In
te
r
n
ation
a
l Jou
rn
al
o
f Po
we
r
Elec
tron
ic
s an
d
D
r
ive S
y
stem
(IJ
PED
S
)
V
o
l.
10, N
o.
4, D
e
c
e
m
ber
201
9,
pp.
1875~
18
84
ISSN: 2088-
8694,
DOI
:
10.11591
/ijpeds.
v10.
i
4.pp1875-1884
1875
Jou
rn
a
l
h
o
me
pa
ge
:
ht
tp:
//i
a
e
score
.
com
/
j
o
u
r
na
l
s
/
i
n
d
e
x
.
p
hp/IJ
PED
S
Research on hybrid SHEPW
M based on different
switch
ing
pattern
s
Tao
J
i
n
g
,
A
l
exan
d
e
r
Ma
klako
v
,
A
n
d
rey R
ad
ion
o
v, S
ergei
B
as
ko
v,
A
le
k
s
an
d
r
a Ku
lmu
k
h
a
meto
va
Dep
a
rtment
of
Mech
at
ro
n
i
cs and
Au
t
o
m
at
i
o
n
, S
ou
th Ur
a
l
St
a
t
e
Un
i
vers
i
t
y
, Ru
s
s
i
a
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
Re
ce
i
v
e
d
Mar
7
,
201
9
Re
vise
d A
p
r
14,
201
9
Ac
ce
p
t
ed
Ap
r
1
9
,
2
019
Th
is
p
ap
er
p
res
e
nt
s
a hyb
rid
pulse
w
idt
h
m
odu
la
t
i
o
n
(
H
P
WM
)
s
t
ra
teg
y
based
on
d
iff
e
rent
switch
i
ng
p
att
e
rns
o
f
s
el
ectiv
e
h
a
rm
o
n
ic
e
limi
n
ati
on
p
ul
se
w
idth
m
o
d
u
l
a
tio
n
(SHEPWM
)
f
or
t
he
t
hree-lev
e
l
n
e
u
t
ral
po
int
cla
m
ped
(
3L
-NP
C
)
con
v
ert
e
r.
S
pecifi
c
lo
w-o
r
d
e
r
harm
o
n
ics
can
b
e
elim
ina
t
ed
b
y
SH
EP
WM
a
t
lo
w
switch
i
ng
f
requ
ency
,
wh
il
e
th
e
rem
a
in
ing
h
i
gh
-ord
er
h
arm
o
n
i
cs
can
b
e
sel
ected
t
o
be
s
imply
filtered
by
addi
ti
onal
h
a
rdware.
L
a
rge
os
c
i
ll
a
t
io
n
wavef
o
rm
u
sually
o
c
c
urs
in
t
he
t
ransi
t
i
on
ins
t
ant
between
t
wo
d
iverse
modul
a
tion
si
t
u
at
ions
,
there
f
or
e
swit
ch
ing
betw
een
d
istinct
s
wi
tchi
ng
pat
t
ern
s
can
b
e
p
r
obl
em
ati
c
i
f
no
eff
ecti
v
e
m
ean
s
is
t
aken
,
esp
ecial
ly
w
hen
th
e
e
f
f
ect
o
f
s
m
o
o
th
a
nd
f
as
t
tran
s
i
ti
on
a
t
a
n
y
tim
e
is
c
o
n
s
i
d
e
ra
ble.
A
un
iv
ersal
an
d
va
li
d
con
t
rol
st
ra
tegy,
which
mai
n
ta
i
n
s
t
h
e
hi
gh-
quality
o
utput
vo
lt
age
and
curren
t
,
is
p
rop
o
sed
an
d
im
plem
ented
in
t
h
i
s
p
a
per
to
a
ddress
th
is
i
ss
ue.
Simu
lati
on
r
es
ults
o
btai
ned
f
r
o
m
M
ATLA
B/S
I
MUL
I
NK
a
r
e
pres
ent
e
d
to
a
n
a
ly
ze
t
h
e
perf
o
r
man
ce
and
v
a
lid
ate
th
e
f
easib
ili
t
y
a
nd
ef
f
ecti
v
enes
s of th
i
s
con
t
rol s
c
hem
e
.
K
eyw
ord
s
:
A
C
-D
C pow
er
con
ve
rters
D
C
-A
C pow
er
con
ve
rters
Me
di
um
v
o
l
ta
g
e
Re
ac
t
i
ve
p
ow
er
c
ontro
l
Va
ri
ab
l
e
sp
eed d
ri
v
e
s
Co
pyri
gh
t © 2
019 In
stit
u
t
e
of Advanced
En
gi
neeri
n
g
an
d
S
c
ien
ce.
All
rights
res
e
rv
ed.
Corres
pon
d
i
n
g
Au
th
or:
Tao
Ji
ng,
D
e
pa
rtem
ent o
f
M
echa
t
ro
n
i
c
s
and
A
u
t
o
ma
ti
on,
S
out
h U
r
al S
tate U
nive
rsity,
76 Le
nin
P
r
.
4
5
4
0
80,
C
he
l
y
a
b
ins
k
,
Russia.
Em
ail:
j
i
n
g
ta
o
1
9
9
4
0
2
14@
gm
ail.c
o
m
1.
I
N
TR
OD
U
C
TI
O
N
F
o
r t
h
e
pa
st fe
w
yea
rs, pow
er con
ve
rters ha
v
e
been de
v
e
l
o
p
i
n
g
t
o
w
a
r
d
s
t
he
d
i
r
e
c
t
i
on
o
f
hi
gh
v
olt
a
g
e
a
n
d
hig
h
po
we
r
fo
r
pu
rpo
s
e
of
i
mp
ro
vin
g
t
h
e
qu
a
l
it
y
a
n
d
ef
fi
ci
e
nc
y
of
p
o
w
e
r
e
qui
pm
en
t
s
a
n
d
s
yst
e
ms.
D
u
e
to
t
he
a
d
v
an
ta
ges
of
t
he
t
hree
-leve
l
n
eu
tr
al
p
o
i
nt
c
la
mpe
d
(
3L-
N
P
C)
c
onve
r
t
er,
i
n
c
l
ud
in
g
h
i
g
h
v
o
l
tag
e
ca
pab
i
lit
y,
l
o
w
dv/d
t
,
low
sw
it
c
h
i
n
g
l
o
ss
es,
goo
d
o
u
t
p
u
t
q
u
al
it
y
a
n
d
low
elec
t
r
om
a
gne
t
i
c
com
p
a
tib
i
l
i
t
y
(EM
C
)
c
o
n
c
ern
s
,
i
t
h
as
b
een
u
se
d
in
m
a
n
y
co
mmerc
i
a
l
a
n
d
i
nd
us
t
r
ia
l
a
p
p
l
ica
t
i
o
n
s
,
for
in
sta
n
ce
,
high
vo
lta
g
e
direc
t
c
ur
rent
(
H
V
D
C
),
h
igh
-
vo
lt
a
g
e
h
i
gh-
pow
e
r
A
C
var
i
a
b
l
e
s
pe
e
d
dr
iv
e
s
a
nd
fle
x
i
b
le
a
c
tra
n
sm
i
ssion
syste
m
s
(F
A
C
TS
) [1–4]
.
The
pu
lse
w
i
d
t
h
mod
u
l
a
t
i
o
n
(P
WM)
co
ntr
o
l
m
e
th
od
is
a
f
a
i
rl
y
cri
t
i
c
al
t
ech
ni
q
u
e
i
n
t
h
e
res
e
a
r
ch
o
f
3L-N
P
C
c
on
ve
rte
r
,
a
nd
pla
y
s
a
vita
l
ro
le
i
n
re
duci
n
g
syst
e
m
s
w
i
tch
i
n
g
l
osses
a
nd
im
prov
i
ng
pow
er
s
yste
m
efficie
n
c
y
.
