TELKOM
NIKA
, Vol.11, No
.11, Novemb
er 201
3, pp. 6329
~6
336
e-ISSN: 2087
-278X
6329
Re
cei
v
ed Ap
ril 22, 2013; Revi
sed
Jun
e
24, 2013; Accepted July 6,
2013
Study on Control Strategies fo
r the Multilevel Cascad
ed
Converters
Lin Xu*
1
, Ya
ng Han
2
1
Sichua
n Electr
ic Po
w
e
r R
e
se
arch Institute, No.
24, Qing
hu
a Roa
d
, Qing
yang D
i
strict, 61007
2 Ch
eng
du
,
Chin
a
2
Universit
y
of E
l
ectron
ic Scien
c
e and T
e
chno
log
y
of
Ch
in
a, No.20
06, Xi
yu
an Ro
ad, W
e
st High-T
e
ch Z
one,
Che
ngd
u, 611
731, Ch
en
gdu,
Chin
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: xul
i
n
198
43
1
@
hotmai
l
.com
A
b
st
r
a
ct
T
he mu
ltilev
e
l
casca
de
d
co
nverters are e
x
tens
ive
l
y a
p
p
lied
for
hi
gh-v
o
ltag
e
and
h
i
gh-p
o
w
e
r
app
licati
ons, w
h
ich
are c
ons
i
dere
d
as
the
most fav
o
ra
ble
topol
og
ies for
the hi
gh
pow
er
ac-driv
e
s a
nd
th
e
high-voltage DC trans
m
i
ssion (HVDC) system
s us
ing t
he
voltage sourc
e
converte
rs (V
SCs). This paper
prese
n
ts the
dc ca
pacitor
b
a
la
ncin
g a
n
d
effective
curr
e
n
t reg
u
lati
on
meth
od
olo
g
i
e
s
for the
multil
eve
l
ca
sca
de
d co
nve
r
te
rs. Th
e
dc-l
i
n
k vo
l
t
ag
e
b
a
l
a
n
c
in
g a
nd ca
pa
ci
to
r
e
nerg
y
e
v
o
l
vin
g
m
e
ch
an
i
s
m
o
f
th
e
MMCC is an
aly
z
e
d
,
an
d an eff
e
ctive c
ontr
o
l s
c
he
me is
devis
ed by uti
l
i
z
i
n
g t
w
o dc capacito
r
voltage c
ontr
o
l
loo
p
s, inc
l
ud
in
g the
total c
a
p
a
citor v
o
ltag
e
control
l
er
(T
C
V
C), the c
apa
citor volt
age
b
a
la
ncin
g co
ntr
o
ll
e
r
(CVBC). T
h
e
p
r
edictiv
e curr
e
n
t contro
ller
is
prop
osed
to
en
hanc
e th
e trac
king
accur
a
cy
of curre
nt co
ntro
l
loo
p
. The
pro
p
o
rtion
a
l-res
o
n
a
n
t contro
ller
(P
RC) is
use
d
a
s
circul
atin
g c
u
rrent
da
mp
in
g co
ntroll
er of
the
mo
du
lar
multi
l
e
vel co
nverter,
w
h
ich is found
to be hig
h
ly ef
fective to mi
ni
mi
z
e
t
he circu
l
ating curr
ent. T
h
e
Electro
m
a
gneti
c
T
r
ansi
ent Pr
ogra
m
(EMT
P) is
utili
z
e
d
for
digit
a
l s
i
mul
a
ti
on
of the
si
ngl
e-ph
ase fiv
e
-l
e
v
e
l
mo
du
lar multil
evel
conv
erter
.
T
he effective
ness of
the
c
ontrol
sch
eme
is v
a
li
date
d
by the
si
mulat
i
o
n
results.
Ke
y
w
ords
: mu
ltileve
l conv
erter, predictiv
e curr
ent contro
l, Dc-link co
ntrol,
EMTP
Copy
right
©
2013 Un
ive
r
sita
s Ah
mad
Dah
l
an
. All rig
h
t
s r
ese
rved
.
