I
nte
rna
t
io
na
l J
o
urna
l o
f
Appl
ied P
o
wer
E
ng
i
neer
ing
(
I
J
AP
E
)
Vo
l.
14
,
No
.
3
,
Sep
tem
b
er
20
25
,
p
p
.
5
8
8
~
5
9
9
I
SS
N:
2252
-
8
7
9
2
,
DOI
:
1
0
.
1
1
5
9
1
/ijap
e
.
v
14
.
i
3
.
pp
588
-
599
588
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//
ija
p
e.
ia
esco
r
e.
co
m/
M
itiga
ting mis
ma
tch
po
we
r los
ses
i
n pho
tov
o
ltaic sy
stems und
er
pa
rtial sha
ding
:
a
co
mpa
ra
tive stud
y
of series
-
pa
ra
lle
l and
a
lternativ
e config
ura
tions
Ra
g
ha
d Adee
b O
t
hm
a
n
,
O
ma
r
Sh
a
ra
f
Al
-
Dee
n
Yehy
a
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zba
k
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Ali A
bb
a
wi
M
o
ha
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Ala
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I
r
a
q
Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
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y:
R
ec
eiv
ed
Au
g
1
1
,
2
0
2
4
R
ev
is
ed
J
an
1
0
,
2
0
2
5
Acc
ep
ted
J
u
n
2
3
,
2
0
2
5
Util
izin
g
t
h
e
p
h
o
to
v
o
lt
a
ic
e
ffe
c
t,
p
h
o
t
o
v
o
lt
a
ic
(P
V)
sy
ste
m
s
a
re
a
p
o
p
u
lar
tec
h
n
iq
u
e
fo
r
c
a
p
tu
r
in
g
so
lar
e
n
e
rg
y
a
n
d
t
u
r
n
in
g
su
n
li
g
h
t
i
n
to
e
lec
tri
c
it
y
.
Ho
we
v
e
r,
e
n
v
iro
n
m
e
n
tal
fa
c
to
r
s,
e
sp
e
c
ially
sh
a
d
e
,
sig
n
ifi
c
a
n
t
ly
imp
a
c
t
p
h
o
to
v
o
lt
a
ic
sy
ste
m
e
fficie
n
c
y
.
S
h
a
d
o
ws
c
a
st
o
n
P
V
p
a
n
e
ls
b
y
su
rro
u
n
d
i
n
g
stru
c
tu
re
s,
tree
s,
a
c
c
u
m
u
late
d
d
ir
t,
c
lo
u
d
s,
a
n
d
d
e
b
r
is
c
a
n
se
rio
u
s
ly
imp
a
ir
th
e
ir
p
e
rf
o
rm
a
n
c
e
.
Th
e
p
u
r
p
o
se
o
f
th
is
stu
d
y
wa
s
to
i
n
v
e
sti
g
a
te
h
o
w
sh
a
d
e
a
ffe
c
ts
p
h
o
t
o
v
o
lt
a
ic
s
y
ste
m
s
u
ti
l
ize
d
in
re
sid
e
n
t
ial
se
tt
i
n
g
s.
S
e
r
i
e
s
-
p
a
ra
ll
e
l
(S
P
)
t
o
p
o
lo
g
y
fo
r
P
V
s
y
ste
m
h
a
v
e
b
e
e
n
in
v
e
stig
a
ted
.
Ad
d
it
i
o
n
a
l
ly
,
in
th
is
wo
rk
,
a
P
V
sy
ste
m
o
f
5
k
W
o
f
t
h
e
re
sid
e
n
c
e
h
o
m
e
h
a
s
b
e
e
n
p
ro
p
o
se
d
a
n
d
m
u
lt
i
c
a
se
s
o
f
s
h
a
d
i
n
g
e
x
a
m
in
e
d
.
Th
r
o
u
g
h
th
e
re
su
lt
s
o
b
tai
n
e
d
w
h
e
n
p
a
rti
a
l
sh
a
d
in
g
wa
s
a
p
p
li
e
d
,
it
wa
s
f
o
u
n
d
th
a
t
t
h
e
h
ig
h
e
st
e
fficie
n
c
y
o
f
t
h
e
sy
ste
m
wa
s
wh
e
n
p
a
rti
a
l
sh
a
d
i
n
g
irrad
i
a
n
c
e
(Ir
=
5
0
0
W/m
2
)
wa
s
a
p
p
li
e
d
to
o
n
e
c
o
lu
m
n
(5
m
o
d
u
les
)
a
s
8
2
.
8
4
%
,
wh
il
e
t
h
e
wo
rst
a
n
d
lea
st
e
q
u
ip
p
e
d
c
a
se
wa
s
wh
e
n
th
e
sh
a
d
i
n
g
wa
s
a
p
p
l
ied
to
th
e
c
o
r
n
e
rs
a
n
d
ra
n
d
o
m
sh
a
d
in
g
a
t
(8
m
o
d
u
les
),
wh
e
re
th
e
e
fficie
n
c
y
d
e
c
re
a
se
d
to
a
p
p
ro
x
ima
tely
3
9
.
2
4
%
a
n
d
4
0
.
6
4
%
re
sp
e
c
ti
v
e
l
y
.
K
ey
w
o
r
d
s
:
E
n
v
ir
o
n
m
en
tal
im
p
ac
t
Par
tial sh
ad
in
g
Ph
o
to
v
o
ltaic
s
h
ad
in
g
PV sy
s
tem
ef
f
icien
cy
So
lar
p
an
el
s
h
ad
o
w
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Om
ar
Sh
ar
af
Al
-
Dee
n
Yeh
y
a
Al
-
Yo
zb
ak
y
Dep
ar
tm
en
t o
f
E
lectr
ical
E
n
g
i
n
ee
r
in
g
,
C
o
lleg
e
o
f
E
n
g
in
ee
r
i
n
g
,
Un
iv
e
r
s
ity
o
f
Mo
s
u
l
Mo
s
u
l
,
I
r
aq
E
m
ail:
o
.
y
eh
y
a@
u
o
m
o
s
u
l.e
d
u
.
iq
1.
I
NT
RO
D
UCT
I
O
N
W
h
en
co
m
p
a
r
ed
to
o
th
er
r
en
ewa
b
le
en
er
g
y
s
o
u
r
ce
s
,
p
h
o
t
o
v
o
ltaic
(
PV
)
s
o
u
r
ce
s
a
r
e
wi
d
ely
u
s
ed
wo
r
ld
wid
e
[
1
]
–
[
5
]
.
PV
ce
lls
ar
e
u
s
ed
in
s
o
lar
p
h
o
to
v
o
ltaic
s
y
s
tem
s
to
co
n
v
er
t
s
o
lar
r
ad
iatio
n
in
to
e
n
er
g
y
,
h
e
n
ce
f
o
s
ter
in
g
t
h
e
g
lo
b
al
g
r
o
wth
o
f
th
e
PV
s
ec
to
r
[
6
]
.
T
h
e
t
o
tal
in
s
talled
PV
ca
p
ac
ity
wo
r
ld
wid
e
at
th
e
en
d
o
f
2
0
1
8
was
4
8
0
GW
,
an
d
p
r
o
jectio
n
s
in
d
icate
t
h
at
ca
p
ac
ity
will
r
e
ac
h
2
,
8
4
0
GW
b
y
2
0
3
0
[
7
]
.
T
h
e
am
o
u
n
t
o
f
s
o
lar
r
ad
iatio
n
th
at
a
PV
m
o
d
u
le'
s
ce
lls
r
ec
eiv
e
af
f
ec
ts
th
e
m
o
d
u
le's
p
er
f
o
r
m
a
n
ce
[
8
]
,
[
9
]
.
Pas
s
in
g
clo
u
d
s
an
d
tall
o
b
jects
s
u
r
r
o
u
n
d
i
n
g
th
e
PV
ar
ea
ca
n
ca
u
s
e
s
h
ad
e,
wh
ich
is
o
n
e
o
f
th
e
tr
ig
g
er
ca
u
s
es
f
o
r
PV
p
er
f
o
r
m
a
n
ce
d
ec
lin
e
[
1
0
]
.
I
n
h
o
m
es
with
s
h
ad
ed
ar
ea
s
,
s
o
lar
en
er
g
y
s
y
s
tem
s
ca
n
b
e
q
u
ite
s
u
cc
ess
f
u
l
th
an
k
s
to
a
v
ar
iety
o
f
tactics
an
d
tech
n
o
lo
g
ical
ad
v
an
ce
m
e
n
ts
.
To
ac
h
iev
e
th
e
r
eq
u
ir
ed
v
o
ltag
e
an
d
cu
r
r
e
n
t
lev
el,
a
s
er
ies/
p
ar
allel
co
m
b
in
atio
n
o
f
PV
m
o
d
u
les
f
o
r
m
s
a
s
o
lar
p
h
o
to
v
o
ltaic
ar
r
a
y
[
3
]
,
[
1
1
]
–
[
1
4
]
.
