Internati
o
nal
Journal of P
o
wer Elect
roni
cs an
d
Drive
S
y
ste
m
(I
JPE
D
S)
V
o
l.
5, N
o
. 3
,
Febr
u
a
r
y
201
5,
pp
. 44
1
~
45
2
I
S
SN
: 208
8-8
6
9
4
4
41
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
Improved Torqu
e
Cont
rol Perf
ormance i
n
Direct Torqu
e
Control using Optimal Switching Vectors
Muhd Z
h
arif
Rifqi Z
uber
Ahmadi
1
,
Auz
a
ni Jidin
2
, Maaspa
liza
A
z
ri
3
, Khairi
Rahim
4
, Tole S
u
tik
n
o
5
1,2,3,4
Faculty
of Electrical
Engin
e
ering,
Facu
lty of Electrical Engin
eering
,
Un
iv
ersiti Tekn
ik
al
Malaysia Mela
k
a
Hang
Tu
ah
Jay
a
,76
100
Durian
Tun
g
g
a
l, Melak
a
Malaysia
5
Depa
rt
m
e
nt
of
El
ect
ri
cal
En
g
i
neeri
n
g,
U
n
i
v
ersi
t
a
s A
h
m
a
d Dahl
a
n
,
Y
ogy
a
k
art
a
,
I
n
d
o
n
esi
a
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Nov 3, 2014
Rev
i
sed
Jan
6, 2
015
Accepte
d
Ja
n 19, 2015
Th
is p
a
p
e
r
p
r
esen
ts th
e sign
ifi
cant im
provem
ent of Direct Torque
C
ont
r
o
l
(D
TC
)
of 3-
p
h
ases i
n
d
u
c
tion m
ach
ine using a Cascade
d
H-
Bid
g
e
Mu
ltilev
e
l Inv
e
rter (CHMI). Th
e l
a
rg
est torqu
e
ripp
le and
vari
a
b
l
e
s
w
i
t
c
hi
n
g
fre
q
u
enc
y
are
kn
o
w
n
as t
h
e
m
a
jo
r
pr
obl
em
foun
d
e
d
in
DTC o
f
in
du
ction
m
o
to
r. As a resu
lt, it can
d
i
min
i
sh
th
e
p
e
rf
or
m
a
n
ce in
du
ction
m
o
to
r
con
t
ro
l. Th
eref
or
e, th
e conven
tio
n
a
l
2
-
l
e
vel
i
nve
rt
er
has bee
n
repl
a
ced wi
t
h
C
H
M
I
t
h
e i
n
or
der t
o
i
n
cre
a
se
the
perform
a
nce of t
h
e m
o
tor eith
e
r
i
n
dynam
i
c or st
eady-state
co
nd
itio
n. By u
s
ing
th
e m
u
ltilev
e
l in
v
e
rter, it can
p
r
od
u
c
e a
m
o
re
sel
ect
i
on
of t
h
e v
o
l
t
a
ge
vect
ors
.
Besides
that, it can m
i
nimize the
to
rq
u
e
ri
p
p
l
e ou
tpu
t
as well a
s
in
cr
ease the efficiency by re
duci
ng the
swi
t
c
hi
n
g
fre
q
u
ency
o
f
t
h
e
i
nve
rt
er.
The
sim
u
l
a
t
i
on m
odel
of
t
h
e
pr
o
pose
d
m
e
t
hod
has
bee
n
d
e
vel
o
ped
an
d
t
e
st
ed by
u
s
i
n
g M
a
t
l
a
b
soft
ware
. Its im
pro
v
em
ents were
also verified via
experim
e
ntal
resu
lts.
Keyword:
Casc
ad
ed H-
Bri
d
g
e
D
i
re
ct
T
o
rq
ue
Co
n
t
ro
l
In
du
c
t
ion
m
ach
in
e
Mult
ilev
e
l In
ver
t
er
Swi
t
c
h
i
ng Ve
ct
or
Copyright ©
201
5 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
u
h
d
Z
h
a
r
i
f
R
i
fqi
Z
ube
r
A
h
m
a
di
Faculty of Elec
trical Engineering
Un
i
v
ersiti Tekn
ik
al Malaysia Melak
a
H
a
ng
Tu
ah
Jay
a
, 761
00
Du
r
i
an
Tun
g
g
a
l, Melak
a
Malaysia
Em
a
il: zh
arifri
fq
i@stud
en
t.u
t
e
m
.ed
u
.
m
y
1.
INTRODUCTION
In t
h
e
m
i
ddl
e
1980
’s, a simpl
e
cont
rol
st
r
a
t
e
g
y
t
o
enhance perform
ance of i
nduct
i
o
n
m
o
t
o
r was
prop
osed by
Takahashi
and Noguchi
. The co
nt
rol
st
rat
e
gy
i
s
pop
ul
arly
kno
wn as Di
rect
Torque C
ont
rol
(
D
TC
)
[1]
.
Thi
s
m
e
t
hod gradual
l
y
repl
aci
ng t
h
e t
r
adi
t
i
onal
m
e
t
hod of Fi
el
d
Ori
e
nted C
ont
rol (FOC
) proposed b
y
F.Bla
s
k
h
e
[2
]. At earl
y
stag
es
, th
e FOC was ex
ten
s
iv
e
y
u
s
ed
to
estab
lis
h
e
d
th
e co
n
t
ro
l o
f
AC q
u
a
n
tities o
f
st
at
or fl
ux, current
s and volt
a
ges by
usi
ng vect
or cont
rol
app
r
oach. H
o
w
e
v
e
r
,
t
h
i
s
s
c
h
e
me
i
s
c
o
mp
l
i
c
a
t
e
d
d
u
e
to
th
e ex
isten
c
e o
f
fram
e
tran
sfo
r
m
a
tio
n
,
cu
rren
t co
n
t
roll
er and re
quires
knowle
dge of
m
achine pa
ra
meters.
In
DTC
,
t
h
e
t
o
rq
ue a
nd
fl
u
x
are co
nt
rol
l
e
d i
n
de
pe
nde
nt
l
y
, i
n
w
h
i
c
h t
h
ei
r
de
m
a
nds are sa
t
i
s
fi
ed
sim
u
l
t
a
neousl
y
by
c
h
oosi
n
g
sui
t
a
bl
e
v
o
l
t
a
ge
vect
o
r
s a
ccor
d
i
n
g t
o
t
h
e
di
gi
t
i
zed
s
t
at
us p
r
od
uce
d
fr
om
hy
st
eresi
s
c
ont
rol
l
e
rs
. U
n
l
i
k
e
t
h
e F
O
C
,
t
h
e
t
o
r
que a
n
d fl
ux a
r
e c
ont
rol
l
ed b
a
sed
o
n
p
r
o
d
u
ci
n
g
t
h
e c
u
r
r
ent
com
pone
nt
s (d
-q a
x
i
s
com
ponent
o
f
st
at
or
cur
r
ent
re
fer
r
i
ng t
o
e
x
ci
t
a
t
i
on refe
re
nce fra
m
e
) whi
c
h re
s
u
l
t
s
i
n
co
m
p
lex
m
a
th
e
m
atical eq
u
a
tio
n
s
.
