TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 12, No. 12, Decembe
r
2014, pp. 80
8
5
~ 809
1
DOI: 10.115
9
1
/telkomni
ka.
v
12i12.67
18
8085
Re
cei
v
ed Au
gust 19, 20
14
; Revi
sed O
c
t
ober 2
2
, 201
4; Acce
pted
No
vem
ber 8,
2014
Effect of Switching Frequency in DTC Based Switched
Reluctance Motor Drive
P.Srini
v
as
Dept. of Electri
c
al Eng
g
., Univ
ersit
y
C
o
ll
eg
e of Engg., Osmani
a Univ
ersit
y
, H
y
d
e
rab
ad, Indi
a
email: sriniv
as
p.eed
ou@
gma
i
l.com
A
b
st
r
a
ct
Since
the
mag
neti
z
i
n
g c
har
ac
teristics ar
e
hi
ghly
no
n-li
ne
ar
in
n
a
ture, th
e
torque
rip
p
l
e
is
hi
gh
i
n
the Sw
itched Reluct
ance M
o
tor (SRM). The torqu
e
ri
pp
le can be
mi
n
i
mi
z
e
d by us
in
g a novel co
n
t
rol
techni
qu
e cal
l
ed D
i
rect T
o
rq
ue C
ontro
l (D
T
C
). In DT
C techn
i
qu
e, torq
ue is c
ontro
lle
d dir
e
ctly thro
u
g
h
control of magnitude of
the flux-link
a
ge and change
in speed of the stator flux
vector. The flux and torque
are
mai
n
tai
ned
w
i
thin set hys
t
eresis b
ands.
T
h
is
pap
er a
naly
z
e
s
perfor
m
a
n
ce
of the
DT
C base
d
dri
v
e
ma
inly
in ter
m
s of the tor
que ri
pp
le i
n
MAT
L
AB/SIMULINK envir
on
me
nt
an
d res
u
lts are d
i
scu
sse
d
ela
borate
l
y. T
he pa
per a
l
so
analy
z
e
s
the
effect
of these tw
o bands
on sw
itching
freque
ncy of th
e
converter.
Ke
y
w
ords
:
sw
itched re
lucta
n
c
e mot
o
r, direc
t
torque c
ontro
l
,
sw
itching frequency, torqu
e
r
i
ppl
e
Copy
right
©
2014 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
Switche
d
Rel
u
ctan
ce Moto
r
d
r
ives are
cons
i
dered
as
an alte
rnative
to the
conve
n
tional
motor d
r
ives i
n
variabl
e sp
eed ap
plications b
e
cau
s
e
of advantage
s such as
si
mple me
cha
n
i
cal
stru
cture,
no
windi
ng or m
agnet
on roto
r,
high
spee
d operation,
wi
de spe
ed ope
rating ra
nge
etc.
Becau
s
e
of d
oubly salie
nt stru
cture
a
n
d
highly non
-li
near ma
gneti
c
cha
r
a
c
teri
st
ics, th
e to
rqu
e
ripple i
s
high
[1, 2].
The torq
ue ri
pple redu
ctio
n of SRM driv
e usin
g Di
re
ct Torque
Co
n
t
rol is p
r
op
osed in [3].
But this method requi
re
s a new
wind
ing schem
e
whi
c
h is exp
ensive a
nd i
n
co
nvenient.
To
overcome
th
e above
di
sadvantag
es,
a novel
DT
C te
chniq
u
e
is p
r
o
p
o
s
e
d
in [4, 5].
This
techni
que
cl
e
a
rly de
scri
be
s the
differen
c
e
between
DTC a
pplied
to Indu
ction
motor
and
DTC
as
applie
d to SRM. This al
so clea
rly anal
yses t
he p
e
rf
orma
nce of SRM drive u
s
ing
conve
n
tional
Hystersi
s
Current
Control tech
niqu
e an
d
the ne
w DT
C sch
e
me. It also
proves
that usin
g DTC
techni
que t
o
rque
rippl
es can b
e
minimi
zed
to
a
gre
a
ter exten
d
t
han
whe
n
co
mpared to t
h
e
Hysteresi
s
Current Cont
rol method [6
-8]. The
nov
el DTC te
ch
nique p
r
e
s
en
ted in [4, 5] is
s
i
mulated in [9, 10].
