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.
1852~
18
62
ISSN: 2088-
8694,
DOI
:
10.11591
/ijpeds.
v10.
i
4.pp1852-1862
1
8
52
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
A sm
art cascaded H-bridge
multilevel inverter w
i
th An
optimized modu
l
ation techniques
increasing the qua
lity and
reducing harm
onics
Y
o
us
s
e
f
B
a
bk
r
a
ni
,
A
h
m
e
d
N
a
dd
a
m
i
,
Mo
ha
med
Hi
lal
Dep
a
rtem
ent
o
f
Elect
rical En
g
ineer
in
g,
U
n
i
vers
ity
o
f
H
assan
1ST
N
ati
o
n
a
l F
acu
lty o
f S
c
ien
ce and
Techn
i
cal
, M
o
ro
cco
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
R
e
ce
i
v
e
d
Mar
20,
2
0
1
9
Re
vise
d Ju
n 1
0
,
2019
A
c
c
e
pte
d
J
u
l
8
,
2019
Th
e
w
o
rl
d
com
m
u
n
i
ty
r
el
ied
h
eavi
l
y
on
f
o
s
s
i
l
s
e
nergi
e
s
bu
t
ju
st
a
f
t
e
r
t
h
e
b
i
g
oi
l
cri
s
is
t
h
e
u
se
o
f
re
n
e
wab
l
e
energ
y
h
a
s
g
reat
ly
i
ncreased
a
n
d
ha
s
be
c
o
me
th
e
m
a
in
i
nteres
t of
m
an
y
co
untries
f
o
r
i
t
s
man
y a
dvan
t
ag
es
s
uc
h
a
s
:
m
i
n
i
ma
l
im
p
act
o
n
t
h
e
env
i
ron
m
en
t
,
r
en
ewab
le
g
enerat
or
s
requ
irin
g
less
maintena
nce
than
t
raditional
ones
a
nd
it
has
also
a
g
reat
i
mpact
o
n
economy
.
It
i
s
eas
y
to
get
ch
arm
e
d
b
y
t
he
a
dv
antag
e
s
of
u
si
ng
t
h
e
r
en
ewabl
e
r
es
ources
bu
t
w
e
m
u
s
t
als
o
b
e
aware
o
f
t
hei
r
d
is
adv
a
ntag
es.
O
n
e
o
f
t
h
e
m
a
j
or
d
isad
van
tag
e
s
i
s
t
hat
the
renewable
energy
r
esources
a
re
i
ntermitte
nt
a
nd
t
hus
t
h
ey
h
ave
l
e
d
sci
e
ntists
t
o
dev
e
lo
p
new
sem
i
c
o
nd
ucto
r
po
wer
con
v
erters
a
m
o
ng
wh
ic
h
a
r
e
the
mu
ltilevel
i
n
verter.
In
t
his
paper
a
new
smart
multi-
l
e
vel
invert
e
r
i
s
pro
p
o
s
ed
s
o
as
t
o
increas
e
i
t
s
levels
acco
rd
in
g
to
t
he
u
ser’s
n
e
e
d
s
a
nd
a
l
s
o
to
avo
i
d
t
h
e
im
p
a
c
t
o
f
shad
es
a
nd
t
he
i
n
t
ermi
tten
ce
o
n
p
h
o
t
o
v
o
lt
ai
c
pan
e
ls
.
W
e
a
l
s
o
p
r
o
p
o
s
e
a
m
o
d
i
f
i
c
a
t
i
o
n
o
n
t
h
e
m
u
l
t
i
c
a
r
r
i
e
r
a
i
m
i
n
g
t
o
r
e
d
u
c
e
th
e
harm
o
n
ics
.
T
h
i
s
m
o
difi
cati
on
i
n
t
r
odu
ces
a
s
in
usoi
dal
wav
e
c
o
m
pa
red
with
trap
ezoid
al
m
ulti
-carrier
t
o
gen
e
rate
t
h
e
p
ul
ses.
I
n
o
r
der
to
o
bt
ai
n
the
line
vo
lt
ages
a
n
d
t
he
t
ot
al
h
arm
o
nic
di
sto
r
ti
ons
(
THD)
M
ATLAB/S
I
M
U
LI
NK
is used.
K
eyw
ord
s
:
C
a
sc
ad
ed
H b
ri
dg
e
P
h
a
s
e
dis
p
o
s
it
i
on
P
h
a
s
e
op
pos
i
t
i
on
dis
p
osit
io
n
Sm
a
r
t
Mult
i-le
ve
l
in
ve
rter
To
tal H
a
rm
on
i
c
s
D
i
st
or
t
i
o
n
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:
Ba
bkran
i Y
ous
sef,
D
e
pa
rtem
ent o
f
E
lectr
i
c
a
l E
n
gi
nee
r
in
g,
University of
Hassan
1ST,
Fa
cult
y
o
f
S
cie
n
ce
and Te
c
h
n
i
ca
l
,
S
ettat,
Em
ail:
y.bab
k
r
a
ni@
g
ma
i
l
.
c
o
m
1.
I
N
TR
OD
U
C
TI
O
N
The
w
o
rl
d
aro
u
n
d
us
h
a
s
c
ha
nge
d
co
ns
ider
a
b
l
y
o
ve
r
t
h
e
pa
st
2
0
y
e
a
rs.
A
s
f
oss
i
l
f
u
e
l
s
be
com
e
m
ore
expe
ns
i
v
e
a
n
d
t
o
u
ghe
r
to
f
i
nd
a
n
d
a
l
so
b
ec
ause
e
nerg
y
fue
l
s
r
e
l
a
t
e
d
a
ct
i
v
i
ties
ha
v
e
l
e
d
t
o
si
gn
i
f
ica
n
t
e
n
v
i
r
o
n
m
e
n
t
a
l
d
a
m
a
g
e
s
[
1
]
.
T
h
u
s
i
t
i
s
a
w
i
s
e
r
d
e
c
i
s
i
o
n
f
o
r
g
o
v
e
r
n
me
nts
a
ll
aro
u
n
d
t
he
w
or
l
d
t
o
red
u
c
e
t
he
ir
d
e
p
e
nd
en
cy
on
s
u
c
h
t
ra
di
t
i
o
n
a
l
t
yp
e
s
o
f
en
erg
y
a
n
d
re
pl
a
c
e
it
w
ith
o
t
h
er
s
o
u
r
c
e
s
of
e
n
e
rg
y
th
at
c
an
b
e
saf
e
r,
che
a
per
clea
ne
r
a
nd
rene
w
a
ble,
s
ol
a
r
e
nerg
y
is
u
n
d
en
ia
bl
y
o
n
e
o
f
th
ese
so
u
r
ce
s,
u
sing
s
ol
ar
r
a
d
i
a
tio
n
t
o
p
r
od
u
c
e
th
e
h
eat
a
n
d
el
ect
ri
cit
y
[
2
]
.
So
l
a
r
e
n
e
r
gy
d
e
m
a
nd
h
a
s
g
row
n
b
y
25%
a
n
n
u
al
l
y
dur
ing
the
pa
st
2
0
yea
r
s
[3].
H
ow
ever
,
it
s
u
t
ili
za
tio
n
ha
s
m
e
t
differ
e
n
t
d
i
f
f
i
c
ul
t
ie
s
the
m
a
j
o
r
one
s
a
r
e
po
w
e
r
qual
ity
a
n
d
t
he
in
t
e
rm
i
t
te
nt o
f re
new
a
ble
ene
r
gy r
e
so
urce
s [4
].
P
o
w
e
r
Q
u
ali
t
y
has
bee
n
a
p
r
o
b
l
e
m
e
ver
s
i
n
c
e
e
l
ec
trica
l
p
ow
er
w
a
s
in
ve
nte
d
a
n
d
i
n
re
c
e
nt
y
e
a
rs,
it
has
bec
o
m
e
t
h
e
m
a
i
n
i
n
t
e
res
t
o
f
r
e
sea
r
che
r
s
w
ho
ar
e
st
il
l
c
onc
e
r
n
e
d
a
bo
u
t
f
in
din
g
w
ays t
o
r
e
duc
e it
s ne
gat
i
v
e
in
flue
nce
o
n
e
lectr
i
c
a
l
dev
i
c
e
s.
