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
. 14
6~
15
5
I
S
SN
: 208
8-8
6
9
4
1
46
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
An Implement
a
ti
on M
ech
anisms of SVM Control St
rategies
Applied to Five Levels Casc
aded Multi-Level Inverters
Mohammed Yaichi*,
Mohammed-Karim Fellah**
* Photovoltaic Pumping Team, R
e
search
Unit in
Renewable
Ener
gies in
the
Sahar
a
n Medium UR
ER/MS-Adrar,
CDER
** Inte
llig
ent
Co
ntrol
and
Ele
c
tri
cal
Power S
y
st
e
m
s Laborator
y,
Djilla
li
Li
abes U
n
iversit
y
of Sidi-
B
el-Abbes
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Dec 26, 2013
Rev
i
sed
Mar
20
, 20
14
Accepte
d Apr 1, 2014
In the
are
a
of th
e en
erg
y
con
t
rol
with high vo
lta
ge and power
,
th
e m
u
ltil
eve
l
invert
ers
cons
tit
ute a r
e
l
a
tiv
el
y recen
t res
e
arc
h
orient
ation
.
The curr
en
t
applications of
this technolog
y
are in
th
e domain
s
of the high
vo
ltag
e
(over
hundred kV), v
a
riab
le speed dr
ives, tr
ansport
and distribution
of a good
quality
of electrical energy
(HVDC,
FACTS
sy
stem,
.
.
.
.
)
.
To improve the
output voltag
e
f
o
r such inverters
,
man
y
different modulati
on strategies have
been dev
e
lop
e
d. Am
ong these strateg
i
es,
the SVM (Sp
ace Ve
cto
r
Modulation)
. Th
e techn
i
que pro
v
ide th
e nearest switching vecto
r
s sequence
to the ref
e
ren
ce
vector
without involvi
ng tr
igono
metric fun
c
tions
and provid
e
the add
ition
a
l a
dvantag
es of superior harm
onic
qualit
y.
In th
is paper,
w
e
anal
yz
e diff
ere
n
t m
echanis
m
s
of th
e output voltage s
y
nth
e
sis and th
e
problem of
even order h
a
rmonic produ
ction
.
With the propo
sed a n
e
w
traj
ector
y S
V
M
,
which can
elim
inat
e al
l the
eve
n
order harm
oni
cs
for five
levels inver
t
er
. Show clearly how
to d
e
duc
e th
e tr
aj
ector
i
e
s
from
the
sequences allow
i
ng to have b
e
tter
performan
ces among several possible
traj
ector
ies.
It
is
dedic
a
ted
to
the
appli
cat
ion of
tw
o part
icul
ar
traj
e
c
tori
es.
Keyword:
Cascad
ed Mu
lt
ilev
e
l Inv
e
rter
SVM
(
Space
ve
ct
or m
o
d
u
l
a
t
i
on)
Traject
ory
Harm
oni
cs
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
oham
m
ed Y
a
i
c
hi
,
Ph
ot
o
vol
t
a
i
c
P
u
m
p
i
ng Team
, Ph
ot
o
vol
t
a
i
c
C
o
n
v
e
r
si
o
n
Di
vi
si
on
,
R
e
search
U
n
i
t
i
n
R
e
ne
wa
bl
e
Ener
gi
es i
n
t
h
e
Saha
ra
n M
e
di
um
UR
ER
/
M
S-A
d
ra
r,
Al
geri
a
Em
a
il: ya
ich
i
_
m
o
h
a
mmed
@
yah
o
o
.
fr
1.
INTRODUCTION
Th
e m
a
in
in
terest o
f
th
e m
u
lti
lev
e
l in
v
e
rters
is th
e rem
a
rk
ab
le i
m
p
r
ov
em
e
n
t o
f
t
h
e sp
ectral q
u
a
lity o
f
its output signals. Multilevel inve
rters ca
n reach the in
crea
sing dem
a
nd
for powe
r
qu
ality and power
ratings
al
on
g wi
t
h
l
o
w
e
r ha
rm
oni
c di
st
ort
i
o
n an
d l
e
s
s
er el
ect
rom
a
gnet
i
c
i
n
t
e
rfe
ren
ce (EM
I
)
.
T
h
i
s
spect
r
u
m
i
s
, by
far
,
relativ
ely b
e
tter th
an
t
h
e classical two
lev
e
ls
in
v
e
rter
[1
]-[5
]
.
