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1.
I
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RO
D
UCT
I
O
N
R
ec
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tly
,
s
o
lar
p
h
o
to
v
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ltaic
(
PV)
en
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g
y
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as
em
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ed
as
a
f
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s
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b
s
titu
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r
tr
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g
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s
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s
.
Po
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s
ar
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o
r
co
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v
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tin
g
s
o
lar
e
n
er
g
y
in
t
o
elec
tr
ical
en
er
g
y
[
1
]
.
C
o
m
p
ar
ed
to
two
-
lev
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in
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ter
s
,
m
u
ltil
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(
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s
)
ar
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esp
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p
r
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ed
f
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r
th
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h
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ce
d
wav
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o
r
m
q
u
ality
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r
ed
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ce
d
f
ilter
in
g
r
eq
u
ir
em
en
t
s
,
lo
wer
ed
to
tal
h
ar
m
o
n
ic
d
i
s
to
r
tio
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(
T
HD)
,
lo
wer
v
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ltag
e
s
tr
ess
ac
r
o
s
s
th
e
s
witch
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an
d
lo
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elec
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m
a
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n
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ter
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c
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(
E
MI
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p
r
o
p
ag
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n
is
s
u
e
[
2
]
,
[
3
]
.
T
h
is
lead
s
to
lo
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in
g
th
e
s
ize
an
d
ex
p
en
s
e
o
f
ML
I
s
b
y
e
n
ab
lin
g
th
e
u
s
e
o
f
d
ev
ices
with
lo
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r
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g
s
[
4
]
.
Fo
r
g
r
i
d
-
c
o
n
n
ec
ted
ML
I
s
,
it
is
im
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o
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tan
t
t
h
at
th
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u
tp
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v
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e
T
HD
m
ee
ts
ex
is
tin
g
I
E
E
E
s
tan
d
ar
d
s
[
5
]
.
T
o
d
o
th
is
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a
n
elev
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lev
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is
u
s
u
ally
n
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d
ed
,
r
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in
a
co
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esp
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n
d
in
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is
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in
th
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es
n
u
m
b
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an
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co
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p
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.
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in
d
ev
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co
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n
t
in
tr
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ce
s
co
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p
lex
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,
ex
p
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es,
an
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esp
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wh
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aim
in
g
f
o
r
ele
v
ated
v
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ltag
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lev
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[
6
]
.
T
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e
n
eu
tr
al
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clam
p
ed
(
NPC
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,
f
ly
in
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c
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s
(
FC
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,
an
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ca
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H
-
b
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ar
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th
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co
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v
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tio
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al
M
L
I
to
p
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lo
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an
d
h
a
v
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b
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n
ex
clu
s
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s
ed
an
d
im
p
lem
en
ted
f
o
r
v
ar
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ap
p
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s
[
7
]
.
NPC
an
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FC
ex
p
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is
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v
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cr
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[
8
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.
T
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m
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s
witch
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DC
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s
[
9
]
.
Switch
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ea
s
es
th
e
s
witch
es
n
u
m
b
er
[
1
0
]
.
I
n
s
p
ite
o
f
th
is
,
th
e
o
u
tp
u
t
v
o
ltag
e
o
f
t
h
is
d
esig
n
h
as
a
T
HD
o
f
1
6
.
6
6
%,
m
a
k
in
g
it
ess
en
tial
to
u
s
e
b
i
g
g
er
f
ilter
s
to
f
u
lf
il
t
h
e
I
E
E
E
r
eq
u
i
r
e
m
en
ts
.
A
v
a
r
iety
o
f
1
7
-
le
v
el
i
n
v
er
ter
s
h
av
e
b
ee
n
in
v
esti
g
ated
in
th
e
liter
atu
r
e
to
ac
h
iev
e
a
co
m
p
r
o
m
is
e
b
etwe
en
m
in
im
izin
g
s
witch
co
u
n
t
an
d
r
ed
u
ci
n
g
th
e
to
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
i
n
th
e
o
u
t
p
u
t
v
o
lta
g
e.
Var
io
u
s
in
v
er
ter
to
p
o
lo
g
ies
th
at
h
av
e
b
ee
n
p
r
o
p
o
s
ed
ar
e
p
r
esen
ted
in
[
1
1
]
–
[
1
3
]
.
Ho
wev
er
,
th
ese
d
esig
n
s
s
u
f
f
er
f
r
o
m
h
i
g
h
v
o
ltag
e
s
tr
ess
.
T
r
ad
itio
n
al
ap
p
r
o
ac
h
e
s
to
d
esig
n
in
g
a
1
7
-
lev
el
in
v
er
ter
,
s
u
ch
as
em
p
lo
y
i
n
g
C
HB
u
n
its
,
n
ec
es
s
itate
a
m
in
im
u
m
o
f
eig
h
t
u
n
its
co
n
n
ec
t
ed
in
s
er
ies
with
3
2
s
witch
es
an
d
eig
h
t
is
o
lated
in
p
u
t
DC
s
o
u
r
ce
s
,
m
ak
in
g
th
e
s
y
s
tem
ex
p
en
s
iv
e,
b
u
lk
y
,
an
d
co
m
p
licated
.
Alter
n
ativ
e
17
-
lev
el
to
p
o
lo
g
y
th
at
u
tili
ze
s
f
o
u
r
b
id
ir
ec
ti
o
n
al
s
witch
es,
ten
u
n
id
ir
ec
ti
o
n
al
s
witch
es,
f
o
u
r
ca
p
ac
ito
r
s
,
an
d
f
o
u
r
d
io
d
es
to
p
r
o
d
u
ce
17
-
le
v
el
o
u
tp
u
t
v
o
ltag
e
in
[
1
4
]
.
T
h
is
d
esig
n
r
e
q
u
ir
ed
an
is
o
l
ated
f
ly
b
ac
k
co
n
v
er
ter
t
o
p
r
o
d
u
ce
two
id
en
tical
is
o
lated
DC
s
o
u
r
ce
s
f
o
r
s
u
p
p
ly
in
g
th
e
p
r
o
p
o
s
ed
in
v
er
te
r
.
I
n
th
is
m
o
d
if
ied
in
v
er
ter
,
th
e
co
m
p
o
n
e
n
t
-
to
-
lev
el
r
atio
is
v
er
y
h
ig
h
,
wh
ich
af
f
ec
ts
th
e
s
ize,
co
s
t,
an
d
ef
f
icie
n
cy
o
f
th
e
in
v
er
ter
.
On
th
e
b
asis
o
f
im
p
r
o
v
e
d
s
er
i
es
-
p
ar
allel
co
n
v
er
s
io
n
,
a
n
o
v
e
l
ca
s
ca
d
ed
SC
ML
I
is
s
u
g
g
ested
in
[
1
5
]
.
O
n
ly
1
0
s
witch
es
ar
e
n
ee
d
ed
to
g
en
er
ate
1
7
o
u
tp
u
t
lev
els,
b
u
t
two
s
ep
ar
ate
DC
s
o
u
r
ce
s
ar
e
n
ee
d
ed
.
S
im
ilar
ly
,
[
1
6
]
p
r
esen
ts
a
n
ew
1
7
L
in
v
er
ter
w
ith
f
o
u
r
is
o
lated
DC
s
o
u
r
ce
s
.
W
it
h
ju
s
t
o
n
e
DC
s
u
p
p
ly
,
1
2
s
witch
es,
f
iv
e
d
io
d
es,
an
d
f
o
u
r
ca
p
ac
ito
r
s
,
th
e
1
7
-
le
v
el
to
p
o
lo
g
y
s
h
o
wn
in
[
1
7
]
ac
h
iev
ed
a
n
8
-
v
o
ltag
e
g
ain
.
