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Mu
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ML
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s
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ality
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s
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in
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p
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d
m
ed
i
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m
-
v
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ltag
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ap
p
licatio
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s
[
1
]
-
[
3
]
.
T
h
e
k
ey
b
en
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its
o
f
m
u
ltil
ev
el
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v
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[
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[
7
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ted
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[
8
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-
[
9
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.
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1
1
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.
On
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in
m
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HD)
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I
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Ma
in
tain
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is
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to
in
cr
ea
s
e
s
y
s
tem
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f
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,
r
ed
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ce
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es
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d
im
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al
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ality
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B
y
m
in
im
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th
e
T
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n
o
t
o
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l
y
is
th
e
in
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p
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I
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5
1
9
with
g
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co
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n
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p
p
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s
,
r
en
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b
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s
,
an
d
in
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s
tr
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o
to
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d
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Sin
u
s
o
id
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ls
e
wid
th
m
o
d
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latio
n
(
SP
W
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is
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e
o
f
th
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m
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s
t
co
m
m
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ly
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s
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co
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tr
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s
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d
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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&
Dr
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N:
2088
-
8
6
9
4
A
n
a
lysi
s
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f c
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s
ca
d
ed
H
-
B
r
id
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mu
ltil
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s
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s
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S
P
WM
w
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…
(
A
z
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A
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s
)
1741
to
its
s
im
p
licity
an
d
ef
f
ec
tiv
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n
ess
in
g
en
er
atin
g
s
m
o
o
th
o
u
t
p
u
t
wav
ef
o
r
m
s
[
1
2
]
,
[
1
3
]
.
Ho
wev
er
,
co
n
v
en
tio
n
al
SP
W
M
tech
n
iq
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es,
p
ar
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s
in
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g
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to
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ize
T
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wh
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p
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s
.
Pre
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s
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th
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d
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ca
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ier
SP
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M,
s
elec
t
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h
ar
m
o
n
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elim
in
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(
SHE)
,
an
d
s
p
ac
e
v
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to
r
m
o
d
u
latio
n
(
SVM)
,
ea
ch
with
ad
v
an
tag
es
an
d
lim
itatio
n
s
[
1
4
]
-
[
1
6
]
.
Fo
r
in
s
tan
ce
,
SVM
p
r
o
v
id
es
b
etter
h
ar
m
o
n
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ed
u
ctio
n
b
u
t
in
v
o
lv
es
co
m
p
lex
co
m
p
u
tatio
n
s
[
1
5
]
,
wh
ile
SHE
r
eq
u
ir
es
s
o
lv
in
g
n
o
n
lin
ea
r
eq
u
atio
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s
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m
ak
i
n
g
r
e
al
-
tim
e
im
p
lem
en
tatio
n
ch
alle
n
g
in
g
[
1
6
]
-
[
1
7
]
,
an
d
im
p
lem
en
tatio
n
o
f
m
u
lti
-
ca
r
r
ier
SP
W
M
r
eq
u
ir
es
co
m
p
le
x
co
m
p
u
tatio
n
al
p
r
o
ce
s
s
in
g
b
ec
au
s
e
it
u
tili
ze
s
m
u
ltip
le
ca
r
r
ier
s
to
g
eth
er
with
co
m
p
a
r
is
o
n
lo
g
ic
[
1
8
]
.
Desp
ite
th
ese
ad
v
a
n
ce
s
,
f
u
r
th
er
im
p
r
o
v
em
en
ts
in
T
HD
r
ed
u
ctio
n
an
d
v
o
ltag
e
q
u
ality
ar
e
n
ee
d
ed
f
o
r
h
ig
h
-
p
er
f
o
r
m
an
ce
ap
p
licatio
n
s
.
Pre
v
io
u
s
wo
r
k
s
in
d
icate
th
at
in
cr
ea
s
in
g
th
e
n
u
m
b
er
o
f
lev
el
s
in
C
HM
I
s
im
p
r
o
v
es
v
o
ltag
e
q
u
ality
b
u
t
also
in
c
r
ea
s
es
cir
cu
it
co
m
p
lex
ity
a
n
d
co
m
p
u
tatio
n
al
d
em
a
n
d
f
o
r
co
n
tr
o
l
tec
h
n
iq
u
es
[
1
0
]
-
[
1
1
]
,
[
1
9
]
.
