TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 12, No. 12, Decembe
r
2014, pp. 81
0
4
~ 811
3
DOI: 10.115
9
1
/telkomni
ka.
v
12i12.68
92
8104
Re
cei
v
ed
Jul
y
23, 201
4; Revi
sed Septe
m
ber
28, 201
4; Acce
pted
Octob
e
r 14, 2
014
A Novel Technique for Vector Control of Single-Phase
Induction Motors Based on Rotor Field-Oriented
Control
Mohammad
Janna
ti*, Sajad Abdollah
z
ade
h
Anb
a
r
a
n, Nik Rum
z
i Nik Idris, Mohd Junai
d
i
Abdul Aziz
UT
M-PROT
O
N
F
u
ture Drive L
abor
ator
y
,
F
a
c
u
lt
y
of Electrica
l
Engi
neer
in
g,
Univers
i
ti T
e
knolo
g
i Mal
a
ysia,
UT
M Skudai, 813
10 Jo
hor, Mala
ysi
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: m_jan
nat
yy@
yah
oo.com
A
b
st
r
a
ct
T
he Vari
abl
e F
r
equ
ency C
ont
rol (VF
C
) techn
i
qu
es such
as
scalar a
nd v
e
ctor contro
l meth
ods ar
e
reco
mme
nde
d in nu
mer
ous in
dustria
l
a
n
d
do
mestic
a
ppl
icat
ions. T
h
ey ca
n
provi
d
e
the
sa
ving
en
ergy
an
d
cost econ
omy
for Induction
Motors (IMs). Due to
asy
m
metric
al ch
a
r
acteristics of singl
e-p
has
e IMs,
conve
n
tio
nal
v
e
ctor co
ntrol
meth
ods
for th
ree-p
hase
IMs can
not
be
dir
e
ctly a
ppl
ie
d t
o
si
ngl
e-ph
ase
IMs.
T
h
is study
ai
ms to i
m
pr
ove
p
e
rformanc
e of
the si
n
g
l
e
-ph
a
s
e IMs driv
e s
ystem. H
ence,
a n
o
vel
contr
o
l
appr
oach
base
d
on R
o
tor F
i
eld-Orie
nted c
ontrol (RF
O
C)
w
a
s develo
p
e
d
for singl
e-p
h
a
se IMs. F
o
r thi
s
purp
o
se, trans
formati
on
matr
ices are a
ppl
ie
d to t
he mac
h
ine e
q
u
a
tions.
It is show
n b
y
apply
i
ng th
e
s
e
transformatio
n
matric
es to the un
ba
lanc
e
d
equ
atio
ns
o
f
single-
ph
ase
IM results in set of bala
n
c
ed
equ
atio
ns w
i
th backw
ard a
n
d
forw
ard comp
one
nts. T
her
efore, by so
me
mo
dific
a
tions
i
n
the co
nventi
ona
l
RF
OC meth
od
for three-p
has
e IM, vector control of
sin
g
l
e
-
phas
e IM can
be d
one. T
h
e prop
osed
meth
o
d
de
mo
nstrates
reaso
nab
ly g
o
od sp
ee
d a
n
d
torque
resp
o
n
ses w
i
th sati
sfactory tracki
ng ca
pa
bil
i
ty. In
contrast to pre
v
ious stu
d
ies
o
n
F
O
C for singl
e-ph
as
e IMs or
unb
ala
n
ce
d tw
o-ph
as
e IMs, the su
ppos
itio
n
of
L
qs
/L
ds
=(M
q
/M
d
)
2
has n
o
t be
en
taken i
n
to
acco
unt in
the
pro
p
o
sed
t
e
chn
i
q
u
e
.
It is show
n th
e effect of us
in
g
this sup
positi
o
n is refl
ected
on the
motor
torque
an
d he
nce sp
ee
d os
cillati
ons. D
u
e
to goo
d track
i
n
g
capa
bil
i
ty of propos
ed driv
e system, this co
ntrol tech
n
i
qu
e
can be a w
e
ll
-suited ca
ndi
d
a
te for appl
icat
ion
w
here precis
e mov
e
of IM in requ
ired suc
h
a
s
cutting, knurli
ng an
d defor
mation pr
ocess
e
s.
Ke
y
w
ord:
a n
o
vel tech
ni
que
, single-
ph
ase
inducti
on
mot
o
r,
rotor field-
orie
nted co
ntrol, transfor
m
at
io
n
mat
r
ic
es
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
Single-pha
se
Induction M
o
tors
(IMs) are
on
e of the most co
mmon IMs
whi
c
h are
broa
dly use
d
in both industrial an
d ho
use
hold ap
pli
c
ation
s
. They
used in drye
rs, co
mpressors,
fans, washi
n
g machine
s
and ma
ny other a
ppli
c
atio
ns. Ge
nerally, single
-
ph
ase IMs have t
w
o
windi
ng
s. These
windin
g
s
are in
space qua
dra
t
e and hav
e different resi
stan
ce
s a
n
d
impeda
nces
(these moto
rs ca
n be
con
s
ide
r
ed a
s
u
nbala
n
ced two-ph
ase IMs) [1]. Since both
stator
win
d
in
gs in
the
sing
le-ph
a
se IMs
are fe
d by th
e sa
me p
o
we
r supply, they
are
unb
alan
ce
operated
and
are
very
su
sceptible i
n
t
he
spee
d to
rque p
u
lsatio
ns. If a
conv
entional ve
ct
or
control
strate
gy for th
ree
-
p
hase IM i
s
ap
plied
to
the
si
ngle-pha
se
o
r
unb
alan
ce
d t
w
o-pha
se
IM
s,
signifi
cant oscillations in the s
peed and t
o
rque output
will be pr
oduced [2-6]. Ther
efore, studying
singl
e-p
h
a
s
e
or u
nbal
an
ce
d two
-
ph
ase
machi
ne
driv
es h
a
ve b
e
e
n
arou
sed i
n
cre
a
si
ng i
n
terest
among
re
sea
r
ch
ers over th
e past de
ca
d
e
s [2-2
0].
