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Dec
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20
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p
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A
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sin
g
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-
p
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se
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y
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m
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h
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lev
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t
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t
v
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e
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rm
wit
h
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ste
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s,
th
is se
tu
p
u
se
s m
e
re
ly
se
v
e
n
p
o
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r
sw
it
c
h
e
s,
two
d
io
d
e
s,
a
n
d
two
D
C
su
p
p
li
e
s.
A
g
re
a
ter
n
u
m
b
e
r
o
f
ste
p
s
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re
a
c
h
iev
e
d
in
o
u
tp
u
t
v
o
lt
a
g
e
th
r
o
u
g
h
su
g
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ste
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ircu
it
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sm
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ll
e
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u
m
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e
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o
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o
m
p
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ts
t
h
a
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o
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h
e
r
e
x
ist
in
g
m
u
lt
i
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l
i
n
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rter
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LI
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t
o
p
o
lo
g
ies
.
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fin
e
r
o
u
t
p
u
t
wa
v
e
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rm
t
h
a
t
is
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lo
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to
a
sin
u
so
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d
a
l
sh
a
p
e
is p
ro
d
u
c
e
d
with
les
s
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tal
h
a
rm
o
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ic
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ist
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rti
o
n
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HD
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b
e
c
a
u
se
o
f
th
e
g
re
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ter
n
u
m
b
e
r
o
f
ste
p
s
in
th
e
o
u
tp
u
t
v
o
lt
a
g
e
.
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u
rth
e
rm
o
re
,
i
t
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ro
l
o
n
g
s
th
e
sw
it
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h
e
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li
f
e
ti
m
e
a
n
d
lo
we
rs
th
e
v
o
lt
a
g
e
stre
ss
a
c
ro
ss
t
h
e
m
,
in
c
re
a
sin
g
re
li
a
b
i
li
ty
.
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n
a
d
d
it
io
n
,
th
e
sy
ste
m
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ro
d
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c
e
s
fe
we
r
sw
it
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h
e
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th
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ss
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ry
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re
su
lt
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g
i
n
lo
we
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p
o
we
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lo
ss
e
s a
n
d
in
c
re
a
se
d
e
fficie
n
c
y
.
Th
is g
u
a
ra
n
tee
s th
e
su
g
g
e
ste
d
sy
ste
m
'
s s
m
a
ll
siz
e
a
n
d
in
e
x
p
e
n
si
v
e
c
o
st.
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c
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m
p
a
riso
n
b
e
twe
e
n
th
e
su
g
g
e
ste
d
to
p
o
l
o
g
y
a
n
d
th
e
m
o
st cu
rre
n
t
M
LI
to
p
o
l
o
g
ies
h
a
s b
e
e
n
c
o
n
d
u
c
ted
t
o
h
i
g
h
li
g
h
t
th
e
k
e
y
c
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m
p
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e
n
ts
o
f
t
h
e
p
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p
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se
d
to
p
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o
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y
.
Th
e
s
u
g
g
e
ste
d
t
o
p
o
lo
g
y
h
a
s
b
e
e
n
c
o
n
tro
ll
e
d
u
si
n
g
th
re
e
d
isti
n
c
t
c
o
n
tr
o
ll
i
n
g
sc
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m
e
s
a
re
p
h
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se
d
i
sp
o
siti
o
n
-
p
u
lse
wid
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m
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d
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(
PD
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WM
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,
p
h
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se
o
p
p
o
siti
o
n
d
isp
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ti
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-
P
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(
P
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a
n
d
a
l
tern
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ti
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p
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se
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siti
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n
d
isp
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sit
io
n
-
P
WM
(
APOD
-
P
WM
)
.
K
ey
w
o
r
d
s
:
H
MLI
m
o
d
u
latio
n
tech
n
iq
u
es
Switch
in
g
s
tr
ess
T
o
tal
h
ar
m
o
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ic
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is
to
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tio
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T
o
tal
s
tan
d
in
g
v
o
ltag
e
Vo
ltag
e
s
tr
ess
r
ed
u
ctio
n
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
R
am
y
a
Gan
esan
Dep
ar
tm
en
t o
f
E
lectr
ical
an
d
E
lectr
o
n
ics E
n
g
in
ee
r
i
n
g
,
Facu
lty
o
f
E
n
g
in
ee
r
in
g
an
d
T
ec
h
n
o
lo
g
y
SR
M
I
n
s
titu
te
o
f
Scien
ce
an
d
T
ec
h
n
o
lo
g
y
,
R
am
ap
u
r
am
C
a
m
p
u
s
R
am
ap
u
r
am
,
C
h
en
n
ai,
T
am
il
Nad
u
,
I
n
d
ia
E
m
ail:
r
am
y
ag
@
s
r
m
is
t.e
d
u
.
in
1.
I
NT
RO
D
UCT
I
O
N
DC
-
AC
co
n
v
er
ter
s
ar
e
a
cr
u
cial
co
m
p
o
n
e
n
t
o
f
elec
tr
ical
p
o
wer
s
y
s
tem
s
th
at
p
r
o
v
i
d
e
ch
an
g
ea
b
le
f
r
eq
u
e
n
cy
an
d
m
a
g
n
itu
d
e
in
o
u
tp
u
t.
Mu
ltil
ev
el
i
n
v
er
ter
s
h
a
v
e
b
ec
o
m
e
v
er
y
p
o
p
u
lar
,
p
ar
ti
cu
lar
ly
in
th
e
r
ea
lm
o
f
DC
/AC
co
n
v
er
ter
s
,
ac
ad
em
ic
an
d
in
d
u
s
tr
y
r
esear
ch
.
