In
te
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ation
a
l Jou
rn
al
o
f Po
we
r
Elec
tron
ic
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d
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ive S
y
stem
(IJ
PED
S
)
V
o
l.
11, N
o.
1, Mar
ch 20
20,
p
p.
213~
2
1
9
IS
S
N
: 2088-
86
94,
D
O
I
:
10.11
59
1
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v11
.
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1.pp
2
13-
21
9
213
Jou
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a
l
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pa
ge
:
ht
tp:
//i
j
p
eds.i
a
esco
re
.com
Stabilization of t
he stator and
rotor flux linkage of
the induc
tion
motor in the asynch
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onous el
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c
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regulation
Vl
a
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L
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k
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Al
ek
sandr
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.
A
n
ik
i
n
,
Al
ek
sa
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d
r
A. Bal
d
e
n
k
ov
Dep
a
rtem
ent
of
t
h
e
oreti
cal f
u
n
d
a
men
t
als of
e
lect
rical
e
ngi
neeri
ng,
S
outh
Ura
l
S
tate
U
n
i
versit
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,
R
u
ssia
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
Re
ce
i
v
e
d
Ju
l
1
1,
201
9
Re
vise
d N
ov
8
, 2019
A
c
c
e
pte
d
D
ec 3,
201
9
The
arti
c
l
e
is
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c
onti
nuation
of
t
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a
utho
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s
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or
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on
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o
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E
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r
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s
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e
pro
cess
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s
of
s
eq
uent
ial
accelerat
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of
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e
e
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ine
to
f
ix
ed
s
peeds
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erlo
ad
a
n
d
l
o
a
d
sh
eddi
ng
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n
each
o
f
t
h
em
w
ere
sim
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la
t
e
d.
A
t
t
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s
am
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tim
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c
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t
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y
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fici
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f
each
t
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s
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x
p
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m
e
ntal
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udies
,
th
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c
and
eff
i
cien
cy
o
f
a
m
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s
table
scal
ar
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ont
rol
was
si
gnif
icantl
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improved by
t
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e
use of dynami
c
p
ositive
f
eedback on stat
or
curr
ent.
K
eyw
ord
s
:
Ma
them
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l
m
odel
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Po
sit
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e f
e
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d
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ack
Rot
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and sta
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f
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ontro
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r
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a
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co
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ol
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o
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en acces
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ti
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n
d
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B
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pon
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th
or:
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e
k
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. A
n
i
ki
n
,
D
e
pa
rtem
ent o
f
t
he
ore
tic
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l
fu
nda
me
nta
l
s
o
f
e
l
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ctr
i
ca
l en
g
i
n
e
e
r
i
ng
,
S
out
h U
r
al S
tate U
nive
rsity,
7
6
,
Le
n
i
n
p
rosp
e
k
t
,
Ch
e
ly
a
b
in
s
k
, Ru
ssi
a. 4
54
080
Em
ail:
ani
k
i
n
a
s
@
s
u
s
u.
ru
1.
I
N
TR
OD
U
C
TI
O
N
I
n
r
e
cent
year
s,
a
g
r
o
u
p
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f
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n
g
i
neer
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at
t
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S
out
h
Ural
S
t
a
te
U
ni
versi
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y
(
S
U
SU
),
h
eade
d
b
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r
of.
K
o
d
k
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V
.
L
.
h
a
s
car
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m
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t
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c
dr
ive
s
w
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t
h
frequ
enc
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c
o
n
t
r
ol
(A
ED
F
C).
Oper
at
i
n
g
ex
per
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e
n
ce
of
s
uc
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dri
v
es
s
h
o
w
s
t
hat
it
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r
from
alw
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bl
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to
o
b
t
a
i
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t
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ra
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ter.
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ase
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on
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s
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t
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ma
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ma
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l
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y
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T
h
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r
e
s
u
l
t
s
o
f
t
h
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x
p
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p
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t
e
d
i
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t
h
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a
r
t
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c
l
e
s
p
u
b
lishe
d
in
R
ussia
n
a
nd
fore
ig
n
pu
b
l
ic
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t
ions
[
1
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2
]
.
A
TV
32
a
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A
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V
71
fre
que
nc
y
c
o
nve
rter
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from
S
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c
tr
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e
used
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s
bas
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c
equ
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pme
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t.
T
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m
a
i
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re
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t
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on
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v
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d
b
ack
on
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h
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st
at
or
curr
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(D
P
F
)
[3,
4
]
.
Th
is
f
e
e
dbac
k
i
nc
lu
de
s
a
d
ynam
i
c
l
i
n
k
t
ha
t
prov
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s
t
he
n
ec
es
sary
g
a
i
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fac
t
ors
f
o
r
the
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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8
8
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86
94
I
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J
P
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w
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r
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V
o
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11,
N
o.
1
,
Mar
202
0
:
213
–
21
9
21
4
c
o
r
r
e
ctive
fe
e
d
bac
k
i
n
the
lo
w
fr
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ncy
r
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w
it
h
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u
t
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ist
u
r
b
i
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g
t
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s
ta
bi
lit
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of
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r
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ve.
The
l
i
m
ited
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b
i
l
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o
f
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dr
i
v
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doe
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o
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a
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I
R
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p
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s
t
o
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f
fe
ct
iv
ely
s
o
lv
e
th
e
i
r p
r
ob
l
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ms.
2.
PROBLEM
D
E
F
INI
T
IO
N
VFD
re
sear
ch usin
g
the
Ma
t
l
a
b / Sim
u
li
nk packa
g
e i
s
dev
ote
d
t
o
a l
a
r
g
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numbe
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of
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The
m
a
i
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p
a
rt
o
f
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h
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a
n
a
ly
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s
a
n
d
i
m
p
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ov
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t
h
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dynami
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ch
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r
ac
t
e
r
i
st
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c
s
o
f
s
uc
h
s
y
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t
em
s
[5-
8
]
,
a
nd
s
o
m
e
of
t
he
m
ar
e
e
q
u
i
ppe
d
w
i
t
h
s
ens
o
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ess
c
o
ntr
o
l
[9,
1
0
]
.
