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i
o
n
.
A
p
r
i
m
ar
y
o
b
s
t
a
c
l
e
i
n
t
es
t
i
n
g
MP
P
T
alg
o
r
i
t
h
m
s
l
ie
s
i
n
t
h
e
r
e
q
u
i
r
e
m
e
n
t
f
o
r
a
r
e
al
PV
p
a
n
e
l
,
a
s
t
h
e
f
l
u
ct
u
a
t
i
n
g
n
at
u
r
e
o
f
s
o
l
a
r
e
n
e
r
g
y
m
a
k
e
s
i
t
d
i
f
f
i
c
u
l
t
t
o
e
s
t
a
b
l
is
h
c
o
n
s
i
s
t
e
n
t
a
n
d
c
o
n
t
r
o
l
l
e
d
c
o
n
d
it
i
o
n
s
f
o
r
e
f
f
e
c
t
i
v
e
f
e
as
i
b
il
i
t
y
ass
e
s
s
m
e
n
t
.
T
o
f
a
c
il
i
ta
t
e
t
h
e
r
es
ea
r
c
h
a
n
d
t
e
s
t
i
n
g
o
f
M
P
P
T
a
l
g
o
r
it
h
m
s
,
t
h
e
d
e
v
e
l
o
p
m
e
n
t
o
f
a
P
V
e
m
u
l
a
t
o
r
i
s
c
r
u
c
i
a
l
.
A
k
e
y
f
e
a
t
u
r
e
o
f
s
u
c
h
e
m
u
l
a
t
o
r
s
i
s
t
h
ei
r
c
a
p
a
b
i
l
i
t
y
t
o
s
i
m
u
la
t
e
t
h
e
e
l
e
ct
r
i
c
a
l
c
h
a
r
a
ct
e
r
is
t
i
cs
o
f
PV
p
a
n
e
ls
u
n
d
e
r
a
n
y
u
s
e
r
-
d
e
f
i
n
e
d
e
n
v
i
r
o
n
m
e
n
t
a
l
s
c
e
n
a
r
i
o
.
T
h
e
f
u
n
d
am
e
n
tal
co
m
p
o
n
e
n
ts
o
f
a
PV
em
u
lato
r
in
cl
u
d
e
a
DC
-
DC
co
n
v
er
ter
an
d
an
in
te
g
r
ated
PV
m
o
d
el
o
p
er
atin
g
with
in
a
clo
s
ed
-
lo
o
p
co
n
tr
o
l
s
y
s
tem
.
T
h
e
PV
m
o
d
el
ca
n
b
e
d
ev
elo
p
e
d
th
r
o
u
g
h
m
eth
o
d
o
l
o
g
ies
s
u
ch
as
n
u
m
er
ical
m
o
d
el,
lo
o
k
-
u
p
tab
les
(
L
UT
s
)
,
p
iece
wis
e
lin
ea
r
f
u
n
ctio
n
s
,
o
r
n
e
u
r
al
n
etwo
r
k
ap
p
r
o
ac
h
es.
N
u
m
er
ic
al
m
o
d
elin
g
tech
n
iq
u
es
a
r
e
wi
d
ely
ad
o
p
ted
in
th
e
d
ev
elo
p
m
en
t
o
f
PV
m
o
d
els,
p
r
im
ar
ily
attr
ib
u
ted
to
th
eir
r
o
b
u
s
tn
ess
,
tr
ac
ea
b
ilit
y
,
ac
cu
r
ac
y
,
an
d
f
lex
ib
ilit
y
.
T
h
e
s
in
g
le
d
io
d
e
eq
u
iv
alen
t
cir
cu
it
m
o
d
el
r
ep
r
esen
ts
a
p
ar
ticu
lar
ly
co
m
m
o
n
n
u
m
er
ical
ap
p
r
o
ac
h
,
lar
g
ely
d
u
e
to
its
in
h
er
en
t
s
im
p
licity
[8
]
-
[
1
7
]
.
Ho
we
v
er
,
a
s
ig
n
if
ica
n
t
d
r
awb
ac
k
o
f
em
p
lo
y
in
g
c
o
m
p
lex
n
u
m
e
r
ical
m
o
d
els
is
th
eir
p
o
ten
tially
h
ig
h
co
m
p
u
tatio
n
al
b
u
r
d
en
.
W
h
ile
th
e
L
UT
m
eth
o
d
is
also
f
r
eq
u
e
n
tly
em
p
lo
y
e
d
,
it
p
r
esen
ts
s
ig
n
if
ican
t
d
r
awb
ac
k
s
,
in
clu
d
in
g
a
s
u
b
s
tan
tial
m
em
o
r
y
r
e
q
u
ir
em
en
t
f
o
r
th
e
m
icr
o
co
n
tr
o
ller
a
n
d
a
lack
o
f
in
h
er
en
t
f
lex
ib
ilit
y
[
1
8
]
,
[
1
9
]
.
I
ts
ac
cu
r
ac
y
r
eq
u
ir
es
lar
g
e
d
ata
s
to
r
ag
e
an
d
lack
s
ad
a
p
tab
ilit
y
,
n
ee
d
in
g
n
ew
d
atasets
f
o
r
ea
ch
p
an
el
an
d
ch
an
g
in
g
co
n
d
itio
n
s
.
B
y
em
p
lo
y
in
g
a
c
u
r
v
e
-
f
itti
n
g
p
r
o
ce
d
u
r
e,
th
e
p
iece
wis
e
lin
ea
r
m
et
h
o
d
r
e
p
r
esen
ts
th
e
o
u
tp
u
t
c
h
ar
ac
ter
is
tic
cu
r
v
e
o
f
a
PV
p
an
el
t
h
r
o
u
g
h
a
s
er
ies
o
f
d
is
cr
ete
lin
ea
r
s
eg
m
en
ts
[
2
0
]
,
[
2
1
]
.
W
h
ile
th
e
ac
cu
r
ac
y
o
f
t
h
e
p
iece
wis
e
li
n
ea
r
m
eth
o
d
im
p
r
o
v
es
with
an
in
cr
ea
s
ed
n
u
m
b
er
o
f
s
eg
m
en
ts
,
its
p
r
ac
tical
f
lex
ib
ilit
y
is
lim
ited
b
y
th
e
n
ee
d
f
o
r
th
e
en
tire
PV
o
u
tp
u
t
ch
ar
ac
ter
is
tic,
r
ath
er
th
an
r
ea
d
ily
ac
ce
s
s
ib
le
d
atash
ee
t
v
alu
es.
T
h
e
n
eu
r
a
l
n
etwo
r
k
m
eth
o
d
o
lo
g
y
is
n
o
t
as
f
r
e
q
u
en
tly
em
p
lo
y
ed
in
PV
em
u
lato
r
d
ev
elo
p
m
e
n
t
d
u
e
to
its
d
ep
e
n
d
en
ce
o
n
tr
ain
in
g
d
ata
o
b
tain
e
d
f
r
o
m
ex
is
tin
g
d
atasets
[
2
2
]
.
W
h
ile
th
e
h
ar
d
war
e
im
p
lem
en
tatio
n
o
f
a
PV
m
o
d
e
l
em
p
lo
y
in
g
a
p
h
y
s
ical
d
io
d
e
o
f
f
er
s
a
d
ir
ec
t
r
e
p
r
esen
tatio
n
[
2
3
]
,
it
s
u
f
f
e
r
s
f
r
o
m
s
ig
n
if
ican
t
ef
f
icien
c
y
lo
s
s
es
attr
ib
u
ted
to
d
io
d
e
th
er
m
a
l
is
s
u
es,
r
eq
u
ir
in
g
ac
tiv
e
c
o
o
lin
g
to
m
itig
ate
p
er
f
o
r
m
an
ce
d
e
g
r
ad
atio
n
.
A
p
o
wer
c
o
n
v
e
r
ter
with
a
PV
m
o
d
el
e
m
b
ed
d
ed
in
its
clo
s
ed
-
lo
o
p
co
n
t
r
o
l
ar
c
h
itectu
r
e
s
e
r
v
es
as
th
e
p
o
wer
s
o
u
r
ce
f
o
r
a
PV
em
u
lat
o
r
in
ten
d
e
d
f
o
r
r
ea
l
-
w
o
r
ld
ap
p
licatio
n
s
.
T
h
e
DC
-
DC
b
u
ck
co
n
v
er
ter
to
p
o
lo
g
y
is
th
e
m
o
s
t
em
p
lo
y
ed
p
o
wer
c
o
n
v
er
ter
ar
ch
itectu
r
e
in
th
e
d
ev
elo
p
m
e
n
t
o
f
PV
em
u
lato
r
s
[
1
1
]
,
[
1
3
]
-
[
1
5
]
,
[
2
4
]
-
[
2
7
]
.
T
h
e
DC
-
DC
b
u
ck
c
o
n
v
er
ter
is
wid
ely
u
s
ed
in
PV
em
u
lato
r
d
ev
el
o
p
m
e
n
t
f
o
r
its
cir
cu
it
an
d
c
o
n
tr
o
l
s
im
p
licity
,
r
eq
u
ir
in
g
f
ewe
r
c
o
m
p
o
n
en
ts
.
Ad
d
itio
n
ally
,
it
c
an
ef
f
ec
tiv
ely
em
u
late
a
b
r
o
ad
s
p
ec
tr
u
m
o
f
PV
o
u
tp
u
t
c
h
ar
ac
ter
is
tics
,
p
r
o
v
i
d
ed
th
e
in
p
u
t
v
o
ltag
e
ex
ce
e
d
s
th
e
PV
p
an
el'
s
o
p
en
-
cir
cu
it
v
o
ltag
e.
W
h
ile
[
1
2
]
u
tili
ze
s
a
SEPI
C
co
n
v
er
ter
with
b
ac
k
s
tep
p
in
g
co
n
tr
o
l,
its
s
y
s
tem
d
esig
n
co
m
p
lex
ity
e
x
ce
e
d
s
th
at
o
f
th
e
b
u
ck
co
n
v
er
ter
d
u
e
to
th
e
in
c
o
r
p
o
r
atio
n
o
f
ad
d
itio
n
al
L
C
elem
en
ts
.
Desp
ite
it
s
b
en
ef
its
in
ter
m
s
o
f
f
o
o
tp
r
in
t,
is
o
latio
n
,
an
d
p
o
we
r
ex
te
n
s
ib
ilit
y
[
2
8
]
,
th
e
Sin
g
le
-
Mo
d
e
Po
wer
Su
p
p
ly
(
SMPS)
co
n
v
er
ter
im
p
lem
en
tatio
n
is
m
o
r
e
c
o
m
p
lex
an
d
in
v
o
lv
es
h
ig
h
e
r
co
s
ts
.
Desp
ite
th
e
in
teg
r
atio
n
o
f
AC
/DC
s
u
p
p
lies
an
d
in
v
er
ter
s
in
co
m
p
lete
s
y
s
tem
s
,
MPPT
alg
o
r
ith
m
test
in
g
o
f
ten
r
eq
u
ir
es
o
n
ly
a
DC
-
DC
co
n
v
er
ter
,
as
th
ese
alg
o
r
ith
m
s
ar
e
f
r
eq
u
e
n
tly
d
ev
el
o
p
ed
u
s
in
g
a
DC
-
DC
b
o
o
s
t c
o
n
v
er
ter
[
2
9
]
-
[
3
1
]
.
T
h
e
r
esu
lt
[
8
]
,
em
u
latio
n
o
f
p
o
ly
cr
y
s
tallin
e
PV
p
an
els
an
d
am
o
r
p
h
o
u
s
PV
p
an
el
ar
e
ca
r
r
ied
o
u
t.
T
h
r
ee
m
o
d
ellin
g
tech
n
iq
u
es
ar
e
ex
p
lo
r
ed
f
o
r
th
r
ee
t
y
p
es
o
f
s
o
lar
ce
ll
tech
n
o
lo
g
ies
,
n
am
ely
Am
o
r
p
h
o
u
s
,
C
d
T
e
an
d
M
o
n
o
-
Si
[
2
8
]
.
