I
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rna
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io
na
l J
o
urna
l o
f
E
lect
rica
l a
nd
Co
m
p
ute
r
E
ng
in
ee
ring
(
I
J
E
CE
)
Vo
l.
10
,
No
.
1
,
Feb
r
u
ar
y
2020
,
p
p
.
223
~
232
I
SS
N:
2
0
8
8
-
8708
,
DOI
: 1
0
.
1
1
5
9
1
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i
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.
v
1
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i
1
.
pp
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3
-
232
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[
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to
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ativ
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[
5
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.
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[
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[
7
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8
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.
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
10
,
No
.
1
,
Feb
r
u
ar
y
2
0
2
0
:
223
-
232
224
in
[
9
]
f
o
r
o
f
f
-
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e
id
en
ti
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o
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o
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M
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n
v
er
g
e
d
ir
ec
tl
y
to
t
h
e
g
lo
b
al
m
i
n
i
m
a.
P
SO,
d
if
f
er
en
tial
e
v
o
lu
tio
n
(
DE
)
,
an
d
s
o
m
e
o
f
t
h
eir
r
ec
en
t
v
ar
ia
n
t
s
f
o
r
in
s
it
u
e
f
f
icie
n
c
y
d
eter
m
i
n
atio
n
o
f
in
d
u
ctio
n
m
o
to
r
w
i
th
o
u
t
p
er
f
o
r
m
i
n
g
n
o
-
lo
ad
test
ar
e
p
r
esen
ted
i
n
[
1
3
]
.
A
n
i
m
p
r
o
v
ed
P
SO
ca
ll
ed
S
y
s
te
m
at
ic
Mu
tatio
n
b
a
s
ed
P
ar
ticle
S
w
ar
m
Op
ti
m
izatio
n
[
1
4
]
is
ap
p
lied
t
o
p
ar
am
eter
esti
m
atio
n
an
d
e
f
f
icien
c
y
d
eter
m
i
n
atio
n
,
s
o
th
at
p
ar
am
eter
v
ar
iatio
n
ef
f
ec
t
is
ta
k
e
n
i
n
to
ac
c
o
u
n
t.
A
d
y
n
a
m
ic
r
ea
l
-
co
d
ed
g
en
etic
a
lg
o
r
ith
m
i
s
ap
p
lied
in
[
1
5
]
to
esti
m
ate
t
h
e
b
o
th
o
f
elec
tr
ical
an
d
m
ec
h
an
ical
p
ar
am
eter
s
.
I
n
[
1
6
]
a
n
e
w
m
e
th
o
d
is
p
r
o
p
o
s
ed
f
o
r
th
e
p
ar
a
m
eter
s
e
s
ti
m
atio
n
o
f
th
e
s
q
u
ir
r
el
-
ca
g
e
in
d
u
ct
io
n
m
o
to
r
s
(
in
th
e
s
i
n
g
le
-
ca
g
e
an
d
d
o
u
b
le
-
ca
g
e
m
o
d
els)
b
ased
o
n
ar
tif
icial
n
e
u
r
al
n
et
w
o
r
k
(
A
N
N)
an
d
ad
ap
tiv
e
n
eu
r
o
f
u
zz
y
in
f
er
e
n
ce
s
y
s
te
m
(
A
NFI
S).
T
h
e
m
et
h
o
d
p
r
o
p
o
s
ed
in
[
1
7
]
,
is
b
ased
o
n
th
e
d
if
f
er
en
tial
e
v
o
lu
t
io
n
alg
o
r
ith
m
.
I
t
esti
m
ate
s
t
h
e
p
ar
a
m
eter
s
o
f
t
h
e
eq
u
i
v
alen
t
elec
tr
ical
cir
cu
it,
s
u
ch
as
s
tato
r
a
n
d
r
o
to
r
r
esis
tan
ce
s
an
d
leak
a
g
e
i
n
d
u
c
-
ta
n
ce
s
,
t
h
e
m
a
g
n
etiz
in
g
i
n
d
u
cta
n
ce
,
a
n
d
also
m
ec
h
an
ical
p
ar
a
m
eter
s
,
s
u
c
h
as
m
o
m
en
t
o
f
in
er
tia
an
d
th
e
f
r
ict
io
n
co
ef
f
i
cien
t.
T
h
e
p
er
f
o
r
m
a
n
ce
o
f
th
i
s
tech
n
iq
u
e
is
ev
al
u
ated
f
o
r
th
r
ee
d
if
f
er
e
n
t
in
p
u
t
s
ig
n
al
s
:
cu
r
r
en
t
s
ig
n
al
o
f
a
p
h
ase
ass
o
ciate
d
w
ith
t
h
e
s
p
ee
d
m
ea
s
u
r
ed
f
r
o
m
atac
h
o
g
en
er
at
o
r
,
cu
r
r
en
t
s
ig
n
al
o
f
a
p
h
ase
ass
o
ciate
d
w
it
h
th
e
s
p
ee
d
ac
q
u
ir
ed
f
r
o
m
a
to
r
q
u
e
m
e
ter
,
an
d
o
n
l
y
th
e
c
u
r
r
en
t
s
i
g
n
a
l
o
f
o
n
e
p
h
ase.