A
l
ot
o
f
w
o
r
k
i
s
dev
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ted
t
o
i
m
p
r
o
vi
n
g
t
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g
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f
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e
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cy
o
f
c
o
n
v
er
ter
s
i
n
A
E
D
F
R
[
11-
13]
H
ow
eve
r
,
t
h
e
m
ode
ls
o
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elec
tr
ic
m
o
to
r
s
u
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d
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t
he
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and
t
h
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o
f
m
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tor
s
i
ncor
p
o
r
a
te
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in
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on
tr
o
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s
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a
r
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t
w
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s
a
m
e
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s
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u
m
p
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r
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o
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,
no
one
d
ispu
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s
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h
e
pr
esence
o
f
t
h
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ina
c
c
u
r
aci
e
s
a
n
d
a
s
sum
p
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[
14-
20]
.
The
r
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ch
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ly
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a
l
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,
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I
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know
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.
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R
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por
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R
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U
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p
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s
r
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ar
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F
ebr
u
a
r
y
14,
201
9
P
r
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o
r
V
.
L.
K
o
d
k
i
n
A
d
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N
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Re
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U
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ver
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In
f
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T
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nol
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s
,
Me
ch
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c
s
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Op
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r
g
,
R
uss
i
a.
S
uch
sem
i
na
r
s
a
r
e
c
onduc
te
d
u
nde
r
the
gu
ida
n
c
e
o
f
P
r
ofessor
A
.
K
ozyar
uk.
W
i
t
h
i
n
t
he
ir
f
r
a
m
e
w
o
r
k
,
lea
d
i
n
g
sc
ie
nt
i
s
ts
o
f
Russ
ia
i
n
t
h
e
f
i
e
l
d
of
e
l
e
c
tr
ic
d
ri
ve
g
ive
an
a
ssessm
ent o
f
m
ode
rn r
esea
rch.
Du
ri
ng
t
h
e
d
i
s
cu
s
s
i
o
n
,
c
oll
e
ag
u
e
s
a
g
reed
w
i
t
h
t
h
e
ma
in
r
esul
t
s
o
f
t
he
r
esea
r
c
h.
T
he
y
cl
a
r
ifie
d
t
h
a
t
t
h
e
c
o
n
c
l
u
s
i
o
n
s
m
a
d
e
a
r
e
t
r
u
e
,
f
i
r
s
t
o
f
a
l
l
,
f
o
r
s
e
n
s
o
r
l
e
s
s
v
e
c
t
o
r
c
o
n
t
r
o
l
,
w
h
i
c
h
i
s
u
s
e
d
i
n
m
o
s
t
f
r
e
q
u
e
n
c
y
c
o
n
v
erter
s
(
Sc
hne
i
d
er
E
l
e
c
t
ric,
D
anfo
ss,
Vac
on,
e
tc.)
a
nd
t
h
er
e
f
o
re
,
t
h
e
stu
d
i
es
h
av
e
a
g
r
ea
t
p
r
ac
t
i
c
a
l
m
e
a
n
i
n
g.
O
ne
o
f
t
h
e
lea
d
in
g
sc
i
e
ntis
ts
i
n
t
h
is
f
i
e
ld
A
.
Us
ol
tse
v.
s
ug
g
e
s
t
e
d
t
he
a
dva
n
t
a
g
es
o
f
the
pr
o
pos
ed
co
rrectio
n
scheme:
th
e
DPF,
wh
ich
do
es
n
ot
c
au
se
i
n
s
tab
ili
ty
d
u
e
t
o
t
he
d
y
n
am
i
c
link,
p
r
o
v
i
de
s
de
e
p
sta
b
i
l
i
z
a
t
i
o
n
o
f
t
he
m
ag
ne
tic
c
ou
p
l
i
n
g
of
t
he
r
ot
or
,
w
h
i
c
h
p
l
a
y
s
a
m
a
j
o
r
r
o
le
i
n
t
h
e
f
o
r
m
atio
n
of
t
he
t
or
q
u
e
of
an
a
sy
n
c
h
r
onou
s
sho
r
t
-
ci
r
c
uit
e
d
e
l
e
c
t
r
i
c
mot
o
r
.
A
c
c
o
r
d
i
n
g
to
A
.
U
soltse
v
,
the
au
t
hor
s
ca
n
ver
i
f
y
t
hese
r
e
s
u
l
ts
by
m
ode
l
i
ng
t
h
e
p
r
o
ce
sse
s
i
n
A
E
D
F
R
.
I
t
s
h
o
u
l
d
b
e
note
d
t
hat
s
u
c
h
a
n
ass
u
mpt
i
on
ve
r
y
l
og
ica
l
l
y
e
x
p
l
ai
ns
a
ll
th
e
result
s.
T
heref
o
re,
af
ter
th
is
s
emi
n
ar,
t
h
e
task
w
as
t
o
co
n
d
u
c
t
a
c
om
p
a
r
a
t
i
ve
s
i
m
u
l
a
t
i
o
n
o
f
a
s
ync
hr
on
o
u
s
e
l
e
c
tr
ic
d
r
i
ve
s
w
i
t
h
d
i
f
f
e
r
e
nt
c
on
tr
o
l
s
ys
t
e
m
s
.
