
e
an
d
s
p
ee
d
o
f
th
e
MP
PT
alg
o
r
ith
m
.
Fu
r
t
h
er
m
o
r
e,
h
ill
c
li
m
b
in
g
(
H
C
)
MP
P
T
alg
o
r
ith
m
h
as
b
ee
n
ch
o
s
en
to
tr
ac
k
th
e
MP
P
d
u
r
in
g
s
u
d
d
en
l
y
ch
a
n
g
i
n
g
s
o
lar
ir
r
ad
ian
ce
.
On
l
y
DC
-
DC
b
o
o
s
t
co
n
v
er
ter
u
s
ed
in
Sta
n
d
-
Alo
n
e
P
V
s
y
s
te
m
w
it
h
f
i
x
ed
lo
ad
r
esis
to
r
is
co
n
s
id
er
ed
h
er
e.
2.
M
P
P
T
F
O
R
ST
AND
-
A
L
O
N
E
P
V
SYS
T
E
M
WI
T
H
L
O
A
D
RE
S
I
S
T
ANC
E
I
n
S
A
P
V
s
y
s
te
m
,
th
e
b
atter
y
i
s
cr
u
cial
f
o
r
p
o
w
er
f
lo
w
m
an
ag
e
m
e
n
t
if
t
h
e
lo
ad
d
e
m
a
n
d
s
a
co
n
s
ta
n
t
v
o
ltag
e.
Ho
w
e
v
er
,
in
s
o
m
e
ap
p
licatio
n
s
li
k
e
h
ea
t
in
g
,
co
o
k
in
g
an
d
w
ater
p
u
m
p
i
n
g
s
y
s
te
m
w
h
er
e
th
e
c
h
an
g
e
i
n
th
e
lo
ad
v
o
ltag
e
w
ill
n
o
t
af
f
e
ct
th
e
r
eliab
ilit
y
o
f
t
h
e
s
y
s
te
m
,
th
e
b
atter
y
i
s
n
o
t
n
ee
d
ed
.
I
n
th
o
s
e
ap
p
licatio
n
s
,
th
e
b
atter
y
is
n
o
t
ap
p
lied
to
r
ed
u
ce
co
s
t,
f
r
eq
u
en
t
m
ain
ten
a
n
ce
a
n
d
en
v
ir
o
n
m
en
tal
i
s
s
u
es
ca
u
s
ed
b
y
b
atter
y
u
s
a
g
es
[
2
,
3
]
.
T
h
e
m
ai
n
o
b
j
e
ctiv
e
o
f
t
h
e
s
y
s
te
m
is
to
o
b
tain
p
o
w
er
f
r
o
m
t
h
e
P
V
ar
r
ay
as
m
u
c
h
as
p
o
s
s
ib
l
e
w
it
h
o
u
t
h
a
v
i
n
g
to
r
eg
u
late
t
h
e
o
u
tp
u
t
v
o
lta
g
e
a
n
d
cu
r
r
e
n
t.
A
s
p
er
m
ax
i
m
u
m
p
o
w
er
tr
an
s
f
er
th
eo
r
e
m
,
m
ax
i
m
u
m
p
o
w
er
is
tr
an
s
f
er
r
e
d
to
th
e
lo
a
d
w
h
en
eq
u
i
v
ale
n
t
lo
ad
r
esis
tan
ce
r
ef
er
r
ed
to
th
e
in
p
u
t
ter
m
i
n
als
o
f
th
e
co
n
v
er
ter
(
R
in
)
i
s
m
atc
h
t
o
th
e
i
n
ter
n
al
r
esis
ta
n
ce
o
f
P
V
ar
r
a
y
at
MP
P
(
R
MPP
)
.
Fi
g
u
r
e
1
s
h
o
w
s
s
u
c
h
a
s
y
s
te
m
.
H
C
M
P
P
T
P
WM
G
EN
ER
A
TO
R
P
V
M
O
D
U
L
E
R
E
S
I
S
TO
R
(
R
L
)
+
-
+
-
I
PV
V
PV
D
u
ty
C
Y
c
l
e
P
WM
S
i
g
n
a
l
DC
-
D
C
BO
O
S
T
C
O
N
V
ER
T
ER
R
in
Fig
u
r
e
1
.
B
lo
ck
d
iag
r
a
m
o
f
M
P
PT
s
tan
d
-
alo
n
e
P
V
s
y
s
te
m
s
w
it
h
lo
ad
r
esis
to
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
,
Vo
l.
9
,
No
.
3
,
Sep
tem
b
er
2
0
1
8
:
1
0
3
8
–
1
0
5
0
1040
2
.
1
.
P
V
ce
ll m
o
deli
ng
I
n
th
i
s
w
o
r
k
,
t
h
e
s
i
m
u
latio
n
s
m
o
d
el
o
f
P
V
s
y
s
te
m
i
s
b
ased
o
n
M
A
T
L
A
B
/S
i
m
u
lin
k
s
i
m
u
lato
r
d
ev
elo
p
ed
in
[
2
1
,
2
2
]
,
w
h
ich
u
tili
ze
d
a
t
w
o
-
d
io
d
e
P
V
ce
ll m
o
d
el
as d
ep
icted
in
Fig
u
r
e
2.
Fig
u
r
e
2
.
A
T
w
o
-
d
io
d
e
m
o
d
el
o
f
P
V
ce
ll
I
t
is
ch
o
s
e
n
d
u
e
to
its
s
u
p
er
io
r
ac
cu
r
ac
y
,
p
ar
ticu
lar
l
y
at
lo
w
i
r
r
ad
ian
ce
lev
el
[
2
1
]
.
A
n
u
m
b
er
o
f
s
er
ies
-
p
ar
allel
co
n
n
ec
ted
P
V
m
o
d
u
le
s
ar
e
u
s
ed
to
f
o
r
m
a
P
V
ar
r
a
y
f
o
r
a
d
esire
d
v
o
lta
g
e
a
n
d
c
u
r
r
en
t
lev
el.
