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o
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e
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t
h
e
se
in
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e
rters
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o
m
m
o
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ly
e
x
h
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it
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e
c
a
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se
th
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y
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k
g
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a
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ic
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latio
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n
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l
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ter
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c
lam
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d
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CI)
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p
e
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tes
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g
ri
d
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c
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n
e
c
ted
th
re
e
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p
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se
tran
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s
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h
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ic
(T
LP
V)
a
p
p
li
c
a
ti
o
n
s.
H
o
we
v
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th
e
p
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d
in
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rter
su
c
c
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ss
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ll
y
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d
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ts
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tro
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m
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s.
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is
m
a
k
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s
it
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p
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sim
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ti
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r
tran
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o
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m
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s
P
V
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p
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d
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y
,
th
e
trad
it
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n
a
l
f
u
ll
-
b
rid
g
e
(
F
B)
in
v
e
rter
with
th
re
e
p
h
a
se
s
,
wh
e
n
c
o
m
p
a
re
d
to
t
h
e
F
C
in
v
e
rter
,
h
a
s
v
e
ry
h
ig
h
lea
k
a
g
e
c
u
rre
n
t.
S
imu
lati
o
n
re
su
l
ts
v
a
li
d
a
te
th
e
F
C
in
v
e
rter’s
a
b
il
it
y
t
o
m
in
imiz
e
lea
k
a
g
e
c
u
rre
n
t.
K
ey
w
o
r
d
s
:
Fil
ter
-
clam
p
ed
in
v
er
ter
Fu
ll
-
b
r
id
g
e
in
v
er
ter
Gr
id
-
co
n
n
e
cted
in
v
e
r
ter
L
ea
k
ag
e
cu
r
r
en
t
r
e
d
u
ctio
n
T
L
PV in
v
er
ter
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
:
S.
Ven
k
ata
Pad
m
av
ath
i
Dep
ar
tm
en
t o
f
E
lectr
ical
,
E
lec
tr
o
n
ics
,
an
d
C
o
m
m
u
n
icatio
n
E
n
g
in
ee
r
in
g
,
GSC
E
GI
T
AM
(
Dee
m
ed
to
b
e
Un
iv
e
r
s
ity
)
Hy
d
er
ab
ad
,
T
elan
g
a
n
a,
I
n
d
ia
E
m
ail:
v
s
aty
av
a@
g
itam
.
ed
u
1.
I
NT
RO
D
UCT
I
O
N
Dir
ec
t
cu
r
r
en
t
(
DC
)
p
r
o
d
u
ce
d
b
y
p
h
o
t
o
v
o
ltaic
(
PV
)
m
o
d
u
le
s
is
p
r
o
ce
s
s
ed
b
y
s
witch
ed
-
m
o
d
e
p
o
wer
co
n
v
er
ter
s
,
en
a
b
lin
g
q
u
ick
er
co
n
tr
o
l
r
esp
o
n
s
es
th
an
th
o
s
e
o
f
o
th
er
r
en
ewa
b
le
en
er
g
y
s
o
u
r
ce
s
.
B
o
th
th
e
ex
p
an
s
io
n
o
f
d
is
tr
ib
u
ted
s
o
lar
en
er
g
y
with
in
co
m
m
u
n
ities
an
d
lar
g
e
in
v
estme
n
ts
in
m
eg
awa
tt
-
s
ca
le
ce
n
tr
al
PV
p
lan
ts
h
av
e
b
ee
n
s
p
u
r
r
ed
b
y
th
ese
b
en
e
f
its
[
1
]
,
[
2
]
.
Dif
f
er
en
t
f
r
o
m
o
th
e
r
r
en
ewa
b
le
e
n
er
g
y
s
y
s
tem
s
,
PV
in
v
er
ter
s
h
av
e
u
n
iq
u
e
f
ea
tu
r
es.
T
h
r
ee
-
p
h
ase
in
v
er
ter
s
ca
n
e
m
p
lo
y
s
m
aller
ca
p
ac
itiv
e
f
ilt
er
s
wh
ile
m
ain
tain
in
g
co
n
s
ta
n
t
v
o
ltag
e
b
ec
au
s
e
,
in
th
e
DC
co
n
n
ec
ti
on
,
th
ey
d
o
n
o
t
en
c
o
u
n
ter
d
o
u
b
le
-
lin
e
-
f
r
eq
u
en
cy
r
i
p
p
les,
u
n
lik
e
s
in
g
le
-
p
h
ase
s
y
s
tem
s
[
3
]
–
[
6
]
.
T
h
is
im
p
r
o
v
es
s
y
s
tem
r
eliab
ilit
y
.
T
h
e
co
s
t
o
f
s
o
lar
en
e
r
g
y
is
s
tr
o
n
g
l
y
im
p
ac
ted
b
y
th
e
ef
f
icien
cy
,
d
e
p
en
d
a
b
ilit
y
,
an
d
co
s
t
-
ef
f
ec
tiv
en
ess
o
f
th
e
n
u
m
er
o
u
s
in
v
e
r
ter
s
th
at
m
ak
e
u
p
lar
g
e
-
s
ca
le
PV
s
y
s
tem
s
.