To im
prove m
u
ch m
o
re quality of electrical en
ergy, we a
p
ply the space
vector m
odulation (SVM
)
strateg
y
wh
ich stan
d
s
ou
t b
e
cau
se it o
ffers sig
n
i
fi
can
t fl
ex
ib
ility to
o
p
ti
mize switch
i
n
g
wav
e
fo
rm
s, an
d
because it is well suited
for i
m
ple
m
entation on a
digital c
o
m
puter [1], [2], [6]-[9]. T
h
e t
echni
que
provi
de the
nearest
s
w
i
t
c
h
i
ng
vect
or
s se
que
nce t
o
t
h
e
refere
nce
vec
t
or an
d cal
cul
a
t
e
s t
h
e on
-st
a
t
e
durat
i
ons
of t
h
e
respective s
w
i
t
ching state vectors
without invol
ving trigonom
e
tric f
unctions and provide the a
d
ditional
ad
v
a
n
t
ag
es of
su
perior h
a
rmo
n
i
c
q
u
a
lity. It
will b
e
stu
d
i
ed
on
a fi
v
e
lev
e
ls cascad
ed
th
ree-ph
ase inv
e
rter.
Thi
s
c
o
n
v
e
r
t
e
r
con
s
i
s
t
s
o
f
a
se
ri
es-c
on
nect
i
o
n
of
t
w
o
4-
qua
dra
n
t
c
o
n
v
ert
e
r
by
pha
se [
2
]
.
Th
e im
p
l
e
m
en
tatio
n
of
SVM
p
r
od
u
c
es,
for
so
m
e
cases, ev
en order
h
a
rm
o
n
i
cs.
W
e
will p
r
opo
se a
new traje
c
tory
SVM
for the
cascade
d
inverter, allowing to
elimin
ate th
e e
v
en
o
r
de
r
harm
oni
cs
fr
om
t
h
e
o
u
t
p
u
t
vo
ltag
e
an
d resu
lting
i
n
a so
l
u
tion
wh
ere th
e nu
m
b
er
o
f
co
mm
u
t
a
tio
n
and
h
e
n
c
e th
e switch
i
n
g
lo
sses
m
a
y
be re
duce
d
i
n
t
h
e i
n
v
e
rt
e
r
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
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:
208
8-8
6
9
4
An Impleme
n
tation
Mec
hanis
m
s of
SV
M C
o
ntrol
Strate
gie
s
Applied t
o
Fi
ve Levels… (Mohamme
d
Yaic
hi)
14
7
2.
PRI
NCI
PLE OF
S
V
M APP
L
IED
FO
R FI
VE
LEVELS INVE
RTER
S
Fi
gu
re
1 s
h
o
w
s t
h
e si
m
p
l
i
f
i
e
d ci
rc
ui
t
of a
f
i
ve l
e
vel
s
casc
a
ded i
n
vert
er
.
The
out
put
vol
t
a
ge o
f
t
h
e
inve
rter
of a
phase, c
h
aracteri
ze its state.
It
i
s
de
fi
ne
d
by
t
h
e f
o
rm
ul
a (1
)
[
2
]
.
U
U
11
K
'
11
K
12
K
'
12
K
o
a
b
c
n
'
a
i
b
'
i
c
'
i
11
i
21
i
31
i
12
i
22
i
32
i
U
13
K
'
13
K
14
K
'
14
K
U
21
K
'
21
K
22
K
'
22
K
23
K
'
23
K
24
K
'
24
K
U
31
K
'
31
K
32
K
'
32
K
U
33
K
'
33
K
34
K
'
34
K
Fi
gu
re
1.
Si
m
p
l
i
f
i
e
d ci
rc
ui
t
di
agram
of
3
-
p
h
a
s
e 5
-
l
e
vel
s
cas
caded
i
n
vert
e
r
V
2U not
e
d
4
if
K
,K
′
and K
,K
′
closed
U no
t
ed
3
if K
,K
′
a
n
d
K
,K
clos
e
d
0
not
ed
2
ifK
,K
′
and K
′
,K
clos
ed
U no
t
ed
1
if
K
,K
and
K
′
,K
clos
ed
2U not
e
d
0
if K
′
,K
and
K
′
,K
closed
(1)
w
ith
s = a, b or c;
d =
1
,
2,
3:
re
prese
n
t the
num
b
er of the
phase
(leg).
Th
eo
retical to
o
l
s allo
wing
ev
alu
a
ting
and
id
en
tifyin
g
th
e representatio
n
o
f
t
h
e v
ecto
r
s and
co
mm
u
t
at
io
n
s
(h
ex
ag
on
al stru
cture) is correspo
nd
ing
to
th
e
v
ectors
o
f
ou
tpu
t
of th
e 2
lev
e
ls and
M
u
ltilev
e
l
i
nve
rt
ers
ha
ve
been
st
u
d
i
e
d
i
n
det
a
i
l
by
[2]
,
[
6
]
,
[
1
0]
.