Desp
ite th
e DTC si
m
p
lici
t
y,
it
is k
n
o
wn
t
o
h
a
v
e
two
maj
o
r prob
lem
s
, n
a
m
e
ly v
a
riab
le switch
i
ng
fre
que
ncy
a
nd
l
a
rge t
o
r
que
ri
ppl
e.
The
s
e p
r
obl
em
s t
h
at
ha
ve ari
s
e
n
due t
o
t
h
e
u
n
p
r
edi
c
t
a
bl
e t
o
r
q
ue a
n
d fl
ux
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 5
,
No
. 3
,
Febru
a
r
y
20
15
:
441
–
4
52
44
2
cont
rol
be
havi
or
f
o
r
va
ri
o
u
s
ope
rat
i
n
g c
o
n
d
i
t
i
ons i
n
hy
st
e
r
esi
s
o
p
erat
i
o
n.
O
bvi
ou
sl
y
,
m
a
ny
rese
arc
h
er
s ha
ve
extensi
v
ely propose
d
s
o
m
e
/m
inor a
d
justm
e
nts to m
i
nim
i
ze the
problem
s.
S
p
ace
vector m
odulation te
chni
que
i
s
one of t
h
e
p
o
p
u
l
a
r m
e
t
hod
s t
o
over
c
om
e
t
h
e pr
obl
em
. Thi
s
way
i
s
wi
del
y
used by
researche
r
s i
n
o
r
der t
o
achieve
greate
r
perform
a
nce m
o
tor as was reported i
n
[3]. The m
a
jor
different
betwee
n
DTC hystere
s
is base
d
an
d DTC-SVM is th
e ho
w t
o
g
e
n
e
rate t
h
e
stato
r
vo
ltag
e
r
e
fere
nce.
I
n
D
T
C-SVM
,
th
e stator voltage refere
nce
can be p
r
o
d
u
c
e
d by
cal
cul
a
t
i
ng wi
t
h
i
n
a sam
p
l
i
ng t
i
m
e
[4, 5]
. B
y
doi
n
g
so, i
t
can p
r
o
d
u
ce t
h
e co
nst
a
nt
swi
t
c
hi
n
g
as
o
p
p
o
se
d t
h
e
DT
C
-
hy
st
eresi
s
b
a
sed.
H
o
we
ver
,
t
o
ge
ne
rat
e
t
h
e st
at
or
v
o
l
t
a
ge re
fere
nces i
n
v
o
l
v
e
the com
p
lex calculation and
burde
n
the proc
essor
de
vice.
Anothe
r im
provem
ent used is
a variable
hys
t
eresis
ban
d
.
B
a
si
cal
l
y
, w
h
en
re
d
u
c
e
t
h
e
ba
nd
wi
dt
h
hy
st
eresi
s
ba
nd
, t
h
e
t
o
rq
ue
ri
p
p
l
e
ha
s al
so
bec
o
m
e
m
i
nim
i
ze.
Ev
en
so, th
e
po
ssib
ility to
select th
e rev
e
rse v
o
ltag
e
v
ect
o
r
can
b
e
o
c
cu
rred
wh
enev
er th
e torq
u
e
ch
ang
e
s
rapi
dl
y
at
t
h
e ext
r
em
e condi
t
i
ons
(i
.e.
at
ve
r
y
l
o
w s
p
eed
s).
Thi
s
m
ean, o
v
e
rsh
o
o
t
an
d
un
ders
h
oot
of t
o
r
que t
o
vary
o
u
t
s
i
d
e t
h
e hy
st
eresi
s
ba
nds m
i
ght
be h
a
ppe
ne
d. A
s
a resul
t
,
t
h
e e
x
t
r
em
e t
o
rque
ri
p
p
l
e
i
s
pr
od
uce
d
d
u
e
to
th
e in
app
r
op
riate selectio
n
vo
ltag
e
v
ect
o
r
. To
im
p
r
o
v
e th
e switch
i
ng
frequ
en
cy, t
h
e d
ith
ering
meth
od
is
use
d
[
6
,
7]
. Th
i
s
m
e
t
hod
was
appl
i
e
d
wi
t
h
i
n
ject
i
ng t
h
e
hi
g
h
swi
t
c
hi
n
g
f
r
e
que
ncy
o
f
t
h
e
err
o
r c
o
m
pone
nt
f
o
r
flux
and
to
rque. Ho
wev
e
r, it still a
l
so
n
o
t
main
tain
s th
e switch
i
ng
frequ
e
n
c
y.
Furth
e
rm
o
r
e,
m
a
n
y
k
i
n
d
s
o
f
t
echni
q
u
e we
r
e
ado
p
t
e
d i
n
DTC
dri
v
es i
n
orde
r t
o
o
v
ercom
e
the proble
m
as
well as
enha
nce the excellent
perform
a
nce of m
o
tor drives
s
u
ch as
[8,
9].
In
recen
t
years, th
e
research
es
on
DTC drives u
tilizin
g
m
u
ltilev
e
l in
v
e
rter b
e
co
m
e
th
e ho
t top
i
c fo
r
pr
o
v
i
d
i
n
g t
h
e
m
o
re excel
l
e
nt
and
p
r
eci
si
o
n
of sel
ect
i
o
n
vo
l
t
a
ge vect
o
r
t
o
im
pro
v
e D
T
C
per
f
o
r
m
a
nce[1
0
-
1
2]
.
In g
e
n
e
ral, m
u
ltilev
e
l in
v
e
rter can
b
e
catego
r
ized
in
three layo
u
t
s, n
a
m
e
ly, CHMI, n
e
utral po
in
t cap
a
cito
r
m
u
l
tilev
e
l in
v
e
rter an
d
flyin
g
cap
acito
r mu
ltilev
e
l in
v
e
rt
er as was repo
rted
[1
3,
1
4
]
. Th
e all
k
i
nd
s
of
m
u
l
tilev
e
l h
a
v
e
d
i
fferen
t
co
nfigu
r
ation
s
, n
u
m
b
e
r of
switch
i
ng
d
e
vices,
switch
i
ng
states/v
ectors
and
arran
g
e
m
e
n
t
s.
Mu
ltilev
e
l in
verter can
offer sig
n
i
fican
t
adv
a
n
t
ag
es to
im
p
r
ov
e DTC
p
e
rfo
r
m
a
n
ce, especiall
y
fo
r m
e
di
um
an
d hi
gh
-
p
o
w
er
v
o
l
t
a
ge a
ppl
i
cat
i
on.
Fu
rt
he
rm
ore, i
t
al
so ca
n o
p
erat
e at
hi
g
h
vol
t
a
ge
an
d
pr
od
uc
e
l
o
we
r harm
oni
c
(i
.e.
sl
o
p
e of
vol
t
a
ge
ch
an
ge
d dv/
dt
)[
1
5
]
.
In t
h
i
s
pa
per, t
h
e DTC
per
f
o
r
m
ances, i
n
t
e
r
m
s of t
o
r
q
ue ri
ppl
e,
harm
oni
c
s
di
st
ort
i
o
n a
n
d swi
t
c
hi
ng
fre
que
ncy
wer
e
im
pro
v
e
d
by
ap
pl
y
i
ng a
p
pr
op
ri
at
e sel
ect
i
o
n
o
f
vol
t
a
ge
vect
o
r
s
of
fere
d i
n
C
H
M
I
t
o
pol
ogy
.
