Internati
o
nal
Journal of P
o
wer Elect
roni
cs an
d
Drive
S
y
ste
m
(I
JPE
D
S)
V
o
l.
6, N
o
. 3
,
Sep
t
em
b
e
r
2015
, pp
. 60
3
~
61
4
I
S
SN
: 208
8-8
6
9
4
6
03
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJPEDS
The Operating Improvement
of the Supply Source and the
Optimization of PWM Control
Far
o
uk
H
a
dj
Benali, G
h
ale
m
Bachir,
F
o
u
a
d
Az
z
o
uz
Electrotechnic D
e
partment,
El
ectrical Eng
i
neerin
g Faculty
USTO-MB El
Mnaou
a
r BP 1505, Bir
El Djir
31000 Oran
Algeria
Article Info
A
B
STRAC
T
Article histo
r
y:
Received
May 14, 2015
Rev
i
sed
Au
g 6, 201
5
Accepted Aug 20, 2015
In this paper the operating improve
ment of the supply
source and the
optimization of PWM control are pr
oposed. A comparison (based on the
bett
er operat
i
ng in term
s of input vo
ltage) be
twe
e
n the m
u
ltilev
e
l inverters
(NPC m
u
ltilevel
invert
er and H
bridge inv
e
rt
er)
is studied.
Then
two contro
l
strateg
i
es (th
e
S
P
WM and the suboptim
al PWM) are
appli
e
d to
th
e m
u
ltil
evel
inverter which has the better voltag
e
perform
ance. At las
t
a
com
p
aris
on
between
thes
e two control techn
i
ques ba
sed
on two essential points, th
e TH
D
and the output v
o
ltag
e
value. A
comparison between our r
e
sults
and r
e
sults
taken
from
lit
er
ature
is also pr
e
s
ented in
this p
a
per
.
S
i
m
u
la
tions
are
carr
i
ed
out using PSIM
environment.
Keyword:
H bridge
conver
t
er
Mu
ltilev
e
l in
v
e
rter
N
P
C co
nv
er
te
r
PWM
SPW
M
THD
Copyright ©
201
5 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
Far
o
u
k
Ha
dj
B
e
nal
i
,
Electrotechnic Depa
rtm
e
nt,
Electrical Engi
neeri
n
g Fac
u
lty,
USTO-MB Univ
ersity,
El Mn
aou
a
r
B
P
150
5, Bir
El
D
j
i
r
3
100
0 Or
an
A
l
g
e
r
i
a.
E-
m
a
i
l: f
a
r
ouk0
409
@ho
t
m
a
il
.co
m
1.
INTRODUCTION
The i
n
c
r
easi
n
g
use i
n
i
n
d
u
st
r
y
of st
at
i
c
devi
ces t
o
co
n
v
ert
ener
gy
, cal
l
e
d
st
at
i
c
conve
rt
e
r
s,
bri
n
gs
o
u
t
m
o
re and m
o
re di
st
ur
ban
ce pr
o
b
l
e
m
s
at
th
e
m
a
in
electric
a
l g
r
id
lev
e
l. Th
u
s
t
h
ere is tod
a
y an
in
crease in
th
e
v
o
ltag
e
THD.
To
reso
lv
e t
h
is prob
lem
,
m
u
lt
ile
vel
i
nve
rt
er st
ruct
u
r
es we
re
de
vel
o
ped
.
Initially, created
bot
h to put several switche
s in se
ri
es a
nd
to accurately ensure t
h
e
volta
ge
withsta
nd
acros
s t
h
em
. Therea
ft
er t
h
ese
con
v
ert
e
r
s
ha
ve sh
ow
n i
n
t
e
r
e
st
i
ng p
r
o
p
e
r
t
i
e
s on t
h
e o
u
t
p
ut
wave
fo
rm
s [1]
.
The
o
u
t
p
u
t
of m
u
lti
lev
e
l in
verter is a staircas
e
wav
e
,
wh
ich
is nearly sin
u
so
i
d
al [2
].
Th
e m
u
ltilev
e
l
in
v
e
rters still requ
ire m
a
n
y
i
m
p
r
o
v
em
en
t
s
an
d
op
ti
m
i
z
a
tio
n
in
th
e co
n
t
ro
l area.