H
a
r
m
onics
a
r
e
a
n
im
port
a
nt
f
a
c
t
o
r
i
n
p
o
w
er
qua
li
t
y
a
nd
a
l
s
o
t
o
ma
i
n
ta
in
st
a
b
le
p
ow
er
s
up
p
l
y
perfor
m
a
n
ce
[
5],
so
t
he
i
nver
t
e
r
s
w
ith
h
a
r
m
o
n
ic
s
r
e
duct
i
on
is
r
equired
m
u
lti
lev
e
l
in
verter
s
ar
e
gain
i
ng
c
e
l
e
b
rit
y
f
or
P
ho
t
o
v
o
l
t
a
ic
(
P
V
)
syste
m
s
d
ue
t
o
the
r
e
duce
d
t
o
t
a
l
h
a
r
m
oni
c
d
i
s
t
or
ti
o
n
s
o
f
the
o
u
t
p
u
t
s
ign
a
l
a
n
d
the
l
o
w
vo
ltage
s
tre
s
s
of
p
ow
e
r
s
w
itc
he
s.
I
t
p
r
od
u
c
e
s
a
l
m
o
s
t
a
si
nusoi
d
a
l
vo
lt
ag
e
at
t
he
ou
tpu
t
[
6]
.
In
a
dd
iti
o
n
,
tw
o-l
e
ve
l
i
n
ve
rters
ar
e
e
xpose
d
t
o
t
h
e
r
m
a
l
s
tre
s
se
s
cre
a
te
d
by
c
on
ve
rt
ing
t
h
e
f
u
ll
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
El
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
A sm
art c
a
sc
a
d
ed
H
-
brid
ge
m
u
l
tile
ve
l i
n
v
e
r
ter w
ith
An o
p
t
i
m
ize
d
m
o
d
u
la
ti
o
n
tec
h
… (
B
abk
ra
ni
Yo
usse
f)
1
853
vo
lta
ge
i
m
p
os
ed
b
y
t
h
e
co
n
tin
u
o
u
s
s
o
u
rc
e,
s
o
t
h
e
per
f
orm
a
nce
a
n
d
li
fe
tim
e
o
f
i
ts
c
om
pone
n
t
s
a
r
e
ac
t
u
a
l
l
y
affec
t
e
d
.
In
t
h
i
s
scen
a
r
io,
a
new
sm
art
m
u
lti
lev
e
l
in
ver
t
e
r
i
s
prop
ose
d
w
it
h
a
m
o
d
i
f
i
e
d
c
om
ma
nd
s
y
ste
m
aim
i
n
g
t
o
re
d
u
c
e
mor
e ha
rm
oni
c
s
o
n t
h
e o
u
t
pu
t sig
n
a
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d
a
l
s
o i
t wi
l
l
a
l
l
o
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ry so
l
ar pane
l
i
n th
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stem
to
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te
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d
e
p
e
nde
n
t
l
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s
o
the
to
t
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ergy
sy
st
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m
w
il
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no
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x
c
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ss
i
v
e
l
y
a
ffe
c
t
ed
b
y
sha
d
es
a
nd
inte
rmit
te
nt
.
Ca
sca
d
e
d
H
-
b
rid
g
e
m
u
lt
ilev
e
l
is
f
ou
nd
t
o
be
a
t
t
ra
ct
i
v
e
for
our
sm
art
i
n
ve
rter
b
ec
a
u
se
it
uses
t
he
s
am
e
tech
n
o
l
o
gy
in s
er
i
e
s “
f
ull
H
-
B
r
id
ges”
t
o
pr
od
uce
in
verte
d
A
C
fr
o
m
s
ep
a
r
at
e DC
so
u
r
ce
s [7
].
Thi
s
p
a
p
er
p
res
e
nt
s
a
p
r
opo
si
tio
n
o
f
a
sma
r
t
ca
sc
ad
ed
h
-b
ri
dg
e
mu
l
t
i
-
l
e
ve
ls
i
nve
rt
er
w
i
t
h
the
pos
si
b
i
l
ity
o
f
i
n
cr
easi
n
g
the
l
e
vel
s
a
c
c
o
rd
in
g
to
t
he
n
ee
d
o
f
t
he
u
s
e
r.
M
u
lti
p
l
e
m
u
l
ti-ca
rrier
S
P
W
M
me
t
hod
s
for
ca
scade
d
h
-br
i
dge
a
re
a
na
lyz
e
d
a
n
d
c
o
mp
a
r
ed
w
ith
t
he
c
on
ve
n
t
i
ona
l
S
P
WM
t
ec
hn
i
q
u
e
.
Those
ca
rrier
s
ar
e
bei
n
g
im
p
l
em
ente
d
w
i
t
h
d
iffer
e
n
t
s
i
n
us
oida
l
d
i
sp
os
it
io
ns
P
D
,
P
O
D
and
A
P
O
D
a
nd
w
i
t
h
d
i
ffe
ren
t
fre
que
nc
ies.
2.
MULT
I-
L
E
V
EL INVERT
ER
2.1.
Inductio
n
m
o
t
o
r
s
B
i
g
ele
c
t
ric
e
n
erg
i
es
u
se
s
i
n
cl
u
d
e
a
d
vanc
e
d
power
e
lec
t
ro
ni
c
s
i
n
v
erte
r
to
e
nc
o
unte
r
t
he
h
i
g
h
dem
a
nd
s.
A
s
a
resul
t
,
m
u
l
t
il
evel
v
ol
t
a
ge
i
nver
t
er
h
as
b
e
e
n
pr
es
en
t
e
d
as
a
n
a
l
t
e
rn
at
ive
i
n
h
i
g
h
po
wer
a
n
d
me
dium
v
o
l
t
a
g
e
c
ir
cumst
a
nc
e
s
[
8].
A
mult
i
l
e
v
el
c
o
n
v
er
t
e
r
no
t
o
n
ly
a
tt
ai
ns
h
i
g
h
po
we
r
a
sse
ssmen
ts
,
but
a
l
s
o
it
i
nc
rea
s
es
t
h
e
p
e
r
form
anc
e
of
t
he
w
ho
le
s
truct
u
re
i
n
term
s
of
h
a
r
m
oni
c
s
[
9].
M
any
pre
s
e
n
t
schem
e
s
inc
o
rp
ora
t
e
the
use
o
f
i
nd
uc
tion
mo
t
o
rs
a
s
m
a
i
n
s
o
u
rc
e
f
o
r
trac
tion
in
e
le
ctric
v
e
h
i
c
l
es,
th
ose
dr
i
v
e
r
r
equ
i
re
adva
nc
e
d
p
o
w
er
e
lectr
onic
i
n
verter
s,
to
att
a
i
n
t
he
ir hi
g
h po
w
e
r
d
eman
d
s
.
The
m
u
l
t
i
l
e
v
el
v
ol
t
a
ge
i
nver
t
er
s
s
t
r
u
ct
ure
a
l
l
o
w
s
t
hem
t
o
g
rasp
t
h
i
s
h
i
gh
v
olt
a
ge
r
e
q
ui
re
me
nt
w
itho
u
t
t
he
u
sage
o
f
t
r
ansform
e
r
s
[
10]
,
e
s
pec
i
a
l
l
y
h
i
g
h
v
o
lta
ge
v
e
h
i
c
l
e
d
riv
e
s
wh
e
r
e
el
ect
ro
ma
g
n
e
ti
c
in
t
e
rfe
r
enc
e
(
EMI) a
nd low
t
o
tal ha
rm
o
n
i
c
d
i
s
tor
t
i
o
n (
T
H
D
)
o
f t
he
o
u
t
pu
t
vol
ta
ge
ar
e
vita
l
.
The
ge
nera
l
u
t
i
l
i
t
y
o
f
the
m
u
ltile
ve
l
i
nver
t
er
i
s
to
c
rea
t
e
a
d
e
s
i
r
ed
v
o
l
ta
g
e
f
rom
m
u
lt
i
p
le
l
eve
l
s
of
d
c
vo
lta
ge
s,
f
or
t
hi
s
rea
s
o
n
,
m
u
lti
lev
e
l
in
ve
rte
r
s
c
a
n
e
a
s
i
l
y
d
eli
v
e
r
t
h
e
hi
g
h
p
o
w
er
n
ec
es
sary
t
o
l
a
rg
e
elec
t
r
i
c
al
V
e
hic
l
e
s
,
h
y
b
ri
d
V
e
h
i
c
l
es or
a
n
y
m
o
t
o
r i
n
ve
r
t
er
t
ec
h
n
o
l
og
y
use
d
m
ai
nly i
n
a
r
eas
o
f hig
h
ener
g
y
c
o
n
s
um
pt
ion
su
ch
as a
i
r c
o
n
d
iti
oni
ng
.
