Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
6, N
o
. 2
,
A
p
r
il
201
6, p
p
.
47
4
~
48
3
I
S
SN
: 208
8-8
7
0
8
,
D
O
I
:
10.115
91
/ij
ece.v6
i
2.9
146
4
74
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
/
IJECE
Switching F
O
C Meth
od for Vect
or Control of Single-Phase
Induction Motor Drives
Mohammad
Jann
ati
*
,
Nik
Rumz
i Nik I
d
ris*,
Mohd
Juna
idi
Abdul Azi
z
*
,
To
le Sutikno**
,
M
.
Gha
n
ba
ri**
*
* UTM-PROTON Future Driv
e
Laborator
y
,
Faculty
of
Elec
trical Engin
eering
,
U
n
iver
siti Teknologi Malay
s
ia,
81310 Skudai, Johor Bahru, Malay
s
ia
** Departmen
t
o
f
Electr
i
cal
Engineer
ing
,
Faculty
of Industr
ial
Technolog
y
,
Univ
er
sitas Ahmad Dahlan,
Yog
y
ak
arta 551
64, Indonesia
*** Departmen
t
of Electr
i
cal
Eng
i
neer
ing, Aliab
a
d Katoul
Bran
ch
, Islamic Azad U
n
iversity
, Aliabad Katoul, Ir
an
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Oct 10, 2015
Rev
i
sed
D
ec 28
, 20
15
Accepte
d
Ja
n 12, 2016
This paper prop
oses a novel vector
contro
l method based on Rotor flux
Field-Orien
t
ed
Control (RFOC) for single-ph
ase Induction
Motor (IM)
drives. I
t
is sho
w
n that
in
a rotating r
e
fer
e
nce
frame, th
e sing
le-phase IM
equations can be separated in
to fo
rward and backward equ
a
tions with
balan
ced s
t
ru
ct
ures
. In order
to ac
com
m
o
date for
thes
e f
o
rward an
d
backward equ
a
tions, a driv
e sy
stem consistin
g of two RFOCs that ar
e
switched interchangeab
ly
, is
proposed
. Alter
n
ativ
ely
,
these two RFOC
algorithm
s
c
a
n
be sim
p
lified
a
s
a
single FOC algorithm. The an
aly
s
is,
controller design
and simulation of th
e proposed techn
i
que showed that it is
feasible for
single-phase
IM driv
e for
high p
e
rfor
m
ance
appli
cat
io
ns
.
Keyword:
AC D
r
ives
H
i
gh
p
e
rf
or
m
a
n
ce
ap
p
lications
Single
-
phase i
n
duction m
o
tor
Switching FOC
Vector c
ontrol
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
:
M
oham
m
ad Jannat
i
,
UTM
-
PR
OT
O
N
F
u
tu
re
Dri
v
e
Lab
o
rat
o
ry
,
Faculty of Electrical
En
gi
nee
r
i
n
g
,
Un
i
v
ersiti Tekn
o
l
o
g
i
Malaysia,
8
131
0 Sk
ud
ai,
Jo
hor
Bah
r
u
,
Malaysia.
Em
a
il: j
a
n
n
a
ti
m
9
4
@
yah
o
o
.
co
m
1.
INTRODUCTION
Sin
g
l
e-ph
ase In
du
ction
Mo
tor (IM
) is o
n
e
of th
e m
o
st
applicable electrical
m
achines whi
c
h are
use
d
in
lo
w power
d
o
m
estic an
d
in
du
strial app
licatio
n
s
. Th
is
electrical
m
o
tor can be use
d
in vac
uum
clea
ners
,
washers, co
m
p
ressors,
fan
s
an
d
etc.
Gen
e
rally, a s
i
n
g
l
e-p
h
ase IM h
a
s tw
o
m
a
in
an
d
aux
iliary win
d
i
ng
s and
i
t
s
operat
i
o
n n
eeds o
n
e o
r
t
w
o ca
paci
t
o
rs
.