T
o
esti
m
ate
t
h
e
eq
u
i
v
ale
n
t
cir
c
u
i
t
p
ar
a
m
eter
s
,
is
p
r
esen
ted
i
n
[
1
8
]
an
o
p
tim
iza
tio
n
ap
p
r
o
ac
h
b
ased
o
n
s
w
ar
m
,
w
ic
h
i
s
ca
lled
t
h
e
A
r
ti
f
icial
B
ee
C
o
lo
n
y
(
A
B
C
)
o
p
ti
m
iz
atio
n
.
b
y
t
h
is
ap
p
r
o
ac
h
.
T
w
o
d
if
f
er
e
n
t
eq
u
i
v
ale
n
t
cir
cu
its
ar
e
i
m
p
le
m
e
n
ted
f
o
r
th
e
p
ar
a
m
eter
esti
m
atio
n
s
c
h
e
m
e;
o
n
e
w
it
h
p
ar
allel
an
d
t
h
e
o
th
e
r
w
it
h
s
er
ies
m
ag
n
etiza
tio
n
cir
cu
it.
I
n
s
p
ite
o
f
th
eir
e
f
f
ec
t
iv
e
n
es
s
to
s
o
lv
e
co
m
p
lex
n
o
n
-
li
n
ea
r
o
p
ti
m
izatio
n
p
r
o
b
lem
s
,
t
h
e
ev
o
lu
tio
n
ar
y
m
et
h
o
d
s
ar
e
c
h
ar
ac
ter
ized
b
y
p
r
e
m
atu
r
e
co
n
v
er
g
e
n
ce
a
n
d
th
e
y
ar
e
g
r
ee
d
y
i
n
co
m
p
u
ti
n
g
ti
m
e
.
T
h
er
ef
o
r
e,
a
r
ec
en
t
g
lo
b
al
o
p
ti
m
izat
io
n
tech
n
iq
u
e,
ca
lled
Alien
o
r
m
e
th
o
d
h
a
s
b
ee
n
p
r
o
p
o
s
ed
an
d
in
tr
o
d
u
ce
d
i
n
a
n
y
s
tu
d
ie
s
[
1
9
-
2
1
]
.
I
t
w
as
s
u
cc
e
s
s
f
u
l
l
y
u
s
ed
to
s
o
l
v
e
d
i
f
f
er
e
n
t
k
in
d
s
o
f
e
n
g
in
ee
r
i
n
g
p
r
o
b
le
m
s
[
2
2
-
2
5
]
.
T
h
is
m
et
h
o
d
is
b
ased
o
n
tr
an
s
f
o
r
m
i
n
g
t
h
e
m
u
ltid
i
m
en
s
io
n
al
p
r
o
b
le
m
to
o
n
e
-
d
i
m
e
n
s
io
n
al
p
r
o
b
lem
.
I
n
t
h
is
ca
s
e
t
h
e
g
lo
b
al
m
i
n
i
m
u
m
s
ea
r
ch
b
ec
o
m
es
s
i
m
p
ler
.
T
h
is
p
ap
er
p
r
o
p
o
s
es
an
o
p
ti
m
izatio
n
ap
p
r
o
ac
h
b
ased
o
n
A
lie
n
o
r
m
et
h
o
d
,
to
esti
m
a
t
e
in
d
u
ctio
n
m
ac
h
in
e
p
ar
a
m
eter
s
.
T
h
e
o
p
t
i
m
izatio
n
p
r
o
ce
s
s
s
tar
ts
w
it
h
tr
an
s
f
o
r
m
i
n
g
t
h
e
m
u
lt
id
i
m
e
n
t
io
n
el
p
r
o
b
lèm
e
to
o
n
e
-
d
i
m
en
tio
n
al
o
n
e.
So
,
t
h
e
elec
tr
ical
a
n
d
m
ec
h
a
n
ical
p
ar
am
eter
s
ar
e
g
iv
e
n
f
u
n
c
tio
n
o
f
o
n
e
v
ar
iab
le.
Usi
n
g
o
n
l
y
t
h
e
s
tar
tin
g
s
tato
r
cu
r
r
en
t
a
n
d
th
e
co
r
r
esp
o
n
d
in
g
p
h
ase
v
o
lta
g
e,
b
o
th
elec
tr
ic
al
an
d
m
ec
h
a
n
ical
p
ar
am
eter
s
ar
e
d
eter
m
i
n
ed
.
T
h
is
is
ac
co
m
p
li
s
h
ed
b
y
m
in
i
m
izatio
n
o
f
th
e
q
u
ad
r
atic
o
u
tp
u
t
er
r
o
r
b
etw
ee
n
th
e
m
ea
s
u
r
ed
cu
r
r
en
t
a
n
d
th
e
co
m
p
u
ted
o
n
e.
