Int
ern
at
i
onal
Journ
al of
P
ower E
le
ctr
on
i
cs a
n
d
Drive
S
ystem
(I
J
PE
D
S
)
Vo
l.
11
,
No.
4
,
Decem
be
r 202
0
, p
p.
217
3
~
218
2
IS
S
N:
20
88
-
8694
,
DOI: 10
.11
591/
ij
peds
.
v11.i
4
.
pp217
3
-
218
2
2173
Journ
al h
om
e
page
:
http:
//
ij
pe
ds
.i
aescore.c
om
Experim
ental d
etermi
nati
on of su
boptim
al p
aram
eters f
or
energy
-
effici
en
t
control
of an i
nduction m
oto
r
V
alen
tin
a
S
. Gou
n
,
Aleks
andr S
. Aniki
n
,
Aleksey
A.
Bakin
South Ura
l
S
t
at
e
U
nive
rsity
(NRU
)
,
Russ
ia
n
Fed
era
t
ion
Art
ic
le
In
f
o
ABSTR
A
CT
Art
ic
le
history:
Re
cei
ved
Feb
3
, 2
0
20
Re
vised
A
pr
2
6
, 2
0
20
Accepte
d
J
ul
9
, 20
20
The
art
i
cle
pr
ese
nts
the
resul
ts
of
expe
r
imental
st
udie
s
of
the
au
to
ma
tic
spe
ed
cont
rol
sys
te
m
(
AS
CS
)
of
an
ind
uct
ion
mo
tor
(I
M).
Prel
im
in
ary
expe
ri
me
nt
al
studie
s
hav
e
sh
own
tha
t
the
st
at
or
cur
ren
t
m
i
nim
um
(pow
er
fac
tor)
is
a
suboptim
al
crite
rion.
Opti
ma
l
in
te
rms
of
cont
ro
l
is
the
r
ated
po
wer
factor.
Te
sts
of
IM
wit
h
a
thyri
stor
vo
lt
ag
e
conve
r
te
r
(TVC),
as
a
po
wer
sourc
e,
were
conduc
t
ed
on
an
installatio
n
created
at
the
depa
rt
me
nt
.
A
ma
th
em
a
ti
c
al
mode
l
of
AS
C
S
IM
cor
respo
nding
to
th
e
e
xper
imental
se
t
up
has
b
ee
n
deve
lop
ed.
To
d
et
er
mi
ne
the
m
a
in
func
ti
on
al
d
e
pende
nc
es
of
IM,
such
as
stat
or
vo
lt
ag
e,
st
at
or
cur
ren
t,
po
wer
fa
ct
or,
torqu
e
on
the
shaft
,
a
progra
m
for
appr
oximat
ing
e
xper
imental
d
at
a
by
po
lynom
i
al
s
was
dev
el
op
ed.
Us
ing
th
e
deve
lop
ed
ma
th
em
a
ti
c
al
mod
el
,
the
reg
ul
at
ory
c
har
acte
rist
ic
of
I
M
tha
t
was
opti
mal
fro
m
an
ene
rgy
point
of
vie
w
was
ob
tain
ed.
The
ne
ce
ss
ar
y
indicat
o
rs
of
IM
and
TVC
are
d
eterm
in
ed
(
thyri
stor
con
trol
angl
e
,
st
at
or
vo
ltage,
sta
tor
cur
ren
t)
to
cha
n
ge
ex
isti
ng
set
tings
in
orde
r
to
save
el
e
ct
ri
c
e
ner
gy.
The
result
s
of
expe
r
i
me
nt
al
studi
es
a
re
pr
ese
nt
ed,
t
he
gra
ph
show
s
an
opt
im
i
ze
d
ver
sion
of
th
e
fo
rm
of
th
e
r
egul
a
tory
ch
aracteristic
ac
cor
d
ing
to
t
he
cri
t
eri
on
of
mi
n
im
um
ele
ct
ri
c
en
erg
y
con
sumpti
on.
Ke
yw
or
d
s
:
Ind
uction m
otor
Po
ly
nomial
de
pende
ncies
Power fact
or
Pr
op
or
ti
onal
c
on
t
ro
l l
a
w
Th
yr
ist
o v
oltag
e co
nv
e
rter
This
is an
open
acc
ess arti
cl
e
un
der
the
CC
BY
-
SA
l
ic
ense
.
Corres
pond
in
g
Aut
h
or
:
Aleksa
ndr S.
A
nik
in
,
Dep
a
rteme
nt of T
heoreti
cal
fundame
ntals
of ele
ct
rical
en
gi
neer
i
ng,
South
Ural
Sta
te
U
ni
ver
sit
y,
76, Le
nin p
ros
pek
t,
Chel
yab
i
ns
k, R
us
sia
. 4
5408
0
Emai
l:
an
ikina
s@susu
.ru
1.
INTROD
U
CTION
In
m
od
e
r
n
c
onditi
ons,
the
pro
blem
of
e
ne
rgy
sa
ving
du
rin
g
op
e
rati
on
of
as
ynch
ron
ou
s
el
ect
ric
dr
i
ves
with
va
r
ia
ble
loa
d
is
be
coming
especi
al
ly
acute
[
1
,
2
].
To
so
l
ve
t
his
pro
blem,
it
is
necessa
ry
to
pr
ov
i
de
energ
y
-
e
ff
ic
ie
nt
op
e
rati
on
of
an
in
duct
ion
m
otor
(
I
M
)
in
t
he
entire
ra
ng
e
of
cha
nges
in
the
loa
d
mome
nt.
F
or
this,
it
is
neces
sary
to
deter
mine
su
c
h
pa
ram
et
ers
of
th
e
mot
or
at
wh
ic
h
it
will
de
velo
p
th
e
re
quire
d
momen
t
with
a
minim
um
co
nsum
ptio
n
of
el
ect
ric
e
nerg
y.
F
or
e
xa
mp
le
,
a
num
be
r
of
st
ud
ie
s
in
this
area
[
3
-
6]
sh
ow
that
w
he
n
unde
rloa
ding
due
to
a
dec
rease
in
t
he
a
mp
li
tu
de
of
t
he
sup
ply
volt
age
of
t
he
MI
at
a
c
onsta
nt
fr
e
qu
e
nc
y,
a
minimu
m
of
losses
ca
n
be
ob
ta
ine
d,
i.e
.
pro
vid
e
ene
r
gy
-
sa
ving
op
e
ra
ti
on
an
d
re
duc
e
m
otor
heati
ng.
T
he
a
uthors
i
nd
ic
at
e
that
the
mode
of
“mi
nimum
sta
tor
cu
rr
e
nt”
is
cl
os
e
in
ene
rgy
in
dicat
ors
to
the
mode
of mini
mu
m
losse
s in
the IM,
not tak
ing
i
nto
ac
co
unt t
he valu
e
of
the po
wer fact
or.
The
sci
entifi
c
t
eam
l
ed
by
N.
F.
Ilyi
nsky
(Mosc
ow
P
ower
En
gin
eeri
ng
I
nst
it
ute)
[7,
8]
s
howe
d
that
du
e
to
t
he
re
gula
ti
on
of
the
amplit
ude
of
t
he
sup
ply
volt
age
of
c
onsta
nt
fr
e
que
ncy,
w
hen
for
te
ch
nolog
ic
al
reasons
,
f
or
a
sign
ific
a
nt
pa
rt
of
t
he
ope
rati
ng
c
ycle,
t
he
load
mome
nt
is
2
...
3
ti
mes
le
ss
than
t
he
rate
d
It
i
s
po
s
sible
t
o
sa
ve
up
t
o
15%
of
e
nergy
c
onsu
me
d,
re
duce
m
otor
heati
ng
by
1.5
.
