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2243
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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N
:
2
0
8
8
-
8
694
I
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t J
P
o
w
E
lec
&
Dr
i
S
y
s
t,
Vo
l.
12
,
No
.
4
,
Dec
em
b
er
2021
:
224
3
–
2
2
5
0
2244
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p
e,
th
e
r
eliab
ilit
y
of
th
e
p
o
w
er
s
u
p
p
l
y
of
s
i
n
g
le
-
p
h
a
s
e
s
w
itc
h
ab
le
lo
ad
d
ec
r
ea
s
es;
T
h
e
m
ea
s
u
r
i
n
g
a
n
d
co
m
m
u
t
atio
n
co
m
p
lex
of
t
h
ese
d
ev
ices
s
ee
m
s
r
ath
er
co
m
p
lica
ted
.
A
n
o
t
h
er
m
iti
g
ati
o
n
m
eth
o
d
is
th
e
u
s
e
of
s
p
ec
ial
tr
an
s
f
o
r
m
er
s
s
u
c
h
as
a
th
r
ee
-
p
h
ase
or
th
r
ee
-
p
h
ase
tr
an
s
f
o
r
m
er
or
Sco
tt
an
d
Stein
m
etz
tr
a
n
s
f
o
r
m
er
s
[7
]
-
[
1
0
]
.
T
r
an
s
f
o
r
m
er
b
alan
c
ed
th
r
ee
-
p
h
a
s
e
can
r
ed
u
ce
en
er
g
y
lo
s
s
es
by
r
ed
u
cin
g
th
e
a
m
p
li
tu
d
es
of
h
ar
m
o
n
ics,
r
ed
u
ci
n
g
t
h
e
r
esi
s
tan
ce
.
T
h
is
in
cr
ea
s
e
s
th
e
w
o
r
k
i
n
g
lif
e
of
en
er
g
y
s
o
u
r
ce
s
in
n
et
w
o
r
k
s
w
i
th
p
h
ase
m
is
alig
n
m
e
n
t
s
.
T
h
e
d
ev
ices
ar
e
d
esig
n
ed
to
in
cr
ea
s
e
th
e
r
eliab
ilit
y
of
au
to
n
o
m
o
u
s
g
en
er
ato
r
s
an
d
co
n
s
u
m
er
s
w
h
en
th
e
lo
ad
s
ar
e
asy
m
m
etr
ical
an
d
f
o
r
b
alan
cin
g
p
h
ase
v
o
ltag
e
s
by
d
ec
r
ea
s
i
n
g
t
h
e
r
esi
s
tan
ce
of
t
h
e
ze
r
o
s
eq
u
e
n
ce
,
so
t
h
at
t
h
e
s
a
m
e
p
h
a
s
e
b
i
as
in
th
e
v
o
lta
g
e
is
eli
m
i
n
ated
,
w
h
ic
h
h
ap
p
en
s
m
ai
n
l
y
d
u
e
to
th
e
as
y
m
m
etr
y
of
th
e
lo
ad
cu
r
r
en
t
s
p
h
as
es.
R
ea
cti
v
e
p
o
w
er
co
m
p
e
n
s
at
io
n
ca
n
be
p
er
f
o
r
m
ed
u
s
i
n
g
a
s
y
n
c
h
r
o
n
o
u
s
g
e
n
er
ato
r
to
g
en
er
ate
or
co
llect
r
ea
cti
ve
p
o
w
er
,
but
it
h
as
t
h
at
d
is
ad
v
a
n
ta
g
e:
t
h
e
h
ig
h
co
s
t
of
i
n
s
tal
latio
n
,
m
ai
n
ten
a
n
ce
,
a
n
d
co
m
p
lex
o
p
er
atio
n
.
S
y
n
c
h
r
o
n
o
u
s
g
en
er
ato
r
s
ar
e
o
f
te
n
u
s
ed
to
co
n
ce
n
tr
ate
co
m
p
e
n
s
atio
n
w
it
h
a
lar
g
e
ca
p
ac
ita
n
ce
,
an
d
a
co
m
p
en
s
atio
n
ca
p
ac
ito
r
o
v
er
co
m
es
th
e
d
i
s
ad
v
an
ta
g
e
s
of
a
s
y
n
c
h
r
o
n
o
u
s
g
e
n
er
ato
r
,
b
u
t
th
e
d
r
a
w
b
ac
k
is
o
n
l
y
f
o
r
u
s
e
w
it
h
t
h
e
s
y
s
te
m
's
b
an
d
w
id
t
h
s
m
all,
s
e
n
s
iti
v
e
to
v
o
ltag
e
c
h
a
n
g
e
s
.
C
o
m
b
i
n
ed
b
alan
cin
g
d
ev
ices
a
l
w
a
y
s
g
i
v
e
th
e
b
est
r
es
u
lt;
h
o
w
e
v
er
,
th
e
y
ar
e
b
ec
o
m
i
n
g
m
o
r
e
co
m
p
le
x
in
th
e
ca
lcu
latio
n
,
an
d
th
e
n
u
m
b
er
of
co
m
p
en
s
ati
n
g
co
m
p
o
n
en
t
s
n
ec
es
s
ar
y
f
o
r
to
tal
co
m
p
en
s
atio
n
r
eq
u
ir
es
m
o
r
e.
T
h
e
co
s
t
of
th
e
co
m
p
en
s
atio
n
s
y
s
te
m
al
s
o
in
cr
ea
s
es.
C
o
n
s
id
er
in
g
th
e
g
r
o
w
i
n
g
d
em
a
n
d
f
o
r
p
o
w
er
s
y
s
te
m
s
f
o
r
m
ea
s
u
r
es
to
i
m
p
r
o
v
e
en
er
g
y
q
u
al
it
y
a
n
d
r
ed
u
ce
th
e
co
s
t
of
i
n
v
est
m
e
n
ts
a
n
d
m
ai
n
ten
a
n
ce
co
s
t
s
of
p
o
w
er
q
u
alit
y
i
m
p
r
o
v
e
m
e
n
t
s
y
s
te
m
s
,
we
n
ee
d
p
r
o
p
o
s
als
th
at
en
s
u
r
e
lo
w
-
co
s
t
s
y
m
m
etr
iz
atio
n
of
th
r
ee
-
p
h
ase
s
y
s
te
m
s
[
1
0
]
-
[
1
5
]
.