To gua
ra
nt
ee
the efficient use of ener
gy
,
t
h
e i
nvest
i
g
at
i
on o
f
di
ffe
re
nt
si
ngl
e
-
p
h
ase IM
d
r
i
v
e schem
e
s have been i
n
crea
s
e
d by researc
h
ers. In these drives the single-pha
se
IM,
with
ou
t cap
acito
r, is treat
ed
as
an asymmetric 2-phase
IM [1].
D
i
f
f
e
r
e
n
t
conver
t
er
topo
log
i
es h
a
v
e
b
een pr
opo
sed to
supp
ly sin
g
l
e-
ph
ase m
ach
in
e, for
ex
am
p
l
e,
one
-l
eg
i
n
vert
er [
2
]
,
2-l
e
g
i
nve
rt
er
[1]
,
[
3
]
3
-
l
e
g i
nve
r
t
er [
4
]
,
[
5
]
a
n
d
4
-
l
e
g i
n
ve
rt
er
[6]
.
T
h
i
s
pa
per
i
nvest
i
g
at
es t
h
e use of
2-l
e
g i
nve
rt
er as s
h
o
w
n i
n
Fi
gu
re 1
fo
r fee
d
i
n
g t
h
e
si
ngl
e-
ph
ase I
M
. Thi
s
co
nfi
g
urat
i
o
n
i
s
i
ndi
cat
ed
f
o
r
hi
g
h
per
f
o
rm
ance a
ppl
i
cat
i
o
n
s
[
1
]
,
[
3
]
(
I
t
sh
oul
d
be
poi
nt
ed
out
t
h
at
t
h
e
f
o
cu
s gi
ve
n h
e
r
e
i
s
o
n
t
h
e d
e
t
a
i
l
e
d an
al
y
s
i
s
and
desi
gn
o
f
t
h
e
vect
or
co
nt
r
o
l
st
ra
t
e
gy
f
o
r
si
n
g
l
e
-p
hase
IM
dri
v
es)
.
Fi
el
d-
Ori
e
nt
e
d
C
ont
r
o
l
(
F
OC
)
m
e
t
hod i
s
wi
d
e
l
y
used f
o
r i
m
pl
em
ent
i
ng h
i
gh
per
f
o
r
m
a
nce vect
o
r
co
nt
r
o
l
o
f
si
n
g
l
e
-
p
h
a
se IM
dri
v
es. T
h
i
s
m
e
t
h
o
d
ha
s bee
n
i
n
creasi
n
gl
y
a
d
o
p
t
e
d a
s
t
h
e s
t
anda
rd c
o
nt
r
o
l
t
echni
q
u
e f
o
r
i
n
d
u
st
ri
al
de
m
a
nds
[
1
],
[3
],
[7
]-
[16
]
.
On
e
o
f
th
e m
a
i
n
d
r
awb
a
ck
s in th
e p
r
esen
ted
FOC m
e
th
od
s to
con
t
ro
l sin
g
l
e-ph
ase IM driv
es is u
s
ing
th
e sup
p
o
s
ition
of (
M
d
/
M
q
)
2
=
L
ds
/
L
qs
(
L
ds
,
L
qs
,
M
d
,
M
q
indicate the stator and
rot
o
r d-
q axes
sel
f
a
nd m
u
t
u
al
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
6, No
. 2, A
p
ri
l
20
16
:
47
4 – 4
8
3
47
5
i
n
d
u
ct
ances
) [
1
]
,
[3]
,
[
7
]
-
[
1
5]
.
It
can be
n
o
t
e
d t
h
at
f
o
r si
m
p
l
i
f
y
i
ng vect
or c
ont
rol
e
quat
i
o
n
s
i
n
si
n
g
l
e
-p
ha
se IM
th
e su
ppo
sition
o
f
(
M
d
/
M
q
)
2
=
L
ds
/
L
qs
is u
s
ed
.