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h
is
in
ter
est
co
m
es
f
r
o
m
a
v
ar
iety
o
f
ad
v
an
ta
g
es
th
at
m
u
ltil
ev
el
in
v
er
ter
s
h
av
e
o
v
e
r
tr
ad
itio
n
al
in
v
er
ter
s
,
wh
ich
r
ed
u
ce
s
th
e
o
u
tp
u
t
wav
ef
o
r
m
'
s
h
ar
m
o
n
ic
c
o
n
ten
t
with
a
lo
t
o
f
s
tep
s
in
th
e
o
u
tp
u
t
v
o
ltag
e
wav
ef
o
r
m
.
Mo
r
eo
v
er
,
th
e
p
h
y
s
ical
d
im
en
s
io
n
s
o
f
th
e
AC
s
id
e
f
ilter
elem
en
ts
ar
e
r
ed
u
ce
d
.
I
n
ad
d
itio
n
,
th
e
o
u
tp
u
t
wav
e
f
o
r
m
'
s
lar
g
e
s
tep
co
u
n
t
ex
te
n
d
s
th
e
life
tim
e
o
f
th
e
s
witch
in
g
co
m
p
o
n
en
ts
an
d
lo
wer
s
th
eir
v
o
ltag
e
s
tr
ess
an
d
d
v
/d
t
r
ate,
im
p
r
o
v
in
g
s
y
s
tem
r
eliab
ilit
y
.
Fo
r
th
e
s
am
e
o
u
tp
u
t
p
o
wer
lev
el,
th
e
m
o
r
e
s
tep
s
in
t
h
e
wav
ef
o
r
m
o
f
o
u
tp
u
t
v
o
ltag
e
h
a
v
e
th
e
b
en
ef
it
o
f
r
ed
u
cin
g
th
e
s
witch
in
g
d
ev
ices'
r
atin
g
wh
en
co
m
p
ar
ed
to
a
co
n
v
en
tio
n
a
l
co
n
v
er
ter
.
T
h
is
lo
wer
s
th
e
m
u
ltil
ev
el
in
v
er
ter
(
MLI
)
s
y
s
tem
'
s
co
s
t
an
d
s
ize
an
d
m
ak
es
it
m
o
r
e
p
ac
k
ag
ea
b
le
[
1
]
.
T
h
r
ee
m
ajo
r
c
ateg
o
r
ies
o
f
tr
ad
itio
n
al
ML
I
s
:
ca
s
ca
d
ed
H
-
b
r
i
d
g
e
m
u
ltil
ev
el
in
v
er
ter
s
(
C
HB
-
ML
I
s
)
,
f
ly
in
g
ca
p
ac
ito
r
m
u
ltil
ev
el
in
v
er
te
r
s
(
FC
-
ML
I
s
)
,
an
d
n
eu
tr
al
p
o
i
n
t d
io
d
e
clam
p
ed
m
u
ltil
ev
el
in
v
er
ter
s
(
NPC
-
ML
I
s
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
14
,
No
.
4
,
Dec
em
b
er
20
25
:
1
0
2
3
-
1
0
3
4
1024
H
y
b
r
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m
w
i
t
h
li
m
i
t
e
d
s
w
it
ch
e
s
a
n
d
DC
v
o
lt
a
g
e
s
o
u
r
c
e
s
.
R
e
g
a
r
d
i
n
g
t
h
is
,
n
u
m
e
r
o
u
s
t
o
p
o
l
o
g
i
es
wi
t
h
s
y
m
m
e
tr
i
c
a
l
a
n
d
a
s
y
m
m
et
r
i
c
a
l
c
o
n
f
i
g
u
r
a
t
i
o
n
s
h
a
v
e
b
e
e
n
p
r
e
s
e
n
t
e
d
[
2
]
,
[
3
]
.
S
e
v
e
r
a
l
i
n
n
o
v
a
t
i
v
e
t
o
p
o
l
o
g
i
es
w
i
t
h
a
r
a
n
g
e
o
f
a
p
p
l
i
c
at
i
o
n
s
h
a
v
e
b
e
e
n
p
u
b
l
i
s
h
e
d
i
n
t
h
is
f
i
eld
s
i
n
c
e
t
h
e
i
n
i
t
i
al
a
tt
e
m
p
t
a
t
t
h
e
M
L
I
w
a
s
p
r
o
v
i
d
e
d
i
n
1
9
8
1
w
i
t
h
t
h
r
e
e
-
l
ev
e
l
N
PC
.
T
h
e
a
u
t
h
o
r
s
i
n
[
4
]
-
[
7
]
p
r
e
s
e
n
t
e
d
n
e
w
M
L
I
t
o
p
o
l
o
g
i
e
s
w
i
t
h
1
3
a
n
d
1
7
le
v
e
l
s
o
f
o
u
t
p
u
t
a
n
d
d
i
f
f
e
r
e
n
t
m
o
d
u
l
a
t
i
o
n
s
c
h
e
m
es
,
a
n
d
t
h
e
y
a
r
e
s
u
i
t
a
b
le
f
o
r
r
e
n
e
w
a
b
l
e
a
p
p
l
ic
a
t
i
o
n
s
.
H
y
b
r
i
d
m
u
l
t
i
l
e
v
el
i
n
v
e
r
t
e
r
d
es
i
g
n
a
n
d
a
n
a
l
y
s
is
f
o
r
as
y
m
m
e
t
r
i
c
i
n
p
u
t
v
o
l
t
a
g
e
s
h
a
v
e
b
e
e
n
p
r
e
s
e
n
t
e
d
i
n
[
8
]
,
[
9
]
.
