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V
p
an
el
s
.
Fo
r
t
h
e
b
at
ter
y
c
h
ar
g
i
n
g
cu
r
r
e
n
t
co
n
tr
o
l
o
f
t
h
e
Q
Z
SI,
t
h
er
e
ar
e
s
ev
er
al
ch
alle
n
g
es
f
o
r
t
h
e
co
n
tr
o
ller
d
esig
n
as
f
o
llo
w
s
:
(
1
)
B
o
th
o
u
tp
u
t
v
o
lta
g
e
an
d
t
h
e
b
atter
y
ch
ar
g
in
g
cu
r
r
e
n
t
o
f
th
e
Q
Z
SI
s
y
s
te
m
w
it
h
b
atter
y
h
a
v
e
to
b
e
co
n
tr
o
lled
b
y
t
h
e
s
h
o
o
t
-
t
h
r
o
u
g
h
s
t
ate,
w
h
ic
h
m
a
k
es
th
e
d
esi
g
n
o
f
a
s
tead
y
a
n
d
f
a
s
t
r
eg
u
lato
r
m
o
r
e
d
if
f
ic
u
l
t
[
1
8
,
2
1
]
.
(
2
)
Sim
i
lar
to
t
h
e
b
o
o
s
t
co
n
v
er
ter
,
t
h
e
Q
Z
SI
o
p
er
atin
g
i
n
t
h
e
co
n
ti
n
u
o
u
s
-
co
n
d
itio
n
m
o
d
e,
w
h
ich
li
m
it
s
th
e
b
an
d
w
id
th
o
f
t
h
e
co
n
tr
o
l
ler
an
d
m
a
k
es
th
e
d
y
n
a
m
ic
r
e
p
ly
o
f
t
h
e
s
y
s
te
m
s
lu
g
g
is
h
,
an
d
(
3
)
.
Nu
m
er
o
u
s
co
n
tr
o
l
m
et
h
o
d
s
to
ac
h
ie
v
e
f
ast
r
esp
o
n
s
e
a
n
d
s
m
al
l
o
v
er
s
h
o
o
t
h
av
e
b
ee
n
p
r
o
p
o
s
ed
f
o
r
th
e
n
o
n
li
n
ea
r
s
y
s
te
m
co
n
tr
o
l
[
2
0
]
.
Am
o
n
g
th
e
m
,
n
o
n
li
n
ea
r
-
ca
r
r
ier
co
n
tr
o
l
a
n
d
o
n
e
-
c
y
cle
co
n
tr
o
l
h
av
e
b
ee
n
f
o
u
n
d
p
r
ac
tical
i
n
s
o
m
e
ap
p
licatio
n
s
.
Ho
w
e
v
er
,
eith
er
m
eth
o
d
h
a
s
s
o
m
e
li
m
itat
io
n
s
.
Gi
v
en
b
atter
y
cu
r
r
en
t
co
n
tr
o
l
m
eth
o
d
s
w
as
s
eld
o
m
i
n
v
esti
g
ated
i
n
t
h
e
lit
er
atu
r
e
,
h
o
w
e
v
er
t
h
e
i
n
v
er
ter
p
er
f
o
r
m
a
n
ce
is
s
til
l
s
u
f
f
er
in
g
d
u
e
to
t
h
e
s
i
n
g
le
ca
p
ac
ito
r
s
s
tab
ilit
y
.
He
n
ce
,
in
t
h
is
p
ap
er
is
tr
y
i
n
g
to
co
v
er
th
e
r
esear
ch
g
ap
b
y
u
s
i
n
g
t
w
o
ca
p
ac
ito
r
b
atter
ies
an
d
Ne
w
P
W
M
tech
n
iq
u
e
s
an
d
p
r
in
cip
les
ar
e
p
r
o
p
o
s
ed
t
o
co
n
tr
o
l
th
e
n
e
w
en
er
g
y
s
to
r
ed
QZ
SI
w
h
en
ap
p
lied
to
th
e
P
V
p
o
w
er
s
y
s
te
m
.
T
h
e
y
ca
n
co
n
tr
o
l
t
h
e
i
n
v
er
ter
o
u
tp
u
t
p
o
w
er
an
d
m
an
a
g
e
t
h
e
b
atter
y
p
o
w
e
r
s
i
m
u
l
tan
eo
u
s
l
y
.
T
h
e
o
p
er
atin
g
p
r
in
cip
le
a
n
d
p
o
w
er
f
lo
w
o
f
t
h
is
s
y
s
te
m
ar
e
an
al
y
ze
d
.
T
h
e
Si
m
u
lated
a
n
d
ex
p
er
i
m
e
n
tal
r
es
u
lts
t
h
r
o
u
g
h
u
s
i
n
g
th
e
p
la
n
n
ed
0
.
2
-
k
W
p
r
o
to
t
y
p
e
v
alid
ate
t
h
e
p
r
o
p
o
s
ed
an
al
y
tic
m
o
d
el
an
d
t
h
e
d
esig
n
m
et
h
o
d
.
I
n
ad
d
itio
n
,
th
is
p
ap
er
an
al
y
ze
s
all
o
f
t
h
e
f
u
n
ctio
n
in
g
s
tate
s
f
o
r
a
QZ
SI
a
n
d
ca
lcu
late
s
th
e
p
o
w
er
lo
s
s
.
2.