Fo
r
a
s
tr
in
g
w
it
h
N
n
u
m
b
er
o
f
m
o
d
u
les i
n
s
er
ie
s
(
N
cell
)
,
th
e
o
u
tp
u
t c
u
r
r
en
t o
f
t
h
e
ce
ll is
g
i
v
en
b
y
:
I
=
I
PV
−
I
o1
[
e
xp
(
V
+
IR
s
a
1
V
T1
)
−
1
]
−
I
o2
[
e
xp
(
V
+
IR
s
a
2
V
T2
)
−
1
]
−
(
V
+
IR
s
×
N
c
el
l
IR
p
×
N
c
el
l
)
(
1
)
w
h
er
e
I
o1
a
n
d
I
o2
ar
e
th
e
r
e
v
e
r
s
e
s
at
u
r
atio
n
c
u
r
r
en
t
s
o
f
d
io
d
e
1
(
D
1
)
an
d
d
io
d
e
2
(
D
2
)
,
r
esp
ec
tiv
el
y
;
V
T1
an
d
V
T2
ar
e
th
e
th
er
m
al
v
o
ltag
es
o
f
r
esp
ec
ti
v
e
d
io
d
es;
a
1
an
d
a
2
r
ep
r
esen
t
th
e
d
io
d
e
id
ea
lit
y
co
n
s
tan
ts
.
I
n
th
is
w
o
r
k
,
5
P
V
m
o
d
u
le
s
ar
e
co
n
n
ec
ted
i
n
a
s
in
g
le
s
er
ies
s
t
r
in
g
a
n
d
p
r
o
v
id
es
ab
o
u
t
2
9
9
.
3
W
as
n
o
m
in
al
m
ax
i
m
u
m
o
u
tp
u
t
p
o
w
er
u
n
d
e
r
s
o
lar
ir
r
ad
ian
ce
o
f
1
0
0
0
W
/m
2
at
s
tan
d
ar
d
test
co
n
d
itio
n
(
ST
C
)
,
as
s
h
o
w
n
i
n
Fig
u
r
e
3
.
T
h
e
P
V
m
o
d
u
le
is
s
i
m
u
lated
u
s
i
n
g
B
P
MSX
-
6
0
m
o
d
el
an
d
its
s
p
ec
if
icatio
n
s
at
S
T
C
ar
e
tab
u
lated
in
T
ab
le
1.
M
o
d
u
l
e
A
(
G
A
)
M
o
d
u
l
e
B
(
G
B
)
M
o
d
u
l
e
C
(
G
C
)
M
o
d
u
l
e
D
(
G
D
)
M
o
d
u
l
e
E
(
G
E
)
B
y
p
a
s
s
D
i
o
d
e
B
y
p
a
s
s
D
i
o
d
e
B
y
p
a
s
s
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o
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e
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o
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e
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e
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u
r
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3
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Fiv
e
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o
d
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les i
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es u
n
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er
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lectr
ical
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d
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t ST
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r
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t
e
r
s
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l
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e
s
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m
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m
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r
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V
o
l
t
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g
e
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t
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mp
p
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1
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r
r
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n
t
a
t
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A
O
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r
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t
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g
e
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c
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1
V
S
h
o
r
t
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r
c
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i
t
c
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r
r
e
n
t
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8
A
T
e
mp
e
r
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t
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r
e
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e
f
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i
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c
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mp
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r
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t
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r
a
t
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e
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T
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r
a
t
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g
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e
r
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u
r
e
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I
n
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r
m
al
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h
en
th
e
s
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lar
ir
r
ad
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ce
o
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tire
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V
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n
i
f
o
r
m
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h
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n
d
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r
r
en
t
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v
o
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e
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-
V)
c
u
r
v
e
s
ex
h
ib
it
s
a
s
in
g
l
e
g
lo
b
al
MP
P
as
d
ep
icte
d
in
Fi
g
u
r
e
4
.
T
o
s
i
m
u
late
th
e
f
a
s
t
c
h
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g
i
n
g
s
o
l
ar
ir
r
ad
ian
ce
,
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w
o
d
i
f
f
er
e
n
t
le
v
els
o
f
ir
r
ad
ian
ce
w
er
e
s
elec
te
d
,
1
)
h
ig
h
e
s
t
(
P
o
in
t
A
,
G=
1
0
0
0
W
/
m
2
)
an
d
lo
w
est
(
P
o
in
t
B
,
G=
3
0
0
W
/m
2
)
.
T
h
e
ch
ar
ac
ter
is
tic
s
v
ar
iatio
n
o
f
P
-
V,
I
-
V
an
d
o
p
ti
m
a
l
in
ter
n
a
l
r
esis
ta
n
ce
cu
r
v
e
s
o
f
t
h
is
P
V
ar
r
ay
f
o
r
th
ese
t
w
o
ir
r
ad
ian
ce
lev
els
ar
e
s
h
o
w
n
in
Fig
u
r
e
4
.
I
t
ca
n
b
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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Desi
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ith
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h
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n
th
e
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ad
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ce
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d
ec
r
ea
s
es
f
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o
m
1
0
0
0
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/m
2
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3
0
0
W
/m
2
.
A
s
a
r
es
u
lt,
R
MP
P
in
cr
ea
s
ed
f
r
o
m
2
4
.
6
to
8
4
.
4
w
h
ic
h
is
ca
lc
u
lated
u
s
i
n
g
;
R
M
P
P
=
V
M
P
P
I
M
P
P
(
2
)
I
t
is
n
o
t
p
r
ac
tical
to
ch
a
n
g
e
t
h
e
lo
ad
r
esis
ta
n
ce
m
a
n
u
a
ll
y
at
an
y
m
o
m
e
n
t
t
h
e
s
o
lar
ir
r
ad
ian
ce
ch
a
n
g
e
s
[
2
3
]
.
T
h
er
ef
o
r
e,
MPPT
al
g
o
r
ith
m
h
as
b
ee
n
d
esig
n
ed
to
co
n
t
in
u
o
u
s
l
y
ad
j
u
s
ts
t
h
e
d
u
t
y
c
y
c
l
e
o
f
th
e
co
n
v
er
ter
,
in
o
r
d
er
to
m
atc
h
th
e
in
p
u
t
r
e
s
is
ta
n
ce
to
t
h
e
in
ter
n
al
r
es
is
ta
n
ce
o
f
P
V
ar
r
a
y
at
MP
P
(
R
in
=R
MPP
)
,
a
n
d
h
e
n
ce
ex
tr
ac
ts
m
ax
i
m
u
m
av
a
ilab
le
p
o
w
er
.
