Internati
o
nal
Journal of P
o
wer Elect
roni
cs an
d
Drive
S
y
ste
m
(I
JPE
D
S)
Vol
.
7
,
No
. 2,
J
une
2
0
1
6
,
pp
. 39
7~
41
5
I
S
SN
: 208
8-8
6
9
4
3
97
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
Modelling and Simulation of a Se
nsorless Control of a True
Asymm
e
tric Cas
c
ade H-B
r
idge
Multilevel Inverter PMSM
Dri
v
es
Kamel Saleh, Mar
k
Sumner
An-Najah Na
tio
nal Univ
ersit
y
P
a
lestin
e,
Univers
i
t
y
of
Nottingh
a
m
, UK
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Aug 5, 2015
R
e
vi
sed M
a
r
8,
2
0
1
6
Accepted
Mar 22, 2016
This paper
intro
duces a n
e
w method to
tr
ack
the
salien
c
y
of
an A
C
motor fed
b
y
a multilev
e
l
converter
through
meas
uring th
e d
y
namic curr
ent r
e
sponse of
the motor
line currents due th
e
IGBT
switching
actions. The method uses
only
th
e fundamental PWM waveform (i
.e th
ere is no modification to th
e
operat
i
on of th
e m
u
ltilev
e
l co
nverter) sim
i
l
a
r
to the fundam
e
ntal PWM
method proposed for a 2-level converter
. Simulation results are
provided to
dem
ons
trate the
perform
anc
e
of
the co
mplete sensorless speed control of a
P
M
m
o
tor driven b
y
s
u
ch a
con
v
erter ov
er a wi
de s
p
eed rang
e.
F
i
nall
y th
e
paper in
troduces a comparison between
the
2-level conver
t
er and th
e
m
u
ltilevel
converter in
term
s of the redu
ction
of t
h
e tot
a
l h
a
rm
oni
c distort
i
on
(THD) using th
e fundamental
P
W
M method in
both cases.
Keyword:
2-l
e
vel
co
n
v
ert
e
r
Mu
ltilev
e
l co
nv
erter
Sens
orl
e
ss
co
n
t
rol
SVP
W
M
THD
Copyright ©
201
6 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
:
Kam
e
l Saleh
,
An-Naj
ah
Natio
n
a
l Un
iv
ersity
Palestin
e,
Un
i
v
ersity of
No
tting
h
a
m
,
UK.
Em
a
il: k
a
m
e
l.s
a
leh
@
n
a
j
a
h
.
edu
1.
INTRODUCTION
Sens
orl
e
ss
co
nt
r
o
l
o
f
m
o
t
o
r
dri
v
es
usi
n
g
t
w
o l
e
vel
co
n
v
ert
e
r
s
ha
s be
en wi
del
y
res
earche
d
fo
r
syste
m
s e
m
p
l
o
y
in
g
stand
a
rd
t
w
o
lev
e
l con
v
erters.
At lo
w an
d
zero
sp
eed
,
so
m
e
fo
rm
o
f
ad
d
ition
a
l ex
ci
tatio
n
h
a
s
b
e
en
p
r
op
osed
, su
ch
as the in
jectio
n of
a h
i
gh fr
equ
e
n
c
y (
H
F)
vo
ltag
e
or
cu
rr
en
t
[1
-3
] or
t
h
e inj
ect
io
n
of
test pulses [4-6]. Howe
ver, these t
echn
i
qu
es in
trod
u
ce si
gn
ifican
t add
itio
n
a
l curren
t
d
i
sto
r
tion
eith
er
d
u
e
to
th
e inj
ected si
g
n
a
ls th
em
selv
es (as in th
e HF inj
ec
tion
m
e
th
od
s and
t
h
e
INFORM m
e
th
o
d
[4
]) or
du
e
to
th
e
i
n
sert
i
o
n
of
t
h
e m
i
nim
u
m
pul
se wi
dt
h i
n
t
h
e o
p
erat
i
o
n
of
th
e driv
e system
wh
en
app
l
yin
g
th
e Fu
nd
amen
tal
P
W
M
E
x
ci
t
a
t
i
o
n
m
e
t
hod
(FP
E
)
[6]
.
Thi
s
di
st
ort
i
o
n ca
uses
au
di
bl
e
n
o
i
s
e,
t
o
r
q
ue
pul
sat
i
ons
a
n
d
i
n
cre
a
s
es t
h
e
syste
m
losses.
Th
e m
u
ltilev
e
l
con
v
e
rter can ach
iev
e
a
h
i
g
h
e
r
v
o
ltag
e
an
d power capab
ility with
co
nv
en
tio
n
a
l
swi
t
c
hi
n
g
de
vi
ces com
p
ared
t
o
t
w
o l
e
vel
con
v
e
r
t
e
rs, an
d i
s
no
w use
d
for hi
gh
po
w
e
r dri
v
es [7
, 8, 9]
.
Mu
ltilev
e
l co
nv
erters e
m
p
l
o
y
switch
i
n
g
d
e
v
i
ces co
nn
ected
in
a ch
ain
,
wh
ich
sequ
en
tially
switch
d
i
fferent DC
vol
t
a
ge
s acr
oss
t
h
e m
o
t
o
r u
s
i
ng
a spe
c
i
a
l
PWM
t
ech
ni
q
u
e
,
t
o
c
r
eat
e a st
eppe
d
o
u
t
p
ut
v
o
l
t
a
ge. T
h
e
par
t
i
c
ul
a
r
st
ruct
u
r
e o
f
so
m
e
of t
h
ese co
nve
rt
ers
of
fers
si
gni
fi
cant
pot
ent
i
a
l
for i
m
provi
ng se
ns
orl
e
ss cont
rol
o
f
m
o
t
o
rs,
as t
h
ey
em
pl
oy
H bri
d
ge ci
r
c
ui
t
s
wi
t
h
a re
l
a
t
i
v
el
y
l
o
w DC
l
i
nk vol
t
a
ge.
