Int
ern
at
i
onal
Journ
al of
P
ower E
le
ctr
on
i
cs a
n
d
Drive
S
ystem
(I
J
PE
D
S
)
Vo
l.
11
,
N
o.
4
,
Decem
be
r 202
0
, p
p.
1826
~
18
34
IS
S
N:
20
88
-
8694
,
DOI: 10
.11
591/
ij
peds
.
v11.i
4
.
pp18
26
-
18
34
1826
Journ
al h
om
e
page
:
http:
//
ij
pe
ds
.i
aescore.c
om
Inducti
on dri
ve syst
em with
DSTA
TCOM
based as
ymmetri
c
twin co
nvert
er
P A
n
ush
a, B
V Raja
nn
a
Depa
rtment
o
f
E
le
c
tri
c
al a
nd
Ele
ct
roni
cs
Engi
n
eering,
Na
la
nd
a
In
stit
ute of Engin
e
eri
ng
and Te
chn
ology,
Ind
ia
Art
ic
le
In
f
o
ABSTR
A
CT
Art
ic
le
history:
Re
cei
ved
Oct
29
, 201
9
Re
vised
A
pr
2
6
, 2
0
20
Accepte
d
J
ul
10
, 2
0
20
High
power
d
e
ma
nds
are
usu
al
ly
m
et
by
a
dvanc
ed
power
e
lectr
oni
cs
conve
rt
ers
in
seve
ral
large
uti
lity
and
e
lectr
i
c
driv
es
a
ppli
c
at
ions.
Applic
a
ti
ons
fro
m
high
power
d
rive
s
commonly
uses
soluti
on
b
ase
d
multi
pulse
and
mu
lt
i
l
eve
l
conv
ert
e
rs.
A
com
mon
DC
l
ink
with
a
tl
e
ast
one
vol
ta
g
e
source
conve
rt
er
(VS
C)
wor
king
with
a
lmos
t
funda
m
enta
l
sw
it
ch
ing
fre
quenc
y
are
us
ed
in
conve
r
te
rs
of
mu
lt
ipu
lse
ty
pe,
and
e
ac
h
ou
t
put
modul
e
is
conn
ecte
d
wit
h
th
e
multipul
se
tr
ansforme
r
in
serie
s.
Wh
en
co
mpa
red
to
tha
t
of
solut
io
n
with
sing
le
-
VS
C,
Sever
al
VS
Cs
gene
rat
in
g
diffe
r
ent
tri
gger
ing
pulse
s
are
adj
used
in
orde
r
to
a
chi
ev
e
cur
r
ent
inj
e
cte
d
with
low
spec
ified
to
ta
l
h
arm
oni
c
distor
tion
(
THD
)
with
l
oss
es
of
abr
idged
sw
it
chi
ng
.
Huge
struc
ture
in
com
p
le
x
it
y
and
exp
ensiv
e
cost
expe
ndi
ture
o
f
the
mul
ti
pu
lse
tra
ns
forme
r
is
the
m
aj
or
limit
at
ion
o
f
th
is
sche
me.
DC
li
nk
spl
i
t
ca
pa
ci
tors
in
a
ddit
ion
ar
e
eli
mi
nated
by
mo
difyi
ng
the
top
ology
of
the
ci
rcu
it
.
Thus,
the i
ndepe
nd
ent
v
ol
ta
ges
of the
DC
ca
pa
ci
tor
ar
e
co
ntrol
le
d
and
dec
re
ase
d
in
n
u
mbe
r
and
th
e
flo
w
of
thi
rd
h
arm
o
nic
cur
r
ent
co
mp
onent
in
th
e
tra
nsformer
is
el
iminated.
Th
e
sche
m
e
of
th
e
design
ed
co
ntrol
ler
is
depe
nding
on
th
e
der
iv
ed ma
th
e
ma
tica
l
sys
te
m mode
l
.
Simul
ai
o
n
observa
ti
on
is
used
to
check
the
sche
me
p
er
forma
nc
e
and
ef
fic
i
en
cy
in
a
de
ta
iled
way
with
driv
e cont
r
ol
t
ec
hniqu
e.
Ke
yw
or
d
s
:
Com
pen
sat
or of stat
ic
type
Converte
r of
volt
age s
ource
Ind
uction m
otor
dr
ive
Inver
te
r of
H
-
bri
dge ty
pe
Inver
te
rs of ca
scade
d
ty
pe
Pu
lse
widt
h
m
odulati
on
met
hod
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
:
B V
Ra
ja
nna,
Dep
a
rtme
nt of
Ele
ct
rical
an
d
Ele
ct
ro
nics
E
nginee
rin
g,
Nalan
da Ins
ti
tu
te
o
f
En
gin
e
eri
ng and
Tech
no
logy,
Satt
enap
al
li
, G
un
t
ur
-
52
2438, An
dhra
Pr
a
des
h,
I
nd
ia
.
Emai
l:
r
aj
an
na
bv@
ng
i.ac
.in
1.
INTROD
U
CTION
In
te
rc
onnecti
on
of
ma
ny
sta
t
ion
s
an
d
cent
r
es
of
l
oa
ds
i
n
con
te
m
pora
ry
powe
r
s
ys
te
ms
are
do
ne
by
the
power
networks
of
exte
nded
tra
ns
missi
on
a
nd
distri
buti
on
w
hich
a
re
com
plex
in
nat
ur
e
.
