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.
11, N
o.
1, Mar
ch 20
20,
p
p.
151~
1
5
9
ISSN: 2088-
8694,
DOI
:
10.115
91/ijpeds.
v11.
i
1.151-159
151
Jou
rn
a
l
h
o
me
pa
ge
:
ht
tp:
//i
j
p
eds.i
a
esco
re
.com
Design a ni
n
e-level modular mul
tilevel converter for DC rai
lway
electrification system
C
.
L.
To
h
1
, P.
C. Ooi
2
1
Dep
a
rt
m
e
nt of E
l
ect
rical
a
nd Ele
c
t
r
on
ic
E
ngin
e
eri
n
g
,
U
niv
e
rsiti
Ten
aga N
a
sio
n
al, M
a
l
ay
si
a
2
D
e
p
a
rtm
e
n
t
o
f El
ectri
cal an
d
E
lectro
ni
c En
g
i
neerin
g, Univers
it
y
o
f
No
ttin
gh
am
M
alays
i
a,
M
al
ay
s
i
a
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
Re
ce
i
v
e
d
Ju
n
1
,
2019
Re
vise
d Ju
l 2
2
,
201
9
A
c
c
e
pte
d
A
ug 1,
201
9
A
recup
e
rati
ng
co
nvert
er
i
s
hi
ghly
d
e
m
a
nd
ed
i
n
tracti
on
p
o
wer
s
u
b
station
to
del
i
v
e
r
th
e
brak
in
g
en
ergy
g
en
erated
b
y
a
t
r
actio
n
vehicle.
C
on
ven
tio
nal
vo
lt
age
so
urce
inv
e
rter
h
ad
b
ee
n
im
p
l
em
en
ted
in
t
h
e
t
racti
on
po
wer
st
ati
o
n.
However
,
l
arge
A
C
line
filters
m
ust
be
i
nstal
l
ed
t
o
improve
t
he
q
uality
o
f
AC
vo
lt
ages
a
n
d
c
u
rrent
s.
T
h
i
s
pape
r
p
r
opo
ses
t
o
i
n
s
t
a
ll
a
n
i
n
e-l
e
vel
M
o
dul
ar
Multilevel
Conver
t
er
(
MMC)
as
a
r
e
c
uperat
i
ng
c
onver
t
er.
T
h
e
mai
n
aim
is
t
o
elim
in
a
t
e
the
n
eed
o
f
AC
l
in
e
fi
lt
ers
while
p
ro
du
cin
g
g
o
od
q
u
a
l
ity
o
f
AC
vo
lt
age
an
d
cu
rrent
w
avef
o
r
m
s
.
T
h
e
M
M
C
i
s
d
e
si
gn
ed
a
n
d
m
o
d
el
led
u
s
i
n
g
MATLAB
/
S
i
mulink
S
i
mula
ti
on
t
ool.
A
centralized
c
ontrol
o
f
bal
a
n
ci
ng
a
ll
th
e
su
b-m
o
du
l
e
capa
c
i
t
o
r
v
o
l
t
a
ge
l
evel
i
s
pro
p
os
ed
w
it
h
T
h
i
r
d
H
arm
oni
c
Vol
t
age
Inj
ection
Level
Shifted
Pulse
W
i
dt
h
M
o
dul
a
t
i
on
(
T
H
V
I-L
S
PWM
)
tech
ni
que.
Th
e
s
i
m
u
l
a
ti
on
resu
lt
s
prov
e
t
h
at
w
ith
t
he
a
p
p
l
i
cati
o
n
o
f
MMC
,
good
q
uality
o
f
ac
vol
t
age
s
a
nd
c
urrent
s
are
bei
n
g
produced.
Th
e
Total
Harm
o
n
ic
D
isto
rti
on in
dex
e
s are
f
o
un
d
l
e
ss th
an 3.
5
%
wit
ho
ut u
si
ng
a
ny
AC
li
ne
f
ilt
ers
in
t
he
s
yst
e
m.
I
n
ad
dition,
t
he
c
lass
ic
D
C
l
i
nk
c
a
p
acit
a
nce
h
a
s
also
bei
n
g
eli
m
inat
ed
.
K
eyw
ord
s
:
Ca
pac
i
t
o
r
volta
ge
bala
n
c
i
ng
con
t
ro
l
H
a
r
m
onic
miti
gat
i
on
L
e
v
e
l
s
h
i
f
te
d
P
W
M
Mo
dua
r
M
u
l
til
e
v
el
C
o
n
v
e
r
ter
Th
ird ha
rmon
i
c
vol
t
a
ge i
njec
tio
n
Th
is
is a
n
o
p
en acces
s a
r
ti
cle u
n
d
e
r t
h
e
CC
B
Y
-S
A
li
cens
e
.
Corres
pon
d
i
n
g
Au
th
or:
C
.
L. Toh,
D
e
pa
rtme
nt
o
f
El
e
c
t
rica
l
and
Ele
c
t
ron
i
c E
n
g
i
nee
r
in
g,
Uni
v
ersi
ti
T
e
n
aga
Na
si
o
n
a
l
,
Jala
n
IK
RA
M
-
U
N
I
TEN, 43
0
00 K
a
ja
ng,
S
e
l
a
n
g
o
r,
M
alay
si
a.
Em
ail:
chue
n
l
i
n
g
@
uni
ten.
ed
u
.
m
y
1.
I
N
TR
OD
U
C
TI
O
N
Ele
c
t
ric
trai
ns
d
raw
ma
ssive
pow
e
r
f
r
o
m
t
h
e
u
t
ili
ty
g
r
i
d
to
a
cc
el
e
r
at
e
f
r
om
s
t
a
nd
sti
l
l
.
T
h
e
y
a
r
e
t
h
en
wo
rk
ed
a
s
g
e
n
e
rat
o
rs
u
pon
rea
c
h
in
g
n
e
xt
p
a
s
se
ng
er
s
t
a
t
i
on
.
It
i
s
predic
te
d
t
h
a
t
a
ppr
oxim
a
te
ly
5
0
%
o
f
t
h
e
reg
e
n
e
ra
ti
ve
b
ra
kin
g
e
n
e
rg
y
c
a
n
be
r
epro
du
c
e
d
[
1
-
3
]
.
Th
e
re
ge
ner
a
t
i
ve
e
ne
r
g
y
ha
d
bee
n
s
tore
d
us
i
n
g
on
b
o
ard
o
r
w
a
y
side
e
ner
g
y
st
or
a
g
e
sys
t
e
m
[
4-7].
These
syst
e
m
s
a
re
f
u
lly
e
qu
i
p
ed
w
it
h
d
i
ffe
r
en
t
e
n
erg
y
so
t
r
age
modu
le
s,
such
as ba
t
te
ries,
fuel
cel
l,
f
lyw
h
eel
s,
a
nd
u
ltra
capa
c
i
tors.
Al
t
e
rn
ati
v
e
l
y
,
t
h
e
r
e
g
e
n
e
r
at
iv
e
e
n
ergy
c
a
n
b
e
t
r
an
s
m
it
t
e
d
b
a
c
k
t
o
t
he
pow
er
g
rid
w
i
t
h
o
u
t
u
s
i
ng
ene
r
g
y
s
tora
ge
e
lem
e
n
t
s
[
8
-1
0].
F
i
gur
e
1
(
a
)
ill
ustra
t
es
o
n
e
o
f
t
h
e
r
ec
up
e
r
ati
v
e
c
o
n
v
er
te
r
syste
m
p
ro
p
o
se
d
in
[
8].
A
lth
o
u
gh
a
co
n
v
en
t
i
o
na
l
V
o
l
t
a
g
e
S
ource
I
nve
rte
r
(
VS
I)
i
s
cap
a
b
l
e
t
o
del
i
v
er
t
h
e
e
ner
gy
b
a
ck
t
o
the
p
o
w
e
r
gri
d
,
a
n
i
ns
tal
l
a
tio
n
o
f
A
C
f
ilter
s
i
s
a
mus
t
.
T
h
e
s
e
f
i
l
t
er
s
a
r
e
us
ed
t
o
s
u
p
p
re
ss
u
n
d
es
ired
h
ar
monic
s
c
o
mp
on
en
ts.
In
o
rd
er
t
o
el
imi
n
a
t
e
th
e
AC
f
ilt
e
rs,
t
h
i
s
p
ap
e
r
p
r
op
ose
s
t
o
re
pl
a
c
e
th
e
co
nv
en
tio
n
a
l
V
S
I
wi
t
h
a
M
o
du
lar
Mu
l
t
i
l
e
v
e
l
C
o
n
v
er
te
r (MMC)
as show
n
i
n
F
ig
ure
1 (
b
).
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
nt
J
P
o
w
E
l
e
c
&
D
r
i
S
yst
V
o
l.
11,
N
o.
1
,
Mar
202
0
:
151
–
15
9
15
2
(a)
(b
)
F
i
gur
e
1.
(
a)
R
e
c
upe
r
a
ti
n
g
c
o
nve
r
t
er
s
yste
m
pr
o
pose
d
i
n
[
8
]
,
(
b
)
Pr
opose
d
r
e
c
uper
a
t
i
ng
c
o
n
v
er
t
e
r
sys
t
e
m
us
ing
m
odula
r
m
ulti
le
ve
l
co
n
v
er
t
e
r
(
M
MC)
2.
