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s
e
to
li
n
es
t
h
er
m
al
li
m
it)
o
v
er
a
lo
n
g
d
is
tan
ce
i
n
a
p
o
w
er
s
y
s
te
m
,
w
it
h
o
u
t
ad
v
er
s
el
y
a
f
f
ec
tin
g
th
e
s
tab
ilit
y
an
d
s
ec
u
r
i
t
y
m
ar
g
in
,
ca
n
b
e
ac
h
ie
v
ed
th
r
o
u
g
h
a
f
a
s
t
p
o
w
er
f
lo
w
co
n
tr
o
l.
Vo
lta
g
e
s
tab
ilit
y
d
ep
en
d
s
o
n
t
h
e
ab
ilit
y
o
f
t
h
e
p
o
w
er
s
y
s
te
m
to
m
ai
n
tai
n
ac
c
ep
tab
le
v
o
ltag
e
f
o
r
th
e
s
y
s
te
m
b
u
s
e
s
u
n
d
er
n
o
r
m
al
co
n
d
itio
n
s
,
a
n
d
,
also
,
in
th
e
f
ac
e
o
f
d
i
s
tu
r
b
an
ce
s
.
I
n
o
t
h
er
w
o
r
d
s
,
af
ter
a
n
in
cid
en
ce
o
f
d
is
tu
r
b
a
n
ce
,
i.e
.
an
in
cr
ea
s
e
i
n
d
e
m
a
n
d
lo
ad
an
d
/o
r
s
y
s
te
m
c
h
ar
ac
ter
is
tic
c
h
an
g
e
s
,
th
e
s
y
s
te
m
m
a
y
f
ac
e
v
o
lta
g
e
i
n
s
tab
ilit
y
,
w
h
ic
h
m
a
y
ca
u
s
e
a
n
u
n
co
n
tr
o
llab
le
d
ev
iatio
n
o
f
v
o
ltag
e
[
4
]
.
T
h
e
f
ail
u
r
e
o
f
p
o
w
er
s
y
s
te
m
s
to
p
r
o
v
id
e
th
e
r
eq
u
ir
ed
r
ea
ctiv
e
p
o
w
er
i
s
t
h
e
m
ai
n
ca
u
s
e
o
f
i
n
s
tab
ilit
y
.
T
h
e
r
ef
o
r
e,
co
n
s
id
er
in
g
th
e
r
ea
cti
v
e
p
o
w
er
s
ec
u
r
it
y
m
ar
g
i
n
ca
n
i
n
cr
ea
s
e
t
h
e
r
el
i
ab
ilit
y
o
f
th
e
s
y
s
te
m
an
d
p
r
ev
en
t
a
n
y
p
o
s
s
ib
le
b
lack
o
u
ts
.
F
AC
T
S
o
b
tain
ed
a
w
ell
-
k
n
o
w
n
r
ep
u
tatio
n
f
o
r
h
i
g
h
e
r
co
n
tr
o
llab
ilit
y
i
n
p
o
w
er
s
y
s
te
m
s
b
y
m
ea
n
s
o
f
p
o
w
er
elec
tr
o
n
ic
d
ev
ices.
T
h
e
f
ir
s
t
ap
p
licatio
n
o
f
F
AC
T
S
d
ev
ices
i
s
a
f
ast
p
o
w
er
f
lo
w
co
n
tr
o
l
an
d
v
o
lta
g
e
s
tab
ilit
y
,
w
h
ic
h
ca
n
h
elp
to
i
m
p
r
o
v
e
th
e
s
y
s
te
m
s
ec
u
r
it
y
[
5
]
-
[
8
]
.
I
n
th
is
p
ap
er
,
an
ef
f
ec
tiv
e
ac
co
n
ti
n
g
e
n
c
y
d
is
p
atc
h
o
v
er
a
d
ay
a
h
ea
d
p
er
io
d
b
ased
o
n
th
e
s
ec
u
r
it
y
-
co
n
s
tr
ain
ed
u
n
it
co
m
m
it
m
en
t
(
SC
U
C
)
m
o
d
el
i
s
p
r
o
p
o
s
ed
.