Re
li
abilt
y
of
th
e
powe
r
qual
it
y
need
not
to
be
al
wa
ys
bet
te
r
eve
n
if
t
he
reli
abili
ty
of
gen
e
rati
on
of
power
is
good
[
1].
Custome
rs
sho
uld
get
t
he
e
ne
rgy
flo
w
with
un
i
nterru
ptio
n
with
a
fi
ne
le
ve
l
of
sin
usoida
l
volt
age
mag
ni
tud
e
and
freq
ue
ncy
pro
vid
e
d
by
t
he
distrib
utio
n
s
ys
te
m
of
powe
r.
M
an
y
l
oad
s
in
the
power
di
stribu
ti
on
s
ys
t
ems
wh
ic
h
are
part
ic
ularly
no
n
-
l
inear
will
co
nsi
der
a
bly
af
fec
t
the
power
qual
it
y
[2].
T
he
Power
Ele
ct
ronics
dev
ic
es
e
ployi
ng
te
c
hniq
ues
of
quic
k
c
on
trolle
d
force
c
om
m
utati
on
ar
e
more
use
f
ul
and
ef
fecti
ve
and
mit
igati
on
of
unfa
vourable
im
pacts
on
t
he
P
Q
i
n
powe
r
in
du
st
ries
durin
g
the
past
few
de
cades
we
re
a
vo
i
ded
by
c
onve
ntional
mea
ns
[
3]
.
Co
mp
e
ns
at
or
s
in
P
Q
are
cl
assifi
ed
mainly
into
tw
o
typ
es
.
Pr
e
ven
t
ion
o
f
harmo
nics
is
done
e
ff
e
ct
ive
ly
by
t
he
firs
t
typ
e
w
hich
is
the
shu
nt
co
nn
ect
e
d
c
ompen
sat
ion
dev
ic
e.
The
disto
rted
vo
lt
age
s
a
nd
volt
age
sa
gs
at
the
s
ys
te
m
si
de
cause
d
by
th
e
fa
ults
in
the
powe
r
tra
nsm
issi
on
sy
ste
m
a
re
co
r
rected
by
t
he
s
econd
ty
pe
whic
h
is
the
serie
s
co
nn
ect
e
d
de
vice,
w
hich
ha
s
an
e
dg
e
over
the
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
Ind
uction drive
system wi
th
DSTATC
OM b
ase
d asy
mm
et
ric
tw
in convert
er
(P
A
nusha
)
1827
sh
unt
ty
pe
[
4],
these
qual
it
ie
s
in
qu
al
it
y
of
powe
r
mig
ht
le
ad
t
o
irre
gula
r
operati
ons
of
a
meniti
es
or
e
ve
n
the
dev
ic
es
with
protect
io
n
a
re
tr
ipp
e
d.
Ge
ne
rati
on
or
A
bsor
pt
ion
of
Re
act
iv
e
P
ow
e
r
Co
ntr
ol
is
do
ne
by
t
he
us
e
of
c
onver
te
rs
employin
g
te
c
hnolog
y
of
F
ACTS
de
vice
wh
ic
h
is
li
nke
d
i
n
pa
rall
el
t
o
t
he
sy
ste
m
of
power
known
a
s
sta
ti
c
synch
ron
ous
com
pensat
or
(S
T
ATCO
M)
[5
-
7].
In
je
ct
io
n
of
Re
act
ive
powe
r
to
the
powe
r
sy
ste
m
m
akes
the
ST
ATCO
M
works
in
th
e
capaci
ti
ve
m
od
e
.
A
co
mm
on
DC
li
nk
with
at
le
ast
on
e
volt
ag
e
so
urce
c
onve
rter
(
VS
C)
w
orkin
g
wit
h
al
m
os
t
f
unda
ment
al
switc
hing
f
r
equ
e
nc
y
are
use
d
in
c
onve
rt
ers
of
mu
lt
ipu
lse
ty
pe
,
a
nd
eac
h
outp
ut
m
odule
is
co
nn
ect
e
d
with
t
he
mu
lt
ipu
lse
tra
ns
f
ormer
i
n
series
[8
-
10
]
.
Wh
e
n
c
ompa
re
d
to
that
of
so
l
ution
with
sin
gl
e
-
VS
C,
Se
veral
VS
Cs
ge
nerat
ing
diff
e
re
nt
trigg
e
rin
g
pu
ls
es
are
adjuse
d
i
n
orde
r
to
ac
hieve
cu
rr
e
nt
injec
te
d
with
l
ow
s
pecified
TH
D
(tota
l
harmo
nic
dist
or
ti
on)
with
l
osse
s
of
abr
i
dg
e
d
swit
chin
g.
H
uge
structu
re
i
n
c
omplexit
y
an
d
ex
pe
ns
ive
c
os
t
e
xp
e
ndit
ure
of
th
e
m
ul
ti
pu
lse
trans
forme
r
is t
he
maj
or li
mit
at
ion
of this sc
he
me
[11
-
1
4
].
In
ca
se
of
ST
ATCO
M
with
a
mu
lt
il
evel
co
nv
e
rter,
the
re
i
s
no
s
ource
of
powe
r
or
a
ny
c
ircuit
in
DC
floati
ng
capaci
tor
du
e
t
o
gal
va
nical
isolat
ion
an
d
s
houl
d
be
co
nnect
ed
with
each
of
the
casca
ded
H
-
bri
dge
conve
rters
[1
5
].