T
h
is
s
tr
u
ctu
r
e
m
i
tig
ates
v
o
ltag
e
s
tr
ess
o
n
d
ev
ices
an
d
h
as
th
e
ab
ilit
y
to
r
estrict
th
e
h
ig
h
in
r
u
s
h
cu
r
r
en
t
b
y
em
p
l
o
y
in
g
th
e
q
u
asi
-
s
o
f
t
ch
ar
g
e
m
eth
o
d
.
Ho
wev
e
r
,
it
i
s
im
p
o
r
tan
t
t
o
o
b
s
er
v
e
th
at
t
h
e
t
o
tal
sta
n
d
i
n
g
v
o
lt
a
g
e
(
T
SV
)
is
r
elativ
ely
h
i
g
h
.
An
o
th
er
1
7
-
L
b
ased
SC
ML
I
is
i
llu
s
tr
ated
in
[
1
8
]
,
tailo
r
ed
f
o
r
r
en
ewa
b
le
en
er
g
y
ap
p
licatio
n
s
.
B
y
u
s
in
g
f
ewe
r
s
witch
es,
ca
p
ac
ito
r
s
,
an
d
d
r
iv
er
s
,
th
e
d
esig
n
s
im
p
lifie
s
th
e
s
y
s
tem
wh
ile
r
ed
u
cin
g
co
s
ts
.
T
h
e
in
v
er
ter
s
tr
u
ctu
r
e
h
as
th
e
ab
ilit
y
t
o
s
elf
-
b
alan
ce
ca
p
ac
ito
r
v
o
ltag
e
lev
els
an
d
an
in
h
er
e
n
t
v
o
ltag
e
-
b
o
o
s
tin
g
ca
p
ab
ilit
y
with
f
o
u
r
DC
s
u
p
p
lies
.
T
h
e
co
n
f
ig
u
r
atio
n
in
[
1
9
]
ca
n
g
e
n
er
ate
1
7
le
v
els
o
f
v
o
ltag
e
with
a
s
in
g
le
s
o
u
r
ce
co
n
f
ig
u
r
atio
n
.
I
t
u
s
es
f
iv
e
ca
p
ac
ito
r
s
with
f
iv
e
d
io
d
es
an
d
1
0
s
witch
es,
an
d
it
is
ab
le
to
b
o
o
s
t
th
e
in
p
u
t
v
o
ltag
e
u
p
to
8
tim
es.
W
h
ile
in
[
2
0
]
,
th
e
i
n
v
er
ter
h
as
th
e
ab
ilit
y
to
b
o
o
s
t
th
e
in
p
u
t
v
o
ltag
e
u
p
to
4
tim
es
b
y
u
s
in
g
j
u
s
t
1
2
s
witch
es
an
d
3
ca
p
ac
ito
r
s
.
W
ith
ten
s
witch
es
an
d
f
o
u
r
is
o
lated
DC
s
o
u
r
c
es,
th
e
to
p
o
lo
g
y
in
[
2
1
]
p
r
esen
ted
a
n
o
v
el
s
in
g
le
-
p
h
ase
ML
I
b
ased
o
n
a
ca
s
ca
d
e
co
n
n
ec
tio
n
to
p
r
o
d
u
ce
an
o
u
tp
u
t
v
o
ltag
e
with
1
7
lev
els
.
A
d
d
itio
n
ally
,
it
o
f
f
e
r
s
th
e
p
o
ten
tial to
e
x
ten
d
to
h
ig
h
er
v
o
ltag
e
lev
els b
y
u
s
in
g
a
ca
s
c
ad
e
co
n
n
ec
tio
n
.
T
h
is
p
ap
er
s
u
cc
ess
f
u
lly
ex
te
n
d
ed
a
p
r
e
-
e
x
is
tin
g
n
in
e
-
le
v
e
l
m
u
ltil
ev
el
in
v
er
ter
[
2
2
]
to
a
1
7
-
lev
el
to
p
o
lo
g
y
f
o
r
g
r
id
-
co
n
n
ec
ted
p
h
o
to
v
o
ltaic
s
y
s
tem
s
with
lo
w
e
r
T
HD
a
n
d
t
h
e
a
b
ilit
y
to
lim
it t
h
e
ca
p
ac
ito
r
in
r
u
s
h
cu
r
r
en
t.
T
h
is
p
a
p
er
p
r
o
p
o
s
ed
a
s
in
g
le
-
p
h
ase
17
-
lev
el
ca
s
ca
d
ed
s
witch
ed
ca
p
ac
ito
r
ML
I
(
C
SC
-
ML
I
)
to
p
o
lo
g
y
co
n
n
ec
ted
to
a
s
in
g
le
DC
b
u
s
b
ar
c
o
llecto
r
f
o
r
a
m
u
lti
-
ar
r
a
y
p
h
o
to
v
o
ltaic
s
y
s
tem
with
g
r
id
in
teg
r
at
io
n
.
T
h
e
p
r
im
ar
y
o
b
jectiv
es
o
f
th
is
p
ap
er
ar
e
:
i
)
T
o
ac
h
ie
v
e
a
b
alan
ce
b
etwe
en
th
e
d
ev
ice
c
o
u
n
t
a
n
d
th
e
o
u
t
p
u
t
v
o
ltag
e
T
HD
with
less
co
u
n
t
o
f
p
o
we
r
s
u
p
p
lies
,
ad
d
r
ess
in
g
a
r
esear
ch
g
ap
;
ii
)
T
o
g
en
e
r
ate
s
ev
en
t
ee
n
o
u
t
p
u
t
v
o
ltag
e
lev
els
with
a
b
o
o
s
tin
g
ab
ilit
y
o
f
2
tim
es
u
s
in
g
m
in
im
u
m
n
u
m
b
er
s
o
f
s
witch
es
;
iii
)
T
o
m
in
im
ize
th
e
s
u
b
jecte
d
v
o
ltag
e
s
tr
ess
an
d
r
ated
cu
r
r
e
n
t o
n
s
witch
es
;
iv
)
T
o
ac
h
iev
e
s
elf
-
v
o
ltag
e
b
ala
n
cin
g
o
f
ca
p
ac
ito
r
s
with
o
u
t u
s
in
g
au
x
iliar
y
cir
cu
its
;
an
d
v
)
T
o
m
in
im
ize
th
e
f
ilter
in
g
n
ee
d
s
.
T
h
is
p
ap
er
is
o
r
g
an
ized
as
f
o
llo
ws:
i)
Sectio
n
2
p
r
esen
ts
th
e
co
n
f
ig
u
r
atio
n
d
escr
ip
tio
n
o
f
th
e
p
r
o
p
o
s
ed
17
-
lev
el
C
SC
-
ML
I
with
a
s
in
g
le
DC
b
u
s
;
ii)
T
h
e
s
in
g
le
-
p
h
a
s
e
co
n
tr
o
l
m
eth
o
d
o
lo
g
y
is
illu
s
tr
ated
in
s
ec
tio
n
3
;
iii)
T
h
e
th
eo
r
etica
l
an
aly
s
is
o
f
th
e
p
r
o
p
o
s
ed
C
SC
-
ML
I
is
ex
p
lain
ed
in
s
ec
tio
n
4
;
iv
)
A
co
m
p
ar
ativ
e
s
tu
d
y
is
p
r
esen
ted
i
n
s
ec
tio
n
5
;
v
)
T
h
e
r
esu
lts
an
d
d
is
cu
s
s
io
n
ar
e
s
h
o
wn
in
s
ec
tio
n
6
;
v
i)
Fin
ally
,
s
ec
tio
n
7
p
r
esen
ts
th
e
co
n
clu
s
io
n
.
