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nte
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lect
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Driv
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s
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J
P
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Vo
l.
9
,
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.
3
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Sep
tem
b
er
2
0
1
8
,
p
p
.
13
30
~
13
37
I
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N:
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8
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.
1
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9
1
/
i
j
p
ed
s
.
v9
.i
3
.
pp
13
30
-
13
37
1330
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ultilevel Inv
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m
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ted
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h
is
p
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p
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r.
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h
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lp
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o
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icie
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w
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o
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s
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ste
m
.
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o
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o
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e
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ti
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z
e
th
e
sy
ste
m
u
p
to
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ted
M
P
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c
o
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a
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a
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d
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it
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s
p
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d
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e
m
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n
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m
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n
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d
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ted
i
n
su
c
h
a
w
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y
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a
t
if
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p
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se
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b
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e
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se
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ts m
a
k
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K
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w
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:
C
ascad
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-
b
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id
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PV
MP
PT
Co
p
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©
201
8
In
s
t
it
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te o
f
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d
v
a
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S
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Al
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rig
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C
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s
p
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ing
A
uth
o
r
:
S
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etap
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m
a
P
an
ig
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i,
Dep
ar
te
m
en
t
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f
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lectr
ical
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d
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lectr
o
n
ics E
n
g
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Natio
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al
I
n
s
tit
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te
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h
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am
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ar
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8
3
1
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1
4
E
m
ail: d
ip
a.
tat@
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m
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co
m
1.
I
NT
RO
D
UCT
I
O
N
Fro
m
t
h
e
la
s
t
co
u
p
le
o
f
y
ea
r
s
r
en
e
w
ab
le
en
er
g
y
s
o
u
r
ce
s
ar
e
g
r
o
w
i
n
g
e
x
te
n
s
i
v
el
y
to
f
u
lf
ill
th
e
e
n
er
g
y
d
em
a
n
d
o
f
co
n
s
u
m
er
s
.
Am
o
n
g
t
h
e
d
i
f
f
er
en
t
en
er
g
y
s
o
u
r
ce
s
,
s
o
lar
en
er
g
y
is
t
h
e
m
o
s
t
r
eli
ab
le
an
d
s
u
s
tai
n
ab
le
o
n
e
[
1
]
-
[
3
]
.
W
ith
th
e
w
id
e
d
ev
elo
p
m
e
n
t o
f
p
o
w
er
elec
tr
o
n
ics
tech
n
o
lo
g
y
it b
ec
o
m
es
ea
s
ier
to
in
te
g
r
ate
v
ar
io
u
s
P
V
in
v
er
ter
s
w
it
h
t
h
e
u
tili
t
y
g
r
i
d
.
A
P
V
-
i
n
v
er
ter
is
t
h
e
m
a
in
co
m
p
o
n
en
t
f
o
r
i
n
te
g
r
atio
n
in
a
g
r
id
-
co
n
n
ec
te
d
ap
p
licatio
n
.
I
t c
o
n
v
er
t
s
t
h
e
D
C
p
o
w
er
a
v
ailab
le
f
r
o
m
s
o
lar
p
an
el
i
n
to
A
C
p
o
w
er
t
h
a
t i
s
f
e
d
in
to
an
u
t
ilit
y
g
r
id
.
P
V
p
an
els
ar
e
co
n
n
ec
ted
eit
h
er
in
s
er
ie
s
o
r
p
ar
allel
o
r
b
o
th
to
o
b
ta
in
th
e
r
eq
u
ir
ed
v
o
lta
g
e
a
n
d
p
o
w
er
.
T
h
is
ar
r
an
g
e
m
en
t
is
ca
lled
a
s
ce
n
tr
alize
d
P
V
in
v
er
ter
.
B
u
t
th
e
r
eq
u
ir
e
m
e
n
t
o
f
h
i
g
h
v
o
lta
g
e
D
C
ca
b
le
b
et
w
ee
n
P
V
p
an
el
an
d
in
v
er
ter
li
m
its
it
s
u
s
ag
e.
T
ill
n
o
w
d
if
f
er
en
t
t
y
p
e
s
o
f
P
V
in
v
er
ter
s
ar
e
d
ev
elo
p
ed
b
a
s
ed
o
n
P
V
m
o
d
u
l
e
co
n
n
ec
te
d
m
et
h
o
d
,
u
tili
za
t
io
n
o
f
tr
a
n
s
f
o
r
m
er
an
d
n
u
m
b
er
o
f
p
o
w
er
s
ta
g
es
[
4]
.
Am
o
n
g
t
h
e
v
ar
io
u
s
in
v
er
ter
to
p
lo
g
ies
th
e
m
u
ltil
e
v
el
in
v
er
ter
co
n
f
ig
u
r
a
tio
n
is
p
a
y
i
n
g
th
e
atte
n
tio
n
o
f
th
e
r
esear
ch
er
s
w
o
r
ld
w
i
d
e
f
o
r
lar
g
e
s
ca
le
ap
p
licatio
n
s
.
B
ec
au
s
e
o
f
it
s
m
u
lt
ile
v
el
s
tr
u
ct
u
r
e
th
e
o
u
tp
u
t
w
a
v
ef
o
r
m
o
b
tai
n
ed
in
t
h
e
g
r
id
s
id
e
m
u
s
t
b
e
s
in
u
s
o
id
al
w
it
h
less
h
ar
m
o
n
ic
s
co
n
ten
t
[5
]
.
I
t
d
o
es
n
o
t
r
eq
u
ir
e
an
y
b
u
lk
y
lo
w
f
r
eq
u
en
c
y
tr
a
n
s
f
o
r
m
er
f
o
r
its
in
te
g
r
atio
n
w
it
h
t
h
e
g
r
id
.
Mo
r
eo
v
er
,
b
ec
au
s
e
o
f
th
e
r
eq
u
ir
e
m
en
t
o
f
i
n
d
iv
id
u
a
l
DC
s
o
u
r
c
e
f
o
r
ea
ch
H
-
b
r
id
g
e
co
n
f
i
g
u
r
atio
n
,
t
h
e
v
o
lta
g
e
co
n
tr
o
l
ca
n
b
e
d
o
n
e
in
d
i
v
id
u
al
l
y
.
A
s
i
n
g
le
p
h
ase
s
ev
e
n
le
v
el
C
HB
co
m
p
r
is
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o
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th
r
ee
H
-
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r
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s
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c
h
f
ed
b
y
m
u
ltip
le
s
tr
in
g
s
o
f
P
V
p
a
n
els
th
r
o
u
g
h
t
h
eir
o
w
n
i
n
d
iv
id
u
al
H
-
b
r
id
g
e
is
p
r
ese
n
ted
in
Fi
g
u
r
e
1
.
I
n
s
u
c
h
ar
r
an
g
e
m
en
t,
th
e
in
d
i
v
id
u
al
MP
P
T
,
ca
lle
d
d
is
tr
ib
u
ted
MPPT
tec
h
n
iq
u
e
is
ap
p
lied
to
tr
ac
k
th
e
e
x
tr
e
m
e
p
o
w
er
o
f
ea
ch
P
V
p
an
el
[
6
].
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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P
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w
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&
Dr
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S
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s
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I
SS
N:
2
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8
8
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694
A
N
o
ve
l A
p
p
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o
a
ch
fo
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g
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id
in
t
eg
r
a
tio
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o
f Ca
s
ca
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H
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Mu
ltil
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ter
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(
S
w
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p
a
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P
a
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1331
2.
SYST
E
M
DE
SCRI
P
T
I
O
N
2
.
1
.
M
o
du
la
r
ca
s
ca
ded H
-
bridg
e
m
ultilev
el
inv
er
t
er
A
s
ev
e
n
le
v
el
C
HB
i
n
v
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ter
p
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d
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ce
s
th
e
o
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tp
u
t
v
o
lta
g
e
v
alu
e
s
(
le
v
els)
w
i
th
r
esp
ec
t
t
o
n
eg
ati
v
e
ter
m
i
n
al
o
f
t
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e
ca
p
ac
ito
r
s
.
I
f
n
r
ep
r
esen
ts
th
e
n
u
m
b
er
o
f
s
t
ep
o
f
p
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ase
v
o
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g
e
w
i
th
r
esp
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t
to
th
e
n
e
g
ati
v
e
ter
m
i
n
al
o
f
t
h
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in
v
er
ter
,
th
e
n
t
h
e
n
u
m
b
er
o
f
s
tag
e
s
k
b
et
w
ee
n
t
w
o
p
h
ase
s
ac
r
o
s
s
lo
ad
is
r
ep
r
esen
ted
as,
Fig
u
r
e
1
.
