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59
1
G
W
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20
1
8
[1
]
.
M
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,
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f
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ti
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wi
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[2
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.
T
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.
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[4
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.
T
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t
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F
AC
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de
vi
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wo
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m
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F
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,
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[6
]
.
W
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n
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r
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m
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d
el
i
b
er
at
e
d
i
n
al
l
o
cat
i
o
n
i
ssu
e
.
A
n
a
p
o
r
t
i
o
n
o
f
t
h
e
e
x
p
r
e
s
s
e
d
g
o
a
l
s
i
n
t
h
e
l
i
t
e
r
a
t
u
r
e
a
r
e
:
n
e
t
w
o
r
k
l
o
a
d
a
b
i
l
i
t
y
e
n
h
a
n
c
e
m
e
n
t
,
l
i
n
e
t
h
e
r
m
a
l
c
o
n
s
t
r
a
i
n
t
s
v
i
o
l
a
t
i
o
n
[7
]
.
S
o
m
e
i
nt
e
r
e
s
ti
ng s
t
udi
e
s
a
r
e
f
oc
us
e
d on t
he
i
n
ve
s
t
i
ga
ti
on of
l
os
s
r
e
duc
t
i
on
,
vol
t
a
ge
pr
of
i
l
e
e
nha
nc
e
m
e
nt
[8
,
9
]
,
v
o
l
t
a
g
e
s
t
a
b
i
l
i
t
y
i
m
p
r
o
v
e
m
e
n
t
,
f
u
e
l
c
o
s
t
r
e
d
u
c
t
i
o
n
[
10
]
,
r
e
l
i
v
i
n
g
t
r
a
n
s
m
i
s
s
i
o
n
l
i
n
e
c
on
ge
s
t
i
o
n
[1
1
]
an
d
e
n
h
an
ce
m
en
t
av
ai
l
ab
l
e t
r
an
s
f
er
c
ap
ab
i
l
i
t
y
(
A
T
C
)
[
12
]
.
E
ac
h
o
f
t
h
e a
b
o
v
e
s
t
at
ed
o
b
j
ect
i
v
es
en
h
an
ce
p
o
w
e
r
s
y
s
t
e
m
p
er
f
o
r
m
an
ce.
B
e
t
h
at
as
i
t
m
ay
,
i
m
p
r
o
v
em
en
t
i
n
o
n
e
g
o
al
d
o
es
n
'
t
g
u
ar
an
t
ee
a
s
i
m
i
l
a
r
up
g
r
a
de
i
n
ot
he
r
s
.
Al
o
ng
t
he
s
e
l
i
n
es
,
n
o
n
e
o
f
t
h
e ex
p
r
e
s
s
ed
s
p
eci
al
i
zed
g
o
al
s
can
'
t
b
e
s
u
r
r
e
n
d
e
r
e
d
i
n t
he
a
l
l
oc
a
t
i
on
of
F
AC
T
S
c
ont
r
ol
l
e
r
.
T
he
r
e
f
or
e
,
t
he
a
l
l
oc
a
t
i
on o
f
F
A
C
T
S
c
o
nt
r
ol
l
e
r
due
t
o
one
or
m
or
e
ob
je
c
t
i
ve
s
w
hi
l
e
not
t
a
ki
n
g i
nt
o t
h
o
ug
ht
t
h
e
c
os
t
of
t
he
d
e
vi
c
e
s
i
s
n
ot
a
pr
a
c
t
i
c
a
l
o
n
e
.
I
n
d
e
t
a
i
l
,
t
h
e
o
p
t
i
m
a
l
a
l
l
oc
a
t
i
on
of
F
AC
T
S
c
ont
r
ol
l
e
r
s
h
o
ul
d
be
e
xp
r
e
s
s
e
d a
s
m
ul
t
i
-
o
bje
c
t
i
ve
opt
i
m
i
z
a
ti
on (
M
O
P
)
i
s
s
ue
f
r
om
bot
h
eco
n
o
m
i
cal
an
d
t
ech
n
i
cal
p
o
i
n
t
s
o
f
v
i
e
w
s
.
F
u
r
t
h
e
r
m
o
r
e,
m
o
s
t
o
f
t
h
e
p
r
es
e
n
t
r
e
s
ear
ch
ar
e
es
t
ab
l
i
s
h
ed
o
n
a
s
up
p
os
i
t
i
on
t
ha
t
t
he
r
e
i
s
no
va
r
i
a
t
i
o
n
i
n
t
he
de
m
a
nd
l
oa
d
ove
r
t
i
m
e
.
T
he
s
e
a
pp
r
oa
c
he
s
ha
ve
be
e
n
c
a
r
r
i
e
d
o
u
t
un
de
r
a
f
i
xe
d
l
oa
d
p
r
of
i
l
e
o
r
ove
r
l
oa
de
d
c
on
di
t
i
ons
.
C
ons
i
de
r
i
ng
u
nc
e
r
t
a
i
nt
y
o
f
t
he
i
n
put
pa
r
a
m
e
t
e
r
s
of
t
he
po
we
r
s
y
s
t
e
m
,
va
r
i
o
us
m
e
t
hods
ha
ve
be
e
n
pl
a
n
ne
d f
o
r
e
s
t
i
m
a
t
i
n
g
t
h
e
s
t
a
t
e
o
f
t
h
e
p
o
w
e
r
s
y
s
t
e
m
.
T
h
e
m
o
s
t
p
e
r
f
e
c
t
t
e
c
h
n
i
q
u
e
i
s
M
o
n
t
e
Ca
r
l
o
s
i
m
u
l
a
t
i
o
n
(
M
C
S
)
,
w
hi
c
h
i
s
us
ua
l
l
y
us
e
d a
s
s
t
a
nda
r
d m
e
t
hod
[
13]
.
M
C
S
p
r
o
vi
de
s
t
he
m
os
t
pr
o
pe
r
out
c
om
e
s
b
ut
t
h
e
c
a
l
c
u
l
a
t
i
o
n
i
s
m
u
c
h
t
i
m
e
-
e
x
h
a
u
s
t
i
o
n
;
t
h
u
s
,
i
t
i
s
n
o
t
a
p
p
r
o
p
r
i
a
t
e
f
o
r
r
e
a
l
t
i
m
e
i
m
p
l
e
m
e
n
t
a
t
i
o
n
.
So
a
s
t
o
d
i
m
i
n
i
s
h
t
h
e
c
o
m
p
u
t
a
t
i
o
n
a
l
e
x
e
r
t
i
o
n
r
e
l
a
t
e
d
w
i
t
h
s
i
m
u
l
a
t
i
o
n
-
b
as
e
d
s
t
r
at
eg
i
es
,
an
al
y
t
i
cal
an
d
es
t
i
m
at
i
o
n
t
e
c
hni
q
ue
s
ha
ve
be
e
n u
t
i
l
i
z
e
d.
A
p
pr
o
xi
m
a
t
i
on m
e
t
hods
c
ons
i
s
t
of
P
E
M
[
14
]
.
Cu
m
u
l
a
n
t
m
e
t
h
o
d
(
CM
)
i
s
p
r
e
s
e
n
t
l
y
t
h
e
i
l
l
u
s
t
r
a
t
i
v
e
o
f
a
n
a
l
y
t
i
c
a
l
p
r
o
c
e
d
u
r
e
s
[
15
]
.
In
[
16
]
a
p
r
oba
bi
l
i
s
t
i
c
t
e
c
hni
qu
e
s
f
or
t
he
s
i
z
i
ng
o
f
m
u
l
t
i
p
l
e
F
A
CT
S
c
o
n
t
r
o
l
l
e
r
i
n
p
o
w
e
r
s
y
s
t
e
m
s
f
o
r
s
t
e
a
d
y
-
s
t
a
t
e
vol
t
a
ge
pr
of
i
l
e
i
m
pr
ove
m
e
nt
us
i
ng
M
C
S
t
e
c
hni
q
ue
a
r
e
us
e
d.
I
n
[1
7
]
a
l
s
o,
opt
im
a
l
a
l
loc
a
ti
on of
F
A
C
T
S
c
ont
r
oll
e
r
s
t
o
m
i
nim
iz
e
the
c
os
t
of
ge
ne
r
a
ti
on
wa
s
s
ol
ve
d by di
f
f
e
r
e
nt
ia
l
e
vol
ut
i
on a
l
gor
i
th
m
DE
i
n c
oinc
i
de
nc
e
w
it
h
M
ont
e
C
a
r
l
o s
im
u
l
a
t
i
o
n
(
D
E
-
MC
S
)
t
a
k
i
n
g
i
nt
o a
c
c
ount
unc
e
r
t
a
i
n
ty
i
n l
oa
d a
nd
wi
nd ge
ne
r
a
t
i
o
n out
put
.
