In
te
r
n
ation
a
l Jou
rn
al
o
f Po
we
r
Elec
tron
ic
s an
d
D
r
ive S
y
stem
(IJ
PED
S
)
V
o
l.
10, N
o.
1, Mar
ch 20
19,
p
p.
211~
2
1
8
IS
S
N
: 2088-
86
94,
D
O
I
:
10.11
59
1
/ij
ped
s
.
v10
.
i
1.pp
2
11-
21
8
211
Jou
rn
a
l
h
o
me
pa
ge
:
ht
tp:
//i
a
e
score
.
com
/
j
o
u
r
na
l
s
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i
n
d
e
x
.
p
hp/IJ
PED
S
Performance identificati
on
of th
e asynchronous el
ectric drives
by th
e
spectrum of roto
r
currents
Vl
a
d
i
m
i
r
L
.
Ko
d
k
i
n
,
Al
ek
sandr
S
.
A
n
ik
i
n
,
Al
ek
sa
n
d
r
A. Bal
d
e
n
k
ov
D
e
partm
e
nt
of
T
h
eoret
i
cal
F
unda
m
e
ntals
o
f
Electri
cal E
ng
in
eeri
n
g, Sou
th Ura
l S
t
ate Univers
ity,
R
u
ssi
a
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
R
e
c
e
i
v
e
d
Au
g
2
3
,
2
018
Re
vise
d O
c
t
9,
2018
A
c
c
e
pte
d
N
ov 3,
201
8
Th
e
ef
fici
ency
o
f
anal
yzin
g
th
e
rot
o
r
current
s
of
a
s
y
n
c
hron
ou
s
electri
c
d
r
ives
with
f
re
qu
e
n
c
y
c
on
trol
i
s
su
b
s
ta
n
t
ia
te
d
in
t
he
a
rti
c
le
.
To
a
sse
s
s
t
h
e
q
u
a
l
i
t
y
o
f
to
rqu
e
g
enerati
o
n
i
n
t
h
e
e
ngi
ne
i
t
is
s
ug
gest
ed
t
o
us
e
t
h
e
sp
ec
tr
a
l
a
na
ly
sis
o
f
th
ese
curren
t
s
an
d
th
e
f
u
nda
m
e
n
t
al
h
armo
nic,
a
s
th
e
m
o
s
t
accu
ra
te
"conf
o
r
m
i
ty
"
of
s
lip
i
n
an
a
sy
nch
r
on
ous
m
otor.
Th
e
p
r
op
o
s
ed
m
et
ho
d
sh
ow
ed
t
hat
"se
n
s
o
rl
ess
vect
or"
con
t
ro
l
l
eads
to
t
h
e
a
p
p
e
a
ran
c
e
o
f
hi
gh
-
f
r
equ
e
ncy harm
on
ics
w
ith
s
i
gnif
i
cant amp
l
i
t
u
d
e. Bec
au
se of
t
h
es
e
harm
on
ics,
a
no
n-s
i
nu
so
id
a
l
e
lect
rom
a
gn
eti
c
m
om
ent
is
c
reat
ed
a
n
d
t
h
e
p
erf
orm
a
n
ce
of
th
e
d
r
iv
e
i
s
d
ecreased
.
T
h
e
m
o
st
e
ff
ect
iv
e
m
e
th
o
d
o
f
t
o
rqu
e
g
en
erat
ion
i
s
t
h
e
f
r
equ
e
ncy
co
nt
rol
w
i
t
h
p
o
s
itive
stat
or
c
u
rrent
f
eed
back
.
This
c
ont
rol
is
do
m
i
n
a
ted
by
p
ro
no
un
ced
h
ar
m
oni
c
co
m
ponent
s,
w
hich
i
ndi
cates
t
h
e
pro
x
i
m
ity
o
f
t
his
stru
cture
t
o
l
i
n
ear
a
nd
s
ig
nificant
l
y
b
e
tt
er
cont
r
o
ll
ab
i
l
ity
o
f
th
e
driv
es,
w
h
i
c
h
m
a
kes
promis
i
n
g
th
eir
u
s
e
in
h
ig
h-t
ech
m
echan
isms,
in
p
a
r
t
i
c
ul
a
r
,
in
i
n
d
u
s
tr
i
a
l
r
o
bo
ts
.
S
i
mu
la
t
i
on
a
nd
e
xp
e
r
im
e
n
t
s
c
o
nf
ir
m
the
p
r
op
ose
d
t
he
ore
t
ic
a
l
pro
po
s
itio
n
s
.
K
eyw
ord
s
:
F
r
equenc
y
con
t
ro
l
Rotor
curr
ent
S
l
i
p
-
r
i
n
g
rot
o
r
mo
t
o
r
Spe
c
tral
a
na
ly
s
i
s
V
a
r
i
a
b
l
e
freq
u
e
nc
y dr
ive
Co
pyri
gh
t © 2
019 In
stit
u
t
e
of Advanced
En
gi
neeri
n
g
an
d
S
c
ien
ce.
All
rights
res
e
rv
ed.
Corres
pon
d
i
n
g
Au
th
or:
Al
e
k
sand
r S
. A
n
i
ki
n
,
D
e
pa
rtme
nt
o
f
The
o
reti
ca
l F
u
nda
me
n
t
a
l
s
o
f
Ele
c
t
rica
l
Engi
ne
eri
n
g,
S
out
h U
r
al S
tate U
nive
rsity,
76,
L
en
in pro
s
p
ek
t,
Che
l
y
ab
i
n
sk,
45
4
0
80,
R
uss
i
a.
Em
ail:
ani
k
i
n
a
s
@
s
u
s
u.
ru
1.
I
N
TR
OD
U
C
TI
O
N
O
n
e
o
f
t
he
i
m
por
tan
t
a
ss
umpt
i
o
n
s
o
n
w
h
ic
h
me
tho
d
s
of
d
e
s
cri
b
in
g
a
n
d
a
n
a
l
y
z
i
n
g
A
C
m
o
t
o
r
s
i
s
base
d
is
t
he
a
s
s
ump
t
i
o
n
of
s
inus
o
i
dal
curr
ent
s
o
f
the
ro
tor
an
d
s
t
a
tor
[
1
]-[4].