A
d
d
itio
n
ally
,
ex
is
tin
g
s
tu
d
ies
lack
a
co
m
p
r
eh
e
n
s
iv
e
co
m
p
ar
is
o
n
o
f
h
o
w
a
m
u
lti
-
s
in
u
s
o
id
al
r
ef
e
r
e
n
ce
in
SP
W
M
af
f
ec
ts
th
e
p
er
f
o
r
m
an
ce
o
f
C
HM
I
s
ac
r
o
s
s
d
if
f
er
en
t le
v
els.
T
h
is
s
tu
d
y
p
r
esen
ts
a
co
m
p
ar
ativ
e
an
aly
s
is
o
f
C
HM
I
w
ith
m
u
lti
-
r
ef
e
r
en
ce
s
in
u
s
o
i
d
a
l
SP
W
M
,
ex
p
lo
r
in
g
its
p
er
f
o
r
m
an
ce
ac
r
o
s
s
f
iv
e,
s
ev
en
,
n
in
e,
elev
en
,
t
h
ir
teen
,
an
d
f
if
tee
n
lev
els.
T
h
e
k
ey
co
n
tr
ib
u
tio
n
s
o
f
th
is
wo
r
k
in
clu
d
e:
i
)
Pro
p
o
s
in
g
a
m
o
d
if
ied
SP
W
M
tech
n
iq
u
e
th
at
em
p
lo
y
s
m
u
ltip
le
r
ef
er
en
ce
s
in
u
s
o
id
al
s
ig
n
als
in
s
tead
o
f
a
s
in
g
le
r
ef
e
r
en
ce
,
e
n
h
an
ci
n
g
v
o
ltag
e
q
u
ali
ty
an
d
r
e
d
u
cin
g
T
HD
[
2
0
]
-
[
2
3
]
;
ii
)
Per
f
o
r
m
in
g
a
d
etailed
p
er
f
o
r
m
an
ce
ev
alu
atio
n
th
r
o
u
g
h
MA
T
L
AB
Simu
lin
k
s
im
u
latio
n
s
to
an
aly
ze
h
o
w
d
if
f
er
en
t
in
v
er
te
r
lev
els
af
f
ec
t
T
HD
an
d
wav
ef
o
r
m
q
u
ality
[
2
4
]
;
an
d
iii
)
C
o
m
p
ar
in
g
th
e
r
esu
lts
with
co
n
v
en
tio
n
al
SP
W
M
tech
n
iq
u
es,
d
em
o
n
s
tr
atin
g
th
a
t
th
e
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
ac
h
i
ev
es
lo
wer
T
HD
an
d
im
p
r
o
v
ed
v
o
ltag
e
p
r
o
f
iles
,
m
ak
in
g
it su
itab
le
f
o
r
h
ig
h
-
p
o
wer
ap
p
licatio
n
s
[
1
1
]
,
[
2
4
]
,
[
2
5
]
.
2.
CIRCU
I
T
CO
NF
I
G
URA
T
I
O
N
O
F
CASCADED H
-
B
RI
DG
E
I
NV
E
R
T
E
R
S
T
h
e
to
p
o
lo
g
y
o
f
th
e
ca
s
ca
d
e
d
C
HM
I
is
f
o
r
m
ed
b
y
ca
s
ca
d
in
g
H
-
b
r
id
g
e
co
n
v
en
tio
n
al
i
n
v
er
ter
s
,
as
d
ep
icted
in
Fig
u
r
e
1
.
T
h
e
s
witch
in
g
s
tates
an
d
o
u
tp
u
t
v
o
lta
g
e
VAB
o
f
th
e
H
-
b
r
id
g
e
in
v
e
r
ter
ar
e
d
ep
icted
in
T
ab
le
1
.