T
h
e
g
en
er
ate
d
o
u
t
p
u
t
p
o
wer
h
as
a
d
ir
ec
t
an
d
in
v
er
s
e
r
elatio
n
s
h
ip
with
th
ese
two
p
ar
am
eter
s
(
ir
r
a
d
iatio
n
an
d
tem
p
er
atu
r
e,
r
esp
ec
tiv
ely
)
.
As
a
r
esu
lt,
"tem
p
er
atu
r
e
"
an
d
"ir
r
a
d
iatio
n
"
v
ar
iab
les ar
e
i
m
p
o
r
ta
n
t w
h
en
i
t c
o
m
es to
PV sy
s
tem
s
'
ab
ilit
y
to
g
en
e
r
ate
elec
tr
icity
.
Par
tial sh
ad
in
g
c
o
n
d
itio
n
s
(
PS
C
)
o
r
n
o
n
-
h
o
m
o
g
e
n
o
u
s
ir
r
ad
iatio
n
r
ef
er
s
to
v
a
r
y
in
g
ir
r
ad
iatio
n
lev
els with
in
a
PV stru
c
tu
r
e
[
1
5
]
–
[
1
8
]
.
T
h
e
p
er
f
o
r
m
an
ce
o
f
s
o
lar
p
h
o
to
v
o
ltaic
s
y
s
tem
s
i
s
g
r
ea
tly
r
ed
u
ce
d
b
y
s
h
ad
in
g
,
wh
ich
also
lo
wer
s
s
y
s
tem
s
tab
ilit
y
an
d
en
er
g
y
p
r
o
d
u
ctio
n
.
I
n
ar
ea
s
with
s
h
ad
o
w,
awa
r
en
ess
,
m
o
n
ito
r
in
g
,
a
n
d
s
y
s
tem
ad
ju
s
tm
e
n
ts
ar
e
ess
en
tial
f
o
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
Mit
ig
a
tin
g
mis
ma
tch
p
o
w
er lo
s
s
es in
p
h
o
to
vo
lta
ic
s
ystems
u
n
d
er p
a
r
tia
l
…
(
R
a
g
h
a
d
A
d
ee
b
Oth
ma
n
)
589
ef
f
ec
tiv
en
ess
.
Ph
o
to
v
o
ltaic
s
y
s
tem
s
,
p
h
o
to
v
o
ltaic
m
o
d
u
les,
r
ec
o
n
f
ig
u
r
atio
n
,
PV o
r
ien
tatio
n
,
an
d
t
h
e
im
p
ac
t o
f
s
o
ilin
g
an
d
p
ar
tial
s
h
ad
in
g
o
n
s
o
lar
en
er
g
y
o
u
tp
u
t
ar
e
th
e
m
ain
to
p
ics
o
f
th
e
s
tu
d
y
.
I
t
d
i
s
cu
s
s
es
th
e
n
eg
ativ
e
ef
f
ec
ts
th
at
p
ar
tial
s
h
ad
e
an
d
d
u
s
t
ac
cu
m
u
latio
n
h
a
v
e
o
n
th
e
p
er
f
o
r
m
a
n
ce
o
f
PV
m
o
d
u
les,
h
ig
h
lig
h
tin
g
th
e
n
ec
ess
ity
o
f
cr
ea
ti
v
e
way
s
t
o
o
p
tim
ize
en
er
g
y
[
5
]
,
[
1
9
]
–
[
2
2
]
.
I
f
o
p
er
ated
in
ac
c
o
r
d
a
n
ce
with
ec
o
lo
g
ical
g
o
v
er
n
an
ce
p
r
in
cip
les,
s
o
lar
h
o
m
e
s
y
s
tem
s
ca
n
s
u
cc
es
s
f
u
lly
en
d
e
n
er
g
y
p
o
v
er
ty
an
d
co
n
tr
ib
u
te
to
en
v
ir
o
n
m
en
tal
p
r
eser
v
atio
n
;
h
o
wev
er
,
a
r
ef
o
r
m
o
f
g
o
v
er
n
a
n
ce
is
r
eq
u
ir
e
d
f
o
r
lo
n
g
-
ter
m
s
u
s
tain
ab
ilit
y
[
2
3
]
.
B
ec
au
s
e
p
h
o
to
v
o
ltaic
s
y
s
tem
s
r
ely
o
n
d
ir
ec
t
s
u
n
s
h
in
e
to
cr
e
ate
elec
tr
icity
,
th
ey
a
r
e
p
ar
tic
u
lar
ly
v
u
ln
er
ab
le
t
o
s
h
ad
e
co
m
p
a
r
ed
to
o
th
e
r
en
er
g
y
p
r
o
d
u
cin
g
s
y
s
tem
s
.
Sig
n
if
i
ca
n
t
p
o
wer
lo
s
s
es
an
d
in
ef
f
ici
en
cies
in
th
e
s
y
s
tem
ca
n
r
esu
lt
f
r
o
m
ev
en
a
s
in
g
le
m
o
d
u
le
i
n
a
PV
ar
r
ay
b
ein
g
p
ar
tially
s
h
ad
ed
.
I
t
is
ess
en
tial
to
co
m
p
r
eh
e
n
d
h
o
w
s
h
ad
in
g
af
f
ec
ts
PV
s
y
s
tem
p
er
f
o
r
m
an
ce
in
o
r
d
er
to
m
ax
im
iz
e
en
er
g
y
y
ield
,
o
p
tim
ize
d
esig
n
,
an
d
g
u
ar
a
n
tee
th
e
f
in
an
cial
s
u
s
tain
ab
ilit
y
o
f
s
o
lar
en
er
g
y
p
r
o
jects.
T
h
is
in
tr
o
d
u
ctio
n
ex
am
in
es
th
e
way
s
in
wh
ich
s
h
ad
e
im
p
ac
ts
th
e
ef
f
icien
c
y
o
f
p
h
o
to
v
o
ltai
c
s
y
s
tem
s
an
d
p
r
o
v
id
es
tip
s
f
o
r
r
e
d
u
cin
g
th
ese
ef
f
ec
ts
t
o
im
p
r
o
v
e
s
y
s
tem
p
er
f
o
r
m
an
ce
as a
wh
o
le.
T
h
e
cu
r
r
en
t
s
tu
d
y
ex
am
in
es
h
o
w
s
o
lar
PV
ar
r
a
y
o
u
tp
u
t
p
o
wer
v
a
r
ies
with
ir
r
ad
iatio
n
l
ev
el
(
at
a
co
n
s
tan
t
tem
p
er
atu
r
e)
.
A
s
o
lar
PV
ar
r
ay
'
s
o
u
tp
u
t
p
o
wer
u
n
d
er
u
n
if
o
r
m
illu
m
in
atio
n
c
o
n
d
itio
n
s
h
as
a
p
ea
k
p
o
in
t
th
at
co
r
r
esp
o
n
d
s
to
its
m
ax
im
u
m
p
o
wer
.
A
n
o
n
-
h
o
m
o
g
en
e
o
u
s
ir
r
ad
iatio
n
s
ce
n
ar
io
r
esu
lts
in
a
lo
wer
p
e
ak
p
o
wer
g
en
er
atio
n
.
Mism
atch
lo
s
s
(
M
L
)
is
th
e
ter
m
u
s
ed
to
d
escr
ib
e
th
e
v
ar
iatio
n
in
g
en
er
ate
d
o
u
tp
u
t
p
o
wer
u
n
d
er
u
n
if
o
r
m
an
d
n
o
n
-
h
o
m
o
g
en
eo
u
s
ir
r
ad
iatio
n
lev
els
[
2
4
]
.
No
n
-
h
o
m
o
g
en
e
o
u
s
ir
r
ad
iatio
n
r
e
d
u
ce
s
PV
f
ac
ilit
ie
s
'
o
u
tp
u
t
p
o
wer
g
e
n
er
atio
n
an
d
e
f
f
icien
cy
.
2.
SI
G
NIF
I
CAN
T
O
F
T
H
I
S S
T
UDY
Ph
o
to
v
o
ltaic
s
y
s
tem
s
'
ef
f
icie
n
cy
ca
n
b
e
s
ev
er
ely
h
ar
m
ed
b
y
s
h
ad
in
g
.
T
h
e
p
o
wer
o
u
tp
u
t
o
f
a
p
h
o
to
v
o
ltaic
ar
r
a
y
ca
n
b
e
s
ig
n
if
ican
tly
d
ec
r
ea
s
ed
b
y
p
a
r
tially
s
h
ad
in
g
ev
e
n
o
n
e
s
o
lar
p
a
n
e
l.
T
h
is
is
d
u
e
to
th
e
f
ac
t
th
at
ce
lls
th
at
ar
e
s
h
a
d
ed
g
en
er
ate
less
cu
r
r
en
t,
an
d
in
a
s
e
r
ies
co
n
n
ec
tio
n
,
t
h
e
lo
west
g
en
er
atin
g
ce
ll
s
ets
th
e
cu
r
r
en
t
lim
it.