The sel
ect
i
o
n
of t
h
e a
p
p
r
o
p
ri
at
e ve
ct
or
s
de
pen
d
s
o
n
t
h
e m
o
t
o
r o
p
e
r
at
i
ng c
o
ndi
t
i
ons
w
h
i
c
h
i
n
here
nt
ly
det
e
rm
i
n
ed by
t
h
e out
put
st
a
t
us o
f
7
-
l
e
vel
of t
o
r
que
hy
st
eresi
s
com
p
ara
t
or. T
h
e ap
pl
i
c
at
i
on o
f
si
m
p
le DTC
st
ruct
u
r
e an
d f
a
st
i
n
st
ant
a
neo
u
s co
nt
r
o
l
wi
t
h
hi
gh co
nt
r
o
l
b
a
nd
wi
dt
h of
fer
e
d i
n
hy
st
eresi
s
based D
T
C
can be
retain
ed. Th
is
p
a
p
e
r is organized
b
y
section
as fo
llowed
;
Sectio
n
II
d
e
scrib
e
d
abou
t th
e con
cep
t
o
f
DTC-
hy
st
eresi
s
ba
s
e
d, Sect
i
on
II
I p
r
ese
n
t
s
t
h
e
t
o
p
o
l
o
gy
an
d
swi
t
c
hi
n
g
ve
ct
ors a
v
ai
l
a
bl
e
i
n
C
H
M
I
t
o
pol
ogy
,
Sect
i
on I
V
di
scusses t
h
e
pr
o
pos
ed sel
ect
i
o
n o
f
vect
o
r
s in DTC-CHM
I
; Sectio
n
VI
p
r
esen
ts th
e sim
u
latio
n
resul
t
s
t
o
s
h
o
w
t
h
e i
m
pro
v
em
ent
s
of
fere
d a
n
d
fi
nal
l
y
Sect
i
o
n
VI
I
gi
ves
t
h
e
co
ncl
u
si
on
.
2.
CO
NCEPT
O
F
DT
C-
HYST
ERESIS B
A
S
E
D
D
T
C
h
a
s a simp
le stru
ctur
e co
nf
igu
r
ation as show
n in Figur
e
1
,
yet it is su
p
e
r
i
or
t
o
en
han
ce t
o
rq
ue
and
fl
u
x
c
o
nt
r
o
l
,
i
n
t
e
rm
s of
fast
dy
nam
i
c
and
rel
i
a
bl
e
c
o
ntrol due to the hysteresis
o
p
er
atio
n. By do
i
n
g so,
t
h
e ap
p
r
o
p
ri
at
e
sel
ect
i
on
o
f
v
o
l
t
a
ge
vect
o
r
s
can i
n
de
pen
d
e
n
t
l
y
cont
rol
b
o
t
h t
o
rq
ue a
n
d f
l
ux.
T
h
ere
f
o
r
e,
i
t
can
of
fer a
fast
er i
n
st
ant
a
neo
u
s c
ont
rol
of t
o
r
q
u
e
and
fl
u
x
bas
e
d. Sel
ect
i
o
n
v
o
l
t
a
ge
vect
or
o
r
swi
t
c
hi
n
g
st
at
e ca
n
b
e
ob
tain
ed fro
m
th
e lo
ok-up
tab
l
e as
was
tab
u
l
ated in
Ta
ble I.
Where, i
n
t
h
e s
w
itching ta
ble contains three
m
a
i
n
com
pone
nt
s,
nam
e
l
y
t
h
e st
at
us
of
t
o
r
que
,
fl
u
x
a
n
d
s
t
at
us fl
u
x
o
r
i
e
nt
at
i
on
f
o
r
sel
ect
i
ng t
h
e a
p
p
r
op
ri
at
e
swi
t
c
hi
n
g
st
at
e
.
T
h
e s
w
i
t
c
hi
n
g
st
at
es a
r
e c
h
oosi
n
g
based
on
th
e requ
iremen
t of t
o
rqu
e
an
d stato
r
fl
u
x
,
eith
er
to increase
or
decrease a
n
d also stator
fl
u
x
s
ect
or. In or
der t
o
m
a
ke
t
h
e
de
cision either to increase or de
crease
can be
obt
ai
ne
d fr
om
t
h
e 3-l
e
vel
an
d 2
-
l
e
v
e
l
hy
st
eresi
s
o
f
t
o
r
q
ue an
d st
at
or fl
ux
, res
p
ect
i
v
el
y
.
B
e
si
des t
h
at
,
t
h
e est
i
m
a
t
e
d val
u
e of fl
ux a
n
d t
o
r
que ca
n b
e
pro
d
u
ce fr
om
t
h
e cal
cul
a
t
i
on of v
o
l
t
a
ge an
d
curre
nt
com
p
o
n
ent
.
In
p
o
w
er ci
rcu
i
t
s
, t
h
e
vol
t
a
ge
so
urce
i
n
vert
e
r
i
s
per
f
o
r
m
e
d by
IGB
T
de
v
i
ce. The
sc
he
m
a
t
i
c
di
agram
o
f
3-
pha
se v
o
l
t
a
ge
sou
r
ce i
n
vert
e
r
i
s
real
i
zed i
n
Fi
gu
re 2
.
Acc
o
r
d
i
n
g t
o
t
h
ese
fi
gu
res, t
h
e i
n
vert
er
has co
nt
ai
ned
six
switch
m
o
des to
op
erate in
th
e 3-p
h
a
se i
n
du
ction
m
achine. The
r
e
f
ore, it can ge
ne
rat
e
ei
ght
v
o
l
t
a
ge
space
vectors, as illustrated in Figure 3.
Eac
h
vol
t
age space vec
t
or,
has a thre
e switching state, [Sa,Sb,Sc]. Six
active
voltage
vector (
to
)
an
d
t
w
o
no
n-
act
i
v
e o
r
ze
ro
vol
t
a
ge vect
o
r
(
and
) c
o
rres
p
on
d
i
ng
to
[
0
0
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Im
pr
oved
T
o
rq
ue C
ont
r
o
l
Per
f
orm
a
n
ce i
n
Di
rect
Tor
q
ue C
o
nt
rol
usi
n
g …
(
M
u
h
d
Zh
ari
f
R
i
f
q
i
Zu
ber A
h
m
adi
)
44
3
0]
an
d
[1
1
1]
,
res
p
ect
i
v
el
y
.
Each s
w
i
t
c
hi
n
g
devi
ce m
u
st
be c
o
m
p
l
e
m
e
n
t
i
ng eac
h
ot
he
r
fo
r
(u
p
p
er a
n
d
l
o
we
r
switch
)
to
avo
i
d
sh
ort circu
it
co
nd
itio
ns.
S
a
V
DC
1
0
S
b
1
0
S
c
1
0
d
q
+
-
v
a
v
b
v
c
v
n
IM
VSI
Fi
gu
re
2.
Sc
he
m
a
t
i
c
di
agram
of
VS
I
Fi
gu
re 3.
