Int
ern
at
i
onal
Journ
al of
P
ower E
le
ctr
on
i
cs a
n
d
Drive
S
ystem
s
(
IJ
PEDS
)
Vo
l.
12
,
N
o.
1
,
M
a
r 202
1
, p
p.
228
~
240
IS
S
N:
20
88
-
8694
,
DOI: 10
.11
591/
ij
peds
.
v12.i
1
.
pp
228
-
240
228
Journ
al h
om
e
page
:
http:
//
ij
pe
ds
.i
aescore.c
om
A
r
evie
w o
n harm
on
i
cs el
imi
na
ti
on i
n real ti
me for
casca
ded H
-
br
i
dge
multile
vel i
nvert
er usin
g parti
cle
swarm
optimiz
ation
Muhamm
ad
Tayy
ab
Yaqoob
1
,
M
oh
d
. K
ha
ir
il
Rahm
at
2
,
Siti
Ma
r
w
angi
Moham
ad
Mah
arum
3
,
Ma
zl
ih
am M
ohd.
Su’ud
4
1,2
El
e
ct
ri
ca
l
Eng
i
nee
ring
Section,
Univer
siti
K
u
a
l
a
L
u
m
p
u
r
,
B
r
i
t
i
s
h
M
a
l
a
y
s
i
a
n
I
n
s
t
i
t
u
t
e
,
S
e
l
a
n
g
o
r
,
M
a
l
y
s
i
a
3
El
e
ct
roni
cs
T
echnology
Sec
ti
on,
Univer
sit
i
K
u
a
l
a
L
u
m
p
u
r
,
B
r
i
t
i
s
h
M
a
l
a
y
s
i
a
n
I
n
s
t
i
t
u
t
e
,
S
e
l
a
n
g
o
r
,
M
a
l
y
s
i
a
4
Univer
siti
Kual
a
Lu
mpur, Mala
ysian
Franc
e
Ins
ti
tute,
Sela
n
gor,
Malysia
Art
ic
le
In
f
o
ABSTR
A
CT
Art
ic
le
history:
Re
cei
ved
M
a
y
1,
20
20
Re
vised
Jan
4
, 20
21
Accepte
d
Ja
n
24
, 2
0
21
Rene
wabl
e
en
er
gy
has
a
gre
at
i
mport
an
ce
for
p
ower
gene
r
at
ion
as
it
does
no
t
use
the
foss
il
s
f
uel
s.
Ene
rgy
ge
ner
ated
fro
m
a
lterna
t
ive
ene
rgy
source
s
are
wea
the
r
d
epe
nd
ent
.
To
g
ene
r
ate
a
continuous
power
to
me
e
t
the
lo
a
d
req
uirement
s,
B
at
t
ery
en
erg
y
st
ora
ge
sys
te
m
ar
e
used.
Pow
er
conve
rsion
proc
ess
must
be
muc
h
eff
icient
as
poss
ibl
e
to
c
onver
t
th
e
DC
stored
en
erg
y
int
o
AC.
Thi
s
c
onver
sion
proc
e
ss
is
usuall
y
do
ne
by
th
e
he
lp
of
inve
rt
ers.
Thi
s
pap
er
g
ives
the
brie
f
over
vie
w
on
three
ma
in
c
at
egor
ie
s
of
multil
ev
e
l
inve
rt
er
l
ike
ca
s
ca
ded
h
-
bridg
e,
neut
ra
l
poin
t
c
lamped
and
fly
in
g
ca
p
ac
i
tor
mul
tilevel
inve
r
t
er
and
h
ighl
igh
t
s
the
ir
adva
nt
ag
es
which
c
an
als
o
hel
p
th
e
schola
rs
to
dee
p
ly
expl
ore
the
c
at
egor
ie
s
o
f
mu
lt
ilevel
inve
rt
er.
Harm
on
ic
el
imination
is
usuall
y
don
e
b
y
cont
rol
li
ng
t
he
sw
it
chi
ng
a
ngle
s
of
the
inve
rt
er.
Amon
g
al
l
the
sw
it
c
hing
angles
te
c
hnique
s,
sel
ecti
ve
har
mon
ic
el
imination
pu
lse
width
modulat
ion
(SH
EPWM)
technique
is
wi
del
y
used
,
tha
t
h
as
al
so
d
iscussed
in
th
is
pa
per
.
Furth
erm
or
e
,
to
elimi
n
at
e
the
har
monics
using
SH
EPWM
,
it
has
th
e
set
o
f
nonli
ne
ar
tr
ans
ce
nden
ta
l
equati
ons,
the
se
set
of
equa
t
ions
ca
n
b
e
ef
fiece
in
t
ly
solved
by
th
e
opti
m
izati
on
m
et
hods.
The
most
e
f
f
i
c
i
e
n
t
a
n
d
r
e
l
i
a
b
l
e
o
p
t
i
m
i
z
a
t
i
o
n
m
e
t
h
o
d
l
i
k
e
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
h
a
s
b
e
e
n
d
i
s
c
u
s
s
e
d
w
i
t
h
m
u
l
t
i
p
l
e
o
b
j
e
c
t
i
v
e
f
u
n
c
t
i
o
n
s
i
n
t
h
i
s
p
a
p
e
r
.
T
h
i
s
p
a
p
e
r
w
i
l
l
h
e
l
p
t
h
e
s
c
h
o
l
a
r
s
t
o
u
n
d
e
r
s
t
a
n
d
t
h
e
f
i
n
e
s
t
c
a
t
e
g
o
r
y
of
multil
evel
inve
rt
er
for
har
monic
e
li
m
in
at
ion
in te
r
ms of
eff
i
cienc
y
and
o
utput
qu
al
i
ty.
Ke
yw
or
d
s
:
Ca
scaded H
-
bri
dg
e
M
ulti
le
vel in
v
e
rter
Partic
le
sw
a
rm
opti
miza
ti
on
Sele
ct
ive h
a
rm
on
ic
s
eli
minati
on
This
is an
open
acc
ess arti
cl
e
un
der
the
CC
BY
-
SA
l
ic
ense
.
Corres
pond
in
g
Aut
h
or
:
M
oh
d.
K
hairil
Ra
hm
at
Ele
ct
rical
En
gi
neer
i
ng Secti
o
n,
B
riti
sh
M
al
aysian
Insti
tute
U
ni
ver
sit
y K
ua
la
Lu
m
pur (
UniKL)
Ku
al
a
Lu
mpur
,
M
al
a
ys
ia
Emai
l:
mkhairi
l@u
nik
l.e
du.m
y
1.
INTROD
U
CTION
Energ
y
ge
ne
rati
on
process
us
i
ng
f
os
sil
s
f
uels
are
not
co
ns
id
ered
as
a
n
e
ff
e
ct
ive
meth
od
a
s
it
eff
ect
s
the
e
nv
i
ronme
nt
a
nd
cl
imat
e.
Re
ne
wab
le
en
ergy
source
s
(
RES)
pro
duce
d
t
he
e
nerg
y
w
it
h
nea
rly
zer
o
carbo
n
emissi
ons
[
1
]
-
[
3].
The
powe
r
gen
e
rati
on
fro
m
t
hese
sou
rce
s
ar
e
weathe
r
de
pende
nt.
This
is
t
he
reas
on
e
nerg
y
gen
e
rated f
r
om
RES
needs
to b
e
sto
re
in
ene
rgy
sto
rag
e d
e
vices
(ESD
)
li
ke
batte
r
y,
f
uel
cel
l,
su
pe
r
cap
aci
tors
et
c.
E
nergy
st
ored
in
these
sto
rag
e
de
vices
ar
e
in
direct
cu
rrent
(
DC)
form,
w
her
ea
s
mo
stl
y
a
ppli
ances
w
ork
s
in
al
te
rn
at
in
g
current
(
AC)
form,
A
de
vice,
t
hat
is
us
ed
t
o
c
onve
rt
DC
i
nto
AC,
cal
le
d
in
ve
rter
relat
es
to
RES
or
ES
D
to
m
eet
the
a
ppli
ances
re
qu
i
rem
ents
[4
]
,
[
5].
I
nv
e
rters
a
re
us
e
d
f
or
gr
i
d
-
c
onnecte
d,
f
le
xib
le
al
te
rn
at
ing
c
urren
t
t
ran
s
missi
o
ns
s
ys
te
ms
(FACTS)
,
beca
use
of
it
s
l
ow
c
os
t,
flexi
bili
ty,
an
d
e
ff
ect
ive
ne
ss
f
or
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
ow Elec
& Dri S
ys
t
IS
S
N: 20
88
-
8
694
A Revi
ew
on h
ar
m
onic
s eli
mi
nia
ti
on in
re
al
ti
me
for c
as
c
aded
H
-
br
id
ge
…
(
Mu
ham
m
ad T
ayy
ab Y
aqoob
)
229
powe
r
co
nvers
ion
it
is
getti
ng
a
n
at
te
ntio
n
for
the
sch
olar
s
[6
]
-
[
12].
Gr
i
d
c
onnected
I
nverter
s
inc
reas
es
the
sign
ific
a
nce i
n photo
volt
ai
c cel
ls, w
in
dm
il
ls,
wh
ic
h wil
l occ
upy
t
he
la
r
ger
-
scal
e
phot
ovoltai
c
cel
ls [13].
Dev
ic
es
that
use
s
al
te
rn
at
i
ng
cu
rr
e
nt
a
re
s
mart
dev
ic
es
,
l
igh
ti
ngs,
m
otors
a
re
powe
red
by
i
nv
e
rters
[14
]
-
[
17]
.
Ene
rgy
util
iz
at
ion
of
c
ompress
ors
an
d
ot
her
e
le
ct
ro
nic
e
qu
i
pme
nt’s
ca
n
be
done
by
c
ombinin
g
inv
e
rters
with
varyin
g
it
s
s
witc
hing
f
re
quency
[
18].
Mo
reover
,
it
al
so
co
ntro
ls
the
vo
lt
age
sta
bili
ty
a
nd
var
ia
ti
on
in
vo
lt
age
in
el
ect
rical
power
syst
ems
[
15
]
,
[
18
]
-
[
20]
.
D
ue
t
o
th
ese
cha
ng
e
s,
li
feti
me
an
d
qu
a
li
ty
of
the
de
vices
ma
y
get
af
fected
by
varyin
g
the
torque
a
nd
rip
ples
of
el
ect
rical
app
li
ances
.
Inver
te
rs
has
man
y
adv
a
ntage
s;
ho
wev
e
r,
t
he
la
r
ge
num
be
r
of
unwa
nted
harmo
nics
ap
pea
r
at
the
outp
ut
of
mu
lt
il
evel
inv
e
rter
wh
ic
h
ef
fect
the
el
ect
rical
and
mecha
nical
par
ts
of
the
s
ys
te
ms
[
21
]
-
[
24]
.