MO
DULAR MULTILEVEL CONVERTE
R
Mo
d
u
la
r
M
u
l
t
i
l
e
ve
l
Co
nver
t
e
r
h
ad
b
ee
n
w
i
de
l
y
u
se
d
i
n
H
i
g
h
V
o
l
t
a
g
e
D
irect
Cu
r
r
e
n
t
(
HVDC
)
tr
a
n
smiss
i
on
a
nd
me
di
um
vo
l
tage
d
r
i
ves
a
p
p
l
i
c
a
t
ions
[
1
1
,
1
2]
.
T
he
m
od
ul
ar
str
uct
u
r
e
o
f
the
M
M
C
o
ff
er
s
hi
g
h
sc
ala
b
i
lit
y
t
o
r
e
ach
h
i
g
her
r
a
nge
o
f
p
o
w
e
r
s
a
nd
vo
lta
ge
s.
I
n
ad
di
t
i
on
,
s
o
me
b
ul
ky
a
n
d
c
o
st
l
y
c
o
m
p
onen
t
s
in
the
pow
er
c
on
ver
s
i
on
s
y
ste
m
s
uc
h
a
s
t
r
a
n
s
f
o
r
m
e
r
,
dc-
l
i
nk
capa
c
i
ta
nce
a
n
d
pa
ssi
ve
f
i
lter
s
can
b
e
e
l
im
ina
t
e
d
.
L
a
t
e
l
y
,
ap
pli
c
a
t
ion
o
f
MMC
h
ad
b
een
e
x
t
end
e
d
to
r
a
i
l
w
a
y
e
l
ect
ri
f
i
c
a
t
i
o
n
s
y
stem
[
13]
.
MM
C
ha
s
be
e
n
in
te
gra
t
e
d
i
n
A
C
r
ailway
e
l
e
c
t
rifica
t
i
o
n
s
ys
tem
as
S
tati
c
Fr
equ
enc
y
C
onve
r
t
er
(
S
F
C)
o
r
Ra
ilw
a
y
P
ow
e
r
C
o
n
d
i
t
i
oner
(R
PC)
[14,
15].
Th
is
p
a
p
er
w
ill
pr
esen
t
t
h
e
a
p
p
lica
t
i
o
n
o
f
M
M
C
a
s
a
r
e
c
u
p
e
r
a
t
i
n
g
c
o
n
v
e
r
t
e
r
i
n
DC
r
ai
lway
e
l
e
ctrifica
tio
n
s
y
ste
m
.
The
fo
llo
win
g
s
ec
t
i
o
n
w
i
l
l
b
ri
ef
ly
i
n
t
rod
u
ce
t
h
e
op
era
t
ion
a
l
p
r
i
n
cip
a
l
wi
th
it
s
con
t
r
o
l
an
d
m
odu
la
tio
n
t
e
c
h
n
i
que.
2
.
1
.
Opera
t
io
n
a
l
pri
n
cipa
l
The
pow
er
c
ircui
t
o
f
a
ni
ne-l
eve
l
M
o
dul
a
r
M
u
l
tile
ve
l
C
o
nver
t
e
r
is
i
l
l
us
tr
ate
d
i
n
F
i
gur
e
2.
A
t
hr
ee
-
p
h
a
s
e
M
M
C
c
o
n
s
i
s
t
s
o
f
s
i
x
e
q
u
i
v
a
l
e
n
t
a
r
m
s
.
E
a
c
h
a
r
m
o
f
t
h
e
c
o
n
v
e
r
t
e
r
co
nt
ai
ns
f
ou
r
un
it
s
of
i
d
e
nti
cal
s
ub
-
m
o
d
u
l
e
a
n
d
a
u
n
i
t
o
f
a
r
m
i
n
d
u
c
t
a
n
c
e
,
L
ar
m
.
T
h
es
e
co
mpo
n
en
t
s
a
re
c
onn
ect
e
d
i
n
se
r
i
es.
T
h
e
a
r
m
in
du
ct
a
n
c
e
is
u
s
ed
t
o
l
i
mit
th
e
c
h
an
gin
g
r
at
e
o
f
A
C
cu
rre
n
t
,
i
a
,
A
u
n
i
t
o
f
s
ub-
mo
du
le
i
s
co
nf
i
g
ur
ed
b
y
on
e
pair
o
f
I
G
BT
sw
itc
h
a
n
d
a
c
a
pa
ci
tor
.
F
igu
r
e
2
(
b
)
i
l
l
us
tr
a
t
e
s
t
he
pow
e
r
c
ir
c
ui
t
of
a
s
ub
-
m
o
d
u
l
e
.
I
n
gen
e
ral
t
h
e
IGBTs
a
r
e
sw
itc
he
d
c
o
mp
lem
e
nt
a
r
ily.
By
t
ur
n
i
n
g
o
n
S
x
(
gate
s
w
i
t
c
h
i
ng
c
o
nt
r
o
l
s
i
gna
l
is
s
e
t
t
o
l
o
gi
c
1)
,
the
su
b-
mod
ule
vo
l
t
age
le
vel
is
e
qu
i
v
ale
n
t
to
t
he
c
a
p
ac
i
t
or
v
o
l
t
a
ge
l
e
v
el
(
v
SM
=
v
c
)
.
C
o
nve
r
s
el
y,
t
he
s
u
b
-
m
od
ule
vo
lt
age
is
e
qua
l
to
z
e
r
o
v
o
lt
if
S
x
’
i
s
tr
ig
ger
e
d
on.
S
inc
e
al
l
t
h
e
s
u
b-
m
o
d
u
l
e
i
s
c
on
ne
cted
i
n
se
r
i
es,
th
e
arm
v
o
lt
a
g
es,
v
RS
a
nd
v
TU
c
an
b
e d
e
t
e
rmin
ed
a
s:
v
RS
∑
(
1
)
v
TU
∑
(
2
)
Where
p
r
epr
e
sent
s
phase
-
l
eg
a
-
b
-
c
.
T
he
p
o
l
e
volta
ge
o
f
ea
c
h
pha
se
c
an
b
e
de
r
i
ved
a
s
:
v
p
o
=
=
(
3
)
The
A
C
c
ur
r
e
nt
f
or
pha
se
l
e
g
-
a
c
a
n
b
e
expr
e
s
se
d
i
n
(
4
)
It
i
s
h
i
gh
lig
h
t
e
d
t
ha
t
a
tota
l
of
s
ix
m
o
d
u
la
t
i
n
g
w
a
v
es
a
re
u
se
d
t
o
co
ntr
o
l
eac
h
a
r
m
o
f
t
he
M
M
C
.
The
c
o
ncep
t
of
g
e
n
er
a
t
i
o
n
thir
d
har
m
onic
v
o
lta
ge
i
njec
tio
n
mod
u
l
a
ti
on
wav
e
s,
l
e
v
el
s
hi
f
t
e
d
p
ulse
wi
dt
h
mo
dul
a
t
i
o
n
and
cap
a
c
i
t
o
r
vo
lt
ag
e
b
a
la
n
c
ing
co
nt
rol
me
t
h
od
w
ill
be
f
ur
ther
e
x
p
l
a
i
n
ed
i
n
the
fo
l
l
owi
n
g
sub
se
c
t
i
on.
2.
2.
Th
ir
d
h
armon
i
c
vo
lt
a
g
e
in
j
ect
i
o
n
m
o
d
u
l
at
ion
wa
ve
Thi
r
d
h
a
r
m
on
ic
v
olt
a
g
e
i
n
j
e
c
t
i
on
pul
se
w
id
th
m
od
ul
at
i
o
n
t
e
c
h
n
i
q
ue
i
s
basi
cal
l
y
e
x
t
ende
d
fr
om
the
c
l
ass
i
c
Si
n
u
so
ida
l
P
u
l
se
-Wi
d
th-
M
od
ula
t
i
o
n
(
S
P
W
M).
As
i
l
l
u
s
t
r
a
t
e
d
in
F
ig
ur
e
3
(
a
)
,
t
he
t
h
i
r
d
h
ar
m
oni
c
vo
l
t
age
i
n
jec
t
i
on
w
a
ve
,
v
re
f
,
i
s
p
r
o
d
u
ce
d
b
y
s
um
min
g
u
p
t
h
e
pur
e
si
nu
so
ida
l
w
ave,
v
a1
,
that
nor
ma
l
l
y
u
s
ed
i
n
S
P
WM
w
it
h
its
t
hir
d
o
r
d
e
r
h
ar
m
onic
c
o
mp
one
n
t
s
[
1
6,
1
7
]
.
The
ma
i
n
a
d
van
t
a
g
e
is
t
o
inc
r
ea
se
t
he
m
aximum
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
P
o
w
Elec
&
D
r
i
S
y
st
I
S
S
N
:
2088-
86
94
Desig
n
a
n
i
ne
-
l
ev
el mo
du
l
a
r mul
tile
ve
l c
o
nv
erter
for
DC
ra
i
l
w
a
y
elec
tr
if
i
c
ati
on sy
ste
m
(C.