It
was
shown
i
n
[16
]
using
t
h
is assu
m
p
tio
n is reflected
i
n
th
e
t
o
r
que r
e
sp
o
n
s
e
of t
h
e si
n
g
l
e
-
pha
se IM
d
r
i
v
e
sy
st
em
. In [1
6
]
, a
m
e
t
hod
fo
r
In
di
rect
R
o
t
o
r
fl
ux F
O
C
(
I
R
F
OC
)
o
f
sing
le-ph
a
se IM with
ou
t u
s
ing
(
M
d
/
M
q
)
2
=
L
ds
/
L
qs
has been pr
esent
e
d.
Ho
we
ver
,
t
h
e i
n
t
r
od
uce
d
m
e
tho
d
i
n
[1
6]
i
s
e
x
t
r
em
el
y
depe
nd
s
on
m
o
t
o
r param
e
t
e
rs
vari
at
i
o
ns.
Thi
s
st
u
d
y
sh
ows t
h
e si
n
g
l
e
-p
hase IM
c
a
n be m
odel
e
d as t
w
o
bal
a
nced ci
rc
ui
t
s
(f
or
war
d
a
n
d
back
wa
rd ci
rc
ui
t
s
). B
a
se
d
o
n
t
h
i
s
si
m
p
l
i
f
y
i
ng,
a n
o
v
el
v
ect
or c
ont
rol
m
e
t
hod
fo
r si
n
g
l
e
-
phase
IM
base
d o
n
FO
C algo
r
ith
m
an
d
w
i
t
h
ou
t usin
g
(
M
d
/
M
q
)
2
=
L
ds
/
L
qs
i
s
present
e
d (s
wi
t
c
hi
n
g
FOC
)
. T
h
i
s
pape
r i
s
or
ga
ni
zed as
fo
llows: After
in
trodu
ctio
n
i
n
sectio
n
1
,
in
sectio
n
2, d-
q m
odel
of si
ngl
e
-
pha
se IM
i
s
p
r
esent
e
d
.
Ne
xt
,
sect
i
on
3 desc
ri
bes t
h
e
devel
o
pm
ent
of t
h
e F
O
C
al
g
o
ri
t
h
m
,
fol
l
o
w
e
d by
p
r
esent
i
ng
pr
o
pose
d
s
w
i
t
c
hi
n
g
FOC
schem
e
f
o
r
v
ector
co
ntr
o
l
o
f
sing
le-p
h
a
se I
M
dr
ives. Th
e
p
e
rf
orman
ce of
th
e
p
r
esen
ted m
e
t
h
od
is an
alyzed
an
d
checke
d
usi
n
g
M
a
t
l
a
b/
Sim
u
l
i
nk
so
ft
wa
re i
n
sect
i
on
4 a
n
d s
ect
i
on
5 c
o
n
c
l
u
des t
h
e
pape
r.
Fi
gu
re 1.
Si
n
g
l
e
-p
hase IM
dr
i
v
e sy
stem
(2-le
g
in
ve
rter)
2.
MODELING
OF SINGLE
-PHASE IM
Neg
l
ecting
th
e co
re saturation
,
th
e d-q
m
o
d
e
l o
f
th
e sing
le-p
h
a
se
IM in
th
e statio
n
a
ry referen
c
e
fram
e
(su
p
ersc
ript “
s
”
)
ca
n
be
sh
ow
n a
s
t
h
e
f
o
l
l
o
wi
ng
eq
uat
i
ons
[
15]
:
(
1
)
In (1
),
v
s
ds
,
v
s
qs
are the stator
d-q a
x
es voltage
s,
i
s
ds
,
i
s
qs
are the stator d-q a
x
es currents
,
i
s
dr
,
i
s
qr
are the
rot
o
r d-q axes
currents
,
λ
s
ds
,
λ
s
qs
are the stator d-q a
x
es fluxes and
λ
s
dr
,
λ
s
qr
are the rotor d-q axes
fluxes.
r
ds
,
r
qs
,
r
r
indicate the
s
t
ator a
n
d rotor
d-q a
x
es
resist
ances.
