I
nte
rna
t
io
na
l J
o
urna
l o
f
P
o
w
er
E
lect
ro
nics
a
nd
Driv
e
Sy
s
t
e
m
(
I
J
P
E
DS
)
Vo
l.
8
,
No
.
1
,
Ma
r
ch
2
0
1
7
,
p
p
.
93
~
99
I
SS
N:
2
0
8
8
-
8
6
9
4
,
DOI
: 1
0
.
1
1
5
9
1
/
i
j
p
ed
s
.
v8
i
1
.
p
p
9
3
-
99
93
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ia
e
s
jo
u
r
n
a
l.c
o
m/o
n
lin
e/in
d
ex
.
p
h
p
/I
JP
E
DS
No
n
-
i
terative
Wi
de
-
m
o
dula
tion
-
i
n
dex
Sw
itching
-
a
ng
le
Ca
lcula
tion Tech
nique
s for
15
-
l
ev
el
Bina
ry
Ca
sca
ded
H
-
b
r
idg
e Multil
e
v
el Inv
erte
r
J
.
A.
So
o
1
,
M
.
S.
Chy
e
2
,
Y.
C
.
T
a
n
3
,
S.
L
.
O
ng
4
,
J
.
H
.
L
eo
ng
5
,
T
.
Su
t
i
k
no
6
1
-
3,
5
CERE
/E
M
A
D/P
ECO,
S
c
h
o
o
l
o
f
El
e
c
tri
c
a
l
S
y
ste
m
s E
n
g
in
e
e
rin
g
,
Un
iv
e
rsity
M
a
la
y
sia
P
e
rli
s,
M
a
l
a
y
sia
4
S
c
h
o
o
l
o
f
M
icro
e
lec
tro
n
ic E
n
g
in
e
e
rin
g
,
Un
iv
e
rsit
y
M
a
la
y
sia
P
e
rli
s,
M
a
lay
si
a
6
El
e
c
tri
c
a
l
En
g
in
e
e
rin
g
De
p
a
rtm
e
n
t
,
Un
iv
e
rsit
as
A
h
m
a
d
Da
h
lan
,
I
n
d
o
n
e
sia
Art
icle
I
nfo
AB
ST
RAC
T
A
r
ticle
his
to
r
y:
R
ec
e
iv
ed
Sep
2
6
,
2
0
1
6
R
ev
i
s
ed
Dec
0
2
,
2
0
1
6
A
cc
ep
ted
Dec
1
2
,
2
0
1
6
Ca
sc
a
d
e
d
H
-
b
rid
g
e
m
u
lt
il
e
v
e
l
in
v
e
rter
(CHBMI)
is
a
b
le
t
o
g
e
n
e
ra
te
a
sta
irca
se
AC
o
u
tp
u
t
v
o
lt
a
g
e
w
it
h
lo
w
s
w
it
c
h
in
g
lo
ss
e
s.
T
h
e
s
w
it
c
h
in
g
a
n
g
les
a
p
p
li
e
d
t
o
t
h
e
CHBMI
h
a
v
e
to
b
e
c
a
lcu
late
d
a
n
d
a
rra
n
g
e
d
p
ro
p
e
r
ly
in
o
rd
e
r
to
m
in
i
m
ize
th
e
to
tal
h
a
r
m
o
n
ic
d
isto
rti
o
n
(T
HD
)
o
f
th
e
o
u
tp
u
t
v
o
lt
a
g
e
w
a
v
e
f
o
r
m
.
In
th
is
p
a
p
e
r,
tw
o
n
o
n
-
it
e
ra
ti
v
e
sw
it
c
h
in
g
-
a
n
g
le
c
a
lcu
latio
n
tec
h
n
iq
u
e
s
a
p
p
li
e
d
f
o
r
a
1
5
-
lev
e
l
b
in
a
ry
a
s
y
m
m
e
tri
c
CHBMI
a
r
e
p
ro
p
o
se
d
.
Bo
th
tec
h
n
i
q
u
e
s
e
m
p
lo
y
a
g
e
o
m
e
tri
c
a
p
p
ro
a
c
h
t
o
e
stim
a
te
th
e
sw
it
c
h
in
g
a
n
g
les
,
a
n
d
th
e
re
f
o
re
,
th
e
g
e
n
e
ra
t
e
d
e
q
u
a
ti
o
n
s
c
a
n
b
e
so
lv
e
d
d
irec
t
ly
w
it
h
o
u
t
it
e
ra
ti
o
n
s,
w
h
ich
a
re
u
su
a
ll
y
ti
m
e
-
c
o
n
su
m
in
g
a
n
d
c
h
a
ll
e
n
g
i
n
g
to
b
e
im
p
le
m
e
n
ted
in
re
a
l
-
ti
m
e
.
A
p
a
rt
f
ro
m
th
is,
b
o
th
tec
h
n
iq
u
e
s
a
re
a
l
so
a
b
le
to
c
a
lcu
late
th
e
sw
it
c
h
in
g
a
n
g
les
fo
r
a
w
id
e
ra
n
g
e
o
f
m
o
d
u
latio
n
in
d
e
x
.
T
h
e
p
ro
p
o
se
d
c
a
lcu
lati
o
n
tec
h
n
iq
u
e
s
h
a
v
e
b
e
e
n
v
a
li
d
a
ted
v
ia
M
AT
LAB
sim
u
latio
n
a
n
d
e
x
p
e
rime
n
t.
K
ey
w
o
r
d
:
As
y
m
m
etr
ic
m
u
l
tile
v
el
in
v
er
te
r
B
in
ar
y
m
u
lt
ilev
e
l in
v
er
ter
C
ascad
ed
H
-
B
r
id
g
e
Mu
ltil
e
v
el
i
n
v
er
ter
No
n
-
I
ter
ati
v
e
Co
p
y
rig
h
t
©
201
7
In
s
t
it
u
te o
f
A
d
v
a
n
c
e
d
E
n
g
i
n
e
e
rin
g
a
n
d
S
c
ien
c
e
.
All
rig
h
ts
re
se
rv
e
d
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
J
.
A
.
So
o
,
Sch
o
o
l o
f
E
lectr
ical
S
y
s
te
m
s
E
n
g
i
n
ee
r
i
n
g
,
Un
i
v
er
s
it
y
Ma
la
y
s
ia
P
er
lis
,
0
2
6
0
0
A
r
au
,
P
er
lis
,
Ma
la
y
s
ia.
E
m
ail: so
o
.
ed
m
u
n
d
@
g
m
a
il.c
o
m
1.
I
NT
RO
D
UCT
I
O
N
C
ascad
ed
H
-
b
r
id
g
e
m
u
ltil
e
v
el
in
v
er
ter
(
C
HB
MI
)
h
as
d
r
a
w
n
in
cr
ea
s
ed
atten
tio
n
in
r
ec
en
t
d
ec
ad
es
o
w
i
n
g
to
its
m
o
d
u
lar
it
y
an
d
lo
w
s
w
itc
h
in
g
lo
s
s
e
s
[1
]
-
[
4]
.