At
MP
P
,
th
e
d
u
t
y
c
y
cle
o
f
th
e
co
n
v
er
ter
is
ca
lc
u
lated
as
[
3
]
;
D
M
P
P
=1
−
√
R
M
P
P
R
L
(
3
)
B
y
as
s
u
m
i
n
g
a
lo
s
s
les
s
co
n
v
er
ter
(
P
PV
=P
out
)
,
th
e
o
u
tp
u
t
v
o
ltag
e
(
V
o
ut
)
o
f
th
e
co
n
v
er
ter
at
MPP
is
d
eter
m
in
ed
as;
V
out
=
V
m
pp
1
−
D
m
pp
(
4
)
P
o
i
n
t
A
P
o
i
n
t
B
I
SC
V
OC
M
P
P
Z
o
n
e
M
P
P
Zo
n
e
D
m
p
p
=
0
.
34
R
m
p
p
=
84
.
4
D
m
p
p
=
0
.
64
R
m
p
p
=
24
.
6
Fig
u
r
e
4
.
(
a)
I
–
V
an
d
P
–
V
cu
r
v
es o
f
P
V
ar
r
a
y
at
t
w
o
ir
r
ad
ian
ce
lev
el
at
ST
C
2
.
2
.
H
ill cli
m
bin
g
(
H
C)
M
P
P
T
a
lg
o
rit
h
m
T
h
e
g
o
al
o
f
em
p
lo
y
i
n
g
MP
PT
is
to
ex
tr
ac
t
m
ax
i
m
u
m
p
o
w
er
f
r
o
m
P
V
A
r
r
a
y
at
an
y
v
ar
y
i
n
g
at
m
o
s
p
h
er
ic
co
n
d
itio
n
s
e
s
p
ec
iall
y
s
o
lar
ir
r
ad
ian
ce
c
h
an
g
es
.
T
o
d
o
s
o
,
MPPT
alg
o
r
ith
m
p
er
tu
r
b
s
th
e
d
u
t
y
c
y
cle
o
f
t
h
e
DC
-
DC
co
n
v
er
t
er
to
m
atc
h
th
e
r
esis
tan
ce
o
f
lo
ad
as
s
ee
n
b
y
th
e
s
o
u
r
ce
(
R
in
)
to
t
h
e
i
n
ter
n
a
l
o
p
tim
a
l
r
esi
s
ta
n
ce
o
f
P
V
A
r
r
a
y
(
R
MPP
)
.
I
n
t
h
is
w
o
r
k
,
t
h
e
co
n
v
e
n
tio
n
al
H
ill
C
li
m
b
i
n
g
alg
o
r
ith
m
as
d
is
c
u
s
s
ed
in
[
4
,
2
4
-
28]
h
as
b
ee
n
ap
p
lie
d
to
tr
ac
k
t
h
e
MP
P
w
h
e
n
s
u
b
j
ec
ted
to
s
u
d
d
en
c
h
an
g
es
in
s
o
lar
ir
r
ad
ian
ce
.
HC
alg
o
r
ith
m
o
f
f
er
s
n
u
m
b
er
o
f
a
d
v
an
ta
g
es:
1
)
it
s
i
m
p
lifie
s
t
h
e
tr
ac
k
in
g
s
tr
u
ct
u
r
e,
2
)
it
r
ed
u
c
es
th
e
co
m
p
u
tat
io
n
ti
m
e,
an
d
3
)
n
o
tu
n
in
g
e
f
f
o
r
t
i
s
n
ee
d
ed
f
o
r
th
e
P
I
g
ain
s
[
2
8
]
.
P
r
ac
tically
,
it
ca
n
r
ep
lace
th
e
ex
p
en
s
i
v
e
MP
PT
co
n
tr
o
ller
w
it
h
lo
w
er
co
s
t c
o
n
t
r
o
ller
w
h
ile
m
ai
n
tai
n
i
n
g
s
i
m
il
ar
o
p
tim
u
m
r
e
s
u
l
ts
.
I
n
HC
,
at
ea
c
h
iter
atio
n
i,
th
e
alg
o
r
ith
m
s
tar
ts
s
e
n
s
in
g
t
h
e
v
o
ltag
e,
V(
i)
an
d
cu
r
r
en
t,
I
(
i)
o
f
P
V
ar
r
a
y
an
d
th
e
co
r
r
es
p
o
n
d
in
g
p
o
w
er
,
P
(
i)
=
V(
i)
×I
(
i)
is
th
en
ca
lcu
l
ated
.
Nex
t,
t
h
e
d
u
t
y
c
y
cle
(
D)
o
f
t
h
e
co
n
v
er
ter
is
p
er
tu
r
b
ed
b
y
an
in
cr
e
m
en
t
o
f
d
u
t
y
c
y
cle
s
tep
s
ize
(
D
step
)
,
a
n
d
th
e
r
es
u
lt
in
g
c
h
an
g
e
o
f
p
o
w
er
,
P
=
P
(
i+1
)
-
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
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t J
P
o
w
E
lec
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Dr
i
S
y
s
t
,
Vo
l.
9
,
No
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3
,
Sep
tem
b
er
2
0
1
8
:
1
0
3
8
–
1
0
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0
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P
(
i)
is
o
b
tain
ed
.
I
f
th
e
P
is
p
o
s
itiv
e,
th
e
n
p
er
t
u
r
b
atio
n
i
s
in
th
e
r
ig
h
t
d
ir
ec
tio
n
,
an
d
m
o
r
e
p
er
tu
r
b
atio
n
is
ap
p
lied
in
t
h
e
s
a
m
e
d
ir
ec
ti
o
n
to
r
ea
ch
t
h
e
MP
P
.
T
h
e
p
er
tu
r
b
atio
n
d
ir
ec
tio
n
i
s
r
ev
er
s
ed
if
P
is
n
e
g
ati
v
e,
a
n
in
d
icatio
n
t
h
at
t
h
e
tr
ac
k
in
g
i
s
m
o
v
ed
a
w
a
y
f
r
o
m
th
e
MP
P
.
T
h
e
f
lo
w
c
h
ar
t
o
f
t
h
e
H
C
alg
o
r
ith
m
i
s
s
h
o
w
n
i
n
Fig
u
r
e
5.