Field-Orie
nte
d
Control
(F
OC) meth
od
s are
we
ll e
s
ta
blish
ed
at hig
h
pe
rform
a
n
c
e vecto
r
control of IM
s. Thi
s
controlling te
chni
q
ue ha
s
som
e
advantag
es
su
ch a
s
wid
e
ran
ge of
sp
eed
control, accu
rate sp
eed
regulatio
n an
d very
fast dynamic resp
onse. It has been
sug
gested
usin
g Rotor
F
i
eld-O
r
ie
nted Control (RFO
C)
metho
d
b
a
s
ed
on
hyste
r
esi
s
cu
rre
nt controlle
r i
n
[4
-
5], [7]. Using
hysteresi
s
current control
l
er h
a
s
so
m
e
dra
w
b
a
ck in
a light lo
ad
con
d
ition. In
[8],
FOC of
singl
e-ph
ase IM usin
g cu
rrent
double
se
q
uen
ce contro
ller to elimin
ate the torq
ue
pulsation
s ha
s be
en p
r
e
s
ented. Howe
ver, cu
rr
ent
doubl
e sequ
ence controller i
s
a
com
p
lex
controlle
r due
to usin
g PI controlle
rs and
extensiv
e on
-line
com
puta
t
ion. To solve
the asso
ciat
ed
probl
em
s in [
7
, 8], in [9, 10] de
cou
p
li
ng vecto
r
co
ntrol of
singl
e-ph
ase IM
based o
n
RF
OC
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
A Novel T
e
ch
nique for Ve
ctor Cont
rol of Single-Ph
a
se
Induction Mo
tors… (Mo
h
a
m
m
a
d Jann
ati)
8105
strategy
with
optimum op
eration
of this mo
tor
und
er Max T/A (torque
per
a
m
pere) h
a
s
been
prop
osed. It wa
s sh
own in
[2-5], [11-14]
by usi
ng
tra
n
sformation matrices,
the RFO
C
eq
uati
ons
of the unbala
n
ce
d two-ph
ase IM ca
n be tran
sform
ed into a structure of equ
ations, whi
c
h
are
simila
r to the RFO
C
equ
ations of the three-p
h
a
s
e
IM. Howeve
r, in the pro
c
e
ss o
f
calculatio
n the
RFO
C
equ
ations, the ba
ckwa
rd com
pone
nts
of the stato
r
voltage equ
atio
ns have b
e
en
negle
c
ted [2
-3], [11]. Negl
ecting th
e ba
ckwa
rd
com
p
onent
s is
refl
ected i
n
the
spe
e
d a
nd th
e
torque dyn
a
m
ic re
spo
n
se
s of the drive system
[12
-
14]. Gene
ral
problem
s en
cou
n
tere
d in the
vector
co
ntrol
of sin
g
le-pha
se IM
s have
been
disc
u
ssed in [1
5] an
d finally, a F
O
C m
e
thod f
o
r a
symmetri
c
al t
w
o-pha
se
IM
inste
ad
of
asymmet
r
ical
two-pha
se
IM ha
s b
een
pro
p
o
s
ed.
T
h
e
prop
osed m
e
thod in [15]
can not b
e
u
s
ed for ve
ctor
control
of sin
g
le-p
ha
se
IM with
two une
qual
main and a
u
x
iliary windin
g
s o
r
unbal
a
n
ce
d two ph
ase IM
s. In [16-1
9
], feedforward de
co
upling
scheme fo
r vector
cont
rol
of single
-
ph
a
s
e IMs h
a
s
b
e
en presente
d
. In [16],
Indirect Stator Fi
eld-
O
r
ie
n
t
ed
Co
ntr
o
l (
I
SF
OC
)
fo
r
s
i
n
g
l
e-
p
has
e
IM
u
s
ing
DS110
4
was
discu
s
sed a
n
d
implem
ente
d
.
In [17], feedforwa
rd
de
coup
ling metho
d
for si
ngle
-
ph
a
s
e IM with
est
i
mation of rotor spee
d ba
sed
on moto
r mo
del ha
s be
en
pre
s
ente
d
. T
he present
ed
method fo
r sp
eed
sen
s
o
r
le
ss ve
ctor
co
n
t
rol
of single
-
p
h
a
s
e IM in [17]
has b
een d
e
velope
d wit
h
estimatio
n
of stator resi
stan
ce in [18
]. In
[19], Speed
sensorle
ss F
O
C of
sin
g
le
-p
hase IM
usi
n
g
ad
aptive sli
d
ing mode
-m
odel refe
ren
c
e
adaptive sy
stem strate
gy has be
en stu
d
i
ed.