C
a
scad
e
i
n
v
e
rte
r
s
are
p
e
rf
ec
t
f
o
r
a
n
i
n
d
u
ct
i
on
m
o
tor
this
c
on
fi
gu
rat
i
o
n
giv
e
s
many
a
dv
an
t
a
g
e
s
su
ch
as [11]
:
a)
It m
akes
i
n
d
uc
t
i
o
n
m
otor
s
a
f
e
r
/han
dy f
o
r in
duc
t
i
o
n
m
otor
pow
e
r
system
.
b)
No e
l
e
ctrom
a
g
n
et
ic
i
n
t
er
fer
e
n
c
e
.
c)
H
i
ghe
r e
ffic
i
e
n
cy is a
t
t
a
ine
d
com
par
e
d t
o
l
o
w
volta
ge m
o
t
ors.
d)
Low
vo
l
t
age
s
w
i
t
c
h
i
n
g de
v
i
c
e
s a
r
e used.
e)
N
o
un
b
ala
n
c
e
c
har
g
e pr
o
b
le
m
i
n
d
rive
m
od
e
or
c
har
g
e m
ode.
2.2.
B
a
sic
stru
ct
ur
e
A
c
a
sca
d
ed
m
ul
t
i
le
v
e
l
i
n
ver
t
e
r
i
s
a
power
e
lectr
o
n
i
c
d
e
v
i
ce
m
a
d
e
t
o
c
r
eate
a
de
s
i
r
e
d
A
C
v
ol
ta
ge
f
r
o
m
s
ev
e
r
al
of DC
v
ol
t
a
g
e
s th
e
st
r
u
c
t
ure is com
po
sed of s
eve
r
a
l H
-
brid
g
e
s c
o
n
v
erter
s
i
n ser
i
e
s
c
on
ne
c
t
i
on as
gi
ve
n
in
F
i
g
ur
e
1
i
t
g
o
t
m
an
y
a
dva
n
t
a
g
es
i
t
c
a
n
rea
c
h
hi
g
h
v
ol
t
a
g
e
a
nd
hi
g
h
p
ow
er
w
itho
u
t
t
ra
nsform
ers
and
w
ith
a
r
e
m
ar
kable
i
m
pr
ovem
e
nt
o
f t
h
e
sp
e
c
t
ra
l
qua
l
i
t
y
[
12]
.
The
v
o
lta
ge
l
e
v
el
s
L
of
t
he
c
a
s
cade
d
H
i
n
v
e
rter
i
s
def
i
ne
d
by
L
=
2
N
+
1
,
w
h
e
r
e
N
i
s
t
h
e
n
u
m
b
e
r
o
f
D
C
source
s
The
m
o
re
H
i
nve
r
t
ers
are
use
d
t
he
m
or
e
le
vel
s
o
f
t
h
e
o
u
t
pu
t
w
a
v
ef
o
r
m
a
r
e
cre
a
t
e
d
and
th
e
sh
a
p
e
bec
o
me
s
ap
pro
x
im
ate
t
o
s
in
us
oi
da
l w
a
veform
.
Th
e ou
tpu
t
vol
t
a
g
e
ca
n
b
e exp
r
e
sse
d
a
s
:
V
o
u
t
=
V
1
+
V
2
+
V
3
+
…
.
.
+
V
n
.
E
a
c
h
f
u
l
l
b
r
i
d
g
e
i
n
v
e
r
t
e
r
c
a
n
g
e
nera
t
e
t
hree
l
e
v
el
s
-V
dc
,
0
and
+
V
dc
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
: 208
8-
869
4
Int J
Pow El
ec &
D
ri
S
yst
Vol
. 10,
N
o.
4, Dec 2019
:
1852 – 186
2
1
854
F
i
gure
1.
S
truc
t
u
r
e
of a
Casca
d
ed H
B
r
i
d
g
e
2.3.
Carr
ier-
based
mod
u
lation
s
ch
eme
s
Mo
st
c
a
rrier
-b
ased
P
WM
s
c
h
e
m
e
s
f
or
c
as
ca
ded
H-br
id
g
e
m
ult
i
-le
v
e
l
i
nver
t
e
r
s
desce
nd
from
t
he
c
a
rri
e
r
d
i
s
po
s
iti
on
s
c
h
eme
[13
]
F
o
r
a
n
L
l
e
vel
ca
sc
a
d
e
d
i
nv
e
r
t
e
r,
L
-1
t
riangular
c
arrier
s
is
u
sed
w
i
th
t
he
s
am
e
fre
que
nc
y
an
d
am
plit
ud
e
so
t
ha
t
t
h
e
y
f
u
l
l
y
o
c
c
u
p
y
t
he
r
an
ge
[
14
].
A
s
ingle
reference
s
i
nus
o
idal
s
i
g
na
l
with
low
fr
eq
uenc
y is bee
n c
o
n
t
in
u
ousl
y
c
om
pare
d
w
i
t
h
e
a
c
h c
a
rr
i
e
r
t
o
determ
i
n
e
t
h
e
swi
t
c
h
e
d
d
ev
ice.
Thr
ee
ca
rrier dispos
i
tio
n
P
W
M
st
r
a
te
g
i
es a
re
w
ell kn
ow
n
and r
e
f
ere
n
ced
[1
5
]
:
a)
P
h
ase
dis
posi
t
i
on
(P
D
)
,
ca
rrier
s
a
r
e
in
t
h
e
sam
e
phase
F
igu
r
e
2
.
b)
P
h
ase
op
pos
iti
on d
i
s
p
osi
t
i
o
n
(P
O
D
)
, c
arrie
r
s a
bove
z
ero
are
180
° pha
se
shi
fted
w
ith
t
h
o
s
e
bel
o
w
c)
A
l
te
rna
t
ive p
h
a
se
op
pos
i
t
i
o
n di
sp
os
i
t
i
on (A
P
O
D), w
here
the
car
r
iers
a
re
alter
n
ate
l
y 18
0
°
phase
s
hif
t
e
d
I
n
t
h
i
s
pa
per,
d
iffere
n
t
m
u
lti-c
a
rr
i
e
r
shapes
(
Tria
ngu
la
r,
T
ra
p
ezo
i
d
al)
a
r
e
u
s
ed
a
n
d
t
he
p
er
for
m
a
n
ces
are
a
n
alyze
d
t
o
prove
t
he be
s
t
tech
n
i
q
u
es [
16
]
The
re
su
lts
a
r
e
o
bta
i
ned
w
h
e
n
u
si
n
g
t
h
o
se
t
ec
hn
ique
s
w
i
t
h
d
iffe
re
nt
s
in
u
s
oi
d
a
l
di
sp
osit
i
o
n
s
P
D
PWM
,
POD
PWM
a
nd AP
O
D
PW
M
.
Figure
2(a
)
.
Trian
g
u
lar
m
u
lti-
ca
rrier
s w
ith P
hase
d
isp
o
s
iti
o
n
(
PD
)
arrange
m
e
nt
F
i
gure
2(b).
Tra
p
ez
oi
da
l
mult
i-ca
rriers
w
i
t
h
P
ha
se
dis
po
si
t
i
on
(P
D
)
a
rr
angem
e
nt.
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
El
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
A sm
art c
a
sc
a
d
ed
H
-
brid
ge
m
u
l
tile
ve
l i
n
v
e
r
ter w
ith
An o
p
t
i
m
ize
d
m
o
d
u
la
ti
o
n
tec
h
… (
B
abk
ra
ni
Yo
usse
f)
1
855
The
eq
uat
i
on (1)
for
trape
z
o
i
dal c
a
rr
i
e
r c
a
n be in
s
er
t
e
d i
n
D
S
P
d
e
f
i
n
ed
a
s
:
Whe
r
e
A
is the
a
m
p
l
i
t
u
de
a
n
d
T
i
s
t
he pe
r
io
d
of
t
he
c
arrie
r
sig
na
l.
U
t
⎩
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎧
0
t
t1
A
/2
t
1
t
t2
A
/
2
t
2
tt
3
A
/
2
t
3
tt
4
A
/2
t
4
t
t5
t
5
tt
6
(
1
)
3.
T
H
E TO
TA
L HARMONIC
ANALY
Z
E
The
t
o
tal
har
m
on
ic
d
i
s
t
o
rt
ion
s
(
TH
D)
a
re
e
val
u
a
t
ed
t
hrou
gh
a
l
l
t
h
e
mo
du
l
a
t
i
o
n
t
e
c
hni
qu
es
a
nd
f
o
r
vari
ous freq
u
e
n
c
i
e
s
.
To
a
c
q
uire
t
he
s
pec
t
r
u
m
o
f
t
he
o
u
t
put
v
o
lta
ge
(
TH
D
)
F
a
s
t
F
o
ur
i
e
r
Tra
n
sf
orm
(
F
F
T
)
is
a
pp
lied
[
17]
.