T
h
er
e
ar
e
tw
o
ca
te
g
o
r
ies
o
f
C
HB
MI
:
(
a)
s
y
m
m
etr
ic
an
d
(
b
)
asy
m
m
etr
ic.
I
n
s
y
m
m
etr
ic
C
HB
MI
,
th
e
D
C
s
o
u
r
ce
v
o
ltag
e
s
in
al
l
HB
s
ar
e
id
en
tical
w
h
i
ls
t
as
y
m
m
etr
ical
C
HB
MI
h
a
s
d
if
f
er
en
ce
D
C
s
o
u
r
ce
v
o
lta
g
e
le
v
els.
Fo
r
a
g
i
v
en
n
u
m
b
er
o
f
HB
,
an
as
y
m
m
e
tr
ic
C
HB
MI
is
ab
le
to
p
r
o
d
u
ce
a
s
tair
ca
s
e
AC
o
u
tp
u
t
v
o
ltag
e
w
a
v
e
f
o
r
m
w
i
th
a
h
i
g
h
er
n
u
m
b
er
o
f
v
o
ltag
e
lev
e
l
th
an
t
h
at
o
f
a
s
y
m
m
etr
ic
C
H
B
MI
[
5
]
-
[
8
].
Gen
er
ally
,
a
s
tai
r
ca
s
e
A
C
o
u
tp
u
t
v
o
lta
g
e
w
a
v
ef
o
r
m
w
i
th
a
h
ig
h
er
n
u
m
b
er
o
f
v
o
lta
g
e
le
v
el
is
e
x
p
ec
ted
to
p
r
o
d
u
ce
lo
w
er
to
tal
h
ar
m
o
n
ic
d
i
s
to
r
tio
n
(
T
HD)
.
Ho
w
e
v
er
,
t
h
e
T
HD
o
f
th
e
s
tair
ca
s
e
A
C
o
u
tp
u
t
v
o
lta
g
e
w
av
e
f
o
r
m
ca
n
b
e
co
m
e
v
e
r
y
h
i
g
h
if
t
h
e
s
w
i
tch
in
g
an
g
l
es
ar
e
n
o
t
p
r
o
p
e
r
ly
ar
r
an
g
ed
[
3
]
.
C
o
n
v
en
t
io
n
all
y
,
a
s
et
o
f
n
o
n
-
li
n
ea
r
tr
an
s
ce
n
d
e
n
tal
eq
u
atio
n
s
i
n
v
o
l
v
i
n
g
tr
i
g
o
n
o
m
etr
ic
eq
u
at
io
n
s
h
as
to
b
e
s
o
lv
ed
to
o
b
tain
th
e
s
w
i
tch
i
n
g
an
g
les.
I
n
[
9
]
-
[
1
1
]
,
iter
ativ
e
m
et
h
o
d
s
ar
e
em
p
l
o
y
ed
to
s
o
lv
e
t
h
es
e
n
o
n
-
li
n
ea
r
tr
an
s
ce
n
d
en
tal
eq
u
atio
n
s
.
Ho
w
e
v
er
,
s
o
lv
i
n
g
t
h
es
e
eq
u
atio
n
s
u
s
in
g
i
ter
ativ
e
m
e
th
o
d
s
ca
n
b
e
t
i
m
e
-
co
n
s
u
m
i
n
g
an
d
ch
al
len
g
i
n
g
to
b
e
p
er
f
o
r
m
ed
in
r
ea
l
-
ti
m
e.
M
o
r
eo
v
er
,
if
th
e
in
it
ial
co
n
d
itio
n
s
o
f
t
h
e
s
w
itc
h
i
n
g
an
g
le
s
ar
e
n
o
t c
o
r
r
ec
tl
y
ch
o
s
e
n
,
t
h
e
n
u
m
b
er
o
f
iter
atio
n
c
y
cl
es
ca
n
b
e
v
er
y
lar
g
e
a
n
d
t
h
e
al
g
o
r
ith
m
m
a
y
f
ail
to
co
n
v
er
g
e,
lead
i
n
g
to
n
o
s
o
lu
t
io
n
s
.
I
n
[
1
2
]
,
th
e
au
t
h
o
r
p
r
o
p
o
s
ed
t
w
o
n
o
n
-
i
ter
ativ
e
m
et
h
o
d
s
to
esti
m
ate
t
h
e
s
w
itc
h
in
g
a
n
g
les
ac
co
r
d
in
g
to
th
e
s
i
n
e
f
u
n
ctio
n
.
Ho
w
ev
er
,
t
h
e
m
et
h
o
d
s
e
m
p
lo
y
ed
in
[
1
2
]
can
o
n
l
y
ca
lcu
late
th
e
s
w
it
c
h
i
n
g
a
n
g
le
s
at
a
s
p
ec
if
ic
m
o
d
u
latio
n
i
n
d
ex
,
an
d
th
er
eb
y
ca
n
n
o
t
b
e
ap
p
lied
d
ir
e
ctl
y
in
ap
p
licatio
n
s
th
at
r
eq
u
ir
e
a
w
id
er
m
o
d
u
lati
o
n
in
d
ex
r
an
g
e
.
I
n
t
h
is
p
ap
er
,
t
w
o
n
o
n
-
iter
at
iv
e
s
w
itc
h
in
g
an
g
le
ca
lc
u
latio
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
IJ
PEDS
Vo
l.
8
,
No
.
1
,
Ma
r
ch
2
0
1
7
:
93
–
99
94
tech
n
iq
u
es
f
o
r
a
15
-
le
v
el
b
in
a
r
y
a
s
y
m
m
etr
ic
C
HB
MI
ar
e
p
r
o
p
o
s
ed
.
T
h
e
tech
n
iq
u
es
ar
e
a
b
le
to
ca
lcu
late
t
h
e
s
w
itc
h
in
g
an
g
les
f
o
r
a
w
id
e
r
an
g
e
o
f
m
o
d
u
latio
n
in
d
e
x
.
B
o
th
tec
h
n
iq
u
e
s
h
av
e
b
ee
n
v
al
id
ated
v
ia
M
A
T
L
A
B
s
i
m
u
lat
io
n
an
d
e
x
p
er
i
m
e
n
tal
r
esu
lt
s
.
2.
P
RO
P
O
SE
D
SW
I
T
CH
I
N
G
ANG
L
E
C
AL
C
UL
A
T
I
O
N
T
E
CH
NI
Q
U
E
I
n
[
6
]
,
tw
o
n
on
-
iter
ati
v
e
m
e
th
o
d
s
ar
e
p
r
esen
ted
.