In the majorit
y
of the previously propos
ed FOC
cont
rol methods f
o
r
controlling singl
e-
pha
se o
r
un
balan
ce
d two-ph
ase IMs, for si
mplifying of FOC equation
s
,
the assum
p
tion
L
qs
/
L
ds
=(
M
q
/
M
d
)
2
has bee
n use
d
[7-1
0], [15-18], [20
]. As mentioned befo
r
e, usin
g this
assumptio
n
is refle
c
ted in
the oscillation
s of
sp
eed a
n
d
hen
ce the t
o
rqu
e
re
sp
on
se
s of the dri
v
e
system. In
[12-1
4
], an
e
x
act mod
e
l f
o
r
RFO
C
of the two-p
h
a
se
IM with
out a
s
sumpti
on
L
qs
/
L
ds
=(
M
q
/
M
d
)
2
ha
s be
en
pro
p
o
s
ed. T
he p
r
op
osed
drive
system in [12,
13] is
sensitive to
regul
ation of
PI controll
er
coe
ffici
ents.
More
over, th
e propo
sed
method i
n
[1
4], is very
co
mlex
due to the usi
ng two p
r
allel
FOC alg
o
rith
ems. In th
is study, a novel scheme fo
r vector
co
ntrol
of
singl
e-p
h
a
s
e
IM based o
n
the RFO
C
an
d without assumption
L
qs
/
L
ds
=(
M
q
/
M
d
)
2
is p
r
o
p
os
ed
a
n
d
che
c
ked by
MATLAB sim
u
lation
s.
2.
Model of IM (Three
-
Phas
e
and Single-Phase IM)
The eq
uation
s
of the IM (three
-p
ha
se a
nd si
n
g
le
-pha
se IM) in the
stationa
ry ref
e
ren
c
e
frame (sup
erscript “
s
’’)
ca
n be de
scribe
d as follo
wing
equation
s
[3]:
Stator and rot
o
r volta
ge eq
uation
s
:
(
1
)
Stator and rot
o
r flux eq
uati
ons:
(
2
)
Electrom
agn
etic torqu
e
eq
uation
s
:
(
3
)
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 : 8104 – 81
13
8106
Whe
r
e,
v
s
ds
,
v
s
qs
,
i
s
ds
,
i
s
qs
,
i
s
dr
,
i
s
qr
,
λ
s
ds
,
λ
s
qs
,
λ
s
dr
and
λ
s
qr
are the
d-q axes voltag
es,
current
s,
and
fluxes of the stator a
nd rot
o
r,
r
ds
,
r
ds
and
r
r
denote the
d-q axes
stat
or and
rotor
resi
stan
ce
s
. L
ds
,
L
qs
,
L
r
,
M
d
an
d
M
q
d
enote
the stato
r
, th
e rotor self a
n
d m
u
tual i
n
ducta
nces.
r
is the
machi
n
e
spe
ed.
e
is t
he ele
c
trom
a
gnetic to
rque,
l
is the loa
d
torque,
J
i
s
the mome
nt of inertia and
F
is
visco
us fri
c
ti
on coefficie
n
t. For thre
e-pha
se IM we have:
r
ds
=r
qs
=r
s
,
L
ds
=L
qs
=L
s
=L
ls
+
3/2
L
ms
,
M
d
=M
q
=M
=
3/
2
L
ms
and for
singl
e-p
h
a
s
e
IM we h
a
ve:
r
ds
≠
r
qs
,
L
ds
≠
L
qs
,
M
d
≠
M
q
.
As can be
se
en from
equatio
ns
(1
)-(3), in
ge
n
e
ral,
the
structure of th
e thre
e-p
h
a
s
e and
si
ngle
pha
s
e m
a
chine
equatio
ns a
r
e
the same.
3.
Problem Sta
t
emen
t in Vect
or Control of Single-Ph
ase IMS
In RFO
C
techniqu
e for ve
ctor
control o
f
IMs,
by using followin
g
m
a
trix (co
n
vent
ional or
balan
ce
d tra
n
sformation
matrix), IM e
quation
s
a
r
e
transfe
r
red to
the rotating
referen
c
e fra
m
e
[21]:
(
4
)
Whe
r
e,
θ
e
is the angle b
e
twee
n the stationary refe
re
nce fra
m
e an
d rotating ref
e
ren
c
e frame
(in
this pap
er
su
perscript
e
in
dicate
d that the equ
ation
s
are in the
rotating refe
re
nce frame
)
. By
applying (4) t
o
the singl
e-p
hase IM equa
tions, the followin
g
equati
ons a
r
e obtai
ned.
