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Driv
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I
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20
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2744
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Ass
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sy
stem config
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tions
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a
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d
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h
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o
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lt
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e
n
u
se
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n
th
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lar
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ll
sy
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m
in
th
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rk
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o
u
r
t
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p
e
s
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u
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p
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ircu
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li
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o
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e
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e
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a
c
t
o
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ri
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s
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V
sy
ste
m
fa
il
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ty
p
e
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n
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s
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e
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rm
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n
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e
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s
e
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p
h
a
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d
in
t
h
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d
y
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ATLAB
is
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se
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),
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a
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1
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s (I
-
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h
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teristics
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th
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TCT
to
p
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l
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g
y
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K
ey
w
o
r
d
s
:
Fau
lt d
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n
o
s
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Gr
o
u
n
d
f
au
lt
Po
wer
v
o
ltag
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r
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PV c
o
n
f
ig
u
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atio
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s
PV p
an
els f
au
lt a
n
aly
s
is
T
h
is i
s
a
n
o
p
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n
a
c
c
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ss
a
rticle
u
n
d
e
r th
e
CC B
Y
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SA
li
c
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se
.
C
o
r
r
e
s
p
o
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ing
A
uth
o
r
:
Om
ar
Sh
ar
af
Al
-
Dee
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Yeh
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a
A
l
-
Yo
zb
ak
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Dep
ar
tm
en
t o
f
E
lectr
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n
g
i
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in
g
,
C
o
lleg
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in
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r
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Un
iv
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ity
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s
u
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aq
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y
eh
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a@
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m
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u
l.e
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u
.
iq
1.
I
NT
RO
D
UCT
I
O
N
T
h
e
g
lo
b
al
r
e
n
ewa
b
le
en
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g
y
m
ar
k
et
h
as
s
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n
tr
em
en
d
o
u
s
tech
n
o
lo
g
ical
ad
v
an
ce
m
e
n
ts
d
u
e
to
th
e
n
eg
ativ
e
clim
ate
im
p
licatio
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s
o
f
f
o
s
s
il
f
u
el
-
b
ased
p
o
wer
f
ac
ilit
ies.
T
h
e
in
cr
ea
s
ed
g
o
v
er
n
m
en
tal
in
ce
n
tiv
es
an
d
o
n
g
o
in
g
tech
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o
l
o
g
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v
a
n
ce
m
en
ts
aim
ed
at
lo
wer
i
n
g
c
ar
b
o
n
f
o
o
tp
r
in
ts
h
av
e
m
ad
e
d
i
s
tr
ib
u
ted
g
e
n
er
atio
n
(
DG)
u
s
in
g
r
en
ewa
b
le
r
eso
u
r
c
es
in
cr
ea
s
in
g
ly
ap
p
ea
lin
g
[
1
]
,
[
2
]
.
T
h
e
wo
r
ld
wid
e
e
n
er
g
y
d
e
m
an
d
p
e
r
p
er
s
o
n
is
r
is
in
g
as
a
r
esu
lt
o
f
th
e
ac
ce
ler
atio
n
o
f
in
d
u
s
tr
ial
ex
p
an
s
io
n
an
d
th
e
o
n
g
o
in
g
r
is
e
in
en
er
g
y
co
n
s
u
m
p
tio
n
.
T
h
is
clea
r
ed
th
e
p
ath
f
o
r
in
-
d
ep
th
s
tu
d
y
o
f
n
o
v
el
g
r
ee
n
p
o
wer
tec
h
n
o
lo
g
ies,
in
clu
d
in
g
g
e
o
th
er
m
al,
b
io
m
ass
,
h
y
d
r
o
,
win
d
,
an
d
s
o
lar
p
o
wer
.
T
h
ese
tech
n
o
lo
g
ies ar
e
s
af
e
a
n
d
s
u
s
t
ain
ab
le.
R
esear
ch
o
n
r
en
ewa
b
le
e
n
er
g
y
tech
n
o
lo
g
y
is
p
r
im
ar
ily
co
n
ce
r
n
e
d
with
co
n
v
er
tin
g
r
en
ewa
b
le
r
eso
u
r
ce
s
in
to
elec
tr
ical
en
e
r
g
y
to
s
u
p
p
o
r
t
co
n
s
u
m
er
lo
ad
s
o
r
th
e
u
tili
ty
g
r
id
[
3
]
.
Ov
er
th
e
p
ast
f
ew
y
ea
r
s
,
th
e
s
o
lar
co
m
p
an
y
h
as
g
r
o
wn
q
u
ick
ly
,
with
p
h
o
to
v
o
ltaic
(
PV)
s
y
s
tem
s
s
ee
in
g
th
e
m
o
s
t
ex
p
an
s
io
n
.
On
e
o
f
th
e
m
o
s
t
im
p
o
r
tan
t
way
s
to
im
p
r
o
v
e
th
e
PV
s
y
s
tem
'
s
life
s
p
an
,
d
ep
en
d
ab
ilit
y
,
an
d
ef
f
icien
c
y
is
to
id
en
tify
an
d
an
ticip
ate
d
if
f
er
e
n
t
d
ef
ec
ts
[
4
]
,
[
5
]
.
PV
m
alf
u
n
cti
o
n
s
,
in
clu
d
in
g
p
ar
tial
s
h
ad
o
win
g
,
b
y
p
ass
-
d
io
d
e
m
alf
u
n
ctio
n
s
,
PV
m
o
d
u
le
d
e
g
r
ad
atio
n
,
an
d
wir
in
g
p
r
o
b
lem
s
,
s
ig
n
if
ican
tly
im
p
ac
t
p
o
wer
o
u
tp
u
t
a
n
d
r
esu
lt
in
d
if
f
er
en
t
p
ea
k
s
in
a
PV
s
y
s
tem
'
s
P
-
V
cu
r
v
es
[
6
]
,
[
7
]
.
A
f
ew
th
in
g
s
n
ee
d
to
b
e
m
ad
e
s
u
r
e
o
f
in
o
r
d
er
to
m
ax
im
ize
th
e
am
o
u
n
t
o
f
e
n
er
g
y
h
a
r
v
ested
b
y
p
h
o
to
v
o
ltaic
s
y
s
tem
s
:
o
p
tim
al
ir
r
ad
ian
ce
lev
els,
lo
w
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
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Po
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&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
A
s
s
es
s
men
t o
f th
e
efficien
cy
a
n
d
p
erfo
r
ma
n
ce
o
f
d
iffer
en
t P
V
s
ystem
…
(
R
a
g
h
a
d
A
d
ee
b
O
th
ma
n
)
2745
tem
p
er
atu
r
es
f
o
r
PV
ce
lls
,
p
r
o
p
er
p
o
s
itio
n
in
g
an
d
o
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ie
n
tatio
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o
f
th
e
p
an
els
t
o
war
d
t
h
e
s
u
n
,
an
d
av
o
id
in
g
ar
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s
o
f
s
h
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e.
T
h
e
d
e
p
en
d
a
b
ilit
y
an
d
ef
f
icien
cy
o
f
th
e
en
tire
PV
in
s
tallatio
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ar
e
lo
wer
ed
b
y
d
i
r
t,
s
n
o
w,
an
d
s
an
d
,
wh
ich
o
b
s
cu
r
e
s
o
lar
ir
r
a
d
iatio
n
.
Fo
r
th
is
r
ea
s
o
n
,
th
e
co
n
n
ec
tio
n
s
b
etwe
en
PV
m
o
d
u
les
an
d
th
e
clea
n
lin
ess
o
f
PV
p
an
els
p
lay
a
cr
itical
r
o
le
in
th
e
p
r
o
d
u
ctio
n
o
f
e
n
er
g
y
.
R
eg
u
lar
m
ain
ten
an
ce
an
d
d
iag
n
o
s
is
ar
e
in
cr
ea
s
in
g
ly
im
p
o
r
tan
t
f
o
r
th
is
r
ea
s
o
n
.
T
h
e
r
elev
a
n
ce
o
f
PV
s
y
s
tem
s
h
as
in
cr
ea
s
ed
d
u
e
t
o
t
h
e
s
o
lar
in
d
u
s
tr
y
'
s
tr
em
en
d
o
u
s
r
is
e
in
r
ec
en
t
y
e
ar
s
.
T
o
im
p
r
o
v
e
s
o
lar
PV
ar
r
ay
d
e
p
en
d
a
b
ilit
y
,
ef
f
icien
c
y
,
an
d
s
af
ety
,
f
au
lt
an
aly
s
is
is
ess
en
tial.
I
f
f
au
lts
g
o
u
n
d
etec
ted
,
p
o
wer
g
e
n
er
ati
o
n
m
ay
b
e
r
ed
u
ce
d
,
s
y
s
tem
ag
in
g
m
ay
s
p
ee
d
u
p
,
an
d
th
e
a
v
ailab
ilit
y
o
f
th
e
en
ti
r
e
s
y
s
tem
m
ay
b
e
in
jeo
p
ar
d
y
[
8
]
.
Glo
b
al
in
s
tallatio
n
s
o
f
lar
g
e
-
s
ca
le
s
o
lar
PV p
o
wer
p
lan
ts
h
a
v
e
g
r
o
wn
im
p
r
ess
iv
ely
q
u
ic
k
ly
in
th
e
last
s
ev
er
al
y
ea
r
s
.
Sin
ce
th
e
m
ajo
r
ity
o
f
th
ese
s
y
s
tem
s
h
av
e
m
u
lti
-
MW
r
atin
g
s
an
d
ca
p
ab
ilit
ies,
th
ey
ar
e
m
ad
e
u
p
o
f
th
o
u
s
an
d
s
o
f
m
o
d
u
les
d
is
p
er
s
ed
o
v
er
h
ec
tar
es
o
f
la
n
d
[
9
]
.
Kee
p
in
g
an
ey
e
o
n
all
th
ese
elem
en
ts
s
ep
ar
ately
is
tim
e
-
co
n
s
u
m
in
g
,
ex
p
en
s
iv
e,
an
d
f
r
eq
u
en
tly
n
o
t
f
ea
s
ib
le.
Acc
o
r
d
in
g
to
i
n
v
esti
g
atio
n
s
,
a
n
u
m
b
er
o
f
f
ac
to
r
s
,
in
clu
d
in
g
ex
ten
d
ed
o
u
t
d
o
o
r
o
p
er
atio
n
,
p
o
o
r
m
ain
ten
an
ce
,
e
n
clo
s
u
r
e
is
s
u
es,
th
er
m
al
cy
clin
g
,
g
r
o
u
n
d
in
g
is
s
u
es,
an
d
co
r
r
o
s
iv
e
co
n
d
itio
n
s
,
ca
n
ca
u
s
e
PV
m
o
d
u
les
to
d
eter
io
r
a
te
p
r
em
atu
r
ely
[
1
0
]
.
T
h
e
ad
v
a
n
tag
es
o
f
f
r
ee
s
o
lar
en
er
g
y
f
o
r
th
e
e
n
v
ir
o
n
m
en
t
a
n
d
ec
o
n
o
m
y
h
av
e
m
ad
e
t
h
e
PV
s
ec
to
r
m
o
r
e
well
-
k
n
o
wn
i
n
r
ec
en
t
y
ea
r
s
.
T
h
e
to
tal
in
s
talled
PV
ca
p
ac
ity
is
an
ticip
ated
to
in
cr
ea
s
e
to
4
3
8
GW
b
etwe
en
2
0
1
7
an
d
2
0
2
2
[
1
1
]
.