Figure
2. Spac
e vector stat
es fo
r 5-le
vels
in
v
e
rter
Fi
gu
re 2 s
h
ow
s al
l
t
h
e swi
t
c
hi
n
g
vect
ors
(
61
vect
o
r
s)
of
a fi
ve l
e
vel
s
i
nve
rt
er l
a
bel
l
e
d wi
t
h
t
h
e
p
o
s
ition
of th
e equ
i
v
a
len
t
switch
i
n
g
states (1
25 states)
[2
]
,
[10
]
-[12
]. These v
ect
o
r
s
o
f
vo
ltag
e
d
i
v
i
de th
e
α
β
p
l
an
e in
to
9
6
triang
u
l
ar portio
n
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
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-86
94
I
J
PED
S
Vo
l. 4
,
No
. 2
,
Jun
e
2
014
:
14
6
–
15
5
14
8
It is the task of the m
odula
t
or (S
VM) to
de
term
ine which position the switches shoul
d assum
e
(switchi
ng stat
e) i
n
t
h
e
α
,
β
plane
,
the
duration needed
(duty cy
cle)
an
d th
e tri
a
n
g
u
l
ar area i
n
wh
ich it is, i
n
order to synt
hesize the
refe
rence
voltage
vector
[
2
]
,
[
6
]
.
T
h
e
ge
ner
a
l
i
zed al
g
o
ri
t
h
m
bei
ng
use
d
t
o
determ
ine, for
the he
xagonal
structure, t
h
e e
x
act position
of the
vector of
refe
rence
(detection of
neares
t three
vect
o
r
s a
n
d
d
u
t
y
cy
cl
es com
put
at
i
o
n
)
was
de
vel
o
ped
an
d
st
udi
e
d
i
n
det
a
i
l
i
n
[
2
]
,
[5]
,
[
8
]
and
[
1
3]
.
3.
PRINCIPLE AND MECH
ANISM OF T
R
AJ
ECT
O
RY
AND
SELECTION OF T
H
E VE
CTORS
OF ST
ATE OF THE FI
VE LEVELS
INVERTERS
3.
1.
Des
cri
pti
o
n
Figure
3 illustrates a subset
of a
five
level space
vector
plot, a
n
d Ta
ble
1 summ
arises all possi
ble
sequ
en
ces
fo
r t
h
is sub
s
et th
at
ach
iev
e
t
h
e requ
ired
m
i
n
i
m
u
m o
f
th
ree
swit
ch
ing
tran
sition
s
per
p
h
a
se leg
in
a
switch
i
ng
p
e
ri
o
d
, i.e. if
we
locate the exact triangle where
is lo
cated
, limited
b
y
so
m
e
so
rt th
ree
switching stats
(s
1
, s
2
, s
3
) in
on
e switch
i
ng
i
n
terv
als T
e
, t
h
en
th
e sequ
en
ce is g
i
v
e
n
like co
n
tinu
a
tion
:
s
1
s
2
s
3
s
1
s
3
s
2
s
1
[
2
],
[1
0
]-[1
2
]
.
Figure
3. Subs
et of 5 le
vels
s
p
ace vector diagram
Tab
l
e
1
.
Po
ssible sequ
en
ces in fiv
e
lev
e
ls sp
ace
vect
o
r
s
u
bse
t
(See
Fi
g
u
re
3
)
. R
e
verse
are
not
sh
ow
n
T
r
iangle Sequences
+
12
(a
)
(
a
)
43
2
t
o
4
3
1
t
o
421
t
o
3
2
1
321
t
o
421
t
o
4
3
1
t
o
4
32
321
t
o
3
2
0
t
o
3
1
0
t
o
210
210
t
o
3
1
0
t
o
3
2
0
t
o
321
a(
i
)
a(
i
i
)
a
(
ii
i)
a(
i
v
)
1
(a
)
431
t
o
421
t
o
32
1
t
o
320
320
t
o
32
1
t
o
421
t
o
431
a(
v
)
a(
v
i
)
2
(a
)
421
t
o
3
2
1
t
o
320
t
o
3
1
0
310
t
o
32
0
t
o
321
t
o
4
2
1
a(
v
i
i
)
a(
v
i
i
i
)
(b
)
42
1
t
o
4
2
0
t
o
410
t
o
3
1
0
310
t
o
410
t
o
4
2
0
t
o
4
21
b(
i
)
b(
i
i
)
1
(c
)
43
1
t
o
4
2
1
t
o
420
t
o
3
2
0
320
t
o
420
t
o
4
2
1
t
o
4
31
c(
i
)
c(
i
i
)
2
(c
)
421
t
o
420
t
o
32
0
t
o
310
310
t
o
32
0
t
o
420
t
o
421
c
(
ii
i)
c(
i
v
)
(d)
4
3
1
t
o
4
3
0
t
o
4
2
0
t
o
3
2
0
320
t
o
420
t
o
4
3
0
t
o
4
31
d(
i
)
d(
i
i
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
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SN
:
208
8-8
6
9
4
An Impleme
n
tation
Mec
hanis
m
s of
SV
M C
o
ntrol
Strate
gie
s
Applied t
o
Fi
ve Levels… (Mohamme
d
Yaic
hi)
14
9
3.2.