Ho
wev
er
,
t
h
ese
tech
n
o
l
o
g
ies
u
tili
ze
f
u
ll
-
ce
ll
tech
n
o
lo
g
y
in
th
e
s
tu
d
y
.
W
h
ile
p
r
io
r
f
u
ll
-
ce
ll
PV
em
u
lato
r
s
ac
h
iev
e
m
u
lti
-
p
ea
k
PV
cu
r
v
es,
th
e
h
alf
-
c
u
t
ce
ll
PV
p
an
el
f
ea
tu
r
es
a
d
is
tin
ct
to
p
o
lo
g
y
,
w
h
ich
is
twice
th
e
n
u
m
b
er
o
f
s
u
b
-
s
tr
in
g
s
co
m
p
ar
ed
to
a
co
n
v
en
tio
n
a
l
p
an
el
o
f
th
e
s
am
e
s
ize.
T
h
is
f
u
n
d
am
e
n
tal
ch
an
g
e
d
ictates
th
at
th
e
eq
u
iv
alen
t
s
i
n
g
le
d
io
d
e
m
o
d
el
eq
u
atio
n
s
a
n
d
th
e
r
esu
ltin
g
m
u
lti
-
p
ea
k
c
h
ar
ac
ter
is
tics
u
n
d
er
PS
C
s
ar
e
in
h
er
e
n
tly
d
if
f
er
e
n
t
an
d
ca
n
n
o
t
b
e
ac
cu
r
ately
r
e
p
licated
b
y
s
im
p
le
r
escalin
g
o
f
a
f
u
ll
-
ce
ll
m
o
d
el.
T
h
e
p
r
o
p
o
s
ed
m
o
d
el
is
n
o
v
el
b
ec
au
s
e
it
is
d
er
iv
ed
f
r
o
m
f
ir
s
t
p
r
in
cip
les
o
f
th
is
s
p
ec
if
ic
elec
tr
ical
ar
ch
itectu
r
e,
en
s
u
r
in
g
h
ig
h
f
id
elity
f
o
r
th
is
m
o
d
er
n
tech
n
o
lo
g
y
.
T
h
e
c
u
r
r
en
t
liter
atu
r
e
,
as
h
ig
h
lig
h
ted
b
y
th
e
s
u
m
m
ar
y
o
f
em
u
lato
r
s
tu
d
ies
in
T
ab
le
1
,
r
ev
ea
ls
a
cr
itical
tech
n
ical
g
ap
,
wh
ich
is
th
e
ab
s
en
ce
o
f
a
co
m
p
r
eh
e
n
s
iv
e
PV
em
u
lato
r
m
o
d
el
v
alid
ate
d
f
o
r
th
e
u
n
iq
u
e,
m
u
lti
-
p
ea
k
o
u
tp
u
t
ch
ar
ac
ter
is
tics
o
f
th
e
in
cr
ea
s
in
g
ly
p
r
e
v
alen
t
h
alf
-
cu
t
ce
ll
tech
n
o
lo
g
y
u
n
d
e
r
co
m
p
lex
p
a
r
tial
s
h
ad
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g
.
T
o
th
e
b
est
o
f
th
e
au
th
o
r
s
'
k
n
o
wled
g
e,
n
o
p
r
io
r
em
u
lato
r
h
as v
alid
ated
a
n
u
m
er
ical
m
o
d
el
s
p
ec
if
ically
f
o
r
h
al
f
-
cu
t c
ell
p
an
els u
n
d
e
r
PS
C
s
.
T
h
is
p
ap
er
p
r
esen
ts
a
h
alf
-
c
u
t
ce
ll
-
b
ased
PV
em
u
lato
r
d
esig
n
ed
to
em
u
late
th
e
m
u
lti
-
p
ea
k
ed
o
u
tp
u
t
ch
ar
ac
ter
is
tics
o
f
h
alf
-
cu
t
ce
ll
PV
p
an
els
u
n
d
er
PS
C
s
.
Utilizi
n
g
a
s
im
p
lifie
d
y
et
ac
c
u
r
ate
s
in
g
le
-
d
io
d
e
m
o
d
el,
a
DC
-
DC
b
u
ck
c
o
n
v
er
te
r
with
an
in
te
g
r
ated
n
u
m
e
r
ical
PV
m
o
d
el
in
its
clo
s
ed
-
l
o
o
p
co
n
tr
o
l
with
a
co
n
v
en
tio
n
al
PI
co
n
tr
o
ller
en
s
u
r
es
r
o
b
u
s
t
an
d
r
ap
id
r
esp
o
n
s
e.
T
h
e
m
ajo
r
c
o
n
tr
ib
u
tio
n
s
o
f
th
is
p
ap
er
a
r
e
p
r
esen
ted
b
elo
w:
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
Dev
elo
p
men
t o
f n
u
merica
l m
o
d
el
-
b
a
s
ed
p
h
o
to
v
o
lta
ic
emu
la
t
o
r
fo
r
h
a
lf
-
cu
t c
ell
P
V
…
(
J
o
r
d
a
n
S
.
Z.
Lee
)
345
-
Dev
elo
p
m
en
t o
f
a
h
ig
h
ly
ac
cu
r
ate
n
u
m
er
ical
m
o
d
el
s
p
ec
if
ic
ally
d
esig
n
ed
to
em
u
late
th
e
c
o
m
p
lex
an
d
m
u
lti
-
p
ea
k
P
-
V
ch
ar
ac
ter
is
tics
o
f
h
al
f
-
cu
t c
ell
PV p
an
els u
n
d
er
PS
C
s
.
-
Simu
latio
n
o
f
d
if
f
e
r
en
t
s
h
ad
i
n
g
p
atter
n
s
t
o
s
h
if
t
t
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e
m
ax
i
m
u
m
p
o
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k
to
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ar
io
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s
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n
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o
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t
h
e
P
-
V
cu
r
v
e.
-
Desig
n
an
d
h
ar
d
war
e
v
alid
at
io
n
o
f
th
e
m
o
d
el
th
r
o
u
g
h
a
co
s
t
-
ef
f
ec
tiv
e
an
d
h
ig
h
-
f
id
e
lity
PV
em
u
lato
r
p
r
o
to
ty
p
e
u
s
in
g
t
h
e
r
ap
id
co
n
t
r
o
l p
r
o
t
o
ty
p
in
g
T
I
L
AUNCHXL
-
F2
8
3
7
9
D
m
icr
o
co
n
tr
o
ller
an
d
PI
co
n
tr
o
ller
.
B
y
p
r
o
v
id
in
g
a
h
ig
h
-
f
id
elity
p
latf
o
r
m
f
o
r
r
e
p
r
o
d
u
cin
g
d
y
n
am
ic
s
h
ad
in
g
ef
f
ec
ts
,
th
is
wo
r
k
s
ig
n
if
ican
tl
y
f
ac
ilit
ates th
e
r
ig
o
r
o
u
s
test
in
g
o
f
MPPT
alg
o
r
ith
m
s
an
d
g
r
id
in
teg
r
atio
n
s
tr
ateg
ies f
o
r
PV sy
s
tem
s
u
tili
zin
g
th
e
in
cr
ea
s
in
g
ly
p
r
e
v
alen
t h
alf
-
cu
t
ce
ll tec
h
n
o
lo
g
y
.
T
ab
le
1
.
Su
m
m
a
r
y
o
f
r
ec
e
n
t stu
d
ies f
o
r
PV
em
u
lato
r
s
with
p
ar
tial sh
ad
in
g
em
u
latio
n
ab
ilit
y
R
e
f
e
r
e
n
c
e
Ty
p
e
o
f
P
V
m
o
d
e
l
i
mp
l
e
m
e
n
t
a
t
i
o
n
met
h
o
d
P
S
C
s e
m
u
l
a
t
i
o
n
i
m
p
l
e
me
n
t
a
t
i
o
n
met
h
o
d
H
a
r
d
w
a
r
e
p
r
o
t
o
t
y
p
e
S
o
l
a
r
c
e
l
l
c
u
t
t
i
n
g
t
e
c
h
n
o
l
o
g
y
[
1
1
]
(
2
0
2
0
)
N
u
meri
c
a
l
m
o
d
e
l
-
B
u
c
k
c
o
n
v
e
r
t
e
r
F
u
l
l
c
e
l
l
[
1
2
]
(
2
0
2
0
)
N
u
meri
c
a
l
m
o
d
e
l
-
S
EPI
C
F
u
l
l
c
e
l
l
[
1
9
]
(
2
0
2
0
)
Lo
o
k
-
u
p
t
a
b
l
e
Lo
o
k
-
u
p
t
a
b
l
e
B
u
c
k
c
o
n
v
e
r
t
e
r
F
u
l
l
c
e
l
l
[
2
8
]
(
2
0
2
2
)
N
u
meri
c
a
l
m
o
d
e
l
/
Lo
o
k
-
u
p
t
a
b
l
e
-
S
M
P
S
F
u
l
l
c
e
l
l
[
2
5
]
(
2
0
2
2
)
N
u
meri
c
a
l
m
o
d
e
l
P
a
r
t
i
a
l
s
h
a
d
i
n
g
a
d
j
u
s
t
e
r
B
u
c
k
c
o
n
v
e
r
t
e
r
F
u
l
l
c
e
l
l
C
u
r
r
e
n
t
w
o
r
k
N
u
meri
c
a
l
m
o
d
e
l
P
r
o
p
o
se
d
h
a
l
f
-
c
u
t
c
e
l
l
n
u
meri
c
a
l
mo
d
e
l
B
u
c
k
c
o
n
v
e
r
t
e
r
H
a
l
f
-
c
u
t
c
e
l
l
2.
M
E
T
H
O
D
2
.
1
.
P
V
ce
ll r
e
f
er
ence
curr
ent
equa
t
io
n
T
h
e
eq
u
iv
ale
n
t
elec
tr
ical
m
o
d
el
o
f
a
PV
ce
ll
,
as
illu
s
tr
ated
in
Fig
u
r
e
1
,
co
n
s
is
ts
o
f
a
p
ar
allel
co
m
b
in
atio
n
o
f
a
cu
r
r
e
n
t
s
o
u
r
ce
an
d
a
p
-
n
ju
n
ctio
n
d
io
d
e,
co
n
n
ec
ted
in
s
er
ies
with
a
r
es
is
tan
ce
.
T
o
r
ed
u
ce
co
m
p
u
tatio
n
al
co
m
p
lex
ity
w
h
ile
m
ain
tain
in
g
ac
ce
p
tab
le
ac
cu
r
ac
y
,
th
e
s
h
u
n
t
r
esis
tan
ce
co
m
p
o
n
en
t
is
n
eg
lecte
d
in
th
is
m
o
d
el
[
3
2
]
.
T
h
e
p
h
o
to
cu
r
r
en
t
i
n
d
u
ce
d
b
y
s
o
lar
ir
r
ad
ian
ce
is
r
e
p
r
esen
ted
b
y
th
e
cu
r
r
en
t
s
o
u
r
ce
,
an
d
th
e
s
em
ico
n
d
u
cto
r
ju
n
ctio
n
p
r
o
p
er
ties
o
f
th
e
PV
ce
ll
ar
e
m
o
d
eled
b
y
th
e
p
-
n
d
io
d
e.
Po
wer
lo
s
s
es
with
in
th
e
PV c
el
l a
r
e
r
ep
r
ese
n
ted
b
y
th
e
s
er
ies r
esis
tan
ce
(
R
se
)
in
th
e
eq
u
iv
alen
t c
ir
cu
it.
Ap
p
ly
in
g
Kir
ch
h
o
f
f
'
s
cu
r
r
en
t
law
to
th
e
PV
ce
ll
eq
u
iv
alen
t
cir
cu
it
m
o
d
el
y
ield
s
th
e
PV
ce
ll
r
ef
er
en
ce
cu
r
r
e
n
t
(
I
PV
)
eq
u
atio
n
,
as
p
r
esen
ted
in
(
1
)
.