Ph
o
to
v
o
ltaic
(
PV)
ar
r
ay
f
au
lt
a
n
aly
s
is
is
th
o
u
g
h
t
to
b
e
cr
u
cial
f
o
r
r
aisi
n
g
th
e
s
y
s
tem
'
s
ef
f
icien
cy
an
d
s
af
ety
.
I
n
ad
d
itio
n
t
o
d
ec
r
ea
s
in
g
ef
f
icien
cy
,
f
au
lts
s
h
o
r
ten
a
s
y
s
tem
'
s
life
s
p
an
[
1
2
]
.
PV
p
an
els
ar
e
b
ec
o
m
in
g
m
o
r
e
an
d
m
o
r
e
co
m
m
o
n
.
T
h
eir
f
laws,
r
is
k
s
,
an
d
h
az
ar
d
s
ar
e
in
cr
ea
s
in
g
ly
b
ein
g
u
s
ed
as
a
f
o
ca
l
p
o
i
n
t
f
o
r
r
esear
ch
to
lo
wer
ass
o
ciate
d
r
is
k
s
an
d
ac
cid
en
ts
[
1
3
]
.
Desp
ite
th
e
s
tead
y
in
cr
ea
s
e
in
th
e
wo
r
ld
'
s
PV
ca
p
ac
ity
,
d
ef
ec
t
d
etec
tio
n
in
PV
s
y
s
tem
s
i
s
s
t
ill
a
n
ee
d
th
at
h
as
n
o
t
r
ec
eiv
ed
en
o
u
g
h
atten
tio
n
[
1
4
]
.
B
ec
au
s
e
o
f
its
m
an
y
s
af
ety
f
ea
tu
r
es,
NE
C
ar
ticle
6
9
0
is
ex
ten
s
iv
ely
u
s
ed
wo
r
ld
wid
e
i
n
th
e
co
n
tex
t
o
f
lin
e
-
lin
e
(
L
L
)
an
d
lin
e
-
g
r
o
u
n
d
(
L
G)
f
au
lt
d
etec
tio
n
in
PV
ar
r
ay
s
.
Sad
ly
,
r
ep
o
r
ts
in
th
e
liter
atu
r
e
also
in
d
icate
th
at
NE
C
6
9
0
s
tan
d
ar
d
s
h
av
e
lim
its
wh
en
it
co
m
es
to
id
en
tify
in
g
L
L
a
n
d
L
G
er
r
o
r
s
[
1
5
]
–
[
1
7
]
.
Def
ec
t
id
en
tific
atio
n
in
s
o
lar
PV
ar
r
ay
s
is
an
es
s
e
n
tial
d
u
ty
to
b
o
o
s
t
PV
s
y
s
tem
s
'
d
ep
en
d
ab
ilit
y
,
e
f
f
ec
tiv
en
ess
,
an
d
s
ec
u
r
ity
.
U
n
clea
n
ed
f
au
lts
in
PV
ar
r
ay
s
n
o
t
o
n
ly
r
esu
lt
in
p
o
wer
lo
s
s
es
b
u
t
also
h
av
e
th
e
p
o
ten
tial
to
g
en
er
ate
s
af
ety
co
n
ce
r
n
s
an
d
f
ir
e
th
r
ea
ts
if
im
p
r
o
p
er
f
a
u
lt
d
etec
tio
n
is
ca
r
r
ied
o
u
t
[
1
8
]
.
R
eg
r
etf
u
lly
,
co
m
p
ar
ed
to
th
e
lig
h
tn
in
g
-
f
ast
p
r
o
g
r
ess
m
a
d
e
in
th
e
f
ield
o
f
m
ax
im
u
m
p
o
wer
p
o
in
t
tr
ac
k
in
g
th
u
s
f
a
r
,
awa
r
e
n
ess
o
f
PV
d
ef
ec
t
d
etec
tio
n
is
co
m
p
ar
ativ
ely
q
u
ite
s
lo
w
,
m
ax
im
u
m
p
o
we
r
p
o
in
t
tr
ac
k
i
n
g
(
MPPT)
[
1
9
]
.
Mo
d
er
n
r
ese
ar
ch
o
n
f
au
lt
d
iag
n
o
s
is
in
PV
ar
r
ay
s
is
d
r
iv
en
b
y
th
e
in
cr
ea
s
in
g
p
r
ev
alen
ce
o
f
PV
s
y
s
tem
s
in
m
o
d
er
n
elec
tr
icity
g
r
id
s
[
2
0
]
.
E
lectr
ical
f
a
u
lts
in
PV
ar
r
ay
s
,
esp
ec
ially
L
G
an
d
L
L
f
a
u
lts
,
p
o
s
e
a
s
ig
n
if
ican
t
o
b
s
tacle
to
th
e
r
ap
id
a
d
v
an
ce
m
en
t
o
f
PV
p
o
wer
g
e
n
er
atio
n
wo
r
ld
wid
e.
T
h
e
r
ef
o
r
e
,
g
iv
e
n
th
e
n
u
m
e
r
o
u
s
u
n
iq
u
e
o
p
er
a
tin
g
ch
ar
ac
ter
is
tics
o
f
PV
-
p
r
o
d
u
cin
g
s
y
s
tem
s
,
a
th
o
r
o
u
g
h
s
tu
d
y
o
f
th
e
c
o
m
p
atib
ilit
y
o
f
th
e
L
L
/LG
f
au
lt
p
r
ev
en
tio
n
s
tan
d
ar
d
s
s
p
ec
if
ie
d
f
o
r
PV
ar
r
ay
s
is
n
ec
ess
ar
y
[
2
1
]
.
Gr
o
u
n
d
f
a
u
lts
h
av
e
th
e
p
o
ten
t
ial
to
g
o
u
n
n
o
ticed
an
d
r
esu
lt
in
s
ig
n
if
ican
t
h
ar
m
to
b
o
th
th
e
PV
ar
r
a
y
an
d
th
e
s
u
r
r
o
u
n
d
i
n
g
e
n
v
ir
o
n
m
en
t
b
ec
au
s
e
o
f
c
er
tain
lim
it
atio
n
s
in
tr
ad
itio
n
al
d
etec
tio
n
p
r
o
ce
d
u
r
es.
Similar
cir
cu
m
s
tan
ce
s
co
u
ld
o
cc
u
r
in
t
h
e
ev
en
t
o
f
lin
e
-
to
-
lin
e
er
r
o
r
s
[
2
2
]
.
W
h
en
an
y
DC
ca
r
r
y
in
g
co
n
d
u
ct
o
r
in
o
n
e
o
f
th
ese
s
y
s
tem
s
u
n
in
ten
tio
n
ally
co
n
n
ec
ts
to
th
e
ea
r
th
o
r
a
g
r
o
u
n
d
ed
s
u
r
f
ac
e,
a
g
r
o
u
n
d
f
au
lt
o
cc
u
r
s
.
W
h
en
g
r
o
u
n
d
f
au
lts
ar
is
e,
d
c
leak
a
g
e
b
ec
o
m
es
m
o
r
e
in
ten
s
e
an
d
tr
av
els
ac
r
o
s
s
th
e
ea
r
th
o
r
o
th
er
co
n
d
u
ctiv
e
p
ath
way
s
b
ef
o
r
e
co
m
i
n
g
b
ac
k
to
th
e
s
o
u
r
ce
[
1
7
]
.
PV
in
s
tallatio
n
s
co
m
p
ly
with
s
tan
d
ar
d
s
s
u
ch
as
I
E
E
E
Stan
d
ar
d
1
3
7
4
,
Natio
n
al
E
l
ec
tr
ic
C
o
d
e
(
NE
C
)
6
9
0
,
a
n
d
E
u
r
o
p
ea
n
I
n
ter
n
atio
n
al
E
lectr
o
T
ec
h
n
ical
C
o
m
m
is
s
io
n
Stan
d
ar
d
(
I
E
C
)
6
2
5
4
8
.
L
L
an
d
L
G
f
au
lt
d
ete
ctio
n
f
ea
tu
r
es
h
a
v
e
also
b
ee
n
in
clu
d
ed
to
p
o
wer
co
n
v
er
s
io
n
e
q
u
ip
m
e
n
t
(
PC
E
)
s
af
ety
s
tan
d
ar
d
s
s
u
ch
as
I
E
C
6
2
1
0
9
-
1
,
I
E
C
6
2
1
0
9
-
2
,
an
d
Un
d
e
r
wr
iter
s
L
ab
o
r
ato
r
ies
UL
1
7
4
1
in
r
ec
e
n
t
y
ea
r
s
.
T
h
u
s
,
a
th
o
r
o
u
g
h
an
a
ly
s
is
o
f
th
ese
s
tan
d
ar
d
s
'
ab
il
it
y
to
id
en
tify
L
L
a
n
d
L
G
er
r
o
r
s
is
also
n
ec
ess
ar
y
.
W
h
ile
th
er
e
a
r
e
m
a
n
y
P
V
a
r
r
a
y
p
r
o
b
le
m
s
,
s
o
m
e
h
a
v
e
r
ec
ei
v
e
d
m
o
r
e
a
tte
n
t
io
n
t
h
a
n
o
t
h
e
r
s
,
i
n
c
lu
d
i
n
g
li
n
e
-
to
-
li
n
e
f
a
u
lts
(
L
L
F)
,
g
r
o
u
n
d
f
a
u
lts
(
GF
)
,
a
r
c
f
a
u
lts
(
AF)
,
a
n
d
h
o
t s
p
o
t
f
au
l
ts
(
HSF
)
[
2
3
]
.
I
n
th
is
p
a
p
er
,
d
if
f
er
e
n
t
ty
p
es
o
f
PV
f
au
lts
h
av
e
b
ee
n
ap
p
lied
to
a
s
o
lar
ce
ll
s
y
s
tem
.
Fo
u
r
ty
p
es,
s
u
ch
as
in
tr
a
-
lin
e
to
lin
e,
cr
o
s
s
-
lin
e
to
lin
e,
lin
e
to
g
r
o
u
n
d
,
an
d
o
p
en
cir
cu
it
f
au
lt,
th
ese
f
au
lts
wer
e
ap
p
lied
in
th
is
wo
r
k
.
T
h
is
p
r
o
p
o
s
ed
PV
s
y
s
t
em
co
n
s
is
ts
o
f
a
5
×
5
m
atr
ix
o
f
PV
ar
r
ay
s
.
T
h
e
s
im
u
latio
n
r
esu
lts
o
f
th
e
f
o
u
r
m
eth
o
d
o
l
o
g
ies
(
SP
–
T
C
T
–
HC
–
B
L
)
u
n
d
er
v
ar
io
u
s
f
au
lt
ca
s
es
ar
e
p
r
esen
ted
in
MA
T
L
AB
.
T
h
e
o
b
tain
ed
r
esu
lts
ar
e
co
m
p
ar
ed
in
ter
m
s
o
f
th
e
(
I
-
V)
cu
r
v
e
an
d
P
-
V
cu
r
v
e
all
f
au
lt
s
ce
n
ar
io
s
.
I
n
s
tan
d
ar
d
test
co
n
d
itio
n
(
STC)
(
ir
r
ad
ian
ce
1
0
0
0
W
/m
2
,
ce
ll
tem
p
er
atu
r
e
2
5
°C
)
th
e
f
o
u
r
to
p
o
lo
g
ies
g
iv
e
th
e
s
a
m
e
(
I
-
V)
an
d
(P
-
V)
ch
ar
ac
ter
is
tics
.
2.
