Internati
o
nal
Journal of P
o
wer Elect
roni
cs an
d
Drive
S
y
ste
m
(I
JPE
D
S)
V
o
l.
5, N
o
. 3
,
Febr
u
a
r
y
201
5,
pp
. 36
6
~
37
3
I
S
SN
: 208
8-8
6
9
4
3
66
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
Adoption of Park’s Transforma
tion for Inverter Fed Drive
J
aya
rama
Pradeep*, R
.
D
e
va
na
t
h
a
n
**
* Department of
Electrical and
Electron
i
cs Eng
i
neering, Sath
y
a
bama University
** Departmen
t
o
f
Electr
i
cal
and
Electroni
cs Eng
i
neering
,
Hindustan University
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Oct 17, 2014
R
e
vi
sed Dec 8,
2
0
1
4
Accepte
d Ja
n
2, 2012
Park’s transform
a
tion in th
e c
ontext of
ac m
achin
e is app
lie
d to obta
i
n
quadratur
e voltages for the 3-p
h
ase balanced
voltag
e
s. In the case of
a
inverter fed
driv
e, on
e can
adopt Park’s
transfor
mation to d
i
rectly
d
e
riv
e
th
e
quadratur
e voltages in terms simplified
fun
c
tio
ns of switching
parameters.
This is the m
a
in
result of the p
a
p
e
r wh
ich can be
applied
to model based and
predic
tive
contr
o
l of e
l
e
c
tri
cal
m
ach
ines.
Sim
u
lation
results
are used
t
o
compare the n
e
w dq voltage modelling
r
e
sponse to conven
tion
a
l direct –
quadratur
e (dq)
axes modelling
respons
e in dir
ect
torque
contr
o
l – space
vector modulation scheme. Th
e proposed
model is compact, d
e
creases
the
computation co
mplexity
and time. The m
odel
is useful especially
in model
based control i
m
p
lem
e
nted in real t
i
m
e
, in te
rm
s of a
sim
p
lified set o
f
switching p
a
rameters.
Keyword:
Di
rect
t
o
rq
ue
c
ont
rol
d
-
q
m
o
d
e
llin
g
Park’s Tra
n
s
f
orm
a
tion
Perm
an
en
t m
a
g
n
e
t m
o
to
r
Space Vector Modulation
Copyright ©
201
5 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
Jayaram
a
Pradeep,
Depa
rt
m
e
nt
of
El
ect
ri
cal
and
El
ect
roni
cs
E
n
gi
nee
r
i
n
g,
Sath
yab
a
m
a
Un
iv
ersity,
Jep
p
i
aar
Naga
r
,
Ol
d M
a
m
a
l
l
a
pu
ram
R
o
ad, C
h
en
nai
-
6
0
0
11
9.
Em
a
il: j
a
ya_
7
p
rad
e
ep
@yah
oo.co
.i
n
1.
INTRODUCTION
In t
h
ree
-
phase
machines us
ua
lly the behavi
or and
perform
a
nce are
desc
ribed and a
n
alyzed by thei
r
vol
t
a
ge a
nd c
u
rre
nt
equat
i
o
ns
. The coe
ffi
ci
e
n
t
s
of t
h
e di
ff
erent
i
a
l
equat
i
ons
whi
c
h des
c
ri
bes t
h
e dy
n
a
m
i
c
b
e
h
a
v
i
or
o
f
the
m
ach
in
es are ti
m
e
v
a
ryin
g
[1
],
[2
] (ex
c
ept wh
en
th
e
ro
t
o
r is station
a
ry
). Th
e m
a
th
e
m
atical
m
odel
l
i
ng of s
u
ch a sy
st
em
tend
s t
o
be co
m
p
l
e
x as t
h
e flux l
i
n
ka
ges, i
n
duce
d
v
o
l
t
a
ges
,
and c
u
r
r
e
n
t
s
cha
n
g
e
co
n
tinuo
usly as th
e
system is in relative m
o
tio
n
.