I
n
o
r
d
er
to
in
v
esti
g
a
te
th
e
f
ea
s
ib
ilit
y
o
f
t
h
e
p
r
o
p
o
s
ed
esti
m
at
io
n
m
et
h
o
d
,
test
s
o
n
t
w
o
b
e
n
ch
m
ar
k
f
u
n
ct
io
n
s
a
n
d
o
n
t
h
e
m
ac
h
in
e
s
i
m
u
lated
d
ata
h
a
v
e
b
ee
n
ac
h
eiv
ed
.
T
h
is
alg
o
r
ith
m
h
a
s
b
ee
n
tes
te
d
ex
p
er
i
m
en
tal
l
y
b
y
u
s
i
n
g
m
ea
s
u
r
ed
d
ata
f
r
o
m
a
1
.
5
KW
i
n
d
u
ctio
n
m
ac
h
i
n
e.
T
o
v
er
if
y
t
h
e
e
f
f
ec
tiv
e
n
es
s
o
f
th
e
p
r
o
p
o
s
ed
m
eth
o
d
,
t
h
e
o
b
tain
ed
r
es
u
lts
ar
ec
o
m
p
ar
ed
w
i
t
h
t
h
e
G
A
tech
n
iq
u
e
r
esu
lt
s
an
d
th
e
m
ea
s
u
r
ed
o
n
es
.
T
h
e
p
ap
er
is
o
r
g
an
ized
as
f
o
l
lo
w
s
.
Sectio
n
2
p
r
esen
ts
t
h
e
r
esear
ch
m
eth
o
d
.
I
n
t
h
i
s
s
ec
tio
n
it
f
i
n
d
s
,
th
e
i
n
d
u
c
tio
n
m
ac
h
i
n
e
m
o
d
el,
th
e
id
en
ti
f
icat
io
n
m
et
h
o
d
an
d
a
clar
i
f
icatio
n
o
f
t
h
e
Al
ien
o
r
m
e
th
o
d
.
T
h
e
m
et
h
o
d
is
u
s
ed
to
d
eter
m
in
e
s
i
m
u
lta
n
eo
u
s
l
y
th
e
elec
tr
ic
al
an
d
m
ec
h
a
n
ical
p
ar
a
m
ete
r
s
o
f
an
in
d
u
ctio
n
m
ac
h
in
e
f
r
o
m
t
h
e
m
ea
s
u
r
ed
cu
r
r
en
t
a
n
d
t
h
e
co
r
r
esp
o
n
d
in
g
p
h
a
s
e
v
o
ltag
e.
R
e
s
u
lts
a
n
d
d
is
c
u
s
s
io
n
ar
e
s
u
m
er
ized
in
S
ec
tio
n
3
,
w
h
er
e,
t
h
e
s
i
m
u
latio
n
an
d
th
e
ex
p
e
r
i
m
en
tal
r
esu
lt
s
ar
e
g
iv
e
n
to
s
h
o
w
t
h
e
v
al
id
it
y
o
f
th
e
d
ev
elo
p
ed
m
et
h
o
d
.
T
h
e
p
a
p
er
i
s
co
m
p
leted
b
y
a
co
n
cl
u
s
i
o
n
in
S
ec
tio
n
4
.
2.
RE
S
E
ARCH
M
E
T
H
O
D
2
.
1
.
I
nd
uct
io
n
m
a
ch
ine
m
o
d
el
Fo
r
th
is
s
t
u
d
y
,
it
h
a
s
u
s
ed
th
e
I
M
m
at
h
e
m
atica
l
m
o
d
el
(
p
ar
k
s
’
m
o
d
el)
p
r
esen
ted
as
f
o
llo
w
b
y
u
s
i
n
g
th
e
u
s
u
al
h
y
p
o
t
h
es
is
(
t
h
e
s
a
tu
r
atio
n
ef
f
ec
t
an
d
s
k
i
n
ef
f
e
ct
ar
e
n
e
g
lecte
d
,
o
n
l
y
o
n
e
s
p
ac
e
h
ar
m
o
n
ic
is
co
n
s
id
er
ed
,
th
e
air
g
ap
co
n
s
ta
n
t)
.
T
h
e
p
r
esen
t i
n
d
u
ct
io
n
m
ac
h
in
e
eq
u
at
io
n
s
ar
e
r
elate
d
to
a
r
ef
er
en
ce
lin
k
ed
to
th
e
s
tato
r
[
1
]
.