T
h
es
e
to
p
o
l
o
g
i
e
s
a
d
d
r
e
s
s
t
h
e
d
e
s
i
g
n
o
f
a
s
i
n
g
l
e
-
p
h
as
e
h
y
b
r
i
d
m
u
lti
l
e
v
e
l
i
n
v
e
r
t
e
r
f
o
r
a
s
t
a
n
d
a
l
o
n
e
s
y
s
t
e
m
u
s
i
n
g
a
s
y
m
m
e
t
r
i
c
a
l
v
o
lt
a
g
e
i
n
p
u
t
s
o
u
r
c
es
a
n
d
t
h
r
e
e
-
l
e
v
e
l
T
-
t
y
p
e
,
d
i
o
d
e
cl
a
m
p
e
d
l
e
g
s
,
a
n
d
H
-
b
r
i
d
g
e
M
L
I
.
I
n
c
o
m
p
a
r
is
o
n
to
t
r
a
d
i
t
i
o
n
al
t
o
p
o
l
o
g
i
es
,
th
i
s
ar
ch
itectu
r
e
r
eq
u
i
r
es
f
ewe
r
s
witch
es
t
o
r
e
a
c
h
t
h
e
o
u
t
p
u
t
v
o
l
t
a
g
e
l
e
v
e
l
.
A
n
as
y
m
m
e
t
r
i
c
c
o
n
f
i
g
u
r
a
ti
o
n
f
o
r
t
h
e
15
-
l
e
v
e
l
t
o
p
o
l
o
g
y
i
s
p
r
o
p
o
s
e
d
i
n
[
1
0
]
.
T
h
is
to
p
o
lo
g
y
n
atu
r
ally
p
r
o
d
u
ce
s
b
o
th
p
o
s
i
tiv
e
an
d
n
eg
ativ
e
c
y
cles
with
o
u
t
th
e
n
ee
d
f
o
r
an
e
x
tr
a
H
-
b
r
id
g
e
u
n
it,
th
u
s
lo
wer
in
g
th
e
in
v
er
ter
'
s
o
v
er
all
s
tan
d
in
g
v
o
ltag
e
.
A
r
ec
en
tly
d
esig
n
ed
m
u
ltil
ev
e
l
in
v
er
ter
with
a
h
ex
ad
v
o
ltag
e
-
b
o
o
s
tin
g
ca
p
a
b
ilit
y
h
as
b
ee
n
p
r
esen
ted
in
[
11
]
.
I
t
u
s
es
a
s
in
g
le
s
o
u
r
ce
with
ju
s
t
f
o
u
r
teen
s
witch
es,
t
w
o
d
i
o
d
e
s
,
a
n
d
f
o
u
r
c
a
p
a
c
i
t
o
r
s
t
o
c
r
e
a
t
e
a
1
3
-
l
e
v
e
l
w
a
v
e
f
o
r
m
.
B
y
co
n
n
ec
tin
g
th
e
DC
s
o
u
r
ce
an
d
c
a
p
ac
ito
r
s
in
p
ar
allel
at
m
u
ltip
le
p
o
in
ts
d
u
r
in
g
a
n
o
p
er
atio
n
a
l
cy
cle,
d
u
r
in
g
th
e
in
v
er
ter
'
s
s
wi
tch
in
g
,
p
r
o
p
er
m
a
g
n
itu
d
e
o
f
th
e
v
o
ltag
e
at
th
e
ca
p
ac
ito
r
s
is
m
ain
tain
ed
.
I
n
[
12
]
,
[
13
]
,
th
er
e
is
an
o
th
er
to
p
o
lo
g
y
th
at
aim
s
to
m
in
im
ize
th
e
n
u
m
b
er
o
f
s
witch
in
g
d
e
v
ices
.
A
p
r
o
to
ty
p
e
o
f
a
n
in
e
-
lev
el
q
u
ad
r
u
p
le
b
o
o
s
t
in
v
e
r
ter
(
NQBI)
to
p
o
lo
g
y
is
s
h
o
wn
i
n
[
14
]
,
wh
ich
r
u
n
s
o
n
a
s
in
g
l
e
s
o
lar
p
h
o
t
o
v
o
ltaic
s
o
u
r
ce
an
d
u
s
es
less
s
witch
es,
ca
p
ac
ito
r
s
,
an
d
d
io
d
es.
W
ith
th
e
h
elp
o
f
th
is
to
p
o
lo
g
y
,
th
e
v
o
ltag
es
o
f
th
e
two
ca
p
ac
ito
r
s
ar
e
ef
f
ec
tiv
ely
b
ala
n
ce
d
,
g
iv
in
g
th
e
o
u
tp
u
t
n
in
e
v
o
ltag
e
lev
els.
A
n
ew
m
u
ltil
ev
el
in
v
er
ter
to
p
o
lo
g
y
p
r
esen
ted
in
[
15
]
,
f
o
r
m
u
ltil
e
v
el
v
o
ltag
e
g
e
n
er
atio
n
,
s
tack
e
d
v
o
lta
g
e
s
o
u
r
ce
s
tak
en
f
r
o
m
s
in
g
le
DC
lin
k
an
d
s
er
ies
-
co
n
n
ec
ted
ca
p
ac
ito
r
s
.
A
d
etailed
an
aly
s
is
o
f
a
p
e
n
cil
-
s
h
ap
ed
(
PS
)
9
-
lev
el
i
n
v
er
ter
with
r
ed
u
ce
d
co
m
p
o
n
en
ts
th
at
was
co
n
s
tr
u
c
ted
with
ju
s
t
two
DC
s
o
u
r
ce
s
was
p
r
o
v
id
ed
i
n
[
16
]
.
An
an
al
y
s
is
o
f
th
e
b
en
ef
its
an
d
d
r
awb
ac
k
s
o
f
m
u
ltil
ev
el
i
n
v
er
ter
to
p
o
lo
g
ies
in
elec
tr
ic
v
eh
icle
ap
p
licatio
n
s
was
p
u
b
li
s
h
ed
in
[
17
]
.
