Intern
ati
o
n
a
l
Jo
u
r
n
a
l
of
P
o
we
r El
ec
tr
on
i
c
s
an
d D
r
i
v
e
S
y
stem
(I
JPE
D
S)
V
o
l.
11
, N
o
. 2, Jun
e
20
20
, pp
. 10
55
~1
064
I
SSN
:
208
8-8
6
9
4
, D
O
I:
10.
115
91
/i
jp
e
d
s.v
1
1
.i2
.
p
p10
55-
1064
1
0
55
Jo
urn
a
l
h
o
me
pa
ge
: h
t
t
p
:/
/ijpe
d
s.
i
a
e
s
c
o
re.
c
o
m
Super-tw
i
sting slid
ing
m
o
de
controll
ers bas
e
d on D-PSO
optimization for temperature co
ntrol of an induction cooking
system
A
b
de
ldja
l
il Abd
e
l
k
ad
er
Mekk
i
1
,
A
b
del
k
a
d
er
K
a
ns
ab
2
,
Mo
ha
m
e
d
m
a
tal
l
a
h
3
,
Zinel
aabi
d
ine Boudjema
4
,
Mo
u
l
ou
d Fel
i
ac
hi
5
1,
2,
4
Dep
a
r
t
m
e
nt
Lab
o
r
a
to
r
y
L
.
G
.
E.E
.
R
,
U
n
i
v
er
si
t
y
o
f
Has
s
ib
a
B
e
nb
ou
ali
,
Al
g
e
r
i
a
3
Un
ivers
i
ty o
f
D
j
ila
l
i
Bou
n
aa
ma
, K
h
emis
milian
a
,
A
l
ger
i
a
5
IR
EEN
A
-IUT
,
CR
TT,
B
d
de
l’u
n
ive
r
si
té
, Fra
n
ce
A
r
ticle In
fo
A
B
S
T
RAC
T
A
r
tic
le
h
i
st
o
r
y:
Re
ce
ive
d
A
p
r 10
, 20
19
Re
vise
d N
o
v
8
,
20
19
Acc
e
pt
e
d
Dec 22
, 20
19
In
this
study
,
w
e
perfo
rm
th
e
con
t
rol o
f
th
e
te
mp
erature
ev
olu
t
io
n
v
e
rsus
time
o
f
i
n
d
u
c
t
i
on c
ooki
ng
sy
st
em
using
a
su
pe
r t
w
i
s
ti
n
g
sli
d
in
g
m
o
de
co
nt
rol (S
T-
SMC) bas
e
d
on
Dynam
i
c Par
t
icl
e
Sw
arm
O
p
t
i
mi
zati
on (D
-PSO).
Fi
rst
,
we
wil
l
determine
t
h
e evol
u
t
ion of
the te
mperat
ur
e in the mi
ddle of the pan
bo
ttom u
s
ing
th
e F
E
M
metho
d
.
The fo
un
d
te
m
p
eratu
r
e
ex
ce
eds
th
e limi
t o
f
th
e d
e
sir
e
d
co
ok
ing
temp
era
t
u
r
e
(15
0
-2
00°
C). S
e
co
nd
, to
limit
te
mpera
t
ure
i
n
c
r
ea
s
e
,
a (ST
-
SMC) m
e
th
od com
b
in
e
d
w
i
t
h
a (D
-
P
SO
)
algor
ithm is used
t
o
get
t
h
e
d
e
sired temper
at
ure.
Part
i
c
l
e
s Swarm
Optimi
z
ati
o
n
(D-PSO) method
i
s
u
s
e
d
t
o
op
timiz
e
the
pa
ram
e
ters o
f
t
h
e
ga
i
n
o
f
(ST
-
SMC)
a
nd
im
pro
v
e
it
s
performance.
The si
m
u
l
a
ti
on res
u
lt
s
s
h
ow
that
the
use of
the optimized super
tw
is
ting
slid
in
g
mo
de
co
ntro
ller
helps
to
a
c
hiev
e
a d
e
sir
e
d v
a
lu
e
o
f
co
ok
ing
.
Ke
yw
ords:
I
ndu
c
tio
n co
okin
g
M
a
g
n
e
t
o
-
th
erma
l
F
i
n
i
t
e
el
eme
n
t me
th
od
P
a
r
t
i
c
le
sw
a
r
m op
tim
iz
at
io
n
S
u
p
e
r-
tw
ist
i
ng
slid
i
n
g mo
d
e
Th
is
is a
n
o
p
en
acces
s a
r
ticle
un
d
e
r the
C
C
B
Y
-SA
licens
e
.
Corres
p
o
n
din
g
A
u
t
h
or:
A
b
d
e
ld
ja
li
l Abd
e
lk
ad
e
r
M
e
kki,
Depa
rt
eme
n
t
o
f
El
ect
rot
e
ch
ni
c, La
bo
ra
t
o
ry
L.G.E.E
.
R
,
U
n
i
v
e
r
sity
of
H
a
ssib
a
Be
nbou
a
li,
Ch
le
f 0
200
0,
A
l
g
e
r
i
a
Emai
l:
a.a
b
del
k
ade
r
me
k
k
i@
u
n
i
v
-c
hle
f
.dz
1.
IN
TR
O
DUCTION
N
o
w
a
days
,
D
o
mest
i
c
i
nduc
t
i
o
n
c
o
o
k
e
r
s (IC) a
r
e
mo
re
a
n
d
mo
re
use
d
du
e
to
i
t
s
he
at
ing
ra
pidi
t
y
,
sa
f
e
t
y
a
n
d
en
erg
e
tic
ef
fi
ci
en
cy
.
Th
e me
ch
a
n
i
s
m
of (I
C)
c
o
n
t
ai
n
s
an
in
duc
to
r
wh
ic
h
i
s
p
l
ac
ed
on
a sup
por
t
wi
th a
ma
t
e
ri
a
l
of fe
rri
t
e
, a
n
d t
h
e
pan
whi
c
h i
s
a fe
rro
m
agne
ti
c met
a
l di
sc, as
depi
ct
ed i
n
Fi
gu
re
1
.
The
c
u
rre
n
t
d
e
n
s
i
t
y g
e
n
e
ra
te
d by t
h
e in
du
c
t
or pro
d
u
c
e
s
a v
a
r
y
i
n
g m
a
gn
e
t
i
c
f
i
e
l
d
,
wh
ic
h ind
u
c
e
s
e
ddy
cu
rre
n
ts on
t
h
e
pa
n b
o
t
t
om
cause
i
t
hea
t
i
n
g by
Jo
ul
e e
f
fe
c
t
.
[
1
].
O
n
t
h
e
ot
her
han
d
, t
h
e
v
a
ri
at
i
on c
ont
rol
of t
h
e t
e
m
p
erat
u
r
e i
n
t
h
e
pa
n's
bot
t
o
m i
s
di
ffi
c
ul
t
bec
a
u
s
e
of t
h
e
n
onl
i
n
e
a
rit
y
of t
h
e
c
h
a
r
ac
te
ri
sti
c
s
ma
gnet
i
c
a
n
d e
l
e
c
t
r
i
c
of
fe
rrom
a
gnet
i
c m
a
t
e
ria
l
of t
h
e
pa
n [2], a
n
d
t
h
e hi
g
h
f
r
eq
u
e
nc
y
cu
rre
n
t
of the
in
duc
t
o
r ,
t
hat
'
s w
h
y i
t
's
not
ea
sy
t
o
o
b
ta
i
n
a
n
acc
urat
e
mat
h
e
m
a
t
i
c
a
l
mo
del
th
a
t
ca
n
b
e
u
s
e
d
fo
r our
st
ud
i
e
d d
e
v
i
c
e
[3],
F
o
r th
is re
aso
n
, ou
r w
o
rk
fo
cu
se
s
on
con
t
ro
l
l
in
g t
h
e
c
o
ok
i
ng
t
e
mpera
t
ure
by
i
m
ple
m
ent
i
n
g
a
t
e
c
hni
q
u
e
c
a
l
l
ed
supe
r t
w
i
s
ti
ng
sl
idi
n
g
m
ode
c
ont
rol
(S
T-S
M
C
)
,
t
h
e
a
i
m o
f
t
h
is
te
ch
ni
q
u
e i
s
t
o
se
l
ect
a
n
a
ppr
op
ri
at
e
in
pu
t
c
u
rre
n
t
w
h
i
c
h
c
a
n
gi
ve
s
u
it
abl
e
co
o
k
i
n
g t
e
mpe
r
at
ure
.
The
su
pe
r-tw
is
t
i
n
g
sli
d
i
n
g m
ode
a
l
g
o
r
it
hms is
one
of t
h
e
most
imp
o
rt
a
n
t
a
p
proac
h
e
s
a
n
d
the
m
o
st
wi
del
y
use
d
S
l
idi
n
g
mo
de
c
o
ntr
o
l
(S
T
-
S
M
C
)
de
si
g
n
e
d
to
w
o
rk
a
nd c
o
n
t
rol
o
f
nonl
i
n
e
a
r
s
y
st
em
s
ha
v
i
ng
a
n
i
m
po
rt
a
n
t
u
n
ce
rta
i
n
t
y c
o
ndi
ti
ons
[
4
,
5]. T
h
e p
r
i
n
ci
pal
i
d
e
a
o
f
t
h
e s
upe
r-
twi
s
t
i
ng
sli
d
i
n
g
m
o
de c
o
nt
ro
l
i
s
t
o
f
o
r
c
e
th
e
slid
i
n
g
v
a
r
i
a
b
le
and
it
s d
e
r
i
v
a
tiv
e t
o
z
e
ro
in
a
f
i
n
i
te
ti
me
in o
r
d
e
r
to
b
e
a
b
le to
rem
o
v
e
t
h
e c
h
atte
ri
n
g
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
088
-8
6
94
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
, Vol.
11
,
No
.
