Internati
o
nal
Journal of P
o
wer Elect
roni
cs an
d
Drive
S
y
ste
m
(I
JPE
D
S)
Vol
.
4
,
No
. 2,
J
une
2
0
1
4
,
pp
. 26
5~
27
3
I
S
SN
: 208
8-8
6
9
4
2
65
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
Sliding Mode Contr
o
l of
Thr
e
e Levels Back-T
o-Back
VSC-
HVDC System Using Space
V
e
ctor
Modulation
Bouafia S
a
ber
*
, Be
naiss
a
Abselkad
er*, B
o
uz
idi Mans
our*
,
*
*
, Ba
rkat
Sa
id***
* Depart
em
ent o
f
El
ectr
i
c
a
l
Engi
neering
,
In
tel
lig
ent Con
t
rol
&
El
ectr
i
ca
l P
o
wer S
y
s
t
em
s
L
a
borato
r
y, Unive
r
s
i
t
y
of
Djilal
i
Liab
es, Si
di Be
l Abbes,
Al
geria
** Departmen
t
o
f
Electr
i
cal
Engineering
,
Univ
ers
i
t
y
of
Kas
d
i M
e
r
b
ah Ouargl
a,
Al
geria
*** Departemen
t of
Electr
i
cal
En
gi
neer
ing, M’sila University
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Ja
n
3, 2014
Rev
i
sed
Feb
28
, 20
14
Accepted
Mar 12, 2014
In this stud
y
,
a s
liding mode strateg
y
proposed to
control a thr
ee levels Back-
to-Back High V
o
ltage Dir
ect Current (HVDC) s
y
stem based on the three-
level voltag
e
source conv
erter (
V
SC).
The voltage-balancing
co
ntrol of two
split DC capacitors of the VSC-HVDC sy
stem is achiev
e
d using
three-lev
e
l
space vec
t
or m
odulation with ba
l
a
ncing strat
e
g
y
based on the effe
ctiv
e use of
the redund
ant s
w
itching states
of the
i
nverter
voltag
e
vectors. Finally
,
a
complete simulation of the VSC-HVDC sy
stem validates
th
e efficiency
of
the proposed strateg
y
law. Compared to the co
nvention
a
l contr
o
l, Slidin
g
Mode Control
scheme for the VSC-
HVDC sys
t
em
s
hows
the att
r
ac
tive
advantages such
as offer
i
ng hig
h
tr
acking
accur
a
cy
, fast d
y
namic r
e
sponse
and good ro
bustness.
Keyword:
Slid
in
g m
o
d
e
co
n
t
ro
ller
Back-to-Back
VSC-HVDC
syste
m
Cap
acito
rs vo
ltag
e
s
b
a
lan
c
i
n
g
Mu
ltilev
e
l sp
ace v
ector
m
odul
at
i
o
n
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
:
B
oua
fi
a Sa
ber
,
Depa
rtem
ent of Elect
ri
cal
E
n
gi
nee
r
i
n
g,
In
tellig
en
t C
ontro
l & Electrical Power System
s Lab
o
r
atory,
Un
i
v
ersity of
Dj
ilali Liab
es,
Sid
i
Bel Abb
e
s
Si
di
B
e
l
A
b
bes
2
2
0
0
0
, B
P
89
Al
ge
ri
a.
Em
ail: boua
fia.sabe
r@gm
ail.
com
1.
INTRODUCTION
High
Vo
ltag
e
d
i
rect Curren
t
(HVDC
) power tran
sm
issio
n
syste
m
s an
d
tech
no
log
i
es co
nstitu
te a k
e
y
appl
i
cat
i
o
n
of
t
h
e p
o
w
er
el
ec
t
r
o
n
i
c
s t
ech
n
o
l
ogy
t
o
el
ect
ri
c
a
l
po
we
r
net
w
or
ks.
T
h
e ec
on
om
i
c
s of
bul
k
po
we
r
transm
ission by unde
rground
m
eans is increasingly m
oving in
favor of
direct curre
nt. T
h
e HVDC links have
th
e ab
ility to
ex
ert in
stan
taneo
u
s po
wer con
t
ro
l in
n
e
i
g
hb
oring
AC syste
m
s [1
]-[2
]. Great m
a
n
y
research
effo
rts
h
a
v
e
b
e
en
d
i
rected toward
s
realizin
g HVDC m
o
d
e
l
s
fo
r
stab
ility stu
d
i
es and
p
o
wer fl
o
w
s [2
].
Fundam
e
ntally, two HVDC technologies are availabl
e [3
]
;
(i) th
e co
nv
en
tio
n
a
l th
yrist
o
r-b
a
sed
lin
e
comm
utated conve
r
ter
(LCC)
HVDC wh
ich
is a
well-p
r
ov
en techn
o
l
o
gy with
th
e first
app
licatio
n
i
n
1
954
in
G
o
tland
, Sw
eden
. (
ii)
V
S
C-H
V
D
C
, wh
ich
is a r
e
lativ
ely
n
e
w techno
logy u
n
d
e
r
r
a
p
i
d
dev
e
lop
m
en
t. Th
e
V
S
C
tech
no
log
y
was in
itially d
e
v
e
lo
p
e
d
for drive tech
no
log
i
es du
e to
si
g
n
i
fican
t in
crease i
n
v
o
ltag
e
and
p
o
wer
rat
i
ngs
o
f
sem
i
con
duct
o
rs
, s
u
ch
as t
h
e i
n
s
u
l
a
t
e
d
gat
e
bi
pol
a
r
t
r
a
n
si
st
o
r
(
I
GB
T
)
, t
h
e
VSC
-
H
VDC
s
c
hem
e
started
to
fi
n
d
ap
p
lication
s
in
th
e late 1
9
9
0
s
,
esp
ecia
lly wh
ere th
e in
terconn
ected
AC n
e
t
w
orks h
a
d
low sh
ort-
circu
it lev
e
ls
or wh
ere a
sm
al
l
fo
o
t
p
r
in
t
w
a
s req
u
i
r
e
d [4
]-
[5
].