Sw
it
chi
ng
f
reque
ncy
plays
a
vital
ro
le
to
mi
nimi
ze
the
ha
rm
on
i
cs,
Be
cause
of
high
am
plit
ud
e
of
fun
dame
ntal
fr
eq
ue
ncy,
ha
rm
on
ic
s
hav
i
ng
lo
w
order
bec
om
es
more
har
m
f
ul
for
the
sy
ste
m.
T
he
pr
ese
nc
e
of
unw
ante
d
ha
rm
onic
s
c
an
al
so
be
re
duced
by
reducin
g
t
he
s
witc
hing
l
os
se
s
prese
nt
in
the
pow
er
switc
he
s.
L
ow
order
ha
rm
on
ic
s
at
th
e
outp
ut
of
m
ul
ti
le
ve
l
inv
e
rter
gen
e
ra
te
the
co
mp
le
x
pro
blems
s
pec
ia
ll
y
at
the
dist
rib
ution
side
w
hen
this
in
ve
rter
relat
es
to
th
e
gr
i
d
[25
]
-
[
26]
.
P
ower
qu
al
it
y
at
t
he
outp
ut
of
i
nverter
al
s
o
get
a
ff
ect
ed
by
t
hes
e
distu
rb
a
nces
li
ke
fluct
uations
an
d
harmo
nics
[27].
To
overc
om
e
these
pro
blem
s,
re
searc
hers
hav
e
c
om
e
up
with
ma
ny
te
chn
i
qu
e
s
that
dep
e
nds
on
modu
la
ti
on
of
the
ou
t
put
waveform
to
mi
nimize
the
harm
on
ic
s
,
w
hich
makes
the
i
nv
e
rter
m
or
e
reli
a
ble
a
nd
eff
ic
ie
nt
[
28].
A
sp
eci
al
ty
pe
of
in
ve
rter
that
giv
es
the
nea
rly
sin
usoid
al
w
avefor
m
at
the
ou
t
pu
t
a
re
cal
le
d
the
mu
lt
il
evel
inve
rters.
This
i
dea
has
bee
n
intr
oduce
d
i
n
1980s
,
the
wor
d
m
ul
ti
in
mu
lt
il
evel
inv
e
rter
mean
s
that
it
con
sist
s
of
mu
lt
i
ste
ps
wa
veform
at
t
he
ou
t
pu
t.
H
arm
onic
s,
el
ect
r
oma
gn
et
ic
i
nterf
e
ren
ce
,
a
nd
qua
li
ty
i
n
inv
e
rters
are
di
rectl
y
relat
ed
to
the
switc
hi
ng
f
reque
ncy,
le
sser
the
s
witc
hi
ng
f
re
qu
e
nc
y
will
yield
the
bette
r
eff
ic
ie
nc
y
of
inv
e
rter
[
29]
.
The
m
ulti
le
vel
in
ver
te
r
main
ly
has
th
ree
typ
e
s,
fl
ying
c
apacit
or
(F
C)
,
diod
e
cl
a
mp
ed
(
DC)
an
d
casca
d
e
d
H
-
bri
dge
(CHB).
T
his
pa
per
disc
us
ses
the
ha
rm
onic
el
imi
nation
i
n
CHB
mu
lt
il
evel
in
ve
rter
as
it
is
mo
st
s
uitable
t
yp
e
f
or
re
ne
w
able
e
nergy
a
ppli
cat
ion
s.
T
o
con
t
ro
l
t
he
s
w
it
ching
fr
e
qu
e
nc
y
of
this
in
ver
te
r
the
re
are
tw
o
po
s
sibil
it
ie
s,
sel
ect
ive
ha
rm
on
ic
el
imi
nation
(
S
HE)
an
d
s
pace
vecto
r
con
t
ro
l
(SVC)
.
W
he
reas
S
H
E
w
orks
on
hi
gh
s
witc
hi
ng
fr
e
qu
e
nc
y
a
nd
SV
C
w
orks
on
a
lo
w
s
witc
hing
fr
e
qu
e
nc
y.
P
ulse
wi
dth
m
odul
at
ion
te
ch
ni
que
w
orks
on
hi
gh
s
witc
hi
ng
f
re
qu
e
nc
y
a
nd
s
w
it
ches
of
the
in
ver
te
r
commuta
te
s
m
ulti
ple
ti
mes
in
one
cycle [
30]
,
an
d
s
witc
h
is comm
utate
d
ei
ther
on
ce
or
tw
ic
e
in
low
swit
chin
g
fr
e
qu
e
nc
y.
For
high
powe
r
a
nd me
dium
pow
er a
pp
li
cat
ions
SH
E is
m
os
tl
y use
d process.
This
pap
e
r
give
s
the
br
ie
f
ov
erv
ie
w
of
basi
c
co
nf
ig
urat
io
ns
of
mu
lt
il
eve
l
inv
erte
rs
(MLI),
pr
os
a
nd
cons
a
nd
recen
tl
y
resea
rc
h
t
ha
t
has
be
en
done
on
t
hr
ee
m
ai
n
ty
pes
of
MLI.
T
he
t
yp
es
that
are
discusse
d
i
n
this
pa
pe
r
a
re
neu
t
ral
po
i
nt
cl
ampe
d
(
NP
C)
,
flying
capaci
to
r
(F
C)
,
a
nd
cas
caded
H
-
B
rid
ge
(C
HB)
Mult
il
evel
inv
e
rter.
M
od
ul
at
ion
te
chn
i
que
li
ke
Sele
ct
ive
har
m
onic
el
imi
nation
pulse
width
m
odula
ti
on
(SHE
PWM)
has
been
discusse
d
i
n
detai
l
an
d
t
he
rece
nt
arti
cl
es
relat
ed
t
o
t
his
te
ch
nique
has
be
e
n
s
ummari
ze
d
he
re.
Fu
rt
hermo
re,
t
he
a
dvanta
ges
of
opti
miza
ti
on
meth
ods
li
ke
PS
O
an
d
G
A
ov
e
r
m
os
tl
y
use
d
nume
ric
al
methods
new
t
on
r
ap
hso
n
(N
R
)
a
nd
la
t
est
pa
pers
has
been
s
ummari
z
ed
i
n
t
his
pape
r.
Fun
dame
ntal
co
nce
pts
a
nd
t
yp
e
s
of
m
ulti
le
vel
i
nv
e
rter
is
pres
ented
Sect
io
n
2.
W
he
reas
Se
ct
ion
3
c
ov
e
rs
the
sel
ect
ive
harmo
nic
te
c
hniq
ues
.
The
la
te
st
pa
pe
rs
w
hich
us
e
s
par
ti
cl
e
swa
r
m
opti
miza
ti
on
(
PS
O)
meth
od
s
f
or
ha
rm
onic
el
imi
nation
hav
i
ng
diff
e
re
nt object
ive fu
nctions h
as b
ee
n
s
umma
rized i
n
sect
io
n 4.
2.
MU
LT
ILE
VE
L IN
VERTE
R
M
ulti
le
vel
in
ve
rter
giv
es
t
he
near
l
y
sin
usoid
al
wav
e
form
at
the
outp
ut
by
ta
kin
g
the
se
ve
ral
volt
age
so
urces
as
a
n
input.
It
has
man
y
ad
va
nta
ges
as
c
ompar
ed
to
c
onve
ntion
al
tw
o
-
le
vel
inv
e
rter
w
hic
h
use
s
fun
dame
ntal
switc
hing
fr
e
quency
pulse
width
mod
ulati
on
(
PWM
)
a
ppr
oach.
M
ulti
le
ve
l
inv
e
rter
is
us
e
d
t
o
gen
e
rate
the
ne
arly
sin
usoidal
wav
e
f
or
m
ei
th
er
from
a
n
E
S
D
or
di
rectl
y
f
r
om
DC
powe
r
gen
e
rati
on
pla
nt
li
ke
Photo
vo
lt
ai
c
c
el
ls.
The
main
adv
a
ntage
of
mu
lt
il
evel
in
ve
rter
is
t
hat
the
increme
nt
in
num
ber
of
le
vels
le
ads
to
the
inc
reme
nt
in
ou
t
pu
t
vo
lt
age
an
d
sta
irc
ase
wav
e
form
.
T
he
sta
irca
se
wav
e
f
or
m
s
up
ports
t
he
re
du
c
ti
on
i
n
total
har
m
onic
distor
ti
on
(
TH
D)
.
Q
ualit
y
of
Stai
rcase
wa
ve
form
is
hi
gh
i
n
te
rms
of
ha
rm
on
ic
s
reducti
on
an
d
low
vo
lt
age
st
ress
am
ong
power
s
witc
hes
.
Thr
ee
main
ty
pes
of
m
ulti
le
vel
inv
e
rters
ha
ve
bee
n
a
pp
li
ed
i
n
medium
a
nd
hi
gh
-
po
wer
a
pp
li
ca
ti
on
s
li
ke
ne
utral
point
cl
ampe
d
(
NP
C
),
flying
ca
pacit
or
(F
C)
an
d
ca
scade
d
H
-
br
i
dg
e
(CH
B)
mu
lt
il
evel
inv
e
rter.
The
num
ber
of
re
qu
i
red
c
omp
on
e
nt
s
in
CHB
is
le
s
ser
tha
n
the
ot
her
t
wo
te
chn
iq
ues
.
De
ta
il
s
of
the
nu
mb
e
r
of
c
omp
on
e
nts
can
be
sh
ow
n
in
Ta
ble
1.
It
al
so
s
hows
t
he
dif
fere
nce
in
diff
e
re
nt
M
LI
topolo
gies.
As
CHB
re
qu
i
res
a
le
ast
num
be
r
of
c
ompone
nt
s
that
e
na
bles
it
s
sim
ple
str
uctu
re
with
al
mo
st
m
inu
te
co
mp
le
xity.
A
dd
it
io
nally,
with
a
le
ast
num
be
r
of
c
omp
on
e
nts
it
ca
n
al
s
o
deli
ver
powe
r
for
high
volt
ag
e
powe
r
a
pp
li
c
at
ion
s
as
co
mpa
red
t
o
oth
e
r.
Additi
on
al
l
y,
merit
s
an
d
de
merit
s
of
th
ree
typ
es
of
inv
e
rter a
re sh
own
i
n
Ta
ble
2
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8
694
In
t J
P
ow
Ele
c
&
D
ri
S
ys
t,
V
ol
.
12
, N
o.
1
,
Ma
rch
20
21
:
228
–
240
230
Table
1.
C
omp
ariso
n
of m
ulti
le
vel inverte
rs
te
chn
iq
ues
Top
o
lo
g
y
Po
wer
Switch
es
Clampin
g
Dio
d
es
Clampin
g
Cap
acito
rs
DC Bu
s
Cap
acito
rs
NPC
2
(
L
-
1)
(L
-
1
)
(
L
-
2)
0
(L
-
1)
FC
2
(
L
-
1)
0
(L
-
1
)
(
L
-
2
)/2
(L
-
1)
CHB
2
(
L
-
1)
0
0
(L
-
1
)/2
2.1.