T
h
e
lev
el
o
f
th
e
C
H
MI
is
d
eter
m
in
ed
u
s
in
g
th
e
f
o
r
m
u
la
=2
+1
,
wh
e
r
e
n
r
ep
r
e
s
en
ts
th
e
n
u
m
b
er
o
f
lev
els in
th
e
in
v
er
ter
,
m
is
th
e
n
u
m
b
er
o
f
d
is
tin
ct
DC
s
o
u
r
ce
s
,
an
d
s
=2
(
n
−
1
)
is
u
s
ed
to
ca
lcu
late
th
e
n
u
m
b
er
o
f
s
witch
es
r
eq
u
ir
ed
f
o
r
a
g
i
v
en
lev
el
o
f
C
HM
I
[
2
5
]
.
T
h
e
co
m
p
ar
is
o
n
o
f
co
m
p
o
n
e
n
t
r
eq
u
i
r
em
en
ts
f
o
r
5
to
1
5
lev
els
o
f
th
e
ca
s
ca
d
ed
H
-
b
r
id
g
e
in
v
er
te
r
is
p
r
o
v
i
d
ed
in
T
ab
le
2
.
Fig
u
r
e
2
s
h
o
ws
th
e
c
o
n
f
ig
u
r
atio
n
o
f
th
e
ca
s
ca
d
ed
H
-
b
r
i
d
g
e
in
v
er
ter
p
e
r
p
h
ase
f
o
r
5
,
9
,
a
n
d
1
5
lev
el
s
.
T
h
e
o
u
tp
u
t
v
o
ltag
e
(
V
AB
)
is
th
e
s
u
m
m
atio
n
o
f
ea
ch
o
u
tp
u
t
f
r
o
m
ea
ch
H
-
b
r
id
g
e
in
v
er
ter
.
Fo
r
a
t
h
r
ee
-
p
h
ase
s
y
s
tem
,
th
e
o
u
tp
u
t
o
f
th
r
ee
id
en
tical
s
tr
u
ctu
r
es
o
f
s
in
g
le
-
p
h
ase
C
HM
I
ca
n
b
e
co
n
n
ec
ted
in
eith
e
r
a
wy
e
o
r
d
elt
a
co
n
f
ig
u
r
atio
n
.
Fig
u
r
e
3
illu
s
tr
ates
th
e
s
ch
e
m
atic
d
iag
r
am
o
f
a
wy
e
-
co
n
n
ec
ted
m
-
lev
el
C
HM
I
with
s
ep
ar
ate
DC
s
o
u
r
ce
s
(
v
d
c)
f
o
r
a
5
-
lev
el
C
HM
I
.
T
h
e
lin
e
v
o
ltag
es
ar
e
ex
p
r
ess
ed
in
ter
m
s
o
f
two
-
p
h
ase
v
o
ltag
es.
Fo
r
in
s
tan
ce
,
th
e
v
o
ltag
e
b
etwe
en
p
h
ase
A
an
d
p
h
ase
B
,
d
en
o
te
d
as
,
is
ca
lcu
lated
u
s
in
g
th
e
(
1
)
:
=
−
(
1
)
wh
er
e,
is
th
e
lin
e
v
o
lta
g
e
is
th
e
v
o
ltag
e
o
f
p
h
ase
A
with
r
esp
ec
t
to
th
e
n
eu
tr
al
p
o
in
t
N,
is
th
e
v
o
ltag
e
o
f
p
h
ase
B
with
r
esp
e
ct
to
th
e
n
eu
tr
al
p
o
in
t N
.
Fig
u
r
e
1
.
H
-
b
r
id
g
e
co
n
v
en
tio
n
al
in
v
er
ter
to
p
o
lo
g
y
an
d
s
witch
in
g
s
tate
(
S3
an
d
S4
ar
e
in
co
m
p
lem
en
tar
y
s
tates to
S1
an
d
S2
,
r
esp
ec
tiv
e
ly
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
3
,
Sep
tem
b
er
20
25
:
174
0
-
1
7
5
1
1742
T
ab
le
1
.