T
h
ese
ce
lls
lo
s
e
p
o
wer
in
s
tead
o
f
p
r
o
d
u
cin
g
it
wh
en
th
ey
a
r
e
s
h
ad
ed
,
wh
ich
co
u
ld
ca
u
s
e
o
v
er
h
ea
tin
g
an
d
d
am
a
g
e.
B
ec
au
s
e
th
e
s
h
ad
ed
a
n
d
u
n
s
h
ad
ed
ce
lls
in
a
PV
ar
r
ay
o
p
er
ate
at
d
i
f
f
er
en
t
l
o
ca
tio
n
s
o
n
th
eir
c
u
r
r
e
n
t
-
v
o
ltag
e
(
I
-
V
)
ch
ar
ac
ter
is
tics
,
s
h
ad
in
g
r
esu
lts
in
m
is
m
atch
lo
s
s
es.
T
h
e
PV
a
r
r
ay
'
s
(
I
-
V
)
cu
r
v
e
is
im
p
ac
ted
b
y
s
h
ad
in
g
,
wh
ich
m
ak
es
it
m
o
r
e
ch
allen
g
in
g
f
o
r
th
e
m
ax
im
u
m
p
o
wer
p
o
in
t
tr
ac
k
in
g
(
MPPT
)
alg
o
r
ith
m
t
o
d
eter
m
in
e
th
e
ac
t
u
al
m
ax
im
u
m
p
o
wer
p
o
in
t.
As
a
r
esu
lt,
en
e
r
g
y
co
n
v
er
s
io
n
is
l
ess
ef
f
ec
tiv
e.
W
h
en
o
n
e
p
a
n
el
is
s
h
ad
ed
in
a
s
er
ies
co
n
f
ig
u
r
atio
n
,
t
h
e
cu
r
r
en
t
f
lo
w
in
g
th
r
o
u
g
h
th
e
en
tire
s
tr
in
g
is
im
p
ac
ted
.
Sh
ad
in
g
in
a
p
ar
allel
ar
r
an
g
em
en
t
m
a
y
r
esu
lt
in
an
u
n
eq
u
al
p
o
wer
d
i
s
tr
ib
u
tio
n
an
d
p
o
s
s
ib
le
o
v
er
l
o
ad
in
g
o
f
th
e
s
h
ad
e
d
p
an
els.
Sin
ce
th
e
s
er
ies
-
p
ar
all
el
(
SP
)
ar
r
a
n
g
em
en
t
is
f
r
e
q
u
e
n
tly
u
s
ed
in
r
ea
l
-
wo
r
ld
s
o
lar
s
y
s
tem
s
,
th
e
ar
ticle'
s
m
ain
g
o
al
is
to
d
em
o
n
s
tr
ate
its
b
en
ef
its
an
d
s
u
itab
ilit
y
f
o
r
r
ed
u
cin
g
th
e
im
p
ac
ts
o
f
p
ar
tial
s
h
ad
o
win
g
.
Alth
o
u
g
h
ad
d
itio
n
al
d
esig
n
s
s
u
ch
as
to
tal
cr
o
s
s
-
tied
(
T
C
T
)
,
b
r
id
g
e
lin
k
(
B
L
)
,
an
d
h
o
n
e
y
co
m
b
(
HC
)
a
r
e
s
ig
n
if
ican
t,
th
e
y
ar
e
n
o
t
in
clu
d
e
d
in
th
is
s
tu
d
y
.
T
h
e
co
m
p
a
r
ativ
e
s
tu
d
y
o
f
o
th
e
r
co
n
f
ig
u
r
atio
n
s
is
lef
t
as
a
p
o
s
s
ib
le
d
ir
ec
tio
n
f
o
r
f
u
tu
r
e
r
esear
c
h
as th
is
wo
r
k
at
tem
p
ts
to
o
f
f
er
a
th
o
r
o
u
g
h
in
v
esti
g
atio
n
o
f
th
e
SP
co
n
f
ig
u
r
at
io
n
.
3.
SYST
E
M
CO
NF
I
G
URA
T
I
O
N
Ph
o
to
v
o
ltaic
s
y
s
tem
s
tar
g
et
s
o
lar
en
er
g
y
,
wh
ic
h
is
r
en
ewa
b
le
en
er
g
y
an
d
is
ab
u
n
d
a
n
t in
alm
o
s
t e
v
er
y
p
lace
.
B
y
u
s
in
g
th
is
en
er
g
y
,
h
o
m
eo
wn
e
r
s
ca
n
r
ed
u
ce
th
eir
d
ep
en
d
en
ce
o
n
co
n
v
e
n
tio
n
al
f
o
s
s
il
f
u
els,
r
ed
u
ce
p
o
llu
tio
n
,
co
n
tr
ib
u
te
to
s
u
s
tain
ab
ilit
y
,
an
d
r
ed
u
ce
th
eir
ca
r
b
o
n
f
o
o
tp
r
i
n
t.
E
co
n
o
m
ically
,
th
e
u
s
e
o
f
s
o
lar
en
er
g
y
p
r
o
d
u
ce
s
s
ig
n
if
ican
t
r
ed
u
ctio
n
in
t
h
e
b
ills
o
f
elec
tr
icity
in
p
r
o
s
p
ec
tiv
e
lo
n
g
ter
m
.
I
n
th
is
w
o
r
k
,
a
PV
s
y
s
tem
o
f
5
k
W
f
o
r
h
o
m
e
p
ur
p
o
s
es h
as b
ee
n
s
u
g
g
ested
as sh
o
wn
in
Fig
u
r
e
1
.
Fig
u
r
e
1
.
PV sy
s
tem
f
o
r
h
o
m
e
ap
p
licatio
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
14
,
No
.
3
,
Sep
tem
b
er
20
25
:
5
8
8
-
599
590
3
.
1
.
P
V
pa
nels
In
o
r
d
er
to
s
u
p
p
ly
5
k
W
in
u
n
i
f
o
r
m
s
h
ad
in
g
co
n
d
itio
n
s
,
2
0
PV
p
an
els
ar
e
co
n
n
ec
ted
as
5
PV
p
an
els
i
n
s
er
ies
with
4
s
u
ch
g
r
o
u
p
s
in
p
ar
allel
,
as
s
h
o
wn
in
Fig
u
r
e
2
.
T
h
e
o
u
tp
u
t
(
I
-
V)
an
d
(
P
-
V)
c
u
r
v
es
f
o
r
ea
ch
p
an
el
with
ir
r
ad
ian
ce
o
f
5
0
0
an
d
1
0
0
0
W
/m
2
ar
e
s
h
o
wn
in
Fig
u
r
e
3
.
T
ab
le
1
d
escr
ib
es
th
e
s
p
ec
if
ic
atio
n
o
f
ea
c
h
p
an
el.
In
o
r
d
e
r
to
o
b
tain
t
h
e
d
esire
d
p
o
wer
p
r
o
d
u
ctio
n
u
n
d
er
c
o
n
s
is
ten
t
s
h
ad
in
g
co
n
d
itio
n
s
,
th
e
PV
s
y
s
tem
is
co
n
s
tr
u
cted
with
p
an
els
co
n
n
e
cted
in
s
er
ies
an
d
p
ar
allel.
Fo
r
m
ax
im
u
m
ef
f
icien
cy
,
ea
ch
p
a
n
el
r
u
n
s
at
its
id
ea
l
v
o
ltag
e
an
d
c
u
r
r
en
t
lev
els.
I
n
o
r
d
er
to
en
s
u
r
e
t
h
at
th
e
s
y
s
tem
ca
n
s
atis
f
y
th
e
p
o
wer
r
eq
u
ir
e
m
e
n
t,
th
e
s
er
ies
s
etu
p
r
aises
th
e
to
tal
v
o
ltag
e
wh
ile
t
h
e
p
ar
allel
co
n
n
ec
tio
n
im
p
r
o
v
es
th
e
cu
r
r
en
t
o
u
tp
u
t.
T
em
p
e
r
atu
r
e
ch
an
g
es
af
f
ec
t
th
e
p
an
els'
p
er
f
o
r
m
an
ce
b
y
s
lig
h
tly
d
ec
r
ea
s
in
g
v
o
ltag
e
an
d
s
lig
h
tly
in
cr
e
asin
g
cu
r
r
e
n
t,
u
n
d
er
s
co
r
in
g
th
e
s
ig
n
if
ican
ce
o
f
th
e
r
m
al
m
an
a
g
em
en
t.
T
h
e
s
y
s
tem
'
s
p
er
f
o
r
m
an
ce
cu
r
v
es
s
h
o
w
h
o
w
wel
l
it
ad
ap
ts
to
v
ar
ied
s
u
n
s
h
in
e
s
itu
atio
n
s
an
d
h
o
w
r
e
liab
le
it is
at
v
ar
io
u
s
ir
r
ad
ian
c
e
lev
els.
3
.
2
.
DC
t
o
DC
bo
o
s
t
co
nv
er
t
er
T
h
e
c
o
n
v
e
r
te
r
is
a
s
i
g
n
if
ica
n
t
s
tag
e
b
e
twe
en
b
o
t
h
th
e
PV
p
a
n
els
a
n
d
t
h
e
i
n
v
e
r
te
r
.