For s
u
ch a c
o
m
p
lex electrical m
achine analysis,
math
e
m
atica
l
tran
sform
a
t
i
o
n
s
[3
]-[6
]
are o
f
ten
u
s
ed
to
sep
a
rate or d
e
co
up
le th
e v
a
riab
les and
to so
lv
e
eq
u
a
tion
s
involv
i
n
g
tim
e v
a
ryin
g
qu
an
tities b
y
referring
all v
a
riab
les to
a co
mm
o
n
referen
ce
fram
e
eith
er
st
at
i
onary
o
r
r
o
t
a
t
i
ng.
Am
on
g t
h
e
vari
ous
m
e
t
hods a
v
ai
l
a
bl
e f
o
r t
r
a
n
s
f
o
r
m
a
t
i
on, t
h
e w
e
l
l
kno
w
n
[
8
]
,
[
9
]
are:
C
l
arke T
r
an
sf
o
r
m
a
ti
on a
n
d
Pa
rk
Tra
n
s
f
o
r
m
a
ti
on
B
y
pr
ope
r sel
e
ct
i
on
of
t
h
e
ref
e
rence
f
r
am
e, it
i
s
po
ssib
l
e t
o
sim
p
lify co
n
s
id
erab
ly th
e com
p
lex
i
t
y
of
th
e m
a
th
e
m
a
t
i
cal
m
ach
in
e mo
d
e
l.
While these tran
sfo
r
m
a
tio
n
s
were i
n
itially d
e
v
e
lo
p
e
d
fo
r th
e an
alysis and
sim
u
lation of
ac
m
achines, they are now
ex
trem
ely
u
s
eful to
o
l
s in
th
e dig
ital co
n
t
ro
l of su
ch
m
ach
in
es. As
di
gi
t
a
l
co
nt
r
o
l
t
echni
q
u
es
are
ext
e
nde
d t
o
t
h
e c
o
nt
rol
o
f
t
h
e c
u
r
r
e
n
t
s
, t
o
rq
ue a
n
d
fl
u
x
of
suc
h
m
achines,
t
h
e
need for com
p
act, accurate machine m
odels
is obvi
ous
.
Gene
ral
l
y
w
h
i
l
e
m
odel
l
i
ng a
dri
v
e, t
h
e 3
-
φ
vol
t
a
ge
s
V
a
, V
b
, V
c
a
r
e
gene
r
a
t
e
d t
h
ro
u
gh a
swi
t
c
hi
n
g
m
odel
of t
h
e i
nve
rt
er.
Usi
n
g
Par
k
s t
r
ans
f
or
m
a
t
i
on, q
u
ad
ra
t
u
re v
o
l
t
a
ges
V
d
, V
q
are t
h
en
obt
ai
ne
d f
r
om
V
a
, V
b
,
V
c
. I
n
t
h
i
s
pap
e
r, we p
r
ese
n
t
a new ap
pr
oac
h
t
o
obt
ai
n
V
d
, V
q
v
o
ltag
e
s d
i
rectly in
ter
m
s
o
f
a si
m
p
lifie
d
form
o
f
switch
i
ng
param
e
ters o
f
t
h
e i
n
v
e
rter. This resu
lt
i
s
m
a
de
p
o
ssi
bl
e
by
com
b
i
n
i
n
g t
h
e swi
t
c
hi
ng
e
q
uat
i
o
n
s
and
t
h
e
Par
k
s t
r
ans
f
orm
a
t
i
on and
usi
n
g s
o
m
e
re
gul
ari
t
y
f
o
un
d i
n
t
h
e
coe
f
fi
ci
ent
s
i
n
vol
v
e
d.
Thi
s
m
e
t
h
o
dol
ogy
whi
c
h gi
ves
V
d
, V
q
d
i
rectly in
term
s o
f
a sim
p
lified
set o
f
switch
i
n
g
p
a
ram
e
ters will b
e
u
s
eful in
an
y
m
odel
l
i
ng of i
nve
rt
er
base
d
dri
v
e, es
peci
al
l
y
i
n
t
h
e co
nt
ex
t
of re
al
t
i
m
e
cont
rol
.