Am
ong these,
the Diode clam
ped, and the cascade
d
H-br
i
dge inverte
r
are the two
m
a
in differe
n
t
m
u
ltilevel
i
nve
rt
er st
ruct
ures
whi
c
h ar
e used i
n
i
n
d
u
st
ri
al
appl
i
cat
i
ons wi
t
h
se
p
a
rat
e
dc so
urc
e
s. In
di
o
d
e-cl
am
ped
i
nve
rt
er t
h
e
r
e i
s
a pr
obl
em
of
capaci
t
o
r
v
o
l
t
a
ge bal
a
nci
n
g a
nd t
h
i
s
p
r
o
b
l
e
m
i
s
overc
om
e i
n
cascade
d
H
-
b
r
i
d
ge
in
v
e
r
t
er
[
3
], [4
],
[5
].
A
m
o
n
g
th
e con
t
ro
l
str
a
teg
i
es
, w
e
d
i
stin
gu
ish
four
PW
M
struct
ures; t
h
e SPWM, the
SVP
W
M
[
6
]
,
t
h
e SHE
W
PM
[7]
an
d t
h
e su
bo
pt
i
m
al
m
odul
at
i
on. T
h
i
s
wo
rk i
s
de
di
ca
t
e
d t
o
t
h
e per
f
o
rm
ance
im
pro
v
em
ent
s
of
i
n
vert
er
v
o
l
t
a
ge a
n
d
t
h
e
o
p
t
i
m
i
zati
on
of
P
W
M
c
ont
r
o
l
st
rat
e
gi
es.
Evaluation Warning : The document was created with Spire.PDF for Python.
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. 3, Sep
t
em
b
e
r
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:
60
3 – 614
60
4
2.
MULTILEVE
L
INVERTE
R
2.
1.
Ne
utr
a
l
P
o
i
n
t
Cl
amped
Inver
t
er
The NPC converter is one
of the re
feren
c
e stru
ctures in
th
e m
u
lti
lev
e
l
co
nv
ersion
(see Fig
u
re 1).
Thi
s
co
nve
rt
er
uses t
h
e seri
es
con
n
ect
i
on
of
swi
t
c
hes. T
h
e vol
t
a
ge
di
st
ri
b
u
t
i
on ac
ros
s
t
h
e swi
t
c
hes i
s
carri
e
d
out
by
diodes c
o
nnected at m
i
ddle
point.
Th
e
vo
ltag
e
acro
ss th
e cap
aci
to
rs are all eq
ual to
)
1
(
N
E
, E is th
e ov
erall
d
i
rect
v
o
ltag
e
.
Th
e
nu
m
b
er of lev
e
ls is co
m
p
u
t
ed
b
y
th
e fo
llo
wi
n
g
fo
rm
u
l
a [8
]:
1
P
N
(
1
)
N:
N
u
m
b
er of vol
t
a
ge
l
e
vel
s
P:
N
u
m
b
er o
f
c
o
m
p
l
e
m
e
nt
ary
swi
t
c
h
pai
r
s
pe
r
phase
.
Fig
u
re. 1 shows an NPC
three lev
e
l inv
e
rter.
Fi
gu
re
1.
Th
re
e l
e
vel
n
e
ut
ral
di
o
d
e-cl
am
ped
l
e
gs
Tabl
e 1
sh
o
w
s
t
h
e rel
a
t
i
o
n
s
hi
p bet
w
ee
n t
h
e
al
l
o
wed
swi
t
c
h
con
f
i
g
u
r
at
i
ons
and
t
h
e
out
put
vol
t
a
ges
o
f
a th
ree lev
e
l
d
i
o
d
e
-clam
p
ed
leg
:
Tabl
e 1.
T
h
ree
l
e
vel
ne
ut
ral
di
ode
-cl
a
m
p
ed l
e
g
rel
a
t
i
ons
hi
ps
bet
w
ee
n s
w
i
t
c
h c
o
n
f
i
g
urat
i
o
n
s
an
d
o
u
t
p
ut
vol
t
a
ge
s
Switch state
K1 K2
K3
K4
Vao(V)
1 1
0
0
E
/
2
0 1
1
0
0
0 0
1
1
-
E
/2
2.