Q
UA
SI
-
Z
SO
URCE
I
NV
E
R
T
E
R
C
o
n
v
en
t
io
n
al
QZ
SI
,
Q
Z
SI
w
i
t
h
b
atter
y
co
n
n
ec
ted
ac
r
o
s
s
C
2
an
d
Q
Z
SI
w
i
th
b
atter
y
co
n
n
ec
ted
ac
r
o
s
s
C
1
as
s
h
o
w
n
i
n
Fi
g
u
r
e
1
,
Fig
u
r
e
2
,
an
d
Fig
u
r
e
3
.
B
o
th
th
e
v
o
ltag
e
an
d
cu
r
r
en
t
f
ed
QZ
S
I
s
ca
n
b
e
co
n
tr
o
lled
u
s
i
n
g
m
et
h
o
d
s
u
s
ed
to
co
n
t
r
o
l
th
e
tr
ad
itio
n
a
l
Z
SIs.
R
e
g
ar
d
les
s
o
f
th
e
co
n
tr
o
l stra
te
g
y
u
s
ed
,
f
o
r
th
e
v
o
lta
g
e
f
ed
Z
SI
a
n
d
Q
Z
SI
s
,
t
h
e
o
p
er
atio
n
ca
n
b
e
li
s
ted
i
n
to
t
h
r
ee
m
o
d
es
;
ac
tiv
e,
ST
,
an
d
n
o
n
-
ST
m
o
d
e.
I
n
A
cti
v
e
m
o
d
e,
o
n
e
an
d
o
n
l
y
o
n
e
d
ev
ice
i
n
ea
ch
p
h
a
s
e
le
g
co
n
d
u
ct
s
.
D
u
r
in
g
th
e
ac
ti
v
e
m
o
d
e,
th
e
i
n
v
er
ter
is
co
n
tr
o
lled
in
th
e
s
a
m
e
m
an
n
er
as
a
s
tan
d
ar
d
VSI
.
T
h
e
S
T
m
o
d
e
o
cc
u
r
s
w
h
en
b
o
th
s
w
itc
h
e
s
in
at
least
o
n
e
p
h
ase
co
n
d
u
ct.
T
h
e
v
o
ltag
e
ac
r
o
s
s
t
h
e
i
n
v
er
ter
d
u
r
in
g
t
h
i
s
m
o
d
e
is
ze
r
o
.
T
h
e
d
is
co
n
tin
u
o
u
s
m
o
d
es
ca
n
o
cc
u
r
w
h
e
n
th
e
i
n
d
u
cto
r
s
,
L
1
an
d
L
2
,
h
a
v
e
a
s
m
all
v
a
lu
e
r
elativ
e
to
o
th
er
s
y
s
te
m
p
ar
a
m
eter
s
.
I
n
g
en
er
al,
t
h
e
d
is
co
n
ti
n
u
o
u
s
m
o
d
es
o
cc
u
r
s
w
h
e
n
th
e
in
v
er
ter
is
g
ated
as
i
f
i
n
t
h
e
ac
ti
v
e
m
o
d
e,
b
u
t o
n
e
p
h
ase
c
u
r
r
en
t i
s
g
r
ea
ter
th
a
n
o
r
eq
u
al
to
th
e
s
u
m
o
f
th
e
in
d
u
cto
r
cu
r
r
en
ts
.
I
n
th
i
s
s
itu
a
tio
n
,
n
o
cu
r
r
en
t
f
lo
w
s
th
r
o
u
g
h
th
e
d
io
d
e,
D1
.
Fo
r
th
e
c
u
r
r
en
t
f
ed
Z
SI
an
d
QZ
SI
s
,
th
e
o
p
er
atio
n
ca
n
b
e
d
iv
id
ed
in
to
m
o
d
es
in
a
s
i
m
il
ar
m
a
n
n
er
.
I
n
th
e
ac
ti
v
e
m
o
d
e
o
n
e
an
d
o
n
l
y
o
n
e
u
p
p
er
d
ev
ice,
a
n
d
o
n
e
a
n
d
o
n
l
y
o
n
e
lo
w
er
d
ev
ice
co
n
d
u
ct.
Du
r
in
g
th
e
ac
ti
v
e
m
o
d
e,
th
e
i
n
v
er
ter
is
co
n
tr
o
lled
in
t
h
e
s
a
m
e
m
a
n
n
er
a
s
a
s
ta
n
d
ar
d
C
SI.
D
u
r
in
g
t
h
e
ST
m
o
d
e,
th
e
en
t
ir
e
u
p
p
er
a
n
d
/o
r
all
o
f
th
e
lo
w
er
s
w
itc
h
es
ar
e
g
ated
o
f
f
.
D
u
r
i
n
g
th
e
d
is
c
o
n
tin
u
o
u
s
m
o
d
e,
t
h
e
s
w
i
tch
e
s
ar
e
g
ated
as
i
f
in
a
n
ac
ti
v
e
s
t
ate,
b
u
t
o
n
e
li
n
e
-
to
-
lin
e
v
o
lta
g
e
is
g
r
ea
ter
th
a
n
o
r
eq
u
al
to
t
h
e
s
u
m
o
f
th
e
ca
p
ac
ito
r
v
o
ltag
e
s
.
W
h
e
n
t
h
i
s
o
cc
u
r
s
,
t
h
e
d
io
d
e,
D
1
,
co
n
d
u
cts
a
n
d
th
e
in
v
er
ter
b
eh
av
es
as
i
f
it
is
an
o
p
en
cir
cu
it
.