In
o
r
de
r t
o
veri
fy
ou
r
m
odel
out
put
V
d
, V
q
usi
n
g t
h
e
pr
o
p
o
se
d m
e
t
hod,
we u
s
e t
h
e i
n
st
ance o
f
Di
rect
t
o
r
que c
o
nt
r
o
l
(DTC
) o
f
per
m
anent
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Ado
p
tion
o
f
Park’
s
Tran
sforma
tio
n fo
r In
vert
e
r Fed Drive (Ja
y
arama
Prad
eep
)
36
7
m
a
gnet synchronous m
o
tor (PMSM) em
ploying s
p
ace
v
ector m
odulation
(S
VM) t
echni
que
. W
e
c
onsi
d
e
r
PM
SM
beca
us
e o
f
i
t
s
ad
va
nt
a
g
e
ove
r
ot
he
r e
l
ect
ri
cal
m
achi
n
es a
n
d
of i
t
s
wi
de a
p
pl
i
cat
i
ons
[1
0]
,
[1
1]
.
The
rest of t
h
e pa
per is
organized a
s
follows:
Sectio
n
2
g
i
v
e
s a simp
le in
trod
u
c
tion
to Vo
ltag
e
so
urce
inv
e
rter.
Section
3
d
e
scrib
e
s th
e conven
tio
n
a
l
d-q
v
o
ltag
e
m
o
d
e
llin
g
o
f
PMSM. Sectio
n
4
exp
l
ain
s
the
pr
o
pose
d
a
d
op
t
i
on
of
Par
k
’s t
r
ans
f
orm
a
t
i
on t
o
rec
o
nst
r
uc
t
d
-
q
vo
ltag
e
s
d
i
rectly. In Secti
o
n 5, th
e d-q
vo
ltag
e
s
are sim
u
lated
u
s
ing
Matlab
/
Si
m
u
lin
k
an
d
th
e resu
lts ob
t
a
ined a
r
e c
o
mpare
d
with
those ob
tain
ed u
s
in
g
t
h
e
pr
o
pose
d
m
ode
l
.
Sect
i
o
n
6
c
o
ncl
u
des t
h
e
pa
per
.
2.
SWITCHING
STATES OF VOLTAGE
SOURCE INVERTER
Th
e
po
w
e
r
d
e
vices o
f
th
e vo
ltag
e
sou
r
ce inver
t
er
a
r
e ass
u
med in i
d
eal c
o
ndition:
the
voltage ac
ross
th
e switch
is zero wh
en
th
e switch
e
s
are con
d
u
c
ting
an
d th
ere will b
e
volta
g
e
acro
ss t
h
e switch wh
en
it is in
ope
n circ
uit in the bloc
king mode
. The
r
efore
,
each inverte
r
leg can
be re
pres
ented as a
n
ideal switch. It give
s
th
e po
ssib
ility to
con
n
ect th
e
th
ree ph
ase
wi
n
d
i
n
g
s of th
e
m
o
to
r to
p
o
s
iti
v
e
or n
e
g
a
tiv
e ter
m
in
als o
f
th
e d
c
l
i
nk (
V
dc
)
.
T
h
us t
h
e
eq
ui
val
e
nt
sch
e
m
e
for t
h
ree-
p
h
ase
i
nve
rt
er a
n
d
p
o
ssi
bl
e ei
ght
com
b
i
n
at
i
ons
of t
h
e
swi
t
c
hes i
n
t
h
e
i
nve
rt
er a
r
e s
h
ow
n i
n
Fi
gu
re
1.
Fi
gu
re
1.
Ei
g
h
t
Pos
s
i
b
l
e
S
w
i
t
c
hi
n
g
st
at
es
of
Vol
t
a
ge
S
o
u
r
c
e
I
nve
rt
er
Th
e
relatio
n b
e
tween
t
h
e switch
i
ng
states and
th
e in
v
e
rter vo
ltag
e
o
u
t
pu
ts in
term
s
o
f
ph
ase
and
lin
e
vol
t
a
ge
s i
s
gi
v
e
n i
n
Ta
bl
e 1
.
Tabl
e 1. Swi
t
c
hi
n
g
pat
t
e
rns
a
n
d
o
u
t
p
ut
vect
ors
Voltage vector
s
Switching
vectors
L
i
ne to neutr
a
l
voltage
Line to line voltage
S
a
S
b
S
c
V
an
V
bn
V
cn
V
ab
V
bc
V
ca
V
0
0
0
0
0
0
0
0
0
0
V
1
1 0
0
2/3
-
1
/3
-
1
/3
1
0
-
1
V
2
1
1
0
1/3
1/3
-
2
/3
0
1
-
1
V
3
0
1
0
-
1
/3 2/3
-
1
/3
-
1
1
0
V
4
0
1
1
-
2
/3
1/3
1/3
-
1
0
1
V
5
0
0
1
-
1
/3
1/3
2/3
0
-
1
1
V
6
1
0
1
1/3
2/3
1/3
1
-
1
0
V
7
1
1
1
0
0
0
0
0
0
3.