L
ds
,
L
qs
,
L
r
,
M
d
,
M
q
de
n
o
t
e
t
h
e
st
at
or a
n
d
r
o
t
o
r
d-
q a
x
es sel
f
and m
u
tual inductances
.
r
is
th
e m
o
to
r sp
eed
.
τ
e
,
τ
l
a
r
e el
ect
rom
a
gnet
i
c
t
o
r
que a
n
d l
o
a
d
t
o
rq
ue.
J
,
F
are
the
m
o
men
t
o
f
in
ertia and
v
i
scous friction
co
efficien
t respectively.
3.
SWITC
H
IN
G
FO
C METH
OD FO
R VECTOR
C
O
NT
ROL OF
S
I
N
G
LE-PH
ASE IM
In t
h
i
s
sect
i
o
n
,
a n
ovel
m
e
t
hod
f
o
r
vect
o
r
cont
rol
of si
ng
l
e
-p
hase IM
d
r
i
v
es
base
d o
n
IR
FOC
i
s
propose
d
. In t
h
e RFOC strat
e
gy it is neces
sary that th
e
machine equat
i
ons t
r
ans
f
er to the
rotating
refe
renc
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Sw
i
t
c
hi
n
g
F
O
C
Met
ho
d f
o
r
Vect
or C
ont
r
o
l
of
Si
n
g
l
e
-P
h
a
s
e
I
n
d
u
ct
i
o
n M
o
t
o
r D
r
i
ves (
M
.
Jan
n
a
t
i
)
47
6
fram
e
. Fo
r th
i
s
pu
rpo
s
e, t
h
e tran
sform
a
tio
n
m
a
trix
as
sh
own
in equ
a
t
i
o
n
(2) is applied
to
th
e m
a
ch
in
e
equat
i
o
ns
[
17]
:
e
e
e
e
e
s
T
cos
sin
sin
cos
(2
)
In
(2
), s
u
pers
cr
ipt “
e
” indicate
s
that the e
quat
i
ons a
r
e in t
h
e
rotating re
fere
nce fram
e. Moreover, “
θ
e
”
is the angle be
tween the
stationa
ry
an
d r
o
t
a
t
i
ng re
fere
nce
fram
e
s. B
y
appl
y
i
ng
(2
) t
o
t
h
e eq
uat
i
o
ns
o
f
t
h
e
single-phase IM
(equations (1)),
e
q
ua
tions (3a) and
(
3b) are obtained:
e
qr
e
dr
e
qs
e
ds
e
qr
e
dr
e
qs
e
ds
v
v
v
v
e
qr
e
dr
e
qs
e
ds
q
d
q
d
r
e
q
d
r
e
q
d
q
d
q
d
e
qs
ds
qs
ds
qs
ds
e
q
d
e
q
d
qs
ds
e
qs
ds
qs
ds
v
v
v
v
e
qr
e
dr
e
qs
e
ds
r
r
r
r
e
q
d
q
d
r
e
r
r
e
r
r
q
d
r
e
q
d
q
d
q
d
e
qs
ds
qs
ds
qs
ds
e
q
d
e
q
d
qs
ds
e
qs
ds
qs
ds
e
qs
e
ds
i
i
i
i
dt
d
M
M
M
M
M
M
dt
d
M
M
dt
d
M
M
M
M
dt
d
L
L
r
r
L
L
M
M
dt
d
M
M
L
L
dt
d
L
L
r
r
i
i
i
i
dt
d
L
r
L
dt
d
M
M
M
M
L
dt
d
L
r
M
M
dt
d
M
M
dt
d
M
M
M
M
dt
d
L
L
r
r
L
L
M
M
dt
d
M
M
L
L
dt
d
L
L
r
r
v
v
0
0
2
2
0
0
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
0
0
(3a
)
s
qr
s
dr
s
qs
s
ds
e
e
e
e
e
e
e
e
e
e
e
e
e
e
e
e
e
qr
e
dr
e
qr
e
dr
e
qs
e
ds
e
qs
e
ds
i
i
i
i
i
i
i
i
i
i
i
i
cos
sin
0
0
sin
cos
0
0
cos
sin
0
0
sin
cos
0
0
0
0
cos
sin
0
0
sin
cos
0
0
cos
sin
0
0
sin
cos
(3
b)
In
(
3
a)
, “
ω
e
” is th
e ang
u
l
ar
velo
city o
f
th
e
ro
tor fiel
d
orie
nted
re
fere
nce
fram
e
. As ca
n
be see
n
,
in
g
e
n
e
ral, equ
a
tio
n
(3
a) in
cludes two
term
s (fo
rward
term
: s
u
p
e
rscrip
t “+
e
” and bac
k
war
d
t
e
rm
: supers
cri
p
t
“-
e
”). Eac
h
term
represe
n
ts a ba
lanced e
q
uation whe
r
e rota
t
e
s
i
n
t
h
e
fo
rwa
r
d
or
bac
k
wa
r
d
d
i
rect
i
on as
sh
o
w
n i
n
Fi
gu
re 2.