I
n
t
he
c
o
u
r
s
e
o
f
t
h
is
s
imu
l
ati
o
n,
i
n
a
d
d
i
t
i
on
t
o
t
h
e
s
p
ee
d
a
n
d
c
u
r
r
e
nt
o
f the
m
o
tor
,
it
is al
s
o
ne
ce
ssa
r
y
t
o
c
on
tr
o
l
i
ts
m
ag
ne
t
i
c f
l
ux.
The
r
esul
ts o
f th
is w
or
k
a
r
e gi
ven
i
n
t
his
art
i
c
l
e
.
3.
S
O
LUTI
ON
The
s
i
mula
t
i
o
n
w
a
s
car
r
i
ed
o
u
t
i
n
the
S
i
mul
i
nk
a
p
pl
i
c
a
t
ion
of
t
h
e
M
ATLAB
so
f
t
ware.
As
i
n
th
e
pr
ev
io
u
s
s
t
udie
s
o
f
t
h
e
a
u
th
or
s,
f
or
t
he
f
ir
s
t
v
er
si
on,
A
ED
F
R
w
a
s
per
f
or
m
e
d
usin
g
the
sta
nda
r
d
m
ode
l
of
t
he
V
F
D
w
ith
v
ec
tor
c
o
nt
r
o
l
[
2
1
–
23]
F
igur
e
1
.
T
he
a
ut
h
o
r
o
f
t
h
e
m
od
e
l
i
s
P
r
ofessor
H
o
an
g
Le-
H
uy,
P
r
o
fessor
a
t
the
D
e
pa
r
t
me
n
t
o
f
El
e
c
t
r
i
ca
l
En
gi
neer
ing
a
n
d
C
o
mpu
t
e
r
E
n
g
i
n
ee
r
i
ng
, L
av
a
l
Un
i
v
e
rsi
t
y
, Qu
e
b
ec
, C
a
n
ada.
F
i
gur
e
1.
M
o
d
e
l
of
V
F
D
w
it
h
vector
c
o
n
tr
o
l
a
nd
t
h
e
m
o
d
u
l
e
"
V
ect
or
c
ontr
o
l"
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
St
abi
l
i
zat
i
on o
f
the
stat
or a
nd
ro
tor f
l
u
x
l
i
nk
a
g
e
of t
h
e
in
duc
t
i
o
n
m
o
t
o
r
…
(V
lad
i
m
i
r L
.
Kodki
n
)
21
5
To
s
tu
dy
the
sc
alar
c
o
n
tro
l
s
ys
tem
F
i
gur
e
2,
t
he
m
ode
l
of
P
rofe
ss
or
L
o
u
is
D
esa
n
te
s
(Lou
is-
A
.
D
e
ssain
t)
f
rom
t
h
e
s
t
a
t
e
e
n
gi
n
eer
i
n
g
sc
h
o
o
l
(
Éco
l
e
de
t
ec
hn
olo
g
i
e
s
u
p
é
ri
eu
re
)
in
M
o
n
t
r
ea
l
(Qu
e
b
e
c
,
C
an
ad
a)
was
used
[
24,
25]
.
To
i
nc
rea
s
e
t
h
e
eff
i
c
i
ency
o
f
t
h
e
form
ati
on
o
f
t
he
e
lec
t
r
o
ma
g
n
e
tic
t
orque
,
pos
it
ive
fe
ed
bac
k
o
n
t
h
e
roo
t
m
ea
n
square
(
r
m
s)
v
al
ue
o
f
the
st
a
t
or
c
urr
en
t
w
a
s
i
n
tr
od
u
c
e
d
i
n
t
o
the
c
ontr
o
l
syste
m
F
igure
3.
F
i
gur
e 2.
S
chem
e
of sc
a
lar
contr
o
l m
ode
l
F
i
gure
3.
S
c
h
em
e of a
s
ca
l
a
r c
o
n
t
ro
l
m
o
de
l w
i
t
h
po
s
it
ive
fee
dba
ck
S
i
mulat
i
o
n
of
p
roce
sse
s
o
f
s
e
que
n
tia
l
acc
el
er
ation
t
o
s
pee
d
s
c
o
rre
s
p
ond
in
g
to
t
h
e
s
up
pl
y
voltage
fre
que
nc
y
o
f
1
0
-
20
-
30
-
40
–
50
H
z
w
a
s
c
arr
i
e
d
o
u
t
,
at
eac
h
s
pe
e
d
o
f
r
o
ta
t
i
o
n
a
l
oa
d
w
a
s
dra
w
n.
T
he
ang
u
l
ar
v
el
oc
it
y
of
t
he
m
o
t
or
s
ha
ft
a
n
d
t
he
r
m
s
v
a
l
ues
o
f
t
he
r
ot
o
r
a
nd
s
t
a
to
r
fl
ux
l
i
n
kag
e
s
a
n
d
t
h
e
st
a
t
o
r
curr
ent
w
e
re
c
on
tro
l
l
e
d.
T
he
r
ms
v
alues
w
e
re
c
alcu
late
d
fr
om
t
h
e
pro
j
e
c
tio
ns
o
n
t
h
e
d
an
d
q
a
x
es
o
f
the
corr
espo
n
d
in
g
si
gna
ls,
whic
h
are
availa
b
l
e
for
me
asurem
e
n
t
in
t
h
e
m
od
el
o
f
an
a
s
y
n
c
h
r
o
nou
s
el
ect
ri
c
mo
t
o
r.
Th
e
la
st
s
ig
n
a
l
i
s
r
equ
i
re
d
to
e
v
a
lu
at
e
th
e
e
f
fi
ci
en
cy
o
f
th
e
d
ri
ve.