M
E
T
H
O
D
AND
T
O
O
L
S
Sin
g
le
PV
ce
ll
ca
n
p
r
o
d
u
c
e
tin
y
g
en
e
r
ated
p
o
wer
a
n
d
f
o
r
h
ig
h
p
o
wer
p
r
o
p
o
s
es
o
r
g
r
id
co
n
n
ec
tio
n
s
,
a
g
r
o
u
p
o
f
p
ar
allel
an
d
s
er
ies
ar
r
an
g
em
e
n
ts
o
f
PV
ce
lls
to
p
r
o
d
u
ce
th
e
r
e
q
u
ir
ed
p
o
wer
f
o
r
s
u
ch
ap
p
licatio
n
s
.
T
h
ese
k
in
d
s
o
f
ar
r
a
n
g
em
e
n
ts
ar
e
ca
lled
PV
m
o
d
u
les
wh
ich
th
ey
f
o
r
m
t
h
e
PV
p
an
els.
I
n
th
is
wo
r
k
a
PV
p
an
el
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.
16
,
No
.
4
,
Dec
em
b
er
20
25
:
2744
-
2
7
5
6
2746
with
s
p
ec
if
icatio
n
lis
ted
in
T
a
b
le
1
h
as
b
ee
n
u
s
ed
as
s
h
o
wn
in
Fig
u
r
e
1
.
A
co
llectio
n
o
f
li
n
k
ed
s
o
lar
m
o
d
u
les,
ea
ch
with
m
an
y
s
o
lar
p
an
els,
is
ca
lled
a
s
o
lar
ar
r
ay
.
Ph
o
to
v
o
ltaic
ar
r
ay
s
,
an
o
t
h
er
n
a
m
e
f
o
r
s
o
lar
ar
r
ay
s
,
a
r
e
er
ec
ted
to
s
u
p
p
ly
en
o
r
m
o
u
s
am
o
u
n
ts
o
f
e
n
er
g
y
to
r
esid
en
tial a
n
d
co
m
m
er
cial
s
tr
u
ctu
r
es.
I
n
th
is
w
o
r
k
,
MA
T
L
AB
/Si
m
u
lin
k
was
u
s
ed
to
m
o
d
el
a
5
×
5
PV
ar
r
a
y
f
o
r
v
ar
i
o
u
s
PV
ar
r
a
y
to
p
o
lo
g
ies,
w
h
er
e
ea
c
h
m
o
d
u
le
co
n
s
is
ts
o
f
3
6
ce
lls
co
n
n
ec
ted
in
s
er
ies.
A
b
y
p
ass
d
i
o
d
e
is
lin
k
ed
to
ev
er
y
m
o
d
u
le.
B
y
co
n
tr
o
llin
g
th
e
o
u
tp
u
t
v
alu
e
o
f
th
e
v
o
ltag
e
s
o
u
r
c
e
(
1
1
2
V)
to
lin
ea
r
ly
in
cr
ea
s
e,
th
e
o
u
tp
u
t
cu
r
r
e
n
t
an
d
v
o
ltag
e
o
f
th
e
PV strin
g
ar
e
r
ec
o
r
d
e
d
,
th
e
ass
o
ciate
d
d
ata
is
th
en
en
ter
ed
in
to
th
e
MA
T
L
AB
wo
r
k
s
p
ac
e
to
p
r
o
d
u
ce
th
e
(
I
-
V)
c
h
ar
ac
ter
is
tic
cu
r
v
e.
A
b
lo
ck
i
n
g
d
i
o
d
e
is
u
s
ed
in
th
e
PV
s
tr
in
g
'
s
o
u
tp
u
t
to
p
r
ev
e
n
t
n
eg
ativ
e
cu
r
r
en
ts
f
r
o
m
o
cc
u
r
r
in
g
.
As
illu
s
tr
ated
in
Fig
u
r
e
2
,
t
h
e
im
p
ac
t
o
f
th
e
m
o
s
t
f
r
eq
u
e
n
t
f
la
ws
in
th
e
PV
ar
r
ay
ch
ar
ac
ter
is
tics
o
n
th
e
ar
r
a
y
'
s
p
er
f
o
r
m
a
n
ce
was stu
d
ied
at
ST
C
in
co
n
s
tan
t w
ea
th
er
cir
cu
m
s
tan
ce
s
.
T
ab
le
1
.
PV m
o
d
u
le
s
p
ec
if
icat
io
n
s
(PV
mo
d
u
l
e
)
p
a
r
a
m
e
t
e
r
V
a
l
u
e
M
a
x
i
m
u
m
p
o
w
e
r
(
P
M
A
X
)
1
7
0
W
V
o
l
t
a
g
e
a
t
ma
x
i
m
u
m
p
o
w
e
r
(
V
m
p
)
1
8
.
3
V
C
u
r
r
e
n
t
a
t
ma
x
i
mu
m
p
o
w
e
r
(
I
mp
)
9
.
2
9
A
O
p
e
n
c
i
r
c
u
i
t
v
o
l
t
a
g
e
(
V
o
c
)
2
2
.
4
V
S
h
o
r
t
c
i
r
c
u
i
t
c
u
r
r
e
n
t
(
I
sc)
1
0
.
2
2
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
.
2
9
V
/
°
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
A
/
°
C
M
a
x
i
m
u
m
p
o
w
e
r
(
P
M
A
X
)
1
7
0
W
Fig
u
r
e
1
.
PV p
a
n
el
an
d
n
am
e
p
late
s
p
ec
if
icatio
n
Fig
u
r
e
2
.
(
I
-
V)
&
(
P
-
V)
test
in
g
cir
cu
it o
f
PV
ar
r
ay
m
o
d
ellin
g
v
ia
MA
T
L
AB
/Si
m
u
lin
k
3.
P
V
ARRA
Y
T
O
P
O
L
O
G
I
E
S
T
h
e
to
p
o
lo
g
y
o
f
s
er
ies
an
d
p
ar
allel
PV
p
an
els
h
as
s
o
m
e
d
r
awb
ac
k
s
,
s
u
ch
as
less
cu
r
r
en
t
an
d
v
o
ltag
e.
T
h
er
ef
o
r
e,
m
an
y
c
o
n
fig
u
r
atio
n
s
o
f
PV
ar
r
ay
s
h
av
e
b
ee
n
p
r
o
p
o
s
ed
in
th
is
f
ield
th
at
wh
ich
is
co
m
m
o
n
ly
ca
teg
o
r
ized
as
[
2
4
]
:
3
.
1
.
Series
-
pa
ra
llel (
SP)
Alth
o
u
g
h
a
s
er
ies
-
p
ar
allel
PV
m
o
d
el
co
n
n
ec
tio
n
ca
n
n
o
t
im
p
r
o
v
e
v
o
ltag
e
a
n
d
cu
r
r
en
t
r
a
n
g
e
at
th
e
s
am
e
tim
e,
it
is
s
till
p
r
ef
er
r
ed
b
ec
au
s
e
o
f
its
lo
w
co
s
t,
m
i
n
im
al
elec
tr
ical
lo
s
s
es,
g
o
o
d
d
e
p
en
d
ab
ilit
y
,
an
d
it
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
A
s
s
es
s
men
t o
f th
e
efficien
cy
a
n
d
p
erfo
r
ma
n
ce
o
f
d
iffer
en
t P
V
s
ystem
…
(
R
a
g
h
a
d
A
d
ee
b
O
th
ma
n
)
2747
d
if
f
er
s
f
r
o
m
th
e
s
er
ies
to
p
o
lo
g
y
in
th
at
it
h
as
f
ewe
r
m
is
m
atch
lo
s
s
es.
B
ec
au
s
e
it
h
as
f
e
wer
s
er
ies
m
o
d
u
les
th
an
th
e
to
tal
n
u
m
b
er
o
f
s
e
r
ies
m
o
d
u
les
co
n
n
ec
ted
in
a
to
p
o
lo
g
ical
s
er
ies
.
As
s
ee
n
in
Fig
u
r
e
3
,
a
n
ar
r
an
g
em
e
n
t
o
f
f
iv
e
m
o
d
u
les
co
n
n
ec
ted
i
n
s
er
ies
co
m
p
ly
in
g
s
tr
in
g
s
f
iv
e
o
f
th
ese
s
tr
in
g
s
jo
in
ed
in
p
ar
allel
to
o
b
tain
th
e
SP
co
n
f
ig
u
r
atio
n
.
T
h
e
m
o
s
t p
o
p
u
lar
co
n
f
ig
u
r
atio
n
,
s
er
ies
-
p
ar
allel,
is
s
im
p
le
to
u
tili
ze
.
Alth
o
u
g
h
th
e
s
er
ies
an
d
p
ar
allel
co
n
f
i
g
u
r
at
io
n
s
in
cr
ea
s
e
th
e
PV
s
y
s
tem
's
o
v
er
all
o
u
tp
u
t,
th
ey
h
av
e
t
h
e
d
is
ad
v
an
tag
e
o
f
b
ein
g
less
ef
f
ec
tiv
e
wh
en
th
er
e
is
p
ar
tial sh
ad
o
win
g
.
3
.
2
.
T
o
t
a
l c
ro
s
s
t
ied (
T
CT
)
Un
lik
e
SP
,
th
e
T
C
T
co
n
f
ig
u
r
a
tio
n
is
r
etr
ie
v
ed
f
r
o
m
th
e
to
p
o
lo
g
y
o
f
SP
,
alth
o
u
g
h
it
is
m
o
r
e
d
if
f
icu
lt
to
im
p
lem
en
t.
As
s
ee
n
i
n
Fig
u
r
e
4
,
it
f
ea
t
u
r
es
a
cr
o
s
s
-
r
o
ws
a
n
d
cr
o
s
s
-
co
lu
m
n
s
c
o
n
n
ec
te
d
a
r
r
an
g
em
e
n
t
wh
e
r
e
th
e
to
tal
v
o
ltag
e
a
n
d
to
tal
cu
r
r
en
t
ar
e
eq
u
al
th
r
o
u
g
h
o
u
t
al
l
r
o
ws
an
d
all
c
o
lu
m
n
s
,
r
esp
ec
tiv
ely
.
T
h
e
T
C
T
s
ch
em
e
h
as
th
e
d
r
awb
ac
k
o
f
h
av
in
g
m
o
r
e
tim
es
th
a
n
SP
,
wh
ich
r
aises
ca
b
le
lo
s
s
es
ev
en
th
o
u
g
h
it
p
er
f
o
r
m
s
b
etter
th
an
SP
in
ter
m
s
o
f
s
h
ad
in
g
an
d
m
is
m
atch
lo
s
s
es.
Fig
u
r
e
3
.
SP
t
o
p
o
lo
g
ies o
f
(
5
×
5
)
PV a
r
r
ay
Fig
u
r
e
4
.
T
C
T
t
o
p
o
lo
g
ies o
f
(
5
×
5
)
PV a
r
r
ay
3
.
3
.
B
ridg
e
l
ink
ed
(
B
L
)
T
h
e
b
r
id
g
e
-
lin
k
ed
to
p
o
lo
g
y
,
as
illu
s
tr
ated
in
Fig
u
r
e
5
,
is
d
e
r
iv
ed
f
r
o
m
T
C
T
an
d
h
as
th
e
ad
v
an
tag
es
o
f
r
eq
u
ir
i
n
g
f
ewe
r
co
n
n
ec
tio
n
s
,
r
eq
u
ir
in
g
less
tim
e
to
b
u
ild
th
e
wir
in
g
,
an
d
h
av
in
g
f
ewe
r
ca
b
le
lo
s
s
es
;
h
o
wev
er
,
u
n
d
e
r
s
h
ad
in
g
co
n
d
i
tio
n
s
,
it h
as a
n
eg
ativ
e
im
p
ac
t
o
n
th
e
to
tal
v
o
ltag
e
an
d
cu
r
r
en
t.