The si
mulatio
n
and a
nalysi
s
of DT
C b
a
sed 4 ph
ase 8
/
6 SRM drive
for co
nsta
nt torqu
e
load i
s
analy
z
ed in
[11]. T
h
is p
ape
r
anal
yzes the
pe
rforma
nce of
DTC
ba
sed
dri
v
e for
Fan
lo
ad.
Perform
a
n
c
e
analysi
s
of
DTC ba
se
d
SRM d
r
iv
e u
s
ing
sim
p
lified Torque E
q
uation a
nd F
E
A
model
s i
s
di
scu
s
sed in
[1
2]. This p
ape
r presents th
e variatio
n of
swit
chin
g fre
quen
cy in
DTC
based d
r
ive
for differe
nt combi
nati
ons of
Flu
x
and Torque Hy
stere
s
is b
and
s
in
MATLAB/SIMULINK envi
r
o
n
ment.
2. Principle
of DT
C
The m
a
them
atical e
quatio
ns
of DT
C [4,
5] as ap
plie
d to SRM
a
r
e
discu
s
sed
h
e
re. T
he
instanta
neo
u
s
voltage a
c
ross the motor windin
g
is gi
ven by:
(1)
)
,
(
dt
i
d
Ri
v
Whe
r
e
(
,i)
is
the phas
e
flux link
a
ges
as
a func
tion of rotor pos
i
tion
θ
and
stator current
i.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 12, Decem
ber 20
14 : 8085 – 80
91
8086
Expanding E
quation (1) re
sults in Equ
a
tion (2
)
(2)
)
,
(
)
,
(
d
t
d
i
d
t
di
i
i
Ri
v
The differe
ntial mech
ani
cal
energy obtai
ned [5] is sh
o
w
n in Equatio
n (3)
)
3
(
)
,
(
d
W
d
i
i
dW
f
m
The insta
n
tan
eou
s torqu
e
e
quation i
s
def
ined a
s
:
)
4
(
d
dW
T
m
Thus, by sub
s
tituting (4
) in
to (3) the exp
r
essio
n
for th
e instanta
neo
us torq
ue p
r
o
ductio
n
of an SRM ph
ase
can b
e
written as:
)
5
(
)
,
(
f
W
i
i
T
This i
s
a
rare
ly used va
ria
n
t of conve
n
tional torque
equatio
n. Du
e to satu
ratio
n
in the
SRM, the influen
ce of
the se
con
d
term in
(5) is negli
g
ibl
e
. Therefore
,
by using
this
approximatio
n, the followin
g
equatio
n for torque p
r
od
u
c
tion may be
obtaine
d as:
(6)
)
,
(
i
i
T
In SRM, unip
o
lar d
r
ives
are normally u
s
ed
and thu
s
the cu
rrent in a moto
r ph
ase i
s
alway
s
positi
v
e. Hence, from eq. (6) t
he sign of
th
e torque i
s
d
i
rectly relat
e
d
to the sign o
f
. In othe
r wo
rds to p
r
o
d
u
c
e a
po
sitive torqu
e
, the
st
ator flux a
m
p
litude mu
st in
cre
a
se
relative to th
e roto
r po
siti
on, wh
ere
a
s
to pr
od
uce a
negative torque the
ch
an
ge in
stator f
l
ux
sho
u
ld d
e
cre
a
se
with
respect to the
rotor movem
e
nt. A positive
value of
may be
defined a
s
flux
acc
e
leration
, wh
ere
a
s
a negative v
a
lue of
may be defined
as
flux
deceleration.
The DT
C techniqu
e is cl
ea
rly explained i
n
[4, 5].
Asymmetri
c
al
converte
r is popula
r
ly used
for the SRM drive
s
. The co
nverte
r for one
pha
se is
sh
o
w
n in Fig
u
re
1 Whe
n
bot
h the switch
es a
r
e turne
d
ON, the
state is defin
e
d
as
‘magneti
z
ing’
(state 1).
When on
e switch is tu
rn
e
d
ON an
d othe
r is turn
ed O
FF, the state
is
defined
as ‘freewheelin
g’ (state 0).
