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.
2, June
2
01
9, pp.
831~
8
4
1
IS
S
N
: 2088-
86
94,
D
O
I
:
10.11
59
1
/ij
ped
s
.
v10
.
i
2.pp
8
31-
84
1
831
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
An adaptable different-levels
cascaded
h-brid
g
e i
n
verter
analysis for PV
grid
-connected
systems
A
d
n
a
n
H
u
s
s
ei
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Ali,
H
a
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sa
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Sa
lma
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Ha
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l
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Abdulw
a
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Ab
dulra
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i
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Tech
nical
Univ
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rsi
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cal Ins
tructor
s
T
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ining Ins
ti
tu
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e
,
I
r
aq
Art
i
cl
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fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
R
e
ce
i
v
e
d
Jun 30,
2018
Re
vise
d A
ug
2
1
,
201
8
A
c
c
e
pte
d
D
ec 11,
2
0
1
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M
u
lti
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in
v
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rs (M
L
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av
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ed p
op
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t
he l
as
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f
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a
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e
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u
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t
of
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h
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i
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l
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o
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l
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r
m
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nic
distorti
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s
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r
o
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t
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u
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s
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s
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-Bridg
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i
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gh
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s
e
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ase
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hb
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lt
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PV
To
tal ha
rmo
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ic
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istort
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o
n
s
th
d
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:
A
dna
n
H
u
sse
i
n
A
l
i
,
Mi
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Te
ch
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Un
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ni
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a
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Instr
uc
tor
s
T
rain
i
n
g
Insti
t
ute
,
Ba
gh
da
d,
I
ra
q
Em
ail:
aaddnnaan
n63@yahoo.com
1.
I
N
TR
OD
U
C
TI
O
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C
u
rre
ntly,
an
i
nt
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r
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ter
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in
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t
i
o
n
,
no
noi
se
a
nd
n
o
f
u
el
c
o
s
t
[1].
O
n
e
o
f
the
s
ourc
e
s
o
f
e
ne
rg
y
w
h
ic
h
i
s
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id
ly
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row
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g
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t
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s, e
sp
ecial
l
y
i
n gr
i
d
-
c
on
nec
t
e
d
a
pp
l
i
ca
tions.
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n
t
h
e
l
a
s
t
f
e
w
d
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c
a
d
e
s
,
a
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co
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d
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w
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pria
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or
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s
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ai
l
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.
S
i
n
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e
t
h
e
1
960
’s
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u
lti
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v
e
l
inv
e
rte
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s
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ave
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e
e
n
a
r
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s
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a
rc
h
ar
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w
hi
c
h
h
as
a
t
t
r
a
cted
the
interes
t
o
f
many
[
2
].
I
n
the
l
i
t
e
ratu
re
,
va
ri
ou
s
t
opo
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o
g
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c
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,
an
d
fl
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aci
to
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add
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tio
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to
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c
a
s
c
a
de
d
H
-
Br
idge
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r
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e
x
i
st
[
3]
.
F
o
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e
v
ery
to
p
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o
g
y
,
th
e
r
e
a
r
e
advan
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age
s
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it
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[
4].
In
t
h
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sa
me
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n
,
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wi
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t
o
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d
i
s
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for
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gre
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ter am
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he s
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of t
he clam
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ma
de
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al
C
H
-
B
r
id
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r
ises first
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n
the m
a
r
k
et [5].
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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0
8
8
-
86
94
I
n
t
J Po
w
Elec
&
Dr
i
Sy
st,
Vo
l. 1
0
,
No
. 2
,
Ju
n
e
2
019
:
8
31
–
8
4
1
83
2
A
m
ong
t
h
e d
i
f
f
er
ent
c
onve
n
t
i
ona
l t
opo
l
o
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y
f
or
M
L i
n
ver
t
er
s,
t
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o
pol
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f
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s
ca
d
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d
H-B
r
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d
g
e
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e
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e
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s
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s
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l
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th
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or
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volta
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e
v
e
l
n
um
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fec
t
e
d
.
The
desig
n
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m
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t
er
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ha
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r
e
se
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c
asc
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H-br
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e
l
l
s
[
6
]
.
T
h
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o
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g
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t
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s
e
o
f
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w
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3
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5
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(
B
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eq
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to
c
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th
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l n
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(
L):
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=
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ଵ
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(1
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a
t
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N=
4
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l
i
n
v
er
t
e
r
al
on
gs
i
d
e
its
m
e
c
ha
n
i
s
m
f
or
s
witc
hi
n
g
.
The
CH-
Br
i
dge
M
L
I
s
c
a
n ba
s
i
c
a
l
l
y
b
e
des
i
gna
te
d as
a
s
um
of
the
c
l
assi
c
t
w
o
-
l
e
v
e
l
b
r
i
d
g
e
,
w
i
t
h
A
C
s
t
ermi
n
a
l
s
t
h
a
t
are
se
que
n
tia
ll
y
linke
d
f
o
r
t
h
e
p
u
r
p
ose
of
s
y
n
t
he
s
i
z
i
n
g
t
he
o
u
t
p
u
t
w
a
ve
f
o
r
m
s.
T
he
s
ymm
e
tr
ica
l
9
-
l
e
v
e
l
i
nve
r
t
er
'
s
powe
r
c
irc
u
i
t
t
hat
c
o
mprise
s
fo
ur
c
e
lls
o
f
C
H
B
i
s
i
ll
ustra
t
ed
i
n
F
i
gur
e
2.