I
n
dio
de
cl
a
mp
e
d
to
polo
gy
the
re
are
ei
gh
te
e
n
s
witc
he
s
co
ntro
ll
e
d
w
it
h
diodes
wh
i
ch
are
antiparall
el
in
add
it
io
n
with
e
igh
te
en
diodes
w
hich
le
ads
t
o
a
great
er
nu
mb
e
r
of
c
omp
on
e
nts.
T
his
to
po
l
ogy
can
be
ma
de
w
it
h
a
small
er
num
ber
of
c
ompone
nts
w
hich
consi
sts
of
12
con
t
ro
ll
ed
s
witc
hes
with
a
ntip
arall
el
diodes
by
t
he
t
opolog
y
as
s
hown
in
Fig
ure
1
[
1
6
].
F
or
sim
ple,
eas
y
la
yout
struct
ur
e
an
d
f
or
re
duci
ng
c
ircuit
dr
i
ver
dif
ficult
y,
Semico
nduc
tor
s
witc
hes
ar
e re
placed
by
VS
Cs i
n
this
to
po
l
ogy [
1
7
].
Conver
sio
n
of
AC
P
owe
r
int
o
DC
P
ow
e
r
r
equ
i
res
P
ower
-
Ele
ct
ronics
te
chnolo
gies
with
ma
na
ging
sk
il
ls.
The
st
ruct
ur
e
a
nd
desi
gn
of
C
omp
onent
in
the
to
po
logy
of
T
win
Converte
r
to
pology
is
obse
rved
[
2]
wh
ic
h
is
li
ke
topolo
gy
of
op
en
-
e
nded
tra
nsfo
rme
r.
I
n
ord
er
t
o
ac
hieve
on
l
y
t
hr
ee
-
le
ve
l
operati
on,
V
SCs
of
bo
t
h
are
maint
ai
ned
with
e
qual
volt
ages
of
DC
-
li
nk
i
n
topolo
gy
of
tw
in
co
nv
e
rter
.
To
e
ns
ure
f
ou
r
-
le
vel
op
e
rati
on
with
re
du
ce
d
TH
D
with
le
sse
r
filt
er
re
qu
i
reme
nt
s
of
the
ci
rcu
i
t
[1
8
]
,
regulat
ion
of
volt
age
at
DC
-
li
nk
of
VS
C
-
2
made
1/2
of
V
SC
-
1
in
t
he
op
en
-
e
nded
t
rans
forme
r
to
polo
gy
that
has
not
been
obse
rv
e
d
in
case
of
t
opolog
y
of
three
-
le
vel
twi
n
co
nverte
r.
Se
ries
co
nnect
ed
capaci
tors
in
a
string
sub
div
id
e
the
sin
gle
DC
bu
s
into
num
ber
of
vo
lt
a
ge
le
vels
in
the
di
od
e
-
cl
amped
in
ve
rter
t
opolog
y.
F
or
s
witc
hing
e
ach
le
g
of
th
e
ph
a
se
ou
t
pu
t t
o
s
om
e
of these
levels
of
vo
lt
age
[
19
],
matri
x o
f
se
micond
ucto
r
s
witc
hes
a
nd
dio
de
s ar
e
used
.
Ca
pacit
or
ba
nk
pairs
in
eac
h
VS
C
must
r
equ
i
re
the
balancin
g
of
the
vo
lt
age
s,
i
f
th
e
ope
n
-
e
nd
e
d
trans
forme
r
-
c
onnected
ci
rc
ui
t
equ
i
pp
e
d
w
it
h
a
s
plit
-
cap
aci
tor
a
rr
a
nge
ment
w
hich
t
her
e
fore
le
a
d
to
the
regulat
ion
of
vo
lt
age
s
in
two
pai
r
of
DC
capaci
tor
s.
To
reduce
t
he
thir
d
-
harmo
nic
an
d
DC
curren
t
com
pone
nts,
a
com
plex
c
ontr
oller is
require
d [2
0
].
On
l
y
pa
ir
of
DC
li
nk
s
in
t
wo
VS
Cs
is
use
d
without
s
pl
it
-
capaci
tor
a
r
rangeme
nt
to
ov
e
rc
om
e
this
dr
a
w
back
in
pro
posed
as
ymmet
ric
twi
n
co
nv
e
rter
to
polo
gy
wh
ic
h
re
duces
the
T
H
D
c
urren
t
c
ompon
ents
i
n
the grid
by c
ho
os
in
g
t
he
tw
o VSCs
DC
-
li
nk
vo
lt
age
s
with a
conv
e
nient
ra
t
io [2
1
-
3
2
]
as
s
how
n
in
Fig
ure
2
.
Figure
1. ST
A
TCOM h
avi
ng
four le
vel c
onne
ct
ed
with a
n op
e
n
-
e
nd
e
d
t
ran
s
f
or
m
er
Figure
2. ST
A
TCOM wit
h
a t
win
-
co
nverter
asym
metri
c to
po
l
ogy
2.
PROP
OSE
D MULTIL
EVE
L IN
VERTE
R
TOP
OLOG
Y
2.1.
Pri
ncipl
e of
oper
ati
on
Pair
of
VS
Cs
c
on
ta
ine
d
i
n
the
pro
posed
m
ulti
le
vel
asym
metri
c
-
twin
-
c
onve
rter
to
polo
gy
a
s
sho
wn
i
n
Figure
2.