T
h
e
b
o
o
s
t
co
n
v
e
r
t
er
h
e
r
e
h
as
t
o
r
a
is
e
th
e
PV
o
u
tp
u
t
v
o
lt
a
g
e
t
o
v
al
u
es
o
f
i
n
v
e
r
t
er
i
n
p
u
t
v
o
lt
ag
e
a
n
d
i
n
t
h
is
s
t
a
g
e
,
t
h
e
MPP
T
c
o
n
t
r
o
ll
er
is
d
esi
g
n
t
o
p
r
o
v
i
d
e
a
s
u
it
ab
le
d
u
t
y
r
ati
o
(
D
)
t
o
t
h
e
c
o
n
v
e
r
te
r
to
ex
tr
ac
t
m
ax
im
u
m
p
o
w
e
r
f
r
o
m
PV
p
a
n
els
d
u
r
i
n
g
th
e
d
a
y
,
as s
h
o
w
n
i
n
Fi
g
u
r
e
4
.
T
h
e
p
a
r
am
ete
r
o
f
s
u
ch
a
c
o
n
v
e
r
te
r
i
n
t
h
is
w
o
r
k
is
s
h
o
wn
i
n
T
ab
l
e
2
.
I
n
o
r
d
e
r
to
m
ax
im
ize
th
e
PV
s
y
s
tem
's
p
o
wer
an
d
ac
h
iev
e
o
p
tim
al
p
er
f
o
r
m
an
ce
,
m
a
x
im
u
m
p
o
wer
p
o
in
t
tr
ac
k
in
g
is
a
n
ec
ess
ar
y
p
r
er
eq
u
is
ite.
B
ec
au
s
e
o
f
its
f
u
n
d
am
e
n
tal
s
tr
u
ctu
r
e,
a
n
u
m
b
e
r
o
f
r
esear
ch
er
s
h
av
e
u
s
ed
th
e
p
er
tu
r
b
atio
n
an
d
o
b
s
er
v
atio
n
(
P&
O)
an
d
i
n
cr
em
e
n
tal
co
n
n
ec
tiv
ity
(
I
C
)
m
eth
o
d
s
f
o
r
MPPT
m
o
d
elin
g
.
C
o
m
p
ar
ed
to
th
e
P&
O
MPPT
m
eth
o
d
,
th
e
I
C
-
MPPT
alg
o
r
ith
m
ca
n
tr
ac
k
ch
an
g
i
n
g
co
n
d
itio
n
s
m
o
r
e
q
u
ick
ly
;
h
o
wev
er
,
it
r
eq
u
ir
es
a
co
s
tly
an
d
co
m
p
lex
c
o
n
tr
o
ller
a
n
d
g
en
er
ates
s
o
m
ewh
at
u
n
s
tead
y
o
u
tp
u
t
p
o
wer
.
I
n
co
n
tr
ast,
th
e
P&
O
alg
o
r
ith
m
'
s
o
u
tp
u
t
p
o
wer
v
ar
ies
ar
o
u
n
d
MPPT.
A
p
er
tu
r
b
a
n
d
o
b
s
er
v
e
(
P&
O)
c
o
n
tr
o
l
alg
o
r
ith
m
is
p
r
o
p
o
s
ed
in
th
is
s
tu
d
y
.
I
t
r
eq
u
ir
es f
ewe
r
p
ar
am
e
ter
s
,
is
in
ex
p
en
s
iv
e,
s
im
p
le
to
d
ep
lo
y
,
a
n
d
r
ea
d
ily
ad
ap
tab
le
to
in
cr
ea
s
e
ef
f
icien
c
y
.
I
t
is
n
ec
ess
ar
y
to
m
ain
tain
th
e
o
p
er
atin
g
p
o
in
t
(
v
o
ltag
e
an
d
cu
r
r
en
t
)
o
f
th
e
PV
ar
r
ay
at
th
e
m
ax
im
u
m
p
o
wer
p
o
in
t
(
MPP)
b
y
m
o
d
if
y
in
g
th
e
d
u
ty
r
atio
o
f
th
e
b
o
o
s
t
co
n
v
e
r
ter
u
s
in
g
th
e
P&
O
tech
n
iq
u
e.
T
h
is
is
b
ec
au
s
e
th
e
co
n
tin
u
o
u
s
v
ar
iatio
n
o
f
ir
r
a
d
ia
n
ce
th
r
o
u
g
h
o
u
t
th
e
d
ay
r
e
s
u
lts
in
s
u
p
p
ly
a
d
ju
s
tab
le
v
alu
es o
f
b
o
th
v
o
ltag
e
an
d
cu
r
r
en
t f
r
o
m
PV c
ells
.
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
6
11
16
2
7
12
17
3
8
13
18
4
9
14
19
5
10
15
20
Fig
u
r
e
2
.
(
5
*
4
)
PV p
an
el
s
y
s
te
m
Fig
u
r
e
3
.
I
-
V
an
d
P
-
V
cu
r
v
es
o
f
PV p
an
el
at
ir
r
ad
ian
ce
o
f
5
0
0
an
d
1
0
0
0
W
/m
2
T
ab
le
1
.
PV p
an
el
p
ar
am
eter
s
(PV
p
a
n
e
l
)
p
a
r
a
me
t
e
r
V
a
l
u
e
M
a
x
i
m
u
m
p
o
w
e
r
(
P
M
A
X
)
2
5
0
.
0
0
2
W
V
o
l
t
a
g
e
a
t
ma
x
i
m
u
m
p
o
w
e
r
(
V
m
p
)
3
0
.
6
V
C
u
r
r
e
n
t
a
t
ma
x
i
mu
m
p
o
w
e
r
(
I
mp
)
8
.
1
7
A
O
p
e
n
c
i
r
c
u
i
t
v
o
l
t
a
g
e
(
V
o
c
)
3
7
.
6
2
V
S
h
o
r
t
c
i
r
c
u
i
t
c
u
r
r
e
n
t
(
I
sc)
8
.
5
9
A
Te
mp
e
r
a
t
u
r
e
c
o
e
f
f
i
c
i
e
n
t
o
f
V
o
c
(
K
v
)
-
0
.
3
5
6
4
%/
o
C
Te
mp
e
r
a
t
u
r
e
c
o
e
f
f
i
c
i
e
n
t
o
f
I
sc
(
K
i
)
0
.
0
5
3
7
2
5
%
/
o
C
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
Mit
ig
a
tin
g
mis
ma
tch
p
o
w
er lo
s
s
es in
p
h
o
to
vo
lta
ic
s
ystems
u
n
d
er p
a
r
tia
l
…
(
R
a
g
h
a
d
A
d
ee
b
Oth
ma
n
)
591
Fig
u
r
e
4
.
B
o
o
s
t c
o
n
v
er
ter
with
(
P&
O)
MPPT
alg
o
r
ith
m
T
ab
le
2
.
B
o
o
s
t
co
n
v
er
ter
p
ar
a
m
eter
s
B
o
o
st
c
o
n
v
e
r
t
e
r
p
a
r
a
me
t
e
r
s
V
a
l
u
e
s
I
n
d
u
c
t
a
n
c
e
(
L)
2
.
2
9
4
mH
C
a
p
a
c
i
t
o
r
1
0
0
µ
F
DC
–
l
i
n
k
c
a
p
a
c
i
t
o
r
7
0
0
µ
F
S
w
i
t
c
h
i
n
g
f
r
e
q
u
e
n
c
y
5
k
H
z
3
.
3
.
DC
t
o
AC
inv
er
t
er
W
h
en
o
b
tain
in
g
a
n
AC
p
o
wer
s
ig
n
al
f
r
o
m
r
e
n
ewa
b
le
en
er
g
y
s
o
u
r
ce
s
(
s
u
ch
as
a
b
atter
y
o
r
s
o
lar
p
an
el)
,
th
e
in
v
er
ter
is
th
o
u
g
h
t
to
b
e
t
h
e
m
o
s
t
cr
u
cial
co
m
p
o
n
en
t.
DC
/A
C
in
v
er
ter
s
ca
n
b
e
co
n
f
i
g
u
r
ed
with
a
h
al
f
o
r
co
m
p
lete
H
-
b
r
i
d
g
e
to
p
o
lo
g
y
,
d
ep
en
d
i
n
g
o
n
th
e
g
eo
m
etr
y
o
f
th
e
p
o
we
r
elec
tr
o
n
ic
s
witch
es.
T
h
is
wo
r
k
u
s
ed
s
in
g
le
p
h
ase
u
n
iv
er
s
al
b
r
i
d
g
e
i
n
v
er
ter
with
p
o
wer
o
f
5
k
W
,
in
p
u
t v
o
ltag
e
o
f
4
0
0
v
o
lts
,
an
d
o
u
tp
u
t v
o
ltag
e
2
2
3
v
o
lts
.
T
h
e
in
v
er
ter
co
n
v
er
ts
th
e
DC
b
o
o
s
t
co
n
v
er
ter
v
o
ltag
e
to
an
AC
v
o
ltag
e
ap
p
lied
to
th
e
lo
ad
.