T
h
e
co
m
p
l
ex
it
y
of
co
n
s
u
m
p
tio
n
p
atter
n
s
ca
u
s
e
s
d
if
f
ic
u
lt
y
an
d
e
v
en
i
m
p
o
s
s
ib
ilit
y
to
cr
ea
t
e
a
g
en
er
al
m
et
h
o
d
f
o
r
op
ti
m
i
zin
g
th
e
u
n
b
alan
ce
d
s
y
s
te
m
.
T
h
e
d
esig
n
of
u
n
i
v
er
s
al
s
y
m
m
etr
izi
n
g
s
y
s
te
m
s
r
eq
u
ir
es
a
co
m
b
in
at
io
n
of
s
e
v
er
al
ap
p
r
o
ac
h
es
an
d
s
e
v
er
al
d
ev
ices.
T
h
is
lead
s
to
an
in
cr
ea
s
e
in
t
h
e
co
s
t
of
cr
ea
tio
n
an
d
m
ain
ten
a
n
ce
.
F
o
r
ex
a
m
p
le,
in
m
a
n
y
ca
s
es,
f
o
r
in
d
u
s
tr
ial
lo
a
d,
th
e
r
ep
ea
tab
ilit
y
of
lo
ad
ch
ar
ac
ter
is
tic
s
(
in
cl
u
d
in
g
th
ei
r
asy
m
m
etr
y
)
is
o
b
s
er
v
ed
at
d
if
f
er
e
n
t
ti
m
e
s
ca
les
f
r
o
m
d
ail
y
to
an
n
u
al.
T
h
is
cir
cu
m
s
ta
n
ce
m
ak
e
s
it
p
o
s
s
ib
l
e
to
s
i
m
p
li
f
y
an
d
r
ed
u
ce
t
h
e
c
o
s
t
of
s
y
m
m
etr
izatio
n
s
y
s
te
m
s
,
w
h
ic
h
is
e
s
s
e
n
tial
s
in
ce
in
v
e
s
t
m
e
n
t
co
s
t
s
ar
e
t
h
e
u
s
er
'
s
p
r
i
m
ar
y
co
n
ce
r
n
w
it
h
i
n
t
h
e
ac
ce
p
tab
le
q
u
alit
y
of
ele
ctr
ic
s
y
s
te
m
s
.
W
it
h
th
ese
a
n
al
y
s
e
s
,
we
d
escr
ib
e
t
h
e
m
eth
o
d
o
lo
g
y
f
o
r
o
p
ti
m
iz
i
n
g
th
r
ee
-
p
h
ase
s
y
s
te
m
s
o
p
er
a
tin
g
in
as
y
m
m
etr
ic
m
o
d
e
s
.
In
m
ee
ti
n
g
th
e
r
eq
u
ir
e
m
en
ts
f
o
r
th
e
q
u
alit
y
of
th
e
t
h
r
ee
-
p
h
ase
p
o
w
er
s
y
s
te
m
a
n
d
th
e
in
v
est
m
e
n
t
co
s
t
s
,
th
is
ap
p
r
o
ac
h
ai
m
s
to
r
ed
u
ce
th
e
n
u
m
b
er
of
r
ea
cti
v
e
p
o
w
er
c
o
m
p
e
n
s
at
io
n
d
ev
ice
s
[
1
5
]
-
[
2
0
]
.
2.
RE
S
E
ARCH
M
E
T
H
O
D
2
.
1
.
Ne
w
pro
po
s
ed
f
ra
ct
i
o
na
l
-
po
ly
no
m
ia
l
f
un
ct
io
n
s
Ass
u
m
e
th
at
we
h
av
e
a
t
h
r
ee
-
p
h
a
s
e
cir
cu
it
co
n
s
is
tin
g
of
(
n
+1
)
n
o
d
es
an
d
m
(
n
+1
<
m
)
b
r
an
ch
an
d
d
escr
ib
ed
by
th
e
m
atr
i
x
of
li
n
k
n
o
d
es
[
1
0
-
2
0
]
:
11
12
1
=
21
22
2
1
2
Vec
to
r
of
th
e
co
n
d
u
cta
n
ce
of
t
h
e
b
r
an
ch
e
s
is
=
dia
g
(
1
,
2
,
…
)
Vec
to
r
s
of
cu
r
r
en
t
a
n
d
elec
tr
o
m
o
tiv
e
f
o
r
ce
s
o
u
r
ce
s
is
f
o
r
m
u
l
ated
as
=
(
1
,
2
,
…
)
=
(
1
,
2
,
…
)
T
h
e
n
o
d
e
v
o
ltag
e
eq
u
atio
n
s
ar
e
w
r
itte
n
in
m
atr
i
x
f
o
r
m
as:
[
1
8
]
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
I
SS
N:
2
0
8
8
-
8
694
N
ew p
r
o
p
o
s
ed
fr
a
ctio
n
a
l
-
p
o
ly
n
o
mia
l fu
n
ctio
n
s
:
n
ew r
ec
o
mme
n
d
a
tio
n
f
o
r
o
ve
r
co
me
th
e
…
(
Q.
S
.