C
o
n
f
ig
u
r
atio
n
o
f
s
i
n
g
le
p
h
ase
g
r
id
-
co
n
n
ec
ted
P
V
s
y
s
te
m
[7
]
k
= 2
n
+1
(
1
)
I
f
th
e
D
C
-
li
n
k
v
o
ltag
e
s
ar
e
eq
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al,
at
th
e
lo
ad
s
id
e
7
-
lev
el
v
o
ltag
e
ca
n
b
e
o
b
tain
ed
.
T
h
e
o
u
tp
u
t
v
o
ltag
e
ca
n
b
e
r
ep
r
esen
ted
b
y
th
e
u
p
co
m
in
g
eq
u
atio
n
s
:
1
=
(
11
-
13
)
.
1
=
P
1
.
1
2
=
(
21
-
23
)
.
2
=
P
2
.
2
(
2
)
w
h
er
e
r
ep
r
esen
ts
th
e
s
w
itc
h
i
n
g
s
tate
o
r
it
ca
n
b
e
ON,
0
o
r
OFF.
P
1
a
n
d
P
2
r
ep
r
esen
t
th
e
d
is
cr
ete
v
alu
es
h
av
i
n
g
t
h
e
v
al
u
es
o
f
-
1
,
0
,
+1
.
Fo
r
lin
ea
r
izatio
n
,
co
n
ti
n
u
o
u
s
s
w
itc
h
in
g
f
u
n
c
tio
n
s
1
an
d
2
[
-
1
,
1
]
ar
e
tak
e
n
i
n
p
lace
o
f
th
e
f
u
n
ctio
n
s
P
1
an
d
P
2
[
8
]
[
9
].
E
q
u
atio
n
s
(
3
)
r
e
p
r
esen
t
th
e
d
y
n
a
m
ic
b
eh
a
v
io
r
o
f
th
e
s
y
s
te
m
t
h
at
is
r
ep
r
esen
ted
as:
=
1
(
1
1
+
2
2
−
−
)
1
=
1
1
(
1
−
1
)
(
3
)
2
=
1
1
(
2
−
2
)
Du
e
to
t
h
e
p
r
esen
ce
o
f
i
s
o
lated
DC
s
o
u
r
ce
in
ca
s
e
o
f
C
HB
,
in
d
ep
en
d
en
t
MP
P
T
co
n
t
r
o
l
ca
n
b
e
p
o
s
s
ib
le
an
d
u
t
m
o
s
t
p
o
w
er
ca
n
b
e
o
b
tain
ed
f
r
o
m
t
h
e
e
n
tire
s
y
s
te
m
m
o
r
e
e
f
f
icie
n
tl
y
.
Ne
v
er
th
eles
s
,
s
i
n
ce
t
h
e
p
o
s
s
ib
ilit
y
o
f
i
n
d
ep
en
d
en
t
v
o
l
tag
e
co
n
tr
o
l
th
r
o
u
g
h
ea
ch
H
–
b
r
id
g
e,
th
er
e
i
s
a
p
o
w
er
i
m
b
al
an
ce
.
T
h
is
p
r
o
b
le
m
ca
n
b
e
clas
s
i
f
ied
in
to
t
w
o
clas
s
es
:
1
)
i
n
ter
p
h
a
s
e
(
clu
s
ter
ed
)
p
o
w
er
i
m
b
ala
n
ce
,
w
h
en
p
o
w
e
r
g
en
er
at
ed
b
y
ea
c
h
p
h
ase
is
n
o
t
eq
u
al
;
a
n
d
2
)
in
ter
b
r
id
g
e
(
in
d
iv
id
u
al)
p
o
w
er
i
m
b
alan
ce
,
w
h
ic
h
h
ap
p
en
s
w
h
en
b
r
id
g
e
s
co
n
n
ec
ted
to
th
e
s
a
m
e
p
h
ase
leg
g
e
n
er
a
tes
a
n
u
n
eq
u
al
p
o
w
er
.
I
f
t
h
is
s
y
s
te
m
ca
n
n
o
t
b
e
co
n
s
id
er
ed
s
er
io
u
s
l
y
,
d
c
-
li
n
k
v
o
ltag
e
w
il
l
f
lo
at
lead
in
g
to
v
o
ltag
e
d
is
to
r
tio
n
at
th
e
g
r
id
s
i
d
e.
B
ec
au
s
e
o
f
th
e
in
ad
eq
u
ate
ir
r
ad
ian
ce
o
b
tain
ed
f
r
o
m
s
u
n
,
v
ar
y
in
g
te
m
p
er
atu
r
e
an
d
u
s
a
g
e
o
f
t
h
e
P
V
p
an
el
s
f
r
o
m
lo
n
g
t
i
m
e
,
t
h
er
e
is
a
n
u
n
b
ala
n
ce
d
p
o
w
er
s
u
p
p
l
y
to
th
e
C
HB
,
ca
u
s
in
g
u
n
b
ala
n
ce
d
cu
r
r
en
t
at
t
h
e
g
r
id
s
id
e.
T
h
er
ef
o
r
e
th
is
i
s
s
u
e
i
s
c
o
n
s
id
er
ed
s
er
io
u
s
l
y
w
it
h
t
h
e
d
esi
g
n
i
n
g
o
f
s
u
itab
le
co
n
tr
o
ller
s
o
th
at
at
th
e
g
r
id
s
i
d
e
b
alan
ce
d
cu
r
r
en
t is ac
h
ie
v
e
d
[
1
0
]
[
1
1
].
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
,
Vo
l.
9
,
No
.
3
,
Sep
tem
b
er
2
0
1
8
:
13
30
–
13
37
1332
3.
CO
NT
RO
L
ST
R
AT
E
G
Y
P
V
m
is
m
atc
h
es
is
v
er
y
h
az
a
r
d
o
u
s
p
r
o
b
lem
in
ca
s
e
o
f
lar
g
e
P
V
s
y
s
te
m
.
Hen
ce
f
o
r
th
,
f
o
r
u
t
m
o
s
t
p
o
w
er
ex
tr
ac
tio
n
f
r
o
m
t
h
e
s
y
s
te
m
a
c
o
n
tr
o
l
s
ch
e
m
e
i
s
es
s
en
t
iall
y
n
ee
d
ed
.
Gen
er
all
y
t
w
o
co
n
tr
o
l
s
ch
e
m
e
i
s
p
r
o
p
o
s
ed
in
th
is
p
ap
er
(
i)
MPPT
co
n
tr
o
l
(
ii)
I
n
v
er
ter
co
n
tr
o
l.
3
.
1
.
M
P
P
T
co
ntr
o
l
T
o
s
h
o
w
t
h
e
r
eq
u
ir
e
m
e
n
t
o
f
MP
PT
,
1
8
5
W
P
V
p
an
el
is
c
o
n
s
id
er
ed
th
at
is
co
n
n
ec
ted
t
o
ea
ch
H
-
b
r
id
g
e
o
f
le
v
el
m
u
l
tile
v
el
i
n
v
er
ter
o
f
a
t
h
r
ee
p
h
a
s
e
s
y
s
te
m
.
T
h
e
P
-
V
a
n
d
I
-
V
c
u
r
v
es
f
o
r
1
8
5
W
p
an
el
is
s
i
m
u
lated
i
n
M
A
T
L
A
B
/SIM
UL
I
NK
e
n
v
ir
o
n
m
e
n
t
a
n
d
ar
e
s
h
o
w
n
i
n
Fi
g
u
r
e
2
.
T
h
e
v
ar
io
u
s
p
lo
ts
at
d
if
f
er
e
n
t
r
ad
iatio
n
s
ar
e
s
h
o
w
n
.
E
ac
h
C
HB
in
v
er
ter
is
co
n
n
ec
ted
to
1
8
5
W
s
o
lar
p
an
el
an
d
f
o
r
a
s
in
g
le
p
h
ase
s
y
s
te
m
n
-
C
HB
in
v
er
ter
s
ar
e
co
n
n
ec
ted
i
n
s
er
ies.