CONVE
NTIONAL d-q
MODELLING
The stator
voltage com
p
onents a
pplied to t
h
e electrical
machine ar
e est
i
m
a
t
e
d usi
ng t
h
e swi
t
c
hi
n
g
states and dc
link voltage
(V
dc
) as
fo
llo
ws:
V
a
=
(2
S
a
-S
b
-S
c
)
V
b
=
(2
S
b
-S
a
-S
c
)
V
c
=
(2
S
c
-S
a
-S
b
)
(
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.
5
,
No
.
3
,
Feb
r
uar
y
201
5 :
3
66 –
37
3
36
8
Figu
re
2.
P
h
as
or
dia
g
ram
sho
w
in
g a
b
c a
n
d
d
-
q
re
fere
nce
fr
am
e
Fi
gu
re 2
re
pr
esent
s
t
h
e p
h
a
sor di
a
g
ram
of 3-
φ
r
o
tating m
achine in
dq
re
fere
nce
fram
e
. For
t
r
ans
f
o
r
m
i
ng t
h
e t
h
ree
p
h
ase
v
o
l
t
a
ges i
n
t
o
di
rect
-q
ua
drat
ure
(
d
-
q
)
a
x
es
v
o
l
t
a
ges,
Pa
r
k
s t
r
a
n
s
f
o
r
m
a
ti
on i
s
ap
p
lied.
Par
k
s t
r
a
n
s
f
o
r
m
a
t
i
on o
f
phas
e
v
o
l
t
a
ges i
s
gi
ven
by
:
=
(
2
)
Where
are the
electrical angl
e of
phase
a
with res
p
ect to
th
e refe
re
nce
fra
m
e
.
4.
RECO
NST
R
UCTE
D
d
-
q VOLTA
GES BY
A
D
A
PTI
N
G PA
RK
’S TRA
N
SF
OR
MATI
ON
The t
h
ree
phas
e voltages
,
,
w
h
i
c
h a
r
e e
x
p
r
ess
e
d i
n
t
e
rm
s of
swi
t
c
hi
n
g
st
at
e
s
i
n
(1
) ca
n
be
put
in
m
a
trix
form
as fo
llo
ws,
2
1
1
12
1
1
1
2
(
3
)
B
y
appl
y
i
ng P
a
rks t
r
a
n
sf
o
r
m
a
t
i
on as
m
e
nt
ione
d i
n
(
2
) o
n
b
o
t
h
si
des o
f
t
h
e (3
) i
t
i
s
pos
si
bl
e t
o
tran
sform
th
ree p
h
a
se ti
m
e
v
a
ryin
g
v
a
riab
le in
to
ti
m
e
in
v
a
rian
t v
a
riab
les in
term
s o
f
qu
adrature and
d
i
rect
axes as
follows
,
V
V
cos
θ
cos
θ
c
o
s
θ
sin
θ
sin
θ
s
i
n
θ
∗
2
1
1
12
1
1
1
2
(4
)
The a
b
ove
eq
u
a
t
i
on ca
n
be si
m
p
li
fi
ed t
o
Eq
uat
i
o
n
(
5
)
an
d
(6
) as
bel
o
w:
V
q
=
(
S
a
+
√
3
-
) S
b
-
√3
sin
θ
e
+
) S
c
)
(5
)
V
d
=
(
S
a
-
√
3
+
) S
b
+
(
√
3
-
)S
c
)
(6
)
Sub
s
titu
tin
g fo
r switch
i
ng
state v
a
lu
es
o
f
,
,
, u
s
i
n
g
Eq
ua
t
i
on
(
5
)
&
(
6
),
t
h
e
Ta
bl
e
2
i
s
com
puted as
below:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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S
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:
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8-8
6
9
4
Ado
p
tion
o
f
Park’
s
Tran
sforma
tio
n fo
r In
vert
e
r Fed Drive (Ja
y
arama
Prad
eep
)
36
9
Tab
l
e
2
.