Whe
n
both the
switche
s
are turned OF
F,
the
state is
defin
ed
as ‘dem
agn
e
t
izing’ (state -1). The 4 p
hase
Asymm
e
trical
conve
r
ter can hav
e a total of
81
possibl
e Spa
c
e Voltage
Vectors. But in orde
r to apply DT
C to SRM, eigh
t Space Voltage
Vectors that are sepa
rate
d by 45
0
are sufficie
n
t. The eight Space
Voltage Vectors that lie in the
cente
r
of eigh
t secto
r
s
N =
1,
2…8, are
shown in Figu
re 2.
As
in
the co
n
v
entional DT
C schem
e,
if
the stato
r
flux
linkage
lie
s i
n
the
k
th
zo
ne
, whe
r
e
k =
1 to 8 , the mag
n
itude
of the flux can
be i
n
crea
sed by u
s
ing t
he switching
vectors V
k+1
a
nd
V
k-1
and can
be de
crea
sed
by usi
ng the
vectors V
k+2
and V
k-2
. He
nce,
whe
nev
er the
stato
r
flux-
linka
ge rea
c
h
e
s its u
ppe
r li
mit in the hysteresi
s
b
and,
it is red
u
ced
by applying
voltage vecto
r
s
whi
c
h are directed to
ward the cente
r
of t
he flux vector spa
c
e an
d vice-ve
r
sa [5].
As detaile
d p
r
eviou
s
ly, the torque i
s
con
t
roll
ed by an
accele
ration
or de
cel
e
ratio
n
of the
stator flux rel
a
tive to the rotor movem
e
nt. Hen
c
e,
if an incre
a
se in torqu
e
is
required, volta
ge
vectors th
at
advan
ce th
e
stato
r
flux-li
n
ka
ge i
n
th
e
directio
n of
rotatio
n
a
r
e
sel
e
cte
d
. T
h
is
cor
r
e
s
p
ond
s
t
o
sel
e
ct
io
n
of
v
e
ct
o
r
s
V
k+1
and V
k+2
for
a
stator flux-linkage
in
the
k
th
zo
ne.
If a
decrea
s
e
in
torq
ue i
s
required, volt
age ve
ctors are a
pp
lied
whi
c
h
de
ce
lerate
th
e
st
ator
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
E
f
f
e
ct
of
S
w
itchin
g Fre
que
nc
y in DT
C B
a
se
d S
w
it
ch
e
d
Relu
ct
an
ce
Mot
o
r D
r
iv
e (
P
.
S
riniva
s)
8087
f
l
ux
-linka
ge v
e
ct
or.
T
h
is
co
rre
sp
ond
s t
o
t
he v
e
ct
o
r
s V
k-
1
and V
k-2
in the k
th
zone [5
]. Based on t
he
output of the torqu
e
and flu
x
hystere
s
is b
l
ocks,
ap
pro
p
r
iate Spa
c
e Voltage Vecto
r
s are
sele
cte
d
.
Figure 1. Asymmetrical
Converte
r
Figur
e 2. Defi
nition of SRM
motor voltag
e
v
e
ct
or
s f
o
r D
T
C
3. Simulation and Analy
s
is of
Dire
ct Torque Control
of
SRM
The
compl
e
te
Non
-
line
a
r m
odel of the
4-pha
se
8/6 S
R
M with Di
re
ct
Torq
ue
Controller i
s
sho
w
n in Fig
u
re 3(a). The
spe
c
ification
of the
SRM is given in Appendix A. The model co
nsist
s
of electri
c
al
system, me
chani
cal sy
ste
m
, posit
ion
sensi
ng blo
c
k, Asymmetrical conve
r
ter
and
DTC blo
c
k.
Figure 3
(
b
)
shows th
e int
e
rnal
blo
c
k o
f
SRM. Fig
u
re 3(c)
sho
w
s the o
ne
pha
se
model.
Figure 3(a
)
. Simulation mo
del of DTC b
a
se
d
drive
Figure 3(b
)
. Internal bl
ock
Figure 3(c).