T
his
assum
p
t
i
on
i
s
m
a
de
i
n
the
deri
va
ti
on
o
f
t
h
e
Clo
ss
form
ul
a
,
t
he
c
on
str
u
ct
i
o
n
of
v
ec
t
o
r
d
i
a
gra
m
s,
t
he
d
eri
v
at
i
o
n
o
f
v
ec
t
o
r
c
o
n
t
rol
a
n
d
DTC technology
(
Di
r
e
ct
Torque C
ontr
ol)
[5]-[12]. The non-
s
inus
o
i
d
a
l
na
t
ure
of t
hese c
u
rre
nts i
s
re
m
e
m
be
red
on
ly
w
he
n
ana
l
yz
ing
t
h
e
i
n
te
rfere
nce
c
r
ea
t
e
d
b
y
e
lec
t
r
i
c
d
r
ives
.
H
o
w
e
ve
r,
i
n
rea
l
i
t
y,
n
o
n
-si
nus
o
i
da
l
c
u
rre
nt
s
grea
t
l
y
redu
c
e
the
ef
f
ic
ie
nc
y
of
a
sy
nc
hro
n
o
u
s e
l
e
c
t
ric
dri
v
es,
reduc
in
g
t
h
e
e
ffe
ct
ive
torq
ue.
Exa
m
p
l
es
o
f
t
h
e
re
com
m
e
nded
use
of
S
c
hne
i
d
er-
E
l
e
ct
ric
fre
que
nc
y
c
onve
rters
in
t
he
r
ota
t
io
n
mec
h
an
i
s
ms
o
f
to
we
r
cra
n
es
a
re
k
no
wn
.
Opera
t
o
r
s,
t
ry
in
g
t
o
a
ppl
y
wind
c
o
m
p
e
nsa
t
i
o
n
mo
d
e
,
a
t
w
hi
ch
t
h
e
y
try
t
o
s
t
a
rt
t
he
d
ri
ve
3
-4
time
s
p
e
r
s
e
c
o
n
d
,
c
l
a
i
me
d.
t
ha
t
t
h
e
ve
c
t
or-c
o
n
t
r
o
l
le
d
dr
ive
"
d
o
e
s
n
o
t
ha
ve
t
i
m
e"
t
o
w
o
rk o
u
t
t
he
m
ode,
a
l
t
h
ou
g
h
"
ol
d" dr
i
ve
s
w
i
t
h
c
o
n
ta
c
t
or
c
ircui
t
s per
f
orm
e
d the
s
e ta
sks.
These
e
x
a
mp
le
s w
e
re
exp
l
a
i
ne
d
b
y
t
he
i
nex
p
er
i
e
nc
e
of
t
he
ope
rat
o
rs,
how
e
v
er,
in
v
i
e
w
of
t
he
p
rop
o
se
d
stud
ies
[13],
[1
4],
the
s
e
conc
l
u
s
i
o
n
s
sh
ou
ld
b
e r
e
vise
d
.
2.
PROBL
E
M
DEFINI
T
I
ON
I
t
i
s
ra
the
r
d
iffic
u
l
t
t
o
e
s
tim
at
e
the
s
p
ec
tra
l
c
ompo
si
tio
n
of
t
h
e
sta
t
or
c
urr
e
nt
s,
w
hi
c
h
a
r
e
t
he
m
ost
ac
cessi
ble
i
n
a
sy
nchro
n
o
u
s
e
l
e
ctr
i
c
dr
ives,
si
n
c
e
in
t
he
m
the
p
r
e
dom
i
n
a
n
ce
of
t
he
f
u
n
d
am
enta
l
(
c
a
rrier)
fre
que
nc
y
i
s
v
ery
sig
n
i
fica
nt
[
15]-[
18].
A
s
hor
t-c
i
r
c
u
i
t
e
d
rot
o
r
i
s
n
ot
a
va
ila
b
l
e
for
me
as
uri
n
g
cur
r
en
ts
i
n
it,
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, Vol. 10,
N
o.
1, Mar
c
h 2
0
1
9
:
21
1 –
21
8
21
2
there
f
ore,
t
o
id
e
n
t
i
f
y
the
pro
c
esses
in
a
n
in
d
u
ct
i
o
n
m
o
t
o
r
.
T
he
s
ta
n
d
w
i
t
h
a
sli
p
-rin
g
r
o
t
or
i
n
duc
t
i
o
n
m
otor
w
a
s
c
r
ea
t
e
d,
i
n
t
o
w
hose
rot
o
r
circ
u
i
ts
c
ur
ren
t
s
e
n
sors
w
er
e
m
o
u
n
t
e
d
.
The
sc
hem
a
t
i
c
d
i
a
g
ram
of
t
h
i
s
s
t
a
nd
i
s
show
n
i
n
F
i
g
u
r
e
1.
T
his
sta
nd
i
n
c
l
u
d
es
t
he
freque
nc
y
co
nver
t
e
r
(UZ1),
w
hi
c
h
r
egulates
s
peed
o
f
s
l
ip-r
i
ng
in
duc
t
i
on
m
o
t
o
r
(M1).
T
he
s
pe
ed
d
a
t
a
w
e
r
e
o
b
t
a
i
ne
d
fro
m
an
e
nco
d
e
r
(
B
R
)
l
o
c
a
t
e
d
o
n
t
h
e
m
o
t
o
r
s
h
a
f
t
.
T
h
e
st
a
nd
a
l
low
s
t
o
re
g
i
ster
s
ync
hro
n
o
u
s
di
a
g
r
a
m
s
o
f
ro
tat
i
o
n
spe
e
d
a
nd
r
o
tor
curre
n
t
s
i
n
s
tat
i
c
a
nd
tr
a
n
s
i
en
t
proce
s
se
s,
a
n
d
the
so
ftw
a
re
t
o
t
h
e
d
i
gi
ta
l
U
S
B
osci
l
l
osc
ope
H
a
n
te
k
D
S
C-
20
90
(P
G
)
m
a
k
es
it
p
o
ss
i
b
le
t
o
perform
spect
r
a
l analysis of sign
als, including rotor
curr
ents
[1
9],
[20].
F
i
g
u
r
e
1
.
S
c
hem
a
t
i
c
d
i
agra
m of t
he
s
t
a
nd
It
sho
ul
d
b
e
not
e
d
th
a
t
th
e
f
r
e
q
u
e
nc
y of t
he r
ot
or c
urre
n
t
is
v
ery
tig
ht
l
y
c
onne
c
t
e
d
w
ith
t
he
sl
i
p i
n
the
mo
t
o
r,
i
.e
.
wi
t
h
a
d
i
s
c
r
ep
an
cy
b
et
we
en
t
h
e
s
p
eed
o
f
ro
t
a
ti
o
n
o
f
t
he
e
lec
t
roma
gne
t
i
c
fie
l
d
of
t
he
s
tat
o
r
and
t
h
e
me
cha
n
ic
al
s
pe
ed
o
f
r
o
ta
tio
n
of
t
he
r
o
t
or.