..
2
ti
mes,
increa
se
powe
r
factor
at
l
ow
l
oad
by
30%.
Ther
e
f
or
e,
by
lowe
rin
g
t
he
volt
age
a
cr
os
s
the
sta
t
or
wi
nd
i
ng
s
t
o
0.7
U
n
for
t
he
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8
694
In
t J
P
ow
Ele
c
&
D
ri
S
ys
t,
V
ol
.
11
, N
o.
4
,
D
ecembe
r
2020
:
217
3
–
218
2
2174
hal
f
loa
d
mode
or
to
0.4
Un
f
or
t
he
idle
mod
e,
it
is
possible
to
en
sure
e
nergy
-
ef
fici
ent
operati
on
of
the
mo
to
r,
and
hen
ce
the
whole
el
ect
ric
dr
i
ve.
H
ow
e
ve
r,
t
he
e
xperim
ental
res
ults
a
nd
real
pract
ic
al
rec
om
me
nd
at
ion
s
wer
e
not
pr
ese
nted b
y
the
a
uth
ors.
As
you
know,
el
ect
rical
energy
in
t
he
I
M
i
s
trans
mit
te
d
by
a
mag
netic
f
ie
ld.
T
he
am
pl
it
ud
e
of
t
he
mag
netic
flu
x
mainly
de
pend
s
on
the
am
plit
ud
e
of
the
volt
age
acr
os
s
t
he
sta
tor
windin
gs
a
nd
is
pract
ic
al
ly
ind
e
pende
nt
of
the
mate
rial
and
dime
ns
io
ns
of
t
he
co
re.
T
hus,
a
ny
mode
of
ope
rati
on
of
the
IM
c
an
be
represe
nted
as
nominal
f
or
s
om
e
a
bs
tract
mo
to
r
of
th
e
c
orres
pondin
g
powe
r.
F
or
a
ny
nomi
nal
m
ode,
the
gen
e
rali
zed
e
ne
rgy
ef
fici
enc
y
par
a
mete
r
is
the
po
wer
facto
r,
w
hich
is
det
ermine
d
by
t
he
best
rati
o
of
c
urren
t
a
nd
volt
age.
T
he
pu
rpose
of
t
his
w
ork
is
to
dem
onstrat
e
by
pract
ic
al
exa
mp
le
that
the
maxim
um
pow
er
fact
or
is
the
mo
st
opt
imal
crit
erion
f
or
e
nsuring
e
ne
rgy
-
e
ff
ic
ie
nt
op
e
rati
on
of
th
e
IM
i
n
an
y
m
od
e
.
To
ac
hie
ve
this
go
al
,
a
mat
he
mati
cal
model
was
c
reated,
p
r
el
imi
nar
y
cal
culat
ion
s
of
th
e
sp
ee
d
c
on
tr
ol
l
oop
of
the
I
M
with
a
thyrist
or
volt
age
co
nverte
r
(
TVC)
wer
e
ca
rr
ie
d
out,
a
nd
the
opti
mal
co
ntr
ol
cha
racter
ist
ic
of
the
I
M
was
theo
reti
cal
ly buil
t.
2.
PROBLE
M
DE
FINITIO
N
In
m
os
t
cases
,
I
M
w
orks
i
n
t
wo
m
odes:
cl
os
e
to
nomi
nal,
an
d
cl
os
e
t
o
i
dle
(l
ow
loa
d
mode)
.
T
he
go
al
of
this
w
ork
is
to
c
reate
an
ine
xp
e
ns
i
ve
and
eas
y
-
to
-
m
anag
e
AS
CS
,
a
s
well
as
a
li
near
iz
ed
m
odel
of
I
M
dr
i
ve
for
deter
minin
g
fee
db
a
ck
c
oe
ff
ic
ie
nts
an
d
sta
bili
ty
s
tud
ie
s
A
s
uitab
le
area
of
a
ppl
ic
at
ion
of
I
M
with
a
minimu
m
of
powe
r
c
onsum
pt
ion
a
re
t
he
me
chan
is
ms
w
ork
ing
with
va
riab
le
load
,
in
the
"i
dling
-
rated
load"
mode.
T
o
so
l
ve
this
prob
le
m
,
in
the
case
of
small
an
d
me
di
um
-
siz
ed
m
otors,
it
is
nece
ssa
ry
to
c
reate
a
n
easy
-
to
-
us
e,
bu
t
ac
cur
at
e
mat
hem
a
ti
cal
mo
del
"Prop
or
ti
onal
r
egu
la
to
r
–
IM
–
load".
T
he
ma
themat
ic
al
model
is
base
d
on
t
he
st
at
ic
and
dyna
mic
cha
racteri
sti
cs
of
AS
C
S.
The
mathe
ma
ti
cal
mo
del
of
IM
with
TVC
for
the
study
of
ste
a
dy
-
sta
te
an
d
tra
ns
ie
nt
process
es
is
base
d
on
po
l
ynom
ia
l
de
pende
ncie
s
on
the
m
ode
pa
rameters
[
9
-
12
].
The
model
is
base
d
on
e
xp
e
rim
ental
data
of
I
M
of
var
i
ous
powe
rs.
A
s
an
e
xam
ple
of
t
he
impleme
ntati
on
of
su
c
h
a
s
ys
te
m,
a
sec
ond
-
order
s
ys
te
m
with
fee
dba
cks
on
the
r
ot
at
ion
al
fr
e
que
ncy
a
nd
sta
tor
c
urren
t i
s presente
d.
It
was
pr
act
ic
al
ly
establi
sh
e
d
th
at
in
su
c
h
a
sy
s
te
m,
with
the c
al
culat
ed
coe
ffi
ci
ents
of the stat
ic
s
pe
ed
c
on
t
ro
ll
er
and fee
dbacks
,
the sta
bili
ty is
within t
he
e
ngineeri
ng r
e
qu
i
re
ments.
3.
THE
ORETI
C
AL R
E
SEA
C
HES
The
a
pp
li
cat
io
n
of
T
VC
is
us
e
d
to
c
on
t
rol
the
volt
a
ge
at
a
const
ant
fr
e
qu
e
nc
y.
In
the
stu
dy
of
pro
portion
al
c
on
t
ro
l
sy
ste
ms
with
a
pr
e
deter
mined
c
on
t
ro
l
char
act
e
risti
c,
that
is,
with
a
st
and
a
r
d
pro
port
ion
al
vo
lt
age
re
gula
tor
,
the
mai
n
prob
le
m
is
t
o
determine
the
f
unct
ion
s
of
the
re
fer
e
nce
si
gn
al
,
the
tra
ns
fe
r
f
unct
i
on
of the T
VC,
and the
ope
rati
ng p
a
rameters
of
IM.
The
de
velo
pme
nt
a
nd
im
pro
veme
nt
of
A
S
CS
f
or
the
r
ot
at
ion
of
I
M
w
it
h
TVC
is
e
xpedie
nt
to
be
performe
d
by
cal
culat
ion
an
d
e
xperime
ntati
on
.
T
he
mat
he
mati
cal
desc
ription
of
AS
CS
can
be
ve
r
y
di
ver
se.
In
cal
culat
in
g
stu
dies
of
I
M
t
ran
sie
nt
proces
ses,
syst
ems
of
li
nea
r
diff
e
re
ntial
eq
uations
desc
ribing
t
he
el
ements
of
A
SCS
are
widel
y
use
d.
It
s
hould
be
note
d
that
the
c
har
ac
te
risti
c
transient
proces
ses
a
re
the
processes
of
i
ns
ta
nta
neous
i
ncr
easi
ng
an
d
dec
reasi
ng
of
load.
