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.
9
,
No
.
3
,
Sep
tem
b
er
2
0
1
8
,
p
p
.
1
1
5
7
~
1
1
6
5
I
SS
N:
2
0
8
8
-
8
6
9
4
,
DOI
: 1
0
.
1
1
5
9
1
/
i
j
p
ed
s
.
v9
.i
3
.
pp
1
1
5
7
-
1
1
6
5
1157
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ia
e
s
co
r
e.
co
m/jo
u
r
n
a
ls
/in
d
ex
.
p
h
p
/
I
JP
E
DS
Ev
a
lua
tion o
f
Sel
ective
H
a
r
m
o
n
ic
Eli
m
ina
ti
o
n
P
ulse
Widt
h
M
o
dula
tion Tech
nique f
o
r
Unipola
r Single
-
Phas
e
H
-
Bridg
e
Inv
erte
r:
Co
m
pa
ra
tive Study
H
us
s
a
in At
t
ia
El
e
c
tri
c
a
l,
El
e
c
tro
n
ics
&
Co
m
m
u
n
ica
ti
o
n
En
g
in
e
e
ri
n
g
De
p
t.
,
A
m
e
r
ica
n
Un
iv
e
rsity
o
f
Ra
s
A
l
Kh
a
ima
h
Am
e
rica
n
Un
iv
e
rsit
y
o
f
Ra
s
A
l
Kh
a
im
a
h
,
Un
i
Em
irat
A
ra
b
Art
icle
I
nfo
AB
ST
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
Dec
13
,
2
0
1
7
R
ev
i
s
ed
Ma
y
10
,
2
0
1
8
A
cc
ep
ted
J
u
l
1
,
2
0
1
8
In
t
h
is
p
a
p
e
r,
a
d
e
tailed
c
o
m
p
a
ra
ti
v
e
stu
d
y
a
b
o
u
t
e
v
a
lu
a
ti
n
g
t
h
e
si
n
g
le
-
p
h
a
se
in
v
e
rter
p
e
rf
o
r
m
a
n
c
e
b
a
se
d
o
n
se
lec
ti
v
e
h
a
r
m
o
n
ic
e
li
m
in
a
ti
o
n
p
u
lse
w
id
th
m
o
d
u
latio
n
(
S
HE
P
W
M
)
tec
h
n
i
q
u
e
is
p
re
se
n
ted
.
S
e
t
o
f
n
o
n
li
n
e
a
r
e
q
u
a
ti
o
n
s
a
re
d
e
riv
e
d
,
f
o
u
r
g
ro
u
p
s
o
f
sw
it
c
h
in
g
a
n
g
les
a
re
c
a
lcu
late
d
u
sin
g
th
e
n
u
m
e
rica
l
it
e
r
a
ti
v
e
m
e
th
o
d
o
f
Ne
w
to
n
-
Ra
p
h
so
n
.
T
h
e
se
a
n
g
les
a
r
e
re
p
re
se
n
ti
n
g
th
e
id
e
a
l
so
lu
ti
o
n
s
to
e
li
m
in
a
te
th
e
lo
w
o
rd
e
r
h
a
rm
o
n
ics
f
ro
m
in
v
e
rter
o
u
tp
u
t
v
o
l
tag
e
a
n
d
lo
a
d
c
u
rre
n
t.
In
v
e
rter
e
ff
e
c
ti
v
e
n
e
ss
is
e
v
a
lu
a
ted
b
y
c
o
m
p
a
rin
g
th
e
p
e
r
f
o
r
m
a
n
c
e
b
a
se
d
o
n
S
HE
P
W
M
a
n
d
b
a
s
e
d
o
n
th
e
c
o
n
v
e
n
ti
o
n
a
l
c
o
n
sta
n
t
sw
it
c
h
in
g
f
re
q
u
e
n
c
y
P
W
M
(CS
F
P
W
M
)
tec
h
n
iq
u
e
.
S
a
m
e
p
a
ra
m
e
ters
se
tt
in
g
is
s
e
lec
t
e
d
w
it
h
c
o
n
sid
e
rin
g
th
e
c
o
n
sta
n
t
sw
it
c
h
in
g
f
re
q
u
e
n
c
y
v
a
lu
e
f
o
r
e
a
c
h
c
a
se
se
p
a
ra
tel
y
a
s
e
q
u
iv
a
len
t
to
t
h
e
n
u
m
b
e
r
o
f
sw
it
c
h
in
g
a
n
g
les
.
M
o
re
o
v
e
r,
d
if
fe
re
n
t
ra
ted
lo
a
d
p
o
w
e
rs
a
re
in
v
e
stig
a
ted
to
e
x
p
lain
th
e
m
e
rit
o
f
S
HE
P
W
M
w
it
h
in
h
ig
h
p
o
w
e
r
a
p
p
li
c
a
ti
o
n
s.
M
AT
LAB
/
S
im
u
li
n
k
sim
u
latio
n
re
su
lt
s
a
re
c
lea
rl
y
in
d
ica
ti
n
g
th
e
p
ri
o
rit
y
o
f
th
e
S
H
E
P
W
M
a
t
a
ll
g
ro
u
p
s
o
f
c
a
lcu
late
d
a
n
g
les
a
n
d
a
t
d
if
f
e
re
n
t
lo
a
d
p
o
w
e
r
a
s w
e
ll
.
K
ey
w
o
r
d
:
Fu
n
d
a
m
e
n
tal
c
o
m
p
o
n
e
n
t
L
o
ad
p
o
w
er
MA
T
L
A
B
No
n
li
n
ea
r
e
q
u
atio
n
s
Selectiv
e
h
ar
m
o
n
ic
e
li
m
i
n
atio
n
S
w
itc
h
in
g
a
n
g
le
s
T
o
tal
h
ar
m
o
n
ic
s
d
is
to
r
tio
n
Un
ip
o
lar
h
-
b
r
id
g
e
i
n
v
er
ter
Co
p
y
rig
h
t
©
201
8
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
.
Al
l
rig
h
ts re
se
rv
e
d
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Hu
s
s
ai
n
A
ttia,
E
lectr
ical,
E
lectr
o
n
ics &
C
o
m
m
u
n
icat
io
n
E
n
g
i
n
ee
r
in
g
Dep
t.
,
Am
er
ica
n
Un
i
v
er
s
i
t
y
o
f
R
as
Al
Kh
ai
m
ah
,
R
as
A
l K
h
ai
m
a
h
,
1
0
0
2
1
,
Un
i E
m
ir
at
A
r
ab
E
m
ail:
h
attia
@
a
u
r
ak
.
ac
.
ae
1.
I
NT
RO
D
UCT
I
O
N
E
f
f
ec
tiv
e
i
n
v
er
ter
i
s
c
h
ar
ac
te
r
ized
b
y
o
n
l
y
lo
w
cu
r
r
en
t
to
t
al
h
ar
m
o
n
ic
d
is
to
r
tio
n
(
T
HD)
,
an
d
lo
w
s
w
itc
h
in
g
lo
s
s
es
f
o
r
i
m
p
r
o
v
e
d
ef
f
ic
ien
c
y
[
1
]
-
[
3
]
.
P
u
ls
e
W
id
th
Mo
d
u
latio
n
(
P
W
M)
b
ased
in
v
er
ter
s
(
s
in
g
le
p
h
ase
an
d
th
r
ee
p
h
ase)
an
d
P
W
M
b
ased
DC
-
DC
co
n
v
er
ter
s
ar
e
w
id
el
y
co
n
s
tr
u
cted
an
d
u
s
ed
b
ec
au
s
e
o
f
th
e
s
i
m
p
lic
it
y
o
f
th
e
P
W
M
d
r
iv
e
p
u
ls
es
g
e
n
er
atio
n
,
w
h
er
ea
s
to
h
av
e
b
etter
T
HD
lev
el
o
f
lo
ad
cu
r
r
en
t,
th
e
v
al
u
e
o
f
s
w
itc
h
in
g
f
r
eq
u
e
n
c
y
n
ee
d
s
to
b
e
i
n
cr
ea
s
ed
.
O
n
t
h
e
o
th
er
h
a
n
d
,
h
i
g
h
s
w
itc
h
i
n
g
f
r
eq
u
en
c
y
r
ep
r
ese
n
ts
a
tr
ad
eo
f
f
w
it
h
i
n
s
w
itc
h
i
n
g
lo
s
s
es
in
t
h
e
in
v
er
ter
s
w
itc
h
e
s
an
d
T
HD
th
at
lead
in
g
to
th
e
d
i
f
f
ic
u
lt
y
to
u
s
e
f
o
r
h
i
g
h
p
o
w
er
ap
p
licatio
n
s
d
u
e
to
th
e
s
w
itc
h
in
g
lo
s
s
es li
m
itat
io
n
[
4
]
-
[
8
]
.
So
th
er
e
is
li
m
itatio
n
o
f
u
s
i
n
g
co
n
s
ta
n
t
s
w
i
tch
i
n
g
f
r
eq
u
e
n
c
y
p
u
ls
e
w
id
t
h
m
o
d
u
latio
n
(
C
SF
P
W
M)
o
r
ca
r
r
ier
m
o
d
u
lated
P
W
M
(
C
P
W
M)
lik
e
Sin
u
s
o
id
al
P
W
M
(
SP
W
M)
f
o
r
h
i
g
h
p
o
w
er
ap
p
l
icatio
n
s
d
u
e
to
th
e
li
m
ita
tio
n
s
o
f
s
w
itc
h
i
n
g
f
r
e
q
u
en
c
y
a
n
d
s
w
itc
h
i
n
g
lo
s
s
e
s
.