[1
0]
uses H
-
B
r
i
dge
s co
nne
ct
ed i
n
series with
2-Lev
e
l inv
e
rter
wh
ich
are used
t
o
g
e
n
e
rate
a small v
o
ltag
e
p
l
u
s
es
u
s
ed
on
ly to
track th
e salien
c
y
p
o
s
ition
,
t
h
is tech
n
i
q
u
e
ach
iev
e
a
g
ood
senso
r
less
resu
lts at th
e sam
e
t
i
m
e red
u
c
e sign
ifican
tly th
e
cu
rrent
d
i
sto
r
tion
du
e t
o
th
e
u
s
e of small v
o
ltag
e
pu
lses.
Prev
io
u
s
research
es in
t
o
sen
s
o
r
less m
u
ltilev
e
l d
r
i
v
es u
s
ed
a
speci
al
m
u
l
t
i
l
e
vel
t
o
pol
ogy
w
h
ere t
h
e H
-
B
r
i
dge
s we
re
used
onl
y
f
o
r ge
ne
r
a
t
i
ng t
h
e
v
o
l
t
a
ge p
u
l
s
es t
o
t
r
a
c
k t
h
e
sal
i
e
ncy
[1
0]
and
wer
e
ad
de
d
t
o
a co
nve
nt
i
o
nal
2
-
l
e
vel
c
o
n
v
ert
e
r
.
I
n
t
h
i
s
pape
r a
new t
e
chni
que i
s
pr
o
pos
ed
to
track
t
h
e salien
c
y in
an
y m
o
to
r
d
r
iv
en b
y
an
y m
u
lti
lev
e
l conv
erter topo
log
y
with
ou
t
d
i
stu
r
b
i
ng
t
h
e
ope
rat
i
o
n of t
h
e
m
u
l
t
i
l
e
vel
conve
rt
er.
At
t
h
e sam
e
tim
e i
t
reduce
s
t
h
e cur
r
e
n
t
di
st
ort
i
o
n as
soci
at
ed wi
t
h
t
h
e 2-
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
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088
-86
94
I
J
PED
S
Vo
l. 7,
No
.
2,
Ju
ne 20
16
:
397
–
4
15
39
8
Lev
e
l sen
s
orless techn
i
qu
es
sig
n
i
fican
tly th
rou
g
h
m
a
k
i
n
g
use of the small v
o
ltag
e
step
s of th
e mu
ltilev
e
l
in
v
e
rter
o
u
t
pu
t as ex
citatio
n
vo
ltag
e
s.
2.
THE MULTILEVEL TOPOLO
GY
A
ND
OPERA
T
ION
Lip
o
[7
] pro
poses a m
u
ltilev
e
l to
po
log
y
wh
i
c
h
u
s
es two
cascad
ed
H
b
r
i
d
g
e
circu
its
p
e
r
p
h
a
se. Th
e
fi
rst
has a
hi
gh
DC
l
i
n
k
v
o
l
t
a
ge, a
n
d em
pl
o
y
s
GT
Os
or
I
G
C
T
s as t
h
e s
w
i
t
c
hi
ng
d
e
vi
ces
whi
c
h a
r
e c
ont
rol
l
e
d
at
rel
a
t
i
v
el
y
l
o
w f
r
eq
ue
ncy
.
The sec
o
n
d
us
es a l
o
we
r DC
l
i
nk v
o
l
t
a
ge
(f
or e
x
am
pl
e 1/
2
of t
h
e GT
O
D
C
l
i
nk
vol
t
a
ge
) a
n
d e
m
pl
oy
s IGB
T
s
wi
t
h
a
hi
g
h
er
swi
t
c
hi
ng
f
r
e
que
ncy
.
Thi
s
o
p
erat
i
o
n
o
f
I
G
B
T
an
d
IGC
T
m
eet
s
wi
t
h
t
h
e
feat
ur
es o
f
eac
h
par
t
i
c
ul
ar o
n
e.
F
o
r ex
am
pl
e t
h
e IGC
T
c
a
n
bl
o
c
k
hi
g
h
vol
t
a
g
e
s b
u
t
i
t
has
a
sl
ow
switch
i
ng
actio
n
wh
ile th
e IGBT can
swit
ch
v
e
ry
q
u
i
ck
ly b
u
t
h
a
s sm
al
l v
o
ltag
e
b
l
o
c
k
i
ng
cap
a
b
ilities. The
co
m
b
in
atio
n
o
f
th
ese circu
its
can
p
r
ov
id
e a go
od
qu
a
lity v
o
l
tag
e
wav
e
form fo
r
h
i
gh
vo
ltag
e
ap
p
lication
s
.
In T
h
i
s
pa
per,
a sim
i
l
a
r t
opol
ogy
i
s
use
d
b
u
t
wi
t
h
usi
n
g a com
b
i
n
at
i
ons
of
2V (
4
00
V)
and
V(
2
0
0
V
)
as DC
s
o
urce
v
o
l
t
a
ge l
e
vel
s
as
sh
ow
n i
n
Fi
g
u
r
e
1.
Fi
gu
re
1.
Hy
br
i
d
asy
m
m
e
t
r
i
c
cascade
d
H-B
r
i
dge
seve
n l
e
v
e
l
con
v
e
r
t
e
r
Th
e
n
u
m
b
e
r
o
f
lev
e
ls th
at can
b
e
g
e
n
e
rated u
s
ing
th
is topo
log
y
will b
e
7
(3V,
2
V
, V,
0
,
-V, -2
V, -
3V
) al
t
h
o
u
g
h
onl
y
2
H-B
r
i
d
ges a
r
e
use
d
i
n
eac
h l
e
g.
Th
i
s
i
s
d
u
e t
o
t
h
e
asy
m
m
e
t
r
i
c
DC
so
urce
l
e
vel
s
use
d
.