T
h
e
m
ain
cir
cu
it o
f
th
e
two
-
s
tag
e
lo
ad
-
c
o
n
n
ec
ted
PV sy
s
tem
is
d
escr
ib
ed
in
Fig
u
r
e
5
.
Fig
u
r
e
5
.
PV
s
y
s
tem
m
o
d
el
i
n
MA
T
L
AB
4.
P
V
A
RRAY
U
ND
E
R
P
AR
T
I
AL
S
H
A
DING
T
h
e
s
y
s
tem
o
f
s
o
lar
ce
lls
ca
n
p
r
o
v
id
e
s
u
f
f
icien
t
am
o
u
n
t
o
f
en
er
g
y
f
o
r
h
o
m
e
ap
p
licatio
n
i
n
s
tan
d
ar
d
u
n
if
o
r
m
ir
r
ad
ian
ce
co
n
d
itio
n
s
.
T
h
is
k
in
d
o
f
en
er
g
y
ca
n
b
e
af
f
ec
ted
d
ir
ec
tly
b
y
s
h
ad
i
n
g
co
n
d
itio
n
s
an
d
its
d
u
r
atio
n
d
u
r
in
g
th
e
d
a
y
.
Ob
v
i
o
u
s
ly
,
th
e
s
o
lar
ar
r
a
y
is
ex
p
o
s
ed
to
s
h
ad
o
w,
wh
ic
h
n
eg
ativ
e
ly
af
f
ec
ts
th
e
s
o
lar
p
an
el
elec
tr
ical
p
o
we
r
o
u
tp
u
t.
A
PV
ar
r
a
y
ty
p
ically
co
n
s
is
ts
o
f
m
an
y
m
o
d
u
les
co
n
n
ec
ted
t
o
o
n
e
a
n
o
th
er
in
b
o
th
s
er
ies
an
d
p
ar
allel
co
n
f
ig
u
r
atio
n
s
.
PV
ar
r
ay
s
ar
e
s
aid
to
b
e
u
n
d
er
p
h
o
to
v
o
ltaic
s
h
ad
e
co
n
tr
o
l
if
m
an
y
ce
lls
in
s
id
e
a
m
o
d
u
le
ar
e
s
h
ad
ed
.
Par
tial
s
h
ad
in
g
lo
wer
s
th
e
cu
r
r
en
t
f
o
r
PV
ce
ll
s
th
at
ar
e
s
h
ad
ed
wh
ile
p
r
o
d
u
cin
g
h
i
g
h
cu
r
r
en
ts
f
o
r
th
e
o
th
er
u
n
s
h
a
d
e
d
ce
lls
s
in
ce
ea
c
h
PV
ce
ll'
s
cu
r
r
en
t
with
in
a
m
o
d
u
le
is
d
ep
en
d
en
t
o
n
th
e
s
u
n
'
s
b
r
ig
h
tn
ess
.
As
d
em
o
n
s
tr
ated
in
Fig
u
r
e
6
,
th
e
ce
lls
u
n
d
er
s
h
a
d
in
g
f
u
n
ctio
n
i
n
th
e
r
e
v
er
s
e
b
i
as
zo
n
e
an
d
m
ain
tain
th
e
s
am
e
cu
r
r
en
t
as
th
e
n
o
n
-
s
h
ad
ed
m
o
d
u
les
s
in
ce
th
e
cu
r
r
e
n
t
f
lo
w
th
r
o
u
g
h
ev
e
r
y
m
o
d
u
le
c
o
n
n
ec
ted
in
s
er
ies
m
u
s
t b
e
eq
u
al.
T
h
e
r
ev
er
s
e
v
o
ltag
e
ac
r
o
s
s
th
e
PV
m
o
d
u
le'
s
ce
ll
s
ca
u
s
es
th
em
to
ab
s
o
r
b
en
e
r
g
y
wh
e
n
th
ey
a
r
e
s
h
ad
ed
.
As
a
r
esu
lt,
th
e
ar
r
ay
'
s
o
u
tp
u
t
p
o
wer
is
d
ec
r
ea
s
ed
.
T
h
is
en
er
g
y
is
tr
an
s
f
o
r
m
ed
in
to
h
ea
t,
wh
i
ch
co
u
ld
lead
to
th
e
s
h
ad
o
wed
ce
lls
'
th
er
m
al
b
r
ea
k
d
o
wn
an
d
th
e
cr
ea
tio
n
o
f
a
h
o
ts
p
o
t.
T
h
e
PV
s
tr
in
g
th
at
is
s
h
ad
ed
m
ay
h
av
e
an
o
p
en
cir
cu
it
d
u
e
to
ce
ll
b
r
ea
k
d
o
wn
b
r
o
u
g
h
t
o
n
b
y
t
h
is
ty
p
e
o
f
h
ea
t
b
r
ea
k
d
o
wn
.
W
ith
b
y
p
ass
d
io
d
es,
th
is
h
o
ts
p
o
t
ef
f
ec
t
ca
n
b
e
av
o
id
ed
.
B
y
p
ass
d
io
d
es
ar
e
u
s
ed
to
s
to
p
n
eg
ativ
e
v
o
ltag
e
f
r
o
m
m
an
if
esti
n
g
.
T
h
e
m
ain
r
ea
s
o
n
s
f
o
r
p
ar
tial sh
ad
in
g
o
cc
u
r
r
e
n
ce
ca
n
lis
t a
s
f
o
llo
ws
[
2
5
]
,
[
2
6
]
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
14
,
No
.
3
,
Sep
tem
b
er
20
25
:
5
8
8
-
599
592
i)
Ph
y
s
ical
o
b
s
tacle
s
:
n
ea
r
b
y
b
u
i
ld
in
g
o
b
jects,
tr
ee
s
,
o
r
s
tr
u
ctu
r
es
th
at
ca
s
t
th
eir
s
h
ad
o
ws
o
n
t
h
e
s
o
lar
p
a
n
els.
I
t
is
p
o
s
s
ib
le
f
o
r
th
e
s
h
ad
in
g
to
b
e
co
m
p
lete
o
r
p
ar
tial,
as
th
is
s
itu
atio
n
is
lik
ely
to
o
cc
u
r
at
a
ce
r
tain
tim
e
o
f
th
e
d
ay
.
ii)
Mo
d
u
le
m
is
m
atch
:
E
v
er
y
PV
s
y
s
tem
m
ay
co
n
s
is
t
o
f
m
an
y
PV
p
an
els
co
n
n
ec
ted
i
n
s
er
ies
to
r
ea
ch
th
e
d
esire
d
v
o
ltag
e,
i
f
s
h
ad
i
n
g
h
ap
p
en
ed
o
n
e
p
a
n
el,
th
e
n
t
h
e
s
tr
in
g
p
er
f
o
r
m
an
ce
will
b
e
af
f
ec
ted
wh
er
e
t
h
e
s
tr
in
g
cu
r
r
en
t
will b
e
lim
ited
to
a
v
alu
e
o
f
th
e
cu
r
r
en
t
o
f
th
e
w
ea
k
est p
an
el
th
at
was m
o
s
t e
x
p
o
s
ed
to
th
e
s
h
ad
o
w.
iii)
C
ell
co
n
f
ig
u
r
atio
n
:
T
h
e
c
o
n
f
ig
u
r
atio
n
o
f
s
o
lar
p
an
els
is
u
s
u
ally
co
n
s
is
tin
g
s
m
all
ce
lls
an
d
if
s
h
ad
in
g
tak
en
p
lace
o
n
s
in
g
le
o
r
m
o
r
e
ce
lls
th
at’
s
lead
to
r
ed
u
ctio
n
in
p
an
e
l o
u
tp
u
t
p
o
wer
.
A
well
k
n
o
win
g
o
f
s
u
ch
ca
u
s
es
ca
n
g
u
i
d
e
r
esear
ch
e
r
s
to
d
esig
n
PV
s
y
s
tem
s
th
at
ar
e
m
o
r
e
r
esil
ien
t
to
p
ar
tial
s
h
ad
in
g
an
d
m
ax
im
izin
g
th
eir
o
v
er
all
e
f
f
icien
cy
an
d
e
n
er
g
y
p
r
o
d
u
ctio
n
.
Par
tial
s
h
ad
i
n
g
ca
u
s
es
r
ed
u
ctio
n
in
ef
f
icien
cy
o
f
PV
s
y
s
tem
.
T
h
e
s
h
ad
ed
ce
lls
p
r
o
d
u
ce
less
p
o
wer
th
an
th
e
u
n
s
h
a
d
ed
ce
lls
,
wh
ich
lead
s
to
r
ed
u
ce
th
e
o
v
e
r
all
o
u
tp
u
t
p
o
wer
o
f
P
V
s
y
s
tem
.
