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ch
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45
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p
ap
er
is
th
e
d
esig
n
o
f
co
n
v
en
tio
n
al
in
v
er
ter
-
d
r
iv
en
PMSM
d
r
iv
e
s
in
E
P
S
ap
p
licatio
n
s
.
Sectio
n
s
1
an
d
2
d
escr
ib
e
th
e
in
tr
o
d
u
ctio
n
a
n
d
m
ath
em
atica
l
m
o
d
el
o
f
PMSM,
s
ec
tio
n
3
d
escr
ib
es
th
e
s
im
u
latio
n
m
o
d
el
an
d
an
a
ly
s
is
,
an
d
s
ec
tio
n
4
d
escr
ib
es
d
esig
n
co
n
s
id
er
atio
n
s
.
Sectio
n
s
5
an
d
6
p
r
esen
t
ex
p
er
im
en
tal
r
esu
lts
an
d
co
n
cl
u
s
io
n
r
esp
ec
tiv
ely
.
2.
MA
T
H
E
M
AT
I
CA
L
M
O
D
E
L
O
F
P
M
S
M
2
.
1
.
Ro
t
o
r
re
f
e
re
nce
f
ra
m
e
P
M
S
M
T
he
m
o
d
ellin
g
o
f
th
e
PMSM
m
ac
h
in
e
h
as
b
ee
n
p
r
esen
ted
h
en
ce
f
o
r
th
in
th
e
r
o
to
r
r
ef
e
r
en
c
e
f
r
am
e.
I
n
a
PMSM,
th
e
r
o
to
r
is
a
p
er
m
a
n
en
t
m
ag
n
et
with
o
u
t
an
y
win
d
in
g
s
an
d
h
e
n
ce
th
er
e
ar
e
n
o
eq
u
atio
n
s
ass
o
ciate
d
with
th
e
r
o
to
r
.
T
h
e
3
-
φ
s
tatio
n
ar
y
‘
a
b
c’
f
r
am
e
ca
n
b
e
tr
a
n
s
f
o
r
m
ed
in
t
o
2
-
φ
s
y
n
c
h
r
o
n
o
u
s
ly
r
o
tatin
g
‘
d
q
’
f
r
am
e,
with
th
e
h
elp
o
f
a
b
c
→
d
q
tr
an
s
f
o
r
m
atio
n
s
.
I
n
th
e
‘
d
q
’
f
r
am
e
,
th
e
s
tato
r
h
as two
win
d
in
g
s
: d
-
ax
is
win
d
in
g
an
d
q
-
ax
is
win
d
in
g
;
a
n
d
th
e
d
-
ax
is
win
d
in
g
is
alig
n
ed
with
t
h
e
m
ag
n
etic
p
o
le
a
x
is
.
C
o
n
s
id
er
th
e
PMSM
m
ac
h
in
e
r
u
n
n
in
g
at
th
e
s
p
ee
d
o
f
‘
ω
r
’
,
in
th
e
an
ti
-
clo
c
k
wis
e
d
ir
ec
tio
n
.
T
h
e
D
-
ax
is
in
d
u
ce
d
v
o
ltag
e
is
(
1
)
.
=
+
−
(
1
)
T
h
e
Q
-
ax
is
in
d
u
ce
d
v
o
ltag
e
is
s
h
o
wn
in
(
2
)
-
(
5
)
.
=
+
−
(
2
)
=
+
(
3
)
=
(
4
)
=
(
5
)
T
h
e
to
r
q
u
e
eq
u
atio
n
is
(
6
)
.
=
3
2
p
2
(
λ
d
−
λ
q
)
(
6
)
Pu
t in
(
7
)
.
=
3
2
p
2
[
(
λ
d
+
λ
)
−
L
q
]
(
7
)
=
3
2
p
2
[
(
L
d
−
)
+
λ
]
(
8
)
=
3
2
p
2
(
L
d
−
)
(
9
)
=
3
2
p
2
λ
(
1
0
)
=
3
2
p
2
λ
(
1
1
)
Hen
ce
th
e
elec
tr
o
m
ag
n
etic
to
r
q
u
e
p
r
esen
t
in
a
r
o
u
n
d
r
o
to
r
p
e
r
m
an
en
t
m
ag
n
et
s
y
n
ch
r
o
n
o
u
s
m
ac
h
in
e
is
n
o
th
in
g
b
u
t
th
e
f
ield
to
r
q
u
e
wh
ich
is
p
r
esen
t
d
u
e
to
th
e
p
er
m
an
en
t
m
ag
n
et
f
lu
x
lin
k
a
g
e,
λm
.