T
h
e
f
ir
s
t
m
eth
o
d
ca
lcu
lates
t
h
e
s
w
itc
h
i
n
g
an
g
les
a
t
ea
ch
in
ter
ce
p
tio
n
p
o
in
t
b
et
w
e
en
a
s
in
e
w
a
v
e
f
o
r
m
an
d
th
e
h
al
f
h
ei
g
h
t
o
f
ea
ch
s
tep
p
ed
o
u
tp
u
t
v
o
ltag
e
le
v
el,
w
h
il
s
t
in
t
h
e
s
ec
o
n
d
m
et
h
o
d
th
e
s
w
itc
h
i
n
g
an
g
les
ar
e
ca
lcu
lated
f
r
o
m
h
al
f
o
f
t
h
e
s
w
i
tch
i
n
g
a
n
g
les
o
b
tain
ed
u
s
i
n
g
th
e
f
ir
s
t
m
e
th
o
d
.
Sin
ce
b
o
th
m
eth
o
d
s
e
m
p
lo
y
g
eo
m
et
r
y
ap
p
r
o
ac
h
to
esti
m
ate
t
h
e
s
w
itc
h
i
n
g
an
g
les,
t
h
e
g
en
er
ated
eq
u
atio
n
s
ca
n
b
e
s
o
lv
ed
d
ir
ec
tl
y
.
Ho
w
ev
er
,
b
o
th
m
et
h
o
d
s
ar
e
o
n
l
y
ab
le
to
esti
m
ate
t
h
e
s
w
itc
h
i
n
g
an
g
le
s
at
a
s
p
ec
if
ic
m
o
d
u
la
t
io
n
in
d
ex
.
I
n
th
is
p
ap
er
,
b
o
th
m
et
h
o
d
s
h
a
v
e
b
ee
n
ex
te
n
d
ed
to
en
ab
le
th
e
ca
lcu
latio
n
o
f
s
w
itc
h
i
n
g
an
g
le
s
o
v
er
a
w
id
e
m
o
d
u
la
tio
n
i
n
d
ex
r
an
g
e
ap
p
lied
to
a
1
5
-
lev
el
b
in
ar
y
as
y
m
m
etr
ic
C
HB
MI
.
T
h
e
p
r
o
p
o
s
ed
s
w
itc
h
in
g
-
a
n
g
le
ca
lc
u
latio
n
tech
n
iq
u
es
,
r
e
f
er
r
ed
as
C
T
A
a
n
d
C
T
B
in
t
h
is
p
ap
er
,
ar
e
g
iv
e
n
i
n
E
q
u
atio
n
s
1
an
d
2
,
r
esp
ec
tiv
el
y
.
1
1
s
in
56
a
M
1
2
3
s
in
56
a
M
1
3
5
s
in
56
a
M
1
4
7
s
in
56
a
M
1
5
9
s
in
56
a
M
1
6
11
s
in
56
a
M
1
7
13
s
in
56
a
M
(
1
)
1
1
1
s
in
2
5
6
a
M
1
2
13
s
in
2
5
6
a
M
1
3
15
s
in
2
5
6
a
M
1
4
17
s
in
2
5
6
a
M
1
5
19
s
in
2
5
6
a
M
1
6
1
1
1
s
in
2
5
6
a
M
1
7
1
1
3
s
in
2
5
6
a
M
(
2
)
w
h
er
e
θ
1
,
θ
2
,
θ
3
,
θ
4
,
θ
5
,
θ
6
a
n
d
θ
7
ar
e
s
w
i
tch
in
g
a
n
g
les.
T
h
e
m
o
d
u
la
tio
n
in
d
e
x
(
M
a
)
in
E
q
u
atio
n
s
1
a
n
d
2
is
g
iv
e
n
b
y
1
DC
28
a
V
M
V
(
3
)
DC
1
1
2
3
4
5
6
7
4
c
os
c
os
c
os
c
os
c
os
c
os
c
os
V
V
(
4
)
w
h
er
e
V
1
is
th
e
f
u
n
d
a
m
e
n
tal
v
o
ltag
e
o
f
th
e
s
tair
ca
s
e
AC
o
u
tp
u
t
v
o
lta
g
e
w
av
e
f
o
r
m
w
h
ic
h
ca
n
b
e
ca
lc
u
lated
u
s
i
n
g
E
q
u
atio
n
4
,
an
d
V
DC
is
t
h
e
m
a
g
n
it
u
d
e
o
f
ea
ch
s
tep
p
ed
o
u
tp
u
t v
o
lta
g
e
le
v
el.
3.
SWI
T
CH
I
N
G
P
A
T
T
E
RN
O
F
15
-
L
E
VE
L
B
I
N
ARY
AS
Y
M
M
E
T
RIC
CASCAD
E
D
H
-
B
RIDG
E
M
UL
T
I
L
E
VE
L
I
N
VE
R
T
E
R
Fig
u
r
e
1
(
a)
s
h
o
w
s
th
e
as
y
m
m
etr
ic
C
HB
MI
w
i
th
t
h
e
D
C
s
o
u
r
ce
v
o
ltag
e
lev
e
ls
in
cr
ea
s
e
i
n
a
b
in
ar
y
f
as
h
io
n
.
T
h
e
to
tal
n
u
m
b
er
o
f
th
e
in
v
er
ter
o
u
tp
u
t
v
o
lta
g
e
lev
el
(
m
)
is
d
ep
en
d
en
t
o
n
t
h
e
t
o
tal
n
u
m
b
er
(
s
)
o
f
in
d
ep
en
d
en
t D
C
s
o
u
r
ce
w
h
ic
h
ca
n
b
e
d
eter
m
i
n
ed
by
1
21
s
m
(
5
)
E
ac
h
ef
f
ec
ti
v
e
o
u
tp
u
t
v
o
ltag
e
lev
el
(
V
DC
-
i
)
r
esp
ec
tiv
e
to
i
-
th
s
w
i
tch
i
n
g
an
g
le
(
θ
i
)
at
t
h
e
f
ir
s
t
q
u
ad
r
an
t
o
f
th
e
C
HB
MI
is
g
i
v
e
n
b
y
DC
14
1
DC
i
iV
V
m
(
6
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PEDS
I
SS
N:
2
0
8
8
-
8
694
N
o
n
-
iter
a
tive
W
id
e
-
mo
d
u
la
tio
n
-
in
d
ex
S
w
itch
in
g
-
a
n
g
le
C
a
lcu
la
tio
n
Tech
n
i
q
u
es
.
.
.
.
(
J.
A
.
S
o
o
)
95
(
a)
(
b
)
Fig
u
r
e
1
.
(
a)
B
lo
ck
d
iag
r
a
m
o
f
15
-
lev
el
b
in
ar
y
a
s
y
m
m
etr
ic
C
HB
MI
(
b
)
Ou
tp
u
t v
o
lta
g
e
w
av
e
f
o
r
m
o
f
1
5
-
lev
el
b
i
n
ar
y
as
y
m
m
etr
ic
C
HB
MI
T
ab
le
1
.