The
pai
r
of
2
-
le
ve
l
VS
Cs
will
ha
ve
t
he
outp
ut
volt
age
diff
e
r
ence
eq
ual
t
o
LV
side
vo
lt
a
ge
by
connecti
ng
differentia
l
trans
f
ormer
LV
windi
ng
s
am
ong
the
m.
G
rid
ha
ving
three
ph
a
ses
is
connecte
d
th
r
ough
HV
wi
nd
i
ngs
s
et
in
patte
rn
of
sta
r.
T
he
S
TA
TCOM
in
put
fi
lt
er
inducta
nce
s
are
go
verne
d
by
t
he
tra
nsfo
rmers
Leaka
ge
i
nduc
ta
nces.
The
t
wo
-
le
vel
outp
ut
in
div
i
du
al
ly
pro
vid
e
d
by
the
op
e
rati
on
of
both
VS
Cs
with
separ
at
e
DC
li
nk
s
. T
ra
ns
f
orm
er L
V win
ding
s Volt
ages a
re
expresse
d
i
n V
SCs volt
age
ou
tpu
t as
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IS
S
N
:
2088
-
8
694
In
t J
P
ow
Ele
c
&
D
ri
S
ys
t,
V
ol
.
11
, N
o.
4
,
D
ecembe
r
2020
:
18
26
–
18
34
1828
=
1
1
−
2
2
+
1
2
=
1
1
−
2
2
+
1
2
(1)
=
1
1
−
2
2
+
1
2
Wh
e
re
is t
he LV
windin
g p
ha
se
-
A
volt
age
1
1
is t
he VSC
-
1
po
le
volt
age
2
2
is t
he VSC
-
2
po
le
volt
age a
nd
1
2
is t
he
t
wo VS
Cs t
erminals
ne
gative
dif
fer
e
nce
vo
lt
ag
e re
s
pecti
vely
.
The
s
um
mati
on
of
the
c
urre
nts
in
the
L
V
ph
a
se
windi
ng
will
be
zero
a
s
two
VS
Cs
ha
ve
sep
arate
DC
li
nks.
+
+
=
0
(2)
Also
,
s
um
mati
on of
volt
ages
at
p
arti
cula
r
in
sta
nt v
al
ues
i
n gr
i
d
is
0.
+
+
=
0
(3)
Additi
on of
wi
nd
i
ng volt
ages
at
LV
si
de
e
xpresse
d
as
+
+
=
(
+
+
)
−
(
+
+
)
−
(
+
+
)
(4)
wh
e
re
R
is R
es
ist
ance at L
V Win
ding,
L
is t
he
LV Wi
nd
i
ng Lea
kag
e
Inducta
nce
,
N
LV
/N
H
V
in
dic
at
es r
at
io
of
tu
r
ns
.
In
se
rtin
g
(
2) a
nd (3) i
n (
4)
yi
el
ds
+
+
=
0
(5)
In
se
rtin
g win
din
g v
oltages
at
LV
si
de fr
om
e
qu
at
io
n (
1)
i
nt
o
e
qu
at
io
n (
5)
giv
es
1
2
=
−
1
3
(
1
1
−
2
2
)
−
1
3
(
1
1
−
2
2
)
−
1
3
(
1
1
−
2
2
)
(6)
In
se
rtin
g
1
2
valu
e in
(1) gives
(
)
=
1
3
(
2
−
1
−
1
−
1
2
−
1
−
1
−
1
2
)
(
1
1
−
2
2
1
1
−
2
2
1
1
−
2
2
)
(7)
The
(
7)
giv
es
the
relat
ion
be
tween
volt
age
s
at
t
he
LV
w
in
ding
a
nd
po
l
e.
Ba
se
d
on
the
sta
te
of
cond
uction
of
swiches
in
VSC
-
1
an
d
V
SC
-
2,
the
volt
ages
occ
ur
at
P
ole
are
decide
d.
A
possible
di
f
fer
e
nt
switc
hes
sta
te
s
co
mb
i
natio
n
is
eq
ual
t
o
2
6
=
64.
T
he
pe
rformance
will
be
a
nalyz
ed
i
n
a
bette
r
wa
y
b
y
choosi
ng
co
nv
en
ie
nt
rati
o
of
VS
Cs
DC
l
ink
volt
ages,
V
DC
1:
V
DC
2=
1:0
.
366
a
s
obse
rv
e
d
i
n
[
2
4
].
With
rep
e
ct
to
switc
hing
of
uniq
ue
sta
te
s,
th
e
volt
age
plo
t
of
spa
ce
vecto
r
is
draw
n
by
us
in
g
pro
per
DC
li
nk
vo
lt
age
rati
o
a
s
show
n
in
Fig
ur
e
3.
Stat
es
of
swichi
ng
t
otall
y
co
ns
ist
s
of
64.
Ou
t
of
the
se
sta
te
s
of
s
witc
hing,
Vo
lt
age
s
of
th
e
phase
w
hich
are
uniq
ue
st
at
es
of
s
witc
hi
ng
are
49
a
nd
Steps
of
volt
ages
obser
ve
d
at
the
vo
lt
age
s
of
t
he LV si
de
a
re
25.