2
,
Jun
e
2
020
: 1
055 –
10
64
1
056
e
f
f
e
ct
du
e to t
h
e
d
i
sco
n
t
inuou
s
c
o
n
t
ro
l a
c
t
i
o
n
w
h
ile
r
e
ta
i
n
ing
t
h
e k
e
y
be
n
e
fi
ts of th
e
cl
ass
i
ca
l sli
d
ing
mod
e
cont
rol
[6
, 7]
.
The
c
h
oic
e
of ga
in
pa
ramet
e
rs o
f
the
su
pe
r t
w
i
s
ti
ng
sl
i
d
in
g
mode
c
o
ntr
o
l has
an
i
n
fl
ue
nc
e
o
n
t
h
e
c
o
n
t
r
o
lle
r perfo
rm
an
c
e
,
wh
e
r
e
op
tim
a
l
g
a
in p
a
ra
me
ter
s
g
u
ar
a
n
tee th
e stab
ilit
y
a
nd rob
u
stn
e
ss
of
t
h
e
sy
s
t
e
m
and
gi
ve a
fast
resp
o
n
se. Va
ri
ous o
p
t
i
m
i
z
a
t
i
on t
e
c
hni
que
s are
use
d
t
o
o
p
ti
miz
e
gai
n
pa
ra
me
te
rs o
f
the
sl
i
d
ing
mode
co
nt
rol
l
e
r
, suc
h
as t
h
e
genet
i
c
a
l
g
o
ri
t
h
m an
d
part
i
c
l
e
swa
r
m o
p
t
i
m
iz
at
ion [
8
-1
1
]
. I
n
thi
s
pape
r, t
h
e
sup
e
r t
w
i
s
ti
n
g
gai
n
para
me
te
rs are
opti
m
i
zed usi
n
g
D
yna
mi
c
P
a
rti
c
le
Swa
r
m O
p
t
i
m
i
z
at
ion (
D
-P
S
O
) [
12].
Th
is
a
l
g
o
r
ith
m is
cho
s
e
n
due
t
o
i
t
s e
a
s
y i
m
p
l
e
m
en
ta
tio
n
,
sp
eed
, a
nd be
c
a
u
s
e
it
is a
pro
m
isin
g too
l
f
o
r
desi
g
n
in
g
opt
i
m
a
l
c
o
n
t
ro
l
l
e
r
s
o
v
e
r
othe
r
opt
imi
zat
i
on t
ech
ni
q
u
es.
The
simul
a
t
i
on
res
u
lt
s of u
n
c
ont
rol
l
ed a
n
d
cont
rol
l
e
d
m
o
del
s
a
r
e
c
o
m
p
a
r
e
d
, whe
r
e t
h
e
use
o
f
(ST
-
S
M
C
base
d
D-P
S
O
) met
hod i
s
sh
ow
n
t
o
gi
v
e
g
o
o
d
r
e
s
u
lts i
n
te
rm
s
o
f
re
li
ab
i
lity
,
an
d sta
b
ili
ty
p
e
r
f
o
r
m
a
n
c
e.
Thi
s
p
a
pe
r i
s
o
r
g
a
ni
se
d
a
s
fol
l
ows: i
n
se
ct
i
on
2,
mo
del
l
i
n
g
and
fi
nit
e
el
e
m
e
n
t
ana
l
ysi
s
a
r
e p
r
ese
n
te
d.
The
ev
ol
ut
io
n
of t
e
m
p
erat
u
r
e
i
n
the
pa
n’s
b
o
tt
om
is
det
e
rmi
n
e
d
i
n
sec
t
i
o
n
3. A
s
u
it
abl
e
c
o
o
k
in
g t
e
m
p
era
t
u
r
e
usin
g s
u
per t
w
i
s
t
i
ng
sl
i
d
in
g
mo
de
(ST
-
S
M
C
)
an
d
(D
-P
S
O
)
t
e
c
h
niq
u
e
i
s
present
e
d i
n
se
ct
ion
4 a
n
d t
h
e
r
e
sul
t
s
o
f
s
i
mu
la
ti
on
ar
e
sh
own
in s
e
c
tio
n
5
.
F
i
n
a
lly,
t
h
e
c
o
n
c
lu
s
i
on
is p
r
ese
n
ted
in
S
e
c
t
io
n
6
.
2.
M
A
GN
ET
O-TH
ER
MAL
FI
NI
TI ELE
MEN
T
ANA
LYSIS
To
f
u
rt
her e
n
h
a
nce
t
h
e
pe
rformance
o
f
t
h
e
i
n
d
u
ct
i
o
n c
o
oki
ng
h
o
b,
i
t
is
p
r
i
m
ordi
al
t
o
det
e
rmi
n
e
t
h
e
evol
ut
ion
o
f
th
e
t
e
mperat
ure
as a fu
nc
ti
o
n
of
t
i
m
e w
h
ic
h
i
s
at
t
h
e same t
i
m
e
t
h
e i
m
a
g
e of th
e
e
v
olut
i
o
n
o
f
t
h
e
i
nduc
ed
c
u
rren
t
s
ge
n
e
ra
te
d b
y
t
h
e
i
n
d
u
ct
or.
The
ma
the
m
a
t
i
c
al
mo
del
of th
e
i
n
duct
i
o
n
he
at
ing i
s
c
o
mp
o
s
ed
o
f
t
w
o
part
s: t
h
e
first
pa
rt i
s
th
e
eq
uat
i
o
n
of
ma
g
n
et
o
-
d
y
n
a
m
ic
s w
h
ic
h is
base
d on
ha
r
m
o
n
i
c
t
i
me
va
ri
at
i
on,
w
h
ere
a
s
th
e
seco
nd
is
th
e
th
erma
l
eq
u
a
ti
on
w
i
th
a
tr
an
si
t t
i
me
v
a
r
i
a
t
io
n.
The
mat
h
emat
ic
al
model
of t
h
e
p
h
y
si
ca
l
phe
n
o
me
no
n
of t
h
e
in
d
u
ct
i
o
n
co
o
k
i
n
g s
y
ste
m
is
2d
a
x
isym
me
tr
ic. U
s
i
n
g th
e
ma
gn
e
t
ic
po
ten
t
i
a
l
A, it
c
a
n
b
e
mo
d
e
l
l
ed
by
t
h
e
coup
le
d mag
n
e
t
o
-th
e
r
m
a
l
fo
rm
ul
at
i
o
n
[
1
3]
gi
ve
n
b
y
:
(1)
t
T
C
q
T
p
m
2
(2)
A
A
r
q
2
2
1
(3)
Whe
r
e:
is
th
e
magn
et
ic
v
e
ct
or po
te
n
t
i
a
l
,
a
r
e
th
e r
a
d
i
al
di
sta
n
ce
fr
om
the
a
x
is
and
th
e
tim
e
re
sp
e
c
tiv
e
l
y
.
,
,
are
t
h
e
ma
gnet
i
c rel
u
ct
i
v
it
y,
t
h
e e
l
ect
ri
c
c
o
n
duct
i
vi
ty
, a
nd
t
h
e a
n
g
u
la
r f
r
eq
ue
nc
y,res
p
ect
i
v
el
y
is
th
e
c
u
rr
en
t
de
n
s
it
y
and
th
e te
mp
er
at
u
r
e
r
e
sp
e
c
t
i
v
e
ly.
C
p
m
,
,
a
r
e th
e
th
er
ma
l
con
d
u
c
ti
v
ity,
th
e masse
d
e
nsi
t
y
,
an
d
th
e
sp
ecif
i
c
h
e
a
t
,
r
e
spec
ti
v
e
l
y
Th
e r
e
so
lu
tio
n o
f
th
e
s
e l
a
st eq
u
a
ti
on
s
w
ith
th
e f
i
n
i
te
el
em
en
t
met
hod r
e
qu
i
r
e
s
t
h
e
u
s
e
of
th
e
bo
u
nda
ry c
o
n
d
i
t
i
ons
i
n
t
h
e
b
o
rde
r
s
of th
e
pa
n
w
h
ic
h
a
r
e
of
t
h
e
Ne
uma
n
n
t
y
pe
(4)
,
a
n
d
t
h
e
b
o
u
n
d
ar
y
c
o
nd
iti
o
n
s
for
t
h
e
e
l
e
c
t
r
o
m
a
g
ne
ti
c
eq
u
a
ti
on
s
a
r
e o
f
t
h
e D
i
r
i
c
h
let
ty
p
e
(5
).
T
T
h
n
T
n
(4)
(A
=
0)
(5)
whe
r
e :
h i
s
t
h
e
c
o
n
v
ec
ti
on
c
o
ef
fi
ci
ent
Tn i
s
t
h
e
a
m
bi
ent
t
e
mp
era
t
ur
e
The
pa
n mat
e
ri
al
i
s
made
o
f
st
a
i
nl
ess-st
ee
l
t
h
e p
r
o
p
ert
i
e
s
of
whi
c
h
a
r
e
gi
ve
n i
n
[1
3].
The
c
o
n
v
ect
i
o
n
c
o
e
f
fic
i
e
n
t
h i
n
t
h
e
p
a
n b
o
t
t
om has
a no
nli
n
ea
r val
u
e d
u
e
to
t
h
e
c
o
n
v
ec
t
i
on
e
f
fec
t
of
t
h
e ai
r
ne
arb
y
.
In
t
h
i
s
w
o
rk,
i
n
o
r
de
r t
o
sim
p
l
i
fy
the
la
tt
e
r
phe
n
o
me
no
n
we a
s
su
me
t
h
a
t
h
has c
o
nst
a
n
t
val
u
e
al
on
g of ra
dius
o
f
t
h
e
pa
n [1
4
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
IS
SN:
208
8-8
6
9
4
Su
per
-
t
w
i
s
t
i
ng
sl
i
d
i
ng m
o
de c
ont
r
o
ll
ers base
d
on
D
-
P
S
O
o
p
t
i
m
izat
i
o
n
f
o
r … (A
bdel
d
jal
i
l Ab
del
k
a
d
e
r
M
e
k
k
i
)
1
057
3.