1. Introduc
tion
Multilevel vo
ltage-sou
r
ce
conve
r
ters (VSCs)
all
o
w a
si
gnificant
red
u
cti
on of the
harm
oni
c co
ntent of the output
voltag
e as
com
pared to the tra
d
itional two
-
l
e
vel VSCs [
1
].
Among va
rio
u
s
multilevel t
opolo
g
ies [2], the fai
r
ly
recently propo
se
d mo
dula
r
m
u
ltilevel cascade
conve
r
ter
(M
MCC) [3] ha
s many attra
c
tive pro
perti
es. As the n
a
me sugg
est
s
, the topolo
g
y is
modula
r
and
ea
sily scal
a
b
le in
term
s of volt
age
l
e
vels. It con
s
ist
s
of
N i
dentical
seri
es-
con
n
e
c
ted su
b-mo
dule
s
pe
r arm, whi
c
h
bring
s
flexibili
ty to
the circu
i
t design, an
d
result
s in lo
w
-
voltage step
s [4, 5].
In high-voltag
e application
s
, N may be as high a
s
sev
e
ral hu
ndred,
which i
s
idea
l choice
for hig
h
-volta
ge hi
gh-po
we
r a
pplication
s
, su
ch
as hig
h
-voltage
d
c
transmissio
n
(HV
D
C), hig
h
-
power m
o
tor
drives, a
nd el
ectri
c
railway
sup
p
lie
s [5-8]
.
The gri
d
-co
nne
cted MM
CC m
a
y act a
s
a
rectifie
r, an i
n
verter, a
n
in
ducto
r, an
d a
cap
a
cito
r,
d
epen
ding on the
pha
se
dif
f
eren
ce between
the su
pply voltage a
nd
current. Thi
s
i
m
plies that the MM
CC i
s
req
u
ire
d
to
achi
eve rigi
d
and
stable voltag
e control of all the floating dc
capa
citors under all o
p
e
r
ating conditi
ons.
This pa
per p
r
esents the
dc-li
n
k
cap
a
citor
balan
cin
g
and effecti
v
e current re
gulation
methodol
ogie
s
for th
e MM
CC. T
he o
r
g
anization of t
h
is p
ape
r i
s
as follo
ws. Section
2 p
r
e
s
ents
the system d
e
scriptio
n of t
he MMCC sy
stem, inclu
d
in
g the m
odelin
g and analy
s
i
s
of the MMCC.
Section 3 p
r
ese
n
ts the control st
rateg
i
es of
the M
M
CC, in
cludi
ng the su
m cap
a
cito
r voltage
controlle
r (SCVC), the differen
c
e capa
cit
o
r voltage
co
ntrolle
r (DCV
C), the pre
d
ictive current loop
controlle
r (PCC) and the
circulat
in
g cu
rre
nt dampin
g
controller
(CCDC). Secti
on 4 pre
s
ent
s the
simulatio
n
re
sults. And
se
ction 5 con
c
lu
des thi
s
pap
e
r
.
Evaluation Warning : The document was created with Spire.PDF for Python.
e-ISSN: 2
087-278X
TELKOM
NIKA
Vol. 11, No
. 11, Novemb
er 201
3: 632
9 – 6336
6330
2. Mathema
t
i
cal Modeling
for Modular
Multilev
e
l Conv
erter
Figure 1
sh
o
w
s the
circui
t diagram of
the si
ngle
-
ph
ase
mod
u
lar multilevel
cascad
ed
conve
r
ter (M
MCC). To
de
rive the
math
ematical
m
ode
l o
f
th
e MMC
c
o
n
v
er
te
r
,
le
t u
s
co
ns
id
er
a
gene
ric conv
erter with
N sub-m
odul
es
p
e
r a
r
m, e
a
ch arm
i
s
co
ntrol
l
ed with
the modulatio
n
in
dex
m
(
t
), where
m
(
t
)=0 mea
n
s
that all sub
-
mod
u
le
s in the arm a
r
e b
y
-passe
d, an
d
m
(
t
)=1 de
n
o
tes
all the sub
-
m
odule
s
in the
arm are inserted. T
he ideal
capa
citan
c
e
of the arm is
denote
d
as:
,
/
ud
d
c
CC
N
(1)
Figure 1. Circuit Diagram o
f
the Single-p
hase MMCC
Topolo
g
y
Whe
r
e
C
u,d
denote
s
the
capa
citan
c
e of
each chopp
er
cell. The
r
e
f
ore, the follo
wing
equatio
ns
hold for the u
pper a
nd lo
wer leg current
s:
,
()
()
(
)
dc
u
uu
u
du
t
mt
i
t
dt
C
(2)
,
()
()
()
dc
d
dd
d
du
t
mt
i
t
dt
C
(3)
Whe
r
e
m
u
(
t
) and
m
d
(
t
),
u
dc,u
(
t
) and
u
dc,d
(
t
),
i
u
(
t
) and
i
d
(
t
) de
no
te the modul
ation index, the
cap
a
cito
r voltage
s and
currents of the
up
per an
d lower arm, re
spe
c
ti
vely.