M
an
y
s
t
a
nd-
a
l
one
D
C
sour
ce
s
tha
t
c
a
n
be
g
o
t
t
e
n
f
r
om
f
ue
l
c
e
l
l
s,
b
at
ter
i
es
o
r
s
o
la
r
ce
l
l
s
ar
e
r
e
q
uir
e
d
b
y
t
he
C
H
B
i
nve
r
t
er
.
I
t
i
s
po
ssi
b
le
f
or
t
hr
e
e
va
r
i
ous
v
ol
t
a
g
e
o
u
t
pu
t
ste
p
s,
0
a
s
a
r
e
fer
e
nc
e
,
(
+V
dc)
,
a
nd
(
−
V
dc
)
to
b
e
g
e
ne
r
a
te
d
w
i
th
c
ombi
n
i
n
g
a
n
y
o
f
t
h
e
f
o
u
r
sw
itc
hes
o
f
e
ac
h ce
ll
,
a
s
s
how
n i
n
Ta
b
le
1
f
or
C
la
ss
ic
H
-
B
ri
dg
e
M
L
I
.
Th
e
tot
a
l
nu
mb
er o
f
th
e
ind
i
vid
u
a
l
c
o
n
v
er
ter
ou
t
p
uts
ca
n
be
u
se
d
in
d
er
iv
i
n
g
t
h
e
A
C
o
u
t
pu
t.
U
sin
g
a
n
n
=
2
N
+
1,
t
he
v
o
l
t
a
ge
l
eve
l
'
s
n
umbe
r
i
n
ou
t
p
u
t
p
ha
se
c
an
b
e
de
f
i
ne
d,
w
he
r
e
a
n
um
b
e
r
of
D
C
s
our
c
e
s
i
s
de
no
te
d
b
y
N
.
F
o
r
e
x
am
ple,
w
i
t
h
n
ine
l
e
vel
s
,
ther
e
is
a
f
luc
t
ua
t
i
on
o
f
t
he
o
utp
u
t
vo
lta
ge
f
r
o
m
(
−4V
d
c)
t
o
(
+
4V
d
c
).
F
i
gur
e
1.
(
a)
F
i
v
e
-
le
vel
(
b
)
n-
l
e
vel
I
n
ver
t
er
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
An
a
d
a
p
t
a
b
le
d
iffe
re
n
t
-
l
e
v
e
l
s casc
ade
d h-br
i
d
ge
i
n
ve
rte
r
a
n
a
l
y
si
s
…
(
H
assan S
a
l
m
a
n H
a
m
ad)
83
3
F
i
gur
e 2.
P
ow
e
r
c
irc
u
i
t
f
or 9-
l
e
v
el
Tab
l
e
1.
S
w
itc
hi
n
g
m
echa
n
ism
for c
l
a
ssi
c
h-br
i
d
ge
MLI
T
i
m
e
+
v
e
H
a
l
f
C
y
cl
e
-
v
e
H
a
l
f
C
y
c
l
e
Ou
tp
u
t
s
V1
(
V
1
+
V
2
)
(
V1
+V2
+
V3
)
(
V
1
+
V2
+V
3
+
V
4
)
V1
(
V
1
+
V
2
)
(
V1
+V2
+V
3
)
(V
1
+
V
2
+
V3
+V4
)
B
r
idge
A
S
A
1
SA
4
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
B
r
i
d
ge
B
Sb
1
Sb
4
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
B
r
idge
C
Sc
1
Sc
4
0
0
1
1
0
0
1
1
1
1
1
1
1
1
1
1
B
r
idge
D
S
d
1
Sd
4
0
0
0
1
0
0
0
1
1
1
1
1
1
1
1
1
Inv
e
rsion Sp
1
B
r
idge
S
p2
Sp
3
Sp
4
1
1
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
1
1
1
1
1
0
0
0
0
C
o
m
p
a
r
ed
t
o
f
l
y
i
ng
s
c
apac
i
t
o
r
o
r
di
o
d
e
s
c
l
a
m
ped
MLI
t
o
p
o
lo
gie
s
,
the
ca
sc
ade
d
H
b
rid
g
e
MLI
ar
e
si
m
p
ler
due
t
o
some
a
dvantages
whi
c
h
it
possess
l
ike
switching
re
du
nd
an
cy
,
au
to
ma
ti
c
vo
lt
ag
e
d
i
st
rib
u
tio
n,
sma
l
le
r
d
v
/d
t
s
t
r
e
ss,
a
bsenc
e
o
f
hi
gh-
rate
d
c
a
pac
i
t
o
rs
a
n
d
d
io
d
es
a
s
w
e
l
l
a
s
the
ne
e
d
f
or
m
inim
um
n
um
ber
of
com
p
o
n
e
n
t
s
[
7
]
.
The
ma
i
n
f
o
c
us
o
f
th
is
m
anus
crip
t
is
t
o
i
n
v
e
sti
gate
t
h
e
s
i
n
g
l
e
p
h
ase
CH
B
per
f
orm
a
n
c
e
s
o
f
M
L
I
w
h
i
c
h
a
n
i
n
p
u
t
s
o
u
r
c
e
s
s
t
a
r
t
e
d
f
r
o
m
l
e
v
e
l
5
t
o
9
a
r
e
a
p
h
o
t
ov
o
lta
ic
c
e
ll.