Looku
p Tab
l
e fo
r V
d
and V
q
B
y
i
n
spect
i
on
of Ta
bl
e 2,
we
can d
r
aw Ta
bl
e 3 by
seg
r
egat
i
ng t
h
e e
n
t
r
i
e
s
i
n
t
e
rm
s of t
h
e ort
h
o
g
o
n
al
fu
nct
i
o
ns
cos
θ
and
sin
θ
.
Tabl
e
3.
V
d
and V
q
i
n
t
e
rm
s of
si
ne a
n
d c
o
s
i
ne f
u
nct
i
o
n
u
n
d
er
va
ri
o
u
s s
w
i
t
chi
n
g
st
at
es
S
w
itching
States
V
q
V
d
S
a
S
b
S
c
0 0
0
0 0
0
0
1 0
0
2
3
cos
0 0
2
3
sin
1 1
0
3
cos
√
3
sin
θ
√
3
cos
3
sin
0 1
0
3
cos
√
3
sin
θ
√
3
cos
3
sin
0 1
1
2
3
cos
0 0
2
3
sin
0 0
1
3
cos
√
3
sin
θ
√
3
cos
3
sin
1 0
1
3
cos
√
3
sin
θ
√
3
cos
3
sin
1 1
1
0 0
0
0
Defi
nin
g
V
q
,V
d
as
i
n
(
8
) bel
o
w, we ha
ve:
V
V
=
α
α
cos
β
β
s
i
n
(
7
)
Whe
r
e
α
i
and
β
i
i
=
1,
2 a
r
e t
h
e
swi
t
chi
n
g
param
e
t
e
rs
defi
ned
i
n
t
e
rm
s of s
w
i
t
c
hi
ng
st
at
es as i
n
Tabl
e
4.
We ca
n
dra
w
T
a
bl
e 4
by
t
a
ki
n
g
dat
a
f
r
om
Tabl
e 3
as
fol
l
o
w
s
:
S
w
itching
States
V
q
V
d
S
a
S
b
S
c
0 0
0
0 0
1 0
0
cos
sin
1 1
0
√
3
sin
θ
c
o
s
sin
θ
√
3
cos
0 1
0
√
3
sin
θ
c
o
s
sin
θ
√
3
cos
0 1
1
cos
sin
0 0
1
√
3
sin
θ
c
o
s
√
3
cos
s
i
n
θ
1 0
1
cos
θ
√
3
sins
sin
θ
√
3
cos
1 1
1
0 0
Evaluation Warning : The document was created with Spire.PDF for Python.
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S
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:
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94
I
J
PED
S
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l.
5
,
No
.
3
,
Feb
r
uar
y
201
5 :
3
66 –
37
3
37
0
Tabl
e
4.
α
and
β
value
s
f
o
r
V
d
and V
q
un
der
v
a
r
i
ou
s
sw
itch
i
ng
states
S
w
itching
States
V
q
V
d
S
a
S
b
S
c
α
1
β
1
α
2
β
2
0 0
0
0 0
0
0
1 0
0
2
3
0 0
2
3
1 1
0
1
3
1
√
3
1
√
3
1
3
0 1
0
1
3
1
√
3
1
√
3
1
3
0 1
1
2
3
0 0
2
3
0 0
1
1
3
1
√
3
1
√
3
1
3
1 0
1
1
3
1
√
3
1
√
3
1
3
1 1
1
0
0
0
0
Fu
rt
h
e
r
b
y
in
sp
ectio
n
o
f
Table 4
,
we
n
o
ticed
t
h
at fo
r all switch
i
ng
states
α
1
β
2
,
α
2
β
1
.
Eq
u
a
tion (7)
can
thu
s
b
e
rewritten
as,
V
q
V
dc
α
1
cos
θ
e
α
2
sin
θ
e
(
8
)
V
d
V
dc
α
2
cos
θ
e
α
1
sin
θ
e
(
9
)
Whe
r
e
α
1
and
α
2
ar
e as
gi
ve
n i
n
T
a
bl
e 5
.
Tabl
e 5.