Selectiv
e
Har
m
o
n
ic
E
li
m
in
atio
n
Mo
d
u
la
tio
n
(
SHEM
)
r
ep
r
esen
ts
o
n
e
o
f
p
r
ec
alcu
lated
p
r
o
g
r
a
m
m
ed
P
W
M
(
PP
W
M)
th
at
it
r
ep
r
esen
t
s
an
ef
f
ec
ti
v
e
alter
n
ati
v
e.
T
h
e
p
r
in
cip
le
o
f
S
HE
M
ad
o
p
ts
ch
o
o
s
i
n
g
t
h
e
s
w
i
tch
i
n
g
an
g
le
s
b
ased
o
n
t
h
e
d
e
s
ir
ed
h
ar
m
o
n
ic
s
to
r
e
m
o
v
e
f
r
o
m
t
h
e
f
u
n
d
a
m
e
n
ta
l
w
av
e
f
o
r
m
[
9
]
.
T
h
e
m
er
it
s
o
f
SHEM
b
ased
i
n
v
er
ter
o
v
e
r
C
SF
P
W
M
b
ased
in
v
er
ter
ca
n
b
e
b
r
ief
ed
b
y
lo
w
er
s
w
itc
h
i
n
g
lo
s
s
e
s
d
u
e
to
t
h
e
lo
w
er
n
u
m
b
er
o
f
co
m
m
u
t
atio
n
s
o
f
i
n
v
er
ter
’
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
,
Vo
l.
9
,
No
.
3
,
Sep
tem
b
er
2
0
1
8
:
1
1
5
7
–
1
1
6
5
1158
s
w
itc
h
es
p
er
r
ef
er
en
ce
c
y
c
le,
s
u
itab
il
it
y
f
o
r
h
i
g
h
p
o
w
er
ap
p
licatio
n
s
d
u
e
to
th
e
lo
w
er
s
w
it
ch
in
g
lo
s
s
es
w
h
ic
h
lead
in
g
to
lo
w
er
s
tr
es
s
o
n
t
h
e
s
y
s
te
m
’
s
s
w
i
tc
h
e
s
,
h
ig
h
p
o
w
er
co
n
v
er
s
io
n
f
r
o
m
t
h
e
D
C
li
n
k
s
u
p
p
l
y
v
o
lta
g
e
d
u
e
to
th
e
p
o
s
s
ib
ilit
y
o
f
d
esi
g
n
i
n
g
th
e
w
o
r
k
i
n
g
co
n
d
itio
n
s
o
f
o
v
er
m
o
d
u
latio
n
,
p
o
s
s
ib
ilit
y
o
f
u
s
in
g
lo
w
er
DC
li
n
k
ca
p
ac
ito
r
d
u
e
to
th
e
lo
w
r
ip
p
l
e
in
t
h
e
DC
lin
k
s
u
p
p
l
y
c
u
r
r
en
t,
,
ca
p
ab
ilit
y
o
f
u
s
in
g
GT
O
th
y
r
i
s
to
r
s
f
o
r
h
ig
h
p
o
w
er
ap
p
licatio
n
s
d
u
e
to
th
e
lo
w
er
n
u
m
b
er
o
f
s
w
itc
h
es
’
c
o
m
m
u
tatio
n
s
p
er
r
ef
er
e
n
ce
c
y
cle,
ca
n
ce
lin
g
t
h
e
lo
w
o
r
d
er
h
ar
m
o
n
ic
s
r
e
m
o
v
e
s
t
h
e
p
o
s
s
ib
il
it
y
o
f
r
eso
n
a
n
ce
w
it
h
lo
w
f
r
eq
u
e
n
c
y
d
ev
ice
s
s
u
c
h
a
s
li
n
e
f
il
ter
s
[
1
0
]
-
[
2
0
]
.
I
n
[
1
0
]
,
A
s
in
g
le
p
h
ase
co
n
v
er
ter
is
p
r
esen
ted
b
ased
u
s
in
g
SHEM
b
ased
o
n
Un
i
f
ied
P
o
w
er
Flo
w
C
o
n
tr
o
ller
(
UP
FC
)
,
th
e
co
n
v
e
r
ter
eli
m
in
a
tes
t
h
e
lo
w
o
r
d
er
h
ar
m
o
n
ics
o
f
5
t
h
7
th
1
1
th
a
n
d
1
3
th
b
y
o
f
f
li
n
e
ca
lcu
lati
n
g
t
h
e
s
w
i
tch
in
g
a
n
g
l
es
o
f
1
0
d
if
f
er
e
n
t
m
o
d
u
latio
n
in
d
ices
u
s
in
g
Gen
etic
A
l
g
o
r
ith
m
.
T
h
e
co
n
v
er
ter
p
er
f
o
r
m
a
n
ce
is
e
v
al
u
ated
b
y
co
m
p
ar
in
g
w
it
h
t
h
e
s
i
n
u
s
o
id
al
P
W
M
(
SP
W
M)
b
ased
co
n
v
er
ter
,
an
d
th
e
co
m
p
ar
is
o
n
d
e
m
o
n
s
tr
ated
t
h
at
th
e
S
HE
M
b
ased
co
n
v
er
t
er
is
co
m
p
letel
y
eli
m
i
n
ated
th
e
f
o
u
r
lo
w
o
r
d
er
h
ar
m
o
n
ics.
Fo
r
in
d
u
ct
io
n
m
o
to
r
s
f
ee
d
in
g
t
h
r
ee
p
h
a
s
e
P
W
M
in
v
er
ter
ap
p
licatio
n
s
,
h
ar
m
o
n
ic
el
i
m
in
at
io
n
p
r
o
ce
s
s
in
p
r
esen
ted
i
n
[
1
1
]
b
ased
o
n
p
ar
ticle
s
w
ar
m
o
p
ti
m
i
za
tio
n
(
P
SO)
.
No
n
lin
ea
r
tr
a
n
s
ce
n
d
en
tal
eq
u
atio
n
s
ar
e
p
r
esen
ted
to
h
av
e
ac
cu
r
at
e
s
elec
tiv
e
h
ar
m
o
n
ics
eli
m
i
n
a
tio
n
u
p
to
th
e
2
3
r
d
o
r
d
e
r
f
r
o
m
th
e
w
a
v
e
f
o
r
m
o
f
in
v
er
ter
v
o
ltag
e.
T
h
e
p
r
ec
is
e
s
o
lu
tio
n
s
ar
e
o
b
tain
ed
af
ter
s
ev
er
al
iter
atio
n
s
o
f
t
h
e
p
ar
ticl
e
s
w
ar
m
al
g
o
r
ith
m
co
n
v
er
g
in
g
p
r
o
ce
s
s
an
d
t
h
e
lo
w
o
r
d
er
h
ar
m
o
n
ics
ar
e
s
u
cc
es
s
f
u
ll
y
atte
n
u
ated
.
Selec
tiv
e
h
a
r
m
o
n
ic
eli
m
i
n
atio
n
is
d
o
n
e
in
[
1
2
]
b
ased
o
n
P
W
M
m
o
d
u
latio
n
tech
n
iq
u
e
b
y
wh
ich
t
h
e
ca
r
r
ier
w
a
v
e
f
o
r
m
i
s
m
o
d
i
f
ied
b
ased
o
n
a
ce
r
tain
p
r
o
ce
s
s
i
n
s
tead
o
f
n
u
m
er
ical
p
r
o
ce
s
s
o
f
o
p
ti
m
izati
o
n
.
T
h
e
m
et
h
o
d
is
ev
al
u
ated
i
n
[
1
2
]
b
y
co
m
p
ar
i
n
g
w
it
h
ca
r
r
ier
p
u
ls
e
w
id
t
h
m
o
d
u
latio
n
.
An
o
p
ti
m
u
m
s
w
it
ch
in
g
p
att
er
n
s
g
en
er
atio
n
s
p
r
ese
n
ted
i
n
[
1
3
]
f
o
r
v
o
ltag
e
co
n
tr
o
lled
in
v
er
ter
ap
p
licatio
n
s
.
I
n
t
h
is
s
t
u
d
y
,
8
n
o
tc
h
a
n
g
le
s
ar
e
d
eter
m
i
n
ed
b
ased
o
n
n
e
u
r
al
n
et
w
o
r
k
m
eth
o
d
f
o
r
d
i
f
f
er
e
n
t
m
o
d
u
latio
n
in
d
ice
s
to
eli
m
in
a
te
th
e
lo
w
o
r
d
er
h
ar
m
o
n
ic
s
til
l
in
cl
u
d
in
g
t
h
e
2
2
th
h
ar
m
o
n
ic.
Si
m
u
latio
n
r
esu
lts
co
n
f
ir
m
ed
th
e
f
u
ll
y
e
li
m
in
a
ti
o
n
o
f
th
e
m
e
n
tio
n
ed
h
ar
m
o
n
i
cs.
A
ce
r
tain
SHEP
W
M
tech
n
iq
u
e
is
p
r
o
p
o
s
ed
in
[
1
4
]
,
[
1
5
]
t
o
g
en
er
ate
P
W
M
p
u
ls
e
s
f
o
r
i
n
v
er
ter
g
ate
d
r
iv
i
n
g
b
ased
o
n
R
es
u
lta
n
t
m
et
h
o
d
.
T
h
is
m
et
h
o
d
s
o
lv
e
s
a
s
et
o
f
n
o
n
li
n
ea
r
eq
u
atio
n
s
to
id
en
ti
f
y
an
d
d
eter
m
in
e
t
h
e
s
w
itc
h
i
n
g
a
n
g
les.
P
W
M
p
u
l
s
e
s
ar
e
d
r
iv
i
n
g
a
f
u
ll
-
b
r
id
g
e
s
in
g
le
-
p
h
ase
i
n
v
er
ter
’
s
s
w
itc
h
es t
h
r
o
u
g
h
u
n
ip
o
lar
s
tr
a
teg
y
w
ith
o
u
t n
ee
d
i
n
g
o
f
t
h
e
in
itial g
u
es
s
.