A
n
ew
to
p
o
lo
g
y
an
d
s
u
r
v
ey
with
less
n
o
o
f
s
witch
in
g
d
ev
ices
wa
s
p
r
esen
ted
in
[
1
8
]
,
[
1
9
]
.
Mu
h
am
m
ad
et
a
l
.
[
20
]
p
r
esen
ted
an
a
d
ap
tiv
e
h
y
b
r
i
d
co
n
tr
o
l
s
tr
ateg
y
in
co
n
ju
n
cti
o
n
with
a
ca
s
ca
d
ed
r
ed
u
ce
d
s
witch
s
y
m
m
etr
ical
m
u
ltil
ev
el
in
v
er
ter
to
e
f
f
icien
tly
an
d
s
tead
ily
in
ject
p
o
wer
p
r
o
d
u
ce
d
f
r
o
m
d
is
tr
ib
u
ted
en
er
g
y
r
eso
u
r
ce
s
in
to
th
e
u
tili
ty
g
r
id
.
I
n
th
is
p
ap
er
,
a
u
n
iq
u
e
h
y
b
r
id
ML
I
to
p
o
lo
g
y
with
a
n
en
h
an
c
ed
H
-
b
r
i
d
g
e
u
n
it
is
p
r
esen
ted
.
T
h
is
s
etu
p
g
en
er
ates
an
o
u
tp
u
t
v
o
ltag
e
with
9
s
tep
s
u
s
in
g
ju
s
t
7
s
witch
es,
2
d
io
d
es,
an
d
2
DC
s
o
u
r
ce
s
.
C
o
m
p
ar
ed
to
th
e
tr
ad
itio
n
al
ap
p
r
o
ac
h
,
th
e
s
u
g
g
ested
s
y
s
tem
ac
h
iev
es
s
e
v
er
al
o
u
tp
u
t
s
tep
s
with
f
ew
er
co
m
p
o
n
e
n
ts
an
d
f
ac
ilit
ates
v
er
s
atile
o
p
er
atio
n
.
B
y
co
n
tr
asti
n
g
th
e
s
u
g
g
es
ted
s
y
s
tem
with
th
e
r
ec
en
tly
d
ev
elo
p
e
d
ML
I
to
p
o
lo
g
ies,
th
e
u
n
iq
u
en
ess
o
f
th
e
s
u
g
g
ested
s
y
s
tem
h
as
b
ee
n
d
em
o
n
s
tr
ated
.
T
h
e
s
u
g
g
ested
to
p
o
l
o
g
y
will
also
b
e
s
u
itab
le
f
o
r
o
th
er
d
o
m
ai
n
s
s
u
ch
as
r
e
n
ewa
b
le
e
n
er
g
y
(
s
o
lar
,
win
d
,
an
d
tid
al)
,
g
r
id
-
to
-
v
eh
icle
(
G2
V)
,
an
d
v
eh
icle
-
to
-
g
r
id
(
V
2
G)
.
T
h
is
to
p
o
lo
g
y
o
u
tp
e
r
f
o
r
m
ed
th
e
o
th
er
d
esig
n
s
wh
en
th
e
n
u
m
b
er
o
f
d
is
tin
ct
co
m
p
o
n
en
ts
was c
o
n
s
id
er
ed
.
T
h
is
p
ap
er
is
d
iv
id
ed
s
tr
u
ct
u
r
ally
as
f
o
llo
ws:
Sectio
n
1
p
r
esen
ts
a
liter
atu
r
e
r
ev
iew
an
d
an
in
tr
o
d
u
ctio
n
h
as
b
ee
n
p
r
o
v
i
d
ed
;
th
e
ex
is
tin
g
an
d
s
u
g
g
e
s
ted
h
y
b
r
id
s
y
s
tem
,
in
clu
d
i
n
g
its
s
tr
u
ctu
r
e
an
d
s
witch
in
g
s
ce
n
ar
io
s
,
is
d
escr
ib
ed
in
s
ec
tio
n
2
.
T
o
illu
s
tr
ate
th
e
m
ajo
r
f
ea
tu
r
es
o
f
th
e
s
u
g
g
ested
s
y
s
tem
,
s
ec
tio
n
3
will
c
o
m
p
a
r
e
it
wit
h
a
f
ew
c
u
r
r
en
t
to
p
o
lo
g
ies.
S
ec
tio
n
4
h
as
o
u
tlin
ed
th
e
v
ar
i
o
u
s
co
n
tr
o
l
m
eth
o
d
s
f
o
r
th
e
s
u
g
g
ested
s
y
s
tem
.
I
n
s
ec
tio
n
5
,
th
e
r
esu
lts
an
d
th
e
d
is
cu
s
s
io
n
ar
e
g
iv
en
.
I
n
s
ec
tio
n
6
,
th
e
wo
r
k
'
s
co
n
clu
s
io
n
is
p
r
esen
ted
.
2.
NE
W
T
O
P
O
L
O
G
I
CA
L
H
Y
B
RID
M
U
L
T
I
L
E
V
E
L
I
NVE
RT
E
R
(
H
M
L
I
)
2
.
1
.
Desig
n o
f
t
he
s
y
s
t
em
T
h
e
s
u
g
g
ested
n
o
v
el
n
i
n
e
-
le
v
el
h
y
b
r
id
m
u
ltil
ev
el
in
v
er
te
r
s
y
s
tem
is
d
ep
icted
in
Fig
u
r
e
1
.
T
h
e
s
u
g
g
e
s
t
e
d
d
esig
n
in
clu
d
ed
th
r
ee
d
io
d
es,
D1
,
D2
,
D3
,
an
d
t
wo
DC
s
o
u
r
ce
s
(
Vd
c1
=
3
V
an
d
Vd
c
2
=
V
)
,
in
ad
d
itio
n
to
s
ev
en
p
o
wer
s
witch
es
(
S1
to
S7
)
.