I
t
pr
ese
n
ts
a
s
ym
me
t
r
i
c
t
ype
i
n
v
e
rt
e
r
w
ith
a
r
ed
u
c
ti
on
i
n
swi
t
c
h
a
m
ou
nt
.
It
c
on
si
st
s
o
f
t
wo
vol
t
a
g
e
s
ource
s
a
n
d
fou
r
s
wi
t
c
h
e
s
f
o
r
e
ach
c
e
l
l
and
genera
te
s
5,
7
,
a
n
d
9
lev
e
l
s
out
p
u
t
w
a
v
e
for
m
d
uri
ng
s
y
mm
etr
ic
o
per
a
tio
n.
M
ore
s
o
,
i
t
c
o
n
ce
nt
r
a
te
s
o
n
tech
n
o
l
o
gie
s
o
f
inve
r
t
er
t
o
c
o
nnec
t
p
h
o
t
o
v
o
l
t
a
i
c
pa
nel
s
t
o
a
si
n
g
l
e-p
h
a
s
e
g
r
id.
A
re
lated
works
ar
e
exp
l
aine
d
in
S
ect
io
n
I
I
.
The
s
u
gge
st
e
d
t
op
o
l
ogy
for
di
ffe
re
nt
m
e
t
h
ods
o
f
c
a
lc
u
l
a
t
i
n
g
t
h
e
sw
it
c
h
in
g
are
of
fer
e
d
i
n
Section
III.
T
h
e
sim
ul
a
tion
resu
lts
a
re discus
s
ed
i
n
Secti
o
n
IV
.
The
conc
lu
si
on w
a
s
gi
v
e
n
in S
ec
t
i
o
n
V
.
2.
REL
A
TE
D
WORK
S
Base
d
on
the
review
o
f
l
ite
rature
i
n
t
h
e
p
r
e
v
i
o
us
p
a
g
es,
i
t
i
s
evi
d
e
n
t
th
at
e
ffor
ts
a
re
m
ade
b
y
m
any
rese
arc
h
ers
t
o
p
ro
pose
no
ve
l
i
n
ve
rter
t
op
o
l
o
g
ie
s
or
t
o
m
o
d
i
fy
t
he
o
l
d
one
s.
T
he
purp
o
se
o
f
d
o
i
n
g
t
h
is
i
s
t
o
impro
v
e
the
q
u
a
l
i
t
y
o
f
e
n
er
gy
t
hat
i
s
a
va
ila
b
l
e
a
t
t
he
t
erm
i
n
a
l
s
of
i
n
v
er
t
e
rs
.
D
u
e
t
o
t
he
a
b
ili
ty
o
f
c
a
s
ca
de
d
H
-
bri
dge
m
u
lti-le
ve
l
i
n
ve
rter
t
o
han
d
l
e
h
i
gh-p
o
w
e
r
a
s
w
e
ll
a
s
i
t
s
r
e
l
i
a
b
i
l
i
t
y
,
w
h
i
c
h
i
s
a
s
a
r
e
s
u
l
t
o
f
i
t
s
m
o
d
u
l
a
r
to
pol
o
gy,
it
ha
s
bee
n
r
ega
r
de
d
a
s
one
o
f
th
e
bes
t
a
va
ila
bl
e
mul
tile
ve
l
in
ve
rter
t
o
p
o
l
og
i
e
s.
D
ue
t
o
t
h
is,
i
s
con
s
i
d
ere
d
as
a
more c
apable
o
p
tio
n
whi
c
h ca
n be
exte
n
de
d
to a
l
l
o
w
gri
d
c
on
ne
c
tio
n
tha
t
i
s
trans
f
or
me
r-less.
R
odri
g
uez
e
t
a
l.
[
8]
,
ha
ve
p
r
o
v
i
de
d
a
de
scr
i
p
t
io
n
of
t
he
m
ost
s
ig
ni
fi
can
t
met
hod
s
o
f
c
on
t
r
ol
a
nd
modu
la
ti
o
n
w
h
i
c
h
h
e
de
sig
n
e
d
f
or
a
f
am
ily
o
f
c
o
n
v
er
ters
w
hi
c
h
i
nc
l
u
de
s
pac
e
-ve
c
t
or
m
od
u
l
at
i
on,
m
ult
i
-le
v
e
l
selec
t
i
v
e
h
a
rmon
ics
e
l
i
m
i
n
a
t
ion
a
n
d
mul
til
e
v
el
s
i
n
u
s
o
i
da
l
p
u
lse
w
i
d
th
m
odu
la
ti
o
n
(
SP
WMs).
The
PWM
rege
nera
t
i
ve
r
ecti
f
ier
s
w
e
r
e
intro
duce
d
b
y
Rodr
ig
ue
z
et
a
l.
[
9]
i
n
w
h
i
c
h
t
h
e
y
w
e
r
e
a
b
l
e
t
o
impr
o
v
e
the
p
o
w
e
r
fa
ct
or
a
s
w
e
l
l
a
s
r
e
duce
i
npu
t
har
m
on
ics.