One ph
ase model
v
+
-
vm
4
v
+
-
vm
3
v
+
-
vm
2
v
+
-
vm
1
to
r
q
u
e
the
t
a
Di
s
c
r
e
t
e
,
T
s
=
1e
-00
6
s.
pow
e
r
gu
i
1
cu
r
r
e
n
t
G1
1
G1
2
G2
1
G2
2
G3
1
G3
2
G4
1
G4
2
V+
V_
A1
A2
B1
B2
C1
C2
D1
D2
c
o
n
ver
t
e
r
t
T
o
W
o
r
k
sp
ace
8
T_
r
e
f
Sp
e
e
d
2
V1
V2
V3
V4
Lo
a
d
To
rq
ue
To
rq
ue
C
u
rre
nt
Fl
ux
Sp
e
e
d
T
o
t
a
l
To
rq
ue
Th
e
t
a
SR
M
-
K
0.
25
Fl
u
x
_
r
e
f
T_
r
e
f
Tc
a
l
Fl
ux
_
r
e
f
Fl
ux
e
s
Ga
t
i
n
g
S
i
g
n
a
l
s
DT
C
Cl
o
c
k
120
V
-
K-
Te
t
a
6
Th
e
t
a
5
To
t
a
l
To
r
q
u
e
4
S
p
eed
3
Fl
ux
2
Cu
r
r
e
n
t
1
T
o
r
que
Th4
V4
T4
C4
F3
P
h
ase
4
Th3
V3
T3
C3
F3
P
h
ase
3
Th2
V2
T2
C2
F2
P
h
ase
2
Th1
V1
F1
C1
T1
P
h
ase
1
mo
d
K T
s
z-
1
K T
s
z-1
60
-K
-
B
-
K-
1/
J
-
K-
5
Lo
a
d
To
r
q
u
e
4
V4
3
V3
2
V2
1
V1
4
4
fl
ux
I(
A
)
3
T1
2C
1
1
F1
TTB
L
-K
-
R
K T
s
z-
1
IT
B
L
2V
1
1
Th
1
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 12, Decem
ber 20
14 : 8085 – 80
91
8088
Mesh
plots
of two Lo
okup t
able
s
are sho
w
n in Fi
gu
re
4(a
)
an
d Figu
re 4
(
b). Fi
gure 5(a
)
sho
w
s the
fo
ur p
h
a
s
e A
s
y
mmetrical
co
nverter u
s
ing
IGBT switch
es. O
ne l
eg
o
f
the convert
e
r i
s
sho
w
n in Fig
u
re 5
(
b). IGB
T
swit
che
s
are use
d
as
the
controll
able
swit
che
s
in th
e conve
r
ter.
The torq
ue computation bl
ock is sho
w
n
in Figure 6.
It contain
s
Flu
x
transform
ation blo
ck, Sector
sele
ction
blo
c
k an
d Flux m
agnitud
e
an
d
com
putat
ion
block. Th
e fu
nction
of Flux
tran
sform
a
tion
block i
s
to convert fluxes in four p
hases into
two p
hases [8]. Th
e Secto
r
sel
e
ction blo
c
k h
a
s
informatio
n a
bout the eigh
t secto
r
s. Ba
sed o
n
t
he a
ngle, the Sector sel
e
ctio
n block outp
u
ts the
pre
s
ent
se
cto
r
nu
mbe
r
of t
he
stator flux
vector. T
he M
A
TLAB pro
g
ram takes sector nu
mbe
r
, flux
increa
se
or d
e
crea
se
sig
n
a
l an
d to
rque
increa
se
o
r
de
c
r
e
a
s
e
s
i
gna
l as
th
e in
puts
a
n
d
ge
n
e
r
a
te
s
the re
qui
red
gate
signal
s
to the IGBT
s of the
conv
erter to a
ppl
y approp
riate
Space volta
ge
vectorT
he
DT
C sch
e
me i
s
simulate
d by
sele
cting
th
e
followin
g
set of 8 Spa
c
e v
o
ltage ve
ctors.
V
1
= (-1
010
), V
2
= (-1
-11
1
),
V
3
= (0-
101
), V
4
= (1-1
-11
)
, V
5
= (10-1
0
)
,
V
6
= (11
-
1-1),
V
7
= (01
0
-
1
), V
8
= (-
111
-1
).
Figure 4(a
)
. Mesh pl
ot of flux-cu
r
rent-a
ngle
Figure 4(b
)
. Mesh pl
ot of Torq
ue-cu
rre
n
t-angl
e
Figure 5(a
)
. Asymmetri
c
al converte
r
Fi
gure 5(b
)
. One leg of th
e conve
r
ter
Figure 6. Torque computat
ion blo
c
k
0
20
40
60
0
0.