T
hey
dif
fer
i
ns
ig
nifica
ntly
(8
–
10
%
)
of
t
he
values
of
t
he
r
otati
on
sp
ee
d
of
the
I
M
from
i
ts
values
in
the
ste
ad
y
sta
te
.
I
n
the
stu
dy
of
su
c
h
m
odes,
th
e
us
e
of
li
near
m
od
e
ls
of
A
SCS
gi
ves
a
fairl
y
go
od
ag
reeme
nt
betwee
n
t
he
c
al
culat
ed
a
nd
ex
pe
rime
ntal
da
ta
.
A
good
re
su
lt
is
a
desc
riptio
n
of
the
cha
racter
ist
ic
s
of
AS
CS
el
ements
by
poly
nomial
de
pe
nd
e
ncies
base
d
on
exp
e
rime
ntal
da
ta
[13
-
17].
A
structu
ral
dia
gr
a
m
that
sat
isfact
or
il
y
desc
r
ibes
the
tra
ns
i
ent
proces
ses
in
I
M
wh
e
n
it
is
fe
d
from
TVC
is
s
how
n
in
Fig
ure
1,
w
he
re
TC
V
-
th
yr
ist
or
c
onve
rter,
SS
-
sp
ee
d
se
nsor,
CS
-
current
sens
or,
PPCC
-
pulse
-
ph
a
se c
on
tr
ol
c
ircuit
.
Figure
1
.
Bl
oc
k diag
ram of
th
e A
SCS
IM
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
ow Elec
& Dri S
ys
t
IS
S
N: 20
88
-
8
694
Experime
nta
l
det
ermin
ation of
subopti
m
al
para
meters
for
e
ner
gy
-
ef
fi
ci
en
t
con
tr
ol
of…
(
V
alentin
a S. G
oun)
2175
The mo
ment
of r
e
sist
ance
of the c
onsume
r w
as d
esc
ribe
d b
y
the
ex
pressi
on:
М
с =
k
c
n
(1)
wh
e
re
kc
is
the
pr
opor
ti
on
al
it
y
facto
r
of
the
consu
mer
set
ti
ng.
A
n
eval
uation
of
the
ef
fe
ct
of
re
du
ce
d
volt
ag
e
on
t
he
dy
nami
c
par
a
mete
rs
of
I
M
wa
s
car
ried
out
usi
ng
th
e
dev
el
op
e
d
m
at
hemati
cal
mo
del
of
AS
CS
IM.
I
n
the
devel
oped
m
odel
t
he
dif
f
eren
ti
al
e
qu
at
i
on
s
of
th
e
mo
s
t
sig
nificant
el
ements
of
the
AS
CS
are
us
e
d
i
n
the
fo
ll
owin
g form
[18]:
(TIM
p +
1)
M
=
k
(w0
–
w),
(2)
M
–
M
c
=
p
w/
Js,
wh
e
re
J
s
is
t
he
total
m
om
e
nt
of
ine
rtia
of
th
e
I
M
with
t
he
dr
i
ve;
TI
M
-
the
el
ect
r
om
a
gnet
ic
ti
me
c
onsta
nt
o
f
IM
; k
is
the
rig
idit
y
mod
ulu
s o
f
the
li
ne
arize
d
mec
han
ic
al
c
har
act
erist
ic
;
w0
–
s
yn
c
hro
no
us
r
otati
on
al
s
pe
ed;
w
is
the c
urren
t
r
otati
on
al
s
pee
d
.
The
fi
rst
eq
ua
ti
on
de
scribe
s
the
li
near
mec
han
ic
al
ch
arac
te
risti
c
of
the
IM
i
n
the
wor
king
zo
ne
,
wh
e
re t
he
sli
p s v
a
ries f
r
om
0 t
o
sк
р. The
se
cond
e
quat
io
n i
s a r
igi
dly
m
odifie
d mec
han
i
cal
li
nk
.
Ba
sed on t
he
e
xp
e
rime
ntal da
ta
, th
e
fo
ll
owin
g
ass
umpti
ons
wer
e
ma
de:
•
The
main
funct
ion
al
dep
e
nde
nc
ie
s w
ere
d
e
scr
ibed b
y
sec
ond
-
orde
r p
olynomi
al
s;
•
It
is
assu
me
d
that
the
val
ve
s
are
sin
gle
–
op
e
rati
on
th
yri
stors
,
i
n
w
hi
ch
only
switc
hing
can
be
con
t
ro
ll
ed
.
Th
e
th
yr
ist
or
is
t
urne
d
off
insta
ntly
by
softwa
re
w
hen
the
c
onditi
on
f
or
the
cu
rrent
dro
p
that i
s curre
ntly
flo
wing th
rough
t
he
th
yri
stor t
o
ze
ro is m
et
;
•
Wh
e
n
c
al
culat
ing
the
th
yr
ist
or
is
c
onside
red
as
a
n
i
deal
va
lve,
t
he
s
witc
hi
ng
ti
me
of
w
hi
ch
ca
n
be
neg
le
ct
e
d
(
(tp
<0.006sec
).
•
We
al
so
neg
le
ct
the
vo
lt
age
drop
on
the
op
e
n
th
yr
ist
or
(V
<
1.5%
of
the
maxim
um
switc
hing
vo
lt
age
). Co
nse
qu
e
ntly,
the
T
VC ca
n be r
e
pr
esen
te
d as a
n
a
mp
li
f
ying li
nk;
•
IM is a
n
a
per
io
dic li
nk of t
he se
co
nd ord
e
r [
18];
•
The
pro
pose
d
qua
li
ty
crit
er
ion
–
po
wer
fa
c
tor
–
is
al
s
o
w
ritt
en
in
t
he
form
of
a
se
cond
–
or
der
po
l
ynom
ia
l
de
pendin
g o
n
the
IM
par
a
mete
rs
and loa
d.
The
se
nsor
s
of
the m
od
e
pa
ra
mete
rs
a
re
des
cribe
d by al
ge
br
ai
c e
quat
ions
:
Vbfw =
kbf
w
w,
V
bf
i =
kbf
i
Is
(3)
Without
al
lowa
nce
f
or
discre
te
ness
in
sig
na
l
extracti
on
[2]
.
The
ro
le
of
th
e
sta
ti
c
sp
eed
c
on
t
ro
ll
er
i
s
performe
d
by
t
he
AS
CS
with
a
tra
nsmi
ssio
n
facto
r
δ
(sl
ope
of
t
he
s
a
wtooth
),
w
hich
is
numerical
ly
eq
ual
to
the
recip
ro
cal
of
the
gain
.
Th
e
va
lues
of
δ
a
nd,
kbf
w,
kbfi
are
c
hose
n
by
t
he
res
ults
of
a
nalysis
a
nd
s
ynthesis,
procee
ding
fro
m
the
pro
visio
n
of
s
pecifie
d
dynamic
pr
op
e
rtie
s
of
the
ci
r
cuit
[
15
-
19].