The
sim
u
l
a
t
i
on
re
sul
t
s
of
s
c
a
l
ar
c
ontro
l
w
itho
u
t
f
ee
d
b
a
c
k
are
show
n
i
n
F
i
gure
4,
o
f
the
vec
t
or
c
o
n
tr
ol
w
i
t
h
a
s
in
gl
e
s
p
eed
c
on
tou
r
(
wi
t
h
o
u
t
a
fl
ux
lin
ka
ge
c
o
n
t
o
u
r
)
-
i
n
F
i
g
u
re
5
a
nd
sca
l
ar
c
on
tro
l
w
ith
p
osit
i
v
e
f
ee
d
b
ack
o
n
t
h
e
r
m
s
val
u
e
of
t
he
s
ta
tor
c
u
rrent
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
11,
N
o.
1
, Ma
r
202
0
:
213
–
21
9
21
6
and
a
dy
nam
i
c
lin
k
-
in
F
ig
ur
e
6.
A
t
the
sa
m
e
t
im
e,
s
pe
ci
al
a
t
t
e
n
t
i
on
w
a
s
pai
d
t
o
the
c
h
an
ge
i
n
the
s
t
ator
a
n
d
rot
o
r
flu
x
e
s
a
t
the
mom
e
nt
o
f
l
o
ad
i
ng.
T
he
d
ev
ia
ti
o
n
s
of
t
he
r
o
tor
a
n
d
st
ator
u
n
d
e
r
l
oa
d
fr
om
t
he
v
a
l
ues
a
t
id
l
e
for
diffe
rent
f
req
u
e
n
ci
es of t
h
e
su
pp
l
y
v
ol
ta
ge
w
ith
d
iffe
r
e
nt c
o
n
tr
ol
a
lg
ori
t
hm
s a
r
e
show
n in Ta
b
el.
1
.
F
i
gur
e 4.
Mo
d
e
ll
ing
pr
oce
s
se
s in a
n asy
n
chr
ono
us
e
lec
t
ric
dri
v
e
w
ith
s
cal
a
r
c
ont
r
o
l
w
ith
ou
t fee
dba
c
k
F
i
gure
5.
M
od
e
l
l
i
ng pr
oc
esse
s in
a
n a
s
y
n
chr
o
n
o
u
s ele
c
t
ric
dri
v
e
w
it
h ve
ct
or c
on
t
r
ol
s
yst
e
m
Tab
l
e
1. The
de
v
ia
tio
ns va
l
ue
s
of
t
he
ro
t
or
a
nd s
t
at
or
f
l
ux u
n
d
er
l
oad f
o
r differe
n
t
f
re
que
ncie
s
of t
he
s
upp
l
y
v
ol
ta
ge
and
c
o
n
t
rol sys
t
e
m
C
o
n
t
r
o
l
sy
st
e
m
M
a
x
i
m
u
m
d
ev
iati
o
n
s
o
f
ro
tor
/ stato
r
flu
x
e
s, V
•
s
10
H
z
20
H
z
30
H
z
40
H
z
50
H
z
S
c
a
l
a
r
c
ontrol
w
ith
out
f
e
e
db
ac
k
-0,2/
-0
,
2
-
0
,
09/
-0
,
1
1
-
0
,
05/
-0
,
0
5
-
0
,
03/
-0
,
0
3
-
0
,
04/
-0
,
0
3
V
e
ctor
c
ontrol
w
ith
a
s
ingle
sp
e
e
d
c
o
n
tou
r
0,
06/
0,
1
-
0
,
03/
-0
,
0
4
-
0
,
05/
-0
,
0
6
-
0
,
03/
-0
,
0
3
-
0
,
03/
-0
,
0
3
S
c
a
l
a
r
c
ontrol with
DPF
-0,1/
-0
,
1
-
0
,
03/
-0
,
0
3
-
0
,
03/
-0
,
0
3
-
0
,
03/
-0
,
0
3
-
0
,
04/
-0
,
0
2
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
St
abi
l
i
zat
i
on o
f
the
stat
or a
nd
ro
tor f
l
u
x
l
i
nk
a
g
e
of t
h
e
in
duc
t
i
o
n
m
o
t
o
r
…
(V
lad
i
m
i
r L
.
Kodki
n
)
21
7
F
i
gur
e 6.
Mo
d
e
ll
ing
pr
oce
s
se
s in a
n asy
n
chr
ono
us
e
lec
t
ric
dri
v
e
w
ith
s
cal
a
r
c
ont
r
o
l
w
ith
ou
t fee
dba
c
k
In
s
ca
l
a
r
co
nt
r
o
l
,
t
h
e
m
ax
i
m
um
p
o
ssibl
e
v
a
lu
e
of
s
t
a
nd
a
r
d
IR
-com
pensa
t
i
on
w
a
s
es
tab
l
i
s
he
d
(w
hich
ma
int
a
ins
s
t
a
b
i
lit
y).
A
t
t
he
s
a
m
e
tim
e,
t
he
s
ca
tt
e
r
o
f
sta
t
or
a
n
d
r
o
t
o
r
f
l
u
x
e
s
a
t
l
o
w
s
p
e
e
d
(
3
0
r
a
d
/
s
)
i
s
i
n
t
h
e
regi
on
of
0
,2
V
•
s
,
and
de
c
r
e
a
ses
to
0
,1
V
•
s
w
it
h
a
n
i
ncre
as
e
i
n
s
p
e
e
d
t
o
n
o
m
i
n
a
l
(
1
5
7
r
a
d
/
s
)
.
W
i
t
h
t
h
e
in
t
r
od
uc
ti
on
of
t
he
D
P
F
,
the
fl
ow
d
e
v
ia
t
i
o
n
s
d
u
r
in
g
ac
cel
e
r
ati
o
ns
a
nd
loa
d
s
urge
s
do
not
e
xce
e
d
0,1 V
•
s.