It
d
ete
r
mine
s
not
o
n
l
y
w
h
e
t
he
r
t
h
e
ta
r
g
et
o
f
p
o
w
e
r
c
o
nve
rs
io
n
can
b
e
re
al
iz
ed,
bu
t
a
l
s
o
t
he
f
i
n
a
l
ou
tpu
t
q
ua
l
i
t
y
o
f
the
vo
l
t
a
g
e
a
n
d
c
u
rre
nt
.
H
e
nc
e,
t
he
p
erfo
rm
an
ce
c
har
a
c
t
e
r
is
t
i
c
s
o
f
a
p
o
wer
con
v
er
t
e
r
(e
.g.,
vo
lta
ge
q
ua
lit
y
and
p
o
w
e
r
fac
t
or
)
grea
t
l
y
de
pe
n
d
o
n
t
h
e
se
le
ct
i
on
o
f
the
a
p
p
r
opria
te
m
o
dula
t
i
o
n
s
t
r
a
te
gy
a
n
d
modi
fic
a
t
i
on
o
f
its o
per
a
t
i
n
g
para
me
ters
[
5–
8].
The
l
o
w
sw
itc
hi
ng
fre
q
uenc
y
sh
ou
l
d
b
e
spe
c
ia
l
l
y
pai
d
a
t
t
e
n
t
i
o
n
to
t
he
h
ig
h
po
we
r
a
p
pli
c
at
ion
s
,
w
h
ic
h
i
s
i
n
c
h
a
r
ge
o
f
t
h
e
hi
g
h
-
e
ffic
ie
ncy
o
f
s
ystem
as
w
el
l
a
s
t
h
e
re
duc
t
i
on
in
s
w
i
tc
hi
n
g
l
o
ss
[9].
M
o
d
u
l
at
io
n
me
tho
d
s
l
i
k
e
c
a
rr
i
e
r-ba
s
e
d
s
i
n
us
o
i
da
l
p
u
l
s
e
w
i
dth
m
o
d
u
l
a
ti
on
(C
B-S
P
WM)
and
spa
c
e
v
ec
tor
pu
l
s
e
w
i
d
t
h
mo
d
u
l
a
t
i
on
(
SVPWM
)
a
re
c
o
m
mo
n
l
y
not
s
ui
t
a
bl
e
f
o
r
the
ap
pl
i
c
a
t
i
o
ns
w
he
re
t
he
s
w
itc
h
i
n
g
f
re
q
u
e
n
cy
i
s
bel
o
w
1
kH
z
.
T
he
l
ow
-order
h
a
r
m
o
n
i
c
s
w
il
l
oc
cur
i
n
t
he
s
ide
b
a
n
d
n
e
a
r
t
h
e
c
a
r
r
i
e
r
f
r
e
q
u
e
n
c
y
,
s
o
t
h
a
t
t
h
e
h
i
g
h
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
10,
N
o.
4
, Dec
201
9 :
1
8
7
5
– 1
884
1
876
di
st
ort
i
o
n
w
i
l
l
b
e
pro
d
u
ce
d
i
n
t
he
o
u
t
p
u
t
v
ol
ta
ge
a
n
d
c
ur
r
e
nt.
N
e
ver
t
h
e
l
e
ss,
s
e
l
ect
ive
harm
on
i
c
e
lim
ina
t
io
n
pu
lse
w
i
d
t
h
m
o
d
u
l
at
i
on
(S
H
E
P
W
M),
w
h
i
c
h
ca
n
be
u
til
iz
ed
t
o
de
cre
ase
the
sw
itc
h
i
n
g
l
osse
s
a
n
d
f
u
rt
h
e
r
incre
a
se
t
he
r
elia
b
ili
t
y
a
n
d
e
ffic
ie
ncy
of
p
o
w
e
r
c
onve
rters
w
h
i
le
b
e
u
til
i
z
e
d
w
i
t
h
g
o
od
pow
e
r
q
ual
i
t
y
i
n
l
ow
sw
it
c
h
i
n
g
fre
q
u
enc
y
s
i
t
ua
t
i
o
n
s,
a
s
one
o
f
th
e
pr
efe
rred
m
odu
la
t
i
on
s
t
ra
t
e
gi
e
s
f
or
h
ig
h
p
o
w
e
r
con
v
e
r
ter
s
[
1
0
–
12].
This
s
trat
egy
c
a
n
be
r
ea
l
i
z
e
d
b
y
me
ans
of
t
he
s
o
l
u
t
i
o
n
f
o
r
s
o
l
vi
ng
a
s
et
o
f
non
lin
ear
a
n
d
t
r
an
s
cen
d
e
ntal
equa
t
i
o
n
s,
a
nd
ty
p
i
cal
m
e
t
ho
d
s
ha
v
e
bee
n
d
e
a
lt w
i
th i
n n
u
m
e
r
o
us
p
ap
e
r
s
[
1
3
–16
].
The
h
ybr
id
S
H
E
P
W
M
pr
ese
n
ted
i
n
t
h
i
s pa
pe
r
c
o
mbi
n
es
one
s
w
i
tch
i
n
g
pa
tt
er
n
w
i
th
a
no
th
e
r
one
.
T
h
e
ma
in
f
ea
tur
e
s
of
t
h
i
s
mo
du
la
ti
o
n
s
tr
a
t
eg
y
ar
e
the
sm
o
o
t
h
a
nd
ra
p
i
d
sw
i
t
c
h
in
g
tra
n
sit
i
o
n
and
the
r
e
duc
t
i
o
n
i
n
swit
c
h
i
n
g
loss
es.
The
t
r
ans
i
t
i
on
c
o
ndi
t
i
ons
can
b
e
r
e
g
u
l
a
t
ed
b
y
c
han
g
i
n
g
t
he
c
ombi
na
t
i
o
n
o
f
t
w
o
sw
itc
h
i
ng
pat
t
erns.
F
u
r
t
h
e
rm
ore
,
t
h
i
s
h
ybr
id
S
H
E
P
W
M
i
s
b
a
s
e
d
o
n
a
ve
rsa
t
i
le
a
n
d
e
f
f
ec
t
i
ve
a
l
g
ori
t
hm,
w
h
ic
h
i
s
v
ery
con
v
e
n
ie
n
t
t
o
im
pl
e
m
e
n
t
and
proc
ess.
A
nd
it
is
a
unive
rsa
l
a
nd
com
p
rehe
nsi
v
e
so
l
u
t
i
on
for
di
ffe
re
nt si
t
u
a
tions.
I
n
t
hi
s
pa
pe
r,
t
he
f
ea
si
b
i
l
ity
a
nd
e
ffe
c
t
i
ve
ne
s
s
o
f
t
h
e
h
ybr
id
S
H
EP
WM
p
r
o
p
o
se
d
is
r
e
s
e
a
r
c
hed.
T
he
r
e
s
t
o
f
t
h
e
p
a
p
e
r
i
s
o
r
g
a
n
i
z
e
d
a
s
follows.
S
ection
I
I
p
r
e
sents
the
est
a
b
l
ishm
ent
o
f
S
HEPWM
m
a
t
h
em
atic
a
l
mode
l
for
3L
-N
P
C
c
o
nver
t
e
r
.
The
o
retica
l
p
a
r
t
o
f
p
r
o
p
o
se
d
hybr
i
d
S
HEPWM
mo
du
l
a
ti
on
s
t
r
a
t
egy
and
trans
i
tion
s
chem
e
are
introduced
i
n
Secti
on
III.
I
n
S
ection
I
V
,
s
imu
l
a
t
i
o
n
resul
t
s
a
r
e
a
n
a
l
yz
ed
a
nd
i
t
s
s
moot
h
and
fas
t
tra
nsi
t
i
o
n
is als
o
p
ut
f
orw
a
r
d
in t
h
is sec
tio
n.