B
ec
au
s
e
o
f
th
eir
g
r
ea
ter
ef
f
icien
cy
,
th
r
ee
-
p
h
ase
PV
in
v
er
ter
s
ar
e
m
o
r
e
ap
p
r
o
p
r
i
ate
f
o
r
h
ig
h
-
p
o
wer
ap
p
licatio
n
s
,
d
esp
ite
th
e
f
ac
t t
h
at
r
esid
en
tial d
is
tr
ib
u
ted
g
e
n
er
atio
n
o
f
te
n
u
s
es si
n
g
le
-
p
h
as
e
in
v
er
ter
s
[
7
]
,
[
8
].
T
r
an
s
f
o
r
m
e
r
less
p
h
o
to
v
o
ltaic
(
T
L
PV)
in
v
er
te
r
s
m
ay
ex
p
er
i
en
ce
s
ig
n
if
ican
t
leak
ag
e
cu
r
r
e
n
ts
d
u
e
to
th
e
co
n
d
u
ctiv
e
c
h
an
n
el
an
d
s
tr
ay
ca
p
ac
itan
ce
th
at
d
ev
elo
p
s
b
etwe
en
th
e
g
r
o
u
n
d
an
d
th
e
PV
ar
r
ay
[
9
]
–
[1
1
]
.
Dep
en
d
in
g
o
n
wh
et
h
er
th
e
s
o
lar
ce
ll
is
th
in
-
f
ilm
,
p
o
ly
cr
y
s
t
allin
e,
o
r
m
o
n
o
cr
y
s
tallin
e,
th
e
v
alu
e
o
f
th
is
p
ar
asit
ic
ca
p
ac
itan
ce
u
s
u
ally
f
alls
b
etwe
en
6
0
an
d
1
6
0
n
F/k
W
[
1
2
]
.
I
n
ad
d
itio
n
to
en
d
an
g
er
in
g
th
e
s
af
ety
o
f
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
.
3
,
Sep
tem
b
er
20
2
6
:
1553
-
1
5
6
3
1554
m
ain
ten
an
ce
wo
r
k
er
s
,
lea
k
a
g
e
cu
r
r
en
t
ca
n
lead
to
in
c
r
ea
s
ed
h
ar
m
o
n
ic
d
is
to
r
tio
n
i
n
th
e
lin
e
cu
r
r
en
t,
in
ter
f
er
en
ce
o
f
c
o
m
m
o
n
-
m
o
d
e
,
an
d
ex
tr
a
lo
s
s
es
in
th
e
s
y
s
tem
.
T
h
er
e
f
o
r
e,
in
ter
n
atio
n
al
r
eg
u
latio
n
s
estab
lis
h
r
ig
o
r
o
u
s
r
estrictio
n
s
o
n
leak
ag
e
cu
r
r
en
t.
Fo
r
in
s
tan
ce
,
th
e
leak
ag
e
cu
r
r
e
n
t
R
MS
v
alu
e
m
u
s
t
s
tay
b
elo
w
3
0
0
m
A
in
ac
co
r
d
an
ce
with
th
e
VDE
0
1
2
6
-
01
-
0
1
s
t
an
d
a
r
d
[
13
]
,
[
14
].
B
ased
o
n
th
is
b
ac
k
g
r
o
u
n
d
,
n
u
m
er
o
u
s
r
esear
ch
ef
f
o
r
ts
h
av
e
f
o
cu
s
ed
o
n
r
ed
u
cin
g
leak
a
g
e
c
u
r
r
en
t
an
d
en
h
an
cin
g
ef
f
icien
c
y
in
T
L
PV
in
v
er
ter
s
.
I
n
[
15
]
,
a
m
eth
o
d
was
in
tr
o
d
u
ce
d
w
h
er
e
an
a
d
d
i
tio
n
al
p
o
wer
s
witch
d
is
co
n
n
ec
ts
th
e
PV
a
r
r
ay
f
r
o
m
th
e
DC
s
id
e
to
m
in
im
iz
e
leak
ag
e
cu
r
r
e
n
t.
Ho
we
v
er
,
th
is
s
witch
ca
u
s
es
s
ig
n
if
ican
t
p
o
wer
lo
s
s
es
s
in
ce
it
o
p
er
ates
at
a
h
ig
h
f
r
eq
u
en
c
y
.
I
n
th
r
ee
-
p
h
ase
PV
s
y
s
tem
s
,
t
h
e
leak
ag
e
cu
r
r
e
n
t
was
ef
f
ec
tiv
ely
d
ec
r
ea
s
ed
b
y
ad
d
in
g
two
ad
d
itio
n
al
s
witch
es
to
th
e
tr
ad
itio
n
al
f
u
ll
-
b
r
i
d
g
e
(
FB
)
in
v
er
ter
ar
r
an
g
em
e
n
t
in
[
16
]
an
d
[
17
].
I
n
n
e
u
tr
al
-
p
o
in
t
clam
p
e
d
in
v
er
ter
an
d
FB
i
n
v
er
ter
to
p
o
lo
g
ies
,
an
ad
d
itio
n
al
m
eth
o
d
d
escr
ib
e
d
in
[
18
]
co
n
n
ec
ts
th
e
g
r
id
'
s
n
eu
tr
al
p
o
in
t
to
th
e
DC
co
n
n
ec
tio
n
'
s
m
id
way
.