PRO
C
EDU
R
E
CA
L
CUL
A
T
ION A
N
D
D
E
T
E
RM
I
N
A
T
ION OF
TH
E
T
E
MP
ER
A
T
URE
EVOL
UAT
I
O
N
The
p
r
o
p
o
se
d
mo
del
i
s
a
n
i
n
duct
i
o
n
co
o
k
i
n
g
s
y
st
em,
whi
c
h is c
o
m
p
ose
d
of t
h
ree
pa
rt
s. T
h
e first
o
n
e
i
s
t
h
e pa
n w
h
ic
h
i
s
t
h
e
pa
rt t
o
be
he
at
e
d
. T
h
e
sec
ond
part i
s
t
h
e ai
r ga
p, a
n
d t
h
e la
st
pa
rt
is t
h
e ind
u
c
t
or
whi
c
h
has
fo
ur sl
ot
s
c
onta
i
ni
ng
t
h
e
exc
i
t
i
ng
coi
l
s
a
s
sh
o
w
n
i
n
Fi
gu
re
1 a
n
d
F
i
gure
2
.
T
h
e
geo
m
et
ri
cal
a
nd
p
hysi
c
a
l
p
a
rame
te
r
s
a
r
e sh
ow
n i
n
Tab
l
e
1,
ex
cep
t
t
h
e
v
a
l
u
e
of th
e c
u
rr
en
t
d
e
nsit
y
wh
ic
h is
equ
a
l
t
o
(2
.5
*1
0
6
A/
m
2
) in
this work.
Tabl
e 1. Pa
ra
m
e
t
e
rs
o
f
s
y
st
em
Symbol
e Magnit
ude
Qua
n
tity
R
Ra
dius of
p
a
n
140m
m
e
1+
e
2
I
nductor
thic
kn
e
s
s
3
.
8m
m
e
3
Ga
p
thic
kness
4m
m
e
4
Conta
i
ner
thic
knes
s
3m
m
d
i
, i=
1
...9
D
i
sta
n
ce
s
1
5
.5
5
m
m
e
2
coi
l
s
thic
kness
2m
m
µ
f
Fe
rr
ite
re
l
a
tive
p
e
r
me
abil
ity
2500
f F
r
e
quenc
y
20*1
0
3
Hz
J
Curr
e
n
t
densit
y
2.
5
*10
6
A/m
2
λ
Th
erm
a
l
c
onductivi
t
y
26 W/m
*
°K
h Convec
tion
co
e
f
f
i
ci
en
t
20 W/m
2
°C
ρ
m
M
a
sse
densit
y
7700K
g
/m
3
C
p
Spec
if
ic he
at
460 J/K
g
.°C
Fi
gu
re
1. Di
me
nsi
o
ns of s
y
ste
m
u
s
ed
Fi
gu
re
2.
M
o
d
e
l
syst
em use
d
in t
h
e P
r
o
g
ra
m
Th
e
m
a
gn
e
t
o-
t
h
e
r
ma
l
c
a
l
c
u
la
tio
n
s
of
th
e
indu
c
t
io
n
c
ook
ing sy
ste
m
a
r
e
g
i
ve
n
b
y
fo
llow
i
ng
step
s:
a.
S
t
e
p
1
:
i
n
it
ia
liz
at
io
n
of
t
h
e
ma
gne
t
i
c
ré
l
u
ct
i
v
i
t
y, t
h
e
el
ec
t
r
i
c
co
nd
u
c
t
i
vit
y
,
a
nd t
h
e t
e
m
p
e
r
a
t
u
r
e
T
0
0
0
,
,
b.
S
t
e
p
2
: c
a
l
cu
la
tio
n
o
f
th
e
ma
gn
et
ic v
e
cto
r
pote
n
ti
al
(
A) by
us
e of
(
1
)
.
c.
St
ep
3
:
cal
c
u
l
a
t
i
on of t
h
e he
at
so
urc
e
d
e
nsit
y
i
s
g
i
ve
n b
y
(2)
a
nd
(3
).
d.
St
ep
4
:
cal
c
u
l
a
t
i
on of t
h
e
t
e
mpe
r
at
ure
w
h
e
r
e
we
use
a ti
m
e
st
ep
of 10
(s
) .
If
75
0
°
go
b
a
c
k
t
o
st
ep
2
o
r
el
se
go
to
s
t
ep
5.
e.
S
t
e
p
5
: d
i
sp
lay
o
f
th
e
r
e
su
lts
.
The
si
mul
a
t
i
o
n
re
sul
t
s
obt
ai
n
e
d
a
r
e s
how
n i
n
Fi
g
u
r
e 3
a
n
d
Fi
gu
re
4.
It is
cl
ear
fr
om t
h
ose Fi
gu
res
th
a
t
t
h
e t
e
mp
era
t
u
r
e evo
l
u
t
ion on
th
e p
a
n
’
s bo
tto
m
e
x
c
e
e
d
s
th
e a
ppr
op
r
i
a
t
e v
a
l
u
e
of
co
ok
i
n
g.
Th
is is
cause
d
by
the
va
ri
at
i
o
n of
the
el
ect
roma
gne
ti
c
pr
ope
rt
i
e
s
of the
syst
em s
u
c
h
as
t
h
e el
ec
tric
al
resi
st
ivi
t
y
ρ
(T
) and
t
h
e
ma
gn
e
tic
p
e
r
m
e
a
b
ilit
y
μ
r(
T
)
.
0
0.
05
0.
1
0.
25
0.
3
0.
35
di
s
t
anc
e
f
r
om
c
ent
er
(m
)
t
h
i
ckn
e
ssc(
m
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
088
-8
6
94
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
, Vol.
11
,
No
.
2
,
Jun
e
2
020
: 1
055 –
10
64
1
058
Fi
gu
re
3. Tem
p
era
t
u
r
e e
v
ol
ut
i
on ve
rsu
s
t
i
me
F
i
gu
re
4.
Te
mpe
r
at
ure
di
stri
b
u
t
i
on o
n
pa
n
’
s
bot
to
m
4.
TEMPERATU
R
E
REGU
LATION
B
e
c
a
use t
h
e i
n
duct
i
o
n
co
o
k
i
n
g s
y
st
em
i
s
a
c
o
u
p
l
e
d
no
nli
n
e
a
r
unce
r
t
a
i
n
sy
st
em, i
t
's
not
e
a
sy t
o
ha
ve
a
n
ac
c
u
ra
te
ma
th
em
at
ic
al mo
d
e
l
th
at
c
a
n
b
e
u
s
ed
t
o
c
o
n
t
ro
l
th
e temp
er
atu
r
e
o
f
t
h
e
p
a
n [3
].
Fo
r th
is
re
ason
,
and
in
orde
r
t
o
c
ont
rol
the
t
e
m
p
erat
ure
of the
pan
a
n
d
t
o
get
a
n
a
p
pr
opria
t
e
t
e
mpe
r
at
ure
of
coo
k
i
n
g, a
s
o
l
u
t
i
on
by
t
h
e
use
o
f
D-P
S
O
t
e
ch
ni
que
i
s
a
ppl
i
e
d
t
o
se
le
ct
o
p
t
i
m
a
l
gai
n
pa
rame
t
e
rs
o
f
s
u
per
t
w
ist
i
n
g
sl
idi
n
g
mo
de
cont
rol
l
e
r,
wh
ere
t
h
e
o
p
ti
mi
z
e
d
S
T
-S
MC i
s
e
m
pl
oye
d t
o
c
ont
rol t
h
e
t
e
mpe
r
a
t
ur
e of
t
h
e de
vi
c
e
w
h
i
c
h is
sho
w
n i
n
fi
gu
re
5.
F
i
gu
re
5. Bl
oc
k
dia
g
ram of
t
h
e ST-S
MC
ba
s
e
d
D-P
S
O
for
t
h
e
c
o
o
k
i
n
g
i
n
d
u
ct
i
o
n
4.1.
Su
per-tw
ist
i
ng
slidin
g
mo
d
e
co
ntro
l
sup
e
r
-
t
w
i
s
t
i
ng
sl
idi
ng
mo
de a
l
go
ri
t
h
ms i
s
o
n
e
of t
h
e
mo
st
i
m
p
o
rt
a
n
t
ap
proa
che
s
a
n
d the
most
u
s
ed
amo
n
g
t
h
e
fa
mi
l
y
o
f
H
O
S
M
al
go
ri
t
h
ms
,a
n
d
i
t
i
s
desi
gne
d t
o
wo
rk
a
n
d
c
ont
rol
n
o
nl
i
n
ea
r
unce
r
t
a
i
n
s
y
ste
m
s
[1
5].
The
pri
n
ci
pal
i
d
e
a
of
t
h
is
al
go
ri
thm
i
s
t
o
dri
v
e
t
h
e
sli
d
i
n
g
varia
b
le
a
n
d
i
t
s
deri
v
a
t
i
ve
to
ze
ro
i
n
fini
t
e
ti
me
,
in
o
r
d
e
r
to
b
e
ab
le
t
o
r
e
mov
e
ch
a
tte
ri
ng
ef
fe
c
t
d
u
e
to th
e
d
i
sc
on
t
i
n
uou
s
con
t
r
o
l a
c
t
i
o
n.