Each l
e
vel
can
be
gene
rat
e
d
b
y
a speci
fi
c
sw
i
t
c
hi
ng
o
f
eac
h
H-B
r
i
d
ge acc
o
r
di
ng
t
o
t
a
bl
e 1
:
Tabl
e
1. R
e
l
a
t
i
o
n
bet
w
een
o
u
t
put
v
o
l
t
a
ge a
n
d
out
put
o
f
eac
h cel
l
i
n
seve
n
l
e
vel
asy
m
m
e
t
r
i
c
Hy
b
r
i
d
casc
a
ded
H
-
Br
i
d
g
e
co
nver
t
er
Output voltage
H-
Br
idge 1
H-
Br
idge 2
3V 2V
1V
2V 2V
0V
V 0V
1V
0 0V
0V
-V
0
V
-1
V
-2
V -2
V
0
V
-3
V -2
V
-1
V
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
Mo
del
l
i
ng a
n
d
Si
m
u
l
a
t
i
o
n of
a
Se
ns
orl
e
ss
C
o
nt
rol
of
a
Tr
ue Asym
met
r
i
c
C
a
sca
d
e H-Bri
d
g
e
…
(
K
amel
Sa
l
e
h)
39
9
The wa
veform
obtaine
d from
each H-B
r
idge in
on
e
fundamental pe
riod is
shown in Fi
gure 2.
Fi
gu
re
2.
O
p
er
at
i
on
of
t
h
e s
e
v
e
n l
e
vel
asy
m
m
e
t
r
i
c
hy
bri
d
c
a
scade
d
H-
bri
d
ge c
o
n
v
e
r
t
e
r.
2.
1. Sp
ace Vec
t
or
M
o
d
u
l
a
ti
o
n
f
o
r 7-L
e
vel
I
n
ver
t
er
C
onsi
d
er t
h
e
7
l
e
vel
casca
de
H-B
r
i
d
ge c
o
n
v
e
rt
er s
h
ow
n i
n
Fi
g
u
re
2.
T
h
e
p
o
ssi
bl
e
o
u
t
p
ut
v
o
l
t
a
ges
t
h
at
can be
ge
nerat
e
d fr
om
each l
e
g are
3V
, 2V
, V
,
0,
-V
,
-2
V an
d -
3
V
.
Acco
r
d
i
n
g t
o
t
h
e swi
t
c
hi
ng st
at
e of
each cell in the
m
u
ltilevel
converter, it is possible to ge
ne
rate 2
7
switchi
ng
states in a spac
e plane as
shown i
n
Fi
gu
re 3. T
h
e no
des re
pre
s
en
t
t
h
e t
i
p
s of t
h
ese vect
ors (
b
as
ic vectors) in t
h
e plane
.
For exam
ple;
the node that
has t
h
e swi
t
c
hi
ng
pat
t
e
rn
(3
,0
,-
1) m
eans t
h
at
t
h
e H-B
r
i
dge
s
i
n
phase a ge
nerat
e
s +3
V, i
n
p
h
ase b
gen
e
rat
e
s
0V
an
d i
n
phas
e
c ge
ne
rat
e
s –
V
. T
h
e
sam
e
out
p
u
t
v
o
l
t
a
ge
o
f
t
h
e
i
n
vert
er
c
a
n
be
gene
rat
e
d
by
ot
her
swi
t
chi
n
g
pat
t
e
rns
f
o
r e
x
am
pl
e (2
,-
1,
-2
) a
n
d
(
1
,
-
2
,
-
3
)
.
M
a
ny
m
e
t
hod
s p
r
o
p
o
se
d i
n
usi
n
g s
p
ace
ve
ct
or m
o
d
u
l
a
t
i
on
o
f
m
u
ltilevel inverter [11, 12, 13].T
he m
e
thod that is adopt
ed in this work
is propose
d
in [11], as it has the
following feature:
It is ve
ry
sim
p
le an
d e
ffective
.
The
o
u
t
p
ut
v
o
l
t
age co
nt
ai
ns
m
i
nim
u
m
di
st
ort
i
o
n
.
The i
n
p
u
t
c
u
r
r
e
nt
ha
s m
i
nim
u
m
curre
nt
di
st
ort
i
o
n.
It is g
e
n
e
ral and
ap
p
licab
le to
an
y lev
e
l.
Returni
n
g to
Figure 3, eac
h
vector i
n
s
p
ace
is gene
rate
d ac
cording t
o
the
voltage
ge
ne
ra
ted from
the c
e
lls in
pha
ses A
,
B
a
nd C
.
T
h
ese v
ect
ors ca
n
be t
r
ans
f
orm
e
d i
n
t
o
αβ
co
o
r
di
nat
e
s (6
0
0
coordinate syste
m
) ac
cordi
ng
to
th
e
fo
llo
wi
ng
eq
u
a
tion
s
:
V
α
Vc
o
s
θ
V
sin
θ
√
3
(1
)
V
β
2V
sin
θ
√
3
(2
)
Whe
r
e V
α
an
d
V
β
are the c
o
ordinates
of t
h
e
vector V in the
60
0
co
ord
i
n
a
te syste
m
, V
and
θ
are t
h
e am
plitude
an
d
ph
ase ang
l
e o
f
t
h
e referen
ce
v
ecto
r
respectiv
ely. To
illu
strate th
is tran
sfo
r
m
a
tio
n
,
Fig
u
re 3
is con
s
id
ered
ag
ain
.
All th
e
switch
i
ng
p
a
ttern
s th
at g
e
n
e
rate V
1
i
n
t
h
e c
o
o
r
di
nat
e
s s
h
o
w
n i
n
Fi
gu
re
3 w
h
i
c
h are
(
2
,0,
-
2)
,
(3,1,-1
)
an
d
(1
,-1,-3
)
will b
e
represen
ted
b
y
th
e po
in
t (2
,2
) in
αβ
c
o
or
di
nat
e
sy
st
e
m
usi
ng
(1
) a
nd
(2
).
Repeating for
all the
vect
ors in space, the
ne
w c
o
ordinate sy
ste
m
will be as shown in
Figure
4.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
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088
-86
94
I
J
PED
S
Vo
l. 7,
No
.
2,
Ju
ne 20
16
:
397
–
4
15
40
0
Fi
gu
re
3.
The
a
v
ai
l
a
bl
e s
w
i
t
c
h
i
ng
st
at
es an
d c
o
r
r
es
po
n
d
i
n
g
v
ect
or
of
t
h
e
sev
e
n l
e
vel
SV
P
W
M
st
at
e di
a
g
ram
Fi
gu
re
4.