(5)
Whe
r
e:
(
6
)
As ca
n be
se
en, in ge
nera
l
, Equation (5
) in
cl
ude
s
fo
rward an
d ba
ckwa
rd
com
p
onent
s
(for
war
d
: +
e
and b
a
ckward: -
e
). G
ene
ration of ba
ckward comp
o
nents i
n
the
singl
e-p
h
a
s
e
IM
equatio
ns i
s
becau
se of di
fferent pa
ram
e
ters i
n
the
single-pha
se I
M
model
(
r
ds
≠
r
qs
,
L
ds
≠
L
qs
and
M
d
≠
M
q
; there
are not the
s
e terms in th
e three
-
ph
ase IM)
.
To sol
v
e this pro
b
l
e
m, in this st
udy,
transfo
rmatio
n matri
c
e
s
a
s
p
r
op
osed i
n
[12-14],
are used. Th
e
goal of u
s
in
g
these
matri
c
es i
s
removin
g
ba
ckward
com
p
o
nents.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
A Novel T
e
ch
nique for Ve
ctor Cont
rol of Single-Ph
a
se
Induction Mo
tors… (Mo
h
a
m
m
a
d Jann
ati)
8107
4.
Proposed M
e
thod
for Ve
ctor Control of Single-Ph
ase IM Bas
e
d
on RFO
C
As mention
e
d
before, du
e to the asymmetric
al ch
ara
c
teri
stics
of single
-
ph
a
s
e IM, the
conve
n
tional
transfo
rmatio
n matrix for t
h
ree
-
p
h
a
s
e I
M
can
not be
use
d
for
sin
g
le-p
ha
se IM
. In
this pap
er, b
a
se
d on prop
ose
d
tran
sformation matr
i
c
es in [12
-
14],
an exact mo
del for RF
OC of
singl
e-p
h
a
s
e
IM is presented. The
tran
sform
a
ti
on
matrices fo
r stato
r
voltage a
nd
curren
t
variable
s
a
r
e
as follo
wing e
quation
s
[12-14]:
Tran
sfo
r
m
a
tion m
a
trix for
stator
voltage
s:
(7)
Tran
sfo
r
m
a
tion m
a
trix for
stator
current
s:
(8)
Usi
ng p
r
o
p
o
s
ed t
r
an
sformation mat
r
i
c
e
s
(Eq
uatio
n (7
) a
nd
(8)) th
e u
n
b
a
lan
c
ed
equatio
ns
of singl
e-pha
se IM (Equ
ation (1)-(3
)) chang
e into
b
a
lan
c
ed
equ
a
tions [3]. A
fter
simplifying, th
e RF
OC
equ
ations
of sin
g
l
e-ph
ase
IM u
s
ing
pro
p
o
s
e
d
tran
sformati
on matri
c
e
s
a
r
e
gaine
d a
s
foll
owin
g eq
uati
ons
(in
RFO
C
meth
od, th
e roto
r flux vector is
align
ed with
d-axis;
λ
dr
e
= |
λ
r
| and
λ
qr
e
=
0):
(
9
)
In Equation
(9),
T
r
(
T
r
=
L
r
/
r
r
) is
the rotor time
c
o
ns
t
ant. Moreover, the
s
t
ator
voltage
equatio
ns a
r
e
obtained a
s
:
(
1
0
)
Whe
r
e:
(
1
1
)
As can
be
se
en fro
m
(9)
a
nd (10),
usi
n
g propo
s
e
d
transfo
rmatio
n
matri
c
e
s
, the RF
OC
equatio
ns of
single
-
p
h
a
s
e IM are o
b
tained a
s
RFO
C
eq
uat
ions
of thre
e-ph
ase IM. The
equatio
ns
of
RFO
C
fo
r three-p
h
a
s
e IM
and
blo
ck
d
i
agra
m of IRFOC
of thre
e-ph
ase IM
are
sho
w
n in Equ
a
tion (12
)
, (1
3) and Fi
gure
1 resp
ectivel
y
[21].
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 : 8104 – 81
13
8108
(
1
2
)
Whe
r
e:
(
1
3
)
Figure 1. Block di
agram of
IRFOC for th
ree
-
ph
ase IM
The differe
nce betwe
en Equation (9) a
nd (10
)
and
RFO
C
equ
ations of thre
e-pha
se IM
(Equatio
n (12
)) is that in E
quation (9) a
nd (10
)
we h
a
ve:
r
qs
,
M
q
,
L
qs
and backward co
mpo
n
ents
(
s
up
er
sc
r
i
p
t
-
e
)
but
in
t
he RFO
C
e
quation
s
of three
-
ph
ase IM,
we hav
e:
r
s
,
M
=3/
2
L
ms
,
L
s
=L
ls
+3/
2
L
ms
and
we do
not have ba
ckward
co
mpo
n
ents.