The
s
upe
r t
w
i
s
ti
ng
sli
d
i
n
g m
o
de
co
nt
rol
ha
s
bee
n
de
ve
lo
pe
d t
o
w
o
rk o
n
l
y
w
i
t
h
syst
ems
w
i
t
h
rel
a
t
i
v
e
deg
r
e
e
e
qual
t
o
o
n
e, w
i
t
h
the
pu
rp
o
s
e
t
o
re
d
u
c
e
the
c
h
at
te
ri
ng whi
l
e
co
ns
ervi
ng t
h
e p
r
o
p
ert
i
es o
f
a tra
d
i
t
i
onal
sl
id
in
g
mo
d
e
. On
e mo
re ad
va
n
t
a
g
e
of
t
h
is
l
a
tte
r
is
th
a
t
t
h
e
i
r
i
m
p
l
e
m
e
n
ta
t
i
o
n
n
e
e
d
s on
ly
th
e kn
ow
le
dge
of
the
sign
o
f
t
h
e
sl
id
i
ng va
ri
abl
e
(s)
[
1
6
]
whi
c
h i
s
gi
ve
n by
1
⟨
0
0
0
1
⟩
0
(6)
Thi
s
l
a
t
t
e
r
al
go
ri
t
h
m
has
be
e
n
re
prese
n
t
e
d
b
y
t
h
e
c
ont
rol
l
a
w
,
u
(
t
)
,
w
h
ic
h
is c
o
m
pose
d
o
f
t
w
o
pa
rt
s
.
Th
e
firs
t on
e
i
s
a
d
i
sc
on
tin
uo
u
s
tim
e d
e
r
i
va
tiv
e
(
u1) a
nd th
e
se
co
nd
par
t
i
s
a c
o
n
t
i
n
u
o
u
s
f
u
n
c
t
i
on
o
f
t
h
e
sli
d
i
ng va
ri
a
b
l
e
(u
2).T
he traj
ec
torie
s
o
f
t
h
e
supe
r t
w
ist
i
n
g a
l
go
ri
t
h
m
i
n
t
h
e
pha
se
pl
a
n
e
a
r
e cha
r
ac
te
ri
ze
d
b
y
a
spiral
m
o
veme
nt
a
r
o
u
n
d
t
h
e
o
r
i
g
in
o
f
t
h
e
sli
d
i
ng
va
ri
abl
e
[1
7].
Le
t’s
Co
nsi
d
er
a
no
nli
n
ea
r
s
y
ste
m
g
i
ven
by
(1
) whe
r
e
a
,
b
,
c
ar
e unk
nown
fu
n
c
t
i
on
s,
x
i
s
th
e s
t
at
e,
and
u,
y
a
r
e
t
h
e c
o
ntr
o
l
i
nput
and
t
h
e
c
o
nt
rol
l
e
d
o
u
t
p
ut
re
sp
e
c
t
i
v
el
y
,
,
,
,
(7)
0
10
0
20
0
30
0
400
500
60
0
0
10
0
20
0
30
0
40
0
50
0
60
0
70
0
80
0
ti
m
e
(
s
)
te
m
p
eratu
r
e
(
C
°
)
0
0.
02
0.
04
0.
0
6
0.
08
0.
1
0.
12
0.
14
500
550
600
650
700
750
800
di
st
a
n
c
e f
r
o
m
c
e
n
t
er
(
m
)
t
e
m
per
at
ur
e /
(
C
°
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
IS
SN:
208
8-8
6
9
4
Su
per
-
t
w
i
s
t
i
ng
sl
i
d
i
ng m
o
de c
ont
r
o
ll
ers base
d
on
D
-
P
S
O
o
p
t
i
m
izat
i
o
n
f
o
r … (A
bdel
d
jal
i
l Ab
del
k
a
d
e
r
M
e
k
k
i
)
1
059
The
pu
rpose
i
s
t
o
get
a
c
o
ntr
o
l i
nput
fu
nct
i
on
y
y
f
y
*
,
wh
ic
h
f
o
r
c
e
s
t
h
e
sy
s
t
em
t
r
a
j
ect
o
r
i
e
s to th
e
ori
g
in o
n
t
h
e
p
h
ase pla
n
e
of
s
l
idi
ng v
a
ri
abl
e
0
*
y
y
i
n
a
f
i
n
i
te
ti
me
.
The sta
nda
rd form of t
h
e
c
ont
rol l
a
w to
co
nt
rol
t
h
e
out
p
u
t
y
in s
u
p
e
r-t
wi
st
al
go
ri
t
h
m ca
n be
gi
v
e
n by:
)
(
)
(
2
*
1
1
1
s
sign
K
u
u
s
sign
s
K
u
r
(8)
Whe
r
e t
h
e
sl
idi
n
g
va
ri
abl
e
is
is de
fi
ne
d as:
y
y
s
*
(9)
k1
a
n
d
k
2
a
r
e
c
ont
rol
l
e
r
gai
n
s
r
= 0.5.
To
d
r
iv
e th
e
t
r
a
j
e
c
t
o
r
ie
s
o
n
to th
e
sl
id
i
n
g man
i
fo
ld
s
s
˙
=
0
i
n
fi
ni
t
e
t
i
me, t
h
e ga
ins
k
1
a
n
d
k2
m
u
st
veri
fy the
f
o
llo
wi
ng
in
equ
a
li
ty
:
m
M
m
m
2
2
4
,
(10
)
Wh
en
u
s
ing
t
h
e
su
p
e
r
tw
isti
n
g
co
n
t
ro
l
l
a
w
,
it
is
no
t n
e
ce
ssar
y
t
o
k
now
th
e
ti
me
d
e
r
i
v
a
tiv
e
in
fo
r
m
a
tio
n of
th
e
sl
id
i
n
g v
a
r
i
a
b
le
[
1
7
]
.
M
o
re
o
v
e
r, i
t
is no
t
n
e
c
e
ss
a
r
y t
o
kn
ow t
h
e
i
n
f
o
rm
at
io
n r
e
lat
i
ng t
o
th
e
ot
he
r s
y
st
em
p
a
ra
me
te
rs
. T
h
e
l
a
t
t
e
r
al
l
o
ws
t
h
e sim
p
l
i
fic
a
t
i
on o
f
t
h
e
co
mput
at
i
on o
f
t
h
e c
ont
rol
l
er a
n
d al
so
t
h
e
r
e
d
u
c
ti
on
o
f
t
h
e
nu
mb
er of sen
s
or
s.
4.2.
Pa
rt
ic
le
swa
r
m o
p
t
i
miz
a
ti
on
In 1
995
, Eb
erha
r
t
an
d
K
e
nn
e
d
y
,
d
e
v
e
lop
e
d
a
n
a
l
go
r
ith
m call
e
d
p
s
o, th
e id
e
a
of
wh
ic
h
w
a
s ex
trac
ted
from t
h
e
m
o
ve
ment
of a
grou
p of ani
m
al
s su
ch as
a
sc
ho
ol
of fi
s
h
or a
sw
arm of
bi
rds
…
et
c [1
8].
Th
e
d
e
fi
n
itio
n
of th
is a
l
go
r
ith
m is s
i
mil
a
r
to
t
h
at
of
the
g
e
n
e
ti
c a
l
g
o
r
i
t
h
m wh
e
r
e th
e
p
opu
l
a
ti
o
n
is
c
a
lle
d
"sw
a
r
m
"
wh
ich
in
cl
ud
es a
nu
mb
e
r
of "ind
i
v
idu
a
ls" c
a
l
l
ed
p
a
r
tic
le
s [19
]
. Mor
e
ov
e
r
, e
a
c
h
p
a
rt
icl
e
po
sitio
n
is
re
prese
n
t
e
d
b
y
a n
u
mbe
r
of pa
ramet
e
rs t
o
be
opti
m
i
z
e
d
.
Furt
he
rmore,
e
ach
pa
rti
c
le
of
t
h
e
swa
r
m
e
x
plo
r
e
D-di
me
n
s
i
ona
l
spac
e
i
n
orde
r
t
o
sea
r
ch
t
h
e
best
p
o
s
i
t
i
on
whi
c
h gi
ve t
h
e be
st fi
t
n
e
ss fu
n
c
t
i
on [2
0
]
.
The
be
st
pa
rti
c
l
e
p
o
si
ti
on
tha
t
gi
ves t
h
e
be
st
fi
t
n
ess
va
l
u
e
,
n
a
med
as
(best
)
,
i
s
kno
w
n
a
s
t
h
e pe
rs
ona
l
i
n
format
i
on of eac
h
pa
rt
ic
le
[20
]
.
On t
h
e
oth
e
r ha
n
d
t
h
e
bes
t
parti
c
l
e
po
sit
i
ons t
h
at
gi
ve
a
best
fi
t
n
ess
f
u
n
c
ti
on
amo
n
g
a
l
l
pa
rt
i
c
l
e
s (p
best
) i
s
na
me
d as
(gbe
st
)
[2
1].
D
-
P
S
O
i
s
one
of t
h
e
fa
mi
l
y
o
f
pso
al
g
o
ri
th
ms, a
n
d
it
i
s
c
h
aract
erise
d
by
t
h
e
use
of a
T
i
me Va
ryi
n
g
cog
n
i
t
i
ve
(c
1)
and
a
s
o
c
i
a
l
c
o
mp
one
nt
(c
2).
T
his i
s
deve
l
o
pe
d
fo
r t
h
e
p
u
rpos
e
of i
m
pr
o
v
i
n
g t
h
e
pe
rformanc
e
of st
an
da
rd P
S
O
al
g
o
r
i
t
h
m
[1
2].
Let
’
s
c
o
n
s
id
er N
is n
u
mb
er
of p
a
r
t
ic
le
s,
a
n
d
D
is th
e
d
i
men
s
io
n o
f
ea
ch
p
a
rt
ic
le,
wh
i
c
h rep
r
esen
t
t
h
e
nu
mbe
r
of
va
ri
a
b
le
s of t
h
e
s
y
s
t
em.
Th
e
po
s
itio
n
an
d t
h
e v
e
lo
ci
t
y
v
e
c
t
or
o
f
th
e
N
p
a
r
t
i
c
l
e
s
a
t
i
t
er
a
tio
n
k
ar
e r
e
s
p
ec
tiv
e
l
y
r
e
p
r
e
s
e
n
ted
a
s
X
X
X
X
k
D
i
k
i
k
i
k
i
,
2
,
1
,
,
,
,
(11
)
V
V
V
V
k
D
i
k
i
k
i
k
i
,
2
,
1
,
,
,
,
(12
)
Whe
r
e i=
1…..
