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
. 32
8~
33
9
I
S
SN
: 208
8-8
6
9
4
3
28
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
Enhanced Torque Control and
Reduced Switching Frequency
in Direct Torque Control Utiliz
ing Optimal Switching Strategy
for Dual-Inverter Supplied Drive
M. Kh
airi
R
a
him
1
, Auz
a
ni
Jidin
2
, T
o
le S
u
tikn
o
3
1,2
F
acult
y
of
Ele
c
tri
cal
Eng
i
neer
i
ng, Univers
i
ti
Te
knikal Malay
s
ia
Melaka (U
Te
M),
Me
la
ka,
Malaysia
3
Department of Electrical
Eng
i
n
eering
,
Univ
er
sitas Ahmad Dahlan (UAD), Yog
y
akarta, Indon
esia
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Dec 24, 2015
Rev
i
sed
Ap
r
20
, 20
15
Accepte
d
May 3, 2016
Direct Torque
Control (DTC)
of
induction
machine h
a
s receiv
e
d wid
e
acc
eptan
c
e
in m
a
n
y
adjus
t
abl
e
s
p
eed driv
e app
l
i
cat
ions
due to
it
s
s
i
m
p
lic
i
t
y
and high perfor
m
ance torque control.
However
,
the DTC using
a common
two-leve
l inv
e
rt
er poses two
m
a
jo
r problems such as h
i
gher switchin
g
frequency
(or po
wer loss) and larger torque ripple. These problem
s are due to
inappropriate vo
ltag
e
vectors which
are selected
among a limited
number of
voltag
e
vectors available
in two-level
i
nver
t
er
. Th
e proposed res
e
arch aims to
formulate
an optimal switching
strate
g
y
using D
u
al-Inver
t
er Sup
p
lied Driv
e
for high performances of DTC. B
y
usi
ng dual-inverter supplied, it provides
greater number of voltage vecto
r
s which
can offer m
o
re options to selec
t
the
most appropriate voltage
ve
ct
or
s.
T
h
e mo
st
a
p
p
r
opriate voltage vectors
should able to pr
oduce minimum torque sl
op
e but sufficient to
satisf
y
torq
u
e
dem
a
nds. The
id
entifi
c
a
tion is
ac
com
p
lishe
d b
y
u
s
ing an equation
of rate of
change of to
rque which is derived
from the induction machin
e eq
uations.
The
proposed strateg
y
also introduces a bl
ock of modification of torque error
status which is responsible to modif
y
th
e status su
ch that it can d
e
termine the
m
o
st optim
al voltag
e
ve
ctors f
r
om
a look-up
tabl
e,
accord
ing
to m
o
tor
operating cond
itions. Th
e imp
r
oveme
nts obtained are
as f
o
llows; 1)
minimization of
switching fr
equency
(re
du
ce pow
er loss),
and 2) r
e
duction of
torque ripple. S
o
me improveme
nts obtai
ned in
the proposed strateg
y
wer
e
verifi
ed vi
a
e
xperimentations.
Keyword:
Di
rect
t
o
rq
ue
c
ont
rol
D
u
al
-
i
nv
er
ter su
pp
lied
I
ndu
ctio
n m
a
c
h
in
es
Mu
ltilev
e
l in
v
e
rter
Ope
n
-en
d
win
d
in
g
in
ve
rter
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
s:
Auza
ni
Ji
di
n
Facu
lty of Electrical Eng
i
n
eerin
g
,
Un
iv
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: au
zan
i@u
t
em
.ed
u
.
m
y
To
le Su
tikn
o
Depa
rt
m
e
nt
of
El
ect
ri
cal
Engi
neeri
n
g
,
Fac
u
l
t
y
of
I
n
d
u
st
ri
al
Tech
nol
ogy
,
U
n
i
v
e
r
si
t
a
s A
h
m
a
d
Dahl
a
n
UA
D 3r
d
C
a
m
pus
,
Ja
nt
u
r
a
n
, Um
bul
har
j
o, Y
ogy
a
k
art
a
5
5
1
6
4
,
In
d
onesi
a
Em
a
il: to
le@ee.u
a
d
.
ac.i
d
1.
INTRODUCTION
No
wa
day
s
, t
h
e
t
y
pe o
f
AC
m
o
t
o
r w
h
i
c
h i
s
k
n
o
w
n
t
o
of
fer l
o
w
m
a
i
n
tenance
,
ru
g
g
e
d
a
n
d
hi
gh
-
efficiency, is
pre
f
era
b
le for
many
in
du
stri
al ap
p
lication
s
. Sin
c
e 197
0’s,
seve
ral
vector control techniques
were pro
p
o
s
ed wh
ich
m
a
in
ly
ai
m to
p
r
ov
id
e ex
cellen
t
dyn
amic co
n
t
rol p
e
rfo
r
m
a
n
ce, co
m
p
arab
le to
th
at
o
b
t
ain
e
d
in
DC
m
o
to
r driv
es. At early
stage, the
vector
cont
rol known as
fi
el
d ori
e
nt
ed co
nt
r
o
l
(F
O
C
) was
in
trodu
ced b
y
[1
] wh
ich enab
les th
e co
n
t
ro
l
o
f
torqu
e
an
d fl
u
x
using th
eir
resp
ectiv
e cu
rren
t prod
u
c
i
n
g
com
pone
nt
s, i
.
e.
∗
and
∗
i
n
sy
nch
r
on
o
u
s re
fe
rence
fram
e
. Ho
we
ver
,
t
h
e
FOC
m
e
t
hod r
e
qui
res a f
r
am
e
tr
an
sf
or
m
e
r
,
sp
eed inf
o
r
m
at
i
o
n,
k
now
ledg
e o
f
m
ach
in
e param
e
ters an
d
cu
rren
t con
t
ro
llers to
estab
lish
t
h
e
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
:
328
–
3
39
32
9
cont
rol
o
f
t
o
r
q
ue an
d fl
u
x
. La
t
e
r, t
h
e di
rect
t
o
r
q
ue co
nt
r
o
l
(DTC
) m
e
t
hod
was i
n
t
r
od
uce
d
i
n
t
h
e
m
i
d of 19
8
0
’
s
b
y
[2
]. Co
m
p
ared
to
FOC, DTC h
a
s lesser sen
s
itiv
ity o
n
p
a
ram
e
ter v
a
riatio
n
s
du
e to
te
m
p
eratu
r
e chan
g
e
s,
sin
ce it d
o
e
s n
o
t
to
tally d
e
p
e
nd
on
m
ach
in
e p
a
ram
e
ters to
esti
m
a
te t
h
e con
t
ro
l p
a
ra
m
e
ters. Du
e
to
its
sim
p
licity and fast instantane
ous c
ont
rol pe
rform
a
nce,
the DTC schem
e
gradually replaces the FOC for
m
a
ny
i
n
d
u
st
ri
al
a
ppl
i
cat
i
ons.
Ho
we
ver
,
t
h
e DTC
has
m
a
jo
r d
r
aw
bac
k
s
such as l
a
rg
er t
o
r
que ri
pp
l
e
and vari
a
b
l
e
swi
t
c
hi
n
g
fre
que
ncy
bec
a
use
of
hy
st
er
esi
s
ope
rat
i
o
n
i
n
co
nt
r
o
l
l
i
ng t
h
e st
at
or
fl
u
x
and t
o
r
q
ue. Se
veral
t
ech
ni
cal
pape
rs
were
pr
op
ose
d
t
o
m
i
nim
i
ze the p
r
o
b
l
e
m
s
and i
m
pro
v
e further t
h
e DTC
perform
a
nces. These include
s
the
i
m
p
r
ov
em
en
t o
f
fl
u
x
esti
m
a
ti
o
n
[3
], sen
s
o
r
l
e
ss driv
e[4
]
,
t
o
rqu
e
cap
a
b
ility
for
wid
e
sp
eed
rang
es
[5-6
], to
rq
ue
dy
nam
i
c
cont
r
o
l
i
n
fl
u
x
wea
k
eni
n
g
re
gi
o
n
[7]
,
red
u
ct
i
o
n of
t
o
r
q
ue
ri
ppl
e
[8
-
9
]
an
d
a con
s
t
a
nt
s
w
i
t
c
hi
n
g
fre
que
ncy
[1
0-
12]
.
Am
ong va
rious
m
odifications of DTC
,
the
adapta
tion
of
space vect
or
m
odulation (S
VM) in DTC
structure
has
received wi
dely accepta
nce
due to its
featur
e
s
can offe
r
gre
a
t reduction
of torque
ripple
and a
con
s
t
a
nt
swi
t
c
hi
n
g
f
r
eq
ue
nc
y
[13]
[
11]
.