Ho
wev
er
,
th
is
ar
r
an
g
em
e
n
t n
ee
d
s
m
o
r
e
s
witch
es th
an
th
e
tr
a
d
itio
n
al
FB
in
v
er
ter
.
I
n
s
tu
d
y
[
7
]
,
a
th
r
ee
-
p
h
ase,
f
u
ll
-
b
r
id
g
e
r
ec
tifie
r
with
ze
r
o
-
v
o
ltag
e
t
o
p
o
lo
g
y
was
s
u
g
g
est
ed
,
wh
ich
u
s
es
twelv
e
m
o
r
e
d
io
d
es
a
n
d
two
m
o
r
e
s
witch
es
th
an
th
e
t
y
p
ical
FB
in
v
er
ter
.
Desp
ite
its
ef
f
ec
tiv
en
ess
,
th
is
d
esig
n
g
r
ea
tly
r
aises
s
y
s
tem
co
s
ts
an
d
p
o
wer
lo
s
s
es.
A
f
ast
r
ec
o
v
er
y
d
io
d
e
an
d
a
m
o
d
u
latio
n
ap
p
r
o
ac
h
in
ten
d
ed
to
k
ee
p
u
p
a
s
tead
y
c
o
m
m
o
n
-
m
o
d
e
v
o
ltag
e
(
C
MV
)
an
d
o
n
e
o
f
a
Z
-
s
o
u
r
ce
in
v
e
r
ter
'
s
ch
ar
ac
ter
is
tics
i
s
its
ab
ilit
y
to
lo
wer
leak
ag
e
cu
r
r
en
t
s
h
o
wn
in
[
19
]
.
Similar
t
o
th
is
,
th
e
r
ed
u
ce
d
c
o
m
m
o
n
-
m
o
d
e
v
o
ltag
e
PW
M
(
R
C
MV
-
P
W
M)
tech
n
iq
u
es su
g
g
ested
in
[
2
0
]
p
r
o
v
i
d
e
b
ip
o
lar
o
u
tp
u
t v
o
ltag
e
b
u
t h
a
v
e
d
is
a
d
v
an
tag
es in
clu
d
in
g
h
ig
h
s
witch
in
g
lo
s
s
es,
v
o
ltag
e
s
p
ik
es,
an
d
s
ig
n
if
ica
n
t
cu
r
r
en
t
r
ip
p
les
ac
r
o
s
s
f
ilter
in
d
u
cto
r
s
,
wh
ich
ev
en
tu
all
y
r
ed
u
ce
ef
f
icien
cy
.
A
n
ew
s
p
ac
e
-
v
ec
to
r
m
o
d
u
latio
n
(
SVM)
m
eth
o
d
f
o
r
th
r
ee
-
p
h
ase
T
-
ty
p
e
in
v
er
ter
s
was
p
r
o
p
o
s
ed
i
n
[2
1
]
to
f
u
r
th
e
r
m
in
im
ize
le
ak
ag
e
cu
r
r
en
t.
Ho
wev
er
,
T
-
ty
p
e
in
v
er
ter
s
r
e
q
u
ir
e
m
o
r
e
co
m
p
o
n
en
ts
th
an
co
n
v
en
tio
n
al
in
v
er
ter
s
tr
u
ct
u
r
es.
Fil
ter
-
c
lam
p
ed
(
FC
)
in
v
er
ter
s
ar
e
d
ef
in
ed
in
th
is
s
tu
d
y
as
in
v
er
ter
s
etu
p
s
th
at
lin
k
th
e
g
r
id
-
s
id
e
f
ilter
'
s
n
eu
tr
al
p
o
in
t
t
o
th
e
DC
lin
k
'
s
m
id
p
o
in
t
.
An
in
v
er
ter
with
th
r
ee
p
h
ases
f
o
r
a
5
0
-
k
W
tr
an
s
f
o
r
m
er
less
s
y
s
tem
th
at
r
ed
u
ce
s
leak
ag
e
cu
r
r
e
n
t
b
y
co
n
n
ec
tin
g
th
e
n
eu
tr
al
p
o
in
t
o
f
t
h
e
f
ilter
to
th
e
DC
-
lin
k
'
s
m
id
way
in
[
22
]
it wa
s
p
r
esen
ted
.
Fo
r
v
ar
iab
le
-
s
p
ee
d
m
o
to
r
d
r
iv
es,
an
o
th
er
in
s
tan
ce
o
f
attac
h
i
n
g
an
L
C
f
ilter
to
th
e
DC
-
lin
k
m
id
p
o
in
t
h
as
b
ee
n
in
v
esti
g
ated
[
2
3
]
.
Nev
er
th
eless
,
f
in
d
in
g
s
f
r
o
m
[
2
3
]
a
r
e
n
o
t
d
ir
ec
tly
s
u
itab
le
f
o
r
T
L
PV
s
y
s
tem
s
em
p
lo
y
in
g
L
C
L
f
ilter
s
.