2.
H B
r
i
d
ge
Inve
rter
Th
is con
v
e
rsion
stru
ct
u
r
e family is th
e first
o
n
e
d
e
scri
b
e
d in
literature as
a m
u
lti
lev
e
l con
v
e
rsion
stru
cture. Th
e
p
r
i
n
cip
l
e of th
is to
po
log
y
is t
o
pu
t in
series
sev
e
ral sing
le p
h
a
se two
lev
e
l b
r
idg
e
s in
H. Each
i
nve
rt
er i
s
fed
by
a di
rect
so
u
r
ce E,
an
d c
o
m
pos
ed
o
f
f
o
ur s
w
i
t
c
hes
whi
c
h
are u
n
i
d
i
r
ect
i
o
nal
i
n
v
o
l
t
a
ge a
n
d
bi
-
d
i
rection
a
l in
cu
rren
t. It is an
asso
ciatio
n between an
IGBT
an
d a
d
i
od
e con
n
ected
in an
ti-p
a
rallel [9
], [10
]
.
These
bridges
are c
o
nnecte
d
to se
parate
voltage
s
o
urces
.
The num
b
er of source
s
is equal
t
o
the
num
ber of
b
r
i
d
ges.
1
2
D
N
(
2
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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9
4
Th
e op
era
tin
g imp
r
o
v
emen
t of
th
e
su
pp
ly
sou
r
ce an
d
th
e op
timiza
tion
o
f
PWM
co
n
t
ro
l
(
F
ar
ouk
H
a
dj
B
e
nal
i
)
60
5
N:
N
u
m
b
er of vol
t
a
ge
l
e
vel
s
D:
N
u
m
b
er of si
ngl
e p
h
ase br
i
dges
pe
r pha
s
e
The st
r
u
ct
ure
of a m
u
l
t
i
l
e
vel
i
nvert
er ba
se
d o
n
the serie
s
connection of H bridges (s
ingle phase
in
v
e
rter
o
r
p
a
rt
ial cell) is shown in
Figu
re 2.
Fi
gu
re
2.
Th
re
e l
e
vel
casca
de
d
H-
bri
dge
l
e
g
Tabl
e 2
sh
o
w
s
t
h
e rel
a
t
i
o
n
s
hi
p bet
w
ee
n t
h
e
al
l
o
wed
swi
t
c
h
con
f
i
g
u
r
at
i
ons
and
t
h
e
out
put
vol
t
a
ges
o
f
a th
ree lev
e
l cascad
ed
leg inverter.
Tabl
e
2. T
h
ree
l
e
vel
cascade
d
H-
bri
dge
l
e
g
re
l
a
t
i
onshi
ps
bet
w
een
swi
t
c
h c
o
n
f
i
g
urat
i
o
ns
a
n
d
o
u
t
p
ut
vol
t
a
ges
Switch state
K1 K2
K3
K4
Vao(V)
1 0
1
0
E
1 1
0
0
0
0 1
0
1
-
E
C
onsi
d
eri
ng t
h
e sam
e
DC
so
urce
v
o
l
t
a
ge, i
t
can be see
n
t
h
at
eve
n
casca
ded i
nve
rt
er
o
u
t
p
ut
v
o
l
t
a
ge
am
pl
i
t
udes a
r
e
great
er
he
re t
h
an i
n
t
h
e
di
ode
-cl
a
m
p
ed.
3.
SIMULATION RESULTS
In
o
r
de
r t
o
c
o
m
p
are bet
w
ee
n
t
h
e t
w
o t
o
p
o
l
ogi
es
(
N
PC
a
n
d
H
bri
dge
),
si
m
u
l
a
t
i
ons a
r
e
carri
ed
o
u
t
t
o
con
f
i
r
m
t
h
e ve
raci
t
y
of
Tabl
e
s
1 a
n
d
2 c
onc
erni
ng
t
h
e
rel
a
t
i
ons
hi
p
bet
w
ee
n t
h
e
al
l
o
we
d
s
w
i
t
c
h c
o
n
f
i
g
ur
at
i
o
n
an
d
th
e ou
tpu
t
v
o
ltag
e
.