The
TH
D
is c
a
l
cu
la
te
d
usin
g
the
fol
l
ow
in
g equa
tio
n (
2
) [18
]
:
∑
(
2
)
Where
:
n
is
t
h
e
ha
r
m
o
nic
or
de
r.
v
n
i
s
t
h
e
r
o
o
t
me
a
n
s
q
u
a
r
e
(
R
M
S
)
v
a
l
u
e
of
th
e
n
th
har
moni
c
com
pone
n
t
.
v
1
is the
(RMS
) va
l
u
e
of t
he f
un
dam
e
n
t
a
l
c
om
pone
n
t
.
The
out
p
u
t
vo
l
t
age
w
a
ve-f
orm
s
F
i
gur
e
3
an
d
the
to
ta
l
har
m
onic
d
ist
o
rt
io
ns
F
igur
e
4a,
b
a
re
a
cquire
d
for
bo
th
t
y
p
es
o
f
mul
t
i-ca
rriers.
F
i
gure
3. T
h
e
ou
t
pu
t v
o
l
t
a
g
e w
a
ve-
f
orm
s
F
i
gure
4 (a
). FF
T
A
na
l
y
si
s of
the
O
utpu
t us
i
ng
Tri
a
ng
ul
a
r
c
arr
i
e
r
s
F
i
gure
4
(b).
F
F
T
A
nal
y
sis
o
f
the
O
ut
p
u
t
usi
ng
m
odif
i
e
d
Tra
p
ezoi
d
a
l
car
riers
Evaluation Warning : The document was created with Spire.PDF for Python.
ISS
N
:
208
8-
8
6
9
4
I
n
t
J
P
o
w
Elec
&
D
r
i
S
y
st
V
ol
.
10,
N
o.
4
,
D
e
c
201
9
:
185
2
–
18
6
2
1
856
The
Ta
ble
1
r
e
sum
e
s
all
h
a
r
m
onics
d
i
s
t
o
r
t
io
n
r
e
su
lts
f
or
b
ot
h
m
ulti-carrier
t
echn
iq
u
e
s
w
ith
di
ff
er
e
n
t
fr
e
q
u
e
ncie
s
.
Table
1
.
T
he
h
a
r
monic
d
i
stor
tio
n
a
n
a
l
y
s
es.
Tec
hnique
s
Dis
p
o
s
itions
F
r
e
que
n
c
i
e
s
Ph
as
e
D
i
spositions
Ph
as
e
opposite
disposi
tio
n
A
l
t
e
r
n
ati
v
e
pha
s
e
opposite
disposi
tio
n
Tr
ia
n
g
ula
r
1
KHz
8
.
27%
8
.
28%
9
.
45%
2
K
H
Z
7.
87%
8
.
68%
8
.
14%
T
r
ape
zoid
1
KHz
6
.
71%
7
.
39%
7
.
20%
2
K
H
Z
6.
59%
7.
06%
6
.
74%
It
c
o
n
f
irms
t
h
a
t
th
e
b
e
st
p
erfo
r
m
an
ce
f
o
r
t
r
i
a
ngu
l
a
r
carr
i
e
rs
i
s
w
h
e
n
p
h
a
s
e
d
i
s
p
o
s
i
t
i
o
n
w
i
t
h
2
K
H
z
f
r
e
que
n
c
y
is
u
s
e
d
and
af
ter
usi
ng
t
h
e
t
r
apez
o
i
da
l
ca
r
r
i
er
s
bet
t
er
r
esults
a
r
e
o
b
t
a
i
ne
d
w
i
t
h
a
g
ai
n
o
f
1
.
28%
.
So
i
t
i
s
c
lea
r
t
ha
t
this
n
e
w
m
odifi
c
a
t
io
n
i
s
b
e
s
t
su
it
ed
f
or
C
a
sc
a
d
ed
M
u
lti-Le
vel
w
ith
t
he
im
pr
o
v
em
ent
of
t
he
o
utp
u
t
sig
n
a
l
q
ua
l
ity
w
h
i
c
h
m
a
k
es
it
mor
e
s
u
i
t
a
bl
e
fo
r
bo
t
h
s
t
a
nd
a
l
on
e
a
n
d
g
r
id
co
nn
e
c
t
e
d
sy
s
t
ems.
4.
S
M
ART M
U
LTI-L
E
V
E
L
I
NVERT
ER
4.
1.
Sh
a
d
e
s
I
n
m
ost
s
o
lar
ph
oto
v
o
l
t
a
i
c
(
P
V)
s
yst
e
ms
it
co
n
t
a
i
ns
a
b
o
u
t
6
t
o
3
0
p
a
n
el
[
19],
to
e
nco
u
n
ter
th
e
vo
l
t
age
ne
ce
ssi
ti
e
s
o
f
t
h
e
s
y
st
e
m
’
s
i
nver
t
e
r
,
so
lar
ar
r
a
ys
a
r
e
us
ua
lly
a
l
i
e
n
ated
i
n
t
o
s
t
r
i
n
g
s
o
f
s
o
lar
pa
n
e
ls
b
u
t
th
ose
str
i
n
g
s
a
r
e
usua
lly
c
o
n
si
st
e
d
f
or
m
mor
e
t
ha
n
o
n
e
sin
g
l
e
p
anel
[
2
0
].
I
f
s
ha
de
i
s
on
e
v
en
o
ne
o
f
th
e
pane
ls
i
n
the
st
r
i
ng,
t
h
e
o
u
t
pu
t
o
f
the
e
n
tir
e
stri
ng
w
i
l
l
be
r
e
duce
d
t
o
ne
ar
l
y
z
e
r
o
[
2
1
]
f
or
a
s
lo
n
g
a
s
t
h
e
s
h
ad
ow
s
t
a
nd
s
the
r
e.
I
n
som
e
c
a
ses,
a
s
ha
d
o
w
doe
s
n
o
t
esse
nt
i
a
lly
n
ee
d
t
o
de
sc
e
n
t
o
n
a
w
ho
l
e
p
a
n
el,
e
v
e
n
j
ust
one
c
e
ll
cou
l
d
cr
u
s
h
th
e
ou
tp
u
t
o
f
th
e
p
a
n
e
l
a
n
d
tu
rn
o
ff
th
e
e
n
t
i
re
s
tring
a
nd
bec
o
me
s
a
r
e
ceiver
tha
t
w
i
l
l
he
a
t
u
p
a
nd
lea
d
t
o
a
loss
o
f
pr
od
uc
ti
on
or
e
ven
w
o
r
s
e
F
i
gur
e
5
[
2
2]
.
F
i
gur
e
5.
E
ffe
c
t
o
f
sha
d
es
o
n
ph
o
t
ov
ol
ta
ic
p
anel
s
The
s
m
a
r
t
m
ulti
le
ve
l
i
n
v
e
r
t
er
F
ig
ur
e
6
pr
o
pose
d
i
n
th
is
p
a
p
er
wi
ll
h
av
e
th
e
po
s
s
ib
il
i
t
y
o
f
i
n
c
re
asi
ng
leve
ls
o
f
t
h
e
o
u
t
p
ut
a
cc
or
d
i
n
g
t
o
the
nee
d
o
f
t
h
e
u
s
er
m
ai
n
l
y
a
cc
o
r
din
g
t
o
th
e
nu
mb
er
o
f
co
nt
i
nuo
us
D
C
sour
c
e
s
ava
i
l
a
bl
e
a
nd
a
l
so
a
c
c
or
d
i
n
g
t
o
t
h
e
p
o
w
e
r
de
sir
e
d.
I
n
t
hi
s
w
a
y
it
w
i
l
l
al
low
e
v
er
y
so
lar
pane
l
i
n
t
he
sys
t
em
t
o
oper
a
te
i
n
d
e
p
e
n
den
t
l
y
a
nd
the
t
o
t
a
l
ene
r
g
y
s
yste
m
w
i
l
l
not
b
e
e
x
ce
ssi
v
e
l
y
a
ffec
t
e
d
b
y
any
sh
ad
ed
pa
ne
ls an
d
a
t t
h
e
sam
e
t
im
e
i
t
can
b
e r
e
plac
ed by
a
st
ora
g
e
bat
te
r
y
.
The
use
r
w
i
l
l
ha
ve
m
u
l
t
i
p
l
e
of
h
-
b
r
i
dge
c
ar
ds
F
igur
e
7,
t
h
o
se
c
ard
s
c
an
b
e
in
se
rt
ed
i
n
an
ot
h
e
r
c
a
rd
w
i
t
h
s
l
o
t
s
t
o
incr
e
a
se
t
he
l
e
v
el
s;
t
he
n
u
m
be
r
of
i
nse
r
ted
car
d
m
u
s
t
b
e
the
sam
e
a
s
the
co
nt
inu
o
u
s
so
u
r
ce
s di
sp
ose
d
.