LV
si
de vo
lt
ag
es of li
ne
a
re a
rtic
ulate
d
in
vo
lt
ages of po
le
wh
ic
h gives
E
ab
,
E
bc
,
and
E
ca
by (1)
=
−
=
1
1
−
2
2
−
1
1
+
2
2
=
−
=
1
1
−
2
2
−
1
1
+
2
2
=
−
=
1
1
−
2
2
−
1
1
+
2
2
(8)
Vo
lt
age
wa
veforms
Ea
b
,
Ebc
and
Ec
a
a
re
ha
ving
7
dif
fer
e
nt
ste
ps
li
ke
th
e
numb
e
r
of
li
ne
volt
a
ge
ste
ps
obser
ve
d
in
the
Diode
cl
amped
fou
r
l
evel
mu
lt
il
evel
co
nv
erte
r
bas
ed
on
the
sta
te
s
of
s
witc
hing
f
or
V
DC
1
=
2
V
DC
2.
Wa
ve
forms
of
the
li
ne
volt
ages
a
re
ha
ving
nin
e
diff
e
re
nt
ste
ps
li
ke
t
he
num
be
r
of
li
ne
ste
p
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
Ind
uction drive
system wi
th
DSTATC
OM b
ase
d asy
mm
et
ric
tw
in convert
er
(P
A
nusha
)
1829
vo
lt
age
s
obse
r
ved
i
n
Di
ode
c
la
mp
ed
f
our
le
vel
mu
lt
il
evel
conve
rter
wit
h
rati
o
of
vo
lt
age
of
ca
pacit
ors
ha
vi
ng
100(
V
DC
1:
V
DC
2:
V
DC
3)
=
33:6
6:33
for
366
V
DC
1
=
1000
V
DC
2.
Th
us
,
the
e
quival
ent
pr
opos
e
d
s
chem
e
of a fo
ur
-
le
vel
conve
rter is
ob
ta
ined.
Figure
3. Pro
pose
d
to
polo
gy
sh
owin
g Sp
ace
v
ect
or
diag
ra
m w
it
h f
ourty
nin
e
uniq
ue
sta
te
s
2.2.
PWM
St
r
ateg
y
Ba
sed
on
the
25
s
witc
hing
sta
te
s
giv
e
n
by
e
qu
at
io
n
(
7),
th
e
volt
age
Ea
a
t
the
L
V
si
de
t
akes
one
of
the
switc
hing
s
ta
te
s.
The
te
ch
nique
of
P
WM
us
ed
a
nd
wa
ve
form
of
m
odul
at
ion
decide
s
the
switc
hing
s
ta
te
.
PWM
te
ch
niques
ge
ne
rall
y
employe
d
in
hi
gh
power
a
pp
li
cat
ion
s
a
re
c
arr
ie
r
-
ba
sed
P
W
M
(CB
-
P
W
M
)
or
sp
ace
vect
or
m
odulati
on
(S
V
M
)
a
nd
S
el
ect
ive
harmo
nic
el
imi
nation
meth
od
(
SHEM
).
T
he
dyna
mic
re
s
pons
e
of
the
S
HE
M
PWM
te
c
hn
i
que
is
slo
w
an
d
thu
s
it
s u
se
is
li
mit
ed.
Secto
r
i
den
ti
ficat
io
n
al
gorithm
is requ
ired
i
n
the
S
V
M
m
ulti
le
vel
co
nverte
r
reali
zat
ion
.
T
he
im
pleme
nta
ti
on
is
m
ulti
fa
cet
ed
du
e
t
o
t
he
presence
of
la
r
ge
numb
e
r
of
se
ct
or
s
.
Th
us
,
t
he
pro
pose
d
topolo
gy
us
es
the
Ph
ase
-
S
hife
d
(PS)
C
B
-
PWM
te
c
hniq
ue.
Oup
ut
volt
age
s
of
Ea
1
g
1,
Eb
1
g
1,
Ec
1
g
1,
Ea
2
g
2,
Eb
2
g
2,
a
nd
Ec
2
g
2
f
or
eve
r
y
in
ver
te
r
are
ha
vi
ng
t
he
ind
ivi
du
al
wa
ve
forms
of
m
od
ulati
on
as
e
x
pe
ct
ed
by
t
he
c
ontr
oller
of
t
his
PWM
te
ch
nique
em
ploye
d.
Stat
es
of
s
witc
hing
are
determi
ne
d
for
t
he
c
or
respo
nd
i
ng
in
ver
te
r
dev
ic
es
by
c
ompa
rin
g
eac
h
wa
veform
of
modu
la
ti
on
wi
th
a
wa
veform
of
ca
rr
ie
r
wh
i
ch
is
same
as
t
he
te
c
hn
i
qu
e
of
ph
a
se
s
hifted
car
rier
b
ase
d
PWM
employe
d
by
H
-
br
i
dg
e
c
onve
rters
of
casca
ded
ty
pe
[1
5,
1
6
].
A
ddit
ion
of
volt
ages
of
ind
i
vidual
c
onve
rter
giv
es
r
es
ultant
ac v
oltage
wa
ve
form f
or
t
wo
H
-
br
i
dg
e
s
per
ph
a
se.
Th
us
, th
e
wa
ve
forms of
ca
rr
ie
r
are
phase
-
s
hi
fted
f
r
om
eac
h othe
r
by
180
0
to el
imi
nate the fre
quenc
y
harmo
nics
of
c
arr
ie
r
.
Since
th
e
two
ac
volt
ages
diff
e
re
nce
giv
es
t
he
re
su
lt
ant
wa
vefo
rm,
the
phase
s
hifti
ng
of
carrier
is
not
r
equ
i
red
i
n
cas
e
of
as
ymmet
r
ic
twin
co
nver
te
r
topolo
gy.