W
h
en
s
o
lar
ir
r
ad
ian
ce
c
h
an
g
es,
th
e
tr
ac
k
i
n
g
s
p
ee
d
to
r
e
ac
h
n
e
w
MP
P
u
s
i
n
g
co
n
v
e
n
tio
n
al
H
C
alg
o
r
ith
m
d
ep
en
d
s
m
a
in
l
y
o
n
t
w
o
v
ar
iab
les,
1
)
th
e
d
u
t
y
c
y
cle
s
tep
s
ize
(
D
step
)
,
an
d
2
)
th
e
MP
PT
s
am
p
li
n
g
ti
m
e
(
T
S
_MPPT
)
w
h
ic
h
i
s
t
h
e
t
i
m
e
g
i
v
e
n
to
t
h
e
MP
P
T
to
r
ea
d
all
t
h
e
i
n
p
u
t
s
a
n
d
s
o
l
v
e
all
t
h
e
ca
lc
u
latio
n
s
in
v
o
l
v
ed
i
n
th
e
a
lg
o
r
it
h
m
a
t e
a
ch
ap
p
lied
d
u
t
y
c
y
cle
(
D)
.
L
ar
g
e
D
step
w
i
ll i
n
cr
ea
s
e
t
h
e
MP
P
tr
ac
k
in
g
s
p
ee
d
b
u
t
th
e
p
o
w
er
lo
s
s
es
a
ls
o
i
n
cr
ea
s
e
s
d
u
e
to
t
h
e
lar
g
e
o
s
c
illatio
n
a
r
o
u
n
d
MP
P
.
Sm
a
ll
D
step
w
i
ll
r
ed
u
ce
p
o
w
er
lo
s
s
e
s
o
s
cillatio
n
ar
o
u
n
d
MP
P
b
u
t
th
e
tr
ac
k
in
g
s
p
ee
d
w
il
l
b
e
lo
w
.
Hen
ce
,
th
e
tr
ad
e
-
o
f
f
h
av
e
to
b
e
m
ad
e
to
in
cr
ea
s
e
th
e
o
v
er
all
MP
PT
ef
f
icie
n
c
y
.
I
n
th
i
s
s
t
u
d
y
,
D
step
is
s
e
t
at
1
0
%
d
u
r
in
g
ex
p
lo
r
atio
n
p
r
o
ce
s
s
an
d
is
s
et
at
0
.
5
%
d
u
r
in
g
ex
p
lo
itatio
n
p
r
o
ce
s
s
.
Me
an
w
h
ile,
lar
g
e
T
S
_MPPT
w
i
ll r
ed
u
ce
th
e
MP
P
tr
ac
k
in
g
s
p
ee
d
a
n
d
v
ice
v
er
s
a.
Du
e
to
th
e
s
tep
ch
a
n
g
e
i
n
ir
r
ad
ian
ce
,
P
V
v
o
ltag
e
an
d
cu
r
r
en
t
w
ill
u
n
d
er
g
o
a
tr
an
s
ie
n
t
r
esp
o
n
s
e
b
ef
o
r
e
s
h
o
r
tl
y
r
ec
o
v
er
i
n
g
to
it
s
n
e
w
s
tead
y
-
s
ta
te
co
n
d
itio
n
[
1
7
,
2
8
,
2
9
]
.
T
h
e
s
ettlin
g
ti
m
e
(
T
S
ettling
)
o
f
v
o
ltag
e
an
d
cu
r
r
en
t
d
ep
en
d
s
m
u
c
h
l
y
o
n
th
e
cir
cu
it
co
m
p
o
n
en
t
s
i.e
ca
p
ac
ito
r
an
d
in
d
u
cto
r
,
w
h
ic
h
w
ill
b
e
d
is
cu
s
s
ed
f
u
r
t
h
er
in
t
h
e
n
e
x
t
s
ec
tio
n
.
Fo
r
ac
cu
r
ate
MPPT
,
T
S
_MPPT
m
u
s
t
b
e
d
esig
n
ed
to
b
e
g
r
ea
ter
th
an
T
S
ettlin
g
a
n
d
all
r
ea
d
in
g
s
a
n
d
ca
lcu
lat
io
n
s
i
n
v
o
lv
ed
in
alg
o
r
it
h
m
m
u
s
t
b
e
co
m
p
leted
w
it
h
i
n
t
h
is
s
p
ec
i
f
ie
d
p
er
io
d
.
Oth
er
w
i
s
e,
th
e
alg
o
r
it
h
m
m
ig
h
t
f
ail
to
p
er
f
o
r
m
i
n
th
e
r
eq
u
ir
ed
m
a
n
n
er
.
Y
E
S
I
f
P
(
i
)
>
P
(
i
-
1
)
I
n
i
t
i
a
l
i
z
a
t
i
o
n
S
t
a
g
e
S
e
t
i
=
1
;
S
l
o
p
e
=
1
;
D
ref
=
0
.
1
V
(
i
-
1
)
=
I
(
i
-
1
)
=
P
(
i
-
1
)
=
0
;
i
=
i
+
1
S
e
n
d
D
(
i
)
=
D
(
i
-
1
)
+
D
s
t
e
p
×
S
l
o
p
e
S
e
n
se
V
(
i
)
&
I
(
i
)
C
a
l
c
u
l
a
t
e
P
(
i
)
=
V
(
i
)
×I
(
i
)
C
o
m
p
l
e
m
e
n
t
S
l
o
p
e
s
i
g
n
NO
S
t
a
r
t
U
p
d
a
t
e
P
(
i
-
1
)
=
P
(
i
)
,
I
(
i
-
1
)
=
I
(
i
)
&
D
(
i
-
1
)
=
D
(
i
)
S
e
n
d
D
(
i
)
=
D
ref
S
e
n
s
e
V
(
i
)
&
I
(
i
)
C
a
l
c
u
l
a
t
e
P
(
i
)
=
V
(
i
)
×I
(
i
)
Fig
u
r
e
5
.
Flo
w
c
h
ar
t o
f
co
n
v
e
n
tio
n
al
H
C
MP
P
T
A
lg
o
r
it
h
m
.
3.
DE
S
I
G
N
O
F
DC
-
DC
B
O
O
ST
CO
NVE
RT
E
R
Fo
r
Stan
d
-
A
lo
n
e
P
V
s
y
s
te
m
s
[
3
0
]
,
a
DC
-
D
C
b
o
o
s
t
co
n
v
er
te
r
is
in
ter
f
ac
ed
b
et
w
ee
n
t
h
e
P
V
ar
r
ay
an
d
th
e
lo
ad
r
esi
s
ta
n
ce
as
s
h
o
w
n
i
n
F
ig
u
r
e
1
.