N
J=
1,2…
D
At
e
ach
it
e
r
at
i
o
n
(k)
a.
A
p
a
r
t
i
c
le
updat
e
s
it
s p
o
s
itio
n
an
d v
e
l
o
c
i
ty
b
y
th
e
fo
ll
o
w
ing
eq
u
a
tion
s
[22
-
24
]
X
Gbest
rand
C
X
pbest
rand
C
V
V
k
ij
k
j
k
ij
k
ij
k
ij
k
ij
W
2
2
1
1
1
(13
)
V
X
X
k
ij
k
ij
k
ij
1
1
(14
)
b.
The
b
e
st
po
sit
i
o
n
t
h
at
gi
ves
th
e
be
st
fi
tne
s
s
funct
i
o
n o
f
it
pa
rt
i
c
l
e
is give
n
a
s
:
pbest
pbest
pbest
pbest
k
D
i
k
i
k
i
k
i
,
2
,
1
,
,
,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
088
-8
6
94
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
, Vol.
11
,
No
.
2
,
Jun
e
2
020
: 1
055 –
10
64
1
060
c.
The
b
e
st
parti
c
l
e
t
h
at
gi
ves
t
h
e best
fit
n
ess
funct
i
on a
m
on
g
a
l
l
pa
rt
i
c
l
e
s
i
s
gi
ve
n as:
Gbest
Gbest
Gbest
Gbest
k
D
k
k
k
j
,
,
2
1
V
k
ij
i
s
t
h
e ve
loc
i
t
y
of
pa
rt
ic
le
i
at
i
t
era
t
i
on k
W
is
th
e
we
igh
t
ing
fu
n
c
ti
on
C
1
,
C
2
are
t
h
e
ac
cel
er
at
i
o
n c
o
e
f
fi
ci
ent
s
rand
1
,
rand
2
are
ra
n
d
o
m
nu
mbe
r
s be
tw
ee
n
0a
nd
1
X
k
ij
is
th
e
p
o
s
iti
on
o
f
p
a
r
t
i
c
l
e
i at it
er
at
io
n
k
pbest
k
ij
is
t
h
e
B
e
st
posi
t
i
on
of pa
rt
ic
le
i
a
t
i
t
e
r
a
t
i
on
k
Gbest
k
j
is
th
e
Be
st
p
o
s
i
t
io
n
o
f
th
e
sw
ar
m
u
n
til ite
r
at
i
o
n k
W
h
ere
c1
, c
2
an
d
W
a
r
e c
o
mp
u
t
ed
by
th
e fo
llo
w
in
g :
0
.
4
2
1
C
C
(15
)
C
ite
r
iter
C
C
C
min
1
min
1
max
1
1
ma
x
(16
)
C
ite
r
iter
C
C
C
min
2
min
2
max
2
2
ma
x
(17
)
W
W
W
iter
iter
iter
W
min
min
max
max
max
(18
)
Whe
r
e:
ietr
,
are
t
h
e
cu
rre
n
t
i
t
e
ra
t
i
on
numb
e
r
a
nd t
h
e max
i
mum
n
u
mbe
r
of
i
t
e
ra
ti
ons
re
spec
ti
vel
y
C
max
1
,
C
min
1
are
t
h
e
ma
xi
ma
l and
mi
ni
ma
l co
gni
t
i
ve
coe
f
fi
ci
ent
s
res
p
ec
t
i
vel
y
C
max
2
,
C
min
2
are
t
h
e
ma
xi
ma
l and
mi
ni
ma
l soci
al
c
o
effic
i
e
n
t
s
re
spe
c
t
i
ve
ly
W
max
,
W
min
are
t
h
e
ma
xi
ma
l and
mi
ni
ma
l wei
g
ht
in
g
fu
n
c
t
i
on re
spect
i
v
el
y
At
e
ach
it
er
a
t
io
n
(k)
,
t
h
e
po
si
tio
n
an
d t
h
e
vel
o
ci
ty
o
f
e
a
c
h
it
h
p
a
r
t
ic
le
a
r
e upd
a
t
e
d
u
s
in
g (1
3-1
4
),
and
th
e
n
w
e
ev
al
u
a
t
e
t
h
e
ob
je
ct
ive
fu
n
c
ti
on
[
25].
Th
e r
e
su
lt
s are
c
o
mp
ar
ed b
e
tw
e
e
n
: th
e n
e
w pb
e
s
t
(b
e
s
t posit
io
n
fo
r t
h
e pa
rti
c
le
I at
the
curre
n
t i
t
era
t
ion)
w
i
t
h
the
ol
d P
b
e
s
t
(the
be
st
po
si
ti
on fo
r t
h
e pa
rt
i
c
l
e
i
at i
t
e
r
at
ion
(k
-
1
)
)
,
th
en
we
sele
ct
t
h
e o
p
t
i
m
al p
b
e
st
.
In
th
e
sa
me
w
a
y
w
e
c
o
mp
a
r
e t
h
e
ne
w Gb
e
s
t
w
i
th o
l
d
G
b
e
s
t,
th
en
w
e
se
le
ct
t
h
e op
tim
al
Gb
e
s
t . The f
l
ow
ch
a
r
t
of
p
r
op
o
s
e
d
te
c
h
ni
q
u
e
is g
i
v
e
n in
F
i
gu
r
e
6.
4.3.
Ap
plication o
f
D
-
PSO fo
r ST-
S
MC
ga
in
p
a
ramet
e
rs to
ind
u
ct
i
o
n coo
k
ing
The
in
du
ct
i
o
n
coo
k
i
n
g
s
y
st
em is mo
del
e
d b
y
fi
nit
e
e
l
e
m
e
n
t a
n
al
ysi
s
and t
h
e t
e
m
p
era
t
ure
was
ca
lc
ula
t
e
d
i
n
t
h
e b
o
t
t
om o
f
t
h
e
pa
n, a
s
e
xpla
i
ne
d
i
n
se
ct
ion
3
A
pa
rt
i
c
l
e
s
w
a
r
m o
p
t
i
mi
za
ti
on i
s
u
s
e
d
i
n
t
h
i
s
w
o
rk
i
n
orde
r t
o
c
hoose
the
opt
i
m
um
gai
n
pa
ramet
e
r
s
of s
u
per-twi
st
ing sl
idi
ng
mo
d
e
c
ontr
o
ll
er (K
1,
K2
).T
h
erea
f
t
e
r
, a
t
e
ach i
t
e
r
a
t
i
on ste
p
, t
h
e
opti
m
iz
e
d
co
nt
rol
l
e
r
has be
e
n
u
s
e
d
t
o
c
ont
ro
l
t
h
e
e
v
ol
ut
i
on o
f
te
mpe
r
at
ure
o
n
t
h
e
bot
to
m of
t
h
e pa
n, a
s
s
h
o
w
n in
Fi
g
u
r
e
5.
In
thi
s
wo
r
k
:
a.
the
o
p
t
i
m
i
z
a
t
i
o
n
pro
b
le
m ca
n be
fo
rm
ul
at
ed
b
y
Mi
ni
miz
i
n
g
t
h
e foll
o
w
i
n
g fit
n
ess fu
nct
i
o
n
NT
i
i
obj
T
T
T
K
K
f
1
*
*
2
1
,
(19
)
Whe
r
e:
Is th
e to
ta
l
o
f
nu
mb
e
r
e
l
e
m
e
n
t
of me
sh
b.
Ea
ch
p
a
rt
ic
le
i
s
r
e
p
r
e
s
en
ted
by
two
p
a
r
a
meter
s
w
h
ich
,
fo
r
t
h
e
d
i
me
nsion
of
sy
st
em
(
D
=
2
),
a
r
e
K
K
K
i
2
1
,
c.
The
b
e
st
po
sit
i
o
n
t
h
at
gi
ves
th
e
be
st
fi
tne
s
s
funct
i
o
n o
f
it
h
pa
r
tic
le
i
s
d
e
f
i
ne
d
a
s
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t
J
P
o
w
Elec
& Dri
Sy
st
I
SSN
: 208
8-8
6
9
4
S
u
p
e
r-
twi
s
tin
g
sli
d
in
g mod
e
c
o
n
t
ro
lle
rs b
a
s
ed
o
n
D-
PS
O
opti
m
iza
t
i
o
n fo
r
…
(
A
b
d
e
ld
ja
li
l Abd
e
lk
ad
e
r
Me
kk
i)
1
061
pb
es
t
pb
es
t
pb
es
t
k
K
i
k
K
i
k
i
2
,
1
,
,
d.
The
best
pa
rt
ic
l
e
t
h
at
gi
ve
s
t
h
e best
fi
t
n
ess f
unc
t
i
o
n
a
m
ong
al
l
pa
rt
ic
le
s
i
s
de
fi
ne
d
a
s
Gb
e
s
t
Gbest
Gbe
s
t
k
K
k
K
k
2
1
,
A
su
p
e
r
t
w
isti
ng
co
n
t
r
o
l a
l
g
o
rith
m
is
e
m
p
l
oy
ed
to
co
ntr
o
l th
e ou
tpu
t
tem
p
er
at
ure of the
system to the
de
si
r
e
d
valu
e
,
w
h
ic
h nee
d
o
n
l
y
t
h
e
me
as
ure
m
e
n
t
of
t
h
e
t
e
mpe
r
a
t
u
r
e
o
n
t
h
e pa
n'
s
bott
o
m. F
o
r t
h
at
p
u
r
pos
e,
The
S
T
-
S
M
te
mpe
r
at
ure
c
ont
r
o
ll
er
i
s
gi
ven
bel
o
w:
)
(
)
(
2
*
1
1
1
S
si
g
n
K
J
J
S
si
g
n
S
T
K
J
T
T
r
(2
0)
W
h
e
r
e
th
e
c
u
rre
n
t
d
e
n
s
i
t
y J
is c
o
n
s
id
er
ed
as
th
e
ou
tpu
t
o
f
th
e
ST-SM
C
cont
ro
l
l
e
r
.
