Internati
o
nal
Journal of P
o
wer Elect
roni
cs an
d
Drive
S
y
ste
m
(I
JPE
D
S)
V
o
l.
4, N
o
. 3
,
Sep
t
em
b
e
r
2014
, pp
. 36
3
~
37
5
I
S
SN
: 208
8-8
6
9
4
3
63
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJPEDS
A Survey and Experimen
t
al Verif
i
cati
on of M
o
dular Multi
l
evel
Converters
Sreedhar Madichetty*, Das
g
upta
Abhijit*, Sivaji Jinka**
*School of
Electrical Eng
i
ne
erin
g, KIIT University
** VIT University
Article Info
A
B
STRAC
T
Article histo
r
y:
Received
Ma
r 4, 2014
Rev
i
sed
Ap
r
23
, 20
14
Accepted
May 15, 2014
This art
i
cl
e pri
m
a
ril
y
brings to
lim
e
light the Multi-lev
e
l con
v
erters
rev
i
ew
and specif
i
call
y the form
and
function of m
odular m
u
ltil
ev
el conv
erter
(MMC) with t
h
eir modulation
,
design
consid
erations, balancing issues,
control s
c
hem
e
s, and
appl
ic
atio
ns. This
arti
cle
intends to
m
a
ke
a d
e
ta
ile
d
anal
ysis of M
M
C with their
control
l
er r
e
la
t
e
d issues in co
m
p
rehensive
manner. It is an approach for MMC
design and
modulation schemes in eas
y
manner. Furth
e
r
m
ore, a
five lev
e
l MMC
hav
e
b
een d
e
signed with optimal
controller and v
e
rified b
y
its experiment
al r
e
sults and explor
ed. In
addition
to
that
, th
is
appro
a
ch draws
s
t
r
a
teg
i
c
conclusions
o
n
MMC towards making th
e
s
y
stem
m
o
re rob
u
st in op
era
tion,
less com
p
lex
in
design and
con
t
r
o
l.
Keyword:
MMC
MMC Co
n
t
ro
ller
Survey On
M
M
C
Copyright ©
201
4 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
M
a
di
chet
t
y
Sre
e
dha
r,
Sch
ool
o
f
El
ec
t
r
i
cal
En
gi
neer
i
ng,
KI
IT Uni
v
er
sity
.
Em
a
il: sreed
h
a
r.8
0
3
@
g
m
ail.c
m
1.
INTRODUCTION
Many inve
stigations in the
field
of m
odula
r
m
u
lti-level inverters ha
ve le
d to
succes
sful operation i
n
HVDC system
s. In rec
e
nt tim
es, in
t
h
e
po
wer t
r
ansm
i
ssion
era,
f
o
r
ve
r
y
l
o
n
g
di
st
a
n
c
e
s, hi
gh
v
o
l
t
a
g
e
DC
(H
VDC
) t
r
an
s
m
i
ssi
on l
i
n
es base
d o
n
cu
rre
nt
so
urce i
n
ve
rt
ers (C
S
I) a
n
d v
o
l
t
a
ge so
u
r
ce i
nvert
e
r
s (
V
SI
) are
found to be
offering m
o
re econom
ic and cost
effectiv
e power transm
ission. But,
recently HVDC transm
ission
syste
m
s
based on VSI have r
eceived i
n
crea
sing attention
due t
o
m
a
ny
opportunities li
ke the
gri
d
ac
cess of
weak
AC
net
w
or
ks, i
nde
pe
nd
ent
co
nt
r
o
l
of
act
i
v
e and
reac
t
i
v
e po
we
r, s
u
ppl
y
o
f
pa
ssi
v
e
net
w
or
ks a
n
d bl
ac
k
start capa
b
ility, hi
gh dy
nam
i
c
pe
rform
a
nce
a
n
d sm
all space requir
em
ents [1]-[3].
In
p
a
rticu
l
ar,
th
e no
v
e
l
p
o
wer con
v
e
rter to
po
log
y
fo
r MMC h
a
s been
in
tensiv
el
y research
ed,
devel
ope
d, a
n
d valuate
d
against
m
a
ny features lik
e high m
odularity, sim
p
le scalability,
low expe
nse of
filters, rob
u
s
t co
n
t
ro
l, sim
p
le in
d
e
si
g
n
and
red
und
an
cy.
This co
nv
erter is
co
m
p
o
s
ed
b
y
id
en
tical power cells
connected i
n
s
e
ries, each
one built up
wit
h
standard c
o
m
ponents, e
n
a
b
li
ng t
h
e connection to
high
voltage
pol
es
.
Al
t
h
o
u
g
h
t
h
e M
M
C
an
d
deri
ved
t
o
p
o
l
o
gi
es
of
f
e
r se
veral
a
d
vant
a
g
es,
si
m
u
l
t
a
neo
u
sl
y
t
h
ey
al
so
i
n
t
r
o
d
u
ce a m
o
re com
p
l
e
x des
i
gn
of t
h
e p
o
w
e
r ci
rcui
t
an
d c
ont
rol
goal
s
,
w
h
i
c
h
have
bee
n
t
h
e m
a
i
n
reaso
n
f
o
r
t
h
e rece
nt
a
n
d
o
n
g
o
i
n
g
resea
r
ch
. F
u
rt
herm
ore, M
e
di
um
V
o
lta
g
e
Co
nv
er
te
r
s
ar
e
an
in
terestin
g area for t
h
e
appl
i
cat
i
o
n o
f
M
M
C
s. Thi
s
p
a
per i
s
or
ga
ni
zed i
n
fo
u
r
sectio
n
s
. Section
-
1 in
trodu
ces th
e MMC. Sectio
n
-2
di
scuss
e
s t
h
e d
i
ffere
nt
t
o
p
o
l
o
gi
es an
d m
odu
l
a
t
i
on t
echni
qu
es. Sect
i
o
n
-
3 sho
u
l
d
di
scus
s t
h
e di
f
f
ere
n
t
co
nt
r
o
l
t
echni
q
u
es
, fa
ul
t
t
o
l
e
ra
nt
o
p
erat
i
o
n a
n
d
i
t
s
expe
ri
m
e
nt
al
ve
ri
fi
cat
i
on a
n
d fi
nal
l
y
concl
u
si
o
n
wi
t
h
recom
m
endat
i
ons
are
p
r
ovi
d
e
d.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
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.
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,
Sep
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em
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e
r
2
014
:
36
3 – 375
36
4
Figure
1
.