I
n
th
e
ac
tiv
e
s
tate
t
h
e
cu
r
r
en
t
f
lo
w
s
th
r
o
u
g
h
th
e
v
o
ltag
e
s
o
u
r
ce
to
th
e
f
ir
s
t
i
n
d
u
cto
r
th
e
n
t
h
e
s
ec
o
n
d
i
n
d
u
cto
r
an
d
f
in
a
ll
y
to
t
h
e
s
o
u
r
ce
v
ia
t
h
e
lo
ad
.
T
h
e
d
io
d
e
is
f
o
r
w
ar
d
b
iased
an
d
allo
w
s
t
h
e
cu
r
r
en
t
f
lo
w
.
I
n
ST
m
o
d
e
th
e
b
o
th
t
h
e
i
n
d
u
cto
r
s
ar
e
alr
ea
d
y
c
h
ar
g
ed
,
th
e
cu
r
r
en
t
f
lo
w
s
f
r
o
m
ca
p
ac
ito
r
C
1
t
h
r
o
u
g
h
th
e
i
n
d
u
cto
r
L
1
a
n
d
f
r
o
m
ca
p
ac
ito
r
C
2
th
r
o
u
g
h
t
h
e
i
n
d
u
cto
r
L
2
.
Fo
r
t
h
ese
r
ea
s
o
n
s
Q
Z
SI
is
u
s
ed
i
n
s
tead
o
f
o
th
er
Z
VSI
s
.
I
n
ad
d
itio
n
,
th
e
in
ter
m
itte
n
t
a
n
d
u
n
s
ch
ed
u
led
ch
ar
ac
ter
is
tic
s
o
f
s
o
lar
p
o
w
er
li
m
it
t
h
e
ap
p
licab
ilit
y
o
f
P
V
s
y
s
te
m
s
.
T
h
er
ef
o
r
e,
ad
d
itio
n
o
f
an
en
er
g
y
s
to
r
ag
e
s
y
s
te
m
(
E
SS
)
to
P
V
p
o
w
er
g
e
n
er
atio
n
to
m
a
k
e
it
s
o
u
tp
u
t
p
o
w
er
co
n
ti
n
u
o
u
s
,
s
tab
le,
a
n
d
s
m
o
o
th
W
ith
o
u
t
r
eq
u
ir
e
m
en
ts
o
f
a
n
y
ad
d
itio
n
al
d
c/d
c
co
n
v
er
ter
s
o
r
co
m
p
o
n
en
ts
,
t
h
e
QZ
SI
w
it
h
e
n
er
g
y
s
to
r
ag
e
w
as
f
ir
s
t
p
r
o
p
o
s
ed
f
o
r
P
V
s
y
s
te
m
i
n
[
1
]
,
[
2
]
.
B
y
co
n
n
ec
t
in
g
t
h
e
b
atter
y
i
n
p
ar
allel
w
ith
ca
p
ac
ito
r
C
2
[
2
]
o
f
th
e
Q
Z
SI,
t
h
is
s
y
s
te
m
is
ab
le
to
d
o
th
e
f
o
llo
w
in
g
s
i
m
u
lta
n
eo
u
s
l
y
.
a.
P
r
o
d
u
ce
th
e
d
esire
d
o
u
tp
u
t a
c
v
o
ltag
e
to
t
h
e
g
r
id
/lo
ad
[
2
0
]
b.
R
eg
u
late
t
h
e
b
atter
y
s
ta
te
o
f
c
h
ar
g
e
(
SO
C
)
an
d
c.
C
o
n
tr
o
l th
e
P
V
p
an
el
o
u
tp
u
t p
o
w
er
(
o
r
v
o
ltag
e)
to
m
ax
i
m
ize
en
er
g
y
p
r
o
d
u
ctio
n
.
B
u
t
it
h
as
a
b
i
g
d
is
c
h
ar
g
i
n
g
p
o
w
er
li
m
itatio
n
d
u
e
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
-
8
694
IJ
PEDS
Vo
l.
7
,
No
.
3
,
Sep
tem
b
er
2
0
1
6
:
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-
825
820
–
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1
1
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ss C
1
1.
O
u
t
p
u
t
p
o
w
e
r
c
o
n
t
i
n
u
o
u
s,
s
t
a
b
l
e
,
a
n
d
smo
o
t
h
i
n
sp
i
t
e
f
l
u
c
t
u
a
t
i
n
g
i
n
p
u
t
b
y
P
V
p
a
n
e
l
2.
P
r
o
d
u
c
e
t
h
e
d
e
si
r
e
d
o
u
t
p
u
t
a
c
v
o
l
t
a
g
e
t
o
t
h
e
g
r
i
d
/
l
o
a
d
3.
R
e
g
u
l
a
t
e
t
h
e
b
a
t
t
e
r
y
st
a
t
e
o
f
c
h
a
r
g
e
(
S
O
C
)
1.
O
u
t
p
u
t
p
o
w
e
r
c
o
n
t
i
n
u
o
u
s
,
st
a
b
l
e
,
a
n
d
s
mo
o
t
h
i
n
s
p
i
t
e
o
f
f
l
u
c
t
u
a
t
i
n
g
i
n
p
u
t
b
y
P
V
p
a
n
e
l
2.
P
r
o
d
u
c
e
t
h
e
d
e
si
r
e
d
o
u
t
p
u
t
a
c
v
o
l
t
a
g
e
t
o
t
h
e
g
r
i
d
/
l
o
a
d
3.
R
e
g
u
l
a
t
e
t
h
e
b
a
t
t
e
r
y
st
a
t
e
o
f
c
h
a
r
g
e
(
S
O
C
)
4.