Sw
itch
in
g
P
atter
n
o
f
15
-
lev
el
B
in
ar
y
A
s
y
m
m
e
tr
ic
C
HB
MI
O
u
t
p
u
t
L
e
v
e
l
(V)
H
B
D
C
S
o
u
r
c
e
(
V
)
S
w
i
t
c
h
e
s
V
DC
2
V
DC
4
V
DC
S1
S2
S3
S4
S5
S6
S7
S8
S9
S
1
0
S
1
1
S
1
2
7
V
DC
✔
✔
✔
1
0
0
1
1
0
0
1
1
0
0
1
6
V
DC
✔
✔
1
1
0
0
1
0
0
1
1
0
0
1
5
V
DC
✔
✔
1
0
0
1
1
1
0
0
1
0
0
1
4
V
DC
✔
0
0
1
1
0
0
1
1
1
0
0
1
3
V
DC
✔
✔
1
0
0
1
1
0
0
1
1
1
0
0
2
V
DC
✔
1
1
0
0
1
0
0
1
1
1
0
0
V
DC
✔
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
-
V
DC
✔
0
1
1
0
0
0
1
1
0
0
1
1
-
2
V
DC
✔
0
0
1
1
0
1
1
0
0
0
1
1
-
3
V
DC
✔
✔
0
1
1
0
0
1
1
0
0
0
1
1
-
4
V
DC
✔
1
1
0
0
1
1
0
0
0
1
1
0
-
5
V
DC
✔
✔
0
1
1
0
1
1
0
0
0
1
1
0
-
6
V
DC
✔
✔
1
1
0
0
0
1
1
0
0
1
1
0
-
7
V
DC
✔
✔
✔
0
1
1
0
0
1
1
0
0
1
1
0
N
o
t
e
:
“
0
”
i
s OF
F
,
“
1
”
i
s ON
T
h
e
s
w
itc
h
i
n
g
p
atter
n
o
f
a
1
5
-
lev
el
b
i
n
ar
y
as
y
m
m
etr
ic
C
HB
MI
r
esp
ec
tiv
e
to
ea
ch
s
tep
p
ed
o
u
tp
u
t
v
o
ltag
e
lev
el
is
s
h
o
w
n
i
n
T
ab
le
1
.
T
h
e
h
ig
h
est
o
u
tp
u
t
v
o
lta
g
e
lev
el
o
f
t
h
e
i
n
v
er
ter
i
s
V
DC7
w
h
ic
h
is
th
e
s
u
m
o
f
th
e
i
n
d
ep
en
d
en
t
D
C
s
o
u
r
ce
s
(
V
DC
+
2
V
DC
+
4
V
DC
)
.
Sin
ce
th
e
o
u
tp
u
t
v
o
lta
g
e
w
a
v
e
f
o
r
m
o
f
t
h
e
i
n
v
er
ter
p
o
s
s
ess
es
t
h
e
ch
ar
ac
ter
is
tic
o
f
h
al
f
-
w
a
v
e
s
y
m
m
etr
y
,
o
n
l
y
s
ev
e
n
s
w
itc
h
i
n
g
a
n
g
les
in
t
h
e
f
ir
s
t
q
u
ad
r
an
t
ar
e
n
ee
d
ed
to
b
e
ca
lcu
lated
.
E
ac
h
s
w
itc
h
in
g
a
n
g
le
co
r
r
esp
o
n
d
s
t
o
ea
ch
ef
f
ec
ti
v
e
o
u
tp
u
t
v
o
ltag
e
lev
el
a
s
s
h
o
w
n
i
n
Fig
u
r
e
1
(
b
)
.
4.
SI
M
UL
AT
I
O
N
A
ND
E
XP
E
RIM
E
NT
AL
R
E
S
UL
T
S
T
ab
le
2
s
h
o
w
s
t
h
e
p
ar
a
m
eter
s
u
s
ed
in
t
h
e
s
i
m
u
latio
n
an
d
ex
p
er
i
m
e
n
tal
s
et
u
p
f
o
r
a
1
5
-
le
v
el
b
in
ar
y
as
y
m
m
etr
ic
C
HB
MI
.
T
h
e
in
v
er
ter
co
n
s
is
t
s
o
f
t
h
r
ee
HB
s
a
n
d
th
e
DC
s
o
u
r
ce
s
ar
e
s
et
at
1
0
V,
2
0
V,
an
d
4
0
V
,
r
esp
ec
tiv
el
y
.
T
w
el
v
e
s
w
itc
h
e
s
ar
e
u
s
ed
a
n
d
s
w
itc
h
ed
at
5
0
Hz.
Fig
u
r
e
2
s
h
o
w
s
t
h
e
M
A
T
L
A
B
s
i
m
u
la
tio
n
r
esu
lt
s
ca
lcu
la
ted
u
s
i
n
g
C
T
A
a
n
d
C
T
B
.
T
h
e
T
HD
is
co
m
p
u
te
d
b
y
2
2
1
n
n
V
TH
D
V
(
7
)
w
h
er
e
V
n
is
th
e
n
-
th
h
ar
m
o
n
i
c
o
f
th
e
o
u
tp
u
t
v
o
lta
g
e
w
a
v
e
f
o
r
m
.
B
ased
o
n
t
h
e
s
i
m
u
latio
n
r
es
u
lts
s
h
o
w
n
i
n
Fig
u
r
e
2
,
C
T
A
an
d
C
T
B
ar
e
a
b
le
to
ca
lcu
late
t
h
e
s
w
itc
h
i
n
g
an
g
le
s
f
o
r
a
w
id
er
r
an
g
e
o
f
m
o
d
u
latio
n
i
n
d
ex
.
T
h
e
h
ig
h
e
s
t
m
o
d
u
lat
io
n
in
d
e
x
ac
h
iev
ab
le
f
o
r
C
T
A
an
d
C
T
B
ar
e
0
.
8
9
an
d
0
.
9
7
,
r
esp
ec
tiv
el
y
,
w
h
ils
t
t
h
e
lo
w
e
s
t
p
o
s
s
ib
le
m
o
d
u
lat
io
n
i
n
d
ex
f
o
r
C
T
A
an
d
C
T
B
ar
e
0
.
0
3
an
d
0
.
1
1
,
r
esp
ec
tiv
el
y
.
B
esid
es,
C
T
A
i
s
ab
le
to
p
r
o
v
id
e
V
D
C
V
o
u
t
A
C
L
o
a
d
S
1
S
2
S
3
S
4
S
5
S
6
S
7
S
8
S
9
S
1
0
S
1
2
S
1
1
2
V
D
C
4
V
D
C
t
V
o
u
t
1
2
3
4
5
6
7
2
3
2
2
2
DC
V
1
DC
V
3
DC
V
4
DC
V
5
DC
V
6
DC
V
7
DC
V
0
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
IJ
PEDS
Vo
l.
8
,
No
.