I
n
t
i
m
e
p
a
s
t
,
t
he
a
p
p
l
i
ca
t
i
o
n
of
m
ult
ile
ve
l
a
c
tive
rec
tif
i
e
rs
w
as
bas
i
ca
ll
y
ma
de
i
n
h
i
gh
p
ow
er
i
nd
us
tria
l
ap
p
l
i
c
at
i
on,
h
i
gh
v
o
l
t
a
ge
a
p
p
l
i
ca
tio
ns,
ow
in
g
to
t
he
c
apa
b
il
ity
o
f
t
h
e
app
l
ied
v
o
l
t
a
g
e
dispe
n
s
i
n
g
t
hro
u
g
h
m
any
ca
sc
ade
d
p
ow
e
r
d
evic
e
s
,
t
he
re
fore
a
ddre
ssi
ng
t
h
e
iss
u
e
o
f
t
heir
l
i
mit
a
ti
on
v
o
lta
g
e
a
s
well
a
s
e
n
abl
i
ng
th
e
ex
c
l
u
s
io
n
of
out
-pu
t
s
y
s
t
e
m
transform
e
r
s
o
f
m
e
dium
t
ow
ard
hig
h
vo
lta
ge
s.
T
h
e
p
er
form
anc
e
o
f
t
h
e
m
u
lt
ile
v
e
l
a
c
t
ive
re
ct
ifiers
i
s
be
tte
r
t
h
an
t
ha
t
of
t
h
e
t
w
o
-
l
e
v
e
l
s
P
W
Ms
in
verter
s
rela
te
d
t
o
t
o
t
a
l
h
armon
i
cs
d
istor
t
i
o
n,
a
nd
w
i
t
h
-o
u
t
u
si
n
g
p
as
si
ve
f
i
l
t
ers
w
h
ic
h
are
expe
nsi
v
e,
b
u
l
ky
and
dece
p
tive
;
t
h
i
s is be
c
a
u
se
t
he
ir ou
t
pu
t v
o
lta
ge
i
s
in
t
he f
orm
of
m
odula
t
ed
s
t
a
i
r
case
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
Int J
Pow
El
ec &
D
ri
S
yst
,
Vol
.
10,
N
o.
2
, June 2019: 831
–
84
1
83
4
I
n
2003,
A
lo
nso
O
.
e
t
al.
[10]
p
re
sente
d
a
nove
l
sc
hem
e
o
f
c
o
n
t
r
o
lli
n
g
a
nd
prop
ort
i
ona
te
P
WM
f
o
r
t
h
e
CH-b
ridg
e
mu
lt
il
ev
el
i
nv
e
r
t
e
r
u
s
ed
f
or
g
ri
d
conn
e
c
t
e
d
p
hot
o
vo
lt
aic
sy
st
em.
Th
ro
ugh
b
y
uti
l
i
z
i
n
g
th
i
s
con
t
ro
l
lin
g,
v
a
r
i
o
us
p
o
w
er
l
e
v
el
s
a
r
e
pro
v
i
d
ed
b
y
eac
h
H-
brid
g
e
m
od
u
l
e
,
t
here
by
al
l
o
w
i
ng
ea
ch
m
o
d
u
l
e
to
in
de
pen
d
e
n
t
l
y
t
rac
k
t
he
m
a
x
im
um
p
ow
er
p
o
i
nt
o
f
c
o
r
r
esp
o
n
d
i
n
g
P
V
A.
F
u
r
t
h
e
r
mo
r
e
,
mu
l
t
il
ev
el
P
W
M
in
verter
s,
w
hi
c
h
a
re
a
pp
r
o
pri
a
te
f
or
u
si
n
g
i
n
inde
pe
n
d
en
t
P
V
g
r
i
d
-c
onnec
t
e
d
p
o
w
e
r
i
n
v
e
rt
ers
fo
r
PV
u
n
i
t
s
w
e
r
e
de
v
elo
p
e
d
by K
a
ng et a
l
.
[
11]. A stra
t
egy f
o
r sw
itc
h
i
n
g
a
f
i
ve level
C
HB
M
LI esse
n
tia
l freq
u
e
n
cy t
o PV
syste
m
s
tha
t
a
re
i
nde
pe
nde
n
t
w
as
p
rop
o
sed
by
O
z
dem
i
r
e
t
a
l.
[
12
]
thro
ug
h
the
se
lec
t
i
on
of
t
he
s
w
i
tc
hin
g
ang
l
es
i
n
a w
a
y tha
t
it
can
e
l
i
minate
t
he ha
r
m
oni
c
s
w
it
h
lo
w
e
r
order.
I
n
ad
d
i
t
i
on
t
o
t
he a
dva
n
t
age
o
f
ha
v
in
g t
h
e ca
pa
b
ili
ty for m
axim
i
z
in
g
th
e po
wer
acq
u
i
r
ed
f
ro
m
P
VAs
,
a
ML
i
n
v
er
ter
is
a
lso
ca
pab
l
e
of
d
ecr
easi
ng
t
h
e
s
t
re
ss
o
f
v
o
l
t
a
ge
d
ev
ice
a
s
w
e
l
l
as
t
o
gen
e
rate
a
l
ow
e
r
out
p
u
t
,
tha
t
i
s
a
v
o
lta
ge
h
ar
moni
c
d
i
stort
i
on
m
ore
e
f
ficie
n
t.
I
n
t
h
e
ar
e
a
o
f
r
e
ne
w
a
ble
e
n
erg
i
e
s
J
os
h
e
t
a
l.