Wi
t
h
v
ect
or
c
o
n
t
r
ol
,
t
h
e
m
e
a
n
v
a
l
ue
o
f
t
h
e
fl
ow
d
e
v
i
a
ti
on
s
is
a
l
s
o
0
,
1
V
•
s
,
b
u
t
a
t
t
h
e
s
a
m
e
t
i
m
e
,
t
h
e
r
e
i
s
a
hi
gh-
fre
q
uenc
y
c
o
mpo
n
e
n
t
i
n
t
he
s
ta
tor
flo
w
.
A
tte
nt
ion
s
h
o
u
l
d
b
e
pa
i
d
t
o
t
h
e
sta
t
or
c
urr
e
nts,
w
hic
h
a
re
t
he
grea
tes
t
i
n
vec
t
or
c
on
tro
l
a
n
d
m
in
i
m
al
i
n
D
P
F
Tabel
2.
T
h
u
s,
t
h
e
sim
u
lat
i
on
clea
r
l
y
sh
ow
ed
t
ha
t
i
n
t
he
elec
tr
ic dr
i
ve
w
it
h D
F
T the
flow
sta
b
i
l
i
z
a
t
i
on
is
p
ra
ct
i
c
a
l
l
y
a
t
t
h
e
sam
e
l
ev
el a
s the
vec
t
or
c
ontr
o
l.
Tab
l
e
2. The
va
l
ue
s
of
s
ta
tor cur
r
ents u
n
d
er
loa
d
for differe
nt
f
re
qu
en
c
i
es
o
f
t
h
e sup
p
l
y
vol
tage
an
d
c
o
n
tr
ol sy
s
tem
C
ontrol sy
ste
m
Sta
t
or c
urr
e
nt
under
loa
d
,
A
10
Hz
2
0
H
z
30
H
z
40
H
z
50
Hz
Sc
al
a
r
c
ontrol
w
ith
out
f
e
e
d
b
a
c
k
1
0
8
7,
5
7,
5
9
V
e
c
t
or
c
ontrol
w
ith
a
s
i
ngle
sp
e
e
d
c
o
n
tou
r
1
4
13
1
2
13
1
3
S
c
a
l
ar
c
o
n
t
ro
l with DP
F
8
7
7
7
,5
8
,5
I
n
a
d
d
i
t
i
on,
p
roc
e
sses
i
n
a
d
rive
w
it
h
ve
c
t
o
r
c
on
t
r
o
l
w
ith
a
s
p
e
e
d
e
r
r
o
r
o
f
2
a
n
d
4
%
a
r
e
s
i
m
u
l
a
t
e
d
F
i
gure
7,
8
. Th
e simu
lat
i
o
n
re
sults
a
re ver
y v
i
sua
l
. Wi
t
h
t
he i
n
t
ro
d
u
ct
i
on o
f
an err
o
r
r
a
te o
f 2
%
i
n
t
o t
h
e si
gna
l
F
i
gure
7,
t
he
c
on
tro
l
l
o
s
e
s
o
p
e
ra
tion
a
t
a
s
pe
ed
c
orr
e
sp
o
n
d
i
ng
t
o
t
he
f
re
q
u
e
ncy
o
f
t
he
s
ta
tor
v
o
l
t
a
g
e
o
f
4
0
H
z
,
and
wit
h
a
n
er
ror
of
4
%
-
30
H
z
F
i
gure
8
.
Large
sta
t
or
c
urrents
a
re
a
v
ery
ser
i
ous
problem
for
drives
i
n
trans
por
t a
nd p
o
w
e
r
c
o
m
p
lexe
s,
w
he
re
t
he lo
a
d
is
n
on-de
ter
m
ini
s
tic
.
Th
us,
t
h
e
mo
d
e
l
i
n
g
o
f
pr
oce
sses
w
i
t
h
c
o
n
t
rol
o
f
f
l
u
x
l
i
n
kage
f
u
lly
c
on
fi
r
m
e
d
t
he
a
ss
um
p
t
i
on
of
P
r
ofessor
A
.
U
sol
t
se
v,
a
nd
e
x
p
l
a
i
ne
d
the
rea
s
on
for
t
h
e
sig
n
i
f
i
can
t
ad
va
n
t
a
g
es
o
f
the
prop
ose
d
D
P
F
over
trad
it
iona
l
a
l
g
o
r
it
hms.
Y
ou
ca
n
im
p
l
em
en
t
th
is
c
orrec
t
ion,
w
it
h
out
a
ny
c
han
g
e
s
in
t
h
e
c
i
r
c
u
it
s
a
n
d
al
gori
t
h
m
s
of
s
ta
nd
ard
fre
que
nc
y
c
o
n
v
erte
rs,
on
a
pro
g
r
a
m
m
a
ble
l
o
g
i
c
co
ntr
o
l
ler.
T
his
m
a
kes
the
w
i
des
p
re
ad
u
s
e
o
f
t
h
e
pro
pose
d
c
or
rec
t
i
o
n
ava
ila
ble
i
n
a
l
m
os
t
an
y
elec
tr
ic
d
ri
ve.
The
a
ut
hors
a
r
e
gra
t
eful
t
o
t
h
e
sem
i
na
r
at
t
h
e
Na
t
i
o
n
a
l
R
e
s
e
a
r
ch
U
ni
v
e
rsi
t
y
o
f
In
fo
rmati
o
n
Te
chno
l
o
g
i
es,
M
ech
a
n
i
c
s
a
n
d
O
p
t
i
c
s
,
a
n
d
e
s
p
e
c
i
a
l
l
y
t
o
P
r
ofessor
A
.
U
soltse
v
,
w
ho is
c
ons
i
d
e
r
ed
t
he
a
ut
h
o
r
of
t
he
i
dea
of
th
is sim
ul
a
tio
n.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
11,
N
o.