H
o
we
ve
r, t
h
e a
d
apt
a
t
i
on
of S
V
M
i
n
creases t
h
e com
p
l
e
xi
t
y
whi
c
h
som
e
how
de
gr
ades t
h
e acc
ura
c
y
of
co
nt
r
o
l
p
e
rf
orm
a
nce an
d
dy
nam
i
c t
o
rq
ue c
ont
rol
per
f
o
rm
ance.
Lately, th
e applicatio
n
o
f
m
u
ltilev
e
l in
v
e
rter h
a
s
g
a
in
ed
pop
u
l
arity in
i
m
p
r
ov
ing
DTC p
e
rfo
r
m
a
n
ces
d
u
e
to
its attractiv
e featu
r
es,
wh
ich
are as follo
ws,
1
)
low vo
ltag
e
stress
on
switch
i
n
g
d
e
v
i
ces wh
ich
allo
ws t
o
ope
rat
e
at
hi
g
h
-
v
o
l
t
a
ge a
nd c
u
r
r
ent
ope
rat
i
o
ns,
2) l
o
w
ha
r
m
oni
c curre
nt
or
v
o
l
t
a
ge di
st
ort
i
o
n (i
.e
. d
u
e
t
o
l
o
w
⁄
or
⁄
)
wh
ich eli
m
in
ates th
e u
s
e
o
f
filter an
d
3) im
p
r
o
v
e
d
efficien
cy an
d
t
o
rq
u
e
d
y
n
a
m
i
c
p
e
rform
a
n
ce with
op
tim
a
l
s
e
lectio
n
of vo
ltag
e
v
ector
s.
Th
e th
ird
feat
u
r
e can
b
e
o
ffered
as t
h
e mu
ltilev
e
l
in
v
e
r
t
er
un
i
q
uely p
r
ov
id
es
g
r
eater
nu
m
b
er
of
vo
ltag
e
vectors, as c
o
m
p
ared to
that av
ailab
l
e in
the
con
v
e
n
t
i
onal
i
nve
rt
er.
Thi
s
pr
o
v
i
d
es m
o
re
de
grees
o
f
f
r
eedom
t
o
sel
ect
t
h
e m
o
st
opt
im
al
vect
ors
am
ong
v
ectors av
ailab
l
e to
ach
iev
e
ex
cellen
t
DTC p
e
rfo
r
m
a
n
c
es. Th
ere are th
ree typ
e
s o
f
m
u
ltilev
e
l
in
v
e
rter
no
rm
al
ly
used i
n
AC
dri
v
es,
nam
e
ly
cascaded H-
b
r
i
d
ge [1
4]
, neut
ral
poi
nt
cl
am
ped [1
5
]
and fl
y
i
ng ca
paci
t
o
r
[1
6]
.
Thi
s
pa
pe
r p
r
o
pos
es a si
m
p
l
e
, y
e
t
si
gni
fi
ca
nt
, m
e
t
hod
of
opt
i
m
al
swi
t
c
hi
ng st
rat
e
gy
i
n
t
h
e DTC
-
hy
st
eresi
s
base
d i
n
d
u
ct
i
o
n
m
a
chi
n
e t
o
pr
od
u
ce fast
t
o
rq
ue
d
y
n
am
i
c
cont
r
o
l
an
d t
o
re
duce
swi
t
c
hi
n
g
fre
q
u
ency
as wel
l
as
t
o
rq
ue
ri
p
p
l
e
.
Al
l
im
pro
v
em
ent
s
obt
ai
ne
d
i
n
t
h
e p
r
o
p
o
se
d m
e
t
h
o
d
a
r
e
veri
fi
ed
vi
a e
xpe
ri
m
e
nt
al
resu
lts.
2.
BASIC
CONCEPT OF DT
C
Ove
r
t
h
e
past
t
h
ree
deca
des,
DTC
m
e
t
hod
was i
n
t
r
o
duce
d
by
Taka
has
h
i
and
N
o
g
u
c
h
i
[
2
]
i
s
depi
ct
e
d
in
Fig
u
re 1. In
th
e co
nv
en
tional DTC stru
cture, it e
m
p
l
o
y
s a p
a
ir of h
y
steresis co
m
p
arato
r
; o
n
e
u
tilizes
a two
-
l
e
vel
hy
st
eresi
s
com
p
arat
or f
o
r co
nt
r
o
l
l
i
ng
t
h
e st
at
or fl
u
x
and t
h
e ot
he
r
one uses a t
h
ree-l
e
vel
hy
st
e
r
esi
s
co
m
p
arato
r
fo
r con
t
ro
lling
th
e to
rq
u
e
. Th
e
o
u
tp
u
t
statu
s
of
hysteresis co
m
p
arato
r
s (
and
) and
stator
flux
po
sition
(secto
r
) are
u
s
ed to
tabu
lated
a
lo
ok
-up
tab
l
e
with
m
o
st o
p
t
i
m
al v
o
ltag
e
v
e
cto
r
s as sugg
ested
b
y
[2], s
o
t
h
e a
p
propriate voltage
vectors a
b
le t
o
co
n
t
ro
l bo
th torqu
e
and
stator flux
, resp
ectively.
Fi
gu
re
1.
St
r
u
c
t
ure
of
B
a
si
c D
T
C
-
hy
st
eresi
s
base
d I
n
duct
i
o
n M
a
c
h
i
n
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
En
ha
nce
d
T
o
r
que
C
o
nt
rol
a
n
d
Re
d
u
ced
Sw
i
t
chi
n
g
Fre
q
u
e
n
cy i
n
Di
rect
…
.
(
Mu
h
d
K
hai
ri
Bi
n A
b
d
R
ahi
m
)
33
0
In
DTC, t
h
e traj
ectory of stato
r
flux
is con
t
ro
lled
t
o
fo
rm
a circu
l
ar l
o
cus b
y
con
t
ro
lling
th
e
rad
i
al
com
pone
nt
o
f
st
at
or s
u
ch
t
h
at
i
t
s
ri
ppl
e
(o
r e
r
r
o
r
)
i
s
re
st
ri
ct
ed
wi
t
h
i
n
t
h
e
p
r
ede
f
i
n
e
d
ban
d
(o
r
up
pe
r an
d
l
o
we
r
bands
)
of the t
w
o-level
hysteresis com
p
arat
or as
de
pi
cted in
Figure 2. E
v
ery
s
ector, t
h
ere are t
w
o
possible
vol
t
a
ge
vect
ors
use
d
t
o
co
nt
r
o
l
t
h
e st
at
or
fl
ux
. F
o
r e
x
am
pl
e,
t
h
e vect
ors
̅
and
̅
are tang
en
tial to
th
e
flux
at
the boundaries
betwee
n Sect
or
I and
I
I
,
and
bou
nd
ar
ies betw
een
Secto
r
I
I
a
nd II
I, res
p
ectively
.
Th
u
s
,
thes
e
vectors are us
ed to control
the stator fl
ux, whe
n
the stator fl
ux
vector
lies in
Secto
r
II.
In
th
is sect
o
r
, th
e
vector
̅
i
s
use
d
t
o
i
n
c
r
ease
t
h
e
st
at
or fl
u
x
;
o
n
t
h
e ot
he
r ha
nd
,
t
h
e
vect
or
̅
is s
w
itched to
dec
r
ease t
h
e
stator
flux. Mea
n
whi
l
e, in the
case
of torque
control, t
h
e sam
e
vo
ltag
e
v
ector
used
t
o
co
n
t
ro
l stato
r
flux
(eith
er
̅
or
̅
) is selected
to
in
crease t
h
e
to
rq
u
e
t
o
its d
e
man
d
.
Wh
en
t
h
e torqu
e
d
e
man
d
is satisfied, th
e app
lication
of
zero voltage
vector
(eithe
r
̅
or
̅
) is switch
e
d
to
d
ecrease th
e to
rqu
e
. No
te
t
h
at
t
h
e
st
at
o
r
fl
ux
m
ovem
e
nt
i
s
ideally halted each tim
e
the zero
voltage
vector is sel
ecte
d
. By ensuring the torque a
n
d fl
ux e
r
rors
within
t
h
ei
r re
spect
i
v
e hy
st
eresi
s
ba
nds
, t
h
e
n
a
dec
o
u
p
l
e
d
co
nt
r
o
l
of
t
o
rq
ue a
n
d
st
at
or
fl
u
x
a
b
l
e
t
o
be acc
om
pli
s
he
d
in
DTC.
Fi
gu
re 2.
Tra
j
e
c
t
o
ry
of St
at
or
Fl
ux
wi
t
h
o
p
t
i
m
al
vol
t
a
ge ve
ct
ors sel
ect
i
o
n
3.