(
1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
A
lien
o
r
meth
o
d
a
p
p
lied
to
in
d
u
ctio
n
ma
ch
i
n
e
p
a
r
a
mete
r
s
id
en
tifi
ca
tio
n
(
La
tifa
K
h
emic
i
)
225
W
h
er
e:
[
]
(
2
)
[
]
(
3
)
[
]
(
4
)
[
]
(
5
)
T
h
e
m
ec
h
a
n
ical
eq
u
atio
n
is
g
i
v
en
a
s
f
o
llo
w
:
(
6
)
(
)
(
7
)
(
8
)
T
h
e
d
y
n
a
m
ic
m
o
d
el
w
it
h
f
o
u
r
elec
tr
ical
p
ar
am
e
ter
s
an
d
t
w
o
m
ec
h
a
n
ical
p
ar
a
m
eter
s
is
f
o
r
m
u
lated
b
y
th
e
f
o
llo
w
i
n
g
s
et
(
9
)
:
{
(
)
(
)
(
9
)
C
o
n
s
eq
u
en
tl
y
,
t
h
e
p
ar
a
m
eter
s
v
ec
to
r
is
g
i
v
e
n
b
y
:
[
]
T
h
u
s
,
th
e
I
M
is
c
h
ar
ac
t
er
ized
b
y
th
e
p
ar
a
m
eter
s
v
ec
to
r
.
T
h
is
v
ec
to
r
is
o
b
tain
ed
f
r
o
m
th
e
m
ea
s
u
r
e
m
e
n
t o
f
t
h
e
cu
r
r
e
n
t a
n
d
th
e
co
r
r
esp
o
n
d
in
g
v
o
lta
g
e
ap
p
lied
to
th
e
m
ac
h
i
n
e.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
10
,
No
.
1
,
Feb
r
u
ar
y
2
0
2
0
:
223
-
232
226
2
.
2
.
I
dentif
ica
t
io
n m
et
ho
d
T
o
esti
m
ate
th
e
p
ar
a
m
eter
s
v
e
cto
r
,
th
e
o
b
j
ec
tiv
e
f
u
n
ctio
n
E
is
m
in
i
m
ized
b
y
th
e
A
lie
n
o
r
m
et
h
o
d
.
T
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
m
i
n
i
m
ize
th
e
q
u
ad
r
atic
er
r
o
r
b
etw
e
en
th
e
ex
p
er
i
m
e
n
tal
cu
r
r
e
n
t
a
n
d
th
e
ca
lcu
late
o
n
e
.
T
h
e
o
b
j
ec
tiv
e
f
u
n
ctio
n
i
s
g
iv
e
n
b
y
:
∑
(
)
(
1
0
)
W
h
er
e
n
is
th
e
n
u
m
b
er
o
f
t
h
e
ex
p
er
i
m
e
n
tal
v
alu
e
s
.
T
h
e
u
s
ed
id
en
tif
ica
tio
n
m
eth
o
d
is
p
r
esen
ted
in
F
ig
u
r
e
1
.
T
o
esti
m
ate
t
h
e
v
ec
to
r
o
f
p
ar
a
m
eter
s
,
th
e
o
b
j
ec
tiv
e
f
u
n
ctio
n
E
is
m
i
n
i
m
ized
b
y
u
s
in
g
t
h
e
A
lie
n
o
r
m
et
h
o
d
.
I
cali
Re
a
l
In
d
u
c
ti
o
n
m
a
c
h
in
e
In
d
u
c
ti
o
n
m
a
c
h
in
e
m
a
th
e
m
a
ti
c
a
l
m
o
d
e
l
E
s
ti
m
a
tio
n
o
f
p
ar
am
eter
s
b
y
A
lie
n
o
r
m
et
h
o
d
I
m
esi
U
E
<
P
v
y
es
no
Fig
u
r
e
1
.
B
lo
ck
d
iag
r
a
m
o
f
t
h
e
i
d
en
tific
atio
n
m
et
h
o
d
2
.
3
.
T
he
Alieno
r
m
et
ho
d
T
h
e
A
lien
o
r
m
e
th
o
d
is
b
ased
o
n
tr
an
s
f
o
r
m
i
n
g
a
m
u
l
ti
-
di
m
en
s
io
n
al
o
p
ti
m
izatio
n
p
r
o
b
le
m
to
a
o
n
e
d
i
m
en
s
io
n
al
o
p
ti
m
izatio
n
p
r
o
b
le
m
u
s
in
g
a
r
ed
u
cin
g
tr
an
s
f
o
r
m
atio
n
[
2
1
]
.
T
h
e
b
ased
r
ed
u
cin
g
tr
a
n
s
f
o
r
m
at
io
n
u
s
e
t
h
e
p
r
o
p
er
ties
o
f
t
h
e
A
r
ch
i
m
ed
es
’
s
p
ir
al
[
2
2
]
,
w
h
er
e
v
ar
iab
les
ar
e
d
eter
m
in
ed
b
y
th
e
ir
p
o
lar
co
o
r
d
in
ates.
F
o
r
ex
a
m
p
le:
w
h
en
i
t h
as t
w
o
v
ar
iab
les
x
1
an
d
x
2
.