I
n
s
p
lit
DC
lin
k
th
r
ee
-
p
h
ase
p
h
o
t
o
v
o
ltaic
s
y
s
tem
s
,
n
eu
tr
al
-
p
o
i
n
t
clam
p
ed
an
d
FB
to
p
o
lo
g
ies
wer
e
e
x
am
in
ed
in
[
18
]
an
d
[
24
]
,
r
esp
ec
tiv
ely
,
b
u
t
th
ese
d
esig
n
s
ar
e
n
o
t
id
ea
l
f
o
r
th
r
ee
-
p
h
ase
th
r
ee
-
wir
e
g
r
id
s
th
at
lack
a
n
eu
tr
al
c
o
n
d
u
ct
o
r
.
Ad
d
itio
n
ally
,
s
p
lit
DC
lin
k
s
a
n
d
ex
tr
a
s
witch
es
h
av
e
b
ee
n
s
u
g
g
ested
f
o
r
PV
in
v
er
ter
s
th
at
ar
e
s
in
g
le
-
p
h
ase
in
[
25
]
an
d
[
26
]
.
A
h
alf
-
b
r
id
g
e
s
in
g
le
-
p
h
ase
ze
r
o
-
v
o
lt
ag
e
s
tate
r
ec
tifie
r
was
p
r
esen
t
ed
i
n
[
26
]
;
i
n
th
is
,
an
ac
tiv
e
s
witch
an
d
d
io
d
e
r
ec
tifie
r
co
n
n
ec
t
th
e
DC
-
li
n
k
m
id
way
to
t
h
e
in
v
er
te
r
'
s
o
u
tp
u
t
.
I
n
a
s
o
lar
p
h
o
to
v
o
ltaic
s
y
s
tem
co
n
n
ec
t
ed
to
th
e
g
r
i
d
with
two
s
tag
es
an
d
th
r
ee
p
h
ases
with
o
u
t
a
tr
an
s
f
o
r
m
er
to
ef
f
ec
tiv
ely
lo
wer
lea
k
ag
e
cu
r
r
en
t,
a
f
ilter
-
clam
p
e
d
in
v
e
r
ter
t
o
p
o
lo
g
y
was u
s
ed
in
[
27
].
Ap
p
licatio
n
o
f
th
e
f
ilter
-
clam
p
ed
in
v
er
te
r
in
Fig
u
r
e
1
,
d
ep
i
ctin
g
T
L
PV
g
r
id
-
co
n
n
ec
ted
t
h
r
ee
-
p
h
ase
s
y
s
tem
s
,
i
s
th
e
m
ain
to
p
ic
o
f
t
h
is
wo
r
k
.
I
n
th
is
co
n
f
ig
u
r
atio
n
,
A
DC
/
DC
b
o
o
s
t
co
n
v
er
ter
th
at
co
n
n
ec
ts
th
e
DC
lin
k
to
th
e
PV
ar
r
ay
m
ay
b
e
p
o
s
itio
n
ed
,
an
d
to
th
e
DC
lin
k
'
s
m
id
p
o
in
t
,
an
L
C
L
f
ilter
is
lin
k
ed
[
28
].
T
h
is
ar
r
an
g
em
e
n
t
h
elp
s
to
s
ig
n
if
ic
an
tly
r
ed
u
ce
leak
ag
e
cu
r
r
en
t,
en
h
an
ce
th
e
q
u
ality
an
d
ef
f
ici
en
cy
o
f
th
e
c
u
r
r
en
t
o
u
tp
u
t,
a
n
d
m
i
n
im
ize
DC
-
lin
k
ca
p
ac
ito
r
v
o
ltag
e
r
ip
p
les.
L
z
g
S
3
B
D
1
D
3
D
2
D
5
S
6
D
4
D
6
S
4
S
2
A
C
L
x
g
L
y
g
S
1
G
r
i
d
B
o
o
s
t
C
o
n
v
e
r
t
e
r
P
V
C
D
C
S
b
L
B
D
B
S
5
C
P
E
V
D
C
P
N
L
x
z
L
y
z
L
z
z
C
f
R
f
V
x
g
V
y
g
V
z
g
n
C
D
C
Fig
u
r
e
1
.
Fil
ter
-
clam
p
e
d
g
r
i
d
-
co
n
n
ec
ted
t
h
r
ee
-
p
h
ase
tr
an
s
f
o
r
m
er
less
p
h
o
to
v
o
ltaic
s
y
s
tem
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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8
6
9
4
I
mp
leme
n
ta
tio
n
o
f filter
-
cla
mp
ed
to
p
o
l
o
g
y
fo
r
t
r
a
n
s
fo
r
merles
s
th
r
ee
-
p
h
a
s
e
P
V
…
(
Mo
h
a
m
med
A
b
d
u
lla
h
)
1555
T
h
e
p
r
o
p
o
s
ed
f
ilter
-
clam
p
e
d
in
v
er
ter
(
FC
I
)
to
p
o
lo
g
y
d
if
f
er
s
f
r
o
m
p
r
e
v
io
u
s
ly
r
ep
o
r
ted
in
v
er
te
r
s
tr
u
ctu
r
es
in
s
ev
er
al
way
s
.