Referrin
g to Figure 1, wh
en only the
singl
e-p
h
a
s
e
leg is
con
s
i
dere
d
, the relation
s
among
i
u
,
i
d
and the circul
a
t
ing curre
n
t
i
z
0
can be de
riv
ed as:
0
2
ud
z
ii
i
，
0
2
L
uz
i
ii
，
0
2
L
dz
i
ii
(4)
Hen
c
e, the lo
ad cu
rrent is repre
s
e
n
ted a
s
:
L
ud
ii
i
(5)
From Fig
u
re
1, accordi
ng to the Kirch
h
o
ff’s Voltage Law (KVL
):
,
2
du
eu
e
u
d
c
u
v
Vd
i
Ri
L
m
u
u
dt
(6)
,
2
dd
ed
e
d
d
c
d
v
Vd
i
Ri
L
m
u
u
dt
(7)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
e-ISSN:
2087
-278X
Study on Con
t
rol Strategie
s
for the Multi
l
evel
Ca
scad
ed Co
nverte
rs (Lin Xu
)
6331
Whe
r
e
u
v
de
notes the vol
t
age at the
cent
er
of the
conve
r
ter leg
,
and
R
e
a
nd
L
e
den
ote t
he
effective se
ries re
si
stan
ce
and buffer in
ducta
nce for each arm.
From Equ
a
tio
n
(6) a
nd Equ
a
tion (7
), we
get:
,,
0
00
22
ud
c
u
d
d
c
d
zd
ze
z
e
mu
m
u
di
V
uR
i
L
dt
(8)
,,
22
2
ud
c
u
d
d
c
d
ee
L
vL
mu
m
u
RL
di
ui
dt
(9)
Whe
r
e
u
z
0
denotes the volt
age drop a
c
ross the
R
e
an
d
L
e
due to the circulatin
g curre
n
t
i
z
0
. From
Equation (8)
and Equatio
n
(9), we g
e
t:
,,
[(
)
(
)
]
()
dc
u
d
c
d
uu
d
d
dc
du
t
u
t
N
mi
m
i
dt
C
(10)
,,
[(
)
(
)
]
()
dc
u
d
c
d
uu
d
d
dc
du
t
u
t
N
mi
m
i
dt
C
(11)
The mod
u
lati
on index
m
u
and
m
d
can be
denoted a
s
:
0
1
2
vz
u
d
uu
m
V
,
0
1
2
vz
d
d
uu
m
V
(12)
Let:
,,
(
)
()
()
dc
u
d
c
d
dc
ut
u
t
u
t
(13)
,,
()
()
()
dc
u
d
c
d
d
c
ut
u
t
u
t
(14)
Substituting
Equation (12)-(1
4) into Equ
a
tion (9
)-(10
)
, we get:
0
0
()
2
[(
1
)
]
dc
v
L
z
z
dc
d
d
du
t
u
i
u
N
i
dt
C
V
V
(15)
00
()
2
1
[(
)
]
2
dc
z
v
z
L
dc
d
d
du
t
u
u
i
N
i
dt
C
V
V
(16)
From Equation (8), we get:
,,
0
0
22
ud
c
u
d
d
c
d
zd
ee
z
mu
m
u
di
V
LR
i
dt
(17)
The se
co
nd term can be d
enoted a
s
:
0
,,
11
(
)
(
)
()
()
24
2
zv
u
d
c
u
d
d
c
d
dc
dc
dd
uu
mu
m
u
u
t
u
t
VV
(18)
Hen
c
e, Equat
ion (17
)
can b
e
rewritten a
s
:
00
0
1
(
)
()
()
24
2
zd
z
v
e
dc
dc
z
ee
d
e
d
e
e
di
V
u
u
R
ut
ut
i
dt
L
L
V
L
V
L
L
(19)
Evaluation Warning : The document was created with Spire.PDF for Python.