In
[1
8
]
a
m
u
l
t
i
-
o
b
j
e
c
t
i
v
e
f
u
n
c
t
i
o
n
w
a
s
pr
o
pos
e
d f
or
opt
i
m
a
l
a
l
l
oc
a
t
i
on of
a
UP
F
C
i
n p
owe
r
s
y
s
t
e
m
c
ons
i
d
e
r
e
d
t
he
m
a
xi
m
i
z
a
t
i
o
n
o
f
s
y
s
t
e
m
p
r
e
d
i
c
t
a
b
i
l
i
t
y
a
n
d
m
i
n
i
m
i
z
a
t
i
o
n
a
c
t
i
v
e
p
o
w
e
r
l
o
s
s
u
s
i
n
g
N
S
G
A
-
I
I
.
H
o
w
ev
e
r
,
t
h
e
s
e p
ap
er
s
h
a
v
e n
o
t
p
ai
d
a
t
t
e
nt
i
on t
o
a
n
d
t
he
l
oa
d
c
or
r
e
l
a
t
i
on
o
n
p
ow
e
r
s
y
s
t
e
m
.
T
hi
s
pa
pe
r
pr
e
s
e
nt
s
a
n a
p
p
r
oa
c
h ba
s
e
d o
n m
ul
ti
-
ob
je
c
t
i
ve
f
u
nc
t
i
o
ns
f
o
r
s
ol
vi
n
g t
h
e
a
l
l
o
c
a
t
i
o
n
pr
o
bl
e
m
of
F
A
C
T
S
de
vi
c
e
s
c
ons
i
de
r
i
ng
hi
g
h pe
ne
t
r
a
t
i
o
n l
e
ve
l
of
w
i
n
d e
ne
r
gy
u
nde
r
u
n
c
e
r
t
a
i
nt
i
e
s
i
n de
m
a
nd
a
nd
wi
nd
ge
ne
r
a
t
i
on
o
ut
p
ut
.
M
or
e
ove
r
,
t
he
l
oa
d c
or
r
e
l
a
t
i
o
n i
s
c
ons
i
de
r
e
d.
T
he
pr
o
po
s
e
d a
l
g
or
i
t
hm
M
OP
S
O
w
i
t
h c
om
bi
ne
d 2
P
E
M
(
M
O
P
S
O
–
P
E
M
)
i
s
i
n
t
r
o
duc
e
d
f
o
r
F
AC
T
S
c
ont
r
ol
l
e
r
a
l
l
oc
a
t
i
on p
r
obl
e
m
un
d
e
r
unc
e
r
t
a
i
nt
i
e
s
.
T
hi
s
pa
pe
r
p
r
o
pos
e
s
t
he
us
e
o
f
2
P
E
M
i
ns
t
e
a
d o
f
M
C
S
,
be
c
a
us
e
P
E
M
i
s
m
uc
h
f
a
s
t
e
r
t
ha
n
M
C
S
i
n s
ol
vi
n
g
p
r
o
b
a
b
i
l
i
t
y
o
p
t
i
m
a
l
p
o
w
e
r
f
l
o
w
(P
O
P
F
) p
r
o
b
l
e
m
s
.
T
he
r
e
m
inde
r
of
t
he
pa
pe
r
i
s
o
r
ga
ni
z
e
d a
s
f
o
l
l
o
w
s
:
m
o
d
e
l
i
n
g
o
f
t
h
e
u
n
c
e
r
t
a
i
n
t
i
e
s
i
s
g
i
v
e
n
i
n
s
e
c
t
i
o
n
2
.
M
a
t
h
e
m
a
t
i
c
a
l
m
o
d
e
l
i
n
g
o
f
F
A
CT
S
i
s
p
r
e
s
e
n
t
i
n
s
e
c
t
i
on
3.
T
he
2P
E
M
f
or
P
P
F
c
a
l
c
ul
a
t
i
o
n
i
s
de
f
i
ne
d i
n
s
e
c
t
i
on
4
.
T
he
pr
o
bl
e
m
f
or
m
ul
a
t
i
on i
s
p
r
e
s
e
nt
i
n s
e
c
t
i
on 5.
T
he
p
r
o
p
os
e
d
(
M
OP
S
O
–
2
P
EM
)
i
s d
e
sc
r
i
b
ed
i
n
s
ect
i
o
n
6
.
I
n
s
ect
i
o
n
7
,
cas
e s
t
u
d
y
an
d
t
h
e
s
i
m
u
l
a
t
i
o
n
r
e
s
u
l
t
s
a
r
e
p
r
e
s
e
n
t
e
d
.
Co
n
c
l
u
s
i
o
n
s
a
r
e
p
r
e
s
e
n
t
e
d
i
n
s
e
c
t
i
o
n
8
.
2.
MO
DE
L
I
N
G
O
F
S
Y
S
T
E
M
U
N
C
E
RT
A
I
N
T
I
E
S
T
he
s
y
s
t
e
m
l
oa
ds
a
r
e
m
ode
l
e
d a
s
P
Q
b
us
e
s
w
i
t
h
de
f
i
ni
t
e
a
c
t
i
ve
a
nd
r
e
a
c
t
i
ve
p
o
w
e
r
a
nd
t
he
w
i
nd
f
a
r
m
out
put
i
s
m
ode
l
e
d a
s
ne
ga
t
i
ve
l
oa
d
.
F
a
m
ous
l
y
,
t
he
l
o
a
ds
o
ug
ht
n
o
t
t
o
b
e c
o
n
s
i
d
er
ed
as
a
d
et
er
m
i
n
i
s
t
i
c
v
al
u
e.
R
at
h
er
,
t
h
ey
ar
e g
e
n
e
r
al
l
y
d
e
m
o
n
s
t
r
a
t
ed
as
a t
y
p
i
c
a
l
o
f
G
a
u
s
s
i
a
n
p
r
o
b
a
b
i
l
i
t
y
d
e
n
s
i
t
y
f
u
n
c
t
i
o
n
(
P
D
F
)
w
h
os
e
m
e
a
n is
e
qui
v
a
l
e
nt
t
o a
n e
x
pe
c
t
e
d
va
l
ue
.
I
n ut
m
os
t c
a
s
e
s
,
t
he
s
t
a
nda
r
d de
vi
a
t
i
on o
f
t
he
P
DF
i
s
a
f
r
a
c
t
i
on
of
t
h
e
e
s
t
im
a
t
e
d l
oa
d va
l
ue
.
I
n t
hi
s
s
t
udy
t
he
l
oa
d
i
n e
a
c
h bus
i
s
de
m
ons
t
r
a
t
e
d
wi
t
h m
e
a
n (
µ)
eq
u
al
t
o
t
he
ba
s
e
l
oa
d
a
n
d
s
t
a
nda
r
d
de
vi
a
t
i
o
n
(
σ
)
i
s
a
s
s
um
e
d
t
o
b
e
±
7
%
o
f
t
he
ba
s
e
l
oa
d.
T
h
e
no
r
m
a
l
di
s
t
r
ibut
i
o
n
of
t
he
l
oa
d
de
m
a
nd
(
d
)
i
s
pr
e
s
e
nt
e
d
a
s
[
1
9,
20]
:
F
(
d
)
=
1
σ
√
2
π
∗
ex
p
−
(
d
−
μ
)
2
2
σ
2
(
1
)
w
he
r
e
,
t
he
va
r
i
a
t
i
on o
f
wi
n
d
po
w
e
r
o
ut
p
ut
i
s
a
n u
nc
e
r
t
a
i
n
pa
r
a
m
e
t
e
r
,
w
hi
c
h c
a
n
be
m
od
e
l
e
d us
i
ng
hi
s
t
or
i
c
a
l
da
t
a
r
e
c
or
ds
o
f
t
he
w
i
n
d
s
pe
e
d.
I
n
t
hi
s
wo
r
k,
va
r
i
a
t
i
o
n
o
f
t
h
e
w
i
n
d
s
pe
e
d,
v
,
i
s
m
o
d
e
l
e
d
u
s
i
n
g
W
e
i
b
u
l
l
P
D
F
a
s
f
o
l
l
o
w
[
21
]
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-
87
08
In
t
J
E
l
e
c
&
C
om
p
E
n
g,
V
o
l
.
10
,
No
.
4
,
A
ug
us
t
20
2
0
:
38
98
-
391
0
3
900
(
)
=
−
1
−
(
2
)
w
h
e
re
k
i
s
s
h
ap
e
p
a
r
am
et
er
an
d
c
:
i
s
s
cal
i
n
g
p
ar
am
et
er
m
/
s
.