[
1
3
]
h
a
d
sug
g
es
t
e
d
ML
I,
w
hich
i
s
capa
b
l
e
o
f
reduc
i
n
g
the
d
i
me
n
s
ions
o
f
o
ut
pu
t
f
i
l
t
e
r
as
w
e
l
l
as
i
n
f
l
u
en
cing
t
h
e
pert
urba
ti
on
s
t
h
at
o
c
c
u
r
a
s
a
r
esul
t
of
t
he
d
a
r
ke
nin
g
o
f
cl
o
ud
of
v
ar
i
a
tio
n
in
s
e
a
s
o
ns,
whi
l
e
a
m
o
d
i
fie
d
p
hase
di
sp
os
it
ion
P
W
M
w
a
s
pro
pos
ed
b
y
Me
i
e
t
a
l
.
[
1
4
]
fo
r
un
it
s
o
f
M
L
I
w
h
i
c
h
w
a
s
e
m
plo
y
e
d
a
t
P
V
g
rid
con
n
ec
ted
for
the
p
u
r
pose
of
a
c
h
ie
v
i
n
g
b
ala
n
ce
i
n
t
he
d
yn
am
ic
c
apa
c
i
t
o
r
v
o
l
tage
w
it
h
o
u
t
re
q
u
iri
ng
a
d
di
tio
na
l
com
p
en
sat
i
on
si
gna
l.
A
d
is
t
i
nc
t
D
C
s
ource
i
s
n
e
e
d
e
d
by
the
Ca
sc
a
d
e
H
-
brid
ge
M
LI,
be
s
i
de
s
i
t
lim
i
t
s
the
perform
ance
t
hi
s
M
L
I
w
h
e
n
i
t
is
a
va
ila
b
l
e
[1
5].
H
o
w
e
ver
,
i
n
t
h
e
c
a
s
e
o
f
P
V
sy
st
em
s,
it
is
a
s
tri
k
in
g
cha
r
ac
t
e
ris
tic
a
s
i
t
e
nha
nce
s
t
he
a
ssem
b
l
i
n
g
o
f
s
o
l
a
r
ce
ll
s
in
a
n
u
m
b
er
o
f
i
nde
pe
n
d
e
n
t
ge
ner
a
t
o
rs.
V
a
r
i
o
u
s
P
W
M
m
e
t
h
o
d
s
s
u
c
h
a
s
o
p
t
i
m
i
z
e
d
s
t
e
p
p
e
d
w
a
v
e
f
o
r
m
(
O
H
S
W
)
a
n
d
s
e
l
e
c
t
i
v
e
harm
o
n
ic
s
e
l
im
i
n
a
t
i
o
n
PW
M
ar
e
sup
por
t
e
d by
the
CH
B-
M
L
I [1
6]
.
3.
SUGGE
S
TED
T
OPO
L
O
G
Y
The
su
g
g
este
d
to
pol
o
gy
a
c
c
o
m
p
lishe
d
b
y
r
educ
i
ng
the
nu
m
b
er
o
f
c
on
tro
l
l
i
ng
sw
i
t
c
h
e
s
i
s
de
scri
be
d
here
.
A
review
o
f
pas
t
s
t
u
d
i
es
,
show
s tha
t
t
h
e
f
oc
us o
f
pre
v
io
u
s
r
e
sea
r
che
r
s
ha
s bee
n
d
e
a
l
i
n
g
w
ith
a
r
e
duc
tio
n
of
s
ize
a
n
d
c
o
m
pon
e
n
t
s
o
f
MLI
,
w
it
h
the
pur
pose
o
f
r
e
d
uci
n
g
sw
i
tc
he
s
thro
ug
h
t
h
e
us
e
of
I
n
v
ersi
on
B
r
i
dge
.
The
c
u
r
r
ent
l
y
pro
pose
d
d
es
i
gn
fo
cuse
s
o
n
m
i
nim
u
m
n
u
m
ber
of
s
w
i
t
ch
es
w
h
i
c
h
h
a
v
e
so
me
d
i
s
adva
n
t
ag
e
s
rela
t
e
d
to
t
he
s
e
t
op
o
l
o
g
i
e
s
.
O
n
e
o
f
s
u
c
h
li
m
i
tat
i
o
ns
i
s
us
in
g
a
b
id
i
r
ect
i
o
n
a
l
swit
ch
w
h
i
c
h
i
n
c
u
r
s
extra
co
st
asi
d
es
t
he
a
bs
e
n
ce
o
f
e
ven
s
ource
s
of
v
olt
a
ge
.
Mor
e
s
o,
t
he
p
ro
po
se
d
t
o
pol
ogy
o
ff
e
r
s
a
b
e
tt
e
r
a
nd
s
i
m
p
l
er
mo
d
u
l
a
r
fo
rm
i
n
c
o
mp
ari
s
on
t
o
th
e
sy
mmet
ri
ca
l
mu
lti
l
e
v
el
i
nv
e
r
t
e
r
;
the
to
p
o
l
o
gy
als
o
a
llow
s
t
r
a
ns
i
s
t
o
r
sw
it
c
h
es
t
o
c
onne
c
t
w
i
t
h
ea
ch
o
t
h
e
r
,
an
d
it
a
lso
pr
ov
i
d
e
s
p
ara
l
le
l
d
i
o
d
e
s
as
i
llus
t
ra
t
e
d
in
F
i
gure
3.