Se
ve
n l
e
vel
SV
P
W
M
st
at
e di
ag
ra
m
i
n
αβ
co
or
di
nat
e
s
To
d
e
termin
e th
e lo
catio
n
o
f
th
e
referen
c
e vo
ltag
e
V
_ref
, t
w
o qu
an
tities will b
e
u
s
ed
wh
ich
are :
V
i
n
t
V
(3
)
V
i
n
t
V
(4
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Mo
del
l
i
ng a
n
d
Si
m
u
l
a
t
i
o
n of
a
Se
ns
orl
e
ss
C
o
nt
rol
of
a
Tr
ue Asym
met
r
i
c
C
a
sca
d
e H-Bri
d
g
e
…
(
K
amel
Sa
l
e
h)
40
1
Wh
ere i
n
t() i
s
a l
o
wer i
n
teg
e
r fun
c
tio
n.
After th
ese tw
o
v
a
lu
es are calcu
l
ated
, it is po
ssib
l
e to iden
tify i
n
wh
ich
p
a
ir
of t
r
iang
les th
e refe
ren
c
e vo
ltag
e
ex
ist.
For ex
am
p
l
e
∆
CBA o
r
∆
CBD
acco
r
din
g
t
o
Fi
gu
r
e
4. Th
e
coo
r
di
nat
e
s
of
t
h
e t
h
ree
ot
he
r
vect
o
r
s ca
n
be
cal
cul
a
t
e
d acc
o
r
di
ng
t
o
t
h
e f
o
l
l
owi
n
g e
q
uat
i
o
ns:
V
,
V
V
1
,
V
V
,V
V
,V
1
V
,V
V
1
,
V
1
(5
)
Th
e ex
tra
d
e
termin
atio
n
of t
h
e triang
le wh
ere th
e
refere
nce
vect
o
r
e
x
i
s
t
s
c
a
n
be ac
hi
eve
d
usi
n
g
t
h
e
fol
l
o
wi
n
g
criterio
n
:
V
e
x
ist
in∆CBDi
f
V
V
V
,V
V
e
x
ist
in∆CB
Ai
f
V
V
V
,V
(6
)
2.
2. Ch
oosing the
Switc
h
ing Sequence
The switchi
ng pattern for ea
ch ba
sic vect
or will be chosen accordi
ng t
o
what is calle
d ‘All m
ean
Method’
[11].
In t
h
is m
e
thod an eq
uivale
nt
mean switching state is us
e
d
for eve
r
y basic
space
vector.
If the
num
ber o
f
t
h
e swi
t
c
hi
n
g
pat
t
e
rns t
h
at
ge
ner
a
t
e
a speci
fi
c basi
c vect
or i
s
od
d t
h
en t
h
e m
e
an swi
t
c
hi
ng wi
l
l
be
th
e m
i
d
d
l
e o
n
e
wh
ile if t
h
e nu
m
b
er of th
e switch
i
ng
p
a
tte
rn
s is ev
en
t
h
en th
e m
ean
switch
i
ng
will b
e
th
e t
w
o
swi
t
c
hi
n
g
pat
t
e
rns
i
n
t
h
e m
i
ddl
e. F
o
r i
n
st
a
n
ce, t
h
e
vect
or
wh
ose t
i
p
has
t
h
e co
o
r
di
nat
e
s
(0
,
1
)
has
6
di
f
f
ere
n
t
switch
i
ng
p
a
ttern
s (3,3,2), (2
,2
,1
), (1,1,0), (0,0
,-1
)
,
(-1
,
-1,-2) and
(-2
,
-2,-3
)
. Th
e m
ean
switch
i
n
g
patterns will
be (
1
,
1
,
0
) a
nd
(0
,0
,-
1)
. A
not
her e
x
am
pl
e i
s
t
h
e vect
o
r
w
h
ose t
i
p
has t
h
e
coo
r
di
nat
e
(
1
,
1
)
has fi
ve di
f
f
ere
n
t
switch
i
ng
p
a
ttern
s (3
,2
,1), (2
,1
,0
), (1,0,-1
)
, (0
,-1,-2
)
an
d
(-1
,-2,-3
). Th
e
mean
switc
h
i
ng
p
a
ttern
will b
e
(1
,0
,-
1). T
h
e m
ean s
w
itching
patterns
for all the
vectors i
n
s
p
ace
for
7-le
vel converter is s
h
own Figure
2 in
brown.
C
onsi
d
eri
n
g
t
h
e swi
t
c
hi
ng
se
que
nce,
t
h
e
r
e a
r
e t
w
o
ge
neral
req
u
i
r
em
ent
s
:
-
The t
r
a
n
si
t
i
on
fr
om
one swi
t
c
hi
n
g
st
at
e t
o
anot
her i
s
achi
e
ved
by
swi
t
c
hi
n
g
o
n
l
y
one
H-B
r
i
d
ge i
n
o
n
e
leg
.
-
Th
e
tran
sitio
n
o
f
V
_ref
fr
om
one sect
o
r
t
o
an
ot
he
r o
r
f
r
om
one t
r
i
a
n
g
l
e
t
o
anot
her
req
u
i
r
es no
ne
or t
h
e
m
i
nim
u
m
num
ber
o
f
s
w
i
t
c
hi
n
g
.