Fi
v
e
lev
e
l th
ree ph
ase sing
le star ch
opp
er ce
ll b
a
sed
M
o
du
lar M
u
lti Lev
e
l co
nverter an
d its sub
-
m
odul
e
co
nf
igu
r
ation
Fi
gu
re
2.
D
o
ub
l
e
st
ar t
h
ree
ph
ase fi
ve
l
e
vel
M
o
d
u
l
a
r
Mu
lti Lev
e
l con
v
e
rter
Fi
gu
re
3.
Si
n
g
l
e
del
t
a
t
h
ree
ph
ase fi
ve
l
e
vel
Mo
du
lar M
u
lti Lev
e
l con
v
e
rt
er
2.
MO
DUL
AR
MUL
T
I-LEVEL
CONVER
TER
T
O
POL
OGIES
AN
D
MO
DUL
A
T
I
O
N
TECHNIQUE
S
There a
r
e m
a
n
y
topologies are existing in literature
, a
f
ter
careful revie
w
,
based
on func
tion and its
ap
p
licab
ility, it h
a
s b
e
en
d
i
v
i
ded
as fo
llo
ws:
a)
Si
ngl
e st
ar bri
d
ge
cel
l
s
(
SSB
C
)
b)
Si
ngl
e del
t
a
bri
dge
cel
l
s
(S
DB
C
)
c)
Doub
le star cho
p
p
e
r cells(DSCC)
d)
Doub
le star
brid
g
e
cells(DSB
C)
The
vital diffe
r
ence
bet
w
een
the chopper a
n
d
bri
dge
cells
are the
s
w
itche
s in
place
of c
a
pacitors
as
prese
n
t
e
d
i
n
be
l
o
w s
u
b-m
o
d
u
l
e
co
nfi
g
u
r
at
i
o
n
,
Fi
g
u
r
e
1 [
4
]
-
[
10]
,
[
37]
.
Single star,
Double star choppe
r cells are shown
i
n
Fi
g
u
r
e 1. T
h
e cur
r
e
nt
fl
o
w
i
n
g t
h
ro
u
gh t
h
e R
pha
se t
o
p l
i
m
b
, b
o
t
t
o
m
lim
b, ci
rcul
at
i
ng c
u
r
r
ent
a
nd R
pha
se cur
r
e
n
t
s
are
rep
r
ese
n
t
e
d
by
‘i
’, ‘
’, ‘
’, ‘i
r
’
r
e
sp
ectiv
ely. By v
i
r
t
u
e
of
K
C
L on
Figu
r
e
1
;
i
(1)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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4
A
Survey and Experime
ntal
Verification of Modul
ar M
u
ltilevel Converte
rs (Sree
d
har
M
adic
h
etty)
36
5
(
2
)
(
3
)
The ci
rcul
at
i
n
g
curre
nt
co
nsi
s
t
s
of bot
h al
t
e
rnat
i
ng c
u
r
r
ent
s
(ac) com
pone
nt
s and
di
rect
cur
r
ent
(
d
c
)
com
pone
nt
s as
f
o
l
l
o
ws:
(
4
)
Th
is circu
l
ating
cu
rren
t
is the un
iqu
e
feature
o
f
th
is t
o
po
l
o
g
y
. Th
is cu
rren
t
co
n
s
ists
of bo
th DC
&
AC
c
o
m
pone
nt
, w
h
e
r
e t
h
e
DC
com
pone
nt
i
s
:
=
(5)
Whe
r
e ‘i
o
’ is t
h
e to
tal ou
tpu
t
cu
rren
t
In
o
r
de
r t
o
fi
n
d
out
vol
t
a
ge f
o
r t
h
e
‘R
’
pha
se, K
V
L i
s
ap
pl
i
e
d t
o
Fi
g
u
re
1.
The
n
t
h
e
v
o
l
t
a
ge ac
ro
s
s
the R phase t
op lim
b, ‘V
’a
nd resistance
, R
top
, for bo
ttom li
m
b
, ‘
’ and resista
n
ce,
R
low
, circulating
currents
, ‘
’, with
su
pp
ly v
o
ltag
e
,
‘V
dc
’,
‘
V
’ rep
r
esen
ts
t
h
e vo
ltag
e
of
lim
b ‘n
’,
an
d
’
N
’
re
prese
n
ts t
h
e
num
ber of
m
odul
es
.
V
tr
=
-
∑
–
L
top
.
– R
top
. i
tr
(6)
V
lr
=-
+
∑
+ L
low
.
+ R
low
. i
lr
(7)
A
p
p
l
yin
g
(1
)
& (2
) in
Equ
a
tio
n (6
) and
(7
)
,
w
e
h
a
v
e
:
Th
e t
o
tal ‘R’ ph
ase ac ou
tpu
t
v
o
ltag
e
‘V
acout
’ is equ
a
tion
(6
) + (7
),
V
acout
= ½
[
∑
∑
] –
L
top+low
.
– R
top
+
low
. i
r
(8)
I
n
v
e
r
d
ict, th
e ou
tpu
t
v
o
ltage d
e
p
e
n
d
s
upon
th
e cu
rr
en
t
‘
i
r
’
an
d th
e d
i
f
f
e
r
e
n
c
e of
volta
g
e
in
th
e
m
odul
es. F
r
om
Eq
uat
i
o
n
(8
),
as l
o
ng
as t
h
e
L
top+low
will b
e
p
r
esen
t i
n
th
e
circu
it; lo
sses
will o
c
cu
r; t
h
e
o
u
t
p
u
t
v
o
ltag
e
will
v
a
ry.
This circ
ulating c
u
rrent ca
n
be expres
sed as:
L
tot
.
R
tot
. i
cir
=
-
∑
∑
=
(9)
As sh
o
w
n i
n
t
h
e Equat
i
on
(9
)
, ‘L
tot
.