F
inal
l
y the
co
nc
lu
si
o
n
s
are
give
n
i
n
S
e
c
tion
V
.
2.
E
S
TABLISH
MENT
O
F SHEP
WM M
AT
H
E
MATIC
A
L
MODE
L
FOR
3L
-
N
PC CONVERTER
The
F
i
g
u
r
e
1
s
how
s
the
top
o
l
og
y
of
3
L-N
P
C
co
n
v
er
t
e
r.
T
he
D
C-b
u
s
v
olt
a
g
e
i
s
d
i
vi
de
d
i
n
to
t
h
r
ee
leve
ls (
V
dc
/
2
,
0
,
and
-
V
dc
/2)
as w
e
l
l
as out
p
u
t
pha
se
vo
l
t
a
ge.
F
i
gure
1.
Top
o
l
og
y
of
3
L
-
N
P
C c
o
nverter
.
The
o
u
t
p
ut
p
ha
se-
A
volta
ge,
for
ins
t
a
n
ce
, c
an be
e
xpresse
d
as:
/2
,
,
1
,
,
,
0
0,
,
1
,
,
,
0
/2,
,
1
,
,
,
0
(
1
)
Here
,
t
h
e
ma
i
n
a
tt
e
n
ti
on
i
s
fo
cu
sed
on
t
h
e
ou
tpu
t
p
h
a
se
-A
v
olt
a
ge
V
AO
.
Th
roug
h
a
r
t
i
f
i
ci
al
arr
a
ngem
e
nt
o
f
sw
itc
h
i
n
g
a
ng
l
e
s
f
o
r
S
H
EP
WM,
w
e
c
an
o
bta
i
n
t
h
e
c
om
mon
ou
tpu
t
p
hase-A
v
o
l
t
a
ge
w
a
ve
form
s
of
t
he
3
L-N
P
C
co
nv
er
t
e
r
as
s
how
n
in
F
ig
ure
2.
T
he
n
u
m
b
er
o
f
el
i
m
inate
d
h
a
r
m
o
n
i
c
s
i
s
deter
m
i
n
ed
b
y the
num
ber
of
s
w
i
t
c
h
i
n
g
a
n
g
l
e
s.
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
R
e
searc
h
o
n
h
y
br
id SH
EPW
M
base
d
on d
i
ffe
re
nt
s
w
i
t
c
h
i
n
g pa
t
t
e
r
ns
(T
ao
Jin
g
)
1
877
(a)
(b)
F
i
g
u
r
e
2.
The
c
o
mm
on ou
t
p
u
t
pha
se-
A
vol
t
a
g
e
w
aveform
s
o
f
t
h
e
3L
-N
P
C
con
ve
rter.
(a
)
N
=
e
ven,
(b)
N
= odd.
A
c
cordi
n
g
t
o
D
i
r
i
c
h
l
e
t
t
heor
e
m
,
the
fo
ll
ow
in
g
F
ourier
series
c
a
n
be
o
b
t
aine
d
for
t
h
e
a
b
o
v
e
o
u
t
pu
t
pha
se-
A
vol
tag
e
w
aveform
:
0
1
()
[
s
i
n
(
)
c
o
s
(
)
]
2
AO
n
n
n
A
Vt
A
n
t
B
n
t
(
2
)
wher
e,
2
0
1
()
s
i
n
(
)
(
)
nA
O
A
Vt
n
t
d
t
(
3
)
2
0
1
()
c
o
s
(
)
(
)
nA
O
BV
t
n
t
d
t
(
4
)
The
F
o
urier
a
n
aly
s
i
s
o
f
a
b
o
v
e
ou
t
p
ut
v
ol
ta
ge
w
a
v
efor
m
ca
n
be
c
o
ns
trai
ne
d
t
o
t
he
f
irs
t
q
u
a
r
t
e
r-c
ycle
bec
a
u
s
e
of
t
he
e
ve
n
qua
r
t
er-
w
ave
s
y
m
m
e
try
a
n
d
o
d
d
h
a
l
f
-
w
a
ve
s
ym
met
r
y
of
t
h
e
out
pu
t
vol
t
a
g
e
w
avef
o
r
m,
and
he
nce
o
n
l
y
odd-
orde
r ha
rm
oni
c
s
a
r
e
e
xi
ste
n
t
w
ith
o
u
t e
v
e
n
-
o
r
de
r ha
rm
o
n
ic
s.
0,
∑
1
cos
,
0
(
5
)
wh
ere
N
i
s
the
num
b
e
r
of
s
w
i
tc
hin
g
a
n
g
les
w
i
t
h
in
t
he
f
i
r
st
quar
t
e
r-c
yc
le
o
f
t
h
e
f
u
n
d
a
m
e
n
ta
l
p
e
ri
od,
and
α
1
,
α
2
,
...,
α
N
w
h
i
ch satis
fy (6)
below.
12
0
...
9
0
N
(
6
)
H
e
re,
t
h
e
m
o
d
u
la
t
i
o
n
i
nde
x
M
i
s
de
fi
ne
d
a
s
t
he
r
a
d
io
o
f
the
fu
n
d
am
ent
a
l
a
m
pl
i
t
u
d
e
of
t
he
o
u
tpu
t
vo
lta
ge
A
1
divided by ha
l
f
o
f
t
h
e
D
C
v
o
l
tage
V
dc
/2,
t
h
a
t
is,
1
/2
dc
A
M
V
(7
)
I
n
t
he
s
ymm
e
t
r
ic
t
hr
ee
-p
hase
s
ystem
,
t
he
t
r
i
p
l
e-
order
har
m
onic
s
c
a
n
b
e
c
a
nce
lle
d
by
eac
h
o
t
her
a
u
to
ma
ti
cal
ly
,
a
n
d
t
h
e
no
nt
ripl
e-o
r
d
e
r
h
a
rmo
n
i
c
s
w
ill
b
e
el
imi
n
a
t
e
d
b
y
se
l
e
c
t
i
n
g
op
tim
al
s
witc
h
i
n
g
a
n
g
le
s
α
1
,
α
2
,
.
.
.,
α
N
thro
u
gh
(8) be
l
o
w
wit
h
m
od
ul
a
t
i
on
in
de
x
M
.
⎩
⎪
⎨
⎪
⎧
∑
1
cos
∑
1
cos
5
0
M
∑
1
cos
0
(
8
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
10,
N
o.
4
, Dec
201
9 :
1
8
7
5
– 1
884
1
878
wh
ere
n
is the
hi
ghe
s
t
o
rder
har
monic
nee
d
e
d
to be
e
lim
ina
t
e
d
,
and
12
[,
,
,
]
N
.
O
b
v
i
o
u
s
l
y
,
t
h
i
s
e
q
ua
tio
n
se
t
is
non
l
i
nea
r
a
nd
transc
e
n
d
e
nta
l
,
a
n
d
t
he
s
w
i
tc
hi
n
g
a
n
g
le
s
ca
n
be
con
v
e
n
ie
n
t
ly s
ol
ve
d by
t
he
fs
olve
function
in the MATLA
B
in
or
d
e
r
t
o s
i
m
p
li
f
y
t
he
c
alc
u
la
t
i
o
n
p
r
o
cedu
r
e
a
nd
take
f
u
l
l
ad
van
t
age
of
t
he
h
ig
h
c
o
mp
uta
t
i
o
n
a
l
per
f
orm
a
nc
e
of
c
o
m
p
u
t
e
r
,
t
h
e
r
efore
muc
h
c
om
pu
t
a
ti
o
n
e
ffor
t
ca
n be
d
one w
ith ea
s
e
.
The
f
ina
l
res
ul
ts of e
a
c
h
sw
i
tc
hi
n
g
ang
l
e
for S
H
EP
WM o
bta
i
ne
d ar
e a
p
p
l
i
e
d to c
ontro
l
t
h
e
o
u
t
p
u
t
w
a
v
e
f
o
r
m
w
i
t
h
t
h
e
e
l
i
m
i
n
a
t
i
o
n
o
f
s
p
e
c
i
f
i
c
l
o
w
-
o
r
d
e
r
harmon
ics.