1
0.2
0.
3
0
10
20
30
The
ta
(D
e
g
.
)
Fl
ux
-
l
i
n
k
a
g
e
(W
bt
)
C
u
r
r
e
n
t (A
)
0
20
40
60
0
10
20
30
-1
0
0
10
T
h
et
a (
D
e
g
.)
C
u
r
r
e
n
t (A
)
To
r
q
ue
(
N
m
)
10
D2
9
D1
8
C2
7
C1
6
B2
5
B1
4V
_
3
A2
2V
+
1
A1
G4
1
G4
2
V+
V-
C1
C2
B
r
_
C
onv
4
G31
G32
V+
V-
C1
C2
B
r
_
C
onv
3
G21
G22
V+
V-
C1
C2
B
r
_
C
onv
2
G11
G12
V+
V-
C1
C2
B
r
_
C
onv
1
8
G4
2
7
G41
6
G3
2
5
G31
4
G2
2
3
G21
2
G1
2
1
G11
4
C2
3
C1
2
V-
1
V+
g
C
E
IG
B
T
1
g
C
E
IGB
T
D1
D
2
G1
2
1
G1
1
1
Ga
t
i
n
g
Si
g
n
a
l
s
M
A
TLA
B
Fun
cti
o
n
pu
l
s
e
s
1
alp
h
a
_
f
l
u
x
be
t
a
_
f
l
u
x
fl
u
x
_m
a
g
an
g
l
e
f
l
ux
m
a
g
&
a
n
gl
e
fl
u
x
B
e
ta
_
f
l
u
x
b
e
taflux_
cal
f
l
ux
A
l
ph
a
_
f
l
ux
al
p
h
afl
u
x
_
c
a
l
A
ngl
e
S
e
c
t
o
r
S
e
cto
r
_C
al
cula
t
o
r
MA
T
L
A
B
Fu
nc
t
i
o
n
MA
T
L
A
B
F
c
n
T_
re
f
T_
c
a
l
fl
u
x
_
r
e
f
f
l
u
x
_ca
l
F_
B
H
T_
B
H
Flux h
y
ste
r
e
s
i
s
&
To
r
q
u
e
h
y
s
t
e
r
e
s
i
s
4F
l
u
x
e
s
3
Fl
ux
_
r
e
f
2
T
cal
1
T_
r
e
f
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
E
f
f
e
ct
of
S
w
itchin
g Fre
que
nc
y in DT
C B
a
se
d S
w
it
ch
e
d
Relu
ct
an
ce
Mot
o
r D
r
iv
e (
P
.
S
riniva
s)
8089
The
singl
e ph
ase
mod
e
l ha
s two loo
k
up
tabl
es. ITBL
is the
flux-current-a
ngle
(
λ
- i -
θ
)
look up
table
and
TTBL
is t
he to
rque
–
cu
rrent –
ang
le (
T-
i -
θ
) l
ook up
table.
Th
ese L
ookup
tables are fo
rmulated
by condu
cting
Fin
i
te Element
A
nalysi
s
(FEA) whi
c
h
is di
scussed
cl
early
in
[13]. The sa
me is repe
ated for the
re
maining
pha
ses b
u
t each
pha
se is
displaced from
one
other by the stroke a
ngle. T
he stro
ke a
n
g
l
e for 4 pha
se
8/6 SRM is 1
5
0
.
3. Results a
nd Analy
s
is
The p
e
rfo
r
m
ance of th
e
DT
C b
a
se
d SRM
driv
e is an
alyze
d
in M
a
tlab/
Simulink
environ
ment. The effect of
variation of flux
and torq
u
e
hysteresi
s
band
s on
swi
t
ching frequ
e
n
cy
of the convert
e
r is an
alyze
d
.
Table 1 shows the variatio
n of switchi
n
g freque
ncy
of the switchi
ng device
with the flux
hystere
s
i
s
ba
nd an
d torq
u
e
hysteresi
s
band. It is
o
b
s
erve
d that for certai
n co
mbination
s
where
the flux and t
o
rqu
e
hyste
r
e
s
is
ban
ds
are
highe
r t
he
switchi
ng fre
q
uen
cy is lo
w.