No
v
el
f
i
v
e
lev
e
ls
v
o
lta
g
e
s
o
u
r
ce
in
v
er
ter
(
VSI
)
is
p
r
esen
ted
in
[
1
6
]
b
ased
o
n
SHEP
W
M
t
ec
h
n
iq
u
e.
Set
o
f
n
o
n
li
n
ea
r
eq
u
atio
n
s
ar
e
s
o
lv
ed
to
d
eter
m
i
n
e
t
h
e
s
witch
i
n
g
a
n
g
le
s
t
h
r
o
u
g
h
h
ig
h
co
n
v
er
g
e
n
ce
s
p
ee
d
n
u
m
er
icall
y
p
r
o
ce
s
s
.
Si
m
u
lat
io
n
r
es
u
lts
d
e
m
o
n
s
tr
ate
th
e
ad
v
an
ta
g
e
o
f
SHE
P
W
M
o
v
er
th
e
co
n
v
e
n
tio
n
al
P
W
M.
I
n
[
1
7
]
,
[
1
8
]
,
th
e
o
p
ti
m
izatio
n
p
r
o
ce
s
s
o
f
th
e
d
if
f
er
en
tial
e
v
o
lu
tio
n
m
et
h
o
d
is
ad
o
p
t
ed
to
d
eter
m
i
n
e
t
h
e
o
p
tim
ized
p
o
s
itio
n
s
o
f
t
h
e
s
witch
i
n
g
a
n
g
les
a
s
a
n
o
b
j
ec
tiv
e
o
f
SHE
P
W
M
tech
n
iq
u
e
w
h
e
r
ea
s
th
e
co
n
ce
p
t
o
f
A
r
ti
f
icial
Ne
u
r
al
Net
w
o
r
k
s
(
A
NN)
is
p
r
o
p
o
s
ed
in
[
1
9
]
to
o
p
tim
ize
t
h
e
s
w
itc
h
i
n
g
an
g
le
s
p
o
s
itio
n
s
d
eter
m
in
at
io
n
to
b
e
u
s
ed
f
o
r
H
-
b
r
id
g
e
in
v
er
ter
’
s
s
w
i
tch
e
s
g
at
es d
r
iv
in
g
.
I
n
t
h
is
p
ap
er
,
th
e
SHE
P
W
M
tech
n
iq
u
e
an
g
les
g
e
n
er
atio
n
an
d
p
r
o
ce
s
s
e
x
ec
u
tio
n
ar
e
e
x
p
lain
ed
in
d
etails,
an
d
th
e
n
th
e
i
n
v
er
ter
p
er
f
o
r
m
a
n
ce
ef
f
ec
t
i
v
e
n
ess
i
s
ev
alu
ated
b
y
co
m
p
ar
i
n
g
w
it
h
th
e
co
n
v
e
n
tio
n
al
co
n
s
ta
n
t
s
w
itc
h
in
g
f
r
eq
u
e
n
c
y
P
W
M
(
C
SF
P
W
M)
tech
n
iq
u
e.
T
h
e
n
u
m
er
ical
tech
n
iq
u
e
o
f
Ne
w
to
n
-
R
ap
h
s
o
n
[
2
0
]
is
ad
o
p
ted
th
r
o
u
g
h
o
f
f
l
in
e
iter
ati
v
e
p
r
o
ce
s
s
to
d
eter
m
in
e
d
i
f
f
er
en
t
s
tr
in
g
s
o
f
a
n
g
le
s
f
o
r
d
if
f
er
e
n
t
m
o
d
u
latio
n
in
d
ice
s
,
all
t
h
ese
v
alu
e
s
ar
e
s
a
v
ed
in
lo
o
k
-
u
p
tab
les
(
L
UT
)
w
it
h
i
n
M
A
T
L
A
B
/
Si
m
u
li
n
k
p
r
o
g
r
a
m
.
T
h
e
co
m
p
ar
is
o
n
s
ar
e
d
o
n
e
b
y
a
n
al
y
zin
g
lo
ad
v
o
lta
g
e
a
n
d
cu
r
r
en
t
w
a
v
ef
o
r
m
s
,
T
o
tal
H
ar
m
o
n
ic
Dis
to
r
tio
n
(
T
HD)
as
w
ell
as
h
ar
m
o
n
ic
s
p
ec
tr
u
m
p
ar
ticu
lar
l
y
at
l
o
w
o
r
d
er
h
ar
m
o
n
ics
a
t
d
i
f
f
er
e
n
t
lo
ad
p
o
w
er
.
Fo
r
p
r
ec
is
e
ev
alu
a
tio
n
,
t
h
e
eq
u
iv
a
len
t
C
S
F
P
W
M
s
w
itc
h
in
g
f
r
eq
u
e
n
c
y
i
s
s
elec
ted
f
o
r
ea
ch
co
m
p
ar
is
o
n
i
n
d
iv
id
u
all
y
b
ased
o
n
th
e
n
u
m
b
er
o
f
s
w
itc
h
i
n
g
an
g
le
o
f
SHE
P
W
M
tech
n
iq
u
e.
T
h
e
an
al
y
s
i
s
i
n
d
icate
s
t
h
e
h
i
g
h
l
y
p
r
io
r
it
y
o
f
SHE
P
W
M
o
v
er
C
SF
P
W
M
esp
ec
ia
ll
y
f
o
r
h
ig
h
le
v
el
o
f
p
o
w
er
ap
p
licatio
n
s
.
2.
S
WI
T
CH
I
N
G
AN
G
L
E
S DE
T
E
RM
I
NAT
I
O
N
T
h
e
m
et
h
o
d
o
f
Ne
w
to
n
-
R
ap
h
s
o
n
is
ad
o
p
ted
to
d
eter
m
i
n
e
t
h
e
p
o
s
itio
n
s
o
f
t
h
e
s
in
g
le
-
p
h
a
s
e
H
-
b
r
id
g
e
in
v
er
ter
’
s
s
w
itc
h
es
s
w
i
tch
i
n
g
an
g
le
s
f
o
r
t
h
e
ai
m
o
f
eli
m
i
n
at
in
g
t
h
e
lo
w
o
r
d
er
h
ar
m
o
n
ics
o
f
d
if
f
er
e
n
t
an
g
le
s
s
tr
in
g
s
a
s
f
o
llo
w
s
;
(
3
th
,
5
th
)
,
(
3
th
,
5
th
,
7
th
,
9
th
,
1
1
th
)
,
(
3
th
,
5
th
,
7
th
,
9
th
,
1
1
th
,
1
3
th
)
,
an
d
(
3
th
,
5
th
,
7
th
,
9
th
,
1
1
th
,
1
3
th
,
1
5
th
,
1
7
th
)
at
r
a
n
g
e
o
f
m
o
d
u
lat
io
n
i
n
d
ex
(
MI
)
v
alu
es
.
Fo
r
t
h
e
f
ir
s
t
s
tr
i
n
g
o
f
s
w
itc
h
i
n
g
a
n
g
les
(
∅
1
,
∅
2
,
an
d
∅
3
)
w
h
ic
h
w
i
ll
b
e
d
eter
m
i
n
ed
b
y
iter
atio
n
m
et
h
o
d
u
s
i
n
g
Ne
w
to
n
R
ap
h
s
o
n
a
lg
o
r
ith
m
p
r
o
ce
s
s
[
2
0
]
,
th
is
p
r
o
ce
s
s
i
s
s
tar
ted
f
r
o
m
E
q
.
(
1
)
,
o
b
tain
in
g
t
h
e
s
et
o
f
th
e
n
o
n
li
n
ea
r
eq
u
atio
n
s
,
an
d
th
en
s
o
l
v
e
t
h
ese
eq
u
atio
n
s
s
et
.
S
a
m
e
p
r
o
ce
s
s
is
r
ep
ea
ted
to
h
av
e
th
e
o
t
h
er
s
o
l
u
tio
n
s
o
f
t
h
e
o
t
h
er
an
g
les
s
ets
f
o
r
ex
tr
a
lo
w
o
r
d
er
h
ar
m
o
n
ics
el
i
m
in
at
io
n
.
Fi
g
u
r
e
1
s
h
o
w
s
th
e
to
p
o
lo
g
y
o
f
th
e
i
n
v
er
ter
w
h
ic
h
ad
o
p
ted
th
e
u
n
ip
o
lar
P
W
M
s
tr
ateg
y
i
n
o
r
d
er
to
r
ed
u
ce
th
e
s
tr
ess
on
t
h
e
i
n
v
er
te
r
’
s
s
w
it
ch
es
[
1
]
,
[
2
]
.
Fo
r
SHE
P
W
M,
Fig
u
r
e
2
s
h
o
w
s
t
h
e
s
h
ap
e
o
f
t
h
e
lo
ad
v
o
ltag
e
(
V
AO
)
w
h
ich
e
x
p
lain
s
f
iv
e
s
w
itc
h
in
g
an
g
les.
Du
e
to
w
av
e
s
y
m
m
etr
y
q
u
ar
ter
w
av
e
f
o
r
m
[
2
1
]
;
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
I
SS
N:
2088
-
8
694
E
va
lu
a
tio
n
o
f S
elec
tive
Ha
r
mo
n
ic
E
limin
a
tio
n
P
u
ls
e
W
id
th
Mo
d
u
la
tio
n
Tech
n
iq
u
e
…
(
Hu
s
s
a
in
A
ttia
)
1159
(
)
=
∑
s
in
(
)
∞
=
1
(
1
)
w
h
er
e
b
n
=
0
f
o
r
ev
en
n
,
w
h
er
e
as f
o
r
o
d
d
n
;
=
4
∫
2
0
s
in
(
)
(
)
(
2
)
Fig
u
r
e
1
.