T
he
in
verter
r
epre
senta
t
io
n
dia
g
r
a
m
of
t
he
C
H
-
bri
dge
s
truc
tur
e
o
f
t
he
g
rid
con
n
e
c
t
i
on
P
V
s
yst
e
ms
a
p
p
e
a
r
s
i
n
F
i
gure
3.
A
t
o
p
o
l
og
y
of
t
he
c
asca
de
d
MLI
c
o
mpr
i
se
s
of
n-
con
n
e
c
t
ed
H
-brid
g
e
i
n
verter
s
ser
i
a
lly
a
n
d
e
a
c
h
D
C
lin
k
can
b
e
fed
w
i
th
a
sm
a
ll c
h
ai
n o
f
P
V
pan
e
ls
[
1
7
].
F
i
gure
3.
C
H
B
c
ircui
t
dia
gr
a
m
MLI
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
An
a
d
a
p
t
a
b
le
d
iffe
re
n
t
-
l
e
v
e
l
s casc
ade
d h-br
i
d
ge
i
n
ve
rte
r
a
n
a
l
y
si
s
…
(
H
assan S
a
l
m
a
n H
a
m
ad)
83
5
4.
DESIGN S
I
M
ULAT
ION,
A
NALYSIS,
A
ND
RES
U
L
T
S
The
ca
sc
ade
d
H
-Bridge
M
LI
c
i
r
cui
t
w
hi
c
h
c
a
n
b
e
des
i
gne
d
us
in
g
M
AT
LAB/
S
i
mulink
i
s
discussed
in
t
h
i
s
sec
t
io
n.
M
ore
so,
the
fi
g
u
re
s
for
a
ll
l
e
ve
ls
i
l
l
us
tra
t
e
t
he
s
i
m
u
l
ate
d
o
utp
u
t
vol
ta
ge
,
TH
D
a
nd
c
u
rrent
ana
l
ys
is
a
s
w
e
l
l
a
s
t
h
e
ou
t
p
u
t
v
o
lta
ge
w
i
t
h
e
qua
l
s
t
e
p
w
av
e
f
orm
f
or
e
le
ve
n-
l
e
vel
casc
a
d
e
d
H
-
Bri
d
g
e
i
n
v
erter
.
5,
7
and
9-Lev
e
ls
s
w
i
t
c
h
i
n
g
o
f the
CH
B
M
L
I
as
s
how
n i
n
Ta
b
le
2.
Ta
ble
2: 5,
7 a
nd 9-Le
vel
s
sw
itc
h
i
ng
o
f
t
he
C
H
B
M
LI
V (
O
UT)
5 le
v
e
ls
7
l
e
v
e
l
s
9 le
v
e
ls
S5
S
6
S7
S
8
S9
S
10
S
11
S
12
S
13
S
14
S
15
S
16
4V
P
1
0
0
1
1
0
0
1
1
0
0
1
3V
P
1
0
0
1
1
0
0
1
1
1
0
0
2V
P
1
0
0
1
1
1
0
0
1
1
0
0
V
P
1
1
0
0
1
1
0
0
1
1
0
0
0
V
1
1
0
0
1
1
0
0
1
1
0
0
-V
P
0
0
1
1
0
0
1
1
0
0
1
1
-
2
V
P
0
1
1
0
0
0
1
1
0
0
1
1
-
3
V
P
0
1
1
0
0
1
1
0
0
0
1
1
-
4
V
P
0
1
1
0
0
1
1
0
0
1
1
0
4.1.
Fiv
e
-l
ev
el
i
nv
e
r
ter
F
i
gure
4(a)
i
l
l
us
trates
t
he
m
ode
l
of
s
im
u
l
a
tio
n
for
t
h
e
F
i
ve-
l
e
vel
c
a
sca
d
e
i
n
ver
t
e
r
c
ircui
t
c
on
te
n
t
8
IG
BT
g
r
i
d
c
o
n
n
e
c
te
d
P
V
s
yste
m.
I
n
orde
r
fo
r
IG
BT’s
t
o
i
n
verts
D
C
t
o
A
C
,
8
p
u
l
s
e
s
a
r
e
r
e
q
u
i
r
e
d
.
F
i
g
u
r
e
4
(
b
)
repr
esents
t
he
out
pu
t
s
i
gna
l
TH
D
,
t
he
8
P
W
M
s
ig
na
l
for
IG
BT
i
s
e
x
pl
aine
d
in
F
ig
ur
e
4(c)
a
nd
F
i
g
u
re
4
(d)
ill
us
trates
t
he
o
ut
p
u
t
v
o
l
ta
ge a
nd
Curren
t
.
The
sim
u
l
a
tio
n
m
o
de
l
c
o
mpr
i
ses
tw
o
H
-
brid
ges
w
h
i
c
h
nom
ina
l
D
C
v
o
l
tag
e
s
up
po
sed
to
b
e
6
5
V
,
in
add
i
tio
n
to
t
he
P
WM
i
nve
rte
r
w
hic
h
c
o
n
tro
l
t
he
s
yste
m
c
o
n
n
e
c
t
ed
t
o
th
e
gr
id,
a
l
so,
a
m
u
lti-le
ve
l
s
t
eppe
d
ou
tpu
t
v
o
l
tage
can
b
e
a
c
h
i
e
v
e
d
a
nd
a
har
m
onic
s
c
o
u
ld
b
e
r
e
duce
d
.