2.
CO
NF
I
G
URA
T
I
O
N
D
E
SC
RIPT
I
O
N
Sin
g
le
-
p
h
ase
p
h
o
to
v
o
ltaic
m
u
l
ti
-
ar
r
a
y
s
in
g
le
DC
b
u
s
b
ar
c
o
llecto
r
C
SC
-
ML
I
in
v
er
ter
is
illu
s
tr
ated
in
Fig
u
r
e
1
.
T
h
e
co
n
f
ig
u
r
atio
n
d
ep
icted
in
Fig
u
r
e
1
in
cl
u
d
es
i
n
d
ep
en
d
en
t
p
h
o
t
o
v
o
ltaic
ar
r
ay
s
lin
k
ed
to
a
s
in
g
le
DC
b
u
s
b
ar
v
ia
DC
-
DC
b
o
o
s
t
co
n
v
er
ter
s
p
e
r
f
o
r
m
in
g
m
a
x
i
m
u
m
p
o
wer
p
o
in
t
tr
ac
k
in
g
(
MPPT)
in
d
ep
en
d
en
tly
f
o
r
ea
c
h
p
h
o
t
o
v
o
ltaic
a
r
r
ay
.
T
h
e
DC
b
u
s
is
th
en
co
n
n
ec
t
ed
to
th
e
p
r
o
p
o
s
ed
ca
s
ca
d
ed
s
witch
ed
ca
p
ac
ito
r
m
u
ltil
ev
el
in
v
er
ter
(
C
SC
-
ML
I
)
.
T
o
en
s
u
r
e
p
r
o
p
er
o
p
er
atio
n
o
f
th
e
C
SC
-
ML
I
,
an
is
o
lated
s
o
u
r
ce
m
u
s
t
f
e
ed
ea
c
h
ce
ll
o
f
th
e
C
SC
-
ML
I
.
So
,
f
ly
b
ac
k
DC
-
DC
co
n
v
er
ter
s
with
a
tu
r
n
r
atio
o
f
1
:1
a
r
e
p
u
t
b
etwe
en
th
e
DC
b
u
s
an
d
th
e
in
d
iv
id
u
al
C
SC
-
ML
I
ce
lls
d
u
e
t
o
th
eir
s
im
p
licity
,
af
f
o
r
d
a
b
ilit
y
,
an
d
b
u
c
k
-
b
o
o
s
t c
ap
ab
ili
ty
wh
ich
in
cr
ea
s
es
th
e
s
y
s
tem
'
s
f
lex
ib
ilit
y
an
d
o
p
er
atin
g
r
an
g
e.
T
h
is
s
tr
u
ctu
r
e
o
f
f
er
s
th
e
b
en
ef
it
o
f
ev
en
ly
d
is
tr
ib
u
ted
o
u
tp
u
t
p
o
wer
ac
r
o
s
s
th
e
ce
lls
o
f
C
SC
-
ML
I
.
T
h
is
co
n
f
ig
u
r
atio
n
is
p
r
o
p
o
s
ed
in
o
r
d
er
to
elim
in
ate
t
h
e
d
r
awb
ac
k
o
f
th
e
ca
s
ca
d
ed
s
tr
u
ctu
r
e
wh
en
th
e
PV
ar
r
a
y
s
s
u
f
f
er
f
r
o
m
p
ar
tial
s
h
ad
in
g
o
r
n
o
n
-
u
n
if
o
r
m
ir
r
a
d
iatio
n
,
wh
ich
is
th
e
i
n
h
er
e
n
t
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
.
2
,
J
u
n
e
20
25
:
1
0
7
0
-
1082
1072
p
o
wer
im
b
alan
ce
am
o
n
g
ce
lls
in
th
e
ca
s
e
o
f
s
in
g
le
-
p
h
ase
s
y
s
tem
s
.
An
d
co
n
s
eq
u
en
tly
,
an
i
m
b
alan
ce
o
f
p
o
w
er
am
o
n
g
d
if
f
er
en
t p
h
ases
in
th
r
ee
-
p
h
ase
s
y
s
tem
s
[
2
3
]
.
T
h
is
wo
r
k
elim
in
ates th
e
p
er
-
ce
ll p
o
w
er
im
b
alan
ce
in
th
e
C
S
C
-
ML
I
b
y
co
n
ce
n
tr
atin
g
all
p
h
o
to
v
o
ltaic
-
g
en
er
ated
p
o
wer
in
a
s
in
g
le
DC
b
u
s
.
T
r
ad
itio
n
al
f
ly
b
ac
k
an
d
b
o
o
s
t
co
n
v
er
ter
s
h
a
v
e
b
ee
n
u
s
ed
.
2
.
1
.
P
r
o
po
s
ed
1
7
-
lev
el
CSC
-
M
L
I
t
o
po
lo
g
y
des
cr
iptio
n
Fig
u
r
e
1
illu
s
tr
ates
C
S
C
-
ML
I
with
g
r
id
i
n
teg
r
at
io
n
f
o
r
p
h
o
to
v
o
ltaic
s
y
s
tem
s
.
Acc
o
r
d
in
g
to
th
is
f
ig
u
r
e
,
th
e
p
r
o
p
o
s
ed
in
v
e
r
ter
co
n
tai
n
s
twelv
e
u
n
id
ir
ec
tio
n
al
s
witch
es,
s
ix
b
id
i
r
ec
tio
n
al
s
witc
h
es,
f
o
u
r
DC
-
lin
k
ca
p
ac
ito
r
s
(
11
,
12
,
21
,
22
)
,
f
o
u
r
f
lo
atin
g
c
ap
ac
ito
r
s
13
,
14
,
23
,
24
,
f
o
u
r
p
o
wer
d
io
d
e
s
,
an
d
two
s
o
f
t
ch
ar
g
in
g
in
d
u
cto
r
s
(
1
,
2
)
alo
n
g
with
f
r
ee
wh
ee
lin
g
d
io
d
es
(
1
,
2
)
.
T
h
e
s
u
g
g
ested
in
v
e
r
ter
is
s
u
p
p
lied
b
y
two
is
o
lated
DC
s
o
u
r
ce
s
with
a
DC
-
lin
k
v
o
ltag
e
.
I
n
e
ac
h
ce
ll
o
f
C
SC
-
ML
I
,
th
e
v
o
l
tag
e
ac
r
o
s
s
ea
ch
s
er
i
es
-
co
n
n
ec
ted
DC
-
lin
k
ca
p
ac
ito
r
b
ec
o
m
es
eq
u
al
to
(
/
2
)
as
th
ey
ch
ar
g
ed
to
.
T
h
e
s
tr
in
g
s
o
f
f
lo
atin
g
ca
p
ac
ito
r
s
ar
e
ch
ar
g
e
d
to
(
/
2
)
.
So
,
ea
ch
o
f
t
h
em
h
as
a
v
o
ltag
e
eq
u
al
to
(
/
4
)
,
an
d
th
e
y
r
em
ain
c
o
n
s
tan
t
d
u
r
in
g
th
e
o
p
er
atio
n
o
f
th
e
p
r
o
p
o
s
ed
C
SC
-
ML
I
.
T
h
e
p
r
o
p
o
s
ed
in
v
er
ter
h
as
th
e
a
b
ilit
y
to
lim
it
th
e
ca
p
ac
ito
r
ch
ar
g
in
g
cu
r
r
en
t
u
s
in
g
th
e
s
o
f
t
ch
ar
g
in
g
m
eth
o
d
.