R
tot
. i
ci
r
’ is th
e vo
ltage d
r
o
p
i
n
on
e lim
b
th
at can
als
o
b
e
refe
rre
d as
t
h
e
di
ffe
re
nce
bet
w
een
l
o
wer
an
d
up
pe
r arm
vo
l
t
a
ges. T
h
e
o
u
t
c
om
es of t
h
e
a
b
o
v
e e
q
uat
i
o
n
are:
a)
The arm
vol
t
a
ge d
r
op i
s
e
q
u
a
l
t
o
t
h
e di
f
f
er
ence o
f
s
o
u
r
ce
vol
t
a
ge
an
d s
u
m
of v
o
l
t
a
ges
of
u
ppe
r
and
l
o
wer
m
odul
es.
b)
The ‘i
cir
’
depe
n
d
s
up
o
n
t
h
e s
o
urce
v
o
l
t
a
ge
‘
V
dc
’ and
su
m
o
f
cell vo
ltag
e
s.
c)
Conse
q
uently, by addi
ng
or s
ubt
racting the
sam
e
am
ount of
voltage from
both arm
s
will not
resu
lt in an
y
sub
s
tan
tial ch
ange th
e
AC sid
e
out
put
v
o
l
t
a
ge,
b
u
t
i
t
affe
ct
s c
i
rcul
at
i
n
g
cu
rre
nt
.
The
u
ppe
r a
n
d
l
o
we
r arm
vol
t
a
ges i
n
cl
usi
v
e
of
su
b m
o
d
u
l
e
s
are s
h
ow
n i
n
Eq
uat
i
o
n
(
1
0
)
and
(
1
1):
V
tr
=
∑
=
–
V
tr
+
∑
(
1
0
)
V
lr
=
∑
=
+ V
lr
+
∑
(
1
1
)
2.
1.
Modulation S
t
rate
gies
From
the e
xha
ustive s
u
rvey
of literature
, it c
l
assifi
es prim
ar
ily two m
e
thods of m
odulation strate
gies
d
e
p
e
nd
ing
u
pon
th
e op
er
atio
n of
MMC [1
1
]-[
21
].
a)
Zero
v
o
l
t
a
ge
a
ppl
i
e
d
t
o
t
h
e a
r
m
i
nduct
o
rs
.
b)
Vol
t
a
ge
ap
pl
i
e
d t
o
t
h
e a
r
m
i
nduct
o
rs
.
Evaluation Warning : The document was created with Spire.PDF for Python.
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,
Sep
t
em
b
e
r
2
014
:
36
3 – 375
36
6
1)
W
i
t
h
t
h
i
s
st
rat
e
gy
, t
h
e
vol
t
a
g
e
pr
ovi
de
d by
t
h
e u
p
p
er a
nd l
o
we
r i
n
duct
o
rs
are zer
o i
.
e. V
tr
= V
lr
.
Hence
t
h
e
vol
t
a
ge
l
e
vel
s
pr
o
v
i
d
e
d
by
t
h
em
are
0 or
,
he
nc
e t
h
e
n
u
m
b
er
of
l
e
vel
s
o
b
t
a
i
n
ed
fr
om
th
em
is N+1
an
d th
e
nu
m
b
ers of
ins
e
rted ce
lls are consta
nt.
2)
In t
h
i
s
case
,
u
ppe
r an
d l
o
we
r cel
l
s
have
di
ffe
rent
v
o
l
t
a
ge
l
e
vel
s
V
tr
and V
lr
, so as t
o
gene
rat
e
d
i
fferen
t
v
o
ltag
e
acro
ss th
e li
m
b
s. Th
is lead
s to
h
i
gh
er n
u
m
b
e
r of vo
ltag
e
lev
e
ls in
th
e o
u
t
pu
t
v
o
ltag
e
wh
ich
is eq
u
a
l t
o
2
N
+1
.
Here th
e
nu
m
b
ers
of inserted
cells are no
t con
s
tan
t
, wh
ich
m
a
y b
e
equal
t
o
N+1
,
N, N
-
1
.
I
n
t
h
i
s
m
e
t
hod, t
h
e
ci
rcul
at
i
ng c
u
rre
nt
can be c
ont
rol
l
e
d
,
b
u
t
due t
o
t
h
e
p
r
esen
ce
o
f
ci
rcu
l
atin
g
cu
rrents; h
i
g
h
e
r ri
p
p
l
es will
co
m
e
i
n
to
t
h
e p
i
cture. Ho
wev
e
r, to redu
ce th
e
ripple content,
a large
num
b
er
o
f
i
n
d
u
ct
or
s ar
e re
qui
re
d.
C
onsi
d
eri
ng t
h
e fi
ve l
e
vel
s
M
M
C
as represe
n
t
e
d i
n
Fi
gu
re
1, t
h
e s
w
i
t
c
hi
n
g
o
p
erat
i
o
ns a
r
e sho
w
n i
n
t
a
bl
e bel
o
w.
F
o
r
u
n
d
e
rst
a
ndi
ng
p
u
r
p
ose t
h
e
t
op
f
o
u
r
s
w
i
t
c
h
e
s S
1
,S
2
,S
3
,S
4
a
r
e s
h
own as
I
1,
I
2,
I
3,
I
4
and t
h
e
bottom
fo
ur swi
t
c
hes
as
I
6,
I
7,
I
8,
I
9
fo
r a leg
.
In
t
h
e
o
t
h
e
r h
a
nd
, the au
x
iliary switch
e
s are i
n
opp
o
s
ite m
a
n
n
e
r
o
f
t
h
e
m
a
i
n
swi
t
c
hes
wi
t
h
a del
a
y
;
t
h
i
s
i
s
expl
ai
ne
d i
n
Ta
bl
e 2 a
n
d 3
.
In t
h
e Ta
bl
e 1, t
h
e swi
t
c
hi
n
g
st
at
es fo
r
a M
M
I
are sh
own
.
The state o
f
, ‘1
’ in
d
i
cates t
h
e switch
is in
ON con
d
ition
an
d
OFF
fo
r
‘0
’.Pri
m
arily i
t
co
nsists of
‘o
ne’ st
at
e of
‘
V
/
2
’o
ut
p
u
t
v
o
l
t
a
ge and ‘
1
6’
st
at
es of ‘V/
4
’
out
put
v
o
l
t
a
ge
and ‘1
6
’
st
at
es of ‘
0
’
vol
t
a
ge
. The
Tab
l
e 2
sho
w
s
th
e b
a
sic op
eratio
n
s
of red
u
n
d
a
n
c
ies
switch
state co
nd
itio
n of
on
e
u
pper lim
b
.
Fin
a
lly th
e
Tabl
e 3 s
h
ow
s
t
h
e capaci
t
o
r
char
gi
n
g
st
at
u
s
of
u
ppe
r l
i
m
b. Ta
bl
e 2 a
n
d Ta
bl
e 3 i
n
di
cat
es t
h
e re
du
nda
nt
swi
t
c
hi
n
g
a
nd
capaci
t
o
r st
at
u
s
i
n
o
n
e s
ub
m
odul
e .U
pwa
r
d a
r
r
o
w i
ndi
c
a
t
e
s t
h
e capaci
t
o
r c
h
ar
gi
n
g
a
nd el
se
di
scha
rgi
n
g
.