1
,
Ma
r
ch
2
0
1
7
:
93
–
99
96
a
co
n
ti
n
u
o
u
s
s
o
l
u
tio
n
o
v
er
a
w
id
e
m
o
d
u
latio
n
i
n
d
ex
,
w
h
i
ls
t
C
T
B
is
o
n
l
y
ab
le
to
g
iv
e
s
o
lu
tio
n
a
t
ce
r
tai
n
in
ter
v
a
ls
o
f
m
o
d
u
la
tio
n
i
n
d
ex
.
T
h
er
e
is
n
o
s
o
lu
tio
n
at
h
i
g
h
e
r
m
o
d
u
latio
n
in
d
e
x
f
o
r
C
T
A
b
ec
au
s
e
t
h
e
d
o
m
ai
n
o
f
th
e
ar
csin
e
f
u
n
ctio
n
i
s
li
m
i
ted
b
etw
ee
n
-
1
~1
to
g
en
er
ate
th
e
s
w
itc
h
i
n
g
a
n
g
le
s
in
r
ea
l
n
u
m
b
er
.
I
f
a
h
ig
h
er
f
u
n
d
a
m
en
ta
l
v
o
ltag
e
is
r
eq
u
ir
ed
,
C
T
B
ca
n
b
e
co
n
s
id
er
ed
as
it
is
ab
le
to
p
r
o
v
id
e
s
o
lu
tio
n
s
at
h
i
g
h
er
m
o
d
u
latio
n
in
d
e
x
.
T
ab
le
2
.
P
ar
am
eter
s
u
s
ed
in
Si
m
u
latio
n
a
n
d
E
x
p
er
i
m
e
n
tal
Se
tu
p
P
a
r
a
me
t
e
r
s
V
a
l
u
e
s
N
u
mb
e
r
o
f
H
B
3
H
B
D
C
so
u
r
c
e
s
1
0
V
,
2
0
V
,
a
n
d
4
0
V
O
u
t
p
u
t
F
r
e
q
u
e
n
c
y
5
0
H
z
M
o
d
u
l
a
t
i
o
n
I
n
d
e
x
R
e
so
l
u
t
i
o
n
0
.
0
0
1
(
a)
T
HD
ag
ain
s
t
m
o
d
u
lat
io
n
i
n
d
ex
(
b
)
Fu
n
d
a
m
e
n
tal
v
o
ltag
e
a
g
ai
n
s
t
m
o
d
u
la
tio
n
i
n
d
ex
(
c)
S
w
itc
h
i
n
g
a
n
g
les a
g
ain
s
t
m
o
d
u
latio
n
in
d
e
x
Fig
u
r
e
2
.
MA
T
L
A
B
s
i
m
u
latio
n
r
esu
lts
o
f
t
h
e
p
r
o
p
o
s
ed
ca
lcu
latio
n
tech
n
iq
u
es
f
o
r
1
5
-
lev
el
b
in
ar
y
as
y
m
m
etr
ic
C
HB
MI
A
1
5
-
lev
el
b
i
n
ar
y
a
s
y
m
m
etr
ic
C
HB
MI
p
r
o
to
ty
p
e
h
as
b
ee
n
co
n
s
tr
u
cted
a
s
s
h
o
w
n
in
Fi
g
u
r
e
3
.
T
h
e
p
r
o
to
ty
p
e
is
co
n
tr
o
lled
u
s
in
g
a
Mic
r
o
ch
ip
PIC1
8
F4
5
5
0
m
i
cr
o
co
n
tr
o
ller
an
d
tw
el
v
e
p
o
w
er
MO
SF
E
T
g
ate
d
r
iv
er
s
.
T
h
e
HB
s
ar
e
p
o
w
e
r
ed
b
y
th
r
ee
i
n
d
ep
en
d
en
t
D
C
p
o
w
er
s
u
p
p
lies
i.e
.
1
0
V,
2
0
V,
an
d
4
0
V,
0
0
.
1
0
.
2
0
.
3
0
.
4
0
.
5
0
.
6
0
.
7
0
.
8
0
.
9
1
0
2
0
4
0
6
0
8
0
1
0
0
1
2
0
1
4
0
1
6
0
1
8
0
2
0
0
M
o
d
u
l
a
t
i
o
n
I
n
d
e
x
,
m
a
T
o
t
a
l
H
a
r
m
o
n
i
c
D
i
s
t
o
r
t
i
o
n
,
T
H
D
(
%
)
C
T
A
0
0
.
1
0
.
2
0
.
3
0
.
4
0
.
5
0
.
6
0
.
7
0
.
8
0
.
9
1
0
2
0
4
0
6
0
8
0
1
0
0
1
2
0
1
4
0
1
6
0
1
8
0
2
0
0
M
o
d
u
l
a
t
i
o
n
I
n
d
e
x
,
m
a
T
o
t
a
l
H
a
r
m
o
n
i
c
D
i
s
t
o
r
t
i
o
n
,
T
H
D
(
%
)
C
T
B
0
0
.
1
0
.
2
0
.
3
0
.
4
0
.
5
0
.
6
0
.
7
0
.
8
0
.
9
1
0
1
0
2
0
3
0
4
0
5
0
6
0
7
0
8
0
9
0
M
o
d
u
l
a
t
i
o
n
I
n
d
e
x
,
m
a
F
u
n
d
a
m
e
n
t
a
l
V
o
l
t
a
g
e
,
V
1
C
T
A
0
0
.
1
0
.
2
0
.
3
0
.
4
0
.
5
0
.
6
0
.
7
0
.
8
0
.
9
1
0
1
0
2
0
3
0
4
0
5
0
6
0
7
0
8
0
9
0
M
o
d
u
l
a
t
i
o
n
I
n
d
e
x
,
m
a
F
u
n
d
a
m
e
n
t
a
l
V
o
l
t
a
g
e
,
V
1
C
T
B
0
0
.
1
0
.
2
0
.
3
0
.
4
0
.
5
0
.
6
0
.
7
0
.
8
0
.
9
1
0
1
0
2
0
3
0
4
0
5
0
6
0
7
0
8
0
9
0
M
o
d
u
l
a
t
i
o
n
I
n
d
e
x
,
M
a
A
n
g
l
e
s
(
°
)
θ
1
0
0
.
1
0
.
2
0
.
3
0
.
4
0
.
5
0
.
6
0
.
7
0
.
8
0
.
9
1
0
10
20
30
40
50
60
70
80
90
d
a
ta
1
d
a
ta
2
d
a
ta
3
d
a
ta
4
d
a
ta
5
d
a
ta
6
d
a
ta
7
θ
7
θ
6
θ
5
θ
4
θ
3
θ
2
0
.
1
0
.
2
0
.
3
0
.
4
0
.
5
0
.
6
0
.
7
0
.
8
0
.
9
1
0
1
0
2
0
3
0
4
0
5
0
6
0
7
0
8
0
9
0
M
o
d
u
l
a
t
i
o
n
I
n
d
e
x
,
M
a
A
n
g
l
e
s
(
°
)
θ
1
0
0
.