Th
e SPWM co
n
t
ro
l is u
s
ed with
th
e same si
m
u
la
tio
n
p
a
ram
e
ters. PSIM program is
u
s
ed
as
si
m
u
latio
n
environ
m
en
t. Si
mu
latio
n
p
a
ram
e
ters are group
ed
in Tab
l
e 3.
Tabl
e 3. Si
m
u
lat
i
on param
e
t
e
rs
f
o
r
S
P
W
M
c
ont
rol
E (V
)
F
p
(Hz)
F
m
(Hz)
A
p
A
m
220
20k
50
1
1
E:
Direct volta
ge feedi
n
g
the inve
rter
F
p
: Car
r
ier
fre
que
ncy
F
m
:
M
odul
at
i
n
g
fre
que
ncy
A
p
: Carrier am
p
litu
d
e
A
m
: Modulating am
plitude
Evaluation Warning : The document was created with Spire.PDF for Python.
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60
6
3.1.
Sim
u
lati
on E
x
ample
of Three Le
vel
NPC
Sim
u
l
a
t
i
on E
x
am
pl
e of
Th
ree
Level
NPC
i
s
sho
w
n i
n
Fi
gu
r
e
3.
Fi
gu
re
3.
Va
o
vol
t
a
ge
wa
ve
fo
rm
for t
h
ree l
e
vel
N
P
C
(
T
H
D
=
56
,3
9
%;
Vm
ax=1
1
0
V
)
3.2.
Sim
u
lati
on E
x
ample
of Three Le
vel
H Bridge
Sim
u
l
a
t
i
on E
x
am
pl
e of
Th
ree
Level
H B
r
i
d
g
e
i
s
sh
o
w
n
i
n
F
i
gu
re
4.
Fi
gu
re
4.
Va
o
vol
t
a
ge
wa
ve
fo
rm
for t
h
ree l
e
vel
H
b
r
i
d
ge
(
T
HD=
5
6
,
3
9 %
;
Vm
ax =22
0
V
)
4.
AN
ALY
S
IS
O
F
RES
U
LTS
Th
e
ob
tain
ed si
m
u
latio
n
results sh
ow t
h
at th
e
Va
o vo
ltage v
a
lu
e fo
r three lev
e
l
NPC
is equ
a
l to
:
110
1
V
ao
(V
)
;
and Va
o v
o
l
t
a
ge val
u
e f
o
r t
h
ree l
e
vel
H
bri
dge i
s
e
qual
t
o
:
220
2
V
ao
(V
)
, for t
h
e
sam
e
direct
so
ur
ce vo
ltag
e
220
E
(V
)
.
Thus:
2
1
E
V
ao
(
3
)
E
V
ao
2
(
4
)
R
e
l
y
i
ng o
n
t
h
e
obt
ai
ne
d si
m
u
l
a
t
i
on res
u
l
t
s
,
we n
o
t
i
ce t
h
at
t
h
e H
bri
dge i
nve
rt
er e
xpl
oi
t
s
at
m
o
st
t
h
e
di
rect
s
u
p
p
l
y
,
on t
h
e
ot
he
r h
a
nd
t
h
e
NPC
i
nve
rt
er e
x
pl
oi
t
s
o
n
l
y
t
h
e hal
f
of t
h
e
di
rect
sup
p
l
y
, ca
usi
n
g t
h
e
decom
m
i
ssi
oni
ng
o
f
p
o
we
r
of
t
h
e s
u
ppl
y
.
The co
nt
r
o
l
st
r
a
t
e
gi
es (SP
W
M
and su
b
opt
i
m
al
PW
M
)
are
appl
i
e
d t
o
t
h
e
chose
n
m
u
l
t
ilevel
i
nve
rt
e
r
(H
bridge m
u
ltilevel inve
rter) accordi
n
g to t
h
e
obtaine
d
res
u
lts.
0
0
.0
1
0
.
0
2
0
.0
3
0
.0
4
0
.0
5
Ti
m
e
(s
)
0
-5
0
-1
0
0
-1
5
0
50
10
0
15
0
Va
o
(
V
)
0
0
.