The V
S
C
o
f
f
e
rs seve
ral
a
dva
nt
age
s
o
v
e
r
t
h
e LC
C
-
H
VDC
sc
hem
e
[3]
-
[
4]
;
VS
C
uses sel
f
-
com
m
ut
at
ed devi
ces w
h
i
c
h
gi
ve at
t
r
active
features s
u
ch
as: the indepe
nde
nt
c
ont
r
o
l
of act
i
v
e
an
d
r
eact
i
v
e
p
o
wer, t
h
e abilit
y to
supp
ly p
a
ssi
v
e
lo
ad
s and
weak
grid
s, and
th
e ab
ility to
o
p
e
rate with
ou
t ex
tern
al
com
m
ut
ati
on
vol
t
a
ge
. M
o
re
ove
r,
VSC
has
a rel
a
t
i
v
e sm
al
l
foot
pri
n
t
d
u
e t
o
t
h
e sm
all
si
ze of t
h
e h
a
rm
oni
c
filters [3
]-[4
].
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
. 2
,
Jun
e
2
014
:
26
5
–
27
3
26
6
Th
e requ
irem
e
n
t to
m
eet h
i
g
h
vo
ltag
e
lev
e
ls, bo
th
at AC
an
d DC si
d
e
s, of an
HVDC
co
nv
erter
station is best accomm
odate
d by m
u
ltilevel VSC config
urations [4]. They were
i
nve
stigated wi
th the
requ
irem
en
t o
f
q
u
a
lity an
d
efficien
cy in
h
i
gh
po
wer system
s. Th
ey o
ffer
m
a
n
y
ad
v
a
n
t
ag
es su
ch
as in
creased
po
we
r rat
i
n
g,
m
i
nim
i
zed t
h
e
harm
oni
c ef
fec
t
s and
re
d
u
ced
electrom
a
gnetic interfe
rence
(EM
I
) em
ission [
4
]
.
Recently, HVDC conve
r
ter syste
m
s
using full back
- to-bac
k m
u
l
tilevel NPC
conve
r
ters are
being
in
v
e
stig
ated
owing
to
th
eir hig
h
-vo
ltag
e
,
h
i
g
h
-cu
r
ren
t
and staircase-lik
e wav
e
fo
rm
cap
ab
ilities [4
]-[5
]
.
Pu
lse
wi
dt
h
m
odul
at
i
on
(P
W
M
) t
e
chni
que
s are
sho
w
i
n
g
p
o
p
u
l
ari
t
y
t
o
cont
r
o
l
m
u
l
t
i
l
e
vel
i
nve
rt
ers
fo
r
m
u
lt
i
-
m
e
gawat
t
i
n
d
u
s
t
r
i
a
l
appl
i
cat
i
ons
[6]
.
S
p
ace
vect
or m
odul
at
i
on (S
VM
) i
s
one
of t
h
e
m
o
st
popul
ar
P
W
M
tech
n
i
qu
es
g
a
in
ed
in
terest recen
tly. Th
e salient features
of the SVM strate
gy are as follows. i) It m
i
nimize
s
to
tal h
a
rm
o
n
i
c d
i
stortio
n of
th
e ac-si
d
e
v
o
ltag
e
s, throug
h u
tilizatio
n
of
all av
ailab
l
e vo
ltag
e
lev
e
ls
of th
e
VSC. ii) It m
i
nim
i
zes the switching los
s
es
since, ov
e
r
each sam
p
ling period
of the S
V
M
m
odulator,
it uses
th
e three adj
a
cen
t
switch
i
ng
states with
m
i
n
i
m
u
m
ON–O
FF state tran
sit
i
o
n
s
of t
h
e swi
t
ch
in
g
d
e
v
i
ces. iii) It
en
ab
les
d
e
v
e
l
o
p
m
en
t o
f
a
m
e
th
od
fo
r
d
c
-cap
acito
r
v
o
ltag
e
b
a
lan
c
ing
wit
h
ou
t th
e n
e
ed
for aux
iliary po
wer
circu
its and
/
o
r
o
f
flin
e calcu
latio
n
s
[8
].
The c
ont
rol
sy
st
em
pl
ay
s an i
m
port
a
nt
r
o
l
e
i
n
t
h
e
wh
ol
e
H
VDC
sy
st
em
[6]
-
[
8
]
.
G
o
od c
ont
rol
l
e
rs ca
n
im
pro
v
e t
h
e
o
p
erat
i
n
g c
h
ara
c
t
e
ri
st
i
c
s not
onl
y
of
DC
s
y
st
em
it
sel
f
, b
u
t
al
so
of
AC
sy
st
em
s. In
c
ont
rol
theory,
sliding m
ode
control, or
SM
C, is a
nonlinea
r c
ontrol
m
e
thod that
alters the
dy
na
m
i
cs
of a nonlinear
sy
st
em
by
appl
i
cat
i
on o
f
a
di
s
c
ont
i
n
u
o
u
s
c
o
n
t
rol
si
g
n
al
th
at
forces th
e syste
m
to
"slid
e" alo
n
g
a cross-sectio
n
of
t
h
e sy
st
em
'
s
n
o
rm
al
beha
vi
or
[
9
]
-
[
1
0]
.