DUAL-INVE
R
TER SUPPLI
ED DRIVE
TOPOLOGY
In t
h
e
dual
-
i
n
v
e
rt
er su
p
p
l
i
e
d dri
v
e t
o
p
o
l
o
gy
,
t
h
e po
wer f
r
o
m
vol
t
a
ge so
ur
ce i
nvert
er
(V
S
I) are fe
d t
o
b
o
t
h
sid
e
of stato
r
wi
n
d
i
n
g
of in
du
ction
m
a
ch
in
e (eith
er
by two
-
lev
e
l or m
u
l
tilev
e
l in
v
e
rter). Figu
re 3
sh
ows
a du
al-inv
erter
su
pp
lied
con
f
i
g
uration
for ind
u
c
tion
m
ach
in
e.
Noted t
h
at
the DC
source
s
use
d
to power-up the
VSIs are electrical isolated for
pre
v
enting
the dam
a
ge t
o
t
h
e po
wer s
w
i
t
c
hi
ng de
vi
ce
or m
achi
n
e whi
c
h
causes
by the
flow of zero-s
e
que
nce c
u
rre
n
t. In a
ddition, each i
nve
rter DC
s
u
pply voltage is set t
o
hal
f
com
p
ared t
o
t
h
e co
n
v
ent
i
on
al
t
w
o-l
e
vel
s
i
ngl
e-si
ded
su
ppl
i
e
d
(c
on
ve
nt
i
onal
DTC
)
.
Al
t
h
o
u
gh t
h
a
t
, t
h
e
gene
rat
i
o
n am
pl
i
t
ude o
f
o
u
t
p
ut
vol
t
a
ge at
st
at
or wi
ndi
ng i
s
equi
val
e
nt
t
o
t
w
o
-
l
e
vel
i
n
vert
er. D
u
e t
o
t
h
e
po
we
r
i
s
fed
fr
om
bot
h si
ded
o
f
s
t
at
or wi
ndi
n
g
,
t
h
ere
f
o
r
e t
h
e
out
put
v
o
l
t
a
ge
ge
nerat
e
d acr
oss st
at
o
r
wi
n
d
i
n
g i
s
si
m
ilar as av
ailab
l
e in
con
v
en
t
i
o
n
a
l three-level in
v
e
rter
(conv
en
tion
a
l m
u
lti
lev
e
l).
As shown i
n
Figure 3, each of this
two-level inve
rter a
b
le to produce
2
or 8 s
w
i
t
c
hi
ng st
at
e
com
b
i
n
at
i
ons.
H
o
we
ver
,
si
nce t
h
e
s
e
du
al
t
w
o
-
l
e
vel
i
nve
rt
ers a
r
e
co
nnect
e
d
i
n
ope
n
-
en
d
wi
n
d
i
n
g
co
nf
igu
r
ation,
th
e nu
m
b
er
s of sw
itch
i
ng
stat
e com
b
inations
are inc
r
ease
d
t
o
2
2
o
r
64
.
I
n
pr
actice, o
n
l
y
1
9
switch
i
n
g
state co
m
b
in
atio
n
s
are fu
lly u
tilized
, th
is
d
u
e
to
th
e rem
a
in
e
d
switch
i
ng
state co
m
b
in
atio
ns ju
st
ove
rlaps to
others
. The
r
efore, these
18 active voltage ve
ctors and one
zer
o vol
t
a
ge v
ect
or
can be
g
a
t
h
ere
d
into four groups
acco
rding to
their am
plitude
vect
ors
such a
s
zero
voltage
vector
(
̅
), sm
all voltage
vect
ors
(
̅
), m
e
di
u
m
vol
t
a
ge vect
o
r
s
(
̅
) and l
a
r
g
e
vol
t
a
ge vect
or
(
̅
) as illu
strated
in
Fig
u
re 4
(x
= 1
,
2
.
..,
6
)
.
The
bi
na
ry
n
u
m
ber i
s
use
d
t
o
i
ndi
cat
e s
w
i
t
c
hi
n
g
st
at
e c
o
n
d
i
t
i
ons a
n
d
can
be e
x
p
r
esse
d a
s
f
o
l
l
o
ws:
-
1Indicat
e
theup
p
ers
wit
c
h
i
s
t
urn
O
N
0Indica
t
e
t
heuppers
w
it
c
h
is
t
u
rn
O
F
F
(1
)
- a
x
is
- a
x
is
III
I
VI
IV
UB = Up
per
B
a
n
d
LB = L
o
wer
Ba
nd
II
̅
(
011
)
̅
(
000
)
̅
(
101
)
̅
(
100
)
̅
(
110
)
̅
(010)
̅
(
111
)
̅
(
001
)
(
,
,
)
Eigh
t voltag
e
vectors
produced b
y
2-level
VSI
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
:
328
–
3
39
33
1
‘x
’ is t
h
e
refe
r
r
in
g to
the
p
h
a
s
e (
x
= a
,
b,
c)
, ‘y
’
is e
i
t
h
e
r
1
or
2
w
h
i
c
h
r
e
fer
r
ed
t
o
i
nve
rt
er
1
or
2
w
h
i
l
e ‘+’
refe
rre
d t
o
t
h
e
u
ppe
r s
w
i
t
c
h.
It
sh
o
u
l
d
be
not
e
d
t
h
at
t
h
e
l
o
we
r s
w
i
t
c
h f
o
r ea
ch
p
h
ase
of i
nve
rt
er i
s
al
way
s
co
m
p
li
m
e
n
t
ary
to
th
e upp
er switch
.
Fi
gu
re
3.
C
o
nfi
g
u
r
at
i
o
n a
n
d
v
o
l
t
a
ge
vect
o
r
s
pr
o
duce
d
by
ea
ch i
n
ve
rt
er
of
t
w
o
-
l
e
vel
i
n
du
al
-i
nve
rt
er s
u
p
p
l
i
e
d
dri
v
e
Fi
gu
re 4.
V
o
l
t
a
ge vect
o
r
s pr
o
duce
d
by
dual
t
w
o
-
l
e
vel
i
nve
rt
ers
4.
PROP
OSE
D
OPTIMAL
S
W
ITCHI
N
G
STRATEG
Y
Th
is section
will p
r
esen
t
b
r
iefly o
n
ho
w t
h
e p
r
op
o
s
ed
o
p
t
i
m
al switch
i
n
g
strateg
y
in
DTC with
th
e
dual
-
i
n
vert
er s
u
p
p
l
i
e
d
dri
v
e
abl
e
t
o
im
pro
v
e
DTC
per
f
o
r
m
ances whi
c
h
as fol
l
o
ws;
1)
red
u
ct
i
on
of t
o
r
q
ue
ri
p
p
l
e
, 2) m
i
nim
i
zat
i
on of sw
i
t
c
hi
ng f
r
eq
ue
ncy
t
h
at
can i
m
prove p
o
w
er
effi
ci
enci
es.
The o
p
t
i
m
al
swi
t
c
hi
n
g
st
rat
e
gy
i
s
exe
c
ut
ed t
h
r
o
u
g
h
t
h
e m
odi
fi
cat
i
on
o
f
t
o
rq
ue e
r
r
o
r st
at
us ba
s
e
d o
n
e
v
al
uat
i
on
o
f
t
o
rq
ue c
ont
rol
cap
ab
ility for ev
ery app
licatio
n
o
f
am
p
l
itu
d
e
o
f
v
ect
ors an
d op
erati
n
g sp
eed
s
. Based
o
n
th
e
prev
iou
s
,
,
,
,
,
̅
(011)
̅
(000)
̅
(101)
̅
(100)
̅
(110)
̅
(010)
̅
(111)
̅
(001)
̅
(011)
̅
(000)
̅
(101)
̅
(100)
̅
(110)
̅
(010)
̅
(111)
̅
(001)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
En
ha
nce
d
T
o
r
que
C
o
nt
rol
a
n
d
Re
d
u
ced
Sw
i
t
chi
n
g
Fre
q
u
e
n
cy i
n
Di
rect
…
.
(
Mu
h
d
K
hai
ri
Bi
n A
b
d
R
ahi
m
)
33
2
state
m
en
t, it
is
p
o
ssi
b
l
e to
ev
alu
a
te th
e cap
ab
ility o
f
to
rqu
e
co
n
t
ro
l for every sp
eed
reg
i
o
n
b
y
co
m
p
arin
g
th
e
switching fre
quencies obtained from
t
h
e t
o
rq
ue an
d st
at
or
fl
ux hy
st
eresi
s
com
p
arator as shown in Fi
gure
5
(hi
ghl
i
g
ht
ed
b
y
bl
ue
bl
oc
k).