I
n
f
ir
s
t,
th
ese
o
n
es
ar
e
d
eter
m
i
n
ed
as:
an
d
(
1
1
)
T
h
e
r
elatio
n
b
et
w
ee
n
r
a
n
d
θ
ca
n
b
e
f
i
n
ed
b
y
th
e
A
r
c
h
i
m
ed
es’
s
p
ir
al,
w
h
er
e
t
h
e
e
q
u
atio
n
is
.
(
Fix
ed
a
n
d
d
esti
n
ed
to
te
n
d
er
to
ze
r
o
)
.
T
h
en
,
t
h
e
t
w
o
v
ar
iab
les
ar
e
o
b
tain
ed
a
s
f
o
llo
w
:
(
)
(
)
(
1
2
)
Fin
all
y
,
t
h
e
t
w
o
v
ar
iab
les
ar
e
ex
p
r
ess
ed
a
s
a
f
u
n
cti
o
n
o
f
t
h
e
u
n
iq
u
e
v
ar
iab
le
.
T
h
is
r
ed
u
cin
g
tr
a
n
s
f
o
r
m
atio
n
ca
n
b
e
u
s
ed
f
o
r
n
v
ar
iab
les
(
n
>
2
)
.
B
u
t
w
h
e
n
t
h
e
n
u
m
b
er
o
f
v
ar
iab
les
in
cr
ea
s
e,
it
w
i
ll
b
e
d
if
f
ic
u
lt
to
d
eter
m
i
n
e
th
e
f
u
n
ctio
n
s
h
i
(
θ
)
.
B
ec
au
s
e
t
h
e
y
ar
e
n
o
t
o
b
tain
ed
in
o
n
l
y
o
n
e
s
tep
[
2
6
]
,
w
h
er
e
t
h
e
co
m
p
u
ti
n
g
ti
m
e
i
s
p
r
o
p
o
r
tio
n
al
to
th
e
n
u
m
b
er
o
f
v
ar
iab
les.
Af
ter
,
it
h
a
s
p
r
o
p
o
s
ed
m
a
n
y
r
ed
u
ci
n
g
tr
an
s
f
o
r
m
atio
n
s
[
2
7
]
w
h
ich
en
ab
le
u
s
to
d
eter
m
i
n
e
t
h
e
f
u
n
c
ti
o
n
s
h
i
(
θ
)
i
n
o
n
l
y
o
n
ce
,
w
h
ic
h
b
r
in
g
s
b
ac
k
f
o
r
u
s
to
f
ac
ilit
ate
ca
lcu
lat
io
n
s
w
h
en
w
e
h
a
v
e
a
lar
g
e
n
u
m
b
er
o
f
v
ar
iab
les.
T
h
e
A
lie
n
o
r
’
s
m
et
h
o
d
ca
n
b
e
u
s
ed
f
o
r
s
o
lv
i
n
g
a
n
o
p
ti
m
iza
tio
n
p
r
o
b
lem
w
h
ich
i
s
s
u
m
m
ar
ized
as
f
o
ll
o
w
:
(
)
∏
[
]
(
)
(
1
3
)
W
h
er
e
f
is
a
co
n
tin
u
o
u
s
f
u
n
cti
o
n
.
T
h
e
v
ar
iab
les
x
i
ar
e
s
u
b
s
tit
u
te
d
b
y
t
h
e
r
ed
u
cin
g
tr
an
s
f
o
r
m
ati
o
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
A
lien
o
r
meth
o
d
a
p
p
lied
to
in
d
u
ctio
n
ma
ch
i
n
e
p
a
r
a
mete
r
s
id
en
tifi
ca
tio
n
(
La
tifa
K
h
emic
i
)
227
x
i
=h
i
(
θ)
,
i=1
……
……
……
,
n
(
1
4
)
So
,
w
e
o
b
tain
t
h
e
f
o
llo
w
i
n
g
ap
p
r
o
ac
h
ed
p
r
o
b
lem
[
]
(
)
(
1
5
)
W
h
er
e
(
)
(
(
)
(
)
)
,
w
h
ic
h
is
a
f
u
n
ctio
n
w
it
h
a
s
in
g
le
v
ar
iab
le.
is
th
e
m
a
x
i
m
u
m
v
al
u
e
o
f
θ.
T
o
s
o
lv
e
t
h
i
s
o
n
e
-
d
i
m
e
n
s
io
n
a
l
m
in
i
m
izatio
n
p
r
o
b
le
m
,
w
e
ca
n
f
o
l
lo
w
s
tep
s
g
i
v
en
in
[
2
1
,
2
6
]
.
So
th
e
in
ter
v
al
[
]
is
d
is
cr
ed
ited
in
to
N
p
o
in
ts
,
w
ith
a
ch
o
s
en
s
tep
,
w
h
er
e
.
T
h
en
w
e
lo
o
k
f
o
r
th
e
ab
s
o
lu
te
m
i
n
i
m
u
m
i
n
th
e
s
et
(
)
,
w
h
er
e
.
.