T
h
e
m
ax
i
m
u
m
p
o
w
er
g
e
n
er
ated
f
r
o
m
t
h
e
P
V
ar
r
ay
at
s
ta
n
d
ar
d
test
co
n
d
itio
n
(
ST
C
)
is
ab
o
u
t
2
9
9
.
3
W
.
T
h
e
s
p
ec
if
icatio
n
s
o
f
t
h
e
P
V
m
o
d
u
le
(
B
P
-
MSX6
0
)
ar
e
g
iv
e
n
i
n
T
ab
le
1
.
I
n
DC
-
DC
b
o
o
s
t
co
n
v
er
ter
,
f
iv
e
co
m
p
o
n
en
t
s
n
ee
d
s
to
b
e
ch
o
s
en
n
a
m
e
l
y
,
s
w
itc
h
i
n
g
d
e
v
i
ce
,
d
io
d
e,
in
d
u
cto
r
,
ca
p
ac
ito
r
an
d
r
esis
to
r
.
I
n
th
e
s
i
m
u
latio
n
,
a
s
tan
d
ar
d
p
o
w
er
d
io
d
e
an
d
th
e
s
w
itch
in
g
d
ev
ice
o
f
P
o
w
er
-
MO
SF
E
T
ar
e
ch
o
s
en
s
in
ce
t
h
er
e
ar
e
w
id
el
y
u
s
ed
f
o
r
lo
w
to
m
ed
i
u
m
p
o
w
er
ap
p
licatio
n
s
.
T
h
e
s
w
i
tch
i
n
g
f
r
eq
u
en
c
y
is
s
et
at
2
0
k
Hz
af
ter
a
tr
ad
e
-
o
f
f
b
et
w
ee
n
t
h
e
s
w
itc
h
i
n
g
lo
s
s
es
a
n
d
s
ize
o
f
i
n
d
u
cto
r
.
Selectio
n
o
f
o
th
er
co
m
p
o
n
en
t
s
is
d
o
n
e
as t
h
e
f
o
llo
w
i
n
g
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
I
SS
N:
2
0
8
8
-
8
694
DC
-
DC
B
o
o
s
t Co
n
ve
r
te
r
Desi
g
n
fo
r
F
a
s
t a
n
d
A
cc
u
r
a
te
MP
P
T A
lg
o
r
ith
ms in
S
ta
n
d
…
(
N
o
r
a
z
la
n
Ha
s
h
im
)
1043
3
.
1
.
Select
io
n
o
f
t
he
re
s
is
t
o
r
T
h
e
r
elatio
n
s
h
ip
b
et
w
ee
n
lo
a
d
r
esis
tan
ce
(
R
L
)
o
f
b
o
o
s
t
co
n
v
er
ter
an
d
o
p
ti
m
a
l
i
n
ter
n
al
r
e
s
is
ta
n
ce
o
f
PV
ar
r
ay
at
MP
P
(
R
MPP
)
ca
n
b
e
ex
p
r
ess
ed
as
[
3
]
;
R
L
=
R
M
P
P
(
1
-
D
m
pp
)
2
(
5
)
W
h
er
e,
D
m
p
p
is
th
e
co
n
v
er
ter
d
u
t
y
c
y
cle
a
t
m
a
x
i
m
u
m
p
o
w
er
p
o
in
t
(
MP
P
)
.
I
n
o
r
d
er
to
t
r
ac
k
th
e
m
a
x
i
m
u
m
p
o
w
er
,
th
e
lo
ad
r
esis
ta
n
ce
o
f
b
o
o
s
t
co
n
v
er
ter
m
u
s
t
b
e
g
r
ea
t
er
th
an
o
r
eq
u
al
to
o
p
ti
m
al
i
n
ter
n
al
r
esis
tan
ce
o
f
P
V
A
r
r
a
y
at
MP
P
(
R
L
≥
R
MPP
)
,
s
in
ce
t
h
e
r
an
g
e
o
f
d
u
t
y
r
atio
(
D)
is
b
et
w
ee
n
0
to
1
.
T
h
e
tr
a
ck
in
g
o
f
m
a
x
i
m
u
m
p
o
w
er
w
ill
f
ails
if
th
e
ab
o
v
e
co
n
d
itio
n
is
n
o
t
m
et
[
3
]
.
I
n
th
is
w
o
r
k
,
t
h
e
v
al
u
e
o
f
lo
ad
r
esis
tan
ce
i
s
c
h
o
s
en
a
s
R
L
=2
0
0
Ω
,
w
h
ich
is
g
r
ea
ter
t
h
an
t
h
e
i
n
ter
n
al
r
esis
tan
ce
o
f
P
V
ar
r
a
y
at
MP
P
f
o
r
lo
w
est
ir
r
ad
ian
ce
(
3
0
0
W
/m
2
)
an
d
te
m
p
er
atu
r
e
o
f
2
5
°C
(
ST
C
)
as
in
T
ab
le
2
.
I
t
is
a
r
ea
l
r
esis
ta
n
ce
m
ea
s
u
r
e
m
e
n
t
f
o
r
3
0
0
W
r
ated
lo
a
d
b
an
k
av
ailab
le
at
t
h
e
lab
f
o
r
f
u
t
u
r
e
h
ar
d
w
ar
e
e
x
ec
u
t
io
n
.
T
h
is
lo
ad
b
an
k
ac
ts
a
s
a
d
u
m
p
in
g
p
lace
f
o
r
2
9
9
.
3
W
p
o
w
er
g
en
er
ated
f
r
o
m
P
V
ar
r
ay
u
s
ed
in
th
is
w
o
r
k
.
3
.
2
.
Select
io
n o
f
t
he
i
nd
uct
o
r
B
o
o
s
t
in
d
u
cto
r
v
alu
e
is
s
elec
t
ed
b
ased
o
n
t
h
e
m
ax
i
m
u
m
all
o
w
ab
le
c
u
r
r
en
t
r
ip
p
le
w
h
ic
h
o
cc
u
r
s
at
th
e
MP
P
u
n
d
er
h
ig
h
est
s
o
lar
ir
r
ad
ian
ce
(
1
0
0
0
W
/m
2
)
.