1
0
.
2
0
.
3
0
.
4
0
.
5
0
.
6
0
.
7
0
.
8
0
.
9
1
0
10
20
30
40
50
60
70
80
90
d
a
ta
1
d
a
ta
2
d
a
ta
3
d
a
ta
4
d
a
ta
5
d
a
ta
6
d
a
ta
7
θ
7
θ
6
θ
5
θ
4
θ
3
θ
2
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PEDS
I
SS
N:
2
0
8
8
-
8
694
N
o
n
-
iter
a
tive
W
id
e
-
mo
d
u
la
tio
n
-
in
d
ex
S
w
itch
in
g
-
a
n
g
le
C
a
lcu
la
tio
n
Tech
n
i
q
u
es
.
.
.
.
(
J.
A
.
S
o
o
)
97
r
esp
ec
tiv
el
y
.
Fig
u
r
es
4
an
d
5
s
h
o
w
t
h
e
ex
p
er
i
m
e
n
tal
r
es
u
lt
s
o
f
C
T
A
an
d
C
T
B
f
o
r
th
e
in
v
er
ter
.
A
t
th
e
s
a
m
e
m
o
d
u
latio
n
in
d
e
x
,
b
o
th
ca
lcu
latio
n
tec
h
n
iq
u
es
p
r
o
d
u
ce
d
if
f
er
en
t
w
a
v
e
f
o
r
m
s
an
d
T
HD.
T
h
e
T
HD
o
f
th
e
o
u
tp
u
t
v
o
ltag
e
w
a
v
e
f
o
r
m
f
o
r
C
T
B
is
h
ig
h
er
th
a
n
t
h
e
C
T
A
.
T
h
is
is
b
ec
au
s
e
th
e
o
u
tp
u
t
v
o
lt
ag
e
w
av
e
f
o
r
m
h
a
s
a
n
ar
r
o
w
er
g
ap
b
et
w
ee
n
p
o
s
iti
v
e
h
al
f
an
d
n
e
g
ati
v
e
h
a
lf
c
y
cl
e
co
m
p
ar
ed
to
th
at
o
f
C
T
A
,
wh
ich
r
ese
m
b
les
a
s
in
e
w
a
v
e
clo
s
er
.
Fu
r
t
h
er
m
o
r
e,
th
e
n
ar
r
o
w
er
g
ap
o
f
th
e
o
u
tp
u
t
v
o
lta
g
e
w
av
e
f
o
r
m
ap
p
r
o
ac
h
in
g
a
s
q
u
ar
e
w
a
v
e
g
i
v
es
h
ig
h
er
f
u
n
d
a
m
en
t
al
v
o
ltag
e
b
u
t
a
t
th
e
co
s
t
o
f
h
i
g
h
er
T
HD.
B
esid
es
t
h
at,
t
h
e
h
ig
h
er
T
HD
o
f
th
e
C
T
B
is
also
attr
ib
u
ted
to
t
h
e
h
i
g
h
t
h
ir
d
h
ar
m
o
n
ic
at
1
5
0
Hz
in
t
h
e
o
u
tp
u
t
v
o
lta
g
e
wav
ef
o
r
m
.
T
ab
le
3
co
m
p
ar
es
th
e
s
i
m
u
latio
n
a
n
d
ex
p
er
i
m
e
n
tal
d
ata
o
f
b
o
t
h
ca
lc
u
latio
n
tech
n
iq
u
e
s
.
T
h
e
s
i
m
u
la
tio
n
a
n
d
ex
p
er
i
m
e
n
tal
r
esu
lts
ar
e
in
g
o
o
d
ag
r
ee
m
en
t.
T
h
e
d
if
f
er
en
ce
s
b
et
w
ee
n
th
e
C
T
A
a
n
d
C
T
B
ca
n
b
e
clea
r
l
y
o
b
s
er
v
ed
in
T
ab
le
3
w
h
er
e
t
h
e
C
T
A
h
as lo
w
er
T
HD
th
an
t
h
e
C
T
B
at
th
e
s
a
m
e
m
o
d
u
la
tio
n
i
n
d
ex
.
Fig
u
r
e
3
.
(
a)
1
5
-
lev
el
b
in
ar
y
a
s
y
m
m
etr
ic
C
HB
MI
ex
p
er
i
m
en
t setu
p
(
a)
C
T
A
at
m
a
=
0
.
4
0
(
b
)
C
T
B
at
m
a
=
0
.
4
0
(
c)
C
T
A
at
m
a
=
0
.
6
5
(
d
)
C
T
B
at
m
a
=
0
.
6
5
O
u
t
p
u
t
V
o
l
t
a
g
e
,
V
o
u
t
0
0.0
1
0.0
2
0.0
3
0.0
4
-80
-60
-40
-20
0
20
40
60
80
T
i
m
e
,
t
0
0.0
1
0.0
2
0.0
3
0.0
4
-80
-60
-40
-20
0
20
40
60
80
O
u
t
p
u
t
V
o
l
t
a
g
e
,
V
o
u
t
T
i
m
e
,
t
0
0.0
1
0.0
2
0.0
3
0.0
4
-80
-60
-40
-20
0
20
40
60
80
O
u
t
p
u
t
V
o
l
t
a
g
e
,
V
o
u
t
T
i
m
e
,
t
0
0.0
1
0.0
2
0.0
3
0.0
4
-80
-60
-40
-20
0
20
40
60
80
O
u
t
p
u
t
V
o
l
t
a
g
e
,
V
o
u
t
T
i
m
e
,
t
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
IJ
PEDS
Vo
l.
8
,
No
.
1
,
Ma
r
ch
2
0
1
7
:
93
–
99
98
(
e)
C
T
A
at
m
a
=
0
.
8
0
(
f
)
C
T
B
at
m
a
=
0
.
8
0
Fig
u
r
e
4
.
E
x
p
er
i
m
en
tal
r
esu
lt
o
f
o
u
tp
u
t
v
o
ltag
e
w
a
v
e
f
o
r
m
f
o
r
C
T
A
an
d
C
T
B
at
m
o
d
u
latio
n
in
d
ex
0
.
4
0
,
0
.
6
5
an
d
0
.
8
0
(
a)
C
T
A
at
m
a
=
0
.
4
0
(
b
)
C
T
B
at
m
a
=
0
.
4
0
(
c)
C
T
A
at
m
a
=
0
.
6
5
(
d
)
C
T
B
at
m
a
=
0
.
6
5
(
e)
C
T
A
at
m
a
=
0
.
8
0
(
f
)
C
T
B
at
m
a
=
0
.
8
0
Fig
u
r
e
5
.
E
x
p
er
i
m
en
tal
r
esu
lts
o
f
T
HD
an
d
f
u
n
d
a
m
e
n
tal
v
o
lt
ag
e
f
o
r
C
T
A
a
n
d
C
T
B
at
m
o
d
u
latio
n
i
n
d
ex
0
.