Th
erefore, it is p
o
ssible
by som
e
cha
nge
s in
the blo
c
k dia
g
ram
of the
RFO
C
fo
r three-p
h
a
s
e IM
(Figu
r
e
1),
we
can
do v
e
cto
r
control of sin
g
le-p
ha
se IM. Equation (1
0
)
can b
e
re
-written as follo
wing e
quatio
ns:
Stator d-a
x
is
voltag
e:
(
1
4
)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
A Novel T
e
ch
nique for Ve
ctor Cont
rol of Single-Ph
a
se
Induction Mo
tors… (Mo
h
a
m
m
a
d Jann
ati)
8109
Stator q-a
x
is
voltag
e:
(
1
5
)
Based
on Eq
uation (9), (1
4) an
d (1
5),
Fi
gure 2 can
be propo
se
d for IRFO
C of
single
-
pha
se IM. In
this Fi
gu
re,
the n
e
ce
ssary voltage
s for ve
ctor control
of si
n
g
le-p
ha
se IM
are
prod
uced by
PI controllers and Decou
p
ling Ci
rcuit as follows (i
n (16
)
,
v
ds
ref_
d
,
v
ds
ref_
q
,
v
qs
re
f
_
d
,
v
qs
ref_q
are
produ
ced
by u
s
ing PI
controll
ers an
d
v
ds
D_C
,
v
ds
D_C
are prod
uced by usin
g De
cou
p
ling
Circuit as
sho
w
n in Figu
re
1):
(
1
6
)
Whe
r
e:
(17
)
The matrix [
T
s
], in Figure
1 and Fi
gu
re 2 for th
ree
-
pha
se
and
single-pha
se I
M
is a
s
follows
[21]:
T
h
r
e
e
-
ph
as
e
IM:
Sin
g
l
e
-
ph
as
e IM:
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 : 8104 – 81
13
8110
Figure 2. Block di
agram of
the pr
opo
se
d
IRFOC for
si
ngle-pha
se I
M
Figure 2, dep
icts the
pro
p
o
se
d
control
scheme fo
r v
e
ctor
co
ntrol
of singl
e-p
h
a
s
e IM. It
comp
oses a
single
RFO
C
algo
rithm
whi
c
h is a
d
o
p
ted from co
nventional
RFOC
with so
me
modificatio
n
s
and two
swit
ches. In ea
ch
sampli
ng tim
e
swit
che
s
co
nse
c
utively o
p
erate.
5.
Simulations and Re
sults
In this section, MATLAB simulation results
based on
propo
se
d dri
v
e system as shown
in Figu
re
2 for a
sin
g
le-p
hase IM hav
e bee
n p
r
e
s
e
n
ted. A sin
g
l
e
-ph
a
se IM i
s
fed from a
Sine
Pulse
Wi
dth
Modulatio
n
(SPWM) two
-
l
eg Volta
ge S
ource Inverte
r
(VSI) as sh
own in Figu
re 3.
The Ratin
g
s
and pa
ram
e
ters of the
sim
u
lated si
ngle
-
pha
s
e IM are
as follo
ws:
Voltage:110V
,
f
=60Hz, No. of pole
s
=4,
r
ds
=7.
1
4
,
r
qs
=2.
0
2
,
r
r
=4.
1
2
,
L
ds
=0.1885
H,
L
qs
=0.18
44H,
L
r
=
0
.1
82
6H
,
M
q
=
0
.1772H,
J
=0.014
6kg.m
2
Figure 3. Single-p
h
a
s
e IM drive syste
m
Figure 4
sho
w
s th
e si
mula
tion re
sult
s of
the
propo
se
d vecto
r
controller
whe
n
th
e sp
eed
referen
c
e
ch
ange
s fro
m
zero to the
no
minal value
(zero to 18
00
rpm). At time
t=10
s, a loa
d
torque e
qual t
o
1N.m is introdu
ced (step
load). As
sho
w
n in Figu
re
4(a
)
, the motor sp
eed follo
ws
the com
m
an
d sp
eed
accura
cy witho
u
t any oversh
o
o
t and
stead
y-state e
rro
r
even at very
low
spe
ed a
nd
after ap
plying l
oad to
rqu
e
(t
he o
scill
ation
of sp
eed i
s
about 0.2
r
pm
in ste
a
dy-st
a
te
and after ap
pl
ying load torq
ue). Figu
re 4
(
b) and Fi
gure
4(c) illustrate
d the curre
n
ts of stator main
and auxiliary
windi
ng
s and
electrom
agn
etic torqu
e
re
spe
c
tively. It
can be
see
n
from Figu
re 4(c)
that the ele
c
tromag
netic t
o
rqu
e
h
a
s
a
quick
re
spo
n
se
with
no
pulsation
s (t
he o
scill
ation
of
electroma
gne
tic torqu
e
is a
bout 0.25
N.m
in steady
-sta
te and after a
pplying loa
d
torqu
e
). Figu
re
4 illustrates the performance of
the proposed drive sy
stem
is extremely satisfact
o
ry.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
A Novel T
e
ch
nique for Ve
ctor Cont
rol of Single-Ph
a
se
Induction Mo
tors… (Mo
h
a
m
m
a
d Jann
ati)
8111
(a)
(b)
(c
)
Figure 4. Simulation re
sult
s of the pro
p
o
s
ed IR
FO
C method for a
single-pha
se I
M
at nominal
and zero
spe
ed; (a)
spe
e
d
,
(b) stato
r
cu
rre
nts, (c) ele
c
trom
agn
etic
torque
Figure 5 an
d Figure 6
sho
w
the go
od dy
nami
c
behavio
r of the propo
s
ed
RFO
C
techni
que fo
r a
singl
e-p
hase IM in
the differe
nce value
s
of
referen
c
e
speed
and
fo
r a
trape
zoid
al re
feren
c
e
spee
d re
spe
c
tively. In Figure
5, at t=9.5s, a lo
ad torq
ue eq
ual to 0.5N.m
is
applie
d an
d removed
at t=11.5s. It is
e
v
ident fr
om F
i
gure
4-6 tha
t
the pro
p
o
s
e
d
sche
me
ca
n
operate stabl
y at high, low and zero
spe
ed and
p
r
ovid
e the accepta
b
le dynami
c
resp
on
se.