Synthesis
of the re
ference vec
t
or
The
best
way
t
o
sy
nt
hesi
ze t
h
e vol
t
a
ge
re
fer
e
nce
vect
or is
by usi
ng t
h
e nearest three
ve
ctors
(
V
,
V
and
V
) and t
h
eir
duty cycles (
d
,
d
and
d
)
[2
]:
V
d
∙V
d
∙V
d
∙V
(2)
W
i
t
h
th
e ad
d
itio
n
a
l con
s
trai
n
t:
d
d
d
T
(3)
For exam
ple, for t
r
iangles (b) and (d), t
h
ere
are
two
possibl
e seque
n
ces.
For t
r
iangles (a
) and
(c) t
h
e
correct se
que
nce can
be i
d
e
n
tified
from
the
pos
sible al
ternatives by ens
u
ring
t
h
at no
ext
r
a
s
w
itching
tran
sitio
ns
o
c
cu
r wh
en
m
o
v
i
n
g
between
tri
a
n
g
l
es. For
exa
m
p
l
e, sequ
ence c(iii)
(or c(iv
)) sh
ou
ld be u
s
ed
whe
n
m
ovi
n
g
fr
om
t
r
i
a
ngl
e (b) t
o
(c) si
nce
i
t
begi
ns wi
t
h
the sam
e
state
as the sequ
e
n
ce
in
(
b
)
,
or
s
e
qu
e
n
ce
c(i)
(or c(ii))
sh
ou
ld b
e
used
wh
en
m
o
v
i
ng
fro
m
trian
g
l
e (c) to (d
) sin
c
e
it b
e
g
i
ns
with
th
e sam
e
state as th
e
sequ
en
ce in
(d). App
l
yin
g
this p
r
in
ci
p
l
e to
trian
g
l
e (a)
m
eans that sequences a(i) to a
(
iv) ca
nnot be
use
d
because they
will introduce e
x
tra switchi
ng transitions whe
n
m
oving i
n
to t
r
iangle
(c).
Tabl
e
2 s
h
o
w
s
t
w
o s
e
ve
n-
seg
m
ent
swi
t
c
hi
n
g
seq
u
e
n
ces
fo
r
fallin
g in
to reg
i
on
(a
2
).
Table
2. E
x
am
ple of t
w
o swit
ching se
quence
s
Seg
m
ents
Sequence 1
Sequence 2
1
s
t
1
[3
1
0
]
V
1
[
421]
V
2
nd
2
[
320]
V
3
[
321]
V
3
rd
3
[
321]
V
2
[
320]
V
4
th
1
[4
2
1
]
V
1
[
310]
V
5
th
3
[
3
21]
V
2
[
320]
V
6
th
2
[
320]
V
3
[
321]
V
7
th
1
[3
1
0
]
V
1
[
421]
V
It is in
teresting
to no
te th
at
fo
r
sequ
en
ce
1
,
the s
w
itching
sequence
of the three
vect
ors
,
V
,
V
and
V
, in
th
e first t
h
ree
seg
m
en
t ro
tates in
a coun
ter cl
oc
kwise
(CC
W) di
rection i
n
the s
p
a
ce vector
diagra
m
sho
w
n i
n
Fi
g
u
r
e 4,
whe
r
eas f
o
r se
qu
ence 2,
the
switching sequence for
th
ese vect
ors
rotating in a cloc
kwis
e
(C
W)
di
rect
i
o
n
.
T
h
ees
not
at
i
o
ns "+" a
n
d "
-
" i
ndi
cat
e t
h
e
di
r
ect
i
on
of
t
h
e
s
w
i
t
c
hi
n
g
se
q
u
e
n
ce
rot
a
t
i
o
n.
Fi
gu
re
4.
The
s
w
i
t
c
hi
n
g
se
q
u
e
n
ce
rot
a
t
i
o
n
di
r
ect
i
ons i
n
re
gi
on
(a
2
)
W
h
ile
b
a
sing
i
t
self
on
t
h
e sequ
en
ce 1, t
h
e sw
itch
i
ng
sequ
en
ce
for all th
e
trian
g
u
l
ar reg
i
o
n
s
is sho
w
n
in
Figur
e
5
.
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l. 4
,
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. 2
,
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e
2
014
:
14
6
–
15
5
15
0
Fi
gu
re 5.
The
s
w
i
t
c
hi
n
g
se
q
u
e
n
ce rot
a
t
i
o
n di
r
ect
i
ons fo
r SV
M
base
d on
se
que
nce 1
By carrying
o
u
t th
e first sim
u
l
a
tio
n
for:
I
npu
t vo
ltag
e
311
;
The m
odul
at
i
o
n i
n
de
x
0
.
7
and
1
.
1
5
fo
r sam
p
ling
fre
q
u
ency
600
12
and
650
13
.
with
;
: fu
nd
amen
tal freq
u
e
ncy=5
0
Hz.