This
d
iscre
p
a
n
c
y
i
n
the
ind
u
c
tio
n
m
o
tor
de
te
rm
in
e
s
t
he
d
e
v
elo
p
e
d
me
cha
n
ic
al
m
o
m
e
n
t, the
refore
,
in ter
ms of th
e
m
a
gn
it
ude
of t
h
e
sli
p
or
the
fre
que
nc
y of t
h
e
rot
or curre
n
t
, it i
s
p
o
s
s
i
bl
e
to
e
stimat
e
t
h
e
eff
i
cien
c
y
o
f
th
e
fo
r
m
at
i
o
n
o
f
a
m
ech
a
n
i
ca
l
m
o
me
nt
w
it
h
th
is
o
r
tha
t
c
on
tro
l
m
eth
o
d
.
It
i
s
ver
y
d
iffic
u
l
t
t
o
es
t
i
ma
te
t
he
r
eal
s
li
p
i
n
a
d
r
i
ve
w
it
h
a
fre
que
nc
y
co
n
v
er
t
e
r.
T
he
p
oi
nt
i
s
t
h
a
t
w
i
t
h
v
e
c
t
o
r
con
t
ro
l
a
nd
w
i
t
h
t
he
c
orrec
t
e
d
s
c
a
l
a
r,
t
he
s
ta
t
o
r
vol
tag
e
f
re
q
u
e
n
c
y
c
ha
n
g
e
s
.
There
f
ore,
e
ven
if
t
he
s
pe
e
d
o
f
rota
ti
o
n
e
xa
ct
ly
c
orre
spo
nds
t
o
the
prese
t
,
t
h
e
ac
tua
l
s
l
i
p,
i
.
e.
t
he
m
i
s
m
a
t
c
h
betw
ee
n
th
e
rota
t
i
o
n
a
l
s
p
e
e
d
o
f
the
e
l
ec
t
r
oma
gne
t
i
c
fiel
d
o
f
t
he
s
ta
t
o
r
and
th
e
m
echa
n
i
c
a
l
s
pe
e
d
o
f
t
he
r
ot
or
can
t
a
k
e
a
n
y
va
l
u
es.
Conse
que
n
tly,
the
effic
i
e
n
c
y
o
f
t
h
e
m
e
t
h
od
o
f
tor
que
g
ene
r
ati
o
n
i
s
h
i
g
h
e
r
,
the
sm
al
ler
t
h
e
s
l
ip
r
equ
i
re
d
for
a
gi
ve
n m
o
me
nt. A
nd
b
est o
f
al
l
,
t
h
e
re
al sli
p i
s
e
stim
ate
d
b
y
th
e r
o
t
a
ry current
f
requency.
3.
EXPE
RIMENTAL
R
ESEA
RCH
S
i
milar
resu
lts
w
er
e
ob
tai
n
e
d
i
n
e
xper
i
m
e
nt
al
s
tu
d
i
es
o
n
a
la
bo
rat
o
ry
b
en
ch
.
Fig
u
r
e
s
2
-5
s
ho
w
t
h
e
ti
m
e
d
ia
gr
am
s
of
t
he
r
otor
c
urre
nt
s
a
t
i
d
l
e
and
u
nder
t
h
e
sa
me
l
o
a
d
c
l
o
s
e
t
o
t
h
e
n
o
m
i
n
a
l
o
n
e
,
a
s
w
e
l
l
a
s
spec
tra
i
n
dica
tin
g
the
m
a
i
n
f
reque
nc
ies
o
f
t
he
r
ot
or
c
ur
rents
[
2
1
]
,
[22].
Th
e
v
a
l
u
es
o
f
th
e
fu
nd
a
m
e
n
t
a
l
fre
que
nc
ies
u
n
d
er
l
oa
d and
n
o
-l
oad a
r
e
sho
w
n in Ta
b
l
e
1.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
P
o
w
Elec
&
D
r
i
S
y
st
I
S
S
N
:
2088-
86
94
Pe
rform
a
nce
i
d
en
t
i
f
i
c
a
t
i
o
n
of
t
h
e
asy
n
c
h
ro
n
ous e
l
ectr
i
c dr
i
v
e
s
by
the spe
c
t
rum
of
…
(
V
la
dim
i
r
L
.
Kodk
i
n
)
21
3
F
i
gur
e
2.
T
he
d
ia
gr
am
o
f
the
spee
d
and
c
u
r
r
e
nt
o
f
the
r
o
t
o
r
of
a
n
a
sync
hr
o
n
o
u
s
dr
i
v
e
w
ith
v
ec
tor
con
t
r
o
l.
Sp
ectru
m
o
f
t
h
e ro
to
r
cu
rr
en
t sig
n
a
l
F
i
gur
e
3.
T
he
d
ia
gr
a
m
o
f
the
spee
d
and
cur
r
ent
o
f
t
he
r
otor
o
f
an
a
sync
hr
o
n
o
u
s
dr
i
v
e
w
i
t
h
c
lo
sed-
lo
op
ve
ct
or
con
t
ro
l.
Spe
c
trum
of the
rotor
cur
r
ent
sig
n
a
l
F
i
gur
e
4.
D
iagr
a
m
o
f
the
spee
d
and
cur
r
e
n
t
o
f
t
h
e
r
o
t
o
r
of
a
n
a
sync
hr
o
n
o
u
s
d
r
i
ve
w
ith
s
c
a
la
r
c
o
n
t
r
o
l
.
Sp
ectru
m
o
f
t
h
e ro
to
r
cu
rr
en
t sig
n
a
l
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
nt
J
P
ow
E
l
e
c
&
Dr
i
S
y
st,
Vol.
10,
N
o.
1
,
Mar
c
h
2
0
1
9
:
21
1
–
218
21
4
F
i
gur
e
5.
D
i
a
gr
am
o
f
the
spee
d
and
c
u
r
r
e
n
t
o
f
the
r
o
t
o
r
of
a
n
a
sy
nc
hr
o
n
o
u
s
d
r
i
ve
w
ith
s
c
a
lar
c
ontr
o
l
an
d
sta
t
or
c
ur
r
e
nt
f
ee
dbac
k
.
S
p
ect
r
u
m
of
t
he
r
ot
o
r
c
ur
r
e
nt
s
i
gna
l
Ta
b
l
e
1.