=
ℎ
−
(
(
+
(
×
)
)
−
1
)
(
1
)
W
h
er
e
I
ph
is
th
e
p
h
o
to
cu
r
r
en
t
;
I
d
is
th
e
d
io
d
e
r
ev
er
s
e
s
atu
r
atio
n
cu
r
r
en
t;
V
o
is
th
e
o
u
t
p
u
t
v
o
ltag
e;
I
o
is
t
h
e
o
u
tp
u
t c
u
r
r
en
t a
n
d
vt
is
th
e
th
e
r
m
al
v
o
ltag
e.
T
h
e
p
h
o
to
c
u
r
r
en
t is r
ep
r
esen
ted
b
y
(
2
)
:
ℎ
=
(
+
(
@
−
)
)
×
(
)
(
2
)
wh
er
e
G
is
ir
r
ad
ian
ce
in
W
/
m
2
;
G
STC
is
th
e
ir
r
ad
ian
ce
at
s
tan
d
ar
d
test
in
g
co
n
d
itio
n
s
;
α
i
is
th
e
tem
p
er
atu
r
e
co
ef
f
icien
t o
f
s
h
o
r
t
-
cir
cu
it
cu
r
r
en
t;
T
pvc@
deg
is
th
e
o
p
er
atin
g
t
em
p
er
atu
r
e
o
f
th
e
PV
ce
ll
in
d
eg
r
ee
s
C
elsi
u
s
;
an
d
T
STC
at
2
5
°C
.
T
h
e
o
p
er
atin
g
tem
p
e
r
atu
r
e
in
f
lu
en
ce
s
th
e
s
em
ico
n
d
u
cto
r
p
r
o
p
er
ties
o
f
th
e
PV
ce
ll.
T
h
is
tem
p
er
atu
r
e
d
ep
en
d
en
ce
is
r
ep
r
esen
ted
b
y
t
h
e
th
er
m
al
v
o
ltag
e
(
vt
)
,
as d
ef
in
e
d
in
(
3
)
:
=
×
×
@
×
(
3
)
wh
er
e
A
is
th
e
d
io
d
e
i
d
ea
lity
f
ac
to
r
;
k
is
th
e
B
o
ltzm
an
n
co
n
s
tan
t
(
1
.
3
8
x
1
0
-
23
)
;
T
pvc
is
th
e
PV
ce
ll
tem
p
er
atu
r
e
in
Kelv
in
;
N
cs
i
s
th
e
n
u
m
b
er
o
f
PV
ce
lls
co
n
n
ec
ted
in
s
er
ies;
an
d
q
is
th
e
elec
tr
o
n
ch
ar
g
e
(
1
.
6
×
10
-
19
)
.
T
o
p
r
o
v
id
e
s
u
f
f
icien
t
v
o
ltag
e
a
n
d
cu
r
r
en
t,
PV
p
an
els
ar
e
g
e
n
er
a
lly
ass
em
b
led
f
r
o
m
n
u
m
er
o
u
s
PV
ce
lls
in
s
er
ie
s
-
p
ar
allel
ar
r
an
g
em
e
n
ts
.
T
h
e
th
er
m
al
v
o
ltag
e
o
f
th
e
p
an
el
i
n
cr
ea
s
es
with
th
e
n
u
m
b
er
o
f
ce
lls
co
n
n
ec
ted
in
s
er
ies.
B
y
co
m
b
in
in
g
(
1
)
an
d
(
3
)
an
d
r
ea
r
r
an
g
in
g
th
e
e
q
u
atio
n
,
th
e
o
u
tp
u
t
v
o
ltag
e
o
f
t
h
e
PV
p
an
el
ca
n
th
en
b
e
r
ep
r
esen
ted
as
(
4
)
.
=
×
ln
(
ℎ
−
)
+
1
(
4
)
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
:
343
-
3
58
346
Fig
u
r
e
1
.
Sin
g
le
d
io
d
e
s
o
lar
ce
ll m
o
d
el
with
s
er
ies r
esis
tan
ce
At
o
p
en
cir
cu
it
co
n
d
itio
n
s
,
th
e
o
u
tp
u
t
cu
r
r
en
t,
is
ze
r
o
,
an
d
th
e
o
p
e
n
cir
cu
it
v
o
ltag
e,
V
oc
ca
n
b
e
d
er
iv
ed
as
(
5
)
.
=
×
ln
(
ℎ
)
+
1
(
5
)
B
esid
es,
ac
co
r
d
in
g
to
[
3
2
]
,
th
e
d
io
d
e
r
e
v
er
s
e
s
atu
r
atio
n
c
u
r
r
e
n
t c
an
b
e
ca
lc
u
lated
as
(
6
)
.
=
@
+
(
@
−
)
(
(
@
+
(
@
−
)
)
)
−
1
(
6
)
w
h
er
e
@
an
d
@
ar
e
th
e
o
p
en
cir
c
u
i
t v
o
ltag
e
an
d
s
h
o
r
t c
ir
cu
it c
u
r
r
en
t a
t stan
d
ar
d
test
co
n
d
itio
n
(
STC
–
1
0
0
0
W
/m
2
a
n
d
2
5
°C
).
PV
p
an
el
d
atash
ee
ts
co
m
m
o
n
ly
p
r
o
v
id
e
p
ar
am
eter
s
s
u
c
h
as
V
oc
,
I
sc
,
N
cs
,
α
i
,
a
n
d
β
v
ca
n
b
e
ea
s
ily
o
b
tain
e
d
f
r
o
m
t
h
e
PV
m
o
d
u
le
d
atash
ee
t.
Ho
wev
er
,
R
se
,
an
d
A
ar
e
u
s
u
all
y
n
o
t
p
r
o
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id
e
d
.
T
o
d
eter
m
in
e
th
ese
p
ar
am
eter
s
,
t
h
is
r
esear
ch
u
tili
ze
d
th
e
Sy
s
tem
Ad
v
is
o
r
M
o
d
el
p
r
o
v
id
e
d
b
y
NR
E
L
wh
ich
was
im
p
lem
en
ted
th
r
o
u
g
h
th
e
PV
Ar
r
ay
b
lo
c
k
with
in
MA
T
L
AB
Simu
lin
k
.
lib
r
ar
y
.
T
h
e
J
A
So
lar
J
AM
6
0
S0
1
-
3
0
0
/PR
PV
p
an
el
s
er
v
es
as
th
e
b
asis
f
o
r
t
h
is
s
tu
d
y
,
w
ith
its
elec
tr
ical
ch
ar
ac
ter
is
tics
d
ef
in
ed
b
y
th
e
p
ar
am
eter
s
in
T
ab
le
2
.
T
ab
le
2
.
E
lectr
ical
p
a
r
am
eter
s
o
f
J
A
So
lar
J
AM
6
0
S0
1
-
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0
0
/P
R
f
r
o
m
d
atash
ee
t
P
a
r
a
me
t
e
r
V
a
l
u
e
D
i
o
d
e
i
d
e
a
l
i
t
y
f
a
c
t
o
r
,
A
0
.
9
4
9
2
9
Te
mp
e
r
a
t
u
r
e
c
o
e
f
f
i
c
i
e
n
t
o
f
s
h
o
r
t
-
c
i
r
c
u
i
t
c
u
r
r
e
n
t
,
α
i
0
.
0
3
6
Te
mp
e
r
a
t
u
r
e
c
o
e
f
f
i
c
i
e
n
t
o
f
o
p
e
n
-
c
i
r
c
u
i
t
v
o
l
t
a
g
e
,
β
v
-
0
.
2
8
1
N
u
mb
e
r
o
f
c
e
l
l
s
i
n
s
e
r
i
e
s
,
N
cs
60
O
p
e
n
-
c
i
r
c
u
i
t
v
o
l
t
a
g
e
,
V
oc
3
9
.
8
5
V
S
h
o
r
t
-
c
i
r
c
u
i
t
c
u
r
r
e
n
t
,
I
sc
9
.
7
5
A
S
e
r
i
e
s r
e
si
s
t
a
n
c
e
,
R
se
0
.
3
3
7
1
9
Ω
W
h
ile
b
y
p
ass
d
io
d
es
ef
f
ec
tiv
ely
r
ed
u
ce
h
o
ts
p
o
ts
in
p
ar
tia
lly
s
h
ad
ed
PV
p
an
els,
th
eir
ac
tiv
atio
n
r
esu
lts
in
P
-
V
cu
r
v
es e
x
h
ib
itin
g
m
u
lti
-
p
ea
k
s
ch
a
r
ac
ter
is
tic
with
th
e
n
u
m
b
er
o
f
p
ea
k
s
d
ir
e
ctly
co
r
r
esp
o
n
d
in
g
to
th
e
n
u
m
b
er
o
f
ac
tiv
ated
d
io
d
es.
T
h
e
ar
ch
itectu
r
e
o
f
s
tan
d
ar
d
PV
p
an
els
g
en
er
ally
in
clu
d
es
th
r
ee
b
y
p
ass
d
io
d
es
as
s
h
o
wn
in
Fig
u
r
e
2
,
p
ar
titi
o
n
in
g
th
e
PV
p
an
el
in
t
o
th
r
ee
ce
ll
s
tr
in
g
s
.
Sh
ad
in
g
o
f
an
in
d
iv
id
u
al
ce
ll
s
tr
in
g
ac
tiv
ates
o
n
e
o
f
t
h
e
b
y
p
ass
d
io
d
es,
co
n
s
eq
u
e
n
tly
y
ield
in
g
a
P
-
V
c
u
r
v
e
with
a
m
a
x
im
u
m
o
f
th
r
ee
p
ea
k
s
.
Un
d
er
u
n
i
f
o
r
m
ir
r
ad
ian
ce
,
t
h
e
cu
r
r
en
t
o
u
tp
u
t
o
f
a
PV
p
a
n
el
with
N
ug
n
u
m
b
er
s
o
f
ce
ll
s
tr
in
g
at
th
e
s
am
e
ir
r
ad
ian
ce
lev
el
ca
n
b
e
ca
lcu
la
ted
as
(
7
)
.
=
ℎ
−
[
(
(
+
)
)
−
1
]
(
7
)
2
.
2
.
H
a
lf
-
cut
ce
ll
P
V
pa
nels
nu
m
er
ica
l m
o
dellin
g
A
h
alf
-
cu
t
ce
ll
PV p
an
el
c
o
n
ta
in
s
twice
th
e
n
u
m
b
e
r
o
f
ce
lls
c
o
m
p
ar
ed
to
a
f
u
ll
ce
ll
PV
p
an
e
l,
as
ea
ch
ce
ll is
b
is
ec
ted
.
T
h
ese
h
alv
es
th
e
cu
r
r
en
t o
f
ea
ch
PV c
ell,
wh
ile
m
ain
tain
in
g
th
e
PV c
ell
v
o
ltag
e,
r
esu
ltin
g
in
a
g
r
ea
ter
n
u
m
b
er
o
f
ce
ll
s
tr
in
g
s
in
th
e
h
alf
-
cu
t
ce
ll
PV
p
a
n
el.
Similar
to
a
s
tan
d
ar
d
f
u
ll
-
ce
ll
PV
p
an
el,
th
e
h
alf
-
cu
t
ce
ll
PV
p
a
n
els
ty
p
ically
in
teg
r
ate
th
r
ee
b
y
p
ass
d
io
d
es
,
d
iv
id
i
n
g
t
h
e
PV
p
a
n
el
in
to
th
r
ee
ce
ll
s
tr
in
g
s
co
n
n
ec
ted
in
s
er
ies.
Ho
wev
e
r
,
ea
ch
ce
ll
s
tr
in
g
is
f
u
r
th
er
d
iv
i
d
ed
in
to
two
p
ar
allel
ce
ll
s
tr
in
g
s
b
y
ea
c
h
b
y
p
ass
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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t J Po
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E
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&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
Dev
elo
p
men
t o
f n
u
merica
l m
o
d
el
-
b
a
s
ed
p
h
o
to
v
o
lta
ic
emu
la
t
o
r
fo
r
h
a
lf
-
cu
t c
ell
P
V
…
(
J
o
r
d
a
n
S
.
Z.
Lee
)
347
d
io
d
e
,
as
illu
s
tr
ated
in
Fig
u
r
e
2
.