We o
b
t
a
i
n
t
h
e resul
t
s
gi
ve
n i
n
Fi
gu
re 6
.
In t
h
e spect
rum
of o
u
t
p
ut
si
gnal
,
t
h
e a
m
pli
t
ude o
f
fund
am
en
tal is
equ
a
l to
10
0%.
600
1
2
0
.7
600
1
2
1
.15
(a)
650
1
3
0
.7
650
1
3
1
.15
(b
)
Fi
gu
re 6.
W
a
v
e
fo
rm
s
pro
d
u
c
e
d by
t
h
e SVM
seq
u
e
n
ce
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
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:
208
8-8
6
9
4
An Impleme
n
tation
Mec
hanis
m
s of
SV
M C
o
ntrol
Strate
gie
s
Applied t
o
Fi
ve Levels… (Mohamme
d
Yaic
hi)
15
1
By an
alyzin
g
t
h
e sp
ectru
m
o
f
th
e SVM signal o
n
fiv
e
lev
e
l
s
, it is no
ted
t
h
at it is
m
a
d
e
u
p
, in
add
itio
n
t
o
t
h
e
f
u
ndam
e
nt
al
o
n
e
w
h
i
c
h i
s
at
t
h
e
f
r
e
que
ncy
an
d
wh
ose
pea
k
va
l
u
e i
s
e
q
ual
t
o
, com
pone
nt
s
o
f
harm
oni
cs
gat
h
ere
d
i
n
fam
i
l
i
e
s. Ho
we
ver
,
t
h
e a
b
o
v
e
d
i
scusse
d t
r
a
j
e
c
t
o
ry
S
V
M
p
r
o
d
u
ces e
v
en
or
de
r
harm
oni
cs fo
r even
val
u
es of
b
ecau
s
e
o
f
th
e no
-symm
e
try o
f
th
e
ou
tpu
t
vo
ltag
e
.
To e
xplai
n that
, now consi
d
er
the re
g
i
on
(Figu
r
e
7) wh
ich is sy
mm
e
t
rical b
y
repo
rt to th
e
o
r
i
g
in
wit
h
the area re
pres
ented
on
Figure 3.
Whe
n
lies
in
reg
i
o
n
s (a
2
)
and
(a
3
) (w
hic
h
are
180
°
apart in
space), the
sw
itch
i
ng
sequen
ce an
d cor
r
esp
ond
ing
w
a
v
e
f
o
r
m
o
f
are s
h
ow
n i
n
Fi
gu
re
8.
Fi
gu
re 7.
V
re
f
i
n
regi
on
(a
3
)
Fi
gu
re
8.
S
w
i
t
c
hi
n
g
se
q
u
ence
fo
r
V
ref
i
n
re
gio
n
(a
2
) a
n
d (a
3
)
To el
i
m
i
n
at
e even
o
r
der
ha
rm
oni
cs
, t
h
e
wa
v
e
fo
rm
s have t
o
be
o
f
hal
f
-
w
a
v
e sy
m
m
e
t
r
y
.
Obv
i
ou
sly, th
e wav
e
fo
rm
s sho
w
n
i
n
Figure 8
d
o
no
t m
e
e
t
th
is con
d
ition
,
wh
ich
ind
i
cates th
at it
cont
ai
n
s
e
v
en
or
der
ha
rm
oni
cs. T
h
i
s
p
h
e
n
o
m
enon
can
be
m
o
re clearly de
m
onstrated
in Figu
r
e
6(
a)
, wh
er
e the
i
nve
rt
er phas
e
vol
t
a
ge
for one cycle of t
h
e
fundam
ental freque
ncy is s
h
own. None
of t
h
e
wave
form
s is
h
a
lf-wav
e symmetrical.
4.
EVEN
ORDE
R HARMONIC ELIMINA
TI
O
N
(
S
EC
OND
T
RAJ
E
C
TO
RY
)
As
di
scusse
d
earl
i
e
r,
wave
fo
rm
wi
t
h
ha
l
f-wa
v
e sy
m
m
e
t
r
y
does
n
o
t
cont
ai
n any
even
o
r
de
r
harm
oni
cs. T
o
achi
e
ve t
h
i
s
, t
h
e swi
t
c
hi
ng s
e
que
nce s
h
o
u
l
d
be ar
ran
g
e
d
suc
h
t
h
at
t
h
e inve
rt
er p
h
ase
vol
t
a
ge
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
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:
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S
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l. 4
,
No
. 2
,
Jun
e
2
014
:
14
6
–
15
5
15
2
gene
rat
e
d by
i
n
any
t
w
o re
gi
o
n
s sy
m
m
e
t
r
i
cal
t
o
t
h
e ori
g
i
n
of t
h
e s
p
a
ce vect
o
r
di
a
g
ram
shoul
d
ha
ve
mirror im
age.