I
t
i
s a
ssu
m
e
d
t
ha
t
i
n e
a
c
h r
e
g
i
on,
t
he
P
D
F
o
f
wi
nd s
pe
e
d i
s
kn
o
w
n
,
t
he
r
e
f
o
r
e
,
t
he
t
r
a
ns
f
or
m
a
t
i
on of
w
i
n
d
s
pe
e
d
t
o
w
i
n
d
t
u
r
bi
ne
o
ut
p
ut
p
o
w
e
r
i
s
gi
ve
n
by
:
=
⎩
⎪
⎨
⎪
⎧
0
,
−
−
,
,
0
,
o
o
r
r
i
i
v
v
v
v
v
v
v
v
v
v
>
≤
≤
≤
≤
≤
≤
0
(
3
)
w
h
er
e
,
V
i
,
V
o
i
s
t
h
e
c
u
t
-
in
a
nd
c
u
t
-
out
wi
n
d
s
pe
e
d
,
V
r
i
s
t
he
r
a
t
e
d
s
pe
e
d
a
n
d
P
r
i
s
t
he
r
a
t
e
d
po
we
r
.
3.
F
AC
T
S
DE
VI
CE
S
AN
D
M
O
D
E
L
I
N
G
F
A
C
T
S
c
ont
r
o
l
l
e
r
t
e
c
hnol
og
y
i
nc
l
ude
s
a
s
e
t
of
c
o
nt
r
ol
l
e
r
s
t
ha
t
pr
o
vi
de
c
ont
r
ol
o
ve
r
one
or
m
or
e
t
r
a
ns
m
i
s
s
i
on s
y
s
t
e
m
s
pa
r
a
m
e
t
e
r
s
.
T
he
s
e
F
A
C
T
S
c
ont
r
ol
l
e
r
c
a
n c
oo
r
di
na
t
e
wi
t
h c
o
nt
r
ol
uni
t
s
or
o
pe
r
a
t
e
s
t
a
n
d
-
a
l
o
ne
.
F
AC
T
S
c
ont
r
ol
l
e
r
us
e
p
owe
r
e
l
e
c
t
r
oni
c
s
c
o
n
ve
r
t
er
s
.
T
h
es
e
co
n
v
e
r
t
er
s
c
o
n
t
r
o
l
t
h
e
p
o
w
er
f
l
o
w
s
a
nd i
m
pr
o
ve
t
he
u
s
a
ge
o
f
t
h
e
t
r
a
ns
m
i
s
s
i
on
’
s
l
i
ne
s
.
I
n l
i
t
e
r
a
t
ur
e
,
t
he
c
ur
r
e
nt
s
t
e
a
dy
-
s
t
a
t
e
m
o
d
e
l
s
o
f
F
A
CT
S
co
n
t
r
o
l
l
er
can
b
e
cl
as
s
i
f
i
e
d
as
t
w
o
cat
eg
o
r
i
es
:
p
o
w
e
r
i
n
j
ect
i
o
n
m
o
d
el
an
d
v
ar
i
a
b
l
e
r
eact
a
n
ce
m
o
d
el
i
n
g
.
3.
1.
SV
C
m
o
de
l
S
V
C
i
s
us
e
d a
s
a
c
ont
r
ol
l
e
d
s
ou
r
c
e
of
t
he
r
e
a
c
t
i
ve
po
w
e
r
.
T
he
m
a
i
n f
e
a
t
ur
e
of
S
V
C
i
s
t
o pr
o
vi
de
vol
t
a
ge
s
t
a
bi
l
i
t
y
wi
t
ho
ut
us
i
n
g l
a
r
ge
r
e
a
c
t
o
r
s
a
nd
ba
n
ks
o
f
c
a
pa
c
i
t
o
r
s
t
o
a
bs
o
r
b
or
s
u
p
pl
y
r
e
a
c
t
i
ve
p
ow
e
r
.
T
h
u
s
,
a
S
V
C c
o
n
t
r
o
l
i
t
s
i
n
d
u
c
t
i
v
e
o
r
c
a
pa
c
i
t
i
ve
c
ur
r
e
nt
i
n
de
pe
n
de
nt
l
y
o
f
t
he
s
y
s
t
e
m
vo
l
t
a
ge
.
T
h
e
S
V
C
can
co
n
s
u
m
e o
r
i
n
j
ect
r
eact
i
v
e p
o
w
er
i
n
t
h
e co
n
n
ect
ed
b
u
s
.
I
f
t
h
e b
u
s
v
o
l
t
ag
e
i
s
l
ow
e
r
t
ha
n t
he
r
e
q
ui
r
e
d v
o
l
t
a
ge
,
t
h
e
S
V
C i
n
j
e
c
t
s
r
e
a
c
t
i
v
e
p
o
w
e
r
i
n
t
o
t
h
i
s
b
u
s
t
o
i
n
c
r
e
a
s
e
i
t
s
v
o
l
t
a
g
e
;
t
h
i
s
c
a
s
e
i
s
s
i
m
i
l
a
r
t
o
a
c
a
p
a
c
i
t
i
v
e
be
ha
vi
o
r
a
s
s
h
ow
n i
n F
i
gu
r
e
1
(
a
)
H
o
w
ev
er
,
w
he
n t
he
b
u
s
vol
t
a
ge
i
s
a
b
ove
t
he
r
e
qui
r
e
d v
ol
t
a
ge
,
t
he
S
V
C
ab
s
o
r
b
r
eact
i
v
e p
o
w
er
f
r
o
m
t
h
i
s
b
u
s
t
o
d
ecr
eas
e i
t
s
v
o
l
t
ag
e;
t
h
i
s
cas
e i
s
s
i
m
i
l
ar
t
o
i
n
d
u
ct
i
v
e b
e
h
a
v
i
o
r
.
T
h
e
S
V
C
b
u
s
i
n
t
h
e
n
et
w
o
r
k
can
b
e
r
ep
r
es
e
n
t
ed
b
y
ab
s
o
r
b
ed
o
r
i
n
j
ect
ed
r
eact
i
v
e
p
o
w
e
r
.
Th
e
wor
k
i
ng
r
a
ng
e
of
i
s
se
t
-
100
t
o
100
MV
A
R
[2
2
]
.
MV
A
R
i
mi
n
≤
MV
A
R
i
≤
MV
A
R
i
m
ax
(
4
)
3.
2.
T
C
SC
m
o
de
l
T
C
S
C
act
s
as
a s
er
i
es
-
c
o
n
t
r
o
l
l
ed
r
eact
an
ce,
w
h
i
c
h
ai
m
t
o
co
m
p
en
s
at
e t
h
e i
m
p
ed
an
ce o
f
t
h
e
t
r
a
n
s
m
i
s
s
i
o
n
l
i
n
e
s
.
T
h
e
s
w
i
t
c
h
i
n
g
o
f
t
h
e
T
CS
C g
i
v
e
a
m
e
c
h
a
n
i
s
m
t
o
c
o
n
t
r
o
l
p
o
w
e
r
f
l
o
w
,
w
h
i
c
h
a
l
l
o
w
s
r
i
s
i
ng t
he
l
oa
d
of
t
he
e
xi
s
t
i
n
g g
r
i
d.
I
n a
d
d
i
t
i
on,
T
C
S
C
c
a
n da
m
p t
he
i
nt
e
r
a
r
e
a
os
c
i
l
l
a
t
i
on of
t
he
l
a
r
ge
e
l
e
c
t
r
i
c
a
l
ne
t
wor
k,
a
n
d
o
f
f
e
r
s
a
n
op
p
or
t
u
ni
t
y
of
po
w
e
r
f
l
o
w
a
d
jus
t
m
e
nt
in
r
e
s
po
ns
e
t
o
d
i
f
f
e
r
e
nt
c
o
nt
i
n
ge
nc
i
e
s
t
h
at
m
ay
t
ak
e
p
l
ace i
n
el
ect
r
i
cal
ne
t
w
or
k
.
A
l
s
o
,
T
h
e T
C
S
C
can
r
eg
u
l
at
e t
h
e s
t
ead
y
-
s
t
a
t
e
p
o
w
e
r
f
l
o
w
t
o
r
e
t
a
i
n
i
t
w
i
t
h
i
n
t
h
e
l
i
n
e
’
s
t
h
e
r
m
a
l
l
i
m
i
t
s
.
T
h
e T
C
S
C
ar
e co
n
s
i
d
er
e
d
as
a
v
ar
i
ab
l
e r
eact
a
n
ce (
)
w
h
i
c
h
i
s
c
o
n
n
e
c
t
e
d
i
n
s
e
r
i
e
s
w
i
t
h
t
h
e
t
r
a
n
s
m
i
s
s
i
o
n
l
i
n
e
a
s
s
h
o
w
n
i
n
F
i
g
u
r
e
1
(
b
)
.
T
he
va
r
i
a
t
i
on o
f
p
r
ov
ide
r
e
gu
la
tin
g
a
c
tiv
e
p
ow
e
r
thr
oug
h
th
e
t
r
a
n
s
m
i
s
s
i
o
n
l
i
n
e
.
T
CS
C
i
s
i
m
p
l
e
m
e
n
t
e
d
u
s
i
n
g
a
c
o
n
t
r
o
l
l
e
d
s
e
r
i
e
s
r
e
a
c
t
o
r
i
n
p
a
r
a
l
l
e
l
w
i
t
h
a
f
i
x
e
d
s
e
r
i
e
s
c
a
p
a
c
i
t
o
r
.