A
g
e
n
er
al
m
o
d
el
o
f
SF
D
is
in
co
r
p
o
r
ated
in
th
e
p
r
o
p
o
s
ed
SC
UC
f
o
r
m
u
la
tio
n
s
.
GE
NC
Os
w
ill
s
u
b
m
i
t
th
eir
b
id
s
to
th
e
I
SO.
T
h
e
I
SO
w
ill
t
h
en
u
s
e
t
h
is
m
o
d
e
l
to
m
i
n
i
m
ize
t
h
e
b
id
-
b
ased
s
y
s
te
m
o
p
er
atin
g
co
s
t
w
h
ile
m
ai
n
tai
n
in
g
t
h
e
s
y
s
te
m
s
ec
u
r
it
y
a
t
b
o
th
n
o
r
m
a
l
s
tate
an
d
p
r
e
-
d
ef
i
n
ed
co
n
tin
g
e
n
c
y
c
ases
.
T
h
is
p
ap
er
is
o
r
g
an
ized
as
f
o
ll
o
w
s
.
Sectio
n
I
I
p
r
o
v
id
es
an
o
u
tlin
e
o
f
t
h
e
p
r
o
p
o
s
ed
m
o
d
el.
Sectio
n
I
I
I
d
escr
ib
es
th
e
f
o
r
m
u
latio
n
s
o
f
SC
U
C
an
d
SC
OP
F
b
ased
o
n
ac
n
et
w
o
r
k
.
Sectio
n
I
V
p
r
esen
t
s
an
d
d
is
cu
s
s
es
te
s
t
ca
s
es c
o
n
s
id
er
in
g
t
h
e
p
r
ev
ail
i
n
g
co
n
s
tr
ai
n
ts
.
T
h
e
co
n
clu
s
io
n
d
r
aw
n
f
r
o
m
t
h
e
s
t
u
d
y
is
p
r
o
v
i
d
ed
in
Sectio
n
V.
2.
M
O
DE
L
O
UT
L
I
N
E
Fig
u
r
e
1
d
ep
icts
t
h
e
f
lo
w
ch
ar
t
o
f
t
h
e
p
r
o
p
o
s
ed
SC
UC
m
o
d
e
l
th
at
en
co
m
p
a
s
s
e
s
N
C
OP
F
a
n
d
SC
OP
F
w
it
h
ac
co
n
tin
g
e
n
c
y
d
is
p
atch
o
v
er
t
h
e
2
4
-
h
h
o
r
izo
n
.
N
C
OP
F
u
til
izes
th
e
UC
s
o
l
u
tio
n
f
o
r
ca
lc
u
lati
n
g
t
h
e
o
p
tim
a
l
d
is
p
atch
o
f
r
eso
u
r
ce
s
,
m
i
n
i
m
izi
n
g
t
h
e
b
id
-
b
ased
o
p
er
atin
g
co
s
t
at
s
tead
y
s
ta
te.
SC
OP
F
u
tili
ze
s
t
h
e
UC
s
o
lu
t
io
n
f
o
r
ca
lcu
lati
n
g
th
e
o
p
ti
m
al
d
is
p
atch
o
f
u
n
it
s
,
m
in
i
m
izin
g
th
e
b
id
-
b
ased
o
p
er
atin
g
co
s
t
at
p
r
ev
en
ti
n
g
s
y
s
te
m
v
io
latio
n
s
w
h
e
n
co
n
ti
n
g
en
cie
s
o
cc
u
r
.
B
e
n
d
er
s
d
ec
o
m
p
o
s
itio
n
is
u
til
ize
d
to
d
ec
o
m
p
o
s
e
t
h
e
SC
U
C
p
r
o
b
le
m
i
n
to
s
m
a
ller
a
n
d
ea
s
ier
to
s
o
lv
e
s
u
b
p
r
o
b
lem
s
[
9
]
-
[
1
2
]
.