T
h
u
s
,
th
e
h
alf
-
cu
t
ce
ll
PV
p
an
els
h
av
e
a
to
tal
o
f
s
ix
ce
ll
s
t
r
in
g
s
.
No
n
eth
eless
,
th
e
P
-
V
cu
r
v
es
o
f
h
alf
-
c
u
t
ce
ll
PV
p
an
els
s
till
ex
h
ib
it
a
m
ax
im
u
m
o
f
th
r
ee
p
ea
k
s
.
Fig
u
r
e
2
d
ep
icts
th
e
p
ar
allel
co
n
n
ec
tio
n
o
f
in
d
iv
id
u
al
b
y
p
a
s
s
d
io
d
es
to
two
ce
ll
s
tr
in
g
s
.
T
h
e
b
y
p
ass
d
io
d
es
ac
tiv
ate
wh
en
th
e
r
esp
ec
tiv
e
ce
ll
s
tr
in
g
s
ex
p
er
ien
ce
s
h
ad
i
n
g
an
d
r
ed
u
ce
ir
r
ad
ian
ce
.
T
h
e
f
o
r
war
d
v
o
ltag
e
th
r
esh
o
l
d
f
o
r
b
y
p
ass
d
io
d
e
ac
tiv
atio
n
is
0
.
6
V.
Fig
u
r
e
2
.
C
o
m
p
a
r
is
o
n
o
f
f
u
ll
-
c
ell
an
d
h
alf
-
c
u
t c
ell
s
tr
u
ctu
r
es
s
h
o
win
g
p
ar
allel
s
u
b
-
s
tr
in
g
co
n
n
ec
tio
n
s
T
h
e
h
alf
-
cu
t
PV
ce
ll
r
ef
er
e
n
ce
cu
r
r
e
n
t
o
f
th
e
p
ar
allel
c
o
n
n
ec
tio
n
o
f
b
y
p
ass
d
io
d
es
ac
r
o
s
s
p
air
ed
ce
ll
s
tr
in
g
s
ca
n
b
e
d
e
r
iv
ed
as
(
8
)
.
=
[
ℎ1
−
(
(
(
+
(
×
)
)
)
−
1
)
]
+
[
ℎ2
−
(
(
(
+
(
×
)
)
)
−
1
)
]
(
8
)
W
h
er
e,
I
ph1
is
th
e
p
h
o
t
o
cu
r
r
e
n
t
o
f
ce
ll st
r
in
g
1
c
o
n
n
ec
tin
g
to
a
b
y
p
ass
d
io
d
e
,
an
d
I
ph2
is
th
e
p
h
o
to
c
u
r
r
en
t
o
f
ce
ll
s
tr
in
g
2
co
n
n
ec
tin
g
to
th
e
s
am
e
b
y
p
ass
d
io
d
e.
I
f
two
ce
ll
s
tr
in
g
s
s
h
ar
in
g
a
b
y
p
ass
d
io
d
e
ex
p
er
ien
ce
n
o
n
-
u
n
if
o
r
m
ir
r
ad
ian
ce
,
t
h
e
r
esu
ltin
g
v
ar
iatio
n
in
t
h
eir
p
h
o
to
cu
r
r
en
ts
,
I
ph1
an
d
I
ph2
will
v
ar
y
a
cc
o
r
d
in
g
t
o
(
2
)
.
As
th
e
PV
p
an
el
co
m
p
r
is
es
th
r
ee
ce
ll
s
tr
in
g
s
co
n
n
ec
ted
in
s
er
ies,
th
e
V
oc
,
N
cs
,
an
d
R
se
v
alu
es
p
r
o
v
id
e
d
in
T
a
b
le
2
r
eq
u
ir
e
d
iv
is
io
n
b
y
th
r
ee
f
o
r
i
m
p
lem
en
tatio
n
in
(
8
)
.
Fig
u
r
e
3
(
a)
s
h
o
ws
th
e
ir
r
ad
ia
n
ce
d
is
tr
ib
u
tio
n
s
ap
p
lied
to
t
h
e
p
ar
allel
ce
ll
s
tr
in
g
s
o
f
ea
ch
b
y
p
ass
d
io
d
e,
wh
er
e
two
s
p
ec
if
ic
ir
r
a
d
ian
ce
d
is
tr
ib
u
tio
n
s
ar
e
co
n
s
i
d
er
ed
:
G1
=
[
5
0
0
4
0
0
2
0
0
]
;
G2
=
[
3
0
0
2
0
0
1
0
0
]
W
/m
².
T
h
e
tem
p
er
at
u
r
e
o
f
al
l
PV
p
an
els,
T
pvc@
deg
is
s
et
at
2
5
°C
.
B
ased
o
n
th
e
ir
r
a
d
ian
ce
d
is
tr
ib
u
tio
n
s
illu
s
tr
ated
in
Fig
u
r
e
3
(
a)
,
t
h
e
r
esu
ltin
g
m
u
lti
-
s
tep
I
–
V
cu
r
v
es
an
d
m
u
lti
-
p
ea
k
P
–
V
cu
r
v
es
ar
e
p
r
esen
ted
in
Fig
u
r
e
3
(
b
)
.
T
h
e
s
tair
ca
s
e
-
lik
e
I
-
V
c
u
r
v
e
is
attr
ib
u
ted
to
th
e
b
y
p
ass
d
io
d
es
ac
ti
v
atin
g
at
d
if
f
er
e
n
t
cu
r
r
en
t
th
r
esh
o
ld
s
d
ictated
b
y
th
e
ir
r
a
d
ian
ce
lev
els.
B
y
ap
p
ly
in
g
(
2
)
,
I
ph
at
c
o
r
r
esp
o
n
d
in
g
to
d
if
f
e
r
en
t
ir
r
a
d
ian
ce
ca
n
b
e
r
eso
lv
ed
in
t
o
d
is
tin
ct
v
alu
es,
d
en
o
ted
as
I
ph1
to
I
ph6
.
T
h
e
o
p
en
cir
c
u
it
v
o
ltag
e
f
o
r
ea
c
h
ce
ll
s
tr
in
g
u
n
d
er
d
if
f
er
en
t
ir
r
a
d
ian
ce
lev
els,
V
oc_irr_n
,
is
ca
lcu
lated
u
s
in
g
(
5
)
an
d
(
6
)
.
Giv
en
th
at
ea
ch
b
y
p
as
s
d
io
d
e
is
co
n
n
ec
ted
ac
r
o
s
s
two
ce
ll
s
tr
in
g
s
,
two
d
i
s
tin
ct
o
p
en
-
cir
c
u
it
v
o
ltag
es
wi
ll
d
ev
elo
p
wh
e
n
th
ese
s
tr
in
g
s
ex
p
er
ien
ce
d
if
f
e
r
en
t
ir
r
ad
ian
ce
lev
els.
Ho
wev
er
,
o
n
ly
th
e
m
in
im
u
m
o
f
th
ese
two
v
o
ltag
es
is
s
elec
ted
.
T
h
e
lab
e
lled
V
1
to
V
3
ca
n
b
e
ca
lcu
lated
as
(
9
)
.
=
[
∑
_
_
_
=
1
]
−
(
−
)
(
)
(
9
)
W
h
er
e
N
bd
is
th
e
to
tal
n
u
m
b
er
o
f
b
y
p
ass
d
io
d
es
,
a
n
d
V
fd
is
th
e
f
o
r
war
d
v
o
ltag
e
o
f
th
e
b
y
p
ass
d
io
d
e.
T
h
is
eq
u
atio
n
is
cr
itical
as
it
r
ep
r
esen
ts
th
e
t
o
tal
o
p
e
n
-
cir
cu
it
v
o
ltag
e,
wh
ich
is
th
e
s
u
m
o
f
t
h
e
m
in
im
u
m
in
d
iv
id
u
al
o
p
e
n
-
cir
cu
it
v
o
ltag
es
ac
r
o
s
s
ea
ch
b
y
p
ass
d
io
d
e
wh
er
e
co
n
n
ec
ted
ce
ll
s
tr
in
g
s
r
ec
eiv
e
d
if
f
er
en
t
ir
r
ad
ian
ce
lev
els.
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
:
343
-
3
58
348
(
a)
(
b
)
Fig
u
r
e
3
.
Ou
t
p
u
t c
h
ar
ac
ter
is
tics
o
f
a
Half
-
cu
t Cell PV p
an
el
u
n
d
er
PS
C
s
:
(
a)
h
alf
-
cu
t c
ell
P
V
p
an
el
with
two
s
p
ec
if
ic
ir
r
ad
ian
ce
d
is
tr
ib
u
tio
n
s
f
o
r
ea
ch
b
y
p
ass
d
io
d
e;
a
n
d
(
b
)
m
u
lti
-
s
tep
I
-
V
c
u
r
v
e
an
d
m
u
lti
-
p
ea
k
P
-
V
cu
r
v
e
o
f
th
e
h
alf
-
cu
t c
ell
PV p
an
el
u
n
d
e
r
PS
C
,
co
n
f
ir
m
in
g
b
y
p
ass
d
io
d
e
ac
tiv
atio
n
u
n
d
er
P
SC
s
T
h
e
p
r
o
p
o
s
ed
PV
p
an
el
n
u
m
er
ical
m
o
d
el
is
d
etailed
in
th
e
f
o
llo
win
g
th
r
ee
d
is
tin
ct
,
m
o
d
u
lar
ized
alg
o
r
ith
m
s
tag
es
to
en
h
a
n
ce
c
lar
ity
an
d
ad
d
r
ess
co
m
p
lex
ity
co
n
ce
r
n
s
.
T
h
e
m
o
d
el'
s
n
u
m
er
i
ca
l
p
r
o
ce
d
u
r
e
is
to
s
o
lv
e
th
e
s
in
g
le
d
io
d
e
m
o
d
el
an
d
co
m
p
u
te
t
h
e
PV
p
an
el
ch
ar
ac
ter
is
tics
cu
r
v
e.
Alg
o
r
ith
m
Stag
e
1
in
itializes
th
e
p
ar
am
eter
s
an
d
s
ets
u
p
t
h
e
s
in
g
le
d
io
d
e
m
o
d
el.
T
h
is
f
o
u
n
d
atio
n
al
p
r
o
ce
d
u
r
e
ca
lcu
lates
th
e
n
ec
es
s
ar
y
elec
tr
ical
p
ar
am
eter
s
f
r
o
m
th
e
en
v
ir
o
n
m
e
n
tal
an
d
r
ef
er
en
ce
d
ata
an
d
in
itializes
th
e
ar
r
ay
s
r
eq
u
ir
ed
f
o
r
th
e
f
u
ll
I
V
cu
r
v
e
g
e
n
er
atio
n
.
T
h
is
s
ta
g
e
in
v
o
lv
es
th
e
co
m
p
u
tatio
n
o
f
th
e
I
ph
a
n
d
V
oc
f
o
r
ea
ch
ce
l
l
s
tr
in
g
,
co
n
s
id
er
in
g
p
o
ten
tial
ir
r
a
d
ian
ce
n
o
n
-
u
n
if
o
r
m
ity
.
T
h
e
m
o
d
el
tak
es
ir
r
a
d
ian
ce
ar
r
a
y
s
(
G1
an
d
G2
)
a
n
d
a
tem
p
er
atu
r
e
a
r
r
ay
T
pvc@
deg
as
in
p
u
ts
f
o
r
ea
c
h
ce
ll
s
tr
in
g
.
Fo
r
c
ell
s
tr
in
g
s
co
n
n
ec
ted
to
th
e
s
am
e
b
y
p
ass
d
io
d
e,
o
n
e
s
tr
in
g
r
ec
eiv
es
ir
r
ad
ian
ce
G1
,
wh
ile
th
e
o
th
er
r
ec
eiv
es G2
.
T
h
e
p
h
o
to
cu
r
r
en
t
I
ph1_irr
is
co
m
p
u
ted
b
ased
o
n
ir
r
ad
ian
ce
lev
el
G1
,
an
d
I
ph2_irr
is
co
m
p
u
ted
b
ased
o
n
G2
.