T
h
e
d
i
sc
h
a
r
g
i
n
g
b
a
t
t
e
r
y
i
s
l
i
mi
t
e
d
t
o
e
n
s
u
r
e
t
h
a
t
t
h
e
sy
st
e
m
5.
O
p
e
r
a
t
e
s
i
n
t
h
e
C
C
M
a
l
w
a
y
s o
p
e
r
a
t
e
s
i
n
t
h
e
C
C
M
d
u
r
i
n
g
b
a
t
t
e
r
y
c
h
a
r
g
i
n
g
6.
A
w
i
d
e
r
b
a
t
t
e
r
y
d
i
sch
a
r
g
i
n
g
p
o
w
e
r
r
a
n
g
e
7.
C
a
n
b
e
u
se
d
t
o
h
i
g
h
v
o
l
t
a
g
e
1.
O
u
t
p
u
t
p
o
w
e
r
c
o
n
t
i
n
u
o
u
s
,
st
a
b
l
e
,
a
n
d
smo
o
t
h
i
n
s
p
i
t
e
o
f
f
l
u
c
t
u
a
t
i
n
g
i
n
p
u
t
b
y
P
V
p
a
n
e
l
2.
P
r
o
d
u
c
e
t
h
e
d
e
si
r
e
d
o
u
t
p
u
t
a
c
v
o
l
t
a
g
e
t
o
t
h
e
g
r
i
d
/
l
o
a
d
3.
R
e
g
u
l
a
t
e
t
h
e
b
a
t
t
e
r
y
st
a
t
e
o
f
c
h
a
r
g
e
(
S
O
C
)
4.
T
h
e
d
i
sc
h
a
r
g
i
n
g
b
a
t
t
e
r
y
i
s l
i
mi
t
e
d
t
o
e
n
su
r
e
t
h
a
t
t
h
e
sy
st
e
m
5.
O
p
e
r
a
t
e
s
i
n
t
h
e
C
C
M
a
l
w
a
y
s
o
p
e
r
a
t
e
s
i
n
t
h
e
C
C
M
d
u
r
i
n
g
b
a
t
t
e
r
y
c
h
a
r
g
i
n
g
6.
A
w
i
d
e
r
b
a
t
t
e
r
y
d
i
sc
h
a
r
g
i
n
g
p
o
w
e
r
r
a
n
g
e
7.
C
a
n
b
e
u
se
d
t
o
h
i
g
h
v
o
l
t
a
g
e
8
.
R
e
d
u
c
e
s
t
h
e
s
t
r
e
ss o
n
o
n
e
b
a
t
t
e
r
y
9
.
B
e
t
t
e
r
T
H
D
p
e
r
f
o
r
man
c
e
Ma
tr
ix
f
o
r
m
o
f
t
h
e
eq
u
atio
n
s
i
s
af
ter
s
o
l
v
in
g
t
h
e
tr
an
s
f
er
f
u
n
ctio
n
o
f
p
r
o
p
o
s
ed
tw
o
b
atter
y
co
n
n
ec
ted
Q
Z
SI
L
et
[
]
.
[
]
(
1
3
)
[
]
[
]
[
(
)
(
)
(
)
(
)
(
)
]
(
1
4
)
4.
SI
M
UL
AT
I
O
N
ST
U
DY
T
h
e
af
o
r
esaid
en
er
g
y
s
to
r
ed
QZ
SI
a
n
d
its
co
n
tr
o
l
s
c
h
e
m
e
ar
e
p
er
f
o
r
m
ed
in
M
A
T
L
A
B
/
SI
MU
L
I
NK.
T
h
e
m
a
in
s
i
m
u
latio
n
p
ar
a
m
ete
r
s
ar
e:
th
e
q
u
a
s
i
-
Z
-
s
o
u
r
ce
ca
p
ac
ito
r
is
C
1
=
C
2
=
4
0
0
m
icr
o
F;
i
n
d
u
cto
r
is
L
1=
L
2
=
5
0
m
H
;
th
e
g
r
id
lin
e
v
o
lta
g
e
i
s
2
0
8
V,
an
d
th
e
g
r
id
f
r
eq
u
en
c
y
is
5
0
Hz;
th
e
co
m
m
a
n
d
p
e
ak
d
c
-
li
n
k
v
o
l
tag
e,
V
ac
is
f
i
x
ed
as
4
0
0
V.
T
h
e
Sim
u
latio
n
te
s
t
is
ca
r
r
ied
o
u
t
i
n
th
r
ee
ca
s
es,
w
h
er
e
b
atter
y
co
n
n
ec
ted
in
C
1
alo
n
e,
C
2
alo
n
e
a
n
d
b
atter
y
co
n
n
ec
te
d
f
o
r
b
o
th
C
1
an
d
C
2
.
Fo
r
th
e
in
p
u
t
v
o
ltag
e
s
o
u
r
ce
f
o
r
t
h
e
p
r
o
p
o
s
ed
QZ
SI
u
s
e
s
th
e
P
&
O
-
MM
P
T
b
ased
P
V
b
ased
1
k
W
s
tr
u
ct
u
r
e.
T
h
e
s
i
m
u
latio
n
i
n
itia
ll
y
ca
r
r
ied
o
u
t
w
i
t
h
8
0
0
W
P
V
o
u
tp
u
t
w
it
h
4
0
0
V
D
C
-
lin
k
.
T
h
e
test
is
ca
r
r
ied
o
u
t
f
o
r
th
e
v
ar
iatio
n
o
f
th
e
p
o
w
er
a
n
d
v
o
lta
g
e
o
f
t
h
e
P
V
o
u
tp
u
t.