The s
w
i
t
c
hi
ng
seq
u
e
n
ce
use
d
i
n
t
h
i
s
pa
per
co
nsi
s
t
s
of
7
segm
ent
s
i
n
e
ach P
W
M
pe
ri
od;
i
n
ea
c
h
segm
ent
one
vect
o
r
i
s
ap
pl
i
e
d. T
o
m
eet
the
gene
ra
l requ
irem
en
ts for
th
e switch
i
n
g
sequ
en
ce m
e
n
tio
n
e
d
abo
v
e,
t
h
e
fol
l
owi
n
g
co
nsi
d
er
at
i
on s
h
oul
d be
t
a
ken
i
n
t
o
acc
o
u
n
t
w
h
en
choo
sing
the v
ect
ors. T
h
e
vector t
h
at is
ap
p
lied in th
e first seg
m
en
t m
u
st b
e
always th
e
o
n
e
who
h
a
s
an
ev
en nu
mb
e
r
of
sw
itc
h
i
ng
(
t
wo me
a
n
swi
t
c
hi
n
g
pat
t
e
rns
)
. T
h
e
ne
xt
vect
o
r
m
u
st
be cho
s
en i
n
a
w
a
y
such t
h
at
o
n
l
y
one cel
l
i
n
o
n
e l
e
g i
s
s
w
i
t
c
hed t
o
obt
ai
n t
h
e
new
vect
or. T
h
e sa
m
e
t
h
i
ng
m
u
st
be d
one i
n
c
h
o
o
si
n
g
t
h
e t
h
i
r
d vect
o
r
. The f
o
urt
h
vect
o
r
sh
o
u
l
d
b
e
sam
e
as t
h
e fi
r
s
t
one
but
obt
a
i
ned
by
t
h
e ot
her m
ean swi
t
c
hi
n
g
pat
t
e
r
n
.
The fi
ft
h, si
xt
h
and se
ve
nt
h
v
ect
ors
m
u
st b
e
sam
e
as th
e t
h
ird, the second
, t
h
e first resp
ectiv
el
y. To illu
strate th
e switch
i
ng
sequ
en
ce th
at i
s
u
s
ed
i
n
t
h
i
s
pape
r, Fi
gu
re 5.a
,
Fi
g
u
re 5
.
b
,
Fi
g
u
re
6.a, Fi
g
u
re
6.
b, Fi
g
u
re
7.a,
Fi
gu
re 7
b
, Fi
g
u
re 8
.
a, Fi
g
u
r
e
8.b ar
e
use
d
.
If
the
re
f
e
rence
v
o
ltage
V
_re
f
ex
ists i
n
∆
CBD an
d
V
α
V
β
is ev
en
, th
e
switch
i
ng
sequ
en
ce
will b
e
(2
,0
,-
3)
,(
2,
0,
-2
),(
3
,
0
,
-
2).
(
3,
1,-
2
)
,
(
3
,
0
,
-
2
)
,
(
2
,
0
,
-
2
),
(
2
,
0
,-
3
)
. T
h
i
s
case i
s
nam
e
d
by
t
y
pe
0 i
n
t
h
e si
m
u
l
a
t
i
on.
Fig
u
re
5
.
a. Swi
t
ch
in
g seq
u
e
n
c
e u
s
ed
i
n
SVPWM for th
e mu
ltilev
e
l con
v
e
rter
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 7,
No
.
2,
Ju
ne 20
16
:
397
–
4
15
40
2
4
T
C
2
T
D
2
T
B
4
T
C
2
T
B
2
T
D
2
T
C
Fig
u
re
5
.
b
.
Timin
g
d
i
ag
ram
for SVPWM
fo
r th
e m
u
ltilev
e
l co
nv
erter
If the
refe
re
nc
e voltage
V
_re
f
ex
ists in
∆
CBA and
V
α
V
β
is ev
en, th
e switch
i
n
g
se
qu
en
ce
will b
e
(2
,0
,-3),
(3,0,-
3)
, (
3
,
0
,
-
2)
, (
3
,
1
,
-
2),
(
3
,
0
,
-
2),
(
3
,
0
,-
3),
(2,0,-
3)
. T
h
i
s
c
a
se i
s
nam
e
d b
y
t
y
pe 1 i
n
t
h
e
sim
u
l
a
t
i
on.
Fig
u
re
6
.
a. Swi
t
ch
in
g seq
u
e
n
c
e u
s
ed
i
n
SVPWM for th
e mu
ltilev
e
l
4
T
C
2
T
A
2
T
B
2
T
C
4
T
C
2
T
B
2
T
A
Figu
re 6.b. Ti
min
g
d
i
ag
ram
for SVPWM
fo
r th
e m
u
ltilev
e
l
If
the
refe
re
nc
e v
o
ltage
V
_re
f
ex
ists
in
∆
CBD and
V
α
V
β
is o
d
d
,
th
e switch
i
n
g
sequ
en
ce
will b
e
(1,0,-2
)
,
(2,0,-
2)
, (
2
,
1
,
-
2)
. (
2
,
1
,
-
1),
(
2
,
1
,
-
1),
(
2
,
0
,-
2),
(1,0,-
2)
. T
h
i
s
c
a
se i
s
nam
e
d b
y
t
y
pe 1 i
n
t
h
e
sim
u
l
a
t
i
on.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Mo
del
l
i
ng a
n
d
Si
m
u
l
a
t
i
o
n of
a
Se
ns
orl
e
ss
C
o
nt
rol
of
a
Tr
ue Asym
met
r
i
c
C
a
sca
d
e H-Bri
d
g
e
…
(
K
amel
Sa
l
e
h)
40
3
Fig
u
re
7
.
a. Swi
t
ch
in
g seq
u
e
n
c
e u
s
ed
i
n
SVPWM for th
e mu
ltilev
e
l con
v
e
rter
4
D
T
2
B
T
2
C
T
2
D
T
2
C
T
2
B
T
4
D
T
Fig
u
re
7
.
b
.
Timin
g
d
i
ag
ram
for SVPWM
fo
r th
e m
u
ltilev
e
l co
nv
erter
If the
refe
renc
e voltage
V
_ref
ex
ists in
∆
CBA and
V
α
V
β
is o
d
d
, th
e switch
i
ng
sequ
en
ce
will b
e
(2
,0
,-3),
(2,0,-
2)
, (
2
,
1
,
-
2)
, (
3
,
1
,
-
2),
(
2
,
1
,
-
2),
(
2
,
0
,-
2),
(2,0,-
3)
. T
h
i
s
c
a
se i
s
nam
e
d b
y
t
y
pe 3 i
n
t
h
e
sim
u
l
a
t
i
on.