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.
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l
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47
4 – 4
8
3
47
7
Fi
gu
re 2.
F
o
r
w
ard
,
b
ackward
and stationa
ry
refe
rence
frames (“+
e
”: forward,
“-
e
”
:
b
a
ckw
a
rd
and
“
s
”:
st
at
i
onary
)
As can
be se
en from
(3a), the structure
of th
e
forward
and
b
a
ck
ward
term
s is s
i
milar to
th
e
conve
nt
i
onal
3-phase IM
equ
a
t
i
ons. The onl
y
di
fference
bet
w
een for
w
ard
t
e
r
m
s
and conv
ent
i
onal
3-phas
e
IM
eq
u
a
tio
n
s
is that, in
th
e fo
rward
term
s th
ere are:
(
r
ds
+r
qs
)/2, (
L
ds
+L
qs
)/
2 an
d (
M
d
+M
q
)/2 bu
t in
th
e co
nv
en
tio
n
a
l
3-p
h
ase IM
we
have:
r
s
,
L
s
=L
ls
+
1.5
L
ms
and
M=
1.
5
L
ms
. M
o
reover
,
t
h
e
di
ff
erence bet
w
ee
n bac
k
war
d
t
e
r
m
s and
conve
nt
i
onal
3-phase IM
equ
a
t
i
ons i
s
t
h
at
, in t
h
e backwar
d
t
e
r
m
s
t
h
ere are:
(
r
ds
-r
qs
)/2,
(
L
ds
-L
qs
)/2, (
M
d
-M
q
)/2,
r
r
=0,
L
r
=0 and
there are -
i
qs
e
and -
i
qr
e
but
i
n
t
h
e con
v
ent
i
ona
l
3-phase
IM
we have:
L
s
=L
ls
+
1.5
L
ms
,
M=
1.5
L
ms
,
r
r
≠
0,
L
r
≠
0 and there are
i
qs
e
and
i
qr
e
.
The b
l
ock di
agram
of f
o
r
w
ard
an
d
backwa
rd
IRFOC can be s
h
own as
Fi
gure
3 an
d Fi
gure
4 res
p
ect
i
v
el
y
.
Fi
gu
re
3.
B
l
oc
k
di
ag
ram
of f
o
r
w
ar
d
IR
F
O
C
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IJECE
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S
w
itch
i
ng
FOC Meth
od
f
o
r
Vecto
r
C
o
n
t
ro
l o
f
S
i
ng
le-Pha
se In
du
ction
Moto
r Drives (M.
Ja
nna
ti)
47
8
Fi
gu
re
4.
B
l
oc
k
di
ag
ram
of b
ackwa
r
d
IR
FO
C
Therefo
r
e, t
w
o
devel
oped IR
FOC
al
gori
t
h
m
s
wi
t
h
t
w
o for
w
ard an
d back
ward cu
rrent
s can be used
for
vect
or co
nt
rol
of a si
ngl
e-
phase IM
. The
bl
ock di
ag
ram
of t
h
e pr
op
ose
d
IR
FOC
f
o
r si
ngl
e-p
h
ase IM
dri
v
es
i
s
shown i
n
Fi
gure
5. In Fi
g
u
r
e 5, i
n
or
der t
o
al
t
e
rnat
ely
swi
t
c
hed bet
w
een t
h
e for
w
ard
and back
war
d
st
at
es, a
switch is used
where
b
y this switch will consecu
tively change positions in each sa
m
p
ling ti
me.