L
i
k
e
w
is
e
th
e
w
h
o
le
t
h
r
ee
p
h
ase
s
y
s
te
m
i
s
in
teg
r
ate
d
w
it
h
g
r
id
t
h
r
o
u
g
h
in
d
u
cto
r
L
t
h
at
i
s
u
s
ed
to
m
i
n
i
m
ize
t
h
e
s
w
itc
h
in
g
c
u
r
r
en
t
h
ar
m
o
n
ics
a
t
t
h
e
g
r
i
d
s
id
e.
I
n
o
r
d
er
to
r
eso
lv
e
th
e
P
V
m
i
s
m
atch
i
s
s
u
e
d
is
tr
ib
u
ted
MP
PT
co
n
tr
o
l te
ch
n
iq
u
e
i
s
ad
o
p
ted
.
Fig
u
r
e
2
. I
-
V
an
d
P
-
V
ch
ar
ac
t
er
is
tics
o
f
1
8
5
W
P
V
p
an
el
at
d
if
f
er
en
t so
lar
r
ad
iatio
n
s
3
.
1
.
1
.
Dis
t
ribute
d M
P
P
T
co
ntr
o
l
V
ar
io
u
s
MP
P
T
tech
n
iq
u
es
w
e
r
e
d
ev
elo
p
ed
i
n
o
r
d
er
to
ex
tr
em
e
p
o
w
er
f
r
o
m
a
P
V
p
an
el
[
12
].
I
n
th
i
s
p
ap
er
,
I
n
cr
e
m
en
ta
l
co
n
d
u
cta
n
ce
MP
PT
m
et
h
o
d
is
ad
o
p
te
d
to
g
en
er
ate
th
e
d
c
-
li
n
k
v
o
ltag
e
r
ef
er
e
n
ce
f
o
r
in
d
iv
id
u
al
P
V
p
an
e
l.
Her
e
t
h
e
MP
P
p
o
in
t
g
o
es
on
ad
j
u
s
ti
n
g
its
p
o
s
iti
o
n
ir
r
esp
ec
tiv
e
o
f
t
h
e
e
n
v
ir
o
n
m
en
t
ch
an
g
es.
I
n
o
r
d
er
to
tr
ac
k
M
P
P
,
I
n
cr
e
m
en
ta
l
C
o
n
d
u
cta
n
ce
(
I
C
)
m
et
h
o
d
co
m
p
ar
es
t
h
e
r
atio
o
f
in
cr
e
m
e
n
tal
co
n
d
u
ctan
ce
to
in
s
tan
tan
eo
u
s
co
n
d
u
ctan
ce
v
al
u
e
o
f
P
V
m
o
d
u
le.
B
ased
o
n
th
is
v
al
u
e
,
th
e
s
lo
p
e
o
f
P
-
V
ch
ar
ac
ter
is
tic
is
v
a
r
ied
an
d
ac
co
r
d
in
g
to
th
e
ch
an
g
e
in
s
lo
p
e,
d
u
ty
c
y
cle
o
f
co
n
v
er
ter
ca
n
b
e
g
en
er
ated
[
1
3
-
16
].
Fo
r
MPP
tr
ac
k
in
g
,
ap
p
l
y
i
n
g
I
C
alg
o
r
it
h
m
t
h
e
f
o
llo
w
in
g
s
tep
s
ar
e
tak
en
i
n
to
co
n
s
id
er
atio
n
:
a.
W
h
en
=
0
,
th
e
er
r
o
r
is
ze
r
o
a
n
d
ca
n
b
e
f
o
u
n
d
o
u
t .
b.
W
h
e
n
>
0
i.e
>
−
,
th
e
MP
P
d
r
ag
s
to
w
ar
d
s
th
e
le
f
t s
id
e
o
f
th
e
c
u
r
v
e
(
h
av
i
n
g
a
p
o
s
itiv
e
er
r
o
r
)
.
c.
W
h
en
<
0
i.e
<
−
,
th
e
MP
P
d
r
ag
s
to
w
ar
d
s
th
e
r
i
g
h
t sid
e
o
f
t
h
e
cu
r
v
e
(
h
a
v
i
n
g
a
n
eg
a
tiv
e
er
r
o
r
)
.
Af
ter
th
e
MP
P
T
tr
ac
k
in
g
t
h
e
d
c
lin
k
v
o
lta
g
e
r
ef
er
en
ce
i
s
f
o
u
n
d
to
b
e
3
6
.
4
V
as sh
o
w
n
i
n
Fi
g
u
r
e
3
.
Fig
u
r
e
3
.
MP
PT
v
o
ltag
e
o
f
1
8
5
W
P
V
p
an
el
th
r
o
u
g
h
i
n
cr
e
m
e
n
tal
co
n
d
u
c
tan
ce
m
et
h
o
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
I
SS
N:
2
0
8
8
-
8
694
A
N
o
ve
l A
p
p
r
o
a
ch
fo
r
g
r
id
in
t
eg
r
a
tio
n
o
f Ca
s
ca
d
ed
H
-
b
r
id
g
e
Mu
ltil
ev
el
I
n
ve
r
ter
...
(
S
w
eta
p
a
d
ma
P
a
n
ig
r
a
h
i)
1333
3
.
2
.
I
nv
er
t
er
c
o
ntr
o
l
I
t
co
m
p
r
is
e
s
o
f
co
n
tr
o
l
o
f
b
o
t
h
ac
ti
v
e
an
d
r
ea
ctiv
e
p
o
w
er
.
I
t
h
as
t
w
o
d
i
f
f
er
e
n
t
co
n
tr
o
l
lo
o
p
s
:
o
n
e
is
ca
lled
th
e
v
o
ltag
e
co
n
tr
o
l
lo
o
p
th
at
is
u
s
ed
to
s
et
th
e
ca
p
ac
ito
r
v
o
ltag
e
ac
r
o
s
s
ea
ch
d
c
lin
k
a
n
d
o
th
er
o
n
e
is
ca
lled
th
e
cu
r
r
e
n
t
co
n
tr
o
l
lo
o
p
th
at
is
r
e
q
u
ir
ed
f
o
r
th
e
g
e
n
er
atio
n
o
f
th
e
s
i
n
u
s
o
id
al
g
r
id
cu
r
r
en
t.
Fi
g
u
r
e
4
.
s
h
o
w
s
t
h
e
co
n
tr
o
l
s
c
h
e
m
e
f
o
r
th
e
en
tire
s
y
s
te
m
.
T
h
e
s
u
m
o
f
d
c
lin
k
v
o
lta
g
e
1
to
ar
e
co
m
p
ar
ed
w
it
h
r
esp
ec
tiv
e
v
o
ltag
e
r
e
f
er
en
ce
t
o
p
r
o
d
u
ce
th
e
s
u
m
o
f
er
r
o
r
th
at
i
s
p
ass
ed
t
h
r
o
u
g
h
th
e
to
tal
v
o
lta
g
e
co
n
tr
o
ller
lo
o
p
to
g
en
er
ate
th
e
r
ef
er
en
ce
cu
r
r
en
t
.
A
s
r
ea
ctiv
e
p
o
w
er
c
o
m
p
e
n
s
at
io
n
is
n
o
t
tak
e
n
in
to
ac
co
u
n
t
i
n
th
is
p
ap
er
,
h
en
ce
is
ad
j
u
s
ted
to
b
e
ze
r
o
.
T
h
e
p
h
ase
an
g
le
o
f
g
r
id
v
o
ltag
e
θ
is
d
eter
m
in
ed
b
y
a
t
h
r
e
e
p
h
ase
lo
ck
ed
lo
o
p
(
P
L
L
)
.
T
h
e
g
r
id
cu
r
r
en
ts
,
a
n
d
ar
e
p
ass
ed
th
r
o
u
g
h
abc
to
dq
c
o
n
v
er
ter
cir
cu
it
to
g
e
n
er
ate
th
e
,
cu
r
r
en
t
co
o
r
d
in
ates.
T
h
ese
cu
r
r
e
n
t
co
o
r
d
in
ates
ar
e
ag
ain
f
ee
d
to
a
P
I
co
n
tr
o
ller
to
g
e
n
er
ate
t
h
e
m
o
d
u
latio
n
in
d
ex
i
n
dq
co
o
r
d
in
ates
an
d
w
it
h
th
e
h
e
lp
o
f
dq
t
o
a
b
c
co
n
tr
o
ller
m
o
d
u
la
tio
n
in
d
ices
i
n
abc
co
o
r
d
in
ates a
r
e
g
en
er
ated
.
Fig
u
r
e
4
.