V
o
l
t
a
ge vect
o
r
s
a
r
e gene
rat
e
d
by
VSI
V3,
(
110)
V4,
(
010)
V5
,(
011
)
V6,
(
001
)
V1,
(
101)
V2,
(
100)
V7,
(
111)
V0,
(
000)
L
U
T
V
S
I
+
MM
S
a
S
b
S
c
Ψ
sd
Stator
flux and electr
o
m
a
gnetic tor
q
u
e
estim
a
tor
s
-
T
e,ref
+
-
Ψ
s,ref
T
e
Ψ
s
Ψ
s
+
E
Te
T
stat
i
b
i
c
V
DC
i
a
Sector detection
Voltage calculatio
n
Ψ
sq
v
sd
v
sq
i
sd
i
sq
-
+
d-q current calcula
tion
0
1
0
1
-1
HB
Ψ
HB
Te
E
Ψ
Fi
gu
re
1.
C
o
m
p
l
e
t
e
st
ruct
ure
of
DTC
-
Hy
st
er
esi
s
B
a
sed
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 5
,
No
. 3
,
Febru
a
r
y
20
15
:
441
–
4
52
44
4
Table 1. Look-up table
3.
CASCADED H-BRIDGE MULTI
LEVE
L
IN
VERTE
R
(
C
H
M
I
)
C
H
M
I
is one
of t
h
e popul
ar power ci
rcuit t
opol
ogi
es used i
n
hi
gh-power
m
e
d
i
u
m
vol
t
a
ge. These
nam
e
s were given because, it uses
m
u
ltiple
units of power
cells connected
in a ser
i
es
to
operate in
m
e
d
i
u
m
or
hi
gh vol
t
a
ge as well
as
t
o
generat
e
l
o
wer har
m
oni
c r
i
ppl
e. A few i
s
ol
at
ed DC
sources are requi
red for t
h
i
s
i
nvert
er
t
o
sy
nthesi
ze an out
p
u
t
vol
tage wav
e
for
m
. The st
r
u
ct
ure of t
h
i
s
invert
er is sho
w
n i
n
Fi
gure 4
,
whi
c
h
each phase consists of two
H-Bridge. Each cell has
single DC-link source to fe
d the induction
m
o
to
r with
connect
ed i
ndi
vi
duall
y
.
So, for t
h
ree phases
m
o
t
o
r requi
r
e
d t
h
ree isol
ated DC
-l
i
nks. Four swi
t
c
hes off t
h
e
device (Sa+, S
a
-, Sb+ and Sb-) are op
erating when they receive
the sig
n
al fro
m
the gate drives.
B
y
f
o
u
r
swi
t
c
hes
of t
h
e
i
nve
rt
er t
o
t
r
i
gge
r, ca
n
pr
o
d
u
ce t
h
ree
di
scr
e
t
e
out
put
Vab
wi
t
h
t
h
e l
e
vel
+V
dc
f
o
r
(S
1 a
nd
S4
switch
is ON),
-V
dc
f
o
r ( S
2
and S
3
swi
t
c
h i
s
ON
) an
d 0
V
fo
r (al
l
swi
t
c
h OFF
)
. T
h
e n
u
m
ber of vol
t
a
g
e
l
e
vel
,
L f
o
r
C
H
M
I
c
a
n
be
defi
ned
by
L=
2m
+1, whe
r
e m
,
fo
r
num
bers
o
f
H-
bri
dge
cel
l
pe
r
p
h
ases.
F
o
r
a
3
-
l
e
vel
C
H
M
I
,
t
h
e
v
o
l
t
a
ge vect
or
ca
n
ge
nerat
e
3
=
27
di
ffe
re
nt
v
o
l
t
a
ge vect
ors
an
d
3L
(L -
1)
+1=
19
vol
t
a
ge
vect
o
r
s p
r
act
i
ces use
d
i
n
C
H
M
I
t
o
p
o
l
o
gy
. F
i
gu
re 5 s
h
ows t
h
e v
o
l
t
a
ge
vect
or a
v
ai
l
a
bl
e as
sho
w
n i
n
C
H
M
I
o
n
a d
-
q
ax
is
. It
can
b
e
seen
that, th
e ou
ter hex
a
gon
wh
ich
co
n
t
ains 12
voltag
e
v
ectors
with
sing
le switch
i
ng
st
at
e com
b
i
n
at
i
on,
w
h
i
l
e
f
o
r
i
nne
r
he
xag
o
n
whi
c
h c
ont
ai
ns
6
vol
t
a
g
e
vect
o
r
s a
r
e
pr
o
d
u
ced
wi
t
h
t
w
o
co
m
b
in
atio
n
switch
i
ng
state. Th
erefo
r
e,
when
in
crease
t
h
e lev
e
l of m
u
ltil
ev
el inv
e
rter,
m
o
re v
o
ltag
e
vecto
r
s
will b
e
p
r
odu
ced
.
So
th
at, th
e v
o
ltag
e
v
ect
o
r
s can
b
e
catego
r
ized
in
th
ree co
nd
itio
ns (i.e: lo
w sp
eed
,
m
e
d
i
u
m
and
hi
gh
) acc
o
r
di
ng
t
h
e s
p
ee
dy
o
p
e
r
at
i
o
n
.
As a
res
u
l
t
,
the to
tal nu
m
b
er of switch
i
ng s
t
ate becom
e
increas
e
,
an
d it offered th
e m
a
n
y
p
o
ssib
ilities to
i
m
p
r
o
v
e
con
t
ro
l strateg
i
es of i
n
d
u
ctio
n
m
o
to
r.
Stator flux
erro
r
s
t
atu
s
,
Ψ
s
+
Tor
que
erro
r
status,
T
stat
S
ec
I
S
ec
II
S
ec
III
S
ec
IV
S
ec
V
S
ec
VI
1
1
[10
0
]
[11
0
]
[01
0
]
[01
1
]
[00
1
]
[10
1
]
0
[00
0
]
[11
1
]
[11
1
]
[00
0
]
[00
0
]
[11
1
]
-1
[
0
01
]
[
1
01
] [
1
00
]
[
1
10
] [
0
10
] [
0
11
]
0
1
[11
0
]
[01
0
]
[01
1
]
[00
1
]
[10
1
]
[10
0
]
0
[11
1
]
[00
0
]
[00
0
]
[11
1
]
[11
1
]
[00
0
]
-1
[
0
11
]
[
0
01
] [
1
01
]
[
1
00
] [
1
10
] [
1
01
]
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Im
pr
oved
T
o
rq
ue C
ont
r
o
l
Per
f
orm
a
n
ce i
n
Di
rect
Tor
q
ue C
o
nt
rol
usi
n
g …
(
M
u
h
d
Zh
ari
f
R
i
f
q
i
Zu
ber A
h
m
adi
)
44
5
4.
PR
OPOSED
SWITCHING
STRA
TEGY
In t
h
e
pr
op
ose
d
st
rat
e
gy
, a
n
e
w bl
oc
k m
odi
fi
cat
i
on
of t
o
r
que
er
ro
r st
at
u
s
i
s
i
n
t
r
od
uce
d
i
n
t
h
e
DTC
st
ruct
u
r
e
by
i
m
pl
em
ent
i
ng t
h
e
C
H
M
I
t
o
p
o
l
o
gy
, i
s
cal
l
e
d “
O
pt
i
m
u
m
St
atus
Det
ect
i
on
o
r
O
S
D”
. T
h
i
s
bl
oc
k i
s
resp
o
n
si
bl
e t
o
m
odi
fy
t
h
e t
o
r
q
ue er
ro
r st
at
us
), w
h
i
c
h pr
o
duces ne
w
t
o
rq
ue
st
at
u
s
,
)
fo
r
sel
ect
i
ng t
h
e o
p
t
i
m
u
m
swi
t
c
hi
ng vect
ors
.