There
f
ore,
t
h
e
pr
o
pose
d
m
e
t
h
od
m
odi
fi
es t
h
e t
o
r
q
ue e
r
r
o
r
st
at
us (
) to a
new
t
o
r
que e
r
r
o
r st
at
us (
) wi
t
h
o
u
t
r
e
qui
re sp
eed i
n
fo
rm
ati
on a
nd
t
h
e us
e
of a s
p
eed se
nsor.
In
suc
h
a way, t
h
e
si
m
p
licit
y an
d
reliab
ility o
f
co
n
t
ro
l, as featured
i
n
th
e con
v
en
tio
n
a
l
DTC
can
be retain
ed. Tak
i
n
g
i
n
to
acco
unt
t
h
at
, t
h
e s
w
i
t
c
hi
n
g
of a
p
pr
o
p
ri
at
e am
pl
i
t
ude
of
vect
o
r
s
det
e
rm
i
n
ed by
t
h
e m
odi
fi
ed
t
o
r
que
er
ro
r
st
at
us
(Op
tim
u
m
Sta
t
u
s
Detection
)
fo
r ev
ery sp
eed reg
i
on, wh
ic
h as suggeste
d
above, a
b
le
to
redu
cing
th
e
rate o
f
chan
ge o
f
t
o
r
q
ue (t
o i
m
prov
e DTC
perf
o
r
m
a
nces) at
t
h
e sam
e
t
i
m
e
retai
n
s t
h
e cont
r
o
l
of t
o
r
q
ue.
An
ot
he
r
t
h
i
n
g
co
nsi
d
er
ed
by
t
h
e
O
p
t
i
m
al
St
at
us Det
ect
i
on
bl
oc
k
is th
e
n
ecessary
to
switch
th
e lo
ng
est am
p
litu
d
e
(i.e.
= +3 o
r
-
3
) o
f
vect
ors
fo
r a
c
hi
evi
n
g t
h
e fa
st
est
t
o
rq
ue
dy
nam
i
c respon
s
e
whe
n
a s
u
dd
en l
a
r
g
e t
o
rq
u
e
d
e
m
a
n
d
o
c
curs. Th
is d
y
n
a
mic co
nd
itio
n or th
is sud
d
e
n
larg
e t
o
rq
u
e
de
m
a
n
d
can
b
e
easily d
e
tected
b
y
m
easuri
n
g t
h
e
t
o
rq
ue
er
ro
r
(
) using
three-l
e
vel hysteresis
com
p
ar
ator. Th
e
fo
llo
wi
n
g
sub
s
ection
s
will
descri
be t
h
e e
ffect
o
f
di
ffe
r
e
nt
am
pl
i
t
ude of
vol
t
a
ge v
ect
ors t
o
wa
rd
t
o
r
que
dy
na
m
i
c behavi
ors
(DT
C
per
f
o
r
m
a
nces)
and
ot
hers
cr
uc
i
a
l
part
s i
n
t
h
e
pr
o
pose
d
s
c
he
m
e
.
Fi
gu
re
5.
The
s
t
ruct
u
r
e
of
p
r
o
pos
ed
DTC
ut
i
l
i
z
i
ng d
u
al
i
n
v
e
rt
er s
u
ppl
y
dri
v
e
wi
t
h
a
n
opt
i
m
al
st
at
us det
e
ct
i
on
bl
oc
k
4.
1.
E
ffec
t
of
Di
ffere
nt
Am
pl
i
t
ude of
V
o
l
t
age
Vectors
on Torque
Dynamic Behavi
ors
In t
h
i
s
s
ubsect
i
on, t
h
e
rat
e
o
f
t
o
r
que c
h
a
n
g
e
equat
i
o
n (
2
)
i
s
deri
ve
d bas
e
d o
n
a vect
o
r
di
agram
as
sho
w
n i
n
fi
g
u
r
e 6
.
T
h
i
s
eq
uat
i
o
n
i
s
nece
ssary
t
o
a
n
al
y
s
i
s
t
h
e be
ha
vi
or
of
t
o
r
q
ue
d
y
n
am
i
c
for
di
ffe
rent
am
pl
i
t
ude vect
ors a
p
pl
i
cat
i
o
n
s
at
di
ffe
rent
s
p
eed
o
p
er
ations. The
n
, t
h
e following cases
below desc
ribe the
red
u
ct
i
o
n
of
t
o
rq
ue
ri
p
p
l
e
a
n
d s
w
i
t
c
hi
n
g
fr
eque
ncy
obt
ai
ned
wi
t
h
t
h
e
p
r
o
p
o
sed
s
w
i
t
c
h
i
ng
vect
o
r
s
f
o
r
eve
r
y
lev
e
l of sp
eed
o
p
e
ration
as
well as co
m
p
ariso
n
with th
at
o
b
tain
ed
in th
e con
v
e
n
tion
a
l DTC.
(I) Case
1: Propos
ed selection of
vectors at L
o
w-Spee
d
Firstly, let assu
m
e
th
at th
e ro
tor fl
u
x
ang
l
e (
,
) i
s
eq
ui
val
e
nt
t
o
t
h
e
st
at
or
fl
u
x
an
gl
e (
,
),
since the slip very sm
all in
practice.
T
h
ere
f
ore, only the spee
d or a
n
gul
a
r fre
quencies
need to
be considere
d
for th
e secon
d
term in
eq
u
a
tion
(2). At low sp
eed
o
p
e
rati
ons, th
e to
rq
u
e
ten
d
s
to
in
crease rap
i
d
l
y as th
e stato
r
fl
u
x
an
gl
e i
n
c
r
eases at
a hi
ghe
r rat
e
t
h
a
n
t
h
at
of t
h
e r
o
t
o
r fl
ux a
ngl
e,
part
i
c
ul
arl
y
e
m
pl
oy
i
ng t
h
e l
a
rgest
t
a
nge
nt
i
a
l
vol
t
a
ge vect
or
(i
.e.
,
,
9
0
) th
at h
a
s t
h
e lo
ng
est am
p
litu
d
e
.
As it can
be noticed t
h
at
th
e seco
nd
term in
(2
) b
ecomes s
m
a
ller, i.
e. in
sig
n
i
fican
t
red
u
c
ti
o
n
term (at
lo
w sp
eed
op
eration
s
), wh
ich
pr
o
v
es t
h
at
t
h
e rat
e
of
i
n
c
r
em
ent
of
t
o
rq
ue st
r
o
ngl
y
i
n
fl
ue
nced
by
t
h
e a
ppl
i
e
d
vo
l
t
a
ge vect
ors
.
These
co
nd
itio
ns n
o
rmall
y
o
ccu
r in
th
e co
nv
en
tio
nal DTC with
th
e o
n
l
y sin
g
l
e op
tio
n
o
f
am
p
lit
u
d
e
(i.e. th
e lon
g
e
st
am
pl
i
t
ude o
f
v
ect
or) i
n
sel
ect
i
ng act
i
v
e
vol
t
a
ge vect
ors
.