Switch
in
g
s
tates a
n
d
o
u
tp
u
t
v
o
ltag
e
o
f
th
e
H
-
b
r
id
g
e
in
v
er
ter
S1
S2
S3
S4
V
AB
1
1
0
0
+
V
d
c
1
0
0
1
0
0
1
1
0
0
0
0
1
1
-
V
d
c
T
a
b
l
e
2
.
T
h
e
c
o
m
p
a
r
i
s
o
n
o
f
c
o
m
p
o
n
e
n
t
r
e
q
u
i
r
e
m
e
n
t
s
f
o
r
5
t
o
1
5
l
e
v
e
l
s
o
f
t
h
e
c
a
s
c
a
d
e
d
H
-
b
r
i
d
g
e
i
n
v
e
r
t
e
r
p
e
r
p
h
a
s
e
Le
v
e
l
s
D
C
so
u
r
c
e
s
N
o
.
o
f
s
w
i
t
c
h
e
s
5
2
8
7
3
12
9
4
16
11
5
20
13
6
24
15
7
28
(
a)
(
b
)
(
c)
Fig
u
r
e
2
.
T
h
e
co
n
f
ig
u
r
atio
n
o
f
th
e
ca
s
ca
d
ed
H
-
b
r
id
g
e
in
v
er
te
r
p
er
p
h
ase
f
o
r
:
(
a)
5
-
lev
el
C
HM
I
,
(
b
)
9
-
lev
el
C
HM
I
,
an
d
(
c)
15
-
l
ev
el
C
HM
I
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
A
n
a
lysi
s
o
f c
a
s
ca
d
ed
H
-
B
r
id
g
e
mu
ltil
ev
el
in
ve
r
ter
s
u
s
in
g
S
P
WM
w
i
th
…
(
A
z
r
ita
A
lia
s
)
1743
Fig
u
r
e
3
.
T
h
e
co
n
f
ig
u
r
atio
n
o
f
th
e
ca
s
ca
d
ed
H
-
b
r
id
g
e
in
v
er
te
r
f
o
r
5
-
lev
el
p
h
ase
A,
B
,
an
d
C
3.
M
O
DUL
AT
I
O
N
T
E
CH
NIQ
UE
S O
F
CASC
ADE
D
H
-
B
R
I
DG
E
I
N
VE
R
T
E
RS
Nu
m
er
o
u
s
r
esear
ch
e
r
s
in
th
e
p
o
wer
co
n
v
er
ter
tech
n
o
lo
g
ies
f
i
eld
h
av
e
d
e
v
elo
p
e
d
v
ar
io
u
s
m
o
d
u
latio
n
tech
n
iq
u
es
f
o
r
co
n
tr
o
l
s
tr
ateg
ies
f
o
r
m
u
ltil
ev
el
in
v
e
r
ter
s
.
T
h
e
m
o
s
t
well
-
k
n
o
wn
a
n
d
s
tr
aig
h
tf
o
r
war
d
tech
n
iq
u
e
is
s
in
u
s
o
id
al
p
u
ls
e
wid
th
m
o
d
u
latio
n
(
SP
W
M)
.
T
h
e
C
HM
I
ca
n
b
e
co
n
tr
o
lled
u
s
in
g
SP
W
M
tech
n
iq
u
es.
T
o
o
b
tain
th
e
m
u
lti
-
lev
el
o
u
tp
u
t,
m
u
lti
-
ca
r
r
ier
wav
e
s
ig
n
als
ar
e
u
s
ed
an
d
c
o
m
p
ar
e
d
with
a
s
in
u
s
o
id
al
s
ig
n
al
;
th
e
o
b
tain
ed
c
o
m
p
a
r
ed
p
u
ls
es
ar
e
u
s
ed
to
s
witch
o
f
f
th
e
in
v
er
ter
[
2
2
]
.