In
th
is stud
y,
slid
in
g
m
o
d
e
co
n
t
ro
l strategy is
ap
p
lied
to co
n
t
ro
l a th
ree-lev
e
l b
a
ck
-t
o-b
a
ck
VSC-
HVDC syste
m
in
th
e ai
m to
i
m
p
r
o
v
e
its p
e
rform
a
n
ces. It will b
e
u
s
ed
for d
e
v
e
lop
i
ng
the in
stan
tan
e
o
u
s activ
e
and reactive
powers
and
DC
v
o
l
t
a
ge
c
ont
rol
l
ers.
2.
SYSTE
M
ST
RU
CTU
R
E
A
N
D
M
A
THE
M
ATI
C
AL M
O
DEL O
F
VS
C-
HV
DC
BA
CK
-TO-B
A
C
K
SYSTE
M
Fi
gu
re
1 sh
o
w
s a schem
a
t
i
c
rep
r
ese
n
t
a
t
i
on
of a t
h
ree
-
l
e
ve
l
VSC
-
base
d
HV
DC
sy
st
em
. The sy
st
em
com
p
rises two back-to-bac
k
connected
t
h
ree-lev
e
l NPC co
nv
erters un
its. Th
e
DC-link is co
m
p
o
s
ed
o
f
two
n
o
m
in
ally-id
e
ntical cap
acito
rs.
Th
e two
VSC u
n
its sh
are th
e sa
m
e
DC-cap
acito
rs and
in
term
ed
iate n
o
d
es
O
1
are comm
on between
VSC-1
and
VSC-2
.
An
estimate o
f
th
e to
tal switch
i
ng
l
o
ss
es of t
h
e sy
st
e
m
i
s
m
odel
l
e
d
by
resi
st
or
R
p
[4
].
R
p
is no
t shown in
Fi
g
u
re
1
.
Th
e
AC-si
d
e termin
al o
f
eac
h conve
rter is
c
o
nnected to t
h
e corres
p
onding
AC
syste
m
through a series connected
R
and
L
an
d
a th
ree-p
h
ase tran
sfo
r
m
e
r. For sim
p
lic
it
y an
d
witho
u
t
th
e lo
ss
o
f
g
e
n
e
rality, we assu
m
e
th
e
fo
llowing
: i) th
e vo
ltag
e
m
a
g
n
itud
e
s
o
f
both
g
r
i
d
s are t
h
e sa
m
e
; h
o
w
ever, th
e
pha
ses can assum
e
any
val
u
es. i
i
)
The p
o
w
e
r swi
t
c
hes
,
di
ode
s an
d passi
ve com
pon
ent
s
of t
h
e t
w
o VS
C
s
are
co
rr
esp
ond
ing
l
y
identical.
1
O
0
O
2
O
2
C
v
1
C
v
dc
v
1
C
2
C
2
R
2
L
2
ta
v
2
tb
v
2
tc
v
1
ta
v
1
tb
v
1
tc
v
1
R
1
L
2
s
a
v
2
s
b
v
2
s
c
v
2
a
i
2
b
i
2
c
i
1
a
i
1
b
i
1
c
i
1
s
a
v
1
s
b
v
1
s
c
v
Fi
gu
re
1.
T
h
re
e p
h
ase
bac
k
-t
o-
bac
k
t
h
ree l
e
vel
N
P
C
based
VSC
-
H
V
D
C
s
y
st
em
To
av
o
i
d
rep
e
t
itio
n
s
in
th
e
form
u
l
atio
n
,
th
e
q
u
a
n
tities o
f
VSC-1
an
d
AC syste
m
-1
are in
d
e
x
e
d
b
y
k=1
, w
h
i
l
e
t
h
o
s
e of
VSC
-
2 a
nd
AC
sy
st
em
-2 a
r
e i
n
d
e
xe
d
by
k=2
. I
n
t
h
i
s
pape
r, st
at
i
o
n 1 i
s
de
si
g
n
at
ed an
d
chosen as
rectifier station
whi
l
e stati
on
2 i
s
d
e
si
gnat
e
d as i
n
vert
er
st
at
i
o
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Sliding M
o
de
Contr
o
l of
Thr
ee Levels B
a
ck
-To-B
a
ck
V
S
C-HVDC
Syste
m
Using Sp
ace…
(Bouafia
Sabe
r)
26
7
12
k
dk
k
t
d
k
s
d
k
dk
q
k
kk
q
tq
k
s
q
k
k
qk
d
k
kk
dc
dc
pe
q
e
q
di
R
v
v
ii
dt
L
L
di
vv
R
ii
dt
L
L
dv
i
dt
R
C
C
(1)
Whe
r
e
C
eq
=C/
2
is th
e
DC-link
equ
i
v
a
len
t
cap
acito
r. In
th
e
syn
c
hrono
us fra
m
e
,
v
sdk
and
v
sq
k
are the
d,
q
axes c
o
m
ponents of the res
p
ective source voltage
s,
i
dk
and
i
qk
are that of the line curre
n
ts,
v
tdk
and
v
tq
k
are
th
at of th
e conv
erter inp
u
t
voltag
e
s.
v
dc
is t
h
e DC
bu
s
v
o
ltag
e
an
d
i
dc
i
s
eq
ui
val
e
nt
DC
c
u
rre
nt
l
i
k
e i
n
ca
se o
f
to
w
lev
e
l conver
t
er
[
8
].
3.