T
h
e
v
ar
iatio
n
h
a
s
b
ee
n
ac
h
ie
v
ed
th
r
o
u
g
h
v
ar
iatio
n
o
f
th
e
ir
r
ad
iati
o
n
.
A
ll
t
h
e
s
i
m
u
lat
io
n
is
ca
r
r
ied
o
u
t
f
o
r
th
e
s
am
e
v
ar
iatio
n
to
test
t
h
e
p
r
e
d
o
m
i
n
an
ce
o
f
th
e
in
v
er
ter
.
T
h
e
F
ig
u
r
e
7
d
is
p
la
y
s
t
h
e
Ma
t
lab
/SIM
UL
I
NK
s
i
m
u
latio
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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n
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a
n
d
E
fficien
cy
A
n
a
ly
s
is
o
f B
a
tter
y
A
s
s
i
s
t
s
P
V
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(
T.K
.
S
S
a
th
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ya
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r
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y
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n
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821
Diag
r
a
m
f
o
r
Q
Z
SI
w
it
h
B
1
co
n
n
ec
ted
ac
r
o
s
s
C
1
an
d
B
2
co
n
n
ec
ted
ac
r
o
s
s
C
2.
I
n
F
ig
u
r
e
8
,
s
h
o
w
s
t
h
e
P
W
M
co
n
tr
o
l sch
e
m
e
f
o
r
p
r
o
p
o
s
ed
i
n
v
er
ter
.
Fig
u
r
e
7
.
Si
m
u
latio
n
Diag
r
a
m
f
o
r
QZ
SI
w
i
th
B
1
co
n
n
ec
ted
a
cr
o
s
s
C
1
an
d
B
2
co
n
n
ec
ted
ac
r
o
s
s
C
2
Fig
u
r
e
8
.
SVP
W
M
g
en
er
ated
f
o
r
th
e
p
r
o
p
o
s
ed
t
w
o
b
atter
y
co
n
n
ec
ted
Q
Z
SI
T
h
e
Fig
u
r
e
1
1
s
h
o
w
s
t
h
e
ca
p
ac
ito
r
v
o
ltag
e
r
esp
o
n
s
e
(
V
C1
an
d
V
C2
)
,
w
h
en
b
atter
y
co
n
n
ec
ted
o
n
l
y
cr
o
s
s
C
1
an
d
Fi
g
u
r
e
1
2
,
s
h
o
ws
t
h
e
ca
p
ac
ito
r
v
o
ltag
e
r
esp
o
n
s
e,
w
h
en
b
atter
y
co
n
n
ec
ted
o
n
l
y
cr
o
s
s
C
2
.
B
ased
o
n
th
e
r
es
u
lt
s
,
it
co
u
ld
u
n
d
e
r
s
tan
d
th
a
t,
th
r
o
u
g
h
th
e
i
n
v
e
r
ter
s
tab
ilit
y
i
s
in
cr
ea
s
ed
.
T
h
e
ca
p
ac
ito
r
s
’
n
o
t
b
ala
n
ce
d
d
u
e
to
th
e
i
n
f
l
u
en
ce
o
f
th
e
b
atter
y
v
o
lta
g
es
o
n
C
1
a
n
d
C
2
.
Her
e,
C
ap
ac
ito
r
ch
ar
g
i
n
g
a
n
d
d
is
c
h
ar
g
i
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iv
e
s
t
h
e
b
o
o
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ted
v
o
lta
g
e
at
t
h
e
i
n
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er
ti
n
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le
g
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.
W
h
e
n
a
b
att
er
y
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co
n
n
ec
ted
ac
r
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s
s
o
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f
th
e
ca
p
ac
ito
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e
n
th
e
v
o
lta
g
e
t
h
at
ap
p
ea
r
s
ac
r
o
s
s
th
at
ca
p
a
cito
r
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lar
g
e
w
h
e
n
co
m
p
ar
ed
w
ith
t
h
e
o
th
er
ca
p
ac
ito
r
.
T
h
is
s
h
o
w
s
th
at
t
h
e
ca
p
ac
ito
r
h
o
ld
s
lar
g
e
v
o
ltag
e
a
n
d
s
tr
es
s
o
n
it
i
n
cr
ea
s
es.
T
h
e
h
ar
m
o
n
ic
d
is
to
r
tio
n
o
f
th
e
o
u
tp
u
t
at
t
h
e
in
v
er
ter
cir
cu
i
t
is
m
ea
s
u
r
ed
an
d
is
f
o
u
n
d
v
er
y
h
ig
h
.
Hen
ce
t
h
e
d
is
to
r
tio
n
o
f
w
av
e
is
h
ig
h
wh
en
co
m
p
ar
ed
w
it
h
f
u
n
d
a
m
en
ta
l
f
r
eq
u
e
n
c
y
w
h
ic
h
is
s
h
o
w
n
i
n
F
i
g
u
r
e
9
an
d
1
0
.
Fig
u
r
e
9
.
QZ
SI
V
C1
a
n
d
V
C2
p
er
f
o
r
m
an
ce
w
i
th
B
Fig
u
r
e
10
.
QZ
SI
V
C1
an
d
V
C2
p
er
f
o
r
m
a
n
ce
,
w
it
h
af
f
ec
t ir
r
ad
iatio
n
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I
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Fig
u
r
e
11
.
V
C1
an
d
V
C2
p
er
f
o
r
m
an
ce
w
i
th
B
ac
r
o
s
s
C
2
Fig
u
r
e
12
.