Sev
er
al
m
itig
atio
n
s
tr
ateg
ies
h
av
e
b
ee
n
s
u
g
g
ested
to
r
ed
u
ce
th
e
im
p
ac
t
o
f
s
h
ad
in
g
;
PV
s
y
s
tem
s
ca
n
b
e
co
n
s
tr
u
cted
with
b
y
p
ass
d
io
d
es,
o
p
tim
u
m
co
n
f
ig
u
r
a
tio
n
o
f
PV
p
an
els,
o
r
ev
e
n
with
m
icr
o
-
in
v
e
r
ter
s
th
at
m
an
ag
e
ea
ch
p
a
n
el
in
d
e
p
en
d
e
n
tly
[
2
5
]
,
[
2
7
]
.
I
n
th
is
wo
r
k
,
m
u
lti
ca
s
es
o
f
s
h
ad
in
g
(
with
a
s
h
ed
ir
r
ad
ian
ce
o
f
5
0
0
W
/m
2
)
o
n
th
e
PV
ar
r
ay
s
y
s
tem
h
as
b
ee
n
s
u
g
g
ested
as
s
h
o
wn
in
F
ig
u
r
e
7
.
First
ca
s
e
1
,
th
e
s
h
ad
in
g
ac
cr
u
es
o
n
th
e
f
ir
s
t
lef
t
co
lu
m
n
o
f
PV
s
y
s
tem
ar
r
ay
.
T
h
e
s
ec
o
n
d
ca
s
e
2
o
f
s
h
ad
in
g
is
o
n
th
e
c
o
m
p
lete
u
p
p
e
r
r
o
w
o
f
th
e
s
y
s
tem
.
A
ca
s
e
o
f
s
p
o
tted
s
h
ad
ca
s
e
3
is
s
u
g
g
ested
to
b
e
o
n
th
e
m
id
d
le
o
f
PV
s
y
s
tem
with
6
s
h
ad
ed
p
an
els.
W
h
ile
ca
s
e
4
d
escr
ib
ed
th
e
s
h
ad
in
g
o
n
two
co
r
n
e
r
s
o
f
th
e
s
y
s
tem
o
n
e
o
f
th
em
is
th
e
u
p
p
er
r
ig
h
t
co
r
n
er
an
d
th
e
o
th
er
o
n
e
is
its
o
p
p
o
s
ite.
T
h
e
last
ca
s
e
is
a
r
an
d
o
m
s
elec
tio
n
o
f
8
m
o
d
u
les
to
b
e
s
h
ad
e
d
,
a
n
d
t
h
e
m
o
d
u
les
ar
e
(
2
,
4,
8,
11,
1
4
,
16,
18
,
an
d
2
0
)
.
T
est
s
u
ch
ca
s
es
p
r
o
v
id
e
in
d
icatio
n
h
o
w
th
e
s
y
s
tem
is
p
er
f
o
r
m
e
d
u
n
d
er
th
ese
s
h
a
d
in
g
ca
s
es.
Mo
s
t
im
p
o
r
tan
t
s
ig
n
s
to
m
ea
s
u
r
e
th
e
p
er
f
o
r
m
a
n
ce
o
f
PV sy
s
tem
ex
p
lain
as
f
o
llo
ws
[
8
]
,
[
1
8
]
.
Fig
u
r
e
6
.
On
e
s
o
lar
ce
ll is
s
h
ad
ed
wh
en
a
b
y
p
ass
d
io
d
e
is
co
n
n
ec
ted
in
p
ar
allel
with
th
em
Fig
u
r
e
7
.
Sev
er
al
p
atter
n
s
o
f
s
h
ad
in
g
o
n
th
e
PV sy
s
tem
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
Mit
ig
a
tin
g
mis
ma
tch
p
o
w
er lo
s
s
es in
p
h
o
to
vo
lta
ic
s
ystems
u
n
d
er p
a
r
tia
l
…
(
R
a
g
h
a
d
A
d
ee
b
Oth
ma
n
)
593
4
.
1
.
M
is
m
a
t
ch
lo
s
s
(
M
L
)
PP
S
C
r
ep
r
esen
ts
th
e
p
o
wer
g
en
er
atio
n
at
s
p
ec
if
ic
PS
C
s
,
wh
ile
Pm
p
is
th
e
f
r
ac
tio
n
o
f
d
if
f
er
en
ce
b
etwe
en
th
e
m
ax
im
u
m
p
o
wer
g
en
e
r
atio
n
u
n
d
e
r
u
n
if
o
r
m
ir
r
ad
ian
ce
co
n
d
itio
n
s
.
T
h
e
g
lo
b
a
l
m
ax
im
u
m
p
o
wer
p
o
in
t
(
GM
PP
)
at
ea
ch
PS
C
's
m
ax
im
u
m
v
o
ltag
e
(
Vm
p
)
an
d
m
ax
im
u
m
c
u
r
r
e
n
t
(
I
m
p
)
ca
n
b
e
m
u
ltip
lied
t
o
d
eter
m
in
e
th
e
PP
SC
.
=
−
×
100
(
1
)
4
.
2
.
F
ill f
a
ct
o
r
(
F
F
)
Dete
r
m
in
in
g
th
e
o
u
tp
u
t
ef
f
icie
n
cy
o
f
s
o
lar
PV
s
y
s
tem
s
u
n
d
e
r
n
o
n
-
h
o
m
o
g
e
n
eo
u
s
(
p
ar
tial
s
h
ad
o
win
g
)
ir
r
ad
iatio
n
c
o
n
d
itio
n
s
is
co
n
n
ec
ted
to
th
e
FF
p
ar
am
eter
.
T
h
e
FF
o
f
a
s
o
lar
PV
s
y
s
tem
is
d
ef
in
e
d
as
t
h
e
p
er
ce
n
tag
e
o
f
m
a
x
im
u
m
elec
tr
ical
o
u
tp
u
t
p
o
wer
g
en
er
ate
d
i
n
a
n
o
n
-
h
o
m
o
g
e
n
eo
u
s
i
r
r
a
d
iatio
n
s
ce
n
ar
i
o
to
m
ax
im
u
m
r
ate
d
ca
p
ac
ity
.
=
(
∗
)
∗
×
100
(
2
)
I
n
(
2
)
,
V
OC
an
d
I
SC
r
ep
r
esen
t
th
e
o
p
en
cir
c
u
it
v
o
ltag
e
o
f
PV
a
r
r
ay
an
d
s
h
o
r
t
cir
c
u
it
cu
r
r
en
t
o
f
PV
a
r
r
ay
,
r
esp
ec
tiv
ely
.
4
.
3
.
P
er
f
o
r
m
a
nce
ra
t
i
o
(
P
R)
PR
is
d
ef
in
ed
as
th
e
m
ax
im
u
m
g
en
er
ated
o
u
tp
u
t
p
o
wer
d
u
r
in
g
a
n
o
n
-
h
o
m
o
g
en
e
o
u
s
(
p
ar
ti
al
s
h
ad
in
g
)
ir
r
ad
iatio
n
s
itu
atio
n
.
I
t
is
co
m
p
ar
ed
to
th
e
m
a
x
im
u
m
g
e
n
er
at
ed
o
u
tp
u
t
p
o
wer
d
u
r
in
g
a
h
o
m
o
g
en
eo
u
s
(
u
n
if
o
r
m
)
ir
r
ad
iatio
n
s
itu
atio
n
.
=
(
−
ℎ
)
(
ℎ
)
×
100
(
3
)
T
h
e
p
er
f
o
r
m
an
ce
r
atio
(
PR
)
i
s
an
im
p
o
r
tan
t
in
d
icato
r
f
o
r
e
v
alu
atin
g
th
e
e
f
f
icien
cy
o
f
a
s
o
lar
s
y
s
tem
u
n
d
er
r
ea
lis
tic
o
p
er
atin
g
c
o
n
d
itio
n
s
,
esp
ec
ially
wh
en
th
er
e
is
p
ar
ti
al
s
h
ad
in
g
.
I
t
h
elp
s
c
o
m
p
ar
e
s
y
s
tem
p
er
f
o
r
m
an
ce
u
n
d
er
v
a
r
y
in
g
co
n
d
itio
n
s
with
id
ea
l
ir
r
ad
ian
ce
,
r
ev
ea
lin
g
p
o
te
n
tial
o
p
er
atio
n
al
lo
s
s
es.
I
t
i
s
al
s
o
u
s
ed
to
o
p
tim
ize
th
e
d
esig
n
an
d
m
ain
ten
a
n
ce
o
f
s
o
lar
s
y
s
tem
s
to
en
s
u
r
e
th
e
h
i
g
h
est p
o
s
s
ib
le
o
u
tp
u
t.
5.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
o
ev
alu
ate
th
e
p
er
f
o
r
m
an
ce
o
f
a
two
-
s
tag
e
h
o
m
e
(
5
×
4
)
PV
s
y
s
tem
,
a
to
p
o
lo
g
ical
SP
w
as
p
r
o
p
o
s
ed
,
an
d
th
e
ch
ar
ac
te
r
is
tics
o
f
th
is
s
y
s
tem
wer
e
test
ed
u
n
d
er
d
if
f
er
en
t
p
a
r
tial
s
h
ad
in
g
co
n
d
itio
n
s
an
d
th
e
ef
f
ec
t
o
f
th
ese
co
n
d
itio
n
s
o
n
t
h
e
p
e
r
f
o
r
m
an
ce
o
f
th
e
en
tir
e
s
y
s
tem
w
as
o
b
s
er
v
ed
.