α
1
and
α
2
val
u
e
s
un
der
v
a
ri
o
u
s s
w
i
t
c
hi
n
g
st
at
es
S
w
itching States
α
1
α
2
S
a
S
b
S
c
0 0
0
0 0
1 0
0
2
/
3
0
1 1
0
1
/
3
1
/
√
3
0 1
0
1
/
3
1
/
√
3
0 1
1
2
/
3
0
0 0
1
1
/
3
1
/
√
3
1 0
1
1
/
3
1
/
√
3
1 1
1
0 0
Rem
a
rk:
V
q
, V
d
g
i
v
e
n in (8
) and
(9
) id
en
tify t
h
e
quad
r
at
u
r
e v
a
riab
les in term
s of switch
i
ng states
(
r
e
p
r
esen
ted by
α
1
and
α
2
)
an
d th
e con
tin
uou
s v
a
r
i
ab
le
θ
e
.
Thi
s
i
s
a
ne
w
res
u
l
t
de
ri
ve
d
f
r
om
t
h
e
di
rect
approach use
d
in the
pa
per.
5.
SIM
U
LATI
O
N
RESULTS
AN
D A
NAL
Y
S
IS
In
o
r
de
r t
o
c
o
m
p
are t
h
e p
r
o
pos
ed
m
odel
out
put
wi
t
h
t
h
at
of
a i
n
ve
rt
er
out
put
(a
pp
l
i
e
d t
o
t
h
e
m
achine),
sim
u
lation i
n
vol
v
ing space
v
ector m
odulation i
n
a
direct t
o
rque
c
ont
rol sc
hem
e
is em
ployed.
The
schem
a
t
i
c
di
agram
sho
w
n
i
n
t
h
e Fi
g
u
r
e
2 was i
m
pl
em
ent
e
d an
d
sim
u
l
a
t
e
d fo
r
perm
anent
m
a
gnet
sy
nch
r
o
n
o
u
s
m
o
t
o
r i
n
t
h
e
M
a
t
l
a
b-Si
m
u
l
i
nk e
nvi
r
o
nm
ent
usi
ng Si
m
P
ower Sy
st
em
. The i
n
p
u
t
vol
t
a
ge of t
h
i
s
PMSM sim
u
lat
i
o
n
is in
term
s o
f
V
q
,V
d
. Th
is
d
-
q
vo
ltag
e
is
b
u
ilt using
Park
’s tran
sfo
r
m
a
tio
n
wh
ich respo
n
d
s
according to the switc
hing sta
t
es
,
,
as
pe
r
(2
).
The
swi
t
c
hi
ng
st
at
e vari
es
acc
or
di
n
g
t
o
t
h
e
e
r
r
o
r
t
o
rq
ue
and
er
ro
r fl
ux
of t
h
e m
achi
n
e. The
bl
ock
wi
t
h
i
n
t
h
e
da
s
h
e
d
lines i
n
Figure 2 i
ndicates t
h
e algorithm
whic
h
i
n
co
rp
orat
es t
h
e pr
o
p
o
s
ed
di
r
ect
app
r
oa
ch e
m
pl
oy
i
ng (8
) a
n
d
(
9
) a
n
d Ta
bl
e 5 t
o
e
v
al
ua
t
e
d-
q
vol
t
a
ge
s
.
Al
l
t
h
e sim
u
l
a
t
i
ons were pe
rf
or
m
e
d for a 3
-
φ
, 4-
pol
e PM
S
M
m
o
t
o
r un
de
r no l
o
a
d
co
n
d
i
t
i
on as sh
o
w
n i
n
t
h
e
Tabl
e 6.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Ado
p
tion
o
f
Park’
s
Tran
sforma
tio
n fo
r In
vert
e
r Fed Drive (Ja
y
arama
Prad
eep
)
37
1
Tabl
e 6. PM
S
M
param
e
t
e
rs
Rated Phase Voltage
300V
Rated
To
rq
u
e
1
.
7
N
m
M
a
gnetic Flux L
i
n
k
age 0.
1848W
b
Po
le p
a
irs
2
Rated Speed
3000r
p
m
Stato
r
Resistan
ce
4
.
7
6
5
Ω
I
nductance – L
q
0.
014H
I
nductance – L
d
0.
014H
Fi
gu
re
2.