4
0
,
0
.
6
5
,
an
d
0
.
8
0
0
0.0
1
0.0
2
0.0
3
0.0
4
-80
-60
-40
-20
0
20
40
60
80
O
u
t
p
u
t
V
o
l
t
a
g
e
,
V
o
u
t
T
i
m
e
,
t
0
0.0
1
0.0
2
0.0
3
0.0
4
-80
-60
-40
-20
0
20
40
60
80
O
u
t
p
u
t
V
o
l
t
a
g
e
,
V
o
u
t
T
i
m
e
,
t
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PEDS
I
SS
N:
2
0
8
8
-
8
694
N
o
n
-
iter
a
tive
W
id
e
-
mo
d
u
la
tio
n
-
in
d
ex
S
w
itch
in
g
-
a
n
g
le
C
a
lcu
la
tio
n
Tech
n
i
q
u
es
.
.
.
.
(
J.
A
.
S
o
o
)
99
T
ab
le
3
.
Sim
u
latio
n
an
d
E
x
p
er
i
m
e
n
tal
Data
o
f
1
5
-
le
v
el
B
in
ar
y
A
s
y
m
m
e
tr
ic
C
HB
MI
S
i
mu
l
a
t
i
o
n
R
e
su
l
t
s
Ex
p
e
r
i
me
n
t
a
l
R
e
su
l
t
s
M
o
d
u
l
a
t
i
o
n
I
n
d
e
x
(
a
m
)
F
u
n
d
a
me
n
t
a
l
v
o
l
t
a
g
e
(
1
r
m
s
V
)
T
H
D
(
%
)
F
u
n
d
a
me
n
t
a
l
v
o
l
t
a
g
e
(
1
r
m
s
V
)
T
H
D
(
%
)
C
T
A
0
.
4
0
2
5
.
2
1
1
2
.
7
5
2
5
.
5
0
1
2
.
8
0
0
.
6
5
4
1
.
0
3
7
.
3
1
4
1
.
1
0
7
.
4
1
0
.
8
0
5
0
.
4
5
5
.
3
4
5
0
.
4
7
5
.
5
4
C
T
B
0
.
4
0
2
5
.
2
1
1
9
.
6
5
2
5
.
8
0
1
9
.
9
0
0
.
6
5
4
1
.
0
3
1
6
.
1
3
4
1
.
5
6
1
6
.
2
0
0
.
8
0
5
0
.
4
5
1
8
.
8
0
5
1
.
3
1
1
8
.
7
0
5.
CO
NCLU
SI
O
N
I
n
t
h
is
p
ap
er
,
t
w
o
n
o
n
-
iter
ati
v
e
s
w
itc
h
i
n
g
-
a
n
g
le
ca
lc
u
latio
n
t
ec
h
n
iq
u
es
(
C
T
A
a
n
d
C
T
B
)
ap
p
lied
f
o
r
a
15
-
lev
el
b
in
ar
y
a
s
y
m
m
etr
ic
C
HB
MI
ar
e
p
r
o
p
o
s
ed
an
d
v
alid
ated
v
ia
s
i
m
u
latio
n
an
d
ex
p
er
i
m
en
t.
B
o
th
tech
n
iq
u
es
ar
e
ab
le
to
ca
lc
u
l
ate
s
w
itc
h
i
n
g
a
n
g
le
s
f
o
r
a
wid
er
r
an
g
e
o
f
m
o
d
u
lat
io
n
i
n
d
ex
.
B
ased
o
n
th
e
s
i
m
u
lat
io
n
a
n
d
ex
p
er
i
m
e
n
tal
r
esu
lt
s
,
C
T
A
h
as
o
u
tp
u
t
v
o
lta
g
e
w
a
v
ef
o
r
m
w
it
h
lo
w
er
T
HD
th
a
n
C
T
B
at
th
e
s
a
m
e
m
o
d
u
latio
n
i
n
d
ex
.
Ho
w
e
v
er
,
C
T
A
i
s
u
n
ab
le
to
ca
lcu
late
s
w
i
tch
i
n
g
a
n
g
les
at
t
h
e
h
i
g
h
er
r
an
g
e
o
f
m
o
d
u
latio
n
in
d
ex
,
w
h
il
s
t
s
w
it
ch
in
g
an
g
le
s
at
th
at
r
an
g
e
ca
n
b
e
o
b
tain
ed
u
s
i
n
g
C
T
B
tech
n
iq
u
e.
Hen
ce
,
b
o
t
h
tech
n
iq
u
es
ca
n
co
m
p
le
m
e
n
t
ea
ch
o
th
er
to
ca
lcu
late
th
e
s
w
it
ch
in
g
an
g
le
s
f
o
r
a
v
er
y
w
id
e
r
an
g
e
o
f
m
o
d
u
latio
n
in
d
ex
.
F
u
r
th
er
m
o
r
e,
th
e
p
r
o
p
o
s
ed
ca
lcu
latio
n
tec
h
n
iq
u
es
r
eq
u
ir
e
n
eit
h
er
n
o
n
-
tr
an
s
ce
n
d
e
n
tal
eq
u
atio
n
s
n
o
r
iter
atio
n
s
to
o
b
tain
t
h
e
s
w
i
tch
in
g
a
n
g
les.
He
n
ce
,
b
o
th
tec
h
n
iq
u
es
ca
n
b
e
ea
s
il
y
e
x
te
n
d
ed
f
o
r
o
th
er
n
u
m
b
er
o
f
lev
els a
n
d
C
HB
MI
to
p
o
lo
g
ies
w
h
er
e
a
w
id
er
r
an
g
e
o
f
m
o
d
u
l
atio
n
in
d
e
x
is
r
eq
u
ir
ed
.
ACK
NO
WL
E
D
G
E
M
E
NT
S
T
h
is
r
esear
ch
w
a
s
s
u
p
p
o
r
ted
b
y
t
h
e
Sch
o
o
l
o
f
E
lectr
ical
S
y
s
te
m
E
n
g
i
n
ee
r
in
g
(
Un
iM
A
P
)
an
d
th
e
Min
i
s
tr
y
o
f
E
d
u
ca
tio
n
Ma
la
y
s
ia
th
r
o
u
g
h
t
h
e
Fu
n
d
a
m
e
n
tal
R
esear
c
h
Gr
an
t
Sch
e
m
e
(
FR
GS/2
/2
0
1
4
/T
K0
6
/UNI
MA
P
/0
2
/3
)
.
RE
F
E
R
E
NC
E
S
[1
]
S
.
Ch
a
tt
e
rjee
,
“
A
M
u
lt
il
e
v
e
l
In
v
e
rter
b
a
se
d
o
n
S
VP
W
M
T
e
c
h
n
iq
u
e
f
o
r
P
h
o
t
o
v
o
lt
a
ic
A
p
p
li
c
a
ti
o
n
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
P
o
we
r E
lec
tro
n
ics
a
n
d
Dr
ive
S
y
ste
ms
,
v
o
l
/i
ss
u
e
:
3
(
1
)
,
p
p
.