T
h
e
tech
n
iq
u
e
ca
n
b
e
ca
teg
o
r
ized
in
to
lev
el
-
s
h
if
ted
v
ar
iatio
n
s
o
f
P
u
ls
e
W
id
th
Mo
d
u
latio
n
(
PW
M)
,
in
clu
d
in
g
p
h
ase
d
is
p
o
s
itio
n
p
u
ls
e
wid
th
m
o
d
u
latio
n
(
PDPW
M)
,
Ph
ase
o
p
p
o
s
ite
d
is
p
o
s
itio
n
p
u
ls
e
wid
th
m
o
d
u
latio
n
(
PODPW
M)
an
d
alter
n
ativ
e
p
h
ase
o
p
p
o
s
ite
d
is
p
o
s
itio
n
p
u
ls
e
wid
th
m
o
d
u
latio
n
(
APODPW
M)
.
I
n
th
is
p
ap
e
r
,
th
e
tec
h
n
iq
u
e
h
as
b
ee
n
m
o
d
if
ied
b
y
em
p
l
o
y
i
n
g
m
u
ltip
le
r
ef
er
en
ce
s
in
u
s
o
id
al
s
ig
n
als
with
v
ar
y
in
g
am
p
litu
d
es,
co
m
p
ar
ed
with
tr
ian
g
le/r
am
p
wav
es
,
to
g
en
er
ate
th
e
s
witch
in
g
s
ig
n
als
th
at
co
n
tr
o
l
th
e
s
em
ico
n
d
u
ct
o
r
s
witch
es
in
a
tim
ed
s
eq
u
en
ce
.
T
h
is
tec
h
n
iq
u
e
em
p
lo
y
s
2
(
n
-
1
)
/2
r
ef
e
r
en
ce
s
in
u
s
o
id
al
t
o
p
r
o
d
u
ce
th
e
n
-
lev
el
in
v
e
r
ter
o
u
tp
u
t
v
o
ltag
e
p
er
p
h
ase.
T
h
e
am
p
litu
d
e
o
f
th
e
s
in
u
s
o
id
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Le
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Fo
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Fig
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b
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ates
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o
f
S2
,
S1
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an
d
S5
,
r
esp
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.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
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lec
&
Dr
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t
,
Vo
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16
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No
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3
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Sep
tem
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20
25
:
174
0
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1
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5
1
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(
a)
(
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5
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e
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e
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d
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t
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c
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0
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
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n
a
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f c
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T6
T7
T8
T9
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0
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1
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2
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3
T1
4
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5
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6
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7
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8
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9
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0
S1
0
0
↔
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
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0
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1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
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1
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1
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0
0
0
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0
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0
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2
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1
3
0
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0
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1
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1
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1
1
1
1
1
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0
0
0
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0
1
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0
1
1
1
1
S
1
7
0
0
0
0
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0
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1
0
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1
1
1
1
1
1
1
0
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1
0
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1
0
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0
0
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S
1
8
1
1
1
1
1
1
1
1
1
1
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1
1
1
1
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1
9
0
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0
0
0
0
0
0
0
0
0
0
0
S
2
0
1
1
1
1
1
1
↔
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1
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0
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0
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1
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1
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1
1
1
1
1
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2
1
0
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0
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0
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0
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0
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2
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1
1
1
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2
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2
4
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1
1
1
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1
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4.
RE
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
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lec
&
Dr
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s
t
I
SS
N:
2088
-
8
6
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ality
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ll
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it
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n
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m
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ilter
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h
o
u
ld
r
e
n
d
er
it
a
c
o
m
p
lian
t d
esig
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
3
,
Sep
tem
b
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20
25
:
174
0
-
1
7
5
1
1748
Fig
u
r
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
A
n
a
lysi
s
o
f c
a
s
ca
d
ed
H
-
B
r
id
g
e
mu
ltil
ev
el
in
ve
r
ter
s
u
s
in
g
S
P
WM
w
i
th
…
(
A
z
r
ita
A
lia
s
)
1749
T
ab
le
8
.
Var
iatio
n
m
o
d
u
latio
n
in
d
ex
,
le
v
el,
m
ax
im
u
m
v
o
ltag
e
,
an
d
%THD
o
f
l
in
e
v
o
ltag
e
f
o
r
5
,
7
,
9
,
1
1
,
1
3
,
an
d
15
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lev
e
l
s
C
HM
I
M
o
d
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l
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