I
n
th
e
p
r
o
p
o
s
ed
to
p
o
lo
g
y
,
s
ev
en
teen
d
is
tin
ct
lev
els
ar
e
g
en
er
ated
in
th
e
o
u
tp
u
t
v
o
l
tag
e,
in
v
o
lv
in
g
±
2
,
±
1
.
75
,
±
1
.
5
,
±
1
.
25
,
±
,
±
0
.
75
,
±
0
.
5
,
±
0
.
25
,
a
n
d
±
0
b
ased
o
n
t
h
e
s
witch
in
g
s
tates lis
ted
in
T
ab
le
1
.
Fig
u
r
e
1
.
Pro
p
o
s
ed
g
r
id
-
c
o
n
n
e
cted
1
7
-
lev
el
C
SC
-
MLI
T
ab
le
1
.
Switch
in
g
s
tat
es o
f
th
e
p
r
o
p
o
s
ed
1
7
-
lev
el
C
SC
-
MLI
O
u
t
p
u
t
v
o
l
t
a
g
e
l
e
v
e
l
s
11
12
13
14
15
16
17
18
19
21
22
23
24
25
26
27
28
29
13
14
23
24
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
C
C
C
C
0
.
25
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
C
C
C
C
0
.
5
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
C
C
C
C
0
.
75
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
NC
D
C
C
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
D
D
C
C
1
.
25
1
0
1
0
0
0
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1
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0
0
0
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1
0
0
0
1
C
C
NC
D
1
.
5
1
0
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1
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D
D
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C
1
.
75
0
0
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NC
D
D
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2
1
0
0
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1
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D
D
D
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-
0
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1
0
0
C
C
C
C
−
0
.
25
0
0
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1
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1
0
1
1
0
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1
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1
0
0
C
C
C
C
-
0
.
5
0
1
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0
0
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1
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0
C
C
C
C
−
0
.
75
0
0
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1
0
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1
1
0
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1
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0
1
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D
NC
C
C
−
0
1
0
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0
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0
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1
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0
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D
D
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C
−
1
.
25
0
1
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1
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C
C
D
NC
-
1
.
5
0
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0
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0
C
C
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−
1
.
75
0
0
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0
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1
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D
NC
D
D
−
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
D
D
D
D
C
=
c
h
a
r
g
i
n
g
,
D
=
d
i
s
c
h
a
r
g
i
n
g
,
a
n
d
NC
=
n
o
t
c
h
a
n
g
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
S
ev
en
teen
-
leve
l c
a
s
ca
d
ed
s
w
itch
ed
-
ca
p
a
cito
r
mu
ltil
ev
el
in
ve
r
ter fo
r
…
(
Ma
yth
a
m
Ja
s
im
N
a
s
er
)
1073
2
.
2
.
So
f
t
cha
rg
ing
m
et
ho
d
On
e
o
f
th
e
m
ajo
r
d
is
ad
v
an
tag
es
o
f
th
e
s
wi
tch
ed
ca
p
ac
ito
r
-
b
ased
to
p
o
lo
g
ies
is
th
e
ca
p
ac
ito
r
in
r
u
s
h
cu
r
r
en
t
d
u
r
in
g
t
h
e
ca
p
ac
ito
r
'
s
ch
ar
g
in
g
m
o
d
e.
So
,
th
e
cu
r
r
en
t
s
tr
ess
o
n
th
e
s
witch
es will
in
cr
ea
s
e.
T
o
s
o
lv
e
th
is
is
s
u
e,
a
s
o
f
t
ch
ar
g
in
g
m
eth
o
d
h
as
b
ee
n
em
p
lo
y
ed
to
d
ec
r
e
ase
th
e
ca
p
ac
ito
r
s
p
ik
e
cu
r
r
e
n
t.
A
s
o
f
t
c
h
ar
g
in
g
in
d
u
cto
r
(
)
in
p
ar
allel
with
a
f
r
ee
wh
ee
lin
g
d
i
o
d
e
(
)
is
em
p
lo
y
ed
in
t
h
e
ca
p
ac
ito
r
c
h
ar
g
in
g
p
ath
to
r
estrict
th
e
s
p
ik
e
cu
r
r
en
t.
T
h
e
s
m
allest
s
ize
f
o
r
th
e
ch
ar
g
in
g
in
d
u
c
to
r
is
f
ig
u
r
e
d
o
u
t
b
y
(
1
)
wh
er
e
r
ep
r
esen
t
th
e
f
lo
atin
g
ca
p
ac
ito
r
s
an
d
r
ep
r
es
en
t th
e
g
r
id
f
r
eq
u
en
cy
[
2
4
]
.
=
1
(
2
)
2
(
1
)
T
h
e
in
d
u
ct
o
r
r
e
d
u
ce
s
th
e
in
r
u
s
h
cu
r
r
en
t;
h
o
wev
er
,
it
lead
s
to
v
o
ltag
e
s
p
ik
es.
As
a
r
esu
lt,
d
io
d
es
(
1
,
2
)
ar
e
p
lace
d
p
ar
allel
to
t
h
e
in
d
u
cto
r
s
to
m
itig
ate
th
is
o
v
er
v
o
lta
g
e
i
s
s
u
e.
2
.
3
.
P
WM
co
ntr
o
l f
o
r
pro
po
s
ed
1
7
-
lev
el
CSC
-
M
L
I
T
o
p
r
o
d
u
ce
th
e
g
ate
p
u
ls
es
f
o
r
th
e
p
r
o
p
o
s
ed
C
SC
-
ML
I
,
th
e
ca
r
r
ier
-
b
ased
u
n
ip
o
lar
s
in
e
PW
M
tech
n
iq
u
e
h
as
b
ee
n
co
n
s
id
er
ed
ac
co
r
d
in
g
to
th
e
lo
g
ic
cir
cu
it
g
iv
en
in
Fig
u
r
e
2
.
A
s
in
g
le
s
in
u
s
o
id
al
r
ef
er
en
ce
s
ig
n
al
f
ea
tu
r
in
g
an
i
n
v
er
ted
n
eg
ativ
e
h
alf
-
cy
cle
is
u
s
ed
alo
n
g
s
id
e
ei
g
h
t
tr
ian
g
u
lar
ca
r
r
ier
s
ig
n
als
in
o
r
d
e
r
to
r
ed
u
c
e
th
e
n
u
m
b
er
o
f
r
eq
u
ir
e
d
ca
r
r
ier
s
ig
n
als to
th
e
h
alf
as c
o
m
p
ar
ed
with
th
e
n
o
n
in
v
er
te
d
o
n
e.
Hen
c
e,
o
n
ly
eig
h
t c
ar
r
ier
s
ig
n
als
r
ath
er
th
a
n
1
6
a
r
e
u
s
ed
to
co
m
p
a
r
e
with
th
e
r
e
f
er
en
ce
s
ig
n
al
to
p
r
o
d
u
ce
s
witch
in
g
g
ate
p
u
ls
es
f
o
r
th
e
p
r
o
p
o
s
ed
in
v
er
ter
.
E
ac
h
o
f
th
e
ca
r
r
ier
s
ig
n
als h
as a
2
.
5
k
Hz
f
r
eq
u
en
cy
.
I
n
th
is
p
ap
er
,
a
n
ew
h
y
b
r
id
p
u
ls
e
wid
th
m
o
d
u
latio
n
h
as
b
ee
n
p
r
o
p
o
s
e
d
b
ased
o
n
a
c
o
m
b
in
atio
n
o
f
p
h
ase
-
s
h
if
ted
p
u
ls
e
wid
th
m
o
d
u
latio
n
(
PS
-
PW
M)
an
d
lev
el
-
s
h
if
ted
p
u
ls
e
wid
th
m
o
d
u
latio
n
(LS
-
PW
M)
.
Fig
u
r
e
2
.