Neutral
po
in
t c
lamped
multi
le
vel inver
ter
This
ty
pe
of
i
nverter
is
e
ff
ect
i
vely
a
th
ree
-
le
vel
di
ode
cl
am
ped
co
nverte
r
t
hat
wa
s
int
rod
uced
by
Na
bae
et
al
,
[31
].
T
his
ty
pe
of
in
vert
er
has
desi
gn
e
d
t
o
pro
duce
a
small
ha
rm
onic
outp
ut
volt
age
f
or
high
e
ffi
ci
enc
y
var
ia
ble
fr
e
que
ncy
drive
ci
rc
ui
ts.
Pr
ed
om
i
na
ntly
the
th
ree
l
evel
NP
C
is
s
how
n
in Figure
1(
a
),
the furth
e
r
ne
utral
po
i
nt
that
is
gi
ven
at
e
very
le
g
ha
s
in
div
id
ua
l
sta
te
s
that
are,
V
dc/2,
-
Vd
c
/2
an
d
zer
o.
T
o
get
t
he
ou
pu
t
vo
lt
a
ge
of
V
dc/2
a
nd
-
Vd
c/
2,
t
he
s
witc
hes
S
1
S
2
a
nd
S
1’
an
d
S
2’
need
to
be
s
w
it
ch
on
i
n
a
s
pec
ific
patte
rn
to
giv
e
t
he
ou
t
pu
t
wav
e
f
orm
li
ke
a
sta
ir
case.
The
num
ber
of
Ca
pacit
or
s
(C)
a
nd
cl
amping
diodes
(
cd)
for
NP
C
m
ulti
le
vel
inv
e
rter ca
n be
easil
y
fi
ndout
by
(
1
)
an
d
(
2
)
:
=
−
1
(1)
=
∗
(
−
2
)
(2)
Wh
e
reas
Fig
ur
e
1(
b)
s
hows
the
five
-
le
vel
N
PC
m
ulti
le
vel
i
nv
e
rter
[
8
]
.
Th
e
ci
rc
uit
dia
gr
a
m
c
onsist
s
of
four
ca
pacit
ors
for
fi
ve
le
vel
NP
C
desig
n.
C
1
,
C
2
,
C
3
and
C
4
.
Wh
il
e
c
ompari
ng
t
he
N
P
C
with
ot
her
mu
lt
il
evel
i
n
v
e
r
t
e
r
[
3
2
]
-
[
3
4
]
,
t
h
i
s
t
y
p
e
o
f
i
n
v
e
r
t
e
r
h
a
s
w
i
d
e
l
y
u
s
e
d
b
e
c
a
u
s
e
o
f
i
t
s
e
f
f
i
c
i
e
n
c
y
a
n
d
l
e
s
s
e
r
l
e
a
k
a
g
e
c
u
r
r
e
n
t
[3
5
]
,
[
3
6
].
Give
n
th
at
N
P
C
w
orks
on
a
mu
tual
DC
bus
,
the
re
qu
i
reme
nt
of
Ca
pacit
or
of
this
in
ver
te
r
is
reduce
d.
T
his
is
t
he
reason
it
is
fea
sible
f
or
back
-
to
-
bac
k
t
opolog
y;
this
in
ver
te
r
has
few
disa
dvanta
ges
as
we
ll
li
ke
di
ff
ic
ult
y
i
n
real
ti
me
po
wer
fl
ow
[
3
7
]
,
[
3
8
].
Stabil
iz
ing
an
d
balan
ci
ng
t
he
DC
vo
lt
age
of
Ca
pacit
or
is
an
im
portant
factor
t
o
consi
der
f
or
N
PC
d
e
s
i
g
n
.
W
h
e
r
e
a
s
a
s
i
n
g
l
e
s
u
p
p
l
y
g
i
v
e
s
t
h
e
D
C
-
b
u
s
t
o
t
h
e
i
n
v
e
r
t
e
r
a
s
t
h
e
u
p
p
e
r
a
n
d
l
o
w
e
r
l
o
a
d
o
f
t
h
e
D
C
l
i
n
k
c
a
p
a
c
i
t
o
r
i
s
t
h
e
p
r
o
b
l
e
m
.
O
n
e
o
t
h
e
r
s
o
l
u
t
i
o
n
i
s
f
o
r
a
d
d
r
e
s
s
i
n
g
t
h
e
a
b
o
v
e
p
r
o
b
l
e
m
i
s
s
o
l
v
e
d
b
y
[
39
]
,
[
4
0
].
Althou
gh
t
hese
so
luti
ons
ha
ve
high
c
os
t,
de
c
rease
the
powe
r
facto
r,
a
nd
in
creases
the
c
omplexit
y
of
th
e
con
t
ro
l
sy
ste
m.
A
no
t
he
r
passi
ve
ci
rc
uit
has
bee
n
pro
posed
i
n
[
3
8
]
to
inc
rease
the
po
wer
rang
e
of
the
w
ho
le
sy
ste
m
wh
il
e
mainta
i
ni
ng
the
volt
age
sta
bili
zat
ion
and
i
nequali
ty
in
DC
vo
lt
a
ge
sy
ste
m.
A
balance
bo
os
te
r
s
yst
em
is
pro
po
se
d
in
[
4
1
]
,
to
s
olv
e
t
he
sta
bili
zat
ion
pro
blem,
re
la
te
s
to
the
l
oad
in
pa
rall
el
.
Further
t
o
re
duce
vo
lt
a
ge
s
t
r
e
s
s
,
u
n
i
f
o
r
m
i
n
p
u
t
v
o
l
t
a
g
e
a
n
d
o
u
t
p
u
t
v
o
l
t
a
g
e
T
H
D
a
n
o
v
e
l
f
i
v
e
-
l
e
v
e
l
v
o
l
t
a
g
e
s
o
u
r
c
e
i
n
v
e
r
t
e
r
i
s
p
r
e
s
e
n
t
e
d
i
n
[4
2
].
The
m
od
el
pro
po
s
ed
in
[
8
]
doesn
ot
ne
ed
f
urt
her
semic
ondu
ct
or
po
wer
swi
tc
hes
t
o
c
o
nn
e
ct
in
s
eries
t
hu
s
it
ha
s
a
high
-
qual
it
y
ou
tpu
t
vo
lt
ag
e as
com
par
e
d
t
o
c
onve
ntion
al
NPC
.
(a)
(b)
Figure
1. Ne
utr
al
p
oi
nt clam
pe
d
m
ulti
le
ve
in
ver
te
r
(
a
) 3
-
le
ve
l (b)
5
-
le
vel [
8
]
2.2.
Fly
ing capacit
or
m
ultil
evel i
nv
er
ter
Flyin
g
ca
pacit
or
(F
C
-
M
LI
)
ha
s
a
simi
la
r
str
uctu
re
as
N
PC
it
has
been
fi
rs
tl
y
m
od
el
e
d
by
M
a
yner
d
a
nd
Fo
c
h
[
3
2
].
Li
ke
NP
C
us
e
s
th
e
cl
amping
di
ode
the
FC
use
s
a
flying
capa
ci
tor
to
cl
amp
the
de
vice
volt
age.
A
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
ow Elec
& Dri S
ys
t
IS
S
N: 20
88
-
8
694
A Revi
ew
on h
ar
m
onic
s eli
mi
nia
ti
on in
re
al
ti
me
for c
as
c
aded
H
-
br
id
ge
…
(
Mu
ham
m
ad T
ayy
ab Y
aqoob
)
231
three
-
le
vel
an
d
five
-
le
vel
FC
is
sh
ow
n
in
Fi
gure
2.
T
he
st
r
uctu
re
of
th
ree
-
le
vel
N
PC
an
d
FC
a
re
simi
la
r,
bu
t
it
diff
e
rs
in
switc
hing
patte
rn
only.
T
o
pas
s
the
cu
rr
e
nt
for
po
sit
ive
cycle
li
ke
V
dc/2
,
S
1
an
d
S
2
will
work
an
d
f
or
the
ne
gative
D
C
input
li
ke
-
Vd
c/
2
S
1’
a
nd
S2
’
will
be
s
witc
hed
on.
F
or
zer
o
le
vel
ei
ther
S
1
S
1’
or
S2
S
2’
is
s
w
i
t
c
h
e
d
o
n
.
A
n
d
t
o
d
i
s
c
h
a
r
g
e
t
h
e
c
a
p
a
c
i
t
o
r
i
t
w
i
l
l
b
e
d
o
n
e
c
o
r
r
e
s
p
o
n
d
i
n
g
l
y
[
3
3
]
.
T
h
e
q
u
a
n
t
i
t
y
o
f
c
a
p
a
c
i
t
o
r
s
t
h
a
t
i
s
l
i
n
k
e
d
w
i
t
h
D
C
a
n
d
t
h
e
q
u
a
n
t
i
t
y
o
f
a
u
x
i
l
i
a
r
y
c
a
p
a
c
i
t
o
r
s
c
a
n
b
e
f
o
u
n
d
o
u
t
w
i
t
h
t
h
e
h
e
l
p
o
f
(
3
)
a
n
d
(
4
)
,
r
es
pe
ct
ively.
(a)
(b)
Figure
2
.
Flyi
ng
ca
pacit
or m
ul
ti
le
vel inv
erter
(a) 3
-
le
vel
(b) 5
-
le
vel [
8
]
DC
capaci
t
o
rs
=
−
1
(3)
Auxil
a
ry
Ca
pacit
ors
=
−
1
×
−
2
2
(4)
The
inc
reme
nt
in
numb
e
r
of
le
vels
for
FC
-
MLI
inc
rease
s
the
com
plexi
ty
in
co
ntr
olli
ng
t
he
sy
ste
m
.
This
is
the
rea
so
n
num
ber
of
le
vels
nee
ds
t
o
be
op
ti
m
um
so
that
it
gi
ves
the
near
ly
si
nuso
i
dal
outp
ut
and
high
-
performa
nce
c
on
t
ro
ll
er
as
w
el
l
[4
4
].
A
n
al
te
rn
at
ive
s
witc
hing
sta
te
for
a
sp
eci
fic
volt
age
le
vel
of
F
C
-
M
L
I
is
exp
la
ine
d
i
n
T
able
3
an
d
Fig
ur
e
2(b
).
To
s
witc
h
it
f
or
10
10
an
d
0101
first
capaci
to
r
w
il
l
store
an
d
re
le
ase
the
charge,
res
pec
ti
vely.