Th
e s
lid
in
g
v
a
r
i
ab
le
of
t
h
e
p
r
op
o
s
ed
con
t
ro
l
l
er
is th
e
te
mp
e
r
atu
r
e
e
r
ror
T
T
S
i
T
*
(2
1)
Wh
er
e:
T
*
is th
e
d
e
sir
e
d
t
e
mp
er
at
u
r
e
.
T
i
i
s
t
h
e me
as
ured
t
e
mp
er
a
t
u
r
e
in
th
e m
i
dd
le
o
f
th
e
p
a
n’
s
bo
t
t
o
m
K
K
2
1
,
A
r
e
g
a
in
s p
a
rame
te
rs
d
e
te
rm
i
n
e
d
by
D-P
S
O
me
th
od
Th
e
stru
c
t
u
r
e
di
ag
r
a
m o
f
the
pr
opo
se
d
me
thod
s (S
T-
S
M
C
ba
se
d
D
-
PSO
)
an
d (
S
T-SM
C ba
sed
PS
O)
f
o
r
t
h
e
i
nduc
t
i
o
n
co
o
k
in
g s
y
st
e
m
is su
mma
r
iz
ed
i
n
Fi
g
u
re
7.
Fi
gu
re
6.
Fl
o
w
c
h
a
r
t
f
o
r
PS
O a
n
d
D
-
P
S
O
Fi
gu
re
7.
Fl
o
w
c
h
a
r
t
f
o
r
ST
-S
MC
bas
e
d
D-P
S
O a
n
d
PS
O
f
o
r
the
c
o
oki
ng
i
n
duct
i
o
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
088
-8
6
94
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
, Vol.
11
,
No
.
2
,
Jun
e
2
020
: 1
055 –
10
64
1
062
5.
R
E
S
U
LTS
AND D
I
SCU
S
S
I
O
N
To
p
r
o
v
e t
h
e
e
ffe
ct
i
v
e
n
ess
o
f
t
h
e ST
-S
MC c
ont
rol
l
e
r me
t
hod
based
on
D
-
PS
O
a
l
g
o
ri
t
h
m desi
gne
d
t
o
enha
nc
e t
h
e
p
e
rf
orma
nce
of t
h
e i
n
d
u
ct
io
n
coo
k
i
n
g syst
em, we
ha
ve use
d
the
M
A
TLAB
s
o
ft
wa
re
. Th
e
simul
a
t
i
on
res
u
l
t
s of
u
n
c
ont
rol
l
e
d
a
n
d co
nt
rol
l
e
d sy
ste
m
are
c
o
m
p
are
d
in t
e
rms
o
f
re
fere
nce t
r
a
c
ki
n
g
,
te
mp
e
r
atu
r
e
ev
o
l
u
t
io
n
and
robu
s
t
n
e
ss aga
i
n
s
t
th
e
physi
c
a
l
p
a
r
a
m
e
t
e
r
v
a
r
i
at
io
n
s
(re
la
tiv
e
p
e
rm
e
a
b
i
l
ity
,
r
e
s
i
sti
v
ity
,
Th
er
ma
l co
ndu
c
tiv
ity
….
).
Th
e p
a
r
a
me
te
rs of
t
h
e
D
-
PSO
an
d PSO
alg
o
ri
th
ms
a
r
e
sh
own
i
n
ta
b
l
e
2.
Tabl
e 2. Para
m
e
t
e
rs
set
i
n
g
of
D
-
P
S
O
a
n
d
P
S
O
Pa
ram
e
t
e
r
s
of a
l
g
o
r
i
t
h
ms
PS
O
D-
PS
O
P
opulati
on s
i
ze
12
1
2
M
a
x ite
r
a
tion num
ber
45
4
5
C
1
m
i
n,
C1m
a
x
x
2.
075 , 2.
025
C
2
m
i
n,
C2m
a
x
x
2.
025 , 2.
125
W m
i
n,
W
m
a
x
x
0.
4 , 0.
9
C
1
2.
05
F
r
om
e
q
16
C
2
2.
05
F
r
om
e
q
17
Wei
g
ht
in
g
W
x
F
r
om
e
q
18
B
e
fo
re t
h
e
i
m
ple
m
ent
a
t
i
o
n
o
f
the
co
nt
rol
l
e
r
, Fi
g
u
re
3,
an
d F
i
gu
re
4, sh
ows
t
h
at
t
h
e t
e
mpe
r
at
ure
v
e
rsu
s
tim
e
on
th
e
p
a
n
’
s
bo
tt
o
m
e
x
ce
ed
s th
e appr
opr
ia
te
v
a
l
u
e
o
f
co
ok
ing
,
w
h
ich is
up
a
t
th
e Cur
i
e
poi
nt
(7
60
°).
A
f
t
e
r t
h
e i
m
pl
ement
a
t
i
o
n
o
f
t
h
e
prop
ose
d
c
ont
rol
l
e
rs (S
T-S
M
C
ba
sed
D
-
P
S
O
)
, a
nd
(S
T
-
S
M
C
base
d
PS
O
)
, t
h
e
o
p
t
i
m
um
val
u
es
obt
a
i
ne
d
f
o
r sup
e
r-t
wi
sti
n
g sli
d
i
ng mo
de
gai
n
para
me
t
e
rs
(k1
,
k
2
)
,
by
b
o
t
h
D-P
S
O
and
PS
O a
l
go
rit
h
ms,
w
h
ic
h
maxi
miz
e
s
th
e
per
f
o
r
ma
nc
e
of met
h
o
d
s a
r
e
sh
o
w
n i
n
Ta
bl
e.3, w
h
e
r
ea
s t
h
e
cont
rol
l
e
d
t
e
m
p
erat
ures
are
s
h
o
w
n
F
i
gure
8.
Tab
l
e
3
.
G
a
in
pa
rame
ters
ob
tain
e
d
by
D-P
S
O
and
P
S
O
A
l
gori
t
hm
s
k1
k2
Va
lue
of fitne
ss fu
nc
tion
ST
-
S
M
C
-D
-P
S
O
-
0
.
001e
5
-1.
1959e
5
0.
0793
ST
-
S
M
C
-PS
O
-
0
.
0008e
5
-1.
2
e
5
0.
0794
ST
-
S
M
C
500
-12.
03e
4
x
Fi
gu
re
.
8
. Tem
p
era
t
ure e
v
ol
u
t
i
on ve
rsu
s
t
i
me
F
r
o
m
F
i
g
u
re
8
,
we
c
a
n
obse
r
ve t
h
at
t
h
e
de
si
re
d
t
e
mpe
r
at
u
r
e
va
lue
i
s
rea
c
hed
,
w
h
e
r
e
t
h
e t
r
ac
ki
ng
e
rro
r
b
e
tw
e
e
n
th
e con
t
ro
l
l
ed
t
e
mp
era
t
u
r
e
a
n
d
d
e
si
red a
r
e
alm
o
st z
e
r
o
f
r
om
2
0
0
s
at
60
0s.
Th
is
mean
s th
at
th
e
c
h
at
te
ri
ng
ph
en
ome
non
b
ecome
s
zero
.
It can
b
e
n
o
t
ed
that
th
e p
r
opo
s
e
d
me
thod
(S
T-SM
C b
a
se
d
D-
PSO
),
pro
v
i
d
es
re
s
u
l
t
s
t
h
at
ha
ve
a
g
o
o
d
ac
cu
ra
c
y
a
n
d
a
m
o
re
sta
b
le
t
e
mpe
r
a
t
u
r
e
t
h
an
t
h
e
ot
her
me
t
hods
(
S
T-S
M
C
and
ST
-S
MC b
a
sed pso)
.
The
be
st
fi
t
n
es
s
f
unct
i
o
n
val
u
e t
h
at
gi
ve
s t
h
e
o
p
ti
mu
m
gai
n
pa
ra
me
t
e
rs
at
e
a
c
h
i
t
e
ra
t
i
o
n
s
t
e
p
,
fo
r t
h
e
tw
o
p
r
op
ose
d
me
th
od
s, a
r
e
sh
own
in
F
i
gu
r
e
9
.
W
e
can
no
te
f
r
o
m
th
i
s
f
i
gu
r
e
,
th
a
t
th
e
con
v
e
rg
en
c
e
by
D
-
PSO
,
i
s
more
promis
i
ng a
n
d
fast
er t
h
an
PS
O a
l
go
ri
t
h
m,
i
n
te
rm of mi
ni
miz
i
n
g
fi
tne
s
s
fu
nct
i
o
n v
a
lue
.
0
100
20
0
30
0
40
0
50
0
60
0
0
50
10
0
15
0
20
0
25
0
ti
m
e
(
s
)
t
e
m
per
at
ur
e
(
C
°
)
ST
-
S
M
C
b
a
s
e
d
D
-
P
S
O
t
e
m
p
er
at
u
r
e d
e
s
i
r
ed
ST
-
S
M
C
b
a
s
e
d
PS
O
ST
-
S
M
C
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
IS
SN:
208
8-8
6
9
4
Su
per
-
t
w
i
s
t
i
ng
sl
i
d
i
ng m
o
de c
ont
r
o
ll
ers base
d
on
D
-
P
S
O
o
p
t
i
m
izat
i
o
n
f
o
r … (A
bdel
d
jal
i
l Ab
del
k
a
d
e
r
M
e
k
k
i
)
1
063
Fi
gu
re
9. Be
st
fi
tne
ss val
u
e
v
e
rsus
n
u
m
be
r o
f
it
e
r
at
i
o
ns
F
i
gure.