A
s
t
h
e res
u
l
t
,
i
t
cont
ri
b
u
t
e
s t
o
l
a
rger t
o
r
q
ue r
i
ppl
e
∗
3-
le
ve
l Hyst
e
r
e
s
is
Co
m
p
arator
O
p
t
i
mu
m
St
at
us
Dete
ction
2-
le
ve
l Hyst
e
r
e
s
is
Co
m
p
arator
∗
VS
I 1
VS
I 2
IM
Voltage
Calc
ulat
ion
/
/
S
ector
Dete
ction
St
at
or
flux and t
o
r
q
ue
e
s
t
i
m
a
t
o
r
s
Cu
rren
t
Calc
ulat
ion
LU
T
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
:
328
–
3
39
33
3
and
hi
g
h
s
w
i
t
c
hi
n
g
fre
q
u
enc
y
whi
c
h ve
ry
si
gni
fi
ca
nt
due
to
t
h
e
fo
llowi
n
g
fact
o
r
s;
1)
extrem
e increa
se of
to
rq
u
e
sin
c
e that th
e redu
ction
term
in
(2
)
beco
m
e
s
s
m
alle
r as t
h
e s
p
ee
d
decrease
s
, a
nd 2) e
x
trem
e decrease
of t
o
r
q
ue
beca
use
of
sel
ect
i
o
n
of
re
verse
v
o
l
t
a
ge
vect
o
r
s
w
h
i
c
h i
s
ha
p
p
ene
d
w
h
ene
v
er t
h
e
t
o
r
q
ue
err
o
r
t
ouc
hes t
h
e l
o
wer ba
n
d
of t
h
e t
h
ree
-
l
e
vel
hy
st
eresi
s
co
m
p
arat
or. Fo
rt
unat
e
l
y
, t
h
e p
r
o
p
o
sed st
rat
e
gy
has
anot
her
o
p
t
i
on
t
o
em
pl
oy
sho
r
t
e
r am
pl
it
ude
o
f
act
i
v
e v
ect
or
s t
h
at
can sl
ow
do
w
n
t
h
e i
n
cr
em
ent
of l
o
ad
angl
e
and
torqu
e
, as
well. Accord
i
n
g
to (2
), th
e app
licatio
n
o
f
th
e sho
r
ter am
p
lit
u
d
e
of activ
e vecto
r
s
resu
lts in
a
sm
a
ller
m
o
tio
n or in
crease
of
th
e lo
ad
ang
l
e
∆
,
th
u
s
th
e
v
ector th
at
h
a
s th
e sho
r
test am
p
litu
de (b
ased
o
n
th
e
cat
ego
r
i
zat
i
on
of ve
ct
or
s i
n
Fi
gu
re 4 i
s
chos
en i
n
t
h
e p
r
o
p
o
sed m
e
t
hod t
o
red
u
ce t
h
e rat
e
of i
n
cre
a
se o
f
t
o
r
que
. I
n
a
d
di
t
i
on, t
h
e
red
u
ct
i
on
o
f
t
h
e
p
o
si
t
i
v
e t
o
r
q
ue sl
o
p
es i
n
t
h
e
p
r
o
p
o
se
d m
e
t
hod c
ons
eq
ue
nt
l
y
pr
even
t
t
h
e i
n
ci
de
nce
of
un
de
rsh
o
o
t
of t
o
r
que e
r
r
o
r
t
o
t
ouc
h t
h
e l
o
we
r ba
n
d
o
f
hy
st
eresi
s
com
p
arat
or. B
y
em
pl
oy
i
n
g
t
h
e
pr
op
ose
d
vect
o
r
s,
pa
rt
i
c
ul
arl
y
i
n
i
n
cre
a
si
ng
t
h
e t
o
r
q
ue, t
o
r
q
ue
ri
p
p
l
e
a
n
d
swi
t
c
h
i
ng
fr
eq
ue
ncy
can
be
red
u
ce
d.
In
decrea
si
n
g
t
h
e t
o
r
q
ue, ze
r
o
v
o
l
t
a
ge
vect
ors a
r
e c
hose
n
i
n
t
h
e
pr
op
os
ed m
e
t
hod si
m
i
l
a
r t
o
t
h
at
em
pl
oy
ed i
n
t
h
e co
nve
nt
i
o
nal
DTC
.
B
y
sel
e
ct
i
ng t
h
e
zer
o
vect
o
r
s at
l
o
w-
spee
d, t
h
e
rat
e
of
dec
r
ease
of
t
o
r
q
u
e
tu
rn
s ou
t to
b
e
s
m
aller. Th
is can
b
e
pro
v
e
n
b
y
(2), as th
e rate is o
n
l
y d
e
term
in
ed
b
y
th
e seco
nd
or redu
ctio
n
term
in
(2),
wh
ich b
e
co
m
e
s a in
sign
ifican
t term
as th
e
s
p
eed decreases
.
It should be
also note
d
t
h
a
t
the
sel
ect
i
on
of t
h
e
pr
o
p
o
s
ed
v
o
l
t
a
ge
vect
o
r
s are
al
so em
pl
oy
ed to inc
r
ease
or
decrease
sl
o
w
l
y
or t
o
hal
t
t
h
e
st
at
or
flu
x
.
Fi
gu
re
6.
C
o
nt
r
o
l
o
f
st
at
o
r
fl
u
x
vect
o
r
t
o
t
r
ac
k i
t
s
re
feren
c
e (in
t
o
a
co
un
ter clo
c
kwise) with
a su
itab
l
e vo
ltag
e
vector a
pplication
,
,
,
,
,
,
,
,
(2
)
(I
I) C
a
se
2:
Pr
op
ose
d
sel
ect
i
o
n
of
vect
ors
at
M
e
di
um
-Spee
d
At m
e
diu
m
-speed, it is neces
sary to em
ploy voltage
vectors that can avoi
d extrem
e torque cha
n
ges
an
d at th
e
same ti
m
e
, th
e selectio
n
o
f
vo
ltage v
ectors ab
le t
o
retain
th
e capab
ility co
n
t
ro
l
o
f
to
rqu
e
.
In t
h
e ca
se o
f
i
n
creasi
ng
of t
o
rq
ue, i
f
t
h
e l
o
n
g
est
am
pl
i
t
ude of
vol
t
a
ge
vec
t
ors i
s
em
pl
oy
ed (i
.e. t
h
e
sam
e
vol
t
a
ge
vect
o
r
s em
pl
o
y
e
d i
n
t
h
e c
o
n
v
ent
i
o
nal
DTC
)
, t
h
e torque m
a
y increase
ra
pidly,
whic
h c
a
uses a
l
a
rge t
o
r
q
ue ri
ppl
e an
d hi
gh
swi
t
c
hi
n
g
fre
q
u
ency
.
On t
h
e
ot
her ha
n
d
, i
f
t
h
e short
e
st
a
m
pli
t
ude of v
o
l
t
a
ge
vectors is em
ployed, t
h
e i
n
crease of t
o
rque
might
not
be
able t
o
satisfy its dem
a
nd
because the
a
n
gula
r
fre
que
ncy of t
h
e stator
flux
vector cannot be inc
r
eas
ed
fu
rt
h
e
r to
m
a
in
tain
at a d
e
sired
lo
ad
ang
l
e
(
).
There
f
ore,
t
h
e
pr
o
p
o
s
ed m
e
tho
d
em
pl
oy
s
m
e
di
um
am
plit
ude
of
vect
or
s, w
h
i
c
h
can
e
x
t
e
n
d
t
h
e
l
i
m
i
t of
t
h
e
stato
r
flux
an
gu
lar frequ
e
n
c
y
for retain
ing
t
h
e con
t
ro
l capab
ility o
f
to
rqu
e
as well as
av
o
i
d
i
ng
th
e ex
treme
to
rq
u
e
in
creases.
In the ca
se
of
decreasi
n
g the
torque, i
f
ze
ro
vo
lta
ge
vectors
are
em
ployed as i
n
the
conve
n
tional
D
T
C, th
e tor
que m
a
y d
ecr
ease r
a
p
i
d
l
y si
n
c
e th
e r
e
du
ctio
n
o
f
th
e lo
ad angle (
)
occurs
at
higher rate, as
the
st
at
or
fl
u
x
vect
or
i
s
ass
u
m
e
d t
o
be
hal
t
,
whi
l
e t
h
e
rot
o
r
fl
u
x
vect
o
r
c
o
nt
i
n
u
ousl
y
a
p
pr
oac
h
es t
o
t
h
e st
at
o
r
fl
u
x
v
ector
. Th
u
s
, to
slow
do
wn t
h
e r
a
te of lo
ad
an
g
l
e
redu
ction
,
th
e sm
allest a
m
p
litu
d
e
of activ
e
v
ectors (
1
1
) is em
p
l
o
y
ed
in
th
e
p
r
op
osed
m
e
th
o
d
. By selectin
g
th
e
p
r
op
o
s
ed
vo
ltag
e
v
ectors, t
h
e positiv
e and
,
,
,
,
∆
,
≅
̅
,
.∆
,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
En
ha
nce
d
T
o
r
que
C
o
nt
rol
a
n
d
Re
d
u
ced
Sw
i
t
chi
n
g
Fre
q
u
e
n
cy i
n
Di
rect
…
.
(
Mu
h
d
K
hai
ri
Bi
n A
b
d
R
ahi
m
)
33
4
negat
i
v
e
t
o
rq
u
e
sl
o
p
es ca
n
be
re
duce
d
a
n
d c
ons
eq
ue
nt
l
y
m
i
nim
i
zes t
h
e t
o
rq
ue
ri
p
p
l
e
at
t
h
e sam
e
t
i
m
e
reduc
e
t
h
e s
w
i
t
c
hi
n
g
f
r
eq
ue
ncy
.
(I
II
) C
a
se
3:
P
r
op
ose
d
sel
ect
i
o
n
of
vect
ors
at
Hi
g
h
-S
pee
d
At h
i
g
h
-sp
eed, it is requ
ired to
em
p
l
o
y
voltag
e
v
ectors t
h
at can fu
lfill th
e cap
a
b
ility con
t
ro
l of
torque
dem
a
nd. As the spee
d
increases
,
th
e ro
tor flux
ang
u
l
ar v
e
lo
city also
increase
s
; it is therefore t
h
e stator
flux
v
ecto
r
h
a
s to
ro
tate faster, i.e. at
h
i
gh
er
an
gu
lar frequ
e
n
c
ies to m
a
in
ta
in
th
e
d
e
sired lo
ad ang
l
e.