U
n
lik
e
th
e
d
esig
n
s
p
r
esen
ted
in
[
15
]
–
[
17
]
,
[
19
]
,
an
d
[
2
1
]
,
a
s
th
er
e
ar
e
n
o
ex
tr
a
co
m
p
o
n
en
ts
n
ee
d
ed
f
o
r
th
e
F
C
I
.
I
t
p
r
o
d
u
ce
s
a
lin
e
-
to
-
lin
e
v
o
ltag
e
o
u
tp
u
t
th
at
is
u
n
i
p
o
lar
,
as
o
p
p
o
s
ed
t
o
[
2
0
]
,
wh
ich
r
ed
u
ce
s
th
e
lin
e
f
ilter
'
s
v
o
ltag
e
s
tr
ess
an
d
p
o
wer
lo
s
s
es
.
I
n
co
n
tr
ast
to
th
e
s
y
s
tem
s
d
is
cu
s
s
ed
in
[
22
]
an
d
[
27
]
,
a
co
m
p
r
eh
e
n
s
iv
e
m
ath
em
atica
l
m
o
d
el
is
p
r
esen
ted
in
th
is
p
ap
er
,
i
n
clu
d
in
g
th
e
d
ev
elo
p
m
en
t
o
f
a
co
m
m
o
n
-
m
o
d
e
e
q
u
iv
alen
t
c
ir
cu
it
f
o
r
d
etaile
d
an
aly
s
is
.
Mo
r
eo
v
er
,
th
e
p
r
o
p
o
s
ed
FC
I
also
o
p
er
ates
r
eliab
ly
in
th
r
ee
-
p
h
ase,
th
r
ee
-
wir
e
g
r
i
d
s
y
s
tem
s
th
at
lack
a
n
eu
tr
al
co
n
d
u
cto
r
.
T
h
is
p
a
p
e
r
'
s
p
r
im
ar
y
co
n
tr
ib
u
tio
n
s
ca
n
b
e
s
u
m
m
ed
u
p
as f
o
llo
ws:
–
T
h
e
FC
I
i
s
m
o
d
if
ied
with
a
s
p
lit
D
C
lin
k
to
s
u
cc
e
s
s
f
u
lly
lo
wer
leak
ag
e
cu
r
r
en
t
in
th
r
ee
-
wir
e,
th
r
ee
-
p
h
ase
s
o
lar
s
y
s
tem
s
u
s
in
g
an
L
C
L
o
u
tp
u
t f
ilter
;
–
T
o
illu
s
tr
ate
h
o
w
th
e
FC
I
r
ed
u
ce
s
leak
ag
e
c
u
r
r
e
n
t
in
P
V
ap
p
licatio
n
s
,
m
ath
em
atica
l
an
aly
s
is
an
d
a
co
m
m
o
n
m
o
d
e
m
o
d
el
a
r
e
d
ev
elo
p
ed
; a
n
d
–
T
h
e
F
C
I
r
e
d
u
c
es
l
e
a
k
a
g
e
c
u
r
r
e
n
t
w
i
t
h
o
u
t
t
h
e
n
e
e
d
f
o
r
a
d
d
i
t
i
o
n
a
l
p
a
r
ts
l
i
k
e
c
o
m
m
o
n
-
m
o
d
e
c
h
o
k
e
s
o
r
s
w
it
c
h
e
s
.
T
h
e
s
tr
u
ctu
r
e
o
f
th
is
p
ap
er
is
a
s
f
o
llo
ws
:
i)
T
h
e
m
at
h
em
atica
l
an
aly
s
is
an
d
l
ea
k
ag
e
cu
r
r
en
t
m
o
d
ellin
g
ar
e
r
ep
r
esen
ted
in
s
ec
tio
n
2
f
o
r
th
r
ee
-
p
h
ase
T
L
PV
s
y
s
tem
s
u
s
in
g
b
o
th
FB
an
d
FC
in
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er
t
er
s
,
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d
d
is
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s
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th
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o
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th
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p
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s
y
s
tem
;
ii)
Sectio
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3
in
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s
im
u
latio
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d
d
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io
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s
,
r
esp
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tiv
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;
iii)
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d
Sectio
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tu
d
y
with
k
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o
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p
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m
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ce
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.
2.
G
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CAL ANA
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.
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at
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u
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2
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ay
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m
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r
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g
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p
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f
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ated
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ter
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ter
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C
L
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Fig
u
r
e
3
ex
h
ib
its
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e
FB
in
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ter
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s
co
m
m
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m
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r
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e
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d
th
e
in
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ter
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t
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ter
m
in
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(
a
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F
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a
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u
r
e
2
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h
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ase
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Fig
u
r
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3
to
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eter
m
in
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e
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ea
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ag
e
cu
r
r
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d
-
co
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at
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o
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t
r
eq
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ir
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tr
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f
o
r
m
e
r
.
T
h
e
v
o
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ac
r
o
s
s
C
PE
ca
n
b
e
s
tated
f
o
r
ea
ch
p
h
ase
as f
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d
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:
=
−
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,
+
,
,
+
,
−
L
e
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ka
ge
(
1
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
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6
9
4
I
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t J Po
w
E
lec
&
Dr
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s
t
,
Vo
l.
1
7
,
No
.