Fi
gu
re 6 s
hows th
e co
m
p
lete s
t
ru
ctur
e o
f
th
e DTC-CHMI
with
i
n
cl
usi
o
n o
f
O
S
D bl
o
c
k
(
g
ray
col
o
r
)
. Fr
om
the fi
g
u
re
,
i
t
ca
n
be
noticed t
h
at, som
e
different
parts a
s
c
o
m
p
ared
wi
t
h
t
h
e DTC
con
v
e
n
t
i
onal
.
These i
n
cl
ude
t
h
e defi
ni
t
i
on
of t
h
e st
at
o
r
fl
ux
pl
ane
,
cal
cu
l
a
t
i
on of
v
o
l
t
a
ge p
h
ase
fo
r
d a
n
d
q c
o
m
ponent
,
an
d
m
odi
fi
ed t
h
e
l
o
o
k
-
u
p
-t
a
b
l
e
f
o
r
DTC
-
C
H
M
I
. T
h
e
fol
l
o
wi
n
g
s
u
bsect
i
o
n
s
di
scus
s
t
h
e f
u
nct
i
ons
o
r
e
quat
i
o
ns
use
d
t
o
m
odel
t
h
e
part
s.
Fi
gu
re
6
St
r
u
ct
ure
of
D
T
C
-
hy
st
eresi
s
base
d i
n
d
u
ct
i
o
n
m
a
chi
n
e
wi
t
h
t
h
e
pr
o
pose
d
m
odi
fi
cat
i
on
of
flu
x
er
r
o
r
statu
s
T
e,ref
Ψ
s,
r
e
f
M
odi
fic
a
tion of
tor
que
e
rro
r
statu
s
L
ook
-u
p
Tab
l
e
+
I.M
S
a
, S
b
, S
c
, S
d
, S
e
, S
f
Ψ
sd
-
+
-
T
e
Ψ
s
σ
T
i
b
i
c
i
a
Ψ
sq
v
sd
v
sq
i
sd
i
sq
-
3-L
e
ve
l
Hys
t
er
es
i
s
C
ontr
o
lle
r
E
Ψ
E
T
χ
σ
Ψ
2-L
e
ve
l
Hys
t
er
es
i
s
C
ontr
o
lle
r
S
ect
o
r
de
te
c
tion
d-q c
u
rre
nt
cal
cu
l
a
t
i
o
n
Volta
ge
c
a
lc
ula
tion
Sta
t
or flu
x
an
d
el
ect
r
o
m
a
g
n
e
t
i
c
t
o
r
q
u
e
es
t
i
m
at
o
r
s
3-L
e
ve
l
CHMI
σ
T
+
Figure 4. 3-Level CHMI conn
ected to
3-phase in
duction
m
achine.
N
V
DC
V
DC
V
DC
S
a1
+
S
a1
-
S
a2
+
S
a2
-
S
b1
+
S
b1
-
S
b2
+
S
b2
-
S
c1
+
S
c1
-
S
c2
+
S
c2
-
Induction
M
achine
Figure 5.
Vol
t
a
ge vect
o
r
gene
rat
e
d by
t
h
e
3
-
l
e
vel
C
H
M
I
on
d
-
q pl
ane.
(10
100
1)
(00
100
1)
(01
100
1)
(01
100
0)
(
0
11
01
0
)
(01
001
0)
(
0
10
11
0
)
(00
011
0)
(10
011
0)
(10
010
0)
(10
010
1)
(10
000
1)
(
1
01
00
0)
(
0
00
00
1)
(1
000
00
)
(00
010
1)
(
0
00
10
0)
(1
00
010
)
(0
00
01
0)
(010
10
0)
(
0
10
00
0
)
(
0
01
01
0
)
(001
00
0)
(0
10
00
1)
(10
101
0)
(0
00
000
)
(0
10
101
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
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:
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Vo
l. 5
,
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. 3
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a
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441
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44
6
(i)
Definiti
on
o
f
s
ector
flu
x
pl
a
n
e
A secto
r
d
e
fi
n
itio
n
of stato
r
fl
u
x
p
l
an
e in
pro
p
o
s
ed
m
e
th
o
d
is sp
lit
in
to
two
d
i
fferen
t sequ
en
ces and
angle bet
w
een sectors is
m
a
intained to 60 degree
s.
It is because, in i
m
ple
m
enting the CHMI topology
pr
o
duces
m
o
re v
o
l
t
a
ge
vect
o
r
an
d t
h
e
num
ber
of
swi
t
c
hi
ng state als
o
increases. Figure
7. is s
h
owing
a two
di
ffe
re
nt
de
fi
ni
t
i
on o
f
t
h
e st
at
or
fl
u
x
pl
a
n
e t
o
ap
pl
y
i
n
t
h
i
s
researc
h
.
Fi
g
u
r
e 7
(
i
)
i
s
s
h
o
w
n t
h
e
defi
ni
t
i
on o
f
st
at
or
fl
u
x
pl
ane f
o
r m
i
ddl
e spee
d o
p
e
r
at
i
o
n.
In
t
h
i
s
case
,
t
h
e m
i
ddl
e v
o
l
t
a
ge vect
o
r
a
m
pli
t
ude i
s
c
h
ose
n
t
o
increase a
n
d decrease the
flux.
While
for low and
high s
p
e
e
d, t
h
e sect
o
r
defi
ni
t
i
on
of t
h
e st
at
or
fl
u
x
pl
ane a
s
in
Fig
u
re 7
(ii) is u
s
ed
eith
er t
o
increas
e or
decrease flux. T
h
e thres
h
old
va
l
u
e fo
r b
o
t
h
of
t
h
e defi
ni
t
i
on s
t
at
or
fl
u
x
pl
ane
ca
n be det
e
rm
i
n
ed usi
n
g
t
h
i
s
eq
ua
t
i
on;
,
if
σ
T
+
= 0, 1 or
3
,
if
σ
T
+
= 2
(1)
(ii)
Calcul
ati
o
n
of d
and
q c
o
mp
onen
t
B
y
applyi
ng t
h
i
s
t
opol
ogy;
t
h
e vol
t
a
ge co
m
p
onent
can be o
b
t
a
i
n
ed fro
m
t
h
e swi
t
chi
ng patt
ern of t
h
e
3-phase vol
t
a
ge source i
nverter as fol
l
o
ws
V
d
=
V
dc
3
2S
a1
-2
S
a2
-S
b1
+S
b2
-S
c1
+S
c2
(2
)
V
q
=
V
dc
√
3
S
b1
-S
b2
-S
c1
+S
c2
(3
)
(iii)
Mo
dified L
o
o
k
-U
p-T
a
ble
As a sh
o
w
n t
h
e pre
v
i
o
us sect
i
on, l
o
o
k
up t
a
bl
e i
s
an i
m
port
a
nt
pa
rt
i
n
D
T
C
dri
v
e
s
. I
n
t
h
e l
o
ok
-u
p
-
tab
l
e h
a
v
e
th
ree co
nd
ition
s
mu
st b
e
satisfied to
choo
se
th
e
ap
pro
p
riate switch
i
n
g
state, i.e. to
rqu
e
statu
s
, flux
st
at
us and sect
or
. In l
o
ok
-
up
t
a
bl
e wi
t
h
a pr
op
ose
d
st
ru
ct
ure co
nsist o
f
vo
ltag
e
v
ectors
with three di
fference
am
pl
i
t
udes,
(i
.
e
. Sh
o
r
t
,
m
e
dium
and l
o
n
g
)
.