SLIDI
N
G M
O
DE CO
NTR
O
L
OF
B
A
C
K
-TO
-
BA
CK VS
C-H
V
DC
S
Y
STEM
Fi
gu
re
2 s
h
ow
s a sc
hem
a
t
i
c
r
e
prese
n
t
a
t
i
o
n
of
a
VSC
-
base
d
HV
DC
sy
st
e
m
and i
t
s
co
nt
rol
st
ruct
ur
e
diagram
.
The cont
rols of a
VSC-HVDC
syste
m
is b
a
sically th
e co
n
t
ro
l
o
f
th
e transfer
o
f
en
erg
y
with
i
nde
pen
d
e
n
t
c
ont
rol
of
act
i
v
e an
d
react
i
v
e
po
we
r a
n
d
al
so
keep
t
h
e
DC
l
i
nk
v
o
l
t
a
ge a
t
t
h
e d
e
si
re
d l
e
vel
t
o
support t
h
e
require
d
active a
n
d
r
eactiv
e p
o
wer
co
mman
d
s
[5
]-
[6
].
Fro
m
Eq
u
a
tion (1), it is o
b
v
i
ou
s th
at th
e co
nv
erter
is a nonl
i
near and c
o
upled
syste
m
. So a nonlinear
co
n
t
ro
ller
b
a
sed
o
n
th
e
slid
ing
m
o
d
e
m
e
th
od
is
d
e
v
e
lop
e
d
in
th
is secti
o
n.
Th
e system
(1
) is subd
iv
id
ed
i
n
three sub
s
yste
m
s
as fo
llo
ws:
Su
bsyst
e
m 1:
The first
s
u
bsyste
m
is
charact
erized by only one
state
dc
x
v
and
on
ly on
e co
n
t
r
o
l
in
pu
t
1
dc
ui
.
12
dc
dc
pe
q
e
q
dv
i
dt
R
C
C
(2)
Th
e Equ
a
tion
(2
) can b
e
written
as fo
llo
w:
11
1
1
*
11
1
.
()
,
y
fg
dc
d
d
c
xL
h
L
h
u
yh
x
v
v
(3)
Whe
r
e:
11
1
12
,
,
,
dc
dc
f
g
pe
q
e
q
xv
u
i
L
h
L
h
RC
C
Su
bsyst
e
m 2:
The sec
o
nd s
u
bsystem
is als
o
cha
r
acterize
d
by
only
one
state
dk
x
i
and
onl
y
one c
ont
rol
i
n
p
u
t
td
k
uv
.
dk
k
t
d
k
s
d
k
dk
q
k
kk
di
R
v
v
ii
dt
L
L
(4)
Th
e Equ
a
tion
(4
) can also
b
e
written
as fo
llow:
22
2
2
*
22
2
, =
fg
dk
d
d
k
x
Lh
L
h
u
yh
i
y
i
(5)
Whe
r
e:
22
22
,,
1
()
,
=
dk
tdk
ks
d
k
fd
k
q
k
g
kk
k
xi
u
v
Rv
Lh
x
i
i
L
h
LL
L
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
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-86
94
I
J
PED
S
Vo
l. 4
,
No
. 2
,
Jun
e
2
014
:
26
5
–
27
3
26
8
Su
bsyst
e
m 3:
Th
e t
h
ird su
b
s
yste
m
is also
characterize
d
by
one state
qk
x
i
and
onl
y
one
co
nt
r
o
l
i
n
put
tqk
uv
.
dk
k
t
d
k
s
d
k
dk
q
k
kk
di
R
v
v
ii
dt
L
L
(6)
Th
e Equ
a
tion
(6
) can also
b
e
written
as fo
llow:
33
3
3
*
33
3
, =
fg
qk
d
q
k
x
Lh
L
h
u
yh
i
y
i
(7)
Whe
r
e:
33
33
,,
1
()
,
=
qk
t
q
k
ks
d
k
fq
k
q
k
g
kk
k
xi
u
v
Rv
Lh
x
i
i
L
h
LL
L
1
a
i
1
b
i
1
c
i
1
ta
v
1
tb
v
1
tc
v
2
a
i
2
b
i
2
c
i
2
ta
v
2
tb
v
2
tc
v
1
s
a
v
1
s
b
v
1
s
c
v
2
s
a
v
2
s
b
v
2
s
c
v
1
R
1
L
2
R
2
L
1
O
0
O
2
O
2
C
v
1
C
v
dc
v
1
a
i
1
b
i
1
c
i
2
a
i
2
b
i
2
c
i
2
s
a
v
2
s
b
v
2
s
c
v
1
s
a
v
1
s
b
v
1
s
c
v
2
C
v
dc
v
abc
abc
1
d
i
*
1
q
i
1
q
i
1
td
v
1
tq
v
abc
dq
abc
2
dc
ref
v
3
S
dcr
e
f
i
P
xref
i
2
tq
v
2
td
v
2
a
i
2
b
i
2
c
i
1
a
i
1
b
i
1
c
i
2
ref
Q
1
2
3
sd
V
2
2
3
sd
V
2
d
i
2
q
i
1
re
f
Q
dq
2
dc
v
11
S
21
S
*
1
d
i
*
2
q
i
*
2
d
i
12
S
22
S
Figu
re
2.