1
, Ma
r
202
0
:
213
–
21
9
21
8
F
i
gure
7. V
ector
c
on
trol w
i
t
h
spee
d er
ror
of 2%
F
i
gure
8. V
ector
c
on
trol w
i
t
h
spee
d er
ror
of 4%
4.
CONCL
U
S
IONS
The
c
o
nduc
te
d
sim
u
l
a
tio
n o
f
A
ED
F
R w
ith sca
l
a
r
c
o
n
t
ro
l
a
nd posi
t
i
ve fee
dbac
k
o
n
t
h
e sta
t
or
c
urre
nt
show
e
d
t
hat
t
h
i
s
c
orre
ctio
n
a
l
l
o
w
s
s
ta
b
i
l
i
z
i
n
g
t
he
f
l
u
x
li
nk
age
o
f
th
e
r
o
t
o
r
a
n
d
st
ato
r
i
n
a
n
e
l
ect
ri
c
mach
i
n
e.
Th
is
e
nsures
a
m
or
e
efficie
n
t
for
m
a
t
i
o
n
o
f
t
he
e
lec
t
r
o
ma
g
n
e
tic
mom
e
n
t
a
t
low
e
r
s
t
at
or
c
ur
rent
s
an
d
le
ss
abs
o
l
u
t
e
s
l
i
p.
I
n
t
u
rn,
suc
h
a
c
or
rec
t
i
on
im
p
r
oves
the
sta
t
i
c
a
nd
d
ynam
i
c
c
h
ara
c
teris
t
i
c
s
of
a
n
as
ync
hr
ono
us
elec
tr
ic dr
i
ve
w
it
h fr
e
que
nc
y co
ntro
l, an
d
m
a
k
e
s
it
p
o
ss
ible
t
o
u
se
mi
ddl
e
-
cl
a
ss t
e
c
h
n
i
cal
-e
co
no
mi
c
f
r
equ
e
n
c
y
con
v
er
ters
i
n
c
o
mple
x
in
d
u
strial
m
echa
n
i
s
m
s
w
i
t
h
h
i
g
h
d
e
m
ands
o
n
t
h
e
s
t
at
ic
a
nd
d
yna
m
i
c
cha
r
ac
t
e
ris
t
ic
s
o
f
the dr
i
v
e
.
REFE
RENCES
[1]
Ko
dk
in
V
.L.
,
"
E
x
p
e
rim
e
n
t
al
r
esearch
o
f
asy
n
c
h
ro
no
us
e
l
ectri
c
d
r
iv
e
wit
h
p
o
s
iti
v
e
d
y
n
a
mi
c
f
eedback
o
n
s
t
at
o
r
curren
t
”
Int
e
rn
at
ion
a
l
confer
ence o
n
i
n
d
u
s
t
ri
a
l
eng
i
n
eerin
g
A
p
p
l
i
c
a
t
i
ons a
n
d
M
a
nufact
u
rin
g
, ICIE
AM
20
17
–
Pr
oceedi
n
g
s
.-20
17
.
[2]
An
ikin
A
.
S
.
,
"Dy
n
am
i
c
posit
iv
e
cou
p
li
ng
i
n
asyn
chro
no
us
e
l
ectri
c
d
r
iv
es
w
ith
f
requ
ency
c
o
n
t
r
o
l
,
"
Pr
io
r
i
t
i
e
s
of
wor
l
d s
c
ien
c
e
:
exp
erim
ent
a
n
d
scien
t
i
f
i
c
d
i
s
c
us
sio
n
M
a
teria
l
s
of t
h
e
8t
h inter
n
a
t
i
onal
s
c
ient
ific
con
f
er
ence.
Sci
e
ntifi
c
a
nd Pu
blish
i
n
g
Cen
t
er Ot
k
r
y
t
i
e
.
N
o
rth
Charl
e
st
on
,
S
C
,
U
S
A,
p
p
.
1
7
-
18,
-
p
p
.
1
19-1
24,
J
u
n
e
20
15
.
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
St
abi
l
i
zat
i
on o
f
the
stat
or a
nd
ro
tor f
l
u
x
l
i
nk
a
g
e
of t
h
e
in
duc
t
i
o
n
m
o
t
o
r
…
(V
lad
i
m
i
r L
.
Kodki
n
)
21
9
[3]
Ko
dk
in,
V
.
L
.,
A
.
S
.
A
n
i
k
i
n
,
A
.
A.
B
alden
k
o
v
,
“Th
e
d
yn
am
ics
ident
ifi
catio
n
o
f
a
sy
nch
r
on
ous
e
l
ectri
c
d
r
ives
v
i
a
f
r
equ
e
ncy
resp
on
se,
”
Int
e
rna
t
i
o
n
a
l
Jo
urn
a
l
o
f
Po
wer
El
ectro
n
i
cs and Dr
ive Sys
t
ems
(
I
JPEDS)
,
Vol.
1
0
, No
. 1
, p
p
. 66
-
73
,
20
19
.
[4]
Kod
k
in
,
V
.
L
.,
A
.S
.
An
i
k
i
n
,
A.
A.
B
alden
k
o
v
,
“
Perf
o
r
man
ce
i
d
enti
fi
cati
on
o
f
t
h
e
a
s
ynch
r
on
ou
s
el
ec
t
r
ic
d
riv
e
s
by
th
e
sp
ectrum
of
r
o
t
or
c
u
r
ren
t
s,”
In
te
rna
tion
a
l J
o
urna
l o
f
Po
we
r Ele
c
t
ro
nic
s
an
d Driv
e
Sy
ste
m
s
(IJ
P
EDS
)
,
Vol.
1
0
, No
. 1
, p
p
. 21
1
-2
1
8
,
20
1
9
.
[5]
Al
ekseev
V
.
V
,
E
me
l
’
yan
ov
A
.