T
he
v
alue
s
of
t
he
f
u
nda
me
nta
l
f
r
e
q
u
enc
i
es
o
f
the
r
o
t
o
r
c
ur
r
e
nts
u
nder
l
o
ad
a
n
d
a
t
no-
loa
d
C
ontrol
sy
ste
m
no-l
o
a
d
unde
r
loa
d
V
e
c
t
or
c
ontrol
2,
1Hz
6,
25
Hz
V
e
c
t
or
s
p
e
e
d
f
e
e
dbac
k
c
ontrol
2,
1
Hz
8
,
75
Hz
Sc
al
a
r
c
ontrol
w
ith
out
f
e
e
d
b
a
c
k
1
,
69
Hz
4
,
75
Hz
Sc
al
a
r
c
ontrol with
sta
tor
c
u
r
r
e
n
t
f
eed
b
ack
1
,7
5
H
z
3
,5
Hz
A
n
al
ys
is
o
f
t
h
e
spe
c
t
r
a
o
f
r
o
t
o
r
cur
r
en
ts
c
on
v
i
nc
i
ngl
y
s
h
ow
s
t
h
a
t
t
he
f
or
m
a
ti
on
of
t
h
e
n
ece
ssar
y
tor
que
i
n
a
ve
ctor
-
c
o
n
tr
ol
l
e
d
e
l
e
c
tr
ic
d
r
i
ve,
e
v
en
w
hen
th
e
spe
ed
l
o
op
i
s
c
lose
d,
i
s
n
o
t
t
he
m
ost
ef
fe
c
t
i
v
e
,
ther
eas
on
f
o
r
thi
s
i
s
pr
o
b
a
b
l
y
t
he
p
r
e
se
nce
of
s
i
g
n
i
f
i
ca
nt
h
a
r
m
on
i
c
s
at
a
f
r
e
que
nc
y
of
3
t
o
8
H
z
a
s
show
n
i
n
F
i
g
u
r
e
s
2
a
nd
3.
A
tte
nt
i
o
n
s
h
ou
l
d
b
e
dr
aw
n
to
F
i
gur
e
3,
v
e
c
tor
c
ont
ro
l
wit
h
f
e
e
d
b
ack
on
t
h
e
e
ngi
n
e
'
s
r
o
t
a
t
i
o
n
spee
d,
a
fter
t
h
e
l
oa
d
is
t
hr
ow
n
an
d
th
e
spee
d
fai
l
u
r
e
,
the
r
e
gu
l
a
tor
"p
u
l
l
s
"
it,
b
u
t
t
he
r
ot
or
c
ur
r
e
nt
f
r
e
que
nc
y
doe
s
n
o
t
c
han
g
e
,
w
hic
h
i
s
ind
i
ca
tive
n
o
t
of
t
he
e
ff
i
c
ien
c
y
o
f
t
he
t
or
q
u
e
gene
r
a
ti
o
n
a
lg
or
i
t
h
m
for
ve
ct
or
co
nt
r
o
l
,
b
ut
a
bo
ut
a
n
i
n
cre
a
se
i
n
th
e
f
r
e
q
u
e
nc
y
of
t
h
e
s
t
a
t
o
r
v
o
lta
ge
.
It
i
s
t
h
is
s
truc
t
u
re
t
h
a
t
is
i
m
p
le
me
n
t
e
d
i
n
the
dr
ive
c
o
n
t
r
o
l
sc
hem
e
o
f
t
h
e
tur
n
o
f
the
tower
cra
n
e,
w
hich
w
a
s
m
e
nti
o
ned
in
t
he
i
n
t
r
o
duc
tio
n.
T
h
e
e
x
cep
t
i
o
n
a
l
ly
"
t
i
g
h
te
ne
d"
l
oa
d
pa
r
r
y
in
g
pr
o
c
e
ss
i
s
a
ss
oc
i
a
te
d
w
it
h
i
n
suf
f
ic
i
e
nt
t
o
r
qu
e
and
do
e
s
not
a
ll
ow
f
o
r
the
"
q
uic
k
"
st
a
r
t-
up
m
o
des
of
t
he
t
ur
n
ac
t
u
a
t
or
r
e
q
u
i
r
e
d
for
w
i
nd
r
e
ta
r
d
i
ng
a
t
t
e
mpts
.
A
nd
it
sh
o
u
l
d
b
e
r
ecog
n
ize
d
a
s
"gu
i
lt
y"
i
n
t
h
is
s
itua
t
io
n,
a
n
i
n
su
ffic
ie
nt
"
u
n
d
e
r
s
ta
nd
i
ng",
espe
c
i
al
l
y
t
he
n
o
n
l
i
n
ear
it
ies
of
a
n
a
s
ync
hr
o
n
o
u
s
e
le
ctr
i
c
dr
ive
.
To
e
x
p
la
i
n
t
he
se
r
esu
lts,
r
e
m
a
in
ing
w
i
t
h
i
n
t
he
a
ss
um
pti
o
ns
m
ade
a
t
the
b
e
g
i
nni
ng
o
f
th
e
a
r
ti
cle
a
b
o
u
t
the
si
n
u
s
o
i
da
l
c
u
r
r
ent
of
t
he
r
o
t
or
a
n
d
t
he
s
ta
t
o
r
of
a
n
as
yn
chr
o
n
ous
e
lec
t
r
i
c
m
o
t
o
r
un
de
r
fr
e
q
u
e
nc
y
c
o
n
t
r
o
l
,
i
s
ver
y
d
i
f
f
i
cu
l
t
.
H
a
vi
ng
c
onsi
d
e
r
ed
t
h
e
s
pe
ctr
a
o
f
r
o
t
o
r
cur
r
ents,
o
n
e
c
a
n
ma
ke
t
h
e
a
ssumpt
i
on
o
f
t
h
e
pr
esence
o
f
a
m
u
ch
l
ar
ger
spec
t
r
al
c
om
p
o
sit
i
on
of
t
he
r
otor
c
ur
r
e
nt
s
(
a
nd,
c
onse
que
n
t
l
y
,
of
t
h
e
s
tat
o
r
cu
rren
t
s)
u
n
d
e
r
v
ecto
r
c
ont
ro
l
t
h
a
n
i
n
th
e
c
a
se
o
f
a
sc
al
ar
o
n
e
.
I
t
i
s
very
d
iffic
u
lt
t
o
es
ti
ma
te
t
he
i
nf
lue
n
ce
o
n
the
t
o
r
que
o
f
these
"
h
ar
mf
ul
"
har
m
on
ics
by
di
r
e
c
t
s
p
e
ctr
a
l
an
al
ys
is
.