H
-
b
r
id
g
e
s
i
n
g
le
p
h
as
e
in
v
er
ter
l
T
o
tal
Har
m
o
n
ics D
is
to
r
tio
n
(
T
HD)
ca
n
b
e
ca
lcu
lated
u
s
in
g
E
q
.
(
3
)
;
=
√
∑
2
∞
=
2
1
w
h
er
e
V
1
is
th
e
f
ir
s
t
f
u
n
d
a
m
en
tal
co
m
p
o
n
en
t
w
h
ile
V
n
ar
e
th
e
ab
o
v
e
h
ar
m
o
n
ic
co
m
p
o
n
en
ts
[
1
4
]
.
Fo
r
th
e
n
o
tch
es
o
f
th
e
f
i
v
e
an
g
les
o
f
∅
1
,
∅
2
,
∅
3
,
∅
4
,
a
n
d
∅
5
,
w
h
ich
ar
e;
0
≤
∅
1
≤
∅
2
≤
∅
3
≤
∅
4
,
≤
∅
5
≤
2
,
th
e
v
al
u
e
o
f
b
n
ca
n
b
e
ca
lcu
la
t
ed
as f
o
llo
w
s
;
=
4
(
∫
∅
2
∅
1
s
in
(
)
(
)
+
∫
∅
4
∅
3
s
in
(
)
(
)
+
∫
2
∅
5
s
in
(
)
(
)
)
(
4
)
=
4
(
[
−
c
os
(
)
]
∅
2
∅
1
+
[
−
c
os
(
)
]
∅
4
∅
3
+
[
−
c
os
(
)
]
2
∅
5
)
(
5
)
=
4
(
[
−
c
os
(
)
]
∅
2
∅
1
+
[
−
c
os
(
)
]
∅
4
∅
3
+
[
−
c
os
(
)
]
2
∅
5
)
Du
e
to
n
is
o
d
d
d
u
r
in
g
th
e
a
n
a
l
y
s
i
s
an
d
t
h
e
d
eter
m
i
n
atio
n
o
f
b
n
,
so
[
−
c
os
(
)
]
=
0
(
6
)
=
4
[
c
os
(
∅
1
)
−
c
os
(
∅
2
)
+
c
os
(
∅
3
)
−
c
os
(
∅
4
)
+
c
os
(
∅
5
)
]
(
7
)
Fig
u
r
e
2
.
Selectiv
e
Har
m
o
n
ic
E
li
m
i
n
atio
n
P
u
ls
es
w
i
th
U
n
ip
o
lar
PW
M
s
tr
ateg
y
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
,
Vo
l.
9
,
No
.
3
,
Sep
tem
b
er
2
0
1
8
:
1
1
5
7
–
1
1
6
5
1160
I
n
o
th
er
w
o
r
d
s
to
k
ee
p
o
n
l
y
f
i
r
s
t
h
ar
m
o
n
ic
(
V
1
)
an
d
r
e
m
o
v
e
th
e
o
d
d
m
u
l
tip
le
o
f
it,
E
q
.
(
7
)
ca
n
b
e
r
e
-
w
r
ite
i
n
E
q
.
(
8
)
as
s
h
o
w
n
w
it
h
in
th
e
n
o
n
l
in
ea
r
eq
u
atio
n
s
;
4
[
(
∅
1
)
−
(
∅
2
)
+
(
∅
3
)
−
(
∅
4
)
+
(
∅
5
)
]
=
1
(
3∅
1
)
−
(
3∅
2
)
+
(
3∅
3
)
−
(
3∅
4
)
+
(
3∅
5
)
=
0
(
5∅
1
)
−
(
5∅
2
)
+
(
5∅
3
)
−
(
5∅
4
)
+
(
5∅
5
)
=
0
(
7∅
1
)
−
(
7∅
2
)
+
(
7∅
3
)
−
(
7∅
4
)
+
(
7∅
5
)
=
0
(
9∅
1
)
−
(
9∅
2
)
+
(
9∅
3
)
−
(
9∅
4
)
+
(
9∅
5
)
=
0
(
8
)
I
n
itial a
n
g
le
s
o
f
a
s
i
n
g
le
-
p
h
ase
u
n
ip
o
lar
SHE
P
W
M
in
v
er
ter
b
ased
o
n
[
2
2
]
:
∅
=
180
×
2
+
1
(
9
)
w
h
er
e
k
=
1
,
2
,
3,
….
N;
a
n
d
N:
n
u
m
b
er
o
f
an
g
le
s
,
t
h
e
i
n
itial
v
a
lu
e
o
f
th
e
f
iv
e
an
g
le
s
is
a
s
s
h
o
w
n
b
elo
w
w
h
er
ea
s
t
h
e
s
o
l
u
tio
n
s
o
f
th
e
s
e
an
g
les
b
ased
o
n
Ne
w
to
n
-
R
ap
h
s
o
n
Me
th
o
d
[
2
0
]
th
r
o
u
g
h
f
i
v
e
iter
atio
n
p
r
o
ce
s
s
f
o
r
d
if
f
er
e
n
t
m
o
d
u
latio
n
i
n
d
ic
es a
r
e
s
h
o
w
n
i
n
T
ab
le
1
;
∅
0
1
= 16.36ᵒ
,
∅
0
2
= 32.73ᵒ
,
∅
0
3
= 49.1ᵒ
,
∅
0
4
= 65.4
5ᵒ
,
∅
0
5
= 81.8
ᵒ
Fig
u
r
e
3
s
h
o
w
s
f
o
u
r
s
tr
in
g
s
o
f
a
n
g
le
s
w
h
ic
h
r
ep
r
esen
t
a
s
a
s
elec
ti
v
e
h
ar
m
o
n
ic
s
eli
m
i
n
ati
o
n
s
o
lu
tio
n
at
d
if
f
er
e
n
t
m
o
d
u
latio
n
i
n
d
ice
s
.
T
ab
le
1.
A
n
g
le
s
o
lu
t
io
n
s
f
o
r
h
ar
m
o
n
ics el
i
m
in
at
io
n
b
ased
o
n
Ne
w
to
n
-
R
ap
h
s
o
n
Me
t
h
o
d
MI
∅
1
∅
2
∅
3
∅
4
∅
5
0
.
0
1
2
9
.
9
2
4
9
3
0
.
0
7
4
9
5
9
.
8
6
9
9
6
0
.
1
2
9
7
8
9
.
8
5
0
0
0
.
0
3
5
2
9
.
7
2
9
5
3
0
.
2
5
4
3
5
9
.
5
4
1
6
6
0
.
4
5
1
1
8
9
.
4
7
4
9
0
.
1
0
2
9
.
2
3
0
8
3
0
.
7
2
8
7
5
8
.
6
8
1
9
6
1
.
2
8
0
7
8
8
.
4
9
8
3
0
.
1
5
2
8
.
8
3
9
6
3
1
.
0
8
3
0
5
8
.
0
1
1
5
6
1
.
9
1
0
9
8
7
.
7
4
4
7
0
.
2
0
2
8
.
4
3
8
5
3
1
.
4
2
2
8
5
7
.
3
2
9
5
6
2
.
5
3
1
0
8
6
.
9
8
7
3
0
.
2
5
2
8
.
0
3
1
0
3
1
.
7
5
0
0
5
6
.
6
3
6
7
6
3
.
1
4
2
1
8
6
.
2
2
4
8
0
.
3
0
2
7
.
6
1
7
2
3
2
.
0
6
3
1
5
5
.
9
3
2
1
6
3
.
7
4
3
7
8
5
.
4
5
5
7
0
.
3
5
2
7
.
1
9
7
5
3
2
.
3
6
0
4
5
5
.
2
1
4
3
6
4
.
3
3
4
7
8
4
.
6
7
7
9
0
.
4
0
2
6
.
7
7
1
8
3
2
.
6
3
9
6
5
4
.
4
8
1
8
6
4
.
9
1
3
7
8
3
.
8
8
9
2
0
.
4
5
2
6
.
3
4
0
1
3
2
.
8
9
8
3
5
3
.
7
3
2
7
6
5
.
4
7
8
7
8
3
.
0
8
6
6
0
.
5
0
2
5
.
9
0
2
4
3
3
.
1
3
3
3
5
2
.
9
6
4
5
6
6
.
0
2
6
6
8
2
.
2
6
6
6
0
.
5
5
2
5
.
4
5
8
1
3
3
.
3
4
0
8
5
2
.
1
7
4
4
6
6
.
5
5
3
5
8
1
.
4
2
4
1
0
.
6
0
2
5
.
0
0
6
7
3
3
.
5
1
6
0
5
1
.
3
5
8
6
6
7
.
0
5
3
0
8
0
.
5
5
2
3
0
.
6
5
2
4
.
5
4
7
3
3
3
.
6
5
3
0
5
0
.
5
1
2
2
6
7
.
5
1
6
1
7
9
.
6
4
1
3
0
.
7
0
2
4
.
0
7
8
5
3
3
.
7
4
3
6
4
9
.
6
2
8
9
6
7
.
9
2
8
1
7
8
.
6
7
6
0
0
.
7
5
2
3
.
5
9
8
0
3
3
.
7
7
7
2
4
8
.
6
9
9
8
6
8
.
2
6
4
9
7
7
.
6
3
2
1
0
.
8
0
2
3
.
1
0
1
9
3
3
.
7
3
8
1
4
7
.
7
1
1
8
6
8
.
4
8
3
4
7
6
.
4
6
6
9
0
.
8
5
2
2
.
5
8
3
5
3
3
.
6
0
1
5
4
6
.