As
a
r
esu
lt,
th
is
to
p
o
lo
g
y
f
alls
in
to
th
e
g
r
o
u
p
o
f
asy
m
m
etr
ical
ML
I
to
p
o
l
o
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it r
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tes.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
A
s
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l n
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Fig
u
r
e
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Diag
r
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m
illu
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tr
atin
g
th
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s
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g
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ested
1
9
L
h
y
b
r
id
ML
I
ar
ch
itectu
r
e
2
.
2
.
M
o
des
o
f
o
pera
t
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n o
f
p
ro
po
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s
y
s
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em
T
h
e
p
r
o
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o
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ed
s
tr
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e
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d
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ed
to
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ate
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v
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r
m
o
f
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t
v
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ltag
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with
n
in
e
lev
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estricte
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q
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tity
o
f
s
witch
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g
d
ev
ices
an
d
d
c
v
o
ltag
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s
o
u
r
ce
s
.
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r
th
is
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o
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y
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tal
o
f
f
o
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r
p
o
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f
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n
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ativ
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els,
an
d
o
n
e
ze
r
o
lev
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s
witch
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g
s
tate
h
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e
r
esu
lted
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th
e
p
r
o
d
u
ctio
n
o
f
n
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e
d
is
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ct
s
witch
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g
s
tates.
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v
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el
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clu
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th
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m
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s
t
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r
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e
d
ON
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ch
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e
d
esire
d
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el.
Fig
u
r
e
2
p
r
o
v
id
es
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d
etailed
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atio
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o
f
ea
ch
o
f
th
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witch
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g
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ce
n
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io
s
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ep
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ately
.
(
a)
(
b
)
(
c)
(
d
)
(
e)
(f)
(
g
)
(
h
)
Fig
u
r
e
2
.
Deta
iled
o
p
er
atio
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9
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ML
I
at
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er
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t le
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els
: (
a)
Vo
=V
d
c1
,
(
b
)
Vo
=V
d
c2
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(
c)
Vo
=V
d
c1
-
Vd
c2
,
(
d
)
Vo
=V
d
c1
+V
d
c2
,
(
e)
Vo
=
-
Vd
c1
,
(
f
)
Vo
=
-
Vd
c2
,
(
g
)
Vo
=
-
(
Vd
c1
-
Vd
c2
)
,
a
n
d
(
h
)
Vo
=
-
(
Vd
c1
+V
d
c
2
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
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t J Ap
p
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E
n
g
,
Vo
l.
14
,
No
.
4
,
Dec
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er
20
25
:
1
0
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3
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1
0
3
4
1026
T
ab
le
1
s
h
o
ws
th
e
elem
en
ts
t
h
at
ca
n
b
e
u
s
ed
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ch
le
v
el
g
en
er
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n
p
r
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ce
d
u
r
e
[
1
]
.
Fro
m
T
ab
le
1
,
th
e
s
witch
in
g
o
p
er
atio
n
f
o
r
d
if
f
er
en
t
o
u
tp
u
t
lev
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s
h
o
wn
in
Fig
u
r
e
3
.
Fo
r
p
o
s
itiv
e
cy
c
le
th
e
s
witch
es
S1
,
S2
,
S5
,
S6
,
a
n
d
S7
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e
in
O
N
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o
s
itio
n
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n
d
r
em
ain
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n
g
s
w
itch
es
ar
e
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OFF
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o
s
itio
n
,
w
h
er
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s
f
o
r
n
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ativ
e
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cle
s
witch
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S3
,
S4
,
S5
,
S6
,
an
d
S7
ar
e
in
ON
p
o
s
itio
n
an
d
r
em
ain
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g
s
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e
in
OFF
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o
s
itio
n
.
Switch
es
S1
,
S3
,
o
r
S2
,
S4
ar
e
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ON
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o
s
itio
n
an
d
th
e
r
e
m
ain
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g
s
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ar
e
in
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p
o
s
itio
n
to
g
et
ze
r
o
v
o
ltag
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at
th
e
lo
a
d
.
T
ab
le
1
.
Var
io
u
s
o
p
er
atin
g
s
tag
es f
o
r
th
e
s
u
g
g
ested
s
y
s
tem
S
w
i
t
c
h
i
n
g
st
a
t
e
s
V
o
u
t
C
l
o
se
d
l
o
o
p
C
u
r
r
e
n
t
p
a
t
h
1
V
dc
1
+V
d
c
2
S
1
,
S
2
,
S
5
,
a
n
d
S
7
2
V
dc
1
S
1
,
S
2
,
S
7
,
a
n
d
D
2
3
V
dc
1
-
V
dc
2
S
1
,
S
2
,
S
6
,
D
2
,
a
n
d
D
3
4
V
dc
2
S
1
,
S
2
,
S
5
,
a
n
d
D
1
5
0
S
1
,
S
3
o
r
S
2
,
S
4
6
-
V
dc
2
S
3
,
S
4
,
S
5
,
a
n
d
D
1
7
-
(V
dc
1
-
V
dc
2
)
S
3
,
S
4
,
S
6
,
D
2
,
a
n
d
D
3
8
-
V
dc
1
S
3
,
S
4
,
S
7
,
a
n
d
D
2
9
-
(V
dc
1
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dc
2
)
S
3
,
S
4
,
S
5
,
a
n
d
S
7
F
ig
u
r
e
3
.
Switch
in
g
s
ch
em
e
f
o
r
o
n
e
c
y
cle
2
.
3
.
Co
m
pu
t
ing
t
he
t
o
t
a
l st
a
nd
ing
v
o
lt
a
g
e
(
T
SV)
T
h
e
s
elec
tio
n
o
f
a
p
o
wer
d
e
v
i
ce
is
s
ig
n
if
ican
tly
in
f
lu
en
ce
d
b
y
th
e
v
o
ltag
e
s
tr
ess
ac
r
o
s
s
th
e
s
witch
es
.