Hy
b
r
id
-
PW
M
lo
g
ic
cir
cu
it f
o
r
th
e
p
r
o
p
o
s
ed
1
7
-
lev
el
C
S
C
-
MLI
As
s
h
o
wn
in
Fig
u
r
e
2
,
th
e
le
v
el
-
s
h
if
ted
ca
r
r
ier
s
(
11
,
12
,
13
,
14
)
h
av
e
th
e
s
am
e
p
h
ase,
wh
ich
is
co
m
p
ar
ed
with
th
e
ab
s
o
lu
te
v
alu
e
o
f
th
e
r
ef
er
e
n
ce
s
ig
n
al
to
p
r
o
d
u
ce
th
e
g
ate
p
u
ls
es
f
o
r
t
h
e
f
ir
s
t
ce
ll
o
f
C
SC
-
ML
I
.
Similar
ly
,
t
h
e
p
h
ase
-
s
h
if
ted
ca
r
r
ier
s
ig
n
als
(
21
,
22
,
23
,
24
)
wh
o
s
e
o
p
p
o
s
ed
to
le
v
el
-
s
h
if
ted
ca
r
r
ier
s
o
f
th
e
f
ir
s
t
ce
ll
ar
e
c
o
n
tr
asted
with
a
r
e
f
er
en
ce
s
ig
n
al
to
p
r
o
d
u
ce
th
e
s
witch
in
g
p
u
ls
es
f
o
r
th
e
s
ec
o
n
d
ce
ll
o
f
C
S
C
-
ML
I
.
T
h
e
c
o
m
p
ar
is
o
n
b
etwe
en
th
e
ca
r
r
ier
an
d
r
ef
er
e
n
ce
s
ig
n
als
an
d
th
e
p
r
o
d
u
ce
d
1
7
-
L
in
v
e
r
ter
o
u
tp
u
t
v
o
ltag
e
wav
ef
o
r
m
is
p
r
esen
ted
in
Fig
u
r
e
3
.
T
h
e
m
o
d
u
latio
n
i
n
d
ex
ca
n
b
e
ca
lc
u
l
ated
as
(
2
)
.
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
.
2
,
J
u
n
e
20
25
:
1
0
7
0
-
1082
1074
=
̂
(
4
̂
)
(
2
)
H
er
e
̂
,
̂
ar
e
th
e
p
ea
k
v
al
u
es
o
f
th
e
r
ef
er
en
ce
s
ig
n
al
an
d
ea
c
h
ca
r
r
ier
s
ig
n
al,
r
esp
ec
tiv
ely
.
(
a)
(
b
)
Fig
u
r
e
3
.
Hy
b
r
id
-
PW
M
s
ch
em
e
f
o
r
th
e
p
r
o
p
o
s
ed
C
SC
-
MLI
:
(
a)
r
ef
er
e
n
ce
an
d
ca
r
r
ier
s
ig
n
als
an
d
(
b
)
1
7
-
lev
el
C
SC
-
ML
I
o
u
tp
u
t
v
o
ltag
e
wav
ef
o
r
m
3.
CO
NT
RO
L
SCH
E
M
E
On
e
o
f
th
e
a
d
v
an
tag
es
o
f
th
e
p
r
esen
ted
s
in
g
le
-
p
h
ase
p
h
o
to
v
o
ltaic
m
u
lti
-
ar
r
ay
s
in
g
le
DC
-
b
u
s
b
ar
C
SC
-
ML
I
in
v
er
ter
is
th
at
th
e
c
o
n
tr
o
l
s
y
s
tem
ca
n
b
e
ef
f
ec
tiv
ely
s
eg
m
en
ted
a
m
o
n
g
th
e
c
o
n
v
er
ter
s
u
tili
zin
g
co
n
v
en
tio
n
al
co
n
tr
o
l m
eth
o
d
o
l
o
g
ies.
T
h
e
co
n
tr
o
l sch
em
e
o
f
ea
ch
co
n
v
e
r
ter
s
tag
e
is
d
escr
ib
ed
in
th
e
f
o
llo
win
g
s
ec
tio
n
s
.
T
h
e
MPPT
b
o
o
s
t
co
n
v
er
ter
s
p
er
f
o
r
m
a
p
er
tu
r
b
an
d
o
b
s
er
v
e
(
P&
O)
tech
n
iq
u
e
b
y
co
n
tr
o
llin
g
th
e
PV
v
o
ltag
es
as
s
h
o
w
n
in
Fig
u
r
e
4.
T
h
e
P&
O
MPPT
is
u
s
ed
d
u
e
to
its
s
im
p
le
s
tr
u
ctu
r
e
an
d
ea
s
y
im
p
lem
en
tatio
n
an
d
its
alg
o
r
ith
m
p
r
esen
ted
in
[
2
5
]
.
T
h
e
r
ef
er
e
n
ce
v
o
ltag
e
(
∗
)
is
g
en
er
ated
b
y
s
en
s
in
g
th
e
PV
v
o
ltag
e
(
)
an
d
cu
r
r
en
t
(
)
f
o
r
ea
c
h
PV
ar
r
a
y
an
d
u
s
ed
it
to
p
er
f
o
r
m
th
e
M
PP
T
,
wh
ich
is
th
en
co
m
p
ar
ed
with
(
)
an
d
th
e
er
r
o
r
is
en
ter
ed
in
t
o
th
e
P
I
co
n
tr
o
ller
f
o
r
th
e
p
u
r
p
o
s
e
o
f
p
r
o
v
id
in
g
th
e
r
e
q
u
ir
ed
d
u
ty
cy
cle
f
o
r
PW
M
to
g
en
er
ate
th
e
g
ate
p
u
ls
es
f
o
r
th
e
b
o
o
s
t
co
n
v
er
ter
.
T
h
e
in
p
u
t
v
o
ltag
e
o
f
ea
ch
C
SC
-
ML
I
ce
ll
is
k
ep
t
co
n
s
tan
t
b
y
ad
ju
s
tin
g
t
h
e
d
u
t
y
r
atio
o
f
t
h
e
f
ly
b
ac
k
s
witch
u
s
in
g
PW
M
b
ased
o
n
t
h
e
o
u
t
p
u
t o
f
th
e
PI
co
n
tr
o
ller
.
T
h
e
T
HD
lev
el
is
a
s
ig
n
if
ican
t
p
o
wer
q
u
ality
in
d
e
x
f
o
r
g
r
id
-
co
n
n
ec
ted
p
h
o
to
v
o
ltaic
in
v
er
ter
s
.
Acc
o
r
d
in
g
to
b
o
th
th
e
I
E
E
E
an
d
I
E
C
s
tan
d
ar
d
s
,
th
e
T
HD
f
o
r
in
jecte
d
g
r
id
cu
r
r
en
t
s
h
o
u
l
d
b
e
less
th
an
5
%
to
m
in
im
ize
n
eg
ativ
e
ef
f
ec
ts
o
n
o
th
er
u
s
er
s
an
d
th
e
g
r
id
[
2
6
]
.
So
,
th
e
c
u
r
r
en
t
co
n
tr
o
ller
m
u
s
t
b
e
d
esig
n
ed
ca
r
ef
u
lly
to
s
atis
f
y
th
is
r
e
q
u
ir
em
e
n
t.
T
h
e
C
SC
-
ML
I
th
at
ap
p
ea
r
s
in
th
e
th
ir
d
b
lo
c
k
o
f
Fig
u
r
e
4
is
u
s
ed
to
c
o
n
tr
o
l th
e
g
r
i
d
cu
r
r
en
t
(
)
an
d
th
e
s
in
g
le
DC
b
u
s
b
ar
v
o
ltag
e
(
)
.