A
P
W
M
ge
ner
a
tor
b
l
ock
e
x
i
s
t
s
t
ha
t
con
t
a
i
n
para
me
t
e
rs
l
i
k
e
am
p
l
itu
de
,
p
h
ase
de
lay,
a
nd
p
u
l
s
e
wid
t
h
p
er
io
d
fr
om
w
hic
h
a
s
h
a
pe
o
f
the
ou
tp
ut
c
an
be
d
eterm
i
ned.
F
i
gure
4(a
)
.
5-l
e
vel
s
CH
B
Inv
e
r
ter
MA
TLA
B m
ode
l cir
c
u
i
t
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
n
t
J Po
w
Elec
&
Dr
i
Sy
st,
Vo
l. 1
0
,
No
. 2
,
Ju
n
e
2
019
:
8
31
–
8
4
1
83
6
F
i
gur
e
4(
b)
.
Ana
l
ys
is
o
f
F
F
T CH
-
B
r
i
dge
M
LI
Fig
u
r
e
4
(
c)
. Ga
t
ing
p
u
lses g
enerated
o
f
PWM
5
-
lev
e
ls CHB
F
i
gur
e
4(
d)
.
V
olta
ge
a
nd
c
u
r
r
ent
o
u
t
p
u
t
p
h
a
s
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
An a
d
a
p
t
a
b
l
e dif
f
ere
n
t-
lev
e
l
s
c
a
sc
ade
d
h-
bri
dge i
n
ver
ter a
naly
s
is
…
(
H
ass
an Sa
lm
a
n
H
a
m
ad)
83
7
Th
us,
t
h
e
in
ver
t
er
e
f
f
ic
ie
nc
y
c
o
u
l
d
be
i
ncr
e
as
ed,
so
t
he
i
nve
r
t
e
r
n
eed
s
to
p
er
form
w
i
t
h
rel
i
ab
i
l
i
t
y
a
n
d
pr
o
f
ic
ien
t
ly
f
o
r
s
upp
ly
i
n
g
a
w
i
de-
r
ang
i
ng
o
f
A
C
l
oa
ds
by
a
r
e
qui
re
d
po
wer
qu
a
lit
y
a
n
d
vol
ta
g
e
w
h
i
ch
i
s
ne
cessar
y
f
or
e
ff
i
c
ie
n
t
l
oa
d
as
w
e
l
l
as
s
ys
te
m
per
f
o
r
m
a
n
ce
s.
M
a
ny
s
y
s
t
em
a
dva
n
t
a
g
es
like
h
i
g
h
-
p
ow
er
,
low
ha
r
m
onic
dis
t
o
r
ti
o
n
s,
capa
c
i
t
y
o
f
h
i
g
h
-
v
o
l
ta
ge
i
n
a
d
d
i
t
i
on
t
o
l
ow
s
w
i
tc
hi
ng
lo
sses.
A
5
-
l
eve
l
s
ou
tpu
t
v
ol
ta
g
e
a
nd
cur
r
en
t
a
r
e
show
n.
T
he
o
ut
p
u
t
5-
le
v
e
l
i
n
ver
t
er
,
centr
a
l
f
r
e
que
ncy
is
5
0
H
z
.
4.
2.
S
e
ve
n
-
le
vel
In
ve
rt
e
r
A
S
e
ven-
le
v
e
l
s
C
H
B
i
n
v
e
r
te
r
cir
c
uit
c
o
n
t
e
n
t
12
s
w
i
tc
hes
of
I
G
B
T
,
w
h
i
c
h
c
a
n
be
d
i
s
p
l
aye
d
i
n
t
h
e
F
i
g
u
r
e
5
(a)
.
A
n
IGBT’s
n
eed
8
p
uls
e
s
f
o
r
inv
e
rti
n
g
D
C
s
ign
a
l
to
t
h
e
A
C.
F
i
gur
e
5(
b)
r
ep
r
e
sents
the
T
H
D
f
o
r
the
o
u
t
p
ut
v
ol
ta
ge
s
ig
na
l
,
F
igur
e
5(
c
)
e
xp
la
i
n
s
t
h
e
8
P
W
M
si
gna
l
f
o
r
IGBT
a
n
d
f
i
n
a
ll
y
F
i
gu
re
5
(
d
)
sh
ows
the
ou
t
p
u
t
v
ol
t
a
ge
a
nd
Cur
r
e
n
t
.
F
i
g
u
r
e
5
(
a
).
7
-l
ev
els CHB
In
ver
t
er
M
ATLAB
mo
d
e
l
circuit
F
i
gur
e
5(
b)
.
Ana
l
ys
is
o
f
F
F
T CH
-
B
r
i
dge
M
LI
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
n
t
J Po
w
Elec
&
Dr
i
Sy
st,
Vo
l. 1
0
,
No
. 2
,
Ju
n
e
2
019
:
8
31
–
8
4
1
83
8
F
i
gur
e
5(
c)
.
G
a
t
i
n
g
pu
lse
s
g
e
n
e
r
ate
d
o
f
P
W
M
7-
le
vel
s
C
H
B
F
i
gur
e
5(
d)
.
V
olta
ge
a
nd
c
u
r
r
ent
o
u
t
p
u
t
p
h
a
s
e
4
.
3
.
N
i
n
e
-
l
e
v
e
l
i
nv
e
r
t
e
r
A
circui
t
of
n
ine
-
le
vels
C
HB
i
n
v
erter
con
t
e
n
t
16
swi
t
c
h
e
s
o
f
IG
B
T
,
w
h
ich
c
a
n
be
p
r
e
se
nte
d
i
n
t
h
e
F
i
g
u
r
e
6
(
a
)
.