3
,
Sep
tem
b
er
20
2
6
:
1553
-
1
5
6
3
1556
=
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g
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ter
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ac
co
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v
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ltag
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h
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m
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ch
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h
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,
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(
4
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(
5
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(
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ter
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k
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l
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tio
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in
th
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in
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ter
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h
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s
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m
m
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g
th
r
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g
h
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e
p
ar
asit
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p
ath
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f
all
th
r
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(
7
)
.
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a
ka
ge
=
−
(
,
+
,
+
,
)
(
7
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ce
th
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in
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u
tp
u
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it
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I
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p
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as (
1
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)
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(
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,
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tly
,
in
th
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ap
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ain
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1
3
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.
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(
1
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(
1
2
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d
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m
o
n
s
tr
ates
h
o
w
t
h
e
p
ar
asit
ic
ca
p
ac
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ce
C
PE
an
d
th
e
r
ate
o
f
c
h
an
g
e
o
f
t
h
e
v
o
ltag
e
ac
r
o
s
s
it,
r
ep
r
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ted
as d
V
PE
(
t)
/d
t,
a
f
f
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ct
th
e
leak
ag
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en
t.
T
h
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(
1
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–
(
1
3
)
ca
n
b
e
c
o
m
b
in
e
d
to
ex
p
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th
e
p
ar
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ca
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r
'
s
v
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ltag
e
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PE
as (
1
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)
.
=
3
3
+
3
+
2
(
+
)
(
−
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(
1
4
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T
h
e
(
1
4
)
in
d
icate
s
th
at
th
e
p
o
ten
tial
is
d
ir
ec
tly
lin
k
ed
to
th
e
C
MV
.
T
h
er
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e,
wh
en
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C
MV
f
lu
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ates
with
tim
e,
th
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e
ar
e
n
o
tab
le
v
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f
lu
ctu
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n
s
ac
r
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s
th
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p
ar
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p
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r
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ca
u
s
in
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a
lar
g
e
leak
ag
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cu
r
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en
t
b
etwe
en
th
e
g
r
o
u
n
d
an
d
th
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PV
ar
r
a
y
.
Ho
we
v
er
,
in
t
h
e
p
r
o
p
o
s
ed
FC
I
,
th
e
p
ar
asit
ic
ca
p
ac
ito
r
'
s
v
o
ltag
e
V
PE
is
in
d
ep
en
d
en
t
o
f
th
e
C
MV
.
T
h
is
ch
a
r
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ter
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tic
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d
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ts
u
n
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ly
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th
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u
g
h
ly
d
is
cu
s
s
ed
in
s
ec
tio
n
2
.
2
.
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
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mp
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tio
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1557
F
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atic
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o
r
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ed
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h
e
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s
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e
L
C
L
o
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t
f
ilter
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ito
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etu
p
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e
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r
r
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g
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m
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o
n
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m
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e
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u
iv
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t
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it
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s
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ated
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Fig
u
r
e
5
.
Alth
o
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g
h
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e
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ilter
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p
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d
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u
ll
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e
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er
ter
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e
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am
e
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n
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l
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ateg
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,
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eir
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y
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ts
d
if
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er
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e
FC
I
;
th
e
n
eu
tr
al
p
o
in
t
is
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k
ed
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e
DC
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lin
k
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id
way
o
f
th
e
L
C
L
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ilter
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ich
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th
e
r
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g
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m
m
o
n
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o
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e
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e
h
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io
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u
r
e
4
.
T
h
r
ee
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p
h
ase
g
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co
n
n
ec
ted
tr
an
s
f
o
r
m
er
less
f
ilter
clam
p
ed
i
n
v
e
r
ter
Fig
u
r
e
5.
T
h
r
ee
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p
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ase
T
L
PV g
r
id
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co
n
n
ec
ted
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ilter
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p
ed
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er
ter
s
u
s
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c
o
m
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o
n
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e
m
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d
el
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I
SS
N
:
2
0
8
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4
I
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w
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lec
&
Dr
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s
t
,
Vo
l.
1
7
,
No
.
3
,
Sep
tem
b
er
20
2
6
:
1553
-
1
5
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3
1558
T
h
e
co
m
m
o
n
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e
cir
cu
it in
Fig
u
r
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5
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s
u
b
jecte
d
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an
d
KVL
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esti
g
ate
th
e
FC
I
's leak
ag
e
cu
r
r
en
t.
T
h
e
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1
5
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7
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e
th
e
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p
r
ess
io
n
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o
r
th
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g
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atio
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th
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ases
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ile
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ter
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ep
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e
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n
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ib
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t
io
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u
s
'
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o
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e,
wh
ile
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,
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d
en
o
tes
th
e
f
ilter
v
o
ltag
e
o
f
e
ac
h
p
h
ase.
T
h
e
in
d
u
ctiv
e
ter
m
s
ac
co
u
n
t
f
o
r
g
r
o
u
n
d
in
g
in
d
u
c
tan
ce
ef
f
ec
ts
d
u
r
in
g
s
witch
in
g
.
T
h
e
p
h
ase
-
to
-
g
r
o
u
n
d
v
o
ltag
e
a
n
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g
r
o
u
n
d
r
esis
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ce
ter
m
s
r
ep
r
esen
t
th
e
im
p
ac
t
o
f
leak
ag
e
cu
r
r
en
t f
l
o
w.