But,
e
st
i
m
at
in
g
the
fu
n
d
a
m
enta
l
ha
r
m
onic
o
f
t
he
r
o
t
or
c
ur
r
e
nt,
w
h
ic
h
c
o
r
r
e
sp
on
ds
t
o
r
eal
s
l
i
p,
i.
e.
m
ism
a
tc
h
of
t
he
r
ota
tio
na
l
s
p
ee
d
of
t
h
e
st
at
o
r
f
i
e
l
d
a
n
d
m
e
c
h
ani
cal
r
ot
a
tio
n
of
t
h
e
r
ot
o
r
,
it
c
a
n
b
e
co
nc
lude
d
tha
t
t
he
t
or
que
g
e
n
e
r
ati
o
n
ef
fic
i
e
n
cy
i
s
e
ffe
c
t
i
v
e
for
ea
ch
o
f
the
c
o
n
s
i
d
er
ed
c
on
tro
l
m
eth
ods
f
or
a
n
as
y
nc
hr
o
nou
s
m
o
tor
(
v
e
c
t
o
r
,
s
c
a
lar
and
s
c
a
l
a
r
w
i
t
h
d
y
n
am
ic
pos
i
tive
s
t
a
t
or
c
ur
r
e
nt
c
ou
p
l
i
ng)
.
The
r
e
su
l
t
s
of
t
h
e
exp
e
ri
me
n
t
s
as
a
w
ho
l
e
c
oi
n
c
id
e
wi
th
t
he
r
e
sults
o
f
t
h
e
exper
i
m
e
nts
car
r
i
ed
o
ut
e
ar
lier
,
but
t
he
y
c
ontr
a
d
i
ct
th
e
g
en
e
r
a
l
l
y
a
cc
e
p
t
e
d
id
ea
s.
4.
MO
DELI
N
G
P
ROCE
S
S
ES IN A
N
ASYN
C
HRO
N
O
U
S
DR
I
V
E
More
ove
r,
b
efor
e
the
cr
ea
ti
o
n
o
f
t
h
e
st
a
n
d,
t
he
m
o
d
el
o
f
the
e
l
ec
tric
d
ri
ve
b
ase
d
o
n
th
e
in
d
u
c
t
io
n
m
o
tor
an
d
t
h
e
fr
eque
nc
y
co
n
v
er
te
r
w
ith
v
e
c
t
or
c
o
n
t
r
o
l
w
a
s
c
a
r
r
i
e
d
out.
I
n
F
igur
e
6
i
s
s
h
o
w
e
d
t
h
e
sc
h
e
me
o
f
the
AC
d
r
i
ve
s
com
p
il
e
d
i
n
the
S
i
mu
li
n
k
a
pp
l
i
ca
ti
o
n
o
f
t
h
e
MATLA
B
s
o
f
t
w
a
r
e
e
n
v
i
r
o
n
m
e
n
t
,
a
n
d
F
i
g
u
r
e
7
show
s
t
h
e
b
l
oc
k
of
t
he
v
ec
tor
con
t
r
o
l
sys
t
em
.
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
El
e
c
&
D
ri S
yst
I
S
S
N
:
2088-
86
94
Perf
orm
a
nce
i
d
e
n
t
i
f
i
c
a
ti
on
of
the
a
s
y
n
chr
o
n
ous
e
l
ec
t
r
ic
dr
iv
es by
the
spe
c
t
r
u
m
of
… (Vla
dim
i
r L
.
Kodk
i
n
)
21
5
F
i
gure
6.
T
he
m
ode
l
o
f
A
C
d
r
ives w
it
h ve
c
t
or c
ontr
o
l
F
i
gure
7.
T
he
"
V
e
c
t
or
con
tro
l
" bloc
k
The
e
xper
i
m
e
n
t
s
w
e
r
e
c
a
rried
o
u
t
i
n
t
h
e
fo
ll
ow
i
ng
w
a
y:
s
u
cce
ssi
v
e
a
c
cel
erat
io
n
at
i
dl
e
sp
e
e
d
t
o
1
0
,
20,
30,
4
0
a
n
d
50
H
z
a
n
d
a
l
o
a
d
d
r
o
p
a
t
e
ac
h
fre
que
nc
y
re
fer
e
nc
e
.
T
he
l
o
a
d
w
a
s
se
t
b
y
s
tepw
ise
ac
tio
n
equ
a
l
to
t
he
n
omi
n
al
v
al
ue
o
f
t
h
e
m
o
t
o
r
t
o
r
que
.
In
F
igure
8
s
how
s
t
h
e
res
u
l
t
s
o
f
s
imu
l
at
i
o
n
o
f
a
c
c
e
l
e
r
at
io
n
a
n
d
l
o
a
d
sk
et
c
h
e
s
a
t
di
ff
eren
t
s
p
eed
s
o
f
r
o
t
ati
o
n
u
nde
r
v
e
ct
o
r
c
ont
ro
l
,
i
n
F
igu
r
e
9
-
wi
th
s
c
a
l
a
r
wi
th
out
f
eedb
ack
,
i
n
F
i
gure
1
0
-
w
it
h sca
l
ar
c
on
tro
l
w
it
h po
sit
i
ve
f
ee
d
b
ac
k
on t
h
e
s
ta
tor
curr
ent
.
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, Vol. 10,
N
o.
1, Mar
c
h 2
0
1
9
:
21
1 –
21
8
21
6
F
i
gure
8.
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
F
i
gur
e 9.
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
The
frequenc
y
o
f
the
rotor
current
un
d
er l
oa
d
(a
t
a s
p
ee
d o
f
90
r
a
d
/ s)
w
i
t
h
v
e
c
t
or
c
on
t
r
o
l
is 10.6H
z
,
sc
a
l
ar
w
it
hou
t
f
e
edb
a
ck
-
2
.72
H
z
,
s
c
a
l
ar
w
it
h
f
eedb
a
ck
on
th
e
s
ta
tor
c
u
rr
ent
-
1.7
4
H
z
.It
is
o
bv
i
o
u
s
t
ha
t
the
fre
que
nc
y
o
f
t
he
r
ot
or
c
urre
nt
s
is
t
he
l
ow
es
t
in
t
he
m
ode
l
o
f
t
he
s
ys
tem
w
i
t
h
a
p
osit
ive
fee
dbac
k
o
n
the
stat
or
curr
ent, w
hi
l
e
w
or
kin
g
at
l
o
w
speeds i
s
st
a
b
ilize
d
i
n
c
o
mpa
r
iso
n w
i
t
h
s
ca
la
r contro
l
a
nd,
i
n prac
tic
e, the
re
a
r
e
no
s
pee
d
d
i
p
s
i
n
t
h
e
l
oa
d
ske
t
ches,
a
n
d
i
n
c
o
m
pa
riso
n
w
i
t
h
the
vect
or one
-
s
ig
n
i
fica
nt
l
y
s
m
a
ller
fr
e
que
nc
y o
f
the r
o
t
o
r
cur
r
ent a
n
d,
acc
ordi
ngl
y,
re
a
l slip [13],
[23],
[24].