The sel
ect
i
o
n
of
v
o
l
t
a
ge ve
ct
ors
depe
n
d
s
on t
h
e t
o
rq
ue
err
o
r
statu
s
. Fo
r ex
am
p
l
e, wh
en the h
i
gh
sp
eed
co
nd
itio
n m
o
d
e
, th
e torqu
e
erro
r
statu
s
is sel
ected
3 to
i
n
d
i
cate is
h
i
gh
sp
eed as
w
e
ll as is choosin
g
t
h
e long
est v
o
ltag
e
v
ect
or
. Fo
r th
e m
e
d
i
u
m
sp
eed
, t
h
e
to
rq
u
e
er
ror
is
selec
t
t
h
e st
at
us
2
i
s
s
h
o
w
n t
h
e m
o
t
o
r i
n
m
i
ddl
e spe
e
d m
ode.
Fi
nal
l
y
,
at
l
o
w
s
p
ee
d
op
erat
i
o
n,
t
h
e sh
ort
e
st
am
pli
t
u
d
e
vol
t
a
ge
v
ect
or
i
s
sel
ect
ed. T
h
e l
a
bel
i
n
g t
h
e
vol
t
a
ge
v
ect
or
base
d
on
t
h
e
s
p
eed
o
p
e
r
at
i
o
n
as s
h
o
w
n i
n
F
i
gu
re
9
and
Ta
bl
e I
I
s
h
ows
t
h
e
l
o
ok
-u
p t
a
bl
e
o
f
DTC
wi
t
h
p
r
o
p
o
sed
st
ruct
ure
an
d s
t
rat
e
gy
.
I
II
III
IV
V
VI
d
Ψ
sq,1
V
IV
III
II
I
VI
d
Ψ
sd,1
(i
i)
For
mid
d
l
e sp
eed
co
nd
itio
n
(i) For low an
d h
i
g
h
sp
eed
co
nd
ition
s
Fig
u
re 7
.
Differen
c
e
sector defin
itio
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
Im
pr
oved
T
o
rq
ue C
ont
r
o
l
Per
f
orm
a
n
ce i
n
Di
rect
Tor
q
ue C
o
nt
rol
usi
n
g …
(
M
u
h
d
Zh
ari
f
R
i
f
q
i
Zu
ber A
h
m
adi
)
44
7
Tabl
e
2. T
h
e
L
o
o
k
-
U
p
Ta
bl
e
For
D
T
C
dri
v
e
s
by
a
p
pl
i
e
d
Stator flux
erro
r
status,
Ψ
s
+
Tor
que
erro
r
status, T
stat
S
ector
I
S
ector
II
S
ector
III
S
ector
IV
S
ector
V
S
ector
VI
1
3
vsL,2
vsL,3
vsL,4
vsL,5
vsL,6
vsL,1
2 vsM,6
vsM,5
vsM,4
vsM,
3 vsM,
2 vsM,
1
1 vsS,2
vsS,3
vsS,4
vsS,5 vsS,6 vsS,1
0
vsZ,0
vsZ,0
vsZ,0
vsZ,0
vsZ,0
vsZ,0
-1 vsS,6
vsS,1
vsS,
2 vsS,3 vsS,4 vsS,5
-2
vsM,
4 vsM,
3
vsM,
2 vsM,
1 vsM,
6 vsM,
5
-3 vsL,6
vsL,1
vsL,
2 v
s
L
,
3 v
s
L
,
4 v
s
L
,
5
0
3
vsL,3
vsL,4
vsL,5
vsL,6
vsL,1
vsL,2
2 vsM,1
vsM,6
vsM,5
vsM,
4 vsM,
3 vsM,
2
1 vsS,3
vsS,4
vsS,5
vsS,6 vsS,1 vsS,2
0
vsZ,0
vsZ,0
vsZ,0
vsZ,0
vsZ,0
vsZ,0
-1 vsS,5
vsS,6
vsS,
1 vsS,2 vsS,3 vsS,4
-2
vsM,
3 vsM,
2
vsM,
1 vsM,
6 vsM,
5 vsM,
4
-3 vsL,5
vsL,6
vsL,
1 v
s
L
,
2 v
s
L
,
3 v
s
L
,
4
A desc
ri
pt
i
o
n of t
h
e o
p
t
i
m
al
sel
ect
i
on base
d
on t
h
e o
p
erat
i
ng s
p
eed i
s
det
e
rm
i
n
ed from
the be
havi
or
o
f
error statu
s
(flux
an
d to
rqu
e
) an
d to
rqu
e
error as fo
llo
ws:
1)
Sel
ect
i
on o
f
t
h
e l
o
n
g
est
v
o
l
t
a
ge vect
or
ha
pp
ened
, w
h
e
n
t
h
e swi
t
c
hi
n
g
f
r
e
que
ncy
o
f
t
o
rq
ue st
at
us i
s
l
e
s
s
t
h
an t
h
e s
w
i
t
c
h
i
ng
fl
u
x
st
at
u
s
(Tst
at
< Fst
a
t
)
du
ri
n
g
t
h
e t
o
rq
ue
dem
a
nds
or
hi
g
h
s
p
ee
d
ope
rat
i
o
n
.
2)
Selection of the
m
e
diu
m
of the vector
is activ
e wh
en
th
e switch
i
ng
frequ
en
cy of to
rq
ue statu
s
is sl
ig
h
tly
hi
g
h
er
t
h
a
n
t
h
a
t
of
fl
u
x
st
at
us.
3)
The sh
ort
e
st
a
m
pli
t
ude vol
t
a
ge vect
o
r
i
s
ch
ose
n
whe
n
t
h
e
swi
t
c
hi
ng
fre
q
u
ency
o
f
t
o
r
q
u
e
st
at
us i
s
hi
gh
er
t
h
at
fl
u
x
st
at
u
s
(Tst
at
>
Fst
a
t
)
. T
h
i
s
case
o
ccur
r
i
n
g
d
u
ri
n
g
at
l
o
w
spee
d
ope
rat
i
o
n a
n
d
negat
i
ve t
o
r
q
u
e
dem
a
nd
.
5.
E
X
PERI
MEN
T
AL SETUP
Th
e
feasib
ility o
f
t
h
e
D
T
C of
i
m
p
l
e
m
en
tin
g
CH
MI topo
logy in
red
u
c
ed
the to
rq
u
e
ripp
le o
u
t
pu
t and
con
s
t
a
nt
swi
t
c
hi
n
g
f
r
eq
ue
ncy
has bee
n
real
i
zed wi
t
h
a
com
p
le
te d
r
iv
e syste
m
. In
th
e ex
p
e
rim
e
n
t
al t
e
st, th
e
p
r
op
o
s
ed
algo
rith
m
sw
itch
i
n
g
str
a
teg
y
h
a
s co
ndu
cted
b
y
dSPA
CE
d
s
1104
. To
in
ter
f
ace in
r
eal ti
me b
e
tw
een
har
d
ware a
nd
soft
ware sy
st
e
m
,
t
h
e C
ont
r
o
l
Desk
has
bee
n
p
r
o
v
i
d
ed i
n
or
der t
o
easi
l
y
cont
rol
t
h
e
par
a
m
e
t
e
r.