C
onsi
d
er
t
w
o
regi
ons
(a
2
) a
n
d
(a
3
), wh
ich
are symm
e
t
ric
a
l to
th
e orig
i
n
o
f
th
e sp
ace d
i
ag
ram
.
To
m
a
ke t
h
e
wave
fo
rm
of
fo
r
in
re
gio
n
(a
2
) a
m
i
rror
im
age o
f
t
h
at
fo
r
in re
gio
n
(a
3
), t
h
e switch
i
ng
sequence
of t
h
e three vect
ors
,
V
,
V
and
V
, sho
u
l
d
be cha
nge
d
fr
om
it
s ori
g
i
n
al
C
C
W
t
o
C
W
.
The res
u
l
t
a
nt
wave
f
o
rm
of
is show
n in
Figu
r
e
9,
w
h
ich
beco
m
e
s a
m
i
r
r
o
r
e
ste im
ag
e of
th
at sho
w
n
i
n
Figu
r
e
8(
b)
.
It
i
s
wo
rt
h
no
t
i
ng t
h
at
al
t
h
o
u
g
h
t
h
e
wa
vef
o
rm
s of
i
n
F
i
gu
re
9 a
n
d
Fi
gu
re
8
(
a)
see
m
s qui
t
e
diffe
re
nt.
Fig
u
r
e
10
sh
ow
s a n
e
w
sw
itch
i
ng
sequ
en
ce ar
r
a
ng
em
ent, where
the
swi
t
ch
i
n
g
se
que
nc
es, i
n
som
e
areas, a
r
e m
odi
fied
for e
v
e
n
o
r
de
r harm
oni
c el
im
i
n
at
i
on.
Fi
gu
re 9.
Ne
w swi
t
c
hi
n
g
se
q
u
e
nce fo
r
V
ref
i
n
regi
on
(a
2
)
Fi
gu
re 1
0
. Ne
w
s
w
i
t
c
hi
n
g
se
que
nce (sec
on
d
trajectory)
5.
SIM
U
LATI
O
N
AN
D
I
N
TE
RPRE
T
A
TION OF THE
RESULTS
We m
a
de a si
m
u
l
a
t
i
on t
e
st
f
o
r a
fi
ve
l
e
vel
s
i
nve
rt
er s
u
pp
l
y
i
ng an
asy
n
c
h
r
o
no
us m
o
t
o
r
,
f
o
r
(r=
0.
9
,
m
=
25)
, t
h
en
f
o
r
(r=
0.
9,
m
=
26).
I
n
t
h
e Fi
gu
r
e
s 1
1
an
d
1
2
,
we
ha
ve
rep
r
e
s
ent
e
d
t
h
e
o
u
t
put
v
o
l
t
a
ges
,
and its spect
ral anal
ysis, th
e cu
rren
t
and t
h
e
spee
d.
Th
e switch
t
r
igg
e
r sign
al
is p
l
o
tted
in Figure
1
3
.
For
t
h
e
t
r
a
j
ect
ory
1 (Fi
g
u
r
e 11
),
we
not
e
t
h
at th
ere is no symmetry o
f
si
m
p
le v
o
ltag
e
in
h
a
lf-
w
a
v
e
fo
r
ev
en v
a
lu
e
s
of
, th
u
s
, i
n
add
itio
n to
th
e
o
d
d
h
a
rm
o
n
i
cs, th
e
vo
ltag
e
co
n
t
ains bo
th
ev
en
ord
e
r
h
a
rm
o
n
i
cs. In
ad
d
ition
,
th
e harm
o
n
i
c sp
ect
re shows t
h
at al
l th
e ev
en
o
r
d
e
r
h
a
rm
o
n
i
cs are eli
m
in
ated
for
o
dd
, and
g
a
th
er i
n
fam
i
ly cen
tered
aroun
d th
e m
u
ltip
le frequ
e
ncies o
f
∙
.
For
t
h
e
t
r
a
j
ect
ory
2 (Fi
g
u
r
e 12
),
we
not
e
t
h
at th
ere is no symmetry o
f
si
m
p
le v
o
ltag
e
in
h
a
lf-
wave
f
o
r
od
d val
u
es
o
f
, thu
s
, in
add
itio
n to
t
h
e
o
dd h
a
rm
o
n
i
cs, th
e vo
ltag
e
con
t
ains bo
th ev
en order
h
a
rm
o
n
i
cs. In
ad
d
ition
,
th
e harm
o
n
i
c sp
ect
re shows t
h
at al
l th
e ev
en
o
r
d
e
r
h
a
rm
o
n
i
cs are eli
m
in
ated
for ev
en
, and
g
a
th
er i
n
fam
i
ly cen
tered
aroun
d th
e m
u
ltip
le frequ
e
ncies o
f
∙
.