T
h
e
h
i
g
h
er
th
e
i
n
d
u
cto
r
v
a
lu
e,
t
h
e
lo
w
er
is
th
e
r
ip
p
le
o
u
tp
u
t
cu
r
r
en
t
a
n
d
v
ice
v
er
s
a.
T
o
r
ea
lize
a
lo
w
co
s
t
co
n
v
er
ter
,
th
e
lo
w
er
i
n
d
u
cto
r
v
al
u
e
i
s
p
r
ef
er
r
ed
,
b
ec
au
s
e
in
d
u
cto
r
is
t
h
e
m
o
s
t
e
x
p
en
s
iv
e
co
m
p
o
n
en
t
co
m
p
ar
ed
to
th
e
o
th
er
s
.
I
n
th
is
w
o
r
k
,
th
e
s
w
itc
h
i
n
g
f
r
eq
u
e
n
c
y
(
s
)
is
s
et
at
2
0
k
Hz
an
d
th
e
p
er
m
itted
a
m
o
u
n
t
o
f
r
ip
p
le
cu
r
r
en
t
(
I
)
is
s
elec
ted
as
4
0
%
o
f
th
e
in
p
u
t
c
u
r
r
en
t
[
3
1
]
.
Hen
ce
,
th
e
m
i
n
i
m
u
m
v
al
u
e
o
f
in
d
u
cto
r
is
d
eter
m
in
ed
as
[
1
9
,
2
9
]
;
L
min
=
V
m
pp
×
D
m
pp
2
×
∆
I
o
ut
×
=0
.
9
4
8
m
H
(
6
)
Her
e,
a
co
m
m
er
ciall
y
av
ai
lab
le
o
f
1
m
H,
5
m
H
an
d
1
0
m
H
i
n
d
u
cto
r
s
ar
e
ch
o
s
e
n
f
o
r
MP
PT
’
s
tr
an
s
ie
n
t
r
es
p
o
n
s
e
s
tu
d
y
.
Fo
r
e
x
a
m
p
l
e,
1
m
H
b
o
o
s
t
co
n
v
er
ter
c
h
o
k
e
(
1
0
A
,
2
0
k
Hz)
i
s
a
v
a
ilab
le
f
r
o
m
SMP
(
w
ww
.
s
m
p
.
d
e
).
3.
3
.
Select
io
n o
f
t
he
c
a
pa
cit
o
r
I
n
th
is
s
tu
d
y
,
t
h
e
in
p
u
t
a
n
d
o
u
tp
u
t
f
ilter
ca
p
ac
ito
r
(
C
in
&
C
ou
t
)
ar
e
ch
o
s
en
to
m
ee
t
th
e
v
o
lta
g
e
r
ip
p
le
r
eq
u
ir
e
m
en
t o
f
0
.
2
%.
An
ap
p
r
o
x
i
m
ate
e
x
p
r
ess
io
n
f
o
r
th
e
r
eq
u
ir
ed
ca
p
ac
itan
ce
is
g
iv
e
n
as
[
1
9
,
2
9
]
;
C
min
=
V
o
ut
×
D
m
pp
2
×
∆
V
o
ut
×
×
=
4
1
.
7
µF
(
7
)
T
o
s
tu
d
y
t
h
e
e
f
f
ec
t
o
f
t
h
e
ca
p
ac
ito
r
v
alu
e
o
n
t
h
e
tr
a
n
s
ie
n
t
r
esp
o
n
s
e
o
f
MP
P
T
f
o
r
s
tep
ch
an
g
e
i
n
ir
r
ad
ian
ce
,
th
r
ee
(
3
)
p
r
ac
tical
ca
p
ac
ito
r
v
alu
es
a
v
ailab
le
to
s
u
p
p
o
r
t
th
e
v
o
lta
g
e
o
f
2
5
0
V
ar
e
s
elec
ted
i.e
.
,
4
7
μ
F,
1
0
0
μ
F
an
d
2
2
0
μ
F.
Usi
n
g
all
t
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ab
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I
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I
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P
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E
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&
Dr
i
S
y
s
t
,
Vo
l.
9
,
No
.
3
,
Sep
tem
b
er
2
0
1
8
:
1
0
3
8
–
1
0
5
0
1044
(
m
o
d
.
s
tiff
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r
ap
ez
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w
it
h
v
ar
iab
le
ti
m
e
s
tep
an
d
r
elati
v
e
to
ler
an
ce
o
f
1
e
-
6
.
T
h
e
MP
PT
s
am
p
li
n
g
t
i
m
e
(T
S
_MPPT
)
is
s
et
at
0
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2
s
ec
o
n
d
(
2
0
0
m
s
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.
T
o
s
tu
d
y
t
h
e
ef
f
ec
t
s
o
f
b
o
o
s
t
co
n
v
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ter
co
m
p
o
n
e
n
ts
to
w
ar
d
s
MP
PT
tr
an
s
ie
n
t
r
esp
o
n
s
e
d
u
r
i
n
g
s
u
d
d
en
ch
a
n
g
es
i
n
ir
r
ad
ian
ce
,
th
e
s
i
m
u
latio
n
s
ar
e
d
iv
id
ed
in
to
t
w
o
ca
s
e
s
,
1
)
I
n
d
u
cto
r
v
alu
e
is
f
i
x
ed
at
1
m
H
w
h
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d
if
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er
en
t
v
a
lu
e
s
o
f
th
e
ca
p
ac
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ar
e
in
cr
ea
s
ed
ac
c
o
r
d
in
g
l
y
a
s
(
4
7
F
100
F
220
)
,
an
d
2
)
C
ap
ac
ito
r
v
alu
e
is
f
ix
ed
at
4
7
F
w
h
ile
d
if
f
er
en
t
v
a
lu
e
s
o
f
th
e
in
d
u
cto
r
ar
e
in
cr
ea
s
e
d
i.e
(
1
m
H
5
m
H
1
0
m
H)
.
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r
b
o
th
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s
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s
u
d
d
en
d
ec
r
ea
s
e
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n
t
h
e
ir
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ian
ce
is
s
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m
u
lat
ed
f
r
o
m
1
0
0
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2
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0
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2
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a
n
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i
s
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m
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f
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3
0
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1
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2
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Fig
u
r
e
6
.
S
i
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latio
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V
s
y
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w
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th
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T
4
.
1
.