D
iffer
e
ntial
eq
ua
ti
on
s
descr
i
bing
the
con
t
ro
l
lo
op
f
or
the
fr
e
quenc
y
of
ro
ta
ti
on
of
the
I
M
in
t
he
transie
nt
proc
ess
(
M
idle
-
M
no
m,
M
no
m
-
M
idle
)
ta
ke
the
form
:
(L1
/R
1)
p Js =
(
V
set
–
kbfi
Js
–
kb
fw
w
–
ke
w)
/R
1
(4)
p
w/ Js =
M
–
M
c,
wh
e
re
L
1
is
th
e
total
inducta
nce
of
the
sta
to
r
wi
nd
i
ng
;
R
1
–
act
ive
resist
an
ce
of
t
he
sta
to
r
windin
g;
Vset
–
spe
ed
ref
e
ren
ce
si
gnal
;
ke
–
coe
ff
ic
i
ent,
ta
king
int
o
acco
unt
the
inter
nal
pa
ras
it
ic
feedbac
k
on
t
he
fr
e
que
ncy
of
ro
ta
ti
on;
Js
is
t
he
total
m
ome
nt
of
i
ner
ti
a
of
the
I
M
a
nd
loa
d.
Since
the
syst
em
is
a
sec
on
d
–
orde
r
s
ys
te
m,
tw
o
feedbac
ks
a
re
intr
oduce
d
to
e
ns
ure
sta
bili
ty:
curre
nt
an
d
s
pe
ed:
kbfi
a
nd
kbfw
are
t
he
c
urren
t
a
nd
r
ota
ti
on
al
feedbac
k
coe
f
fici
ents,
re
sp
e
ct
ively.
Using
the
the
ory
of
m
od
al
c
on
t
r
ol,
stu
dies
w
e
re
co
nducte
d
on
t
he
sta
bili
ty
o
f
cl
ose
d
l
oop
ope
ra
ti
on
a
nd
t
he
pa
rameters
δ
=
1,
kbfi
=
2,
kbf
w
=
1
[20
-
25]
we
re
ch
os
e
n.
The
pur
po
se
of
ASC
S
is
the
op
ti
mal
functi
onin
g
of
the
c
on
tr
ol
le
d
sy
ste
m
in
the
pr
e
sence
of
an
exter
nal
lo
ad,
as
a
ru
le
,
rand
om
.
The
val
ues
of
the
pa
rameter
s
of
IM
a
nd
TV
C
ente
rin
g
t
he
rig
ht
-
ha
nd
side
s
of
the
e
quat
ion
s
,
i
n
accor
da
nce
with
t
he
rec
om
me
nd
at
io
ns
of
[
19,
26,
27],
were
dete
rmin
e
d
i
n
t
he
f
orm
of
t
he
a
bove
-
me
nt
ion
e
d
functi
onal
depend
e
nces
.
The
value
of
the
re
fer
e
nce
sig
nal
accor
ding
to
t
he
sp
ee
d
of
r
ot
at
ion
Vse
t
is
c
ho
s
en
accor
ding
to
t
he
ex
pe
riment
al
char
act
erist
ic
,
sta
rting
fro
m
the
co
ndit
io
n:
minim
um
i
dle
cu
rr
e
nt
an
d
small
loads
(ma
ximum
powe
r
fact
or)
wh
il
e
maint
ai
nin
g
sta
ble
operati
on
of
the
IM.
The
n
the
con
tr
ol
sig
nal
will
look li
ke:
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8
694
In
t J
P
ow
Ele
c
&
D
ri
S
ys
t,
V
ol
.
11
, N
o.
4
,
D
ecembe
r
2020
:
217
3
–
218
2
2176
Vcs
=
Vset
–
V
bfw
–
V
bf
i
(
5)
The
c
ontr
ol
sign
al
Vcs
is
c
ompare
d
i
n
A
SCS
wit
h
a
s
awto
oth
sig
nal
as
s
how
n
in
Fig
ur
e
2
.
Accor
ding
t
o
the
te
st
re
su
lt
s,
unde
r
ce
rtai
n
a
ssu
m
ptio
ns
T
V
C
withi
n
the
pe
rformance
(Midle
-
Mnom)
of
I
M,
the
ope
rati
ng
r
ang
e
of
t
he
a
ngle
α
of
re
gu
la
ti
on
of
the
Im
pu
lse
–
P
hase
C
on
t
ro
l
Sy
ste
m
(I
PCS
)
within
60
–
90
degrees.
T
he v
oltage at t
he out
pu
t
of TV
C
as
a fu
nction o
f
a
is d
e
fine
d
as:
Vd
=
160
–
1,0
67а
(6)
The
dep
e
nde
nc
e
V
d
(
а)
,
(
w
her
e
V
d
=
V
s
)
,
co
ns
tr
ucted
f
rom
the
e
xper
imenta
l
data,
i
s
show
n
i
n
Figure
3.
Th
e
func
ti
onal
de
pende
ncies
of
the
ex
per
ime
ntal
data
of
t
he
m
oto
r
unde
r
inv
e
sti
gatio
n
we
re
descr
i
bed
by
poly
nomial
sec
ond
-
orde
r
de
pe
nd
e
nces
.
To
determi
ne
t
he
functi
on
of
set
ti
ng
t
he
sig
nal
V
set
(
n)
and the
qual
it
y crit
erio
n
–
t
he p
ow
e
r fact
or, lin
ear
dep
e
ndenc
es w
e
re c
onstr
ucted.
Figure
2. Timi
ng d
ia
gr
a
ms
of open
lo
op ope
rati
on
Figure
3. The
vo
lt
age
at the
outp
ut of T
VC
dep
e
ndin
g on the a
ng
le
of c
ontrol
of
IP
CS
Fig
ure
4. Dia
gram of t
he
e
xp
e
rimental
set
up
4.
PRACTI
CA
L
R
ESE
ARCH
The
ex
per
i
men
ta
l
set
up
c
reated
i
n
t
he
trai
ning
la
borato
ry
m
ade
it
possible
to
buil
d
a
nd
a
nalyze
the
sta
ti
c
char
act
e
risti
cs
of
the
mo
to
r
4A
80
B
6
i
n
idle
an
d
low
lo
ad
m
ode
s.
Stat
ic
cha
ra
ct
erist
ic
s
are
gi
ven
in
Table
1,
Fig
ure
5:
i
dle
a
nd
low
l
oa
d
m
od
es
f
or
opti
mal
set
ti
ng
s
are
c
on
si
der
e
d.
Is
–
sta
tor
phase
c
urren
t
,
cos
φ
–
powe
r
fa
ct
or
,
Vs
–
phase
sta
tor
volt
age,
n
–
r
otor
s
peed,
P
1
–
powe
r
drawn
f
rom
the
su
ppl
y
net
wor
k,
P
2
–
us
ef
ul
powe
r,
M
–
to
rque
de
ve
lop
e
d
by
t
he
mo
to
r;
а
–
t
hyr
ist
or
c
ontr
ol
a
ng
le
.
T
he
w
ork
of
the
m
otor
un
der
reduce
d vo
lt
ag
e is sta
ble.
An
op
ti
mal
c
on
t
ro
l
cha
racteri
sti
c
was
obta
ined
by
th
e
crit
erio
n
of
minim
um
c
urre
nt
wh
il
e
mainta
inin
g
ef
fecti
ve
po
wer
.
On
Fig
ur
e
6:
1
–
is
a
natu
ral
el
ect
ro
mec
han
i
cal
char
act
eris
ti
c;
2
–
idle
res
ponse
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
ow Elec
& Dri S
ys
t
IS
S
N: 20
88
-
8
694
Experime
nta
l
det
ermin
ation of
subopti
m
al
para
meters
for
e
ner
gy
-
ef
fi
ci
en
t
con
tr
ol
of…
(
V
alentin
a S. G
oun)
2177
wh
e
n
c
ha
ng
i
ng
the
ref
e
ren
ce
sign
al
with
ou
t
dr
i
ving
the
loa
d
on
the
sh
a
ft;
char
act
e
risti
c
3
–
co
rr
e
spo
nd
s
to
the
idle
cha
racteri
sti
c
with
a
dr
i
ve
on
t
he
s
haft
;
4
–
c
orres
ponds
t
o
a
c
har
act
erist
ic
with
an
m
oto
r
loa
d
m
om
e
nt
equ
al
to
0.2
of
the
nominal;
char
act
e
risti
c
5
–
c
orres
ponds
to
the
m
om
e
nt
of
mo
t
or
loa
d
e
qual
t
o
0.4
of
the
nominal;
cha
r
act
erist
i
c
6
–
co
rr
es
ponds
to
t
he
m
om
e
nt
of
mo
t
or
l
oad
equ
al
to
0.6
of
the
nomin
al
;
7
–
corres
ponds to
the m
om
e
nt
of
mo
to
r
l
oad eq
ua
l t
o
0.8
of t
he nomi
nal.