V
C1
an
d
V
C2
p
er
f
o
r
m
an
ce
w
i
th
B
ac
r
o
s
s
C
1
V
THD
s
p
ec
tr
a,
w
h
e
n
Q
Z
SI
B
ac
r
o
s
s
C
2
as
s
h
o
w
n
i
n
Fi
g
u
r
e
1
3
,
an
d
in
Fig
u
r
e
1
4
as
s
h
o
w
VT
HD
s
p
ec
tr
a,
w
h
e
n
Q
Z
SI
B
ac
r
o
s
s
C
1
.
T
h
e
F
ig
u
r
e
1
5
an
d
Fig
u
r
e
16
illu
s
tr
atio
n
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th
e
i
n
v
er
ter
ca
p
ac
ito
r
s
b
alan
cin
g
f
o
r
b
o
th
ir
r
itat
io
n
e
f
f
ec
t
a
n
d
c
o
n
s
ta
n
t
s
o
lar
p
o
w
er
.
T
h
e
l
iv
e
v
o
ltag
e
p
r
o
f
ile
f
o
r
p
r
o
p
o
s
ed
p
r
o
p
o
s
ed
t
w
o
b
atter
y
QZ
SI
a
n
d
its
h
ar
m
o
n
ic
s
p
ec
tr
a.
Du
e
to
th
e
ca
p
ac
ito
r
b
alan
ci
n
g
th
e
h
elp
o
f
B
1
a
n
d
B
2
f
o
r
th
e
p
r
o
p
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atter
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ased
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atter
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f
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t
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is
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d
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g
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ter
.
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u
r
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1
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h
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s
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ted
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f
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ter
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atter
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to
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h
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t.
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e
th
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s
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r
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F
ig
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r
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1
4
s
h
o
w
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t
h
e
m
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s
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ter
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t c
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n
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th
e
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h
t
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atter
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n
n
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ted
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r
k
.
T
h
e
MP
PT
ca
n
b
e
i
m
p
le
m
en
ted
th
r
o
u
g
h
ad
j
u
s
ti
n
g
s
h
o
o
t
-
t
h
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o
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g
h
d
u
t
y
r
atio
t
o
ch
an
g
e
t
h
e
P
V
p
an
el
’
s
v
o
ltag
e.
T
h
e
m
o
d
u
latio
n
s
i
g
n
al
i
s
c
o
n
tr
o
lled
to
en
s
u
r
e
a
co
n
s
ta
n
t
o
u
tp
u
t
v
o
lta
g
e.
T
h
e
b
atter
y
w
ill
b
alan
ce
th
e
d
if
f
er
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ce
b
et
w
ee
n
th
e
in
p
u
t
p
o
w
er
an
d
o
u
tp
u
t
p
o
w
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r
.
T
h
e
s
i
m
u
la
ted
an
d
ex
p
er
i
m
e
n
tal
r
es
u
lt
s
v
er
if
ied
th
e
p
r
o
p
o
s
ed
P
V
p
o
w
e
r
g
en
er
atio
n
s
y
s
te
m
.
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n
o
v
e
l
to
p
o
lo
g
y
f
o
r
an
en
er
g
y
-
s
to
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ed
QZ
SI
h
as
b
ee
n
p
r
o
p
o
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ed
to
o
v
er
co
m
e
th
e
s
h
o
r
tco
m
i
n
g
o
f
th
e
e
x
is
tin
g
s
o
l
u
tio
n
s
in
P
V
p
o
w
er
s
y
s
te
m
.
T
h
e
e
f
f
ec
tiv
e
n
es
s
o
f
t
h
e
p
r
o
p
o
s
ed
co
n
tr
o
ller
s
w
er
e
v
er
if
ied
b
y
b
o
th
t
h
e
s
i
m
u
latio
n
an
d
e
x
p
er
i
m
e
n
tal
r
esu
lt
s
.
RE
F
E
R
E
NC
E
S
[1
]
S
.
B.
Kja
e
r,
J.
K.
P
e
d
e
rse
n
,
a
n
d
F
.
Blaa
b
jerg
,
“
A
Re
v
ie
w
o
f
S
in
g
le
-
p
h
a
se
G
rid
-
c
o
n
n
e
c
ted
In
v
e
rters
fo
r
P
h
o
to
v
o
lt
a
ic
M
o
d
u
les
”,
IEE
E
T
ra
n
s.
In
d
A
p
p
li
c
a
t.
,
v
o
l
.
4
1
,
p
p
.
1
2
9
2
-
1
3
0
6
,
2
0
0
5
.
[2
]
C.
B
h
a
ra
ti
ra
ja,
S
.
Ra
g
h
u
,
P.
Ra
o
,
K.R.
S
.
P
a
li
n
iam
y
,
“
Co
m
p
a
ra
ti
v
e
A
n
a
l
y
sis
o
f
Di
ff
e
re
n
t
P
W
M
T
e
c
h
n
iq
u
e
s
to
Re
d
u
c
e
th
e
Co
m
m
o
n
M
o
d
e
Vo
lt
a
g
e
in
T
h
re
e
-
le
v
e
l
Ne
u
tral
-
P
o
i
n
t
-
Clam
p
e
d
In
v
e
rters
f
o
r
V
a
riab
le
S
p
e
e
d
In
d
u
c
ti
o
n
Driv
e
s”
,
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
ms
,
v
o
l.
3
,
Iss
u
e
1
,
P
a
g
e
s
1
0
5
-
1
1
6
,
M
a
rc
h
2
0
1
3
,
[3
]
E.