M
od
ulati
on
w
avefor
ms
with
carrier
wav
e
f
or
m
s
c
ompa
ris
on
for
phase
-
A
as
s
ho
wn
in
Fig
ure
4.
T
he
te
c
hn
i
que
of
PWM
em
ployed
in
the
operati
on
el
imi
nates
the
low
-
or
der
ha
rm
on
ic
s.
Ha
r
monics
wh
ic
h
are
domina
nt
are
twic
e
the
fr
e
quenc
y
of
carrie
r
locat
ed
at
it
s
s
ideba
nd.
The
mag
nitud
e
of
c
arr
ie
r
side
ba
nd
f
reque
ncy
is
too
the
re
but
s
mall
er
tha
n
f
re
qu
e
nc
y
of car
rier.
Figure
4. P
has
e
-
sh
i
fted
ca
rr
ie
r based
P
W
M
t
echn
i
qu
e
s
how
ing
t
he
c
ompar
ison o
f
m
odula
ti
on
wav
e
f
or
m
s
with ca
rr
ie
r
w
a
veforms
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
.
11
, N
o.
4
,
D
ecembe
r
2020
:
18
26
–
18
34
1830
3.
PROP
OSE
D ST
ATC
OM
S
YS
TE
M
EQ
U
IVA
LE
NT
CI
RCUIT
An
E
qu
i
valent
ci
rc
uit
is
deri
ved
f
or
the
pro
po
se
d
ST
A
TCOM
for
a
na
lysis
pur
po
se
as
sho
wn
in Figu
re
5.
Figure
5. The
pro
po
se
d ST
A
TCOM h
avi
ng
an
e
qu
i
valent c
ircuit
d
ia
gr
a
m
Sour
ces
of
V
ol
ta
ge,
Re
sist
an
ces
an
d
I
nduct
ances
a
re
us
e
d
in
the
co
mb
i
na
ti
on
of
se
ries
eq
uiv
al
e
nt
ci
rcu
it
wh
ic
h
r
epr
ese
nts
the
t
ran
s
f
or
me
r.
Pa
ir
of
r
esi
sta
nce
s
R
1
an
d
R
2
locat
ed
acr
os
s
pair
of
DC
li
nks
f
or
modell
ing
l
os
s
es in t
wo VSC
s.
T
he
s
ys
te
m
pro
po
se
d h
as
the
der
i
ved go
ve
rn
i
ng equati
ons as
(
)
=
(
−
0
0
0
−
0
0
0
−
)
(
)
+
(
−
+
−
+
−
+
)
(9)
wh
e
re
L
is e
xpresse
d
in
ω
bl/z
base.
l
is t
he
le
aka
ge
inductanc
e
of
STA
TC
O
M
ωb
is
b
ase
freq
uen
c
y o
f
ST
A
TCOM a
nd
an
d
z
base is im
ped
a
nce
of
bas
e in STATC
O
M
.
Sy
ste
m
va
lues
f
or
al
l
the
vari
ables
a
nd
pa
r
amet
ers
a
re
gi
ven
in
per
-
unit
(
p.u.).
I
nform
at
ion
i
n
t
he
Appe
nd
i
x
is
giv
en
f
or
dq
0
re
fer
e
nce
f
rame
trans
formati
on
of
(
9).
F
rame
of
dq
0
has
va
r
ia
bles
of
the
s
ys
te
m
giv
e
n
as
f
ollo
ws:
(
)
=
(
−
−
−
)
(
)
+
(
−
1
+
2
+
|
|
−
1
+
2
)
(10)
wh
e
re
and
are
d
an
d
q
-
a
xis
current
at
side
of
L
V.
VS
C
-
1
and
VS
C
-
2
a
re
hav
i
ng
c
omp
onents
of
volt
ag
es
giv
e
n
by
(
1
,
1
),
(
2
,
2
).
The
ac
pa
ra
mete
rs
of
t
he
gr
i
d
a
nd
S
TA
TCOM
a
re
i
nterr
el
at
ed
by
E
qu
at
io
n
(10).
T
he
e
qua
ti
on
s
of
insta
ntaneous
po
wer
balance
are
us
e
d
f
or
d
eri
ving
t
he
reli
ance
between
the
pa
ra
mete
rs
of
DC
an
d
ac
of
STATC
O
M.
The
c
onditi
on
of
balance
of
po
wer
betwe
en
the
DC
an
d
ac
li
nk
s
of
V
SC
-
1a
re
giv
e
n by the
f
ol
lowing
(11)
:
1
1
=
3
2
(
1
+
1
)
(11)
The
relat
ion
be
tween
t
he
vo
l
ta
ge
V
DC
1
a
nd
c
urren
t
ps
si
ng
th
rou
gh
DC
-
li
nk
ca
pacit
or
c
1
is
giv
e
n
as foll
ows:
1
=
1
(
1
−
1
1
)
(12)
wh
e
re
C
1
is e
xpress
ed
as
1
/
(
ωb
c
1
z
base).
In
se
rtin
g
I
DC
1from
(11)
1
=
1
(
3
2
1
(
1
+
1
)
−
1
1
)
(13)
simi
la
rly
, VSC
-
2 has
the e
qua
ti
on
of go
verning g
i
ven as
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
Ind
uction drive
system wi
th
DSTATC
OM b
ase
d asy
mm
et
ric
tw
in convert
er
(P
A
nusha
)
1831
2
=
2
(
3
2
2
(
2
+
2
)
−
2
2
)
(14)
the
s
ys
te
m
behavio
ur is gi
ven by the
(1
0)
,
(1
3), a
nd (14).