L. T
oh)
15
3
ou
t
p
u
t
v
ol
ta
g
e
a
m
p
lit
u
d
e
w
ith
ou
t
in
t
r
od
uci
n
g
ad
d
iti
ona
l
s
i
de
ba
n
d
ha
r
m
onic
s
.
I
t
i
s
no
te
d
tha
t
,
t
h
e
con
v
e
nt
iona
l
S
i
nu
so
id
al
P
u
l
se
-Wi
d
th
-M
odul
a
tio
n
(S
PWM
)
t
e
c
h
n
iq
ue
h
as
l
i
m
ite
d
the
line
a
r
m
odu
l
a
t
i
o
n
r
a
nge
t
o:
(a)
(b
)
F
i
gur
e
2.
P
ow
e
r
c
ir
c
u
i
t
o
f
(
a
)
nine
-
l
e
v
e
l
m
od
ular
m
ulti
le
vel
c
o
n
v
er
ter
(
M
M
C
)
,
(
b)
S
ub-
m
odu
le
(
S
M
)
0
<
m
a
1
.
0
(5
)
Where
m
a
in
d
i
cate
s
t
he
a
m
p
li
tu
de
m
o
d
u
l
ati
o
n
i
n
dex.
B
y
intr
o
d
u
c
i
n
g
t
h
e
n
e
w
mo
dul
a
tin
g
wa
ve
,
v
re
f
,
t
h
e
f
und
amen
t
a
l
co
mpon
e
n
t
,
v
a1
,
c
a
n
be
r
aised
u
p
t
o
1
5
%
g
r
e
a
t
e
r
.
This
i
s
ma
inly
d
ue
t
o
the
c
ompe
n
s
a
t
i
on
of
th
ir
d
or
de
r
ha
r
m
oni
c
c
o
m
p
o
n
en
t,
v
a3
,
t
o
r
eg
ul
at
e
v
re
f
w
i
t
h
i
n
t
h
e
r
a
nge
o
f
1.
0.
T
her
e
for
e
,
in
T
H
V
I
-
P
WM
tec
h
n
i
q
u
e
,
t
he
l
inear
m
od
ul
a
t
i
on
r
a
n
g
e
is
e
xt
ende
d
t
o
:
0
<
m
a
1
.
15
(
6
)
The
si
x
un
i
t
s
modu
la
ti
n
g
w
a
v
es
w
hic
h
a
r
e
de
m
a
nde
d
f
o
r
M
M
C
m
o
du
l
a
tio
n
can
b
e
de
r
i
ved
as
:
U
ppe
r
a
r
m m
odu
la
tin
g
w
a
ve
,
re
f
_
p
u
p1
3
(
7
)
Low
e
r
a
r
m
m
odu
la
tin
g
w
a
ve
,
re
f
_
p
l
p1
3
(
8
)
The
p
u
r
e
s
in
usoi
da
l
w
a
ve
e
qu
a
t
i
o
ns
f
or
e
ach
pha
se,
v
p1
,
a
r
e:
v
a1
sin
2
v
b1
sin
2
(
9
)
v
c1
sin
2
The
ap
pr
ox
i
m
a
t
ed
e
x
p
r
e
ssio
n
o
f
t
h
ir
d
or
der
har
m
onic
c
o
mp
one
n
t
,
v
3
,
i
s
a
s f
o
llow
e
d
[1
8]
:
,
,
,
,
(
10)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
11,
N
o.
1
, Ma
r
202
0
:
151
–
15
9
15
4
F
i
gure
3.
(
a) Thir
d
ha
r
m
onic
vo
l
t
age
in
jec
tion
mod
u
l
at
i
n
g w
a
v
e
(
p
h
a
se-a),
(b)
Leve
l shi
f
t
e
d c
a
rr
i
e
r w
a
ves
t
o
b
e
u
s
e
d
for
a
n
in
e
-
le
ve
l
MMC
2.3.
Leve
l
s
h
i
fte
d p
u
l
se
w
id
th
m
odu
l
at
i
o
n
an
d
c
a
p
a
c
i
t
o
r vo
lta
g
e
b
al
an
cin
g
c
on
t
r
ol
The
num
ber
o
f
d
e
m
a
n
d
e
d
t
r
ia
ng
ula
r
car
rier
w
ave
,
v
tr
i
,
i
s
d
epe
n
d
e
d
on
t
h
e
n
u
mbe
r
o
f
sub-
mo
du
l
e
c
o
n
n
e
c
t
e
d
i
n
o
n
e
a
r
m
.
I
n
t
h
i
s
p
a
p
e
r
,
f
o
u
r
u
n
i
t
o
f
c
a
r
r
i
e
r
w
a
v
e
s
w
i
l
l
b
e
u
s
e
d
.
T
h
e
s
e
c
a
r
r
i
e
r
w
a
v
e
s
a
r
e
s
h
i
f
t
e
d
vert
ica
l
l
y
i
n
sa
m
e
pha
se
.
The am
pl
i
t
ud
e of e
ach
car
rier wa
v
e
is
e
q
u
al
ly
d
ivi
d
e
d
a
s foll
o
w
s:
(1
1
)
Whe
r
e
N
r
e
pr
e
s
e
n
t
s
t
he
t
o
t
a
l
n
umbe
r
of
s
ub-
mo
du
le
p
e
r
a
rm.
The
freque
nc
y
o
f
t
h
e
c
a
r
r
i
e
r
w
a
v
e
s
i
s
s
e
t
a
c
c
o
rdi
n
g
to
t
h
e
M
MC
s
w
i
t
c
hi
ng
fre
qu
en
cy
,
f
sw
.
F
i
gure
3
(b
)
show
s
t
h
e
c
a
r
r
ie
r
w
a
ves
nee
d
e
d
f
or
a
n
ine
-
leve
l
MM
C
.
T
h
e
g
at
e
swit
ch
ing
co
nt
rol
si
gn
a
l
s,
G
pui
a
nd
G
pli
w
i
l
l
be
p
r
o
duc
ed
w
he
n
the
fol
l
ow
i
ng
c
o
nd
it
ion
s
are
m
a
tc
h
e
d
:
re
f_
p
u
,
G
pui
= 1
e
lse
G
pui
= 0
(
12
)
re
f_
p
l
,
G
pli
=
1 els
e
G
pl
i
=
0
(
1
3
)
In
g
ene
r
a
l
,
on
l
y
f
our
s
u
b
-m
odu
les
w
i
l
l
b
e
tr
i
g
ge
red
on
per
phas
e
le
g
a
t
e
very
i
ns
t
a
nt
.
T
h
e
sw
itc
h
i
ng
dec
i
si
o
n
of
ea
c
h
sub-m
o
du
le w
i
l
l be
def
ine
d
by Ca
pa
ci
tor
V
o
l
t
ag
e
B
a
la
n
c
in
g (
C
V
B
)
co
ntr
o
l
l
e
r
.
Th
e
co
nt
rol
obj
e
c
t
i
v
e
o
f
t
h
e
C
V
B
con
t
ro
ll
er
i
s
to
r
e
g
ul
at
e
t
h
e
vo
lt
ag
e
l
e
ve
l
of
e
a
c
h
fl
o
a
ti
ng
c
a
p
a
c
i
t
o
r
i
n
p
ermi
tt
ed
v
o
l
t
a
g
e
r
an
g
e
.
In
o
rd
er
t
o
ac
hi
e
v
e
thi
s
,
a
l
l
c
a
p
a
c
i
t
or
v
ol
ta
g
e
s,
v
c
,
and
a
r
m
c
u
rre
nt
s,
i
arm
,
w
ill
b
e
s
a
m
pl
e
d
p
eri
o
d
i
call
y
.
Ea
ch
a
rm
c
a
p
aci
to
r
v
o
lt
ag
e
v
a
lu
e
s
w
il
l
t
he
n
be
s
or
t
e
d
in
a
sce
n
d
i
ng
o
rder
.
If the res
pec
t
i
v
e ar
m curre
nt i
s fo
u
nd
grea
t
e
r
tha
n
ze
r
o a
m
p
e
re
(
i
ua
or
i
la
>
0
A
)
, t
he
ga
t
e
s
w
itc
h-o
n
c
om
m
a
nds
w
ill
be
p
ri
ori
t
i
z
e
d
t
o
t
he
s
u
b
-m
od
ul
e
w
h
ic
h
c
a
p
ac
itor
v
o
l
t
a
g
e
v
a
l
ue
r
a
nke
d
first.
T
he
c
a
p
ac
it
or
o
f
th
i
s
sub-m
odu
le
w
il
l
st
a
r
t
be
in
g
c
h
arge
d
up
up
on
t
r
i
g
ge
ri
n
g
on.
C
on
v
e
r
sel
y
,
by
de
ter
m
ini
n
g
a
nega
tiv
e
arm
curr
ent
(
i
ua
o
r
i
la
<
0
A
),
t
he
s
ub-m
o
du
l
e
w
hic
h
c
a
p
ac
itor
v
o
l
t
a
g
e
va
lue
is
r
anke
d
a
t
bo
ttom
w
i
l
l
b
e
t
u
r
ned
on
for
disc
harg
i
n
g
.