Si
m
u
l
i
nk
bl
oc
k
di
ag
ram
of co
n
v
ent
i
onal
a
n
d
p
r
op
ose
d
m
e
t
hod
Fig
u
re
3
ind
i
cates th
e switch
i
ng
states
,
,
cor
r
es
po
n
d
i
n
g t
o
fl
ux
an
d t
o
rq
ue e
r
r
o
r
fr
om
PM
SM
. Fi
g
u
r
e
4 i
ndi
cat
es t
h
e co
rres
p
on
di
ng s
w
i
t
c
hi
n
g
param
e
t
e
rs
α
1
and
α
2
fo
r
vario
u
s s
w
itchin
g
states
,
,
as per Ta
ble 5. Figure 5
repre
s
ents the c
o
m
p
aris
o
n
o
f
com
put
ed
di
rect
an
d
qua
drat
ure
v
o
l
t
a
ges (a&
c)
whic
h s
h
ow an alm
o
st identical res
p
onse
as m
easur
ed
di
rect
a
n
d
qua
drat
ure
v
o
l
t
a
ge
s (
b
&
d
)
i
n
t
h
e sam
e
fi
g
u
re.
Fi
g
u
re
6 re
p
r
esent
s
t
h
e err
o
r
i
n
c
o
m
put
e
d
a
nd m
easure
d
vol
t
a
ges
of
di
rect
a
n
d
q
u
ad
rat
u
re a
x
es
whi
c
h
i
s
of t
h
e o
r
der
of
1.
4*
1
0
-12
. Figure 7 c
o
m
p
ares the response
s of m
eas
ured
and c
o
m
put
ed
di
rect
an
d q
u
a
d
rat
u
re
axes
vol
t
a
ge
s
whe
n
t
h
e i
n
put
v
o
l
t
a
ge (
V
dc
)
i
s
chan
ge
d t
o
hal
f
t
h
e
rat
e
d
val
u
e at
t
=
0.
3s
an
d d
o
ubl
e t
h
e rat
e
d
v
a
lu
e at t=0
.
62s. Th
e
resu
lts sh
ow th
at th
e
resp
on
ses ar
e al
m
o
st identical
for va
rious
vol
tage cha
n
ges both
for
the conventi
onal and th
e pr
opo
sed
techn
i
qu
es.
Fi
gu
re
3.
S
w
i
t
c
hi
n
g
St
at
es
,
,
Fi
gu
re
4.
α
1
and
α
2
val
u
e
s
un
der
v
a
ri
o
u
s s
w
i
t
c
hi
n
g
states
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l.
5
,
No
.
3
,
Feb
r
uar
y
201
5 :
3
66 –
37
3
37
2
Figu
re
5.
Com
p
aris
on
o
f
c
o
m
pute
d
(a)
Q
u
ad
rature
and
(c
) Direct axes voltage
s
with
th
e m
easu
r
ed (b
)
Qua
d
rature
an
d
(d
)
Direct a
x
es v
o
ltages
Fi
gu
re
6.
Er
ro
r
V
o
l
t
a
ge i
n
c
o
m
put
ed an
d m
easure
d
Fi
gu
re
7.
C
o
m
p
ari
s
on
o
f
c
o
m
put
e
d
a
n
d
m
e
asure
d
v
o
l
t
a
ges
fo
r
vari
ous
i
n
p
u
t
v
o
l
t
a
ge l
e
ve
l
s
6.
CO
NCL
USI
O
N
Thi
s
pa
per
pre
s
ent
s
an ad
o
p
t
i
on o
f
Par
k
’s t
r
ans
f
o
r
m
a
ti
on
for a
n
i
nve
rt
e
r
fed
dri
v
e w
h
i
c
h al
l
o
ws
gene
rat
i
o
n of d-
q vol
t
a
ges di
rect
l
y
i
n
t
e
rm
s
of
swi
t
c
hi
n
g
param
e
t
e
rs. Th
e pr
o
p
o
s
ed
m
odel
has
bee
n
u
s
ed i
n
t
h
e m
odel
bas
e
d co
nt
r
o
l
,
s
u
c
h
as, i
ndi
r
ect
t
o
r
q
ue co
nt
r
o
l
and i
n
t
e
r
n
al
m
odel
c
ont
rol
of
PM
SM
w
h
i
c
h
i
s
ou
r
o
ngo
ing
w
o
rk
.