I
n
t
h
is
b
lo
ck
,
th
e
DC
b
u
s
v
o
ltag
e
(
)
is
co
m
p
ar
e
d
with
th
e
b
u
s
r
ef
er
en
ce
v
o
ltag
es
(
∗
)
an
d
th
e
er
r
o
r
is
ap
p
lied
to
a
PI
co
n
tr
o
ller
with
g
ain
s
=
0
.
2
an
d
=
1
.
5
.
T
h
e
c
o
n
t
r
o
l
l
e
r
o
u
t
p
u
t
d
e
t
e
r
m
i
n
e
s
t
h
e
r
e
f
e
r
e
n
c
e
g
r
i
d
c
u
r
r
e
n
t
(
∗
)
.
T
h
e
n
,
a
p
h
a
s
e
-
l
o
c
k
e
d
l
o
o
p
(
P
L
L
)
t
e
c
h
n
o
l
o
g
y
i
s
e
m
p
l
o
y
e
d
t
o
s
y
n
c
h
r
o
n
i
z
e
t
h
e
co
n
t
r
o
l
s
y
s
t
e
m
f
o
r
t
h
e
p
u
r
p
o
s
e
o
f
g
e
n
e
r
a
t
i
n
g
t
h
e
g
r
i
d
r
e
f
e
r
e
n
ce
c
u
r
r
e
n
t
(
∗
)
[
2
7
]
.
T
h
e
g
r
i
d
c
u
r
r
e
n
t
(
)
t
h
e
n
i
s
c
o
m
p
a
r
e
d
w
i
t
h
t
h
e
r
e
f
e
r
e
n
c
e
v
a
l
u
e
(
∗
)
a
n
d
t
h
e
r
e
s
u
l
t
i
n
g
e
r
r
o
r
s
i
g
n
a
l
i
s
a
p
p
l
i
e
d
t
o
a
p
r
o
p
o
r
t
i
o
n
a
l
-
r
e
s
o
n
a
n
t
(
P
R
)
c
u
r
r
e
n
t
c
o
n
t
r
o
l
l
e
r
w
i
t
h
g
a
i
n
s
=
0
.
3
a
n
d
=
1
5
,
w
h
i
c
h
i
s
e
m
p
l
o
y
e
d
r
a
t
h
e
r
t
h
a
n
a
P
I
c
o
n
t
r
o
l
l
e
r
t
o
g
e
t
r
i
d
o
f
f
r
e
q
u
e
n
c
i
e
s
o
t
h
e
r
t
h
a
n
5
0
H
z
f
r
o
m
t
h
e
c
u
r
r
e
n
t
w
a
v
e
f
o
r
m
[
2
8
]
.
F
i
n
a
l
ly
,
t
h
e
PR
c
o
n
t
r
o
l
l
e
r
o
u
t
p
u
t
i
s
u
s
e
d
as
t
h
e
r
e
f
e
r
e
n
c
e
v
o
l
t
a
g
e
a
n
d
i
s
a
p
p
li
e
d
t
o
t
h
e
h
y
b
r
i
d
-
P
W
M
b
l
o
c
k
.
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
S
ev
en
teen
-
leve
l c
a
s
ca
d
ed
s
w
itch
ed
-
ca
p
a
cito
r
mu
ltil
ev
el
in
ve
r
ter fo
r
…
(
Ma
yth
a
m
Ja
s
im
N
a
s
er
)
1075
Fig
u
r
e
4
.
C
o
n
tr
o
l b
lo
c
k
d
iag
r
a
m
o
f
th
e
p
r
o
p
o
s
ed
C
SC
-
ML
I
with
g
r
id
in
te
g
r
atio
n
f
o
r
PV
s
y
s
tem
4.
T
H
E
O
R
E
T
I
CA
L
ANA
L
YS
I
S
4
.
1
.
V
o
l
t
a
g
e
a
nd
curr
ent
s
t
re
s
s
on
s
wit
ch
ing
dev
ices
T
h
e
m
ax
im
u
m
v
o
ltag
e
s
tr
ess
ac
r
o
s
s
th
e
s
witch
es
o
f
th
e
p
r
o
p
o
s
ed
C
SC
-
ML
I
ca
n
b
e
ex
p
r
ess
ed
as
(
3
)
to
(
6
)
.
19
=
29
=
4
(
3
)
11
=
12
=
21
=
22
=
2
(
4
)
13
=
14
=
17
=
18
=
23
=
24
=
27
=
28
=
(
5
)
15
=
16
=
25
=
26
=
1
.
5
(
6
)
I
n
t
h
e
p
r
o
p
o
s
e
d
C
S
C
-
M
L
I
,
t
h
e
c
h
a
r
g
i
n
g
c
u
r
r
e
n
t
(
)
w
h
i
c
h
h
a
s
h
i
g
h
a
m
p
l
i
t
u
d
e
f
l
o
w
s
t
h
r
o
u
g
h
t
h
e
s
w
i
t
c
h
e
s
(
13
,
14
,
17
,
a
n
d
18
)
i
n
t
h
e
f
i
r
s
t
c
e
l
l
o
f
C
S
C
-
M
L
I
a
n
d
t
h
r
o
u
g
h
t
h
e
s
w
i
t
c
h
e
s
(
23
,
24
,
27
,
a
n
d
28
)
i
n
t
h
e
s
e
c
o
n
d
c
e
l
l
.
S
o
,
t
h
e
c
u
r
r
e
n
t
s
t
r
e
s
s
o
f
t
h
e
s
e
s
w
i
t
c
h
e
s
i
s
h
i
g
h
.
B
u
t
t
h
e
r
e
m
a
i
n
i
n
g
s
w
i
t
c
h
e
s
c
a
r
r
y
o
n
l
y
t
h
e
g
r
i
d
c
u
r
r
e
n
t
(
)
.
T
h
e
m
a
x
i
m
u
m
r
a
t
e
d
c
u
r
r
e
n
t
o
n
e
a
c
h
s
w
i
t
c
h
o
f
C
S
C
-
M
L
I
c
a
n
b
e
m
a
t
h
e
m
a
t
i
c
a
l
l
y
r
e
p
r
e
s
e
n
t
e
d
a
s
(
7
)
a
n
d
(
8
)
.
11
=
12
=
15
=
16
=
19
=
21
=
22
=
25
=
26
=
29
=
(
7
)
13
=
14
=
17
=
18
=
23
=
24
=
27
=
28
=
(
+
)
(
8
)
4
.
2
.
DC
-
lin
k
a
nd
f
lo
a
t
ing
ca
pa
cit
a
nce
des
ig
n
T
h
e
ca
lcu
latio
n
o
f
eq
u
iv
alen
t
DC
-
lin
k
ca
p
ac
itan
ce
is
(
9
)
[
2
2
]
.
−
=
4
∆
(
9
)
As th
e
DC
-
lin
k
ca
p
ac
ito
r
s
o
f
e
ac
h
ce
ll
ar
e
co
n
n
ec
ted
in
s
er
ies
(
1
0
)
.
11
=
12
=
21
=
22
=
2
−
(
1
0
)
W
h
er
e
r
ep
r
esen
t
th
e
i
n
jecte
d
p
o
wer
to
th
e
g
r
id
,
r
ep
r
esen
t
th
e
g
r
id
f
r
eq
u
e
n
cy
an
d
∆
r
ep
r
esen
t
th
e
r
ip
p
le
v
o
ltag
e
(
5
–
1
0
%
o
f
)
.
T
h
e
ca
lcu
latio
n
o
f
f
lo
atin
g
ca
p
ac
itan
ce
is
(
1
1
)
[
2
2
]
.