Fi
gu
re
5.
B
l
oc
k
di
ag
ram
of t
h
e p
r
o
p
o
sed
IR
FOC
fo
r
vect
o
r
co
nt
r
o
l
o
f
si
ng
l
e
-p
hase
IM
d
r
i
v
es
In
Figu
re
5
,
2 to
2
tran
sform
a
t
i
o
n
m
a
trix
([
T
s
]
)
i
s
obt
ai
ned as
(4):
1
0
0
1
s
T
(4
)
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IJEC
E V
o
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.
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. 2, A
p
ri
l
20
16
:
47
4 – 4
8
3
47
9
C
onseq
uent
l
y
, t
o
sim
p
li
fy
proposed F
O
C
i
n
Fi
gure 5
,
si
ngl
e FOC
al
gori
t
h
m
wi
t
h
onl
y
changes i
n
t
h
e
m
o
t
o
r param
e
ters can be
used
for
vect
or c
ont
rol
of
si
ngl
e-p
h
a
se IM
dri
v
es (
s
ee Fi
gure 6
)
.
Fi
gu
re
6.
B
l
oc
k
di
ag
ram
of t
h
e si
m
p
l
i
f
i
e
d pr
op
ose
d
F
O
C
fo
r
vect
or
co
nt
r
o
l
of
si
n
g
l
e
-
pha
se IM
dri
v
es
4.
SIMULATION RESULTS
In
th
is sectio
n, th
e si
m
u
lat
i
o
n
resu
lts b
a
sed
o
n
Fi
g
u
re 5
and
Figu
re 6
is carried
o
u
t
to
valid
ate th
e
pr
o
pose
d
c
ont
rol
st
rat
e
gy
.
A 0
.
2
5
H
p
si
n
g
l
e
-
phase
IM
i
s
dri
v
e
n
by
a
2-l
e
g v
o
l
t
a
ge
so
urce i
nve
rt
er. T
h
e
si
m
u
latio
n
in
vestig
atio
n
is main
ly fo
cu
sed
o
n
th
e m
o
to
r sp
eed
an
d
t
o
rq
ue respo
n
ses. Th
e m
o
to
r p
a
rameters
are s
h
own in T
a
ble 1.
Tabl
e
1. R
a
t
i
n
gs a
n
d
param
e
ters
of
t
h
e si
ngl
e-p
h
ase
IM
Voltage 90V
Fr
equency
(
f
)
60Hz
No. of Poles
4
Power 0.
25Hp
r
ds
7.
14
r
as
2.
02
M
a
0.
1772H
r
r
4.
12
L
ds
0.
1885H
L
as
0.
1844H
J
0.
0146
kg.m
2
F
0.
0N.m
.
s
Fi
gure
7 sh
ow
s t
h
e sim
u
l
a
t
i
on resul
t
s
o
f
t
h
e pro
pos
e
d
controller for a trapezoidal refe
rence spee
d
from
500
rpm
to -500 rpm
.
It is seen th
at the real speed signal are so accura
te that hardly can be
distinguished
from
the corresponding reference speed signal. As can
be seen from
Fi
gure 7, t
h
e
m
a
xim
u
m speed error is
about
1.5
rpm
.
The m
a
in and auxiliary
stator currents and
electro
m
a
gnetic
torque
for trapezoidal reference
speed are al
so
sho
w
n i
n
Fi
g
u
re 7.
As sh
o
w
n f
r
om
Fi
gure 7, t
h
e si
nus
oi
dal
form
of t
h
e st
at
or curr
ent
s
i
s
main
t
a
in
ed
in
th
e d
i
fferen
t
sp
eed
. Moreover, it can
b
e
seen
th
at th
e electro
m
a
g
n
e
ti
c
to
rqu
e
h
a
s a q
u
i
ck
respo
n
se
wi
t
h
no pul
sat
i
ons.