V
u
)
2245
AY
A
U
0
=
−
A
(
J
+
YE
)
(
1
)
T
h
e
n
o
d
e
v
o
ltag
es
can
be
f
o
u
n
d
by
t
h
e
C
r
a
m
er
f
o
r
m
u
la
[
1
9
]
-
[
2
1
]
:
=
d
et
d
et
T
h
e
m
atr
i
x
w
ill
b
e:
=
1
1
,
1
…
1
,
…
1
,
…
1
,
i
,
1
…
,
…
,
…
,
j
,
1
…
,
…
,
…
,
n
,
1
…
,
…
,
…
,
T
h
e
m
atr
i
x
d
eter
m
in
a
n
t
s
of
a
n
d
ar
e
d
ef
in
ed
as
f
o
llo
w
s
:
(
h
e
r
e
an
d
w
er
e
w
it
h
s
ig
n
(
*
)
,
ar
e
r
esu
lt
s
of
th
e
cir
cu
i
t
an
a
l
y
s
is
we
h
av
e
d
o
n
e
on
t
h
e
m
ap
le
s
o
f
t
w
ar
e
,
an
d
d
u
e
to
t
h
e
l
i
m
itatio
n
s
of
p
ap
er
we
w
il
l
n
o
t
p
r
esen
t
in
m
o
r
e
d
etail)
.
de
t
=
0
+
1
1
+
2
2
+
3
1
2
=
0
(
1
+
1
0
1
+
2
0
2
+
3
0
1
2
)
de
t
=
0
,
+
1
,
1
+
2
,
2
+
3
,
1
2
In
g
e
n
er
al,
v
o
ltag
e
s
w
ill
b
e:
=
de
t
de
t
=
0
,
+
1
,
1
+
2
,
2
+
3
,
1
2
0
(
1
+
1
0
1
+
2
0
2
+
3
0
1
2
)
Le
t
α
=
0
⁄
;
=
1
÷
3
an
d
,
=
,
0
⁄
;
;
=
0
÷
3
,
we
h
a
v
e
:
=
d
et
d
et
=
0
,
+
1
,
1
+
2
,
2
+
3
,
1
2
1
+
α
1
1
+
α
2
2
+
α
3
1
2
(
2
)
If
th
e
i
-
th
b
r
an
ch
co
n
n
ec
t
s
t
w
o
n
o
d
es
j
-
th
an
d
k
-
th
,
t
h
e
cu
r
r
e
n
t
f
lo
w
in
t
h
at
f
r
o
m
k
to
j
,
in
g
e
n
er
al,
as
:
=
0
,
+
1
,
1
+
2
,
2
+
3
,
1
2
1
+
α
1
1
+
α
2
2
+
α
3
1
2
(
3
)
C
o
ef
f
icie
n
ts
α
1
…
α
3
in
th
is
ca
s
e
h
a
s
t
h
e
s
a
m
e
v
alu
e
as
t
h
e
co
ef
f
icie
n
ts
of
t
h
e
v
o
ltag
e
s
,
=
1
÷
–
in
d
ex
of
b
r
an
c
h
es
[
2
0
]
-
[
2
4
]
.
2
.
2
.
T
esting
In
th
e
s
ec
o
n
d
ex
p
er
i
m
e
n
t
(
p
r
o
p
o
s
ed
f
u
n
ctio
n
s
)
,
we
p
er
f
o
r
m
ed
as
d
escr
ib
ed
in
s
ec
ti
on
2
.
T
h
e
e
x
a
m
p
le
cir
c
u
it
is
s
h
o
w
n
in
Fi
g
u
r
e
1.
T
h
e
er
r
o
r
b
etw
ee
n
t
w
o
ex
p
er
i
m
e
n
ts
w
a
s
ca
lcu
la
ted
by
th
e
f
o
r
m
u
la
:
(
1
,
2
)
=
100%
|
|
1
(
1
,
2
)
|
−
|
2
(
1
,
2
)
|
1
(
1
,
2
)
|
h
er
e
(
1
,
2
)
=
{
̇
,
(
,
)
(
1
,
2
)
or
̇
,
(
,
)
(
1
,
2
)
}
;
,
=
0
,
4
̅
̅
̅
;
≠
;
=
1
,
2
–
cu
r
r
en
ts
(
v
o
ltag
es)
of
th
e
f
ir
s
t
ex
p
er
i
m
en
t
an
d
th
e
p
r
o
p
o
s
ed
m
et
h
o
d
[
2
5
]
-
[
3
3
]
.
In
Fi
g
u
r
e
2
an
d
Fig
u
r
e
3,
p
r
esen
t
t
h
e
er
r
o
r
s
(
1
,
2
)
of
cu
r
r
en
t
an
d
(
1
,
2
)
of
th
e
v
o
lta
g
e
of
th
e
p
r
o
p
o
s
ed
FP
F
w
it
h
o
u
t
co
n
s
id
e
r
in
g
r
a
n
d
o
m
er
r
o
r
s
(
=
0
)
,
s
u
c
h
as
er
r
o
r
s
of
m
ea
s
u
r
e
m
en
t
or
co
n
s
ta
n
t
ch
a
n
g
e
of
lo
ad
etc.
H
o
w
ev
er
,
th
i
s
ca
s
e
d
o
es
n
o
t
ex
is
t
in
p
r
ac
tice,
so
we
h
ad
tak
en
i
n
to
ac
co
u
n
t
r
an
d
o
m
er
r
o
r
in
th
e
r
an
g
e
of
=
±
0
.
5%
an
d
±
1%
.
T
h
e
er
r
o
r
s
w
er
e
p
r
esen
ted
as
in
Fig
u
r
e
s
4
to
7.
T
h
e
r
o
o
t
m
ea
n
s
s
q
u
ar
e
(
R
MS)
v
al
u
es
of
th
e
er
r
o
r
s
w
e
r
e
ca
lcu
lated
by
th
e
f
o
r
m
u
la,
an
d
th
e
r
es
u
lts
w
i
ll
be
co
n
tai
n
e
d
in
th
e
T
ab
le
1.
=
√
1
1
∑
∑
2
(
1
(
)
,
2
(
)
)
=
1
=
1
h
er
e
,
-
th
e
le
n
g
t
h
s
of
v
ec
to
r
1
,
2
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t,
Vo
l.
12
,
No
.
4
,
Dec
em
b
er
2021
:
224
3
–
2
2
5
0
2246
Fig
u
r
e
1
.
E
x
a
m
p
le
cir
cu
it
Fig
u
r
e
2.
Dep
en
d
en
ce
of
er
r
o
r
in
d
eter
m
i
n
i
n
g
t
h
e
v
alu
e
of
th
e
er
r
o
r
on
r
ea
ctan
c
e’
s
v
alu
e
s
1
,
2
,
w
h
e
n
=
0
%
Fig
u
r
e
3.