3
.
4
.
H
o
ney
co
m
b
(
H
C)
T
h
is
to
p
o
lo
g
y
is
b
ased
o
n
th
e
T
C
T
co
n
ce
p
t,
wh
ich
u
s
es
a
h
o
n
ey
co
m
b
s
tr
u
ctu
r
e
.
As
s
ee
n
in
Fig
u
r
e
6
,
th
e
co
n
n
ec
tio
n
s
h
ap
e
o
f
th
e
ties
d
if
f
er
s
s
lig
h
tly
f
r
o
m
B
L
.
Alth
o
u
g
h
o
u
tp
u
t
p
o
wer
lo
s
s
es
in
th
is
d
esig
n
ca
n
b
e
lo
wer
ed
,
it is
lim
ited
in
th
at
p
o
wer
lo
s
s
es c
an
n
o
t b
e
r
e
d
u
ce
d
in
all
s
h
ad
in
g
c
o
n
d
itio
n
s
.
Fig
u
r
e
5
.
B
L
T
o
p
o
lo
g
ies o
f
(
5
×
5
)
PV a
r
r
a
y
Fig
u
r
e
6
.
HC
T
o
p
o
lo
g
ies o
f
(
5
×
5
)
PV a
r
r
a
y
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
4
,
Dec
em
b
er
20
25
:
2744
-
2
7
5
6
2748
4.
F
AULT
S IN P
V
AR
RAYS
T
wo
ty
p
ical
f
a
u
lt
s
ce
n
ar
io
s
f
o
r
PV
ar
r
ay
s
ex
is
t
[
2
5
]
.
E
lectr
i
ca
l
is
s
u
es
ar
e
th
e
f
ir
s
t,
wh
ile
s
h
ad
e
f
a
u
lt
s
ar
e
th
e
s
ec
o
n
d
.
An
o
m
alies
th
at
ar
is
e
in
th
e
s
y
s
tem
'
s
in
ter
n
al
elec
tr
ical
ar
ch
itectu
r
e
ar
e
th
e
ca
u
s
e
o
f
elec
tr
ical
p
r
o
b
lem
s
.
Ho
wev
e
r
,
ch
an
g
es
in
th
e
ex
ter
n
al
en
v
ir
o
n
m
en
t
an
d
is
o
latio
n
lev
els
ar
e
ca
u
s
in
g
s
h
ad
e
d
ef
ec
ts
[
2
6
]
.
As
s
h
o
wn
in
Fig
u
r
e
7
,
th
e
th
r
ee
m
o
s
t
p
r
ev
alen
t
ty
p
es
o
f
elec
tr
ical
f
au
lts
ar
e
i
)
lin
e
to
l
i
n
e
(
L
-
L),
ii
)
lin
e
to
g
r
o
u
n
d
(
L
-
G)
,
an
d
iii
)
o
p
en
ci
r
cu
it
(
OC
)
.
T
h
ese
is
s
u
es
co
u
ld
lead
to
d
ec
r
ea
s
ed
p
o
wer
p
r
o
d
u
ctio
n
a
n
d
p
o
s
s
ib
ly
ir
r
ev
er
s
ib
le
h
ar
m
to
th
e
p
h
o
to
v
o
ltaic
s
y
s
tem
[
1
7
]
.
W
h
en
th
e
r
e
is
a
s
h
o
r
t
cir
cu
it
b
etwe
en
an
y
two
lo
ca
tio
n
s
in
th
e
PV
ar
r
ay
,
lin
e
-
to
-
lin
e
f
au
l
ts
ar
e
p
r
o
d
u
ce
d
.
Fu
r
th
er
m
o
r
e,
in
ter
esti
n
g
an
d
cr
o
s
s
-
s
tr
in
g
f
au
lts
ar
e
L
L
f
a
u
lts
th
at
o
cc
u
r
in
b
o
th
th
e
s
am
e
s
tr
in
g
an
d
two
d
is
tin
ct
s
tr
in
g
s
.
Sig
n
if
ican
t
p
r
o
b
lem
s
,
s
u
ch
as
p
o
wer
o
u
tag
es,
p
o
s
s
ib
le
d
am
ag
e
to
th
e
PV
m
o
d
u
les,
a
n
d
s
af
ety
r
is
k
s
,
c
an
r
esu
lt
f
r
o
m
th
is
k
i
n
d
o
f
m
alf
u
n
ctio
n
.
L
o
w
ir
r
ad
ian
ce
m
a
k
es
it
ch
allen
g
in
g
to
id
en
tify
L
L
f
au
lts
with
lo
w
lev
els
o
f
m
is
m
atch
f
a
u
l
t
b
ec
au
s
e
th
e
f
au
lt
cu
r
r
en
t
is
o
f
a
s
m
all
s
ize
an
d
g
o
es
u
n
n
o
ticed
.
T
h
e
n
u
m
b
er
o
f
PV
m
o
d
u
les
in
v
o
lv
ed
i
n
th
e
f
a
u
lt
is
in
d
icate
d
b
y
th
is
m
is
m
atch
lev
el.
T
h
e
m
is
m
atch
lev
el
an
d
f
au
lt
p
ath
im
p
ed
an
ce
ar
e
th
e
two
m
ain
f
ac
to
r
s
th
at
d
eter
m
in
e
h
o
w
s
ev
er
e
an
L
L
f
au
lt
is
.
T
h
e
f
au
lt
c
u
r
r
e
n
t
will
b
e
m
in
im
a
l
if
th
e
m
is
m
atch
lev
el
is
lo
w
an
d
th
e
im
p
e
d
an
ce
is
h
ig
h
[
2
7
]
.
T
h
e
co
n
n
ec
tio
n
b
etwe
en
th
e
ea
r
th
g
r
o
u
n
d
co
n
d
u
ct
o
r
(
E
GC
)
an
d
th
e
cu
r
r
en
t
-
ca
r
r
y
in
g
co
n
d
u
cto
r
(
C
C
C
)
is
th
e
u
s
u
al
ca
u
s
e
o
f
L
G
f
au
lts
,
alth
o
u
g
h
th
ey
ca
n
al
s
o
o
r
ig
in
ate
f
r
o
m
in
ter
n
al
PV
ce
ll
f
ailu
r
e
o
r
ca
b
le
in
s
u
latio
n
f
ailu
r
e.
An
L
G
f
a
u
lt
o
cc
u
r
s
d
u
e
to
a
b
l
o
ck
in
g
d
io
d
e
a
n
d
ze
r
o
f
a
u
lt
r
esis
tan
ce
.
Mo
d
u
les
ar
e
id
en
tifie
d
b
y
th
eir
lo
ca
tio
n
in
th
e
PV
ar
r
ay
.
T
h
e
cu
r
r
e
n
t
f
r
o
m
th
e
d
ef
ec
tiv
e
m
o
d
u
les
m
i
g
h
t
ev
e
n
g
o
i
n
two
d
if
f
er
en
t
d
ir
ec
ti
o
n
s
:
eith
er
v
ia
th
e
s
h
o
r
t
-
cir
cu
it
r
o
u
te
o
r
th
r
o
u
g
h
th
e
h
ea
lth
y
m
o
d
u
le.
An
o
p
en
cir
cu
it
d
ef
ec
t
is
an
y
s
itu
atio
n
in
wh
en
th
er
e
is
an
o
p
e
n
cir
c
u
it
b
etwe
en
two
p
an
els
th
at
p
r
ev
e
n
ts
p
o
wer
f
r
o
m
f
l
o
win
g
.
Ma
n
y
f
ac
to
r
s
ca
n
ca
u
s
e
o
v
er
c
u
r
r
en
t
f
au
lts
(
OC
f
a
u
lts
)
,
in
clu
d
in
g
a
b
r
o
k
e
n
ca
b
le
b
etwe
en
two
s
tr
in
g
s
,
an
o
b
ject
f
allin
g
o
n
th
e
p
an
els,
a
b
ad
c
o
n
n
ec
tio
n
b
etwe
en
two
l
o
ca
tio
n
s
,
o
r
a
n
u
n
in
ten
tio
n
al
b
r
ea
k
i
n
a
cu
r
r
en
t
-
ca
r
r
y
in
g
co
n
d
u
ct
o
r
[
1
2
]
.
Ar
c
f
a
u
lts
,
o
n
th
e
o
th
er
h
an
d
,
r
esu
lt
f
r
o
m
o
p
en
cir
cu
it
f
a
u
lts
in
a
s
tr
in
g
o
r
f
r
o
m
in
s
u
latio
n
f
ailu
r
e
b
etwe
en
two
p
o
r
tio
n
s
o
f
ad
jace
n
t
s
tr
in
g
s
.
T
h
e
y
ca
n
o
cc
u
r
in
p
ar
allel
o
r
s
eq
u
e
n
ce
an
d
p
o
s
e
a
s
er
io
u
s
r
is
k
f
o
r
f
ir
e
.
I
n
th
is
wo
r
k
,
f
o
u
r
PV
s
y
s
tem
to
p
o
l
o
g
ies
ar
e
c
o
n
n
ec
te
d
to
b
e
in
v
esti
g
ated
u
n
d
er
f
o
u
r
co
m
m
o
n
elec
tr
ical
f
au
lts
,
as
s
h
o
w
n
in
Fig
u
r
e
7
.
Su
c
h
as:
i)
c
r
o
s
s
s
tr
in
g
lin
e
-
lin
e
f
a
u
lt
,
ii)
i
n
tr
a
s
tr
in
g
lin
e
-
lin
e
f
a
u
lt
,
iii)
l
in
e
to
g
r
o
u
n
d
f
au
lt
,
an
d
i
v
)
o
p
en
cir
c
u
it
f
au
lt
.
T
h
ese
k
in
d
s
o
f
f
au
lts
ar
e
co
n
s
id
er
ed
t
h
e
m
o
s
t
co
m
m
o
n
o
f
elec
tr
ical
f
au
lts
,
with
an
in
cid
en
ce
p
er
ce
n
ta
g
e
o
f
ab
o
u
t
3
0
%
to
6
0
%
o
f
all
f
a
u
lts
,
d
ep
en
d
in
g
o
n
th
e
PV
ce
ll
cir
cu
m
s
tan
ce
s
r
eg
ar
d
in
g
to
th
e
in
s
tallatio
n
an
d
th
e
en
v
ir
o
n
m
en
t
[
2
8
]
.
E
ac
h
o
f
th
e
ch
o
s
en
to
p
o
lo
g
ies
co
n
s
is
ts
o
f
a
PV a
r
r
ay
(
5
×5
)
b
u
ilt in
M
AT
L
AB
/Si
m
u
lin
k
with
s
o
lar
m
o
d
u
les h
av
i
n
g
th
e
d
ata
as lis
ted
in
T
ab
le
1
u
n
d
er
STC.
Fig
u
r
e
7
.
PV
s
y
s
tem
u
n
d
er
f
o
u
r
elec
tr
ical
f
au
lts
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
A
s
s
es
s
men
t o
f th
e
efficien
cy
a
n
d
p
erfo
r
ma
n
ce
o
f
d
iffer
en
t P
V
s
ystem
…
(
R
a
g
h
a
d
A
d
ee
b
O
th
ma
n
)
2749
5.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
h
is
s
ec
tio
n
p
r
esen
ts
th
e
MA
T
L
AB
s
im
u
latio
n
r
esu
lts
f
o
r
th
e
f
o
u
r
tech
n
iq
u
es
(
SP
,
T
C
T
,
HC
,
an
d
B
L
)
u
n
d
e
r
d
if
f
er
en
t
f
au
lt
s
ce
n
ar
io
s
.