Fo
r
a
ch
o
s
en
p
er
m
an
en
t
m
ag
n
et
s
y
n
c
h
r
o
n
o
u
s
m
ac
h
in
e,
th
e
n
u
m
b
er
o
f
p
o
l
es (
p
)
is
co
n
s
tan
t
as we
ll
as
th
e
p
er
m
a
n
en
t
m
ag
n
et
r
o
to
r
f
lu
x
-
lin
k
ag
e
(
λm
).
Hen
ce
,
th
e
elec
tr
o
m
a
g
n
etic
to
r
q
u
e
eq
u
atio
n
f
o
r
th
e
r
o
u
n
d
-
r
o
to
r
PMSM
ca
n
b
e
r
ew
r
itten
as
(
1
2
)
an
d
(
1
3
)
.
T
e=
Ktiq
(
1
2
)
=
3
2
p
2
λ
(
1
3
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
P
erfo
r
ma
n
ce
a
n
a
lysi
s
o
f c
o
n
v
en
tio
n
a
l m
u
ltil
ev
el
in
ve
r
ter d
r
iven
P
MS
M d
r
ive
…
(
R
a
ke
s
h
G.
S
h
r
iw
a
s
ta
va
)
39
T
h
er
ef
o
r
e
,
elec
tr
o
m
a
g
n
etic
to
r
q
u
e
is
(
1
4
)
.
=
+
+
(
1
4
)
3.
SI
M
UL
A
T
I
O
N
M
O
D
E
L
AN
AL
YS
I
S
Fig
u
r
e
1
s
h
o
ws
th
e
Simu
lin
k
m
o
d
el
o
f
a
two
-
le
v
el
in
v
e
r
ter
-
d
r
iv
en
PMSM
d
r
iv
e.
Fig
u
r
es
2
-
4
s
h
o
w
m
o
to
r
r
esp
o
n
s
e
at
2
8
0
r
p
m
,
5
0
0
r
p
m
,
an
d
1
5
0
0
r
p
m
.
Fig
u
r
e
5
s
h
o
ws
a
f
ast
Fo
u
r
ier
tr
an
s
f
o
r
m
(
FFT
)
an
aly
s
is
o
f
a
two
-
lev
el
in
v
er
ter
-
d
r
iv
e
n
P
MSM
d
r
iv
e.
T
ab
le
1
s
h
o
ws
th
e
to
r
q
u
e
r
ip
p
le
an
aly
s
is
o
f
a
t
wo
-
lev
el
in
v
er
ter
.
I
n
Fig
u
r
e
2
,
at
0
.
0
1
s
ec
,
lo
ad
to
r
q
u
e
3
N
-
m
is
a
p
p
lied
a
n
d
r
em
o
v
ed
at
0
.
0
3
s
ec
.
T
h
e
to
r
q
u
e
v
ar
ies
with
th
e
lo
a
d
T
h
e
r
ef
er
en
ce
s
p
ee
d
is
5
0
0
r
p
m
an
d
th
e
f
lu
ctu
atio
n
in
s
p
ee
d
o
n
r
em
o
v
al
o
f
to
r
q
u
e
th
an
s
p
e
ed
r
em
ain
s
co
n
s
tan
t.
Sp
ee
d
,
th
r
ee
-
p
h
ase
s
tato
r
cu
r
r
en
t
,
an
d
elec
tr
o
m
ag
n
etic
to
r
q
u
e
ar
e
co
n
s
tan
t w
ith
s
o
m
e
r
ip
p
l
es a
t 0
.
6
s
ec
.
Fig
u
r
e
1.
Simu
lin
k
m
o
d
el
o
f
t
wo
-
lev
el
in
v
er
ter
-
d
r
iv
e
n
PMSM
d
r
iv
e
(
a)
(
b
)
(
c)
Fig
u
r
e
2
.
Mo
t
o
r
r
esp
o
n
s
e
at
2
8
0
r
p
m
(
a)
r
o
to
r
s
p
ee
d
,
(
b
)
ele
ctr
o
m
ag
n
etic
to
r
q
u
e
,
an
d
(
c)
th
r
ee
-
p
h
ase
s
tato
r
cu
r
r
en
t
0
0
.
0
2
0
.
0
4
0
.
0
6
0
.
0
8
0
.
1
-
5
0
0
50
100
150
200
250
300
T
i
m
e
S
p
e
e
d
[
r
a
d
/
se
c]
0
0
.
0
1
0
.
0
2
0
.
0
3
0
.
0
4
0
.