Fig
u
re
8
.
a. Swi
t
ch
in
g seq
u
e
n
c
e u
s
ed
i
n
SVPWM for th
e mu
ltilev
e
l
4
A
T
2
B
T
2
C
T
2
A
T
2
C
T
2
B
T
4
A
T
Figu
re 8.b. Ti
min
g
d
i
ag
ram
for SVPWM
fo
r th
e m
u
ltilev
e
l
Applying t
h
e s
a
m
e
rules that are use
d
in t
h
e
exam
ples sh
ow
n
i
n
Figu
r
e
5.a,
Figu
r
e
6
.
a, Fig
u
r
e
7.a
and
Fig
u
r
e
8.a i
n
c
h
o
o
si
n
g
t
h
e
swi
t
c
hi
n
g
se
que
nce,
t
h
e swi
t
c
hi
n
g
se
que
nce
fo
r t
h
e
refe
rence
v
o
l
t
a
ge e
x
i
s
t
i
ng i
n
s
ect
or
1
i
s
gi
ve
n i
n
t
a
bl
e 2
w
h
e
r
e
V
α
,V
β
are calculated using (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. 7,
No
.
2,
Ju
ne 20
16
:
397
–
4
15
40
4
Tab
l
e 2
Switchin
g
sequ
en
ce
i
n
sect
o
r
1
fo
r
SVPW
M
used in
th
e m
u
ltilev
e
l co
nv
erter
SECTOR
1
(V
D
,V
D
)
V0/4 V1/2 V2/2 V0/2
V2/2 V1/2 V0/4
(0
,0
)
∆
BCD
(0
,0
,-1
)
(0
,0
,0
) (1
,0
,0
) (1
,1
,0
) (1
,0
,0
) (0
,0
,0
)
(0
,0
,-1
)
∆
BCA
(0
,0
,-1
)
(1
,0
,-1
)
(1
,0
,0
) (1
,1
,0
) (1
,0
,0
)
(1
,0
,-1
)
(0
,0
,-1
)
(1
,0
)
∆
BCD
(0
,-1
,
-1
)
(1
,-1
,
-1
)
(1
,0
,-1
)
(1
,0
,0
)
(1
,0
,-1
)
(1
,-1
,
-1
)
(0
,-1
,
-1
)
∆
BCA
(1
,-1
,
-2
)
(1
,-1
,
-1
)
(1
,0
,-1
)
(1
,0
,0
)
(1
,0
,-1
)
(1
,-1
,
-1
)
(1
,-1
,
-2
)
(2
,0
)
∆
BCD
(1
,-1
,
-2
)
(1
,-1
,
-1
)
(2
,-1
,
-1
)
(2
,0
,-1
)
(2
,-1
,
-1
)
(1
,-1
,
-1
)
(1
,-1
,
-2
)
∆
BCA
(1
,-1
,
-2
)
(2
,-1
,
-2
)
(2
,-1
,
-1
)
(2
,0
,-1
)
(2
,-1
,
-1
)
(2
,-1
,
-2
)
(1
,-1
,
-2
)
(3
,0
)
∆
BCD
(1
,-2
,
-2
)
(2
,-2
,
-2
)
(2
,-1
,
-2
)
(2
,-1
,
-1
)
(2
,-1
,
-2
)
(2
,-2
,
-2
)
(1
,-2
,
-2
)
∆
BCA
(2
,-2
,
-3
)
(2
,-2
,
-2
)
(2
,-1
,
-2
)
(3
,-1
,
-2
)
(2
,-1
,
-2
)
(2
,-2
,
-2
)
(2
,-2
,
-3
)
(4
,0
)
∆
BCD
(2
,-2
,
-3
)
(2
,-2
,
-2
)
(3
,-2
,
-2
)
(3
,-1
,
-2
)
(3
,-2
,
-2
)
(2
,-2
,
-2
)
(2
,-2
,
-3
)
∆
BCA
(2
,-2
,
-3
)
(3
,-2
,
-3
)
(3
,-2
,
-2
)
(3
,-1
,
-2
)
(3
,-2
,
-2
)
(3
,-2
,
-3
)
(2
,-2
,
-3
)
(5
,0
)
∆
BCD
(2
,-3
,
-3
)
(3
,-3
,
-3
)
(3
,-2
,
-3
)
(3
,-2
,
-2
)
(3
,-2
,
-3
)
(3
,-3
,
-3
)
(2
,-3
,
-3
)
(0
,1
)
∆
BCD
(0
,0
,-1
)
(1
,0
,-1
)
(1
,1
,-1
)
(1
,1
,0
)
(1
,1
,-1
)
(1
,0
,-1
)
(0
,0
,-1
)
∆
BCA
(1
,0
,-2
)
(1
,0
,-1
)
(1
,1
,-1
)
(2
,1
,-1
)
(1
,1
,-1
)
(1
,0
,-1
)
(1
,0
,-2
)
(1
,1
)
∆
BCD
(1
,0
,-2
)
(1
,0
,-1
)
(2
,0
,-1
)
(2
,1
,-1
)
(2
,0
,-1
)
(1
,0
,-1
)
(1
,0
,-2
)
∆
BCA
(1
,0
,-2
)
(2
,0
,-2
)
(2
,0
,-1
)
(2
,2
,-1
)
(2
,0
,-1
)
(2
,0
,-2
)
(1
,0
,-2
)
(2
,1
)
∆
BCD
(1
,-1
,
-2
)
(2
,-1
,
-2
)
(2
,0
,-2
)
(2
,0
,-1
)
(2
,0
,-2
)
(2
,-1
,
-2
)
(1
,-1
,
-2
)
∆
BCA
(2
,-1
,
-3
)
(2
,-1
,
-2
)
(2
,0
,-2
)
(2
,0
,-1
)
(2
,0
,-2
)
(2
,-1
,
-2
)
(2
,-1
,
-3
)
(3
,1
)
∆
BCD
(2
,-1
,
-3
)
(2
,-1
,
-2
)
(3
,-1
,
-2
)
(3
,0
,-2
)
(3
,-1
,
-2
)
(2
,-1
,
-2
)
(2
,-1
,
-3
)
∆