Fo
r
e
v
er
y
f
ailu
r
e
s
ce
n
ar
i
o
,
th
e
r
esu
ltin
g
r
esu
lts
ar
e
c
o
m
p
ar
ed
u
s
in
g
th
e
(
I
-
V)
an
d
(
P
-
V)
cu
r
v
es.
As
in
d
ic
ated
in
T
ab
le
2
,
u
n
d
e
r
ty
p
ical
cir
cu
m
s
tan
ce
s
,
all
f
o
u
r
to
p
o
lo
g
ies
at
STC
p
r
o
v
id
e
th
e
s
am
e
(
I
-
V)
&
(
P
-
V)
p
r
o
p
er
ties
.
W
h
en
o
p
er
atin
g
f
a
u
ltles
s
ly
in
all
f
o
u
r
t
o
p
o
lo
g
i
es,
th
e
PV
ar
r
ay
'
s
g
en
er
atin
g
o
u
tp
u
t p
o
wer
is
4
.
2
1
6
3
K
watts (
STC)
at
1
0
0
0
W
/m
2
o
f
ir
r
a
d
ian
ce
an
d
2
5
°C
in
tem
p
er
atu
r
e.
T
ab
le
2
.
PV
a
r
r
a
y
o
u
t
p
u
t
at
ST
C
To
p
o
l
o
g
y
V
o
.
c
(
V
)
I
s.c
(
A
)
V
max
(
V
)
I
max
(
A
)
P
M
P
P
(W)
SP
1
1
1
.
3
5
1
.
7
3
9
1
.
1
6
4
6
.
2
8
4
2
1
6
.
3
TC
T
1
1
1
.
4
5
1
.
7
3
9
1
.
0
1
4
6
.
2
6
4
2
1
6
.
2
7
HC
1
1
1
.
4
5
1
.
7
3
9
1
.
1
0
4
6
.
2
4
4
2
1
6
.
3
BL
1
1
1
.
4
5
1
.
7
3
9
1
.
1
0
4
6
.
2
4
4
2
1
6
.
3
5
.
1
.
Cro
s
s
s
t
ring
lin
e
–
lin
e
f
a
ult
in t
he
P
V
a
rr
a
y
T
h
er
e'
s
a
p
r
o
b
lem
b
etwe
en
t
h
ese
two
s
tr
in
g
s
.
Fig
u
r
e
8
r
esu
lts
d
em
o
n
s
tr
ate
th
at,
f
o
r
th
e
(
P
-
V)
ch
ar
ac
ter
is
tics
,
th
e
wh
o
le
r
an
g
e
o
f
th
e
(
I
-
V)
c
h
ar
ac
ter
i
s
tics
r
em
ain
s
u
n
af
f
ec
ted
in
th
e
SP
to
p
o
lo
g
y
,
ir
r
esp
ec
tiv
e
o
f
th
e
n
u
m
b
er
o
f
p
an
els im
p
ac
ted
b
y
th
e
f
au
lt.
T
h
e
m
ax
im
u
m
p
o
wer
r
ea
ch
e
d
3
6
8
0
.
6
6
watts wh
en
th
e
f
au
lt
b
etwe
en
PV1
an
d
PV
7
o
cc
u
r
r
e
d
b
ec
au
s
e
th
e
v
o
ltag
e
v
alu
e
in
th
e
SP
to
p
o
lo
g
y
wa
s
1
2
.
3
%
lo
wer
th
an
it
was
in
th
e
ty
p
ical
s
ce
n
ar
io
.
Sin
ce
it
is
th
e
c
u
r
r
e
n
t
f
r
o
m
t
h
e
n
o
n
-
f
a
u
lty
s
tr
in
g
s
th
at
ca
n
g
o
s
tr
aig
h
t
in
to
t
h
e
f
au
lty
s
tr
in
g
i
n
th
e
ev
en
t
o
f
a
s
h
o
r
t
cir
cu
it,
a
v
o
id
in
g
th
e
lo
a
d
.
T
h
is
m
a
y
r
esu
lt
in
o
v
e
r
cu
r
r
en
t
in
th
e
im
p
ac
ted
s
tr
in
g
s
,
h
ar
m
in
g
th
ese
m
o
d
u
le
s
.
Similar
to
th
e
SP
to
p
o
lo
g
y
,
th
e
d
ef
ec
t
ca
u
s
es
cu
r
r
en
t
f
r
o
m
n
o
n
-
f
au
lty
s
tr
in
g
s
to
b
e
d
iv
er
ted
i
n
to
th
e
f
au
lty
s
tr
in
g
s
,
b
u
t
th
e
cr
o
s
s
-
ties
allo
w
f
o
r
s
o
m
e
cu
r
r
e
n
t
r
ed
is
tr
ib
u
tio
n
ac
r
o
s
s
th
e
PV
a
r
r
ay
.
Dep
e
n
d
in
g
o
n
th
e
n
u
m
b
er
o
f
p
an
els
im
p
licated
in
t
h
e
f
ailu
r
e,
it
is
d
is
co
v
er
ed
th
at
th
e
o
p
en
cir
cu
it
v
o
ltag
e
in
th
e
T
C
T
to
p
o
lo
g
y
d
ec
r
ea
s
es
d
r
am
atica
lly
.
Sin
c
e
th
e
d
ef
ec
t
was
b
etwe
en
P
V1
an
d
PV1
0
,
th
e
v
o
ltag
e
d
r
o
p
p
e
d
b
y
6
0
.
3
%,
w
h
ich
h
ad
a
s
ig
n
if
ican
t
im
p
ac
t
o
n
th
e
s
y
s
tem
'
s
f
u
n
ctio
n
ality
.
T
h
e
T
C
T
to
p
o
lo
g
y
s
aw
a
r
ed
u
ctio
n
i
n
th
e
m
ajo
r
ity
o
f
th
e
p
o
wer
g
e
n
er
ated
at
t
h
is
f
au
lt.
I
f
t
h
e
m
a
x
im
u
m
p
o
wer
v
alu
e
d
r
o
p
s
t
o
1
4
1
0
.
9
5
watts
wh
en
t
h
e
f
a
u
lt
h
ap
p
en
s
b
etwe
en
PV1
a
n
d
PV1
0
.
T
h
o
u
g
h
,
d
ep
en
d
in
g
o
n
h
o
w
th
e
p
r
o
b
lem
af
f
ec
ts
th
e
s
y
s
tem
,
s
o
m
e
p
o
we
r
m
ig
h
t sti
ll b
e
av
ailab
le
f
r
o
m
u
n
af
f
ec
ted
s
tr
in
g
s
.
B
ec
au
s
e
th
er
e
is
less
ch
an
ce
o
f
a
n
ex
ce
s
s
iv
e
cu
r
r
en
t
in
an
y
o
n
e
s
tr
in
g
d
u
e
t
o
th
e
m
o
r
e
ev
e
n
d
is
tr
ib
u
tio
n
o
f
c
u
r
r
e
n
t
th
r
o
u
g
h
o
u
t
th
e
ar
r
a
y
,
th
e
HC
to
p
o
lo
g
y
p
r
o
v
id
es
s
u
p
er
io
r
p
r
o
tectio
n
f
o
r
th
e
m
o
d
u
les.
I
n
co
m
p
ar
is
o
n
to
SP
an
d
T
C
T
t
o
p
o
lo
g
ies,
th
e
p
o
wer
lo
s
s
is
l
ess
s
ev
er
e,
alth
o
u
g
h
th
e
ar
r
a
y
o
u
tp
u
t
will
s
till
b
e
im
p
ac
ted
.
I
f
th
e
f
au
lt
a
r
is
es
b
etwe
en
PV1
a
n
d
PV1
0
,
th
e
m
ax
im
u
m
p
o
wer
in
HC
d
r
o
p
s
to
1
6
9
4
.
8
3
watts.
Dep
en
d
in
g
o
n
h
o
w
s
er
io
u
s
an
d
wh
er
e
th
e
d
ef
ec
t
is
,
th
e
s
y
s
tem
ca
n
s
till
f
u
n
ctio
n
less
ef
f
icien
tly
.
I
n
B
L
to
p
o
lo
g
y
,
th
e
b
r
id
g
e
c
o
n
n
ec
ti
o
n
s
f
ac
ilit
ate
alter
n
atin
g
cu
r
r
en
t
r
o
u
tes
in
th
e
ev
en
t
o
f
a
cr
o
s
s
-
s
tr
in
g
lin
e
-
lin
e
f
au
lt.
T
h
is
ef
f
ec
tiv
ely
is
o
lates
th
e
f
au
lt
an
d
r
ed
u
ce
s
its
in
f
lu
en
ce
o
n
th
e
r
em
ain
i
n
g
p
o
r
tio
n
s
o
f
th
e
ar
r
ay
.
T
h
e
im
p
ac
t
o
f
a
d
ef
ec
t
o
cc
u
r
r
in
g
i
n
b
o
th
th
e
HC
an
d
B
L
to
p
o
l
o
g
ies
is
co
m
p
ar
ab
le.
W
h
en
th
e
n
u
m
b
e
r
o
f
p
a
n
els
im
p
ac
ted
b
y
th
e
p
r
o
b
lem
r
is
es,
it
is
ev
id
en
t
h
o
w
t
h
e
f
au
lt
r
e
d
u
ce
s
th
e
o
p
e
n
cir
cu
it
v
o
ltag
e
;
n
ev
er
th
eless
,
th
is
ef
f
ec
t is n
o
t a
s
g
r
ea
t a
s
it wo
u
l
d
b
e
in
a
T
C
T
ar
ch
itectu
r
e
.
5
.
2
.
I
ntr
a
s
t
ring
line
–
line
f
a
ult
in t
he
P
V
a
rr
a
y
A
d
ir
ec
t
s
h
o
r
t
cir
cu
it
b
etwe
en
two
p
lace
s
in
th
e
s
am
e
s
tr
in
g
is
ca
u
s
ed
b
y
th
e
d
ef
ec
t.
T
ab
l
e
3
s
h
o
ws
th
e
r
esu
lts
o
f
h
ig
h
lig
h
tin
g
th
e
er
r
o
r
in
ea
c
h
o
f
th
e
f
o
u
r
t
o
p
o
l
o
g
ies.
T
h
is
r
ed
u
ce
s
th
e
n
u
m
b
e
r
o
f
ac
tiv
e
m
o
d
u
les
in
th
e
s
tr
in
g
b
y
cr
ea
tin
g
a
b
y
p
ass
f
o
r
th
e
c
u
r
r
e
n
t
in
th
e
SP
t
o
p
o
lo
g
y
a
r
o
u
n
d
th
e
s
ec
tio
n
o
f
th
e
s
tr
in
g
b
etwe
en
th
e
f
au
lt
s
p
o
ts
.
As
a
r
esu
lt,
th
e
d
am
ag
e
d
s
tr
in
g
'
s
v
o
ltag
e
o
u
tp
u
t
d
r
am
atica
lly
d
ec
r
ea
s
es.
B
ec
au
s
e
th
e
v
o
ltag
e
o
f
th
e
af
f
licted
s
tr
in
g
is
lo
wer
,
th
e
PV
ar
r
ay
'
s
o
v
er
all
p
o
wer
o
u
tp
u
t
is
d
ec
r
ea
s
ed
.