10 sh
ow
s the
c
o
m
p
ar
ison be
t
w
ee
n si
mul
a
t
i
on
resul
t
s before
a
n
d a
f
t
e
r
t
h
e
a
ppli
c
at
ion o
f
t
h
e
pro
pose
d
c
o
ntroll
ers
.
F
r
o
m
t
h
i
s
fi
gu
re
we
can
se
e
t
h
a
t
the
prop
ose
d
me
tho
d
s gi
ve
a goo
d
reg
u
l
a
t
i
on of
te
mp
e
r
atu
r
e
v
e
r
s
u
s
t
i
me
,
d
e
sp
i
t
e
th
e pr
esenc
e
of
lar
g
e
v
a
ri
at
io
n
s
of ph
ysic
al
p
a
r
a
me
ters. W
e
can
see
al
s
o
from
F
i
gure 8
unti
l
F
i
g
u
re 1
0
,
t
h
at
t
h
e S
T
-S
MC wi
th
D
-
P
S
O
gi
ve
bet
t
er resul
t
a
n
t
s
o
f
t
e
mpe
r
at
ure t
h
a
n
t
h
e
S
T
-SM
C
w
i
th
PS
O and
S
T
-SM
C
, in
term
mo
r
e
a
c
c
u
r
a
t
e
r
e
su
lts
,
w
h
ich
si
g
n
i
fi
ca
n
t
th
at
t
h
e ST-SM
C
-D-
PSO
is
more
perfor
m
ance t
h
en
ST-
S
M
C
-
P
S
O
.
Fi
gu
re
1
0
.
Te
mpe
r
at
ure
e
vol
uti
o
n
ve
rs
us
t
i
me
be
f
o
re a
n
d a
f
t
e
r
a
ppl
i
e
d S
T
-S
MC
base
d
D-P
S
O
6.
CO
NCL
U
S
I
O
N
A
n
o
p
t
i
mi
za
ti
o
n
te
ch
ni
que
ha
s
be
e
n
a
d
opt
e
d
f
o
r t
h
i
s
w
o
rk
usi
n
g
t
h
e
D-P
S
O
t
o
se
le
ct
the
a
ppr
op
ri
at
e
gai
n
para
me
te
rs, w
h
i
c
h i
m
pr
o
v
e the
pe
rfo
r
ma
nce o
f
t
h
e
ST
-S
MC
c
o
ntr
o
ll
er, w
h
e
r
e t
h
e
i
m
p
r
o
v
e
d
S
T
-S
MC
is
empl
o
y
e
d
i
n
or
der
to
c
o
nt
rol
t
h
e
te
mpe
r
at
ure
o
f
t
h
e
i
n
duct
i
o
n
c
ooki
n
g
de
vic
e
.
Th
e m
a
in
fe
a
t
u
r
e o
f
th
is S
T
-S
M
C
te
chn
i
que
is th
e
si
mp
lic
it
y
o
f
imp
l
e
m
e
n
ta
ti
o
n
,
and
it
s r
obu
stn
e
ss.
Thi
s
st
u
d
y
s
h
o
w
s t
h
a
t
t
h
e
p
r
o
pos
ed
met
h
od (ST
-
S
M
C ba
se
d
D
-
P
S
O
) gi
ve
s a sta
b
le
p
e
rfo
r
ma
nce wi
t
h
a
go
o
d
t
e
mpera
t
ure
re
gul
at
i
o
n,
des
p
i
t
e the
p
r
ese
n
c
e
o
f
l
a
rge
va
ri
at
i
ons i
n
t
h
e
phy
si
ca
l pa
ra
met
e
r
s
o
f
t
h
e
s
y
st
em
, an
d
al
so i
t
gi
ves a
c
onst
a
nt
ou
t
put
c
o
ok
i
n
g
t
e
mp
e
r
at
ure
(1
50
°C
) w
h
i
c
h
i
s
t
h
e
de
sire
d t
e
mpe
r
at
ure
.
RE
FERE
NC
E
S
[1]
F
.
A
l
l
a
ou
i,
A.
Kans
sab
,
M
.
M
a
ta
llah
,
A.
Zo
ui
, an
d
M.
F
e
liach
i,
"
M
od
e
l
ling
an
d
O
p
timizatio
n of
In
du
ction
Coo
k
in
g
by
the
u
s
e of
M
a
g
n
eto
-
th
ermal F
i
nite
E
l
em
ent A
n
alysis and
Neu
r
al Ne
tw
ork
,
"
in
M
a
t
e
ri
al
s Sci
e
n
c
e
Fo
ru
m
, pp.
25
1-2
59, 20
14
.
[2]
M
.
F
e
liach
i
an
d
G. Dev
e
ley
,
"
M
ag
neto
-th
e
rmal beh
a
v
i
o
r
fin
i
te
elemen
t ana
l
ys
is
fo
r
ferro
m
a
g
n
etic ma
ter
i
als
i
n
i
n
d
u
c
t
io
n h
e
a
t
ing
d
e
vic
e
s
,
"
IE
EE
transact
ions on
m
agnet
ics,
vo
l.
2
7
, pp
. 5
235
-52
3
7
,
19
91
.
[3]
Z
.
Do
ng, Y. Li,
S.
Z
h
a
n
g, a
n
d
F.
Sh
a
n
g
,
"
F
uz
zy
te
mp
era
t
ure
co
ntrol of
ind
u
c
t
i
o
n
coo
k
er
,"
in
I
E
CO
N 20
17-4
3
r
d
An
nu
al Con
f
ere
n
ce o
f
th
e I
E
E
E
In
du
strial Electro
nics
S
o
c
i
ety
, pp. 3
0
5
1
-
3
0
56,
2
017
.
[4]
S
.
Jan
a
rd
han
a
n, M
.
un
N
a
bi
, a
nd P
.
M
.
Tiwar
i
,
"
A
tti
t
u
d
e
con
t
ro
l of m
a
gn
etic
actu
a
ted
s
p
ac
e
c
raft u
s
in
g
su
pe
r-
tw
is
ti
ng
al
gor
i
t
h
m
w
i
t
h
no
nl
in
ear
s
lid
in
g s
u
r
f
a
c
e
,"
i
n
20
12
1
2
th
In
ter
n
a
tiona
l
Wo
rks
h
o
p
on
V
a
r
i
ab
le S
t
ru
ctu
r
e
Sys
t
em
s
, p
p
.
46
-
51, 20
12
.
[5]
A.
Bo
uro
u
i
n
a
,
A
.
Dja
h
b
a
r, A. Cha
k
e
r
, a
n
d
Z. B
oudj
e
m
a
,
"
H
i
gh o
r
d
e
r sli
d
i
n
g
m
ode d
i
re
c
t
to
rqu
e
c
o
n
t
ro
l
of
a
DFIG
su
pp
lied b
y
a
fiv
e
-lev
el
S
V
P
W
M
inv
e
r
t
er
fo
r
th
e
wind
tu
rbin
e,"
Elek
tr
otehn
i
sk
i Ve
s
t
n
i
k,
vol
. 8
5
,
pp
. 26
3-2
7
0
,
20
18
.
[6]
Z
.
Bou
d
j
e
ma
, R. Tal
e
b, Y. Dje
r
iri,
a
n
d A. Ya
h
dou
,
"A no
vel
dire
c
t
to
rq
ue c
o
n
t
ro
l u
s
i
n
g
sec
o
n
d
o
r
d
e
r c
onti
n
uo
u
s
slid
in
g
mo
d
e
o
f
a
do
ub
ly f
e
d
i
ndu
ction
gen
e
r
a
tor for a
w
i
n
d
energ
y
co
nv
ersio
n
sys
t
em,"
T
u
r
k
is
h J
o
ur
na
l
o
f
E
l
ec
t
r
i
c
al En
gine
e
r
i
n
g
&
Comput
e
r
S
c
ie
n
c
e
s
,
v
o
l. 2
5
,
pp.
96
5-9
7
5
,
20
17.
0
5
10
15
20
25
30
35
40
45
0
0.
0
2
0.
0
4
0.
0
6
0.
0
8
0.
1
nu
m
ber
of
i
t
er
at
i
o
n
b
e
st
f
i
t
n
e
ss
va
l
u
e
D
-
PSO
PS
O
0
100
200
300
400
500
600
0
200
400
600
800
ti
m
e
(
s
)
t
e
m
per
at
ur
e (
C
°
)
bef
or
e regul
at
i
o
n
S
T
-
S
M
C
bas
ed
D
-
P
S
O
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
088
-8
6
94
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
, Vol.
11
,
No
.
2
,
Jun
e
2
020
: 1
055 –
10
64
1
064
[7]
M.
K. Kh
a
n
, K.
B.
Go
h
,
a
nd S.
K.
Sp
ur
ge
o
n
, "Se
c
o
nd ord
e
r slid
in
g
m
o
d
e
c
o
n
t
rol of a d
i
e
s
e
l
e
n
g
i
ne
,
"
Asi
an J
o
u
r
nal
of Con
t
r
o
l
,
v
o
l.
5, pp
. 6
14-6
1
9
,
20
03
.
[8]
E
.
Kö
se,
K. Ab
ac
i, H.
Kiz
m
a
z
,
S
.
Aksoy
,
a
n
d M
.
A.
Yal
ç
in,
"Sl
i
di
ng
m
o
d
e
c
ontrol
ba
se
d o
n
g
e
n
e
ti
c
a
l
go
rith
m fo
r
W
S
CC s
y
s
t
ems
include of
SV
C,
"
El
ektr
oni
ka ir Elek
tro
t
ech
n
i
ka
,
v
o
l.
19,
pp.
2
5
-2
8, 2
0
1
3
.
[9]
P.
N. Me
n
on
a
nd
R. Ana
s
ra
j, "Pa
r
ti
c
l
e Swa
r
m
Op
ti
m
i
ze
d Sli
d
i
n
g
Mo
de
Co
nt
ro
l
l
e
r
fo
r a
n
AC-DC
Bo
ost Co
nv
e
r
t
e
r,"
in
20
14
3r
d
In
te
r
n
a
t
iona
l Conf
eren
ce
on
Eco
-
fr
ie
nd
ly
Co
mp
ut
ing
a
nd Comm
un
ica
t
io
n S
y
stems
,
pp. 27
7-2
8
1
, 20
14
.