I
n
th
is
in
s
tan
ce
,
th
e
v
o
ltag
es
ac
r
o
s
s
th
e
L
C
L
f
ilter
's
R
C
b
r
an
ch
es
ar
e
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an
d
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e
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(
1
2
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n
d
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e
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m
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ed
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o
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ac
itan
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PE
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as (
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,
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h
e
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ak
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o
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e
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ilter
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C
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ch
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o
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e
o
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th
e
DC
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lin
k
h
av
e
th
e
m
o
s
t
ef
f
ec
t
o
n
th
e
p
o
ten
tial
VPE.
I
n
co
n
tr
ast
to
a
co
n
v
en
tio
n
al
f
u
ll
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b
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id
g
e
i
n
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er
ter
,
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er
e
d
ep
en
d
s
o
n
th
e
C
MV
(
as
in
d
i
ca
ted
in
(
1
4
)
)
,
th
e
FC
I
to
p
o
lo
g
y
en
s
u
r
es
t
h
at
is
in
d
ep
en
d
en
t
o
f
C
MV
.
As
a
r
esu
lt,
n
o
tr
an
s
ien
t
v
o
ltag
e
is
g
en
e
r
ated
ac
r
o
s
s
th
e
p
ar
asit
ic
ca
p
ac
itan
ce
C
PE
as
a
r
esu
lt
o
f
c
h
an
g
es
i
n
C
M
,
ef
f
ec
tiv
ely
r
ed
u
cin
g
lea
k
ag
e
c
u
r
r
en
t.
I
m
p
u
ls
e
-
lik
e
c
u
r
r
en
ts
a
r
e
s
u
p
p
r
ess
ed
in
t
h
e
FC
I
to
p
o
lo
g
y
b
y
co
n
n
ec
tin
g
th
e
R
C
b
r
an
ch
es
t
o
th
e
g
r
id
f
r
o
m
t
h
e
L
C
L
f
ilter
a
n
d
t
h
e
i
n
v
er
ter
v
ia
in
d
u
cto
r
s
.
As
a
r
e
s
u
lt
,
t
h
e
v
o
ltag
es
ac
r
o
s
s
th
e
R
C
b
r
an
ch
es
d
o
n
'
t
ch
an
g
e
ef
f
ec
tiv
ely
,
elim
in
atin
g
ab
r
u
p
t
tr
an
s
itio
n
s
.
T
h
e
to
tal
v
o
ltag
e
o
f
th
e
th
r
ee
R
C
b
r
an
c
h
es
(
,
+
,
+
,
)
f
o
r
m
s
a
s
m
o
o
th
wav
e
f
o
r
m
w
ith
a
ze
r
o
a
v
er
ag
e
v
alu
e
.
C
o
n
s
eq
u
en
tly
,
th
e
v
o
ltag
e
in
th
e
p
r
o
p
o
s
ed
FC
I
m
ain
tain
s
a
s
tead
y
DC
b
i
as
with
m
in
im
al
r
ip
p
le,
r
esu
ltin
g
in
a
s
ig
n
if
ican
t
r
ed
u
ctio
n
o
f
leak
ag
e
cu
r
r
en
t
s
o
p
p
o
s
ed
to
t
h
e
tr
a
d
itio
n
al
f
u
ll
b
r
id
g
e
in
v
er
ter
.
T
h
is
o
b
s
er
v
atio
n
was
f
u
r
th
er
v
er
if
ie
d
th
r
o
u
g
h
d
etailed
s
im
u
latio
n
p
r
esen
ted
in
t
h
e
s
u
b
s
eq
u
en
t sectio
n
s
.
Fig
u
r
e
6
s
h
o
ws
th
e
s
y
s
tem
's
co
n
f
ig
u
r
atio
n
an
d
its
clo
s
ed
-
lo
o
p
co
n
tr
o
l
s
ch
em
e.
A
P&
O
MPPT
alg
o
r
ith
m
is
u
s
ed
to
tr
ac
k
th
e
PV
ar
r
ay
o
p
er
atin
g
p
o
i
n
t
,
wh
ich
p
r
o
v
id
es
th
e
DC
-
lin
k
r
ef
er
en
ce
vol
ta
ge
∗
.
A
PI
co
n
tr
o
ller
th
e
n
p
r
o
ce
s
s
es th
is
v
o
ltag
e
to
p
r
o
d
u
ce
th
e
ac
tiv
e
-
p
o
wer
r
e
f
er
en
ce
P*
.
Fig
u
r
e
6
.
B
lo
ck
d
iag
r
am
o
f
g
r
i
d
-
co
n
n
ec
ted
th
r
ee
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p
h
ase
tr
an
s
f
o
r
m
er
less
p
h
o
to
v
o
ltaic
s
y
s
tem
with
a
f
ilter
-
clam
p
ed
i
n
v
er
t
er
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
I
mp
leme
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o
f filter
-
cla
mp
ed
to
p
o
l
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g
y
fo
r
t
r
a
n
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fo
r
merles
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th
r
ee
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h
a
s
e
P
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…
(
Mo
h
a
m
med
A
b
d
u
lla
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)
1559
T
h
e
in
v
er
ter
,
o
p
er
atin
g
in
eit
h
er
FB
o
r
F
C
co
n
f
ig
u
r
atio
n
,
in
jects
ac
tiv
e
p
o
wer
in
to
th
e
g
r
id
.