0
10
.
0
20
.
0
30
.
0
4
0
.
0
5
Ti
me (
s
)
0
-
100
-
200
-
300
100
200
300
Vao
(
V
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Th
e op
era
tin
g imp
r
o
v
emen
t of
th
e
su
pp
ly
sou
r
ce an
d
th
e op
timiza
tion
o
f
PWM
co
n
t
ro
l
(
F
ar
ouk
H
a
dj
B
e
nal
i
)
60
7
5.
MO
DUL
ATI
O
N TE
CH
NI
QUES
5.
1.
S
P
W
M
s
t
ra
teg
y
Thi
s
st
rat
e
gy
i
s
base
d o
n
t
h
e
com
p
ari
s
o
n
o
f
a si
ne
wa
ve
refe
rence
v
o
l
t
a
ge
Um
cal
l
e
d
m
odul
at
i
n
g
sig
n
a
l wh
ich
has an
a
m
p
litu
de
Am
and a f
r
e
que
ncy
fm
, t
o
one
or m
o
re t
r
i
a
ngl
e carri
e
r
s Up
whi
c
h ha
v
e
t
h
e
sam
e
am
pli
t
ude
)
1
(
2
N
A
p
and the
sam
e
fre
quency
fp
.
Each c
o
m
p
ari
s
on
gi
ves
0 i
f
t
h
e m
odul
at
i
n
g
s
i
gnal
i
s
hi
g
h
e
r
t
h
an t
h
e ca
rri
er
. Ot
her
w
i
s
e i
t
gi
ves
1
.
The s
u
m
of si
gnals
obtaine
d
from
the com
p
arison
s
g
i
v
e
s the ph
ase
vo
ltage v
a
lu
e of each lev
e
l.
Two
p
a
ram
e
ters typ
i
fy th
is st
rateg
y
[1
1
]
:
Mo
du
latio
n ind
e
x
:
f
f
Q
p
(
5
)
Voltage
adjust
ment coefficient:
A
N
A
r
p
m
)
1
((
(
6
)
The Figure 5 s
h
ows
t
h
e neces
sary
signals
to gene
rate
a five
level
voltage, with
Q=
3
0
an
d
r= 1
.
Fig
u
re
5
.
Referen
ce
v
o
ltag
e
an
d triang
le carriers fo
r a
fiv
e
m
u
l
tilev
e
l in
v
e
rter
(
Q=
20
,
r =
1
)
5.
2. Th
e Su
boptimal
PW
M
Str
a
te
gy
Opt
i
m
al or su
b
opt
i
m
al PW
M
enabl
e
s t
o
re
d
u
ce vol
t
a
ge was
t
e by
i
n
ject
i
on
of ha
rm
oni
c or
der 3 i
n
t
h
e
refe
rence
(m
od
ula
t
i
ng si
g
n
al
) [1
2]
.
The i
n
ject
i
on
of ha
rm
oni
c o
r
de
r 3 at
m
o
d
u
l
a
t
i
ng si
gn
al lev
e
l en
ab
les to
increase the
fundam
ental
max
i
m
u
m
a
m
p
litu
d
e
of th
e
resu
ltin
g
wav
e
,
an
d
con
s
eq
u
e
ntly in
th
e o
u
t
pu
t vo
ltag
e
s
with
ou
t th
e m
o
dulatin
g
am
pl
i
t
ude goe
s bey
o
n
d
A
p
/
2
. Thi
s
ha
rm
oni
c or
der 3 c
ont
ai
ne
d i
n
t
h
e out
p
u
t
v
o
l
t
a
ge of t
h
e i
n
ve
rt
er i
s
eli
m
in
ated
b
y
th
e three-ph
ase system
in
sin
g
l
e and
p
h
ase vo
ltag
e
s
[1
3
]
.
Th
is m
e
t
h
od
is illu
st
rated
b
y
Fi
gu
re 6.
Fig
u
re
6
.