[10]
Z
.
-m
. CHE
N
, W.-j
. MENG, J.
-g
. Z
H
ANG, a
nd J.-c
.
Z
E
NG, "
S
c
h
e
m
e
o
f
sli
d
i
ng
m
o
de c
o
ntro
l b
a
se
d
on m
o
d
i
fie
d
particle sw
ar
m opti
mi
zation,"
Sys
t
ems
En
gin
eerin
g
-
T
h
eor
y
&
Practice,
vo
l.
29
, pp
. 1
37-1
4
1
,
2
009
.
[11]
S.
V.
Te
ja
,
T
.
Sh
a
n
a
v
a
s
,
a
n
d
S.
Pa
tn
aik
,
"
M
od
i
f
ie
d
PS
O ba
se
d
sli
d
i
n
g
-
m
o
d
e
c
ont
rol
l
e
r
pa
ra
m
e
te
rs for b
u
ck
con
v
erter," in
2
012
IE
EE Stu
d
e
n
ts' Con
f
e
r
e
n
ce
on Ele
c
t
ric
a
l, Elec
tron
ic
s an
d Co
m
p
ut
e
r
S
c
ie
n
c
e
, p
p
.
1-4
,
20
12
.
[12]
V.
S
a
nkard
os
s an
d P
.
Geethan
j
a
li, "
P
M
D
C mo
tor
param
e
te
r es
ti
m
a
tion
us
ing
b
i
o-i
n
s
p
ired o
p
tim
i
z
a
t
io
n algo
rith
ms,"
IE
EE Access,
vo
l. 5
,
pp
.
11
24
4-1
1
2
5
4
, 20
17
.
[13]
A.
Ka
n
s
sa
b
,
A.
Z
a
ou
i, a
n
d M. F
e
lia
c
h
i, "M
od
e
ling
a
n
d
o
p
ti
mizat
io
n of
in
du
cti
on c
o
okin
g
by t
h
e
u
s
e
of ma
gn
eto
-
th
erm
a
l fin
i
te
elemen
t
an
a
l
y
s
is an
d gen
e
tic alg
o
ri
th
ms,"
Fro
n
tier
s
of El
ectr
i
ca
l an
d
Ele
c
tron
ic
En
gineering
,
vo
l.
7,
p
p
.
31
2-3
1
7
,
2012
.
[14]
J.
-
k
. B
y
un
,
K.
C
h
oi
, H.
-
S
.
R
o
h
,
and
S
.
-
y
. H
a
hn
, "
O
pt
im
al
de
s
i
gn
pro
cedu
r
e
fo
r a
prac
tical
ind
u
ctio
n
h
e
a
t
in
g
coo
k
er,"
IEE
E
tra
n
s
a
ctio
ns
on
m
a
gnetics
,
vo
l.
3
6
,
pp.
1
3
9
0
-
13
93, 20
00
.
[15]
C. L
a
scu, I
.
Bo
ld
ea, an
d F
.
Bla
a
b
jerg,
"S
u
p
er-tw
i
s
t
ing
slid
in
g
mo
de co
ntr
o
l of
tor
q
ue an
d
f
l
ux
in
p
e
rman
ent
magn
e
t
sy
nch
r
ono
us
ma
chine dr
ives
," in
IECON 201
3-3
9
th An
nua
l Con
f
eren
ce
o
f
th
e
IEEE Ind
u
s
t
rial Electro
nics
S
o
cie
t
y
,
p
p
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71
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17
6
,
20
1
3
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J. L
i
u,
S. Va
z
q
ue
z
,
L.
W
u
, A.
M
a
rq
ue
z,
H
.
Ga
o,
a
n
d
L.
G.
Fra
n
que
l
o
, "E
xte
n
d
e
d
sta
t
e ob
se
rv
e
r-base
d
sl
id
in
g-m
ode
cont
rol for
t
h
ree-phas
e
power
co
nvert
e
rs,"
IEEE Transact
ions
on In
dustrial
Electronics,
vo
l. 6
4
,
p
p
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22
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,
2
016
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[17]
M.
K. Kh
a
n
, S.
K.
Spu
r
ge
o
n
,
a
nd P.
F.
Pu
le
sto
n
, "Ro
b
u
s
t sp
ee
d
co
nt
ro
l o
f
a
n
a
u
tom
o
ti
ve
e
n
gi
ne usi
n
g
se
c
o
nd ord
e
r
s
l
id
in
g mo
d
e
s
,
"
i
n
2
0
0
1
E
u
ro
pe
an
Co
nt
ro
l
Co
nfere
n
c
e
(E
CC)
,
p
p
.
97
4-97
8
,
20
01
.
[18]
M. Alam, K. K
u
mar, and
A. Mathur,
"
E
co
no
mic
lo
ad d
i
sp
atch
co
nsidering
v
a
lv
e-
po
int
effe
cts u
s
i
n
g
time
vary
in
g
con
s
tric
tion
fac
t
or bas
e
d
part
icl
e
s
w
arm
op
ti
m
i
zation
,
"
in
2
015
IEEE
UP S
e
c
t
i
on Co
nf
e
r
e
n
ce
o
n
Ele
c
t
ric
a
l
Com
puter
and
E
l
ec
tr
on
ics
(UPCO
N
)
, p
p
.
1-6,
20
15
.
[19]
Y. S
h
i
an
d
R. C.
Eb
erhart
, "Emp
iric
al st
ud
y of
p
a
rti
c
le
swarm
op
timization
,
"
in
Pro
ceeding
s
of th
e
1
9
9
9
Cong
res
s
o
n
E
v
o
l
ut
io
na
ry
Compu
t
a
t
i
o
n-CE
C9
9 (Ca
t
.
No
.
99
TH84
06
)
,
p
p
.
1
9
4
5
-1
9
5
0
,
1
999.
[2
0]
S.
Ma
nd
al,
S.
Ghsh
a
l
,
R. Kar, D.
M
a
n
d
al, an
d A. S
h
ivare,
"
S
warm in
tellig
e
n
ce
ba
sed
o
p
t
i
m
a
l
l
i
n
e
a
r
fir h
i
gh
pa
ss filt
e
r
de
si
gn
u
s
i
n
g
particle sw
arm
opt
i
mi
zati
on
w
i
th
cons
t
r
icti
o
n
fa
ctor
and
in
erti
a
w
e
igh
t
a
ppro
ach,"
in
201
1
IE
EE
St
ude
nt
Con
f
er
enc
e
on
R
e
s
e
ar
ch a
n
d
Dev
e
lopm
ent
,
20
11,
pp
.
3
5
2
-
3
57.
[20]
M.
Sa
l
i
m
a
n
d
M.
Sa
rv
i,
"In
d
u
c
t
io
n Mo
t
o
r Sp
ee
d Co
n
t
ro
l
Us
i
n
g Indi
rect Z
-
s
o
urce Matr
i
x
Conv
ert
e
r w
ith PSO-PI
Cont
rol
l
e
r
under Various
Br
eak
Conditions,
"
In
t
e
rn
at
io
na
l
J
ourna
l of
P
o
we
r
Ele
c
t
ron
i
c
s
a
nd Driv
e Sy
ste
m
s
(IJP
E
DS)
,
vo
l. 3
,
no
.
1
,
pp
.
41
-5
2
,
2
013
.
[21]
F
.
A
.
H
a
san
an
d
L.
J. R
a
sh
ad,
"F
ractio
na
l-o
r
de
r P
I
D
co
ntro
ller
for
per
m
an
en
t
mag
n
e
t
DC
mo
to
r b
a
sed
on
P
S
O
alg
o
rith
m,"
In
tern
at
io
na
l J
o
urn
a
l of
Po
we
r
El
ec
t
r
o
n
i
c
s an
d
Dri
v
e Sy
ste
m
s (IJP
EDS),
v
o
l
.
1
0
, no
. i4, pp
. 172
4-
17
33
, 2
019
.
[22]
M
.
Bengo
urin
a,
M
.
Ra
h
li, S
.
Saa
d
i,
and
L. Has
s
a
i
n
e
, "P
SO
based D
i
rect
Pow
e
r
C
o
ntr
o
l
for
a Multi
funct
i
onal
Grid
Con
n
ected
P
h
o
t
ov
oltai
c
S
y
stem
, "
In
ter
natio
na
l J
o
u
r
n
a
l of Pow
e
r Ele
c
tro
n
ics
an
d Dr
ive Sys
t
em
(I
JPED
S),
vo
l. 9
,
p
p
.
61
0-6
2
1
,
2018
.
[23]
Y.
Ah
me
d
a
nd
A.
Ho
ba
lla
h, "Ada
pt
iv
e fil
t
e
r-FLC
in
te
g
r
ati
o
n
fo
r t
o
rq
u
e
rip
p
l
e
s min
i
mi
za
ti
on i
n
PMSM u
s
i
n
g
PSO,
"
work,
vo
l. 3, pp
. 4, 20
19
.
[24]
S
.
W. Sh
neen
,
C
.
M
a
o, and
D
.
W
a
ng,
"
A
d
v
an
ced
o
p
tima
l
P
S
O, F
u
zzy
and
P
I
con
t
r
o
ller with P
M
S
M
and
WTGS
at
5H
z
side of
gen
e
rat
i
o
n
a
n
d
50
H
z
S
i
de
o
f
G
r
id
,"
In
te
rn
atio
na
l Jo
urna
l
o
f
Po
we
r E
l
e
c
t
ro
n
i
c
s
a
nd
Driv
e
Sy
st
e
m
s
(IJP
E
DS)
,
v
o
l.
7,
p
p
.
1
73,
2
0
16.
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