Gen
er
ally
,
to
tal
s
tan
d
in
g
v
o
lt
ag
e
(
T
SV)
is
th
e
o
v
er
all
v
o
l
tag
e
s
tr
ess
ac
r
o
s
s
all
p
o
wer
s
witch
in
g
d
ev
ices,
ac
co
u
n
tin
g
f
o
r
all
v
o
ltag
e
s
tep
s
T
SV [
1
]
.
=
∑
=
1
(
1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
A
s
ymm
etri
ca
l n
in
e
-
leve
l h
yb
r
id
mu
ltil
ev
el
in
ve
r
ter d
esig
n
a
n
d
a
n
a
lysi
s
fo
r
… (
Gerr
i R
a
tn
a
ia
h
)
1027
W
h
er
e
is
th
e
n
u
m
b
er
o
f
p
o
we
r
s
witch
in
g
d
ev
ices.
T
h
er
e
ar
e
7
s
witch
in
g
d
ev
ices in
th
e
s
u
g
g
ested
to
p
o
lo
g
y
,
s
o
th
at
(
1
)
ca
n
b
e
m
o
d
if
ied
as
(
2
)
.
=
∑
7
=
1
=
1
+
2
+
3
+
4
+
5
+
6
+
7
(
2
)
On
e
im
p
o
r
tan
t
co
m
p
o
n
en
t
o
f
th
e
to
p
o
lo
g
y
d
esig
n
is
th
e
v
o
ltag
e
s
tr
ess
o
n
th
e
s
witc
h
es.
T
h
e
s
u
g
g
ested
s
tr
u
ctu
r
e
is
s
h
o
wn
in
Fig
u
r
e
1
with
th
e
m
a
g
n
itu
d
e
o
f
DC
s
o
u
r
ce
s
as
Vd
c2
=
V,
Vd
c
1
=
3
V,
th
e
s
witch
es'
v
o
ltag
e
s
tr
ess
is
g
iv
en
b
y
(
3
)
a
n
d
(
4
)
.
1
+
2
+
3
+
4
=
1
+
2
=
3
+
=
4
(
3
)
5
+
6
+
7
=
2
=
(
4
)
C
o
n
s
id
er
in
g
th
e
a
b
o
v
e
e
q
u
ati
o
n
s
,
th
e
T
SV
o
f
th
e
p
r
o
p
o
s
ed
to
p
o
lo
g
y
is
1
9
V
[
1
]
.
T
SV
is
a
m
ea
s
u
r
em
en
t
o
f
ea
ch
s
witch
's
p
er
-
u
n
it
v
o
ltag
e
s
tr
ess
.
I
t
is
th
e
r
elatio
n
s
h
ip
b
etwe
en
th
e
s
witch
es
'
p
ea
k
v
o
ltag
e
s
tr
ess
e
s
o
f
all
s
witch
es a
n
d
p
ea
k
o
u
t
p
u
t v
o
ltag
e
[
4
]
.
T
SV
in
p
.
u
ca
lcu
latio
n
is
g
iv
en
in
(
5
)
.
=
1
+
2
+
3
+
4
+
5
+
6
+
7
1
+
2
=
4
.
75
(
5
)
3.
CO
M
P
ARA
T
I
V
E
S
T
UDY
T
h
e
p
r
o
p
o
s
ed
to
p
o
lo
g
y
m
ain
l
y
co
n
s
is
ts
o
f
two
d
c
v
o
ltag
e
s
o
u
r
ce
s
,
f
iv
e
d
r
iv
i
n
g
cir
c
u
its
,
an
d
s
ev
en
p
o
wer
s
witch
es.
T
h
e
co
m
p
ar
i
s
o
n
with
th
e
m
ajo
r
ity
o
f
th
e
m
o
s
t
r
ec
en
t
to
p
o
l
o
g
ies
is
d
is
p
lay
ed
i
n
T
a
b
le
2
.
W
ith
th
e
ex
ce
p
tio
n
o
f
th
e
to
p
o
lo
g
ies
o
f
f
e
r
ed
in
t
h
e
p
u
b
licatio
n
s
[
2
1
]
-
[
3
3
]
,
th
e
s
u
g
g
ested
to
p
o
lo
g
y
h
as
less
co
m
p
o
n
en
ts
o
v
er
all.
Fewer
s
witch
es,
d
r
iv
er
cir
cu
its
,
an
d
DC
s
o
u
r
ce
s
,
as
well
a
s
th
r
e
e
d
io
d
es
an
d
ze
r
o
ca
p
ac
ito
r
s
,
all
co
n
tr
ib
u
te
to
th
e
s
u
g
g
ested
to
p
o
lo
g
y
'
s
r
ed
u
ce
d
cir
cu
it
f
o
o
t
p
r
in
t
an
d
in
cr
ea
s
ed
to
p
o
lo
g
y
d
ep
en
d
a
b
ilit
y
.
Sam
e
n
u
m
b
er
o
f
p
o
wer
elec
tr
o
n
ic
s
witch
es
in
th
e
to
p
o
lo
g
y
p
r
esen
ted
in
[
3
0
]
,
[
3
2
]
,
b
u
t
[
3
2
]
h
as
m
o
r
e
DC
s
o
u
r
ce
s
th
an
th
e
p
r
o
p
o
s
ed
t
o
p
o
lo
g
y
.
T
h
e
T
SV
an
d
co
s
t
f
ac
to
r
ar
e
also
less
co
m
p
ar
e
d
to
o
th
er
to
p
o
lo
g
ies.