Thi
s
i
s
un
derst
a
nda
bl
e si
nce t
h
e swi
t
c
hi
n
g
p
a
t
t
e
rn ge
nerat
i
on m
echani
s
m
,
i
n
cl
udi
n
g
t
h
e sel
ect
i
on
o
f
th
e statio
n
a
ry
v
ectors and
d
w
ell ti
me calcu
la
tio
n
s
, is th
e sa
m
e
for
bot
h t
r
a
j
ect
o
r
i
e
s. T
h
e
onl
y
di
ffe
rence
i
s
t
h
at
som
e
of t
h
e
s
w
i
t
c
hi
ng
seq
u
e
n
ces are
rearra
nged for the
ne
w tra
j
ectory.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
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S
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8-8
6
9
4
An Impleme
n
tation
Mec
hanis
m
s of
SV
M C
o
ntrol
Strate
gie
s
Applied t
o
Fi
ve Levels… (Mohamme
d
Yaic
hi)
15
3
1250
2
5
,
0.9
,
2
.51%
1300
2
6
,
0.9
,
2
.99%
Fi
gu
re
1
1
.
Si
m
u
l
a
t
i
on
res
u
l
t
s
on
5
l
e
vel
s
i
n
v
e
rt
er
or
dere
d
b
y
t
h
e S
V
M
(t
ra
ject
o
r
y
1
)
1250
2
5
,
0.9
,
2
.72%
1300
2
6
,
0.9
,
2
.29%
Fi
gu
re
1
2
.
Si
m
u
l
a
t
i
on
res
u
l
t
s
on
5
l
e
vel
s
i
n
v
e
rt
er
or
dere
d
b
y
t
h
e S
V
M
(t
ra
ject
o
r
y
2
)
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
:
14
6
–
15
5
15
4
It shou
ld
b
e
po
in
ted ou
t th
at
th
e
d
e
v
i
ce
switch
i
ng
fre
quency of t
h
e SVM tra
j
ectory 2 is
slightly
hi
g
h
er t
h
an
t
h
at
of t
h
e t
r
a
j
ec
t
o
ry
1
f
o
r a
gi
ven
sam
p
l
i
ng f
r
eq
ue
ncy
dat
a
cor
r
es
po
n
d
i
n
g
t
o
o
d
d
.
Ho
we
ver
,
the de
vice s
w
i
t
ching freque
ncy of the
SVM traj
ect
o
r
y
1 is slig
h
tly h
i
gh
er th
an
th
at
of th
e traj
ecto
r
y
2
fo
r a
gi
ve
n sam
p
l
i
n
g
fre
q
u
ency
dat
a
co
rres
p
on
di
n
g
t
o
eve
n
(Figu
r
e 13
).
SVM
T
r
a
j
ect
or
y
1,
m=2
5
SVM
T
r
a
j
ect
or
y
1,
m=2
6
SVM
T
r
a
j
ect
or
y
2,
m=2
5
SVM
T
r
a
j
ect
or
y
2,
m=2
6
Fig
u
re 13
. Sign
als wav
e
forms
of
th
e
switch
attack
K
11
fo
r t
h
e i
n
ve
rt
er
on
f
i
ve l
e
vel
s
6.
CO
NCL
USI
O
N
Two s
p
ace
vec
t
or m
o
dulation traject
or
ies
are propose
d
for five
levels
cas
caded inverte
r
s
.
T
h
e m
a
in
featu
r
e lies in
its ab
ility
to
eli
m
in
ate ev
en
ord
e
r h
a
rm
o
n
i
cs in
th
e inv
e
rter o
u
t
p
u
t
v
o
ltage o
f
th
e m
o
du
lation
trajectory
1 for eve
n
an
d
of
t
h
e m
odul
at
i
o
n
t
r
aject
o
r
y
2 f
o
r
o
d
d
.
C
onsi
d
eri
ng t
h
e sim
i
l
a
r form
of t
h
e he
xa
go
n
a
l
st
ruct
ure
of
t
h
e SVM
f
o
r t
h
e m
u
l
t
i
l
e
vel
inve
rt
ers
,
we
thus
can carry
out a
n
al
gorithm
whic
h uses
either tra
j
ectory 1
or traje
c
t
o
r
y
2, acc
o
r
di
ng
t
o
t
h
e
val
u
e
of
, s
o
as t
o
o
b
t
a
i
n
out
put
si
g
n
al
s w
h
i
c
h c
ont
ai
n
o
n
l
y
od
d
ha
rm
oni
cs, a
n
d
t
h
i
s
fo
r
any
l
e
vel
s
of
v
o
l
t
a
ge.
The adva
ntage
of the SVM techni
que is that
all the
even order
harm
onics can be eliminated. This is
favo
rab
l
e in the in
du
stry app
licatio
n
s
.