Table
1.
T
est
4A80B6:
P
nom
=
1
,
1 k
W,
n
nom
=
920 min
-
1
, id
li
ng and l
ow loa
d
m
odes
with
r
edu
ce
d v
oltage
accor
din
g
t
o
th
e crit
erio
n of t
he
mi
nimum st
at
or
c
urre
nt (m
aximum
powe
r
f
act
or)
М
(
Nm
)
n
(
m
in
-
1
)
V
s
(V)
I
s
(А)
a
(
g
rad)
co
s
φ
P
1
(W)
P
2
(W)
0
,15
975
44
0
,52
108
0
,65
23
15
0
,55
970
4
9
,8
0
,7
1
0
2
,5
0
,78
71
56
0
,75
9
6
7
,5
5
1
,1
0
,8
1
0
1
,2
0
,78
97
76
0
,8
965
5
2
,5
0
,88
100
0
,77
105
81
1
,25
960
5
5
,2
1
,03
9
7
,5
0
,78
161
126
1
,41
9
5
7
,5
5
6
,6
1
,13
9
6
,25
0
,77
184
142
1
,58
955
58
1
,18
95
0
,77
204
157
1
,88
950
5
8
,5
1
,3
9
4
,5
0
,76
245
187
2
,0
9
4
7
,5
5
8
,8
1
,38
9
4
,25
0
,75
264
199
2
,23
945
5
9
,1
1
,45
94
0
,74
268
221
2
,39
9
4
2
,5
6
6
,3
1
,5
8
7
,5
0
,75
315
236
2
,55
940
7
4
,5
1
,55
80
0
,75
293
252
2
,83
935
9
0
,3
1
,68
65
0
,74
331
278
3
,18
930
92
1
,83
6
3
,33
0
,72
428
310
3
,53
925
9
3
,6
1
,95
6
1
,67
0
,72
478
342
3
,9
920
9
5
,3
2
,1
60
0
,70
535
376
(a)
(b)
Figure
5. Test
4A8
0B6
:
P
nom
= 1
,
1 k
W,
n
nom
= 920 mi
n
-
1
, idl
ing
a
nd lo
w
lo
ad
m
odes
with
reduce
d vo
lt
ag
e
accor
ding t
o
th
e crit
erio
n of t
he
mi
nimum st
at
or
c
urre
nt (m
aximum
powe
r
f
act
or)
a)
–
for
а (P
2
)
a
nd b)
–
f
or
Vs,
n, M,
co
sφ,
P
1 (
P2)
Figure
6.
Ele
ct
romecha
ni
cal
c
har
act
erist
ic
s.
IM
4A8
0B6
:
P
nom
= 1
,
1 k
W,
n
n
om
= 920 mi
n
-
1
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8
694
In
t J
P
ow
Ele
c
&
D
ri
S
ys
t,
V
ol
.
11
, N
o.
4
,
D
ecembe
r
2020
:
217
3
–
218
2
2178
An
al
yzin
g
t
he
obta
ine
d
c
harac
te
risti
cs,
it
can
be
no
te
d
t
ha
t
in
eac
h
of
them
t
her
e
is
a
minim
um
corres
pondin
g
to
the
minim
um
val
ue
of
t
he
sta
tor
c
urren
t
(
po
i
nt
B
co
rr
e
s
ponds
to
idli
ng
;
po
i
nt
V
–
to
a
load
of
0.2
f
r
om
nomi
nal;
point
J
–
to
a
loa
d
of
0.4
from
nominal;
point
D
–
t
o
a
l
oad
of
0.6
fro
m
nomi
nal;
Figure
7
sh
ows
a
view
of
the
recomm
end
e
d
el
ect
romecha
nical
c
ha
racteri
sti
cs
of
the
s
ubopti
m
al
I
M
co
ntr
ol
sy
ste
m
accor
ding
to
t
he
crit
erio
n
of
the
m
inim
um
sta
tor
cu
rr
e
nt,
wh
e
re
point
E
pr
act
ic
al
ly
co
r
respo
nd
s
t
o
t
he
rate
d
load
of
I
M
a
nd
point
B
is
cl
os
e
to
t
he
op
ti
mal
value
f
or
the
idle.
Sta
rting
from
point
V
an
d
with
a
f
ur
t
her
increase
in
l
oa
d,
a
n
unsta
ble
mode
of
op
e
ra
ti
on
of
the
s
yst
em
is
ob
se
r
ve
d.
Gr
a
dual
inc
rease
in
the
c
urre
nt
feedbac
k
sig
na
l
(by
a
dju
sti
ng
the
po
te
ntiom
et
er
R8
)
ma
ke
s
it
possible
to
achieve
sta
ble
operati
on,
but
at
the
same
ti
me,
the
amplific
at
io
n
factor
decr
eas
es,
a
nd
the
syst
em
co
ntin
ues
to
operate
at
char
act
e
risti
c
9
a
nd
enters
the
op
e
r
at
ion
m
od
e
s
how
n
by
point
G.
W
he
n
a
ca
pacit
or
C
1
is
i
ntr
oduce
d
i
nto
the
fee
dback
ci
rcu
it
(K
e
y1
ope
ns),
only
t
he
al
te
r
nating
cu
rr
e
nt
feedbac
k
c
ompone
nt
is
in
pu
t
to
D
A
1
(
Fig
ure
.
4)
.
As
s
how
n
by
exp
e
rime
ntal
da
ta
,
the
a
mp
li
fi
cat
ion
f
act
or o
f
the
s
ys
te
m
pra
ct
ic
al
ly
do
es
not
dec
rease
.
I
n
this
case,
t
he
A
SCS
at
the
init
ia
l
op
e
rati
ng
mod
e
c
orrespo
nd
i
ng
t
o
point
B
(
Fig
ure
.
6),
wh
e
n
the
loa
d
inc
reases,
w
orks
on
char
act
e
risti
c
8.
B
y
c
on
t
ro
ll
ing
t
he
ma
gnit
ud
e
of
the
va
riable
c
omponent
of
the
c
urren
t
fee
db
ac
k,
it
i
s
po
s
sible
to
a
chieve
sta
ble
op
e
rati
on
of
the
sy
ste
m
in
the
entire
range
of
c
ha
racteri
sti
c
8
(on
the
segme
nt B
–
E).
(a)
(b)
Fig
ure
7. Test
AOK
2
-
51
-
6
-
T
2:
P
nom
=4 k
W,
n
nom
=955 mi
n
-
1
, id
le
a)
–
f
or
V
s
, Q,
P
1
, n, S (P
2
)
a
nd
b)
–
for
I
s
, c
os
φ
(
P
2
)
Wh
e
n
re
placi
ng
a
sta
ti
c
re
gula
tor
with
a
n
ast
at
ic
on
e
(
w
hen
the
Ke
y2
key
is
opene
d),
the
s
peed
ref
e
ren
ce
sig
na
l
is
sel
ect
ed
s
o
that
IM
idli
ng
works
in
t
he
mode
s
how
n
by
point
I,
w
hi
ch
co
rr
es
pond
s
to
a
ro
ta
ti
onal
s
pee
d
w
r
=
93
1
mi
n
-
1
.