On
ce
th
e
g
lo
b
al
s
o
lu
tio
n
o
f
th
i
s
o
p
ti
m
izatio
n
p
r
o
b
lem
is
o
b
tain
ed
f
o
r
a
,
th
e
r
ed
u
cin
g
tr
an
s
f
o
r
m
a
tio
n
g
iv
e
n
in
(
1
4
)
is
u
s
ed
to
d
ed
u
ce
th
e
v
ar
iab
les
as f
o
ll
o
w
s
:
(
)
(
1
6
)
2
.
3
.
1
.
T
he
us
ed
re
d
ucing
t
ra
ns
f
o
r
m
a
t
io
n
I
n
th
is
p
ar
t
w
e
p
r
ese
n
t
t
h
e
r
ed
u
ci
n
g
tr
an
s
f
o
r
m
atio
n
w
h
i
ch
is
u
s
ed
to
tr
an
s
f
o
r
m
th
e
m
i
n
i
m
ized
f
u
n
ctio
n
to
a
f
u
n
c
tio
n
o
f
o
n
l
y
a
s
in
g
le
v
ar
iab
le.
W
e
h
av
e
u
s
e
th
e
k
o
n
f
é
-
c
h
er
r
u
a
u
lt
[
2
2
]
tr
an
s
f
o
r
m
atio
n
,
w
h
ich
is
d
ef
i
n
ed
b
y
:
(
)
(
⁄
)
[
(
)
(
)
(
)
]
(
1
7
)
T
h
e
C
h
o
ice
o
f
th
e
p
ar
a
m
e
ter
s
is
g
i
v
e
n
as f
lo
w
s
:
w
i
and
ar
e
t
w
o
s
lo
w
l
y
g
r
o
w
in
g
s
eq
u
e
n
ce
s
.
a
i
an
d
b
i
ar
e
th
e
b
o
u
n
d
ed
v
alu
e
o
f
th
e
v
ar
iab
le
x
i
(
[
]
)
.
[
]
.
W
h
er
e
is
th
e
m
a
x
i
m
u
m
v
al
u
e
o
f
θ.
So
,
ea
ch
r
ed
u
ctio
n
tr
an
s
f
o
r
m
atio
n
h
as
a
m
et
h
o
d
f
o
r
ca
lcu
late
t
h
e
θ
max
.
Fo
r
th
is
o
n
e
w
e
ca
n
ca
lcu
la
te
th
e
θ
max
as
f
lo
w
[
2
6
,
2
8
]
:
(
(
)
(
)
)
(
1
8
)
W
h
er
e
:
(
1
9
)
3.
RE
SU
L
T
S
AND
D
I
SCU
SS
I
O
N
3
.
1
.
Si
m
ula
t
io
n r
esu
lt
s
A
n
u
m
er
ical
p
r
o
g
r
a
m
b
ased
o
n
A
lie
n
o
r
m
e
th
o
d
is
ap
p
lied
to
s
i
m
u
ltan
eo
u
s
l
y
a
b
en
ch
m
ar
k
f
u
n
c
tio
n
s
an
d
a
s
i
m
u
lated
d
ata
o
f
an
i
n
d
u
ctio
n
m
ac
h
in
e.
3
.
1
.
1
.
B
ench
m
a
r
k
f
un
ct
io
n
s
T
o
p
r
o
v
e
th
e
v
alid
i
t
y
o
f
t
h
e
K
o
n
f
é
-
C
h
er
r
u
al
t
tr
an
s
f
o
r
m
atio
n
,
w
e
ar
e
b
r
o
u
g
h
t
b
ac
k
to
ap
p
ly
it
o
n
t
w
o
b
en
ch
m
ar
k
f
u
n
c
tio
n
s
.
T
ab
le
1
s
h
o
w
s
th
e
m
i
n
i
m
izat
io
n
p
r
o
b
le
m
s
w
h
ic
h
ar
e
ch
o
s
en
.
T
h
e
r
ed
u
ci
n
g
tr
an
s
f
o
r
m
atio
n
d
ef
i
n
ed
b
y
t
h
e
(
1
7
)
is
u
s
ed
to
d
e
f
in
e
t
h
e
v
ar
ia
b
les
.
W
ith
[
]
w
h
ic
h
i
s
ca
lc
u
lated
ac
co
r
d
in
g
to
(
1
8
)
.
I
n
T
ab
le
2
th
e
v
a
lu
e
s
o
f
an
d
ar
e
illu
s
tr
ated
.
is
ca
lcu
lated
b
y
(
1
8
)
,
(
1
6
)
an
d
is
t
h
e
o
b
tain
ed
s
o
lu
t
io
n
o
f
t
h
e
p
r
o
b
lem
d
e
f
in
ed
b
y
(
1
5
)
.
T
h
e
o
p
ti
m
a
l
s
o
l
u
tio
n
s
ar
e
d
ed
u
ce
d
u
s
in
g
th
e
r
ed
u
cin
g
tr
an
s
f
o
r
m
atio
n
(
1
7
)
w
h
er
e
.