6
2
–
7
3
,
2
0
1
3
.
[2
]
M
.
S
.
Ku
m
a
r
a
n
d
R.
Ka
n
n
a
n
,
“
Util
izin
g
th
e
Op
ti
m
iza
ti
o
n
A
lg
o
rit
h
m
in
Ca
s
c
a
d
e
d
H
-
Brid
g
e
M
u
lt
il
e
v
e
l
In
v
e
rter,
”
T
EL
KOM
NIKA
In
d
o
n
e
si
a
n
J
o
u
rn
a
l
o
f
El
e
c
trica
l
En
g
in
e
e
rin
g
,
v
o
l
/
i
ss
u
e
:
13
(
3
)
,
p
p
.
4
5
8
–
4
6
6
,
2
0
1
5
.
[3
]
B.
Oz
p
in
e
c
i,
e
t
a
l
.
,
“
Ha
r
m
o
n
ic
Op
ti
m
iza
ti
o
n
o
f
M
u
lt
il
e
v
e
l
Co
n
v
e
rters
u
sin
g
Ge
n
e
ti
c
A
l
g
o
rit
h
m
s,”
IEE
E
Po
we
r
El
e
c
tro
n
ics
L
e
tt
e
rs
,
v
o
l
/i
ss
u
e
:
3
(
3
)
,
p
p
.
9
2
–
9
5
,
2
0
0
5
.
[4
]
J.
N.
Ch
ias
so
n
,
e
t
a
l.
,
“
A
Un
if
ied
A
p
p
ro
a
c
h
to
S
o
lv
i
n
g
th
e
Ha
r
m
o
n
ic
El
im
in
a
ti
o
n
E
q
u
a
ti
o
n
s
in
M
u
lt
il
e
v
e
l
Co
n
v
e
rters
,
”
IEE
E
T
r
a
n
sa
c
ti
o
n
s
o
n
P
o
we
r E
lec
tro
n
ics
,
v
o
l
/i
ss
u
e
:
19
(
2
)
,
p
p
.
4
7
8
–
4
9
0
,
2
0
0
4
.
[5
]
J.
S
.
L
a
i
a
n
d
F
.
Z.
P
e
n
g
,
“
M
u
lt
i
lev
e
l
Co
n
v
e
rters
–
A
Ne
w
Br
e
e
d
o
f
P
o
w
e
r
Co
n
v
e
rters
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
In
d
u
stry
Ap
p
li
c
a
ti
o
n
s
,
v
o
l
/i
ss
u
e
:
32
(
3
)
,
p
p
.
5
0
9
–
5
1
7
,
1
9
9
6
.
[6
]
E.
Ba
b
a
e
i,
e
t
a
l.
,
“
A
N
o
v
e
l
S
tru
c
tu
re
fo
r
M
u
lt
il
e
v
e
l
Co
n
v
e
rte
rs
,
”
in
2
0
0
5
I
n
tern
a
ti
o
n
a
l
C
o
n
f
e
re
n
c
e
o
n
E
lec
tri
c
a
l
M
a
c
h
in
e
s an
d
S
y
ste
m
s,
v
o
l.
2
,
p
p
.
1
2
7
8
–
1
2
8
3
,
2
0
0
5
.
[7
]
E.
Ba
b
a
e
i,
e
t
a
l.
,
“
Re
d
u
c
ti
o
n
o
f
DC
V
o
lt
a
g
e
S
o
u
rc
e
s
a
n
d
S
w
it
c
h
e
s
in
A
s
y
m
m
e
tri
c
a
l
M
u
lt
il
e
v
e
l
Co
n
v
e
rters
u
sin
g
a
No
v
e
l
T
o
p
o
lo
g
y
,
”
El
e
c
tric P
o
we
r S
y
ste
ms
Res
e
a
rc
h
,
v
o
l
/i
ss
u
e
:
77
(
8
)
,
p
p
.
1
0
7
3
–
1
0
8
5
,
2
0
0
7
.
[8
]
R.
T
a
leb
,
e
t
a
l
.
,
“
G
e
n
e
ti
c
A
lg
o
r
it
h
m
A
p
p
li
c
a
ti
o
n
i
n
A
s
y
m
m
e
tri
c
a
l
9
-
L
e
v
e
l
In
v
e
rter,”
In
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
Po
we
r E
lec
tro
n
ics
a
n
d
Dr
ive
S
y
ste
ms
,
v
o
l
/i
ss
u
e
:
7
(
2
)
,
p
p
.
5
2
1
–
5
3
0
,
2
0
1
6
.
[9
]
L
.
M
.
T
o
lb
e
rt,
e
t
a
l.
,
“
M
u
lt
il
e
v
e
l
Co
n
v
e
rter
f
o
r
Larg
e
El
e
c
tri
c
Driv
e
s,”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
In
d
u
str
y
Ap
p
li
c
a
ti
o
n
s
,
v
o
l
/i
ss
u
e
:
35
(
1
)
,
p
p
.
3
6
–
4
3
,
1
9
9
9
.
[1
0
]
Y.
L
.
Ka
m
e
s
w
a
ri
a
n
d
O.
C.
S
e
k
h
a
r,
“
F
u
z
z
y
L
o
g
ic
Co
n
tro
ll
e
d
Ha
r
m
o
n
ic
S
u
p
p
re
ss
o
r
in
Ca
sc
a
d
e
d
M
u
lt
il
e
v
e
l
In
v
e
rter,”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Po
we
r E
lec
tro
n
ics
a
n
d
Dr
ive
S
y
ste
ms
,
v
o
l
/i
ss
u
e
:
7
(
2
)
,
p
p
.
3
0
3
–
3
1
0
,
2
0
1
6
.
[1
1
]
T
.
Cu
n
n
in
g
h
a
m
,
“
Ca
s
c
a
d
e
M
u
lt
il
e
v
e
l
In
v
e
rter
s
f
o
r
Larg
e
H
y
b
rid
-
El
e
c
tri
c
V
e
h
icle
A
p
p
li
c
a
ti
o
n
s
with
V
a
rian
t
DC
S
o
u
rc
e
s
,
”
M
.
S
.
T
h
e
sis,
Un
iv
e
rv
sity
T
e
n
n
e
ss
e
e
,
Kn
o
x
v
il
le,
2
0
0
1
.
[1
2
]
F
.
L
.
L
u
o
a
n
d
H.
Ye
,
“
A
d
v
a
n
c
e
d
DC/A
C
In
v
e
rter
s: A
p
p
li
c
a
ti
o
n
s in
Re
n
e
w
a
b
le E
n
e
rg
y
,”
T
a
y
lo
r
&
F
ra
n
c
is,
2
0
1
3
.
Evaluation Warning : The document was created with Spire.PDF for Python.