T
h
e
m
a
s
ter
p
r
o
b
lem
u
s
e
s
t
h
e
a
v
ailab
le
m
ar
k
et
in
f
o
r
m
at
io
n
to
f
i
n
d
t
h
e
o
p
ti
m
al
h
o
u
r
l
y
s
ch
ed
u
le
o
f
u
n
it
s
(
UC
)
b
y
co
n
s
id
er
in
g
th
e
p
r
ev
ail
in
g
U
C
co
n
s
tr
ain
ts
T
h
e
h
o
u
r
l
y
s
o
l
u
tio
n
o
f
U
C
is
u
s
ed
in
t
h
e
s
u
b
p
r
o
b
le
m
s
to
ex
a
m
i
n
e
t
h
e
A
C
n
et
w
o
r
k
co
n
s
tr
ai
n
ts
at
s
tead
y
s
tate
a
n
d
co
n
tin
g
en
c
y
[
1
3
]
-
[
2
4
]
.
T
h
e
s
h
u
n
t
F
AC
T
S
d
ev
ices
ar
e
in
co
r
p
o
r
ated
in
th
e
s
u
b
p
r
o
b
le
m
s
i
f
v
io
latio
n
s
ar
e
d
etec
ted
.
Giv
en
th
e
u
n
it
s
ch
ed
u
le
b
y
t
h
e
UC
s
o
lu
tio
n
,
t
h
e
S
u
b
p
r
o
b
lem
1
w
il
l
ch
ec
k
t
h
e
b
as
e
ca
s
e
n
et
w
o
r
k
f
ea
s
ib
ilit
y
.
I
n
t
h
is
s
u
b
p
r
o
b
le
m
,
s
lac
k
v
ar
iab
l
es
f
o
r
r
ea
l
an
d
r
ea
cti
v
e
p
o
wer
m
is
m
atc
h
es
ar
e
m
i
n
i
m
ized
b
ased
o
n
lin
e
f
lo
w
an
d
Sh
u
n
t
F
A
C
T
S
Dev
ice
s
ad
j
u
s
t
m
e
n
ts
.
T
h
e
p
r
o
p
o
s
ed
B
en
d
er
s
cu
t
in
co
r
p
o
r
ate
s
lack
v
ar
iab
les
f
o
r
th
e
r
ea
l
an
d
r
ea
ctiv
e
p
o
w
e
r
m
is
m
atc
h
t
h
at
is
m
it
ig
ated
b
y
r
ec
alcu
lati
n
g
th
e
u
n
it
s
c
h
ed
u
les.
I
f
NC
OP
F
ca
n
n
o
t
g
u
ar
a
n
tee
t
h
e
s
y
s
te
m
s
ec
u
r
i
t
y
at
s
tead
y
-
s
t
ate
lo
ad
s
h
ed
d
in
g
m
a
y
b
e
u
tili
ze
d
f
o
r
m
a
n
ag
i
n
g
a
f
ea
s
ib
le
s
o
lu
t
io
n
.
A
co
n
v
er
g
ed
b
ase
ca
s
e
p
o
w
er
f
lo
w
will
b
e
ac
h
ie
v
ed
b
ased
o
n
t
h
e
U
C
r
es
u
lt
s
.
T
h
e
co
n
tin
g
e
n
cies
n
et
w
o
r
k
ch
ec
k
s
u
b
p
r
o
b
le
m
,
i.e
.
,
s
u
b
p
r
o
b
lem
2
,
u
s
es
th
e
U
C
s
o
l
u
tio
n
f
o
r
th
e
b
ase
ca
s
e
to
ch
ec
k
th
e
s
y
s
te
m
s
ec
u
r
it
y
i
n
ca
s
e
o
f
co
n
tin
g
en
cie
s
.
Usi
n
g
AC
p
o
w
er
f
lo
w
eq
u
at
io
n
s
,
b
o
th
r
ea
l
an
d
r
ea
ctiv
e
p
o
w
er
m
is
m
atc
h
es
ar
e
m
in
i
m
ized
in
th
i
s
s
u
b
p
r
o
b
lem
.