G
u
b
´
ıa,
P
.
S
a
n
c
h
is,
A
.
Urs
´
u
a
,
J.
L
o
p
e
z
,
a
n
d
L
.
M
a
rro
y
o
,
“
Gr
o
u
n
d
Cu
rr
e
n
t
S
i
n
g
le
-
p
h
a
se
T
ra
n
sfo
rm
e
r
les
s
Ph
o
t
o
v
o
lt
a
ic S
y
ste
ms
”
,
P
ro
g
.
P
h
o
to
v
o
lt
a
ics
:
Re
s.
A
p
p
l.
,
v
o
l.
1
5
,
p
p
.
6
2
9
–
6
5
0
,
2
0
0
7
.
[4
]
T
.
Ke
re
k
e
s,
R.
T
e
o
d
o
re
sc
u
,
a
n
d
U.
Bo
ru
p
,
“
T
ra
n
sf
o
rm
e
r
les
s
Ph
o
to
v
o
lt
a
ic
I
n
v
e
rte
rs
Co
n
n
e
c
ted
t
o
t
h
e
Gr
id
”
,
i
n
P
r
o
c
.
A
P
EC
2
0
0
7
,
p
p
.
1
7
3
3
–
1
7
3
7
,
F
e
b
.
2
5
–
M
a
r.
0
1
,
2
0
0
7
.
[5
]
X
iao
m
e
n
g
S
u
,
Ya
o
ji
e
S
u
n
a
n
d
Ya
n
d
a
n
L
in
,
“
A
n
a
l
y
sis
o
n
L
e
a
k
a
g
e
Cu
rre
n
t
in
T
ra
n
sf
o
r
m
e
r
le
ss
S
in
g
le
-
P
h
a
se
P
V
In
v
e
rters
Co
n
n
e
c
ted
t
o
t
h
e
G
rid
”
,
IEE
E
T
ra
n
s.
2
0
1
1
.
[6
]
S
M
A
,
"
Ca
p
a
c
it
iv
e
Dis
c
h
a
rg
e
Cu
rre
n
ts
-
In
f
o
rm
a
ti
o
n
o
n
t
h
e
S
y
ste
m
L
a
y
o
u
t
f
o
r
T
ra
n
s
f
o
r
m
e
r
les
s In
v
e
rters
"
.
[7
]
C.
Bh
a
ra
ti
ra
ja,
Ha
rsh
a
v
a
rd
h
a
n
Re
d
d
y
,
N.
S
ri
Ra
m
sa
i,
a
n
d
S
u
n
k
a
v
a
ll
i
S
a
t
y
a
S
a
isu
m
a
,
“
F
P
GA
B
a
s
e
d
De
sig
n
a
n
d
V
a
li
d
a
ti
o
n
o
f
A
s
y
m
m
e
tri
c
a
l
Re
d
u
c
e
d
S
w
it
c
h
M
u
lt
il
e
v
e
l
In
v
e
rter,
I
n
ter
n
a
ti
o
n
a
l
J
o
u
rn
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
),
Vo
l.
7
,
No
.
2
,
p
p
.
3
4
0
-
3
4
8
,
Ju
n
e
2
0
1
6
.
[8
]
M
.
Ca
lais
a
n
d
V.
G
.
A
g
e
li
d
is,
"
M
u
lt
il
e
v
e
l
Co
n
v
e
rte
rs
fo
r
S
in
g
le
-
p
h
a
se
Gr
id
Co
n
n
e
c
ted
Ph
o
to
v
o
lt
a
ic
S
y
ste
ms
-
a
n
Ov
e
rv
iew"
,
In
d
u
strial
El
e
c
tro
n
ics
,
1
9
9
8
.
P
r
o
c
e
e
d
in
g
s.
IS
IE
'
9
8
.
IE
EE
In
ter
n
a
ti
o
n
a
l
S
y
m
p
o
siu
m
o
n
,
v
o
l.
1
,
p
p
.
2
2
4
-
2
2
9
,
1
9
9
8
.
[9
]
O.
L
o
p
e
z
,
F
.
D.
F
re
ij
e
d
o
,
A
.
G
.
Ye
p
e
s,
P
.
F
e
rn
a
n
d
e
z
-
Co
m
e
sa
a
,
J
.
M
a
lv
a
r,
R.
T
e
o
d
o
re
sc
u
,
a
n
d
J.
Do
v
a
l
-
Ga
n
d
o
y
,
"
El
im
in
a
ti
n
g
G
ro
u
n
d
Cu
rre
n
t
in
a
T
ra
n
s
f
o
rm
e
r
les
s"
,
IEE
E
T
ra
n
.
E
n
e
rg
y
Co
n
v
e
rs
io
n
v
o
l.
2
5
,
p
p
.
1
4
0
-
1
4
7
,
2
0
1
0
.
[1
0
]
M
.
L
ise
rre
,
F
.
Blaa
b
jerg
,
a
n
d
S
.
Ha
n
se
n
,
"
De
sig
n
a
n
d
Co
n
tr
o
l
o
f
a
n
LCL
-
B
a
se
d
T
h
re
e
-
P
h
a
se
Ac
ti
v
e
Re
c
ti
f
ier
"
,
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
In
d
u
stry
A
p
p
li
c
a
ti
o
n
s
,
v
o
l
.
4
1
,
N
o
.
5
,
S
e
p
tem
b
e
r/Oc
to
b
e
r
2
0
0
5
.
[1
1
]
A
Na
b
a
e
,
I.