This
com
b
ina
t
ion
can
not b
e
se
lected
a
s
the
switch
is un
derutili
zed.
F
o
r th
e
combi
nation
s
in
wh
ich
either flux or
toque hy
steresi
s
is high
cannot
b
e
sel
e
cted
as the
swit
chin
g fre
quen
cy is hig
h
. It is ob
se
rved
that as the h
y
stere
s
is
ban
ds de
crea
se
s, the sw
itchin
g frequ
en
cy of the device
increa
se
s. The
norm
a
l o
pera
t
ing fre
que
ncy ran
ge
of th
e devi
c
e
is
5
kHz - 1
5
kHz. Th
us,
8 %
flux hyste
r
e
s
is
band and 5 %
torque
hysteresi
s
ban
d can be sele
ct
ed
for
thi
s
dri
v
e.
At
lower hystere
s
i
s
b
a
nds,
swit
chin
g freq
uen
cie
s
are h
i
gher
re
sultin
g in highe
r switchi
ng lo
sses an
d red
u
ced efficien
cy.
The p
e
rfo
r
ma
nce
of the DT
C ba
se
d SRM drive
i
s
an
alyzed fo
r a
Fan type lo
ad
of 8 Nm
and at
a refe
ren
c
e
sp
eed
of 800
rp
m.
The a
nalysi
s
is pe
rfo
r
med
for 8% flux h
y
stere
s
is ba
n
d
and 5% to
rq
u
e
hyste
r
e
s
is
band. Fi
gure
7 sh
ows th
e
simulatio
n
wa
veforms of th
e drive
with
DTC
techni
que.
Figure 7
(
a
)
shows the
vari
ation of
stato
r
curr
ent in
al
l the four ph
a
s
e
s
a
s
a
fun
c
tion of
time. It is
ob
served
that
DT
C le
ad
s to
re
gularly
space
d
an
d
peri
odi
c
cu
rre
nts in
all the
pha
se
s. It
is observe
d
the current
is not
dire
ctly controll
e
d
and thus
due to the nonlin
ear m
o
to
r
cha
r
a
c
teri
stics, the
pha
se
cu
rrents a
r
e
nonli
nea
r in
natu
r
e. Th
e
maximum
current a
nd t
h
e
averag
e cu
rrent of each p
hase are 1
3
.8
7 A and 4.85
A resp
ectivel
y
.
Figure 7
(
b
)
sho
w
s the
magnitud
e
of
the
st
ator fl
ux vector.
T
he flux ma
g
n
itude i
s
maintaine
d
at
the referen
c
e value
of 0.
25
Wb
by foll
owin
g a
hyst
ere
s
is ba
nd
of 0.021
Wb, as
again
s
t the set band of 0.020 Wb. Figu
re 7(c)
sho
w
s the total torque re
sp
on
se
. It is obse
r
v
e
d
that the torqu
e
is maintain
ed within the
hyster
e
s
i
s
ba
nd of 0.48 Nm as ag
ainst
the set band
of
0.40 Nm. Th
e cal
c
ul
ated
torque
rip
p
le
is 6.0
0
%.
It is o
b
served
that the a
c
tu
al or cal
c
ul
ated
torque a
nd flux has hig
her erro
r. This
can be attri
but
ed to finite iteration time
of the simulat
i
on.
Figure 7(d
)
shows the loa
d
torque a
nd i
t
varies a
s
the squ
a
re of th
e spe
ed.
The in
stanta
neou
s torque
s of all the fo
ur ph
as
es i
s
sho
w
n i
n
Fi
gure
7(e). Fi
gure
7(f)
sho
w
s the
sp
eed
re
spo
n
se. The
settling time fo
r
st
e
ady state
sp
eed i
s
0.310
se
c. Fig
u
re
7
(
g)
s
h
ows
th
e var
i
a
t
io
n o
f
ψ
α
with
ψ
β
. It
ca
n be
seen
th
at the traje
c
tory of fluxe
s
betwe
en
α
a
nd
β
axes i
s
ci
rcul
ar i
n
n
a
ture.
Figure 7
(
h
)
s
hows th
e d
e
lta an
gle,
whi
c
h vari
es bet
ween
-1
80
0
an
d
+18
0
0
.
Table 1. Vari
ation of Switching Frequ
en
cy with
Flux Hysteresi
s
B
and an
d Torq
ue Hyste
r
e
s
is
Band
S.No.