(
1
01
00
1)
(
0
11
00
1)
(
0
11
00
0
(
0
11
01
0)
(
0
10
01
0)
(
0
10
11
0)
(
00
01
10
)
(
10
01
10
)
(
1
00
10
0)
(
1
00
10
1)
(
1
00
00
1)
(vs
S
,3)
(
0
00
00
1
)
(
1
00
00
0
)
(vs
S
,2)
(
0
00
10
(
vs
S
,
1
)
(
0
00
01
0
(vs
S
,6)
(
0
10
00
0
(vs
S
,5)
(
0
01
00
0
)
(vs
S
,4)
(
1
01
01
0)
(
0
00
00
0)
(
0
10
10
1)
vsL
,
vsL
,
vsL
,
5
vsL
,
6
vsL
,
1
vsL
,
2
vsM,
3
vsM,
4
(
0
01
00
1)
vsM,
5
vsM,
6
vsM,
1
vsM,
2
vsS
,
vsS
,
vsS
,
vsS
,
vsS
,
vsS
,
vs
Z
,
0
Fi
gu
re
9.
V
o
l
t
a
ge
Vect
o
r
a
v
ai
l
a
bl
e i
n
C
H
M
I
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 5
,
No
. 3
,
Febru
a
r
y
20
15
:
441
–
4
52
44
8
The co
nt
r
o
l
Desk a
ppl
i
cat
i
on i
s
very
f
r
i
e
ndl
y
use
r
t
o
confi
g
u
r
e t
h
e
l
a
y
out
experi
m
e
nt
t
o
m
oni
t
o
r t
h
e
expe
ri
m
e
nt
al
r
e
sul
t
.
Fo
r FP
GA
de
vi
ce, t
h
e al
gori
t
hm
blanki
ng t
i
m
es for
3-l
e
vel
C
H
M
I
i
s
const
r
u
c
t
e
d i
n
pr
o
p
er f
o
r p
r
e
v
ent
i
n
g t
h
e sh
ort
ci
rcui
t
at
powe
r
de
vi
ce
circu
it (IGBT). Th
is d
e
v
i
ce is
respon
sib
l
e to
ach
ieve
th
e propo
sed
strateg
y
in
sm
o
o
th
and
successfu
l
. Th
e sam
p
li
n
g
p
e
riod
in
this syste
m
is set
5
0
u
s
with
same th
e
sim
u
l
a
t
i
on sa
m
p
li
ng t
i
m
e. Fi
gu
re 1
0
sh
ow
s t
h
e c
o
m
p
l
e
t
e
har
d
ware
set
u
p
has
been
d
o
n
e. T
h
ree
uni
t
s
o
f
t
h
e
DC-Li
n
k
is set 1
2
0
V fo
r testin
g
DTC-C
H
MI an
d
fo
r
DTC co
nv
en
tional in
v
e
rter is set 2
4
0
V. Th
e m
o
to
r
p
a
ram
e
ters are d
e
term
in
ed
b
a
sed
on
th
e
b
l
ock
e
d
ro
to
r and n
o
l
o
ad
test.
Th
e m
o
to
r p
a
ra
m
e
ter as tab
u
lated
in
Tab
l
e
III.
In the exp
e
rim
e
n
t
, in
du
ction
m
o
tor is cou
p
l
ed
to a DC
m
o
to
r as a lo
ad
. To
co
n
t
ro
l t
h
e lo
ad is by
ap
p
l
ying
th
e
vo
ltag
e
supp
ly at th
e arm
a
tu
re wind
ing
in
the DC m
o
to
r. Th
e DC m
o
to
r
was m
a
n
u
f
actured
b
y
LO
REN
Z
O
and
th
e pow
er r
a
t
i
n
g
is 1.1kW
.
Figure 10. Co
m
p
lete experi
m
e
n
t
al setup
T
a
b
l
e
3
.
M
o
tor
param
e
ters
I
n
du
ction
motor p
a
ramet
ers
Rated
power, P
1.1 kW
Rated
voltage,
V
s
380
V
Ra
ted
curr
ent,
i
s,rated
2.7
A
Ra
ted
s
p
eed
,
ω
m
2800
rpm
S
t
a
t
or r
e
s
i
s
t
anc
e
,
R
s
6.1
Ω
Rotor re
sista
n
ce
,
R
r
4.51
Ω
S
t
a
t
or s
e
lf indu
ctan
ce
,
L
s
306.5
mH
Rotor
s
e
lf
indu
ctan
ce
,
L
r
306.5
mH
Mutual
inductance,
L
m
291.9
mH
Combined
iner
tia, J
0.0565 kg-m
2
Combined
viscous friction, B
0.0245 N.m.s
Number of
pole pairs,
P
2
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
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S
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208
8-8
6
9
4
Im
pr
oved
T
o
rq
ue C
ont
r
o
l
Per
f
orm
a
n
ce i
n
Di
rect
Tor
q
ue C
o
nt
rol
usi
n
g …
(
M
u
h
d
Zh
ari
f
R
i
f
q
i
Zu
ber A
h
m
adi
)
44
9
6.
IMPLEME
N
TATION AND E
X
PE
RIMENTAL
RESULTS
These sect
i
o
n
s
prese
n
t
t
h
e expe
ri
m
e
nt
al resul
t
s
of si
gni
fi
cant
im
provem
e
nt
by
usi
n
g C
H
M
I
con
f
i
g
urat
i
o
n
.
B
e
fo
re t
o
t
h
e al
go
ri
t
h
m
conduct
e
d at
har
d
ware t
e
st
i
n
g, t
h
e si
m
u
l
a
ti
on has bee
n
si
m
u
l
a
t
e
d t
o
m
a
ke sure t
h
e
pr
o
pose
d
st
rat
e
gy
can achi
e
v
e
t
h
e excel
l
e
nt
perf
o
r
m
a
nce
of DTC
dri
v
e
s
vi
a C
H
M
I
. M
a
t
l
a
b
R
2
0
1
1
a ve
rsi
o
n i
s
use
d
as a
t
ool
t
o
c
o
n
f
i
r
m
t
h
at
a st
rategy
. T
h
en
, t
h
e
pr
op
ose
d
s
w
i
t
c
hi
ng
st
rat
e
gy
wa
s
v
e
rified
through
ex
p
e
rim
e
n
t
al
test. So
m
e
test co
nd
iti
o
n
s
were cond
u
c
ted
o
n
D
T
C
-
driv
es con
t
ro
l sch
e
mes to
eval
uat
e
t
h
e p
e
rf
orm
a
nces. The t
w
o di
f
f
e
rent
t
o
pol
ogi
es of i
n
vert
er
and co
nt
r
o
l
schem
e
used in t
h
es
e
ev
alu
a
tion
s
are con
d
u
c
ted as
fo
llo
ws;
i.
C
ont
r
o
l
of
DT
C
-
Hy
st
eresi
s
b
a
sed o
n
th
e 2-lev
e
l conv
en
ti
on
al inv
e
rter.
ii.