T
h
is
s
y
s
tem
was
im
p
lem
en
ted
u
s
in
g
MA
T
L
AB
/S
im
u
lin
k
.
Fro
m
th
e
s
im
u
latio
n
r
esu
lt,
as
s
h
o
wn
i
n
T
ab
le
3
,
we
n
o
te
th
e
o
u
tp
u
t
o
f
th
e
p
h
o
to
v
o
ltaic
ar
r
ay
u
n
d
er
s
tan
d
ar
d
c
o
n
d
itio
n
s
an
d
its
o
u
tp
u
t u
n
d
er
th
e
in
f
l
u
en
ce
o
f
m
u
ltip
le
ca
s
es o
f
p
ar
ti
al
s
h
ad
in
g
.
I
n
d
if
f
er
e
n
t
p
ar
tial
s
h
ad
in
g
ca
s
es,
we
ab
s
o
r
p
tio
n
th
at
th
e
ca
p
ac
ity
o
f
th
e
p
h
o
to
v
o
ltaic
s
y
s
tem
is
n
o
t
af
f
ec
ted
,
ex
ce
p
t
f
o
r
th
e
ca
s
e
1
,
wh
ich
led
to
a
r
ed
u
ctio
n
i
n
th
e
s
h
o
r
t
cir
cu
it
cu
r
r
en
t
(
I
s
.
c)
o
f
th
e
s
y
s
tem
to
(
3
0
.
2
9
5
5
A)
d
u
e
to
th
e
ef
f
ec
t
o
f
p
ar
tial
s
h
ad
in
g
o
n
an
e
n
tire
co
lu
m
n
(
5
p
a
n
el)
with
a
v
alu
e
o
f
(
I
r
=
5
0
0
W
/m
2
)
.
Fig
u
r
e
8
s
h
o
ws
th
e
(
P
-
V
)
c
h
ar
ac
ter
is
tic
o
f
PV
ar
r
ay
u
n
d
e
r
v
ar
io
u
s
p
ar
tial
s
h
ad
in
g
co
n
d
itio
n
s
;
we
n
o
tice
a
d
ec
r
ea
s
e
in
th
e
v
alu
e
o
f
th
e
m
a
x
im
u
m
p
o
wer
p
r
o
v
id
ed
b
y
th
e
p
h
o
to
v
o
ltaic
s
y
s
tem
f
r
o
m
its
v
alu
e
u
n
d
e
r
s
tan
d
ar
d
co
n
d
itio
n
s
(
4
9
8
1
.
8
1
W
)
wh
en
ex
p
o
s
ed
to
v
ar
io
u
s
p
ar
tial
s
h
ad
in
g
s
itu
atio
n
s
.
W
h
en
th
e
PV a
r
r
ay
is
o
p
er
atin
g
at
s
tan
d
ar
d
test
co
n
d
itio
n
(
STC)
(
u
n
if
o
r
m
ir
r
ad
ian
ce
c
o
n
d
itio
n
)
,
th
e
(
P
–
V)
ch
a
r
ac
ter
is
tics
cu
r
v
e
o
f
th
e
ar
r
ay
ex
h
ib
its
a
s
in
g
le
m
ax
im
u
m
p
o
wer
p
o
in
t.
b
u
t,
d
u
r
in
g
p
ar
tial
s
h
ad
in
g
co
n
d
itio
n
s
,
th
e
(
P
-
V
)
c
u
r
v
es
s
h
o
w
a
m
o
r
e
co
m
p
licated
ch
ar
ac
ter
ize
d
b
y
s
ev
er
al
lo
ca
l
an
d
o
n
e
g
lo
b
al
m
ax
im
u
m
p
o
wer
p
o
in
t.
T
h
e
r
esu
lts
s
h
o
w
th
at
th
e
n
u
m
b
er
o
f
p
an
els
ex
p
o
s
ed
to
p
ar
tial
s
h
ad
in
g
an
d
th
eir
l
o
ca
tio
n
p
lay
a
n
im
p
o
r
tan
t
r
o
le
in
th
e
d
ec
r
ea
s
e
th
at
o
cc
u
r
s
in
th
e
v
alu
e
o
f
th
e
m
ax
im
u
m
p
o
wer
o
f
th
e
p
h
o
to
v
o
ltaic
s
y
s
t
em
.
I
n
ca
s
es
4
an
d
5
,
p
ar
tial
s
h
ad
in
g
o
cc
u
r
r
e
d
o
n
th
e
s
am
e
n
u
m
b
er
o
f
m
o
d
els
(
8
p
an
els).
T
h
e
g
lo
b
al
m
ax
im
u
m
p
o
wer
p
o
i
n
t
in
ca
s
e
4
d
ec
r
e
ased
b
y
(
4
1
%)
f
r
o
m
its
v
alu
e
in
STC,
wh
ile
th
e
g
l
o
b
al
m
a
x
im
u
m
p
o
wer
in
ca
s
e
5
d
ec
r
ea
s
ed
b
y
(
4
4
.
8
%)
f
r
o
m
th
eir
v
alu
es
in
STC
d
u
e
to
th
e
d
if
f
er
e
n
ce
in
th
e
lo
c
atio
n
s
o
f
th
e
m
o
d
els u
n
d
er
th
e
in
f
lu
en
ce
o
f
p
a
r
tial sh
ad
in
g
.
Fo
r
th
e
p
er
f
o
r
m
an
ce
an
al
y
s
is
o
f
th
e
PV
ar
r
ay
ch
ar
ac
ter
is
tic
u
n
d
er
a
p
a
r
tial
s
h
ad
in
g
s
itu
atio
n
,
s
ev
er
al
f
ac
to
r
s
o
f
FF
,
ML
,
an
d
PR
wer
e
r
elied
u
p
o
n
.
A
PV
ar
r
a
y
o
f
s
ize
(
5
×4
)
p
r
o
d
u
ce
s
less
o
u
tp
u
t
p
o
wer
.
T
h
e
PV
ar
r
ay
'
s
in
cr
ea
s
ed
p
o
wer
lo
s
s
is
th
e
ca
u
s
e
o
f
t
h
is
d
r
o
p
p
ed
o
u
tp
u
t p
o
wer
.
As s
ee
n
in
Fig
u
r
e
9
,
th
is
ty
p
e
o
f
p
o
wer
lo
s
s
is
ex
p
r
ess
ed
as
ML
.
T
h
e
k
in
d
o
f
s
h
ad
in
g
p
atter
n
h
as
a
s
ig
n
if
ican
t
im
p
ac
t
o
n
ML
.
Du
r
in
g
STCs
,
th
e
ML
was
n
ea
r
ly
ze
r
o
,
th
e
least
ML
as
1
2
.
4
%
was
f
o
u
n
d
in
ca
s
e
1
with
s
in
g
le
GM
P
P
at
4
3
6
2
.
1
7
W
,
th
e
wo
r
s
t
ca
s
e
is
at
ca
s
e
5
with
g
lo
b
al
m
ax
p
o
wer
p
o
in
t a
s
2
7
4
9
.
4
9
W
,
wh
e
r
e
th
e
ML
in
cr
ea
s
ed
t
o
4
4
.
8
%.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
14
,
No
.
3
,
Sep
tem
b
er
20
25
:
5
8
8
-
599
594
Fig
u
r
e
1
0
s
h
o
ws
th
e
ef
f
ec
t
o
f
d
if
f
er
en
t
p
a
r
tial
s
h
ad
in
g
co
n
d
itio
n
s
o
n
th
e
f
ill
f
ac
t
o
r
(
FF
)
o
f
a
PV
s
y
s
tem
.
I
n
th
e
n
o
r
m
al
s
tate
(
n
o
s
h
ad
i
n
g
)
,
th
e
f
ill
f
ac
to
r
r
ea
c
h
es
its
h
ig
h
est
v
alu
e
at
7
6
.
5
%
.
W
ith
s
h
ad
in
g
ap
p
lied
to
ce
r
tain
co
lu
m
n
s
o
r
r
o
ws,
th
e
f
ill
f
ac
to
r
g
r
ad
u
ally
d
ec
r
ea
s
es,
r
ea
ch
in
g
6
7
%
f
o
r
co
l
u
m
n
s
h
a
d
in
g
a
n
d
6
0
.
8
%
f
o
r
r
o
w
s
h
ad
in
g
.
Per
f
o
r
m
an
ce
d
et
er
io
r
ates
f
u
r
t
h
er
with
s
h
a
d
in
g
at
th
e
ce
n
ter
o
r
co
r
n
er
s
,
r
ea
c
h
in
g
its
lo
west
v
alu
e
with
r
an
d
o
m
s
h
a
d
in
g
at
4
2
.
2
%.