e-ISSN: 2
087-278X
TELKOM
NIKA
Vol. 11, No
. 11, Novemb
er 201
3: 632
9 – 6336
6332
Notably,
the
MMCC syste
m
dynami
c
s can
be
de
scri
bed
by Equ
a
tion
(15
)
-(19
), and
the
theoreti
c
al st
eady state point
can b
e
derived. Ho
wever, si
nc
e the coe
fficients in these
differential
e
quation
s
a
r
e
time-varying,
the an
al
ytical sol
u
tion
would n
o
t be
dire
ctly obtai
ned.
Whe
r
ea
s, the
app
roximate
d stea
dy stat
e sol
u
tion of
i
z
0
can be de
rived fro
m
Equation
(19
)
by
a
s
s
u
ming
th
e
u
z
0
is small compared
with
V
d
, thus
we
get:
0
vL
z
d
ui
i
V
(20)
Substituting Equation
(20)
to Equation (16), the
u
z
0
is derived a
s
:
2
0
2
2
dv
z
d
Vu
u
V
(21)
The output vo
ltage
u
v
can b
e
approximat
ed as:
si
n
(
)
vm
uV
t
(22)
In case of act
i
ve rectifier m
ode,
i
L
can be
approxim
ate
d
as:
si
n(
)
Lm
iI
t
(23)
Hen
c
e,
i
z
0
can be derive
d
as:
0
(1
c
o
s
(
2
)
)
2
mm
z
d
VI
it
V
(24)
And
u
z
0
is
rewritten as
:
2
0
(1
c
o
s
(
2
)
)
2
dm
z
d
VV
ut
V
(25)
In case of rea
c
tive power g
eneration mo
de,
i
L
is denot
ed as:
sin(
90
)
Lm
iI
t
(26)
Hen
c
e,
i
z
0
can be derive
d
as:
0
si
n
(
2
)
2
mm
z
d
VI
it
V
(27)
It can be ob
serve
d
from
Equation (24
)
-(27
) tha
t, in either active
rectifier o
r
reactive
comp
en
satio
n
mode,
i
z
0
c
ontain
s
a se
con
d
ord
e
r o
scill
ation term, which
cau
s
e
s
unn
ecessary
circulatin
g cu
rre
nts a
nd p
o
w
er l
o
ss a
c
ro
ss th
e conv
erter arm
s
. Thi
s
effect
can
b
e
minimi
zed
by
usin
g dampi
n
g
controlle
r b
a
se
d on the circul
ating current dampin
g
controlle
r (CCDC).
3. Contr
o
l Strategie
s
of the Modular
Multilev
e
l Conv
erter
The co
ntrol strategy imple
m
ented is a li
near
control whi
c
h aim
s
to operate MMC in the
proximity of t
he lin
ear regi
on. T
w
o
different volt
ag
e
control l
oop
s
a
r
e im
pleme
n
ted, na
mely, the
total capa
cito
r voltage co
ntrolle
r (TCV
C) and the
cap
a
citor voltag
e
balanci
ng co
ntrolle
r (CVB
C),
the T
C
VC
blo
c
k is u
s
ed
to
control the
ov
erall
ene
rgy
of the le
g, an
d the
CVBC
block i
s
used
to
control the ba
lance betwe
e
n
uppe
r and l
o
we
r arm
s
of the MMCC phase-le
g. Not
ably, due to the
non-li
nea
r sy
stem equ
atio
ns, the intera
ction betwee
n
the TCVC
and CVBC lo
ops may lea
d
to
instability. Ho
wever,
sin
c
e
total ene
rgy
and
ene
rgy
balan
ce i
n
teracts dynami
c
ally, the TCV
C
loop is tun
ed
to be about te
n percent of the CVBC
lo
o
p
to achieve t
he de
cou
p
led
control.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
e-ISSN:
2087
-278X
Study on Con
t
rol Strategie
s
for the Multi
l
evel
Ca
scad
ed Co
nverte
rs (Lin Xu
)
6333
3.1. Total Ca
pacitor Volta
g
e Con
t
rolle
r
The total ca
p
a
citor volta
g
e
controller
(T
CVC)
is u
s
ed
to regulate t
he total ene
rgy store
d
in a MM
C co
nverter l
eg. T
y
pically, in a
steady
st
ate
operation, th
e refe
ren
c
e v
a
lue i
s
set to 2
V
d
.