Tabl
e
1. B
a
si
c
Swi
t
c
hi
n
g
O
p
e
r
at
i
o
n
o
f
a
Fi
ve
Level
M
M
C
State
2
S
1
S
2
S
3
S
4
S
5
S
6
S
7
S
8
S
1
S
2
S
3
S
4
S
5
S
6
S
7
S
8
State
1 1 1 1 0
0 0 0
0
0
0 0
1
1 1
1
2
4
1 1 1 0 1
0 0 0
0
0
0 1
0
1 1
1
4
1 1 1 0 0
1 0 0
0
0
0 1
1
1 0
1
1 1 1 0 0
0 0 1
0
0
0 1
1
1 1
0
0 1 1 1 1
0 0 0
1
0
0 0
0
1 1
1
0 1 1 1 0
1 0 0
1
0
0 0
1
0 1
1
0 1 1 1 0
0 1 0
1
0
0 0
1
1 0
1
0 1 1 1 0
0 0 1
1
0
0 0
1
1 1
0
1 0 1 1 1
0 0 0
0
1
0 0
0
1 1
1
1 0 1 1 0
1 0 0
0
1
0 0
1
0 1
1
1 0 1 1 0
0 1 0
0
1
0 0
1
1 0
1
1 0 1 1 0
0 0 1
0
1
0 0
1
1 1
0
1 1 0 1 1
0 0 0
0
0
1 0
0
1 1
1
1 1 0 1 0
1 0 0
0
0
1 0
1
0 1
1
1 1 0 1 0
0 1 0
0
0
1 0
1
1 0
1
1 1 0 1 0
0 0 1
0
0
1 0
1
1 1
0
1 1 1 0 1
0 0 0
0
0
0 1
0
1 1
1
1 1 1 0 0
1 0 0
0
0
0 1
0
1 1
1
1 1 1 0 0
1 0 0
0
0
0 1
1
0 1
1
1 1 1 0 0
0 1 0
0
0
0 1
1
1 0
1
1 1 1 0 0
0 0 1
0
0
0 1
1
1 1
0
0
1 1 0 0 1
1 0 0
1
0
1 0
1
1 0
0
0
1 1 0 0 0
1 1 0
1
0
1 0
0
1 1
0
1 1 0 0 0
0 1 1
1
0
1 0
0
0 1
1
1 1 0 0 1
0 0 1
1
0
1 0
1
0 0
1
1 1 0 0 1
0 1 0
1
0
1 0
1
0 1
0
1 1 0 0 0
1 0 1
1
0
1 0
0
1 0
1
0 1 1 0 1
1 0 0
0
1
0 1
1
1 0
0
0 1 1 0 0
1 1 0
0
1
0 1
0
1 1
0
0 1 1 0 0
0 1 1
0
1
0 1
0
0 1
1
0 1 1 0 1
0 0 1
0
1
0 1
1
0 0
1
0 0 1 1 1
1 0 0
1
0
0 1
0
1 1
0
0 0 1 1 0
1 1 0
1
0
0 1
0
0 1
1
0 0 1 1 0
0 1 1
1
0
0 1
1
0 0
1
0 0 1 1 1
0 0 1
1
0
0 1
1
0 1
0
0 0 1 1 1
0 1 0
1
0
0 1
0
1 0
1
0 0 1 1 0
1 0 1
0
1
0 1
1
0 1
0
1 0 0 1 1
1 0 0
0
1
0 1
0
1 0
1
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4
A
Survey and Experime
ntal
Verification of Modul
ar M
u
ltilevel Converte
rs (Sree
d
har
M
adic
h
etty)
36
7
Tabl
e 2.
B
a
si
c Swi
t
c
hi
n
g
O
p
e
r
at
i
o
n
o
f
a Re
dunda
n
ce Switching State i
n
MMC
State Cur
r
e
nt
Switching
Capacitor
Capacitor
1010
> 0
S
1
D
2
S
4
D
3
Cs
2
Cs
4
1010
< 0
S
2
D
1
S
3
D
4
Cs
4
Cs
2
0110
> 0
S
2
D
1
S
4
D
3
Cs
1
Cs
4
0110
< 0
S
2
D
1
S
4
D
3
Cs
4
Cs
1
0101
> 0
S
2
D
1
S
3
D
4
Cs
1
Cs
3
0101
< 0
S
1
D
2
S
4
D
3
Cs
3
Cs
1
1001
> 0
S
1
D
2
S
3
D
4
Cs
1
Cs
3
1001
< 0
S
2
D
1
S
4
D
3
Cs
3
Cs
2
Tab
l
e 3
.
Basic Cap
acito
r Swit
ch
ing
Op
eratio
n
of
a R
e
d
u
nda
nce S
w
i
t
c
hi
n
g
St
at
e i
n
M
M
I
S
1
S
2
V
ou
t
Cu
rren
t
Po
wer
Cap
acito
r
On Of
f
0
> 0
S
1
Undefined
On Of
f
0
< 0
D
1
Undefined
Of
f On
V
dc
> 0
D
2
Charge
Of
f On
V
dc
< 0
S
2
Discharge
D
u
e to
t
h
e un
ev
en
v
o
ltag
e
d
i
strib
u
tion
in
the leg
s
o
f
a
p
h
a
se, circu
l
ating
cu
rren
ts
w
ill flo
w
thro
ugh
th
e syste
m
. It co
nsists o
f
cu
rren
t h
a
rm
o
n
i
cs wh
ich
d
e
te
ri
orates the system perform
a
nce. Here
, an att
e
m
p
t is
m
a
de t
o
deri
ve
t
h
e c
u
r
r
e
n
t
ha
rm
oni
cs p
r
ese
n
t
i
n
ci
rcul
ating
cu
rren
ts and
its n
ecessary co
n
t
ro
ller to
sup
p
ress
th
e sam
e
. Th
e
in
stan
tan
e
ou
s
v
o
ltag
e
ac
ross the
ca
pacitors are de
note
d
a
s
,
,
,
….
Als
o
the
v
o
ltag
e
d
i
st
ribu
tio
n acro
s
s the cap
acitors is
co
nsid
ered
t
o
be th
e sam
e
.
….
.