BCA
(2
,-1
,
-3
)
(3
,-1
,
-3
)
(3
,-1
,
-2
)
(3
,0
,-2
)
(3
,-1
,
-2
)
(3
,-1
,
-3
)
(2
,-1
,
-3
)
(4
,1
)
∆
BCD
(2
,-2
,
-3
)
(3
,-2
,
-3
)
(3
,-1
,
-3
)
(3
,-1
,
-2
)
(3
,-1
,
-3
)
(3
,-2
,
-3
)
(2
,-2
,
-3
)
(0
,2
)
∆
BCD
(1
,1
,-2
)
(1
,1
,-1
)
(2
,1
,-1
)
(2
,2
,-1
)
(2
,1
,-1
)
(1
,1
,-1
)
(1
,1
,-2
)
∆
BCA
(1
,1
,-2
)
(2
,1
,-2
)
(2
,1
,-1
)
(2
,2
,-1
)
(2
,1
,-1
)
(2
,1
,-2
)
(1
,1
,-2
)
(1
,2
)
∆
BCD
(1
,0
,-2
)
(2
,0
,-2
)
(2
,1
,-2
)
(2
,1
,-1
)
(2
,1
,-2
)
(2
,0
,-2
)
(1
,0
,-2
)
∆
BCA
(2
,0
,-3
)
(2
,0
,-2
)
(2
,1
,-2
)
(3
,1
,-2
)
(2
,1
,-2
)
(2
,0
,-2
)
(2
,0
,-3
)
(2
,2
)
∆
BCD
(2
,0
,-3
)
(2
,0
,-2
)
(3
,0
,-2
)
(3
,1
,-2
)
(3
,0
,-2
)
(2
,0
,-2
)
(2
,0
,-3
)
∆
BCA
(2
,0
,-3
)
(3
,0
,-3
)
(3
,0
,-2
)
(3
,1
,-2
)
(3
,0
,-2
)
(3
,0
,-3
)
(2
,0
,-3
)
(3
,2
)
∆
BCD
(2
,-1
,
-3
)
(3
,-1
,
-3
)
(3
,0
,-3
)
(3
,0
,-2
)
(3
,0
,-3
)
(3
,-1
,
-3
)
(2
,-1
,
-3
)
(0
,3
)
∆
BCD
(1
,1
,-2
)
(2
,1
,-2
)
(2
,2
,-2
)
(2
,2
,-1
)
(2
,2
,-2
)
(2
,1
,-2
)
(1
,1
,-2
)
∆
BCA
(2
,1
,-3
)
(2
,1
,-2
)
(3
,1
,-2
)
(3
,2
,-2
)
(3
,1
,-2
)
(2
,1
,-2
)
(2
,1
,-3
)
(1
,3
)
∆
BCD
(2
,1
,-3
)
(2
,1
,-2
)
(3
,1
,-2
)
(3
,2
,-2
)
(3
,1
,-2
)
(2
,1
,-2
)
(2
,1
,-3
)
∆
BCA
(2
,1
,-3
)
(3
,1
,-3
)
(3
,1
,-2
)
(3
,2
,-2
)
(3
,1
,-2
)
(3
,1
,-3
)
(2
,1
,-3
)
(2
,3
)
∆
BCD
(2
,0
,-3
)
(3
,0
,-3
)
(3
,1
,-3
)
(3
,1
,-2
)
(3
,1
,-3
)
(3
,0
,-3
)
(2
,0
,-3
)
(0
,4
)
∆
BCD
(2
,2
,-3
)
(2
,2
,-2
)
(3
,2
,-2
)
(3
,3
,-2
)
(3
,2
,-2
)
(2
,2
,-2
)
(2
,2
,-3
)
∆
BCA
(2
,2
,-3
)
(2
,2
,-2
)
(3
,2
,-2
)
(3
,3
,-2
)
(3
,2
,-2
)
(2
,2
,-2
)
(2
,2
,-3
)
(1
,4
)
∆
BCD
(2
,1
,-3
)
(3
,1
,-3
)
(3
,2
,-3
)
(3
,2
,-2
)
(3
,2
,-3
)
(3
,1
,-3
)
(2
,1
,-3
)
(0
,5
)
∆
BCD
(2
,2
,-3
)
(3
,2
,-3
)
(3
,3
,-3
)
(3
,3
,-2
)
(3
,3
,-3
)
(3
,2
,-3
)
(2
,2
,-3
)
2
.
3
.
Ca
lculating
the Dwell Time
The dwel
l
t
i
m
e
cal
cul
a
t
i
ons
depe
n
d
on
w
h
et
her
V
α
V
β
is
odd
o
r
ev
en
an
d a
l
s
o
w
h
e
t
h
e
r th
e r
e
f
e
r
e
n
c
e
v
ector ex
ists in
∆CBD
or
∆CB
A
as
fo
llowi
n
g
:
1.
V
D
α
V
D
β
is ev
en
and
the referen
ce
v
o
l
tag
e
ex
ists i
n
∆
CBD
(typ
e 0)
:
T
D
1
V
α
ref
V
D
α
V
β
ref
V
D
β
T
T
B
V
α
ref
V
D
α
T
T
C
T
T
B
T
D
(7
)
2.
V
D
α
V
D
is ev
en
and
the referen
ce
v
o
l
tag
e
ex
ists i
n
∆
CB
A
(typ
e 1)
:
T
A
V
α
ref
V
D
α
V
β
ref
V
D
β
1
T
T
B
V
D
β
1
V
β
ref
T
T
C
T
T
A
T
B
(8
)
3.
V
D
α
V
D
β
is odd
an
d th
e
referen
c
e vo
ltag
e
ex
ists in
∆
CBD
(ty
p
e
2):
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Mo
del
l
i
ng a
n
d
Si
m
u
l
a
t
i
o
n of
a
Se
ns
orl
e
ss
C
o
nt
rol
of
a
Tr
ue Asym
met
r
i
c
C
a
sca
d
e H-Bri
d
g
e
…
(
K
amel
Sa
l
e
h)
40
5
T
B
V
α
ref
V
D
β
T
T
C
V
β
ref
V
D
β
T
T
D
T
T
B
T
C
(9
)
4.