A
m
u
ltil
ev
el
in
v
er
ter
'
s
co
s
t
f
a
cto
r
(
C
F)
is
d
eter
m
in
ed
b
y
th
e
p
r
o
d
u
ct
o
f
T
SV
with
a
co
n
s
tan
t
σ
an
d
th
e
co
s
t
o
f
its
co
m
p
o
n
en
t
p
ar
t
s
.
σ
=
0
.
5
a
n
d
σ
=
1
.
5
ar
e
th
e
co
n
s
tan
t
v
alu
es
c
h
o
s
en
f
o
r
th
e
co
m
p
a
r
is
o
n
th
at
is
s
h
o
wn
b
elo
w.
T
h
e
co
s
t c
o
m
p
o
n
en
t is ca
lcu
lated
as
(
6
)
[
4
]
.
(
)
=
+
+
+
+
+
×
(
6
)
Fro
m
T
ab
le
2
,
th
e
co
m
p
ar
ati
v
e
s
tu
d
y
p
r
esen
ted
i
n
Fig
u
r
e
4
.
T
h
e
X
-
ax
is
is
ta
k
en
as
m
u
ltil
ev
el
in
v
er
ter
to
p
o
lo
g
ies an
d
Y
-
a
x
is
is
tak
en
as n
u
m
b
er
o
f
s
witch
es in
Fig
u
r
e
4
(
a)
,
th
e
n
u
m
b
er
o
f
g
ate
d
r
iv
e
cir
cu
its
in
Fig
u
r
e
4
(
b
)
,
th
e
n
u
m
b
e
r
o
f
ca
p
ac
ito
r
s
in
Fig
u
r
e
4
(
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20
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(
a)
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b
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c)
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d
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e)
Fig
u
r
e
4
.
C
o
m
p
a
r
in
g
ML
I
t
o
p
o
lo
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ies with
(
a)
n
u
m
b
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r
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w
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b
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ate
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m
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SV,
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d
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c
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t f
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r
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M
O
DUL
AT
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N
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CH
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I
n
a
n
ML
I
,
th
e
p
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im
ar
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ate
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s
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at
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s
in
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s
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m
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v
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HD
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th
e
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ca
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d
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in
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ased
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MCS
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t
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d
m
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1
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ag
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th
e
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MI
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m
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u
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s
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ase
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M
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u
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s
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[
3
4
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.
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I
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8
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Ph
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d
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u
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Ph
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RE
SU
L
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AND
D
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T
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D
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h
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9
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s
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if
f
er
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n
t
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
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8
7
9
2
I
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p
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n
g
,
Vo
l.
14
,
No
.
4
,
Dec
em
b
er
20
25
:
1
0
2
3
-
1
0
3
4
1030
m
o
d
u
latio
n
tech
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iq
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es
,
PDPW
M,
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DP
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d
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M,
wer
e
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lo
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ed
in
th
is
r
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ap
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.
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u
r
e
8
s
h
o
ws
o
u
tp
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t
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d
o
u
tp
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t
cu
r
r
e
n
t
u
s
in
g
PDPW
M
s
ch
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e
.
Fig
u
r
e
9
s
h
o
ws
o
u
tp
u
t
v
o
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a
n
d
o
u
tp
u
t
cu
r
r
e
n
t
u
s
in
g
PDPW
M
s
ch
em
e
with
a
f
ilter
.
Fig
u
r
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1
0
s
h
o
ws
o
u
tp
u
t
v
o
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e
an
d
o
u
tp
u
t
cu
r
r
e
n
t
u
s
in
g
PODP
W
M
s
ch
em
e
.
Fig
u
r
e
1
1
s
h
o
ws
o
u
tp
u
t
v
o
ltag
e
an
d
o
u
tp
u
t
cu
r
r
en
t
u
s
in
g
PODPW
M
s
ch
em
e
with
f
ilter
.
Fig
u
r
e
1
2
s
h
o
ws
o
u
t
p
u
t
v
o
lta
g
e
an
d
o
u
tp
u
t
cu
r
r
en
t
u
s
in
g
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W
M
s
ch
em
e
,
an
d
Fig
u
r
e
1
3
s
h
o
ws
o
u
tp
u
t
v
o
ltag
e
an
d
o
u
tp
u
t
c
u
r
r
e
n
t
u
s
in
g
APODPW
M
s
ch
em
e
with
f
ilter
.
T
o
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
(
T
HD)
is
ca
lcu
lated
u
s
in
g
FF
T
an
aly
s
is
in
MA
T
L
AB
/Si
m
u
lin
k
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d
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m
p
a
r
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o
n
r
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e
tab
u
lated
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T
ab
le
3
.
Fig
u
r
e
1
4
s
h
o
ws
T
HD
an
aly
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is
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o
r
PDP
W
M,
Fig
u
r
e
1
5
s
h
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ws
T
HD
an
aly
s
is
f
o
r
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W
M
,
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d
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u
r
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1
6
s
h
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ws
T
HD
an
aly
s
i
s
f
o
r
APO
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ter
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m
p
ar
is
o
n
o
f
th
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ee
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n
tr
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l
s
ch
em
es,
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tech
n
iq
u
e
h
as
lo
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T
HD.
(
a)
(
b
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F
ig
u
r
e
8
.
Su
g
g
ested
HM
L
I
wi
th
PDPW
M
tech
n
iq
u
e:
(
a)
o
u
t
p
u
t
v
o
ltag
e
(V
0
)
an
d
(
b
)
o
u
t
p
u
t c
u
r
r
en
t
(I
0
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(
a)
(
b
)
F
ig
u
r
e
9
.
Su
g
g
ested
HM
L
I
wi
th
PDPW
M
tech
n
iq
u
e
u
s
in
g
f
i
lter
:
(
a)
o
u
tp
u
t v
o
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e
(V
0
)
an
d
(
b
)
o
u
tp
u
t c
u
r
r
en
t
(I
0
)
(
a)
(
b
)
Fig
u
r
e
10
.