(12)
Und
e
r an
y swit
ch
ing
co
nd
ition
s
, t
h
e av
erag
e vo
lta
g
e
acro
ss th
e
u
p
p
e
r arm
switch
e
s are sho
w
n
as:
∆
(
1
3
)
Th
e t
o
tal cap
acito
r
v
o
ltag
e
of
th
e cap
acito
r is sh
o
w
n
i
n
Equatio
n
(3) an
d the d
e
feren
tial cap
acito
r
vol
t
a
ge
i
s
s
h
o
w
n
i
n
t
h
e E
q
ua
t
i
on
(4
), i
n
t
h
e
sam
e
way
Equ
a
t
i
on
(1
6)
,
(1
7)
an
d(
1
8
)
f
o
r t
h
e l
o
we
r l
i
m
b.
….
.
(14)
∆
∆
∆
∆
….
∆
.
(15)
∆
(16)
….
(17)
∆
∆
∆
….
∆
(
1
8
)
The ci
rc
ul
at
i
ng cu
rre
nt
s i
n
t
h
e arm
i
nduct
o
rs c
o
n
s
i
s
t
s
of
bot
h
DC
an
d
AC
com
pone
n
t
s. These AC
com
pone
nt
s ar
e cal
l
e
d as t
h
e
harm
oni
cs,
si
n
ce t
h
o
s
e are
r
o
t
a
t
i
ng
wi
t
h
t
h
e
hi
g
h
er
f
r
eq
ue
n
c
i
e
s i
n
t
h
e
sy
st
em
.
∑
i
∞
(19)
i
i
i
+….
(
2
0
)
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I
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088
-86
94
I
J
PED
S
Vo
l.
4
,
No
.
3
,
Sep
t
em
b
e
r
2
014
:
36
3 – 375
36
8
In
or
der t
o
der
i
ve t
h
e ci
rcul
at
i
ng v
o
l
t
a
ge a
n
d cu
rre
nt
, we
need t
h
e
o
u
t
p
u
t
vol
t
a
ge o
f
a si
ngl
e p
h
ase
fro
m
th
e th
ree
p
h
a
se:
.
.
(21)
.s
i
n
(22)
‘m
’ i
s
t
h
e m
odul
at
i
on i
n
d
e
x
o
f
a si
gnal
.
Yet
agai
n,
t
h
e
act
u
a
l
vol
t
a
g
e
s a
r
e
sho
w
n
bel
o
w:
.
1
.
s
in
∆
(
2
3
)
.
1
.
s
in
∆
(
2
4
)
Th
erefo
r
e, th
e
to
tal v
o
ltag
e
is;
(
2
5
)
1
.
s
i
n
(
1
.
s
i
n
∆
)
(2
6)
∆
∆
.
.
∆
∆
(
2
7
)
In
o
r
de
r t
o
deri
ve t
h
e
di
st
ur
ba
nce
vol
t
a
g
e
f
o
r
t
h
e
up
pe
r a
n
d
l
o
we
r cel
l
capa
c
i
t
o
rs
of
a l
e
g
i
.
e.
∆
∆
;
.
(
2
8
)
.
.
(
2
9
)
At th
is i
n
stan
ce,
∑
∞
(
3
0
)
∑
∞
(
3
1
)
.
(
3
2
)
.
(
3
3
)
∑
.
.
∞
(
3
4
)
∑
.
.
∞
(
3
5
)
….
(
3
6
)
….
(
3
7
)
Now, let’s c
o
nsider a
b
out t
h
e
current
∑
∞
(
3
8
)
→
The
curre
nt
present in the
phase ’a
’
upper a
r
m
→
Dc c
o
m
pone
nt
of
t
h
e c
u
r
r
e
n
t
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I
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S
I
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:
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4
A
Survey and Experime
ntal
Verification of Modul
ar M
u
ltilevel Converte
rs (Sree
d
har
M
adic
h
etty)
36
9
→
Fu
n
d
am
ent
a
l
com
pone
nt
o
f
t
h
e c
u
r
r
ent
.
→
H
a
r
m
o
n
i
c
co
mp
on
en
t of
cu
rr
en
t.
∑
.
∞
(
3
9
)
.
cos
(
4
0
)
∴
Th
e to
tal curren
t
(
4
1
)
∑
.
∞
∑
.
∞
(
4
2
)
Now, let’s co
nsid
er abo
u
t
vo
ltag
e
fo
r ‘N’ mo
du
le in term
s o
f
cap
acitan
ce:
.s
i
n
(
4
3
)
∑
.
∞
∑
.
∞
(
4
4
)
∆
.
.
1
.
s
in
.
∑
∞
.
(
4
5
)
∆
.
.
1
.
s
in
.
∑
∞
.
(
4
6
)
∴
Th
e t
o
tal ‘R’ ph
ase
vo
ltag
e
is
sh
own
in Eq
u
a
tio
n
(47
)
(
4
7
)
By su
b
s
titu
ting Equ
a
tion
(45
)
an
d (46
)
i
n
Equ
a
tio
n (47
)
;
we sh
all
h
a
v
e
∆
∆
.∆
.∆
(
4
8
)
.
.
1
.
s
i
n
.
∑
∞
.
.
.
1
.
s
i
n
.
1
∞
.
(4
9)
.
.
.
.
.
∑
∞
.
.
.
.
.
.
∑
∞
.
(5
0)
From
abo
v
e i
t
can be co
ncl
ude
d t
h
at
, t
h
e
sy
st
em
consi
s
t
s
of b
o
t
h
dc
and ac com
p
o
n
ent
s
. M
o
st
i
m
p
o
r
tan
t
issue h
e
re is th
e st
ead
y state o
f
a syste
m
with
c
o
n
t
ro
ller, i
f
app
lied
.
To
m
a
in
tain
its fu
nd
amen
tal
and
el
im
i
n
at
e t
h
e dc a
n
d ac
com
pone
nt
s,
a co
nt
rol
l
e
r i
s
nee
d
ed t
o
be
im
pl
em
ent
e
d i
n
t
h
e sy
st
e
m
. The
co
n
t
r
o
ller
should
b
e
d
e
sign
ed
so
as to
b
e
fu
lly su
ff
ice th
e Eq
u
a
tion
(5
1)
and
Equ
a
tio
n (5
2)
.
1
sin
1
s
i
n
.