T
hus,
the
si
gn
ific
a
nt
issue
of
FC
is
to
c
on
tr
ol
t
he
c
hargin
g
a
nd
disc
hargin
g
of
th
e
capaci
tors
in
a
sp
eci
fic
ti
me
to
ge
t
the
nearl
y
sin
us
oi
dal
wav
e
f
or
m
at
t
he
outp
ut.
T
he
sign
ific
a
nt
fac
tor
of
FC
ov
e
r
N
PC
is
it
s
ph
a
se
la
ying
s
-
off
.
The
se
phase
la
yi
ng
s
off
hav
e
t
he
qu
al
it
y
to
ei
ther
charge
or
discharge
the
capaci
tor
,
the
powe
r
co
nsum
ption
of
DC
so
urces
t
o
bal
ance
the
c
ontr
ol
sy
ste
m
acr
os
s
ma
ny
le
ve
s
[4
5
].
Ther
e
f
or
e,
FC
ha
s
le
ss
er
volt
age
stres
s,
s
mall
er
siz
e
of
out
pu
t
filt
er
and
le
sse
r
TH
D
[
4
6
].
Although
fe
w
researc
hers
an
d
sc
ho
la
r
s
cl
ai
m
that
FC
is
be
tt
er
than
NP
C
in
te
rms
of
le
s
ser
num
be
r
of
com
pone
nts
bu
t
FC
al
so
has
s
ome
disa
dv
a
ntage
s
to
o
li
ke
the
co
ntr
ol
li
ng
of
cha
r
gin
g
a
nd
disc
hargin
g
of
ca
pacit
or
s
re
qu
i
re
a
com
plex
method
w
hich
le
ads
to
poor
s
witc
hing
e
ff
ic
ie
ncy.
Accor
din
gl
y,
sc
hola
rs
hav
e
co
ntri
bu
t
ed
thei
r
w
ork
to
so
l
ve
these
iss
ues
in
[3
7
]
t
o
minimi
ze
the
vo
lt
a
ge
dist
or
ti
on
at
t
he
in
put
si
de
of
FC
-
MLI.
Furth
er
merit
s
an
d
de
merit
s
of FC a
nd o
t
he
r MLI are
sho
wn in
Table
2
.
Table
2
. Pr
os
a
nd cons
of m
ul
ti
le
vel inv
erte
r
s [4
8
]
Typ
es
Ad
v
an
tag
es
Disad
v
an
tag
es
NPC
-
M
LI
•
Easy
to m
o
d
el
•
Nu
m
b
er
o
f
compo
n
en
ts in
crea
ses
as
o
u
tp
u
t level
in
crea
ses
•
Red
u
ced v
o
ltag
e st
ress and
lesser ha
r
m
o
n
ics [31
]
•
Co
m
p
lex
ity
increa
ses
while b
alan
cin
g
the v
o
ltag
e level
o
f
DC
-
lin
k
Cap
acit
o
r
[3
7
]
FC
-
ML
I
•
Simila
r
p
h
ase so
ou
tp
u
t vo
ltag
e ca
n
b
e ea
sily
balan
ced
an
d
lower dev
ice s
tress [3
7
]
•
Diff
icu
lty
incr
ease
s wh
ile des
ig
n
in
g
at
h
ig
h
er
lev
els
[4
0
]
•
Lesser
THD
•
Need h
u
g
e nu
m
b
er
o
f
Cap
acito
r
•
Lesser the
size of
Ou
tp
u
t f
ilter,
•
No
t ef
fi
cien
t in sw
itch
in
g
f
requ
en
cy
[
3
7
]
•
Red
u
ced n
u
m
b
er
o
f
co
m
p
o
n
en
ts
•
Ins
tallatio
n
cos
t is
h
ig
h
CHB
-
M
LI
•
Relaib
ility
is hig
h
,
fault to
lreant
[4
8
]
•
Every C
ell has
ind
iv
id
u
al DC so
u
rce
[3
7
]
•
Ab
ility
to d
esig
n
easily
f
o
r
h
ig
h
er
n
u
m
b
er
o
f
levels
•
Vo
ltag
e is no
t balan
ce a
m
o
n
g
all
p
h
a
ses
of inv
erter
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8
694
In
t J
P
ow
Ele
c
&
D
ri
S
ys
t,
V
ol
.
12
, N
o.
1
,
Ma
rch
20
21
:
228
–
240
232
Table
3
. E
ffec
t o
f
c
urren
t
pola
rity a
nd sw
it
ch
ing
Stat
es [4
3
]
Vo
ltag
e L
ev
el
Switch
in
g
States
Cu
rr
en
t Path
State of Cap
aci
to
rs
State of Cap
aci
to
rs
1
/2
Vdc
1100
Ia
> 0
S1
,
S2
Un
ch
an
g
ed
0
Ia
< 0
D1
,
D2
Un
ch
an
g
ed
1010
Ia
> 0
S1
,
D1
,
C3
Ch
arges C
1
Ia
< 0
S1
,
C1
,
D1
Disch
arges C
1
101
Ia
> 0
D4
,
C1
,
S2
Disch
arges C
1
-
1
/2
Vdc
Ia
< 0
S2
,
C1
,
D2
Ch
arges C
1
11
Ia
> 0
D3
,
D4
Un
ch
an
g
ed
2.3.
Ca
sc
ad
e
d
H
-
b
ri
dg
e m
ultil
ev
el
invert
er
A
Ca
scade
d
H
-
bri
dge
m
ulti
lev
el
inv
e
rter
(
CHB
-
M
LI
)
is
made
by
c
onne
ct
ing
the
ma
ny
H
-
bri
d
ge
inv
e
rters
i
n
s
uc
h
a
wa
y
t
hat
th
e
outp
ut
of
eve
ry
H
-
bri
dge
sums
up
with
ot
he
r
to
ma
ke
t
he
sta
ir
case
wav
e
for
m
at
the
outp
ut.
Every
H
-
bri
dg
e,
us
uall
y
cal
l
ed
a
cel
l,
has
a
sep
a
rate
DC
sou
rce
as
s
hown
in
Fi
gure
3
[38
].
Diff
e
re
nt
outp
ut
is
usual
ly
be
en
gen
e
rated
by
this
t
yp
e
of
i
nv
e
rter
li
ke
V
dc
,
0
an
d
-
V
dc.
To
get
the
outpu
t
of
Vd
c
S
1
a
nd
S
4
are
s
witc
he
d
on
a
nd
for
-
V
dc
S
2
an
d
S
3
a
r
e
tu
rn
e
d
on.
Since
the
outp
ut
vo
lt
age
of
t
he
CHB
-
M
L
I
is
the
sum
of
al
l
the
h
-
br
i
dg
es
as
gi
ve
n
i
n
(
5
)
.
T
he
numb
e
r
of
le
ve
ls
fro
m
this
t
yp
e
of
in
ver
te
r
can
be
cal
cula
te
d by n = 2
S+1
whe
re
S is the
num
be
r of
DC s
ource
s [4
7
].
=
1
+
2
+
3
+
4
(5)
Figure
3. Ca
sc
aded H
-
br
id
ge mult
il
evel in
ve
rter
[3
7
]
Adva
ntages
of
CHB
-
M
LI
ha
s
bee
n
sta
te
d
i
n
[
8
]
that
incl
ud
e
s
le
sser
c
omp
on
e
nts,
sim
ple
str
uctur
e
,
and
eas
y
s
witc
hing
strat
e
gy.
The
ou
pu
t
volt
age
of
this
inv
e
rter
can
easi
ly
be
adj
ust
by
inc
reasi
ng
an
d
decr
easi
ng
t
he
numb
e
r
of
H
-
bri
dges.
A
s
t
he
ouput
volt
age
l
evels
a
re
cal
cu
la
te
d
by
n
=
2S+
1,
th
at
is
fa
r
m
or
e
than
DC
sourc
e.
The
refor
e
,
this
typ
e
of
i
nverter
ma
kes
th
e
man
uf
act
ur
in
g
proce
ss
m
or
e
cl
ear
and
c
hea
per.
I
n
oth
e
r
w
ords
, C
HB
-
M
LI
is fa
r bett
er th
a
n NP
C
-
M
L
I
a
nd FC
-
MLI i
n
te
r
ms
of
relai
blit
y
a
nd
best f
a
ult t
ol
eran
ce
capab
il
it
y.
Th
ese
ad
va
ntage
s
ass
ist
the
i
nverter
to
pe
rform
bette
r
un
der
l
ower
DC
input
vo
lt
age
[4
8
].
M
ulti
le
vel
in
ve
rters
that
have
been
mentio
ned
i
n
this
pa
pe
r
has
se
ve
ral
adv
a
ntage
s
an
d
disa
dvanta
ge
s.
These
pros
a
nd
c
ons
of
t
hese
in
ver
t
ers
pla
ys
a
sig
nificant
ro
le
in
it
s
dev
el
opme
nt.
T
he
N
PC
-
M
L
I
can
be
use
d
t
o
integrate
it
with
the
gr
id
.
But
du
e
t
o
it
s
incr
ement
in
se
micond
ucto
r
de
vi
ces,
it
is
no
t
con
si
der
e
d
as
a
good
appr
oach
f
or
gri
d
c
onnecte
d
powe
r
s
ys
te
ms
.
Simi
la
r
co
nc
ern
s
ap
pl
y
f
or
FC
-
M
L
I,
t
o
c
on
t
ro
l
t
he
ca
pa
ci
tor
chargin
g
a
nd
di
s
chargin
g
will
be
m
uch
dif
fi
cult
to
desi
gn
it
fo
r
higher
num
ber
of
le
vel
s.
This
pro
blem
has
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
ow Elec
& Dri S
ys
t
IS
S
N: 20
88
-
8
694
A Revi
ew
on h
ar
m
onic
s eli
mi
nia
ti
on in
re
al
ti
me
for c
as
c
aded
H
-
br
id
ge
…
(
Mu
ham
m
ad T
ayy
ab Y
aqoob
)
233
been
a
dresse
d
in
[4
8
]
to
balance
the
ca
pacit
or
vo
lt
a
ge
in
e
cvery
in
div
i
dual
cel
l.
M
et
hod
pr
ese
nted
i
n
[
4
8
]
ha
s
been
te
ste
d
f
or
N
PC
-
M
LI
a
nd
CHB
syst
ems.
T
he
res
ults
o
bt
ai
ned
from
t
his
met
hod
pro
ve
that
it
is
a
pp
l
ic
able
for
me
diu
m a
nd h
i
gh
-
po
wer
a
pp
li
cat
io
ns
. On
the contorar
y a t
hird
harmo
ni
c injec
ti
on
pulse width
mod
ul
at
ion
(THIP
W
M
)
for
seve
n
le
ve
l
ha
s
bee
n
te
ste
d
and
fin
ds
ou
t
t
hat
TH
IPW
M
is
bette
r
tha
n
si
nu
s
oi
dal
pul
se
width
modu
la
ti
on
(
S
PWM)
.