C
o
nt
rol st
ruct
ure
o
f
the th
ree le
vels VSC
-
H
V
D
C
sy
stem
For
,
and
dc
dk
qk
vi
i
, t
h
e surfac
es
S
1
, S
2
and
S
3
are give
n by
t
h
e follo
win
g
e
x
p
r
essi
on:
**
11
1
**
22
2
**
33
3
dc
d
c
i
d
c
d
c
dk
d
k
i
d
k
d
k
qk
q
k
i
q
k
q
k
Sk
v
v
k
v
v
d
t
Sk
i
i
k
i
i
d
t
Sk
i
i
k
i
i
d
t
(8
)
An
d c
o
nse
que
ntly
, their tem
poral
deri
vative
s
are
give
n
by
:
**
11
1
**
22
2
**
33
3
dc
dc
i
d
c
d
c
dk
dk
i
d
k
d
k
qk
qk
i
q
k
q
k
d
Sk
v
v
k
v
v
dt
d
Sk
i
i
k
i
i
dt
d
Sk
i
i
k
i
i
dt
(9
)
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I
J
PEDS
I
S
SN:
208
8-8
6
9
4
Sliding M
o
de
Control of
Three Levels B
a
ck
-To-B
a
ck
V
S
C-HVDC
Syste
m
Using Sp
ace…
(Bouafia
Sabe
r)
26
9
The e
qui
valent
cont
rol ca
n
be
calculated f
r
o
m
the fo
rm
ula
0
S
, and the stabilizing control is
given
to guarantee t
h
e conve
rgence condition
[6]-[11]. Finally, the co
ntrol law is given
by:
*
**
1
11
11
*
**
2
22
22
*
**
3
33
33
1
()
1
()
1
()
dc
i
Vc
f
d
c
d
c
d
c
g
dk
i
t
d
k
f
dk
d
k
dk
g
qk
i
tq
k
f
qk
q
k
qk
g
dv
k
iL
h
v
v
k
s
i
g
n
S
Lh
d
t
k
di
k
vL
h
i
i
k
s
i
g
n
S
Lh
d
t
k
di
k
vL
h
i
i
k
s
i
g
n
S
Lh
d
t
k
(1
0)
Whe
r
e:
12
3
1
2
3
,,,
,
,
,
,
a
n
d
dc
dk
qk
i
i
i
kk
k
k
k
k
k
k
k
are
positive constants.
4.
THREE-LEVEL SPACE
VECTOR MODUL
ATION
A
three-level converter differs fr
om
a conventional t
w
o-level conver
ter in that it is capable
of
pr
o
duci
n
g
th
re
e dif
f
ere
n
t le
v
e
ls o
f
out
put
pha
se
voltage
, W
ith
three possible
output states
for
eac
h of the
three
phases, t
h
ere are a t
o
tal of
27 (33)
possible switch com
b
inations
. The
result of plotting each
of t
h
e
out
put
v
o
ltages
in a
αβ
re
fere
n
ce fram
e
is sh
o
w
n
in
Fig
u
re
3
.
Fig
u
re 4 s
h
ow
s that the 27 switch com
b
inations re
sult in a total of 19 uniq
ue v
o
ltage vecto
r
s sinc
e
som
e
of the
co
m
b
inations p
r
o
duce
the
sam
e
voltage
ve
ctor
.
These di
ffe
ren
t
co
m
b
inations
relate to different
ways of
co
nn
ecting
th
e VS
Cs to the DC bus that
result in t
h
e same voltage
bei
n
g applied t
o
AC system
s. Projection of t
h
e vectors
on a
αβ
co
o
r
di
nates fo
rm
s
a
two
-
lay
e
r he
xa
go
n ce
ntere
d
at the origin
of the
αβ
pla
n
e. Z
e
ro
voltage
ve
ctors a
r
e locate
d
at the
ori
g
in
of t
h
e
plane.
The swi
t
ching states are illu
strated
by 0, 1 and
2
wh
ich denote correspondin
g switching states. Any
sam
p
ling instant the tip of t
h
e voltage
vector is located in a triangle form
ed
by three swit
ching vect
ors
nearest
to the voltage
vector
(Figur
e
3). T
h
e
nea
r
est three
ve
ctors
are c
h
osen
by
determ
ining the triangle
within the
vector space i
n
which t
h
e
desi
re
d
voltage vec
t
or resides.
Th
e r
e
qu
ir
ed
on
du
r
a
tio
n
o
f
each
of the
vect
ors is
determ
ined by
E
q
uation (24). T
h
ese
specify that
the dem
a
nd ve
ctor,
v
ref
, is the geom
etric sum
of the chose
n
three vect
ors (
v
1
, v
2
, v
3
)
m
u
ltiplied by thei
r on-
du
ratio
ns (
d
1
, d
2
, d
3
) and that t
h
eir
on-
durati
ons m
u
st fill the com
p
lete cycle.
11
2
2
3
3
12
3
,
ref
j
re
f
r
e
f
re
f
vd
v
d
v
d
v
T
dd
d
T
vv
e
v
(1
1)
The
next step
is to identify t
h
e ap
p
r
o
p
riate
red
u
nda
nt s
w
itching
st
ates and
ge
nerate th
e switchin
g
pattern to control
voltages
of the
capacit
o
rs. T
h
is requires knowle
dge
of phase
curre
nts a
n
d im
pac
t
s of
diffe
re
nt switc
hin
g
states o
n
dc-si
d
e interm
ediate branch
currents a
n
d c
onseque
ntly capacitor
voltage
s [6]-
[7]
.
u
u
ref
v
1
v
2
v
3
v
Figure
3. Spac
e vector
diagra
m
s
of three-level converter
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN:
2
088
-86
94
I
J
PEDS
Vo
l.
4
,
No
.
2
,
Jun
e
2
014
:
26
5
–
27
3
27
0
5.