∑
∞
0
(51)
∑
∞
0
(
5
2
)
Fr
o
m
th
e Equatio
n
(
5
1
)
an
d Equ
a
tion
(
52)
, it is
f
oun
d
th
at, lo
ad
vo
ltag
e
d
e
p
e
nd
s
up
on
t
h
e cu
rr
en
t
,
diffe
re
nce bet
w
een
uppe
r &
lowe
r capacitors;
depe
n
d
s o
n
l
y
on t
h
e
DC
l
i
nk v
o
l
t
a
ge, t
h
e sum
of t
h
e
arm
vol
t
a
ge
s [
3
6]
.
3.
CONTROLLER
DESIG
N
AN
D
FA
U
L
T
T
O
LERANT
OPERA
T
IO
N
OF
MM
C
On
e im
p
o
r
tan
t
p
r
o
b
l
em
asso
ciated
with
mo
du
lar m
u
ltile
v
e
l con
v
e
rter
is th
e issu
e of circu
l
ating
cu
rren
t at
b
a
lan
ced
and
unb
alan
ced
load
con
d
ition
.
Ma
in
l
y
two
typ
e
s
o
f
co
nd
itio
ns are co
nsid
ered
an
d
as
fo
llows:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l.
4
,
No
.
3
,
Sep
t
em
b
e
r
2
014
:
36
3 – 375
37
0
a)
Und
e
r b
a
lan
c
ed
cond
itio
n
,
o
n
l
y po
sitive seq
u
en
ce
of curren
t
will flo
w
i
n
th
e b
u
ffer
in
du
ctor
/ar
m
i
n
du
ctor
.
b)
Und
e
r
u
n
b
a
lanced
co
nd
ition
,
all p
o
s
itiv
e, n
e
g
a
tiv
e an
d zero sequ
en
ce
o
f
cu
rren
t
will flow.
Fo
r better
und
er
stand
i
ng
, it can
b
r
oa
dly classified as
follows,
a)
In
ner
cu
rre
nt
s
u
p
p
r
essi
o
n
of
a
M
M
C
b)
C
i
rcul
at
i
n
g
cu
r
r
ent
s
u
pp
ressi
o
n
m
e
t
hod
c)
Cap
acito
r vo
ltag
e
b
a
lan
c
i
n
g
meth
od
d)
Sy
nch
r
on
o
u
s S
a
m
p
l
i
ng C
ont
r
o
l
an
d i
t
s
e
ffec
t
e)
Dual Vector
C
ont
rol
f)
Est
i
m
a
t
i
on of
e
n
er
gy
by
usi
n
g
arm
i
nduct
a
nc
e an
d st
ore
d
ca
paci
t
a
nce
Form
t
h
e E
q
ua
t
i
on
(4
9
)
a
n
d
Eq
uat
i
o
n
(
5
0)
one
ca
n
c
oncl
ude
that, as t
h
e arm
inductance increa
ses,
the circulating current dec
r
ea
ses. Due to
thi
s
effect there i
s
an increa
se
in
th
e v
a
l
u
e of
in
ductance
, the
cost
and space requirem
ent w
ill also inc
r
ease.
It urge
s the
need to c
ontrol
the circ
ulating c
u
rrent i
n
ste
a
d
of
i
n
creasi
n
g i
n
d
u
ct
ance.
It
[
2
2]
pr
o
p
o
s
es,
un
de
r bal
a
nce
d
co
n
d
i
t
i
ons
,
negat
i
v
e
seq
u
e
nce c
o
m
pone
nt
o
f
circulating c
u
rrent
in each a
r
m
rotate
s at
double the
lin
e freque
ncy.
So,
∆
control m
e
thod
was
stated
by
tr
an
sf
or
m
i
n
g
th
e a-
c-b
seq
u
e
n
ce w
ith
a doub
le lin
e f
r
e
q
u
e
n
c
y in
to
d-
q
seq
u
e
n
ce at r
o
tat
i
o
n
a
l r
e
fer
e
n
c
e f
r
a
m
e
.
But this m
e
thod
was
not
bee
n
able to elim
inate the ci
rc
ulating c
u
rre
n
t tota
lly at unde
rbal
anced conditions.
As
per
t
h
e a
r
t
i
c
l
e
[2
3]
a
pr
o
pose
d
c
ont
rol
m
e
t
hod
wi
t
h
real
i
z
a
t
i
on
of
i
n
st
ant
a
neo
u
s
p
o
w
er
o
f
eac
h l
e
g
,
a
n
d
al
s
o
an algorithm
to re
duce the
circula
ting
cu
rren
ts and
d-c link
v
o
ltages ripp
les. Un
fo
rt
u
n
a
tely it h
a
s
a
di
sad
v
a
n
t
a
ge o
f
i
n
cl
usi
o
n o
f
do
u
b
l
e
l
i
n
e fre
que
ncy
ri
p
p
l
e
. In
[
24]
,
p
r
op
os
ed
a
-
b
-
c refe
re
nce fram
e
t
o
c
ont
ro
l
t
h
e ci
rcul
at
i
n
g
cur
r
ent
s
b
u
t
have t
h
e di
sa
d
v
ant
a
ge o
f
ge
nerat
i
n
g a
del
a
y
ho
weve
r, i
t
cann
o
t
i
m
pro
v
e t
h
e
tran
sien
t respon
se o
c
cu
rring
in
th
e in
n
e
r b
a
lan
c
in
g
cu
rren
ts. Ag
ain
in
[25
]
pr
op
ose
d
a m
odel
of pre
d
i
c
t
i
v
e
cont
rol
w
h
i
c
h
t
o
o
k
ac
-si
d
e c
u
r
r
ent
,
ci
rc
ul
at
i
ng c
u
rre
nt
s a
n
d s
u
b
-
m
odul
e
vol
t
a
ge
bal
a
nc
i
ng,
by
det
ect
i
n
g
t
h
e
switch status
to
m
i
nimize the cost
function. But, t
h
is study [26]
analyses each individual pha
se’s
i
n
st
ant
a
ne
o
u
s
po
we
r t
o
red
u
ce t
h
e act
i
v
e
p
o
we
r ri
p
p
l
e
, w
h
en
ne
gat
i
v
e s
e
que
nce c
o
m
pone
nt
was
gen
e
rat
e
d
.