T
he c
apa
c
itor
vol
ta
ge
b
a
l
anc
i
n
g
c
o
n
tr
ol
i
s e
x
e
cu
te
d in
p
ara
l
le
l
for
all
ar
ms in
MM
C.
3.
SYS
T
E
M
M
ODELLING
AND RE
S
U
LTS
V
ERIFICAT
ION
I
n
o
r
d
e
r
t
o
e
v
a
l
ua
te
t
he
f
ea
sib
i
l
ity
o
f
the
p
r
o
pose
d
c
on
verte
r
,
t
w
o
s
im
ul
a
t
i
on
mo
de
l
s
a
r
e
c
on
struc
t
e
d
as
s
how
n
in
F
i
gur
e
4
(a)
a
nd
(b).
I
n
F
i
gure
4
(a
),
t
he
c
on
ve
n
t
i
o
n
a
l
V
olt
a
ge
S
our
ce
Inve
rter
(
VS
I)
i
s
implem
e
n
te
d
a
s
a
r
ecu
pe
rat
i
n
g
c
o
nverte
r
.
T
h
e
p
o
w
e
r
circu
i
t
of
t
he
V
SI
c
an
b
e
referr
ed
f
rom
[17]
.
W
h
ereas,
F
i
gure
4 (
b
) show
s
t
h
e
i
n
t
e
gra
t
i
o
n of t
he pr
o
pose
d
M
o
d
u
l
a
r
Mu
l
t
ile
v
e
l C
onve
r
t
er
a
s a r
e
c
upe
ra
ti
n
g
con
v
e
rter.
The
r
e
ge
ne
rat
i
v
e
p
o
w
e
r
prod
uc
ed
b
y
a
br
ak
in
g
r
a
i
l
w
a
y
i
s
m
ode
l
l
e
d
a
s
a
c
on
t
r
o
llab
l
e
v
o
lta
ge
s
ource
.
Li
t
e
rat
u
re
s
had
doc
ume
n
te
d
t
h
at
t
he
d
c
vol
t
a
ge
m
ay
r
i
s
e
u
p
t
o
1
k
V
w
i
t
h
a
p
p
r
o
x
i
m
a
t
e
l
y
1
.
5
k
A
d
c
c
u
r
r
e
n
t
pro
duce
d
i
n
b
r
a
k
i
ng
m
o
de.
O
n
t
he
o
ther
h
a
nd,
t
he
t
r
acti
o
n
p
o
w
e
r
s
u
b
s
t
a
t
i
o
n
a
s
s
h
o
w
n
i
n
F
i
g
u
r
e
1
i
s
si
m
p
li
fie
d
a
s
a
thre
e-pha
se
s
t
a
r
con
n
e
c
te
d
RL
l
oad.
T
he
r
esist
i
ve
l
oa
d
va
lue
is
s
e
t
b
y
try
a
n
d
e
rror
t
o
m
eet
the
r
e
gene
ra
ti
ve
b
ra
ki
n
g
c
u
rrent
lim
i
t
g
iv
e
n
i
n
[1
9].
Con
v
e
r
sel
y,
t
he
m
odel
l
i
n
g
o
f
the
i
n
d
u
c
t
i
v
e
loa
d
i
s
re
fe
rri
n
g
t
o
t
he
f
i
e
ld
d
a
t
a
[1
9
]
.
As
t
h
e
g
e
n
era
t
o
r
i
mp
ed
an
ces
a
nd
r
eac
t
o
rs
i
n
f
o
r
ma
t
i
on
a
re
not
g
i
v
e
n
,
the
impe
da
nce
of
t
he
z
igz
a
g
t
rans
for
m
e
r
i
s
use
d
t
o
es
tim
at
e
th
e
t
r
a
c
t
i
o
n
s
u
b
s
ta
t
i
o
n
t
ota
l
i
m
p
eda
n
c
e
.
Ta
ble
1
prese
n
t
s
t
he
p
ar
am
eter
s
of
t
he
t
ra
nsf
o
rme
r
.
S
i
nc
e
t
h
e
pro
pos
ed
inve
rter
w
ill
be
i
nte
g
r
a
ted
t
o
t
he
s
ec
on
dar
y
st
a
r
w
in
d
i
ng
o
f
t
he
t
rans
fo
r
m
e
r
(
F
i
gur
e
1)
,
the
prim
ary
w
i
n
d
i
n
g
t
o
se
c
o
n
d
a
r
y
sta
r
w
i
n
d
i
ng
%
im
pe
dance
,
%
Z
sY
,
i
s
u
se
d
t
o
e
s
t
im
a
t
e
the
re
ac
t
a
nce
of
t
h
e
t
ra
nsform
er.
B
y
n
e
g
l
e
c
tin
g
t
h
e
re
si
s
t
an
c
e
o
f
t
h
e
t
r
ansfor
m
e
r,
X
sY
,
is
e
stima
t
e
d
a
s
21.8
1
m
Ω us
in
g (14).
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
P
o
w
Elec
&
D
r
i
S
y
st
I
S
S
N
:
2088-
86
94
Desig
n
a
n
i
ne
-
l
ev
el mo
du
l
a
r mul
tile
ve
l c
o
nv
erter
for
DC
ra
i
l
w
a
y
elec
tr
if
i
c
ati
on sy
ste
m
(C.
L. T
oh)
15
5
%
1
0
0
%
(
14)
Where,
P
a
n
d
V
r
epr
e
sent
t
h
e
r
ated
pow
er
i
n
v
o
l
t
-am
p
er
e
a
nd
t
h
e
n
o
m
i
na
l
p
h
ase
v
ol
t
a
ge
i
n
vo
lt.
B
y
usi
n
g
(
1
5
)
t
he
r
ea
c
t
anc
e
o
f
t
h
e
tr
ansform
e
r
is
e
stim
ated
a
p
p
ro
xima
te
l
y
7
0
µ
H
.
T
he
s
im
ula
t
i
o
n
pa
r
a
m
e
ter
s
a
r
e
su
mmari
z
ed
i
n T
a
b
l
e 2
.
(
15)
Ta
b
l
e
1.
P
a
r
a
m
e
t
er
s
of
t
he
z
ig
za
g
tr
ans
f
or
me
r
[
19]
Pa
r
a
m
e
t
e
r
Valu
e
Ra
t
e
d
powe
r
,
P
3300
kV
A
Ra
t
e
d
no
m
i
n
a
l
f
r
e
que
ncy
,
f
50
H
z
Ra
t
e
d
no
m
i
n
a
l
volta
g
e
–
p
r
i
m
a
ry,
V
p,
r
m
s
33
kV
Ra
t
e
d
no
m
i
n
a
l
volta
g
e
–
s
ec
ond
a
r
y
,
V
s,
rm
s
2
×
585
V
Prim
a
r
y
w
i
nding
to
s
ec
onda
ry
d
e
l
t
a
w
inding
%
i
m
pe
d
a
nce
,
%
Z
s
6.
86 %
Prim
a
r
y
w
i
nding
to
s
ec
onda
ry
s
t
a
r
winding
%
im
p
e
d
a
n
c
e
,
%
Z
sY
7
.
01 %
(a)
(b
)
F
i
gur
e
4.
S
imula
t
i
on
m
o
d
e
l
of
r
e
c
uper
a
ti
n
g
c
on
ve
r
t
er
s
yste
m
:
(
a
)
Volt
a
g
e
so
ur
ce
in
v
e
rter
(VSI),
(
b
) Mod
u
lar
mul
t
i
l
e
v
el
c
on
ve
rter
(MM
C)
Ta
ble
2.
S
i
m
u
latio
n
par
a
me
ter
s
V
olta
g
e
S
our
c
e
Inve
rte
r
(
VSI)
M
odula
r
M
ultile
v
e
l
C
onve
rt
e
r
(
MM
C)
DC
l
ink
Vol
t
a
g
e
,
V
dc
9
60
V
820
V
DC l
ink ca
p
a
c
itor,
C
dc
1
m
F
N
A
N
u
mb
er
o
f
p
o
w
e
r
c
el
l
p
e
r
ar
m,
N
NA
4
Ca
p
a
c
ita
n
c
e
p
e
r
sub-m
odule
,
C
SM
NA
18 m
F
Arm
induc
t
o
r
,
L
arm
NA
0.
5 m
H
R
e
s
i
s
t
i
v
e
Lo
a
d
p
er
p
h
a
s
e
,
R
0
.4
Ω
0
.4
Ω
I
n
d
u
c
t
i
v
e
L
o
ad
p
er
p
h
a
s
e
,
L
70
µH
70
µH
Sw
it
c
h
i
ng
Fre
que
n
c
y
,
f
sw
1000
Hz
1000
H
z
A
m
pli
t
ude
M
odula
tion
In
de
x,
m
a
1
.
0
0
1.
15
A
m
pli
t
ude
r
a
t
io
o
f
tria
ngula
r
w
a
v
e
s
,
1
0.
5
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
11,
N
o.