T
h
e
f
i
g
u
r
e
d
em
o
n
s
tr
ates
th
at
th
e
s
h
a
d
in
g
p
atter
n
an
d
l
o
ca
tio
n
s
ig
n
if
ica
n
tly
im
p
ac
t th
e
ef
f
icien
c
y
o
f
a
PV sy
s
tem
,
n
ec
ess
itatin
g
th
e
d
esig
n
o
f
s
y
s
tem
s
th
at
m
in
im
ize
th
e
ef
f
ec
t o
f
s
h
a
d
in
g
,
as sh
o
wn
in
Fig
u
r
e
1
0
.
Fig
u
r
e
1
1
s
h
o
ws
th
e
ef
f
ec
t
o
f
d
if
f
er
en
t
p
a
r
tial
s
h
ad
in
g
co
n
d
i
tio
n
s
o
n
th
e
p
er
f
o
r
m
a
n
ce
r
atio
(
PR
)
o
f
a
p
h
o
to
v
o
ltaic
s
y
s
tem
.
Un
d
er
n
o
r
m
al
co
n
d
itio
n
s
,
with
o
u
t
s
h
ad
i
n
g
,
th
e
s
y
s
tem
ac
h
ie
v
es
a
p
ea
k
p
er
f
o
r
m
an
ce
r
atio
o
f
1
0
0
%.
W
ith
p
ar
tial
s
h
ad
in
g
,
th
is
r
atio
g
r
ad
u
ally
d
ec
r
ea
s
es
,
r
ea
ch
in
g
8
7
.
5
%
f
o
r
s
in
g
le
-
co
lu
m
n
s
h
ad
in
g
an
d
7
9
.
4
%
f
o
r
s
in
g
le
-
r
o
w
s
h
ad
in
g
.
T
h
e
PR
d
ec
r
ea
s
es
f
u
r
th
er
wh
e
n
th
e
ce
n
ter
o
r
co
r
n
er
s
ar
e
s
h
ad
ed
,
r
ea
c
h
in
g
5
8
.
9
%
an
d
5
5
.
1
9
%
f
o
r
r
an
d
o
m
s
h
ad
in
g
.
T
h
e
f
ig
u
r
e
d
em
o
n
s
tr
ates
th
at
s
h
ad
in
g
d
is
tr
ib
u
tio
n
d
ir
e
ctly
af
f
ec
ts
th
e
ef
f
icien
cy
o
f
a
p
h
o
to
v
o
ltaic
s
y
s
tem
,
an
d
th
e
m
o
r
e
ir
r
eg
u
la
r
th
e
s
h
ad
in
g
o
r
th
e
m
o
r
e
cr
itic
al
ar
ea
s
,
th
e
g
r
ea
ter
th
e
p
er
f
o
r
m
an
ce
l
o
s
s
.
T
ab
le
3
.
PV a
r
r
a
y
p
ar
a
m
eter
s
u
n
d
er
p
ar
tial sh
ad
in
g
ca
s
es
P
a
r
t
i
a
l
s
h
a
d
i
n
g
c
a
se
s
V
o.
c
(V)
I
s
.
c
(A)
V
max
(V)
I
max
(A)
P
max
(W)
S
TC
c
o
n
d
i
t
i
o
n
1
8
8
3
4
.
6
1
5
2
.
9
1
8
3
2
.
5
7
4
9
8
1
.
8
1
C
a
se
1
:
P
SC
a
t
c
o
l
u
m
n
1
1
8
8
3
0
.
2
9
5
5
1
5
2
.
9
5
8
2
8
.
5
1
8
4
3
6
2
.
1
7
C
a
se
2
:
P
SC
a
t
r
o
w
1
1
8
8
3
4
.
6
2
1
6
1
2
1
.
4
3
7
3
2
.
5
9
3
9
5
8
.
5
6
C
a
se
3
:
P
S
C
a
t
c
e
n
t
e
r
1
8
8
3
4
.
6
1
7
6
1
5
5
.
2
2
8
2
4
.
5
1
3
8
0
5
.
2
1
C
a
se
4
:
P
S
C
a
t
c
o
r
n
e
r
s
1
8
8
3
4
.
6
1
8
3
8
9
.
9
1
5
4
3
2
.
6
4
2
9
3
5
.
2
C
a
se
5
:
P
S
C
a
t
r
a
n
d
o
m
1
8
8
3
4
.
6
1
7
4
1
6
3
.
9
4
2
1
6
.
7
7
2
7
4
9
.
4
9
Fig
u
r
e
8
.
P
-
V
ch
a
r
ac
ter
is
tic
u
n
d
er
p
a
r
tial sh
ad
in
g
ca
s
es
Fig
u
r
e
9
.
Mism
atch
lo
s
s
f
o
r
p
a
r
tial sh
ad
in
g
ca
s
es
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
Mit
ig
a
tin
g
mis
ma
tch
p
o
w
er lo
s
s
es in
p
h
o
to
vo
lta
ic
s
ystems
u
n
d
er p
a
r
tia
l
…
(
R
a
g
h
a
d
A
d
ee
b
Oth
ma
n
)
595
Fig
u
r
e
1
0
.
Fil
l
f
ac
to
r
lo
s
s
f
o
r
p
ar
tial sh
ad
in
g
ca
s
es
Fig
u
r
e
1
1
.
Per
f
o
r
m
a
n
ce
r
atio
f
o
r
p
ar
tial sh
ad
in
g
ca
s
es
T
h
e
p
h
o
to
v
o
ltaic
s
y
s
tem
was
c
o
n
n
ec
ted
to
t
h
e
s
in
g
le
-
p
h
ase
5
k
W
(
R
-
L
)
h
o
m
e
l
o
ad
.
T
ab
le
4
s
h
o
ws
th
e
ef
f
ec
t
o
f
th
e
v
ar
io
u
s
p
ar
tial
s
h
ad
in
g
s
itu
atio
n
s
at
(
I
r
=
500
W
/m
2
)
.
At
STC,
s
in
ce
th
e
P
V
ar
r
ay
s
y
s
tem
is
o
p
er
atin
g
at
f
u
ll
ca
p
ac
ity
,
th
e
lo
ad
o
p
er
ates
with
a
h
ig
h
ef
f
icien
cy
esti
m
ated
at
9
2
.
1
7
%.
Ho
wev
er
,
wh
en
th
e
PV
ar
r
ay
s
y
s
tem
is
ex
p
o
s
ed
to
d
if
f
er
en
t
ca
s
es
o
f
p
ar
tial
s
h
ad
in
g
,
th
e
lo
ad
p
o
wer
in
th
e
s
y
s
tem
is
af
f
ec
ted
.
Par
tial
s
h
ad
in
g
m
ea
n
s
a
d
ec
r
ea
s
e
in
t
h
e
v
alu
e
o
f
t
h
e
cu
r
r
e
n
t
s
u
p
p
lie
d
b
y
th
e
PV
ar
r
ay
s
y
s
tem
to
th
e
lo
ad
,
as
well
as
a
v
o
ltag
e
d
r
o
p
,
w
h
ich
in
tu
r
n
af
f
ec
ts
th
e
am
o
u
n
t
o
f
p
o
we
r
s
u
p
p
lied
to
th
e
lo
a
d
.
T
h
is
h
as
led
to
a
d
ec
r
ea
s
e
in
th
e
o
v
er
all
e
f
f
icien
cy
o
f
th
e
s
y
s
tem
b
y
d
i
f
f
er
en
t
p
er
ce
n
tag
es
ac
co
r
d
in
g
to
th
e
p
ar
tial
s
h
a
d
in
g
co
n
d
itio
n
to
wh
ich
th
e
s
o
lar
s
y
s
tem
is
ex
p
o
s
ed
.
T
h
r
o
u
g
h
th
e
r
esu
lts
o
b
tain
ed
w
h
en
p
ar
tial
s
h
ad
in
g
was
ap
p
lie
d
,
it
was
f
o
u
n
d
t
h
at
th
e
h
ig
h
est
ef
f
icien
cy
o
f
th
e
s
y
s
tem
was
wh
e
n
p
ar
tial
s
h
ad
in
g
(
I
r
=
5
0
0
W
/m
2
)
was
ap
p
lied
to
o
n
e
c
o
lu
m
n
(
5
p
an
el
s
)
as
8
2
.
8
4
%,
w
h
ile
th
e
wo
r
s
t
an
d
least
eq
u
ip
p
e
d
c
ase
was
wh
en
th
e
s
h
ad
in
g
was
ap
p
lied
to
th
e
c
o
r
n
er
s
a
n
d
r
an
d
o
m
s
h
ad
i
n
g
at
(
8
p
an
els),
wh
er
e
th
e
ef
f
icien
cy
d
ec
r
ea
s
ed
to
a
p
p
r
o
x
im
ately
3
9
.
2
4
%
an
d
4
0
.
6
4
%
r
esp
ec
tiv
e
ly
.
Fig
u
r
e
1
2
s
h
o
ws
th
e
lo
ad
v
o
ltag
e
o
u
tp
u
t,
lo
ad
c
u
r
r
en
t,
an
d
l
o
ad
p
o
wer
at
STC
.
Fig
u
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Evaluation Warning : The document was created with Spire.PDF for Python.