T
h
e
o
p
e
n
-
cir
cu
it
v
o
lta
g
es
d
er
iv
ed
f
r
o
m
I
ph1_irr
an
d
I
p
h2_irr
ar
e
co
m
p
ar
ed
,
an
d
th
e
s
m
aller
o
f
t
h
e
two
is
s
to
r
ed
f
o
r
th
e
co
m
p
u
tatio
n
o
f
I
PVHC
f
o
r
th
e
p
ar
allel
ce
ll
s
tr
in
g
s
.
T
h
is
co
m
p
ar
is
o
n
is
im
p
o
r
tan
t
t
o
th
e
h
alf
-
c
u
t
ar
ch
itectu
r
e,
as
f
i
n
d
in
g
th
e
lim
itin
g
v
o
ltag
e
o
f
th
e
p
a
r
allel
s
u
b
-
s
tr
in
g
s
d
ef
in
es
t
h
e
s
p
ec
if
ic
in
f
lectio
n
p
o
i
n
ts
wh
er
e
b
y
p
ass
d
io
d
es will a
ctiv
ate,
s
ettin
g
th
e
f
o
u
n
d
atio
n
f
o
r
t
h
e
m
u
lti
-
p
ea
k
p
r
o
f
ile.
Alg
o
r
ith
m
s
tag
e
2
h
a
n
d
les
th
e
co
m
p
u
tatio
n
al
g
r
o
u
p
in
g
o
f
ad
jace
n
t
s
tr
in
g
s
with
id
en
tical
ir
r
ad
ian
ce
co
n
d
itio
n
s
to
r
ed
u
ce
r
ed
u
n
d
a
n
t
ca
lcu
latio
n
an
d
d
ef
i
n
es
th
e
cu
r
r
en
t
ca
lc
u
latio
n
lo
g
ic
f
o
r
a
s
p
ec
if
ic
v
o
ltag
e
s
tep
.
Up
o
n
co
m
p
u
tatio
n
o
f
th
e
p
ar
am
eter
s
f
o
r
ea
c
h
PV
p
an
el
m
en
tio
n
ed
in
alg
o
r
ith
m
s
ta
g
e
1
,
th
ey
a
r
e
s
to
r
ed
f
o
r
s
u
b
s
eq
u
en
t
u
s
e
in
I
-
V
cu
r
v
e
g
en
er
atio
n
in
alg
o
r
ith
m
s
tag
e
2
.
T
h
e
co
r
e
co
m
p
u
tatio
n
f
o
r
d
eter
m
in
i
n
g
th
e
cu
r
r
en
t
o
f
th
e
ce
ll
s
tr
in
g
s
in
th
e
n
u
m
er
ical
m
o
d
el
is
p
er
f
o
r
m
ed
in
alg
o
r
ith
m
s
tag
e
2
an
d
s
tep
3
.
At
ea
ch
d
is
cr
ete
v
o
ltag
e
s
tep
,
th
e
n
u
m
er
ical
m
o
d
el
co
m
p
u
tes th
e
ce
ll st
r
in
g
s
'
o
u
tp
u
t c
u
r
r
en
t b
y
iter
atin
g
o
v
er
a
v
o
ltag
e
r
an
g
e
f
r
o
m
1
V
to
th
e
s
u
m
o
f
in
d
iv
id
u
al
ce
ll
s
tr
in
g
o
p
en
-
c
ir
cu
it
v
o
ltag
es.
T
h
e
to
tal
I
PVHC
is
th
e
s
u
m
o
f
th
e
co
m
p
u
ted
p
h
o
to
cu
r
r
en
ts
,
I
ph1_irr
an
d
I
ph2_irr
.
T
h
e
alg
o
r
ith
m
ic
p
r
o
ce
s
s
f
o
r
co
m
p
u
tin
g
th
e
o
u
tp
u
t
cu
r
r
en
t
u
tili
ze
s
th
r
ee
co
n
d
itio
n
al
b
r
an
ch
es
t
o
h
an
d
le
d
if
f
er
e
n
t
s
ce
n
ar
io
s
.
T
h
ese
b
r
an
c
h
es
s
er
v
e
as
th
e
c
o
r
e
m
ec
h
a
n
is
m
f
o
r
m
u
lti
-
p
ea
k
em
u
latio
n
,
m
at
h
e
m
atica
lly
r
ep
licatin
g
th
e
p
h
y
s
ical
ac
tiv
atio
n
o
f
b
y
p
ass
d
io
d
es
to
cr
ea
te
d
is
tin
ct
cu
r
r
en
t
s
tep
s
wh
en
s
h
a
d
ed
s
u
b
-
s
tr
in
g
s
ex
ce
e
d
th
eir
v
o
ltag
e
lim
its
.
Fo
r
s
ce
n
ar
io
3
(
a)
,
wh
e
n
th
e
i
n
s
tan
tan
eo
u
s
v
o
ltag
e,
V
s
u
r
p
ass
es
th
e
s
u
m
m
ed
o
p
e
n
-
cir
cu
it
v
o
ltag
es
o
f
th
e
in
itial
i
ce
ll
s
tr
in
g
s
,
th
e
o
u
tp
u
t
cu
r
r
e
n
t
is
Alg
o
r
ith
m
s
tag
e
1
.
E
s
tab
lis
h
es th
e
b
aselin
e
p
ar
am
ete
r
s
f
o
r
th
e
u
n
iq
u
e
p
ar
allel
s
u
b
-
s
tr
in
g
s
tr
u
ctu
r
e
Pro
ce
d
u
r
e:
I
n
itialize
C
ell
Par
am
eter
s
I
n
p
u
ts
:
I
r
r
ad
ian
ce
1
,
G1
,
I
r
r
a
d
ian
ce
2
,
G2
an
d
tem
p
er
atu
r
e
ar
r
ay
s
,
T
C
o
n
s
tan
t:
A, I
sc@
stc
, V
oc@
stc
, α
i
, β
v
, N
cs
, R
se
, T
stc
, V
fd
,
k,
q
,
N
bd
Dec
lar
e
a
r
r
ay
s
:
I
d
, I
ph1_irr
, I
ph2_irr
, V
oc_irr1
, V
oc_irr2
, I
PVHC
, I
max
Ou
tp
u
t:
I
max
,
th
e
m
ax
im
u
m
cu
r
r
en
t o
f
all
I
-
V
cu
r
v
es f
o
r
ea
ch
v
o
ltag
e
L
o
g
ic
f
lo
w:
1
.
C
alcu
late
p
ar
a
m
eter
s
f
o
r
ea
ch
ce
ll
s
tr
in
g
b
ased
o
n
in
p
u
t
G1
,
G2
,
an
d
T
pvc@
deg
,
u
s
in
g
(
5
)
,
(
6
)
,
an
d
(
8
)
2
.
Sto
r
e
in
th
ei
r
r
esp
ec
tiv
e
v
al
u
es in
I
d
, I
ph1_irr
, I
ph2_irr
, V
oc_irr1
,
V
oc_irr2
3
.
C
o
m
p
ar
e
V
oc_irr1
(
i)
an
d
V
oc_irrw
(
i)
,
an
d
s
to
r
e
t
h
e
s
m
aller
v
al
u
e
b
etwe
en
th
em
as
V
oc_irr_min
.
4
.
I
n
itialize
d
ec
lar
ed
ar
r
ay
s
I
P
VHC
an
d
I
max
.
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
Dev
elo
p
men
t o
f n
u
merica
l m
o
d
el
-
b
a
s
ed
p
h
o
to
v
o
lta
ic
emu
la
t
o
r
fo
r
h
a
lf
-
cu
t c
ell
P
V
…
(
J
o
r
d
a
n
S
.
Z.
Lee
)
349
ass
ig
n
ed
to
a
v
al
u
e
o
f
ze
r
o
.
T
h
is
m
o
d
els
th
e
ac
tiv
atio
n
o
f
l
o
wer
-
ir
r
ad
ia
n
ce
s
tr
in
g
s
ab
o
v
e
th
eir
v
o
ltag
e
lim
it,
ex
clu
d
in
g
t
h
eir
cu
r
r
en
t
f
r
o
m
I
max
.
W
h
ile
s
ce
n
ar
io
3
(
b
)
c
h
ec
k
s
if
th
e
v
o
ltag
e
is
less
th
an
th
e
s
u
m
o
f
th
e
o
p
e
n
-
cir
cu
it
v
o
ltag
es
o
f
all
ce
ll
s
t
r
in
g
s
ex
clu
d
in
g
th
e
N
ug
g
r
o
u
p
ed
s
tr
in
g
s
(
wh
er
e
N
ug
eq
u
als
1
f
o
r
a
d
is
tin
ct
ir
r
ad
ian
ce
i
-
th
s
tr
in
g
)
,
th
e
c
u
r
r
en
t
is
s
et
to
th
e
p
h
o
to
cu
r
r
en
t
o
f
th
e
i
-
th
ce
ll
s
tr
in
g
.
T
h
is
s
im
u
lates
th
e
lo
w
-
v
o
ltag
e
o
p
er
atio
n
o
f
PV
p
a
n
els,
wh
er
e
th
e
o
u
tp
u
t
c
u
r
r
en
t
is
m
ain
ly
d
ictated
b
y
th
e
l
o
wer
i
r
r
ad
ian
ce
o
f
th
e
i
-
th
p
an
el.
As
f
o
r
s
ce
n
a
r
io
3
(
c)
,
th
e
o
u
t
p
u
t
c
u
r
r
en
t
ca
lcu
latio
n
f
o
r
v
o
ltag
es
b
e
y
o
n
d
th
e
d
ef
in
ed
c
o
n
d
itio
n
s
is
co
n
tin
g
en
t o
n
th
e
u
n
if
o
r
m
it
y
o
f
ir
r
ad
ian
ce
ac
r
o
s
s
th
e
ce
ll
s
tr
i
n
g
s
.
Un
d
er
u
n
if
o
r
m
ir
r
ad
ian
ce
(
N
ug
=
N
bd
)
ac
r
o
s
s
th
e
ce
ll
s
tr
in
g
s
,
th
e
o
u
tp
u
t
cu
r
r
en
t
is
ca
lcu
lated
ac
co
r
d
in
g
to
(
8
)
.
W
h
ile
u
n
d
e
r
n
o
n
-
u
n
if
o
r
m
ir
r
ad
ian
ce
ac
r
o
s
s
th
e
ce
ll
s
tr
in
g
s
,
th
e
p
ar
am
eter
s
o
f
in
d
iv
id
u
al
ce
ll
s
tr
in
g
s
ar
e
m
o
d
if
ied
to
ac
c
u
r
ately
m
o
d
el
th
e
ir
r
ad
ian
c
e
ef
f
ec
ts
.
T
h
ese
m
o
d
if
icatio
n
s
en
s
u
r
ed
I
-
V
cu
r
v
es
clo
s
ely
m
atch
th
e
id
ea
l
I
-
V
cu
r
v
es.
(
1
0
)
-
(
1
2
)
ar
e
im
p
o
r
tan
t
f
o
r
co
m
p
u
tin
g
th
e
o
u
tp
u
t c
u
r
r
e
n
t a
t e
ac
h
v
o
ltag
e
in
cr
em
e
n
t
:
=
ℎ
−
[
(
(
+
)
)
−
1
]
(
1
0
)
w
h
er
e
,
=
−
[
∑
_
_
_
−
=
1
]
+
(
−
)
(
)
(
1
1
)
=
{
1
=
1
(
)
(
1
+
12
)
>
1
(
1
2
)
w
h
er
e
V
mod
is
th
e
m
o
d
if
ied
v
o
ltag
e
th
at
ac
co
u
n
ts
f
o
r
v
o
ltag
e
d
r
o
p
s
ac
r
o
s
s
th
e
ac
tiv
ated
b
y
p
ass
d
io
d
es
an
d
V
oc
o
f
th
e
f
ir
s
t
(
i
-
N
ug
)
ce
ll
s
tr
in
g
o
f
th
e
PV
p
a
n
el
;
f
mod
is
th
e
m
o
d
i
f
icatio
n
f
ac
to
r
th
at
c
o
r
r
ec
ts
f
o
r
v
ar
y
in
g
R
se
o
f
th
e
o
p
er
atin
g
ce
ll
s
tr
in
g
an
d
th
e
n
eg
lecte
d
s
h
u
n
t
r
esis
tan
ce
,
R
sh
in
th
e
s
in
g
le
-
d
io
d
e
m
o
d
el
.