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IJECE
ISS
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2088-8708
S
w
itch
i
ng
FOC Meth
od
f
o
r
Vecto
r
C
o
n
t
ro
l o
f
S
i
ng
le-Pha
se In
du
ction
Moto
r Drives (M.
Ja
nna
ti)
48
0
Fi
gu
re
7.
Si
m
u
l
a
t
i
on res
u
l
t
s
o
f
t
h
e
p
r
o
p
o
se
d
cont
rol
l
e
r
f
o
r t
h
e t
r
a
p
ez
oi
dal
refe
rence
spe
e
d
fr
om
t
op t
o
b
o
t
t
o
m
:
St
at
or C
u
r
r
ent
s
, Z
oom
of
St
at
or
C
u
rre
nt
s,
Sp
eed,
Spee
d
Er
r
o
r
,
T
o
r
q
ue
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I
S
SN
:
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088
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08
IJEC
E V
o
l
.
6, No
. 2, A
p
ri
l
20
16
:
47
4 – 4
8
3
48
1
Fi
gure
8 sh
ow
s sim
u
l
a
t
i
on resul
t
s
of t
h
e p
r
o
posed
st
rat
e
gy
for
vect
or c
ont
rol
of
t
h
e si
ngl
e-phase IM
in the nom
i
na
l and zero refe
rence speed
s and
un
d
e
r lo
ad
co
nd
itio
n
.
In
Fi
g
u
r
e 8
,
th
e m
o
to
r is ru
nn
in
g
at th
e
reference spee
d of 0r
pm
. Then at
t
=
3s a st
ep change of 1
8
0
0
rpm
i
s
i
n
t
r
odu
ced. In addi
t
i
on, at
t
=
9s, a step l
o
ad
of
1.2
N
.m
i
s
int
r
od
uced a
nd
at
t
=
11s i
s
rem
oved
.
It
i
s
evi
d
ent
from
Fi
gur
e 8 t
h
at
al
t
hou
gh at
t
h
e m
o
m
e
nt
of
appl
y
i
ng l
o
ad t
h
ere i
s
a sm
all
speed di
p
but
t
h
en i
t
i
s
rest
ored qui
ckl
y
. B
a
sed on
present
e
d resul
t
s
i
n
Fi
gure
8
,
usi
ng p
r
o
pose
d
dri
v
e sy
st
em
,
t
h
e
m
a
xim
u
m
speed err
o
r i
n
nom
i
n
al
speed
and d
u
ri
n
g
l
o
ad con
d
i
t
i
on i
s
about
0.4 r
p
m
.
M
o
reover, t
h
e
m
a
xim
u
m
speed error i
n
zero refer
e
nce speed i
s
abo
u
t
0.1 rpm
.
As show
n fr
o
m
Fi
gure
8 the torque increases accordingly to en
s
u
re that the spe
e
d is m
a
intain
ed
at 1800rpm
.
It can be see
n
from
Fi
gure
7 an
d
Fi
gure
8 t
h
at
t
h
e dy
nam
i
c perfo
rm
ance of t
h
e pr
op
osed c
ont
rol
l
e
r f
o
r t
h
e si
ngl
e-phase
IM
i
s
extre
m
ely acce
ptable.
Fig
u
r
e
8
.
Sim
u
latio
n
r
e
su
lts
of
th
e pr
opo
sed
co
n
t
r
o
ller
i
n
t
h
e no
m
i
n
a
l an
d
zer
o r
e
f
e
r
e
n
ce
sp
eed
s
an
d under
lo
ad
con
d
ition
fro
m
to
p
to
bo
tto
m: Sp
eed, Torqu
e
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IJECE
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S
w
itch
i
ng
FOC Meth
od
f
o
r
Vecto
r
C
o
n
t
ro
l o
f
S
i
ng
le-Pha
se In
du
ction
Moto
r Drives (M.