1
, Ma
r
202
0
:
151
–
15
9
15
6
The
re
cu
pera
ting
c
o
n
v
erter
s
y
ste
m
u
si
ng
V
S
I
is
m
uch
si
mple
c
om
p
are
t
o
M
M
C
.
A
l
l
the
g
a
t
i
n
g
signa
l
s
a
re
g
e
n
er
ate
d
from
the
s
i
nu
soi
d
al
p
u
l
se-
w
idt
h
-m
odu
la
tio
n
(SP
W
M)
b
loc
k
.
F
i
gur
e
5
(
a
)
sho
w
s
the
sim
u
la
t
i
on
r
esul
ts
o
f
the
thr
ee-
phase
m
o
d
u
l
a
t
i
n
g
w
a
ves
an
d
a
tria
n
gul
a
r
w
ave
prod
u
c
e
d
i
nside
t
h
e
S
P
WM
bl
oc
k.
T
he
p
e
a
k
o
f
a
l
l
s
i
nus
o
i
da
l
w
a
ves
a
n
d
t
h
e
t
r
i
a
n
g
u
l
a
r
w
a
ve
a
re
s
et
t
o
1
.
0
p.u.
(
m
a
=
1
.
0
)
.
T
he
s
in
usoi
da
l
w
a
ve
freq
u
enc
y
i
s
se
t
t
o
50 H
z
(referr
i
ng t
o
T
a
b
le
1
,
A
C
l
o
a
d m
o
d
e
lin
g) and the
tria
n
g
u
l
ar
w
a
v
e fre
q
ue
ncy i
s
set
e
q
u
i
va
le
n
t
t
o
t
h
e
sw
i
t
ch
i
n
g
fr
eque
nc
y,
i
.
e
.
1
kH
z.
A
d
c
li
n
k
c
a
pac
ito
r
of
1
m
F
is
i
nte
g
ra
t
e
d
t
o
s
t
a
bi
l
i
z
e
the
dc
l
i
n
k
v
o
lta
ge (pro
d
u
ce
d
by
the
tra
ct
ion rail i
n
rege
n
era
t
i
o
n mo
de)
.
In
th
is sim
ula
t
i
o
n
,
the dc
l
i
n
k
vo
lta
g
e
is
c
o
n
t
r
olla
ble
(assume
d
o
u
t
e
r
c
on
tro
l
l
oo
p
[2
0]
i
s
a
p
pli
e
d).
T
he
ref
o
r
e
t
he
d
c
l
i
n
k
v
o
lta
ge
i
s
r
e
gu
l
a
ted
a
t
96
0 V
.
With t
h
a
t
t
h
e
l
i
ne-t
o-l
i
n
e vo
l
t
age
is
r
e
gula
t
e
d
a
t
585
V
.
O
n
t
he
o
ther
h
a
nd,
M
MC
g
a
t
es
s
i
gna
ls
a
re
f
irs
t
b
ei
ng
d
e
t
e
r
m
i
ne
d
u
s
i
ng
t
h
e
T
H
V
I
-LS
P
W
M
modu
la
ti
o
n
t
ec
hn
ique
(
th
ird
ha
rm
on
i
c
v
o
l
ta
ge
i
n
j
ec
tio
n
l
e
vel
sh
i
f
te
d
pul
se
w
id
th
m
odu
lat
i
on).
F
i
g
u
re
5
(
b)
and
(c
)
show
s
the
c
a
r
r
ier
wa
ves
an
d
m
o
d
u
la
t
i
o
n
w
ave
s
b
e
i
ng
ge
n
e
ra
te
d
f
o
r
u
pper
a
nd
l
o
w
e
r
arm
s
o
f
the
M
M
C
.
Sin
c
e
fo
ur
u
nits
o
f
s
u
b-modu
le
s
a
r
e
con
n
ec
te
d
i
n
s
erie
s
in
eac
h
ar
m
of
M
MC,
fo
ur
u
ni
ts
o
f
tria
ng
u
l
ar
w
av
e
s
a
r
e
d
em
an
d
e
d.
T
he
se
t
ria
n
gu
lar
wa
ves
a
r
e
i
d
en
t
ical
i
n
a
m
plit
ude
a
n
d
p
hase.
The
m
o
d
u
l
a
t
i
o
n
w
a
ve
s
w
h
ic
h
con
s
is
t
of
t
h
e
t
h
i
rd
h
ar
mon
i
c
vol
tage
c
om
p
one
n
t
a
l
l
ow
a
n
inc
r
ea
si
n
g
o
f
ad
d
iti
ona
l
1
5
%
to
t
h
e
modu
l
a
ti
on
i
nd
e
x
.
Th
e
mai
n
a
dv
an
t
a
ge
w
o
u
l
d
b
e
d
e
c
r
ea
si
ng
t
h
e
d
c
l
i
n
k
vo
lta
ge
l
eve
l
t
o
8
20
V
w
h
i
l
e
ma
int
a
in
in
g
th
e
effec
t
ive
line
-
t
o
-
line
v
o
lta
ge
a
t
5
8
5
V
.
Th
e
dc
l
i
nk
c
a
p
a
c
it
or
(
1
m
F
)
is
n
o
t
d
em
and
e
d
w
ith
the
inte
gr
at
ion
of
M
M
C
a
s
rec
upera
tin
g
co
n
v
er
t
e
r.
T
his
is
m
a
i
nl
y
due
t
o
t
h
e
dc
l
in
k
v
o
l
ta
ge
c
a
n
b
e
s
t
a
b
i
l
i
z
e
d
t
h
r
o
u
g
h
t
h
e
s
w
i
t
c
h
i
n
g
a
c
t
i
v
i
t
i
e
s
o
n
e
a
c
h
s
u
b
-
m
o
d
u
l
e
e
i
t
h
e
r
t
o
i
nse
r
t
or
b
y
p
ass
a
n
a
ppr
opria
te
n
u
m
be
r
of
sub-m
odu
les
for
e
a
c
h
p
ha
se
l
e
g
.
Th
us,
ca
pa
cit
o
r
vo
lta
ge
b
alanc
i
ng
c
on
trol
i
s
esse
n
tia
l
t
o
m
ai
nt
ai
n
the
pr
o
p
er
opera
tio
n
of t
h
e
MMC.
(a)
(b)
(c)
F
i
gure
5.
(a
)
S
inuso
i
dal
P
u
lse
Wid
t
h
M
o
d
u
la
t
i
o
n
(S
P
W
M
)
for
VS
I
,
(b)
T
hird H
a
r
m
oni
c
V
o
l
t
a
g
e
Injec
t
i
o
n
Leve
l
S
h
ifte
d
P
u
lse W
i
dt
h
Mod
u
l
at
i
on (TH
V
I-LS
P
W
M)
for
up
p
er
a
rm
MMC,
(
c
)
THV
I-LSP
W
M
f
or
lower
a
rm
M
MC
A
s
s
how
n
in
F
igure
4(b),
the
Capac
itor
V
o
l
t
age
Ba
la
n
c
in
g
C
o
n
t
ro
l
bl
oc
k
w
i
ll
sa
mple
t
he
a
r
m
curr
ents
a
nd
e
a
c
h
s
u
b
-
m
od
ul
e
ca
paci
tor
v
o
l
t
a
ge
v
a
l
ues
p
e
r
i
o
d
ica
l
l
y
.
Aft
e
r
e
x
ec
uti
n
g
th
e
ca
p
a
c
i
to
r
vo
lt
age
bala
nc
i
n
g
c
o
n
t
r
o
l
a
l
gori
t
hm
,
appr
opria
te
g
a
t
e
s
i
gna
ls
w
il
l
the
n
b
e
d
i
s
t
ri
bu
t
e
d
to
t
h
e
c
or
respo
n
d
enc
e
su
b-
modu
les.
F
ig
u
r
e
6
i.
i
l
l
us
trates
t
he
t
rajec
t
o
r
ies
of
uppe
r
and
lower
arm
currents
in
phas
e
l
e
g
-a.
W
h
en
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
D
e
sign
a n
i
ne-
l
e
vel
m
o
du
lar
m
u
lti
leve
l
co
nv
e
r
t
e
r f
o
r D
C
ra
ilw
ay
elec
t
r
if
ic
at
ion
sy
s
t
e
m
(C.
L
.
T
oh)
15
7
t
h
e
con
t
ro
ll
er
i
d
e
nt
i
f
i
e
s
a
p
o
s
it
iv
e
arm
cu
rre
n
t
,
th
e
cap
a
c
i
t
or
vol
t
a
ge
o
f
al
l
sub-m
o
du
les
i
n
t
ha
t
pa
rt
i
c
u
l
a
r
a
rm
w
ill
va
r
y
i
n
a
n
i
nc
rea
s
i
n
g
tr
e
nd.
A
s
ha
rp
d
ec
li
ne
o
f
the
s
e
capa
ci
to
r
vo
lt
a
g
e
s
h
a
p
p
e
n
wh
en
n
e
g
at
i
v
e
a
r
m
c
u
r
r
e
n
t
i
s
d
e
t
e
c
t
e
d
.