Dep
en
d
en
ce
of
er
r
o
r
in
d
eter
m
i
n
i
n
g
t
h
e
v
alu
e
of
th
e
er
r
o
r
on
r
ea
ctan
c
e’
s
v
alu
e
s
1
,
2
,
w
h
e
n
=
0
%
Fig
u
r
e
4.
Dep
en
d
en
ce
of
er
r
o
r
in
d
eter
m
i
n
i
n
g
t
h
e
v
alu
e
of
th
e
er
r
o
r
on
r
ea
ctan
c
e’
s
v
alu
e
s
1
,
2
,
w
h
e
n
=
0
.
5
%
.
Fig
u
r
e
5
.
Dep
en
d
en
ce
of
er
r
o
r
in
d
eter
m
i
n
i
n
g
t
h
e
v
alu
e
of
th
e
er
r
o
r
on
r
ea
ctan
c
e’
s
v
alu
e
s
1
,
2
,
w
h
e
n
=
0
.
5
%
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
I
SS
N:
2
0
8
8
-
8
694
N
ew p
r
o
p
o
s
ed
fr
a
ctio
n
a
l
-
p
o
ly
n
o
mia
l fu
n
ctio
n
s
:
n
ew r
ec
o
mme
n
d
a
tio
n
f
o
r
o
ve
r
co
me
th
e
…
(
Q.
S
.
V
u
)
2247
Fig
u
r
e
6.
Dep
en
d
en
ce
of
er
r
o
r
in
d
eter
m
i
n
i
n
g
t
h
e
v
alu
e
of
th
e
er
r
o
r
on
r
ea
ctan
c
e’
s
v
alu
e
s
1
,
2
,
w
h
e
n
=
1
%
Fig
u
r
e
7.
Dep
en
d
en
ce
of
er
r
o
r
in
d
eter
m
i
n
i
n
g
t
h
e
v
alu
e
of
th
e
er
r
o
r
on
r
ea
ctan
c
e’
s
v
alu
e
s
1
,
2
,
w
h
e
n
=
1
%
T
ab
le
1
.
T
h
e
R
MS
v
al
u
es
of
t
h
e
er
r
o
r
s
d
ep
en
d
on
,
%
0
0
.
5
1
,
,
%
6
.
8
7
·
1
0
-
8
0
.
3
4
1
.
1
4
,
,
%
9
.
0
2
·
1
0
-
10
0
.
7
3
7
.
9
8
We
h
ad
r
ep
ea
ted
ly
ex
ec
u
ted
it
(n
=1
0
0
0
tim
es)
to
ass
e
s
s
er
r
o
r
s
an
d
ac
cu
r
atel
y
r
ec
ei
v
ed
av
e
r
ag
e
er
r
o
r
s
.
̅
(
1
,
2
)
=
1
∑
̅
(
1
,
2
)
=
1
[
%
]
T
h
e
R
MS
v
al
u
es
of
t
h
e
a
v
e
r
ag
e
er
r
o
r
s
ar
e
c
o
n
tain
ed
in
T
ab
le
2.
̅
=
√
1
1
∑
∑
̅
2
(
1
(
)
,
2
(
)
)
=
1
=
1
w
h
er
e
,
-
t
h
e
len
g
t
h
s
of
v
ec
to
r
1
,
2
.
T
ab
le
2
.
T
h
e
d
ep
en
d
en
cies
of
th
e
r
o
o
t
m
ea
n
s
q
u
ar
e
er
r
o
r
s
on
,
%
0
0
.
5
1
̅
,
,
%
6
.
8
7
·
1
0
-
8
1
.
3
1
2
.
5
9
̅
,
,
%
9
.
0
2
·
1
0
-
10
1
.
5
8
3
.
0
1
As
we
can
s
ee
,
th
e
m
o
s
t
s
i
g
n
i
f
ican
t
er
r
o
r
of
th
e
p
r
o
p
o
s
e
d
m
et
h
o
d
is
u
n
d
er
2
%,
w
h
e
n
th
e
m
o
s
t
s
ig
n
i
f
ica
n
t
r
an
d
o
m
er
r
o
r
of
=
0
.
5%
an
d
ab
o
u
t
3%
w
h
en
=
1
%
.
T
h
e
ac
cu
r
ac
y
of
f
r
ac
tio
n
a
l
-
p
o
l
y
n
o
m
ia
l
f
u
n
ctio
n
s
d
ep
en
d
s
on
th
e
er
r
o
r
of
m
ea
s
u
r
e
m
e
n
t.
No
w
ad
a
y
s
,
th
e
d
e
v
elo
p
m
e
n
t
of
m
ea
s
u
r
em
en
t
d
ev
ice
s
wi
th
h
ig
h
q
u
alit
y
m
ak
e
s
a
ti
n
y
er
r
o
r
<
0
.
5%
,
h
o
w
e
v
er
,
in
th
i
s
ar
ticle,
we
n
o
t
o
n
l
y
ta
k
e
i
n
to
ac
co
u
n
t
th
e
er
r
o
r
s
of
m
ea
s
u
r
e
m
en
t
b
u
t
also
i
n
clu
d
in
g
t
h
e
co
n
s
tan
t
c
h
a
n
g
e
of
lo
ad
as
s
h
o
w
n
in
Fi
g
u
r
e
8.
Fig
u
r
e
8
.
T
h
e
co
n
s
tan
t
ch
a
n
g
e
of
lo
ad
s
P
er
m
i
s
s
ib
l
e
ch
a
n
g
e
li
m
its
of
l
o
ad
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t,
Vo
l.
12
,
No
.
4
,
Dec
em
b
er
2021
:
224
3
–
2
2
5
0
22
48
=
|
(
0
)
−
(
1
)
|
(
0
)
=
D
0
100%
d
=
|
−
0
|
w
h
er
e
0
=
(
0
)
-
i
m
p
ed
an
ce
at
th
e
b
eg
in
n
i
n
g
of
t
h
e
ca
lc
u
latio
n
;
(
1
)
-
i
m
p
ed
a
n
ce
at
t
h
e
en
d
of
t
h
e
ca
lcu
latio
n
.