C
ont
r
o
l
of
DT
C
base
d
on
t
h
e
3
-
l
e
vel
C
H
M
I
usi
n
g
pr
o
p
o
s
ed
swi
t
c
hi
ng
st
rat
e
gy
.
Each
test was
p
e
rform
e
d
u
nder th
e sam
e
co
nd
itio
n in
o
r
d
e
r t
o
h
a
v
e
fair co
m
p
arison
s for
b
o
t
h
of inv
e
rter
to
po
log
y
as tabu
lated
in Tab
l
e 4
.
Tabl
e 4.
Co
m
p
a
r
ison
be
tw
e
e
n t
h
e c
o
n
v
e
n
ti
on
al
a
nd pr
op
o
s
e
d
m
e
tho
d
Control
Paramet
ers
Inverter topology
(a)
2-Level
Conventional
I
n
verter
(c) 3-
Level
CHMI
T
o
r
que
ref
e
ren
ce
Change
Low to High
0.7 Nm – 2
.
5 N
m
High to
Low
2.5 Nm – 0
.
7 N
m
Sam
p
ling tim
e,
T
s
50
µs
Torque h
y
s
t
eres
i
s
bandwidth, HB
T
0.36 Nm
Flux h
y
steresis b
a
ndwidth,
HB
i
0.02 Wb
Torque lim
it
,
4 Nm
The t
o
r
q
u
e
,
fl
ux
,
vol
t
a
g
e
ph
ases an
d
cu
rre
nt
wa
ve
fo
rm
resul
t
f
o
r
b
o
t
h
o
f
i
n
ve
rt
er t
o
pol
ogy
a
r
e
sho
w
n i
n
Fi
g
u
r
e 11
. Tw
o di
ffe
rent
re
fere
n
ces of t
o
r
q
ue have
been a
p
p
l
i
e
d for
bot
h of t
h
e i
n
vert
er
. The
si
gni
fi
ca
nt
i
m
pr
o
v
em
ent
i
n
t
e
rm
t
o
rque
ri
ppl
e a
n
d s
w
i
t
c
hi
n
g
pat
t
e
rn
can
be
obt
ai
n
e
d
by
ap
pl
y
i
n
g
t
h
e
pr
o
pose
d
s
w
i
t
c
hi
n
g
st
rat
e
gy
.
A st
ep
ch
an
ge
of
re
fere
nce t
o
rq
ue
(T
re
f
) was
ap
pl
i
e
d fr
om
0.
7 Nm
t
o
2.
5 Nm
at
t=0
.
4s as sh
own
in
Fi
g
u
re
1
1
(i) and
(iii) and 2
.
5
N
m
to
0
.
7Nm
as sh
o
w
n
i
n
Figure 11
(ii) an
d
(iv) fo
r
bo
th
o
f
th
e inv
e
rter .
In in
itially, th
e stato
r
fl
u
x
an
gu
lar v
e
l
o
city as well as
m
o
to
r sp
eed
i
s
slower. So
,
in
th
is
co
nd
itio
n, th
e t
o
rqu
e
error statu
s
is selected
b
e
tween
S
t
=0 a
nd S
t
=1
in
o
r
der to
choo
se the lo
wer am
p
lit
u
d
e
of
vol
t
a
ge vect
or.
W
h
e
n
t
h
e
t
o
r
que refe
re
nce sud
d
e
n
l
y
cha
n
g
e
d
t
o
2.5Nm
,
it can
b
e
seen th
at, th
e torque erro
r
status S
t
=2 m
o
m
e
nt
ari
l
y
for
v
e
ry
sh
ort
of t
i
m
e respo
n
se
d
u
ri
ng t
o
r
que t
r
ansi
ent
was oc
cur
r
i
n
g. T
h
i
s
i
s
sh
o
w
t
h
at
, w
h
e
n
hav
e
a ne
w
dem
a
nd, t
h
e l
o
n
g
est
a
m
pli
t
ude v
o
l
t
a
ge
vect
o
r
i
s
a
p
pl
i
e
d t
o
p
r
o
d
u
c
e
t
h
e fa
st
er
dy
nam
i
c
to
rq
u
e
respon
se to
in
crease.
Based
on
th
e ob
serv
ation
of
th
e exp
e
rim
e
n
t
al resu
lts, it
can be seen that when the
t
o
r
que
refe
re
n
ce cha
nge t
o
l
o
we
r t
h
e m
a
gni
t
ude
, s
u
d
d
enly th
e n
e
g
a
tive lo
ng
est rev
e
rse vo
ltag
e
is
ch
osen.
That m
eans, the torque e
r
ror
status is selected S
t
=-
3 i
n
or
der t
o
q
u
i
c
k re
spo
n
se t
o
reac
h t
h
e dem
a
nd
of t
h
e
m
o
t
o
r. The
r
ef
o
r
e, i
t
sh
ow
s t
h
e
t
o
r
que e
r
r
o
r
st
at
us St
g
r
ad
ual
l
y
change
s f
r
o
m
S
T
=3
↔
2 t
o
S
T
=2
↔
1 a
nd
fi
nal
l
y
to
S
T
=1
↔
0
f
o
r dec
r
easi
n
g t
h
e
out
put
v
o
l
t
a
ge i
n
sat
i
s
fy
i
n
g
t
h
e t
o
r
que
dem
a
nd as t
h
e
st
at
or
fl
u
x
a
n
gul
a
r
vel
o
ci
t
y
red
u
c
e
. The e
ffect
s
of t
o
r
que
ri
p
p
l
e
an
d swi
t
c
hi
n
g
f
r
eq
ue
nc
y
by
appl
y
i
n
g
pr
op
ose
d
s
w
i
t
c
hi
ng
strategy ca
n
be clearly seen in t
h
e m
a
gnified im
ag
e o
f
Fig
u
r
e
12
. By
ob
serv
i
n
g th
e pr
opo
sed sw
itch
i
ng
strateg
y
, it can
be seen
th
at
, th
e
wav
e
fo
rm
fo
r vo
ltag
e
p
h
a
se is to
sho
w
t
h
e leng
th
o
f
sl
o
p
e wh
en to
rq
u
e
referen
ce is
app
lied
.
Th
is is i
n
d
i
cated th
e l
o
n
g
e
st vo
lta
ge
vect
o
r
i
s
ch
ose
n
w
h
e
n
s
u
d
d
e
n
l
y
t
o
r
que
re
fe
rence
ch
ang
e
d
eith
er for forward
o
r
rev
e
rse
con
d
itio
n
op
eratio
n.
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I
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:
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94
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Vo
l. 5
,
No
. 3
,
Febru
a
r
y
20
15
:
441
–
4
52
45
0
(b)
Pr
op
osed s
t
ra
teg
y
(a
)
Co
nve
n
ti
onal
i
n
verter
(i)
(ii)
(iii)
(iv)
Tref
=
0.
7Nm
t
o
2.
5Nm
Tref
=
2.
5Nm
t
o
0.
7Nm
vd
Ia
Ia
vd
vd
Ia
Ia
vd
Figure 11. Experi
m
e
nt
al result for torque referecene wa
s applie
d for condition
Te
Te
Te
Te
Evaluation Warning : The document was created with Spire.PDF for Python.