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
El
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
A sm
art c
a
sc
a
d
ed
H
-
brid
ge
m
u
l
tile
ve
l i
n
v
e
r
ter w
ith
An o
p
t
i
m
ize
d
m
o
d
u
la
ti
o
n
tec
h
… (
B
abk
ra
ni
Yo
usse
f)
1
857
F
i
gur
e 6.
S
ma
rt c
asca
de
d sys
t
em
F
i
g
u
r
e
7
. H-
b
ridge cards
4.2.
H-bridg
e
w
ith driv
er
A
n
o
u
t
pu
t
pu
ls
e
(+
5v)
o
f
a
m
i
croc
o
n
t
r
o
lle
r
i
s
g
ene
r
al
l
y
s
uffic
ie
nt
t
o
dr
ive
a
MO
S
F
ET
ded
i
ca
te
d
to
sma
l
l
signa
l
.
How
e
v
er,
tw
o pr
ob
l
e
ms
a
rise
w
hen
w
o
rk
i
ng w
i
t
h
m
or
e
pow
erful
MO
S
F
ETs:
•
The
c
ontrol s
i
g
n
a
l
o
f t
h
e
3.
3 V
or
5
V
microco
n
t
ro
ll
e
r
s is no
t ofte
n
e
n
o
u
gh.
I
t
i
s
n
e
ces
s
a
ry t
o
a
p
ply
at le
a
s
t
8-12V
t
o
com
p
le
te
l
y
i
gn
ite
the
M
O
S
F
ET
w
h
ich c
a
n
c
a
use
the
i
r de
st
r
u
c
tio
n
[2
3].
•
With
ou
t
dri
v
er
s
M
O
S
F
ET
sw
itc
hi
n
g
c
a
n
c
ause
a
f
e
e
d
b
ac
k
t
o
t
he
c
o
n
t
ro
l
c
i
r
c
ui
t
,
w
hi
l
e
t
he
d
ri
vers
are
de
sig
n
e
d
t
o
hand
le
t
h
i
s pr
ob
l
e
m
[2
4].
S
i
n
c
e
we
w
ill
c
o
nv
e
r
t
vo
l
t
a
ges
hi
gh
er
t
h
a
n
+
30
V
w
e
w
i
l
l
n
e
ed
d
r
i
vers
(
I
R
2
3
0
4
)
in
our
c
irc
u
its
,
it
w
ill
m
a
x
i
mize
t
he
s
w
i
tc
hi
ng
s
p
ee
d
b
y
i
nje
c
t
ing
curr
en
t
s
o
t
ha
t
t
h
e
MO
S
F
ET
s
p
e
n
ds
t
he
l
e
a
s
t
pos
si
b
l
e
t
i
me
i
n
trans
i
t
i
on
tim
e,
and
so w
e
w
ill
have
a
m
inimum
w
aste of ene
r
gy
and
h
e
at
on
co
mp
on
en
ts [25
].
F
o
r
si
m
u
la
ti
o
n
pur
pose
s
,
P
r
ot
e
u
s
IS
IS
w
as
u
se
d
F
i
g
u
re
7
t
o
sim
u
la
te
t
he
H
-bridge
s
ys
t
e
m
a
l
on
gs
i
d
e
the
MO
S
F
ET dri
v
ers,
w
ith mi
c
roc
o
n
t
ro
l
l
er pro
gra
m
m
i
ng and
al
l sw
i
t
c
h
i
ng
dev
i
ce
s.
F
i
gure
8.
H
Bridge
w
ith
M
O
S
F
ET
Driver
s
F
i
gure
9.
The
o
u
t
p
u
t
v
o
l
t
a
g
e
of
t
h
e
H
-
b
rid
g
e
inver
t
e
r
5.
EXPE
RIMENTAL
R
ESULT
S
A
s
f
or
E
xpe
r
i
m
e
nta
l
r
e
s
ul
ts,
the
out
pu
t
vo
l
t
a
ge
d
es
i
gne
d
for
th
e
s
y
ste
m
i
s
23
0
A
C
s
up
p
l
y
F
i
gure
9c
.
In
o
rde
r
t
o
re
a
c
h
i
t
t
he
i
n
p
u
t
s
up
p
l
y
use
d
i
s
34V
f
or
eac
h
di
ff
e
r
e
n
t
i
nver
t
er
s
t
a
ges,
f
or
a
ll
sw
i
t
ch
i
n
g
de
vice
s
MO
S
F
ETs
I
RF
44ZN
are
uti
lize
d
i
n
or
d
e
r
t
o
o
b
t
a
i
n
h
i
gh
e
ff
i
c
ie
nc
y
o
v
er
a
n
ext
e
nsi
v
e
lo
a
d
r
ang
e
.
Th
e
DSP
con
t
ro
l
l
er
o
r
ardu
i
no-m
e
ga
i
s
use
d
t
o
ge
nera
t
e
t
he
s
w
itc
h
i
ng
pu
lses
f
or
s
w
i
t
c
hes
base
d
on
P
O
D
,
A
P
O
D
and
P
D
a
rra
ngem
e
nt
s
for
P
W
M.
T
he
c
a
rrier
s
i
g
nal
s
a
b
o
v
e
a
n
d
be
low
z
e
r
o
a
r
e
l
e
v
e
l
s
s
h
i
f
t
e
d
t
o
r
e
a
l
i
z
e
P
D
,
P
O
D
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
: 208
8-
869
4
Int J
Pow El
ec &
D
ri
S
yst
Vol
. 10,
N
o.
4, Dec 2019
:
1852 – 186
2
1
858
and
A
P
O
D
s
ignal
s
.
A
nd
to
g
e
n
e
r
ate
t
h
e
p
u
l
ses
requ
ired
f
or
t
he
M
O
S
F
E
T
s
w
i
t
c
h
e
s
t
h
e
s
e
s
i
g
n
a
l
s
a
r
e
b
e
e
n
com
p
are
d
c
ont
in
u
o
u
s
ly
w
ith
t
he
re
f
er
ence
si
nus
oi
da
l
sig
n
a
l
.
Whe
n
t
he
i
nve
rter
s
t
a
rts
w
o
rki
ng,
t
he
m
i
c
r
o
co
n
t
ro
ller
ge
n
e
ra
t
e
s
a
5v
s
i
gna
l
to
d
e
t
e
c
t
t
h
e
numbe
r
o
f
c
a
rd
s
in
se
rt
e
d
.
Th
en
,
a
cod
e
o
f
7
dig
i
t
s
r
e
c
e
i
v
ed
w
il
l
b
e
e
q
u
iv
a
l
ent
to
t
h
e
n
u
m
be
r
an
d
t
h
e
lo
c
a
t
i
o
n
o
f
e
ach
ca
rd.
F
o
r
e
x
a
m
pl
e
,
t
he
r
ece
p
t
i
on o
f
0
0
0
0
0
01 code
m
e
a
n
s
th
a
t
o
n
l
y
o
n
e
ca
r
d
i
s
inse
rte
d
a
n
d
t
he l
ocat
i
on
of
t
he
card is in
t
he f
irst slot.
A
f
ter the
tes
t
i
n
g
,
t
he pr
ogra
m
to pro
d
u
ce
the
s
w
i
tc
hin
g
puls
e
s
w
ill
b
e
ge
n
e
r
a
t
e
d
c
o
r
respo
n
d
i
ng
t
o t
h
e
code
l
iste
d
a
n
d
w
i
ll
k
e
e
p
fu
nct
i
o
n
i
n
g
u
nt
i
l
t
he
i
n
v
er
t
e
r’s
s
hu
t
do
w
n
.
A
s
f
or
r
elays
Fi
g
u
re
9
i
t
w
i
ll
l
e
t
t
h
e
curr
ent
fl
ow
i
f
the
r
e
is
no
h-br
idge
car
d
ins
e
rte
d
.
F
o
r
e
v
ery
h
-b
ri
dg
e
ca
rd
t
h
e
f
o
llo
wing
e
qu
i
p
me
nt
’s
T
a
b
l
e
2
is
n
ee
ded
:
Ta
b
l
e
2.
H-br
i
dge
M
ater
i
e
ls.