Co
n
s
e
q
u
e
n
t
l
y
,
t
o
g
u
a
r
a
n
t
e
e
t
h
e
s
y
s
t
e
m
s
t
a
b
i
l
i
t
y
,
i
t
i
s
a
d
v
o
c
a
t
e
t
o
co
m
pe
ns
a
t
e
u
p
t
o c
om
pe
ns
a
t
i
ng
de
gr
e
e
(
)
o
f
t
h
e l
i
n
e
n
o
m
i
n
al
r
eact
an
c
e
v
al
u
e
(
X
li
n
e
)
,
b
ot
h
i
n i
nd
uc
t
i
ve
(
,
)
an
d
t
h
e ca
p
aci
t
i
v
e (
,
)
o
p
er
at
i
n
g
z
o
n
es
.
A
s
a r
es
u
l
t
,
t
h
e t
o
t
al
b
r
a
n
ch
r
eact
a
n
ce (
X
ij
)
i
s
a
s
fo
l
l
o
ws
[2
3
]
.
(
a)
(
b)
F
ig
ur
e
1
.
M
o
d
e
l
s
o
f
F
A
CT
S
c
o
n
t
r
o
l
l
e
r
(
a
)
S
V
C
(b
)
T
C
S
C
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
E
l
e
c
&
C
om
p
E
n
g
I
S
S
N
:
208
8
-
87
08
A
p
r
o
b
a
b
i
l
i
s
t
i
c
m
u
l
t
i
-
ob
je
c
tiv
e
ap
pr
oa
c
h
fo
r
F
A
CT
S
d
e
v
i
c
e
s
a
l
l
o
c
a
t
i
o
n
wi
t
h
…
(
M.
E
L
-
Az
a
b
)
3
901
T
h
e
e
q
u
i
v
al
en
t
r
eact
an
ce
o
f
b
r
an
c
h
i
s
:
=
+
(
5
)
=
(
6
)
w
h
e
re
,
ar
e c
o
m
p
en
s
at
i
o
n
d
eg
r
ee a
n
d
b
r
a
n
ch
r
eact
an
ce
,
r
es
p
ect
i
v
el
y
.
X
TCSC
i
s
t
h
e
T
CS
C
r
eact
an
ce.
T
h
e
d
eg
r
ee
o
f
t
h
e
p
r
act
i
cal
co
m
p
en
s
at
i
o
n
o
f
t
h
e
T
C
S
C
v
a
r
i
es
b
et
w
ee
n
8
0
%
cap
aci
t
i
v
e
an
d
2
0
%
i
n
d
u
c
t
i
v
e
[
23
]
.
4.
P
R
O
B
A
BLI
S
TI
C
LO
A
D
F
LO
W
T
h
e d
et
er
m
i
n
i
s
t
i
c p
o
w
e
r
f
l
o
w
an
al
y
s
i
s
o
f
t
h
e p
er
f
o
r
m
an
ce
o
f
t
h
e s
y
s
t
e
m
r
el
i
es
o
n
cer
t
ai
n
s
p
eci
f
i
c
s
cen
ar
i
o
a
n
d
i
g
n
o
r
e t
h
e
u
n
ce
r
t
ai
n
t
y
w
i
t
h
i
n
t
h
e
p
ar
am
et
er
s
o
f
t
h
e
s
y
s
t
em
an
d
t
h
e
s
t
at
es
.
I
t
c
o
n
s
i
d
e
r
s
t
h
at
al
l
t
h
e
s
t
a
t
e
s
a
r
e
k
n
ow
n a
n
d
f
i
xe
d.
O
n
t
he
ot
he
r
ha
n
d,
a
p
r
o
ba
bi
l
i
s
t
i
c
a
pp
r
oa
c
h
,
e
va
l
ua
t
e
s
t
he
pr
ob
a
bi
l
i
ty
d
i
s
t
r
i
b
u
t
i
o
n
f
o
r
t
h
e u
n
cer
t
ai
n
v
ar
i
a
b
l
es
,
co
n
s
eq
u
e
n
t
l
y
,
w
el
l
r
ef
l
ect
t
h
e d
ef
i
n
i
t
e s
y
s
t
e
m
p
er
f
o
r
m
an
ce.
S
e
v
er
al
m
e
t
hods
f
o
r
p
r
o
ba
bi
l
i
s
t
i
c
l
oa
d f
l
o
w (
P
L
F
)
s
t
udy
ha
ve
be
e
n e
s
t
a
bl
i
s
he
d.
T
he
s
e
m
e
t
hods
f
a
l
l
i
n t
hr
e
e
ba
s
i
c
gr
o
ups
:
a
na
l
y
t
i
c
a
l
m
e
t
hod
s
,
M
C
S
pr
oc
e
d
ur
e
s
,
a
nd a
pp
r
ox
im
a
t
e
m
e
t
hods
.
P
oi
nt
e
s
t
i
m
a
te
m
e
t
hod,
P
E
M
,
i
s
a
s
of
n
o
w t
he
de
l
e
ga
t
e
of
a
p
pr
oxi
m
a
t
e
m
e
t
hods
f
or
P
L
F
c
a
l
c
ul
a
t
i
ons
.
I
n t
hi
s
s
t
udy
,
t
he
t
hr
e
e
-
p
o
i
n
t
e
s
t
i
m
a
t
e
(
2P
E
M
+
1
)
m
e
t
ho
d i
s
a
ppl
i
e
d
he
r
e
t
o
ha
ndl
i
ng
t
he
u
nc
e
r
t
a
i
nt
y
e
f
f
e
c
t
s
[
14
,
24
]
.
T
he
o
r
i
gi
na
l
2
P
E
M
c
a
nn
ot
h
an
d
l
e co
r
r
el
at
ed
u
n
cer
t
ai
n
v
ar
i
ab
l
e.
T
o
s
o
l
v
e t
h
e p
r
o
b
ab
i
l
i
s
t
i
c o
p
t
i
m
al
p
o
w
e
r
f
l
o
w
w
i
t
h
co
r
r
e
l
a
t
e
d
v
a
r
i
a
b
l
e
s
,
t
he
c
o
va
r
i
a
nc
e
m
a
t
r
i
x t
r
a
ns
f
or
m
a
t
i
on m
e
t
h
od
[
25]
i
s
c
o
m
bi
ne
d i
nt
o t
he
or
i
gi
na
l
P
E
M
m
e
t
hod
wa
s
us
e
d.
I
n
t
h
i
s
s
t
u
d
y
t
h
e
c
o
r
r
e
l
a
t
i
o
n
c
o
e
f
f
i
c
i
e
n
t
i
s
s
e
t
t
o
0
.
7
.
4.
1.
(2
m
+
1
)
a
l
g
o
r
i
th
m
S
t
ep
1
:
D
et
e
r
m
i
n
e
t
h
e
n
u
m
b
er
o
f
u
n
ce
r
t
ai
n
p
ar
am
et
er
s
m
.
S
t
e
p
2
:
D
e
t
e
r
m
i
n
e
t
h
e
l
o
c
a
t
i
o
n
s
o
f
c
o
n
c
e
n
t
r
a
t
i
o
n
s
ξ
l
,
1
,
ξ
l
,
2
,
ξ
l
,
3
a
n
d
t
h
e
p
r
o
b
a
b
i
l
i
t
i
e
s
o
f
c
o
n
c
e
n
t
r
a
t
i
o
n
s
W
l,1
,
W
l,2
a
nd
W
l,3
f
o
r
eac
h
v
ar
i
a
b
l
e
.
,
1
=
,
3
2
+
,
4
+
3
∗
1
,
3
2
2
(
7
)
ξ
l
,
2
=
λ
l
,
3
2
−
,
4
+
3
∗
λ
1
,
3
2
2
(
8
)
,
3
=
0
(
9
)
w
h
e
re
,
3
a
nd
,
4
m
e
a
n
t
he
s
ke
w
ne
s
s
a
n
d
k
ur
t
os
i
s
of
t
h
e
r
an
d
o
m
i
n
p
u
t
p
ar
am
et
er
.
λ
i
,
3
=
∫
(
l
i
−
μ
i
)
3
∞
−
∞
f
i
dx
i
σ
i
3
λ
i
,
4
=
∫
(
l
i
−
μ
i
)
4
∞
−
∞
f
i
dx
i
σ
i
4
w
l
,
k
=
(
−
1
)
3
−
/
ξ
,
ξ
,
1
−
ξ
,
2
,
k
=
1
,
2
(
10
)
.