Ne
v
er
th
e
less
,
d
ep
en
d
in
g
o
n
h
o
w
s
er
io
u
s
th
e
er
r
o
r
is
,
s
o
m
e
s
tr
in
g
s
m
ig
h
t
k
ee
p
wo
r
k
in
g
as
th
ey
s
h
o
u
ld
.
I
t
is
o
b
s
er
v
ed
th
at
th
e
s
h
o
r
t
-
cir
cu
i
t
cu
r
r
en
t
was
n
o
t
im
p
ac
ted
b
y
t
h
e
f
au
lt,
ir
r
esp
ec
tiv
e
o
f
th
e
n
u
m
b
er
o
f
p
an
els
im
p
ac
ted
,
an
d
co
n
s
eq
u
en
tly
,
th
e
o
v
er
all
r
a
n
g
e
(
I
-
V)
ch
a
r
ac
ter
is
tics
in
th
e
SP
ar
ch
itectu
r
e
wer
e
n
o
t
im
p
ac
ted
.
allo
ws
th
e
c
u
r
r
en
t
to
b
e
r
ed
is
tr
ib
u
ted
th
r
o
u
g
h
o
u
t
th
e
P
V
ar
r
ay
i
n
th
e
T
C
T
d
esig
n
,
p
o
ten
tially
less
en
in
g
th
e
ef
f
ec
t
o
n
th
e
s
y
s
tem
as
a
wh
o
le.
T
h
e
im
p
ac
ted
s
tr
in
g
'
s
v
o
ltag
e
o
u
tp
u
t
d
ec
r
ea
s
es,
b
u
t b
ec
au
s
e
th
e
c
r
o
s
s
-
ties
en
ab
le
o
th
er
s
tr
in
g
s
t
o
m
ak
e
u
p
f
o
r
th
e
lo
s
s
,
th
e
v
o
ltag
e
a
cr
o
s
s
th
e
ar
r
a
y
is
s
tab
ilized
.
A
s
ig
n
if
ican
t
d
r
o
p
in
th
e
o
p
e
n
cir
cu
it
v
o
ltag
e
is
o
b
s
er
v
ed
to
ch
an
g
e
th
e
(
I
-
V)
ch
ar
ac
te
r
is
tics
o
f
th
e
T
C
T
to
p
o
l
o
g
y
,
d
e
p
en
d
i
n
g
o
n
h
o
w
m
an
y
p
a
n
els
ar
e
af
f
ec
ted
b
y
th
e
f
au
lt.
Fu
r
th
er
m
o
r
e,
th
e
m
ax
im
u
m
v
o
ltag
es
d
r
o
p
p
ed
as
th
e
n
u
m
b
er
o
f
d
ef
ec
tiv
e
p
an
els
in
a
s
tr
in
g
r
o
s
e,
af
f
ec
tin
g
th
e
(
P
-
V
)
ch
ar
ac
te
r
is
tics
o
f
th
is
s
y
s
te
m
.
As
a
r
esu
lt,
wh
e
n
t
h
e
m
al
f
u
n
ctio
n
h
ap
p
en
ed
at
PV,
less
elec
tr
icity
was
g
en
er
ated
at
1
4
1
0
.
4
5
watts
(
1
,
2
,
3
,
4
)
.
T
h
r
ee
s
eq
u
en
tial
PV
m
o
d
els
(
1
,
2
,
an
d
3
)
with
i
n
o
n
e
s
tr
in
g
in
th
e
HC
an
d
B
L
to
p
o
lo
g
ies
ex
p
er
ien
ce
d
s
ig
n
if
ic
an
t
wav
e
d
is
to
r
tio
n
[
1
8
]
a
n
d
o
p
en
cir
cu
it
v
o
ltag
e
r
ea
d
in
g
s
o
u
ts
id
e
o
f
th
e
p
er
m
itt
ed
r
an
g
e
.
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.
16
,
No
.
4
,
Dec
em
b
er
20
25
:
2744
-
2
7
5
6
2750
(
a)
(
b
)
(
c)
(
d
)
(
e)
(f)
(
g
)
(
h
)
Fig
u
r
e
8
.
PV a
r
r
a
y
ch
ar
ac
te
r
is
tics
u
n
d
er
cr
o
s
s
lin
e
–
lin
e
f
au
l
t
:
(
a)
(
I
-
V)
cu
r
v
e
f
o
r
SP
; (
b
)
(
P
-
V)
cu
r
v
e
f
o
r
SP
;
(
c)
(
I
-
V)
cu
r
v
e
f
o
r
T
C
T
; (
d
)
(
P
-
V)
cu
r
v
e
f
o
r
T
C
T
; (
e)
(
I
-
V)
c
u
r
v
e
f
o
r
HC
; (
f
)
(
P
-
V)
cu
r
v
e
f
o
r
HC
;
(
g
)
(
I
-
V)
cu
r
v
e
f
o
r
B
L
;
an
d
(
h
)
(
P
-
V)
cu
r
v
e
f
o
r
B
L
T
ab
le
3
.
PV
a
r
r
a
y
p
er
f
o
r
m
a
n
c
e
u
n
d
er
i
n
t
r
a
li
n
e
–
li
n
e
f
a
u
lt
F
a
u
l
t
lo
c
a
t
i
o
n
To
p
o
l
o
g
y
V
o
.
c
(
V
)
I
s.c
(
A
)
V
max
(
V
)
I
max
(
A
)
P
mp
p
(
W
)
A
t
P
V
1
SP
1
1
1
.
4
5
1
.
7
3
7
9
.
9
5
46
3
6
8
0
.
6
3
TC
T
1
1
1
.
4
5
1
.
7
3
9
5
.
5
5
3
8
.
6
5
3
6
9
2
.
3
8
HC
1
1
1
.
4
5
1
.
7
3
9
3
.
6
6
3
7
.
6
3
5
1
9
.
7
8
BL
1
1
1
.
4
5
1
.
7
3
9
3
.
8
9
3
7
.
8
3
5
4
9
.
4
7
A
t
P
V
(
1
,
2
)
SP
1
1
1
.
4
5
1
.
7
3
9
1
.
0
0
37
3
3
7
6
.
2
6
TC
T
89
5
1
.
7
3
7
6
.
0
7
3
8
.
5
2
9
8
2
.
8
7
HC
1
1
0
.
8
6
5
1
.
7
3
8
3
.
7
5
3
8
.
3
3
3
2
1
0
.
4
3
BL
1
1
0
.
8
6
5
1
.
7
3
8
2
.
0
2
3
8
.
4
1
3
1
5
3
.
3
2
A
t
P
V
(
1
,
2
,
3
)
SP
1
1
1
.
4
5
1
.
7
3
9
1
.
1
0
37
3
3
7
3
.
0
3
TC
T
6
6
.
9
6
5
1
.
7
3
5
6
.
6
3
8
.
2
7
2
1
6
7
.
8
4
A
t
P
V
(
1
,
2
,
3
,
4
)
SP
1
1
1
.
4
5
1
.
7
3
9
0
.
8
6
37
3
3
7
7
.
0
3
TC
T
4
4
.
4
5
1
.
7
3
37
3
8
.
1
1
1
4
1
0
.
4
5
HC
9
7
.
7
5
1
.
7
3
5
9
.
9
9
2
8
.
6
1
7
1
6
.
7
2
A
t
P
V
(
1
,
3
,
4
)
BL
1
0
5
.
5
5
1
.
7
3
6
3
.
7
8
3
8
.
3
8
2
4
4
8
.
1
5
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
A
s
s
es
s
men
t o
f th
e
efficien
cy
a
n
d
p
erfo
r
ma
n
ce
o
f
d
iffer
en
t P
V
s
ystem
…
(
R
a
g
h
a
d
A
d
ee
b
O
th
ma
n
)
2751
5
.
3
.
L
ine
–
g
r
o
un
d f
a
ult
in t
he
P
V
a
rr
a
y
T
ab
le
4
illu
s
tr
ates
th
at
th
e
(
I
-
V)
f
ea
tu
r
es
o
f
t
h
e
SP
to
p
o
lo
g
y
wer
e
u
n
af
f
ec
ted
b
y
t
h
is
f
au
l
t,
r
eg
ar
d
less
o
f
its
lo
ca
tio
n
,
wh
en
it
was
p
r
o
jecte
d
b
etwe
en
th
e
s
tr
in
g
an
d
g
r
o
u
n
d
ce
lls
.
W
h
en
a
lin
e
-
g
r
o
u
n
d
f
au
lt
h
a
p
p
en
s
in
th
e
SP
to
p
o
lo
g
y
,
th
e
im
p
ac
ted
s
tr
in
g
o
r
m
o
d
u
le
m
ay
p
r
o
v
id
e
a
lo
w
-
r
esis
tan
ce
ch
an
n
el
to
th
e
g
r
o
u
n
d
.
T
h
e
cu
r
r
en
t
f
lo
w
th
r
o
u
g
h
th
e
g
r
o
u
n
d
p
ath
m
ay
s
ig
n
if
ican
tly
r
is
e
as
a
r
esu
lt
o
f
th
is
.
A
v
o
ltag
e
im
b
alan
ce
in
th
e
im
p
ac
ted
s
tr
in
g
d
u
e
to
th
e
d
e
f
ec
t
m
ay
r
esu
lt
i
n
a
d
ec
r
ea
s
e
in
th
e
s
tr
in
g
'
s
o
v
er
all
o
u
tp
u
t
v
o
ltag
e.
D
u
e
to
th
e
lo
s
s
o
f
th
e
s
tr
in
g
cu
r
r
en
t
th
at
ca
u
s
ed
th
e
f
au
lt,
we
o
b
s
er
v
e
a
d
ec
r
ea
s
e
in
th
e
m
a
x
im
u
m
c
u
r
r
en
t
v
alu
e
to
3
7
A.
I
n
c
o
n
tr
ast,
th
e
o
p
en
cir
cu
it v
o
ltag
e
r
em
ain
e
d
at
its
n
o
r
m
al
v
alu
e,
with
t
h
e
e
x
ce
p
tio
n
o
f
th
e
last
ca
s
e,
in
wh
ich
PV5
was
im
p
ac
ted
b
y
th
e
f
au
lt
,
an
d
th
e
m
ax
im
u
m
v
o
ltag
e
v
alu
e
was
n
o
ted
to
h
av
e
d
ec
r
ea
s
ed
b
y
1
2
%
f
r
o
m
its
v
alu
e
in
th
e
n
o
r
m
al
ca
s
e.
T
h
e
f
ailu
r
e
at
PV3
to
g
r
o
u
n
d
w
o
u
ld
ca
u
s
e
th
e
m
ax
im
u
m
p
o
w
er
o
u
tp
u
t
to
d
r
o
p
to
3
3
7
5
.
2
3
watts.
W
h
en
u
s
in
g
T
C
T
to
p
o
lo
g
y
,
t
h
e
d
ef
ec
t
m
a
y
ca
u
s
e
th
e
v
o
ltag
e
in
th
e
im
p
a
cted
s
tr
in
g
to
d
r
o
p
,
m
u
ch
lik
e
in
th
e
SP
to
p
o
lo
g
y
.
B
ec
au
s
e
th
e
s
tr
in
g
s
ar
e
in
ter
co
n
n
ec
ted
,
t
h
e
T
C
T
to
p
o
lo
g
y
m
ay
b
e
a
b
le
to
p
ar
tially
allev
iate
th
is
v
o
ltag
e
d
r
o
p
,
b
u
t th
e
o
v
e
r
all
o
u
tp
u
t o
f
th
e
ar
r
ay
will st
ill b
e
im
p
ac
ted
.