P
,
K
o
zyaru
k
A
.
E
.
,
"
A
nal
y
sis
of
t
h
e
dy
nam
i
c
perf
o
r
m
a
n
ce
o
f
a
v
a
r
i
a
bl
e-f
r
e
q
uen
c
y
in
du
ctio
n
mo
tor
dri
v
e
u
s
i
n
g
vari
ou
s
co
nt
rol
st
ru
c
t
u
r
es
a
n
d
a
l
g
o
ri
t
h
ms,
"
R
u
s
s
i
a
n
El
ectrical
En
g
i
neer
in
g
,
Vol.
8
7
. No
. 4
, p
p
. 18
1
-1
8
8
,
20
1
6
.
[6]
Al
ekseev
V
.
V
,
V
ers
h
i
n
i
n
V
.
I,
V
as
ili
e
v B.
Y
u.,
"
D
eterm
i
n
a
ti
on
of
t
h
e
param
eters
of
f
lu
x
lin
kag
e
v
ect
ors in
e
lect
ric
dri
v
es
w
ith
v
ector co
n
tro
l
,"
No
te
s
o
f
th
e M
i
n
i
ng
Ins
t
i
t
ute,
V
o
l
.
1
9
6.
p
p
.
2
22-2
2
5
, 2
01
2.
[7]
Kv
ash
n
in
V
.O,
&
Chered
ni
k
Yu
.
N
,
"
Co
nst
r
uctio
n
o
f
a
m
a
t
h
emati
c
a
l
mo
de
l
o
f
a
n
ind
u
c
tion
m
o
t
o
r
i
n
sy
nc
hro
n
o
u
s
axes
w
i
t
h
tem
p
e
r
a
t
ure
c
o
m
p
en
sa
ti
on
f
or
c
hang
es
i
n
ro
to
r
f
l
u
x
l
i
n
k
ag
e,"
El
e
c
t
r
otech
ni
c
a
l
and
Co
m
p
u
t
er
Sys
t
ems
,
vo
l.
3
,
N
o
.
7
9
,
pp.
2
56
-25
7
,
2
011.
[8]
Al
ekseev
V
.
V,
&
K
ozyaru
k
A.
E
.
"Com
p
a
rativ
e
an
alys
is
o
f
m
o
d
e
ls
f
or
s
y
s
te
m
s
o
f
an
a
u
t
om
at
ed
a
s
y
n
c
hron
ou
s
dri
v
e
wit
h
v
ector
c
on
trol,
"
Russia
n
Electrica
l
E
n
g
i
n
eerin
g
, Vo
l
.
8
4
,
No
. 12
, pp
.
7
02
, 20
1
3
.
[9]
Vas
i
l
i
ev
B
.
Y
u
,
&
Ko
zyaru
k
A
.
E
.
"
Increas
in
g
t
h
e
e
f
f
i
cien
cy
o
f
asy
n
ch
ron
ous
e
l
ectric
dri
v
es
w
ith
d
i
r
ect
t
orq
u
e
con
t
ro
l,"
Bul
l
e
t
in
of
SUSU
.
S
e
r
.
Ene
r
gy
,
V
ol.
13,
N
o
.
2
.
p
p
.
7
5
-8
4
,
201
3.
[10]
M
o
u
s
ta
f
a
Z
air,
&
A
bd
eldej
b
ar
H
azzab,
"
M
RA
S
sp
eed
s
ens
o
rl
ess
vec
t
o
r
co
nt
ro
l
of
i
nd
uc
t
i
on
m
o
t
or
d
ri
ves
usin
g
pred
icti
ve
a
d
a
ptat
io
n
m
echan
is
m,
"
In
tern
a
t
io
nal Jou
r
n
a
l of
P
o
wer E
l
ect
ronics
an
d Dr
ive Sys
t
e
m
s
(
I
JPEDS)
,
V
o
l.
9,
N
o.
4
,
pp.
1
523-15
33
,
2
0
1
8
.
[11]
Mul
d
i
Yuhendr
i
,
Ahyanuardi
A
hya
nuardi,
Aswardi
Asw
ardi.,
"
D
i
rec
t
torque
c
ont
r
ol
s
trat
e
g
y
of
P
M
S
M
e
m
pl
o
y
i
n
g
ul
tra
s
p
ars
e
m
atri
x
co
nvert
er,"
I
n
te
r
n
a
t
io
na
l J
o
u
r
na
l o
f
P
o
w
e
r
E
l
ect
ro
n
i
cs a
n
d
Dr
ive S
y
st
ems (IJPED
S
)
,
Vo
l
.
9
,
No. 1
, p
p
. 64
-
72
,
20
18
.
[12]
Ko
zyaruk
А
.
Е
,
&
R
u
d
ak
ov
V
.
V,
"
Mo
dern
a
nd
p
erspect
iv
e
alg
o
rith
m
i
c
maintenance
is
f
re
q
u
e
nc
y
-re
gu
la
te
d
elect
ric d
r
ives,"
SP
EC
. Sa
i
n
t
Petersburg
, 2
00
4.
[13]
Ot
h
m
ane
S
a
l
a
m
a
,
Ab
del
m
oumen
T
ab
yao
u
i,
M
oh
amed
B
ench
a
g
ra,.
"
C
o
n
t
rol
m
e
th
od
s
o
n
t
hr
e
e
-
p
h
a
se
p
owe
r
con
v
erters
i
n
pho
to
vo
ltai
c
s
y
ste
m
s
,
"
Int
e
rna
t
i
onal
Jou
r
n
a
l
of
P
o
wer
El
ectro
n
i
cs an
d D
r
i
ve Sys
t
em
s (
I
JPED
S
)
,
V
o
l.
9,
N
o.
4
,
pp.