I
f
SC
OP
F
ca
n
n
o
t
g
u
ar
an
tee
th
e
s
y
s
te
m
s
ec
u
r
it
y
at
cr
i
tica
l
co
n
tin
g
e
n
cies,
L
S
m
a
y
b
e
u
t
il
ized
f
o
r
m
a
n
ag
i
n
g
a
f
ea
s
ib
le
s
o
lu
tio
n
.
I
n
o
u
r
ap
p
r
o
ac
h
,
au
g
m
en
ted
L
a
g
r
an
g
ia
n
r
elax
atio
n
(
AL
R
)
i
s
ap
p
lied
to
s
o
lv
e
UC
.
2
.
1
.
Nco
pf
T
h
is
s
ec
tio
n
i
n
F
ig
u
r
e
2
co
n
s
i
s
ts
o
f
o
p
ti
m
al
p
o
w
er
f
lo
w
(
OP
F)
f
o
r
c
h
ec
k
i
n
g
h
o
u
r
l
y
n
et
w
o
r
k
co
n
s
tr
ain
ts
.
T
h
e
OP
F
is
o
p
ti
m
ized
b
y
ap
p
l
y
i
n
g
p
r
i
m
al/d
u
al
i
n
ter
io
r
p
o
in
t
m
et
h
o
d
(
P
DI
P
M
)
.
T
h
e
OP
F
ch
ec
k
s
h
o
u
r
l
y
n
et
w
o
r
k
co
n
s
tr
ain
t
s
to
f
i
n
d
o
u
t
w
h
eth
er
th
e
p
r
o
p
o
s
ed
UC
s
o
lu
tio
n
ca
n
p
r
o
v
id
e
a
co
n
v
er
g
ed
ac
p
o
w
er
f
lo
w
a
n
d
m
ee
t
n
et
w
o
r
k
co
n
s
tr
ain
ts
(
s
u
ch
as
tr
an
s
m
is
s
io
n
f
lo
w
a
n
d
b
u
s
v
o
lta
g
e
li
m
it
s
)
.
I
f
th
e
NC
OP
F
i
s
in
f
ea
s
ib
le,
t
h
e
B
en
d
er
s
c
u
ts
w
il
l
b
e
in
tr
o
d
u
ce
d
i
n
to
th
e
n
e
x
t
U
C
ca
lc
u
latio
n
.
T
h
e
iter
ati
v
e
p
r
o
ce
s
s
b
et
w
ee
n
UC
an
d
t
h
e
s
u
b
p
r
o
b
lem
1
w
il
l
co
n
ti
n
u
e
u
n
til
ac
v
io
lati
o
n
s
ar
e
eli
m
in
ated
.
I
f
th
e
m
ax
i
m
u
m
n
u
m
b
er
o
f
iter
atio
n
s
o
f
t
h
e
N
C
OP
F
i
s
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in
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(
L
S)
is
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ed
to
f
in
d
a
co
n
v
er
g
ed
NC
OP
F so
lu
t
io
n
at
s
tead
y
s
ta
te
[
2
5
]
-
[
3
0
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8792
IJ
A
P
E
Vo
l.
5
,
No
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1
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A
p
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2
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1
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:
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24
2
.
2
.
Sco
pf
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e
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tili
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d
f
o
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ex
a
m
i
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n
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ac
co
n
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g
e
n
cies.
Her
e
w
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s
o
l
v
e
o
p
f
w
it
h
ad
d
itio
n
al
co
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ain
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f
o
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ea
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n
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ased
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er
m
i
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u
s
t
m
en
t
o
f
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ea
l
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o
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er
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e
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er
atio
n
.
O
n
ce
a
co
n
ti
n
g
e
n
c
y
i
s
i
n
tr
o
d
u
ce
d
,
i
f
v
io
latio
n
s
ar
e
n
o
t
eli
m
i
n
ated
w
it
h
i
n
t
h
e
e
m
er
g
e
n
c
y
ti
m
e
b
y
ap
p
l
y
i
n
g
co
n
tr
o
l
v
ar
iab
les
s
u
c
h
as
r
ea
l
p
o
w
er
g
en
er
atio
n
a
n
d
s
h
u
n
t
f
ac
ts
d
ev
ice
s
,
t
h
e
co
n
tin
g
e
n
c
y
w
ill
b
e
lab
eled
as
u
n
co
n
tr
o
lla
b
le
co
n
ti
n
g
e
n
c
y
.