T
h
e
lo
ca
tio
n
o
f
th
e
f
a
u
lt
an
d
th
e
ef
f
icien
cy
o
f
th
e
c
r
o
s
s
-
ties
in
r
ed
is
tr
ib
u
tin
g
th
e
c
u
r
r
en
t
d
eter
m
in
e
h
o
w
m
u
ch
o
f
a
r
ed
u
ctio
n
in
p
o
wer
o
u
tp
u
t o
cc
u
r
s
.
I
t'
s
p
o
s
s
ib
le
th
at
th
e
ar
r
ay
will k
ee
p
r
u
n
n
in
g
less
ef
f
icien
tly
.
T
h
e
f
in
d
i
n
g
s
s
u
g
g
est
th
at
wh
e
n
th
e
f
a
u
lt
was
co
n
ce
n
tr
ate
d
a
t
th
e
s
tar
t
o
f
th
e
s
tr
in
g
an
d
th
e
g
r
o
u
n
d
,
th
e
T
C
T
to
p
o
lo
g
y
s
aw
th
e
lar
g
est
f
all
in
th
e
v
alu
es
o
f
th
e
o
p
en
cir
c
u
it
v
o
ltag
e
a
n
d
s
h
o
r
t
cir
cu
it
cu
r
r
en
t.
T
h
is
,
in
tu
r
n
,
h
ad
an
im
p
ac
t
o
n
t
h
e
(
I
-
V)
ch
ar
ac
ter
is
tics
o
f
th
is
to
p
o
lo
g
y
.
T
h
e
v
o
ltag
e
d
r
o
p
was
n
ea
r
wh
en
th
e
f
au
lt
h
ap
p
en
e
d
b
etwe
en
PV1
an
d
g
r
o
u
n
d
o
r
PV2
an
d
ea
r
th
,
b
u
t
t
h
e
lar
g
est
cu
r
r
e
n
t
v
alu
e
o
cc
u
r
r
ed
wh
en
th
e
f
ailu
r
e
h
ap
p
en
e
d
b
etwe
en
PV1
an
d
g
r
o
u
n
d
b
ec
au
s
e
th
e
s
tr
in
g
cu
r
r
e
n
t
leak
ed
to
g
r
o
u
n
d
.
T
h
e
o
th
er
p
r
o
b
lem
lo
ca
tio
n
s
d
id
n
o
t e
x
p
er
ien
ce
an
y
c
h
an
g
e
in
th
e
m
ax
im
u
m
cu
r
r
en
t
v
alu
e.
5
.
4
.
O
pen
-
circ
uit
f
a
ult
in t
h
e
P
V
a
rr
a
y
T
esti
n
g
an
o
p
en
cir
cu
it
f
a
u
lt with
in
o
n
e
o
f
t
h
e
s
tr
in
g
s
r
e
v
ea
ls
th
at,
as
s
ee
n
in
Fig
u
r
e
9
,
it
i
s
clea
r
h
o
w
f
au
lts
af
f
ec
t
cu
r
r
e
n
t
r
ed
u
ctio
n
in
SP
to
p
o
lo
g
y
.
Du
e
to
th
e
s
tr
i
n
g
cu
r
r
en
t
lo
s
s
wh
er
e
th
e
f
a
u
lt
o
cc
u
r
s
,
th
is
ef
f
ec
t
m
an
if
ests
wh
en
th
e
f
a
u
lt
h
ap
p
en
s
in
an
y
s
tr
in
g
in
s
id
e
t
h
is
to
p
o
lo
g
y
.
T
h
e
d
am
a
g
ed
s
tr
in
g
d
o
esn
'
t
p
r
o
v
id
e
an
y
p
o
wer
;
h
en
ce
,
th
e
o
v
e
r
all
o
u
tp
u
t
o
f
t
h
e
a
r
r
ay
is
d
ec
r
ea
s
ed
ev
en
t
h
o
u
g
h
t
h
e
o
th
er
p
ar
allel
s
tr
in
g
s
ar
e
r
u
n
n
in
g
n
o
r
m
ally
.
T
h
e
am
o
u
n
t
o
f
im
p
a
cted
s
tr
in
g
s
d
ir
ec
tly
co
r
r
elate
s
with
th
e
p
o
wer
lo
s
s
.
T
h
is
is
d
em
o
n
s
tr
ated
b
y
th
e
f
ac
t
th
at
wh
en
a
f
au
lt
o
cc
u
r
s
i
n
o
n
e
s
tr
in
g
,
th
e
m
ax
im
u
m
p
o
wer
v
alu
e
lo
wer
s
f
r
o
m
its
n
o
r
m
al
v
alu
e
o
f
4
2
1
6
.
3
watts
to
3
3
7
3
.
0
1
watts,
an
d
wh
en
a
f
au
lt
o
cc
u
r
s
in
two
s
tr
in
g
s
,
th
e
p
o
wer
d
r
o
p
s
to
2
5
2
9
.
7
8
watts.
T
h
e
c
u
r
r
e
n
t
f
r
o
m
th
e
o
th
er
p
ar
allel
m
o
d
u
les
is
r
e
d
is
tr
ib
u
ted
th
r
o
u
g
h
th
e
o
th
e
r
f
u
n
ctio
n
al
m
o
d
u
les
at
th
e
T
C
T
to
p
o
lo
g
y
wh
en
an
o
p
e
n
-
cir
cu
it
f
au
lt
o
cc
u
r
s
in
o
n
e
o
f
th
e
m
o
d
u
les.
Alth
o
u
g
h
th
e
ar
r
ay
'
s
o
u
tp
u
t
is
d
ec
r
ea
s
ed
,
it
ca
n
s
till
p
r
o
v
id
e
p
o
wer
.
I
n
co
m
p
ar
is
o
n
t
o
th
e
SP
ar
r
a
n
g
em
en
t,
t
h
e
T
C
T
co
n
f
ig
u
r
atio
n
m
in
im
izes
p
o
wer
lo
s
s
b
y
en
a
b
lin
g
s
u
r
r
o
u
n
d
in
g
s
tr
in
g
s
to
a
d
ju
s
t
f
o
r
th
e
v
o
ltag
e
o
f
th
e
m
alf
u
n
ctio
n
in
g
s
tr
in
g
.
C
o
n
s
eq
u
en
tly
,
we
d
is
co
v
er
th
at
th
e
T
C
T
to
p
o
lo
g
y
ex
p
er
ien
ce
d
th
e
least
r
ed
u
ctio
n
in
m
ax
im
u
m
p
o
wer
,
d
r
o
p
p
in
g
to
3
6
9
2
.
3
1
watts.
B
etter
cu
r
r
e
n
t
r
ed
is
tr
ib
u
tio
n
is
p
o
s
s
ib
le
in
th
e
ev
en
t
o
f
an
o
p
e
n
-
cir
cu
it
f
au
lt
with
t
h
e
HC
co
n
f
i
g
u
r
atio
n
.
Sin
ce
th
e
p
r
o
b
lem
ati
c
m
o
d
u
le'
s
cu
r
r
en
t
is
m
o
r
e
ef
f
icien
tly
d
is
tr
ib
u
ted
am
o
n
g
n
ea
r
b
y
m
o
d
u
les,
th
e
im
p
ac
t
o
f
th
e
f
ailu
r
e
is
r
ed
u
ce
d
.
T
h
e
g
r
ea
test
p
o
wer
i
n
th
is
to
p
o
lo
g
y
was
3
4
1
3
.
7
5
watts.
Ho
wev
er
,
in
B
L
T
o
p
o
l
o
g
y
,
th
e
b
r
id
g
e
co
n
n
ec
tio
n
s
p
er
m
it
th
e
cu
r
r
e
n
t
to
tr
av
el
th
r
o
u
g
h
t
h
e
d
ef
ec
tiv
e
s
tr
in
g
in
th
e
e
v
en
t
o
f
an
o
p
en
-
cir
cu
it
m
alf
u
n
ctio
n
.
T
h
e
ar
r
a
y
'
s
o
u
tp
u
t
is
b
ar
ely
ch
an
g
ed
,
an
d
t
h
e
u
n
af
f
ec
te
d
m
o
d
u
les
k
ee
p
r
u
n
n
in
g
.
B
ec
au
s
e
o
f
th
e
way
th
e
B
L
to
p
o
lo
g
y
is
o
lates
th
e
p
r
o
b
lem
atic
m
o
d
u
le,
th
er
e
is
les
s
d
is
tu
r
b
an
ce
to
th
e
r
em
ain
d
er
o
f
th
e
ar
r
ay
'
s
f
u
n
ctio
n
ality
.
T
h
e
m
ax
im
u
m
p
o
we
r
d
r
o
p
s
to
3
4
4
9
.
1
4
ac
c
o
r
d
in
g
to
th
e
r
esu
lts
.
T
ab
le
4
.
PV
a
r
r
a
y
p
er
f
o
r
m
a
n
c
e
u
n
d
er
li
n
e
–
g
r
o
u
n
d
f
a
u
l
t
F
a
u
l
t
l
o
c
a
t
i
o
n
To
p
o
l
o
g
y
V
o
.
c
(
V
)
I
s.c
(
A
)
V
max
(
V
)
I
max
(
A
)
P
mp
p
(
W
)
F
r
o
m PV
1
SP
1
1
1
.
4
5
1
.
7
3
9
1
.
1
0
37
3
3
7
3
.
0
3
TC
T
2
2
.
4
7
4
1
.
3
8
1
8
.
6
9
37
6
9
2
.
9
2
BL
6
8
.
9
2
4
1
.
3
4
3
9
.
2
7
2
8
.
1
7
1
1
0
5
.
2
4
F
r
o
m PV
2
SP
1
1
1
.
4
5
1
.
7
3
9
1
.
0
1
37
3
3
6
8
.
7
8
TC
T
2
1
.
7
3
5
1
.
7
3
1
7
.
7
8
4
6
.
5
8
2
8
.
5
7
BL
6
8
.
0
2
5
1
.
7
3
3
8
.
5
5
2
7
.
9
9
1
0
8
3
.
9
7
F
r
o
m PV
3
SP
1
1
1
.
4
5
1
.
7
3
9
1
.
0
5
37
3
3
7
3
.
0
3
TC
T
4
4
.
1
1
5
1
.
7
3
3
6
.
2
4
46
1
6
7
5
.
6
4
BL
9
0
.
4
1
5
1
.
7
3
3
9
.
0
3
4
6
.
8
5
1
8
2
7
.
9
3
F
r
o
m PV
4
SP
1
1
1
.
4
5
1
.
7
3
9
1
.
2
0
37
3
3
7
5
.
2
3
TC
T
6
6
.
5
5
1
.
7
3
5
4
.
4
0
4
6
.
2
2
5
2
2
.
4
3
F
r
o
m PV
5
SP
1
1
1
.
4
5
1
.
7
3
7
9
.
9
5
3
8
.
9
3
6
8
0
.
6
3
TC
T
8
8
.
9
5
1
.
7
3
7
2
.
8
4
6
.
3
3
3
3
6
9
.
4
HC
1
0
6
.
6
5
1
.
7
3
7
4
.
9
8
4
6
.
4
3
3
4
8
1
.
5
3
BL
1
0
5
.
5
4
5
1
.
7
3
7
6
.
4
9
4
6
.
3
4
3
5
3
9
.
7
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.
16
,
No
.
4
,
Dec
em
b
er
20
25
:
2744
-
2
7
5
6
2752
(
a)
(
b
)
(
c)
(
d
)
(
e)
(f)
(
g
)
(
h
)
Fig
u
r
e
9
.