With
a
n
in
crease
in
loa
d,
I
M
op
e
rati
ng
at
cha
racteri
sti
c
10,
e
nters
a
mode
cl
os
e
to
the
nominal
(
po
i
nt
K)
.
T
he
s
ys
te
m
w
orks
sta
bly
over
the
e
nt
ire
loa
d
range
with
out
intr
oduci
ng
add
it
io
nal
c
urr
ent
fee
dbac
k
(potenti
ome
te
r
R8
is
in
the
off
posit
io
n)
.
T
he
a
bove
theo
ry
an
d
pr
act
ic
al
recomme
nd
at
i
on
s
were
te
ste
d
in
the
trai
ning
la
borato
r
y
of
el
ect
rical
machines
of
S
USU
on
the
mo
t
or
AOK
2
-
51
-
6
-
T
2
(p
a
ra
mete
rs:
220/38
0V,
16
/
10A,
4
kW,
95
5
mi
n
-
1
,
ef
fici
ency
82%,
cos
=
0.
78).
As
a
l
oad,
DC
mo
to
r
ty
pe
2P
N16
0MU
HL
4
(p
a
rameters:
220V,
4.5
kW,
24.2A,
1000/3
000
mi
n
-
1
)
wa
s
us
e
d,
mec
ha
nical
ly
connecte
d
to
t
he
I
M
a
nd
ope
rati
ng
i
n
the
el
ect
ro
ma
gnet
ic
br
a
ke
m
ode.
T
he
po
wer
s
uppl
y
was
pro
vid
e
d
by
a
flo
or
-
m
ounted
in
du
ct
io
n
vol
ta
ge
regulat
or
(
IR)
ty
pe
IR
59/2
2
-
U
3
(
pa
rameters:
16
0kV
A,
380V,
vo
lt
age
regulat
ion
li
mit
s
0
–
38
0V,
m
ai
ns
c
urren
t
310A,
loa
d
c
urr
ent
245A).
T
he
res
ults
of
th
e
te
sts
are
placed
i
n
Table
2,
Fi
gur
e
7
(AOK2
-
51
-
6
-
T
2
te
st:
P
nom
=
4
kW,
n
nom
=
95
5
min
-
1,
i
dling
m
od
e
),
where
V
s
–
is
t
he
volt
ag
e
on
the
sta
tor;
I
s
–
is
the
sta
to
r
c
urr
ent;
P
1
–
c
onsu
me
d
act
iv
e
powe
r;
Q
–
reacti
ve
powe
r
c
ons
umpti
on
;
cosφ
–
is
the
powe
r
fact
or
;
n
–
is t
he
rotat
ion fr
e
quenc
y;
P
2
–
use
f
ul po
wer
;
S
–
is t
otal
pow
er.
The
r
est
res
ults
of
t
he
te
st
ar
e
placed
i
n
Ta
ble
3
a
nd
Fig
ure
8
(
AOK2
-
51
-
6
-
T2
te
st:
P
n
om
=
4
kW,
n
nom
=
9
55
mi
n
-
1,
the
m
od
e
of
small
loads
wh
e
n
the
c
ondi
ti
on
s
of
the
m
inimum
sta
tor
current
a
nd
ma
ximum
powe
r
fact
or
a
re
sat
isfie
d).
F
rom
the
grap
hs
(F
ig
ure.
7b)
it
can
be
see
n
t
ha
t
at
a
minim
um
val
ue
of
t
he
sta
tor
current,
w
hile
mainta
inin
g
powe
r,
the
powe
r
fa
ct
o
r
(
cosφ
(P
2)
)
va
ries
withi
n
small
li
mit
s
and
is
appr
ox
imat
el
y
equ
al
to
t
he
nominal
(corr
es
pondin
g
to
the
rated
loa
d).
T
he
opti
mize
d
s
ta
tor
cu
rr
e
nt
li
near
l
y
dep
e
nds
on the
eff
ect
iv
e
pow
er.
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
ow Elec
& Dri S
ys
t
IS
S
N: 20
88
-
8
694
Experime
nta
l
det
ermin
ation of
subopti
m
al
para
meters
for
e
ner
gy
-
ef
fi
ci
en
t
con
tr
ol
of…
(
V
alentin
a S. G
oun)
2179
Table
2
.
T
est
AOK
2
-
51
-
6
-
T
2: P
nom
=4 k
W,
n
nom
=955 mi
n
-
1
, id
le
.
V
s
(V)
I
s
(А)
P
1
(kW
)
Q
(
k
W
ar)
co
sφ
n
(
m
in
-
1
)
P
2
(
W
)
S
(
VA)
219
2
,5
0
,32
0
,89
0
,34
996
3
,14
951
200
2
,29
0
,30
0
,74
0
,37
995
3
,14
795
180
2
,17
0
,27
0
,60
0
,40
994
3
,13
677
141
1
,75
0
,22
0
,36
0
,52
989
3
,12
427
121
1
,65
0
,20
0
,27
0
,59
985
3
,10
345
110
1
,63
0
,19
0
,23
0
,61
981
3
,09
311
100
1
,53
0
,19
0
,19
0
,72
975
3
,07
265
91
1
,53
0
,18
0
,16
0
,75
969
3
,05
240
80
1
,55
0
,17
0
,13
0
,79
959
3
,02
215
70
1
,63
0
,17
0
,11
0
,86
944
2
,97
198
60
1
,8
0
,16
0
,09
0
,85
919
2
,89
188
51
2
,13
0
,16
0
,09
0
,85
866
2
,70
187
Table
3
.
T
est
AOK
2
-
51
-
6
-
T
2
te
st:
P
nom
=
4 k
W
, n
nom
=
95
5
mi
n
-
1
, t
he
m
ode
of small
loa
ds
wh
e
n
t
he
conditi
ons
of
t
he
mi
nimum st
at
or
c
urre
nt and ma
xim
um p
ower
f
act
or a
re
sat
isfie
d
V
s
(V)
I
s
(А)
М
(
Nm
)
n
(
m
in
-
1
)
Q
(kW
ar)
P
2
(W)
co
sφ
9
5
,3
1
,54
0
,01
970
0
,17
5
0
,19
6
0
,77
9
4
,7
1
,80
0
,11
973
0
,18
0
,24
0
,81
3
9
4
,3
1
,92
2
,0
955
0
,18
0
,26
0
,83
9
3
,6
2
,21
3
,32
942
0
,19
0
,30
0
,84
9
3
,0
2
,42
4
,22
931
0
,20
0
,34
0
,87
9
2
,5
2
,82
6
,06
914
0
,21
0
,39
0
,86
9
2
,0
2
,95
8
,17
906
0
,22
0
,41
0
,87
(a)
(b)
Figure
8. Test
AOK
2
-
51
-
6
-
T
2
te
st:
P
nom
=
4 k
W,
n
nom
=
95
5
mi
n
-
1
, t
he
m
ode
of small
loa
ds
wh
e
n
t
he
conditi
ons
of
t
he
mi
nimum st
at
or
c
urre
nt and ma
xim
um p
ower
facto
r
a
re
sat
isfie
d
a)
–
for
M
, Q,
I
s
,
co
sφ,
n, V
s
(P
2
)
a
nd b)
–
f
or
I
s
, c
os
φ (
P
2
)
5.