C
o
n
tr
o
l sch
e
m
e
f
o
r
m
o
d
u
lar
ca
s
ca
d
ed
H
-
b
r
id
g
e
m
u
ltil
e
v
el
P
V
in
v
er
ter
f
o
r
th
r
ee
-
p
h
ase
s
y
s
te
m
Fo
r
s
i
m
p
licit
y
,
ta
k
e
p
h
ase
a
in
to
co
n
s
id
er
atio
n
.
Du
e
to
i
n
d
iv
id
u
al
MP
PT
co
n
tr
o
l,
th
e
g
en
er
ated
v
o
ltag
e
s
2
to
ar
e
co
n
tr
o
lled
th
r
o
u
g
h
n
-
1
lo
o
p
.
E
ac
h
v
o
ltag
e
c
o
n
tr
o
ller
g
iv
e
s
th
e
m
o
d
u
latio
n
in
d
e
x
p
r
o
p
o
r
tio
n
o
f
o
n
e
H
-
b
r
id
g
e
m
o
d
u
le
in
p
h
ase
a
.
Af
ter
m
u
ltip
lied
b
y
t
h
e
m
o
d
u
latio
n
in
d
ex
o
f
p
h
ase
a
,
n
-
1
mo
d
u
latio
n
in
d
ice
s
ca
n
b
e
g
e
n
er
ated
.
T
h
e
ca
lcu
latio
n
f
o
r
p
h
ase
b
an
d
c
ar
e
also
ap
p
r
o
a
ch
ab
le
in
t
h
e
s
a
m
e
w
a
y
to
d
eter
m
i
n
e
t
h
e
m
o
d
u
lat
io
n
in
d
ices.
A
p
h
ase
s
h
i
f
ted
m
o
d
u
latio
n
s
ch
e
m
e
is
u
s
ed
f
o
r
s
w
itc
h
i
n
g
ea
c
h
H
-
b
r
id
g
e
in
v
er
ter
.
3
.
2
.
1
.
P
ha
s
e
s
hift
ed
m
o
du
la
t
i
o
n sche
m
e
T
h
er
e
ar
e
d
if
f
er
en
t
m
o
d
u
la
tio
n
s
tech
n
iq
u
es
p
r
o
p
o
s
ed
f
o
r
s
w
itch
i
n
g
o
f
m
u
ltil
e
v
el
in
v
er
ter
s
[
1
7
]
-
[
21
]
.
Am
o
n
g
w
h
ic
h
P
S
-
P
W
M
is
m
o
s
t
p
o
p
u
lar
l
y
u
s
ed
to
p
r
o
d
u
ce
P
W
M
co
n
tr
o
l
s
ig
n
al
s
f
o
r
s
w
itc
h
i
n
g
o
f
th
e
in
v
er
ter
s
[
22]
[
23
]
.
A
s
p
ar
tial
s
h
ad
i
n
g
p
h
en
o
m
en
o
n
ca
u
s
es
a
s
er
io
u
s
i
s
s
u
e
in
ca
s
e
o
f
s
w
i
tch
i
n
g
o
f
ca
s
ca
d
ed
in
v
er
ter
,
h
e
n
ce
th
e
m
o
d
u
la
t
io
n
in
d
e
x
o
f
ea
ch
ce
ll
m
u
s
t
b
e
p
r
o
p
e
r
ly
u
p
d
ated
to
co
n
s
id
er
u
n
b
alan
ce
d
co
n
d
itio
n
s
at
d
c
s
id
e
b
y
p
r
o
d
u
cin
g
d
i
f
f
er
e
n
t
m
o
d
u
lati
n
g
s
i
g
n
al
s
.
I
n
o
r
d
er
to
ac
h
iev
e
a
b
alan
ce
d
co
n
d
itio
n
at
g
r
id
s
id
e,
ce
ll
w
it
h
h
i
g
h
p
o
w
e
r
is
ass
ig
n
ed
w
it
h
h
ig
h
m
o
d
u
l
atio
n
i
n
d
ex
a
n
d
w
it
h
lo
w
p
o
w
er
is
ass
ig
n
ed
w
it
h
lo
w
m
o
d
u
latio
n
i
n
d
ex
a
n
d
h
e
n
ce
ea
ch
ce
ll
is
m
o
d
u
lated
in
d
iv
id
u
all
y
u
s
i
n
g
t
h
e
P
W
M,
in
o
r
d
er
to
p
r
o
v
id
e
an
ev
en
p
o
w
er
s
h
ar
in
g
a
m
o
n
g
th
e
ce
lls
.
I
n
P
S
-
P
W
M
all
t
h
e
tr
i
an
g
u
lar
ca
r
r
ier
s
ar
e
h
a
v
e
th
e
s
a
m
e
f
r
eq
u
e
n
c
y
an
d
p
ea
k
-
p
ea
k
a
m
p
lit
u
d
e
an
d
a
p
h
ase
s
h
i
f
t
is
m
ad
e
a
m
o
n
g
a
n
y
t
w
o
i
m
m
ed
iate
ca
r
r
ier
w
a
v
es.
Fo
r
m
Vo
ltag
e
lev
els
,
t
h
er
e
is
n
ee
d
o
f
(
m
-
1
)
c
ar
r
ier
s
ig
n
al
s
an
d
t
h
e
y
ar
e
p
h
a
s
e
s
h
if
ted
w
it
h
a
n
an
g
le
o
f
θ
=
(
3
6
0
°/
m
-
1
)
.
3
.
3
.
P
o
w
er
ba
la
nce
co
ntr
o
l
P
ar
tial sh
ad
in
g
i
s
a
co
m
m
o
n
p
r
o
b
lem
g
e
n
er
all
y
o
cc
u
r
s
i
n
a
l
ar
g
e
P
V
s
y
s
te
m
t
h
at
r
es
u
lt
s
i
n
u
n
eq
u
al
p
o
w
er
g
en
er
atio
n
b
y
t
h
e
P
V
m
o
d
u
les
co
n
n
ec
ted
to
ea
c
h
H
-
b
r
id
g
es
,
lead
in
g
to
u
n
b
alan
ce
d
g
r
id
c
u
r
r
en
t
a
s
s
h
o
w
n
i
n
Fig
u
r
e
5
(
a)
.
Ho
w
e
v
er
,
th
e
ad
d
itio
n
o
f
ze
r
o
s
e
q
u
en
ce
v
o
lta
g
e
in
ea
c
h
p
h
ase,
m
a
n
a
g
e
s
i
n
d
is
tr
ib
u
tio
n
o
f
b
alan
ce
d
p
o
w
er
a
m
o
n
g
th
e
th
r
ee
p
h
ases
s
o
th
at
at
th
e
g
r
id
s
id
e
cu
r
r
en
t
is
b
ala
n
ce
d
as
s
h
o
w
n
in
Fi
g
u
r
e
5
(
b
)
[
2
4
]
.
I
f
∗
is
t
h
e
o
u
tp
u
t
v
o
ltag
e
o
f
th
e
in
v
er
ter
d
u
r
i
n
g
p
ar
tial
s
h
ad
i
n
g
co
n
d
iti
o
n
th
e
n
w
it
h
th
e
i
n
j
ec
tio
n
o
f
,
th
e
o
u
tp
u
t
v
o
lta
g
e
o
f
t
h
e
i
n
v
er
ter
m
o
d
i
f
ied
as,
∗
+
=
(
w
h
er
e
i
=
a
,
b
,
c
f
o
r
th
r
ee
p
h
ase
v
o
lta
g
es).
I
t
is
b
ased
o
n
t
h
e
co
n
ce
p
t
t
h
at
i
f
t
h
r
ee
p
h
ase
u
n
b
alan
ce
d
v
o
lt
ag
es
at
th
e
g
r
id
s
id
e
v
ar
ies
d
i
r
ec
tl
y
ac
co
r
d
in
g
to
u
n
b
ala
n
ce
d
p
o
w
er
,
t
h
e
i
n
j
ec
ted
ze
r
o
s
eq
u
en
ce
v
o
lta
g
e
m
ak
e
s
t
h
e
g
r
id
cu
r
r
en
t
b
alan
ce
d
[
2
5
]
.
Fig
u
r
e
6
.
s
h
o
ws
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
,
Vo
l.
9
,
No
.
3
,
Sep
tem
b
er
2
0
1
8
:
13
30
–
13
37
1334
th
e
m
o
d
u
latio
n
co
m
p
e
n
s
at
io
n
s
ch
e
m
e
u
s
ed
in
co
n
tr
o
l
b
lo
ck
to
b
alan
ce
th
e
g
r
id
cu
r
r
en
t.