Vo
ltag
e
wav
e
fo
rm
s:
wav
e
fo
rm
o
f
th
e
resu
lting
v
o
ltag
e
V
re
(
r
e
d
);
wa
vef
o
rm
of
t
h
e m
odul
at
i
n
g
vol
t
a
ge
V
m
(bl
u
e);
wa
vef
o
rm
of
t
h
e t
h
i
r
d
h
a
r
m
oni
c vol
t
a
ge
V
h3
(g
ree
n
)
0.
01
0.
0
2
0.
03
0.
04
0.
0
5
Ti
m
e
(
s
)
0
-0
.
5
-1
0.
5
1
0
0
.0
1
0
.0
2
0
.
0
3
0
.0
4
0
.0
5
Ti
m
e
(
s
)
0
-0
.
5
-1
-1
.
5
0.
5
1
1.
5
Vh3
(
V
)
Vr
e
(
V
)
Vm
(
V
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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SN
:
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94
I
J
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S
Vo
l.
6, No
. 3, Sep
t
em
b
e
r
2
015
:
60
3 – 614
60
8
Th
e m
o
du
latin
g
is exp
r
essed
as fo
llo
ws:
V
V
V
h
m
re
3
(7
)
)
3
sin(
)
si
n(
3
A
A
V
h
m
re
(8
)
6
3
A
A
m
h
(9
)
V
re
: Resu
ltin
g
v
o
ltag
e
wav
e
form
A
m
: Mo
du
lating
am
p
litu
d
e
A
h3
:
Harm
oni
c
o
r
de
r 3
am
pl
i
t
ude
The H b
r
i
d
ge
3, 5
,
7 an
d 1
5
l
e
vel
i
nve
rt
ers
are im
pl
em
ented i
n
PSIM
en
vi
r
onm
ent
i
n
orde
r t
o
defi
ne
wh
ich
o
f
th
e t
w
o con
t
ro
l strateg
i
es (
SPW
M
and PWM) is
the m
o
st efficie
n
t.
The phase vol
t
age wave
form Vab (V)
with a fu
nd
am
en
tal f
r
e
q
u
e
n
c
y o
f
50
H
z
an
d a sw
itch
i
ng
fre
que
ncy
of
2
0
kHz
i
s
prese
n
t
e
d f
o
r
al
l
si
m
u
l
a
t
i
ons
.
For t
h
e com
p
arison, the T
HD a
nd
the
fundam
ental voltage are
m
easure
d
and pre
s
ented for all
sim
u
l
a
t
i
ons. Fi
gu
re
7
rep
r
ese
n
t
s
H
b
r
i
d
ge
3,
5,
7
an
d
1
5
l
e
vel
i
n
vert
e
r
on
e-l
e
g.
(a)
(b
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
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:
208
8-8
6
9
4
Th
e op
era
tin
g imp
r
o
v
emen
t of
th
e
su
pp
ly
sou
r
ce an
d
th
e op
timiza
tion
o
f
PWM
co
n
t
ro
l
(
F
ar
ouk
H
a
dj
B
e
nal
i
)
60
9
(c)
(d
)
Fi
gu
re
7.
(a
)
3-
l
e
vel
cascade
d
H-
bri
dge
l
e
g,
(
b
)
5
-
l
e
vel
casc
a
ded
H
-
bri
d
ge l
e
g
(c
) 7-l
e
vel
cascade
d
H-
bri
dge
leg
(d
) 15-lev
e
l cascad
ed
H-bridg
e
leg.
6.
SIMULATION RESULTS
6.
1. SPW
M
Si
mul
a
ti
ons
Sim
u
l
a
t
i
on
par
a
m
e
t
e
rs of
SP
WM
c
ont
r
o
l
a
r
e g
r
o
u
p
ed
i
n
T
a
bl
e 4
.
Tabl
e 4. Si
m
u
lat
i
on param
e
t
e
rs
f
o
r
S
P
W
M
c
ont
rol
.
E (V
)
Fp (Hz)
F
m
(Hz)
Ap
A
m
110
20k
50
1
1
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
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-86
94
I
J
PED
S
Vo
l.
6, No
. 3, Sep
t
em
b
e
r
2
015
:
60
3 – 614
61
0
6.
1.