It has been found that the prop
ortio
nal controlle
r
k
p,sum
is sufficient to regulate th
e sum ca
pa
ci
tor
voltage to its referen
c
e. By adding a
n
i
n
tegratio
n
term, the TCVC control is
also effective, b
u
t
the pa
ramete
r sele
ction i
s
cruci
a
l to en
sure
gl
obal
stability unde
r a wi
de o
peration rang
e. For
the sake of
simpli
city, the propo
rtiona
l co
ntro
l i
s
a
good
tra
deo
ff betwee
n
th
e a
c
cura
cy a
n
d
robu
stne
ss.
3.2. Capaci
tor Voltage Balancing Co
ntroller
Referrin
g to Equation (16), the term
i
L
is not produ
ci
ng any avera
ge value si
nce it is an
AC co
mpo
n
e
n
t in stea
dy state. The term also
-2
i
z
0
u
v
/V
d
contributes only by an oscillating term, if
i
z
0
does not have any com
pone
nt with the sam
e
freq
uen
cy as
u
v
. The only qua
ntity that can be
freely vari
ed
without
ca
usi
ng d
e
viation
s
from
u
v
refer
e
nc
e is
i
z
0
.
Therefore,
th
e only
way t
o
influen
ce the
energy balan
ce bet
wee
n
the two a
r
m
s
is to reg
u
late
the circulatin
g cu
rre
nt
i
z
0
. A
sep
a
rate p
r
o
portion
al co
ntrolle
r
k
p,diff
is utilized to reg
u
late the differen
c
e capa
cit
o
r voltage to its
r
e
ferenc
e (z
er
o)
.
3.3. Predictiv
e
Current
Controller (P
CC)
Curre
n
t control of the
MM
CC can
be
made
wi
th
hi
gh b
and
width
,
whi
c
h i
s
crucial
for
redu
ction
of tran
sient
curre
n
ts du
ring fau
l
ts, and
re
du
ction of curre
n
t harmoni
cs. Both the outp
u
t
cur
r
e
n
t
i
L
a
n
d
ci
rculating
current
i
z
0
are
available
for feedb
ack
co
nt
rol. Th
e
differential e
quatio
n
across the g
r
i
d
impeda
nce is de
scribe
d as:
1
[]
LL
Lv
g
di
r
iu
v
dt
L
L
(28)
Whe
r
e
L
an
d
r
L
de
note
s
the gri
d
co
upling i
ndu
ct
ance an
d its equivale
nt resi
stan
ce. L
e
t
v
(
t
)=
u
v
(
t
)
−
v
g
(
t
), the followin
g
equatio
n ca
n be derive
d
:
0
0
()
(
)
0
1
()
(
)
(
)
LL
rr
tt
t
t
LL
LL
t
it
e
i
t
e
v
d
L
(29)
Notably, the
control loop
of the MMCC b
e
lon
g
s
to the typical sample
-d
ata cont
rol
system. Let
t
0
=
kT
s
,
t
=(
k
+1
)
T
s
, the discret
e
rep
r
e
s
entati
on of
Equatio
n (29
)
is de
rived as:
[(
1
)
]
(1
)
1
(1
)
(
)
(
)
LL
ss
s
s
rr
Tk
T
kT
LL
LL
kT
ik
e
i
k
e
v
d
L
(30)
Sinc
e
r
L
is ve
ry sm
all, hen
ce
we
get
[(
1
)
]
1
L
s
r
kT
L
e
, thus th
e follo
wi
ng eq
uation
can be
obtaine
d:
(1
)
1
(
1
)
(
)
[
()
()
]
L
s
s
s
r
T
kT
L
LL
v
g
kT
ik
e
i
k
u
v
d
L
(31)
In orde
r to derive the pre
d
ictive cu
rr
en
t control, the
referen
c
e current for
i
L
(t) a
t
the
k
th
sampli
ng in
stant is rep
r
e
s
e
n
ted as
i
ref
(
k
)=
i
L
(
k
+2), thus the MMCC o
u
tput voltage
u
v
is derive
d
as:
/
(
)
[
(
)
(
1)
]
(
1)
Ls
m
rT
L
m
vr
e
f
L
g
s
L
uk
i
k
e
i
k
v
k
T
(32)
From Equ
a
tion (32
)
, it ca
n be ded
uce
d
that, in ord
e
r to cal
c
ul
ate the MMCC output
voltage
u
v
(
k
),
it is nece
s
sa
ry to predi
ct the value
s
i
L
(
k
+1)
and the
averag
e valu
e of
v
g
(
k
+1)
.