A
cc
o
r
d
in
g
l
y
,
a
p
r
e
-
co
n
t
in
g
e
n
c
y
o
p
er
atin
g
p
o
in
t
is
s
o
u
g
h
t
f
o
r
th
e
u
n
co
n
tr
o
llab
le
co
n
ti
n
g
e
n
c
y
b
y
r
ec
alcu
la
tin
g
t
h
e
u
c.
T
h
e
n
e
w
o
p
er
atin
g
p
o
in
t
th
at
in
cl
u
d
es
p
r
ev
en
t
iv
e
co
n
t
r
o
l
ac
tio
n
s
ca
n
p
r
ev
en
t
s
y
s
te
m
v
io
latio
n
s
in
th
e
e
v
en
t
o
f
th
e
u
n
co
n
tr
o
llab
le
co
n
tin
g
e
n
c
y
.
Me
an
w
h
ile,
p
o
s
s
ib
le
co
r
r
ec
tiv
e
d
is
p
atch
c
o
n
tr
o
ls
w
it
h
i
n
t
h
e
g
i
v
en
e
m
er
g
e
n
c
y
ti
m
e
w
i
ll
eli
m
i
n
ate
s
y
s
te
m
v
io
latio
n
s
f
o
r
an
y
co
n
tr
o
llab
le
co
n
ti
n
g
en
ci
es.
2
.
3
.
Ls
I
f
v
io
latio
n
s
r
es
u
lti
n
g
f
r
o
m
u
n
co
n
tr
o
llab
le
co
n
tin
g
e
n
cie
s
ca
n
n
o
t
b
e
m
it
ig
ated
b
y
av
ailab
le
co
n
tr
o
l
m
ea
s
u
r
es,
ls
w
i
l
l
p
r
o
v
id
e
a
f
e
asib
le
n
co
p
f
/
s
co
p
f
s
o
lu
tio
n
b
ased
o
n
d
ec
r
em
e
n
tal
b
id
s
/co
n
tr
ac
ts
.
T
h
e
id
ea
f
o
r
ap
p
ly
i
n
g
ls
is
to
ad
d
v
ir
t
u
al
g
e
n
er
ato
r
s
at
lo
ad
b
u
s
e
s
w
h
er
e
l
s
is
allo
w
ed
.
T
h
e
ef
f
ec
t o
f
a
v
ir
tu
al
g
en
er
ato
r
is
to
s
h
ed
lo
ca
l
lo
ad
s
f
o
r
r
e
m
o
v
i
n
g
an
y
v
io
latio
n
s
at
s
tead
y
s
t
ate
an
d
co
n
ti
n
g
en
cie
s
.
L
s
at
a
s
u
b
s
ta
tio
n
co
u
ld
r
ep
r
esen
t sev
er
al
c
u
r
tail
m
en
t c
o
n
tr
ac
ts
.
W
e
p
r
o
v
id
e
th
e
f
o
llo
w
i
n
g
f
i
v
e
as
s
u
m
p
tio
n
s
f
o
r
i
m
p
le
m
e
n
ti
n
g
l
s
.
I
n
th
i
s
p
r
o
p
o
s
ed
alg
o
r
ith
m
,
d
em
an
d
b
id
s
ar
e
in
ela
s
tic.
L
s
is
r
ep
r
esen
ted
as
an
u
n
d
esira
b
le
f
u
n
ctio
n
,
an
d
ls
co
n
tr
ac
t
p
r
ices
ar
e
p
r
esu
m
a
b
ly
h
i
g
h
er
th
a
n
g
e
n
er
ati
n
g
u
n
it
b
id
s
.
L
s
i
s
tr
ea
ted
as
th
e
la
s
t
r
eso
r
t
w
h
en
all
o
th
er
o
p
tio
n
s
f
ai
l in
s
ee
k
i
n
g
a
f
ea
s
ib
le
s
o
lu
t
io
n
.