1. Si
mul
a
ti
on Resul
t
s of
H
bri
d
ge 3
L
e
vel
In
verter
: Aspec
t
of Ph
a
s
e
V
o
l
t
age
s V
ab
(V)
Sim
u
l
a
t
i
on E
x
am
pl
e of
H
b
r
i
dge
3
Le
vel
I
n
vert
er:
As
pect
of
Ph
ase
Vol
t
a
ges
V
ab
(
V
)
in
Figu
re 8.
Fi
gu
re
8.
P
h
as
e v
o
l
t
a
ge
wav
e
fo
rm
V
ab
(V
)
for
H
bri
d
ge
3 l
e
v
e
l
s
6.
1.
2. Si
mul
a
ti
on Resul
t
s of
H
B
r
i
d
ge
5
L
e
vel
In
verter
: Aspec
t
of Ph
a
s
e
V
o
l
t
age
s V
ab
(V)
Sim
u
l
a
t
i
on E
x
am
pl
e of
H
b
r
i
dge
5
Le
vel
I
n
vert
er:
As
pect
of
Ph
ase
Vol
t
a
ges
V
ab
(
V
)
in
Figu
re 9.
Fi
gu
re
9.
P
h
as
e v
o
l
t
a
ge
wav
e
fo
rm
V
ab
(V
)
fo
r H
b
r
i
d
ge
5 l
e
vel
s
6.
1.
3. Si
mul
a
ti
on Resul
t
s of
H
B
r
i
d
ge
7
L
e
vel
In
verter
: Aspec
t
of ph
A
s
e
V
o
l
t
age
s V
a
b (V
)
Sim
u
l
a
t
i
on E
x
am
pl
e of
H
b
r
i
dge
7
Le
vel
I
n
vert
er:
As
pect
of
Ph
ase
Vol
t
a
ges
V
ab
(
V
)
in
Figu
re 1
0
.
Fig
u
r
e
10
. Ph
ase
vo
ltag
e
w
a
vef
o
r
m
V
ab
(V
)
for
H b
r
i
d
ge 7
l
e
vel
s
0
0
.0
1
0
.0
2
0
.0
3
0
.0
4
0
.
0
5
Ti
m
e
(
s
)
0
-
100
-
200
-
300
100
200
300
Vab (
V
)
0
0
.0
1
0
.
0
2
0
.03
0
.0
4
0
.
0
5
Ti
m
e
(s)
0
-
100
-
200
-
300
100
200
300
Vab
(
V
)
0
0
.0
1
0
.0
2
0
.0
3
0
.0
4
0
.0
5
Ti
m
e
(
s
)
0
-1
0
0
-2
0
0
-3
0
0
10
0
20
0
30
0
Va
b
(
V
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Th
e op
era
tin
g imp
r
o
v
emen
t of
th
e
su
pp
ly
sou
r
ce an
d
th
e op
timiza
tion
o
f
PWM
co
n
t
ro
l
(
F
ar
ouk
H
a
dj
B
e
nal
i
)
61
1
6.
1.
4 .
Si
mul
a
t
i
on
Resul
t
s
o
f
H bri
d
ge
15
L
e
vel
In
verter
:
Aspec
t
of
Ph
a
s
e V
o
l
t
age
s
V
ab
(V)
Sim
u
l
a
t
i
on E
x
am
pl
e of
H
b
r
i
dge
1
5
Level
I
nve
rt
er:
As
pect
o
f
P
h
ase
V
o
l
t
a
ges
V
ab
(
V
)
in
Figu
re 1
1
.
Fig
u
r
e
11
. Ph
ase
vo
ltag
e
w
a
vef
o
r
m
V
ab
(V
)
for
H b
r
i
d
ge 15l
evel
s
6.
2. PW
M
S
u
b
op
ti
mal
Si
m
u
l
a
ti
ons
Sim
u
l
a
t
i
on par
a
m
e
t
e
rs
of
su
b
opt
i
m
al
PW
M
are gr
ou
pe
d
i
n
Tabl
e 5.
Tabl
e
5.
Si
m
u
lat
i
on
param
e
t
e
rs f
o
r t
h
e
s
u
b
o
p
t
i
m
a
l
PW
M
c
ont
rol
E (V
)
Fp
(Hz)
F
m
(
H
z)
Ap
A
m
Ah
3
110
20k
50
1
1.