T
h
e
iter
ativ
e
p
r
o
ce
s
s
also
ass
e
s
s
e
s
if
th
e
I
o
o
f
th
e
i
-
th
ce
ll
s
tr
in
g
d
r
o
p
s
b
elo
w
th
e
p
h
o
to
c
u
r
r
en
t
o
f
th
e
(
i
+1
)
-
t
h
ce
ll
s
tr
in
g
in
th
e
s
eq
u
en
ce
.
I
n
s
u
ch
in
s
tan
ce
s
,
th
e
lo
o
p
is
ter
m
in
ated
p
r
io
r
to
c
o
m
p
letio
n
to
o
p
tim
ize
co
m
p
u
t
atio
n
al
ef
f
icien
cy
.
Alg
o
r
ith
m
s
tag
e
3
ex
ec
u
tes
th
e
ir
r
ad
ia
n
ce
g
r
o
u
p
in
g
c
h
ec
k
,
th
en
iter
ates
th
r
o
u
g
h
v
o
ltag
e
s
tep
s
,
an
d
f
in
ally
p
er
f
o
r
m
s
c
u
r
r
e
n
t
m
at
ch
in
g
to
d
eter
m
i
n
e
th
e
m
ax
i
m
u
m
cu
r
r
en
t
f
o
r
ea
ch
v
o
lta
g
e
s
tep
.
T
h
is
s
tag
e
in
v
o
lv
es
in
itializin
g
N
ug
to
1
,
with
N
ug
d
en
o
tin
g
th
e
c
o
u
n
t
o
f
ad
jace
n
t
ce
ll
s
tr
in
g
s
r
ec
ei
v
in
g
id
en
tical
to
tal
ir
r
ad
ian
ce
.
T
h
e
t
o
tal
ir
r
ad
ia
n
ce
o
f
s
u
cc
ess
iv
e
ce
ll
s
tr
in
g
s
is
co
m
p
ar
ed
.
I
f
i
d
en
tical,
th
e
N
g
co
u
n
ter
is
in
cr
em
en
ted
,
g
r
o
u
p
in
g
th
ese
s
tr
in
g
s
to
o
p
tim
ize
co
m
p
u
tatio
n
al
ef
f
icien
cy
.
Alg
o
r
ith
m
s
tag
e
3
s
tep
6
:
s
elec
t
th
e
m
ax
im
u
m
c
u
r
r
e
n
t
f
o
r
ea
c
h
v
o
ltag
e
p
o
i
n
t
f
r
o
m
al
g
o
r
ith
m
s
tag
e
2
s
tep
3
.
T
h
is
p
r
o
ce
s
s
y
ield
s
th
e
m
ax
im
u
m
cu
r
r
en
t
a
r
r
ay
,
wh
ich
th
e
m
o
d
e
l
r
etu
r
n
s
as
th
e
I
-
V
cu
r
v
e
f
o
r
t
h
e
h
alf
-
c
u
t
ce
ll
PV
p
an
el
u
n
d
e
r
g
iv
en
co
n
d
itio
n
s
,
ef
f
ec
tiv
ely
co
n
s
tr
u
ctin
g
th
e
f
in
al
m
u
lti
-
p
ea
k
cu
r
v
e
b
y
d
y
n
am
ically
s
elec
tin
g
th
e
d
o
m
in
an
t
cu
r
r
en
t
p
ath
at
ev
er
y
v
o
ltag
e
s
tep
.
Alg
o
r
ith
m
s
tag
e
2
.
C
o
m
p
u
tes
th
e
in
d
iv
id
u
al
"step
s
"
o
f
th
e
c
u
r
v
e
b
ased
o
n
b
y
p
ass
d
io
d
e
lo
g
ic
Pro
ce
d
u
r
e:
C
alcu
late
I
V
cu
r
v
es
I
n
p
u
ts
:
i
(
C
u
r
r
en
t
p
a
n
el
in
d
ex
)
,
V
(
Vo
ltag
e
s
tep
)
,
N
ug
(
Nu
m
b
er
o
f
id
en
tical
a
d
jace
n
t
s
tr
in
g
s
)
,
all
ar
r
ay
s
f
r
o
m
Alg
o
r
ith
m
1
.
Ou
tp
u
t:
I
PVHC
(
i,V
)
(
C
u
r
r
en
t c
o
n
tr
ib
u
tio
n
o
f
th
e
i
-
th
ce
ll st
r
in
g
g
r
o
u
p
at
v
o
ltag
e
V)
L
o
g
ic
Flo
w:
1
.
C
h
ec
k
if
v
o
ltag
e
is
to
o
h
ig
h
: I
f
V
>
s
u
m
(
V
oc_diff_min
(
1
:i))
,
s
et
I
PVHC
(
i,V
)
=
0
.
2
.
C
h
ec
k
lo
w
v
o
ltag
e
r
e
g
io
n
:
E
ls
e
if
V
=
1
o
r
V
<
s
u
m
(
V
oc_diff_min
(
1
:i
-
N
ug
)
)
,
s
et
I
PVHC
(
i,V
)
=
I
ph1_irr
(
i)
+
I
ph2_irr
(
i)
3
.
Fin
al
cu
r
r
e
n
t c
alcu
latio
n
at
o
p
er
atin
g
r
eg
io
n
: E
L
SE
a.
Un
if
o
r
m
co
n
d
itio
n
:
I
f
u
n
if
o
r
m
(
N
ug
= N
bd
)
,
s
et
I
PVHC
(
i,V
)
ac
co
r
d
in
g
to
(
8
)
.
b.
No
n
-
u
n
if
o
r
m
c
o
n
d
itio
n
: I
f
n
o
n
-
u
n
if
o
r
m
,
s
et
I
PVHC
(
i,V
)
ac
co
r
d
in
g
to
(
10
)
,
(
1
1
)
,
a
n
d
(
1
2)
.
c.
Op
tim
izatio
n
ch
ec
k
: I
f
i <
N
bd
an
d
I
PVHC
(
i,V
)
<
I
ph1_irr
(
i)
+
I
ph
2_irr
(
i)
,
b
r
ea
k
t
h
e
lo
o
p
.
4
.
R
etu
r
n
I
PVHC
(
i,V
)
.
Alg
o
r
ith
m
s
tag
e
3
.
Ag
g
r
e
g
ates th
e
s
eg
m
en
ts
to
f
o
r
m
th
e
f
in
al
m
u
lti
-
p
ea
k
c
u
r
v
e
Pro
ce
d
u
r
e:
C
alcu
late
th
e
m
ax
im
u
m
cu
r
r
e
n
t b
y
c
o
m
p
ar
in
g
all
th
e
I
-
V
cu
r
v
es
I
n
p
u
ts
:
N
bd
,
all
ar
r
ay
s
f
r
o
m
Alg
o
r
ith
m
1
,
G1
,
G2
.
Ou
tp
u
t:
I
max
(
m
ax
im
u
m
cu
r
r
e
n
t a
r
r
a
y
/f
in
al
I
-
V
cu
r
v
e)
L
o
g
ic
Flo
w:
1
.
Ou
ter
L
o
o
p
(
PV Str
in
g
Gr
o
u
p
in
g
I
ter
atio
n
)
: FOR
ea
ch
P
V
p
an
el
s
tr
in
g
f
r
o
m
1
to
N
bd
.
2
.
I
n
itialize
g
r
o
u
p
in
g
: N
ug
=
1
.
3
.
I
r
r
ad
ian
ce
Gr
o
u
p
in
g
C
h
ec
k
:
FOR
co
u
n
t
e
q
u
als
i
to
(
N
bd
-
1
)
,
if
G1
(
i
)
+
G2
(
i)
=
G1
(
co
u
n
t
+1
)
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
:
343
-
3
58
350
T
h
e
th
r
ee
m
o
d
u
la
r
ized
alg
o
r
ith
m
s
tag
es
en
ab
le
ac
cu
r
ate
s
im
u
latio
n
o
f
h
alf
-
cu
t
ce
ll
PV
p
an
el
b
eh
av
io
r
u
n
d
er
n
o
n
-
u
n
if
o
r
m
i
r
r
ad
ian
ce
.
T
h
e
u
s
e
o
f
N
ug
o
p
ti
m
izes
co
m
p
u
tatio
n
b
y
g
r
o
u
p
i
n
g
id
e
n
tical
s
tr
in
g
s
.
Fu
r
th
er
m
o
r
e
,
V
mod
an
d
f
mod
en
s
u
r
e
ac
cu
r
ate
I
-
V
cu
r
v
es
e
m
u
latio
n
f
o
r
ce
ll
s
tr
in
g
g
r
o
u
p
s
u
n
d
er
d
if
f
er
e
n
t
ir
r
ad
ian
ce
.
2
.
3
.
P
V
e
m
ula
t
o
r
s
im
ula
t
io
n
in M
A
T
L
A
B
/S
im
uli
nk
T
o
em
u
late
th
e
I
-
V
c
h
ar
ac
ter
i
s
tics
o
f
ty
p
ically
h
ig
h
-
v
o
ltag
e
h
alf
-
cu
t
ce
ll
PV
p
a
n
els,
a
P
V
em
u
lato
r
u
tili
ze
s
a
DC
-
DC
b
u
ck
co
n
v
e
r
ter
to
s
tep
d
o
w
n
th
e
o
u
t
p
u
t
v
o
ltag
e
to
th
e
d
esire
d
o
p
er
ati
n
g
r
a
n
g
e.
T
h
e
b
u
c
k
co
n
v
er
ter
co
n
tr
o
ls
th
e
eq
u
iv
alen
t
r
esis
tan
ce
v
ia
a
f
ee
d
b
ac
k
lo
o
p
,
alig
n
in
g
th
e
o
u
tp
u
t
cu
r
r
en
t
with
th
e
r
ef
er
en
ce
c
u
r
r
en
t
c
o
m
p
u
ted
b
y
th
e
n
u
m
er
ical
m
o
d
el
f
o
r
ac
cu
r
ate
I
-
V
r
e
p
licatio
n
u
n
d
er
v
ar
y
in
g
co
n
d
itio
n
s
.
T
h
e
b
u
ck
co
n
v
er
ter
co
n
s
is
ts
o
f
an
in
d
u
cto
r
,
a
Sch
o
ttk
y
d
io
d
e,
a
ca
p
ac
ito
r
,
an
d
a
MO
SF
E
T
,
wh
er
e
th
e
MO
SF
E
T
f
u
n
ctio
n
s
as
th
e
f
ast
-
s
witch
in
g
elem
en
t
co
n
tr
o
lled
b
y
a
g
ate
d
r
iv
er
.
T
h
e
a
cc
u
r
ac
y
o
f
th
e
PV
em
u
lato
r
d
ep
en
d
s
o
n
c
o
m
p
o
n
en
t
d
esig
n
.
Dete
r
m
in
in
g
t
h
e
c
r
itical
in
d
u
ctan
ce
,
L
,
an
d
o
u
tp
u
t
ca
p
ac
itan
ce
,
C
out
u
s
ed
eq
u
atio
n
s
th
at
wer
e
d
er
iv
ed
b
y
m
o
d
if
y
in
g
th
e
f
o
r
m
u
las
d
escr
ib
ed
in
(
1
3
)
an
d
(
1
4
)
[
3
3
]
.
>
(
1
−
)
2
(
1
3
)
>
1
−
8
2
(
1
4
)
W
h
er
e
lo
ad
r
esis
tan
ce
,
R
load
is
d
eter
m
in
ed
b
ased
o
n
(
1
5
)
.
=
(
)
(
)
(
1
5
)
W
h
er
e
V
MPP(min)
an
d
I
MPP(min)
ar
e
th
e
m
ax
im
u
m
p
o
wer
p
o
in
t
v
o
ltag
e
(
2
8
.