By
usin
g the interpol
ation m
e
thod, the rel
a
tions am
on
g the con
s
e
c
utive three sampling p
o
int
s
o
f
grid voltage
s
are de
rived a
s
:
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e-ISSN: 2
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TELKOM
NIKA
Vol. 11, No
. 11, Novemb
er 201
3: 632
9 – 6336
6334
(2
)
2
(
1
)
(
)
gg
g
vk
vk
vk
(33)
Thus, the la
st
term in Equa
tion (32
)
is de
noted a
s
:
15
3
(1
)
[
(1
)
(
2
)
]
(
)
(
1
)
22
2
gg
g
g
g
vk
vk
vk
vk
v
k
(34)
In ord
e
r to
predict
i
L
(
k
+1), the
v
a
ria
b
le
L
in Eq.(31
) i
s
repla
c
e
d
by it
s no
minal val
ue
L
m
,
thus:
(1
)
(
)
[
(1
)
(
)
]
L
s
m
r
T
L
s
LL
v
g
m
T
ik
e
i
k
u
k
v
k
L
(35)
Therefore, th
e block di
agram of the pre
d
ictive
cu
rren
t control la
w i
s
de
rived a
s
sho
w
n in
Figure 2.
Figure 2. The
Block
Diag
ra
m of the Pred
ictive Curre
n
t Control L
a
w
From
the bl
o
c
k dia
g
ra
m, the o
pen
-loo
p
tran
sfer fun
c
tion of the
cu
rre
nt controll
er
H
(
z
) is
obtaine
d as:
1
()
(1
)
(
1
)
m
L
Hz
Lz
z
(36)
The clo
s
e
d
-l
o
op ch
ara
c
te
ri
stic eq
uation i
s
1+
H
(
z
)=0, hence we g
e
t:
2
2
(1
)
0
(1
)
m
LL
z
Lz
(37)
Therefore, th
e pole
s
are
re
pre
s
ente
d
as:
()
m
zL
L
L
(38)
From Equ
a
tion (38), it can
be obse
r
ved
that, in case
of
L
=
L
m
, we get
z
2
=
0
, indic
a
ting
that the MMCC output current tracks th
e
refere
nce sig
nal in two cy
cles.
3.4. Circulati
ng Curr
ent
Damping Con
t
roller (CCDC)
The p
r
opo
rti
onal-i
nteg
ral
regul
ator
shows
un
sati
sfacto
ry pe
rforma
nce for curre
n
t
tracking
in case of
alternating refere
nce
sig
nal, whi
c
h re
sult
s
in rem
a
rkable
p
h
a
s
e and
amplitude tra
cki
ng erro
rs.