Qua
n
t
iti
e
s
M
a
t
e
r
ia
ls
4
10R
R
e
s
is
tor
s
4
1k
Re
sistors
2
33uF/16
v
c
a
p
ac
iti
e
s
2
I
R
2
304
D
r
ive
r
s
or
I
R
2301
4
I
R
F
Z
4
4N
T
ra
nsistor
s
6
1
N
4007
D
i
ode
s
The
e
x
perim
e
nta
l
p
r
o
to
ty
pe
i
s
i
llus
t
rate
d
o
n
F
ig
ure
10(a
)
a
long
w
it
h
t
h
e
P
C
B
la
y
o
u
t
f
or
e
very
h
-
bri
dge
car
d:
PC
B
des
i
gn on ARES
3D
view of the h-br
idge car
d
F
i
gur
e 1
0
(a
). PC
B
lay
o
u
t f
o
r
h-br
idge
ca
r
ds
F
i
gur
e 1
0
(b)
. Sug
ges
t
e
d
s
m
a
r
t
m
ul
ti-
leve
l
in
ve
rter
F
i
gur
e 1
0
(
c
). V
ol
tage
o
u
t
p
u
t
of fi
ft
e
e
n
m
ul
ti-le
vel i
n
verte
r
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
El
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
A sm
art c
a
sc
a
d
ed
H
-
brid
ge
m
u
l
tile
ve
l i
n
v
e
r
ter w
ith
An o
p
t
i
m
ize
d
m
o
d
u
la
ti
o
n
tec
h
… (
B
abk
ra
ni
Yo
usse
f)
1
859
A
c
cordi
n
g
to
t
hi
s
sys
t
em
,
P
h
ase
di
sp
os
i
t
i
o
n
m
u
lt
i
-
car
rier
m
odul
a
t
i
o
n
t
e
c
h
n
i
que
s
are
us
ed
a
nd
the
ou
tpu
t
a
nd
th
e
pe
rform
a
nc
e
s
a
re
a
na
l
y
z
e
d
.
F
i
gur
e
10(
b)
s
how
s
th
e
su
gge
ste
d
s
m
a
rt
m
ult
i
-
l
e
v
e
l
i
n
v
er
ter
syste
m
m
a
d
e u
p
t
o ana
l
yz
e
th
e
per
f
orm
a
nc
es of
a
casc
a
ded
fi
ftee
n le
ve
ls i
nver
t
e
r
.
Th
is
s
yste
m
i
s
d
ev
ise
d
i
nt
o fo
ur
m
ajor pa
r
ts:
Part
1
:
P
u
l
s
es I
n
put
s, wh
e
re
M
ult
i
-
ca
rri
e
r P
W
M
t
e
c
hni
qu
es are
i
nse
r
te
d (
T
he C
om
ma
nd
par
t
)
P
a
rt 2: D
C
inp
ut
s w
h
e
r
e, P
h
o
to-
v
o
l
taic
D
C
s
ource
s
or
b
at
t
e
ries
a
r
e
used (DC
i
n
p
u
ts)
Pa
rt 3: Rela
ys
w
ill le
t
the c
u
rre
nt
f
l
o
w
if
t
he
re
i
s
no h-
brid
g
e
ca
rd
i
nser
ted.
P
a
rt 4: The
ou
t
p
u
t
v
olta
g
e
a
ft
er
D
C
conve
rsion
(A
C ou
t
p
u
t
)
.
F
o
r
expe
rime
n
t
a
l
a
p
p
lic
at
ion.
T
he
P
WM
s
c
h
em
e
w
a
s
exe
c
u
t
e
d
in
M
O
S
F
E
T
s
I
R
F
Z
4
4
N
u
s
i
n
g
a
n
A
r
dui
n
o
M
e
g
a
256
0
an
d
f
o
r
be
tte
r
c
o
mpa
r
iso
n
,
the
sam
e
c
onf
igura
tio
ns
a
re
u
sed
i
n
t
he
s
i
m
u
l
a
tio
n
an
d
expe
r
i
me
n
t
a
tio
n.
T
he
o
ut
p
u
t
vo
l
t
a
g
e
w
a
ve
form
i
s
s
how
n
i
n
F
i
gure
1
0
(
c).
It
c
an
b
e
se
en
t
h
a
t
th
e
ex
p
e
ri
me
n
t
al
resul
t
m
atc
h
w
i
t
h
sim
u
l
a
tio
n.
A
c
ompa
r
i
son
be
tw
ee
n
t
h
e
c
a
sca
d
e
d
t
o
p
o
lo
gy
o
f
a
se
ve
n
and
a
fiftee
n
m
u
l
t
i-
leve
l
i
nver
t
er
i
s
do
ne
a
n
d
t
he
r
esu
lts
a
r
e
s
h
o
w
n
i
n
Ta
ble
2,
F
i
gu
res
1
1
(
a
-
j
)
w
hi
ch
c
l
e
a
r
l
y
s
hows
t
h
e
perc
en
tage
re
d
uct
i
on
in
t
he t
o
t
al ha
r
m
o
ni
c
d
i
stor
t
i
o
n
by
inc
r
ea
sing
the
n
u
m
b
er
o
f le
ve
ls
“
N
”
.
S
e
ven
leve
l
in
ver
t
er
an
a
l
y
se
s
F
i
f
t
ee
n
le
vel i
n
ve
rte
r
an
a
lyse
s
Fi
gu
re 11
(
a). Mul
t
i
-
carriers P
D
arrang
em
ent
f
o
r a s
e
ven
level
invert
er
Fi
gur
e
1
1(
f). Mu
l
t
i
-c
arri
ers
PO
D
arrangem
ent
f
o
r
a
fi
f
t
een
level
invert
er
Figu
re
11
(
b).
Se
v
e
n mu
lt
i-le
ve
l
in
ve
r
t
e
r
o
utpu
t s
i
g
n
a
l
Fi
gure
1
1(
g).
F
i
fteen
m
u
lti-
l
e
vel
invert
e
r
output
s
i
gnal
F
i
g
u
re
1
1(c).
S
e
ven
mu
lti-l
e
vel
in
verter
T
HD
anal
ysis
o
f
POD
Figure 11(h).
F
i
ft
een multi-
l
e
vel inverter
T
HD anal
ysi
s
o
f
PD
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
: 208
8-
869
4
Int J
Pow El
ec &
D
ri
S
yst
Vol
. 10,
N
o.
4, Dec 2019
:
1852 – 186
2
1
860
Figu
re 11
(
d
)
. Se
v
en mu
l
t
i
-l
ev
el i
nv
ert
e
r THD ana
l
y
s
is o
f
APO
D
F
i
g
u
re 1
1(i
)
. Fifteen m
u
l
t
i
-l
ev
el in
v
erter T
HD anal
ysis
o
f
POD
Figu
re
11
(e
). Se
v
e
n
mul
ti-le
ve
l
in
ve
rte
r
THD a
n
a
l
y
s
is
o
f
APO
D
F
i
g
u
re 1
1(j
)
. Fifteen m
u
l
t
i
-l
ev
el in
v
erter T
HD anal
ysis
o
f
APO
D
6.
RESULT
S
INT
E
RP
RETATION
Ab
ou
t
D
C
/
A
C
c
o
nv
e
r
s
i
on
,
t
h
e
h
a
rmo
n
i
c
a
n
a
ly
si
s
of
outp
u
t
vo
lt
a
g
e
s
is
s
how
n
in
F
i
gure
12,
t
h
e
fi
ftee
n
le
ve
l
s
i
nve
r
t
er
g
e
n
er
at
es
l
e
s
s
T
o
t
a
l
H
a
rm
oni
c
D
i
s
t
ort
i
o
n
(TH
D
)
a
nd
h
i
g
h
e
r
o
u
t
p
u
t
q
ua
li
t
y
f
or
e
very
mult
i-ca
rrier
s
t
echn
i
ca
l
di
s
p
o
s
i
t
i
o
n
(
P
D,
P
OD,
A
POD).
Base
d
on
o
b
ta
i
n
e
d
r
esu
l
t
s
i
ncr
e
asi
ng
t
h
e
n
u
m
b
er
o
f
“
N
”
le
v
e
l
i
n
cr
ease
s
g
re
a
t
l
y
t
he
qua
l
ity
o
f
t
h
e
ou
tpu
t
s
ig
n
a
l
by
r
ed
uci
n
g
the
to
ta
l
harm
onic
d
i
s
t
ort
i
o
n
so
it
clea
r
tha
t
i
nc
re
asi
ng
l
e
ve
ls
m
a
k
es
it
mor
e
s
u
i
ta
b
l
e
f
o
r
app
l
ic
a
ti
ons
w
he
re
e
lec
t
r
o
ma
gne
t
i
c
i
n
te
rfer
ence
(
EMI)
and
low
tota
l
h
a
rm
onic
dis
t
ort
i
o
n
(
TH
D
)
of
th
e
ou
t
p
u
t
v
ol
t
a
ge a
re
v
it
a
l
.