At
m
o
m
e
n
t
1
,
th
e
ca
lcu
latio
n
p
r
o
ce
s
s
is
co
m
p
l
eted
,
an
d
th
e
v
alu
es
(
1
,
2
)
r
ec
ei
v
ed
w
il
l
be
ap
p
lied
to
th
e
co
m
p
en
s
atio
n
s
y
s
te
m
if
d
<
D
.
3.
NUM
E
RICAL
R
E
SU
L
T
S
A
ND
DIS
C
USS
I
O
N
Seq
u
en
c
e
co
m
p
o
n
en
t
s
ar
e
f
o
r
m
u
lated
as
[
2
0
]
-
[
3
7
]:
[
̇
1
(
,
)
(
1
,
2
)
̇
2
(
,
)
(
1
,
2
)
̇
0
(
,
)
(
1
,
2
)
]
=
[
1
1
1
2
1
2
1
]
−
1
∙
[
̇
(
,
)
(
1
,
2
)
̇
(
,
)
(
1
,
2
)
̇
(
,
)
(
1
,
2
)
]
.
(
4
)
w
h
er
e
,
=
1
,
̅
̅
̅
̅
̅
;
≠
;
We
g
o
t:
̇
(
,
)
(
1
,
2
)
=
,
(
,
)
+
,
(
,
)
1
+
,
(
,
)
2
+
,
(
,
)
1
2
1
+
α
1
1
+
α
2
2
+
α
3
1
2
.
(
5
)
Neg
ati
v
e
a
n
d
ze
r
o
s
eq
u
en
ce
co
m
p
o
n
e
n
t
s
ap
p
ea
r
in
as
y
m
m
etr
ical
s
y
s
te
m
s
,
a
n
d
th
e
y
h
av
e
g
r
ea
ter
v
alu
e
s
w
h
en
t
h
e
s
y
s
te
m
is
m
o
r
e
as
y
m
m
etr
ic.
{
|
̇
1
(
,
)
(
1
,
2
)
|
→
|
̇
2
(
,
)
(
1
,
2
)
|
→
|
̇
0
(
,
)
(
1
,
2
)
|
→
,
or
{
1
=
1
/
|
̇
1
(
,
)
(
1
,
2
)
|
→
2
=
|
̇
2
(
,
)
(
1
,
2
)
|
→
3
=
|
̇
0
(
,
)
(
1
,
2
)
|
→
(
6
)
L
et
(
)
=
{
1
,
2
,
3
}
T
h
e
m
u
l
ti
-
o
b
j
ec
tiv
e
o
p
ti
m
izat
io
n
p
r
o
b
lem
can
be
b
r
o
u
g
h
t
b
ac
k
to
m
at
h
e
m
at
ical
f
o
r
m
a
n
d
d
escr
ib
ed
as
f
o
llo
w
[2
]
,
[
1
2
]
(
1
,
2
)
=
{
1
(
1
,
2
)
,
2
(
1
,
2
)
,
3
(
1
,
2
)
}
s
.
t.
(
1
,
2
)
∈
,
w
h
er
e
t
h
e
i
n
teg
er
≥
2
is
th
e
n
u
m
b
er
of
o
b
j
ec
tiv
es,
an
d
t
h
e
s
e
t
is
th
e
f
ea
s
ib
le
s
e
t
of
d
ec
i
s
io
n
v
ec
to
r
s
.
T
h
e
v
alu
ed
v
ec
to
r
of
th
e
o
b
j
ec
tiv
e
f
u
n
ctio
n
is
d
ef
in
ed
as:
:
→
ℝ
T
h
er
ef
o
r
e,
X_
1
is
a
n
o
n
-
d
o
m
i
n
ated
s
o
lu
tio
n
an
d
X_
2
is
an
in
f
er
io
r
s
o
lu
tio
n
.
T
h
e
s
o
lu
tio
n
X_
1
w
ill
be
ca
lled
d
o
m
i
n
ated
s
o
lu
t
io
n
i
f
:
∀
=
1
.
.
3
:
(
1
)
≤
(
2
)
T
y
p
ic
all
y
,
in
th
e
mu
lti
-
o
b
j
ec
tiv
e
o
p
ti
m
izatio
n
p
r
o
b
lem
,
we
o
f
te
n
en
co
u
n
ter
n
o
n
-
d
en
o
m
i
n
ated
s
o
lu
tio
n
s
r
at
h
er
th
a
n
d
e
n
o
m
i
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S
[1
]
J.
J.
G.
W.
D.
S
tev
e
n
so
n
,
P
o
we
r
sy
ste
m
a
n
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lys
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Ne
w
Yo
rk
:
M
c
G
r
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w
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Hill
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1
9
9
4
.
[2
]
C.
L.
F
o
rtes
c
u
e
,
“
M
e
th
o
d
of
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y
m
m
e
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tes
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h
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se
Ne
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s,
”
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n
s.
Am.
In
st.
El
e
c
tr.
En
g
.
,
v
o
l.
XX
XV
II,
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o
.
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ly
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1
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[3
]
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ley
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.
[4
]
M
.
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r
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a
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d
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a
h
u
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m
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.
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o
l.
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5,
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1
2
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8
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2
4
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2
0
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.
[5
]
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Li
,
a
n
d
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A.
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8,
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8,
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.
[6
]
Y.
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ih
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ra
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iy
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z
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wa
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n
d
H.
Ko
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t
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e
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sin
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le
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”
2
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l
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Po
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ra
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]
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K
o
ro
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Ne
im
a
n
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d
K.
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B:
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ter
.
[8
]
N
.
G.
Hin
g
o
ra
n
i
,
a
n
d
L
.
Gy
u
g
y
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,
Un
d
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S
:
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h
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of
Fl
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x
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le
AC
T
ra
n
sm
issio
n
S
y
ste
ms
,
Ne
w
Je
rse
y
:
W
il
e
y
-
IEE
E
P
re
ss
,
1
9
9
9
.
[9
]
Y.
H.
S
o
n
g
,
a
n
d
A
.
T.
Jo
h
n
s
,
Fl
e
x
ib
le
AC
T
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n
sm
issio
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S
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ms
,
Lo
n
d
o
n
:
IEE
E
P
re
ss
,
1
9
9
9
.
[1
0
]
M.