TH
IPW
M
has
le
sse
r
har
m
onic
s
in
t
he
outp
ut
of
MLI
an
d
highest
ou
t
pu
t
powe
r
qual
it
y.
The
idea
pr
opose
d
in
[
8]
us
es
par
ti
cl
e
s
warm
opti
miza
ti
on
(
PSO)
to
fi
nd
out
th
e
opti
mal
switc
hing
an
gl
es
f
or
CHB
-
M
LI
.
F
r
om
t
his
stu
dy
it
is
con
cl
ud
e
d
that
opti
miza
tio
n
meth
ods
giv
e
m
uc
h
bette
r
resu
lt
s
t
han
S
PWM
.
Th
us
,
the
ne
w
scheme
propos
ed
a
fter
this
is
cal
le
d
the
sel
e
ct
ive
ha
rm
oni
el
imi
nation
pul
se
width
m
odul
at
ion
(S
H
EP
WM)
i
n w
hich
t
he
sel
e
ct
ed
ha
rm
onic
s
are mi
nimize
d usi
ng opti
miza
ti
on
met
hods
.
3.
E
F
FECT OF
LOAD V
A
RI
ATIO
N
I
N
H
ARMO
NI
CS
EL
IMINATI
ON
Harmo
nics
in
mu
lt
il
evel
in
ve
rters
pla
ys
a
sign
ific
a
nt
ro
l
e
in
e
ff
ic
ie
nc
y
a
nd
reli
abili
t
y
of
overall
sy
ste
m.
Most
i
mporta
nt
facto
rs
de
pe
nd
i
ng
on
t
he
harmo
ni
cs
are
due
to
non
-
li
near
it
y
of
loa
ds
,
i
n
-
e
ff
i
ci
ent
switc
hing
an
gl
es
f
or
i
nsula
te
d
gate
bi
-
pola
r
tra
ns
ist
or
s
(
I
GBT)
,
pulse
width
wavef
orm
for
ge
ner
at
i
ng
the
require
d
ou
t
put
and
va
riat
ion i
n
reacta
nce o
f
outp
ut
loa
d.
T
he
e
ff
ect
o
f
loa
d
var
ia
ti
on
in
ha
rm
on
ic
el
imi
na
ti
on
sect
ion
furthe
r
div
i
des
i
nto
four
s
ubsect
io
ns
,
sect
ion
on
e
desc
ribes
th
e
eff
ect
of
non
-
li
near
loa
ds
on
harmo
nics,
sec
ti
on
t
wo
br
ie
fl
y
e
xpla
in
t
he
impleme
ntati
on
of
real
-
ti
me
c
al
culat
ion
an
d
imple
mentat
ion
of
switc
hing
a
ngl
es
w
hile
hand
li
ng
t
he
IEEE
51
9
sta
nd
a
r
d
f
or
T
HD,
se
ct
ion
t
hr
ee
de
scri
bes
the
sel
ect
ive
harmo
nic
el
imi
nation
us
in
g
pulse
widt
h
m
odulati
on
te
c
hn
i
qu
e
wh
e
reas
la
st
sect
ion
desc
ribes
the
sig
nif
ic
ance
of sw
it
chi
ng a
ng
le
s
for ha
rm
on
ic
s
minimiz
a
ti
on
in
m
ulti
le
vel in
ver
te
r.
3.1.
Non
-
li
ne
ar
lo
ads
Loa
d
va
riat
ion
plays
a
sig
ni
ficant
r
ole
in
har
m
onic
s
ge
ner
at
io
n,
as
mentio
ned
i
n
[29],
onli
ne
el
imi
nation
of
harmo
nics
ha
s
been
done
usi
ng
modifie
d
PSO
wh
il
e
t
he
loa
d
va
ries
.
N
on
li
nea
rity
in
the
sy
ste
m
a
rises
wh
e
n
t
he
vo
lt
a
ge
a
pp
li
ed
acr
os
s
it
s
te
r
minal
s
has
cha
nged
.
Wh
e
n
t
he
lo
a
d
var
ie
s,
it
cha
nges
the
impeda
nce
that
e
nab
le
s
the
non
-
li
nea
rity
in
t
he
sy
ste
m
no
matt
er
it
is
c
onnected
to
a
pur
e
sin
usoidal
vo
lt
age
so
urce
[
49
]
.
T
hese
no
n
-
li
nea
riti
es
con
ta
ins
the
harmo
nics
that
relat
e
with
the
im
ped
a
nc
e
of
the
i
nv
e
r
te
r
and
the
gr
i
d
th
at
is
connecte
d
t
o
it
[
51].
U
nw
a
nte
d
ha
rm
on
ic
s
be
coming
the
ma
jor
issue
as
th
e
y
a
re
le
adi
ng
due
to
increme
nt
in
powe
r
qu
al
it
y
r
el
at
ed
issues.
Fifth
a
nd
se
ve
nth
harmo
nics
el
imi
nation
ha
s
bee
n
do
ne
in
[
52]
us
in
g
a
new
c
on
t
ro
l
strat
eg
y
in
the
outp
ut
volt
age
o
f
sta
tor.
N
on
-
li
ne
arit
y
i
n
l
oad
s
al
so
a
rises
w
he
n
a
n
inv
e
rter
is
c
on
nected
to
a
di
stribu
te
d
gri
d.
T
he
i
dea
pro
po
s
ed
in
[5
2
]
pro
vid
es
a
n
a
dd
it
io
nal
filt
ering
f
or
harmo
nics
in
non
-
li
near
loa
ds
.
T
his
i
dea
can
be
a
pp
li
ed
f
or
mu
lt
il
evel
in
ver
te
r
or
t
o
an
y
oth
e
r
re
ne
wab
le
energ
y
s
ources
.
Vali
datio
n
of
these
te
ch
ni
ques
are
done
by
impleme
nting
a
three
-
le
vel
ne
utral
po
i
nt
cl
ampe
d
inv
e
rter
t
hat
c
onnect
a
gr
i
d
ha
ving
a
no
n
-
li
nea
r
l
oad.
As
the
non
-
li
near
loa
ds
c
onti
nuously
ge
ner
at
es
harmo
nics
that
eff
ect
s
t
he
performa
nce
the
re
fore,
real
-
ti
me
harmo
nic
el
imi
nation
is
nece
s
sary
to
im
pro
ve
the
sy
ste
m
pe
rformance a
nd sta
bili
ty.
3.2.
Rea
l
-
time
As
descr
i
bed
in
the
ab
ove
se
ct
ion
,
ha
rm
on
i
cs
cha
ng
e
s
as
t
he
non
-
li
ne
arit
y
in
t
he
loa
d
e
xist.
S
uch
a
s
a
th
ree
-
phase
or
sin
gle
-
phas
e
m
otor
va
ries
it
s
pee
d
a
nd
r
eact
ance
with
resp
ect
to
a
lo
ad,
no
n
-
li
nea
ri
ty
i
n
a
sy
ste
m
e
xist
and
it
c
hanges
with
res
pect
to
ti
me.
Cl
os
ed
-
l
oop
dev
ic
es
c
ontr
ol
the
ha
rm
on
ic
s
mu
c
h
bet
te
r
than
op
e
n
as
me
ntion
e
d
i
n
[
5
3
].
M
od
ulati
on
i
ndex
de
pe
nd
e
nt
h
a
ving
cl
os
e
d
loop
c
on
t
ro
ll
ing
has
bee
n
done
f
or
CHB
m
ulti
le
vel
inv
e
rter.
PS
O
is
us
e
d
in
this
pa
pe
r
to
el
imi
nate
the
ha
rm
on
ic
s
by
ha
ving
the
m
odul
at
ion
ind
e
x
as
a
fee
db
ac
k
in
pu
t.
Wh
il
e
i
n
real
-
t
ime
scena
rio
not
on
l
y
the
non
-
li
nea
rity
e
ff
e
ct
s
the
harmo
ni
cs,
DC
input
vo
lt
age
a
lso
plays
a
si
gnific
ant
r
ole
on
t
he
sta
bili
ty
of
the
outp
ut
volt
age
of
a
n
i
nverter
.
T
his
issue
has
been
so
l
ved
by
[
5
4
]
to
main
ta
in
the
TH
D
for
5
th
,
7
th
,
9
th
,
and
11
th
orde
r
harmo
nics
in
seve
n
-
le
vel
i
nverter
.
Stat
e
ta
ble
has
been
ma
de
to
g
ener
at
e
t
he
opti
mu
m
switc
hi
ng
a
ngle
s
a
gain
with
t
he
help
of
a
micr
oc
on
tr
oller
.
Re
-
opti
miza
ti
on
h
as
bee
n
do
ne
in
this pa
per
for
12%
reduct
ion
in TH
D
du
rin
g
fa
ult scen
ario.
Ar
ti
fici
al
n
eu
ral
netw
orks
(AN
N)
a
re
al
s
o
use
d
f
or
re
al
-
ti
me
impleme
ntati
on
of
s
witc
h
in
g
a
ng
le
s
.
PS
O
an
d
ANN
both
ha
s
been
util
iz
ed
i
n
[5
5
]
to
fin
d
ou
t
t
he
best
s
ol
ution
set
f
or
the
known
in
put
vo
lt
a
ges
a
nd
unknow
n
s
witc
hin
g
ang
le
s
. T
he me
thod
pro
po
se
d i
n
[
5
5
] has
b
ee
n vali
dated
in MATL
AB/S
I
M
U
LI
NK.
3.3.
Sele
ctie h
arm
on
ic
eli
mi
nati
on
Thr
ough
S
HE
-
P
WM
met
hod
unwa
nted
ha
rm
on
ic
s
can
be
rem
oved
e
asi
ly
f
r
om
the
outp
ut
of
mu
lt
il
evel
in
ve
rter
[5
6
].
A
tra
ns
ce
nd
e
ntal
e
quat
ion
is
us
e
d
to
mi
nimize
th
e
switc
hi
ng
a
ngle
s
to
mi
nimi
ze
the
harmo
nics
fro
m
the
ou
t
pu
t
[
5
7
].
Howe
ve
r,
Sine
a
nd
Cosine
f
unct
ion
s
c
onta
ins
importa
nt
r
ole
s
an
d
conve
rg
e
nce
t
o
the
opti
mum
ex
planati
on
is
dif
ficult
to
at
ta
in.
To
disc
over
t
he
utmo
st
switc
hing
a
ng
le
s
t
o
minimi
ze
the
unwa
nted
harmo
nics,
div
er
s
e
mathemat
ic
a
l
mo
dels
ha
ve
been
pr
e
sente
d
li
ke
G
orb
ne
r
basis
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8
694
In
t J
P
ow
Ele
c
&
D
ri
S
ys
t,
V
ol
.
12
, N
o.