T
ab
le
3
s
h
o
w
s
t
h
e
g
i
v
en
an
d
th
e
s
i
m
u
lated
s
o
lu
tio
n
s
.
A
cc
o
r
d
in
g
to
th
e
s
i
m
u
lat
io
n
r
es
u
lt
s
p
r
ese
n
ted
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
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8
8
-
8708
I
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p
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,
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10
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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p
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g
I
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N:
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229
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4
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h
o
w
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
10
,
No
.
1
,
Feb
r
u
ar
y
2
0
2
0
:
223
-
232
230
th
e
s
u
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RE
F
E
R
E
NC
E
S
[1
]
E.
C.
Qu
isp
e
,
I.
D
.
L
ó
p
e
z
,
F
.
J.
T
.
E.
F
e
rre
ira,
V
.
S
o
u
sa
,
“
Un
b
a
lan
c
e
d
V
o
lt
a
g
e
s
I
m
p
a
c
ts
o
n
th
e
En
e
rg
y
P
e
rf
o
r
m
a
n
c
e
o
f
In
d
u
c
ti
o
n
M
o
to
rs
,
”
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
E
lec
trica
l
a
n
d
C
o
mp
u
ter
E
n
g
i
n
e
e
rin
g
(
IJ
ECE
)
,
v
o
l.
8
,
n
o
.
3
,
p
p
.
1
4
1
2
-
1
4
2
2
,
Ju
n
2
0
1
8
.
[2
]
J.
Ch
a
tela
in
,
M
a
c
h
in
e
s
é
le
c
tr
iq
u
e
s.
T
ra
it
é
d
’é
lec
tricité
,
P
r
e
ss
e
s
P
o
ly
tec
h
n
iq
u
e
s
R
o
m
a
n
d
e
s
,
L
a
u
sa
n
n
e
,
v
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l.
10
,
1
9
8
3
.
[3
]
V
.
P
.
S
a
k
th
iv
e
l,
R.
B
h
u
v
a
n
e
sw
a
ri
,
S
.
S
u
b
ra
m
a
n
ian
,
“
Ba
c
teria
l
F
o
ra
g
in
g
T
e
c
h
n
iq
u
e
Ba
se
d
P
a
ra
m
e
ter
Esti
m
a
ti
o
n
o
f
In
d
u
c
ti
o
n
M
o
t
o
r
f
ro
m
M
a
n
u
f
a
c
tu
re
r
Da
ta
,
”
El
e
c
tri
c
Po
we
r
Co
mp
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n
e
n
ts
a
n
d
S
y
ste
ms
,
v
o
l.
3
8
,
n
o.
6
,
pp.
6
5
7
–
6
7
4
,
2
0
1
0
.
[4
]
D.G
.
L
u
e
m
b
e
r
g
e
r,
L
in
e
a
r a
n
d
n
o
n
li
n
e
a
r p
r
o
g
ra
mm
i
n
g
,
A
d
d
iso
n
W
e
sle
y
,
1
9
8
9
.
[5
]
M
.
S
.
Ba
z
a
ra
a
,
H.D.
S
h
e
ra
ll
,
a
n
d
C.
M
.
S
h
e
tt
y
,
No
n
li
n
e
a
r
p
ro
g
ra
mm
in
g
th
e
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ry
a
n
d
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lg
o
rith
m
s
,
Jo
h
n
W
il
e
y
&
S
o
n
s i
n
c
.
,
1
9
9
3
.
[6
]
M
.
Bo
u
n
e
k
h
la,
M
.
E
Zaim
,
A
.
Re
z
z
o
u
g
,
“
Co
m
p
a
ra
ti
v
e
stu
d
y
o
f
th
re
e
m
in
i
m
iza
ti
o
n
m
e
th
o
d
s
a
p
p
li
e
d
t
o
t
h
e
in
d
u
c
ti
o
n
m
a
c
h
in
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p
a
ra
m
e
ter
s
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d
e
n
ti
f
ica
ti
o
n
u
si
n
g
tran
sie
n
t
sta
t
o
r
c
u
rre
n
t
,
”
El
e
c
tric
Po
we
r
Co
mp
o
n
e
n
ts
a
n
d
S
y
ste
ms
,
v
o
l.
3
3
,
n
o
.
8
,
p
p
.
9
1
3
-
9
3
0
,
2
0
0
5
.
[7
]
B.
A
b
d
e
lh
a
d
i,
A
.
Be
n
o
u
d
j
it
,
N.
N
a
it
S
a
id
,
“
Id
e
n
ti
f
ica
ti
o
n
o
f
In
d
u
c
ti
o
n
M
a
c
h
in
e
P
a
ra
m
e
ters
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sin
g
a
Ne
w
A
d
a
p
ti
v
e
G
e
n
e
ti
c
A
lg
o
ri
th
m
,
”
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e
c
tric P
o
we
r Co
mp
o
n
e
n
ts
a
n
d
S
y
ste
ms
,
v
o
l.