Su
g
g
ested
HM
L
I
w
ith
PODP
W
M
tech
n
iq
u
e:
(
a)
o
u
tp
u
t v
o
ltag
e
(V
0
)
an
d
(
b
)
o
u
tp
u
t c
u
r
r
en
t
(I
0
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
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E
n
g
I
SS
N:
2252
-
8
7
9
2
A
s
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l n
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ter d
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n
d
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a
lysi
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Gerr
i R
a
tn
a
ia
h
)
1031
(
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(
b
)
Fig
u
r
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1
1
.
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g
g
ested
HM
L
I
w
ith
PODP
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M
tech
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iq
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e
u
s
in
g
f
ilter
: (
a)
o
u
tp
u
t v
o
ltag
e
(V
0
)
an
d
(
b
)
o
u
tp
u
t c
u
r
r
en
t
(I
0
)
(
a)
(
b
)
F
ig
u
r
e
12
.
Su
g
g
ested
HM
L
I
w
ith
APODP
W
M
tech
n
iq
u
e:
(
a)
o
u
tp
u
t
v
o
ltag
e
(V
0
)
an
d
(
b
)
o
u
tp
u
t c
u
r
r
en
t
(I
0
)
(
a)
(
b
)
F
ig
u
r
e
13
.
Su
g
g
ested
HM
L
I
w
ith
APODP
W
M
tech
n
iq
u
e
u
s
in
g
f
ilter
: (
a)
o
u
tp
u
t v
o
ltag
e
(V
0
)
an
d
(
b
)
o
u
tp
u
t c
u
r
r
en
t
(I
0
)
Fig
u
r
e
1
4
.
T
HD
an
aly
s
is
o
f
th
e
p
r
o
p
o
s
ed
HM
L
I
with
PDPW
M
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
14
,
No
.
4
,
Dec
em
b
er
20
25
:
1
0
2
3
-
1
0
3
4
1032
F
ig
u
r
e
15
.
T
HD
an
aly
s
is
o
f
th
e
p
r
o
p
o
s
ed
HM
L
I
with
PODPW
M
Fig
u
r
e
1
6
.
T
HD
an
aly
s
is
o
f
th
e
p
r
o
p
o
s
ed
HM
L
I
with
APODPW
M
T
ab
le
3
.
C
o
m
p
a
r
is
o
n
o
f
T
HD
an
aly
s
is
TH
D
%
PD
-
PWM
P
O
D
-
PWM
A
P
O
D
-
PWM
1
2
.
0
4
1
0
.
2
0
1
3
.
4
9
6.
CO
NCLU
SI
O
N
T
h
is
s
tu
d
y
p
r
esen
ts
a
n
o
v
el
h
y
b
r
id
m
u
ltil
ev
el
in
v
er
ter
to
p
o
lo
g
y
.
I
n
o
r
d
er
to
p
r
o
v
id
e
an
o
u
tp
u
t
v
o
ltag
e,
th
is
n
in
e
-
s
tag
e
d
esig
n
r
eq
u
ir
es
two
DC
s
u
p
p
lies
,
th
r
ee
d
io
d
es,
an
d
s
ev
en
p
o
wer
s
witch
es.
Nu
m
er
o
u
s
p
r
o
p
er
ties
wer
e
p
r
esen
t
in
th
e
s
u
g
g
ested
h
y
b
r
id
s
y
s
tem
,
in
c
lu
d
in
g
lo
w
v
o
ltag
e
s
tr
ess
o
n
t
h
e
p
o
wer
s
witch
es
an
d
a
h
ig
h
o
u
tp
u
t
v
o
ltag
e
n
u
m
b
er
o
f
s
tep
s
with
f
ewe
r
s
witch
es.
T
h
e
p
ap
er
c
o
n
tain
s
th
e
c
o
n
clu
s
io
n
s
f
o
r
e
v
er
y
f
o
r
m
u
la
th
at
was
u
tili
ze
d
to
r
eg
u
late
th
e
s
y
s
tem
ex
p
an
s
io
n
'
s
o
p
er
atio
n
.
Sev
er
al
c
u
r
r
e
n
t
ML
I
to
p
o
lo
g
ies
h
av
e
b
ee
n
co
m
p
ar
e
d
to
th
e
s
u
g
g
e
s
ted
to
p
o
lo
g
y
i
n
ter
m
s
o
f
s
witch
es,
d
io
d
es,
s
o
u
r
ce
s
,
lev
els,
an
d
c
o
s
t
f
ac
to
r
.
Ad
d
itio
n
ally
,
th
is
co
m
p
ar
is
o
n
b
r
o
u
g
h
t
th
e
s
u
g
g
ested
s
y
s
tem
'
s
r
o
b
u
s
tn
ess
ch
ar
ac
ter
is
ti
cs
to
lig
h
t.
T
h
r
ee
d
is
tin
ct
co
n
tr
o
llin
g
s
tr
ateg
ies
,
th
e
PDPW
M,
PODP
W
M
,
an
d
APODPW
M
co
n
tr
o
l
s
ch
em
es
h
av
e
b
ee
n
u
s
ed
to
co
n
d
u
ct
th
e
s
im
u
latio
n
test
.
E
x
ce
llen
t
r
esu
lts
ar
e
o
b
tain
ed
f
o
r
th
r
ee
tech
n
iq
u
es,
an
d
T
HD
o
b
tain
ed
u
s
in
g
FF
T
an
d
m
ee
ts
th
e
h
a
r
m
o
n
ics s
tan
d
ar
d
.
F
UNDING
I
NF
O
R
M
A
T
I
O
N
Au
th
o
r
s
s
tate
n
o
f
u
n
d
in
g
in
v
o
lv
ed
.
Evaluation Warning : The document was created with Spire.PDF for Python.