0
2
V)
an
d
c
u
r
r
e
n
t
(
0.
7
3
7
A
)
o
f
th
e
PV
p
an
el
u
n
d
er
th
e
c
o
n
d
itio
n
o
f
u
n
if
o
r
m
ir
r
ad
ia
n
ce
o
f
1
0
0
W
/m
2
an
d
tem
p
er
atu
r
e
o
f
25
°
C
,
r
esp
ec
tiv
ely
.
C
o
n
s
id
er
in
g
th
e
n
ee
d
f
o
r
r
e
d
u
ce
d
i
n
d
u
ct
o
r
s
ize,
c
o
m
p
at
ib
ilit
y
with
th
e
T
I
m
icr
o
co
n
tr
o
ller
'
s
f
r
eq
u
en
c
y
lim
itatio
n
s
,
an
d
aim
in
g
f
o
r
c
o
n
tin
u
o
u
s
cu
r
r
en
t
m
o
d
e
o
p
er
atio
n
with
m
i
n
im
ized
r
i
p
p
le,
th
e
b
u
c
k
co
n
v
er
te
r
s
p
ec
if
icatio
n
s
an
d
d
esig
n
c
o
n
s
tr
ain
ts
wer
e
estab
lis
h
ed
as su
m
m
ar
ized
in
T
a
b
le
3
.
T
ab
le
3
.
Sp
ec
if
icatio
n
s
an
d
co
n
tr
o
l p
ar
a
m
eter
s
o
f
th
e
PV e
m
u
lato
r
P
a
r
a
me
t
e
r
V
a
l
u
e
S
w
i
t
c
h
i
n
g
f
r
e
q
u
e
n
c
y
,
f
20
k
H
z
I
n
d
u
c
t
a
n
c
e
,
L
2
mH
O
u
t
p
u
t
c
a
p
a
c
i
t
a
n
c
e
,
C
o
u
t
47
µF
M
i
n
i
m
u
m
d
u
t
y
c
y
c
l
e
,
d
m
i
n
0
.
0
5
Ta
r
g
e
t
o
u
t
p
u
t
v
o
l
t
a
g
e
r
i
p
p
l
e
,
γ
1%
T
h
e
PV
em
u
lato
r
m
o
d
el
was
im
p
lem
en
ted
with
in
th
e
MA
T
L
AB
/Si
m
u
lin
k
en
v
ir
o
n
m
en
t
,
u
tili
zin
g
a
b
u
ilt
-
in
b
u
ck
c
o
n
v
e
r
ter
m
o
d
e
l
in
th
e
Simu
lin
k
lib
r
a
r
y
,
as
s
h
o
wn
in
Fig
u
r
e
4
.
T
h
e
h
alf
-
cu
t
ce
ll
PV
p
an
el
n
u
m
er
ical
m
o
d
el
is
in
teg
r
ated
in
to
th
e
b
u
ck
c
o
n
v
e
r
ter
'
s
clo
s
ed
-
lo
o
p
c
o
n
tr
o
l,
w
h
ich
u
tili
ze
s
a
PI
co
n
tr
o
ller
,
as
d
ep
icted
in
Fig
u
r
e
4
,
to
c
o
m
p
u
te
d
u
ty
cy
cle,
D,
f
o
r
MO
SF
E
T
s
witch
in
g
.
T
h
e
d
elib
er
ately
s
elec
ted
s
tan
d
ar
d
PI
co
n
tr
o
ller
s
er
v
es
to
v
alid
ate
t
h
e
p
r
o
p
o
s
ed
m
o
d
el,
d
em
o
n
s
tr
atin
g
its
ab
ilit
y
to
b
e
ac
cu
r
ate
ly
em
u
lated
with
o
u
t
r
elian
ce
o
n
co
m
p
lex
,
h
ig
h
-
c
o
m
p
u
tatio
n
al
-
lo
a
d
co
n
tr
o
l
s
ch
e
m
es.
T
h
e
PV
p
an
el
n
u
m
er
ical
m
o
d
el
is
d
ev
elo
p
e
d
in
th
e
MA
T
L
AB
/Si
m
u
lin
k
en
v
ir
o
n
m
e
n
t
u
s
in
g
a
MA
T
L
AB
f
u
n
ctio
n
b
lo
ck
b
ased
o
n
th
e
th
r
ee
m
o
d
u
lar
ized
alg
o
r
ith
m
s
tag
es
o
f
th
e
p
r
o
p
o
s
ed
h
alf
-
cu
t
ce
ll
PV
p
an
el
n
u
m
er
ical
m
o
d
el.
T
h
e
r
ef
er
en
ce
c
u
r
r
en
t
d
e
r
iv
atio
n
is
b
ased
o
n
t
h
e
b
u
ck
co
n
v
er
te
r
'
s
o
u
tp
u
t
v
o
ltag
e.
T
h
is
in
te
g
r
ated
co
n
tr
o
l
e
n
ab
les
th
e
PV
p
an
el’
s
o
u
tp
u
t
ch
ar
ac
ter
is
tic
em
u
latio
n
ac
r
o
s
s
v
ar
io
u
s
o
p
er
atin
g
p
o
in
ts
.
PI
co
n
tr
o
ller
d
esig
n
r
eq
u
i
r
es
co
n
s
id
er
atio
n
o
f
s
y
s
tem
d
y
n
am
ics,
n
o
n
-
lin
ea
r
ities
,
an
d
d
esire
d
r
esp
o
n
s
e
tim
e.
Pro
p
er
tu
n
in
g
en
h
a
n
ce
s
r
o
b
u
s
t
n
ess
,
s
tab
ilit
y
,
an
d
r
esp
o
n
s
iv
en
ess
f
o
r
ac
cu
r
ate
tr
ac
k
in
g
o
f
th
e
PV
p
an
el'
s
o
p
er
atin
g
p
o
in
t.
T
h
e
PI
co
n
tr
o
ller
co
ef
f
icien
t
is
s
et
t
o
0
.
1
3
f
o
r
th
e
p
r
o
p
o
r
tio
n
al
co
ef
f
icien
t
an
d
4
0
f
o
r
th
e
in
teg
r
al
c
o
ef
f
icien
t
f
o
r
s
im
u
latio
n
in
M
AT
L
AB
/Si
m
u
lin
k
.
+
G2
(
co
u
n
t +
1
)
,
i
n
cr
em
en
t
N
ug
.
4
.
Sk
ip
th
e
f
o
r
lo
o
p
if
h
av
in
g
PV p
an
els with
id
en
tical
ir
r
ad
i
an
ce
: I
n
cr
em
e
n
t i
b
y
N
ug
–
1,
5
.
I
n
n
er
L
o
o
p
(
V
o
ltag
e
Step
I
t
er
atio
n
)
: FOR
ea
ch
v
o
ltag
e
s
te
p
V
f
r
o
m
1
to
s
u
m
(
V
oc_diff_min
):
a.
C
all
Alg
o
r
ith
m
2
to
d
eter
m
i
n
e
I
PVHC
(
i,V
)
.
6.
Ma
x
im
u
m
cu
r
r
e
n
t selec
tio
n
: A
f
ter
b
o
th
l
o
o
p
s
,
FOR
ea
ch
v
o
ltag
e
V
,
s
et
I
max
(
V)
=
m
ax
(I
PVHC
(
:,V
)
)
7
.
R
etu
r
n
I
max
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
Dev
elo
p
men
t o
f n
u
merica
l m
o
d
el
-
b
a
s
ed
p
h
o
to
v
o
lta
ic
emu
la
t
o
r
fo
r
h
a
lf
-
cu
t c
ell
P
V
…
(
J
o
r
d
a
n
S
.
Z.
Lee
)
351
T
h
e
MA
T
L
AB
/Si
m
u
lin
k
s
im
u
latio
n
was
co
n
f
ig
u
r
ed
with
a
f
ix
ed
-
s
tep
s
o
lv
er
an
d
a
s
tep
s
ize
o
f
1
μ
s
.
T
h
is
co
n
f
ig
u
r
atio
n
en
s
u
r
es
co
m
p
ati
b
ilit
y
in
co
m
p
ar
is
o
n
with
th
e
h
ar
d
war
e
r
esu
lts
,
as
th
e
m
icr
o
co
n
tr
o
ller
o
p
er
ates
ex
clu
s
iv
ely
in
f
ix
e
d
-
s
tep
m
o
d
e.
I
r
r
a
d
ian
ce
in
p
u
ts
ar
e
c
o
n
f
ig
u
r
ed
v
ia
th
e
c
o
n
s
tan
t
b
lo
c
k
s
G1
an
d
G
2
as
d
ep
icted
in
Fig
u
r
e
4
.
T
h
e
n
u
m
er
ical
m
o
d
el
r
eq
u
ir
es th
ese
v
alu
es in
an
ar
r
ay
f
o
r
m
at,
wh
er
e
ea
ch
ar
r
ay
elem
en
t
s
p
ec
if
ies th
e
ir
r
ad
ian
ce
f
o
r
a
s
ec
tio
n
o
f
th
e
h
alf
-
c
u
t c
ell
PV p
an
el
,
as sh
o
wn
in
Fig
u
r
e
3
.
A
s
ig
n
al
b
u
ild
er
b
lo
ck
was
e
m
p
lo
y
ed
to
v
ar
y
th
e
lo
a
d
co
n
d
itio
n
,
e
n
ab
lin
g
th
e
g
en
e
r
atio
n
o
f
th
e
f
u
ll
I
V
ch
ar
ac
ter
is
tic
cu
r
v
e.
T
h
e
d
y
n
am
ic
r
esp
o
n
s
e
o
f
th
e
PV
em
u
lato
r
was
ev
alu
ated
b
y
s
u
b
jectin
g
th
e
s
y
s
tem
to
a
s
u
d
d
e
n
s
tep
ch
an
g
e
in
th
e
o
p
e
r
atin
g
s
etp
o
in
t
as
p
r
esen
ted
in
Fig
u
r
e
5
.
T
h
e
s
y
s
tem
ex
h
ib
its
e
x
ce
llen
t
tr
an
s
ien
t
b
eh
av
i
o
u
r
,
with
o
u
tp
u
t
v
o
ltag
e
an
d
cu
r
r
e
n
t
s
u
cc
ess
f
u
lly
r
ea
ch
in
g
s
tead
y
s
tate
with
m
in
im
al
o
v
er
s
h
o
o
t
an
d
a
s
ettlin
g
tim
e
o
f
less
th
an
1
0
m
s
.
T
h
is
h
ig
h
-
s
p
ee
d
d
y
n
am
ic
p
er
f
o
r
m
an
ce
s
er
v
es
to
v
alid
ate
th
e
en
tire
ar
ch
itectu
r
e.
Fig
u
r
e
4
.
PV e
m
u
lato
r
s
im
u
latio
n
m
o
d
el
in
MA
T
L
AB
/Si
m
u
lin
k
with
in
teg
r
ated
h
alf
-
c
u
t PV
p
an
el
n
u
m
er
ical
m
o
d
el
with
in
th
e
cl
o
s
ed
-
lo
o
p
co
n
tr
o
l sy
s
tem
Fig
u
r
e
5.
Dy
n
am
ic
r
esp
o
n
s
e
o
f
PV e
m
u
lato
r
with
PS
C
s
h
o
win
g
<
10
m
s
s
ettlin
g
tim
e
u
n
d
e
r
s
tep
ch
an
g
e
in
th
e
o
p
er
atin
g
s
etp
o
in
t
ch
a
n
g
in
g
f
r
o
m
1
.
9
2
4
Ω
to
2
.
5
3
1
Ω
an
d
to
2
.
8
4
3
Ω
T
o
f
u
r
th
er
ass
ess
th
e
v
iab
il
ity
o
f
th
e
p
r
o
p
o
s
ed
h
alf
-
c
u
t
ce
ll
n
u
m
er
ical
m
o
d
el
f
o
r
r
ea
l
-
tim
e
ap
p
licatio
n
s
,
th
e
co
m
p
u
tatio
n
al
b
u
r
d
en
im
p
o
s
ed
b
y
th
e
m
o
d
el
was
q
u
an
tifie
d
v
ia
h
ig
h
-
r
eso
lu
tio
n
tim
in
g
in
th
e
MA
T
L
AB
s
im
u
latio
n
en
v
i
r
o
n
m
en
t.