1
851-18
65
,
2
0
1
8
.
[14]
Yes
h
in
E
.
K.,
"El
ectrom
ech
anical
s
ys
tem
s
o
f
m
u
ltim
oto
r
d
rives,"
M
o
deling and
controlling
,
S
tat
e
T
ec
h
n
i
cal
Unive
r
sit
y
of
Kuzbas
s,
pp. 247,
2
0
03.
[15]
Research
o
f
au
to
matic
e
lectri
c
dri
v
es
,
e
l
ec
t
r
ical
m
achi
n
es
a
nd
val
v
e
i
n
v
e
rter:
th
emat
ic
d
ig
est
o
f
s
cien
tif
i
c
w
o
rks
under edition of
Lif
anovV
.
A.
, Le
v
i
n
t
ov S
.
D
.
-Chel
y
abi
n
sk:
CP
I
,
1
60,
199
0.
[16]
F
i
g
a
ro
B
.
I,
&
P
avly
achi
k
L
.
B,
"
Regul
ati
n
g
elect
rical
d
ri
ves
o
f
altern
ati
n
g
-
cu
rrent
,
"
M
i
sn
k: T
echn
oper
s
p
ecti
v
a
,
p
p
. 36
3
, 2
00
6.
[17]
S
o
k
o
lo
vs
ky
G
.
G
.,
"El
ectric
d
r
iv
es
o
f
altern
atin
g
cu
rrent
w
it
h
fre
q
ue
n
c
y
re
gu
la
tio
n
,
"
M
: AC
ADE
M
IA
,
p
p
. 26
7
, 2
00
6.
[18]
Us
oltsev
A
.
A,
V
oro
byo
v
N.
V
,
F
e
shi
n
B
.
N.
,
"M
eth
o
d
o
l
ogy
f
or
t
h
e
an
alys
is
o
f
elect
rom
a
gn
ets
o
f
p
ro
cesses
i
n
su
bs
ystem
s
of
a
n
a
ut
om
a
t
ed
elect
ric d
r
ive,
"
Au
to
ma
tio
n an
d
Infor
m
atics
,
Vol.
2
,
No
.
35.
p
p
.
50-53,
2
0
14.
[19]
Us
oltsev
A
.
A.,
"Det
erm
i
natio
n
of
t
he
p
aram
ete
r
s
o
f
t
he
a
sy
nc
hr
o
n
o
u
s
m
o
tor
m
o
d
e
l
accordi
n
g
t
o
t
h
e
r
ef
erence
dat
a
,
"
News of uni
versiti
es,
Ins
t
r
u
ment m
a
k
i
ng
, v
ol.
5
1
,
No.
10
,
p
p
.
3
5
-4
1,
2
00
8.
[20]
Ily
i
n
a
A
.
G
,
&
U
so
lt
sev
A.
A
,
"
O
pt
im
al
m
o
tion
con
t
rol
duri
ng
p
o
s
i
t
i
o
n
in
g
and
i
t
s
m
o
delin
g
in
t
he
M
athL
ab,
"
Si
mulink environ
m
ent, Instr
u
ment
maki
ng
, vo
l
. 5
1,
No
.
6,
pp
.
6
3
-6
8
,
2
00
8.
[21]
Ho
ang
L
e
-H
uy
,
“M
o
d
elin
g
and
si
m
u
l
a
ti
on
of
e
lect
rical
d
rives
u
s
i
ng
M
ATLAB/Si
muli
nk
a
n
d
P
ow
er
S
ys
tem
Blo
c
kset
”,
IE
CON'01
.
27th
An
nual
Confer
ence o
f
t
h
e
IE
EE Ind
u
stri
a
l
El
ectr
o
n
i
cs So
c
i
ety
.
[22]
M
a
r
c
P
e
r
r
o
n
;
H
o
a
n
g
L
e
-
H
u
y
,
“
F
u
l
l
L
o
a
d
R
a
n
g
e
N
e
u
r
a
l
N
e
t
w
o
r
k
E
f
f
i
ci
ency
O
p
tim
i
zati
o
n
o
f
a
n
Ind
u
cti
o
n
M
o
tor
with Vect
or
Con
trol
u
s
i
ng
D
iscont
inuous
P
W
M
”,
IEE
E
In
ter
nati
o
n
a
l Symp
osiu
m
o
n
In
du
stria
l
Ele
c
t
r
o
n
i
c
s
, 20
0
6
.
[23]
Ho
ang
L
e
-Huy
;
G.
S
y
b
ill
e
,
“
M
A
T
LA
B/Si
m
u
lin
k
and
P
S
P
i
ce
a
s
m
od
ell
ing
too
l
s
f
o
r
power
systems
and
powe
r
elect
roni
cs”, P
o
w
er
E
ngin
eering
S
o
ci
ety S
u
mm
er M
eeti
ng, 2
00
0
.
[24]
Lo
uis-A.
D
essaint
,
&
R
og
er
C
ham
p
agne,
"Real-ti
m
e
sim
u
l
a
ti
on
o
f
elect
ric
driv
es,"
Mat
h
em
atics a
n
d Comput
ers
in
Si
mulation
, v
o
l
.
6
3
,
No
. 3-
5
, pp
. 1
73
-1
81
20
0
3
.
[25]
Lo
uis-A.
D
es
saint
,
&
K
a
m
al
A
l
-
Hadd
ad,
"
M
o
d
el
lin
g
and
s
i
m
u
l
a
tion
o
f
elect
ric
m
a
ch
in
e
s
,
c
o
nv
erters
a
nd
s
ystem
s
,"
M
a
th
ematics
and Co
mp
u
t
er
s in
Si
mu
l
a
tio
n,
vol. 6
3,
N
o.
3
-5,
p
p
.
135
-14
3
,
200
3.
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