3
2
,
n
o.
8
,
p
p
.
7
6
7
–
7
8
4
,
2
0
0
4
.
[8
]
B.
A
b
d
e
lh
a
d
i,
A
.
Be
n
o
u
d
ji
t,
a
n
d
N.
Na
it
-
S
a
id
,
“
A
p
p
li
c
a
ti
o
n
o
f
G
e
n
e
ti
c
A
l
g
o
rit
h
m
w
it
h
a
No
v
e
l
A
d
a
p
ti
v
e
S
c
h
e
m
e
f
o
r
th
e
Id
e
n
ti
f
ica
ti
o
n
o
f
In
d
u
c
ti
o
n
M
a
c
h
in
e
P
a
ra
m
e
ters
,
”
IEE
E
tr
a
n
s
a
c
ti
o
n
s
o
n
e
n
e
rg
y
c
o
n
v
e
rs
io
n
,
v
o
l.
2
0
,
n
o
.
2
,
p
p
.
2
8
4
-
2
9
1
,
2
0
0
5
.
[9
]
N.
Be
n
a
ïd
ja,
N.
Kh
e
n
f
e
r,
“
Id
e
n
t
if
ica
ti
o
n
o
f
A
s
y
n
c
h
ro
n
o
u
s
M
a
c
h
in
e
P
a
ra
m
e
ters
b
y
Ev
o
lu
ti
o
n
a
ry
T
e
c
h
n
iq
u
e
s
,
”
El
e
c
tric P
o
we
r Co
mp
o
n
e
n
ts
a
n
d
S
y
ste
ms
,
v
o
l.
3
4
,
n
o
.
1
2
,
p
p
.
1
3
5
9
-
1
3
7
6
,
2
0
0
6
.
[1
0
]
M
A
.
Aw
a
d
a
ll
a
h
,
“
P
a
ra
m
e
ter
Es
ti
m
a
ti
o
n
o
f
In
d
u
c
ti
o
n
M
a
c
h
in
e
s
f
ro
m
Na
m
e
p
late
Da
ta
Us
in
g
P
a
rti
c
le
S
w
a
r
m
Op
ti
m
iza
ti
o
n
a
n
d
G
e
n
e
ti
c
A
lg
o
rit
h
m
Tec
h
n
iq
u
e
s
,
”
El
e
c
tric
Po
w
e
r
Co
mp
o
n
e
n
ts
a
n
d
S
y
ste
ms
,
v
o
l.
3
6
,
n
o
.
8
,
pp.
8
0
1
–
8
1
4
,
2
0
0
8
.
[1
1
]
M.
Bo
u
n
e
k
h
la,
e
t
a
l
.
,
“
Us
in
g
two
P
S
O
stru
c
t
u
re
a
p
p
ro
a
c
h
e
s
to
e
stim
a
te
i
n
d
u
c
ti
o
n
ma
c
h
in
e
p
a
r
a
me
ter
s
,
”
1
3
t
h
E
u
ro
p
e
a
n
C
o
n
fer
e
n
c
e
o
n
P
o
we
r E
lec
tro
n
ics
&
Ap
p
li
c
a
ti
o
n
s (
EP
E)
,
Ba
rc
e
lo
n
a
,
S
p
a
i
n
,
S
e
p
2
0
0
9
.
[1
2
]
V
.
P
.
S
a
k
th
iv
e
l,
R.
Bh
u
v
a
n
e
sw
a
r
i,
S
.
S
u
b
ra
m
a
n
ian
,
“
A
n
I
m
p
ro
v
e
d
P
a
rti
c
le
S
w
a
r
m
Op
ti
m
iza
ti
o
n
f
o
r
In
d
u
c
ti
o
n
M
o
to
r
P
a
ra
m
e
ter De
t
e
r
m
in
a
ti
o
n
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
C
o
mp
u
t
e
r A
p
p
li
c
a
ti
o
n
s
,
v
o
l
.
1
,
n
o
.
2
,
p
p
.
62
-
6
7
,
2
0
1
0
.
[1
3
]
R.
T
h
a
n
g
a
ra
j,
M
.
P
a
n
t
,
C.
T
h
a
n
g
a
Ra
j,
A
K.
Na
g
a
r
,
“
In
S
it
u
Eff
icie
n
c
y
De
ter
m
in
a
ti
o
n
o
f
In
d
u
c
ti
o
n
M
o
t
o
r:
A
c
o
m
p
a
ra
ti
v
e
stu
d
y
o
f
e
v
o
lu
ti
o
n
a
ry
tec
h
n
iq
u
e
s
,
”
Ap
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u
d
issa
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M
.
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o
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6
]
M
.
A
.
Jird
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.
Re
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[1
7
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J.J.
G
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.
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M
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M
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3
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.
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.
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8
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M.
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O.
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.
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