N
o
n
e
t
h
e
less,
t
he
s
ele
c
ti
o
n
o
f
su
i
t
a
b
le
i
n
i
tia
l
val
u
es
i
s
c
r
uci
a
l
for
t
h
e
i
t
era
tive
co
n
v
erge
n
c
e.
A
cc
ordin
g
t
o
refere
nce
[1
7],
t
h
e
i
n
it
ial
v
a
lu
e
s
for
N
swi
t
c
hi
ng
a
n
g
l
e
s (h
e
r
e,
N
=
o
dd)
uni
p
o
l
a
r
S
H
E
P
W
M
ca
n
be
der
i
ve
d
as
3
0
°
1
2
0
°
∙
/
1
∆
3
0
°
1
20°
∙
/
1
∆
9
0°
∆
(
9
)
wh
ere
1
,
2
,
...,
(
1
)
/
2
kN
, and
is an o
p
t
im
a
l
sm
a
ll a
n
gle
, w
hi
c
h
is used
t
o a
v
o
i
d s
i
n
g
u
l
a
ri
t
y
of
fsolv
e
f
unc
t
i
on
.
A
f
t
e
r te
st,
0.3
~
0.5
a
nd som
e
o
t
h
e
r
va
l
ue
s ca
n ensur
e
itera
t
i
ve
c
on
ve
rge
n
c
e
.
F
i
nal
l
y,
s
e
v
era
l
p
ro
gra
m
s
are
w
r
it
te
n
base
d
on M
la
n
gua
ge
i
n
MA
TLA
B
t
o
g
e
t
v
ari
o
us
c
urves
ba
sed
on
d
i
f
fere
n
t
n
u
m
be
rs
o
f
sw
i
t
c
h
i
n
g
a
n
gl
e
s
a
nd
m
o
d
u
l
a
tio
n
inde
x
r
a
nge
s
from
0
t
o
1.
H
e
r
e,
N
=
1
7
a
n
d
N
=
19
are
take
n a
s
t
h
e
e
xam
p
l
e
s,
a
s show
n in
F
i
gur
e
3.
(a)
(b)
F
i
gure
3.
T
he
r
elat
i
on c
u
rves be
t
w
e
e
n
s
w
i
tc
hin
g
a
ng
le (
de
g.)
an
d
modu
la
ti
o
n
in
d
e
x
(
M
)
(a)
N
=
17, (
b)
N
=
19.
3.
PROPO
S
E
D
HYB
R
I
D
SH
EPWM M
O
D
U
L
ATIO
N
STRATE
G
Y
AND TRAN
S
I
T
I
ON SCHE
M
E
3.1.
Prop
ose
d
m
od
u
l
ati
o
n
st
rategy
G
e
nera
lly,
t
h
e
m
a
xim
u
m
n
u
m
b
e
r
of
s
e
l
ec
te
d
harm
o
n
i
c
s
to
b
e
re
mov
e
d
d
ep
end
s
o
n
th
e
a
llo
wa
bl
e
sw
it
c
h
i
n
g
fre
q
u
e
nc
y
o
f
sem
icon
d
u
ct
or
m
odu
les,
w
hich
h
as
t
he
f
o
l
lo
w
i
ng
r
e
l
a
tio
nshi
p
:
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
R
e
searc
h
o
n
h
y
br
id SH
EPW
M
base
d
on d
i
ffe
re
nt
s
w
i
t
c
h
i
n
g pa
t
t
e
r
ns
(T
ao
Jin
g
)
1
879
.m
a
x
1
11
2
sw
f
kN
f
(
1
0
)
wh
ere
k
i
s
t
h
e
m
a
xim
u
m
n
u
m
b
er
o
f
se
lec
t
e
d
h
ar
mo
nic
s
t
o
be
r
em
ove
d
,
f
sw
.m
a
x
i
s
t
h
e
a
l
lo
wab
l
e
sw
it
c
h
i
n
g
fre
q
u
e
nc
y
of sem
icon
d
u
ct
or
m
odu
les,
and
f
1
i
s
th
e
f
un
dam
e
n
t
a
l
f
re
que
nc
y.
Acc
o
rd
ing
t
o
(1
0
)
,
a
un
iv
e
r
sal
mod
u
l
a
ti
on
s
t
r
at
e
g
y
fo
r
a
p
o
w
e
r
c
o
n
v
e
r
t
e
r
li
m
i
te
d
to
a
s
w
i
t
c
h
i
n
g
fre
que
nc
y
o
f
4
50
H
z
(
d
ue
t
o
the
IG
B
T
m
od
ule)
w
i
t
h
d
i
f
fer
e
nt
f
u
n
d
am
en
t
a
l
fr
eq
ue
nc
ie
s
at
M
=
0
~
1
i
s
s
h
o
w
n
in F
ig
ure
4.
F
i
g
u
re
4
. Modu
l
a
ti
o
n
st
rat
e
gy
u
si
ng
S
HEP
W
M i
n
th
e
mo
d
u
l
a
t
ion
re
gion
.
3.2.
Prop
ose
d
t
ran
s
ition
sc
h
e
m
e
Eve
r
y
mom
e
n
t
has
its
c
orr
e
sp
on
d
i
n
g
o
ut
put
s
ta
te
i
n
t
h
e
m
o
dula
t
i
o
n
p
roce
ss
o
f
S
H
EP
WM,
a
s
s
how
n
in
F
igur
e
5.
I
n
order
t
o
i
l
l
us
trate
i
t
s
princ
i
pl
e,
s
e
v
e
r
al
p
ar
a
m
e
ters
a
r
e
d
eterm
i
ned
as
f
o
l
l
o
w
:
N
=
1
9
,
M
=
0
.
8
5
and
f
1
=
1
1
.
8
4
H
z
(
w
h
e
r
e
,
1
18.25
,
2
18
.84
,
3
23
.7
6
,
4
24
.9
0
,
5
29.3
3
,
6
30.9
4
,
7
34
.94
,
8
36.
94
,
9
40.
59
,
10
42.
89
,
11
46.
21
,
12
48.6
4
,
13
51
.4
1
,
14
54.
64
,
15
56
.6
8
,
16
60.
67
,
17
62.
00
,
18
66.
73
,
19
67.
37
).
F
i
gure
5.
P
ha
se vol
ta
ge
w
ave
f
orm
s
of
the 3
L
-
N
P
C
c
onvert
er
durin
g the
mod
u
l
at
i
on pr
oc
ess of
S
H
E
P
W
M
(
N
=
1
9
)
.
The
ou
t
p
u
t
p
h
a
se
v
ol
ta
ge
w
ave
f
orm
s
a
bo
ve
,
in
a
s
e
n
se
,
can
b
e
re
g
a
rd
e
d
a
nd
e
xp
re
ss
ed
a
s
th
e
corr
espo
n
d
in
g
spac
e
vec
t
ors
on
t
h
e
ba
si
s
of
s
pace
v
e
c
t
o
r
repr
es
e
n
t
a
tion
.
In
a
d
dit
i
o
n
,
t
h
e
c
o
r
re
sp
o
ndi
ng
sp
a
ce
v
e
ct
o
r
s
a
n
d
t
h
e
i
r d
u
t
y
c
y
c
l
e
s fro
m
9
0º
t
o
120.1
º
a
re
p
re
se
n
t
ed
in Ta
b
le
1
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
10,
N
o.
4
, Dec
201
9 :
1
8
7
5
– 1
884
1
880
Ta
bl
e
1
.