In t
h
e case
of
i
n
creasi
n
g t
h
e
t
o
r
que
, t
h
e
pr
o
pos
ed m
e
t
hod
has t
o
em
pl
oy
t
h
e l
o
ngest
a
m
pli
t
ude
o
f
vect
o
r
t
o
m
ove qui
ckl
y
t
h
e st
at
or fl
u
x
vect
o
r
t
o
ret
a
i
n
t
h
e
desi
re
d l
o
ad a
n
gl
e and
henc
e ret
a
i
n
s t
h
e co
n
t
rol
of
t
o
r
que
. The se
l
ect
i
on of t
h
e
l
o
n
g
est
am
pl
i
t
ude
of
vect
o
r
is the sa
m
e
as
selected in the conve
n
tional
DTC.
Referri
n
g
to
(2), th
e lon
g
e
st am
p
l
itu
d
e
of
v
e
cto
r
at
h
i
gh
speed
s
will n
o
t
drastically in
crease th
e torqu
e
,
as th
e
reduction term
becom
e
s great
er.
On the othe
r hand, for
reduci
ng t
h
e torque,
the pr
oposed
m
e
thod em
ploys the shortest am
plitude of
vectors, sim
ila
r to t
h
at em
ployed in the
cas
e of m
e
di
u
m
speeds.
As
justi
f
ied in the cas
e of m
e
diu
m
speeds,
t
h
e sel
ect
i
on o
f
t
h
e sh
ort
e
st
am
pli
t
ude of v
e
ct
ors m
a
y sl
ow do
wn t
h
e rat
e
of l
o
a
d
an
gl
e r
e
duct
i
o
n an
d t
o
r
q
ue
slo
p
e
, as
well. No
te th
at, th
e selectio
n
of zero v
ect
o
r
s as em
p
l
o
y
ed
in
th
e conv
en
ti
o
n
al DTC
resu
lts in
a
hi
g
h
er
rat
e
of
l
o
ad a
n
gl
e re
d
u
ct
i
o
n
an
d l
a
r
g
er
ne
gat
i
v
e t
o
r
q
ue sl
o
p
e.
On
t
h
e
ot
he
r
han
d
,
t
h
e sel
e
ct
i
on
of
medium a
m
plitude of voltage
vector
s is not recomm
ended
because it
m
a
y
produce a higher rate of increase
the load a
n
gle, whic
h does
not guara
n
tee to dec
r
ease the
torque
. As
di
scusse
d ab
o
v
e,
t
h
e ne
gat
i
v
e t
o
r
q
ue
sl
ope
o
b
t
a
i
n
ed
i
n
t
h
e
pr
o
pos
ed m
e
t
hod i
s
l
o
we
r, as
com
p
ared t
o
t
h
at
o
b
t
a
i
n
ed
i
n
t
h
e
con
v
e
n
t
i
o
nal
DTC
.
Hence
,
this
wil
l
reduce t
h
e torque
ri
pple as
well as switch
i
ng
freq
u
e
n
c
ies at th
e inv
e
rter.
4.
2.
De
fi
ni
ti
on
o
f
Fl
u
x
Sec
t
o
r
s f
o
r Sel
e
c
t
i
n
g O
p
ti
m
a
l
Ve
ctors
Thi
s
sect
i
on i
n
t
r
o
duces t
w
o
d
e
fi
ni
t
i
ons
of
fl
ux sect
or
fo
r s
e
l
ect
i
ng o
p
t
i
m
a
l
vect
ors
,
i
t
i
s
necessary
i
n
th
e p
r
op
o
s
ed
DTC fo
r en
surin
g
th
e selection
of th
e op
tim
al v
ecto
r
s
with larg
er tang
en
tial flu
x
co
m
p
o
n
en
t are
th
e m
o
st effici
en
t to im
p
r
o
v
e
th
e
DTC
p
e
rfo
r
m
a
n
ces
. Since
th
e propo
sed
DTC u
tilizin
g
the d
u
a
l
-
inverter
supplied
has e
i
ghteen active
vectors,
whic
h can be categorized int
o
th
re
e di
ffe
re
nt
am
pl
i
t
udes a
n
d a
m
ong
t
h
em
,
t
h
ere ar
e si
x
m
e
di
u
m
am
pl
i
t
ude of v
ect
ors w
h
i
c
h a
r
e shi
f
t
e
d
by
3
0
de
grees
wi
t
h
respect
t
o
t
h
e
ot
her
particula
r
vectors
.
Note
t
h
at, there
are t
w
o activ
e v
ect
o
r
s that h
a
ve th
e larg
er tang
en
tial t
o
th
e fl
u
x
co
m
p
on
en
t
for every fl
ux
sector is selected as
shown in Figure
7. The
s
e vectors are e
m
ployed to increase
th
e to
rq
ue, also
e
m
ployed to ei
ther i
n
crease
or
decreas
e th
e
stato
r
flux
.
Due to
th
ese sh
ift
e
d
m
e
d
i
u
m
v
ecto
r
s, it is th
erefore,
t
h
e p
r
o
p
o
sed
D
T
C
has t
o
i
n
t
r
o
duce t
w
o
de
fi
n
i
t
i
ons o
f
fl
ux s
ect
or, as
gi
v
e
n
i
n
Fi
g
u
re
7.
As
sho
w
n by
Fi
g
u
re
7
(a), t
h
e s
h
ort
and t
h
e l
o
n
g
am
pl
i
t
udes
of vec
t
ors ha
ve a sa
m
e
defi
ni
t
i
on
of fl
ux sect
or,
sim
i
l
a
r
t
o
t
h
at
defi
ned
i
n
t
h
e c
o
nve
nt
i
onal
DTC
.
H
o
weve
r, t
h
e m
e
di
um
am
pl
i
t
ude of
vect
ors
usi
n
g
a
di
ffe
rent
defi
ni
t
i
on
of
se
ct
or,
i
n
whi
c
h s
h
i
f
t
e
d
by
3
0
de
gre
e
s
t
o
t
h
at
de
fi
ne
d
i
n
t
h
e c
o
nve
nt
i
onal
DTC
(
o
r
i
n
Fi
gu
re
7
(a)
)
. B
y
i
n
t
r
od
uci
n
g
t
h
e
new de
finition
of the
flux
sector, the
tange
n
tial com
pone
nt
of res
p
ective
two m
e
dium
am
plitude
vectors
will
be si
gni
fi
ca
nt
f
o
r
eve
r
y
fl
ux
s
ect
or.
(a)
(b
)
Fi
gu
re
7.
Pr
o
p
o
se
d T
w
o
Fl
u
x
Sect
o
r
Defi
ni
t
i
ons
f
o
r
(a
)
Op
t
i
m
a
l
Swi
t
c
hi
n
g
of
Sh
o
r
t
an
d
Lo
ng
Am
pl
i
t
ude
of
Vect
o
r
s a
n
d
(
b
) O
p
t
i
m
al
Swi
t
chi
n
g
of
M
e
di
um
A
m
pl
i
t
ude
of
Vect
ors
Sector
I
Sector
II
Sector
II
I
Sector
IV
Sector
V
Sector
VI
- axis
- axis
Sector
I
Sector
II
Sector
II
I
Sector
IV
Sector
V
Sector
VI
- axis
- axis
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
:
328
–
3
39
33
5
4.
3. L
o
ok-
up
T
a
bl
e f
o
r
Sel
ecti
n
g
Op
ti
mal
V
o
l
t
age
Vec
t
ors
Ent
i
r
e i
d
e
n
t
i
f
i
e
d o
p
t
i
m
al
vectors
f
o
r e
v
ery
e
r
ro
r st
at
us a
n
d f
l
ux sect
or t
o
i
m
prove
DTC
p
e
rf
orm
a
nces
are t
h
en t
a
bul
at
ed i
n
t
o
a l
o
ok
-
up t
a
bl
e, a
s
gi
ve
n i
n
Tab
l
e 1
.
Clearly
, th
e lo
ok-up
tab
l
e requ
ires th
ree
in
fo
rm
atio
n
to
select th
e o
p
timal v
ect
ors,
w
h
i
c
h are t
h
e fl
ux e
r
r
o
r st
at
us
,
t
h
e m
odi
fi
ed fl
ux e
r
r
o
r st
at
us
and
f
l
ux
sector
s.