POLY
NOMI
AL D
EPE
N
D
ENCES
OF
THE M
AI
N
P
A
RAMET
ERS
OF I
M
To
dete
rmin
e
the
coe
ff
ic
ie
nt
s
of
po
l
ynomi
al
s
approximat
ing
a
giv
e
n
ar
ray
of
s
ource
po
i
nts,
an
appr
ox
imat
in
g
pro
gr
am
was
wr
it
te
n
in
FO
R
TRAN
.
T
he
ac
ceptable
acc
uracy
of
the
poly
nomial
desc
rip
ti
on
o
f
giv
e
n
a
rr
a
ys
of
input
data
wa
s
achie
ved
by
check
i
ng
the
r
esults
of
cal
c
ulati
on
s
at
c
ontr
ol
points
[
28
,
29
-
34
].
Po
ly
nomial
de
pende
nce
of
th
e
second
degre
e
for
the
to
rqu
e
M
on
the
s
pe
ed
of
the
m
otor
sh
a
ft
n,
t
he
volt
ag
e
of
t
he
th
yr
ist
or
powe
r
s
ource
Vs,
t
he
c
urren
t
co
ns
ume
d
f
rom
the
powe
r
s
ource
Is,
t
he
a
ng
le
of
co
ntr
ol
of
the
IP
CS
а
:
М(n,V
s
,I
s
,а)
= 55,7
19n
–
322,2
05V
s
+
10
40,842I
s
–
376,9
86а
–
0,0
08n
V
s
–
1,
435n
I
s
+
0,01
0n
а
+
1,965Vs
I
s
+ 2
,229V
s
а
+
2,694I
s
а
–
0,0
29n
n +
0,9
99V
s
V
s
–
16,
147I
s
I
s
+ 1,
241а
а
To
s
ol
ve
the
direct
a
nd
in
ve
rse
c
ontrol
pro
blems,
the
par
a
mete
rs
of
li
near
de
pe
ndencies
we
re
determi
ned [
16
]:
М(n,V
s
,I
s
,а)
=
–
0,016
1n + 0
,0964V
s
+ 1,
6638I
s
+ 0,
0988
а,
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8
694
In
t J
P
ow
Ele
c
&
D
ri
S
ys
t,
V
ol
.
11
, N
o.
4
,
D
ecembe
r
2020
:
217
3
–
218
2
2180
The
poly
nomial
d
epe
ndenc
e
of the
po
wer
fac
tor o
n
the
same
p
a
rameters
w
i
ll
b
e wri
tt
en
as
:
cos
φ(
n,
V
s
,I
s
,
а)
= 20,4
79n
–
119,793V
s
+ 4
31,
381I
s
–
137,9
40а +
0,012
n
V
s
–
–
0,638
n
I
s
+
0,019
n
а
+ 1,
122V
s
I
s
+ 0,
727V
s
а
+
1,40
1I
s
а
–
0,012
n
а
+
+ 0,
329V
s
V
s
–
8,5
71I
s
I
s
+ 0,
401а
а,
The
li
nea
r
a
ppr
ox
imat
io
n
ta
ke
s the
form:
cos
φ(
n,
V
s
,I
s
,
а)
= 0,
011n
–
0,0
61V
s
+ 0,
385I
s
–
0,065
а,
The
volt
age
on
the
sta
tor
windin
g
with
sta
ble
mo
to
r
ope
rati
on
a
nd
with
m
inimum
sta
tor
current
a
nd
op
ti
m
um
powe
r
fact
or w
il
l be
w
ritt
en
as:
V
s
(
n,M,
I
s
,а)
= 0,
704n
+ 327
8,2
01M
–
7056,
682I
s
+ 2
9,971
а
–
0,0
01n
n
–
–
68,
340M
M
–
10
6,666
I
s
I
s
–
0,000
3а
а
–
3,4
17n
M
+ 7,
344n
I
s
–
–
0,032
n
а +
197,0
15
M
I
s
–
0,355
M
а
–
0,1
74
I
s
а,
The
li
nea
r
a
ppr
ox
imat
io
n
ta
ke
s the
form:
V
s
(n,M,
I
s
,а)
= 0,
163n
+ 1,
9622M +
1,1
727I
s
–
1,0
749а,
The
c
urre
nt consume
d
f
r
om
t
he powe
r netw
ork for t
he op
ti
mu
m
po
wer fa
ct
or
will
b
e
wr
i
tt
en
as:
I
s
(
n,
M,
V
s
,
а
) =
–
30,68
1n
–
435,9
47M +
18
1,552V
s
+ 205,
114
а
+ 0,
016n
n +
3,267M
M
–
–
0,554
V
s
V
s
–
0,656
1а
а
+
0,465
n
M
–
0,0
030
n
V
s
–
0,0
11
n
а
–
0,0
42
M
V
s
–
–
0,163
M
а
–
1,206
V
s
а,
The
li
nea
r
a
ppr
ox
imat
io
n
ta
ke
s the
form:
I
s
(
n,
M,
V
s
,а)
=
–
0,002
1n + 0
,4147M
+
0,0
144V
s
+ 0,
0177а,
6.
CONCL
US
I
O
NS
An
e
xp
e
riment
al
instal
la
ti
on
was
c
reated
in
the
la
borato
r
y
of
el
ect
rical
e
ng
i
neer
i
ng
of
SU
S
U
a
nd
a
pr
act
ic
al
ver
si
on
of
the
s
ubop
ti
mal
I
M
c
ontr
ol
s
ys
te
m
was
i
mp
le
me
nt
ed
acc
ordin
g
to
the
c
rite
rio
n
of
th
e
minimu
m
sta
t
or
cu
rr
e
nt
us
in
g
t
he
e
xam
ple
of
a
th
ree
-
p
ha
se
I
M
ty
pe
4A8
0B6.
Ex
peri
mental
stu
die
s
of
t
he
sy
ste
m
with
a
sta
ti
c
reg
ulato
r
hav
e
s
how
n
t
hat
it
is
po
ssib
le
to
reduce
th
e
sta
tor
cu
rr
e
nt
of
I
M
by
43%
at
M
c
=
0;
33%
wit
h
M
c
=
0.2
Mn
om
;
20%
at
Мс
=
0,4Мn
om
;
9%
at
М
с
=
0,6
М
no
m;
4%
a
t
М
с
=
0,8
Мn
om
in
com
pa
ris
on w
i
th wo
rk of a
n I
M
at t
he
sam
e
values
of the
m
om
e
nts
of
l
oadi
ng
on a
natu
ra
l characte
risti
c.
A
pr
act
ic
al
ve
r
sion
was
de
velop
e
d
a
nd
a
ma
themat
ic
al
model
of
the
sub
opti
mal
co
ntr
ol
sy
ste
m
for
IM
by
the
c
rite
ria
of
the
mi
ni
mu
m
sta
to
r
c
urren
t
an
d
the
maxi
m
um
pow
er
facto
r,
ope
r
at
ing
with
a
c
on
sta
nt
sp
ee
d
ref
e
ren
c
e
sig
nal
with
a
sta
ti
c
re
gu
la
to
r.
As
I
M
volt
age
c
onve
rter,
TVC
a
nd
IR
wer
e
use
d.
T
he
sp
ee
d
ref
e
ren
ce
was
sel
ect
ed
based
on
the
co
ndit
ion
that
t
he
st
at
or
cu
rr
e
nt
I
M
i
n
t
he
i
dle
is
minimi
ze
d
and
the
m
odes o
f
lo
w
l
oads
(
or
cl
ose
t
o
the
m)
are
sat
isfie
d
[2].