A
n
I
G
BT’
s
n
e
e
d
16
p
u
l
ses
i
n
i
nver
t
i
n
g
D
C
s
i
gna
l
t
o
t
h
e
A
C.
F
igur
e
6(
b)
r
e
p
r
e
se
nts
the
T
H
D
f
o
r
the
o
u
t
p
u
t
v
o
l
t
a
ge
s
ig
na
l,
F
ig
ure
6(c
)
e
x
p
la
ins
the
1
6
P
W
M
s
i
g
n
a
l
f
or
I
G
B
T
a
nd
f
i
na
l
l
y
F
i
g
u
r
e
6
(
d
)
show
s
t
h
e
out
put
v
olta
g
e
a
n
d
C
u
r
r
e
n
t
.
Tab
l
e
3.
9
-
L
eve
l
S
ugge
ste
d
M
LI
s
w
itc
hi
n
g
Mec
h
a
n
ism
Ti
me
P
osi
tive
Ha
lf
Cyc
l
e
N
e
g
a
tiv
e
Ha
lf Cycle
O
u
tput
V
1
V
1
+
V
2
V
1
+
V
2
+
V3
V
1+
V2
+V
3
+
V
4
V1
V
1+
V2
V
1+
V
2
+
V3
V1
+V2
+
V
3+
V
4
Br
id
g
e
A
S
a
1
S
a
4
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
B
r
i
dge
B
S
b
1
S
b
4
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
B
r
i
dge
C
Sc
1
S
c
4
0
0
1
1
0
0
1
1
1
1
1
1
1
1
1
1
B
r
i
dge
D
S
d
1
Sd
4
0
0
0
1
0
0
0
1
1
1
1
1
1
1
1
1
I
nve
r
s
i
o
n
S
p
1
B
r
idge
S
p2
S
p3
S
p4
1
1
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
1
1
1
1
1
0
0
0
0
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
An a
d
a
p
t
a
b
l
e dif
f
ere
n
t-
lev
e
l
s
c
a
sc
ade
d
h-
bri
dge i
n
ver
ter a
naly
s
is
…
(
H
ass
an Sa
lm
a
n
H
a
m
ad)
83
9
F
i
gur
e
6(
a
)
.
9-Leve
l
s
C
H
B
I
n
v
er
ter
MA
TLA
B
m
ode
l
c
i
r
c
u
i
t
F
i
gur
e
6(
b)
.
Ana
l
ys
is
o
f
F
F
T CH
-
B
r
i
dge
M
LI
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
Int J
Pow
El
ec &
D
ri
S
yst
,
Vol
.
10,
N
o.
2
, June 2019: 831
–
84
1
84
0
F
i
gure
6(c
)
.
G
a
t
i
n
g
pu
l
ses
ge
n
e
ra
ted of P
W
M
9-le
v
e
l
s
CH
B
F
i
g
u
r
e
6
(
d
).
V
ol
t
a
ge
a
nd c
u
rrent
o
utp
u
t
ph
a
se
The
s
i
mu
la
ti
o
n
M
A
TLA
B
ha
v
e
b
ee
n
pr
esen
ted
to
n
ume
r
o
u
s
CH
-br
i
dge
t
o
pol
ogi
es
o
f
M
L
Is
f
o
c
u
s
e
s
on
5-
l
e
vel
s
,
7
-
l
e
ve
ls
a
nd
9-le
ve
l
s
.
A
com
p
ar
i
s
o
n
o
f
t
h
ese
to
p
o
l
o
g
ie
s
w
ith
d
e
t
a
ile
d
ha
s
be
en
o
ffe
r
ed
i
n
t
h
is
pape
r
an
d
c
o
n
centra
t
e
d
on
m
a
in
p
ara
m
e
t
e
r
s
such
a
s
sw
itc
hin
g
p
ow
er
d
e
v
i
ces
u
sed
numb
e
r,
T
o
t
al
H
a
r
mo
n
i
c
D
i
stor
tio
n,
t
he stre
s
se
s
ov
er
c
ur
rent a
n
d
vo
l
ta
ge,
and
gat
i
n
g
P
ulses ge
nera
te
d of
P
WM.
5.
CONCLU
S
I
O
N
The
s
i
mu
la
ti
o
n
o
f
fi
ve
l
e
v
el
s,
s
eve
n
l
e
v
el
s,
a
nd
n
i
n
e
leve
l
s
,
i
nv
ert
e
rs
w
ere
ex
e
c
u
t
e
d
i
n
MA
TLA
B/S
I
MILIN
K
,
ba
se
d
o
n
a
pp
l
y
i
ng
stra
i
g
h
t
for
w
ard
c
o
ntro
l
str
a
te
gy
o
f
c
o
n
t
r
o
ll
i
n
g
th
e
IG
BT
s
w
itc
hes
w
ith
s
ui
t
a
ble
ang
l
es
a
t
pr
o
p
e
r
dela
ys.
A
pe
rfe
c
t
spe
c
i
fi
ca
t
i
o
n
of
t
he
C
H
B
M
LI
a
re
a
ch
ieve
d
l
i
ke
h
i
g
h
Evaluation Warning : The document was created with Spire.PDF for Python.