This instanta
neous powe
r begins wit
h
the
positive,
negative and zero seque
n
ce com
ponents with double
fre
que
ncies a
n
d dc c
o
m
pone
nts. T
h
e disa
dvantage
of this
m
e
thod is the
use of a co
m
p
licated PIR not
c
h filter
use
d
to c
o
ntrol each c
o
m
ponent se
pa
rately. Due to
unbalance in t
h
e
uppe
r and l
o
wer arm
of t
h
e
MMC,
circu
l
atin
g curren
ts will d
e
v
e
l
o
p. Th
ese ev
en h
a
rm
o
n
i
cs
and circu
l
ating
cu
rren
ts can
b
e
sup
p
ressed
b
y
u
s
in
g
a
cont
rol
l
e
r an
d desi
g
n
e
d
as f
o
l
l
o
ws.
Re h
(
s) =
.
(
h
=
2,
4,
6…
….)
(53)
H(s
)
=
.
=
.
,
,
…
.
,
,
…
(54)
Bu
t i
cir
will consist of the
DC
com
pone
nts al
so.
H
c
(j
o
) =
.
,
.
,
(55)
B
y
consi
d
e
r
i
n
g t
h
e
up
pe
r ar
m
,
t
h
e out
put
vol
t
a
ge
o
f
t
h
e
up
pe
r arm
i
s
, V
top
= V
dc
/4
,
wh
ich
lies in
bet
w
ee
n:
k
1
*V
to
p
< V
top
< (k
1
+1
)
V
top
; where
k
1
is a po
sitiv
e
in
teg
e
r, K
h
is a p
r
op
ortio
nal co
n
s
tan
t
. In
o
r
der t
o
produce a volt
age ‘V
r
’ at a certain tim
e
, k
1
sub-m
odule capacitors
will be in
sufficie
n
t and if we c
o
nside
r
(k
1
+
1
), sub-m
odule ca
pacitors
then it will ge
nerate
ove
r
voltage. He
nce,
k
1
m
odul
e i
s
t
a
ken
as I
r
t
o
pr
ov
id
e
maj
o
r p
a
r
t
,
and (k
1
+1) is tak
e
n as O
µ
f
o
r
t
h
e r
e
m
a
i
n
i
ng part
.
k
1
=
=
(56)
The
n
the
re
fere
nce
voltage ca
n
be calculate
d as:
V
r_ref
= V
r
– k
1
.
(
5
7
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
A
Survey and Experime
ntal
Verification of Modul
ar M
u
ltilevel Converte
rs (Sree
d
har
M
adic
h
etty)
37
1
In
o
r
de
r t
o
c
o
n
t
rol
t
h
e
v
o
l
t
a
ge
bal
a
nci
n
g
o
f
t
h
e s
u
b m
odul
e
capaci
t
o
r
t
h
e
r
e
are t
w
o
ef
fect
i
v
e
way
s
a)
Vi
rt
ual
l
o
o
p
m
a
ppi
ng
b)
Selectiv
e v
i
rt
ual lo
op
m
a
p
p
i
ng
The ab
ove m
e
nt
i
one
d t
w
o m
e
t
h
o
d
s are bas
e
d o
n
t
h
e com
p
ari
s
on
of t
h
e
capaci
t
o
r
vol
t
a
ge. I
n
t
h
i
s
meth
o
d
a co
unter up coun
ter
meth
o
d
is
d
e
p
l
o
y
ed to
co
n
t
rol th
e m
a
p
p
i
ng
relatio
n
s
wh
ich
will b
e
equ
a
l
to
o
r
less than the
ca
rrier freque
ncy. T
h
e ra
nge
of
cou
n
ter
is 0
-(C
ou
nter
-1
)
[2
7]
-
[
3
5
]
.
Th
e abov
e m
e
t
h
od
is app
licab
le o
n
l
y wh
en
th
e syste
m
is o
p
e
rated
at well b
a
lan
ced
co
nditio
n
s
. Bu
t
the system
will retain s
u
ch a
position in
pra
c
tical due to
variation
in circ
ulating
c
u
rre
n
ts, m
odulation
singles
.
Concl
u
sively,
the accuracy
of t
h
e m
e
t
hod is applicable
here
. From
the
literature
[36]-[37], a m
e
t
h
od i
s
p
r
op
o
s
ed
wh
ere th
ere is a n
e
ed
to
so
rt th
e cap
acito
r
vo
ltages frequ
en
tly resu
ltin
g
con
s
um
p
t
io
n
of m
o
re ti
m
e
& im
ple
m
entation
of a
n
a
voi
dable com
p
licacy in th
e
ha
rdware(c
om
plex at
hi
ghe
r voltage
levels).
Inst
ea
d,
on
ce
t
h
e m
a
xim
u
m
and m
i
nim
u
m
val
u
es o
f
c
a
paci
t
o
r
v
o
l
t
a
ges a
nd t
h
ei
r
cor
r
es
po
n
d
i
n
g
di
rect
i
o
ns can
be pi
cke
d
.
In
o
r
de
r t
o
m
i
nim
i
ze t
h
e del
a
y
of
P
W
M
si
gnal
,
a sy
nchr
o
n
o
u
s
sam
p
l
i
ng cont
r
o
l
i
s
im
pl
em
ent
e
d. Here
[
47]
-
[
5
3
]
,
i
t
i
s
consi
d
er
ed wi
t
h
a c
ont
i
n
u
o
u
s m
odel
i
n
st
ead
o
f
di
sc
r
e
t
e
m
odel
,
d
u
e
t
o
t
h
e
fol
l
o
wi
n
g
a
d
va
nt
ages:
a)
Di
scret
e
m
odel
do n
o
t
al
l
o
w
an anal
y
t
i
cal a
ppr
oac
h
t
o
m
odel
t
h
e convert
er a
nd
des
i
gn t
h
e
cont
rol system
.
b)
Nu
m
e
rical so
lu
tio
ns of sub
-
m
o
du
le with
h
i
ghe
r
nu
m
b
er of s
w
i
t
c
hi
n
g
act
i
o
ns
req
u
i
r
e
co
nsid
erab
le ti
me.
Th
erefo
r
e ad
d
i
n
g
so
m
e
v
o
ltag
e
will n
o
t
affect th
e lo
ad
voltag
e
b
u
t
it will affect th
e cu
rren
t, th
en
th
e
to
tal circu
l
ating
cu
rren
t
will be con
t
ro
lled
and
system
can
main
tain
steady state co
nd
ition
.
-
- R.
-
(
) -
L.
(
) -
=
(57)
=
-
- R.
-
(
) -
L.
(
)
(
5
8
)
+
+
(
) =
(
5
9
)
By
taking
the
d
i
ffere
nce,
=ev
(er
r
o
r
vol
t
a
ge
)
(6
0)
=
– ev -
(
6
1
)
=
+ ev
-
(
6
2
)
So,
= R.