PV
ar
r
a
y
ch
ar
ac
te
r
is
tics
u
n
d
er
o
p
en
cir
cu
it
f
au
lt
:
(I
-
V)
c
u
r
v
e
f
o
r
SP
; (
b
)
(
P
-
V)
cu
r
v
e
f
o
r
SP
;
(
c)
(
I
-
V)
c
u
r
v
e
f
o
r
T
C
T
; (
d
)
(
P
-
V)
cu
r
v
e
f
o
r
T
C
T
; (
e)
(
I
-
V
)
c
u
r
v
e
f
o
r
HC
; (
f
)
(
P
-
V)
cu
r
v
e
f
o
r
HC
;
(
g
)
(
I
-
V)
c
u
r
v
e
f
o
r
B
L
;
an
d
(
h
)
(
P
-
V)
c
u
r
v
e
f
o
r
B
L
5
.
5
.
Co
m
pa
riso
n o
f
perf
o
rma
nce
o
f
t
he
P
V
a
rr
a
y
c
o
nfig
ura
t
io
ns
I
n
o
r
d
e
r
to
co
m
p
ar
e
th
e
p
er
f
o
r
m
an
ce
o
f
th
e
f
o
u
r
to
p
o
lo
g
ies
wh
en
f
au
lts
o
cc
u
r
r
ed
,
th
ese
f
au
lts
wer
e
p
lace
d
in
th
e
s
am
e
lo
ca
tio
n
f
o
r
all
o
f
th
ese
to
p
o
lo
g
ies
at
STC,
an
d
th
e
r
esu
lts
s
h
o
wed
in
Fig
u
r
e
1
0
th
at,
th
e
ef
f
ec
t
o
f
th
e
o
p
en
cir
cu
it f
au
lt b
etwe
en
PV
(
7
,
8
)
i
n
th
e
f
ir
s
t
s
tr
in
g
an
d
PV
(
1
8
,
1
9
)
i
n
th
e
f
o
u
r
th
s
tr
in
g
,
it
led
to
a
d
ec
r
ea
s
e
in
th
e
s
h
o
r
t
-
cir
c
u
it
cu
r
r
en
t
o
f
th
e
p
h
o
to
v
o
ltaic
s
y
s
tem
b
y
4
0
%
f
r
o
m
its
v
alu
e
in
th
e
n
o
r
m
al
s
tate
in
th
e
SP
to
p
o
lo
g
y
,
wh
ile
th
e
v
alu
e
o
f
th
is
cu
r
r
en
t
in
cr
ea
s
ed
b
ey
o
n
d
th
e
p
e
r
m
is
s
ib
le
lim
it
in
th
e
HC
an
d
B
L
to
p
o
lo
g
ies,
a
n
d
th
is
in
t
u
r
n
af
f
ec
ted
th
e
(
I
-
V)
ch
ar
ac
ter
is
tics
o
f
th
is
to
p
o
lo
g
y
.
W
h
ile
i
n
th
e
T
C
T
to
p
o
lo
g
y
,
t
h
e
ef
f
ec
t o
f
th
e
f
au
lt wa
s
lim
ited
an
d
with
in
th
e
n
o
r
m
al
lim
its
o
f
its
(
I
-
V)
ch
ar
ac
te
r
is
tics
.
As
f
o
r
th
e
(
P
-
V)
ch
a
r
ac
ter
is
tics
,
th
e
p
er
f
o
r
m
a
n
ce
o
f
th
e
T
C
T
was
b
etter
th
an
th
e
o
th
er
t
o
p
o
lo
g
y
,
as
it
h
ad
th
e
h
ig
h
est
p
o
wer
g
en
e
r
at
ed
u
n
d
er
th
e
in
f
l
u
en
ce
o
f
th
is
f
au
lt.
As
f
o
r
th
e
SP
,
th
e
p
o
wer
g
en
er
ated
u
n
d
er
th
e
in
f
lu
en
ce
o
f
th
is
f
au
lt
d
ec
r
ea
s
ed
s
ig
n
if
ican
tly
,
r
ea
ch
in
g
4
0
%
o
f
its
v
alu
e
in
th
e
n
o
r
m
al
s
tate.
W
h
en
th
e
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
A
s
s
es
s
men
t o
f th
e
efficien
cy
a
n
d
p
erfo
r
ma
n
ce
o
f
d
iffer
en
t P
V
s
ystem
…
(
R
a
g
h
a
d
A
d
ee
b
O
th
ma
n
)
2753
in
tr
a
-
lin
e
-
lin
e
f
a
u
lt
was
im
p
o
s
ed
b
etwe
en
PV
(
1
,
2
)
in
t
h
e
f
o
u
r
to
p
o
lo
g
ies,
it
led
to
a
d
ec
r
e
ase
in
th
e
v
al
u
e
o
f
th
e
o
p
e
n
ci
r
cu
it
v
o
ltag
e
b
y
4
0
.
3
%
f
r
o
m
its
v
alu
e
in
th
e
n
o
r
m
al
ca
s
e
in
th
e
T
C
T
to
p
o
lo
g
y
.
T
h
e
r
e
was
a
s
ig
n
if
ican
t
d
is
to
r
tio
n
[
2
9
]
in
th
e
ch
a
r
ac
ter
is
tics
o
f
th
e
H
C
to
p
o
lo
g
y
,
d
esp
ite
th
e
clo
s
en
ess
o
f
th
e
r
esu
lts
b
etwe
en
it
an
d
th
e
B
L
to
p
o
lo
g
y
.
T
h
e
(
P
-
V)
ch
a
r
ac
ter
is
tics
u
n
d
er
th
e
in
f
l
u
en
ce
o
f
th
is
f
a
u
lt
wer
e
th
e
b
est
in
th
e
SP
to
p
o
lo
g
y
,
as it g
av
e
th
e
h
ig
h
est
g
en
e
r
ated
p
o
wer
,
as sh
o
wn
in
Fig
u
r
e
1
1
.
W
h
en
th
e
c
r
o
s
s
-
lin
e
–
lin
e
f
au
lt
is
h
ig
h
lig
h
te
d
b
etwe
en
PV1
in
th
e
f
ir
s
t
s
tr
in
g
an
d
PV8
in
t
h
e
s
ec
o
n
d
s
tr
in
g
,
we
n
o
tice
t
h
e
ef
f
ec
t
o
f
th
e
f
au
lt
in
d
ec
r
ea
s
in
g
th
e
o
p
en
cir
cu
it
v
o
ltag
e
in
t
h
e
T
C
T
to
p
o
lo
g
y
,
wh
ic
h
af
f
ec
ted
its
(
I
-
V)
ch
ar
ac
ter
is
tics
as
s
h
o
wn
in
Fig
u
r
e
1
2
.
T
h
is
f
au
lt
also
af
f
ec
ted
th
e
(
P
-
V
)
ch
ar
ac
ter
is
tics
o
f
th
is
to
p
o
lo
g
y
.
T
h
e
(
I
-
V)
a
n
d
(
P
-
V)
ch
ar
ac
ter
is
tics
o
f
th
e
H
C
an
d
B
L
to
p
o
lo
g
ies
ar
e
v
er
y
s
im
ilar
.
Desp
ite
th
e
o
cc
u
r
r
e
n
ce
o
f
d
is
to
r
tio
n
,
th
e
d
y
n
am
ic
an
d
in
tr
icate
in
ter
ac
ti
o
n
s
th
at
o
cc
u
r
with
in
th
e
p
h
o
t
o
v
o
ltaic
ar
r
a
y
as
it
attem
p
ts
to
r
ed
is
tr
ib
u
te
c
u
r
r
e
n
t,
r
eg
u
late
v
o
ltag
e,
an
d
p
r
eser
v
e
o
v
e
r
all
s
y
s
tem
b
alan
ce
ar
e
th
e
m
ain
ca
u
s
e
o
f
th
e
n
o
is
e
s
h
o
wn
in
t
h
e
P
-
V
c
u
r
v
e.
T
h
e
P
-
V
c
u
r
v
e
ex
h
i
b
its
ab
n
o
r
m
alities
o
r
n
o
is
e
d
u
e
t
o
tr
an
s
ien
t
ef
f
ec
ts
,
v
o
ltag
e
v
ar
iatio
n
s
,
a
n
d
h
ar
m
o
n
ic
d
is
to
r
tio
n
s
ca
u
s
ed
b
y
th
es
e
in
ter
ac
tio
n
s
.
Alth
o
u
g
h
th
e
B
L
&
HC
ar
ch
itectu
r
e
is
in
ten
d
ed
t
o
r
e
d
u
ce
th
e
im
p
a
ct
o
f
f
ailu
r
es,
th
e
q
u
ick
m
o
d
if
icatio
n
s
an
d
a
d
ju
s
tm
en
ts
n
ec
e
s
s
ar
y
to
is
o
late
th
e
f
au
lt
an
d
r
ed
is
tr
ib
u
te
p
o
wer
m
ay
ca
u
s
e
m
o
m
e
n
tar
y
d
is
r
u
p
tio
n
s
in
th
e
o
u
tp
u
t
c
h
ar
ac
ter
is
tics
o
f
th
e
s
y
s
tem
,
th
e
HC
wav
e
[
2
9
]
–
[
3
1
]
.
T
h
e
SP
&
B
L
to
p
o
lo
g
y
h
ad
th
e
b
est p
er
f
o
r
m
an
ce
u
n
d
e
r
th
e
in
f
l
u
en
ce
o
f
th
is
f
au
lt.
(
a)
(
b
)
Fig
u
r
e
1
0
.
PV
ar
r
ay
c
h
ar
ac
ter
i
s
tics
u
n
d
er
o
p
en
cir
cu
it f
au
lt:
(
a)
(
I
-
V)
c
u
r
v
e
a
n
d
(
b
)
(
P
-
V)
c
u
r
v
e
(
a)
(
b
)
Fig
u
r
e
1
1
.
PV
ar
r
ay
c
h
ar
ac
ter
i
s
tics
u
n
d
er
in
tr
a
lin
e
–
lin
e
f
au
lt
:
(
a)
(
I
-
V)
c
u
r
v
e
a
n
d
(
b
)
(
P
-
V)
c
u
r
v
e
(
a)
(
b
)
Fig
u
r
e
1
2
.
PV
ar
r
ay
c
h
ar
ac
ter
i
s
tics
u
n
d
er
cr
o
s
s
lin
e
–
lin
e
f
a
u
lt
:
(
a)
(
I
-
V
)
c
u
r
v
e
an
d
(
b
)
(
P
-
V)
c
u
r
v
e
L
in
e
-
to
-
lin
e
f
a
u
lts
in
elec
tr
ical
n
etwo
r
k
s
ca
n
b
e
clo
s
ely
ass
o
ciate
d
with
th
e
PV
s
y
s
tem
's
p
o
wer
cu
r
v
e
s
p
ik
es.
A
s
u
d
d
en
s
h
o
r
t
-
cir
cu
it
co
n
d
itio
n
b
etwe
en
two
p
h
ases
r
esu
lts
in
a
r
ap
id
r
is
e
in
cu
r
r
e
n
t
d
u
r
in
g
a
lin
e
-
to
-
lin
e
f
au
lt.
T
h
is
ca
u
s
es
a
b
r
ief
d
is
r
u
p
tio
n
in
th
e
s
y
s
tem
,
wh
ich
ca
u
s
es
a
s
u
d
d
en
in
cr
ea
s
e
in
p
o
wer
wh
en
th
e
(
a)
(
b
)
Evaluation Warning : The document was created with Spire.PDF for Python.