C
o
r
re
sp
ondi
ng
s
p
a
c
e
v
e
c
t
o
rs of
SH
EP
W
M
(
N
= 19)
a
nd t
h
e
i
r
du
t
y
cyc
l
e
s fr
om 90
°
to 1
2
0
.1°
N
o
.
Dut
y
c
yc
le
S
pac
e
v
e
c
t
or
1
90°
-
91.
02°
[
P
N
N]
2
91.
02
°-
95
.0
3
°
[P
N
O
]
3
95.
03
°-
97
.0
3
°
[P
N
N
]
4
5
6
7
8
9
10
11
12
13
14
15
97.
03
°-
1
00.
66
°
100.
66
°-
102.
9
6
°
102.
96
° -
106.
2
9
°
106.
29
° -
108.
7
2
°
108.
72
° -
111.
4
9
°
111.
49
° -
112.
7
2
°
112.
72
° -
113.
3
6
°
113.
36
° -
114.
7
3
°
114.
73
° -
116.
7
7
°
116.
77
° -
118.
1
0
°
118.
10
°-
119.
4
2
°
119.
42
°-
120.
1
0
°
[P
N
O
]
[P
N
N
]
[P
N
O
]
[P
N
N
]
[P
N
O
]
[P
N
N
]
[O
NN
]
[P
N
N
]
[P
N
O
]
[P
N
N
]
[O
NN
]
[P
N
N
]
When
t
he
hybrid
S
HEP
W
M
method
is
a
dopted,
the
sw
itching
problem
b
e
t
w
e
e
n
t
w
o
d
i
f
f
e
r
e
n
t
S
H
EP
WM
s
w
i
tch
i
ng
pa
tter
n
s
sho
u
l
d
be
n
e
c
e
ssaril
y
c
ons
i
d
ere
d
.
O
n
e
o
f
the
ob
jec
tive
s
o
f
trans
i
tio
n
i
s
t
o
swi
t
c
h
s
moo
t
hly
f
ro
m
on
e
st
at
e
t
o
a
no
th
e
r
,
s
o
a
s
to
p
re
v
e
nt
t
h
e
l
a
r
ge
i
mpu
l
se
c
ur
ren
t
p
r
o
duce
d
a
t
a
tran
si
tio
n
in
sta
n
t
a
nd its
a
dverse
e
ffe
c
t
s
o
n
e
le
ctric
a
l
e
qui
pm
ent
or
p
o
w
e
r
g
r
i
d
.
An
d
a
n
oth
e
r
o
n
e
i
s
t
o
s
wit
c
h
qui
ckl
y
,
so
tha
t
t
he
t
r
a
n
s
i
tio
n
c
a
n
sa
t
i
s
f
y
t
h
e
d
ynam
i
c
resp
onse
de
ma
nd
of
t
h
e
p
o
w
e
r
system
s.
I
n
ot
her
w
o
rds,
s
m
o
ot
h
t
r
a
n
si
ti
o
n
sh
oul
d
b
e
don
e
i
n
on
e
s
w
i
t
c
hi
ng
peri
o
d
[
1
8
–20
].
I
n
o
r
d
er
t
o
re
a
l
iz
e
t
h
e
ab
ov
e
goa
ls,
the
fol
l
o
w
i
ng
tw
o
con
d
i
t
i
o
n
s
a
r
e
g
e
n
e
r
a
l
l
y
r
e
q
u
i
r
e
d
.
I
t
i
s
nec
e
ssary
t
o
e
n
sur
e
t
ha
t
the
pha
se
a
n
g
l
e
an
d
am
pl
itu
de
o
f
the
f
u
n
d
am
en
tal
pha
se
v
o
lta
ge
b
e
f
ore
a
nd
after
trans
i
t
i
on
a
r
e
cons
iste
nt
.
O
t
he
rw
ise
,
t
he
s
u
d
de
n
c
h
a
nge
o
f
t
h
e
fu
nd
amen
tal
ph
a
s
e
vo
lt
ag
e
wil
l
o
ccu
r
,
wh
i
c
h
w
ill
l
e
ad
t
o
o
v
e
rsho
ot o
f
the
ou
t
p
u
t
c
ur
ren
t
.
The
num
ber
o
f
s
w
itc
hi
ng
ac
t
i
o
n
s
s
h
ou
ld
n
o
t
b
e
m
o
re
t
h
a
n
one
.
If
n
o
t
,
it
w
il
l
ha
ve
s
o
m
e
negat
i
v
e
in
flue
nce
on
the
c
o
n
v
erter
,
s
uch
a
s
g
r
eate
r
s
w
i
t
c
h
i
n
g
losse
s,
s
u
dde
n
c
h
a
n
ge
s
in
p
h
a
se
vol
t
a
g
e
a
nd
shor
t pu
lses.
Al
l
of
t
h
e
a
bov
e
co
nsi
d
era
tio
n
s
a
re
v
ali
d
f
o
r
t
h
e
t
ra
n
s
itio
n
f
r
om
p
rev
i
ous
S
H
E
P
W
M
sw
i
t
c
h
i
ng
pat
t
ern
t
o
t
he
c
urr
e
nt
one.
T
h
e
tra
n
si
tio
n
a
l
g
o
ri
t
h
m
is
i
m
p
lem
e
nt
ed
quite
s
i
m
pl
y
,
a
n
d
t
h
e
ma
in
t
a
s
k
i
s
t
o
des
i
g
n
a
“
vec
t
or
d
e
t
e
c
t
o
r”.
Thi
s
d
e
t
ec
tor
(se
e
F
ig
ure
6)
c
ont
i
n
u
o
u
sly
de
t
e
c
t
s
the
ge
ner
a
ted
sta
t
e
s
[
P
]
,
[O
]
and
[N
]
be
t
w
e
e
n
tw
o
sw
itc
h
i
ng
pat
t
erns,
a
n
d
a
t
t
he
m
om
en
t
w
h
en
t
he
s
i
gn
al
o
n
w
h
e
t
her
to
p
e
rform
s
w
i
tc
h
i
ng
trans
i
t
i
on
is
o
n
, the
c
ontr
o
l sy
stem
pe
r
form
s the
tra
n
si
ti
on
if
a
l
l
p
r
e
v
i
o
u
s
c
on
dit
ion
s gi
v
e
n
a
r
e
me
t
.
F
i
gur
e 6.
Bl
o
c
k
dia
gra
m
o
f
prop
osed h
y
b
ri
d
S
H
EP
W
M
trans
it
ion
sc
hem
e
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
P
o
w
Elec
&
D
r
i
S
y
st
I
S
S
N
:
2088-
86
94
Rese
arc
h
o
n
hy
br
i
d
SH
EPW
M base
d
on d
i
f
f
ere
n
t swi
t
c
h
i
ng pa
tte
rns (
T
ao Jin
g
)
1
881
4.
S
I
MULAT
I
O
N
R
E
S
UL
TS
AND
A
NALYSIS
To
v
e
r
if
y
a
nd
eva
l
ua
t
e
t
he
s
t
a
te
s
o
f
o
u
t
pu
t
vo
l
t
a
g
e
a
n
d
cu
r
r
ent
w
avef
o
r
ms
acquire
d
fr
om
3
L-NPC
c
o
n
v
er
ter
usi
ng
t
h
e
pr
o
pos
ed
t
r
a
ns
i
tio
n
sc
hem
e
,
the
si
m
u
la
ti
o
n
st
udy
i
s
i
m
p
l
ement
e
d
in
MA
TLA
B
/
S
I
MU
LI
N
K
pla
t
for
m
.
I
n
o
ur
m
ode
l,
t
he
d
e
f
a
u
lt
s
t
at
e
of
t
h
e
si
gn
al
o
n
wh
eth
e
r
t
o
p
erf
o
rm
sw
itc
h
i
n
g
t
r
a
nsit
i
on
i
s
t
he
r
u
n
n
in
g
st
a
t
us.