T
a
k
a
h
a
sh
i,
a
n
d
H.
Ak
a
g
i,
“
A
Ne
w
N
e
u
tral
-
P
o
in
t
Cl
a
m
p
e
d
P
W
M
In
v
e
rter”
,
IEE
E
T
ra
n
s
.
I
n
d
.
A
p
p
l.
,
v
o
l.
IA
-
1
7
,
No
.
5
,
p
p
.
5
1
8
–
5
2
3
,
S
e
p
.
/Oc
t.
1
9
8
1
.
[1
2
]
M
.
L
ise
rre
,
R.
T
e
o
d
o
re
sc
u
,
a
n
d
F
.
Blaa
b
jerg
,
“
S
tab
il
it
y
o
f
P
h
o
t
o
v
o
l
taic
a
n
d
W
in
d
T
u
r
b
in
e
G
rid
-
c
o
n
n
e
c
ted
In
v
e
rters
f
o
r
a
L
a
r
g
e
S
e
t
o
f
G
rid
Im
p
e
d
a
n
c
e
V
a
lu
e
s”
,
IEE
E
T
ra
n
s.
P
o
we
r E
l
e
c
tro
n
.
,
v
o
l
.
2
1
,
N
o
.
1
,
p
p
.
2
6
3
–
2
7
2
,
Ja
n
.
2
0
0
6
.
[1
3
]
F
.
S
c
h
im
p
f
a
n
d
L
.
No
ru
m
,
"
G
rid
c
o
n
n
e
c
ted
Co
n
v
e
rters
f
o
r
P
h
o
to
v
o
l
taic
,
G
rid
c
o
n
n
e
c
ted
Co
n
v
e
rters
f
o
r
P
h
o
t
o
v
o
lt
a
ic,
S
tate
o
f
th
e
A
rt,
Id
e
a
s
f
o
r
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m
p
ro
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e
n
t
o
f
T
ra
n
s
f
o
rm
e
r
les
s
In
v
e
rters
"
,
No
rd
ic
W
o
rk
sh
o
p
o
n
Po
we
r
a
n
d
In
d
u
stri
a
l
El
e
c
tro
n
ics
,
2
0
0
8
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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g
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n
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a
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fficien
cy
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[1
4
]
B.
P
.
M
c
G
ra
th
,
D.G
.
Ho
l
m
e
s,
a
n
d
IEE
E,
"
A
C
o
mp
a
riso
n
o
f
M
u
lt
ic
a
rr
ier
PW
M
S
tra
teg
ies
fo
r
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sc
a
d
e
d
a
n
d
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tra
l
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in
t
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m
p
e
d
M
u
l
ti
lev
e
l
In
v
e
rte
rs
"
,
IEE
E
P
o
w
e
r
El
e
c
tro
n
ics
S
p
e
c
ialists Co
n
f
e
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n
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e
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o
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s
.
p
p
.
6
7
4
-
6
7
9
,
2
0
0
0
.
[1
5
]
G.
P
ra
k
a
sh
,
S
u
b
ra
m
a
n
i,
C.
Bh
a
ra
t
iraja
,
a
n
d
M.
S
h
a
b
in
,
“
A
L
o
w
Co
st
S
in
g
le
-
p
h
a
se
G
rid
Co
n
n
e
c
ted
R
e
d
u
c
e
d
S
w
it
c
h
P
V
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v
e
rter
b
a
se
d
o
n
T
ime
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ra
m
e
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w
it
c
h
in
g
”
,
In
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
El
e
c
trica
l
P
o
we
r
a
n
d
E
n
e
rg
y
S
y
ste
ms
,
v
o
l.
7
7
,
p
p
.
1
0
0
-
1
1
1
,
M
a
rc
h
2
0
1
6
.
[1
6
]
A
ip
in
g
G
u
o
,
Xu
P
e
n
g
,
Yin
g
y
in
g
Zh
o
u
,
Xia
o
q
i
o
n
g
He
a
n
d
Zelian
g
S
h
u
,
“
T
h
e
M
o
d
u
la
ti
o
n
T
e
c
h
n
iq
u
e
s
in
3
L
-
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C
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sc
a
d
e
Co
n
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e
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r”,
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u
tu
re
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n
e
rg
y
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e
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tro
n
ics
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n
f
e
re
n
c
e
(IF
EE
C).
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v
.
2
0
1
5
.
[1
7
]
L
.
Yu
-
Tzu
n
g
a
n
d
T
.
Yin
g
-
Yu
,
“
Dig
it
a
l
Co
n
tro
l
o
f
a
M
u
lt
i
-
p
h
a
se
In
ter
lea
v
e
d
PW
M
In
v
e
rte
r
wit
h
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in
ima
l
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p
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0
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2
0
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.
[1
8
]
E.
T
w
in
in
g
a
n
d
D.G
.
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lm
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s,
“
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rid
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p
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8
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a
y
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[1
9
]
C.
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w
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p
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1
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5
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3
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n
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2
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.
[2
0
]
C.
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ra
ti
ra
ja,
S.
Ra
g
h
u
,
P.
Ra
o
,
K.R.
S
.
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a
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y
,
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m
p
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Driv
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s”
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ter
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o
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.
[2
1
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C.
Bh
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L
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v
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.
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g
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Dr.
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.
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.
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sh
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De
sig
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p
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rn
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e
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trica
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rin
g
,
v
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l.
1
3
,
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d
it
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o
n
1
,
p
p
5
4
-
6
3
,
2
0
1
3
.
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