+ L.
(
)
(
6
3
)
In
o
r
d
e
r t
o
det
e
rm
i
n
e t
h
e di
f
f
e
rence
v
o
l
t
a
ge
bet
w
ee
n t
h
e
up
per
an
d l
o
wer
capaci
t
o
rs
,
o
n
e
sh
o
u
l
d
fi
n
d
th
e en
erg
y
stored
in th
e cap
a
cito
r.
∈
=
(
∈
)
2
=
N. [
(
∈
/
)
2
]
(
6
4
)
∈
=
(
∈
)
2
=
N. [
(
∈
/
)
2
]
(
6
5
)
Th
e ch
an
g
e
in
en
erg
y
stored
i
n
th
e cap
acito
r
is:
(
∈
) =
.
∈
=
(
+
) (
– ev
-
)
(
6
6
)
(
∈
) =
.
∈
= (
+
) (
+ ev
-
)
(
6
7
)
Th
e t
o
tal en
ergy,
∈
=
∈
+
∈
(68)
=
∈
-
∈
(69)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l.
4
,
No
.
3
,
Sep
t
em
b
e
r
2
014
:
36
3 – 375
37
2
Diffe
re
nce is:
(
∈
) =
2
.
.
(70)
(
∈
) =
.
2
.
(71)
Som
e
im
port
a
n
t
concl
u
si
o
n
s a
r
e:
a)
.
R
e
pr
esent
s
t
h
e
pr
o
duct
o
f
po
we
r
del
i
v
ere
d
,
.
rep
r
esen
ts
th
e lo
sses
o
c
curred
i
n
t
h
e
syste
m
,
.
is the po
wer
d
e
liv
ered to
t
h
e lo
ad
.
b)
In ov
erall, i
f
the
is co
n
t
ro
lled, th
e
syste
m
cap
ac
i
t
o
r
ene
r
gy
can be
c
ont
rol
l
ed.
c)
DC
c
o
m
pone
n
t
o
f
has
no impact
on t
h
e
differe
n
ce
of
c
a
pa
c
ito
r
en
er
g
y
as
th
er
e a
r
e no
D
C
com
pone
nt
s i
n
‘ev
’
. T
h
e DC
com
pone
nt
o
f
can
on
ly b
e
used
to
con
t
ro
l
th
e to
tal cap
acito
r
ener
gy
.
B
u
t
t
h
e AC
c
o
m
pone
nt
of
ha
vi
n
g
t
h
e
f
u
n
d
am
ent
a
l
fre
q
u
ency
as
t
h
e
out
put
vol
t
a
ge
‘ev
’
ca
n
be em
pl
oy
ed
t
o
c
o
ntrol the ca
pacitor e
n
ergy.
d)
The pr
o
duct
o
f
.
ma
k
e
th
e
en
er
g
y
to
ch
a
n
g
e
.
e)
,
sh
all g
i
v
e
th
e sa
m
e
effect bu
t th
is is p
e
rmissib
l
e for sm
a
ll R an
d
L, thu
s
we
n
e
ed
to
devel
o
p
a c
ont
rol
st
rat
e
gy
f
o
r
,
on
ly.
On
e
of o
t
h
e
r
i
m
p
o
r
tan
t
issue asso
ciated
with
MMC HVDC system
i
s
fau
lt to
lerance wh
ile its
ap
p
licab
ility. It p
r
opo
ses HVDC syste
m
, o
f
fers th
e
o
p
e
ratio
n
a
l flex
ib
ility o
f
VSC b
a
sed syste
m
s
in
term
s
o
f
activ
e an
d
reactiv
e p
o
w
e
r co
n
t
ro
l,
b
l
ack
start cap
ab
ility, in
ad
d
ition to
i
m
p
r
ov
ed
ac fau
lt rid
e
-th
r
ough
cap
ab
ility an
d
th
e un
iqu
e
feat
u
r
e
of cu
rren
t-l
i
m
i
tin
g
cap
ab
il
ity d
u
r
i
n
g
d
c
si
d
e
fau
lts. Th
is
[31
]
p
a
p
e
r prop
o
s
ed
a protection sc
hem
e
to im
ple
m
ent fast fault
clearance
a
n
d
aut
o
m
a
t
i
c
recovery
f
o
r n
o
npe
rm
anent
faul
t
s
on
dc
lin
es. By em
p
l
o
y
in
g
d
oub
le th
yristor sw
itches, th
e freewh
eelin
g
effect
of
d
i
odes is
elim
inated and t
h
e
dc-link
fault curre
nt is
allowe
d to
freely d
ecay
to zero.
In order to
m
i
tigate
the circulating curre
nts of the
MMC,
co
m
p
u
t
er sim
u
latio
n
is carried
o
u
t
first
and th
en
v
e
rified
ex
p
e
rim
e
n
t
all
y
with a co
m
b
i
n
atio
n
o
f
rep
e
titiv
e
cont
rol
l
e
r an
d harm
oni
c
el
i
m
inat
i
o
n
t
ech
ni
q
u
e.
Tabl
e
4.
Param
e
t
e
rs U
s
ed
f
o
r
Fi
ve Le
vel
M
M
C
Sim
u
l
a
t
i
on a
n
d
E
xpe
ri
m
e
nt
M
M
C
L
e
vel
Five
DC Voltage
V
dc
=200V Dc
Circu
l
atin
g
Cu
rren
t
ref
e
ren
ce
I
cref
= 0
Arm
I
nductor
s
L
1
=L
2
=L=3 m
H
Switching fr
equen
c
y
S
f
=100 Hz
Capacitor
Value
C=16 µF/400V
Bandwidth of the c
ontroller
2000
Lo
ad
Para
m
e
te
rs
L
r
=10
m
H/R
r
=30
Ω
Gain of Resonant
contr
o
ller
Gr
c
=1250
Resonant fr
equenc
y
of contr
o
ller
ɷ
0
=2
0
00
The sy
st
em
has been t
e
st
ed
wi
t
h
t
h
e pa
ram
e
t
e
rs l
i
s
t
e
d i
n
Tabl
e I
V
. T
h
e expe
ri
m
e
nt
al
set
up
has be
e
n
sho
w
n i
n
Fi
gu
r
e
4.
Fi
gu
re
4.
Ex
pe
ri
m
e
nt
al
set
up
of
fi
ve
l
e
vel
M
M
C
wi
t
h
c
ont
r
o
l
l
e
r
Contr
o
ller
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