F
i
gur
e
7
s
h
ow
s
simu
la
ti
o
n
r
esu
l
t
s
o
f
o
u
t
p
ut
p
ha
se
-
A
v
o
lta
ge
a
n
d
c
u
rre
n
t
a
nd
out
put
l
i
n
e
volt
a
g
e
b
e
fo
re
a
nd
a
fter
t
ran
s
ition
from
SHEPWM
N
=
1
9
t
o
S
H
E
P
W
M
N
=
1
7
in
t
he
c
a
s
e
of
a
pp
l
y
in
g
t
h
e
pr
op
os
e
d
tr
a
n
sit
i
on
sc
he
me
.
F
i
gur
e
7.
S
i
m
u
lat
i
on
r
e
su
l
t
s
o
f
o
u
t
pu
t
p
h
a
s
e-
A
volta
ge
a
n
d
c
ur
r
ent
an
d
ou
t
p
u
t
l
in
e
v
o
l
tag
e
b
efor
e
a
nd
a
f
ter
tr
a
n
sit
i
on
fr
om
S
H
E
P
W
M
N
= 19
to
SH
EP
WM
N
=
1
7
.
Her
e
,
u
ao
a
nd
i
a
r
epr
e
sents
ou
tpu
t
pha
se-
A
v
olta
ge
a
n
d
c
ur
r
e
nt,
r
e
spe
c
t
i
v
e
l
y
,
a
nd
u
ab
i
s
out
pu
t
li
ne
vo
l
t
age.
T
he
h
a
r
m
oni
c
spec
tr
ums of
u
ab
b
e
f
or
e
a
nd
a
f
ter
tr
ans
iti
on ar
e
sh
ow
n in F
ig.
8.
I
t i
s
seen t
h
a
t
t
he l
ow
-
or
d
e
r
har
m
o
n
i
c
s
be
l
o
w
5
0
t
h-
or
der
of
h
a
r
mon
i
c
ar
e
b
o
t
h
e
limi
n
a
t
e
d
,
w
h
i
c
h
i
s
t
h
e
s
a
m
e
a
s
a
f
o
r
e
m
e
n
t
i
o
n
e
d
t
h
eo
re
ti
cal
an
a
ly
si
s.
(a)
(b
)
F
i
gur
e
8.
S
i
m
ulat
i
on
r
e
sul
t
s
o
f
h
ar
monic
s
p
e
c
tr
um
s
of
u
ab
:
a) SHE
P
W
M
N
= 19
,
b
) SH
EP
W
M
N
=
1
7
Ea
ch
o
u
t
pu
t
ph
a
s
e
vo
lt
ag
e
be
fo
re
a
nd
a
ft
er
t
ra
nsit
i
o
n
i
s
s
h
o
w
n
i
n
F
ig
u
r
e
9
.
A
s
can
b
e
s
e
e
n
f
ro
m
F
i
g
u
r
e
9
t
ha
t
the
spa
ce
v
e
c
t
o
r
s
of
t
he prev
i
o
u
s
sta
t
e
an
d
t
h
e
l
a
tte
r
state
a
r
e
the
sa
me
,
so
t
ha
t
the
tra
n
sit
i
on
c
a
n
be
s
moo
t
hl
y
p
e
r
f
or
m
e
d
dur
ing
the
sw
i
t
c
h
ing
pr
ocess
a
t
t
i
m
e
t
=
0
.
2
5s
.
A
nd
t
h
is
t
r
a
n
s
it
i
o
n
f
i
nishe
s
i
n
a
shor
t tim
e.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
10,
N
o.
4
, Dec
201
9 :
1
8
7
5
– 1
884
1
882
(a)
(b)
Fi
g
u
r
e
9
.
Si
m
u
l
at
io
n
re
sult
s of
ea
c
h
o
ut
p
u
t
ph
ase
vo
lt
ag
e
be
f
o
r
e a
nd a
f
ter
t
r
ans
iti
on.
(
a)
Tr
a
nsit
io
n fro
m
SH
E
P
W
M
N
=
19 a
nd S
H
EPW
M
N
=
17
.
(
b
)
Z
o
o
m
o
f
t
r
an
s
i
tio
n
poi
nt
a
t
t
i
m
e
t
=
0
.25s
O
n
e
of
t
he
s
ig
ni
fica
n
t
i
n
d
i
ca
tors
f
or
t
h
e
s
m
oot
h
trans
i
t
i
on
be
t
we
en
dif
fe
rent
S
H
E
P
W
M
swi
t
c
hi
n
g
p
a
tt
e
r
n
s
i
s
t
h
at
t
h
e
re
i
s
no
s
ud
d
e
n
c
h
an
g
e
in
e
a
c
h
ou
tpu
t
ph
ase
c
urr
e
nt
dur
ing
tra
n
si
t
i
on,
i
nc
lu
di
n
g
p
h
a
se
a
n
d
am
plit
ud
e
of
f
un
dam
e
n
t
a
l
,
a
nd
ha
rm
on
i
c
s
of
c
urrents.
F
rom
F
i
g
u
r
e
1
0
,
w
e
c
a
n
easil
y
find
tha
t
s
im
ul
a
tio
n
re
su
lt
s
of
e
a
c
h
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The
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.
A03
.
2
1
.
0011
.
REFE
RENCES
[1]
J.
R
odri
g
u
ez,
S
.
Bern
et,
P
.
S
tei
m
er,
and
I.
L
izam
a,
"
A
su
rvey
o
n
neu
t
ral-p
o
i
n
t-c
l
am
ped
in
verters
,
"
IEEE
Tran
sac
t
io
ns
on
Ind
u
str
i
a
l
Ele
c
tr
on
ic
s
,
vol.
5
7(7
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pp
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u
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ub
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J.
H
oltz
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J
.
R
od
ri
gu
e
z
,
a
nd
G.
B
a
o
m
i
n
g
,
"
M
e
d
iu
m-
vo
l
tage
m
ul
t
i
l
e
vel
conve
r
t
e
rs-Stat
e
o
f
the
art,
chal
leng
es,
and
req
u
i
r
em
ents
i
n
in
du
s
t
ria
l
a
pplicat
io
ns,
"
IEEE T
r
an
sac
t
io
ns on
I
n
d
u
s
tria
l
Ele
c
t
r
o
nic
s
,
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B.
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u,
et
al.
,
"
H
ig
h-po
wer
co
nv
erters
a
n
d
A
C
d
r
ives
,
"
2n
d E
d
iti
o
n
,
p
p
.
4
80
,
New Yo
rk:
Wiley
,
2017
.
[4]
Y.
K
u
c
hero
v
a
n
d
S
.
U
tts,
"
T
he
F
ACTS
a
nd
H
VDC
e
qu
ipmen
t
a
pp
li
ca
t
ion
f
o
r
re
l
i
abili
t
y
,
flexibi
lity
a
nd
con
t
ro
llab
ilit
y
i
n
c
rease
i
n
t
he
m
etro
polit
an
a
rea
p
o
wer
s
y
s
t
em,
"
in
11
th
IE
T
In
t
e
rn
ati
o
n
a
l
Conferen
ce on
AC an
d
DC P
o
wer
Tran
sm
is
s
i
on
,
p
p
.
1-6
,
B
irm
i
ng
ha
m
, 2
01
5.
[5]
H.
S
.
Pat
e
l
an
d
R.
G
.
Hoft,
"Gen
erali
z
e
d
t
ech
ni
ques
o
f
h
armo
ni
c
e
liminatio
n
an
d
vo
lt
age
con
t
ro
l
i
n
t
hyri
s
t
o
r
inverters:
P
art
i-
harmoni
c
e
l
i
minati
on,"
IE
EE T
r
an
sac
t
io
n
s
o
n
In
du
stry
Ap
p
lic
at
io
ns
,
vo
l.
I
A-9
(
3),
pp
.
3
1
0
-
317
,
Ma
y
19
73
.