0
5
0
.
0
6
0
.
0
7
0
.
0
8
0
.
0
9
0
.
1
0
2
4
6
8
10
12
T
i
m
e
[
se
c]
E
l
e
ct
r
o
m
a
g
n
e
t
i
c
T
o
r
q
u
e
s
[
N
.
m
]
se
c]
0
0
.
0
2
0
.
0
4
0
.
0
6
0
.
0
8
0
.
1
-
1
5
-
1
0
-5
0
5
10
15
T
i
m
e
S
t
a
t
o
r
C
u
r
r
e
n
t
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
14
,
No
.
1
,
Ma
r
ch
20
25
:
37
-
45
40
(
a)
(
b
)
(
c)
Fig
u
r
e
3
.
Mo
t
o
r
r
esp
o
n
s
e
at
5
0
0
r
p
m
(
a)
r
o
to
r
s
p
ee
d
,
(
b
)
to
r
q
u
e
,
an
d
(
c)
th
r
ee
-
p
h
ase
s
tato
r
cu
r
r
en
t
I
n
Fig
u
r
e
3
,
a
t
0
.
0
1
s
ec
,
l
o
ad
t
o
r
q
u
e
3
N
-
m
is
ap
p
lied
an
d
r
e
m
o
v
ed
at
0
.
1
5
s
ec
.
T
h
e
to
r
q
u
e
v
ar
ies
with
th
e
lo
ad
T
h
e
r
e
f
er
en
ce
s
p
ee
d
i
s
5
0
0
r
p
m
a
n
d
th
e
f
l
u
ctu
atio
n
in
s
p
ee
d
o
n
r
e
m
o
v
al
o
f
to
r
q
u
e
th
an
s
p
ee
d
r
em
ain
s
co
n
s
tan
t.
Sp
ee
d
,
t
h
r
ee
-
p
h
ase
s
tato
r
cu
r
r
e
n
t
,
an
d
elec
tr
o
m
a
g
n
etic
to
r
q
u
e
a
r
e
co
n
s
tan
t w
ith
s
o
m
e
r
ip
p
les at
0
.
1
5
.
T
h
e
to
r
q
u
e
v
ar
ies
with
th
e
lo
ad
T
h
e
r
e
f
er
en
ce
s
p
ee
d
is
5
0
0
r
p
m
a
n
d
th
e
f
lu
ctu
atio
n
in
s
p
ee
d
o
n
r
em
o
v
al
o
f
to
r
q
u
e
th
a
n
s
p
ee
d
r
em
ain
s
co
n
s
tan
t.
Sp
ee
d
,
th
r
ee
-
p
h
ase
s
tato
r
cu
r
r
e
n
t
,
an
d
elec
tr
o
m
ag
n
etic
to
r
q
u
e
ar
e
co
n
s
tan
t
with
s
o
m
e
r
ip
p
les at
0
.
0
6
s
ec
.
(
a)
(
b
)
(
c)
Fig
u
r
e
4
.
Mo
t
o
r
r
esp
o
n
s
e
at
1
5
0
0
r
p
m
(
a
)
r
o
to
r
s
p
ee
d
,
(
b
)
t
o
r
q
u
e
,
a
n
d
(
c
)
th
r
ee
-
p
h
ase
s
tato
r
cu
r
r
e
n
t
0
0
.
1
0
.
2
0
.
3
0
.
4
0
.
5
0
.
6
0
.
7
0
.
8
0
.
9
1
-
4
0
0
0
-
3
0
0
0
-
2
0
0
0
-
1
0
0
0
0
1000
2000
3000
4000
5000
T
i
m
e
[
se
c]
R
o
t
o
r
S
p
e
e
d
(
r
p
m
)
0
0
.
0
5
0
.
1
0
.
1
5
0
.
2
0
.
2
5
0
.
3
0
.
3
5
0
.
4
0
.
4
5
0
.
5
-5
0
5
10
15
20
25
T
i
m
e
[
se
c]
E
l
e
ct
r
o
m
a
g
n
e
t
i
c
t
o
r
q
u
e
[
N
-
m
]
0
0
.
0
5
0
.
1
0
.
1
5
0
.
2
0
.
2
5
0
.
3
0
.
3
5
0
.
4
0
.
4
5
0
.
5
-
1
5
-
1
0
-5
0
5
10
15
T
i
m
e
[
se
c]
T
h
r
e
e
p
h
a
se
st
a
t
o
r
cu
r
r
e
n
t
[
a
m
p
]
0
0
.
1
0
.
2
0
.
3
0
.