3
=
1
−
1
(
,
4
−
2
,
3
)
(
11
)
S
t
ep
3
:
D
et
e
r
m
i
n
e
t
h
e t
h
r
ee
co
n
cen
t
r
at
i
o
n
s
p
l
,
k
,
k
=1
:
3
f
o
r
eac
h
p
ar
am
et
er
.
p
,
1
=
μ
pl
+
ξ
l
,
1
σ
pl
(
12
)
p
,
2
=
μ
pl
+
ξ
l
,
2
σ
pl
(
13
)
p
l
,
3
=
μ
pl
(
14
)
w
h
e
re
σ
pl
a
nd
μ
pl
ar
e
s
t
an
d
ar
d
d
ev
i
at
i
o
n
a
n
d
t
h
e
m
ean
r
es
p
ect
i
v
el
y
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-
87
08
In
t
J
E
l
e
c
&
C
om
p
E
n
g,
V
o
l
.
10
,
No
.
4
,
A
ug
us
t
20
2
0
:
38
98
-
391
0
3
902
S
t
e
p
4
:
c
a
l
c
u
l
a
t
e
t
h
e
o
b
j
e
c
t
i
v
e
o
u
t
p
u
t
,
f
or
a
l
l
c
onc
e
nt
r
a
t
i
o
ns
us
i
n
g
D
O
P
F
.
,
(
,
)
=
,
(
,
)
(
1
,
1
,
1
,
…
,
,
,
…
,
1
,
)
(
15
)
w
h
e
re
,
=
1
:
3
,
=
1
:
,
x
i
s
t
h
e co
n
cen
t
r
at
i
o
n
[
μ
p1
,
μ
p1
,
μ
p1
,
…
…
,
p
l
,
k
,
…
.
.
,
μ
p1
]
a
n
d
u
i
s
t
h
e
v
e
c
t
o
r
o
f
c
ont
r
ol
va
r
i
a
bl
e
s
.
S
t
e
p
5
:
c
a
l
c
u
l
a
t
e
E
(
Y
)
a
n
d
E
(
Y
2
).
E
(
Y
)
=
∑
∑
(
w
l
,
k
∗
,
(
X
,
u
)
3
k
=
1
m
=
1
(
16
)
E
(
Y
)
2
=
∑
∑
(
w
l
,
k
∗
,
(
X
,
u
)
2
3
k
=
1
m
=
1
)
(
17
)
S
t
e
p
6
:
Ca
l
c
u
l
a
t
e
t
h
e
e
x
p
e
c
t
a
t
i
o
n
a
n
d
s
t
a
n
d
a
r
d
d
e
v
i
a
t
i
o
n
f
o
r
t
h
e
o
b
j
e
c
t
i
v
e
o
u
t
p
u
t
u
s
i
n
g
:
μ
=
E
(
Y
)
(
18
)
σ
=
E
(
2
)
−
(
μ
)
2
(
19
)
5.
P
RO
B
L
E
M
F
O
R
MU
L
A
T
I
O
N
A
ND
O
BJ
EC
TI
V
ES
F
U
N
C
TI
O
N
5
.
1
.
P
ro
b
l
em
s
t
a
t
e
men
t
T
h
e
g
o
a
l
i
n
t
h
i
s
s
t
u
d
y
i
s
t
o
i
m
p
r
o
v
e
t
h
e
e
l
e
c
t
r
i
c
a
l
n
e
t
w
o
r
k
l
o
a
d
a
b
i
l
i
t
y
c
o
n
s
i
d
e
r
i
n
g
s
t
a
t
i
c
s
e
c
u
r
i
t
y
i
n
t
e
r
m
s
of
l
i
ne
loa
di
ng a
n
d v
ol
t
a
ge
l
e
ve
l
t
hr
o
ug
h
opt
i
m
a
l
a
ll
oc
a
t
i
on
of
F
A
C
T
S
c
o
nt
r
ol
l
e
r
.
T
w
o c
a
t
e
g
or
i
e
s
o
f
F
A
CT
S
c
o
n
t
r
o
l
l
e
r
,
n
a
m
e
l
y
T
CS
Cs
a
n
d
S
V
Cs
a
r
e
l
o
c
a
t
e
d
i
n
or
de
r
a
l
l
e
v
i
a
t
e
t
he
b
us
v
ol
t
a
ge
a
n
d
ove
r
l
oa
d
s
vi
ol
a
t
i
on
s
.
T
he
O
P
F
p
r
o
bl
e
m
c
on
s
i
de
r
i
ng t
h
e
pr
e
s
e
nc
e
of
T
C
S
C
a
nd S
V
C
.
T
he
M
OP
c
a
n be
m
a
t
he
m
a
t
i
c
a
l
ly
d
ef
i
n
ed
as
[
26
]
.
M
i
n
i
m
i
z
e
x
i
n
,
(
)
=
{
1
(
)
,
2
(
)
,
…
…
.
(
)
}
(
20
)
S
u
b
jec
t
to
1
(
)
,
2
(
)
,
…
…
(
)
=
0
ℎ
1
(
)
,
ℎ
2
(
)
,
.
.
…
,
ℎ
(
)
≤
0
(
21
)
w
h
e
re
,
i
s
t
he
num
be
r
o
f
o
bje
c
t
i
v
e
f
unc
t
i
ons
,
i
s
t
he
num
be
r
of
i
ne
q
ua
l
i
t
y
c
ons
t
r
a
i
nt
s
a
n
d
i
s
t
he
n
um
be
r
of
e
qua
l
i
t
y
c
o
ns
t
r
a
i
nt
s
.
I
n t
he
M
OP
,
m
or
e
t
ha
n
o
ne
o
bje
c
t
i
v
e
f
unc
t
i
on i
s
be
i
n
g
opt
im
i
z
e
d s
im
ul
t
a
ne
o
us
l
y
.
M
o
s
t
of
t
he
t
im
e
,
one
c
om
m
on s
ol
ut
i
o
n c
o
ul
d n
ot
be
f
ou
n
d f
o
r
a
l
l
t
he
ob
je
c
t
i
ve
f
unc
t
i
o
n
s
i
n
t
h
e s
ear
ch
s
p
a
ce.
I
n
c
o
n
t
r
a
s
t
,
a s
et
of
be
s
t
p
oi
nt
s
c
o
ul
d
be
a
c
hi
e
ve
d
.
T
hi
s
s
e
t
of
p
oi
nt
s
i
s
r
e
f
e
r
r
e
d
a
s
t
he
P
a
r
e
t
o
s
ol
ut
i
o
n s
e
t
.
T
he
va
l
ue
s
of
t
he
P
a
r
e
t
o
o
pt
i
m
a
l
poi
nt
s
i
n
t
he
ob
je
c
t
i
ve
s
p
a
c
e
f
or
m
P
a
r
e
t
o
f
r
ont
i
n
t
he
o
bje
c
t
i
v
e
s
pa
c
e
.
T
he
s
ol
ut
i
o
n
f
o
r
t
h
i
s
ki
n
d
of
pr
o
bl
e
m
s
r
e
qui
r
e
s
p
oi
nt
s
i
n
t
he
o
bje
c
t
i
v
e
s
pa
c
e
s
h
oul
d c
on
ve
r
ge
t
o t
he
P
a
r
e
t
o f
r
o
nt
a
nd
c
ove
r
t
he
f
r
o
nt
[
27
]
.
5.
2.
O
b
je
c
ti
v
e
fu
n
c
ti
o
n
s
I
n
t
h
i
s
s
t
u
d
y
,
t
h
e
o
b
j
e
c
t
i
v
e
f
u
n
c
t
i
o
n
s
c
o
n
s
i
d
e
r
e
d
t
h
e
m
a
x
i
m
i
z
i
n
g
s
y
s
t
e
m
l
o
a
d
a
b
i
l
i
t
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t
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y
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e
m
s
ecu
r
i
t
y
co
n
s
t
r
ai
n
t
,
m
i
n
i
m
i
zi
n
g
t
h
e ex
p
ect
at
i
o
n
o
f
t
he
r
e
a
l
po
we
r
l
os
s
e
s
i
n t
he
t
r
a
ns
m
i
s
s
i
on l
i
ne
s
,
a
n
d
m
i
n
i
m
i
z
i
n
g
t
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e
s
t
a
b
l
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m
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n
t
c
o
s
t
o
f
F
A
CT
S
c
o
n
t
r
o
l
l
e
r
.
5.
2.
1.
M
i
n
i
m
i
z
at
i
on
of
r
e
al
p
ow
e
r
l
os
s
e
s
P
L
T
he
o
bje
c
t
i
ve
i
s
t
o
m
i
nim
i
z
e
the
a
c
t
i
ve
p
ow
e
r
l
os
s
i
n
t
he
t
r
a
ns
m
i
s
s
i
on
ne
t
w
o
r
k
c
a
n
be
f
o
r
m
ul
a
t
e
d
a
s
:
1
(
x
,
u
)
=
∑
[
V
i
2
+
V
j
2
−
2
V
i
V
j
co
s
(
δ
i
−
=
1
)
]
(
22
)
w
h
e
re
a
nd
nl
,
i
s
t
he
c
on
d
uc
t
a
nc
e
of
b
r
a
nc
h
k,
a
n
d
t
he
num
be
r
of
b
r
a
nc
he
s
r
e
s
pe
c
t
i
ve
l
y
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
E
l
e
c
&
C
om
p
E
n
g
I
S
S
N
:
208
8
-
87
08
A
p
r
o
b
a
b
i
l
i
s
t
i
c
m
u
l
t
i
-
ob
je
c
tiv
e
ap
pr
oa
c
h
fo
r
F
A
CT
S
d
e
v
i
c
e
s
a
l
l
o
c
a
t
i
o
n
wi
t
h
…
(
M.