1
,
Ma
rch
20
21
:
228
–
240
234
theo
ry
a
nd
symmet
ric
poly
nomial
s.
A
s
the
se
mathemat
ic
al
mo
dels
c
ompu
te
init
ia
l
gu
e
sses,
s
om
et
ime
s
these
gu
e
sses
are
no
t
accuratel
y
nominate
d
that
su
r
ge
the
c
om
plexity
c
os
t.
High
-
le
vel
inve
rters
are
not
able
to
perform
mu
c
h
ef
fici
ently
us
in
g
these
mathemat
ic
al
methods
[24
]
-
[
26]
.
T
o
ove
rcome
these
issues
op
ti
miza
ti
on
methods
directl
y
us
in
g
A
rtific
ia
l
In
te
ll
igen
ce
te
ch
niques
has
bee
n
us
e
d.
T
he
main
point
of
util
iz
ing
these
al
gorithm
s
ar
e
they
are
no
t
wide
-
ra
ng
i
ng
an
d
no
t
de
pe
nd
s
on
earl
y
su
pp
os
it
ions
he
nce
decr
ease
s
co
m
pu
ta
ti
onal
co
st.
Furthe
rm
or
e
,
these
op
ti
miz
at
ion
met
hods
can
easi
ly
w
ork
on
l
ow
cost
DS
P
,
howe
ver
t
her
e
are
ma
ny
othe
r
proce
dures
in
w
hich
s
om
e
of
t
he
bi
o
-
in
s
pire
d
al
gorith
ms
are
P
SO,
GA,
bee
al
gorithm
(BA
)
a
nd
di
ff
e
ren
ti
al
ev
olu
ti
on
(
DE)
[
49
].
N
on
li
near
it
y
in
L
ow
or
der
har
m
onic
s
e
qu
at
io
ns
can
be
fou
nd
out
with
the
hel
p
of
ob
je
ct
ive
f
un
ct
io
ns
.
U
su
al
ly
r
es
earche
rs
us
e
diff
e
ren
t
obje
ct
ive
f
un
ct
io
ns
to
le
ssen
the
harmo
nics.
Di
ver
se
proce
dures
ha
ve
be
en
s
ugge
ste
d
to
cl
a
rify
the
ha
rm
on
ic
el
imi
nation
pro
blem.
The
wav
e
f
or
m
a
t t
he
outp
ut volt
ag
e of m
ulti
le
vel inv
e
rter
us
in
g Fo
ur
ie
r
ser
ie
s
in
S
HE
-
P
WM i
s g
i
ven by
(
6
)
.
(
)
=
0
2
+
∑
(
A
n
cos
2
+
s
in
2
)
=
1
(6
)
w
he
re
a
0
is
th
e
dc
facto
r,
V
n
cha
racteri
ze
s
odd
har
m
oni
cs
and
de
no
te
s
even
ha
rm
onic
s.
T
he
desi
gn
s
of
M
ulti
le
vel
volt
age
sour
ce
i
nverter
de
pe
nd
on
t
he
assem
bly
of
the
ou
t
pu
t
wav
e
f
or
m
,
i.e.,
sin
gle
switc
hi
ng
per
le
vel and
mu
lt
i swit
chi
ng p
e
r l
evel as s
how
n i
n
Fig
ure
4
.
Ca
te
go
r
y
-
a
wa
veform
giv
es
the
ou
t
pu
t
volt
age
bu
t
ha
ving
switc
hi
ng
fre
qu
e
nc
y
mi
nim
um
.
W
he
reas
cat
egory
-
b
use
s
high
switc
hi
ng
f
reque
ncy.
(s
-
1)
li
mit
s
th
e
low
orde
r
unwa
nted
ha
rm
on
ic
s
,
w
he
re
s
is
the
numb
e
r
of
DC
su
pply
t
hat
ar
e
the
input
sid
e
of
the
i
nv
e
rt
er
.
By
i
ncr
easi
ng
t
he
num
ber
of
le
vels
,
qua
li
ty
of
ou
t
pu
t
w
ave
for
m
al
s
o
i
ncr
ea
s
es.
B
ut
t
his
i
nc
reases
the
c
omplexit
y
a
nd
c
ost
of
the
s
ys
te
m
t
hat
tu
r
n
out
to
be
more
c
omplex
.
W
he
reas
in
c
at
egory
-
b
with
ou
t
inc
reasin
g
the
numb
e
r
of
le
vels
ca
n
gi
ve
t
he
bette
r
ou
tp
ut
without
incr
ea
sing
the
c
os
t
a
nd
c
omplexit
y
of
the
s
ys
te
m
[28].
Q
uar
te
r
sy
m
metri
cal
w
avefor
m
is
sho
wn
i
n
F
ig
ure
4
with
al
l
the
co
ns
e
quent
DC
sourc
es
in
t
his
way
eve
n
ha
rm
on
i
cs
bec
om
e
s
th
e
zer
o,
there
f
ore
the
equ
at
io
n f
or
t
he
typ
e
a
wav
e
f
orm ca
n be
give
n
as
.
(a)
(b)
Figure
4. Stai
r
case o
utput
vo
l
ta
ge
wa
ve
form
of se
ven
-
le
vel
M
ulti
le
vel
Inv
erter,
(
a)
sin
gle
sw
it
chi
ng p
e
r l
evel,
(
b) m
ulti
-
switc
hing
per le
vel
(
)
=
(
)
(7)
wh
e
re
V
n
is t
he
Fou
rier c
oeff
ic
ie
nt,
an
d
ca
n be a
rtic
ulate
d
a
s
(
8)
;
=
4
∑
(
)
=
1
(8)
w
he
re,
VD
C
:
is DC
vo
lt
age
,
i
:
is t
he vo
lt
age
so
urce a
nd
n
:
is t
he har
mon
ic
o
r
der
The
wav
e
f
or
m
in
F
ig
ure
4
de
scribes
t
hat
al
l
ang
le
s
sho
uld
be
l
ess
tha
n
90
degree
a
nd
m
us
t
be
i
n
a
n
ascen
ding
orde
r
as
mentio
ne
d i
n
(
9
)
.
1
<
2
<
3
<
4
<
5
<
90
0
(9)
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
ow Elec
& Dri S
ys
t
IS
S
N: 20
88
-
8
694
A Revi
ew
on h
ar
m
onic
s eli
mi
nia
ti
on in
re
al
ti
me
for c
as
c
aded
H
-
br
id
ge
…
(
Mu
ham
m
ad T
ayy
ab Y
aqoob
)
235
The
sel
ect
ive
harmo
nic
eq
ua
ti
on
s
to
el
imi
na
te
nth
orde
r
harmo
nics
can
be
f
ur
t
her
e
xpan
de
d
as
the
set
of
equ
at
io
n sh
ow
n
as
(10)
:
(
1
)
+
(
2
)
+
(
3
)
…
…
.
(
)
=
(
3
1
)
+
(
3
2
)
+
(
3
3
)
…
…
.
(
3
)
=
0
+
(
5
2
)
+
(
5
3
)
…
…
.
(
5
)
=
0
(10)
(
1
)
+
(
2
)
+
(
3
)
…
…
.
(
)
=
0
w
he
re n
is
the
n
umbe
r
of h
ar
monic order
a
nd M
is
the
m
od
ulati
on
in
dex
t
hat d
efin
es
t
he
pu
lse
wi
dth
rat
io o
f
the
switc
hing
wa
ve
form f
or
I
GBTS
of
t
he
in
ve
r
te
r.
3.4.
Sw
itchi
ng ang
le
s
Sw
it
chin
g
a
ng
le
s
plays
a
si
gn
i
ficant
r
ole
for
ge
ne
rati
ng
wav
e
f
or
m
f
or
I
GBT/M
OSFETs.
O
ptimal
cal
culat
ion
of
switc
hing
a
ng
l
es
reduces
t
he
harmo
nics
f
r
om
the
outp
ut
of
m
ulti
le
vel
inv
e
rter
[
29].
Sele
ct
ed
lowe
r
or
der
ha
rm
on
ic
s
a
re
el
imi
nated
i
n
[
29]
a
nd
th
e
o
ve
rall
total
harm
on
ic
disto
rtion
(T
HD)
is
reduced
b
y
cal
culat
ing
t
he
opti
mal
switc
hing
a
ng
le
s
.
A
lso,
t
he
s
udde
n
cha
ng
e
s
in
th
e
ha
rm
on
ic
s
a
r
e
minimi
ze
d
in
[29
]
by
getti
ng
the
opti
mu
m
s
witc
hing
a
ngle
s
f
r
om
the
lo
okup
ta
bl
es.
T
o
im
pro
ve
the
onli
ne
a
pp
li
cat
ion
of
t
his
sin
gle
-
ph
a
se
m
ulti
le
vel
inv
erte
r,
a
ut
hor
has
pr
e
-
cal
culat
ed
the
swi
tc
hin
g
an
gles
a
t
varyin
g
m
od
ulati
on
i
nd
e
xes
from
0
to
1.
5
th
,
7
th
a
nd
11
th
order
ha
rm
on
ic
s
are
re
du
ce
d
by
[
30]
in
th
ree
phase
hybri
d
casca
de
d
mu
lt
il
evel
i
nverter
.
These
ha
rm
on
i
cs
h
as
bee
n
re
du
ce
d
by
fin
din
g
the
opti
mal
switc
hi
ng
an
gles
us
in
g
m
odifie
d
pa
rtic
le
swa
r
m
op
ti
miza
ti
on
(
M
PS
O
)
met
ho
d.
Ha
rm
on
ic
s
a
re
al
s
o
mi
nimi
zed
i
n
[5
8
]
by
fin
ding
op
ti
ma
l
switc
hing
an
gl
es
us
i
ng
PSO
a
nd
G
A,
in
w
hich
P
S
O
is
f
ound
be
tt
er
than
GA.
Hardwa
re
a
nd
simulat
ion
a
na
lysis
has
bee
n
do
ne
to
com
par
e
both
resu
lt
s.
Deter
minati
on
of
s
witc
hing
a
ng
le
s
has
al
so
do
ne
in
[
59
]
with
the
hel
p
of
PSO
f
or
harmo
nics
min
imi
zat
ion
in
th
ree
phase
five
le
vel
mu
lt
il
eve
l
inv
erter
by
s
olv
in
g
the
t
ransce
ndental
eq
ua
ti
on
s.
Anothe
r
c
omp
ariso
n
of th
ree
op
ti
miza
ti
on m
et
hods
li
ke [5
8
]
has
b
ee
n don
e for
sel
ect
ive
harmo
nic mini
miza
ti
on
in
[5
6
]
.
I
n
t
his
pa
pe
r
c
ompa
rison
of
new
t
on
raphs
on
(N
R
),
PSO
a
nd
GA
has
bee
n
do
ne
and
P
SO
fou
nd
bette
r
than
the
oth
er
tw
o
al
gorith
ms.