The propo
rtio
nal re
son
ant
(PR)
cu
rre
nt controlle
r, on the other ha
nd,
achi
eves
excellent tra
c
kin
g
pe
rform
ance for the
al
ternating
sign
al, whi
c
h mimi
cs the PI regul
ator
impleme
n
ted
in the
synchron
ou
s rotating refere
nce
frame
(SRRF) with
the f
o
llowin
g
tra
n
s
fer
function:
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
e-ISSN:
2087
-278X
Study on Con
t
rol Strategie
s
for the Multi
l
evel
Ca
scad
ed Co
nverte
rs (Lin Xu
)
6335
,0
,0
22
()
iz
PR
p
z
n
k
Gs
k
s
(39)
W
h
er
e th
e
pa
r
a
me
te
rs
k
p,
z
0
and
k
i,
z
0
are p
r
op
ortion
a
l
and
resona
nt gain,
and
ω
n
den
otes the
angul
ar freq
u
ency of the target alte
rnat
ing sign
al
, which impli
e
s t
he se
con
d
order ha
rmo
n
ic in
the pre
s
e
n
t case. Th
an
ks t
o
the infinite open
-loo
p gai
n introdu
ce
d
by the PR re
gulator, the
zero
steady-state t
r
ackin
g
erro
r is reali
z
e
d
for
the alternatin
g sign
al at 10
0Hz.
4. Simulation Resul
t
s an
d Discus
s
io
ns
To valid
ate t
he effe
ctiven
ess of
the
control
s
t
rategies
, the digital s
i
mulation of the
singl
e-p
h
a
s
e
five-level M
M
CC
co
nvert
e
r is
ca
rri
ed
out usi
ng t
he Elect
r
om
agneti
c
Tran
sient
Program (E
MTP-ATP).
The sy
stem
para
m
eters
are: the buff
e
r ind
u
cta
n
ce and resi
st
ance
L
e
=
4
.5mH,
R
e
=0.02O
hm,
V
d
=800V, the
dc-li
n
k
cap
a
c
itor valu
e
C
dc
=
2
.5mF, the grid induc
t
anc
e
L
s
=
1
.5mH,
V
grid
=220V (RMS), the cap
a
citor refe
re
n
c
e d
c
-lin
k vo
ltage
V
dc,ref
=4
00V, the T
C
VC
controlle
r gai
n
k
p,sum
=12, the CVBC
co
ntrolle
r gain
k
p,diff
=1.2, the circulating
current dampi
ng
controller (CCDC) gain
k
p,
z
0
=
1
.5,
k
i,
z
0
=2
00.
Figure 3. The
Simulation Result
s of t
he MMCC und
er Active Rectifi
e
r Mod
e
(a)
without an
d (b)
with circulating curren
t damping co
ntrolle
r.
Figure 3 sho
w
s the
simul
a
tion re
sults of
the
MMCC u
nder
active re
ctifier mod
e
. And the
grid
volta
ge unde
rgo
e
s o
u
tage
s
du
rin
g
t
=
0
.1s
and
t
=0.2
s. Th
e dc-lin
k
ca
pacito
r
volta
ges
u
dc
1
~
u
dc
4
, the load cu
rrent
i
L
, the load voltage
v
Load
, the grid voltage
v
g
, an
d the circul
atin
g
cur
r
e
n
t
i
z
0
can be observe
d. In Figure 3, the peak a
c
tive curre
n
t referen
c
e
i
L,ref
=50A, it can
be
observed i
n
Figure 3(a) t
hat t
he d
c
-lin
k capa
citor v
o
ltage
s ar
e stable both i
n
steady
state
and
transi
ent p
r
o
c
e
ss, a
nd th
e ci
rculating
curre
n
t i
z
0
shows obvious
second
order oscillation
with
positive d
c
off
s
et with
out th
e ci
rc
ulating
current controller. Howeve
r, whe
n
the circulating curre
n
t
controlle
r is a
c
tivated, the se
con
d
ord
e
r
comp
one
nt is eliminated, a
s
sh
own in Figure 3
(
b
)
.
5. Conclusio
n
The dc
capa
citor bal
an
ci
ng and effective curre
nt regul
ation m
e
thodol
ogie
s
for the
modula
r
m
u
ltilevel ca
scad
ed conve
r
ter (MM
C
C) a
r
e propo
se
d i
n
this
pap
er.