155
0.
1925
6.
2.
1. Si
mul
a
ti
on Resul
t
s of
H
B
r
i
d
ge
3
L
e
vel
In
verter
: Aspec
t
of Ph
a
s
e
V
o
l
t
age
s V
ab
(V)
Si
m
u
latio
n
Resu
lts of
H
b
r
i
d
ge 3
Lev
e
l
Inv
e
rter: Asp
ect of
Ph
ase Vo
ltag
e
s V
ab
(V
) in
Fig
u
re
1
2
.
Fig
u
r
e
12
. Ph
ase
vo
ltag
e
w
a
vef
o
r
m
V
ab
(V
)
for
t
h
e
H
bri
dge
3 l
e
vel
s
0
0
.0
1
0
.0
2
0
.0
3
0
.0
4
0
.0
5
Ti
m
e
(
s
)
0
-1
0
0
-2
0
0
-3
0
0
10
0
20
0
30
0
Va
b
(V
)
0
0
.
0
10
.
0
20
.
0
30
.
0
4
0
.
0
5
Ti
me
(
s
)
0
-1
0
0
-2
0
0
-3
0
0
10
0
20
0
30
0
Va
b (
V
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l.
6, No
. 3, Sep
t
em
b
e
r
2
015
:
60
3 – 614
61
2
6.
2.
2. Si
mul
a
ti
on Resul
t
s of
H
B
r
i
d
ge
5
L
e
vel
In
verter
: Aspec
t
of Ph
a
s
e
V
o
l
t
age
s V
ab
(V)
Si
m
u
latio
n
Resu
lts of
H
b
r
i
d
ge 5
Lev
e
l
Inv
e
rter: Asp
ect of
Ph
ase Vo
ltag
e
s V
ab
(V
) in
Fig
u
re
1
3
.
Fig
u
r
e
13
. Ph
ase
vo
ltag
e
w
a
vef
o
r
m
V
ab
(V
)
for
t
h
e
H
bri
dge
5 l
e
vel
s
6.
2.
3.
Si
mul
a
ti
on
Resul
t
s
of
H B
r
i
d
ge
7
l
e
v
e
l
Inver
t
er:
A
s
pect
o
f
Ph
ase
V
o
l
t
ages
V
ab
(V
)
Si
m
u
latio
n
Resu
lts of
H
b
r
i
d
ge 7
Lev
e
l
Inv
e
rter: Asp
ect of
Ph
ase Vo
ltag
e
s V
ab
(V
) in
Fig
u
re
1
4
.
Fig
u
r
e
14
. Ph
ase
vo
ltag
e
w
a
vef
o
r
m
V
ab
(V
)
for
t
h
e
H
bri
dge
7 l
e
vel
s
6.
2.
4. Si
mul
a
ti
on Resul
t
s of
H
B
r
i
d
ge
1
5
L
e
vel
In
verter
: Aspec
t
of Ph
a
s
e
V
o
l
t
age
s V
ab
(V)
Si
m
u
latio
n
Resu
lts of
H
b
r
i
d
ge 15
Lev
e
l Inverter: Aspect
of Phase
Voltages V
ab
(V
) i
n
Fi
gu
re
1
5
.
Fig
u
r
e
15
. Ph
ase
vo
ltag
e
w
a
vef
o
r
m
V
ab
(V
)
for
t
h
e
H
bri
dge
1
5
l
e
vel
s
0
0
.0
1
0
.0
2
0
.
0
3
0
.0
4
0
.0
5
Ti
me
(
s
)
0
-1
0
0
-2
0
0
-3
0
0
10
0
20
0
30
0
Va
b (
V
)
0
0
.
0
1
0
.0
2
0
.0
3
0
.
0
4
0
.0
5
Ti
me (
s
)
0
-
100
-
200
-
300
100
200
300
Vab (
V
)
0
0
.0
1
0
.0
2
0
.0
3
0
.0
4
0
.0
5
Ti
m
e
(
s
)
0
-
100
-
200
-
300
100
200
300
Va
b (
V
)
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