I
n
th
is
tec
h
n
iq
u
e,
th
e
w
ei
g
h
ted
m
i
n
-
m
ax
m
et
h
o
d
is
ad
o
p
te
d
.
T
h
e
w
e
ig
h
ted
r
atio
o
f
u
n
b
ala
n
ce
d
p
o
w
er
in
ea
c
h
p
h
ase
is
ca
lc
u
lated
b
y
th
e
f
o
r
m
u
la,
=
(
4
)
(
a)
(
b
)
Fig
u
r
e
5
.
Vec
to
r
d
iag
r
am
s
o
f
g
r
id
cu
r
r
en
t b
alan
c
in
g
(
a)
w
i
th
o
u
t (
b
)
w
it
h
in
j
ec
tin
g
ze
r
o
s
eq
u
en
ce
co
m
p
o
n
en
t
w
h
er
e
is
th
e
a
v
er
ag
e
o
f
t
h
e
in
j
ec
ted
p
o
w
er
i
n
t
h
r
ee
p
h
ase
s
an
d
is
th
e
in
v
er
ter
p
o
w
er
in
ea
c
h
p
h
ase.
T
h
en
th
e
ze
r
o
s
eq
u
e
n
ce
m
o
d
u
latio
n
in
d
e
x
0
ca
n
b
e
ca
lcu
lated
b
y
th
e
f
o
r
m
u
la,
0
=
0
.
5
{m
a
x
(
.
,
.
,
.
)
+
m
i
n
(
.
,
.
,
.
)}
(
5
)
w
h
er
e
,
,
ar
e
th
e
m
o
d
u
la
tio
n
i
n
d
ices
o
f
p
h
a
s
e
a
,
b
an
d
c
d
ete
r
m
in
ed
b
y
t
h
e
cu
r
r
e
n
t
lo
o
p
co
n
tr
o
ller
.
Af
ter
d
eter
m
i
n
i
n
g
t
h
e
m
o
d
u
lat
io
n
in
d
ices t
h
e
m
o
d
u
latio
n
in
d
ex
o
f
ea
ch
p
h
ase
is
m
o
d
if
ied
a
s
,
′
=
-
0
.
Fi
g
u
r
e
6
.
Sch
e
m
e
f
o
r
m
o
d
u
la
ti
o
n
co
m
p
en
s
a
tio
n
t
h
r
o
u
g
h
w
ei
g
h
ted
m
i
n
-
m
a
x
m
eth
o
d
.
4.
RE
SU
L
T
S AN
D
AN
AL
Y
SI
S
A
s
e
v
e
n
lev
e
l
th
r
ee
p
h
a
s
e
ca
s
ca
d
ed
m
u
ltil
e
v
el
i
n
v
er
ter
is
i
n
itiall
y
s
i
m
u
lated
w
i
th
1
8
5
W
o
f
P
V
p
an
el
as
d
c
s
o
u
r
ce
in
MA
T
L
A
B
/SIM
U
L
I
NK
en
v
ir
o
n
m
e
n
t.
A
ll
P
V
p
an
els
ar
e
o
p
er
ated
at
1
0
0
0
W
/
2
an
d
at
25
0
C
.
At
ti
m
e
t=0
.
8
s
ec
d
u
e
t
o
p
ar
tial
s
h
ad
i
n
g
p
an
el
1
an
d
2
o
f
p
h
a
s
e
a
g
et
th
e
r
ad
i
atio
n
o
f
6
0
0
W/
2
.
Fro
m
Fi
g
u
r
e
7
(
a)
.
it
s
h
o
w
s
t
h
at
th
e
MP
P
v
o
ltag
e
o
b
tain
ed
f
r
o
m
p
an
el
3
o
f
p
h
a
s
e
a
is
3
6
.
4
w
h
ile
d
u
e
to
p
ar
tial
s
h
ad
i
n
g
p
an
el
1
an
d
2
g
iv
e
th
e
MP
P
v
o
ltag
e
o
f
3
6
V.
T
h
e
M
P
P
v
o
ltag
e
o
b
tain
ed
in
p
h
ase
b
is
s
h
o
w
n
in
Fi
g
u
r
e
7
(
b
)
.
I
t
s
h
o
w
s
t
h
at
p
ar
tial
s
h
ad
i
n
g
ef
f
ec
t
t
h
e
MP
P
v
o
lta
g
e
o
f
p
h
a
s
e
a
o
n
l
y
,
w
h
er
ea
s
t
h
e
o
t
h
er
t
w
o
p
h
ases
ar
e
n
o
t
af
f
ec
ted
b
y
t
h
e
e
n
v
ir
o
n
m
e
n
t
al
is
s
u
es.
P
h
a
s
e
c
u
r
r
en
t
o
b
t
ain
ed
o
f
p
h
ase
a
u
n
d
er
d
is
tr
ib
u
ted
MP
PT
is
s
h
o
w
n
in
F
ig
u
r
e
7
(
c)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
I
SS
N:
2
0
8
8
-
8
694
A
N
o
ve
l A
p
p
r
o
a
ch
fo
r
g
r
id
in
t
eg
r
a
tio
n
o
f Ca
s
ca
d
ed
H
-
b
r
id
g
e
Mu
ltil
ev
el
I
n
ve
r
ter
...
(
S
w
eta
p
a
d
ma
P
a
n
ig
r
a
h
i)
1335
Fig
u
r
e
7
(
a)
.
DC
lin
k
v
o
ltag
e
o
b
tain
ed
u
n
d
er
d
is
tr
ib
u
ted
MP
PT
o
f
p
an
el
s
1
an
d
2
o
f
p
h
ase
a
u
n
d
er
p
ar
tial
s
h
a
d
i
n
g
co
n
d
it
io
n
.
Fi
g
u
r
e
7
(
b
)
.
DC
lin
k
v
o
lta
g
e
o
f
p
h
a
s
e
b
o
b
tain
ed
u
n
d
er
d
is
tr
ib
u
ted
MP
PT
.
Fig
u
r
e
7
(
c)
.
P
h
ase
cu
r
r
en
t o
b
tain
ed
o
f
p
h
a
s
e
a
u
n
d
er
d
is
tr
ib
u
ted
MP
PT
.
P
o
w
er
o
b
tain
e
d
f
r
o
m
ea
c
h
p
h
ase
i
s
s
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o
w
n
i
n
Fi
g
u
r
e
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(
d
)
.
Fro
m
ti
m
e
t=0
to
t=0
.
8
s
ec
,
p
o
w
er
ex
tr
ac
ted
f
r
o
m
t
h
r
ee
p
h
a
s
e
ar
e
ap
p
r
o
x
im
ate
l
y
5
3
5
W
an
d
at
t=0
.
8
s
ec
b
ec
au
s
e
o
f
ch
a
n
g
e
in
r
ad
iatio
n
,
p
o
w
er
ex
tr
ac
ted
f
r
o
m
p
h
a
s
e
a
is
3
4
0
W
ca
u
s
in
g
a
t
h
r
ee
p
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ase
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n
b
alan
ce
d
p
o
w
er
.
Fo
r
th
is
p
u
r
p
o
s
e,
th
e
m
o
d
u
la
tio
n
s
ch
e
m
e
w
it
h
ze
r
o
s
e
q
u
en
ce
v
o
ltag
e
i
n
j
ec
tio
n
is
ad
o
p
ted
.
Fig
u
r
e
7
(
d
)
.
P
o
w
er
ex
tr
ac
ted
f
r
o
m
t
h
r
ee
p
h
ases
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
,
Vo
l.
9
,
No
.
3
,
Sep
tem
b
er
2
0
1
8
:
13
30
–
13
37
1336
Af
ter
ze
r
o
s
eq
u
e
n
ce
v
o
ltag
e
i
n
j
ec
tio
n
t
h
e
i
n
v
er
ter
o
u
tp
u
t
v
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ltag
e
i
s
s
h
o
w
n
i
n
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g
u
r
e
7
(
e)
.
It
s
h
o
w
s
at
t=0
.
8
s
ec
,
d
u
e
to
ze
r
o
v
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ltag
e
i
n
j
ec
tio
n
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v
o
lta
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at
t
h
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g
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id
s
id
e
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o
m
e
s
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m
b
ala
n
ce
t
h
at
ca
u
s
i
n
g
a
b
ala
n
ce
d
g
r
id
cu
r
r
en
t a
s
s
h
o
w
n
in
Fig
u
r
e
7
(
f
)
.