D
C
-
C
A
P
AC
ITOR
V
O
LTAGES BA
LA
NC
ING STRATEGY
In a three-phase three
-
level
VSC
converter, t
h
e total energy
E
of DC-link capacitors
is
[7]:
22
12
()
2
CC
C
Ev
v
(1
2)
Whe
n
all capa
c
itor voltages
are bala
nced,
the total ene
r
gy
E reache
s
its m
i
nim
u
m
of
2
mi
n
4
dc
EC
v
,
[7]
-
[
8]
. T
h
is c
o
n
d
ition
is called the m
i
nim
u
m
energy
pr
operty whic
h ca
n be
used as the basic princi
ple for
DC
-ca
p
acitor
voltage
balanci
ng a
nd c
ont
rol.
The ad
opte
d
cont
rol m
e
thod sho
u
l
d
m
i
nim
i
ze the qua
drati
c
cost
fu
nctio
n
J
as
sociated with vol
t
age de
viation
of
the DC
-ca
p
a
c
itors [8]
.
The
cost
f
u
nction
is
de
fine
d
as f
o
llows:
22
12
2
CC
C
J
vv
(1
3)
Where:
,1
,
2
2
dc
Cj
Cj
v
vv
j
B
a
sed on pr
o
p
e
r
selection o
f
red
u
nda
nt
s
w
itchin
g states o
f
bot
h
VSC
uni
ts,
J
can
be m
i
nim
i
zed, if
capacitor
volt
a
ges are m
a
in
tained at voltage refe
re
nce
values of
v
dc
/2
. The m
a
them
atical condit
i
on to
min
i
miz
e
J
is:
2
12
((
)
(
)
)
0
Cx
x
vi
k
i
k
(1
4)
Whe
r
e
2
C
v
is the voltage
drift
at sa
m
p
ling
peri
od
k
. C
u
r
r
ents c
o
m
ponents
x=
1,2
,
3
ar
e
co
m
p
u
t
e
d
f
o
r
diffe
re
nt
com
b
inatio
ns of
adjace
nt red
u
nda
nt
s
w
itch
in
g states ov
er
a sam
p
lin
g
p
e
r
i
od
an
d
th
e b
e
st
com
b
ination
which m
a
ximize
(14) is selected.
6.
R
E
SU
LTS AN
D ANA
LY
SIS
To
validate the
de
velo
ped
ste
a
dy
state m
odel and
a c
ont
rol
strategy
, its
p
e
rf
orm
a
nce an
d r
o
bu
stness
are analyzed whe
n
applied SMC of Three
Levels B
ack-
T
o-Bac
k
VSC
-
HV
DC Syst
em
Using Spac
e Vector
Modulation wi
th the
param
e
t
e
rs
prese
n
ted
i
n
Ta
ble
1
[7]
.
Sim
u
lation stu
d
ies
of t
h
e sy
st
em
are exec
ute
d
usin
g
M
A
TLAB
™
/S
IM
UL
IN
K fo
r diffe
re
nt
o
p
er
a
ting
c
o
n
d
iti
ons
,
the
syste
m
was sim
u
lated duri
ng 0.1s
.
The HVDC sy
ste
m
of Figure
1 is capable to inte
rfac
e
the
two AC
sy
stem
s with differ
e
nt nom
inal
fre
que
ncies a
n
d m
a
intain DC
-v
oltage
balan
ce [6]
.
To
de
m
onstrate this capability,
d
yna
m
i
c r
e
sp
on
se o
f
the
syste
m
of Figure
1 to steps
chan
ges i
n
real and
reactive power
de
m
a
nds is c
o
nsidere
d
. T
h
e
nom
inal
fre
que
ncies of
AC
sy
stem
-1
and
AC
system
-
2
of Figure
1 a
r
e
60
Hz
a
n
d 50
Hz respectivel
y
.
Table 1.
Sim
u
lation
Pa
ram
e
ters
Para
m
e
ters
of
the Study Syste
m
Value
E
ach DCC no
m
i
nal power
Each AC s
y
ste
m
n
o
m
inal
voltage
Each AC s
y
ste
m
S
hort Circuit Ratio
No
m
i
nal Frequencies
f
1
No
m
i
nal Frequencies
f
2
Each transform
e
r v
o
ltage ratio
R
1
and
R
2
L
1
and
L
2
No
m
i
nal net DC
voltage
Resistance
R
p
VSC-
1 sa
m
p
ling frequency
VSC-
2 sa
m
p
ling frequency
DC-link Capacitor
C
1
,C
2
110 M
W
138 kV
5
60 Hz
50 Hz
138 kV / 30 kV
40 m
Ω
6 m
H
30 kV
1.
8 K
Ω
2520 Hz
2520 Hz
2000 µF
6.
1.
Re
al
P
o
w
er C
o
n
t
rol
Initially, the s
y
ste
m
is in a
stand
b
y
m
ode of o
p
e
r
ation a
nd
v
dcref
is set
to 30kV. B
o
th VSCs units
ope
rate at unit
y
po
wer f
actor
. At t = 0.
04 s
up t
o
0
.
0
7
s,
P
ref2
is change
d
as a step corre
sponding to a
powe
r
c
h
a
n
g
e
f
r
o
m
0
t
o
1
0
Mw
,
f
r
o
m
A
C
s
y
s
t
em
-
1
t
o
A
C
S
y
s
t
em
-
2
.
A
t
t
=
0
.