E
L
-
Az
a
b
)
3
903
5.
2.
2.
M
axi
m
i
z
at
i
on
of
t
h
e
s
ys
t
e
m
l
o
ad
ab
i
l
i
t
y
T
h
e
l
o
a
d
a
b
i
l
i
t
y
o
f
e
l
e
c
t
r
i
c
a
l
n
e
t
w
o
r
k
i
s
t
h
e
a
b
i
l
i
t
y
f
o
r
s
w
e
l
l
i
n
g
a
s
m
u
c
h
a
s
c
o
n
c
e
i
v
a
b
l
e
t
h
e
p
o
w
e
r
t
r
an
s
m
i
t
t
ed
b
y
t
h
e n
et
w
o
r
k
t
o
t
h
e c
u
s
t
o
m
er
s
,
an
d
k
eep
i
n
g
t
h
e el
ect
r
i
cal
n
et
w
o
r
k
i
n
a s
af
e s
t
at
e i
n
t
er
m
s
o
f
br
a
nc
h
l
oa
di
n
g
a
n
d
vol
t
a
ge
l
e
ve
l
s
.
M
a
x
i
m
i
z
e
(
23
)
T
h
e
l
o
ad
f
act
o
r
,
i
s
de
f
i
ne
d
a
s
f
ol
l
ow
s
:
=
∗
[
(
)
]
(
24
)
=
∗
[
(
)
]
(
25
)
∈
[
1
,
]
(
26
)
w
h
e
re
,
ar
e
t
h
e
act
i
v
e
a
n
d
r
ea
ct
i
v
e
l
o
a
d
d
em
an
d
at
l
o
a
d
b
u
s
i
r
es
p
ect
i
v
el
y
.
T
he
o
bje
c
t
i
ve
f
unc
t
i
o
n
i
s
ba
s
e
d
on
i
n
de
xe
s
c
a
l
c
ul
a
t
i
ng
t
he
s
y
s
t
e
m
l
oa
da
bi
l
i
t
y
i
s
e
xp
r
e
s
s
e
d
a
s
:
2
(
,
)
=
1
(
27
)
5
.
2
.
3
.
F
A
C
TS
i
n
s
t
a
l
l
a
t
i
o
n
c
o
s
t
A
n
ot
he
r
ob
je
c
t
i
ve
f
unc
t
i
on
t
o
be
c
ons
i
de
r
e
d,
i
s
m
i
nim
i
z
i
ng
t
he
F
AC
T
S
c
o
n
t
r
ol
l
e
r
e
s
t
a
bl
i
s
hm
e
nt
c
os
t
t
h
at
can
b
e
cal
cu
l
at
ed
as
f
o
l
l
o
w
s
:
3
(
,
)
=
1000
∗
∗
(
28
)
w
h
e
re
i
s
t
h
e
e
s
t
a
b
l
i
s
h
m
e
n
t
c
o
s
t
o
f
F
A
C
T
S
c
o
n
t
r
o
l
l
e
r
i
n
U
S
$
/
K
V
A
R
a
n
d
W
h
er
e
i
s
t
h
e
i
n
s
t
a
l
l
e
d
v
a
l
u
e
o
f
t
h
e
F
A
CT
S
c
o
n
t
r
o
l
l
e
r
i
n
M
V
A
r
.
T
h
e
c
o
s
t
o
f
T
CS
C a
n
d
S
V
C c
a
n
b
e
c
a
l
c
u
l
a
t
e
d
a
c
c
o
r
d
i
n
g
t
o
t
h
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f
o
l
l
o
w
i
n
g
[7
]
:
=
0
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0003
2
−
0
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3051
+
127
.
38
US
$
/
K
V
A
r
(
29
)
=
0
.
0015
2
−
0
.
7130
+
153
.
75
US
$
/
K
VA
r
(
30
)
5.
3.
C
o
ns
t
r
a
i
nt
s
T
he
o
bje
c
t
i
ve
f
unc
t
i
o
n
i
n
E
q.
20
i
s
s
ub
je
c
t
e
d
t
o
t
he
p
o
we
r
s
y
s
t
e
m
e
qua
l
i
t
y
a
nd
i
ne
qua
l
i
t
y
c
on
s
t
r
a
i
nt
s
a
s
fo
l
l
o
ws
:
5.
3.
1.
E
q
u
al
i
t
y
c
on
s
t
r
ai
n
t
s
T
h
e
e
q
ua
l
i
t
y
c
ons
t
r
a
i
nt
s
of
t
h
e
O
P
F
i
nc
l
udi
n
g
wi
n
d
f
a
r
m
s
a
r
e
t
he
p
o
we
r
f
l
ow
e
q
ua
t
i
o
ns
a
s
f
ol
l
ow
s
:
P
i
=
P
gi
+
P
w
i
−
P
Di
(
31
)
Q
i
=
Q
gi
+
Q
w
i
−
Q
Di
(
32
)
w
h
e
re
,
a
n
d
ar
e
t
h
e
b
u
s
act
i
v
e
an
d
r
eact
i
v
e
p
o
w
er
i
n
j
ect
i
o
n
s
can
b
e
e
x
p
r
es
s
ed
as
:
=
V
i
V
j
j
∈
N
B
G
ij
co
s
θ
ij
+
B
ij
si
n
θ
ij
i
∈
N
B
(
33
)
=
V
i
V
j
j
∈
N
B
G
ij
s
i
n
θ
ij
−
B
ij
c
os
θ
ij
i
∈
N
B
(
34
)
5.
3.
2.
I
ne
qu
a
l
i
t
y
c
o
ns
t
r
a
i
nt
s
T
h
e
s
e
c
o
n
s
t
r
a
i
n
t
s
a
r
e
i
m
p
o
s
e
d
o
n
r
e
l
e
v
a
n
t
v
a
r
i
a
b
l
e
s
t
o
e
n
s
u
r
e
t
h
a
t
t
h
e
y
s
a
t
i
s
f
y
p
h
y
s
i
c
a
l
l
i
m
i
t
s
o
f
t
he
de
vi
c
e
s
.
A
c
t
i
ve
a
nd
r
e
a
c
t
i
ve
p
ow
e
r
s
up
pl
i
e
d
by
e
a
c
h
ge
ne
r
a
t
or
a
nd
ge
ne
r
a
t
or
vol
t
a
ge
s
a
r
e
l
i
m
i
t
e
d
t
o
i
t
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-
87
08
In
t
J
E
l
e
c
&
C
om
p
E
n
g,
V
o
l
.
10
,
No
.
4
,
A
ug
us
t
20
2
0
:
38
98
-
391
0
3
904
m
a
xim
u
m
a
nd
m
i
nim
u
m
va
lue
.
W
h
er
e,
g
e
n
er
at
o
r
act
i
v
e
p
o
w
er
(
P
gi
),
re
a
c
t
i
v
e
p
o
we
r (
Q
gi
)
a
nd v
ol
t
a
ge
m
a
gni
t
ude
s
(
V
gi
).
≤
(
)
≤
,
,
∈
(
35
)
≤
(
)
≤
,
,
∈
(
36
)
≤
≤
,
∈
(
37
)
T
r
a
n
s
f
o
r
m
e
r
t
a
p
s
s
e
t
t
i
n
g
,
t
k
,
h
a
v
e
m
i
n
.
a
n
d
m
a
x
.
s
e
t
t
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n
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l
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m
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t
s
a
r
e
s
t
a
t
e
d
a
s
:
≤
≤
,
∈
(
38
)
S
e
c
u
r
i
t
y
l
i
m
i
t
s
:
T
h
e
s
e
c
o
n
s
t
r
a
i
n
t
s
i
n
c
l
u
d
e
t
h
e
l
i
m
i
t
s
o
n
l
o
a
d
b
u
s
;
v
o
l
t
a
g
e
m
a
g
n
i
t
u
d
e
s
,
a
n
d b
r
a
n
c
h f
low
l
i
m
i
t
s
t
h
e
y
a
r
e
s
t
a
t
e
d
a
s
,
≤
E
(
)
≤
,
i
∈
N
B
(
39
)
(
)
≤
,
i
∈
N
L
(
40
)
T
h
e
s
e
t
t
i
n
g
p
a
r
a
m
e
t
e
r
s
f
o
r
F
A
CT
S
c
o
n
t
r
o
l
l
e
r
a
r
e
r
e
s
t
r
i
c
t
e
d
b
y
t
h
e
i
r
l
i
m
i
t
s
a
s
f
o
l
l
o
w
:
−
0
.