(a)
(b)
Figure 5. Simulation re
sult
s of the pro
p
o
s
ed
IRFO
C method for a
single-pha
se I
M
in the
differen
c
e val
ues of spee
d; (a) spee
d, (b
) elect
r
oma
g
n
e
tic torqu
e
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 : 8104 – 81
13
8112
(a)
(b)
Figure 6. Simulation re
sult
s of the pro
p
o
s
ed IR
FO
C method for a trape
zoid
al ref
e
ren
c
e
spe
e
d
;
(
a
)
s
p
ee
d
,
(
b
) e
l
e
c
tr
oma
gne
tic
to
r
q
ue
Figure 7
sh
ows a
com
pari
s
on
bet
ween th
e
ste
ady-state
el
ectro
m
ag
neti
c to
rque
respon
se
of the propo
se
d
scheme
ba
se
d on Fi
gure 2
with con
s
ide
r
ing of
(
M
q
/
M
d
)
2
=
L
qs
/
L
ds
(e.
g
,
[7-10], [15-18], [20],
[22-24
]) and
witho
u
t
con
s
ide
r
in
g
of (
M
q
/
M
d
)
2
=
L
qs
/
L
ds
. As
c
a
n b
e
s
e
en
fr
om
Figure 7, the
r
e is
a small
magnitud
e
of osc
illation
s at the n
o
m
inal comm
and
spe
e
d i
n
the
electroma
gne
tic torqu
e
re
spon
se when t
he assum
p
tio
n
(
M
q
/
M
d
)
2
=
L
qs
/
L
ds
is used (the oscillations
of ele
c
trom
a
gnetic torq
ue
with
co
nsi
d
ering
of
(
M
q
/
M
d
)
2
=
L
qs
/
L
ds
i
s
a
bout
0.25
N.m a
r
ou
nd
the
averag
e am
ount of 1N.
m
. Moreove
r
, the osc
illa
tions of ele
c
trom
agn
etic torque
with
out
con
s
id
erin
g of
(
M
q
/
M
d
)
2
=
L
qs
/
L
ds
is a
b
out 0.4
N
.m
arou
nd th
e a
v
erage
am
ou
nt of 1
N
.m).
It is
con
c
lu
ded
in
co
mpa
r
ison
with the
p
r
ev
ious c
ontrol
scheme
s
for
FOC of
singl
e-ph
ase o
r
t
w
o-
pha
se IM (e.
g
, [7-10], [15-18], [20], [22-24]), t
he pro
p
o
se
d FOC te
chni
que in thi
s
pap
er is m
o
re
acc
u
rate.
(a)
(b)
Figure 7. Simulation re
sult
s of com
pari
s
on between
t
o
rqu
e
re
sp
on
se in si
ngle
-
p
hase IM; (a)
not
assumin
g
(
M
q
/
M
d
)
2
=
L
qs
/
L
d
s
,
(b) a
s
sumin
g
(
M
q
/
M
d
)
2
=
L
qs
/
L
d
s
6. Conclu
sion
In this
pap
er,
a n
o
vel te
ch
nique
for
sp
e
ed
control of
singl
e-p
h
a
s
e
or u
nbal
an
ce
d two
-
pha
se IM
s
b
a
se
d o
n
RF
OC
ha
s
been
propo
sed.
It is shown
usi
ng u
nbal
an
ce
d tra
n
sfo
r
mat
i
on
matrices th
e
unbal
an
ced e
quation
s
of
si
ngle-pha
se
I
M
can
be tran
sferred i
n
to th
e equ
ation
s
that
have the
sa
me st
ru
cture
as th
e thre
e-ph
ase IM.
Usi
ng thi
s
si
milarity a n
o
v
el vector co
ntrol
method for
si
ngle-pha
se I
M
s whi
c
h i
s
obtaine
d fro
m
the conven
tional vector
control metho
d
for
three
-
ph
ase IMs is
propo
sed. Unli
ke ot
her F
O
C m
e
thod for
singl
e
-ph
a
se IMs,
the pro
p
o
s
e
d
scheme i
n
this pap
er d
o
e
s
not u
s
e th
e sup
p
o
s
ition
(
M
q
/
M
d
)
2
=
L
qs
/
L
ds
. The perf
orma
nce of the
proposed
RF
OC techni
que is highly
satisfactory for
controlling
si
ngl
e-phase I
M
in wide range of
spe
ed.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
A Novel T
e
ch
nique for Ve
ctor Cont
rol of Single-Ph
ase
Induction Mo
tors… (Mo
h
a
m
m
ad Jann
ati)
8113
Referen
ces
[1]
AE F
i
tzgerald,
C Kings
le
y, SD
Umans. Electri
c
Machin
er
y
.