Fig
u
r
e
7
(
e)
.
T
h
r
ee
p
h
ase
in
v
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ter
o
u
tp
u
t v
o
lta
g
e
af
te
r
p
r
o
p
o
s
ed
m
o
d
u
la
tio
n
tec
h
n
iq
u
e
Fig
u
r
e
7
(
f
)
.
Ba
lan
ce
d
th
r
ee
p
h
ase
g
r
id
cu
r
r
en
t
5.
C
O
N
C
L
U
SIO
N
A
t
h
r
ee
p
h
ase
ca
s
ca
d
ed
H
-
b
r
id
g
e
m
u
ltil
e
v
el
P
V
in
v
er
ter
w
it
h
g
r
id
in
te
g
r
atio
n
i
s
p
r
o
p
o
s
ed
in
th
i
s
p
ap
er
.
I
n
o
r
d
er
to
r
e
d
u
ce
th
e
co
m
p
le
x
it
y
an
d
in
cr
ea
s
e
th
e
e
f
f
icien
c
y
d
is
tr
ib
u
ted
MP
PT
is
ap
p
lied
to
ea
ch
P
V
p
an
el.
A
s
p
ar
tial
s
h
ad
i
n
g
is
a
n
i
m
p
o
r
tan
t
p
h
e
n
o
m
e
n
o
n
to
b
e
co
n
s
id
er
ed
i
n
a
lar
g
e
s
ca
le
P
V
s
y
s
te
m
t
h
at
h
a
s
d
ir
ec
t i
m
p
ac
t o
n
g
r
id
cu
r
r
en
t
b
alan
ci
n
g
,
a
m
o
d
u
latio
n
co
m
p
e
n
s
atio
n
s
ch
e
m
e
i
s
p
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p
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s
ed
.
I
t h
elp
s
in
b
alan
ci
n
g
th
e
g
r
id
c
u
r
r
en
t
b
y
i
n
j
ec
tin
g
a
ze
r
o
s
eq
u
e
n
ce
v
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lta
g
e
i
n
p
r
o
p
o
r
ti
o
n
to
p
o
w
er
i
m
b
a
l
nc
e
s
o
t
h
at
m
a
x
i
m
u
m
p
o
w
er
is
ex
tr
ac
ted
.
P
ARAM
E
T
E
RS
T
AK
E
N:
Dc
lin
k
ca
p
ac
ito
r
C=
3
6
0
0
µF
,
I
n
d
u
cto
r
L=
2
.
5
m
H
,
L
o
ad
r
esis
to
r
R
=
0
.
1
Ω
,
Gr
id
r
ated
p
h
ase
v
o
lta
g
e=
6
0
Vr
m
s
,
S
w
i
tch
i
n
g
f
r
eq
u
e
n
c
y
=
1
.
5
Kh
z
RE
F
E
R
E
NC
E
S
[1
]
Bo
se
BK.
P
o
w
e
r
El
e
c
tro
n
ics
,
S
m
a
rt
G
rid
,
a
n
d
Re
n
e
wa
b
le
En
e
rg
y
S
y
ste
m
s.
Pro
c
e
e
d
in
g
s
o
f
th
e
IEE
E
.
No
v
2
0
1
7
;
1
0
5
(1
1
)
:
2
0
1
1
-
2
0
1
8
.
[2
]
P
a
n
ig
ra
h
i
S
,
T
h
a
k
u
r
A
.
Cu
rr
e
n
t
tre
n
d
s
in
p
o
we
r
e
lec
tro
n
ics
fo
r
win
d
a
n
d
so
l
a
r
e
n
e
rg
y
c
o
n
v
e
rs
io
n
sy
ste
ms
.
In
tern
a
ti
o
n
a
l
C
o
n
f
e
re
n
c
e
o
n
P
o
w
e
r
a
n
d
Em
b
e
d
d
e
d
Driv
e
Co
n
tr
o
l
(
ICP
EDC)
.
Ch
e
n
n
a
i,
2
0
1
7
:
2
4
2
-
2
4
7
.
[3
]
De
v
a
sh
ish
,
T
h
a
k
u
r
A
,
P
a
n
ig
ra
h
i
S
,
Be
h
e
ra
RR
.
A
re
v
iew
o
n
win
d
e
n
e
rg
y
c
o
n
v
e
rs
io
n
sy
ste
m
a
n
d
e
n
a
b
li
n
g
tec
h
n
o
l
o
g
y
.
I
n
tern
a
ti
o
n
a
l
C
o
n
f
e
re
n
c
e
o
n
El
e
c
tri
c
a
l
P
o
w
e
r
a
n
d
E
n
e
rg
y
S
y
ste
m
s (ICE
P
ES
)
,
Bh
o
p
a
l,
2
0
1
6
:
5
2
7
-
5
3
2
.
[4
]
Ca
lais
M
,
M
y
rz
ik
J,
S
p
o
o
n
e
r
T
,
Ag
e
li
d
is
V
G
.
In
v
e
rte
rs
fo
r
sin
g
l
e
-
p
h
a
se
g
ri
d
c
o
n
n
e
c
ted
p
h
o
to
v
o
l
ta
ic
sy
ste
ms
-
a
n
o
v
e
rv
iew
:
3
3
rd
A
n
n
u
a
l
IEE
E
P
o
w
e
r
El
e
c
tro
n
ics
S
p
e
c
ialists
C
o
n
f
e
re
n
c
e
.
P
ro
c
e
e
d
in
g
s
(Ca
t.
No
.
0
2
CH3
7
2
8
9
)
,
C
a
irn
s,
Qld
.
2
0
0
2
:
1
9
9
5
-
2
0
0
0
.
[5
]
Ro
d
rig
u
e
z
J,
L
a
i
JS,
P
e
n
g
F
Z.
M
u
lt
il
e
v
e
l
in
v
e
rters
:
A
su
rv
e
y
o
f
to
p
o
l
o
g
ies
,
c
o
n
tro
ls,
a
n
d
a
p
p
li
c
a
ti
o
n
s .
IEE
E
T
ra
n
s
.
In
d
.
El
e
c
tro
n
.
A
u
g
.
2
0
0
2
;
4
9
(4
)
:
7
2
4
–
7
3
8
.
[6
]
T
o
w
n
se
n
d
D,
S
u
m
m
e
r
s
T
J
,
B
e
tz
RE.
Co
n
tro
l
a
n
d
mo
d
u
la
t
io
n
sc
h
e
me
f
o
r
a
c
a
sc
a
d
e
d
H
-
b
rid
g
e
mu
lt
i
-
lev
e
l
c
o
n
v
e
rte
r in
la
r
g
e
sc
a
le p
h
o
t
o
v
o
l
t
a
ic sy
ste
ms
.
P
r
o
c
.
IEE
E
ECCE
.
S
e
p
2
0
1
2
:
3
7
0
7
–
3
7
1
4
[7
]
X
iao
B,
Ha
n
g
L
,
T
o
lb
e
rt
L
M
.
Co
n
tro
l
o
f
th
re
e
-
p
h
a
se
c
a
sc
a
d
e
d
v
o
lt
a
g
e
so
u
rc
e
in
v
e
rte
r
fo
r
g
rid
-
c
o
n
n
e
c
ted
p
h
o
to
v
o
lt
a
ic sy
ste
ms
.
Tw
e
n
t
y
-
E
ig
h
th
A
n
n
u
a
l
IEE
E
A
p
p
li
e
d
P
o
w
e
r
El
e
c
tro
n
ics
Co
n
f
e
re
n
c
e
a
n
d
Ex
p
o
siti
o
n
(A
P
EC)
,
L
o
n
g
Be
a
c
h
,
CA
,
2
0
1
3
:
2
9
1
-
2
9
6
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
I
SS
N:
2
0
8
8
-
8
694
A
N
o
ve
l A
p
p
r
o
a
ch
fo
r
g
r
id
in
t
eg
r
a
tio
n
o
f Ca
s
ca
d
ed
H
-
b
r
id
g
e
Mu
ltil
ev
el
I
n
ve
r
ter
...
(
S
w
eta
p
a
d
ma
P
a
n
ig
r
a
h
i)
1337
[8
]
L
a
i
JS,
P
e
n
g
F
Z.