T
h
e
s
e
b
e
h
a
v
i
o
r
s
a
r
e
c
l
e
a
r
l
y
d
e
p
i
t
c
h
e
d
i
n
F
ig
ure
6
ii
.
The
z
o
om-
i
n
v
i
ew
o
f
ca
p
a
c
i
t
o
r
vo
lta
ge
w
ave
f
orm
s
f
or
s
u
b
-m
odule
s
l
oca
t
e
d
i
n
u
p
p
e
r
a
nd
l
ow
er
a
r
m
s
(
phase-a
)
ar
e
show
n
in
F
i
g
u
r
e
6
iii
and
i
v
.
The
resu
lts
c
o
n
firm
t
ha
t
the
ca
pa
cit
o
r
v
o
l
ta
ge
b
ala
n
c
i
n
g
c
ont
rol
a
l
g
o
ri
thm
ha
d
bee
n
m
od
elle
d
succe
ssfu
lly
s
i
n
ce
a
l
l
t
he
ca
p
acit
o
r
vo
ltage
l
eve
l
s
i
n
o
ne a
rm
are
alterna
t
i
n
g
l
y incre
a
se
d
or de
c
re
ased.
i
i
i
i
ii
i
v
F
i
gure
6.
S
imula
t
i
on r
e
su
l
t
s
for
p
h
a
s
e-a
:
i
) a
r
m
s
’ c
u
rrents,
i
i
)
c
a
pac
itor
v
o
lta
ge o
f su
b-m
odule
s
loca
te
d
i
n
phas
e
l
eg-a
,
i
ii)
z
oo
m
in view
of
v
c_ua[1-4
]
at
ti
m
e in
st
an
t
0
.
98
13
s,
iv)
zo
om
in vie
w
of
v
c_la[
1
-4
]
a
t
t
i
m
e
in
sta
n
t
0.97
7
9
s
Th
e
s
t
eady
st
ate
t
h
ree
ph
a
s
e
vo
lt
ag
e
s
a
nd
c
u
rre
n
t
s
wav
e
f
o
r
m
s
a
r
e
prese
n
te
d
i
n
F
ig
ure
7.
F
or
e
a
s
e
of
com
p
aris
on,
t
h
e
r
e
s
ul
t
s
p
ro
du
ce
d
by
V
S
I
ar
e
tab
u
la
te
d
i
n
c
ol
umn
(
a
)
w
hil
e
c
ol
um
n
(
b
)
is
r
eserve
d
for
M
M
C
resul
t
s.
A
s
sho
w
n
in
F
igur
e
7
(a
)
i.,
the
ph
ase
vo
l
t
a
g
es
g
ene
r
a
te
d
b
y
t
h
e
c
on
ven
t
io
na
l
V
S
I
are
balan
c
e
bu
t
di
st
orte
d.
The
y
ar
e sw
itch
e
d fr
om -⅔
V
dc
to
⅔
V
dc
w
h
i
l
e
t
h
e
l
in
e
-
to
-lin
e
vol
t
a
g
e
wav
e
f
orm
is tri
g
g
er
ed from
V
dc
to
–
V
dc
.
Their
THD
indexe
s
a
r
e
capture
d
us
i
n
g
t
h
e
MA
TLA
B
P
o
w
e
r
gui
F
F
T
A
naysis
T
o
o
l
a
s
68.
70
%.
The
A
C
c
ur
rent
s
a
l
s
o
c
o
n
ta
i
n
l
ar
ge
r
ipp
l
e
and
a
lo
t
of
s
i
d
eba
n
d
h
arm
o
nic
s
c
omp
one
n
t
s.
T
he
THD
i
nde
xes
for
al
l
pha
ses
ar
e
c
l
ose
d
t
o
33.5
1
%
.
In
o
rde
r
t
o
m
i
t
i
ga
t
e
t
he
s
e
ha
rmo
n
ic
d
is
tort
i
o
n,
A
C
fil
t
ers
[2
1,
22]
mu
st
b
e i
m
pl
e
m
en
t
e
d
.
H
o
w
e
ver,
t
h
i
s
pow
er
q
ua
li
t
y
i
ss
ue
can
a
lso
b
e
s
o
l
ve
d
b
y
i
mp
lem
e
n
t
in
g
MMC
a
s
a
rec
upera
t
i
ng
con
v
er
t
e
r
in
T
P
S
S
.
A
s
s
how
n
in
F
ig
ure
7
(b)
i.,
MM
C
m
a
nage
s
t
o
pr
o
d
uc
e
s
i
n
u
s
o
i
d
al
p
ha
se
v
o
lta
ges
an
d
l
i
n
e-to
-li
n
e
v
o
lt
a
g
e
wa
v
e
f
o
rms
wit
h
s
ma
ll
r
ip
pl
e
s
.
Th
e
s
e
vo
lt
a
g
es
d
is
tort
ion
in
de
xes
a
r
e
re
corde
d
l
ess
th
a
n
3.5
%.
I
n
a
d
d
i
t
i
o
n
a
c
lea
n
a
nd
g
o
o
d
qua
l
i
t
y
l
i
n
e
c
u
rre
n
t
s
ha
d
a
l
s
o
b
e
en
g
en
era
t
ed
w
ith
t
he
TH
D
i
nde
x
a
s
l
ow
as 2.
37 %.
A
ll the
TH
D
index
e
s
for
w
a
ve
for
m
s show
n in F
i
gure
7 ar
e summ
arize
d
in Ta
b
l
e 3
.
i
ii
iii
(
a
)
(
b
)
F
i
gur
e 7.
S
i
m
ulat
i
on re
su
l
t
s for
(a
) VS
I, (
b) M
MC.
The
su
b
-
pl
ot
s
show
:
i
)
pha
se
vo
l
tage
w
avef
orm
s
,
i
i
)
l
i
ne
-
t
o-l
i
ne
vo
l
tage,
v
ab
,
wave
form
,
and i
i
i
) pha
se
c
urren
t
w
avef
orm
s
0.
96
0.
96
5
0.
97
0.
9
7
5
0.
98
0.
98
5
0.
9
9
0.
9
9
5
1
-5
00
0
50
0
v
sa
, v
sb
, v
sc
[V
]
ti
m
e
(
s
)
0.
96
0.
96
5
0.
97
0.
9
7
5
0.
98
0.
98
5
0.
9
9
0.
9
9
5
1
-10
0
0
0
10
00
i
sa
, i
sb
, i
sc
[A
]
ti
m
e
(
s
)
0.
96
0.
96
5
0.
97
0.
9
7
5
0.
98
0.
98
5
0.
9
9
0.
9
9
5
1
-10
0
0
0
10
00
v
ab
[V]
ti
m
e
(
s
)
0.
96
0.
9
6
5
0.
9
7
0.
975
0.
98
0.
9
8
5
0.
99
0.
995
1
-5
00
0
50
0
ti
m
e
(
s
)
0.
96
0.
9
6
5
0.
9
7
0.
975
0.
98
0.
9
8
5
0.
99
0.
995
1
-1
00
0
0
10
00
ti
m
e
(
s
)
0.
96
0.
9
6
5
0.
9
7
0.
975
0.
98
0.
9
8
5
0.
99
0.
995
1
-1
00
0
0
10
00
ti
m
e
(
s
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
11,
N
o.
1
, Ma
r
202
0
:
151
–
15
9
15
8
Tab
l
e
3. Tota
l
h
arm
o
n
i
c dis
t
o
r
tion
in
de
xes c
o
mpa
r
ison
be
t
w
ee
n v
o
l
t
a
ge
s
our
ce
inve
rt
er (VS
I)
and
mod
u
l
ar
mult
ile
ve
l
co
nve
rter
(MMC)
V
S
I
M
M
C
P
h
a
s
e
vol
t
a
g
e
dist
o
rtio
n,
TH
D
v
6
8.
70
%
3.
29
%
L
i
ne
-
l
i
n
e
volt
a
ge
d
ist
o
r
t
i
on,
TH
D
v
6
8.
71
%
3.
14
%
P
h
as
e
cu
r
r
en
t
d
i
s
t
o
r
t
i
o
n
,
TH
D
i
3
3.
51
%
2.
37
%
4.
CONCL
U
S
ION
Th
is
p
aper
p
rop
o
se
s
t
o
r
ep
l
ace
a
c
o
n
v
en
t
i
o
n
a
l
r
ecu
pe
rati
n
g
c
on
v
erter
sys
t
em
w
ith
a
n
i
n
e
-
lev
e
l
Mo
du
la
r
M
u
l
t
ileve
l
C
onve
rte
r
(
MM
C)
.
The
op
e
r
a
t
i
o
nal
pr
i
n
c
i
pa
l
o
f
t
h
e
M
M
C
ha
d
bee
n
p
re
se
nte
d
i
n
br
i
e
f
to
ge
ther
w
i
t
h
a
fe
asi
b
l
e
c
o
n
t
r
o
l
an
d
m
o
dul
a
t
i
o
n
t
e
c
h
ni
q
u
e
.