T
h
e
f
o
llo
win
g
e
q
u
atio
n
s
d
em
o
n
s
tr
ate
h
o
w
th
e
g
r
i
d
-
s
y
n
c
h
r
o
n
iz
atio
n
cu
r
r
en
ts
ar
e
co
m
p
u
ted
in
α
β'
s
s
tatio
n
ar
y
r
ef
er
en
ce
f
r
am
e
f
r
o
m
th
e
r
ea
ct
iv
e
an
d
ac
tiv
e
p
o
wer
c
o
m
m
an
d
s
.
∗
=
1
(
2
+
2
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(
∗
+
∗
)
(
1
7
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=
1
(
2
+
2
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∗
−
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(
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8
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A
t
t
h
e
L
C
L
f
il
t
e
r
'
s
g
r
i
d
s
i
d
e
,
V
g
i
s
m
o
n
i
t
o
r
e
d
,
a
n
d
a
t
i
n
v
e
r
t
e
r
t
e
r
m
i
n
a
ls
,
t
h
e
p
h
a
s
e
c
u
r
r
e
n
t
s
a
r
e
s
e
n
s
e
d
(
F
i
g
u
r
e
6
)
.
T
h
is
s
en
s
in
g
ar
r
an
g
e
m
en
t im
p
r
o
v
es c
o
n
tr
o
l a
cc
u
r
ac
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b
y
p
r
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id
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g
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r
ec
is
e
v
o
ltag
e
a
n
d
cu
r
r
en
t f
ee
d
b
ac
k
.
3.
SI
M
UL
A
T
I
O
N
R
E
S
UL
T
S
AND
DIS
CUSS
I
O
NS
T
o
ev
alu
ate
th
e
FC
I
p
er
f
o
r
m
an
ce
,
a
co
m
p
r
e
h
en
s
iv
e
s
im
u
latio
n
m
o
d
el
was
cr
ea
ted
in
MA
T
L
AB
/S
im
u
lin
k
,
p
ar
ticu
la
r
ly
its
ef
f
ec
tiv
en
ess
in
s
u
p
p
r
ess
in
g
leak
ag
e
cu
r
r
e
n
t.
B
o
th
in
v
er
ter
to
p
o
lo
g
ies
—
th
e
FB
an
d
th
e
FC
,
s
h
o
wn
ea
r
lier
in
Fig
u
r
e
s
2
a
n
d
4
wer
e
m
o
d
ele
d
with
in
t
h
e
s
a
m
e
f
r
am
ewo
r
k
f
o
r
co
m
p
ar
ativ
e
e
v
alu
atio
n
.
Fig
u
r
es
7
an
d
8
d
e
p
ict
th
e
g
r
id
cu
r
r
en
ts
in
th
r
ee
p
h
ases
f
o
r
th
e
f
u
ll
b
r
id
g
e
an
d
th
e
f
ilter
-
clam
p
ed
i
n
v
er
ter
,
r
esp
ec
tiv
ely
.
F
ig
u
r
e
s
7
a
n
d
8
s
h
o
w
t
h
e
s
im
u
lated
g
r
id
cu
r
r
e
n
ts
in
t
h
r
ee
p
h
ases
o
f
a
B
6
in
v
er
ter
a
n
d
a
B
6
clam
p
ed
in
v
e
r
ter
p
lo
tted
ag
ain
s
t
tim
e.
All
th
r
ee
p
h
ase
c
u
r
r
e
n
ts
ar
e
s
in
u
s
o
id
al
an
d
b
alan
ce
d
,
with
eq
u
al
m
ag
n
itu
d
e.
E
ac
h
wav
ef
o
r
m
is
p
h
ase
-
s
h
if
ted
b
y
1
2
0
°
,
wh
ich
is
ch
a
r
ac
ter
is
tic
o
f
a
th
r
ee
-
p
h
ase
s
y
s
tem
.
Sm
all
r
ip
p
les ap
p
ea
r
b
ec
au
s
e
o
f
th
e
in
v
er
ter
'
s
s
witch
in
g
ac
t
io
n
.
Fig
u
r
es
9
a
n
d
1
0
illu
s
tr
ate
th
e
v
o
ltag
e
ac
r
o
s
s
th
e
s
tr
ay
ca
p
ac
i
tan
ce
(
)
f
o
r
b
o
th
in
v
er
ter
ty
p
e
s
.
T
h
e
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ile
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u
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s
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ay
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ig
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u
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10
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ates
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ter
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u
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.
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ter
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2
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8
8
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4
I
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lec
&
Dr
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,
Vo
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1
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3
,
Sep
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b
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20
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6
:
1553
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atin
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u
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ase
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lated
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ase
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I
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ig
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.
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a
n
s
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m
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r
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e
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h
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ase
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ase
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g
r
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PV sy
s
tem
s
.
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
.
3
,
Sep
tem
b
er
20
2
6
:
1553
-
1
5
6
3
1562
F
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