=
,
∆
(
1
1
)
As th
e
f
lo
atin
g
ca
p
ac
ito
r
s
o
f
e
ac
h
ce
ll
ar
e
co
n
n
ec
ted
in
s
er
ies
(
1
2
)
.
13
=
14
=
23
=
24
=
2
(
1
2
)
W
h
er
e
,
is
th
e
m
ax
im
u
m
m
a
g
n
itu
d
e
o
f
g
r
id
cu
r
r
en
t
an
d
∆
is
ac
ce
p
tab
le
v
o
ltag
e
r
ip
p
le
(
2
–
5
%
o
f
4
)
in
th
e
f
lo
atin
g
ca
p
ac
ito
r
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.
16
,
No
.
2
,
J
u
n
e
20
25
:
1
0
7
0
-
1082
1076
5.
CO
M
P
ARA
T
I
V
E
S
T
UDY
T
o
d
em
o
n
s
tr
ate
th
e
ef
f
ec
tiv
e
n
ess
o
f
th
e
s
u
g
g
ested
1
7
-
lev
el
C
SC
-
ML
I
,
a
co
m
p
ar
is
o
n
b
etwe
en
th
e
p
r
o
p
o
s
ed
in
v
er
ter
an
d
o
th
e
r
e
x
is
tin
g
1
7
L
-
ML
I
s
is
illu
s
tr
ated
in
T
ab
le
2
.
T
h
e
co
m
p
ar
is
o
n
is
m
ad
e
in
te
r
m
s
o
f
th
e
n
u
m
b
er
o
f
v
o
ltag
e
le
v
els
(
)
,
in
p
u
t
DC
s
o
u
r
ce
(
)
,
s
witch
es
(
)
,
d
io
d
es
(
)
,
an
d
ca
p
ac
ito
r
s
(
)
ar
e
tak
e
n
in
to
ac
co
u
n
t.
Ad
d
itio
n
ally
,
th
e
lim
itatio
n
o
f
ca
p
ac
ito
r
'
s
in
r
u
s
h
cu
r
r
en
t
ca
p
ab
ili
ty
,
co
n
n
ec
tio
n
to
th
e
g
r
id
an
d
T
SV h
av
e
b
ee
n
in
clu
d
ed
i
n
th
e
co
m
p
ar
is
o
n
.
T
h
e
ter
m
T
SV is ca
lcu
lated
as
(
1
3
)
.
=
∑
=
11
(
1
3
)
W
h
er
e
th
e
is
th
e
s
witch
n
u
m
b
er
an
d
is
th
e
v
o
ltag
e
ac
r
o
s
s
th
e
s
witch
.
T
SV
is
an
ess
en
tial
f
ac
to
r
in
an
aly
zin
g
th
e
f
ea
s
ib
ilit
y
o
f
a
t
o
p
o
lo
g
y
,
as it is a
n
in
d
ir
ec
t i
n
d
icato
r
o
f
th
e
s
witch
es'
r
atin
g
s
.
T
h
e
h
ig
h
er
th
e
T
SV,
th
e
h
ig
h
er
th
e
r
atin
g
an
d
co
s
t
o
f
th
e
u
s
ed
I
GB
T
.
Am
o
n
g
th
e
p
r
esen
ted
1
7
-
lev
el
to
p
o
lo
g
ies,
th
e
p
r
o
p
o
s
ed
to
p
o
l
o
g
y
h
as
a
s
u
p
er
io
r
T
SV,
wh
ich
it
h
as
a
v
alu
e
o
f
1
6
.
5
.
I
n
[
3
0
]
,
to
p
o
lo
g
y
h
as
a
lo
w
v
alu
e
o
f
T
SV,
b
u
t
it
r
e
q
u
ir
es
a
h
ig
h
er
n
u
m
b
er
o
f
DC
s
o
u
r
c
es.
W
h
ile
in
[
1
2
]
,
[
2
4
]
,
T
SV
v
alu
e
is
q
u
ite
h
i
g
h
.
C
o
m
m
o
n
C
HB
,
NPC
,
an
d
FC
co
n
f
ig
u
r
atio
n
s
n
ec
ess
itate
n
u
m
er
o
u
s
c
o
m
p
o
n
en
ts
to
p
r
o
d
u
c
e
1
7
v
o
ltag
e
le
v
els.
T
h
is
lim
itatio
n
m
ak
es
th
em
u
n
ec
o
n
o
m
ical
f
o
r
s
ev
er
al
ap
p
licatio
n
s
.
I
n
[
1
6
]
,
[
1
8
]
,
[
2
1
]
17
-
lev
el
to
p
o
lo
g
ies
ar
e
in
v
en
ted
with
a
lo
wer
n
u
m
b
er
o
f
s
witch
es
b
u
t
th
e
lar
g
e
n
u
m
b
er
o
f
in
p
u
t
DC
s
o
u
r
ce
s
is
a
d
r
awb
ac
k
o
f
t
h
ese
to
p
o
lo
g
ies.
Fu
r
th
er
ML
I
to
p
o
l
o
g
ies
with
a
s
in
g
le
DC
s
o
u
r
ce
f
o
r
1
7
-
le
v
el
ar
e
ex
p
l
o
r
ed
in
[
1
2
]
,
[
1
4
]
,
[
1
7
]
,
[
2
0
]
,
[
3
2
]
,
[
3
3
]
,
th
ese
d
esig
n
s
s
u
f
f
e
r
f
r
o
m
h
ig
h
v
o
ltag
e
s
tr
ess
.
Ma
n
y
p
r
esen
ted
i
n
v
er
ter
s
h
a
v
e
a
h
ig
h
er
g
ain
f
ac
to
r
th
an
th
e
p
r
o
p
o
s
ed
o
n
e,
b
u
t
th
e
y
s
u
f
f
er
f
r
o
m
v
er
y
h
ig
h
v
o
ltag
e
s
tr
ess
ac
r
o
s
s
s
witch
es,
m
ak
in
g
th
em
u
n
s
u
itab
le
f
o
r
h
i
g
h
-
v
o
ltag
e
ap
p
licatio
n
s
.
I
n
co
m
p
ar
is
o
n
to
th
e
o
th
er
s
tr
u
ctu
r
es
p
r
esen
ted
in
T
ab
le
2
,
th
e
p
r
o
p
o
s
ed
C
SC
-
ML
I
d
em
o
n
s
tr
ates
a
n
o
tab
le
a
b
ilit
y
to
lim
it
th
e
ch
ar
g
in
g
s
p
i
k
e
cu
r
r
e
n
t.
As
m
en
tio
n
e
d
in
th
e
ab
o
v
e
ta
b
le,
it
was
o
b
s
er
v
ed
th
at
o
n
ly
th
e
s
tr
u
ctu
r
es
p
r
esen
ted
in
[
1
2
]
,
[
1
4
]
,
[
1
7
]
,
[
2
4
]
,
[
3
3
]
,
ca
n
p
r
o
v
id
e
th
is
s
ig
n
if
ican
t
f
ea
tu
r
e.
I
n
s
u
m
m
a
r
y
,
w
h
atev
er
t
h
e
co
m
p
lex
ity
o
f
th
e
s
witch
ar
r
an
g
em
en
ts
,
th
e
n
u
m
b
e
r
o
f
DC
s
o
u
r
ce
s
,
o
r
th
e
h
ig
h
v
o
ltag
e
s
tr
ess
,
ea
ch
to
p
o
l
o
g
y
p
r
esen
ts
its
o
wn
ch
allen
g
es.
T
ab
le
2
.