A
u
th
ors
c
h
o
o
se
t
o
bala
nc
e
t
h
e
vo
l
t
a
g
e
le
ve
l
o
f
the
ca
pac
i
t
o
r
in
e
ac
h
s
ub-m
o
d
u
l
e
as
t
he
m
ain
co
n
t
ro
l
o
b
je
c
tive
.
A
s
imple
c
o
nt
r
o
l
a
l
g
o
ri
t
h
m
ha
d
bee
n
pro
pose
d
t
o
ke
ep
a
l
l
t
he
c
apa
c
itor
v
o
l
t
a
ges
fluc
t
u
a
t
e
w
i
t
h
in
a
to
ler
a
nc
d
ban
d
.
Be
s
i
de
s,
t
he
c
o
n
c
e
p
t
o
f
t
h
i
r
d
harm
on
ic
v
o
l
t
a
ge
i
nje
c
t
i
on
l
e
ve
l
s
h
i
f
ted
pu
lse
w
i
d
t
h
m
odu
la
tio
n
(
T
H
V
I
-
L
S
P
W
M
)
t
e
c
h
n
i
q
u
e
h
a
d
b
e
e
n
di
sc
usse
d.
T
he
s
imu
l
a
t
i
o
n
res
u
l
t
s
o
f
t
he
M
M
C
h
as
c
o
n
firm
ed
t
ha
t
t
he
A
C
l
i
ne
f
i
l
t
e
r
a
n
d
dc
lin
k
c
a
p
ac
i
t
or
a
re
pos
si
b
l
e
t
o
b
e
elimi
n
a
t
e
d
.
Th
e
pro
duce
d
v
o
l
tage
s
an
d
c
u
r
r
ent
s
a
re
n
ear
ly
s
in
uso
i
da
l
w
i
th
t
he
T
o
t
a
l
H
arm
onic
D
i
stor
tio
n (
T
H
D
)
i
n
d
e
x
es re
c
orde
d less t
h
an
3
.5
%
.
ACKNOW
LEDG
E
MEN
T
S
Th
e
au
th
o
r
s
are
pl
e
a
s
e
d
to
e
xp
ress
t
h
e
i
r
a
pprec
i
a
ti
on
t
o
th
e
Mi
ni
st
r
y
o
f
Ed
u
cati
o
n
(M
O
E
),
M
a
l
a
y
s
i
a
for
sp
o
n
sor
i
n
g
the
F
u
nd
a
m
e
n
ta
l
R
e
sear
ch
G
ra
nt
S
che
m
e
(F
R
G
S
)
t
o
c
ond
uc
t
this
r
e
s
e
a
rc
h.
P
rojec
t
C
o
d
e
:
F
R
G
S
/1/
2
01
6
/
TK
04
/U
N
I
TEN
/02/
1.
REFE
RENCES
[1]
V.
G
e
l
m
a
n,
"
Braki
n
g
Energ
y
R
ecup
e
r
a
ti
on
-
Revers
ib
le
T
hyri
s
t
o
r-
Control
l
ed
R
ectifiers,"
IEEE V
e
hicular
T
echn
o
lo
gy M
agaz
ine
, v
ol
.
4
,
n
o
. 3
,
p
p
. 8
2
- 89
,
2
0
0
9
.
[2]
H.
I
baio
nd
o
,
A
.
Ro
m
o
,
"
K
in
e
t
ic
E
nerg
y
Reco
very
o
n
Railway
S
yst
e
m
s
w
it
h
F
eed
back
t
o
the
Gri
d
,"
i
n
14
th
Int
e
rna
t
i
o
n
a
l
Power Electr
onics
an
d M
o
tio
n Co
n
t
ro
l
Confer
ence
, Oh
r
i
d
,
p
p
. 9
4-9
7
, 20
1
0
.
[3]
S
-
H
S
o
n
g
,
S
-
J
Jang,
H
-J
B
ang
,
C
-Y
W
on
,
"
R
eg
enerati
o
n
i
n
v
e
rter
s
ystem
f
o
r
DC
t
ract
ion
w
i
th
h
a
r
m
oni
c
red
u
ct
ion
capab
ili
ty," in
3
0
th
An
nu
al Confer
ence o
f
t
h
e IEEE
Ind. El
ectr
o
n
i
cs
Soci
e
ty
,
Bu
san
,
p
p.
146
3-1
468,
2
00
4.
[4]
P
.
A
rb
o
l
eya,
P
.
Bid
a
gu
ren,
U
.
Arm
e
nd
ariz,
"En
e
rgy
i
s
o
n
bo
ard:
En
e
r
gy
s
to
ra
ge
a
nd
o
the
r
a
lte
r
na
tive
s
in
m
o
d
e
r
n
li
ght
r
ai
lw
a
y
s,
"
I
E
E
E
E
l
ectrification M
a
gazine
, v
ol.
4
,
no
. 3
pp
.
3
0-4
1
,
2
01
6.
[5]
J.
S
wansan,
J
.
S
m
a
tl
ak,
"State-o
f-
t
h
e
-
a
r
t
i
n
L
i
g
h
t
R
a
i
l
A
l
te
r
n
a
t
i
ve
P
o
w
er
S
upp
li
es,
"
i
n
AP
TA
/T
R
B
20
15
Ligh
t Ra
il
Con
f
eren
ce
, pp
. 1
-1
6, 20
1
5
.
[6]
G.
V
,
"Energ
y
s
t
orag
e
th
at
m
a
y
b
e
to
o
go
od
t
o
b
e
t
ru
e:
C
om
p
a
ris
o
n
b
etween
w
ay
sid
e
s
t
o
rage
a
n
d
r
ev
e
r
s
i
b
l
e
thyristor
controlled rect
ifiers f
or
heavy rail
,"
IEEE
V
e
h.
T
e
ch
no
l. M
a
g
.,
v
o
l
.
8
,
n
o
.
4
,
p
p
.
7
0
-
80
,
2013
.
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F.
C
i
cca
rel
l
i
,
D
.
Iannuzzi
,
K.
K
ondo, L
.
Frat
e
lli,
"
L
i
ne-vol
tag
e
con
t
rol
b
a
s
e
d
on
way
s
id
e energ
y
s
to
rage s
ys
tem
s
f
o
r
tra
m
wa
y n
e
twor
k
s
,"
IEE
E
Tr
ans. o
n
P
o
wer
El
ectroni
cs
, v
ol
. 31
,
n
o. 1,
p
p
.
88
4-8
9
9, 20
1
6
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[8]
W.
A
.
G
.
d
e
Ja
ger,
M
.
H
u
i
zer,
E
.
K
.
H.
v
an
d
er
P
ols,
"
Implemen
t
ati
o
n
of
acti
v
e
reg
e
n
e
rat
i
on
u
ni
t
i
n
a
t
ract
io
n
substa
ti
on," in
16th
Eu
ro
pea
n
Co
nf
e
r
ence o
n
P
o
wer
El
ectr
o
n
i
cs and
Ap
p
l
icati
o
n
s
,
L
a
p
p
ee
nran
t
a
, p
p. 1-9
,
2
0
1
4
.
[9]
D.
C
o
r
nic,
"
Efficien
t
recovery
o
f
braki
n
g
en
ergy
t
hro
ugh
a
r
ev
e
rsib
le
d
c
s
ubstat
i
o
n
,
"
i
n
E
l
ectrica
l Sys
t
ems for
Aircr
aft
,
R
a
ilway
an
d S
h
ip Propul
si
on
,
Bol
o
g
n
a,
pp.
1
-9,
2
010.
[10]
S
-
J
Jan
g
,
C-Y
Cho
i
,
C-H
Bae,
S
-H
S
on
g,
C
-Y
W
o
n
,
"S
tu
dy
of
r
eg
en
er
ati
o
n
p
o
w
e
r
co
nt
ro
l
i
nvert
er
f
o
r
D
C
t
r
acto
n
with
acti
v
e
po
wer
filter
abi
lity,"
i
n
3
1
st
A
nnua
l Co
n
f
erence
o
f
IEEE In
dustria
l Elect
ro
n
i
cs S
o
ciet
y
,
R
a
l
e
i
g
h
,
pp
.
1
271
-12
7
7
, 2
005
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[11]
B.
G
em
m
e
ll,
J
.
Dorn
,
D.
R
etzm
an
n,
D
.
S
o
era
n
gr,
"
P
ro
sp
ec
t
s
o
f
M
u
lt
ilevel
VSC
Technol
ogies
f
o
r
Powe
r
Transmissi
on," in
pr
oc IE
EE
/PES
T
&
D Conf.
Exp
o
., pp
.
1
-16
,
2
0
0
8
.
[12]
S
.
K
o
u
r
o
,
M
.
M
a
l
i
n
o
w
s
k
i
,
K
.
G
o
p
a
k
u
m
a
r
,
J
.
P
o
u
,
L
.
G
.
F
r
a
n
q
u
e
l
o
,
B
.
W
u
,
J
.
R
o
d
r
i
g
u
e
z
,
M
.
A
.
P
e
r
e
z
,
J
.
I
.
L
e
o
n
,
"Re
cen
t
adv
a
m
ces
a
nd
i
n
d
u
strial
a
ppl
icatio
ns
o
f
m
u
ltil
e
v
el
c
on
v
ert
e
rs,"
IE
E
E
. Tr
ans
.
on
Ind
.