The
fre
que
nc
y
of
t
he
r
o
t
or
c
urre
nt
s is the
l
ow
e
s
t
in
t
he
m
o
d
e
l
of
t
h
e
s
yst
e
m
wi
th
a
p
os
iti
ve
f
e
e
d
b
ack
on
t
h
e
sta
t
or
c
ur
rent,
w
h
ic
h
ind
i
ca
tes
a
m
o
re
e
ff
i
c
i
e
n
t
a
l
g
or
it
hm
f
or
t
he
f
orm
a
ti
on
of
a
m
ec
hani
ca
l
m
o
m
e
nt.
A
t
t
ha
t,
i
n
c
o
m
p
ariso
n
w
i
t
h
t
h
e
sc
a
l
ar
c
o
n
t
ro
l
in
a
n
e
l
ec
tric
d
ri
ve
w
ith
a
p
osi
t
i
v
e
s
t
a
t
or
c
u
r
ren
t
c
on
nect
i
on,
work
a
t
l
o
w
s
p
ee
d
s
i
s
s
t
a
b
il
i
z
e
d
a
nd,
i
n
pr
ac
ti
c
e
,
th
ere
ar
e
n
o
s
pe
ed
d
i
p
s
i
n
t
he
case
o
f
l
oa
d
s
u
rges,
and
i
n
com
p
aris
on
w
ith the
v
e
c
t
o
r
t
h
er
e
are
sign
i
f
ic
ant
l
y
l
o
we
r
freque
nc
ies
of
t
he
r
ot
or
c
urre
nt
a
nd
,
acc
or
di
ngl
y,
t
h
e
fre
que
nc
y
of
r
eal
s
l
i
p.
A
na
l
y
t
i
c
w
a
y
to
e
xp
la
in
a
n
d
,
e
v
en
m
or
e
so
.
to
p
re
di
c
t
t
hi
s
situ
a
t
i
o
n
i
s
a
l
m
o
s
t
impo
ssi
ble
,
s
o
let
'
s
t
u
r
n
t
o e
xpe
rime
n
t
s.
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
El
e
c
&
D
ri S
yst
I
S
S
N
:
2088-
86
94
Perf
orm
a
nce
i
d
e
n
t
i
f
i
c
a
ti
on
of
the
a
s
y
n
chr
o
n
ous
e
l
ec
t
r
ic
dr
iv
es by
the
spe
c
t
r
u
m
of
… (Vla
dim
i
r L
.
Kodk
i
n
)
21
7
F
i
gure
1
0
.
Mo
del
lin
g
proce
s
s
e
s
in
a
n
asy
n
ch
ron
ous e
lec
t
ric
driv
e
wi
th
s
ca
la
r c
o
n
t
rol
w
i
th
fe
ed
bac
k
on t
h
e
st
a
t
or
c
u
r
rent
5.
CONCL
U
S
IONS
Th
us,
t
h
e
s
p
ec
t
r
a
l
a
na
l
y
s
i
s
of
t
he
r
o
t
or
c
urre
nts
of
a
n
asy
n
c
h
r
on
ou
s
el
e
c
t
r
i
c
d
ri
v
e
h
as
s
hown
t
h
a
t
t
h
e
most e
ffec
t
i
ve
m
etho
d o
f
torq
u
e
gene
ra
ti
o
n
w
il
l
be freque
n
c
y c
o
n
t
r
o
l
w
ith
posit
i
v
e sta
t
or
c
urr
e
nt fee
dba
ck.
A
s
t
he
s
pec
t
ra
l
ana
l
ys
is
s
ho
w
s
,
this
c
o
n
tr
ol
i
s
d
o
mina
te
d
b
y
p
r
o
n
o
u
n
c
e
d
harm
o
n
i
c
c
om
po
ne
nt
s,
w
h
ic
h
i
n
d
i
ca
te
s
the
pro
x
i
m
i
ty
o
f
th
i
s
s
tr
uc
ture
t
o
l
i
ne
ar
a
nd
s
i
g
n
i
fica
nt
ly
b
e
t
te
r
co
ntr
o
lla
b
ili
t
y
o
f
t
h
e
d
r
ive
s
,
w
h
ic
h m
a
ke
s prom
isi
ng
the
i
r
use
in
h
ig
h-
t
e
c
h
m
e
c
hani
sms, in pa
r
ti
cul
a
r, i
n
i
ndu
st
ri
al
robo
ts.
REFE
RENCES
[1]
Us
oltsev
, A.A
,
“Vect
or co
n
tro
l
of
asy
n
ch
ron
ous m
ot
ors
,
” T
u
to
ria
l
.
-
S
pb
.
:
I
TMO,
1
2
0
p
,
2
0
0
2
.
h
t
tp
:
/
/
s
e
r
vo
mo
to
r
s
.ru/d
o
c
u
me
nta
t
io
n/
fre
q
ue
n
c
y_
c
o
n
t
rol_o
f
_
a
sy
nc
h
ronous_m
o
t
o
rs
/chas
t
upr.pd
f
[2]
P
o
zd
eev,
A.D
,
“
El
e
c
t
r
om
ag
netic
and
elect
rom
echan
ical
p
rocess
e
s
in
freq
u
en
cy-
c
on
tro
l
l
e
d
asyn
chro
no
us
e
lect
ric
dri
v
es,
”
-
Cheb
oks
a
r
y
:
Publish
i
ng h
o
u
s
e Ch
uvash U
n
i
versit
y
,
172
p
,
1
99
8
.
[3]
So
ko
lov
s
k
y
,
G
.
G
. AC e
l
e
c
tr
ic
d
rive
s wi
th
f
re
qu
e
n
c
y
c
on
trol.
-
M
os
cow:
"
ACADEM
IA
"
,
267
p
,
2006
.
[4]
Srinivas
G
angi
s
h
etti,
T
arakal
yani
S
andipamu
,
“Di
f
f
e
rent
C
on
trol
S
chem
es
f
o
r
S
ens
o
r
L
e
ss
V
ect
or
C
o
n
t
r
ol
o
f
In
du
c
t
io
n
Mo
to
r,”
Int
e
rn
a
t
i
o
n
a
l
Jour
nal of
Po
wer El
ectr
oni
c
s
a
nd Dri
ve
S
y
st
em
(
I
JPE
D
S
)
,
V
o
l
.
8
,
No
.
2
,
pp
.
7
12~
7
21,
J
une
2
01
7.
[5]
Kod
k
in
V
.
L.,
An
ik
in
A
.