I
t
sh
ou
ld b
e
no
ted
t
h
at, t
h
e lo
ok-
up
tab
l
e is v
a
lid fo
r fo
ur-
q
u
a
d
r
an
t of
op
er
ation
.
Tabl
e
1.
Sel
ect
i
on
o
f
t
h
e
M
o
st
O
p
t
i
m
a
l
of
Vo
l
t
a
ge Vect
ors i
n
P
r
o
p
o
se
d M
e
t
h
o
d
Stator
flux
erro
r sta
t
u
s
,
To
rq
u
e
erro
r
status,
Sector
I
Sector
II
Sector
III
Sector
IV
Sector
V
Sector
VI
1
3
̅
̅
̅
̅
̅
̅
2
̅
̅
̅
̅
̅
̅
1
̅
̅
̅
̅
̅
̅
0
̅
̅
̅
̅
̅
̅
-1
̅
̅
̅
̅
̅
̅
-2
̅
̅
̅
̅
̅
̅
-3
̅
̅
̅
̅
̅
̅
0
3
̅
̅
̅
̅
̅
̅
2
̅
̅
̅
̅
̅
̅
1
̅
̅
̅
̅
̅
̅
0
̅
̅
̅
̅
̅
̅
-1
̅
̅
̅
̅
̅
̅
-2
̅
̅
̅
̅
̅
̅
-3
̅
̅
̅
̅
̅
̅
5.
IMPLEME
N
TATION AND E
X
PE
RIMENTAL
RESULT
These
sections
presents
the c
o
m
p
arative analysis of
perform
ances,
i
n
t
e
r
m
s of swi
t
c
hi
n
g
fre
que
ncy
,
t
o
r
que ri
ppl
e
and t
o
rq
ue dy
nam
i
c cont
r
o
l
bet
w
een t
h
e
con
v
e
n
t
i
onal
DTC
an
d t
h
e
pro
p
o
se
d DT
C
.
The
com
p
lete expe
rim
e
ntal set-up has
bee
n
realized as
show
n
i
n
Fi
gu
re
8.
Fu
r
t
herm
ore, t
h
e
c
ont
rol
al
go
ri
t
h
m
s
are
execut
e
d on
a dSP
A
C
E
1
1
0
4
wi
t
h
sam
p
l
i
ng peri
od
o
f
50µ
s.
Fi
gu
re
8.
C
o
m
p
l
e
t
e
d
r
i
v
e sy
st
em
of t
h
e e
xpe
ri
m
e
nt
set
-
up
Th
e
p
a
ram
e
ter
s
of th
e indu
ctio
n m
o
to
r an
d
DTC
d
r
i
v
e
use
d
i
n
t
h
i
s
e
x
peri
m
e
nt
are t
a
bul
at
ed i
n
Tabl
e
2
.
It sh
ou
ld
be n
o
t
ed
th
at th
e iso
l
ated
DC-Link
vo
ltage so
urce is set at 1
2
0
V,
to
conduct dual-inve
rter
su
pp
lied
driv
e. Th
e en
tire
p
e
rform
a
n
ces anal
ysis for the
propos
ed a
n
d
t
h
e
con
v
e
n
t
i
onal
DTC
were pe
rf
orm
e
d
un
de
r sam
e
op
erat
i
n
g
co
n
d
i
t
i
ons
i
n
o
r
de
r t
o
have
fai
r
com
p
ari
s
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
En
ha
nce
d
T
o
r
que
C
o
nt
rol
a
n
d
Re
d
u
ced
Sw
i
t
chi
n
g
Fre
q
u
e
n
cy i
n
Di
rect
…
.
(
Mu
h
d
K
hai
ri
Bi
n A
b
d
R
ahi
m
)
33
6
Tabl
e
2.
In
d
u
ct
i
on M
a
c
h
i
n
e
a
n
d
co
nt
r
o
l
para
m
e
t
e
rs
Induction Machi
n
e
PARAMETER
VALUE
Rated power
,
P
1.
1 kW
Rated speed
,
2800 r
p
m
Stator resistance
,
6.
1
Ω
Rotor resistance,
6.
2293
Ω
Stator
self inductance,
0.
4797
9 m
H
Rotor
self inductan
ce,
0.
4797
9 m
H
M
u
tual inductance,
0.
4634 m
H
Nu
m
b
er
s of pole pair
s,
P
2
The Convent
i
onal and P
r
oposed
DTC
T
o
r
que Rated
4Nm
Flux Rated
0.
8452W
b
T
o
r
que hy
ster
esis
band,
0.
36Nm
Flux hy
ster
esis band,
0.
02W
b
Som
e
t
e
st
has bee
n
car
ri
ed
out
t
o
eval
uat
e
t
h
e pe
rf
o
r
m
a
nces i
m
pro
v
e
m
ent
s
obt
ai
ne
d u
s
i
n
g t
h
e
pr
o
pose
d
D
T
C
schem
e
vi
a expe
ri
m
e
nt
al
resul
t
s
, as wel
l
as com
p
ari
s
on
wi
t
h
t
h
e co
nv
ent
i
onal
2-l
e
ve
l
DT
C
schem
e
. In t
h
i
s
fi
rst
case, a st
ep chan
ge o
f
refe
rence t
o
rq
u
e
from
0.9 Nm
t
o
2.5 Nm
i
s
appl
i
e
d f
o
r pr
o
pos
ed
DTC
sc
hem
e
. From
Fi
g
u
re
9, t
h
e sel
ect
i
o
n
of
ap
p
r
o
p
ri
a
t
e am
pl
it
ude
o
f
vol
t
a
ge
ve
ct
ors
,
as
su
g
g
es
t
e
d i
n
pr
o
pose
d
sche
m
e
, can
be
obs
erve
d
fr
om
t
h
e pat
t
e
r
n
o
f
wa
vef
o
rm
of
pha
se st
at
or
vol
t
a
ge
w
h
i
c
h e
x
hi
bi
t
s
t
h
e i
n
crem
ent
of t
h
e f
u
ndam
e
nt
al
com
pone
nt
fo
r sat
i
s
fy
i
n
g t
h
e hi
g
h
e
r
t
o
r
q
ue dem
a
nd,
as t
h
e
m
o
t
o
r spee
d
i
n
creases
. As
sho
w
n by
e
x
p
e
ri
m
e
nt
al
resul
t
s
obt
ai
ne
d i
n
t
h
e p
r
o
p
o
sed
DTC
(i
n Fi
g
u
r
e
9)
, t
h
e sel
ect
i
on
o
f
app
r
op
ri
at
e am
pl
i
t
ude o
f
vect
ors i
s
base
d o
n
t
h
e regi
o
n
of
speed o
p
e
r
at
i
ons
, w
h
i
c
h i
s
as fol
l
o
ws 1
)
at
l
o
w-
spee
d t
h
e
p
r
o
pos
ed
DTC
s
w
i
t
c
hes
bet
w
e
e
n
zer
o
(
0
)
and sh
or
t
(
1
) am
p
litu
d
e
s of vo
ltag
e
vect
o
r
s,
2
)
at
m
e
di
um
-speed
t
h
e
pr
o
pose
d
DTC
em
pl
oy
es t
h
e s
h
ort
(
1
) a
n
d
t
h
e m
e
di
um
(
2
)
am
pl
i
t
udes of
vol
t
a
ge
vect
o
r
s,
a
n
d
3)
at
hi
gh
-s
peed
t
h
e
p
r
o
p
o
sed
DTC
appl
i
e
s
t
h
e
l
o
n
g
(
3
)
and th
e
short (
1
) am
pl
i
t
ude
s o
f
v
o
l
t
a
g
e
vect
o
r
s.
T
h
e
pr
o
pose
d
DTC
al
so
ret
a
i
n
s t
h
e im
port
a
nt
fe
at
ure
of
t
h
e
con
v
e
n
t
i
onal
DTC
t
h
at
i
s
t
o
p
r
o
v
i
d
e
a
q
u
i
c
k t
o
r
que
dy
n
a
m
i
c cont
r
o
l
.
The m
a
gni
fi
e
d
res
u
l
t
s
as
de
p
i
ct
ed i
n
Fi
gu
res
9
sh
o
w
n
t
h
e l
o
n
g
e
s
t
am
pl
it
ude
of
v
o
l
t
a
ge
ve
ct
or i
s
su
d
d
e
n
l
y
ap
pl
i
e
d
d
u
ri
ng
t
o
r
q
ue
dy
nam
i
c
co
nd
itio
n, i.e.
a su
dd
en
large to
rqu
e
d
e
m
a
n
d
(h
i
g
h
ligh
t
ed
b
y
red
do
tted
lin
e).