Ca
s
e
1
(
L
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m
H
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7
F
1
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2
2
0
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Fig
u
r
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7
(
a)
s
h
o
w
s
t
h
e
tr
ac
k
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g
o
f
d
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t
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c
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cle,
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lta
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e,
cu
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n
t,
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d
p
o
w
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t
h
e
P
V
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r
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s
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n
tio
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al
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al
g
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ith
m
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o
r
a
s
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d
en
d
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r
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e
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r
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V
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2
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atio
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p
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ch
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at
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t
A
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6
4
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5
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7
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4
9
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2
9
9
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3
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ter
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A
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5
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at
1
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in
F
ig
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r
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7
(
a)
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t,
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ce
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l
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d
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r
ea
s
ed
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m
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0
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0
0
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2
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m
0
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6
4
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PP
A
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to
0
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5
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4
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d
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0
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3
4
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.
A
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t
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in
cr
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e
f
r
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m
3
0
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to
4
6
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8
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to
6
6
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3
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d
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8
2
.
3
W
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On
ce
it
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ter
s
t
h
e
zo
n
e
o
f
MP
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B
,
th
e
ex
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lo
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n
p
r
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ce
s
s
is
u
s
ed
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r
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ch
tr
u
e
MP
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h
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ch
is
8
2
.
5
W
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n
th
is
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s
e,
th
e
MP
PT
tr
ac
k
in
g
s
p
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d
is
8
0
0
m
s
(
T
S
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×
4
s
tep
s
)
.
T
h
e
tr
ac
k
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s
p
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d
ca
n
b
e
i
m
p
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b
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ci
n
g
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th
e
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t
r
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e
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d
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t.
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u
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r
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t
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f
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h
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ar
e
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as
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u
la
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3
.
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h
en
t
h
e
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p
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v
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s
e,
T
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m
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s
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n
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r
l
y
f
r
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m
1
0
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m
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to
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n
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0
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0
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f
4
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s
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th
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ll
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r
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ito
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t
h
e
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S
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u
s
t
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ed
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n
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er
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ate
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d
h
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r
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s
es
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e
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k
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g
s
p
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d
.
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w
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s
e,
t
h
e
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o
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ith
m
w
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l
m
ea
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e
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t
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n
g
to
i
n
co
r
r
ec
t
MP
P
d
etec
tio
n
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A
s
f
o
r
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n
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er
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p
r
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p
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ito
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h
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it
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e
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a
m
e
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n
d
itio
n
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m
o
s
t
0
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lta
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n
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er
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a
n
d
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o
f
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r
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e
n
t
u
n
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er
s
h
o
o
t.
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x
t,
t
h
e
MP
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T
tr
an
s
ien
t
r
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n
s
e
u
n
d
er
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d
d
en
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n
cr
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e
in
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ce
is
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n
v
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s
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ated
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g
u
r
e
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-
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.
T
h
e
P
V
ar
r
ay
is
s
i
m
u
la
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at
i
r
r
ad
ian
ce
,
G=
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0
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/m
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at
t
h
e
b
eg
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n
i
n
g
o
f
t
h
e
s
i
m
u
latio
n
.
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t
s
tead
y
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tate
co
n
d
itio
n
,
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is
o
s
cillates
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o
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d
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P
at
p
o
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3
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,
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6
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9
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t
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in
s
ta
n
t,
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h
e
ir
r
ad
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ce
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s
u
d
d
en
l
y
i
n
cr
ea
s
ed
to
1
0
0
0
W
/m
2
.
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o
r
it
h
m
s
tar
t
s
ea
r
c
h
in
g
th
e
n
e
w
MP
P
A
b
y
i
n
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g
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h
e
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u
t
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cle
f
r
o
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0
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3
4
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4
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e
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o
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8
0
0
m
s
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4
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tep
s
in
cl
u
d
in
g
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i
tiali
s
e
s
tep
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.
Fig
u
r
e
8
(
b
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s
h
o
w
s
th
e
zo
o
m
ed
v
o
ltag
e
a
n
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r
r
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ith
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u
r
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d
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r
r
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t
o
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er
s
h
o
o
t
to
1
9
5
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r
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it
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s
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e
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o
r
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p
ac
ito
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o
t
o
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s
er
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ed
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v
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e
a
s
s
ee
n
i
n
Fig
u
r
e
8
(
b
)
.
T
settling
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o
r
4
7
F,
1
0
0
F a
n
d
2
2
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F c
ap
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ito
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s
ar
e
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s
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s
a
n
d
2
4
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s
r
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ec
ti
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el
y
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S
_
M
P
P
T
=
200
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e
p
=
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.
005
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S
_
M
P
P
T
=
200
ms
Z
oom
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n
Z
oom
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n
S
t
e
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dy S
t
a
t
e
D
=
0
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64
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0
.
54
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0
.
44
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=
0
.
34
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=
30
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P
=
46
.
8
W
P
=
66
.
3
W
P
=
82
.
3
W
P
=
2
9
9
.
3
W
I
=
3
.
49
A
V
=
85
.
7
A
D
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.
64
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xpl
or
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t
i
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e
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=
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.
06
A
I
=
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09
A
I
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1
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11
A
V
=
62
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4
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V
=
82
.
3
V
V
=
43
.
1
V
V
=
27
.
2
V
(
a
)
(
b
)
(
c
)
(
d
)
M
P
P
B
4
s
t
e
p
s
Fig
u
r
e
7
.
(
a)
T
h
e
tr
ac
k
in
g
o
f
D,
V
PV
, I
PV
,
an
d
P
PV
d
u
r
in
g
a
s
u
d
d
en
d
ec
r
ea
s
e
in
ir
r
ad
ian
ce
Z
oom
I
n
(
F
i
g
.
7
b
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(
a
)
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b
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nde
r
S
hoo
t
(
US
)
S
e
t
t
l
i
ng T
i
m
e
(
T
s
e
t
t
l
i
ng
)
Fig
u
r
e
7
.
(
b
)
T
h
e
zo
o
m
ed
i
m
a
g
e
o
f
V
PV
&
I
PV
in
t
h
e
i
n
ter
v
al
o
f
2
s
–
2
.
2
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
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n
t J
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o
w
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3
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tem
b
er
2
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1
8
:
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3
8
–
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0
5
0
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oom
I
n
Z
oom
I
n
S
t
e
a
dy
S
t
a
t
e
D
=
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.
34
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=
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44
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54
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.
64
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ode
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s
t
e
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n
i
t
i
a
l
i
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e
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te
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T
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_
M
P
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T
=
200
ms
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=
83
.