Yo
u
n
g
,
T
h
e
T
e
c
h
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ica
l
W
riter
’
s
Ha
n
d
b
o
o
k
,
Ca
li
f
o
rn
ia
:
U
n
iv
e
rsity
S
c
ien
c
e
,
1989.
[1
1
]
L.
T
h
é
v
e
n
in
,
Exte
n
si
o
n
of
O
h
m’s
la
w
to
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o
mp
lex
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tro
mo
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irc
u
it
s
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A
n
n
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les
.
3e
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ries
.
10:
2
2
2
–
2
2
4
.
[1
2
]
L.
T
h
é
v
e
n
in
,
On
a
n
e
w
th
e
o
re
m
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y
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mic
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tricity
.
S
c
ien
c
e
s.
9
7
:
1
5
9
–
1
6
1
.
[1
3
]
J.
E.
Brit
tai
n
,
“
T
h
e
v
e
n
in
'
s
th
e
o
re
m
,
”
in
IEE
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S
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e
c
tru
m
,
v
o
l.
2
7
,
n
o
.
3,
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p
.
42
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,
M
a
rc
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o
i:
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0
.
1
1
0
9
/
6
.
4
8
8
4
5
.
[1
4
]
E.
L.
No
rto
n
,
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De
sig
n
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f
in
it
e
n
e
tw
o
rk
s
f
o
r
u
n
if
o
rm
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re
q
u
e
n
c
y
c
h
a
ra
c
teristic
,
”
Be
ll
Lab
o
ra
to
ries
,
Ne
w
J
e
rse
y
,
U.S
,
T
e
c
h
n
ica
l
Rep
o
rt
T
M
2
6
–
0
–
1
8
6
0
,
1
9
2
6
.
[1
5
]
K.
M.
Ch
a
n
d
y
,
U.
He
rz
o
g
,
a
n
d
L.
W
o
o
,
“
P
a
ra
m
e
tri
c
A
n
a
l
y
sis
of
Qu
e
u
in
g
Ne
tw
o
rk
s,
”
in
IBM
J
o
u
rn
a
l
of
Res
e
a
rc
h
and
De
v
e
lo
p
me
n
t
,
v
o
l.
19,
n
o
.
1,
pp.
36
-
4
2
,
Ja
n
.
1
9
7
5
,
d
o
i:
1
0
.
1
1
4
7
/rd
.
1
9
1
.
0
0
3
6
.
[1
6
]
R
.
C
Do
rf
,
a
n
d
J
.
A
S
v
o
b
o
d
a
,
Ci
rc
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T
h
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s
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in
In
tro
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u
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ti
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tri
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NJ:
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h
n
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n
s.
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p
.
1
6
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0
7
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[1
7
]
A.
S.
A
d
a
lev
,
M.
Ha
y
a
k
a
wa
,
a
n
d
N.
V.
Ko
r
o
v
k
in
,
“
I
d
e
n
ti
f
ica
ti
o
n
of
e
lec
tri
c
c
ircu
it
s:
p
r
o
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lem
s
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n
d
m
e
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o
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s
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ti
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ra
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h
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n
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e
m
e
n
t,
”
2
0
0
5
I
EE
E
I
n
ter
n
a
ti
o
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l
S
y
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o
si
u
m
on
Circ
u
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ts
a
n
d
S
y
ste
ms
,
2
0
0
5
,
pp.
9
8
0
-
9
8
3
V
o
l
.
2,
d
o
i:
1
0
.
1
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CA
S
.
2
0
0
5
.
1
4
6
4
7
5
4
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
E
lec
&
Dr
i
S
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s
t,
Vo
l.
12
,
No
.
4
,
Dec
em
b
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2021
:
224
3
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2
2
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0
2250
[1
8
]
A.
S.
A
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a
lev
,
N.
V.
K
o
ro
v
k
in
,
a
n
d
M.
Ha
y
a
k
a
w
a
,
“
Us
in
g
L
in
e
a
r
Re
latio
n
s
Be
tw
e
e
n
Ex
p
e
rime
n
tal
Ch
a
ra
c
teristics
in
S
ti
f
f
Id
e
n
ti
f
ica
ti
o
n
P
r
o
b
lem
s
of
L
in
e
a
r
Circu
it
T
h
e
o
ry
,
”
in
I
EE
E
T
ra
n
sa
c
ti
o
n
s
on
Circ
u
it
s
and
S
y
ste
ms
I:
Reg
u
l
a
r
Pa
p
e
rs
,
v
o
l.
5
5
,
n
o
.
5,
p
p
.
1
2
3
7
-
1
2
4
7
,
Ju
n
e
2
0
0
8
,
d
o
i
:
1
0
.
1
1
0
9
/T
CS
I.
2
0
0
8
.
9
2
4
9
0
8
.
[1
9
]
T.
S.
S
h
o
re
s,
A
p
p
li
e
d
L
in
e
a
r
Al
g
e
b
ra
a
n
d
M
a
trix
A
n
a
lys
is
,
Be
rli
n
,
G
e
r
m
a
n
y
:
S
p
r
in
g
e
r
S
c
ien
c
e
&
Bu
sin
e
ss
M
e
d
ia,
2
0
0
7
.
[2
0
]
C
.
B.
Bo
y
e
r,
A
Histo
ry
of
M
a
th
e
ma
ti
c
s
,
2
n
d
e
d
.
,
H
o
b
o
k
e
n
,
Ne
w
J
e
rse
y
:
W
il
e
y
,
1968
,
p
p
.
4
3
1
.
[2
1
]
L
.
G
.
S
to
k
v
is,
(1
9
1
4
)
.
On
t
h
e
c
re
a
ti
o
n
of
3
h
a
rm
o
n
ics
in
th
e
a
lt
e
r
n
a
to
rs
as
a
re
su
lt
of
p
h
a
se
i
m
b
a
lan
c
e
.
Re
p
o
rts.
v
o
l.
1
5
9
:
p
.
4
6
.
Co
m
p
tes
Re
n
d
u
s.
v
o
l.
1
5
9
:
p
.
4
6
.
[2
2
]
K
.