V
D
α
V
D
β
is odd
an
d th
e
referen
c
e vo
ltag
e
ex
ists in
∆
CB
A
(ty
p
e3
):
T
B
V
D
β
1
V
β
ref
T
T
C
V
D
α
1
V
α
ref
T
T
A
T
T
B
T
C
(1
0)
5.
The algorithm
that illustrates th
e proc
edure for applying the space ve
c
t
or m
odulation in a
m
u
ltilevel
in
v
e
rter will
b
e
:
-
Tran
sf
orm
t
h
e
refe
rence
vol
t
a
ge t
o
sect
or
1 by
subt
ract
i
ng
t
h
e val
u
e (
n
-
1
)
*
6
0
° f
r
o
m
t
h
e angl
e o
f
t
h
e
refe
rence
v
o
l
t
a
ge whe
r
e n
i
s
t
h
e num
ber of
s
ect
or.
-
Calculate
V
α
ref
,
V
β
_
ref
acc
or
di
n
g
t
o
(1
),
(
2
)
-
Specify t
h
e tria
ngle
where
the
refe
renc
e
voltage e
x
ists according to (5),(6)
-
C
h
o
o
se t
h
e s
w
i
t
chi
n
g
se
que
nc
e fr
om
Tabl
e 2
-
Calculate the dwell tim
e
accordi
n
g to
(7), (8),
(9), (10)
-
Transform
the switching sequence
t
o
the s
ector whe
r
e the refere
nce
voltage exists according to
Table 3
Tabl
e
3. R
e
l
a
t
i
o
n
o
f
s
w
i
t
c
hi
n
g
st
at
es i
n
di
ffe
rent
sect
ors
Sector Switching
state
1 Va
Vb
Vc
2
-Vb
-Vc
-Va
3 Vc
Va
Vb
4
-Va
-Vb
-Vc
5 Vb
Vc
Va
6
-Vc
-Va
-Vb
2.
4. Sens
ored
Opera
ti
o
n
of a Casc
ade
H
-
Bridg
e
Multil
ev
el
In
verter
PMSM Drive
Fi
gu
re
9 s
h
o
w
s t
h
e vect
or c
ont
rol
st
r
u
ct
u
r
e pr
o
pose
d
fo
r
t
h
e cascad
e
H-B
r
i
d
ge m
u
l
t
i
l
e
vel
i
nvet
e
r
PM
SM
d
r
i
v
e
s
y
st
em
when
u
s
i
ng
an
enc
o
der
f
o
r
fee
dba
ck
i.e in
sen
s
o
r
ed
m
o
d
e
. Th
e simu
latio
n of t
h
e cascad
e
H-Bri
d
g
e
m
u
lt
ilev
e
l in
v
e
ter
PMSM driv
e
h
a
s
b
een
ca
r
r
i
e
d o
u
t
usi
n
g t
h
e S
A
B
E
R
si
m
u
l
a
t
i
on pac
k
age. T
h
e
si
m
u
latio
n
resu
lts in
Figu
re
1
0
sh
ow t
h
e
feasib
ility o
f
th
e syste
m
. It can b
e
seen fro
m
th
e fi
g
u
re t
h
at
at lo
w
spee
ds t
h
e
de
m
a
nd
vol
t
a
ge
i
s
sm
all
and
he
nce
onl
y
t
h
e
H
-
B
r
i
d
ges sy
nt
h
e
si
zed
V(
20
0
V
) are
use
d
t
o
g
e
nerat
e
suc
h
a voltage
.
W
h
e
n
the s
p
eed is increas
ed, the
de
m
a
n
d
vo
ltag
e
is increased
and
all th
e H-Bridg
e
s are
swi
t
c
he
d i
n
or
der t
o
ge
nerat
e
t
h
i
s
dem
a
nd v
o
l
t
a
ge i
n
a
way
t
h
at
t
h
e H
-
B
r
i
dge sy
nt
hi
ze
d t
h
e v
o
l
t
a
ge
2V
(
4
0
0
V
)
has s
w
i
t
c
hi
n
g
f
r
eq
ue
ncy
eq
ual
s
t
h
e
fu
n
d
am
ent
a
l
Figure
9. Vect
or control topo
logy
using m
u
lti level space
vector
PW
M
for m
u
lt
ilevel inverter
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 7,
No
.
2,
Ju
ne 20
16
:
397
–
4
15
40
6
Figure
10.
Spe
e
d ste
p
s in se
nsore
d
m
ode
usi
n
g S
p
ace
vector m
odulation
for 7-level inve
rter
3.
TRACKING THE
SALIE
N
CY
IN MULT
ILEVEL INVERTER
It is
p
o
s
sib
l
e t
o
track
t
h
e sali
en
cy using
the PW
M
sign
als
in
a m
u
ltilev
e
l in
verter in
similar way to
th
at in
trodu
ced
in
[6
]
for a 2
-
lev
e
l inv
e
rt
er withou
t in
t
e
rru
p
ting
t
h
e
m
u
l
tilev
e
l in
v
e
rter
n
o
rm
al o
p
e
ration
because
of t
h
e
test vectors.
Figure
11 s
h
ows the Ty
pe
0 switchi
ng sequence
. T
h
e sta
t
or circ
uit when the
vectors V1, V2
and V0
are
app
l
i
e
d a
r
e s
h
o
w
n i
n
Fi
g
u
r
e
12
.
a
, 1
2
.
b
a
n
d
12
.
c
res
p
ect
i
v
el
y
.
dt
di
V
b
)
2
(
dt
di
V
c
)
2
(
dt
di
V
a
)
2
(
4
0
T
2
1
T
2
2
T
2
0
T
2
1
T
2
2
T
4
0
T
dt
di
V
b
)
0
(
dt
di
V
c
)
0
(
d
t
di
V
a
)
0
(
dt
di
V
b
)
1
(
dt
di
V
c
)
1
(
dt
di
V
a
)
1
(
Figure 11. Swi
t
ching
se
que
nc
e
for Type 0
i
n
sector 1 in t
h
e
m
u
l
tilevel space diagram
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