M
c
Gra
w
-
Hil
l. 20
03.
[2]
M Jannati, E F
a
lla
h.
Mode
li
ng
and Vector Co
ntrol of Unb
a
l
a
nc
ed i
nducti
on
motors (fa
u
lty three p
has
e
or sing
le p
h
a
s
e ind
u
ctio
n motors)
. 1st. Confer
ence
o
n
Po
w
e
r El
ec
tronic & Drive
S
y
stems
&
T
e
chnolog
ies (
PEDST
C). 2010; 208-2
11.
[3]
M Jannati, NR
N Idris, Z
Salam.
A New
Method for Mo
d
e
lin
g a
nd Vect
or
Contro
l of Unb
a
la
nce
d
Inductio
n
Moto
rs
. IEEE Energy
Co
nvers
i
on
Con
g
ress an
d
Ex
p
o
siti
on. 20
12; 362
5-3
632.
[4]
M Jann
ati, A
Mona
di, NR
N
Idris, MJA Azi
z
, AAM
F
audz
i. Vector Co
nt
rol of F
a
u
l
t
y
T
h
ree-Phase
Inductio
n
Moto
r
w
i
th a
n
Ada
p
t
i
ve Sli
d
in
g Mod
e
Contro
l.
Pr
z
Elektrotech
. 2
0
13; 89(1
2
): 116
-120.
[5]
M Jann
ati, A
Mona
di, N
R
N
Idris, MJA A
z
iz, AAM F
a
u
d
zi. Sp
eed
Se
nsorl
e
ss Vect
or Co
ntrol
of
Unb
a
la
nce
d
T
h
ree-Ph
ase In
d
u
ction M
o
tor
w
i
th Adaptiv
e Sli
d
in
g Mod
e
Co
n
t
rol.
Internatio
n
a
l Jo
urna
l of
Pow
e
r Electron
ics and Dr
ive S
ystems (IJPED
S)
. 2014; 4(3): 406-
418.
[6]
M Jannati, N
R
N
Idris, MJA Aziz. Indirect Ro
tor F
i
eld-Orie
nted Co
ntrol of F
aul
t-T
o
lerant D
r
ive S
y
stem
for T
h
ree-Pha
s
e Ind
u
ctio
n
Motor
w
i
th
R
o
tor R
e
sistanc
e Estimati
on
Using
EKF
.
TE
L
K
OM
N
I
KA
Indon
esi
an Jou
r
nal of Electric
al Eng
i
ne
eri
n
g
.
2014; 1
2
(9): 6
633-
664
3.
[7]
MBR Correa,
CB Jacob
i
na,
AMN Lima, ER
C da Silv
a. Ro
tor F
l
ux Orient
ed Co
ntrol of a
Singl
e Phase
Inductio
n
Moto
r Drive.
IEEE Transacti
ons o
n
Industria
l Elect
r
onics
. 20
00; 4
7
(4): 832-
84
1.
[8]
MR Corr
ea,
C
B
Jaco
bin
a
, E
RCD S
ilva,
AM
N Lim
a
. Vect
or contro
l strate
g
i
es for
sin
g
l
e
-p
hase
in
ducti
on
motor drive s
y
s
t
ems.
IEEE
Trans. Ind. Electron.
2004; 5
1
(5): 107
3-10
80.
[9]
S Vaez-Z
ade
h
,
SR Haroon
i.
Decou
p
li
ng V
e
ctor Contro
l of Si
ngl
e-Ph
as
e Inductio
n
Motor Drives
.
Procee
din
g
s of
36th IEEE Conferenc
e on Po
w
e
r
Electro
n
ics
Specia
lists PESC. 2005; 7
33-
738.
[10]
S Reic
y
,
S Va
ez-Z
ade
h.
Vector Control of Sing
le-Ph
a
se Inducti
on Mach
ine
w
i
t
h
M
a
x
i
mu
m T
o
r
q
u
e
Operatio
n
. In IEEE ISIE. Dubrovnik, Cro
a
tia.
2005; 9
23-9
2
8
.
[11]
M Jannati, E F
a
lla
h.
A New
Method for Sp
eed Se
nsorl
e
s
s
Vector
Control of Sing
le-Ph
a
se Inducti
o
n
Motor Usin
g Extende
d Kal
m
a
n
F
ilter
. Conf. Proc. Of
ICEE. 2011; 1-5.
[12]
M Jann
ati, NR
N Idris, MJA Aziz.
A new
method for
RF
OC of Inductio
n
M
o
tor un
der
ope
n-ph
ase fa
ult
.
In Industrial El
ectronics Soc
i
e
t
y
,
IECON. 201
3; 2530-
25
35.
[13]
M Jann
ati, NR
N Idris, MJA Aziz, A Mona
di,
AAM
F
audzi.
A Novel Sc
he
me for Red
u
cti
on of T
o
rque
and S
pee
d Ri
ppl
e in R
o
tor
F
i
eld Orie
nte
d
Co
ntro
l of
Sing
le Ph
ase
Inductio
n
Mot
o
r Base
d o
n
Rotational T
r
ansformations.