8
≤
≤
0
.
2
,
∈
(
41
)
−
1
0
0
M
V
Ar
≤
Q
i
S
VC
≤
1
0
0
M
V
Ar
,
i
∈
N
S
VC
(
42
)
T
h
e
l
o
ad
f
act
o
r
i
s
c
o
n
t
r
o
l
l
e
d
b
y
i
t
s
b
o
u
n
d
a
r
i
e
s
a
s
:
1
≤
≤
(
43
)
5.
3.
3.
A
c
o
ns
t
r
a
i
nt
ha
ndl
i
ng
t
e
c
hni
q
ue
I
n
o
r
de
r
t
o e
f
f
i
c
i
e
nt
l
y
ha
n
dl
e
t
he
c
o
ns
t
r
a
i
nt
s
,
a
c
o
ns
t
r
a
i
ne
d
d
om
i
na
nc
e
c
o
nc
e
pt
i
s
us
e
d i
n
t
hi
s
pa
pe
r
[
28
]
.
T
h
e
s
o
l
u
t
i
o
n
o
f
t
h
e
c
o
n
s
t
r
a
i
n
t
ℳ
d
o
m
i
n
a
t
e
t
h
e
s
o
l
u
t
i
o
n
o
f
t
h
e
c
o
n
s
t
r
a
i
n
t
,
i
f
a
ny
of
t
he
f
ol
l
owi
n
g
c
o
n
d
i
t
i
o
n
s
i
s
a
c
h
i
e
v
e
d
:
−
Bo
t
h
s
o
l
u
t
i
o
n
s
ℳ
a
n
d
a
r
e
f
e
a
s
i
bl
e
s
ol
ut
i
ons
,
a
n
d
s
ol
ut
i
o
n
ℳ
d
o
m
i
n
a
t
e
s
s
o
l
u
t
i
o
n
.
−
S
o
l
u
t
i
o
n
ℳ
i
s
f
e
a
s
i
b
l
e
a
n
d
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l
u
t
i
o
n
i
s
n
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t
.
−
Bo
t
h
s
o
l
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t
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o
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ℳ
a
nd
a
r
e
i
nf
e
a
s
i
bl
e
,
b
ut
s
ol
ut
i
on
ℳ
h
a
s
a
l
e
s
s
e
r
c
o
n
s
t
r
a
i
n
t
v
i
o
l
a
t
i
o
n
.
I
n
t
hi
s
s
t
udy
,
t
he
ove
r
a
l
l
c
o
ns
t
r
a
i
nt
s
vi
ol
a
t
i
o
n
c
a
n
b
e
c
o
n
s
i
d
er
e
d
as
:
=
.
=
1
+
.
=
1
(
44
)
,
i
s
t
h
e
f
a
c
t
o
r
i
n
d
i
c
a
t
i
n
g
v
i
o
l
a
t
i
o
n
l
i
m
i
t
s
,
a
r
e
a
s
s
oc
i
a
t
e
d t
o t
he
l
i
ne
l
oa
di
ng
a
nd
t
h
e
l
i
n
e
s
v
o
l
t
a
g
e
l
e
v
e
l
.
=
1
;
(
)
≤
1
−
(
)
.
;
(
)
>
(
45
)
=
1
;
1
.
1
≥
(
)
≥
0
.
95
[
μ
(
1
−
(
)
]
;
ℎ
(
46
)
w
h
e
re
(
)
a
nd
.
ar
e t
h
e e
x
p
ect
ed
ap
p
a
r
en
t
p
o
w
e
r
a
n
d
t
h
er
m
al
l
i
m
i
t
g
en
er
at
ed
b
et
w
ee
n
b
u
s
es
p
a
n
d q.
Υ
an
d
µ
ar
e
a
s
m
al
l
p
o
s
i
t
i
v
e
co
n
s
t
an
t
[7
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
E
l
e
c
&
C
om
p
E
n
g
I
S
S
N
:
208
8
-
87
08
A
p
r
o
b
a
b
i
l
i
s
t
i
c
m
u
l
t
i
-
ob
je
c
tiv
e
ap
pr
oa
c
h
fo
r
F
A
CT
S
d
e
v
i
c
e
s
a
l
l
o
c
a
t
i
o
n
wi
t
h
…
(
M.
E
L
-
Az
a
b
)
3
905
6.
S
O
L
UT
I
O
N
AP
P
RO
AC
H
6.
1.
Mu
l
ti
-
o
b
j
ect
i
v
e
p
a
r
t
i
cl
e
s
w
a
rm
o
p
t
i
mi
z
a
t
i
o
n
T
h
e
b
a
s
i
c
p
a
r
t
i
c
l
e
s
w
a
r
m
o
p
t
i
m
i
z
a
t
i
o
n
a
l
g
o
r
i
t
h
m
i
s
d
e
v
e
l
o
p
e
d
e
x
p
l
o
i
t
i
n
g
s
o
c
i
a
l
m
o
d
e
l
s
i
m
u
l
a
t
i
o
n
s
.
T
he
m
e
t
hod
i
s
de
ve
l
ope
d
w
i
t
h
i
ns
pi
r
a
t
i
o
n
f
r
om
f
l
oc
ki
n
g
o
f
bi
r
ds
a
n
d
s
c
h
o
ol
i
ng
o
f
f
i
s
h.
T
he
P
S
O
m
e
t
hod
wa
s
f
i
r
s
t
d
e
s
i
g
ne
d t
o s
i
m
ul
a
t
e
be
h
a
vi
o
r
o
f
bi
r
ds
s
e
a
r
c
hi
ng
f
or
f
oo
d i
n a
b
o
un
de
d
a
r
e
a
.
A s
i
ngl
e
bi
r
d
wo
ul
d f
i
nd
f
o
o
d
t
h
r
o
u
g
h
s
o
c
i
a
l
c
o
o
p
e
r
a
t
i
o
n
w
i
t
h
o
t
h
e
r
b
i
r
d
s
i
n
t
h
e
f
l
o
c
k
,
i
.
e
.
,
w
i
t
h
i
t
s
n
e
i
g
h
b
o
r
s
.
T
h
e
p
a
r
t
i
c
l
e
s
w
a
r
m
opt
i
m
i
z
a
ti
on a
l
go
r
i
t
hm
w
i
t
h dy
na
m
i
c
ne
i
gh
b
or
h
oo
d t
o
pol
ogy
f
o
r
e
v
e
r
y
pa
r
t
i
c
l
e
(
i
=
1
,
2
,
…
.
.
,
N
)
c
an
b
e
d
es
cr
i
b
ed
as
[
29
]
.
(
+
1
)
=
[
(
)
+
1
(
)
−
(
)
+
2
(
)
−
(
)
]
(
47
)
(
+
1
)
=
(
+
1
)
(
48
)
w
h
er
e
(
)
∈
ℝ
i
s
t
h
e
p
o
s
i
t
i
o
n
o
f
i
t
h
p
a
r
t
i
c
l
e
a
t
t
i
m
e
t
,
(
)
∈
ℝ
i
s
t
he
be
s
t
p
os
i
t
i
on
a
c
hi
e
ve
d
by
t
he
i
t
h
p
a
r
t
i
c
l
e
u
n
t
i
l
t
i
m
e
t
,
(
)
∈
ℝ
i
s
t
he
b
e
s
t
pos
i
t
i
o
n a
c
hi
e
ve
d by
i
t
h
p
a
r
t
i
c
l
e
a
n
d
i
t
s
n
e
i
g
h
b
o
r
s
u
n
t
i
l
t
i
m
e
t
,
(
)
∈
ℝ
i
s
t
h
e
r
a
t
e
o
f
p
o
s
i
t
i
o
n
c
h
a
n
g
e
(
v
e
l
o
c
i
t
y
)
o
f
t
h
e
i
t
h
p
a
r
t
i
c
l
e
a
t
t
i
m
e
t
,
a
nd
N
i
s
t
he
nu
m
be
r
of
p
a
r
t
i
c
l
e
s
i
n
t
h
e
s
w
a
r
m
.
T
h
e
c
o
e
f
f
i
c
i
e
n
t
s
1
(
)
∈
[
0
,
1
−
]
a
nd
2
(
)
∈
[
0
,
2
−
]
ar
e
n
-
di
m
e
ns
i
o
na
l
u
n
i
fo
rm
v
e
c
t
o
r
s
w
i
t
h
r
a
n
d
o
m
d
i
s
t
r
i
b
u
t
i
o
n
r
e
f
e
r
r
e
d
t
o
a
s
s
o
c
i
a
l
a
n
d
c
o
g
n
i
t
i
v
e
l
e
a
r
n
i
n
g
c
o
e
f
f
i
c
i
e
n
t
s
,
r
es
p
ect
i
v
el
y
.
T
h
ey
d
et
e
r
m
i
n
e
t
h
e r
el
at
i
v
e
s
i
g
n
i
f
i
can
ce
o
f
s
o
ci
al
an
d
co
g
n
i
t
i
v
e
co
m
p
o
n
e
n
t
s
.