Ha
rm
on
ic
s
el
imi
nat
io
n
is
not
only
do
ne
i
n
m
ulti
le
vel
inve
rter
,
it
has
al
s
o
el
imi
nated
in
[
59
]
t
hroug
h
m
odular
m
ulti
lev
el
in
ver
te
r
us
ing
sta
ir
-
case
modu
la
ti
on
str
at
egy
with
t
he
help
o
f
PSO.
S
witc
hing
losse
s
an
d
th
e
stress o
n
de
vi
ce
has
al
so
r
e
du
ce
d
i
n
this p
aper
f
or h
ig
h
-
pow
e
r
e
nergy
c
onve
rsion
app
li
cat
io
ns
by
re
duci
ng
dv
/
dt
losses
.
F
rom
f
ig
ure
4
pul
ses
of
s
witc
hing
pa
tt
ern
ca
n
be
visu
al
iz
ed.
Sw
it
ch
s
1
and
s2
will
w
ork
f
or
t
he
sec
ond
hal
f
c
ycle
wh
e
re
as
s5
an
d
s
6
a
re
s
witc
hed
on
for
pos
it
ive
half
c
ycle
rest
al
l
switc
hes
are
h
igh
an
d
l
ow
f
or
a
ce
rtai
n
ti
me
per
io
d
to
make
a
near
l
y
sin
usoidal
wa
ve
f
orm
at
the
ou
t
pu
t
as
sh
ow
n
in
F
ig
ure
5.
Figure
5
.
S
witc
hing
pu
lse
s
of
sta
ir
-
case m
ulti
le
vel inverte
r
[5
6
]
4.
PAR
TI
CLE S
WA
RM OPTI
MIZATI
ON (
PSO)
This
sect
io
n
pro
vid
es
t
he
br
ie
f
over
view
of
mu
lt
il
evel
inv
e
rter
e
ff
ic
ie
ncy
a
nd
it
s
re
li
abili
ty
by
reducin
g
the
harmo
nics
us
i
ng
op
ti
miza
ti
on
al
gorithm
P
SO
.
Fi
rin
g
a
ngle
s
or
s
witc
hing
a
ngle
s
f
or
the
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8
694
In
t J
P
ow
Ele
c
&
D
ri
S
ys
t,
V
ol
.
12
, N
o.
1
,
Ma
rch
20
21
:
228
–
240
236
IG
BTS/
MOSF
ETS
pla
ys
a
n
i
mporta
nt
ro
le
to
ge
ner
at
e
the
near
l
y
si
nuso
i
da
l
outp
ut
wa
ve
form
at
t
he
outpu
t
of
a
mu
lt
il
evel
in
ver
te
r
.
T
he
s
wi
tc
hin
g
losses
a
re
al
so
de
pe
ndent
on
t
he
fi
rin
g
a
ng
le
s.
T
hes
e
firin
g
a
ngle
s
can
be
cal
culat
ed
usi
ng
mat
hemati
ca
l
te
chn
iq
ues
or
bio
-
ins
pire
d
i
ntell
igent
al
go
rithms.
O
ptimi
zat
ion
met
h
od
s
li
ke
PSO
ha
s
been
mo
st
widel
y
use
d
al
gorithm
for
mi
nimizi
ng
the
harmo
nics
in
mu
lt
il
evel
i
nv
e
rter.
H
arm
on
ic
s
al
so
ge
ner
at
e
d
du
e
t
o
no
n
-
li
ne
arit
y
in
the
lo
ad.
T
his
no
n
-
li
near
it
y
is
beca
us
e
of
the
reac
ti
ve
and
var
ia
ti
on
i
n
the
loa
d.
U
nc
ontr
ollable
an
d
non
-
li
near
loa
d
pro
duces
t
he
harmo
nics
t
hat
eff
e
ct
s
the
in
ve
rter
sta
bili
ty
a
nd
it
s
eff
ic
ie
nc
y.
Harmo
nics
pro
duc
es
by
t
he
loa
d
can
be
reduce
d
by
re
-
opti
mizi
ng
t
he
switc
hi
ng
a
ngle
s.
Re
a
l
-
ti
me
cal
culat
ion
of
switc
hing
a
ng
l
es
bec
om
es
ne
cessar
y
to
inc
r
ease
the
in
v
ert
er
ef
fici
ency
a
nd
it
s
reli
abili
ty.
As
the
c
ompu
ta
ti
on
ti
me
of
P
S
O
is
muc
h
hi
gher
,
the
refo
re
sch
olars
ha
ve
pr
e
-
sto
red
the
values
of
swit
chin
g
ang
le
s
at
va
rio
us
m
odulati
on ind
e
xes
i
n
lo
ok
-
up
ta
bles.
T
he
ps
e
udo
c
ode
of
PS
O
ca
n
be
s
how
n
i
n
Fi
gure
6.
I
ts
com
p
utati
onal
ti
me
dep
e
nd
s
on
t
he
num
be
r
of
it
erati
ons
and
s
earc
h
sp
ace
li
ke
in
the
init
ia
l
sta
ge
this
al
gorithm
init
ia
li
zes
it
s
acce
le
rati
on
pa
rame
te
rs
c
1,
c
2
an
d
W
max
a
nd
W
min.
The
m
ov
ement
of
a
pa
r
ti
cl
e
is
cal
culat
ed by
(
11
)
.
̈
+
1
=
̈
+
1
+
[
1
1
̈
(
−
̈
)
]
+
[
2
2
̈
(
−
̈
)
]
(11)
̈
+
1
=
̈
+
̈
+
1
(12)
w
he
re,
+
1
is t
he
inerti
a
weig
ht a
nd it
is g
i
ven by
(13)
:
+
1
=
−
[
m
ax
−
m
in
]
(13)
The
pa
rtic
le
w
hich
fi
nd
s
the
best
posit
ion
a
s
co
mpa
re
d
t
o
ot
her
s
per
s
on
al
best
after
updatin
g
the
po
sit
io
n
a
nd
ve
locit
y,
that
pa
rtic
le
will
store
it
s
posit
ion
a
t
PBest
.
The
updatin
g
proces
s
will
co
ntin
ue
unti
l
the
pa
rtic
le
s
reaches
at
the
end
point
of
the
it
erati
on.
I
n
[
6
1
]
P
SO
al
gorithm
is
pro
po
s
ed
for
ha
r
monic
el
imi
nation
in
mu
lt
il
evel
inv
e
rters
us
in
g
the
ob
je
ct
ive
fun
ct
ion
gi
ve
n
in
(14).
T
he
met
hod
pro
po
se
d
in
this
pap
e
r
is
usual
l
y
use
d
for
la
r
ge
var
ia
ble
fr
e
quenc
y
dr
i
ves
(
VFDs)
,
uninte
r
up
ta
ble
powe
r
su
p
plie
s
(
UPS)
and
gr
i
d
co
nn
e
ct
ed
ren
e
wab
le
e
ne
rgy
s
ys
te
m.
M
et
ho
d
pro
po
sed
in
[
5
0
]
ma
inly
f
ocuses
on
co
mputat
iona
l
ti
me
and
re
qu
ire
le
ss
ti
me
to
reac
h
to
global
mi
nimu
m
.
Same
ob
je
ct
ive
functi
on
w
hich
is
us
e
d
in
[6
1
]
,
is
uti
li
zed
by
[
6
1
]
to
re
du
ce
the
ha
rm
onic
s
usi
ng
mod
ul
ar
m
ulti
le
vel
conve
rter.
I
n
[
6
1
]
mod
ular
m
ulti
le
vel
co
nve
rter
is
pro
po
se
d
f
or
hi
gh
po
wer
ap
pl
ic
at
ion
s
a
nd
m
ai
nly
fo
c
us
es
on
el
imi
natin
g
the
harmo
nics
with
uneq
ual
i
nput
of
DC
s
ources.
T
he
te
ch
ni
qu
e
presente
d
i
n
this
pa
per
is
al
so
a
ble
to
simpl
if
y
the
s
witc
hing
ang
le
s
with
the
help
of
a
ng
le
r
otati
on
sche
me.
T
he
init
ia
l
values
of
par
ti
cl
es
to
s
olv
e
the
set
of
non
-
li
near
tra
nsc
en
den
ta
l
e
qu
at
ion
s
is cal
culat
ed b
y
new
t
on r
a
phs
on
s
(
NR)
meth
od. Fur
t
her the
sw
it
chi
ng angl
es h
as
b
ee
n o
ptimi
zed by PS
O
.
(
1
,
2
,
3
)
=
[
=
1
1
cos
(
−
)
]
2
+
[
=
1
2
c
o
s
(
3
−
)
]
2
+
⋯
+
[
=
1
cos
(
(
2
−
1
)
)
]
2
(14)
Total
ha
rm
on
i
c
disto
rtion
is
the
sig
nificant
con
ce
r
n
f
or
th
e
sch
olars,
the
refor
e
t
he
for
mu
la
of
TH
D
has
bee
n
util
iz
ed
by
resea
rchers
a
s
a
n
obje
c
ti
ve
f
unct
ion
i
n
[
5
2
].
Ha
rm
onic
s
orde
r
nu
mb
e
r
5
th
,
7
th
,
11
th
a
nd
13
th
a
re
bei
ng
el
imi
nated
in
[
50
]
.
T
he
an
gles
cal
culat
e
d
f
rom
the
ob
je
ct
ive
functi
on
gi
ven
in
(
15
)
a
re
impleme
nted
i
n
mic
ro
c
ontr
oller
f
or
ex
per
i
m
ental
an
d
valid
at
ion
pur
po
se
s.
Same
obje
ct
iv
e
f
un
ct
io
n
has
been
us
e
d
in
[
5
1
]
to
furthe
r
mi
nim
iz
e
the
ha
rm
onic
on
dif
fer
e
nt
load
c
onditi
on
s.
T
he
te
ch
nique
pr
ese
nted
i
n
[10
3]
has
bee
n
st
or
e
in
look
up
ta
ble
wh
ic
h
ma
kes
it
po
ssi
ble
for
r
eal
ti
me
har
m
onic
minimi
zat
ion.
O
utco
me
of
thi
s
pap
e
r has
bee
n vali
date
d via s
imulat
ion
s
and
experime
nts.
=
[
1
1
2
(
)
2
]
1
2
×
100
(15)
=
|
3
⋅
28
−
1
|
4
+
|
5
|
2
+
|
7
|
2
(16)
In
[6
2
]
a
detai
le
d
co
mp
a
rati
ve
study
of
Ne
wton
Ra
phs
on
method,
Ge
ne
ti
c
Algortihm
and
PS
O
has
been
donde
for
harmo
nic
min
imi
zat
ion
in
m
ulti
le
vel
inv
ert
er.