M
ietti
n
e
n
,
N
o
n
li
n
e
a
r
M
u
l
ti
o
b
j
e
c
ti
v
e
Op
ti
miza
ti
o
n
,
B
o
sto
n
:
S
p
ri
n
g
e
r
,
1
9
9
9
.
[2
3
]
N.
S
rin
iv
a
s
a
n
d
K.
De
b
,
“
M
u
il
ti
o
b
jec
ti
v
e
Op
ti
m
iza
ti
o
n
Us
in
g
No
n
d
o
m
in
a
ted
S
o
rt
in
g
in
G
e
n
e
ti
c
A
l
g
o
rit
h
m
s,"
in
Evo
lu
ti
o
n
a
ry
Co
mp
u
t
a
ti
o
n
,
v
o
l.
2,
n
o
.
3,
p
p
.
2
2
1
-
2
4
8
,
S
e
p
t.
1
9
9
4
,
d
o
i:
1
0
.
1
1
6
2
/ev
c
o
.
1
9
9
4
.
2
.
3
.
2
2
1
.
[2
4
]
K.
De
b
,
A.
P
ra
tap
,
S.
A
g
a
r
wa
l
a
n
d
T.
M
e
y
a
riv
a
n
,
"A
f
a
st
a
n
d
e
li
ti
s
t
m
u
lt
io
b
jec
ti
v
e
g
e
n
e
ti
c
a
lg
o
rit
h
m
:
NSG
A
-
II,
”
in
IEE
E
T
ra
n
s
a
c
ti
o
n
s
on
Evo
lu
ti
o
n
a
ry
Co
mp
u
ta
ti
o
n
,
v
o
l.
6,
no.
2,
p
p
.
1
8
2
-
1
9
7
,
A
p
ril
2
0
0
2
,
d
o
i:
1
0
.
1
1
0
9
/
4
2
3
5
.
9
9
6
0
1
7
.
[2
5
]
Ho
n
g
b
in
g
F
a
n
g
,
Qia
n
W
a
n
g
,
Yi
-
Ch
e
n
g
Tu
a
n
d
M
a
rk
F
Ho
rste
m
e
y
e
r
,
“
An
e
ff
ici
e
n
t
n
o
n
-
d
o
m
in
a
ted
so
rti
n
g
m
e
th
o
d
f
o
r
e
v
o
lu
ti
o
n
a
ry
a
lg
o
rit
h
m
s
,
”
Evo
l
Co
mp
u
t.
,
v
o
l.
1
6,
n
o
.
3,
pp.
3
5
5
-
384
,
2
0
0
8
,
1
0
.
1
1
6
2
/ev
c
o
.
2
0
0
8
.
1
6
.
3
.
3
5
5
.
[2
6
]
G.
Na
d
a
k
u
d
it
i,
V.
S
h
a
rm
a
a
n
d
R.
Na
re
sh
,
“
A
p
p
li
c
a
ti
o
n
of
non
-
d
o
m
in
a
ted
so
rti
n
g
g
ra
v
it
a
ti
o
n
a
l
se
a
rc
h
a
lg
o
rit
h
m
w
it
h
d
isru
p
t
io
n
o
p
e
ra
to
r
f
o
r
sto
c
h
a
stic
m
u
lt
io
b
jec
ti
v
e
sh
o
rt
ter
m
h
y
d
ro
th
e
rm
a
l
s
c
h
e
d
u
li
n
g
”
,
I
ET
Ge
n
e
ra
ti
o
n
,
T
ra
n
sm
issio
n
&
Distrib
u
ti
o
n
,
v
o
l.
10,
n
o
.
4,
pp.
8
6
2
-
9
7
2
,
M
a
rc
h
2
0
1
6
,
d
o
i:
1
0
.
1
0
4
9
/
ie
t
-
g
td
.
2
0
1
4
.
1
1
3
7
.
[2
7
]
S.
G
e
rb
e
x
,
R.
Ch
e
rk
a
o
u
i
a
n
d
A.
J.
G
e
r
m
o
n
d
,
“
Op
ti
m
a
l
lo
c
a
ti
o
n
of
m
u
lt
i
-
t
y
p
e
F
A
C
T
S
d
e
v
ice
s
in
a
p
o
w
e
r
s
y
ste
m
by
m
e
a
n
s
of
g
e
n
e
ti
c
a
lg
o
rit
h
m
s,
”
IE
EE
T
ra
n
sa
c
ti
o
n
s
on
P
o
we
r
S
y
ste
ms
,
v
o
l.
1
6
,
n
o
.
3,
p
p
.
5
3
7
-
5
4
4
,
A
u
g
.
2001,
d
o
i
:
1
0
.
1
1
0
9
/
5
9
.
9
3
2
2
9
2
.
[2
8
]
X
.
-
P
.
Zh
a
n
g
,
C
.
Re
h
tan
z
,
a
n
d
B
.
P
a
l,
F
lex
ib
le
AC
T
ra
n
sm
issio
n
S
y
ste
ms
:
M
o
d
e
ll
in
g
a
n
d
Co
n
tro
l
,
B
e
rli
n
:
S
p
ri
n
g
e
r
-
V
e
rlag
Be
rli
n
He
id
e
l
b
e
rg
,
2
0
0
6
.
[2
9
]
E
.
A
c
h
a
,
C
.
R.
F
u
e
rte
-
Esq
u
iv
e
l,
H
.
Am
b
riz
-
P
e
rre
z
,
a
n
d
C
.
A
n
g
e
le
s
-
Ca
m
a
c
h
o
,
FA
CT
S
.
M
o
d
e
ll
i
n
g
a
n
d
S
imu
l
a
ti
o
n
in
Po
w
er
Ne
two
rk
s
,
En
g
lan
d
:
Jo
h
n
W
il
e
y
&
S
o
n
s
L
td
,
2
0
0
4
.
[3
0
]
N.
V.
Ko
r
o
v
k
in
,
V.
L.
Ch
e
c
h
u
ri
n
,
a
n
d
M.
Ha
y
a
k
a
w
a
,
In
v
e
rs
e
p
ro
b
lem
s
in
e
lec
tric
c
irc
u
it
s
a
n
d
e
l
e
c
tro
ma
g
n
e
ti
c
s
,
Ne
w
Yo
rk
:
S
p
rin
g
e
r,
2
0
0
6
.