4
0
.
5
0
.
6
0
.
7
0
.
8
0
.
9
1
-
4
0
0
0
-
3
0
0
0
-
2
0
0
0
-
1
0
0
0
0
1000
2000
3000
4000
5000
T
i
m
e
[
se
c]
R
o
t
o
r
S
p
e
e
d
(
r
p
m
)
0
0
.
1
0
.
2
0
.
3
0
.
4
0
.
5
0
.
6
0
.
7
0
.
8
0
.
9
1
-
1
0
-8
-6
-4
-2
0
2
4
6
8
10
T
i
m
e
[
se
c]
T
h
r
e
e
P
h
a
se
S
t
a
t
o
r
C
u
r
r
e
n
t
[
A
]
0
0
.
1
0
.
2
0
.
3
0
.
4
0
.
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I
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t J Ap
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I
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8
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P
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(
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43
5.
CO
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PS
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.
RE
F
E
R
E
NC
E
S
[
1
]
R
.
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a
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d
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.
B
.
W
a
g
h
,
“
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RS
Dr
.
Ra
k
e
sh
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.
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h
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o
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tai
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d
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h
.
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d
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re
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lec
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d
d
r
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s
fro
m
RT
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Na
g
p
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r
U
n
iv
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rsity
,
(In
d
ia)
in
2
0
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.
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o
c
c
u
p
ied
v
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o
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s
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t
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rv
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t
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e
a
rs.
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is
c
u
rre
n
tl
y
wo
r
k
in
g
a
s
a
p
ro
fe
ss
o
r
in
th
e
De
p
a
rtme
n
t
o
f
El
e
c
tri
c
a
l
En
g
in
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rin
g
,
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o
v
in
d
ra
o
Wan
jari
Co
ll
e
g
e
o
f
E
n
g
i
n
e
e
rin
g
&
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h
n
o
l
o
g
y
,
Na
g
p
u
r
.
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re
se
a
rc
h
in
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sts
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n
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lu
d
e
th
e
a
n
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ly
sis
a
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d
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o
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tr
o
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tri
c
a
l
d
riv
e
s,
p
a
rt
icu
larly
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h
y
b
r
id
,
a
n
d
e
lec
tri
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v
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h
icle
a
p
p
li
c
a
ti
o
n
s.
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c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
ra
k
e
sh
_
sh
riwa
sta
v
a
@re
d
iffma
il
.
c
o
m
.
Dr
.
Pra
v
in
B
.
Po
k
le
b
o
rn
i
n
1
9
7
6
,
re
c
e
iv
e
d
a
B.
E.
d
e
g
re
e
in
El
e
c
tro
n
ics
En
g
i
n
e
e
rin
g
in
1
9
9
8
,
M
.
Tec
h
.
d
e
g
re
e
in
VLS
I
fr
o
m
RTM
Na
g
p
u
r
Un
i
v
e
rsity
,
Na
g
p
u
r
i
n
2
0
0
8
,
a
n
d
a
P
h
.
D.
in
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e
c
tro
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ics
E
n
g
i
n
e
e
rin
g
f
ro
m
RTM
Na
g
p
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r
Un
iv
e
rsity
,
Na
g
p
u
r
in
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0
15
.
Cu
rre
n
tl
y
,
h
e
is wo
rk
in
g
a
s
a
n
a
ss
istan
t
p
ro
fe
ss
o
r
a
n
d
h
e
a
d
o
f
th
e
De
p
a
rtme
n
t
of
El
e
c
tro
n
ic
s
a
n
d
Tele
c
o
m
m
u
n
ica
ti
o
n
s
En
g
in
e
e
rin
g
a
t
P
ri
y
a
d
a
rsh
a
n
i
J.
L.
C
o
ll
e
g
e
o
f
En
g
in
e
e
rin
g
,
Na
g
p
u
r,
In
d
ia.
He
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
p
b
p
o
k
le@
g
m
a
il
.
c
o
m
.
Dr
.
Aja
y
M.
Mend
h
e
g
ra
d
u
a
te
d
in
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e
c
tri
c
a
l
En
g
in
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e
rin
g
fro
m
YCCE,
Na
g
p
u
r.
He
h
a
s
a
p
o
st
-
g
ra
d
u
a
ti
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n
i
n
El
e
c
tr
ica
l
P
o
we
r
S
y
ste
m
s
fro
m
S
S
G
M
CE,
S
h
e
a
g
a
o
n
,
Am
a
ra
v
a
ti
Un
iv
e
rsity
,
a
n
d
a
Dip
lo
m
a
in
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sin
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ss
M
a
n
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g
e
m
e
n
t
fr
o
m
Na
g
p
u
r
Un
i
v
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.