M
u
lt
il
e
v
e
l
c
o
n
v
e
rters
-
a
n
e
w
b
re
e
d
o
f
p
o
w
e
r
c
o
n
v
e
rters
,
IEE
E
T
r
a
n
sa
c
ti
o
n
s
o
n
In
d
u
stry
A
p
p
li
c
a
ti
o
n
s
.
M
a
y
/Ju
n
1
9
9
6
;
3
2
(
3
)
:
p
p
.
5
0
9
-
5
1
7
.
[9
]
V
il
la
n
u
e
v
a
,
Co
rre
a
P
,
Ro
d
rig
u
e
z
J
.
Co
n
tro
l
o
f
a
si
n
g
le
p
h
a
se
H
-
B
rid
g
e
mu
lt
il
e
v
e
l
in
v
e
rte
r
fo
r
g
rid
-
c
o
n
n
e
c
ted
PV
a
p
p
li
c
a
ti
o
n
s
.
1
3
th
In
tern
a
ti
o
n
a
l
P
o
w
e
r
El
e
c
tro
n
ics
a
n
d
M
o
ti
o
n
C
o
n
tro
l
C
o
n
f
e
re
n
c
e
,
P
o
z
n
a
n
,
2
0
0
8
:4
5
1
-
4
5
5
.
[1
0
]
X
iao
B
,
Ha
n
g
L
,
M
e
i
J,
Ril
e
y
C,
T
o
lb
e
rt
L
M
,
Oz
p
in
e
c
i
B
.
M
o
d
u
lar
Ca
sc
a
d
e
d
H
-
Brid
g
e
M
u
lt
il
e
v
e
l
P
V
I
n
v
e
rter
W
it
h
Distrib
u
ted
M
P
P
T
f
o
r
G
ri
d
-
Co
n
n
e
c
ted
A
p
p
li
c
a
ti
o
n
s.
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
I
n
d
u
stry
Ap
p
l
i
c
a
ti
o
n
s
.
M
a
rc
h
-
A
p
ril
2
0
1
5
;
5
1
(2
)
:
1
7
2
2
-
1
7
3
1
.
[1
1
]
S
y
a
fa
ru
d
d
in
.
Pro
b
lem
-
so
lvin
g
mi
sm
a
tch
in
g
l
o
ss
e
s
o
f
p
h
o
t
o
v
o
lt
a
ic
(
PV
)
sy
ste
m
u
n
d
e
r
p
a
rti
a
ll
y
sh
a
d
e
d
c
o
n
d
it
io
n
s
.
M
a
k
a
ss
a
r
In
tern
a
ti
o
n
a
l
Co
n
f
e
re
n
c
e
o
n
E
lec
tri
c
a
l
En
g
in
e
e
rin
g
a
n
d
I
n
f
o
rm
a
ti
c
s (M
ICEE
I)
,
M
a
k
a
ss
a
r
,
2
0
1
4
:
1
-
4.
[1
2
]
S
u
b
u
d
h
i
B
,
P
ra
d
h
a
n
R
.
A
Co
m
p
a
ra
ti
v
e
S
tu
d
y
o
n
M
a
x
im
u
m
P
o
w
e
r
P
o
in
t
T
ra
c
k
in
g
T
e
c
h
n
iq
u
e
s
f
o
r
P
h
o
t
o
v
o
lt
a
i
c
P
o
w
e
r
S
y
ste
m
s .
IEE
E
T
ra
n
sa
c
t
io
n
s o
n
S
u
sta
i
n
a
b
le E
n
e
rg
y
.
Ja
n
2
0
1
3
;
4
(1
)
:
8
9
-
9
8
.
[1
3
]
S
e
ra
D,
M
a
th
e
L
,
Ke
re
k
e
s
T
,
S
p
a
taru
S
V
,
T
e
o
d
o
re
sc
u
R.
On
th
e
P
e
rt
u
rb
-
a
n
d
-
Ob
se
rv
e
a
n
d
I
n
c
re
m
e
n
tal
Co
n
d
u
c
tan
c
e
M
P
P
T
M
e
t
h
o
d
s f
o
r
P
V
S
y
ste
m
s.
IEE
E
J
o
u
r
n
a
l
o
f
Ph
o
to
v
o
lt
a
ics
.
J
u
ly
2
0
1
3
;
3
(
3
)
:
1
0
7
0
-
1
0
7
8
.
[1
4
]
S
o
o
n
T
K
,
M
e
k
h
il
e
f
S
.
A
F
a
st
-
Co
n
v
e
rg
in
g
M
P
P
T
T
e
c
h
n
iq
u
e
f
o
r
P
h
o
t
o
v
o
lt
a
ic
S
y
ste
m
Un
d
e
r
F
a
s
t
-
V
a
ry
in
g
S
o
lar
Irra
d
iatio
n
a
n
d
L
o
a
d
Re
sista
n
c
e
.
I
EE
E
T
ra
n
sa
c
ti
o
n
s
o
n
In
d
u
stria
l
I
n
fo
rm
a
t
ics
.
F
e
b
2
0
1
5
;
1
1
(1
)
:
1
7
6
-
1
8
6
.
[1
5
]
Kish
G
J,
L
e
e
JJ
,
Leh
n
P
W
.
M
o
d
e
ll
in
g
a
n
d
c
o
n
tr
o
l
o
f
p
h
o
to
v
o
lt
a
ic
p
a
n
e
ls
u
ti
li
z
i
n
g
th
e
in
c
re
m
e
n
tal
c
o
n
d
u
c
tan
c
e
m
e
th
o
d
f
o
r
m
a
x
i
m
u
m
p
o
w
e
r
p
o
in
t
trac
k
in
g
.
IET
Ren
e
wa
b
le P
o
we
r
Ge
n
e
ra
ti
o
n
.
Ju
ly
2
0
1
2
;
6
(
4
)
:
2
5
9
-
2
6
6
.
[1
6
]
Kjær
S
B
.
Ev
a
lu
a
ti
o
n
o
f
th
e
“
Hi
l
l
Cli
m
b
in
g
”
a
n
d
th
e
“
In
c
re
m
e
n
tal
Co
n
d
u
c
ta
n
c
e
”
M
a
x
i
m
u
m
P
o
w
e
r
P
o
in
t
T
ra
c
k
e
rs
f
o
r
P
h
o
t
o
v
o
lt
a
ic
P
o
w
e
r
S
y
ste
m
s.
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
En
e
rg
y
C
o
n
v
e
rs
io
n
.
De
c
2
0
1
2
;
2
7
(
4
)
:
9
2
2
-
9
2
9
.
[1
7
]
A
h
m
e
d
L
,
Bo
rg
h
a
te
V
B
.
S
im
p
li
fied
sp
a
c
e
v
e
c
to
r
m
o
d
u
latio
n
tec
h
n
iq
u
e
f
o
r
se
v
e
n
-
lev
e
l
c
a
s
c
a
d
e
d
H
-
b
rid
g
e
in
v
e
rter
.
IET
Po
we
r E
lec
tro
n
ics
.
M
a
rc
h
2
0
1
4
;
7
(3
)
:
6
0
4
-
6
1
3
.
[1
8
]
Ra
b
in
o
v
ici
R,
Ba
i
m
e
l
D,
T
o
m
a
sik
J
,
A
.
Zu
c
k
e
rb
e
r
g
e
r
.
T
h
irt
e
e
n
-
lev
e
l
c
a
s
c
a
d
e
d
H
-
b
rid
g
e
in
v
e
rt
e
r
o
p
e
ra
ted
b
y
g
e
n
e
ric
p
h
a
se
sh
if
ted
p
u
lse
-
w
id
th
m
o
d
u
latio
n
.
I
ET
P
o
we
r E
lec
tro
n
ics
.
S
e
p
t.
2
0
1
3
;
6
(
8
)
:
1
5
1
6
-
1
5
2
9
.
[1
9
]
F
a
ra
h
N,
Laz
i
J.
B.
M
,
T
a
li
b
M
.
Co
m
p
a
ra
ti
v
e
S
tu
d
y
o
f
T
h
re
e
Diff
e
r
e
n
t
T
o
p
o
lo
g
ies
o
f
F
iv
e
-
lev
e
l
In
v
e
rter
w
it
h
S
P
W
M
M
o
d
u
latio
n
T
e
c
h
n
iq
u
e
.
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
P
o
we
r
El
e
c
tro
n
ics
a
n
d
Dr
ive
S
y
ste
m
(
IJ
PE
DS
)
.