Th
e l
o
ng
est am
p
litu
d
e
of
v
o
ltag
e
v
ector is ap
p
lied
to
increase th
e rate o
f
ch
ang
e
of l
o
ad an
gl
e whi
c
h
can pr
ovi
de a fast
t
o
rq
ue dy
n
a
m
i
c
cont
rol
,
as m
e
nt
i
oned
i
n
sect
i
o
n
4.
I
n
th
e seco
nd
case, so
m
e
v
e
r
i
f
i
catio
n
tests w
e
r
e
car
r
i
ed
ou
t w
ith
th
e pr
oposed
op
tim
a
l
sw
itch
i
n
g
and
no
n
-
o
p
t
i
m
al
swi
t
c
hi
n
g
usi
n
g
t
h
e sam
e
exp
e
ri
m
e
nt
al
pl
at
form
and a
co
n
s
t
a
nt
o
f
re
fer
e
nce t
o
r
que
, i
.
e.
at
1.
9
Nm
, for
eve
r
y
spee
d
ope
rat
i
o
n
,
i
.
e.
l
o
w-s
p
eed, m
e
di
um
-speed
an
d
hi
g
h
-
spee
d.
T
h
e e
xpe
ri
m
e
nt
al
pl
at
form
co
m
p
r
i
ses du
al in
v
e
r
t
er
s
f
o
r
o
p
e
n-
end
w
i
ndin
g
s
of
indu
ctio
n m
ach
in
e, wh
er
e th
e
op
ti
mal an
d non
-op
t
i
m
al
switch
i
ng
m
o
des can
b
e
switch
e
d v
i
a
p
r
og
ra
m
o
r
so
ft
ware. Fro
m
th
e resu
lts ob
tain
ed in
Fi
g
u
re
1
0
, initiall
y,
th
e D
T
C activates th
e pr
oposed
o
p
tim
al s
w
itch
i
ng
m
o
d
e
, and
th
en
it activ
ates th
e non
-op
t
i
m
al sw
it
ch
ing
m
ode whi
c
h c
a
n
be re
fer
r
e
d
as t
h
e c
o
n
v
e
n
t
i
onal
DTC
s
w
i
t
c
hi
n
g
.
Fi
g
u
r
e 1
0
(a)
sh
o
w
s t
h
e
wa
vef
o
rm
s of
t
o
r
que
, cur
r
e
n
t
s
and p
h
ase v
o
l
t
a
ge obt
ai
ne
d fr
om
experi
m
e
nt
al
resul
t
s
fo
r
t
h
e case of l
o
w spee
d o
p
era
t
i
ons
.
As
not
i
ced
i
n
Fi
gu
re
10
(a
),
by
em
pl
oy
i
ng
opt
i
m
al
vect
or
s, t
h
e t
o
r
q
u
e
ri
ppl
e i
s
gre
a
t
l
y
red
u
ce
d as t
h
e
rat
e
o
f
increase
of torque is slower.
The effect
of t
o
r
q
ue i
n
crease
due t
o
a
p
p
r
op
ri
at
e vect
or sel
ect
i
on, i
.
e.
wi
t
h
sh
ort
am
pl
i
t
ude, ca
n
be cl
earl
y
see
n
by
m
a
gni
fy
i
ng t
h
e re
sul
t
s
as de
pi
ct
ed i
n
Fi
gu
re
10
(a)
.
From
t
h
e m
a
gni
fi
ed
results, it can
also be see
n
t
h
at the
switch
i
ng
ind
i
cated
b
y
regu
latio
n
of to
rqu
e
is less often
with
th
e
op
ti
m
a
l
switch
i
ng
. Mean
ing
th
at, the selectio
n
o
f
sh
ort v
ect
or
whi
c
h re
duces
sl
ope o
f
t
o
r
q
ue i
n
crease m
a
i
n
l
y
cont
ri
b
u
t
e
s t
h
e
re
duct
i
o
n
o
f
s
w
i
t
c
hi
n
g
fre
q
u
e
ncy
.
Fi
gu
re
1
0
(b
) s
h
ows
t
h
e wa
vef
o
rm
s o
f
t
o
rq
ue,
c
u
r
r
e
n
t
s
a
n
d
pha
se v
o
l
t
a
ge
obt
ai
ne
d f
r
o
m
expe
ri
m
e
nt
al
resul
t
s
f
o
r t
h
e
case of m
e
di
um
speed o
p
er
at
i
ons.
As sh
o
w
n
by
Fi
gu
re 1
0
(
b
)
,
sim
i
l
a
r im
provem
e
nt
s are obt
ai
ned
wi
t
h
t
h
e o
p
t
i
m
a
l
swi
t
c
hi
ng, as cl
e
a
rl
y
be seen t
h
at
t
h
e
t
o
r
que ri
ppl
e a
nd s
w
i
t
c
hi
n
g
f
r
eq
ue
ncy
are g
r
eat
l
y
reduce
d
.
Sam
e
reason i
s
used t
o
j
u
st
i
f
y
t
h
e im
prove
m
e
nt
s,
in
wh
ich th
e
red
u
c
tion
s
are
ob
tain
ed b
y
slowing
d
o
wn
th
e
cha
nge
o
f
t
o
r
q
ue
rat
e
s,
pr
ovided that in the
case of
m
e
di
um
-speed
t
h
e sl
owi
n
g d
o
w
n
o
f
t
o
r
q
ue
rat
e
i
s
cont
ri
b
u
t
ed by
t
w
o c
h
a
nge
s;
ei
t
h
er t
o
i
n
crease
or dec
r
ease
t
h
e t
o
rq
ue
wi
t
h
ap
pr
o
p
ri
at
e ve
ct
ors,
i
.
e. m
e
di
um
and s
h
ort
vectors. T
h
e improvem
ents
have al
s
o
been
v
e
ri
fi
e
d
at
hi
gh-
spee
d o
p
erat
i
o
n as sh
o
w
n i
n
Fi
g
u
r
e 1
0
(c)
.
As can b
e
obse
r
ve
d fr
o
m
m
a
gni
fi
ed re
sul
t
i
n
Fi
gu
re 1
0
(c)
,
the rate of torque
decrease i
s
slow
er th
an
th
at o
b
t
ain
e
d
in
th
e no
n-op
timal switch
i
n
g
.
Th
e slo
w
er rate is
resul
t
e
d
d
u
e t
o
sel
ect
i
on
of
s
h
o
r
t
vect
or
(i
n
s
t
ead
of
usi
n
g
zero
vect
or i
n
t
h
e n
o
n
-
o
pt
im
al
swi
t
c
hi
n
g
)
whi
c
h
reduces t
h
e
rate of
decrease
of loa
d
a
n
gl
e, as
m
e
nt
i
oned i
n
s
ect
i
on
4.
1.
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
:
328
–
3
39
33
7
Fi
gu
re
9.
The
e
xpe
ri
m
e
nt
al
wavef
o
rm
s res
u
l
t
of
To
r
que
(
), pha
se vol
t
a
ge
(
) a
n
d stator current
(
)
fo
r
st
ep c
h
an
ge
of
refe
rence
t
o
rq
u
e
fr
om
0.9
Nm
t
o
2
.
5
Nm
(a)
(b
)
(c)
Fi
gu
re
1
0
. C
o
m
p
ari
s
on
wave
fo
rm
s of T
o
r
q
u
e
(
)
,
stator
cu
rren
t
(
,
,
), a
n
d
pha
se v
o
l
t
a
ge
(
) at
co
nstan
t
torqu
e
fo
r
propo
sed switch
i
ng
an
d no
n-o
p
tim
al
swi
t
ch
in
g strateg
i
es fo
r t
h
ree sp
eed
co
nd
itio
n (a)
Lo
w s
p
eed
co
n
d
i
t
i
on,
(
b
)
M
e
d
i
um
speed c
o
n
d
i
t
i
on a
n
d
(c)
Hi
g
h
s
p
ee
d c
o
ndi
t
i
o
n
Optima
l
Switc
hin
g
Non-
Optima
l
Switc
hin
g
Optima
l
Switc
hin
g
Non-
Optima
l
Switc
hin
g
Mag
n
ifi
e
d I
m
a
g
e
Optima
l
Switc
hin
g
Non-
Optima
l
Switc
hin
g
Optima
l
Switc
hin
g
Non-
Optima
l
Switc
hin
g
Mag
n
ifi
e
d I
m
a
g
e
Optima
l
Switc
hin
g
Non-
Optima
l
Switc
hin
g
Optima
l
Switc
hin
g
Non-
Optima
l
Switc
hin
g
Mag
n
ifi
e
d I
m
a
g
e
Mag
n
ifi
e
d I
m
a
g
e
Evaluation Warning : The document was created with Spire.PDF for Python.