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is
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h
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h
.
D
.
fro
m
S
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S
UT
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S
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h
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P
).
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is wo
r
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p
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c
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m
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il
:
m
e
n
d
h
e
a
jay
1
@
g
m
a
il
.
c
o
m
.
Dr
.
Nitin
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te
d
i
d
g
ra
d
u
a
ti
o
n
in
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e
c
tri
c
a
l
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g
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fro
m
VN
IT,
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g
p
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r
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ra
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lec
tri
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ra
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fro
m
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p
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He
c
a
n
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p
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u
.
i
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8
7
9
2
P
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45
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p
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p
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h
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ra
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rsity
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g
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r
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rre
n
tl
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i
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h
a
.
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c
a
n
b
e
c
o
n
tac
ted
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t
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m
a
il
:
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jen
d
ra
r.
fe
a
t@d
m
ih
e
r.
e
d
u
.
i
n
.
Dr
.
Ra
h
u
l
Ma
p
a
r
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re
c
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d
a
b
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c
h
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lo
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m
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st
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re
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in
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g
in
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m
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a
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it
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a
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h
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le
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v
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rsity
,
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d
ia,
i
n
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0
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a
n
d
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sp
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ly
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a
n
d
a
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h
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d
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g
r
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e
in
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o
m
m
u
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m
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ra
v
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d
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h
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s
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c
a
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h
u
l.
m
a
p
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c
c
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e
r.
i
n
.
Dr
.
Ra
n
jit
Dhu
n
d
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g
ra
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u
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ted
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a
th
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m
a
ti
c
s
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t
h
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n
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te
o
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c
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e
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g
p
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r
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n
d
a
P
h
.
D.
fro
m
RTM
,
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g
p
u
r
U
n
iv
e
rsit
y
.
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is
wo
rk
i
n
g
a
s
a
n
a
ss
istan
t
p
ro
fe
ss
o
r
in
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a
th
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m
a
ti
c
s
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t
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VK
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'
s
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c
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h
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n
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g
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v
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h
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t
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h
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re
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ter
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l
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u
rn
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ls.
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c
a
n
b
e
c
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tac
ted
a
t
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il
:
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n
ji
td
h
u
n
d
e
@g
m
a
il
.
c
o
m
.
Dr
.
H
e
m
a
n
t
R.
Bh
a
g
a
t
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o
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n
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m
a
ste
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s
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re
e
in
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h
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g
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g
fro
m
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,
Na
g
p
u
r
(In
d
ia).
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o
c
c
u
p
ied
v
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rio
u
s
p
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si
ti
o
n
s
to
se
r
v
e
th
e
e
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g
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g
i
n
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u
tes
fo
r
a
b
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u
t
2
2
y
e
a
rs.
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is
c
u
rre
n
tl
y
wo
rk
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g
a
s
a
n
a
ss
o
c
iate
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ro
fe
ss
o
r
in
th
e
De
p
a
rtme
n
t
o
f
M
e
c
h
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n
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o
v
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n
d
ra
o
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n
jari
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f
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n
g
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g
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n
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h
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lo
g
y
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g
p
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r.
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a
tt
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n
d
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d
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ter
n
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ti
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l
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n
d
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ti
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n
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l
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fe
re
n
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e
s.
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is
a
m
e
m
b
e
r
o
f
p
r
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fe
ss
io
n
a
l
b
o
d
ies
su
c
h
a
s IS
T
E.
He
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
h
e
m
a
n
t_
b
p
@y
a
h
o
o
.
c
o
m
.
Dr
.
Ra
m
e
sh
Pa
w
a
se
c
o
m
p
lete
d
h
is
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c
h
e
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tro
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m
m
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a
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c
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Dr.
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b
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e
b
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b
e
d
k
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h
n
o
lo
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i
v
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,
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n
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re
in
2
0
0
8
.
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h
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s
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p
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d
h
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s
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v
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b
a
i
P
h
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le
P
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n
e
Un
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e
rsity
(S
ITRC
Na
sh
i
k
).
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i
s
wo
rk
i
n
g
a
s
a
ss
o
c
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p
r
o
fe
ss
o
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in
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t
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fr
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tv
a
h
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in
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g
,
S
a
n
g
a
m
n
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r
M
a
h
a
ra
sh
tra
(In
d
ia).
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c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
ra
m
e
sh
.
p
a
wa
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@a
v
c
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e
.
o
rg
.
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