S,
“
F
r
e
q
ue
n
c
y
c
o
ntro
l
o
f
a
sy
nc
h
r
on
o
u
s
e
l
ectri
c
driv
e
s
i
n
trans
p
o
r
t,”
20
15
International
Si
ber
i
an Con
f
erence o
n
Co
nt
rol
a
nd
Comm
unica
tio
n
s
(
S
IB
CON)
,
20
15
.
[6]
V.
L.
K
o
dkin,
A
.
S
.
An
ikin
,
Ya.
A
,
“
S
h
m
a
ri
n
Eff
ect
iv
e
Freq
uency
C
on
tro
l
f
o
r
I
ndu
cti
o
n
Elect
ric
D
r
ives
u
n
d
er
Ov
erload
in
g,”
Rus
s
i
an El
ectrical
En
g
i
neer
in
g
,
Vo
l
.
85
,
No
. 1
0,
p
p
. 64
1
–
6
4
4
, 2
01
4.
[7]
Park R., Robert
s
on
B., “T
he react
ances of synchr
onous
m
achi
n
es
,
” Tr. AI
E
E
,
vo
l.
4
7, 19
2
8
.
[8]
M
d
.
Rashed
u
l
I
s
l
am,
Md
.
M
a
ru
f
u
l
Isl
a
m,
M
d
.
K
amal
H
os
sa
in
,
“
P
i
n
t
u
Ku
ma
r
S
a
dh
u
Pe
rfo
r
ma
nc
e
Ana
l
ysi
s
o
f
a
DT
C
and
S
V
M
Based
F
i
el
d-O
r
ient
ati
o
n
Co
n
t
ro
l
In
du
cti
on
M
o
t
o
r
Dri
ve
,”
International Journal
of
Power
El
ectro
n
i
cs
a
n
d
Dr
ive S
y
s
t
em
(
I
JPEDS)
,
Vo
l
. 5
,
No. 3
, p
p
. 33
6
~
3
4
3
, Feb
ruary
20
15
.
[9]
S
h
ev
chenk
o
,
A
.
F
.
a
nd
A
b
d
el’
M
a
ks
ud
S
elim,
S
.
A
.,
“
V
ector
c
o
n
t
r
ol
o
f
st
a
t
or’s
c
urrent
i
n
s
y
n
c
hro
nou
s
m
o
tor
w
i
th
p
e
rma
n
e
n
t ma
gn
e
t
s
for
d
r
owne
d
pu
mp
d
r
i
ve
,”
Na
u
c
h
n. Ve
s
tn
.
No
vo
s
ib
. Go
s
.
Tek
h
n
.
Un
i
v
., no
. 2(
4
3), 20
1
1
.
[10]
Ya
hy
a
Ahme
d
Ala
m
r
i
,
Nik
Ru
mz
i
N
i
k
Id
ris
,
I
bra
h
im
M
oh
d.
A
lso
f
y
a
n
i
,
T
ole
S
u
ti
kn
o,
“
Im
pro
v
ed
S
tat
o
r
F
l
ux
Estimation
f
o
r
D
i
rect
T
or
que
Cont
ro
l
o
f
I
nd
ucti
o
n
M
o
t
o
r
D
rives
,
”
In
te
rn
atio
na
l J
o
u
r
na
l
of Powe
r
Ele
c
t
ron
i
c
s
a
n
d
Dr
ive S
y
s
t
e
m
(
I
JPEDS)
, Vol.
7
, No.
4
,
pp. 10
4
9
~
10
60,
Decem
ber 2
0
1
6
.
[11]
Ko
dk
in
V
.L,
“P
ro
bl
e
m
s
o
f
i
n
t
ro
d
u
ci
ng
freq
u
en
cy
r
egu
l
ati
o
n
in
t
h
e
m
i
nin
g
i
n
d
u
s
t
r
y
/
V.
L.
K
odkin
,
M
.A.
M
a
l
c
her,
A.
S.
An
i
kin,
”
B
u
lle
tin
of
SUS
U
.
se
rie
s
"
E
ne
rgy
"
.
I
ssu
e
.
1
8
.
-
No
.
37
(29
6). -
P
.
1
5
4
, 20
1
2
.
[12]
M
.
J
ann
a
ti
,
N
.
R
.
N.
I
dri
s
,
and
M.
J
.
A
.
A
ziz,
"
S
p
eed
S
e
n
so
rles
s
Fau
l
t
-
Tolerant
D
riv
e
S
ystem
o
f
3
-P
has
e
I
nd
uct
i
on
Mo
to
r
Us
in
g
S
w
itc
hing
E
x
t
e
n
de
d
Ka
lma
n
F
il
te
r"
T
E
L
K
O
M
NIKA
In
don
esi
a
n
Jo
urn
a
l
o
f
Electrical
En
gi
neer
ing
,
vo
l.
12,
2
0
1
4
.
[13]
Ko
dk
in
V
.L,
“
E
xp
erim
ent
a
l
Res
earch
o
f
As
yn
chron
o
u
s
E
l
ectri
c
Dri
v
e
w
ith
P
o
s
i
t
i
v
e
Dy
nam
i
c
F
e
ed
back
o
n
S
t
at
or
Current,”
III Int
e
r
n
a
t
i
o
n
a
l Co
nference
on
Ind
u
st
ri
a
l
Engin
eerin
g
,
A
p
p
l
i
c
ati
o
n
s
and M
anu
fa
cturi
n
g,
I
C
IE
AM
2
0
1
7
– P
r
o
ceedi
ngs
, 201
7.
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, Vol. 10,
N
o.
1, Mar
c
h 2
0
1
9
:
21
1 –
21
8
21
8
[14]
V.L.
K
odk
i
n,
A
.
S
.
Anikin
,
Ya.
A
.
Shm
a
rin,
“
D
yna
m
i
c
Load
D
is
turba
nce
Correcti
o
n
f
o
r
Alterna
t
ive
Cur
r
ent
Elect
ric
Dri
v
es,
”
II Int
e
rn
at
ion
a
l
Co
n
f
eren
ce
o
n
Ind
u
s
t
rial
En
gi
n
eeri
n
g
,
App
l
i
c
ation
s
a
n
d M
anufa
c
turin
g
,
ICIEAM
2
016
–
P
r
oceedi
n
g
s
,
2017.
[15]
Vo
rob
'
ev
,
N
.
N
, T
heo
r
y
of
s
eri
e
s,
4
e
d
.
,
R
ev
ised
.
A
nd
additi
on
a
l
.
-
M
o
s
c
ow:
S
c
ience,
4
08
p,
197
9.
[16]
Bo
nar D.D.,
Kh
ou
ry M.