Ja
nna
ti)
48
2
Figure
9 shows
the com
p
ariso
n
between the
steady-sta
te to
rq
u
e
resp
on
se of th
e RFOC at th
e n
o
m
in
al
reference spe
e
d by
consi
d
eri
ng (
M
d
/
M
q
)
2
=
L
ds
/
L
qs
(
e
.g.
,
[
1
], [3
],
[7
]-
[15
]
)
and
wi
t
hout
co
nsi
d
eri
n
g
(
M
d
/
M
q
)
2
=
L
ds
/
L
qs
(swi
t
c
hi
ng
F
O
C
)
. Lar
g
er t
o
rque
ri
ppl
e can
be seen
w
h
en t
h
e assum
p
t
i
on (
M
d
/
M
q
)
2
=
L
ds
/
L
qs
i
s
used.
It
i
s
con
c
l
uded i
n
com
p
ari
s
on
wi
t
h
t
h
e p
r
evi
o
us sc
hem
e
s for R
F
OC
of
si
ngl
e-
phase IM
dri
v
es, t
h
e
pro
pose
d
co
nt
r
o
l
l
e
r i
n
t
h
i
s
st
udy
gi
ves bet
t
e
r
perf
orm
a
nce.
Figu
re 9. Simu
latio
n
resu
lts
o
f
th
e co
m
p
ariso
n
betwee
n
torqu
e
resp
on
se
at th
e no
m
i
n
a
l referen
c
e sp
eed
; left:
assum
i
ng (
M
d
/
M
q
)
2
=
L
ds
/
L
qs
, ri
ght
:
not
a
ssum
i
ng
(
M
d
/
M
q
)
2
=
L
ds
/
L
qs
.
5.
CO
NCL
USI
O
N
In t
h
i
s
pa
pe
r, a
vect
or c
ont
rol
st
rat
e
gy
fo
r si
n
g
l
e
-
phase
IM
d
r
i
v
es ba
sed
on
In
di
rect
R
o
t
o
r
fl
u
x
Fi
el
d-
Orien
t
ed
Con
t
ro
l is p
r
op
o
s
ed
and
tested
. It was sh
own
th
at th
e sin
g
l
e-p
h
a
se IM equatio
n
s
in
th
e ro
tatin
g
refe
rence
frame can
be
classified as
t
h
e
bal
a
nced
eq
uat
i
o
n
s
. B
a
se
d
on
t
h
i
s
si
m
p
l
i
c
it
y
,
a no
vel
vect
o
r
c
ont
rol
m
e
t
hod u
s
i
n
g t
w
o de
vel
o
pe
d
IR
FOC
al
go
r
i
t
h
m
s
was pro
pos
ed
. As a r
e
sul
t
,
t
h
ese t
w
o al
g
o
ri
t
h
m
s
were
si
m
p
lified
as sin
g
l
e IRFOC alg
o
rith
m
.
Si
m
u
latio
n
resu
lts
sho
w
e
d
t
h
at
t
h
e
pr
op
ose
d
s
w
i
t
c
hi
n
g
F
O
C
st
r
a
t
e
gy
works
well ov
er m
o
st sp
eed
ran
g
e
s an
d und
er lo
ad cond
itio
n.
REFERE
NC
ES
[1]
M.R. Correa
, et
al
.
, "Rotor-flux-
oriented con
t
rol
of a sing
le-ph
a
se indu
ction
motor drive"
,
IEEE Transactions
on
Industrial Electronics
, vo
l. 47, p
p
. 832-841
, Aug. 2000.
[2]
M. Chomat and T.A. Lipo, "A
djus
table-speed
single-phase IM
drive with reduced number of switches",
IEEE
Transaction on I
ndustrial Applications
, vo
l. 39, p
p
. 819-825
, May/Jun. 2003.
[3]
M.B. de Rossiter Corrêa
, et a
l
.
,
"Vector con
t
rol
strateg
i
es for sin
g
le
-phase
induction motor drive
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