6
4
3
3
6
8
.
4
9
8
0
7
5
.
0
9
7
8
0
.
9
0
2
2
.
0
2
7
5
3
3
.
3
2
0
3
4
5
.
4
5
1
3
6
8
.
1
1
2
3
7
3
.
3
3
7
0
0
.
9
5
2
1
.
3
8
8
0
3
2
.
7
6
6
7
4
4
.
0
1
2
9
6
6
.
7
4
6
3
7
0
.
6
4
0
3
1
.
0
0
2
0
.
3
4
5
5
3
1
.
1
2
8
6
4
1
.
5
0
8
4
6
1
.
5
1
6
8
6
4
.
4
1
5
8
3.
CO
M
P
ARATI
VE
S
I
M
UL
AT
I
O
N
R
E
SU
L
T
S
T
h
e
f
o
u
r
an
g
le
s
s
tr
i
n
g
s
ar
e
s
av
ed
in
lo
o
k
u
p
tab
les
L
UT
o
f
MA
T
L
A
B
/
Si
m
u
latio
n
to
b
e
u
s
ed
w
it
h
a
s
u
itab
le
lo
g
ic
co
m
b
in
a
tio
n
to
g
en
er
ate
th
e
P
W
M
p
u
ls
es
at
t
h
e
m
en
tio
n
ed
a
n
g
les
t
h
at
to
e
x
ec
u
te
t
h
e
Selec
tiv
e
Har
m
o
n
ic
E
li
m
i
n
atio
n
P
W
M
(
SHE
P
W
M)
tech
n
iq
u
e.
T
o
ev
alu
ate
th
e
SHE
P
W
M
b
ased
in
v
er
ter
p
er
f
o
r
m
a
n
ce
,
T
o
tal
Har
m
o
n
ic
s
Dis
to
r
tio
n
(
T
HD)
,
an
d
h
ar
m
o
n
ics
s
p
ec
tr
u
m
o
f
t
h
e
lo
ad
v
o
ltag
es
ar
e
co
m
p
ar
ed
w
it
h
t
h
e
co
u
n
ter
p
ar
ts
o
f
C
o
n
s
t
an
t
S
w
i
tch
in
g
Fre
q
u
e
n
c
y
P
W
M
(
C
SF
P
W
M)
b
ased
in
v
er
ter
at
all
o
f
t
h
e
a
n
g
les
s
tr
in
g
s
s
ep
ar
atel
y
co
n
s
id
er
i
n
g
th
e
s
a
m
e
n
u
m
b
er
o
f
s
w
i
tch
i
n
g
an
g
le
f
o
r
ea
ch
ca
s
e.
T
ab
le
I
I
s
h
o
w
s
th
e
in
v
er
ter
p
ar
am
eter
s
in
cl
u
d
i
n
g
t
h
e
s
w
i
tc
h
in
g
f
r
eq
u
en
c
ies
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
I
SS
N:
2088
-
8
694
E
va
lu
a
tio
n
o
f S
elec
tive
Ha
r
mo
n
ic
E
limin
a
tio
n
P
u
ls
e
W
id
th
Mo
d
u
la
tio
n
Tech
n
iq
u
e
…
(
Hu
s
s
a
in
A
ttia
)
1161
T
ab
le
2
.
I
n
v
er
ter
s
ettin
g
p
ar
am
eter
s
P
a
r
a
me
t
e
r
S
H
E
P
W
M
B
a
se
d
I
n
v
e
r
t
e
r
C
S
F
P
W
M
B
a
se
d
I
n
v
e
r
t
e
r
D
C
l
i
n
k
V
o
l
t
a
g
e
(
V
)
3
5
0
V
3
5
0
V
L
o
a
d
1
2
Ω
1
2
Ω
R
a
t
e
d
P
o
w
e
r
5
k
W
5
k
W
M
o
d
u
l
a
t
i
o
n
I
n
d
e
x
(
M
I
)
0
.
9
0
.
9
L
-
F
i
l
t
e
r
1
2
mH
1
2
mH
1
st
C
o
mp
a
r
i
so
n
∅
1
,
∅
2
,
∅
3
f
SW
=
3
0
0
H
z
2
nd
C
o
mp
a
r
i
so
n
∅
1
,
∅
2
,
∅
3
,
∅
4
,
∅
5
f
SW
=
5
0
0
H
z
3
rd
C
o
mp
a
r
i
so
n
∅
1
,
∅
2
,
∅
3
,
∅
4
,
∅
5
,
∅
6
,
∅
7
f
SW
=
7
0
0
H
z
4
th
C
o
m
p
a
r
i
so
n
∅
1
,
∅
2
,
∅
3
,
∅
4
,
∅
5
,
∅
6
,
∅
7
,
∅
6
,
∅
7
f
SW
=
9
0
0
H
z
Fig
u
r
e
3
s
h
o
w
s
t
h
e
co
m
p
ar
is
o
n
o
f
t
h
e
i
n
v
er
ter
o
u
tp
u
t
v
o
lt
ag
e
w
i
th
it
s
Fa
s
t
Fo
u
r
ier
T
r
an
s
f
o
r
m
F
F
T
an
al
y
s
is
o
f
t
h
e
h
ar
m
o
n
ic
s
s
p
e
ctr
u
m
b
et
w
ee
n
t
h
e
SHE
P
W
M
an
d
th
e
C
SF
P
W
M
o
f
th
e
co
n
s
tan
t
s
w
itc
h
i
n
g
f
r
eq
u
en
c
ies a
s
e
x
p
lai
n
ed
i
n
T
ab
le
I
I
.
Fro
m
Fi
g
u
r
e
3
,
t
h
e
lo
w
o
r
d
er
h
ar
m
o
n
ics
eli
m
i
n
atio
n
is
clea
r
l
y
n
o
ticea
b
le
w
it
h
r
esp
ec
t
to
th
e
d
esi
g
n
ed
an
g
le
s
o
f
SHE
P
W
M
co
m
p
ar
ed
to
th
e
u
n
d
esira
b
le
lo
w
o
r
d
er
h
ar
m
o
n
ics
u
s
i
n
g
C
SF
P
W
M.
Mo
r
e
o
v
er
,
th
e
h
ig
h
er
v
alu
e
s
o
f
t
h
e
v
o
lta
g
e
f
u
n
d
am
e
n
tal
s
ar
e
d
e
m
o
n
s
tr
ated
u
s
in
g
SHE
P
W
M.
Fig
u
r
e
4
s
u
m
m
ar
izes
th
e
co
m
p
ar
i
s
o
n
in
ter
m
o
f
i
n
v
er
ter
v
o
lta
g
e
s
h
ap
e
w
i
th
F
FT
an
a
l
y
s
i
s
u
s
in
g
T
ab
le
I
I
p
ar
am
eter
s
s
ett
in
g
.
Fi
g
u
r
e
4
clea
r
l
y
d
e
m
o
n
s
tr
ates
t
h
e
p
r
io
r
ity
o
f
th
e
h
ar
m
o
n
ic
eli
m
i
n
atio
n
tec
h
n
iq
u
e
co
m
p
ar
i
n
g
to
t
h
e
co
n
v
en
t
io
n
al
s
in
u
s
o
id
al
P
W
M
tech
n
iq
u
e.
Fig
u
r
e
5
ad
d
o
th
er
e
x
p
la
n
a
tio
n
o
f
t
h
e
s
i
m
u
la
tio
n
r
e
s
u
l
ts
i
n
ter
m
o
f
T
HD%
le
v
el
s
a
n
d
th
e
f
u
n
d
a
m
en
ta
l v
o
lta
g
e
lev
el
t
h
r
o
u
g
h
w
h
ic
h
th
e
ad
v
a
n
ta
g
es o
f
u
s
in
g
SHE
P
W
M
ar
e
also
s
h
o
wn
.
Fig
u
r
e
6
s
h
o
w
s
lo
ad
cu
r
r
en
ts
w
a
v
e
f
o
r
m
s
w
it
h
FF
T
co
m
p
ar
i
s
o
n
at
m
o
d
u
latio
n
in
d
ex
M
I
=
0
.
9
f
o
r
th
e
ca
s
e
o
f
SHE
P
W
M
o
f
n
i
n
e
an
g
le
s
an
d
C
SF
P
W
M
o
f
9
0
0
Hz
co
n
s
tan
t
s
w
i
tch
in
g
f
r
eq
u
en
c
y
,
Fig
u
r
e
6
d
em
o
n
s
tr
ate
s
t
h
e
d
ata
o
f
5
k
W
r
ated
p
o
w
er
lo
ad
cu
r
r
en
t
wav
ef
o
r
m
s
t
h
r
o
u
g
h
w
h
ich
th
e
e
f
f
ec
tiv
e
n
e
s
s
o
f
SHE
P
W
M
o
v
er
C
SF
P
W
M
is
s
h
o
w
n
i
n
ter
m
o
f
T
HD
an
d
f
u
n
d
am
en
tal
cu
r
r
en
t le
v
el
s
.
Fig
u
r
e
7
d
em
o
n
s
tr
ates
t
h
e
p
o
s
itiv
e
ef
f
ec
t
a
n
d
th
e
p
r
io
r
it
y
o
f
u
s
i
n
g
SHE
P
W
M
in
ter
m
o
f
f
u
n
d
a
m
en
ta
l
cu
r
r
e
n
t
co
m
p
o
n
en
t
a
n
d
T
HD
%
lev
el
s
f
o
r
h
ig
h
p
o
w
er
ap
p
licatio
n
s
.