F
i
gure
12.
TH
D
analys
is for
t
he li
n
e
v
o
lta
ge
s
7.
CONCL
U
S
ION
The
S
P
WM
c
on
tro
l
s
ch
e
m
e
for
t
h
e
f
i
f
t
ee
n
l
e
ve
l
c
a
sca
d
ed
H
b
ridge
i
n
v
e
r
ter
has
be
en
p
r
e
sen
t
ed
i
n
th
i
s
pa
p
er
T
he PD
PWM
m
e
tho
d
ha
s
g
iv
en t
he bet
ter re
su
l
t
s
for
a
ll t
y
pe
s of c
ar
riers,
T
he
r
e
s
ults
i
l
l
ustr
a
t
e
tha
t
aft
e
r m
odi
fyi
n
g
the c
a
rr
iers be
t
t
e
r r
e
sul
t
s
ca
n
be ob
t
a
i
ne
d.
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
El
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
A sm
art c
a
sc
a
d
ed
H
-
brid
ge
m
u
l
tile
ve
l i
n
v
e
r
ter w
ith
An o
p
t
i
m
ize
d
m
o
d
u
la
ti
o
n
tec
h
… (
B
abk
ra
ni
Yo
usse
f)
1
861
Th
e
s
m
a
r
t
mul
t
i
l
e
ve
l
inv
e
rt
er
s
u
g
g
e
st
ed
w
i
l
l
all
o
w
ev
ery
sol
a
r
pa
ne
l
in
t
he
s
y
s
tem
to
o
per
a
te
in
de
pen
d
e
n
t
l
y
a
nd t
h
e t
o
t
a
l e
n
ergy
system
w
i
ll n
o
t
be
e
x
tr
em
ely
affec
te
d by
sh
a
d
es or
so
me
interm
i
t
t
e
n
ce.
A
com
p
ar
ative
stu
d
y
o
f
a
se
ven
a
n
d
f
i
f
t
e
e
n
m
ul
t
i
-
le
ve
l
in
verte
r
i
s
d
one
t
o
i
llu
stra
te
t
he
g
r
e
a
t
impro
v
e
m
e
n
t o
f
t
he
q
ua
li
t
y
si
g
na
l d
u
e
t
o
t
he
N
l
evel
o
f t
h
e
mul
ti
-inv
e
r
t
e
r.
I
t
i
s
c
l
e
a
r
t
h
at
t
hi
s
new
sc
hem
e
i
s
best
s
ui
ted
f
o
r
Casca
d
ed
M
u
l
t
i
-Leve
l
w
i
t
h
the
impr
ove
me
nt
o
f
t
h
e
ou
tpu
t
s
i
g
nal
qua
l
ity w
hic
h
makes
it
more
suita
b
l
e for bo
t
h
sta
nda
lone
an
d
grid c
onne
c
t
e
d
s
ys
tem
s
.
REFE
RENCES
[1]
B Xi
a
o
,
L
Han
g
,
J Mei
,
&
C
R
il
e
y
., "
M
o
d
u
l
ar
C
as
caded H-Brid
g
e
M
ulti
l
e
vel
PV
I
nverter
Wit
h
D
is
t
r
i
buted
M
PP
T
f
o
r
G
r
id
-Co
n
n
ected
A
p
p
licat
ions
I
EEE
T
rans
actions
o
n
Ind
u
st
ry
A
p
p
licati
ons,
"
v
ol
.
5
1
,
n
o
.
2
,
p
p
.
1
72
2-1
731
,
M
a
r-A
pr
2
01
5.
[2]
L
W
a
ng
,
D
Z
h
a
n
g,
Y
W
an
g
,
&
B
W
u
.
,
"P
ower
a
nd
V
ol
tage
B
alan
ce
Co
ntro
l
of
a
N
ov
el
T
h
r
ee-P
h
ase
S
o
li
d-S
t
a
t
e
T
r
ansf
or
mer
Using
M
ul
tilevel
C
a
s
caded
H
-Bridge
Inver
t
ers
f
o
r
Mi
crog
rid
A
ppli
catio
ns
I
EEE
T
ransact
io
ns
o
n
P
o
wer
Elect
ronics,
"
v
ol
.
3
1
,
n
o
.
4,
pp.
3
2
8
9
-
3301,
A
p
r
2
0
1
6
.
[3]
S
S
L
e
t
h
a
,
T
T
h
a
k
u
r
,
&
J
K
u
m
a
r
.
,
"
H
a
r
m
o
n
i
c
e
l
i
m
i
n
a
t
i
o
n
o
f
a
p
h
o
t
o-v
o
ltaic
b
ased
cas
c
a
de
d
H
-
br
id
ge
m
u
lti
lev
e
l
i
n
v
e
r
t
e
r
u
s
i
n
g
P
S
O
(
p
a
r
t
i
c
l
e
s
w
a
r
m
o
p
t
i
m
i
z
a
t
i
o
n
)
f
o
r
i
n
d
u
c
t
i
o
n
m
o
t
o
r
d
r
ive,
"
v
o
l
.
10
7,
n
o.
15,
p
p
.
3
3
5
-3
46,
J
u
l
20
16
.
[4]
A
A
b
d
u
l
r
a
z
z
a
q
a
n
d
A
H
A
l
i
,
"
E
ffici
e
n
cy
P
erf
o
rm
ances
o
f
T
w
o
M
P
P
T
A
l
gori
t
hm
s
f
o
r
P
V
S
y
s
t
e
m
W
it
h
D
i
ff
eren
t
Solar
Panels
Irra
diance
s
s
,
"
In
te
rn
atio
na
l J
o
u
r
na
l
of
Powe
r
E
l
e
c
t
r
o
n
i
c
s
an
d Driv
e
Sy
ste
m
(IJ
P
E
D
S
)
,
vol.
9,
no.
4
,
pp
.
1
7
5
5
-
17
64
,
De
c
20
18
.
[5]
O
.
S
a
la
m
a
,
A.
Ta
b
y
aou
i
,
&
M
.
Bench
a
gr
a,
"
Co
nt
rol
M
e
th
od
s
on
T
h
ree-
ph
ase
P
o
w
e
r
Con
v
ert
e
rs
i
n
P
h
o
t
ovo
lt
aic
Syst
e
m
s
,
"
Int
e
rna
t
i
o
n
a
l Jo
ur
na
l
of
P
o
wer
Elect
ron
i
cs
and
Dri
ve Syst
em
(
I
J
P
ED
S
)
,
vo
l.
9
,
no
.
4,
p
p
.
1
8
5
1
-
18
65
,
D
ec
20
18
.
[6]
M
D
a
bb
aghj
am
a
n
es
h
and
A
M
o
eini
,
"Hi
g
h
P
e
rfo
rm
ance
Con
t
ro
l
of
G
r
id
C
on
nected
C
ascad
e
d
H
-Bri
dge
A
cti
v
e
Rect
ifi
e
r
Based
on
Type
II-Fuzzy
L
ogic
C
ont
roller
w
ith
L
ow
F
re
q
u
e
nc
y
Mod
u
l
a
t
io
n
Te
c
h
n
i
qu
e
,
"
In
ter
nat
io
nal
Jo
ur
na
l of
Elect
rica
l
and
Co
m
puter
En
gi
neer
i
n
g
(
I
JECE)
;
vo
l
.
6
,
n
o
. 2,
p
p
.
48
4-4
9
4
, Ap
r
20
1
6
.
[7]
J
Sa
s
t
ry
,
P
Ba
k
a
s,
H
K
im
,
L
Wa
ng
,
&
A
Ma
rino
po
ulos
.,
"
E
v
a
lua
t
io
n
o
f
cas
caded
H
-bri
dg
e
in
verter
f
o
r
u
t
i
lit
y-
sc
a
l
e
ph
otov
o
lta
ic
syste
ms
,"
Re
n
e
w
a
bl
e
En
e
r
g
y
,
v
o
l
.
69
,
p
p
.
208
-218,
S
e
p
2
014.
[8]
S
y
e
d
M
u
n
v
a
r
A
l
i
,
V
.
V
i
j
a
y
a
k
u
m
a
r
R
e
d
d
y
,
&
M
.
S
u
r
y
a
K
a
l
a
v
a
t
h
i
.