The
d
epe
ndence
o
f
the
volt
age
sig
nal
of
t
he
jo
b
on
the
main
op
e
rati
ng
p
a
rameters
is
const
ru
ct
e
d.
The
sta
ti
c
s
pe
ed
c
ontr
oller
i
n
t
he
ex
pe
rim
ental
set
up
prov
i
des
f
or
loa
d
mome
nts
le
ss
tha
n
the
nominal
w
ork
of
I
M
on
t
he
c
on
t
ro
l
c
ha
racteri
sti
c,
w
hich
a
ppr
ox
imat
es
th
e
opti
mal
c
urv
e
[
2].
T
he
eval
uation
of
t
he
in
flue
nc
e
of
t
he
re
gula
ti
ng
c
har
act
e
risti
c
on
the
main
par
a
mete
rs
of
IM
is
desc
ribe
d
by
po
l
ynomi
al
s
of
the
seco
nd
a
nd
first
degrees.
Stu
dies
of
the
su
boptimal
co
ntr
ol
sy
ste
m
of
I
M
of
ty
pe
4A8
0B6
acco
r
di
ng
t
o
the
crit
eri
on
of
minim
um
sta
tor
cu
rr
e
nt
with
an
ast
at
ic
re
gula
tor
s
howe
d
t
hat
if
at
the
loa
d
m
ome
nts
M
c
=
0.
8
M
no
m
a
nd
M
c
=
0,
t
he
sta
tor
cu
r
ren
ts
of
I
M
w
he
n
w
orki
ng
with
the
ast
at
ic
an
d
sta
ti
c
regul
at
ors
prac
ti
cal
ly
coincide
,
th
en
for
M
c
=
0.6
M
no
m
the
sta
tor
c
urre
nt
of
I
M
,
c
ontr
olled
from
t
he
s
ubopti
mal
sy
ste
m
with
the
ast
at
ic
regulat
or
by
4%,
at
M
c
=
0.4
Мn
om
–
by
10%
,
at
M
c
=
0.2
Мn
om
–
by
14%
m
ore
tha
n
with
t
he
sta
tic
regulat
or.
As
a
res
ult
of
the
st
u
dy
of
the
nat
ure
of
the
el
ect
r
om
ec
han
ic
al
c
har
act
erist
ic
s
(
dep
e
ndence
Is
–
n)
of
the
operati
on
of
I
M
,
c
on
tr
ol
le
d
from
T
V
C
or
IR,
it
w
as
fou
nd
t
hat
each
point
of
the
op
ti
mal
curve
corres
pondin
g
to
the
minim
um
val
ues
of
th
e
sta
tor
cu
rr
e
nt
an
d
the
ma
xi
mu
m
of
t
h
e
power
facto
r,
at
c
on
sta
nt
load
m
om
e
nts,
ra
ng
i
ng
f
rom
nomi
nal
to
i
dle.
C
on
s
eq
ue
ntly,
the
li
nea
rized
opti
mal
con
t
ro
l
c
ha
rac
te
risti
c
al
lows
t
he use
of a stan
da
rd T
VC as a
stat
ic
re
gu
la
to
r [2,
26].
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
ow Elec
& Dri S
ys
t
IS
S
N: 20
88
-
8
694
Experime
nta
l
det
ermin
ation of
subopti
m
al
para
meters
for
e
ner
gy
-
ef
fi
ci
en
t
con
tr
ol
of…
(
V
alentin
a S. G
oun)
2181
REFERE
NCE
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-
ph
ase
asyn
chr
onou
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drive
base
d
on
gen
erali
z
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,
“
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el
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pproa
ch
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stor
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con
tr
oll
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ction
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,”
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nal
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“
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esti
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ti
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th
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-
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n
induc
ti
on
mo
tor,”
Techn
ic
al
E
lec
trodynamic
s
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.
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pp
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56
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20
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[5]
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ai
ev
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tki
n,
“
Compa
r
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Analysis
of
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thods
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ng
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-
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e
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ti
on
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2016.
[6]
Chuang,
H.
G
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Li
,
and
C.
Lee.
"The
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ic
i
enc
y
Improve
m
ent
o
f
AC
Induc
ti
on
Motor
with
Con
stant
Freque
n
cy
Te
chno
logy.
"
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ergy
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vo
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p.
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813
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201
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[7]
Ili
nski,
N
.
"F
req
uenc
y
Conv
ert
er
s
in
Wate
r
Supply
Sys
te
ms
for
Ene
rgy
Sav
ing.
"
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rgy
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n
e
ering:
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nal
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f
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ion
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nski,
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,
“
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o
ac
h
t
o
AC
mot
or
sel
ec
t
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and
chec
king,
”
Pap
er
pr
ese
nte
d
at
the
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EE
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ren
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32
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[9]
V
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,
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A
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B
al
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,
“
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e
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lysis
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th
e
q
ual
it
y
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fr
eq
uenc
y
con
trol
of
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ct
ion
mot
or
ca
rri
ed
ou
t
on
th
e
basis
of
th
e
p
r
oce
ss
es
in the
ro
tor
c
irc
ui
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onfe
renc
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.
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“
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r
e
asing
th
e
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rgy
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icie
ncy
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t
io
n
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hine
s
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th
e
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e
of
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-
O
rie
nt
ed
Magn
et
i
c
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erials
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Die
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Cop
p
er
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el
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ag
e
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th
e
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ansacti
o
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r
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Ko
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Alex
andr
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Anikin
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ndr
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Ba
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nkov,
"N
onlinear
Dynam
ic
s
of
As
ynchr
onou
s
El
e
ct
ri
c
Driv
e:
Engi
n
ee
r
ing
I
nte
rpre
ta
t
ion
an
d
Corre
ct
ion
Te
chn
ique
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9.
[12]
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in
V.L
.
,
A.
S.
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A.
,
B
al
denkov
,
“
Ana
l
ysis
of
stab
il
it
y
of
el
e
ct
ri
c
driv
es
as
non
-
li
ne
ar
sy
stem
s
accordi
ng
to
Popov
criter
i
on
adj
usted
to
a
mpl
it
ud
e
and
ph
ase
fre
qu
enc
y
c
har
acte
rist
ic
s
of
it
s
e
le
m
ent
s,
”
2nd
Inte
rnation
al
Confe
renc
e
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A
ppli
ed
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mat
ic
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S
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.
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,
“
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ene
rgy
s
avi
n
g
opportuni
t
ie
s
i
n
el
e
ct
r
ic
mot
or
drive
n
sys
te
ms
-
Part
1:
Sys
te
m
eff
icienc
y
im
pro
vem
en
t,
”
52nd
I
EE
E/IAS
Indust
rial
and
Comm
erc
ial
Powe
r
Sy
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Techni
cal
Confe
renc
e, I
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d
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2016
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[14]
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ira,
F.J.T.E
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De
Alm
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d
a,
A.T
,
“
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ie
w
on
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rgy
sav
i
ng
opportun
it
i
es
in
e
le
c
tric
mot
o
r
driv
en
sys
tems
-
Part
2:
Reg
ene
r
at
i
on
and
outpu
t
power
red
u
ct
i
on,
”
52nd
I
EE
E
/IA
S
Industrial
and
Comm
erc
ial
Powe
r
Syst
ems
Techni
ca
l
Conf
e
renc
e, I
and
CP
S
,
2016
.
[15]
Donolo,
P.D
.
,
P
ez
z
ani
,
C
.
M.,
B
oss
io
,
G.R.,
D
e
Angelo,
C.
H.
,
D
onolo
,
M
.
A.
,
“
D
era
t
ing
of
indu
ction
mo
tors
due
t
o
power
quality
issues
conside
rin
g
the
mot
or
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