[6]
W
.
F
e
i
,
X
.
D
u
a
n
d
B
.
W
u
,
"
A
g
e
n
e
r
a
l
i
z
e
d
h
a
l
f
-
w
a
v
e
s
y
m
m
e
t
r
y
S
H
E
-
P
W
M
f
o
rmul
a
t
i
on
f
o
r
multi
level
volt
age
inverters,"
I
EEE Transactions
on
Industrial E
l
ect
ronics
,
v
o
l.
5
7
(
9),
pp.
3
0
3
0
-
303
8
,
S
ept
20
10.
[7]
M
.
S
.
A.
D
ahi
d
ah
,
G
.
K
o
n
stan
tino
u
an
d
V
.
G
.
A
g
eli
d
i
s
,
"
A
r
ev
i
e
w
o
f
mul
tilevel
selectiv
e
harmonic
e
limi
n
ation
PW
M:
F
o
r
mulat
i
o
n
s
,
s
o
l
v
i
ng
a
lgo
r
it
hms
,
i
m
p
l
e
m
e
ntatio
n
and
appl
i
cat
io
n
s
,
"
IEEE Tran
s
a
cti
o
ns on Power
El
ectro
n
i
cs
,
vol.
3
0
(8
),
pp.
4
09
1-4
106
,
A
ug
20
15
.
[8]
X.
Z
h
a
ng
a
nd
W
.
Yue
,
"
Ne
ut
ra
l
p
o
in
t
p
o
te
nt
ia
l
ba
la
n
c
e
a
l
g
o
rith
m
f
o
r
t
h
r
ee-l
e
vel
NP
C
i
n
vert
er
b
as
ed
o
n
SHEP
WM,"
El
e
c
troni
cs
L
e
tters
,
vol
.
5
3
(2
3),
p
p
.
15
42
-154
4,
N
ov 2
0
1
7
.
[9]
Y.
Z
ha
n
g
,
Z.
Z
h
a
o
a
nd
J.
Z
h
u
,
"
A
h
y
b
r
id
P
WM
a
pp
lie
d
t
o
hi
gh
-p
ow
er
t
hre
e
-
l
evel
i
nvert
e
r-fed
i
n
duct
ion-
m
o
tor
dri
v
es
,
"
IEEE
T
r
a
n
s
a
ct
ions
on
In
d
u
st
ri
a
l
El
ectr
onics
,
v
o
l
.
58(8
)
,
pp.
340
9-3
4
2
0
,
Aug
20
11
.
[10]
J.
W
an
g
a
n
d
D
.
A
h
m
adi,
"
A
precis
e
a
n
d
p
racti
cal
h
arm
o
n
i
c
elim
i
n
a
t
ion
m
e
t
hod
f
o
r
m
u
ltilev
e
l
inv
e
rters
,
"
IE
EE
T
r
a
n
sa
cti
o
n
s
o
n
In
du
st
ry A
pplicati
ons
,
vol.
4
6(2
)
,
pp
.
8
57
-865,
Mar-A
pr
2
010
.
[11]
D
.
A
h
m
a
d
i
,
K
.
Z
o
u
,
C
.
L
i
,
Y
.
H
u
a
n
g
a
n
d
J
.
W
a
n
g
,
"
A
u
n
i
v
e
r
s
a
l
s
e
l
ecti
v
e
harm
o
n
ic
e
limi
n
a
t
io
n
me
th
od
f
or
h
igh
-
power i
n
ve
rt
ers
,
"
IE
EE
Tra
n
sa
cti
o
n
s
o
n
P
o
wer
El
ectr
o
n
i
cs
,
vol.
26(1
0
),
pp.
2
7
4
3
-
27
52,
O
c
t
2
0
11.
[12]
A.
E
d
pug
an
t
i
a
n
d
A
.
K.
R
ath
o
re,
"
A
s
u
r
vey
of
l
ow
s
wi
tching
f
req
uency
m
o
d
u
l
a
ti
o
n
t
ech
ni
ques
f
o
r
m
e
di
u
m
-vo
l
t
a
ge
m
u
lti
l
evel con
vert
ers,"
IE
EE T
r
a
n
saction
s
on Ind
u
stry
App
l
ications
, vo
l
. 5
1(5
)
,
p
p
. 4
21
2-4
2
2
8
, S
ep
t
-
Oct
2
0
1
5
.
[13]
W
.
Z
h
a
n
g
,
X
.
M
e
n
g
a
n
d
Z
.
L
i
,
"
T
h
e
s
i
m
u
l
a
t
i
o
n
r
e
s
e
a
r
c
h
f
o
r
s
e
l
e
c
tiv
e
h
a
rmo
n
ic
e
l
i
m
i
n
a
ti
on
tech
ni
que
b
as
ed
o
n
genetic
a
lgori
t
h
m
,"
P
r
o
c
eed
in
gs of th
e 33rd
Ch
ines
e Con
t
r
o
l
Co
nf
eren
ce
, Nanj
i
n
g
, p
p.
86
2
8
-
8
6
3
2
, 20
1
4
.
[14]
H.
T
agh
i
zad
eh
a
n
d
M
.
Taraf
d
ar
H
agh
,
"
Harm
on
ic
e
l
i
m
i
na
t
i
on
o
f
ca
sc
ade
mu
ltil
e
vel
in
verters
with
n
oneq
u
al
D
C
so
urces
u
s
i
ng
p
articl
e
s
w
a
rm
o
p
timizati
on,"
IEE
E
Tr
an
sactio
ns on
Ind
u
s
t
ria
l
Electr
onics
,
vo
l
.
5
7(1
1
),
p
p.
3
6
7
8
-
36
84
,
N
o
v
201
0.
[15]
M
.
H
.
E
t
e
s
a
m
i
,
N
.
F
a
r
o
k
h
n
i
a
a
n
d
S
.
H
a
m
i
d
F
a
t
h
i
,
"
C
o
l
o
n
i
a
l
c
o
m
p
e
ti
ti
ve
a
lg
or
i
t
h
m
d
e
v
e
lo
pme
n
t
to
w
a
r
d
h
a
r
mo
ni
c
mini
mization
in
m
ul
t
i
level
inverters,"
IEEE T
r
a
n
s
a
ct
ions
on
I
n
dustrial Inf
o
rmatics
,
vo
l
.
1
1
(
2),
pp
.
4
5
9
-
466,
Ap
r
20
15
.
[16]
A.
K
av
ou
si,
B.
V
a
h
id
i,
R
.
S
a
lehi
,
M
.
K
.
Bak
h
s
h
i
zadeh,
N
.
F
a
r
o
k
h
nia
and
S
.
H
.
F
a
t
h
i
,
"
Ap
p
l
icat
ion
of
t
he
b
ee
algorithm
f
o
r
selecti
v
e
harmon
i
c
e
l
i
minat
i
on
s
trat
egy
i
n
m
u
ltil
evel
i
nv
erters
,"
IE
EE T
r
ans
ac
tio
ns
o
n
Po
wer
El
ectro
n
i
cs
,
vol.
2
7
(4
),
pp.
1
68
9-1
696
,
A
pr
2
01
2.
[17]
Chu
n
h
u
i
W
u
,
Qiron
g
J
iang
a
nd
Ch
un
peng
Z
ha
n
g
,
"An
op
tim
i
z
a
ti
on
m
e
t
hod
f
o
r
t
h
r
ee-level
sel
e
c
t
iv
e
harm
on
ic
e
l
i
m
i
n
a
t
e
d
p
u
l
s
e
w
i
d
t
h
m
o
d
u
l
a
t
i
o
n
(
S
H
E
P
W
M
)
,
"
i
n
Int
e
rn
ati
o
n
a
l
Con
f
er
ence o
n
El
ectri
cal
M
a
ch
ines
a
nd
Sys
t
em
s
,
Nan
jin
g
,
vol.