T
h
e
co
m
p
u
tatio
n
al
l
o
ad
was
m
ea
s
u
r
ed
b
y
is
o
latin
g
th
e
tim
e
r
e
q
u
ir
ed
f
o
r
th
e
m
ic
r
o
co
n
tr
o
ller
to
e
x
e
cu
te
th
e
co
r
e
n
u
m
er
ical
ca
lc
u
latio
n
(
Alg
o
r
ith
m
s
Stag
e
1
to
3
)
to
d
eter
m
in
e
a
s
in
g
le
I
V
c
h
ar
ac
ter
is
tic
p
o
i
n
t.
T
h
e
r
esu
lts
co
n
f
ir
m
an
ex
ce
p
tio
n
ally
lo
w
co
m
p
u
tatio
n
al
lo
a
d
wh
er
e
th
e
m
o
d
el
r
eq
u
ir
es
o
n
ly
ar
o
u
n
d
5
.
2
μ
s
t
o
co
m
p
lete
o
n
e
f
u
ll
ca
lcu
lati
o
n
cy
cle.
T
h
e
r
ap
id
d
y
n
a
m
ic
r
esp
o
n
s
e
an
d
lo
w
co
m
p
u
tatio
n
al
o
v
er
h
ea
d
o
f
t
h
e
n
o
v
el
h
alf
-
c
u
t
ce
ll
n
u
m
er
i
ca
l
m
o
d
el
co
n
f
ir
m
t
h
at
its
co
m
p
lex
ity
d
o
es
n
o
t
im
p
ed
e
r
ea
l
-
tim
e
e
x
ec
u
tio
n
.
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
:
343
-
3
58
352
2
.
4
.
H
a
rdwa
re
im
plem
ent
a
t
io
n
T
h
e
PV
em
u
lato
r
h
a
r
d
war
e
i
m
p
lem
en
tatio
n
c
o
n
s
is
ts
o
f
a
cu
r
r
en
t
-
c
o
n
tr
o
lled
b
u
c
k
co
n
v
er
ter
cir
cu
it
an
d
a
PV
em
u
lato
r
co
n
tr
o
ller
,
as
s
h
o
wn
in
Fig
u
r
e
6
.
Ap
p
r
o
p
r
iate
co
m
p
o
n
e
n
t
r
atin
g
s
elec
tio
n
is
cr
itical
f
o
r
th
e
b
u
ck
co
n
v
er
ter
cir
c
u
it.
Vo
ltag
e
r
atin
g
s
m
u
s
t
b
e
h
ig
h
e
r
th
a
n
th
e
DC
s
o
u
r
ce
v
o
ltag
e
an
d
t
h
e
PV
p
an
el
o
p
e
n
-
cir
cu
it
v
o
ltag
e,
an
d
cu
r
r
e
n
t
r
at
in
g
s
m
u
s
t
s
u
r
p
ass
th
e
PV
p
an
el
s
h
o
r
t
-
cir
cu
it
cu
r
r
e
n
t.
T
h
e
L
C
f
ilter
o
f
th
e
b
u
ck
co
n
v
er
ter
u
tili
ze
d
a
to
r
o
id
al
in
d
u
cto
r
a
n
d
an
elec
tr
o
ly
tic
ca
p
a
cito
r
.
Fig
u
r
e
6
.
Ov
e
r
v
iew
o
f
PV e
m
u
lato
r
h
ar
d
war
e
im
p
lem
e
n
tatio
n
A
MO
SF
E
T
d
r
iv
er
is
r
eq
u
ir
ed
to
in
ter
f
ac
e
th
e
MO
SF
E
T
(
I
R
F7
4
0
)
g
ate
with
th
e
T
I
L
AUNCHXL
-
F2
8
3
7
9
D
m
icr
o
c
o
n
tr
o
ller
.
T
h
e
r
ea
l
-
tim
e
m
icr
o
co
n
t
r
o
ller
'
s
o
u
tp
u
t
s
ig
n
al
h
as
in
s
u
f
f
icien
t
d
r
iv
e
s
tr
en
g
th
f
o
r
th
e
MO
SF
E
T
,
g
iv
en
th
e
b
u
ck
c
o
n
v
er
ter
'
s
h
ig
h
in
p
u
t
v
o
ltag
e
.
T
h
e
I
R
2
1
1
0
MO
SF
E
T
d
r
iv
er
is
u
s
ed
in
th
is
im
p
lem
en
tatio
n
alo
n
g
with
a
b
o
o
ts
tr
ap
cir
cu
it
f
o
r
d
r
iv
in
g
th
e
h
ig
h
-
s
id
e
MO
SF
E
T
[
3
4
]
.
T
h
e
PV
em
u
lato
r
co
n
tr
o
ller
u
tili
ze
s
a
cu
r
r
en
t
s
en
s
o
r
an
d
a
v
o
ltag
e
d
iv
i
d
er
n
etwo
r
k
f
o
r
cu
r
r
en
t
an
d
v
o
ltag
e
s
en
s
in
g
,
r
esp
ec
tiv
ely
.
An
elec
tr
o
n
ic
lo
ad
with
ad
ju
s
tab
le
p
o
wer
d
is
s
ip
atio
n
ca
n
ac
co
m
m
o
d
ate
th
e
PV
em
u
lato
r
'
s
r
esis
tan
ce
o
p
er
atin
g
p
o
in
t.
T
h
e
PV
em
u
lato
r
co
n
tr
o
ller
m
o
d
el
f
o
r
th
e
T
I
L
AUNCHXL
-
F2
8
3
7
9
D
r
ea
l
-
tim
e
m
icr
o
co
n
tr
o
ller
was
d
ev
elo
p
e
d
in
MA
T
L
AB
/Si
m
u
lin
k
.
T
wo
ADC
in
p
u
t
p
in
s
an
d
o
n
e
PW
M
o
u
tp
u
t
p
in
ar
e
ass
ig
n
ed
.
Ou
tp
u
t
v
o
ltag
e
an
d
cu
r
r
en
t
s
ig
n
als
f
r
o
m
th
e
b
u
c
k
co
n
v
er
te
r
cir
cu
it
ar
e
r
ec
eiv
ed
b
y
th
e
r
ea
l
-
tim
e
m
icr
o
co
n
tr
o
ller
'
s
AD
C
in
p
u
t.
T
o
m
atch
th
e
m
icr
o
co
n
t
r
o
lle
r
'
s
3
.
3
V
m
ax
im
u
m
an
alo
g
in
p
u
t
an
d
th
e
1
2
-
b
it
ADC
'
s
4
0
9
6
r
eso
lu
tio
n
,
r
ec
ei
v
ed
v
alu
es
ar
e
s
ca
led
b
y
3
.
3
/
4
0
9
5
.
A
r
esis
tiv
e
v
o
ltag
e
d
iv
i
d
er
n
etwo
r
k
r
e
d
u
ce
s
th
e
b
u
ck
co
n
v
er
ter
'
s
o
u
tp
u
t
v
o
ltag
e
to
a
lev
el
co
m
p
atib
l
e
with
th
e
m
icr
o
c
o
n
tr
o
ller
'
s
an
alo
g
in
p
u
t
r
a
n
g
e.
T
h
e
I
NA2
1
9
DC
cu
r
r
e
n
t
s
en
s
o
r
was
s
elec
ted
f
o
r
its
ac
cu
r
ac
y
an
d
s
tr
aig
h
tf
o
r
wa
r
d
in
te
g
r
at
io
n
.
T
h
e
d
u
t
y
cy
cle
co
m
p
u
ted
b
y
th
e
PI
c
o
n
tr
o
ller
is
a
n
o
r
m
alize
d
v
alu
e
b
etwe
e
n
0
an
d
1
.
Sin
ce
th
e
r
ea
l
-
tim
e
m
icr
o
co
n
tr
o
ller
's
ePW
M
b
lo
ck
r
eq
u
ir
es th
e
d
u
ty
cy
cle
as a
p
er
ce
n
ta
g
e,
th
e
PI
c
o
n
tr
o
ller
'
s
o
u
tp
u
t is scaled
b
y
a
f
ac
to
r
o
f
1
0
0
.
T
h
e
ex
p
er
im
en
tal
s
etu
p
o
f
th
e
PV
em
u
lato
r
h
ar
d
war
e
is
d
ep
icted
in
Fig
u
r
e
7
.
T
h
e
ex
p
er
im
en
tal
h
ar
d
war
e
in
clu
d
es
a
DC
-
DC
b
u
ck
co
n
v
er
ter
cir
c
u
it
with
cu
r
r
en
t
s
en
s
o
r
an
d
v
o
ltag
e
s
en
s
in
g
r
esis
tiv
e
n
etwo
r
k
s
,
an
d
a
T
I
L
AUNCHXL
-
F2
8
3
7
9
D
r
ea
l
-
tim
e
m
icr
o
co
n
tr
o
ller
im
p
lem
en
tin
g
th
e
PV
em
u
lato
r
co
n
tr
o
ller
m
o
d
el.
T
h
e
r
esis
tiv
e
v
o
ltag
e
d
iv
id
er
c
o
m
p
o
s
ed
o
f
R
1
(
1
2
k
Ω
)
a
n
d
R
2
(1
kΩ
)
was
u
s
ed
to
s
ca
le
th
e
o
u
tp
u
t
v
o
ltag
e
d
o
wn
to
th
e
A
DC
lim
it.
A
1
m
s
tim
e
s
tep
was
co
n
f
ig
u
r
e
d
f
o
r
t
h
e
r
ea
l
-
ti
m
e
m
icr
o
c
o
n
tr
o
ller
.
T
h
e
lab
o
r
ato
r
y
p
o
wer
s
u
p
p
l
y
was
u
s
ed
as
th
e
D
C
s
o
u
r
ce
,
an
d
a
3
0
0
W
elec
tr
o
n
ic
lo
ad
s
er
v
ed
as
th
e
v
ar
iab
le
lo
ad
.
T
wo
lab
o
r
at
o
r
y
p
o
wer
s
u
p
p
ly
u
n
its
wer
e
u
tili
ze
d
to
ac
h
iev
e
a
to
tal
s
u
p
p
ly
v
o
ltag
e
o
f
4
0
V,
wh
ich
ex
ce
ed
s
th
e
o
p
en
-
cir
c
u
it
v
o
lta
g
e
o
f
th
e
h
alf
-
c
u
t
ce
ll
PV
p
an
el
s
p
ec
if
ied
in
T
ab
le
2
.
T
h
e
elec
tr
o
n
ic
lo
ad
was
co
n
f
ig
u
r
ed
to
c
u
r
r
en
t
-
c
o
n
tr
o
lled
m
o
d
e
to
s
et
th
e
lo
ad
c
o
n
d
i
tio
n
s
ac
co
r
d
in
g
t
o
th
e
s
im
u
latio
n
r
esu
lts
,
th
er
eb
y
en
ab
lin
g
d
ir
ec
t
co
m
p
ar
is
o
n
.
T
h
e
co
n
tr
o
ller
m
o
d
el
was
d
ep
lo
y
ed
t
o
th
e
r
ea
l
-
tim
e
m
i
cr
o
co
n
tr
o
ller
u
s
in
g
MA
T
L
AB
/S
im
u
lin
k
.
T
h
e
o
u
tp
u
t
v
o
ltag
e
a
n
d
cu
r
r
en
t
o
f
th
e
PV
em
u
lato
r
wer
e
m
o
n
ito
r
e
d
v
ia
th
e
elec
tr
o
n
ic
lo
ad
d
is
p
lay
to
g
e
n
er
ate
PV
ch
ar
ac
ter
is
tic
cu
r
v
es
u
n
d
e
r
s
p
ec
if
ied
lo
ad
co
n
d
itio
n
s
.
T
h
e
PI
co
n
tr
o
ller
'
s
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