[3
1
]
S.
L
i,
Y.
L
i,
J.
S
u
n
,
Q.
Jin
,
a
n
d
X.
L
i,
“
A
n
o
v
e
l
c
o
n
tro
l
a
lg
o
rit
h
m
f
o
r
in
v
e
rter
-
b
a
se
d
d
istri
b
u
te
d
g
e
n
e
ra
ti
o
n
in
u
n
b
a
la
n
c
e
d
th
re
e
-
p
h
a
se
p
o
w
e
r
s
y
ste
m
s,
”
2009
I
n
ter
n
a
ti
o
n
a
l
C
o
n
fer
e
n
c
e
on
S
u
st
a
i
n
a
b
le
Po
we
r
Ge
n
e
ra
ti
o
n
a
n
d
S
u
p
p
ly
,
2
0
0
9
,
p
p
.
1
-
6,
d
o
i:
1
0
.
1
1
0
9
/S
U
P
ERG
EN.
2
0
0
9
.
5
3
4
8
2
7
6
.
[3
2
]
B.
M
a
h
d
a
d
,
T.
Bo
u
k
ti
r
,
a
n
d
K.
S
r
a
iri
,
“
A
T
h
re
e
-
P
h
a
se
P
o
w
e
r
F
lo
w
M
o
d
e
li
z
a
ti
o
n
:
A
T
o
o
l
f
o
r
Op
ti
m
a
l
L
o
c
a
ti
o
n
a
n
d
Co
n
tr
o
l
of
F
A
CT
S
De
v
ice
s
in
Un
b
a
lan
c
e
d
P
o
w
e
r
S
y
ste
m
s,
”
IECON
2
0
0
6
-
3
2
n
d
An
n
u
a
l
Co
n
f
e
re
n
c
e
on
IE
EE
In
d
u
stria
l
El
e
c
tro
n
ics
,
2
0
0
6
,
p
p
.
2
2
3
8
-
2
2
4
3
,
d
o
i:
1
0
.
1
1
0
9
/I
ECON.
2
0
0
6
.
3
4
7
7
6
6
.
[3
3
]
T.
C.
T
ra
n
,
P.
Br
a
n
d
ste
tt
e
r,
V.
H.
Du
y
,
H.
H.
V
o
,
C.
D.
T
ra
n
a
n
d
S.
D.
Ho
,
“
R
o
to
r
T
ime
Co
n
sta
n
t
Esti
m
a
ti
o
n
of
In
d
u
c
ti
o
n
M
o
t
o
r
Us
in
g
On
li
n
e
PI
-
A
d
a
p
ti
v
e
a
n
d
GA
-
A
d
a
p
ti
v
e
M
o
d
e
l,
”
in
I
n
ter
n
a
ti
o
n
a
l
Co
n
fer
e
n
c
e
on
Ad
v
a
n
c
e
d
En
g
i
n
e
e
rin
g
T
h
e
o
ry
a
n
d
A
p
p
li
c
a
t
io
n
s
,
20
1
7
,
p
p
.
8
6
0
-
8
7
1
,
do
i
:
1
0
.
1
0
0
7
/9
7
8
-
3
-
3
1
9
-
6
9
8
1
4
-
4
_
8
3
.
[3
4
]
C.
D.
T
ra
n
,
P.
Bra
n
d
ste
tt
e
r,
M.
H.
C.
Ng
u
y
e
n
,
S.
D.
Ho
,
P.
N.
P
h
a
m
,
a
n
d
B.
H.
Din
h
,
“
An
Im
p
ro
v
e
d
C
u
rre
n
t
-
S
e
n
so
rles
s
M
e
th
o
d
f
o
r
In
d
u
c
ti
o
n
M
o
to
r
Driv
e
s
A
p
p
ly
in
g
H
y
ste
r
e
sis
Cu
rre
n
t
Co
n
tr
o
ll
e
r,
”
In
d
o
n
e
sia
n
J
o
u
rn
a
l
of
El
e
c
trica
l
En
g
in
e
e
rin
g
a
n
d
In
f
o
r
ma
ti
c
s
(
IJ
EE
I)
.,
v
o
l.
9,
n
o
.
1,
p
p
.
130
-
1
4
0
,
2
0
2
1
,
d
o
i:
1
0
.
5
2
5
4
9
/
ij
e
e
i.
v
9
i1
.
1
6
1
9
.
[3
5
]
S.
D.
H
o
,
P.
P
a
lac
k
y
,
M.
Ku
c
h
a
r,
P.
Bra
n
d
ste
tt
e
r
,
a
n
d
C.
D.
T
ra
n
,
“
P
a
rti
c
le
sw
a
r
m
o
p
ti
m
iza
ti
o
n
-
b
a
se
d
sta
to
r
re
sista
n
c
e
o
b
se
rv
e
r
f
o
r
sp
e
e
d
se
n
so
rles
s
in
d
u
c
ti
o
n
m
o
to
r
d
riv
e
,
”
I
n
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
of
El
e
c
trica
l
a
n
d
Co
m
p
u
te
r
En
g
i
n
e
e
rin
g
.,
v
o
l.
1
1
,
n
o
.
1,
p
p
.
8
1
5
-
8
2
6
,
2
0
2
1
,
d
o
i:
1
0
.
1
1
5
9
1
/i
jec
e
.
v
1
1
i1
.
p
p
8
1
5
-
8
2
6
.
[3
6
]
S.
D.
Ho
,
P.
Bra
n
d
ste
tt
e
r,
P.
P
a
lac
k
y
,
M.
Ku
c
h
a
r,
B.
H.
Din
h
,
a
n
d
C.
D.
T
ra
n
,
“
Cu
rre
n
t
se
n
so
rles
s
met
hod
b
a
se
d
on
f
ield
-
o
rien
ted
c
o
n
tro
l
in
in
d
u
c
ti
o
n
m
o
to
r
d
riv
e
,
”
J
o
u
rn
a
l
of
E
lec
trica
l
S
y
ste
ms
.,
v
o
l
.
1
7
,
n
o
.
1,
p
p
.
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