2,
pp.
1
3
4
6
-
135
0,
20
0
5
.
[18]
Y.
W
an
g,
X
.
W
e
n,
X
.
Gu
o,
F
.
Zh
ao
a
nd
W
.
Co
n
g
,
"Th
e
s
m
o
o
t
h
trans
i
t
i
o
n
res
earc
h
o
f
d
i
ff
erent
PW
M
m
o
dulati
ons
f
o
r
v
ecto
r
c
on
trol
o
f
in
ductio
n
m
o
to
r
in
m
edi
u
m
v
o
l
t
age
hig
h
p
o
w
e
r,"
in
Int
e
rn
ati
o
n
a
l
Conference o
n
E
l
ectr
i
c
a
l
M
a
c
hin
e
s and
Sy
s
t
em
s
,
pp.
1
-
5
, B
ei
ji
n
g
201
1
.
[19]
A.
A
.
Ra
dio
n
o
v
,
V
.
R
.
G
a
s
iy
a
r
o
v
a
n
d
A.
S
.
Ma
kla
k
ov
,
"
H
yb
rid
P
W
M
o
n
the
basis
o
f
S
VPWM
a
nd
S
H
E
PWM
for
VS
I
as
p
art
of
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L
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con
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e
r,
"
in
IECON 201
7 -
43r
d An
nual Co
n
f
er
ence
o
f
th
e
IEEE Ind
u
s
t
r
i
al
El
ectro
n
i
cs
S
o
ciety
,
pp.
1
2
3
2
-
12
3
6
,
Beijing
20
17.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
10,
N
o.
4
, Dec
201
9 :
1
8
7
5
– 1
884
1
884
[20]
Y.
Zh
a
ng
,
D.
X
u,
C
.
Yan and
S.
Z
ou
,
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ri
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M
S
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hem
e
f
o
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h
e
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d
Invert
e
r
,
"
IEEE Jo
ur
na
l o
f
Emer
gi
ng
and
Sel
ected T
opi
cs
in Power
El
ectr
o
n
i
cs
,
v
o
l
.
3(4),
p
p
.
1
151
-11
5
9
,
D
ec
201
5.
B
I
OGRAPHIES
O
F AUTHO
RS
Ta
o
J
i
ng
.
2
016
–
D
i
p
l
o
m
a
o
f a
Bachel
or, Zhej
ia
n
g
O
cean
U
ni
versity
,
Chin
a;
2
018
–
D
i
pl
o
m
a
o
f
a
M
a
s
t
er,
S
o
u
t
h
Ural
S
tate
U
nivers
ity,
Ru
ssia;
2
01
8
t
o
p
resen
t
–
D
o
ct
oral
c
a
n
di
date
o
f
th
e
D
e
partm
e
n
t
“
Mechat
ron
i
cs
a
n
d
a
u
t
o
m
atio
n”,
S
o
ut
h
U
r
al
S
t
a
te
U
niv
ersity
,
Rus
s
i
a
.
H
i
s
res
earch
i
n
t
e
res
t
s
in
clu
d
e t
h
e f
i
e
l
d
o
f
p
ow
er elect
roni
cs, m
o
t
or d
rive
s
y
s
tems
and
m
echat
roni
cs.
A
l
exa
nder
Ma
kla
kov.
201
3
–
D
i
plo
m
a
of
a
n
en
gi
neer
,
M
a
gn
ito
go
rsk
St
ate
Tech
nical
U
n
iv
ersi
ty,
Ru
s
s
ia;
20
17
–
P
h
D
(tech
nical
s
cience),
S
outh
Ural
S
t
a
t
e
Univers
ity,
R
u
ssia
;
2015
t
o
p
r
esent
–
Ass
oc
i
a
te
p
ro
fesso
r
o
f
t
he
D
ep
artm
ent
“M
ech
atron
i
cs
a
n
d
a
ut
om
ati
o
n
”
,
S
out
h
Ural
S
t
ate
Un
iversit
y
,
Rus
s
i
a
.
H
i
s
res
earch
i
nteres
ts
i
ncl
u
d
e
t
he
f
i
el
d
of
power
e
lect
roni
cs
a
nd
m
oto
r
d
r
ive
sy
s
t
ems
.
A
ndr
ey
R
a
d
iono
v.
199
7
–
D
i
p
l
o
m
a
o
f
a
n
engi
neer,
M
a
gn
it
ogors
k
S
tat
e
T
echn
i
cal
U
n
ivers
i
ty,
Ru
ssi
a
;
2
00
0
–
P
h
D
(t
echni
cal
s
cience),
Mo
sco
w
S
tat
e
T
ech
nic
a
l
Universi
t
y
(
ME
I
)
,
Rus
s
ia
;
2
0
0
9
–
D
r
.
S
c
.
(
t
e
c
h
n
.
)
,
M
a
g
n
i
t
o
go
rsk
St
ate
T
e
chn
i
cal
U
ni
versity
,
Russi
a
;
2
014
t
o
pres
ent
–
V
i
ce-Recto
r
f
or
E
du
cati
o
n
A
f
f
a
irs,
S
ou
th
U
ral
Stat
e
U
n
iv
ersity,
R
u
s
s
i
a
.
H
is
r
es
earch
i
nt
eres
ts
i
n
clu
d
e the f
i
e
l
d
o
f
power elect
ro
n
i
cs
, m
o
t
o
r d
r
iv
e
sy
st
ems an
d
m
echat
ron
i
cs
.
Se
rg
ei
B
asko
v.
1
99
6
–
Dip
l
o
m
a
o
f
a
n
e
n
gine
e
r
,
Ma
gn
itog
or
sk
S
ta
te
T
e
c
h
n
i
c
a
l
U
n
iversity,
Ru
ssi
a
;
1
99
9
–
P
h
D
(t
echni
cal
s
cience),
Mo
sco
w
S
tat
e
T
ech
nical
U
n
i
v
e
r
s
i
t
y
(
M
E
I
)
,
R
u
s
s
i
a
;
2
0
1
7
t
o
pres
ent
–
A
s
s
o
c
i
at
e
p
r
ofes
sor
of
t
h
e
D
ep
art
m
ent
“
M
echat
roni
cs
a
nd
a
u
t
om
a
tio
n”,
S
outh
U
r
al
S
tat
e
U
niversi
t
y
,
R
uss
i
a.
H
i
s
r
es
earc
h
i
nteres
ts
i
n
c
lud
e
t
h
e
f
iel
d
o
f
power
e
l
ectron
i
cs
a
n
d
motor
drive
sys
t
ems.
Al
e
k
sa
nd
ra
K
ul
mu
kh
a
m
e
tov
a.
2
0
0
8
–
D
i
p
l
o
m
a
o
f
a
n
e
n
g
i
n
e
e
r
,
S
o
u
t
h
U
r
a
l
S
t
a
t
e
U
n
i
v
e
r
s
i
t
y
,
Ru
ssi
a
;
2
0
1
4
–
P
h
D
(t
echni
cal
s
ci
ence),
Uf
a
st
ate
avi
a
ti
on
tech
ni
cal
u
niversit
y
(U
SATU
),
R
u
s
s
i
a
;
2
0
1
4
t
o
p
r
e
s
e
n
t
–
A
s
s
o
c
i
a
t
e
p
r
o
f
e
s
s
o
r
o
f
t
h
e
D
e
p
a
r
t
m
e
n
t
“
M
e
chat
ron
i
cs
a
nd
au
tom
a
tio
n”,
S
outh
Ural
S
tate
U
ni
versi
t
y,
R
ussi
a.
H
is
r
esearc
h
i
n
t
e
r
e
s
t
s
in
c
l
u
d
e
t
h
e
f
ie
ld
o
f
motor
drive
sys
t
ems.
Evaluation Warning : The document was created with Spire.PDF for Python.