I
n
v
er
ter
p
er
f
o
r
m
a
n
ce
i
s
ex
p
lain
ed
d
u
r
i
n
g
i
n
cr
ea
s
i
n
g
t
h
e
lo
ad
p
o
w
er
,
a
n
d
th
e
tec
h
n
i
q
u
e
o
f
SHE
P
W
M
is
p
r
ef
er
r
ed
to
u
s
e
f
d
u
e
to
t
h
e
lo
w
s
w
i
tch
in
g
lo
s
s
e
s
t
h
r
o
u
g
h
t
h
e
lo
w
er
n
u
m
b
er
o
f
s
w
i
tch
e
s
c
o
m
m
u
tatio
n
s
p
er
f
u
n
d
a
m
e
n
tal
p
er
io
d
[
1
]
(
a)
(
b
)
(
c
)
(
d
)
Fig
u
r
e
3
.
Fo
u
r
s
tr
in
g
s
o
f
an
g
le
s
as a
s
elec
ti
v
e
h
ar
m
o
n
ic
s
eli
m
i
n
atio
n
s
o
lu
tio
n
at
d
if
f
er
en
t
m
o
d
u
latio
n
in
d
ice
s
;
(
a)
T
h
r
ee
an
g
les,
(
b
)
Fiv
e
a
n
g
l
es,
(
c)
Sev
en
a
n
g
le
s
,
(
d
)
Nin
e
an
g
le
s
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
M
o
d
u
l
a
t
i
o
n
I
n
d
e
x
(
M
I
)
A
n
g
le
(
d
e
g
.)
&
1
&
2
&
3
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
M
o
d
u
l
a
t
i
o
n
I
n
d
e
x
(
M
I
)
A
n
g
le
(
d
e
g
.)
&
1
&
2
&
3
&
4
&
5
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
M
o
d
u
l
a
t
i
o
n
I
n
d
e
x
(
M
I
)
A
n
g
le
(
d
e
g
.)
&
1
&
2
&
3
&
4
&
5
&
6
&
7
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
M
o
d
u
l
a
t
i
o
n
I
n
d
e
x
(
M
I
)
A
n
g
le
(
d
e
g
.)
&
1
&
2
&
3
&
4
&
5
&
6
&
7
&
8
&
9
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
,
Vo
l.
9
,
No
.
3
,
Sep
tem
b
er
2
0
1
8
:
1
1
5
7
–
1
1
6
5
1162
SHE
P
W
M
(
3
A
n
g
le
s
)
C
SF
P
W
M
(
f
s
=
3
0
0
Hz)
SHE
P
W
M
(
5
A
n
g
les)
C
SF
P
W
M
(
f
s
=
5
0
0
Hz)
SHE
P
W
M
(
7
A
n
g
le
s
)
C
SF
P
W
M
(
f
s
=
7
0
0
Hz)
SHE
P
W
M
(
9
A
n
g
le
s
)
C
SF
P
W
M
(
f
s
=
9
0
0
Hz)
Fig
u
r
e
4
.
I
n
v
er
ter
p
er
f
o
r
m
an
c
e
co
m
p
ar
is
o
n
in
ter
m
o
f
o
u
tp
u
t v
o
ltag
e
s
h
ap
e,
h
ar
m
o
n
ic
s
p
ec
tr
u
m
,
T
HD
lev
el,
an
d
f
u
n
d
a
m
en
tal
co
m
p
o
n
e
n
t v
alu
es;
SHE
P
W
M
(
lef
t
s
id
e)
,
an
d
C
SF
P
W
M
(
r
ig
h
t
s
id
e)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
I
SS
N:
2088
-
8
694
E
va
lu
a
tio
n
o
f S
elec
tive
Ha
r
mo
n
ic
E
limin
a
tio
n
P
u
ls
e
W
id
th
Mo
d
u
la
tio
n
Tech
n
iq
u
e
…
(
Hu
s
s
a
in
A
ttia
)
1163
(a
)
(
b
)
Fig
u
r
e
5
.
C
o
m
p
ar
is
o
n
b
et
w
ee
n
SHE
P
W
M
an
d
C
SF
P
W
M
b
ased
in
v
er
ter
p
er
f
o
r
m
a
n
ce
ter
m
;
(
a)
I
n
v
er
ter
Vo
ltag
e
T
HD%
lev
els,
(
b
)
Fu
n
d
a
m
e
n
tal
v
o
ltag
e
lev
els
SHE
P
W
M
(
9
A
n
g
le
s
)
C
SF
P
W
M
(
f
s
=
9
0
0
Hz)
Fig
u
r
e
6
.
I
n
v
er
ter
p
er
f
o
r
m
an
c
e
co
m
p
ar
is
o
n
in
ter
m
o
f
lo
ad
cu
r
r
en
t,
an
d
h
ar
m
o
n
ic
s
p
ec
tr
u
m
(
a)
(
b
)
Fig
u
r
e
7
.
I
n
v
er
ter
p
er
f
o
r
m
an
c
e
co
m
p
ar
is
o
n
at
d
if
f
er
en
t lo
ad
p
o
w
er
in
ter
m
;
(
a)
Fu
n
d
a
m
e
n
tal
c
u
r
r
en
t c
o
m
p
o
n
en
t,
(
b
)
T
HD
% lev
els
4.
CO
NCLU
SI
O
N
C
o
m
p
lete
s
tep
s
o
f
SHE
P
W
M
s
o
lu
tio
n
s
g
en
er
atio
n
a
n
d
s
in
g
le
-
p
h
a
s
e
u
n
ip
o
lar
in
v
er
te
r
f
u
n
ct
io
n
in
v
e
s
ti
g
atio
n
w
it
h
p
er
f
o
r
m
an
ce
ef
f
ec
ti
v
en
e
s
s
ev
al
u
atio
n
b
ased
o
n
S
HE
P
W
M,
an
d
co
m
p
ar
i
n
g
w
i
th
C
SF
P
W
M
b
ased
in
v
er
ter
all
ar
e
p
r
esen
ted
i
n
t
h
i
s
p
ap
er
.
Fo
u
r
g
r
o
u
p
s
o
f
a
n
g
les
ar
e
g
e
n
er
ated
b
y
d
er
iv
i
n
g
s
ets
o
f
n
o
n
li
n
ea
r
eq
u
atio
n
s
an
d
t
h
en
d
if
f
er
e
n
t
s
tr
i
n
g
s
o
f
a
n
g
le
s
f
o
r
d
if
f
er
e
n
t
m
o
d
u
latio
n
i
n
d
ices
a
r
e
d
eter
m
i
n
ed
u
s
i
n
g
th
e
f
iv
e
-
iter
atio
n
n
u
m
er
ical
m
eth
o
d
o
f
Ne
w
to
n
-
R
ap
h
s
o
n
,
th
e
co
llected
an
g
le
s
ar
e
p
lo
tted
an
d
th
e
e
f
f
ec
ts
a
r
e
an
al
y
ze
d
.
M
A
T
L
A
B
/Si
m
u
li
n
k
is
u
s
ed
to
s
av
e
t
h
ese
an
g
le
s
i
n
lo
o
k
-
u
p
tab
les
(
L
UT
)
an
d
w
ith
a
s
u
itab
le
lo
g
ic
co
m
b
i
n
atio
n
;
S
HE
P
W
M
p
u
ls
es
ar
e
g
e
n
er
ated
to
d
r
iv
e
t
h
e
i
n
v
er
ter
s
w
itc
h
es.
T
h
e
i
n
v
er
ter
o
u
tp
u
t
v
o
lta
g
e
a
n
d
lo
ad
cu
r
r
en
t
th
r
o
u
g
h
L
-
f
ilter
ar
e
ev
alu
ate
d
b
y
t
h
e
co
m
p
ar
is
o
n
w
ith
th
e
co
u
n
ter
p
ar
t
o
f
C
S
F
P
W
M
in
ter
m
o
f
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
,
Vo
l.
9
,
No
.
3
,
Sep
tem
b
er
2
0
1
8
:
1
1
5
7
–
1
1
6
5
1164
h
ar
m
o
n
ic
s
p
ec
tr
u
m
,
f
u
n
d
a
m
en
tal
co
m
p
o
n
e
n
t,
lo
w
o
r
d
er
h
ar
m
o
n
ic
co
m
p
o
n
e
n
t
s
le
v
els
a
n
d
T
HD
lev
el
s
.
B
ased
o
n
th
e
n
u
m
b
er
o
f
g
e
n
er
ated
s
w
itc
h
in
g
a
n
g
les,
t
h
e
co
n
s
t
an
t
s
w
i
tch
in
g
f
r
eq
u
en
c
y
o
f
C
SF
P
W
M
is
f
air
l
y
s
elec
ted
s
u
c
h
as
3
0
0
Hz
f
o
r
th
e
ca
s
e
o
f
th
r
ee
an
g
le
w
h
er
ea
s
9
0
0
Hz
f
o
r
th
e
ca
s
e
o
f
n
in
e
a
n
g
les.
T
h
e
co
llecte
d
s
i
m
u
lat
io
n
r
esu
lts
ar
e
d
e
m
o
n
s
tr
ated
th
e
m
er
its
o
f
SHE
P
W
M
o
v
er
C
SF
P
W
M
an
d
clea
r
ly
e
x
p
lai
n
ed
f
o
r
th
e
ca
s
e
o
f
lo
ad
p
o
w
er
in
cr
ea
s
i
n
g
th
at
to
p
r
o
v
id
e
a
s
u
itab
le
r
ef
er
en
ce
s
tu
d
y
w
h
ic
h
in
d
icate
t
h
e
p
o
s
itiv
e
e
f
f
ec
t
o
f
SHE
P
W
M
f
o
r
h
ig
h
p
o
w
er
ap
p
licatio
n
s
.