C
o
m
p
a
r
is
o
n
o
f
th
e
p
r
o
p
o
s
ed
to
p
o
lo
g
y
in
r
elatio
n
to
o
th
er
1
7
-
lev
el
to
p
o
lo
g
ies
To
p
o
l
o
g
y
(
×
)
C
u
r
r
e
n
t
%
TH
D
G
a
i
n
f
a
c
t
o
r
Li
mi
t
a
t
i
o
n
o
f
i
n
r
u
sh
c
u
r
r
e
n
t
G
r
i
d
c
o
n
n
e
c
t
e
d
C
H
B
17
8
32
0
0
32
-
-
-
-
FC
17
2
32
32
16
32
-
-
-
-
N
P
C
17
2
32
32
16
32
-
-
-
-
[
1
2
]
17
1
14
4
4
82
-
8
Y
e
s
No
[
1
4
]
17
1
14
4
4
24
-
2
Y
e
s
Y
e
s
[
1
6
]
17
4
14
0
4
44
-
4
No
No
[
1
7
]
17
1
12
5
4
34
1
.
6
8
Y
e
s
Y
e
s
[
1
8
]
17
4
14
0
2
48
1
.
6
2
8
No
No
[
2
0
]
17
1
12
2
3
25
2
.
4
7
4
No
No
[
2
1
]
17
4
10
0
0
36
-
2
-
No
[
2
4
]
17
1
13
3
3
53
-
8
Y
e
s
No
[
2
9
]
17
2
11
1
3
36
-
1
.
6
No
No
[
3
0
]
17
6
9
3
1
20
-
4
No
No
[
3
1
]
17
2
14
2
4
40
-
8
No
No
[
3
2
]
17
1
13
3
3
40
-
8
No
No
[
3
3
]
17
1
11
1
3
28
-
4
Y
e
s
No
P
r
o
p
o
se
d
17
2
18
4
8
1
6
.
5
1
.
1
8
2
Y
e
s
Y
e
s
6.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
A
p
r
o
p
o
s
ed
1
7
-
lev
el
C
SC
-
M
L
I
-
b
ased
PV
-
g
r
id
s
y
s
tem
is
s
im
u
lated
u
s
in
g
th
e
MA
T
L
AB
/Si
m
u
lin
k
p
latf
o
r
m
u
n
d
er
d
if
f
e
r
en
t
en
v
ir
o
n
m
en
tal
co
n
d
itio
n
s
.
T
h
e
PV
p
o
wer
in
jectio
n
s
tag
e,
co
m
p
r
i
s
in
g
PV
ar
r
ay
s
an
d
th
eir
co
r
r
esp
o
n
d
in
g
MPPT
b
o
o
s
t
co
n
v
e
r
ter
s
,
h
as
b
ee
n
s
im
u
lated
b
y
lin
k
in
g
th
eir
o
u
tp
u
ts
to
a
s
in
g
le
DC
b
u
s
with
a
ca
p
ac
ito
r
=
2
5
0
0
µF.
On
th
e
o
th
er
s
id
e,
two
f
ly
b
ac
k
c
o
n
v
er
ter
s
wer
e
em
p
l
o
y
ed
to
s
u
p
p
ly
th
e
C
SC
-
ML
I
ce
lls
.
T
h
e
ce
lls
o
f
th
e
p
r
o
p
o
s
ed
in
v
er
ter
h
av
e
b
ee
n
ca
s
ca
d
ed
an
d
co
n
n
ec
ted
to
th
e
g
r
id
th
r
o
u
g
h
a
=
1
m
H.
T
h
e
p
r
o
p
o
s
ed
in
v
e
r
ter
p
ar
am
eter
s
f
o
r
a
3
k
W
p
o
wer
s
y
s
tem
ar
e
b
ein
g
c
o
n
s
id
er
ed
,
with
p
ea
k
in
v
er
ter
o
u
tp
u
t
v
o
ltag
e
=
3
4
0
V
at
a
g
r
i
d
f
r
eq
u
en
cy
=
5
0
Hz.
T
h
e
in
p
u
t
DC
-
lin
k
v
o
ltag
e
=
1
7
0
V
f
o
r
ea
ch
ce
ll
an
d
o
p
er
ates w
ith
a
2
.
5
k
Hz
s
witch
in
g
f
r
eq
u
en
cy
.
T
h
e
s
p
e
ci
f
i
c
a
ti
o
n
s
o
f
t
h
e
PV
m
o
d
u
l
e
s
f
o
r
e
ac
h
P
V
a
r
r
a
y
a
n
d
t
h
e
m
a
i
n
p
a
r
a
m
e
t
e
r
s
o
f
t
h
e
s
i
m
u
l
at
e
d
s
y
s
t
em
a
r
e
s
u
m
m
a
r
i
z
e
d
i
n
T
a
b
l
e
s
3
a
n
d
4
,
r
e
s
p
e
c
t
i
v
el
y
.
I
n
it
i
a
ll
y
,
t
o
d
em
o
n
s
t
r
a
t
e
t
h
e
d
y
n
a
m
i
c
p
e
r
f
o
r
m
a
n
c
e
o
f
t
h
e
p
r
o
p
o
s
e
d
g
r
i
d
-
t
i
e
s
y
s
t
e
m
c
o
n
t
r
o
l
s
c
h
e
m
e
,
t
h
e
s
y
s
t
e
m
's
p
e
r
f
o
r
m
a
n
c
e
i
s
e
v
a
l
u
a
t
e
d
u
n
d
e
r
a
s
o
l
a
r
i
r
r
a
d
i
a
t
i
o
n
s
t
e
p
c
h
a
n
g
e
f
r
o
m
7
0
0
t
o
1
0
0
0
W
/
m
2
a
t
t
=
1
s
.
A
s
t
e
p
c
h
a
n
g
e
i
n
PV
p
o
w
e
r
is
il
l
u
s
t
r
a
te
d
i
n
F
i
g
u
r
e
5
(
a
)
.
A
s
a
n
t
i
ci
p
a
te
d
,
t
h
e
o
u
t
e
r
v
o
l
t
a
g
e
l
o
o
p
e
f
f
e
c
ti
v
e
l
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I
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g
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u
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6
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DC
b
u
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v
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tep
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tem
r
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a)
b
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p
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k
v
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n
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b
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Fig
u
r
e
7
.
Var
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in
g
s
o
lar
i
r
r
ad
ia
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ce
r
esu
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: (
a)
to
tal
PV p
o
wer
,
(
b
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g
r
id
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r
r
en
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n
d
s
ca
led
g
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v
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d
(
c)
v
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ltag
e
ac
r
o
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s
f
lo
atin
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Evaluation Warning : The document was created with Spire.PDF for Python.
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ated
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u
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est
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eq
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al
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f
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7
0
V.
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h
e
r
esu
lts
in
d
icate
th
at
th
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p
r
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p
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ed
C
S
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o
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ates
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ec
tiv
ely
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th
s
tead
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s
tate
an
d
d
y
n
am
ic
c
o
n
d
itio
n
s
.
(
a)
(
b
)
(
c)
(
d
)
(
e)
Fig
u
r
e
8
.
R
esu
lts
u
n
d
er
s
tead
y
-
s
tate
co
n
d
itio
n
s
: (
a)
to
tal
PV
p
o
wer
,
(
b
)
in
v
er
ter
o
u
tp
u
t
v
o
lt
ag
e,
(
c)
g
r
id
cu
r
r
e
n
t a
n
d
s
ca
led
g
r
i
d
v
o
ltag
e,
(
d
)
DC
-
lin
k
ca
p
ac
it
o
r
s
cu
r
r
en
t,
an
d
(
e)
f
l
o
atin
g
ca
p
ac
ito
r
s
cu
r
r
e
n
t
Evaluation Warning : The document was created with Spire.PDF for Python.