Ele
c
tr
onics
,
vol.
57,
no
.
8
,
pp
.
2
5
5
3
-2
010
,
2
01
0.
[13]
D.
R
onanki,
S
.
S
.
Williamson,
"M
odular
M
ul
t
i
l
evel
C
onvert
ers
f
o
r
t
r
ans
p
o
r
ta
tion
el
ectrifi
cati
o
n
:
c
h
a
ll
eng
e
s
an
d
op
po
rtun
ities
,
"
IEEE T
r
an
s
of T
r
an
spo
r
t
a
tio
n Electr
i
fica
t
i
o
n
, v
ol
. 4
,
n
o
. 2
, p
p.
3
99
-40
7
, 2
01
8.
[14]
M.
G
linka,
R
.
M
arqua
r
t
,
"
A
new
AC
/AC
Mu
ltilevel
Co
nverter
Fami
l
y,
"
IEEE T
r
a
n
s.
on
In
d.
Electr
onics
,
v
o
l
.
52
,
no
.
3
,
pp
.
6
6
2
-
6
6
9,
2
00
5.
[15]
Q
.
X
u
,
F
.
M
a
,
Z
.
H
e
,
Y
.
C
h
e
n
,
J
.
M
.
G
u
e
r
r
e
r
o
,
A
.
L
u
o
,
Y
.
L
i
,
Y
.
Y
ue,
"An
a
lys
i
s
an
d
com
p
ari
s
o
n
o
f
mo
dular
Rail
way
P
o
wer
Conditioner
f
o
r
high
-speed
r
ail
w
ay
t
racti
on
sys
t
e
m,"
IEEE
Tran
. O
n
P
o
wer
Elect
ro
n
i
cs
,
vo
l.
3
2,
no
.
8
,
pp
.
6
0
3
1
-6
048
,
2
01
7.
[16]
G
.
G
u
o
,
Q
.
S
o
n
g
,
W
.
Y
a
n
g
,
Y
.
W
a
n
g
,
W
.
L
i
u
,
H
.
R
a
o
,
S
.
X
u
,
"
A
p
p
l
icati
o
n
o
f
t
hird
-ord
er
h
arm
o
n
i
c
volt
a
ge
injection
i
n
a modular
mu
ltilevel
converter,"
IEEE Tr
ans
.
on
Ind. El
ectr
o
n
i
cs
,
vol.
65,
no.
7
,
pp.
5
2
6
0
-
5
2
7
1
,
201
8.
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
D
e
sign
a n
i
ne-
l
e
vel
m
o
du
lar
m
u
lti
leve
l
co
nv
e
r
t
e
r f
o
r D
C
ra
ilw
ay
elec
t
r
if
ic
at
ion
sy
s
t
e
m
(C.
L
.
T
oh)
15
9
[17]
M
.
A
.
Boo
s
t
,
P
.
D.
Z
i
o
g
a
s,
"
State-of
-th
e
-art
carrier
P
W
M
T
echn
i
q
u
es:
A
crit
ical
e
v
a
luat
io
n,"
IE
EE T
r
an
s
.
on
In
d.
Applications
, vo
l
. 2
4,
no
.
2
,
pp
. 2
71
-2
80
,
1
9
8
8
.
[18]
G. Ab
a
d,
P
o
wer electr
o
n
i
cs an
d
el
ectr
i
c dri
v
es
f
o
r tr
acti
on
ap
p
lica
tio
n
s
,
Spain
:
Jo
h
n
W
iley &
Son
s
.
L
t
d
., 2
01
7
.
[19]
M
.
R
a
j
arat
nam
,
P
.
Gu
yard
,
N
.
M
azet,
"P
lan
o
f
I
nst
r
uc
t
i
o
n
-
T
rac
t
i
o
n
P
o
w
e
r
S
u
b
-
S
t
a
t
i
o
n
(
T
P
S
S
)
O
v
e
r
a
l
l
S
y
s
t
e
m
Description,"
Kons
ortiu
m CM
C-COL
A
S
-
UNIW
AY
,
K
uala
L
um
p
u
r,
201
6.
[20]
J.
I
.
Leo
n
,
S
.
V
azq
uez,
L
.
G
.
F
ran
quel
o
,
"
M
u
ltilev
e
l
co
nv
erters
:
con
t
rol
an
d
m
o
du
la
ti
on
tech
ni
qu
es
f
o
r
t
h
e
ir
op
eratio
n
a
n
d
indus
tri
a
l
ap
p
l
ication
s
,
"
Pro
ceedin
gs
o
f
T
h
e
IEEE
,
vo
l.
1
05
, n
o.
1
1,
p
p
.
2
06
6
-
20
81
,
2
0
1
7
.
[21]
B
.
R
M
a
d
h
u
,
M
.
N
.
D
i
n
n
e
s
h
,
B
.
M
.
R
a
v
i
t
h
e
j
a
,
"
D
e
s
i
g
n
o
f
S
h
u
n
t
H
yb
rid
Ac
tiv
e
P
o
w
e
r
F
il
te
r
to
r
e
d
uc
e
h
a
rmon
ic
s
on
A
C
sid
e
due
t
o
no
n-linear
l
oads
,
"
In
ter
natio
na
l Jou
r
n
a
l
of Po
wer
El
ectr
o
n
i
cs an
d
D
r
ive S
y
stem
(IJEPD
S
)
,
v
o
l.
9
,
no
. 4
,
p
p
.
1
92
6-1
9
3
6
, 2
01
8.
[22]
B.
R
ah
im
a,
G
.
A
m
ar,
B.
M
.
T
o
u
f
i
k
,
C.
M
oham
e
d
,
"
Hi
gh
-perf
o
rm
an
ce
acti
v
e
po
we
r
filt
er
i
m
p
lem
e
n
t
ation
b
a
sed
on
pred
icti
ve
c
urren
t
c
o
n
t
r
o
l
,
"
Intern
at
io
nal Jo
ur
nal
of
P
o
wer El
ectron
i
cs
an
d Drive
Syst
em (
I
JEPD
S
)
,
vo
l.
1
0
,
no.
1
,
pp
.
2
77-2
8
7
,
2
0
1
9.
B
I
OGRAPHIES
O
F AUTHO
RS
Chu
e
n
Li
ng
T
o
h
receiv
e
d
th
e
B.
E
n
g
.
an
d
M.
E
n
g
.
d
e
gree
in
e
l
ect
rical
e
n
g
i
n
eering,
b
o
t
h
fro
m
Un
iv
ersi
ti
T
ekn
o
lo
gi
M
a
l
aysia
(UT
M
),
S
ku
dai,
M
al
ays
i
a,
i
n
2002
and
2
0
0
5
r
esp
ectiv
ely
;
a
nd
her
P
h
.D
i
n
El
ectrical
P
ower
E
ng
in
ee
ri
ng
f
ro
m
No
rwegian
Un
iv
ers
i
t
y
o
f
S
cien
ce
a
nd
Te
c
h
n
o
log
y
(NT
N
U),
Tro
n
d
h
e
i
m
,
N
orwa
y,
i
n
20
14
.
Cu
rre
ntly
,
sh
e
i
s
a
S
e
ni
or
L
ect
urer
a
t
th
e
Un
iv
ers
i
ti
T
en
ag
a
Nas
i
o
n
al,
K
a
jang
,
Mal
a
ysia.
H
e
r
teach
in
g
and
r
e
search
i
nteres
ts
i
ncl
ude
t
h
e
fiel
d
o
f
pow
er
e
l
ectron
i
cs
,
mo
to
r
dri
v
e
system
s
an
d
fi
eld
p
r
ogr
a
mma
ble
ga
te
a
rra
y
app
l
i
cati
o
n
s
.
S
h
e
is
a
l
s
o
a
M
e
m
b
er
o
f
IEE
E
P
o
w
er
Elect
ro
nics
S
o
ciet
y
(PELS
)
M
a
l
aysia
Chapter.
P
e
i
Chen
g
Ooi
receiv
e
d
th
e
B.
E
ng
.,
M
.
S
c
.,
a
nd
P
h
.
D.
d
egree
s
i
n
20
01
,
2
0
0
3
,
an
d
20
12
,
resp
ecti
v
ely
.
I
n
2
0
0
5
,
she
jo
in
e
d
t
he
E
lect
rical
a
nd
E
l
ectro
ni
c
E
n
g
i
n
eerin
g
De
part
m
e
nt,
Th
e
Un
iv
ers
i
ty
o
f
N
o
tti
n
g
h
am
M
a
l
ays
i
a
Cam
p
us,
where
s
h
e
is
c
urr
e
n
t
l
y
an
A
sso
ciat
e
P
r
of
es
so
r
.
S
h
e
i
s
a
S
en
io
r
F
e
llow
of
t
h
e
H
i
gher
E
d
u
cati
on
Academ
y
,
U
K
and
has
been
l
ectu
r
ing
in
t
he
elect
rical
and
ele
ct
ro
ni
c areas f
o
r
fif
t
een y
ears.
Evaluation Warning : The document was created with Spire.PDF for Python.