ACK
NO
WL
E
D
G
E
M
E
NT
S
T
h
e
au
th
o
r
s
ap
p
r
ec
iate
t
h
e
f
i
n
an
c
ial
s
u
p
p
o
r
t
p
r
o
v
id
ed
b
y
s
c
h
o
o
l
o
f
e
n
g
i
n
ee
r
i
n
g
,
Am
er
ica
n
Un
i
v
er
s
it
y
o
f
R
as
A
l K
h
ai
m
ah
–
UA
E
,
www
.
au
r
a
k
.
ac
.
ae
/en
/
s
ch
o
o
l
-
of
-
en
g
i
n
ee
r
in
g
/
RE
F
E
R
E
NC
E
S
[1
]
HA
A
tt
ia,
T
KS
F
re
d
d
y
,
HS
Ch
e
,
W
P
He
w
,
A
El
Kh
a
teb
,
“
Co
n
f
in
e
d
Ba
n
d
V
a
riab
le
S
w
it
c
h
in
g
F
re
q
u
e
n
c
y
P
u
lse
W
id
th
M
o
d
u
lat
io
n
(CB
-
VSF
P
W
M
)
f
o
r
S
in
g
le
-
P
h
a
se
In
v
e
rter
w
it
h
L
C
L
F
il
ter”
,
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
P
o
w
e
r
El
e
c
tro
n
ics
,
2
0
1
6
.
[2
]
HA
A
tt
ia,
H
W
P
in
g
,
Y
A
l
-
M
a
s
h
h
a
d
a
n
y
,
“
De
si
g
n
a
n
d
a
n
a
ly
sis
fo
r
h
ig
h
p
e
rf
o
rm
a
n
c
e
s
y
n
c
h
ro
n
ize
d
in
v
e
rter
w
it
h
P
W
M
p
o
w
e
r
c
o
n
tro
l”,
Clea
n
E
n
e
rg
y
a
n
d
T
e
c
h
n
o
lo
g
y
(CE
AT
),
2
0
1
3
IEE
E
Co
n
f
e
re
n
c
e
,
2
6
5
-
2
7
0
.
[3
]
Hu
ss
a
in
A
.
A
tt
ia,
Yo
u
sif
I.
A
l
-
M
a
sh
h
a
d
a
n
y
,
Be
z
a
N.
G
e
tu
,
“
De
sig
n
a
n
d
S
im
u
latio
n
o
f
a
Hig
h
P
e
rf
o
rm
a
n
c
e
S
tan
d
a
l
o
n
e
P
h
o
t
o
v
o
lt
a
ic
S
y
ste
m
,
”
ICREGA
’1
4
–
Re
n
e
wa
b
le
En
e
rg
y
:
G
e
n
e
ra
ti
o
n
a
n
d
A
p
p
li
c
a
ti
o
n
s,
S
p
rin
g
e
r
P
r
o
c
e
e
d
in
g
s in
En
e
rg
y
2
0
1
4
,
p
p
6
8
3
-
6
9
7
.
[4
]
A
tt
ia
Hu
ss
a
in
,
S
a
g
a
f
in
ia
A
li
,
“
No
v
e
l
Disc
re
te
Co
m
p
o
n
e
n
ts
Ba
se
d
S
p
e
e
d
Co
n
tr
o
ll
e
r
f
o
r
In
d
u
c
ti
o
n
M
o
t
o
r”
,
In
tern
a
ti
o
n
a
l
Jo
u
rn
a
l
o
f
P
o
w
e
r
El
e
c
tro
n
ics
a
n
d
Driv
e
S
y
ste
m
s (IJP
EDS
),
V
o
l
.
7
,
Iss
.
4
,
(2
0
1
6
).
[5
]
H
A
tt
ia,
BN
G
e
tu
,
N
Ha
m
a
d
,
“
A
S
tab
le
DC
P
o
w
e
r
S
u
p
p
ly
fo
r
P
h
o
t
o
v
o
lt
a
ic
S
y
ste
m
s”
,
In
t.
J
.
o
f
T
h
e
rm
a
l
&
En
v
iro
n
m
e
n
tal
En
g
in
e
e
rin
g
1
2
(
1
),
(2
0
1
6
)
6
7
-
7
1
.
[6
]
Hu
ss
a
in
A
A
tt
ia,
Am
j
a
d
O
m
a
r,
M
a
e
n
T
a
k
ru
ri,
“
De
sig
n
o
f
d
e
c
e
n
tralize
d
stre
e
t
L
ED
li
g
h
t
d
i
m
m
in
g
s
y
ste
m
”
,
El
e
c
tro
n
ic De
v
ice
s,
S
y
st
e
m
s a
n
d
A
p
p
li
c
a
ti
o
n
s (ICE
DSA
),
2
0
1
6
5
t
h
In
ter
n
a
ti
o
n
a
l
IEE
E
Co
n
f
e
re
n
c
e
,
2
0
1
6
.
[7
]
Hu
ss
a
in
A
.
A
tt
ia,
“
Co
m
p
a
ra
ti
v
e
De
sig
n
o
f
F
u
z
z
y
L
o
g
ic
Co
n
tro
ll
e
r
f
o
r
P
h
o
to
v
o
lt
a
ic
P
a
n
e
l
M
a
x
im
u
m
P
o
w
e
r
P
o
i
n
t
T
ra
c
k
in
g
”
,
2
0
1
7
I
n
tern
a
ti
o
n
a
l
C
o
n
f
e
re
n
c
e
o
n
El
e
c
tri
c
a
l
a
n
d
Co
m
p
u
ti
n
g
T
e
c
h
n
o
l
o
g
ies
a
n
d
A
p
p
li
c
a
ti
o
n
s
(ICE
CT
A
),
978
-
1
-
5
3
8
6
-
0
8
7
2
-
2
/1
7
/$
3
1
.
0
0
©
2
0
1
7
IE
EE
[8
]
H
A
tt
ia,
A
O
m
a
r,
M
T
a
k
ru
ri,
HY
A
li
,
“
P
u
lse
W
id
t
h
M
o
d
u
latio
n
Ba
se
d
De
c
e
n
tralize
d
S
tree
t
L
ED
L
ig
h
t
Dim
m
in
g
S
y
st
e
m
”
,
In
tern
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
P
o
w
e
r
El
e
c
tro
n
ics
a
n
d
Driv
e
sy
st
e
m
s (IJP
EDS
)
,
8
(
3
),
2
0
1
7
,
p
p
.
1
2
3
8
-
1
2
4
7
.
[9
]
L
.
L
i,
D.
Cz
a
rk
o
w
sk
i,
Y.
L
iu
,
a
n
d
P
.
P
i
ll
a
y
,
“
M
u
lt
il
e
v
e
l
S
e
lec
ti
v
e
Ha
r
m
o
n
ic
El
im
in
a
ti
o
n
P
W
M
T
e
c
h
n
i
q
u
e
in
S
e
ries
-
Co
n
n
e
c
ted
Vo
lt
a
g
e
In
v
e
rters
“
,
in
d
u
stry
A
p
p
li
c
a
ti
o
n
s Co
n
f
e
re
n
c
e
,
1
9
9
8
,
U
S
A
,
d
o
i:
1
0
.
1
1
0
9
/IA
S
.
1
9
9
8
.
7
3
0
3
3
4
[1
0
]
K.A
.
Ra
n
i
F
a
th
im
a
,
a
n
d
Dr.T
.
A
.
Ra
g
h
a
v
e
n
d
iren
,
“
De
sig
n
o
f
a
N
o
v
e
l
Co
n
tr
o
l
S
c
h
e
m
e
f
o
r
th
e
Co
n
v
e
rters
o
f
th
e
S
in
g
le
P
h
a
se
Un
if
ied
P
o
w
e
r
F
lo
w
Co
n
tro
ll
e
r
Us
in
g
S
e
lec
ti
v
e
Ha
r
m
o
n
ic
El
im
in
a
ti
o
n
”
,
3
rd
I
n
tern
a
ti
o
n
a
l
Co
n
f
e
re
n
c
e
o
n
P
o
w
e
r,
Co
n
tr
o
l
a
n
d
V
L
S
I
En
g
in
e
e
rin
g
(IC
P
C
V
E'
2
0
1
4
)
Ja
n
.
5
-
6
,
2
0
1
4
D
u
b
a
i
(UA
E),
p
p
.
2
8
-
35
[1
1
]
M
o
h
a
m
e
d
A
z
a
b
,
“
Ha
r
m
o
n
ic
El
imin
a
ti
o
n
i
n
T
h
re
e
-
P
h
a
se
V
o
lt
a
g
e
S
o
u
rc
e
In
v
e
rters
b
y
P
a
rti
c
le
S
w
a
rm
Op
ti
m
iza
ti
o
n
”
,
Jo
u
rn
a
l
o
f
El
e
c
tri
c
a
l
En
g
in
e
e
rin
g
&
T
e
c
h
n
o
lo
g
y
V
o
l.
6
,
No
.
3
,
p
p
.
3
3
4
~
3
4
1
,
2
0
1
1
DO
I:
1
0
.
5
3
7
0
/JE
E
T
.
2
0
1
1
.
6
.
3
.
3
3
4
[1
2
]
Ja
so
n
R.
W
e
ll
s,
X
in
G
e
n
g
,
P
a
tri
c
k
L
.
Ch
a
p
m
a
n
,
P
h
i
li
p
T
.
Kre
in
,
a
n
d
Bre
tt
M
.
Ne
e
,
“
M
o
d
u
lati
o
n
-
Ba
se
d
Ha
r
m
o
n
ic
El
im
in
a
ti
o
n
”
,
IEE
E
T
ra
n
sa
c
ti
o
n
o
n
p
o
w
e
r
El
e
c
tro
n
ics
,
v
o
l
2
2
,
n
o
.
1
,
Ja
n
.
2
0
0
7
,
p
p
.