REFERE
NC
ES
[1]
S Chatter
j
ee. A
Multil
evel
Inv
e
rter
Based on
SVPWM Technique for
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c
Appl
icati
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Internationa
l
Journal of Power Electronics
an
d Dr
ive S
y
s
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em (
I
JPEDS)
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3
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[2]
M Yaichi. An
al
y
s
e d
e
la
te
chn
i
que de m
odula
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ctori
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ll
e
SVM (Space Vector Modul
atio
n) appliqu
ée
au
x
onduleurs multiniveaux
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trical
engineer
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es Un
iversity
of Sidi-B
el-Abbes, Alger
i
a,
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[3]
N Celanovic
.
Space ve
ctor m
odulation and
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ntrol of m
u
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c
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rg,
Virginia. 2000
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iel
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rlin
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[7]
MA Khan, A Iq
bal, SM Ahm
a
d, Z Husain
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l
y
s
is of
Discon
ti
nuous Space Ve
ctor PW
M Tech
niques for
a Sev
e
n-
P
h
as
e Voltag
e
S
ource Inv
e
rt
er.
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n
ternational Jou
r
nal of Pow
e
r El
ectronics and D
r
ive
S
y
stem (
I
JPEDS)
. 2012; 2(2
)
:
203~218.
[8]
N Celanovic
,
D Boro
y
e
v
i
ch
. A fast space-v
ector
m
odula
tion algo
rithm
for m
u
ltile
vel thre
e-phase
convert
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IEEE
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.
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37(2): 637-641.
[9]
N Celanovic, D Boro
y
e
v
i
ch. A
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y
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utr
a
l-point vo
ltag
e
balancing prob
lem in three-
lev
e
l
neutral-point-
c
lamped voltage so
urce PWM inverter.
I
E
EE Transactions on power electronics
.
2
000; 15(2): 242-
249.
[10]
PC Loh, DG Holm
es. A new f
l
ux m
odulation techn
i
que for multil
evel inv
e
rt
er
.
IEEE Transactions on industry
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2; 38(5): 1389-1
399.
[11]
BP
Mcgrath, DG Holm
es, TA Lipo. Optim
ise
d
space
ve
ctor
switching seque
nces for m
u
ltile
vel inver
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.
IEEE
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el
ectr
oni
c
s
. 2003; 18
(6): 1
293-1301.
[12]
DW
Feng,
B Wu,
S Wei,
D Xu.
Space vector modulation for neutral point
clam
ped multil
evel i
n
verter with even
order harmonic
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C
GEI 2004, Nia
g
ara Fa
lls. 2004;
1471-1475.
[13]
T Georgios, A
Georgios. A multi-fun
c
tion gr
id
connected PV
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y
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ee level
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ergy
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011; 85(11): 259
5-2610.
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
An Impleme
n
tation
Mec
hanis
m
s of
SV
M C
o
ntrol
Strate
gie
s
Applied t
o
Fi
ve Levels… (Mohamme
d
Yaic
hi)
15
5
BIOGRAP
HI
ES OF
AUTH
ORS
Mohammed Yaichi was born
on
1980 in
Adrar,
Algeria. He receiv
ed the engin
e
er
degree in
ele
c
tri
cal
engin
e
ering from
the t
h
e Univers
i
t
y
of
Bechar
, Be
char
, Algeri
a,
in 20
03. And the
m
a
gister degree from
Djillali
Liab
es Universi
t
y
, Sidi-Bel-Ab
b
es, Algeri
a in
2006. He is
currently
workin
g toward
the do
ctorate d
e
gree
in
the Power Electronics,
and
the
Photovoltaic
Pum
p
ing
Sy
st
em
, Djillal
i
Liab
es Universit
y
of
Sidi-Bel-Abbes, Algeria.
Since 2009, he is
with the Photov
oltai
c
Pum
p
ing Team
, Rese
arch
Unit in Renew
a
ble
Energies in
The Sahar
a
n
Medium (URER
/
MS) Adrar, Al
ge
ria.
His re
se
a
r
c
h
inte
re
sts
include a stud
y
on performance
improvement of a stand-alone ph
otovoltaic pumping s
y
steme, v
a
ri
able-spe
ed AC m
o
tor drives,
and diff
eren
t m
u
ltil
evel
inv
e
rt
er
circu
it
topologi
es thus its
techniq
u
e of
contro
l P
W
M.
Mohammed-Kar
i
m Fellah
was b
o
rn in Oran
, Alg
e
ri
a, in
1963. He receiv
e
d
the Eng. degr
ee in
Electrical Engin
eering
from University
of Scie
n
ces and
Technolog
y
,
Oran, Algeria, in 1986
,
and The Ph.D. d
e
gree from
Nati
onal Pol
y
t
echni
c Institut
e
of
Lorr
aine (N
ancy
, France) in
1991.
Since 1992
, h
e
is Professor at
th
e University
of
Sidi Bel-Abb
e
s
(Algeria)
and
Member of
the
Intell
igen
t Cont
rol and
Ele
c
tri
cal Power
.
Hi
s current resear
ch interest
includes Power
Electronics, HV
DC links,
and D
r
ives.
Evaluation Warning : The document was created with Spire.PDF for Python.