4.
MA
TL
AB
M
ODELIN
G
A
ND R
ES
ULT
S OF
SI
MU
L
ATIO
N
Thr
ee
dif
fere
nt
scena
rios
a
re
carried
out
in
t
he
sim
ulati
on,
1).
ST
ATC
O
M
of
high
pow
er
em
ploye
d
in
plan
ned
co
nv
e
rter
of
as
ymmet
ric
t
yp
e
.
2).
ST
ATCO
M
of
high
power
with
c
on
t
ro
l
of
r
eact
ive
Powe
r
employe
d
in
pl
ann
e
d
co
nvert
er
of
as
ymmet
ric
ty
pe.
3).
S
TATC
OM
of
high
powe
r
wi
th
in
duct
io
n
m
achine
dr
i
ve
em
ploye
d
in
p
la
nn
e
d co
nv
e
rter
of as
ymmet
ric ty
pe.
4.1.
STATC
OM
of
high p
ow
er
e
mploye
d in
pl
an
ne
d c
onvert
er o
f asymm
et
ri
c type
High
Powe
r
S
TATC
OM
E
m
ployed
in
As
ymmet
ric
Twi
n
Co
nverter
m
odel
in
M
at
la
b/
Simuli
nk
as
sh
ow
n
i
n
Fi
gure
6.
Phase
-
A
gr
i
d
vo
lt
age
at
HV
-
si
de
&
P
hase
-
A
t
ransf
ormer
c
urren
t
at
LV
-
side
as
show
n
i
n
Figure
7
.
I
nput
side
volt
age
of
co
nverter
w
hi
ch
is
nothin
g
bu
t
the
volt
age
s
at
the
pr
ima
r
y
side
t
o
sup
port
the
Asymmetric
C
onve
rter
with c
onve
rter
op
e
rat
ion
s
as s
how
n
i
n
Fi
gure
8.
Figure
6. ST
A
TCOM o
f hig
h p
ow
e
r
e
mp
l
oyed
in
con
ver
te
r
of as
ym
met
ric typ
e
m
od
el
in Matl
ab/Sim
ulink
Figure
7. P
has
e
-
A
grid
volt
ag
e at
HV
-
si
de
&
Ph
as
e
-
A
tra
nsfo
rme
r c
urren
t at
LV
-
s
ide
Figure
8. I
nput
side
volt
age
of
co
nv
e
rter
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
.
11
, N
o.
4
,
D
ecembe
r
2020
:
18
26
–
18
34
1832
An
al
ys
is
of
FF
T
f
or
Ph
a
se
-
A
Current
at
L
V
Side
with
Asymmetric
C
onve
rter
is
13.34%
as
s
how
n
i
n
Figure
9.
A
nal
ys
is
of
FFT
f
or
V
oltage
at
th
e
LV
Side
wit
h
Asymmetric
Co
nv
e
rter
is
41.64%
as
s
hown
in
Figure
10.
Figure
9. A
nal
ys
is
of
FFT
for
Ph
as
e
-
A
C
urr
ent at L
V
Side
Figure
10. A
na
lysis o
f FFT i
n v
oltage at L
V Si
de
4.2.
STATC
OM
of
hig
h
power
with
c
ontrol
of
re
act
i
ve
power
empl
oy
ed
in
planne
d
conver
ter
of
as
ym
metric
ty
pe
STA
TC
O
M
o
f
h
ig
h
powe
r
with
c
ontrol
of r
e
act
ive
po
wer
e
mp
lo
ye
d
i
n
twi
n
c
onve
rter of
asym
metri
c
typ
e
m
od
el
w
hich
ha
s
t
he
P
hase
-
A
gri
d
volt
age
at
HV
-
s
ide
&
P
hase
-
A
t
ran
s
f
or
me
r
cu
rr
e
nt
at
L
V
-
side
as
sh
ow
n
in
Fi
gur
e 11.
Inp
ut
side
vo
lt
age
of
c
onve
rter
wh
ic
h
is
not
hing
but
the
volt
ages
at
the
pr
ima
ry
si
de
t
o
s
uppo
rt
the
Asymmetric
C
onve
rter
with c
on
t
ro
l
of r
eact
i
ve powe
r
with
conve
rter
op
e
r
at
ion
s as
s
how
n
in
Fig
ure
12.
Figure
11. Pha
se
-
A
grid
volt
age at
HV
-
side
& P
hase
-
A
tra
nsfo
rme
r c
urren
t at
LV
-
s
ide
Figure
12. In
put si
de
volt
age
of co
nverter
4.3.
STATC
OM
of
high
p
ower
wi
th
induc
ti
on
m
achine
drive
empl
oy
ed
in
pl
an
ne
d
c
onverter
of
as
ym
metric
ty
pe
The
Ele
ct
r
om
a
gn
et
ic
T
orq
ue,
Sp
ee
d
a
nd
Stat
or
C
urre
nt
of
S
TATC
OM
of
hi
gh
powe
r
with
inducti
o
n
machine
dri
ve
employe
d
i
n plann
e
d
c
onve
rte
r of
a
symmet
ri
c typ
e
as s
how
n
in
Fig
ure
13.
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
Ind
uction drive
system wi
th
DSTATC
OM b
ase
d asy
mm
et
ric
tw
in convert
er
(P
A
nusha
)
1833
Figure
13.