De
c
2
0
1
7
;
8
(4
)
:
1
6
1
2
-
1
6
2
1
.
[2
0
]
Ro
y
D,
sin
g
h
M
,
Ro
y
T
.
A
No
v
e
l
A
p
p
ro
a
c
h
f
o
r
S
p
a
c
e
V
e
c
to
r
B
a
se
d
P
W
M
A
lg
o
rit
h
m
f
o
r
Dio
d
e
Cla
m
p
e
d
T
h
re
e
lev
e
l
V
S
I
F
e
d
I
n
d
u
c
ti
o
n
M
o
t
o
r
Driv
e
.
In
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
Po
we
r
El
e
c
tro
n
ics
a
n
d
Dr
ive
S
y
ste
m
(
IJ
PE
DS
)
.
De
c
2
0
1
7
;
8
(
4
):
1
5
3
4
-
1
5
4
7
.
[2
1
]
Ud
a
k
h
e
P
,
A
tk
a
r
D,
Ch
iri
k
i
S
,
Bo
rg
h
a
te
V
B
.
Co
m
p
a
riso
n
o
f
d
if
f
e
re
n
t
typ
e
s
o
f
S
PW
M
tec
h
n
iq
u
e
s
fo
r
th
re
e
p
h
a
se
se
v
e
n
lev
e
l
c
a
sc
a
d
e
d
H
-
Brid
g
e
in
v
e
rte
r
.
IEE
E
1
st
In
tern
a
ti
o
n
a
l
Co
n
f
e
re
n
c
e
o
n
P
o
w
e
r
El
e
c
tro
n
ics
,
In
telli
g
e
n
t
Co
n
tr
o
l
a
n
d
E
n
e
rg
y
S
y
ste
m
s (ICP
EICE
S
)
,
De
lh
i
,
2
0
1
6
:
1
-
5.
[2
2
]
S
a
h
o
o
S
K,
B
h
a
tt
a
c
h
a
ry
a
T
.
P
h
a
se
-
S
h
if
ted
Ca
rrier
-
Ba
se
d
S
y
n
c
h
ro
n
ize
d
S
i
n
u
s
o
id
a
l
P
W
M
T
e
c
h
n
iq
u
e
s
f
o
r
a
Ca
sc
a
d
e
d
H
-
Brid
g
e
M
u
lt
il
e
v
e
l
In
v
e
rter.
IEE
E
T
ra
n
sa
c
ti
o
n
s o
n
P
o
we
r E
lec
tro
n
ics
.
Ja
n
2
0
1
8
;
3
3
(
1
):
5
1
3
-
5
2
4
.
[2
3
]
S
u
n
X
,
W
a
n
g
B,
Zh
o
u
Y,
W
a
n
g
W
,
Du
H
,
L
u
Z
.
A
S
in
g
le
DC
S
o
u
rc
e
Ca
sc
a
d
e
d
S
e
v
e
n
-
Lev
e
l
In
v
e
rter
In
teg
ra
ti
n
g
S
w
it
c
h
e
d
-
Ca
p
a
c
it
o
r
T
e
c
h
n
iq
u
e
s.
I
EE
E
T
ra
n
sa
c
ti
o
n
s
o
n
In
d
u
stria
l
E
lec
tro
n
ics
,
No
v
.
2
0
1
6
;
6
3
(
1
1
)
:
7
1
8
4
-
7
1
9
4
.
[2
4
]
W
a
n
g
F
,
Le
Y,
M
a
o
W
,
S
h
i
n
e
n
g
Y,
Zh
a
n
g
X
.
P
o
we
r
b
a
l
a
n
c
e
c
o
n
tro
l
sc
h
e
me
o
f
c
a
sc
a
d
e
d
H
-
b
rid
g
e
mu
lt
il
e
v
e
l
in
v
e
rte
r
fo
r
g
rid
-
c
o
n
n
e
c
ti
o
n
p
h
o
t
o
v
o
lt
a
ic
sy
ste
ms
.
IEE
E
8
th
In
tern
a
ti
o
n
a
l
P
o
w
e
r
El
e
c
tro
n
ics
a
n
d
M
o
ti
o
n
Co
n
tro
l
Co
n
f
e
re
n
c
e
(IP
EM
C
-
ECCE
A
sia
)
,
He
f
e
i.
2
0
1
6
:
1
5
3
9
-
1
5
4
5
.
[2
5
]
Yu
Y,
Ko
n
sta
n
ti
n
o
u
G
,
Hre
d
z
a
k
B,
A
g
e
li
d
is
V
G
.
P
o
w
e
r
Ba
lan
c
e
o
f
Ca
sc
a
d
e
d
H
-
Brid
g
e
M
u
lt
il
e
v
e
l
Co
n
v
e
rters
f
o
r
L
a
r
g
e
-
S
c
a
le P
h
o
t
o
v
o
lt
a
ic I
n
teg
ra
ti
o
n
.
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Po
we
r E
lec
tro
n
ics
;
Ja
n
2
0
1
6
;
3
1
(1
):
2
9
2
-
3
0
3
.
B
I
O
G
RAP
H
I
E
S
O
F
AUTH
O
RS
S
w
e
tap
a
d
m
a
P
a
n
ig
ra
h
i
re
c
e
iv
e
d
B
tec
h
d
e
g
re
e
in
El
e
c
tri
c
a
l
a
n
d
El
e
c
tro
n
ics
En
g
i
n
e
e
rin
g
f
ro
m
BP
UT
Od
is
h
a
,
t
h
e
M
T
e
c
h
d
e
g
re
e
f
ro
m
V
S
S
UT
,
Bu
rla,
O
d
ish
a
i
n
t
h
e
y
e
a
r
2
0
1
0
a
n
d
2
0
1
4
re
sp
e
c
ti
v
e
l
y
.
S
h
e
is
c
u
rre
n
tl
y
a
re
se
a
rc
h
S
c
h
o
lar
i
n
t
h
e
De
p
a
rtm
e
n
t
o
f
El
e
c
tri
c
a
l
a
n
d
El
e
c
tr
o
n
ics
En
g
i
n
e
e
rin
g
,
Na
ti
o
n
a
l
In
st
it
u
te
o
f
T
e
c
h
n
o
lo
g
y
Ja
m
sh
e
d
p
u
r.
He
r
a
re
a
o
f
in
tere
st
in
c
lu
d
e
p
o
w
e
r
e
lec
tro
n
ics
a
n
d
re
n
e
w
a
b
le en
e
rg
y
s
y
ste
m
.
Am
a
rn
a
th
T
h
a
k
u
r
re
c
e
i
v
e
d
th
e
B
S
c
(En
g
g
.
)
d
e
g
re
e
in
El
e
c
t
rica
l
En
g
in
e
e
rin
g
f
ro
m
M
IT
,
M
u
z
a
ff
a
rp
u
r,
th
e
M
T
e
c
h
d
e
g
re
e
f
ro
m
II
T
(BHU
),
V
a
ra
n
a
si
a
n
d
th
e
P
h
D
d
e
g
re
e
f
ro
m
De
p
a
rtme
n
t
o
f
El
e
c
rica
l
En
g
in
e
e
rin
g
,
IIT
Kh
a
ra
g
p
u
r
in
1
9
7
9
,
1
9
8
2
a
n
d
1
9
9
7
re
sp
e
c
ti
v
e
l
y
.
He
is
c
u
rre
n
tl
y
a
P
r
o
f
e
ss
o
r
in
t
h
e
De
p
a
rtm
e
n
t
o
f
El
e
c
tri
c
a
l
a
n
d
E
lec
tro
n
ics
E
n
g
in
e
e
rin
g
,
Na
ti
o
n
a
l
In
stit
u
te
o
f
T
e
c
h
n
o
lo
g
y
Ja
m
sh
e
d
p
u
r.
His
a
re
a
o
f
in
tere
st
i
n
c
lu
d
e
p
o
w
e
r
e
lec
tro
n
ics
a
n
d
re
n
e
wa
b
le
e
n
e
rg
y
s
y
ste
m
.
He
is
li
f
e
m
e
m
b
e
r
o
f
th
e
In
d
ian
S
o
c
iety
f
o
r
T
e
c
h
n
ica
l
Ed
u
c
a
ti
o
n
Ne
w
De
lh
i
a
n
d
In
stit
u
ti
o
n
o
f
En
g
in
e
e
rs,
In
d
ia.
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