J
.,
“Real
Infin
it
e
Series
,
”
T
h
e M
a
t
h
ema
t
i
c
al
Asso
ciatio
n
o
f
America
,
2
74
p
.
,
20
06.
[17]
M
e
jl
bro
L,
“
F
ouri
e
r
S
e
ries
a
n
d
S
ystem
s
o
f
Diff
erent
i
a
l
E
q
u
a
t
io
n
s
an
d
Eig
envalu
e
P
r
ob
le
ms:
Guidelines
f
or
S
o
l
u
t
i
ons
o
f
P
r
oblem
s,
”
Le
if M
e
jlbro
&
Ventus Publishing
Aps
, 1
25
p, 20
0
7
.
[18]
Lod
a
y-
Ric
h
a
u
d
M.,
“D
iv
e
r
ge
nt
S
e
r
ie
s,
S
u
m
m
a
b
i
l
i
ty
a
nd
R
e
s
urg
e
nc
e
I
I
.
S
im
p
l
e
a
n
d
M
u
lt
ip
l
e
S
um
ma
b
i
l
i
ty
,
”
S
p
r
i
n
g
e
r
I
n
t
e
r
n
at
i
o
n
a
l
P
u
bl
is
hi
ng
, 27
2
p
, 20
1
6
.
[19]
An
ikin
A
.S
.
D
y
n
a
mi
c
p
o
s
i
tiv
e
c
o
u
p
l
i
n
g
i
n
asy
n
ch
rono
us
e
l
ectric
d
r
iv
e
s
w
i
t
h
f
r
e
qu
e
n
c
y
c
on
tr
o
l
/
А
.
С
.
An
ik
in
,
V
.
L.
Kodkin,
A.A.
B
al
den
kov
//
"Pri
orities
of
w
orl
d
s
ci
ence:
e
xperim
en
t
and
s
c
ientif
ic
d
is
cus
s
i
on"
M
aterial
s
o
f
t
h
e
8
t
h
international
scient
i
f
i
c
c
onf
e
re
nc
e.
S
c
i
ent
i
fi
c
and
P
u
blishin
g
Ce
n
t
er
"
O
t
k
r
yti
e
".
N
orth
C
h
a
rlest
on,
S
C,
U
SA
,
1
7
-18.
-
P
.
1
19-1
24,
J
une
2
0
15.
[20]
V.
L.
K
od
k
i
n,
Y
a.
A.
S
h
m
arin
,
A
.
S.
A
ni
k
i
n
,
A
A
Balden
ko
v,
N
.
A
.
Lo
g
i
n
o
v
a,
“
Co
rrecti
on
of
d
yn
ami
c
m
omen
t
pert
urbat
i
o
n
s
in
e
l
ectric
dri
v
es
o
f
altern
ati
ng
curren
t
”
S
c
i
e
nc
e
o
f
S
US
U.
M
ateri
a
ls
o
f
th
e
68
th
s
c
i
ent
i
fi
c
con
f
erenc
e
,
p
p
8
05
-81
4
, 2
01
6.
[21]
V.
L.
K
od
ki
n
,
A
.
S
.
A
n
i
k
i
n
,
A.
A.
B
alden
k
o
v
,
“
S
pect
ral
Anal
ysis
o
f
R
ot
or
C
urrents
i
n
F
requency-control
l
ed
E
lect
r
i
c
Dri
v
es,
”
2nd
In
t
e
rna
t
i
o
n
a
l
Co
n
f
eren
ce
o
n
A
u
to
ma
ti
on
,
M
echa
n
i
c
al a
n
d
Elect
rical
Eng
i
n
eer
i
n
g
,
AME
E
2
01
7
–
P
r
oceedi
n
g
s
.
–
201
7
[22]
V
.
L
.
K
o
d
k
i
n
,
A
.
S
.
A
n
i
k
i
n
,
A
.
A
.
B
a
l
d
e
n
k
o
v
,
“
T
h
e
a
n
a
l
y
s
i
s
o
f
t
h
e
q
u
ali
t
y
of
t
h
e
f
requen
c
y
con
t
rol
of
i
nd
uctio
n
m
o
t
o
r
c
a
r
r
i
e
d
o
u
t
o
n
t
h
e
b
a
s
i
s
o
f
t
h
e
p
r
o
c
e
s
s
e
s
i
n
t
h
e
r
o
t
o
r
c
i
rcui
t,”
X
I
Inter
n
a
tio
nal S
c
ientif
ic an
d T
e
chn
i
ca
l
Con
f
eren
ce
“
D
yn
am
ics o
f
Sys
t
e
m
s
,
M
echan
is
m
s
an
d
M
a
ch
ines”
–
P
roceedi
n
g
s
– 20
1
7
.
Оms
k
,
14-1
6
.
11.
201
7
[23]
K
o
d
k
i
n
.
V
.
L
,
“
M
e
t
h
o
d
s
o
f
o
p
t
i
m
i
z
i
n
g
t
h
e
s
p
e
e
d
a
n
d
a
c
c
u
r
a
c
y
o
f
o
p
tical
c
o
m
pl
ex
g
u
i
d
a
nce
sy
st
ems
b
a
s
e
d
on
equ
i
v
a
lence
of
a
ut
om
ati
c
c
o
n
t
r
ol
s
yst
e
m
d
o
m
a
in
o
f
attract
ion
an
d
unconditional
stabil
ity
o
f
t
h
ei
r
equiva
lent
circuits,”
P
r
o
cee
d
i
n
g
s of SP
IE - T
h
e In
tern
a
t
io
nal S
o
cie
t
y f
o
r Op
tica
l
E
ngin
eerin
g
.
–
20
16
[24]
V.
L
.
K
od
k
i
n,
A.S
.
A
n
i
k
i
n
,
A
.A
.
B
a
l
d
enk
o
v
,
“
Anal
y
s
i
s
o
f
st
abi
l
i
t
y of
el
ectric drives as n
o
n
-
l
i
n
ear sy
s
t
e
ms
accord
in
g
to
P
op
ov
c
ri
terio
n
a
dj
ust
e
d
to
a
m
p
lit
u
d
e
a
nd
p
h
a
se
f
requ
ency
c
h
aracteri
s
t
i
cs
o
f
it
s
el
e
m
ent
s
,”
2nd Internation
a
l
Co
nfe
r
e
n
c
e
o
n
A
p
p
l
ie
d
Ma
the
m
a
tic
s,
Si
mula
t
i
o
n
,
an
d
Mo
de
lin
g
A
M
S
M
2
0
1
7
– P
r
oceedin
gs
. –
20
17
Evaluation Warning : The document was created with Spire.PDF for Python.