0
7
s
,
P
ref2
is
chan
ge
d f
r
o
m
10
Mw
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PEDS
I
S
SN:
208
8-8
6
9
4
Sliding M
o
de
Contr
o
l of
Thr
ee Levels B
a
ck
-To-B
a
ck
V
S
C-HVDC
Syste
m
Using Sp
ace…
(Bouafia
Sabe
r)
27
1
to -
10M
w; this
cha
nge c
o
rres
p
o
n
d
s to
a p
o
w
er fl
ow
re
versa
l
fr
om
10M
w t
o
-
1
0M
w,
f
r
om
AC
sy
stem
-2 to AC
syste
m
-1.
6.
1. Re
acti
ve Pow
er Co
ntr
o
l
in the fi
rst tim
e
interval,
bet
w
een
0 a
n
d 0.05
s, th
e
system
is in stop m
ode; at t = 0.05 s,
reactive
po
we
r
dem
a
nds o
f
AC
sy
stem
s 1
are c
h
a
nge
d
fr
om
0 to
-5
M
v
ar a
n
d
fr
om
0 t
o
3 M
v
ar
f
o
r ac sy
stem
-2.
Th
e
p
e
rf
or
m
a
n
ce o
f
the pr
opo
sed
SMC contr
o
l will b
e
carr
i
ed
o
u
t
thr
ough
sim
u
latio
n
stu
d
y
as
well
as to be com
p
ared
with that
of line
a
r
co
ntr
o
l. The
res
u
lts un
der t
h
e co
n
v
entio
n
al PI c
ont
rol will be
give
n.
The
n
c
o
m
p
arisons
are
m
a
de between t
h
ese t
w
o controls:
Co
n
t
ro
l
1
:
Slid
in
g m
o
d
e
Con
t
ro
l in
r
o
tating
synchr
ono
us
f
r
a
m
e
.
C
ontr
o
l
2:
C
o
n
v
e
n
tional
PI
cont
rol i
n
r
o
tat
i
ng
sy
nc
hr
on
o
u
s
fram
e
.
Figu
re
4.
Sim
u
lation res
u
lts
o
f
DC
-Lin
k
v
o
ltage
Figu
re
6.
Sim
u
lation res
u
lts
o
f
DC
capa
s
itor
s
v
o
ltages
(a)
u
s
ing
PI
co
ntr
o
l
l
er, (
b
)
usin
g S
M
C
cont
roller
Figu
re
7.
Sy
st
em
resp
on
ses
u
s
ing
PI
co
ntr
o
l
l
er an
d
SM
C
c
ont
rller (a
)
o
f
R
eal po
wer
f
o
r
at AC
sy
stem
1
side , (b) of R
eactive
power
for at
AC syste
m
1 side, (c
)
of
Real power
for at AC
sy
stem
2 side l ,
(d)
of
R
eal p
o
we
r
fo
r at
AC system
2 si
de
0
0.
0
1
0.
02
0.
03
0.
04
0.
05
0.
06
0.
07
0.
08
0.
09
0.
1
2.
98
2.
985
2.
99
2.
995
3
3.
005
3.
01
x 1
0
4
Tim
e
(
s
)
D
C
bus
v
o
l
t
age
(
V
)
v
dc
(
w
i
t
h P
I
c
o
nt
r
o
l
l
e
r
)
v
dc
(
w
i
t
h SM
C
c
ont
r
o
l
l
e
r
)
0
0.
0
1
0.
0
2
0.
0
3
0.
04
0.
0
5
0.
0
6
0.
0
7
0.
0
8
0.
09
0.
1
1.
4
6
1.
4
8
1.
5
1.
5
2
x 1
0
4
(a
)
Time
(
s
)
DC
c
apa
c
t
or
s
v
l
o
t
a
g
e
s
(
V
)
v
c1
v
c2
0
0.
0
1
0.
0
2
0.
03
0.
04
0.
05
0.
06
0.
07
0.
08
0.
09
0.
1
1.
46
1.
48
1.
5
1.
52
x 1
0
4
(b
)
Time
(
s
)
D
C
c
apac
t
o
r
s
vlot
age
s (
V
)
v
c1
v
c2
0
0.
0
1
0.
02
0.
03
0.
04
0.
05
0.
06
0.
07
0.
08
0.
09
0.
1
-2
-1
0
1
2
3
x 1
0
7
Ti
m
e
(
s
)
P
1
an
d P
1
(w
)
(a
)
P
1(
w
i
t
h
P
I
c
o
n
t
rol
l
e
r)
P
1
(
w
i
t
h
SM
C
c
o
nt
r
o
l
l
e
r
)
0
0.
01
0.
02
0.
03
0.
04
0.
05
0.
0
6
0.
0
7
0.
0
8
0.
09
0.
1
-1
-0
.
5
0
0.
5
1
x 1
0
7
Ti
m
e
(
s
)
Q
1
an
d
Q
1
(V
a
r
)
(b
)
Q
1(
w
i
t
h
P
I
c
o
nt
r
o
l
)
Q
1(
w
i
t
h
SM
C c
o
nt
r
o
l
l
e
r
)
0
0.
01
0.
02
0.
03
0.
04
0.
05
0.
0
6
0.
0
7
0.
0
8
0.
09
0.
1
-3
-2
-1
0
1
2
x 1
0
7
Ti
m
e
(
s
)
P
2
an
d P
2
(w
)
(c
)
P
2(
w
i
t
h
P
I
c
ontr
o
l
l
e
r
)
P
2(
w
i
t
h
SM
C
c
ontr
o
l
l
e
r
)
0
0.
01
0.
02
0.
03
0.
04
0.
05
0.
06
0.
07
0.
08
0.
09
0.
1
-1
-0
.
5
0
0.