,
"Coup
led
rando
m
PW
M
te
ch
ni
qu
e
fo
r
du
al
in
ve
rte
r
f
e
d
i
n
d
u
c
tio
n
m
otor
d
r
i
v
e
,"
Int
e
rn
ati
o
n
a
l Jo
ur
nal
o
f
Po
wer
Elect
ro
n
i
cs
a
n
d
D
r
i
ve S
y
stem
(
I
JPEDS)
,
v
o
l.
10
,
n
o
.
1
, Ma
r
2
01
9.
[9]
V
K
G
upt
a
and
R
M
a
h
a
nt
y,
"
Op
timi
zed
s
wit
c
h
i
n
g
s
chem
e
o
f
cas
caded
H
-bri
dge
m
ul
tilevel
i
n
ve
r
t
er
u
sing
P
SO,"
In
ter
n
a
t
io
nal Jour
na
l o
f
Elect
ri
cal Power
&
Ene
r
g
y
Sys
t
em
s
,
v
o
l
.
64
,
p
p
. 6
99
-70
7
, Jan 2
01
5
.
[10]
N
a
yeem
ud
di
n,
T
.
Bram
han
a
nd
a
Redd
y,
&
M
.
Vij
a
y
a
K
um
ar.,
"
Lev
e
l
S
hi
f
t
e
d
D
is
c
o
nt
in
uo
u
s
P
W
M
A
l
g
o
r
i
t
h
m
s
to
M
i
n
i
mize
Co
m
m
o
n
M
o
d
e
V
o
ltag
e
f
o
r
Cascad
e
d
M
u
l
til
e
v
el
I
n
v
ert
e
r
F
ed
I
nduction
M
o
tor
Dr
i
v
e
,
"
International
Jo
ur
na
l of
P
o
we
r
El
ectro
n
i
cs a
n
d
Drive S
y
st
em
(
I
JP
EDS)
, vo
l
9
, n
o
.
2
, Jun
20
1
8
.
[11]
N
.
P
r
abah
aran
a
nd
K
.P
al
anis
amy,
"
An
aly
s
is
a
n
d
i
nt
egrat
i
o
n
o
f
m
u
l
tilevel
i
n
v
e
rt
er
c
onf
i
g
urati
o
n
wit
h
b
oost
co
nv
erters
i
n
a
pho
to
vo
ltai
c
sys
t
em
,"
En
e
r
g
y
C
o
n
v
e
r
sion
an
d
Ma
na
ge
me
nt
,
vo
l.
1
28
,
n
o
.
1
5
,
p
p.
3
2
7
-
34
2,
N
o
v
20
16
.
[12]
M
.
P
ors
e
lv
i
,
K
.
D
eepa,
&
R
.
Mut
h
u
.
,
"F
P
G
A
Based
S
e
lect
iv
e
Harm
o
n
i
c
Elim
in
ati
on
Techn
i
q
u
e
f
o
r
M
u
lti
l
ev
el
Invert
er”
,
Int
e
rnat
ion
a
l
Jou
r
n
a
l of
Po
wer Elect
r
o
n
i
cs
an
d
Dr
i
ve Sys
t
em
(
I
JPED
S
)
, v
o
l
9
, no
. 1
, M
ar 20
1
8
.
[13]
T
P
K
a
k
o
s
i
m
o
s
,
K
P
a
v
l
o
u
,
A
K
l
a
d
a
s
,
&
S
M
a
n
i
a
s
.
,
"
A
s
i
n
g
l
e
-
p
h
a
s
e
n
i
n
e-l
e
vel
in
vert
er
f
or
r
enew
able
e
nerg
y
s
y
s
t
e
m
s
em
ploy
in
g
m
o
d
e
l
pred
ict
i
ve
c
o
n
trol,
"
Energ
y
Co
nver
sio
n
a
nd M
ana
gem
e
nt
,
vo
l
8
9
(
1),
p
p
.
4
27
-4
37
,
Ja
n
20
15
.
[14]
M
C
o
p
p
o
l
a
,
F
D
i
N
a
p
o
l
i
,
&
P
G
u
e
r
r
i
e
r
o
,
"
A
n
F
P
G
A
-
B
a
s
e
d
A
d
v
a
n
c
e
d
Cont
rol
S
t
rateg
y
o
f
a
Grid
-Ti
e
d
P
V
C
HB
Invert
er”,
IEEE T
r
an
sa
c
tio
ns
on
Po
wer E
l
ectro
nics
, vo
l
.
3
1
,
no
.
1
,
p
p
. 8
06
-81
6
, Ja
n
2
01
6.
[15]
S
Vijay
a
M
ad
hav
i
a
nd
G
.
Tu
lasi
R
am
D
a
s
,
"Co
m
parati
ve
S
tu
dy
of
C
o
n
t
ro
lle
rs
f
or
a
n
Iso
l
a
t
e
d
F
ull
Brid
ge
B
oo
st
Co
nv
erter
T
o
p
o
logy
i
n
F
u
el
C
ell
A
p
p
licat
io
n
s
,"
Int
e
rnati
o
n
a
l
J
o
urn
a
l
of Powe
r
Electr
onics
and
Drive S
y
st
em
(I
J
P
E
D
S
)
,
vo
l
9
, n
o. 4
,
Dec
2
0
1
8
.
[16]
Y
Babkran
i,
A
N
add
a
mi
,
S
Hay
a
n
i
,
&
M
H
ilal.
,
"
S
el
ectiv
e-harm
on
i
c
elimin
ati
o
n
w
i
t
h
a
n
op
tim
i
z
e
d
M
u
lti
carrier
M
o
du
lation
Tech
niq
u
es
f
or
C
a
s
cad
ed
H
-Bri
dge
M
u
l
t
i
lev
e
l
Inverter
,"
Jou
r
n
a
l
of A
ppli
e
d
Ma
th
ematics
and
Comput
a
t
i
o
n
, vo
l
.
3
, n
o.
1,
p
p
.
57
4-5
8
2
, 20
1
9
.
[17]
G
.
Vi
dh
ya Kris
h
n
a
n,
M.
V
alan
R
ajk
u
m
a
r, &
C
.H
em
al
atha,
"Mo
d
el
in
g
a
n
d
S
i
m
u
l
a
tio
n o
f
1
3-l
e
vel
Cascaded
H
y
b
ri
d
M
u
lt
il
evel
I
nvert
er
w
ith
l
es
s
n
u
m
b
er
o
f
S
w
it
ches,
"
In
ter
n
a
t
i
o
n
a
l
J
o
ur
nal o
f
Inno
vat
i
ve S
t
udies in
S
c
iences
an
d
E
n
g
i
n
eerin
g
Tec
h
no
lo
gy IS
SN 2
4
55
-48
6
3
(
I
JISS
ET
)
, vo
l
. 2
,
n
o
. 11
, No
v
2
0
1
6
.
[18]
Yu
sn
id
a
Ah
ma
d
Ta
r
m
iz
i,
A
u
z
a
n
i
J
i
d
i
n,
K
a
s
ru
l
A
bdu
l
Karim,
&
T
.
S
u
t
ikn
o
.,
"
A
s
imp
l
e
c
o
nsta
nt
s
witc
hing
f
r
eq
uen
c
y
o
f
d
irect
t
orqu
e
co
ntrol
o
f
b
rush
less
D
C
m
otor,
"
In
t
e
rna
t
i
o
n
a
l Jou
r
nal
of Power
Electr
onics
a
nd Drive
S
y
st
em (
I
JPEDS)
,
vo
l
1
0
, no
. 1
,
Mar 20
19
.
[19]
S
e
l
v
am
uthu
ku
maran,
"
A
Ga
rg
H
yb
rid
Mu
lticarri
er
M
o
d
u
l
ati
o
n
to
R
e
d
u
ce
L
eak
a
g
e
Curren
t
i
n
a
Trans
f
orm
e
rless
Cas
caded
M
ul
tilev
e
l
I
n
v
ert
e
r
f
o
r
Ph
ot
ov
o
l
ta
ic
S
ystem
s
,
”
IEE
E
T
r
ansa
c
ti
ons o
n
Powe
r
E
l
ectron
i
cs
,
vo
l.
3
0
,
n
o.
4
,
Ap
r 20
15
.
[20]
K
i
t
t
ay
a
S
o
msai.
,
"
C
o
n
tro
l
l
e
r
Des
i
g
n
o
f
UPQ
C
f
or
E
nhancin
g
P
o
wer
Q
uality
i
n
Dis
t
ri
but
i
on
S
yste
m,"
In
ter
n
a
t
io
nal Jour
na
l o
f
P
o
wer
El
ectro
n
i
cs
a
n
d
Dr
ive S
y
s
t
em
(
I
JP
EDS)
,
vo
l 9
,
n
o
. 4
, Dec 20
18
.
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