%
Fl
ux-li
n
kage
H
y
s
t
eresi
s Ban
d
%
Tor
que
H
y
s
t
eresi
s Ban
d
S
w
itching
Frequ
e
nc
y
(kHz
)
1 10
10
6.99
2 10
5
14.08
3 8
8
8.69
4 8
5
13.69
5 5
10
7.29
6 5
5
14.49
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 12, Decem
ber 20
14 : 8085 – 80
91
8090
(a) Stator
cu
rrent
(b) Flux ma
g
n
itude
(c
) TotalTo
r
q
ue re
spo
n
s
e
(d) L
oad torq
ue
(e) T
o
rq
ue in
all pha
se
s
(f) Speed
(g) Flux traj
ectory
(h) Delta
an
gl
e
Figure 7. Simulation waveform
s of SRM
drive with Di
rect Torque
Controlle
r
4. Conclusio
n
In DTC, the torqu
e
is cont
rolled di
re
ctly
through the
control of ma
gnitude of th
e flux-
linka
ge an
d the chan
ge in
spe
ed of th
e stator
flux vector.
Th
e DTC ba
sed 4
pha
se
8/6
S
R
M
drive i
s
an
alyzed. T
he va
ri
ation of flux
and to
rq
u
e
h
y
stere
s
is ba
n
d
s o
n
swit
chi
ng fre
que
ncy
o
f
0
.
358
0.
3
6
0
.
362
0
.
364
0.
366
0.
368
0.
37
0.
372
0.
3
7
4
0
5
10
15
T
i
m
e
(
S
ec)
C
u
rre
n
t
(
A
)
Ph
1
Ph
2
Ph
3
Ph
4
0
0.
1
0.
2
0.
3
0.
4
0.
5
0
0.
0
5
0.1
0.
1
5
0.2
0.
2
5
T
i
m
e
(
S
ec)
Fl
u
x
m
a
g
n
i
t
ud
e
(
w
b-
t
u
rn
s
)
0
0.
1
0.
2
0.
3
0.
4
0.
5
0
1
2
3
4
5
6
7
8
9
T
i
m
e
(
S
ec)
To
t
a
l
t
or
que
(
N
m
)
0
0.1
0.
2
0.
3
0.4
0.
5
0
1
2
3
4
5
6
7
8
9
T
i
m
e
(
S
ec)
Loa
dt
or
q
u
e
(
N
m
)
0.
3
5
8
0.3
6
0.3
6
2
0.
3
6
4
0.
3
6
6
0.
368
0.3
7
0.
3
7
2
0.3
7
4
0
2
4
6
8
10
T
i
m
e
(
S
ec)
Torque
(
N
m
)
Ph
1
Ph
2
Ph
3
Ph
4
0
0.
1
0.
2
0.
3
0.
4
0.
5
0
10
0
20
0
30
0
40
0
50
0
60
0
70
0
80
0
X
:
0.
43
42
Y
:
79
6.7
Ti
m
e
(
S
e
c
)
S
p
eed
(
r
p
m
)
-0
.
2
-0
.
1
0
0.
1
0.
2
0.
3
-0
.
2
-0
.
1
0
0.
1
0.
2
0.
3
Fl
ux
a
l
pha
Flux
be
t
a
0
0.1
0.
2
0.3
0.
4
0.
5
-2
0
0
-1
5
0
-1
0
0
-5
0
0
50
10
0
15
0
20
0
Ti
m
e
(
S
e
c
)
D
e
lt
a
a
n
g
le
(
D
e
g
.
)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
E
f
f
e
ct
of
S
w
itchin
g Fre
que
nc
y in DT
C B
a
se
d S
w
it
ch
e
d
Relu
ct
an
ce
Mot
o
r D
r
iv
e (
P
.
S
riniva
s)
8091
the conve
r
ter is
analy
z
ed.