Base
d on
the
cap
a
cito
r
e
n
e
r
gy
evolving mech
ani
sm, an
effectiv
e capa
citor co
ntrol
sche
me
i
s
devise
d
,
whi
c
h
Evaluation Warning : The document was created with Spire.PDF for Python.
e-ISSN: 2
087-278X
TELKOM
NIKA
Vol. 11, No
. 11, Novemb
er 201
3: 632
9 – 6336
6336
inclu
d
e
s
the total cap
a
cito
r voltage cont
roller (TCV
C)
and capa
citor voltage bala
n
cin
g
co
ntroll
er
(CVBC). To
enha
nce the
tracking a
c
curacy of
cu
rre
nt control
loop,
the predi
ctive cu
rrent
controlle
r (P
CC) is
pre
s
e
n
ted. To mini
mize the
circulating curre
n
t of the MMCC, a
n
effective
circulatin
g current da
mp
ing controlle
r (CCDC
) i
s
p
r
op
osed
usin
g p
r
op
ortional
-reson
ant
controlle
r. The simulatio
n
result
s unde
r
active re
ctifier mode a
r
e prese
n
ted for verificatio
n
, wh
ich
sho
w
s perfe
ct capa
citor vo
ltage bala
n
ci
ng co
ntrol an
d pre
c
ise cu
rrent tracking.
Referen
ces
[1]
M Hag
i
w
a
r
a
, H Aka
g
i. C
ontrol
an
d e
x
perime
n
t of
p
u
lse-
w
i
dth
mo
dul
ated m
o
d
u
l
a
r multi
l
eve
l
converters.
IEEE Trans. Power Electron
. 20
09; 24(7): 1
737
–17
46.
[2]
M Hagi
w
a
ra,
K Nishimura,
H Akag
i. A me
dium-vo
l
tag
e
motor driv
e
w
i
t
h
a m
o
d
u
lar m
u
ltilev
e
l
PW
M
inverter.
IEEE Trans. Power Electron
. 20
10;
25(7): 178
6–
1
799.
[3]
H Akagi. Cl
as
sificatio
n
, T
e
rminol
og
y, a
n
d
App
lic
atio
n of the Modu
lar
Multilev
e
l C
a
s
c
ade C
onv
erte
r
(MMCC).
IEEE Trans. Power
Electron
. 20
11;
26(11): 31
19
–
313
0.
[4]
H Peng, M Ha
gi
w
a
r
a
, H Aka
g
i. Mode
lin
g a
nd Ana
l
ys
is of
S
w
itc
h
in
g-Ri
p
p
le Vo
ltag
e on
the DC Li
nk
Bet
w
e
e
n
a D
i
o
de Rectifi
e
r a
n
d
a Mod
u
l
a
r Multilev
e
l C
a
s
c
ade Inv
e
rter (MMCI).
IEEE Trans.
Power
Electron.
20
13;
28(1): 75–
84.
[5]
C Gao, X Jia
ng, Y Li, Z
C
hen, J Liu. A dc-
link vo
ltag
e
self-bal
ance
method for a
dio
de-cl
ampe
d
modu
lar multi
l
e
vel co
nverter
w
i
t
h
minim
u
m numb
e
r of voltage se
nsors.
IEEE Transactions on Power
Electron
ics.
20
13; 28(5): 2
125
-213
9.
[6]
J Gholin
ezha
d. Anal
ysis of ca
scade
d Anal
ys
i
s
of Cascade
d
H-Bridge
Mu
lti
l
evel Invert
er in DT
C-SVM
Inductio
n
Moto
r Drive for F
C
EV.
Journal
of Electrical En
g
i
ne
erin
g an
d T
e
chn
o
lo
gy
. 20
13; 8(2): 30
4-
315.
[7]
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aei. As
ymmetric
Casc
ade
d Multi-
lev
e
l Inve
rter: A S
o
luti
on to Obta
in Hi
gh
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e
r
of Voltag
e
Leve
l
s.
Journ
a
l
of Electrical E
ngi
neer
in
g and
T
e
chnol
ogy.
2
013; 8(2): 3
16-
325.
[8]
MR Ban
aei. R
educti
on
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mpon
ents in
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a
scad
ed T
r
ans
former Multil
ev
el Inverter
Usi
ng T
w
o
DC
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n
a
l of Electrica
l
Engi
neer
in
g an
d T
e
chno
lo
gy
. 201
2; 7(4): 538
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Evaluation Warning : The document was created with Spire.PDF for Python.