Ele
c
trom
a
gnet
ic
torqu
e
, spee
d
a
nd stat
or
c
urre
nt
5.
CONCL
US
I
O
N
Flexible
AC
T
ran
s
missi
onS
yst
ems
(
F
ACTS
)
de
vices
a
re
plan
ned
an
d
i
mp
le
me
nted
i
n
sy
ste
ms
of
powe
r
by
fast
dev
el
opment
i
n
powe
r
el
ect
r
on
ic
s
.
FA
CT
S
de
vices
are
ut
il
iz
ed
for
co
nt
ro
l
powe
r
fl
ow
a
nd
enh
a
nce
s
ys
te
m
sta
bili
ty.
V
SCs
of
t
wo
le
vel
empl
oy
e
d
with
a
hi
gh
-
powe
r
ST
ATC
OM
with
c
on
t
ro
l
of
re
act
ive
po
wer
is
propose
d
a
nd
i
nductio
n
machine
dri
ve
performa
nce
i
s
chec
ked
by
t
he
pr
opos
e
d
s
ys
te
m.
The
c
on
t
ro
l
of
two
DC
li
nk
volt
ages
of
VS
C
s h
as
bee
n
sho
wn
i
n
the
pro
pose
d
to
po
l
ogy. Also, the lo
w cur
rent
distor
ti
on
is
ac
hieve
d
by
sel
e
ct
ing
t
he
DC
l
ink
volt
ages
of
the
tw
o
VS
C
s
with
a
c
onve
nient
rati
o.
DC
-
li
nk
vo
lt
age
re
gula
ti
on
of
tw
o
c
onver
te
r
s
is
done
by
c
on
tr
oller
vo
lt
age
DC
-
li
nk
wh
ic
h
is
plann
e
d
for
e
xtra
ct
in
g
necessa
ry
act
ive
powe
r
of
ut
il
i
ty
there
by
t
ran
s
ferrin
g
t
he
powe
r
a
mon
g
pair
of
c
onve
rters
d
if
fer
e
ntial
ly.
Desig
n
of
pla
nn
e
d
c
onve
rter
impro
ved
in
i
mp
le
me
ntin
g
the
m
odel
in
M
at
la
b/Sim
ulink
syst
em.
Quic
k
an
d
bette
r
re
spo
ns
e
and
bette
r values
of T
HD ar
e obtai
ned whi
ch
a
re
well
w
it
hin
t
he
Sta
ndar
ds
of I
E
EE.
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NCE
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-
le
v
el
o
pen
-
ende
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r
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ase
d
ST
ATCOM
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ere
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ci
t
ty,
“A
co
mpa
r
ison
of
diod
e
-
c
la
mp
ed
and
c
asc
ad
e
d
mul
tilevel
conv
ert
ers
for
a
ST
ATCOM
with
ene
rgy
storag
e,”
I
EE
E
Tr
ans.
Ind.
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e
ct
ron.
,
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K.N.V.
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,
G.
Ranjith
Kum
ar,
Y
.
S.
Anil
Kumar
,
G.
Sa
tya
na
ray
ana,
“
Reali
zation
of
ca
sc
ade
d
H
-
bridge
5
-
Le
v
e
l
mul
tilevel
inve
r
te
r
as
Dynam
ic
Volta
g
e
R
estor
er,
”
Computer
Comm
unic
ati
on
and
Informati
c
s
(ICCCI),
201
3
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rnational
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nfe
renc
e
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vo
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M.
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ar
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el
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B.
Wu,
J.
Rodrigue
z
,
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.
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z,
and
J.
I.
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on,
“R
ecent
a
dvanc
es
and
ind
ustria
l
app
li
c
at
io
ns
of
mu
lt
i
le
v
el
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”
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E
E
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power
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e
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ti
on
er
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g
c
asc
ad
e
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t
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r
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te
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te
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on
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ina
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e
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,
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1
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le
ve
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c
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ad
e
i
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te
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r
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i
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EE
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ans.
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.
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akshmi
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“
I
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m
ent
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b
y
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zz
y
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ro
ll
ed
base
d
IPQ
C
at
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ad
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ti
ons
,
”
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f
ic
i
ent
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r
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lity
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CEE
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nte
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nfe
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and
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.
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ta
r
am
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a
n,
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bus
r
ipple
mi
n
im
i
zation
i
n
ca
sc
ade
d
H
-
br
idge
mu
lt
i
le
v
el
c
onver
te
rs
und
er
stai
rc
ase
mod
ulat
ion,”
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.
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EE IA
S
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,
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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
.
11
, N
o.
4
,
D
ecembe
r
2020
:
18
26
–
18
34
1834
[14]
S.
Vaz
que
z,
J.
I
.
Le
on
,
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M.
C
a
rra
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G.
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anque
lo
,
E
.
Ga
l
van,
M.
R
eye
s,
J.
A.
San
chez,
an
d
E.
Dominguez
,
“Ana
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of
th
e
power
ba
la
nc
e
in
th
e
cells
o
f
a
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evel
c
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ade
d
H
-
br
idg
e
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ans.
Ind
.
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ron.
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[15]
S.
Lu,
S.
Mari
et
hoz
,
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n
e,
“A
symme
trica
l
c
asc
ade
multil
eve
l
conve
r
te
rs
wit
h
nonint
eg
er
o
r
dynam
i
ca
l
ly
ch
a
nging
DC
voltag
e
ratios:
Conc
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