6.
2.
P
r
i
nc
i
pl
e
s
o
f
M
O
P
SO
T
he
M
O
P
S
O i
s
a
n e
xt
e
n
s
i
o
n o
f
o
r
i
gi
na
l
P
S
O
gi
ve
n
by
[
30
]
,
t
ha
t
i
s
c
a
pa
bl
e
of
ha
ndl
i
n
g m
a
ny
ob
je
c
t
i
ve
f
unc
t
i
ons
i
n
one
r
un
.
i
n M
O
P
S
O
,
p
os
i
t
i
on
u
pda
t
e
a
nd
ve
l
oc
i
t
y
u
pda
t
e
e
q
ua
t
i
on
s
ke
e
p
on
s
a
m
e
a
s
i
n
(
4
7)
a
nd
(
4
8)
i
n
P
S
O
.
A
l
l
t
h
e p
ar
am
et
e
r
d
ecl
ar
e
d
ar
e al
s
o
s
a
m
e
ex
cl
u
d
i
n
g
t
h
e
o
b
j
ect
i
v
e f
u
n
ct
i
o
n
.
T
he
c
om
pa
r
i
s
on
of
P
S
O w
i
t
h ot
he
r
he
u
r
i
s
t
i
c
a
l
gor
i
t
hm
s
m
a
ke
s
t
he
o
b
vi
o
us
c
o
nc
e
pt
un
de
r
c
o
ns
i
d
e
r
a
t
i
on
a
P
a
r
e
t
o
s
e
t
r
a
nki
ng
p
r
oc
e
d
ur
e
c
o
ul
d
be
t
he
s
t
r
a
i
ght
w
a
y
t
o
de
ve
l
o
p t
he
s
c
he
m
e
t
o e
xpl
oi
t
t
he
m
ul
t
i
-
o
b
j
e
c
t
i
v
e
opt
i
m
i
z
a
ti
on p
r
o
bl
e
m
s
.
T
he
hi
s
t
or
i
c
a
l
n
ot
a
t
i
on o
f
o
pt
i
m
um
c
a
ndi
da
t
e
s
obt
a
i
ne
d by
a
pa
r
t
i
c
l
e
c
ou
l
d be
ha
n
dl
e
d t
o ke
e
p n
o
n
-
dom
i
na
t
e
d c
a
n
di
da
t
e
s
ge
ne
r
a
t
e
d i
n t
h
e
pr
e
vi
o
us
i
t
e
r
a
t
i
ons
.
B
y
us
i
n
g of
gl
oba
l
a
tt
r
a
c
ti
on
s
t
r
a
t
e
g
i
e
s
unde
r
c
ons
i
de
r
a
ti
o
n a
hi
s
t
or
i
c
a
l not
a
t
i
on f
ound no
n
-
d
om
i
n
a
t
e
d c
a
ndi
da
t
e
s
w
oul
d put
t
hr
ou
g
h
co
n
v
er
g
en
ce ch
ar
act
er
i
s
t
i
c
i
n
t
o
g
l
o
b
al
l
y
n
o
n
-
do
m
i
na
t
e
d
s
ol
u
t
ions
.
T
he
opt
im
i
z
a
ti
on pr
obl
e
m
i
s
a
m
u
l
ti
-
obje
c
ti
ve
opt
i
m
i
z
a
ti
on
w
hi
c
h wa
s
c
o
ns
i
de
r
e
d a
s
a
n e
f
f
e
c
t
i
ve
m
e
t
ho
d t
o
di
s
c
ove
r
y
t
he
opt
i
m
a
l
s
ol
ut
i
on
be
t
w
e
e
n
di
f
f
e
r
e
nt
o
bje
c
t
i
ve
s
.
T
he
d
e
t
a
i
l
e
d pr
oc
e
d
ur
e
s
f
o
r
f
i
ndi
ng t
he
be
s
t
s
ol
ut
i
o
ns
by
o
pt
im
a
l
P
a
r
e
t
o s
e
t
a
r
e
i
nt
r
o
d
uc
e
d
i
n
F
i
gu
r
e
2.
6.
3.
B
es
t
c
o
mp
r
o
mi
s
e
s
o
l
u
t
i
o
n
(B
C
S
)
A
s
s
o
o
n a
s
t
he
P
a
r
e
t
o i
de
a
l
gr
o
u
p i
s
got
,
i
t
i
s
c
o
m
m
ons
e
ns
e
t
o i
n
di
c
a
t
e
s
i
ngl
e
s
ol
u
t
i
on f
r
om
a
ll
s
o
l
u
t
i
o
n
s
t
h
at
m
eet
a f
ew
m
e
an
s
t
o
s
o
m
e ex
p
a
n
d
s
.
F
u
zzy
d
eci
s
i
o
n
-
m
a
ki
ng a
p
pr
oa
c
h i
s
i
nt
e
nd
e
d t
o s
e
pa
r
a
t
e
t
h
e
BCS
.
F
o
r
t
h
i
s
o
p
t
i
m
i
z
a
t
i
o
n
d
u
e
t
o
t
h
e
i
n
accu
r
at
e n
at
u
r
e
o
f
t
h
e d
eci
s
i
o
n
-
m
a
ki
ng pr
o
c
e
s
s
i
nvol
ve
d,
t
he
i
t
h
obje
c
t
i
ve
f
unc
tion
i
s
de
not
e
d
by
a
m
e
m
be
r
s
h
i
p
f
unc
t
i
on
s
p
eci
f
i
ed
as
[
31]
.
=
⎩
⎨
⎧
1
≤
,
,
−
,
−
,
,
<
<
,
0
≥
,
(
49
)
w
h
er
e,
,
a
nd
,
ar
e t
h
e
m
ax
i
m
u
m
an
d
m
i
n
i
m
u
m
v
al
u
e
o
f
t
h
e i
t
h
obje
c
ti
v
e
f
unc
t
i
on a
m
ongs
t
a
ll
non
-
dom
i
na
te
d s
ol
uti
on,
r
e
s
pe
c
ti
ve
ly
.
F
or
i
ndi
vi
dua
lly non
-
d
om
i
na
te
d s
ol
uti
on
k
,
t
he
c
or
r
e
s
p
ondi
n
g
m
e
m
be
r
s
h
i
p
f
unc
t
i
on
i
s
co
n
s
i
d
er
ed
as
:
=
∑
=
1
∑
∑
=
1
=
1
(
50
)
w
h
e
re
m
i
s
t
he
num
be
r
of
n
on
-
dom
i
na
t
e
d s
e
t
,
by
us
i
ng
F
uz
z
y
r
a
n
ki
n
g
m
e
t
hod,
t
he
B
C
S
f
r
om
pa
r
e
t
o f
r
on
t
s
o
l
u
t
i
o
n
s
ca
n
b
e
s
el
ect
ed
a
nd
t
he
be
s
t
s
ol
ut
i
o
n
i
s
t
he
va
l
ue
wi
t
h
hi
g
he
s
t
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-
87
08
In
t
J
E
l
e
c
&
C
om
p
E
n
g,
V
o
l
.
10
,
No
.
4
,
A
ug
us
t
20
2
0
:
38
98
-
391
0
3
906
F
i
gu
r
e
2.
F
l
ow
c
h
a
r
t
o
f
t
h
e
pr
opo
s
e
d
MO
P
S
O
a
lgor
ith
m
6.
4.
P
r
op
os
e
d
s
ol
u
t
i
on
f
or
t
h
e
F
A
CT
S
al
l
oc
a
t
i
on
p
r
o
b
l
e
m
T
h
e
o
p
t
i
m
a
l
a
l
l
o
c
a
t
i
o
n
o
f
T
CS
C
a
n
d
S
V
C
c
o
n
t
r
o
l
l
e
r
i
s
e
x
p
r
e
s
s
e
d
a
s
h
y
b
r
i
d
c
o
n
t
i
n
u
e
s
-
d
i
s
c
r
e
t
e
M
O
P
.
T
he
c
om
pl
e
t
e
pr
o
bl
e
m
i
s
pl
a
nne
d a
s
t
w
o l
e
ve
l
s
.
I
n t
he
up
pe
r
l
e
ve
l
t
he
M
O
P
S
O
l
o
o
k
f
o
r
t
he
be
t
t
e
r
s
ol
ut
i
o
n
t
hr
ou
g
h a
num
be
r
of
f
e
a
s
i
bl
e
s
ol
ut
i
o
ns
,
t
o
g
e
t
t
he
l
oc
a
t
i
on a
nd
r
a
t
i
ng
of
F
AC
T
S
c
o
nt
r
ol
l
e
r
a
n
d t
he
r
e
s
u
l
t
of
t
he
f
i
r
s
t
l
e
ve
l
i
s
pr
oc
e
e
de
d t
o
s
e
c
on
d l
e
ve
l
.
I
n t
he
s
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