6
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I
=
0
.
99
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P
=
82
.
4
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D
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0
.
64
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s
t
e
p
=
0
.
005
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=
96
.
3
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V
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86
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4
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99
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6
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V
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1
0
1
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4
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I
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3
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46
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I
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21
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P
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1
2
2
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1
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1
6
5
.
5
W
P
=
2
2
9
.
6
W
P
=
2
9
9
.
1
W
Fig
u
r
e
8
.
(
a)
T
h
e
tr
ac
k
in
g
o
f
D,
V
PV
, I
PV
,
an
d
P
PV
d
u
r
in
g
a
s
u
d
d
en
i
n
cr
ea
s
e
i
n
ir
r
ad
ian
ce
Z
oom
I
n
(
F
i
g
.
8
b
)
Z
oom
I
n
(
F
i
g
.
8
b
)
(
a
)
(
b
)
O
ve
r
S
hoo
t
(
OS
)
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e
t
t
l
i
ng T
i
m
e
(
T
s
e
t
t
l
i
ng
)
Fig
u
r
e
8
.
(
b
)
T
h
e
zo
o
m
ed
i
m
a
g
e
o
f
V
PV
&
I
PV
in
t
h
e
i
n
ter
v
al
o
f
2
s
–
2
.
2
s
4
.
2
.
Ca
s
e
2
(
C=4
7
F
,
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H
1
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H
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n
t
h
is
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s
e,
th
e
ca
p
ac
ito
r
is
f
ix
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to
it
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o
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ti
m
u
m
v
a
lu
e
o
f
4
7
F.
A
t
2
s
i
n
s
tan
t,
s
o
lar
ir
r
ad
ian
ce
i
s
s
u
d
d
en
l
y
d
ec
r
ea
s
ed
/i
n
cr
ea
s
ed
.
T
h
e
tr
an
s
ien
t
r
esp
o
n
s
e
o
f
MP
PT
is
o
b
s
er
v
ed
b
y
i
n
cr
ea
s
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g
t
h
e
i
n
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u
cta
n
ce
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e
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r
o
m
1
m
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to
5
m
H
a
n
d
t
o
1
0
m
H.
F
ig
u
r
e
9
(
a
-
b
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s
h
o
w
s
th
e
MP
P
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ac
k
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n
g
r
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u
lt
s
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o
r
s
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d
d
en
d
ec
r
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s
es i
n
ir
r
ad
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ce
f
r
o
m
1
0
0
0
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/m
2
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3
0
0
W
/m
2
.
A
s
t
h
e
in
d
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i
n
cr
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s
e,
th
e
s
e
ttli
n
g
ti
m
e
o
f
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h
e
w
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e
f
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r
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s
w
il
l
also
in
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ea
s
e.
T
settling
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o
r
1
m
H
in
d
u
cto
r
is
1
0
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s
,
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h
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T
settling
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o
r
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o
th
5
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d
1
0
m
H
i
n
d
u
cto
r
s
ex
ce
ed
s
t
h
e
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I
n
t J
P
o
w
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lec
&
Dr
i
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s
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SS
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d
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r
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te
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P
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o
r
ith
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S
ta
n
d
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r
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la
n
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s
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im
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1047
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r
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S
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e
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s
.
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r
f
ast
MP
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atio
n
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a
w
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e
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ec
is
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n
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H
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n
d
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r
f
o
r
th
e
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er
ter
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it.
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e
u
n
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er
s
h
o
o
t
f
o
r
1
m
H
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u
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r
is
0
%,
f
o
r
5
m
H
in
d
u
cto
r
is
8
%
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d
f
o
r
1
0
m
H
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d
u
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r
is
1
8
%.
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u
r
r
en
t
u
n
d
e
r
s
h
o
o
t is 1
5
% f
o
r
all
in
d
u
cto
r
s
.
Me
an
w
h
ile,
Fi
g
u
r
e
1
0
(
a
-
b
)
s
h
o
w
s
t
h
e
MP
P
tr
ac
k
in
g
r
es
u
lt
s
f
o
r
s
u
d
d
en
i
n
cr
ea
s
es i
n
ir
r
ad
ian
ce
f
r
o
m
3
0
0
W
/m
2
to
1
0
0
0
W
/m
2
. T
settling
f
o
r
1
m
H
in
d
u
cto
r
is
5
m
s
,
T
settling
f
o
r
5
m
H
i
n
d
u
cto
r
is
2
0
m
s
an
d
T
settling
f
o
r
1
0
m
H
i
n
d
u
cto
r
is
3
7
m
s
.
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lta
g
e
o
v
er
s
h
o
o
t is b
et
w
ee
n
0
to
2
%.
B
ig
g
es
t c
u
r
r
en
t o
v
er
s
h
o
o
t
o
cc
u
r
s
u
n
d
er
s
u
d
d
en
i
n
cr
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s
e
i
n
ir
r
ad
ian
ce
,
r
ea
ch
in
g
a
p
ea
k
o
f
1
9
5
% f
r
o
m
its
s
tead
y
s
tate
v
a
lu
e.
T
h
e
o
v
e
r
all
r
esu
lts
f
o
r
b
o
th
C
ase
1
an
d
C
a
s
e
2
ar
e
tab
u
lated
in
T
ab
le
3
.
Z
oom
I
n
Z
oom
I
n
S
t
e
a
dy S
t
a
t
e
P
=
2
9
9
.
3
W
I
=
3
.
49
A
V
=
85
.
7
A
D
s
t
e
p
=
0
.
005
D
=
0
.
64
T
S
_
M
P
P
T
=
0
.
2
s
D
=
0
.
64
D
=
0
.
54
D
=
0
.
44
D
=
0
.
34
Fig
u
r
e
9
.
(
a)
T
h
e
tr
ac
k
in
g
o
f
D,
V
PV
, I
PV
,
an
d
P
PV
d
u
r
in
g
a
s
u
d
d
en
d
ec
r
ea
s
e
in
ir
r
ad
ian
ce
Z
oom
I
n
(
F
i
g
.
9
b
)
(
a
)
(
b
)
U
nde
r
S
hoo
t
(
US
)
S
e
t
t
l
i
ng T
i
m
e
(
T
s
e
t
t
l
i
ng
)
Evaluation Warning : The document was created with Spire.PDF for Python.