It is ob
se
rved
that a
s
th
e h
y
stere
s
is b
a
n
d
s
de
creases, the
swit
chin
g
freque
ncy of
the device i
n
crea
se
s. Fi
nally, a
com
b
ination a
flu
x
hystere
s
is band and
to
rque
hystere
s
i
s
b
a
nd i
s
sele
cted
ba
sed
on
the
no
rmal
ope
rating fre
que
n
c
y range
of th
e devi
c
e,
whi
c
h
is 5 kHz - 1
5
kHz. Thu
s
, 8 % flux hysteresi
s
ban
d an
d 5 % torque
hystere
s
i
s
ba
nd is sele
cted
for
this drive
Referen
ces
[1]
R Krishn
an.
S
w
itc
h
e
d
Rel
u
ctance M
o
tor
Drives
:
mod
e
lin
g, simul
a
ti
on, an
al
ysis,
desi
gns a
n
d
app
licati
ons, C
RC press. 20
0
1
.
[2]
T
J
E Miller. S
w
i
t
ched Re
lucta
n
c
e Motors and
t
heir Co
ntrol, Magn
a Ph
ysics
& Oxford. 199
3.
[3] PJinu
pun,
PC
KLuk.
Direct
torque co
ntrol for sens
or
less
sw
itched
reluctanc
e motor drives
.
Internatio
na
l C
onfere
n
ce Po
wer Electron
i
cs & Variab
le Sp
e
ed Driv
es. 199
8; 329–
33
4.
[4]
AD Cheok, PH Hoon.
A new
torqu
e
co
ntrol
meth
od for sw
i
t
ched re
lucta
n
c
e motor dr
ive
s
.
26
th
An
n
ual
Conf. IEEE In
dustrial Electronics Societ
y
,
2
000; 38
7–
39
2.
[5]
AD C
heok, Y
F
u
kuda. A
n
e
w
t
o
rq
ue
an
d f
l
u
x
c
ontrol
met
hod
for s
w
itc
h
ed r
e
lucta
n
ce
motor dr
ives.
IEEE Transaction on Power Electronics
. 20
02
; 17(4): 543
–55
7.
[6]
Sutikno T
,
Nik Idris N, Jidin A,
Cirstea M. An I
m
prove
d
F
P
GA Implem
entati
on
of Dir
ect T
o
rque
Co
ntro
l
for Induction M
a
chi
nes.
IEEE Transactio
n
s o
n
Industria
l Informatics
. 201
3
;
9(3): 1280 - 1
290.
[7]
Sutikno T
,
Universitas Ahma
d D, Nik Idris NR, Un
ivers
i
ti T
e
knologi M, Jidin AZ
. Altera
Corpor
ati
o
n
Sdn B, et al. A
Model
of F
P
GA
base
d
Dir
ect T
o
rque Contro
l
l
er.
T
E
LKOMNIKA Indones
ia
n Journ
a
l o
f
Electrical E
ngi
neer
ing
. 2
013;
11(2): 74
7-7
5
3
.
[8]
Sutikno T
,
Idri
s NRN, Jidin
A. A revie
w
of direct
torque
control of in
du
ction motors for sustain
a
b
l
e
relia
bi
lit
y a
nd
ener
g
y
effici
en
t drives.
R
e
n
e
w
able
and
Su
staina
ble
En
er
gy Rev
i
ew
s
. 2
014;
32: 5
48-
558.
[9] HJ
Guo.
Co
ns
ider
ations
of d
i
rect torqu
e
co
ntrol for switched reluctance
m
o
tors.
IEEE I
n
ternational
S
y
mp
osi
u
m on
Industrial El
ec
tronics.
200
6; 232
1–
232
5.
[10]
Gui
y
in
g So
ng,
Z
h
ida
Li, Z
h
e
ngh
an Z
h
ao,
Xi
an
g W
a
n
g
.
Direct torq
ue c
ontrol
of sw
itched r
e
l
u
ctanc
e
m
o
tors.
IEEE Internati
o
n
a
l Co
nferenc
e Electr
ical Mac
h
in
es and S
y
stems
.
200
8
;
338
9-33
92
.
[11]
P Sriniv
as, PVN Prasa
d
. Dir
ect torque c
o
n
t
rol of
4 p
has
e 8/6 s
w
itc
hed
relucta
n
ce m
o
tor driv
e fo
r
constant torque load.
W
o
rld Journ
a
l of Mod
e
ling
and Si
mul
a
tion
, 20
12; 8(
3): 185-1
95.
[12]
P Sriniv
as, P
V
N Pras
ad. C
o
m
par
ative P
e
rformance
Ana
l
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