5
1
x 1
0
7
Ti
m
e
(
s
)
Q
2
an
d
Q
2
(V
a
r
)
(d
)
Q
2
(
w
i
t
h
P
I
c
ont
r
o
l
l
e
r
)
Q
2
(
w
i
t
h
SM
C
c
ont
r
o
l
l
e
r
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN:
2
088
-86
94
I
J
PEDS
Vo
l.
4
,
No
.
2
,
Jun
e
2
014
:
26
5
–
27
3
27
2
Figure 4 a
n
d
5 show
s the
D
C
volta
ge
respons
e w
ith
PI and non
li
near co
ntr
o
ll
e
r
s, w
e
can
observ
e
t
h
at
t
h
e DC-b
us vo
lta
ge is m
a
int
a
in
ed c
l
os
e to
its referen
ce
with g
o
o
d
a
p
p
r
oxim
a
tion, s
t
abi
lity
and
with
ou
t
o
v
ersho
o
t
in
ca
se of SMC
co
ntrol
l
er,
it
is
i
m
portant als
o
to no
te
t
h
a
t
t
h
e
ap
pl
ica
t
i
on of
th
e
prop
osed
re
du
nda
nt
v
ect
ors bas
e
d
thre
e-l
e
ve
l SV
M
co
ntrol
m
a
intai
n
s ca
pac
itors
v
o
lt
ages
b
a
la
nc
ed
to
their references of
v
dc
/2
. Is possible t
o
see
how t
h
e vol
t
a
g
e a
c
ross ea
c
h
ca
pac
i
t
o
r rem
a
ins cons
tant after
the
pert
urba
ti
on
is a
p
p
lie
d.
This res
u
lt
co
nfirm
s
the
eff
ecti
v
e
n
ess of Slidi
n
g
m
ode D
C
vo
lta
ge co
ntrol
l
er.
Figure
7 s
how
s dy
nam
i
c respo
n
se of
th
e s
y
stem
under
v
a
rious
ste
p
s c
h
an
ges
in r
eal
and
reac
ti
ve
p
o
w
er d
e
m
a
n
d
s
o
f
the HVDC syste
m
fo
r SMC an
d
PI co
ntro
llers resp
ectively. We can
sh
o
w
that real
and re
ac
tiv
e
pow
er a
nd
cu
rrent c
o
m
pon
ents
of A
C
sy
stem
1 and
A
C
sy
stem
2
are reg
u
la
te
d
at t
h
e
corresp
on
din
g
referenc
es, a
n
d are w
e
ll
de
c
o
u
p
le
d from
each
ot
her.
(a)
(b
)
Figu
re
8.
Ha
rm
onic
spectr
u
m
of
line c
u
r
r
ent
(a
) with PI
C
o
ntr
o
ller, (b
) with
SM
C
c
o
ntr
o
ller
Figure
8(a) a
nd
8(b) sh
o
w
s harm
onic
spectr
u
m
of line
c
u
rrent
de
m
onstrate t
h
a
t
the
dist
orti
on
in
supp
ly
curre
nt
w
ith
SMC s
t
rate
gy
w
h
ere
t
o
ta
l h
a
rm
onic
dist
orti
on
(TH
D
)
equa
l t
o
1.
57%
is
less t
h
an
in
case
of PI controll
er where
THD=2.00% .
7.
CO
NCL
USI
O
N
In this
pap
e
r,
Slidi
ng
Mo
de
con
t
rol str
a
te
g
y
appli
e
d t
o
a
bac
k
-to-
bac
k
t
h
ree le
ve
l vo
lt
age so
urce
converter HVDC syste
m
u
s
ing s
p
ace vector m
odulati
on.
T
h
e effectiveness of
the proposed contr
o
l
strate
gy
u
nde
r vari
ous
o
p
e
r
atin
g
co
nd
iti
ons
is a
n
a
l
y
z
ed
an
d c
o
m
p
ared w
i
th
c
o
nve
nt
io
nal
c
o
ntrol
l
er
base
d o
n
sim
u
lati
on
st
udi
es i
n
t
h
e
MA
TLA
B™
/SIMU
L
IN
K
enviro
nm
ent.
Si
m
u
latio
n re
sults i
n
d
i
ca
te
tha
t
th
e perfo
rm
ances of SMC strat
e
gy
are
m
u
ch bet
t
e
r tha
n
th
e
abo
v
e l
i
n
ear c
ontr
o
l w
i
t
h
co
nve
nt
io
nal c
o
ntrol
l
er
during acti
v
e a
nd re
acti
v
e
power cha
nge
. The
a
b
sence
of ov
ersho
o
ts
in D
C
v
o
l
t
a
g
es resp
onses
duri
ng
pow
e
r
s chan
ges,
g
o
o
d
trans
i
e
n
t
respons
es an
d low
current
d
i
stor
tio
n d
e
m
onstrates
the
sup
e
riority
of
the
SMC strat
e
gy com
p
ared to
its c
o
unt
e
rpart
trad
itio
n
a
l PI
co
ntro
ller. S
o
SMC schem
e
fo
r the
VSC-HVDC system sh
o
w
s so
me
attractive
adv
a
ntag
es
such
as offeri
ng
hi
gh
trac
ki
ng
acc
uracy
, f
a
st dy
n
a
m
i
c respons
e a
nd
go
od ro
bus
tn
ess.
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a
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F
u
nda
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nta
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(
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z
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H
D=
2.00%
Ma
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%
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unda
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I
J
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S
SN:
208
8-8
6
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4
Sliding M
o
de
Contr
o
l of
Thr
ee Levels B
a
ck
-To-B
a
ck
V
S
C-HVDC
Syste
m
Using Sp
ace…
(Bouafia
Sabe
r)
27
3
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