Rese
arch Jo
urnal of Ap
pli
e
d
Sciences, En
gin
eeri
ng a
n
d
T
e
chnol
og
y
.
201
4; 7(16): 34
05-3
409.
[14]
M Jann
ati, A Mona
di, SA A
nbar
an, NR
N Idris, MJA Aziz
. An Exact Mo
del for
Rotor
F
i
eld-Orie
nte
d
Contro
l of Si
ngl
e-Phas
e In
ductio
n
Motor
s
.
T
E
LKOMNIKA Indon
esi
a
n Jour
nal
of
Electrica
l
Engi
neer
in
g
. 2014; 12(
7): 511
0-51
20.
[15]
D Ja
ng. Pr
obl
e
m
s Incurre
d i
n
a Vector-
C
o
n
trolle
d S
i
n
g
le-P
h
a
se In
ducti
on
Motor, an
d
a P
r
opos
al f
o
r
a
Vector-Co
n
troll
ed T
w
o
-
Phas
e Ind
u
ctio
n M
o
tor as
a
Re
plac
ement.
IE
EE T
r
ansacti
o
n
o
n
P
o
w
e
r
Electron
ics
. 20
13; 28(1): 5
26-
536.
[16]
HB Azza, M J
e
mli, M Bouss
a
k, M Goss. Impl
eme
n
tatio
n
of Sensorle
e
Spee
d Co
ntrol
for
T
w
o-Ph
as
e
Inductio
n
Moto
r Drive Usin
g ISF
O
C Strategy.
IJST
, T
r
ansactions of Ele
c
trical Eng
i
ne
e
r
ing
. 20
11
;
35(E1): 63-
74.
[17]
M Jemli, H Ben Azza, M Boussak. Sens
orless I
ndir
e
ct Stator F
i
el
d Orie
ntation S
p
e
e
d
Control fo
r
Sing
le-Ph
a
se I
nducti
on M
o
to
r Drive.
IEEE
Transactions on
Power Electr
onics
. 20
09
; 24
(6
): 1
6
1
8
-
162
7.
[18]
HB Azza, M Jemli, M Boussak, M Gossa. High
p
e
rformanc
e sens
orless s
pee
d vector co
ntrol of SPI
M
Drives
w
i
th
on-
line stator res
i
s
t
ance estimati
o
n
.
J. Simul
a
t. Practice T
heory
.
2011; 1
9
: 271-
282.
[19]
HB Azza,
N Z
a
idi,
M Jem
li,
M Bouss
a
k, M
Go
ssa. D
e
ve
l
opme
n
t a
nd E
x
p
e
rime
ntal
Ev
alu
a
tion
of
a
Sensor
less Sp
eed C
ontro
l of SPIM Using
Adaptiv
e Sli
d
in
g Mode-M
R
AS
Strateg
y
.
IEE
E
Journa
l o
f
Emer
gi
ng an
d
Selecte
d
T
opic
s
in Pow
e
r Ele
c
tronics
. 201
4; 2(2): 319-
32
8.
[20]
M Jannati, SA Anbar
an, IM
Alsof
y
ani, NRN I
d
ris, MJA Aziz.
Modeli
ng a
nd
RF
OC of faulty three-ph
ase
IM usin
g Exte
n
ded
Ka
lman
F
i
lter for r
o
tor s
p
eed
esti
mation
. In Po
w
e
r E
n
gin
eeri
n
g and
Optimization
Confer
ence (P
EOCO). 2014; 270-
275.
[21]
P Vas. Vector Contro
l of AC Ma
chi
nes. Oxf
o
rd scie
n
ce p
u
b
licati
on. 1
990.
[22]
M Jann
ati, NR
N Idris, MJA A
z
iz. Spee
d Se
n
s
orle
ss F
a
ult T
o
ler
ant Driv
e S
y
stem
of 3-Ph
a
s
e Inducti
o
n
Motor Us
ing
S
w
itc
h
i
ng E
x
t
end
ed
Kalm
an
F
ilter.
T
E
LK
OMNIKA Indo
nesi
an J
our
na
l of E
l
ectric
a
l
Engi
neer
in
g
. 2014; 12(
11).
[23]
M Jan
nati, N
R
N
Idris, MJA A
z
iz
. IF
OC of F
ault
y
Si
ngl
e-Pha
s
e IMs.
T
E
LKOMNIKA Indon
esia
n Jo
urn
a
l
of Electrical En
gin
eeri
n
g
. 20
1
4
; 12(10).
[24]
M Jannati, SH Asgari, NRN Id
ris, MJA Aziz.
S
pee
d Sens
orl
e
ss Direct Rot
o
r Field-Orie
nted Co
ntrol of
Sing
le-Ph
a
se
Inductio
n
M
o
tor Usi
n
g
E
x
tend
ed
Kalm
a
n
F
ilter.
Inter
natio
nal
Jo
urn
a
l
of Pow
e
r
Electron
ics an
d Drive Syste
m
s (IJPEDS)
. 2014; 4(4).
Evaluation Warning : The document was created with Spire.PDF for Python.