3
3
6
-
3
4
0
[1
3
]
K.
T
a
m
il
a
r
a
si,
C.
S
u
g
a
n
th
in
i,
“
Ne
u
ra
l
Ne
t
w
o
rk
Ba
se
d
Op
ti
m
a
l
S
w
it
c
h
in
g
P
a
tt
e
r
n
G
e
n
e
ra
ti
o
n
f
o
r
M
u
lt
i
p
le
P
u
lse
W
id
th
M
o
d
u
late
d
I
n
v
e
rter”
,
In
tern
a
ti
o
n
a
l
Jo
u
r
n
a
l
o
f
M
o
d
e
rn
En
g
in
e
e
rin
g
Re
se
a
rc
h
(IJME
R),
V
o
l.
3
,
Iss
u
e
.
4
,
Ju
l
-
A
u
g
.
2
0
1
3
,
p
p
-
1
9
1
0
-
1
9
1
5
[1
4
]
Ja
m
a
l
A
.
M
o
h
a
m
m
e
d
,
“
Op
ti
m
u
m
S
o
lv
in
g
S
HE
P
W
M
E
q
u
a
ti
o
n
s
f
o
r
S
in
g
le
P
h
a
se
In
v
e
rter
Us
in
g
Re
su
lt
a
n
t
M
e
t
h
o
d
”
,
En
g
in
e
e
rin
g
&
T
e
c
h
n
o
lo
g
y
,
V
o
l
.
2
6
,
N
o
.
6
,
2
0
0
8
,
p
p
.
6
6
0
-
6
7
0
[1
5
]
M
.
Kira
n
k
u
m
a
r
,
A
.
M
a
d
h
u
S
a
in
a
th
,
V
.
P
a
v
a
n
Ku
m
a
r,
“
S
e
l
e
c
ti
v
e
Ha
r
m
o
n
ic
El
i
m
in
a
ti
o
n
b
y
P
ro
g
ra
m
m
a
b
le
P
u
lse
W
id
th
M
o
d
u
lati
o
n
i
n
In
v
e
rters
”
,
In
tern
a
ti
o
n
a
l
Jo
u
r
n
a
l
o
f
En
g
in
e
e
rin
g
T
re
n
d
s a
n
d
T
e
c
h
n
o
lo
g
y
(I
JETT
),
V
o
l.
4
,
Iss
.
4
,
A
p
ril
2
0
1
3
,
p
p
.
1
1
9
6
-
1
2
0
1
[1
6
]
Jia
ji
a
Re
n
Jia
n
z
e
Wan
g
Y
in
g
h
o
n
g
Hu
Ya
n
c
h
a
o
Ji,
“
Re
se
a
rc
h
o
n
S
o
lu
ti
o
n
s
t
o
S
e
lec
ti
v
e
Ha
r
m
o
n
ic
E
li
m
in
a
ted
P
W
M
S
w
it
c
h
in
g
A
n
g
les
f
o
r
No
v
e
l
F
iv
e
lev
e
l
In
v
e
rter
”
,
P
o
w
e
r
a
n
d
En
e
rg
y
En
g
in
e
e
rin
g
Co
n
f
e
re
n
c
e
(
A
P
P
E
EC),
2
0
1
0
A
sia
-
P
a
c
if
ic,
d
o
i
:
1
0
.
1
1
0
9
/A
P
P
EE
C.
2
0
1
0
.
5
4
4
9
0
2
9
[1
7
]
Ay
o
n
g
Hie
n
d
ro
,
“
M
u
lt
i
p
le
S
w
it
c
h
in
g
P
a
tt
e
rn
s
f
o
r
S
HE
P
W
M
In
v
e
rters
Us
in
g
Di
ff
e
re
n
ti
a
l
Ev
o
lu
ti
o
n
A
lg
o
rit
h
m
s”
,
In
tern
a
ti
o
n
a
l
Jo
u
rn
a
l
o
f
P
o
w
e
r
El
e
c
tro
n
ics
a
n
d
Driv
e
S
y
ste
m
(IJP
E
DS),
Vo
l.
1
,
N
o
.
2
,
De
c
e
m
b
e
r
2
0
1
1
,
p
p
.
9
4
~
1
0
3
[1
8
]
N.
Ba
h
a
ri,
Z
.
S
a
lam
,
T
a
u
f
ik
,
“
Ap
p
li
c
a
ti
o
n
o
f
Diff
e
re
n
ti
a
l
Ev
o
l
u
ti
o
n
to
De
term
in
e
th
e
HE
P
W
M
A
n
g
les
o
f
a
T
h
re
e
P
h
a
se
V
o
lt
a
g
e
S
o
u
rc
e
In
v
e
rter”
,
3
6
t
h
A
n
n
u
a
l
Co
n
f
e
re
n
c
e
o
n
IEE
E
In
d
u
str
ial
El
e
c
tro
n
ics
so
c
iety
,
No
v
.
2
0
1
0
,
USA
,
p
p
.
2
6
8
3
-
2
6
8
8
[1
9
]
O.
Bo
u
h
a
li
,
M
.
Be
rk
o
u
k
,
B.
F
ra
n
c
o
is,
C.
S
a
u
d
e
m
o
n
t,
S
.
L
a
b
io
d
,
“
S
o
lv
in
g
Ha
rm
o
n
ics
El
i
m
in
a
ti
o
n
P
ro
b
lem
in
T
h
re
e
-
P
h
a
se
V
o
l
tag
e
c
o
n
tro
ll
e
d
I
n
v
e
rter
u
sin
g
A
rti
f
i
c
ial
Ne
u
ra
l
Ne
t
w
o
rk
s”
,
Jo
u
rn
a
l
o
f
El
e
c
tri
c
a
l
S
y
st
e
m
s,
1
-
1
(2
0
0
5
):
p
p
.
39
-
51
[2
0
]
W
a
h
id
a
h
A
b
d
Ha
li
m
,
Ten
g
k
u
No
o
r
A
rian
a
T
e
n
g
k
u
A
z
a
m
,
Ko
m
a
th
i
A
p
p
las
a
m
y
,
A
u
z
a
n
i
Jid
in
,
“
S
e
le
c
ti
v
e
Ha
r
m
o
n
ic
Elim
in
a
ti
o
n
Ba
se
d
o
n
Ne
w
to
n
-
ra
p
h
so
n
M
e
th
o
d
f
o
r
Ca
sc
a
d
e
d
H
-
b
rid
g
e
M
u
lt
il
e
v
e
l
In
v
e
rterIn
tern
a
ti
o
n
a
l
Jo
u
rn
a
l
o
f
P
o
w
e
r
El
e
c
tro
n
ics
a
n
d
Driv
e
S
y
ste
m
(IJP
EDS
),
Vo
l.
8
,
No
.
3
,
S
e
p
t
e
m
b
e
r
2
0
1
7
,
p
p
.
1
1
9
3
~
1
2
0
2
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
I
SS
N:
2088
-
8
694
E
va
lu
a
tio
n
o
f S
elec
tive
Ha
r
mo
n
ic
E
limin
a
tio
n
P
u
ls
e
W
id
th
Mo
d
u
la
tio
n
Tech
n
iq
u
e
…
(
Hu
s
s
a
in
A
ttia
)
1165
[2
1
]
D.
G
ra
h
a
m
e
Ho
l
m
e
s,
“
P
u
lse
W
id
th
M
o
d
u
latio
n
F
o
r
P
o
w
e
r
Co
n
v
e
rte
rs;
P
ri
n
c
ip
les
a
n
d
P
ra
c
ti
c
e
”
,
IEE
E
P
re
ss
,
A
Jo
h
n
W
il
e
y
&
S
o
n
s,
In
c
.
,
P
u
b
li
c
a
ti
o
n
,
2
0
0
3
.
[2
2
]
S
u
n
J,
G
ro
tsto
ll
e
n
H
(1
9
9
2
)
S
o
l
v
in
g
n
o
n
li
n
e
a
r
e
q
u
a
ti
o
n
s
f
o
r
se
le
c
ti
v
e
h
a
r
m
o
n
ic
e
li
m
in
a
ted
P
W
M
u
sin
g
p
re
d
icte
d
in
it
ial
v
a
lu
e
s.
IE
EE
T
ra
n
s
P
o
w
e
r
El
e
c
tro
n
ics
p
p
.
2
5
9
–
2
6
0
B
I
O
G
RAP
H
Y
O
F
AUTHO
R
Hu
ss
a
in
A
tt
ia
e
a
rn
e
d
h
is
M
.
S
c
.
d
e
g
re
e
in
e
lec
tro
n
ic
e
n
g
in
e
e
r
in
g
f
ro
m
th
e
Un
iv
e
rsit
y
o
f
T
e
c
h
n
o
lo
g
y
,
B
a
g
h
d
a
d
,
in
1
9
9
9
.
He
e
a
rn
e
d
h
is
B.
S
c
.
in
e
lec
tro
n
ic
a
n
d
c
o
m
m
u
n
ica
ti
o
n
e
n
g
in
e
e
rin
g
f
ro
m
th
e
sa
m
e
u
n
iv
e
rsity
in
1
9
9
1
.
Hu
ss
a
in
’s
re
se
a
rc
h
in
tere
sts:
P
o
w
e
r
El
e
c
tro
n
ics
S
y
st
e
m
,
A
C
&
DC
S
p
e
e
d
Co
n
tr
o
l
Driv
e
s,
A
n
a
lo
g
&
Dig
it
a
l
El
e
c
tro
n
ic
Circu
it
s
De
sig
n
,
P
W
M
In
v
e
rters
(sin
g
le p
h
a
se
&
th
re
e
p
h
a
se
s).
Evaluation Warning : The document was created with Spire.PDF for Python.