REFERE
NC
ES
[1]
L
e
e RJ,
Pi
l
l
ay
P,
Ha
rl
ey
RG.
D,Q Refer
e
nce
Frames for the
Simulation of I
nduction Motor
s
.
El
ectr
i
c Pow
e
r
Systems Resear
c
h
(
EPRI
).
1984; 8:
15–26.
[2]
Kraus
e
P
C
. Ana
l
ys
is
of
El
ec
tric
M
achiner
y.
N
e
w
Y
o
rk:
McGraw-Hill, 1994
: 135.
[3]
E Clarke. Cir
c
uit Analy
s
is of
AC
Power S
y
stems.
New Y
o
rk:
Wiley,
1943: I.
[4]
Dobruck
y
B, Pokorn
y
M,
B
e
no
va M.
Instantan
e
ous single-ph
ase s
y
stem pow
er
demonstration
using virtu
a
l
two
phase th
eor
y
.
I
EEE conference on Internation
a
l Schoo
l on
N
onsinusoidal Cu
rrents and Compensation, ISNC
C.
2008: 1-5.
[5]
RH
Park. Two-reaction theor
y
of
s
y
n
c
hronous
machines.
AI
EE T
r
ans.,
1929; 716.
[6]
S
Chattop
a
dh
ya
y
et
a
l
.
El
ectr
i
c
a
l
P
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wer Qual
it
y.
Powe
r Syte
ms,
Springe
r
Science-
Business media
. 2011.
[7]
Analog dev
i
ces.
ADSP-21990: R
e
feren
c
e Frame
Conversions
.
20
02.
[8]
R Krishnan.
El
e
c
tri
c
Motor
Driv
es.
Pr
en
ti
ce Ha
ll
. 2003
.
[9]
BK
Bos
e
. M
oder
n
P
o
w
e
r El
ec
tro
n
ics
and
A
C
D
r
i
v
es
.
Pearson Ed
ucation
,
In
c., 20
02.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Ado
p
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BIOGRAP
HI
ES
OF AUTH
ORS
Jay
arama
Prad
eep
has obtained
her BE
and ME degree fro
m Sa
thy
a
ba
ma
Uni
v
e
r
si
ty
,
Ta
mi
l
n
a
d
u,
Chennai in 199
8 and 2002 respectively
.
She has 14
y
ears of teaching
experien
ce in St. Joseph
’s
College of Engineering
,
Tamiln
a
du, Chennai. She is currently
p
u
rsuing her doctoral degree in th
e
area of H
y
brid
Control of
PMSM in Sath
y
a
bama
Univers
i
t
y
,
Tam
ilnadu
,
Ch
e
nnai.
Her r
e
s
ear
ch
inter
e
s
t
s
ar
e in
t
h
e ar
ea
of P
o
wer
El
ectron
i
cs
and
drives
.
Phone no: 044-2
4501060, fax no: 044- 24500861
,
email:
jay
a
_7pr
adeep@
y
ahoo.co.in
Dr Rajagopalan Devanathan
receiv
ed his P
h
D and M.Sc
(
E
ng) from Queen’s University
,
Kingston, Ontar
i
o, Can
a
da and h
i
s
BE
and ME
fr
om Indian Institute
of
Scien
c
e,
Bangalor
e
, India.
Dr Devanathan has taught at
Nan
y
ang Technological University
(NTU), Singapore for over two
decad
es.
He
has
published
over
120
papers in in
terna
tiona
l and nation
a
l confer
e
n
ce
pro
c
e
e
ding
s
and journals
, an
d has
received a
w
ards
from IEEE E
duca
tion S
o
c
i
et
y and NTU. He has
chaired an
d
co-chaired inter
n
ation
a
l confer
ences organized b
y
I
E
E
E
a
n
d
N
T
U
.
C
u
r
r
e
n
t
l
y
h
e
i
s
a
t
t
a
c
h
e
d
t
o
Hindustan University
, Ch
ennai,
as
Dean (
E
lectri
cal Sciences).
Phone no: 044-2
7474395/ 27474
262, fax
no: 044
-
27474208 email:
d
eanes@hi
ndu
stanuniv.ac.in
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