A
s
Sele
ct
iv
e
harmo
nic
ha
r
monic
el
imi
nation
is
consi
der
e
d
as
a
low
s
witc
hing
f
reque
ncy
m
et
hod.
P
SO
is
f
ound
m
uch
bet
te
r
in
[
6
2
]
by
ut
il
iz
ing
the
ob
j
ect
ive
f
u
n
c
t
i
o
n
g
i
v
e
n
i
n
(
16
)
.
S
a
m
e
o
b
j
e
c
t
i
v
e
f
u
n
c
t
i
o
n
w
i
t
h
s
o
m
e
m
o
d
i
f
i
c
a
t
i
o
n
s
i
n
m
o
d
u
l
a
t
i
o
n
i
n
d
e
x
i
s
util
iz
ed
by
[
59
]
for
volt
age
ha
r
monic
el
imi
nat
ion
an
d
a
c
om
bin
at
io
n
of
PS
O
with
mes
h
a
dap
ti
ve
direct
search
te
c
hn
i
que
has
been
impleme
nted
i
n
this
pa
per
t
o
f
urt
her
imp
rove
the
co
nv
e
r
gan
ce
rate
of
the
pro
po
s
ed
al
gorith
m.
I
n
thi
s
pap
e
r
th
ree
ph
ase
se
ve
n
le
ve
l
CHB
is
sim
ul
at
ed
in
M
A
T
LAB
/S
I
M
U
LI
NK
a
nd
e
xperi
mental
a
nalysi
s
has
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
ow Elec
& Dri S
ys
t
IS
S
N: 20
88
-
8
694
A Revi
ew
on h
ar
m
onic
s eli
mi
nia
ti
on in
re
al
ti
me
for c
as
c
aded
H
-
br
id
ge
…
(
Mu
ham
m
ad T
ayy
ab Y
aqoob
)
237
been
done
us
i
ng
micr
oc
on
t
r
oller
AT
90
C
A
N12
8
with
c
ombinati
on
of
Alte
ra’
s
Cycl
on
e
I
I
FP
GA.
The
pro
po
se
d
te
c
hniqu
e i
n [
59
]
ass
um
es
that the
DC in
put so
urc
e is same t
hro
ugho
ut the e
xpe
riment.
Particle
Swa
rm Op
tim
izatio
n
1.
Ob
jectiv
e f
u
n
ctio
n
(
)
2.
Initialize p
ar
am
et
e
rs
1
,
2
,
,
,
an
d
po
p
u
lat
io
n
3.
Gen
erate
an
initial
p
o
p
u
latio
n
of particles
4.
Evalu
ate the fitnes
s o
f
each p
arti
cle a
n
d
set all
in
itial po
sitio
n
s as
5.
while
(
<
)
o
r
(
!
)
6.
select th
e Gbest
pa
rticle
in
sw
ar
m
,
w
h
ich
has
the m
in
im
u
m
f
itn
ess
valu
e
7.
fo
r
=
1
:
8.
Calcu
late the v
elo
c
ity
of particle
9.
Up
d
ate the po
sitio
n
of partice
10.
end
for
11.
for
=
1
:
12.
ev
alu
ate the fitness
of up
d
ated
particl
e
13.
if
(
)
<
(
)
,
14.
th
en
set curre
n
t po
sitio
n
as
15.
end
if
16.
end
for
17.
find
the b
est p
artic
le.
18.
end whil
e
Figure
6. Pse
udoc
ode
of PS
O
[
50
]
5.
CONCL
US
I
O
N
Eff
ic
ie
nc
y
a
nd
reli
abili
ty
are
the
main
c
onc
ern
s
sp
eci
al
ly
for
m
ulti
le
vel
inv
e
rters.
Ha
r
monic
at
the
ou
t
pu
t
of
m
ulti
le
vel
in
ver
te
r
plays
a
n
im
por
ta
nt
r
ole
for
it
s
reli
abili
ty
a
nd
ef
ficei
enc
y.
U
nw
a
nted
harm
on
ic
s
that
are
genera
te
d
due
t
o
une
f
fici
ent
switc
hi
ng
an
gles
a
nd
nonlinea
rity
in
loads
are
t
he
main
c
on
ce
r
n
f
or
t
he
sch
olars.
T
his
study
bri
efly
e
xp
la
in
s
the
be
st
cat
egor
y
of
mu
lt
il
evel
in
ve
rter
by
te
ll
ing
the
a
dvanta
ge
s
an
d
disad
va
ntages
o
f
eac
h
cat
e
gor
y.
A
s
c
ompa
re
d
t
o
NP
C
a
nd FC,
C
HB
is
m
or
e
reli
a
ble
a
n
d
e
ff
e
ct
ive d
esi
gn
as
it
al
so
c
onsist
s
of
le
sse
r
num
be
r
of
c
ompone
nt
s.
F
or
s
witc
hi
ng
a
ng
le
s
mi
nimiza
ti
on
,
S
HE
PWM
is
e
ff
ect
ive
for
harmo
nic
el
imi
nation.
The
s
et
of
non
-
li
ne
ar
eq
uatio
ns
f
ormed
by
S
H
EPW
M
ca
n
be
easi
ly
so
lve
d
b
y
op
ti
miza
ti
on
method
li
ke
P
SO
.
T
his
pa
pe
r
c
on
cl
ud
e
s
th
at
for
harmo
ni
c
el
imi
nation
in
m
ulti
le
vel
in
ver
te
r
,
CHB
te
chn
i
que
is
bette
r
than
NP
C
an
d
FC
,
for
switc
hing
pur
po
ses
t
he
S
HEPW
M
te
ch
nique
is
bette
r
and
t
o
so
lve
t
he
set
of
nonlinea
r
t
ran
sce
ndental
equ
at
io
ns,
PS
O
gi
ves
prom
isi
ng
re
su
lt
.
T
he
m
ulti
ple
obje
ct
ive
functi
ons that
has
rece
ntly
use
d
by
oth
e
r
sch
olars has
been
discusse
d
a
nd it
s ad
va
ntages h
as b
ee
n
prese
nted
i
n
this
pa
per.
W
hi
le
fo
r
real
ti
me
app
li
cat
io
ns
i
t
can
be
c
oncl
uded
from
ot
her
pap
e
rs
t
hat
the
op
ti
m
um
s
witc
hing
ang
le
s
that
has been
calc
ulate
d
ca
n be st
or
e
d i
n
a l
ook
-
up ta
ble for
b
et
te
r
harm
on
ic
minim
iz
at
ion
.
REFERE
NCE
S
[1]
Strasser
T
.
,
et
al.
,
“
A
r
evi
ew
of
a
rch
itect
ur
es
and
conc
ep
ts
for
in
telli
gen
ce
in
fu
tur
e
el
e
ct
r
ic
en
erg
y
sys
te
ms,
”
IEEE
Tr
ansacti
ons on Indus
trial
E
le
c
tronic
s
,
vo
l.
62
,
n
o.
4
,
pp
.
2424
-
24
38
,
2015
.
[2]
Kama
l
W
.
A.
,
“
Improv
ing
e
ner
gy
ef
ficien
c
y
-
the
cost
-
eff
ective
way
to
m
it
igate
global
warm
ing,”
Ener
gy
Conve
rs
ion
and
Manage
ment
,
vo
l.
38
,
no
.
1
,
pp
.
3
9
-
59
,
1997
.
[3]
Demi
rba
s
M
.
F
.
,
Ba
la
t
M
.
,
“
R
ec
en
t
adva
n
ce
s
on
th
e
produc
tion
and
u
ti
l
ization
tr
ends
of
b
i
ofue
ls:
a
glob
al
per
spec
t
ive,”
En
ergy
Conv
ersion
and
Manag
eme
nt
,
vo
l. 47, no. 1
5
-
16,
pp
.
2371
-
23
81
,
2006
.
[4]
Yuks
el
I
.
,
Kay
gusuz
K.
,
“
Ren
ewa
ble
en
erg
y
source
s
for
cl
e
an
and
sus
ta
i
n
a
ble
ene
rgy
policie
s
in
Tu
rke
y,
”
Re
newab
le
and
Sustainabl
e
Ener
gy
Revi
ews
,
vol
.
15
,
no
.
8
,
pp
.
4
132
-
41
44
,
2011
.
[5]
AbuBakr
S
.
,
Ba
haj
A
.
S.
,
“
Gen
era
t
ing
elec
tri
c
ity
from
the
o
cea
ns,”
Re
n
ewable
and
Sustainabl
e
Ene
rgy
R
evie
w
s
,
vol.
15
,
no
.
7
,
pp
.
3399
-
3
416
,
20
11
.
[6]
Kouro
S,
M
al
i
nows
ki
M.
,
“
R
ec
en
t
adva
n
ce
s
and
industrial
appl
i
c
ations
of
mul
tilev
el
co
nver
te
rs,
”
IE
EE
Tr
ansacti
ons on Indus
trial
E
le
c
tronic
s
,
vo
l. 57, n
o.
8
,
pp
.
2553
-
25
80
,
2010
.
[7]
Mali
nows
ki
M
.
,
Gopakuma
r
K
.
,
Rodriguez
J
.
,
P
ere
z
M
.
A.
,
“
A
survey
on
c
asc
a
ded
mu
lt
i
le
ve
l
i
nver
te
r
s,
”
I
EEE
Tr
ansacti
ons on Indus
trial
E
le
c
tronic
s
,
vo
l. 57, n
o.
7
,
pp
.
2197
-
2
206
,
2010
.
[8]
Rodrígue
z
J
.
,
L
a
i
J
.
S
.
,
Peng
F
.
Z.
,
“
Mult
il
ev
el
i
nver
te
rs:
a
surve
y
of
topol
og
i
es,
cont
rols,
and
ap
pli
c
at
ions
IE
EE
Tr
ansacti
ons on Indus
trial
E
le
c
tronic
s
,
vo
l. 49, n
o.
4
,
pp
.
724
-
7
38
,
2002
.
[9]
Rodrígue
z
J
.
,
e
t
al
.
,
“
Mult
ilevel
volt
ag
e
-
source
-
conve
rt
er
topol
o
gie
s
for
industrial
m
edi
um
-
vo
lt
a
ge
drive
s,
”
IE
E
E
Tra
nsac
ti
ons on
Industria
l
Elec
tr
onic
s
,
vo
l. 54, n
o.
6
,
pp
.
2930
-
29
45
,
2007
.
[10]
Cola
k
I
.
,
Kab
alc
i
E
.
,
B
ayi
ndir
R.
,
“
R
evi
ew
of
mu
lt
ilevel
voltage
source
i
nver
t
er
to
pologi
es
and
co
ntrol
sche
me
s,
”
Ene
rgy
Con
ve
rs
i
on
and
Manag
e
ment
,
vo
l. 52, no
.
2
,
pp
.
1114
-
11
28
,
2011
.
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