Vir
tu
al
u
n
it
s
ar
e
co
n
s
id
er
ed
f
o
r
n
co
p
f
at
s
tead
y
s
tate
an
d
s
co
p
f
at
co
n
tin
g
e
n
c
y
b
ase
d
o
n
th
e
h
o
u
r
l
y
co
m
m
i
t
m
e
n
t o
f
u
n
its
.
I
t is ass
u
m
ed
th
at
ea
ch
lo
ad
b
u
s
p
o
w
er
f
ac
to
r
is
co
n
s
ta
n
t.
T
h
e
r
atio
o
f
s
y
s
te
m
s
p
in
n
i
n
g
/
o
p
er
atin
g
r
eser
v
e
r
eq
u
ir
e
m
e
n
t
to
t
h
e
to
tal
lo
ad
is
as
s
u
m
ed
to
r
em
ai
n
co
n
s
ta
n
t f
o
r
th
e
e
n
tire
ti
m
e.
2
.
4
.
So
lutio
n P
ro
ce
du
re
So
lv
e
u
c.
C
h
ec
k
t
h
e
h
o
u
r
l
y
ac
p
o
w
er
f
l
o
w
d
is
p
atch
a
t
s
tead
y
s
tate
b
y
o
p
f
.
I
f
th
e
h
o
u
r
l
y
o
p
f
i
s
n
o
t
c
o
n
v
er
g
ed
a
n
d
n
u
m
b
er
o
f
iter
atio
n
b
et
w
ee
n
u
c
an
d
th
e
s
u
b
p
r
o
b
le
m
1
(
n
co
p
f
)
is
n
o
t
r
ea
ch
ed
,
b
en
d
er
s
cu
ts
g
o
b
ac
k
to
s
tep
1
f
o
r
r
ec
alcu
latin
g
u
c.
Ot
h
er
w
is
e,
i
f
th
e
h
o
u
r
l
y
o
p
f
co
n
v
er
g
ed
,
p
r
o
ce
ed
to
th
e
s
tep
5
.
I
f
th
e
m
a
x
i
m
u
m
n
u
m
b
er
o
f
ite
r
atio
n
b
et
w
ee
n
u
c
a
n
d
th
e
s
u
b
p
r
o
b
lem
1
(
n
co
p
f
)
is
r
ea
c
h
ed
an
d
th
e
o
p
f
is
n
o
t
co
n
v
er
g
ed
,
u
s
e
t
h
e
f
ea
s
ib
l
e
u
c
r
esu
lt
s
at
th
e
p
r
ev
io
u
s
ite
r
atio
n
as
th
e
f
i
n
al
an
d
g
o
to
th
e
n
ex
t
s
tep
f
o
r
th
e
ls
s
o
lu
tio
n
.
A
d
d
v
ir
t
u
al
g
e
n
er
ato
r
s
to
o
p
f
an
d
o
b
tain
th
e
l
s
s
o
lu
t
io
n
at
s
t
ea
d
y
s
tate.
So
lv
e
s
co
p
f
s
u
b
p
r
o
b
le
m
w
it
h
ad
d
itio
n
al
co
n
s
tr
ai
n
ts
f
o
r
ea
ch
co
n
tin
g
e
n
c
y
.
C
h
ec
k
t
h
e
h
o
u
r
l
y
ac
n
et
w
o
r
k
f
o
r
ea
ch
co
n
ti
n
g
en
c
y
.
I
f
ac
p
o
w
er
f
lo
w
is
n
o
t
co
n
v
er
g
e
d
o
r
n
et
w
o
r
k
(
t
r
an
s
m
is
s
io
n
f
lo
w
s
a
n
d
b
u
s
v
o
ltag
e
s
)
v
io
latio
n
s
ex
i
s
t,
a
n
d
n
u
m
b
er
o
f
i
ter
atio
n
b
et
w
ee
n
u
c
an
d
t
h
e
s
u
b
p
r
o
b
le
m
2
(
s
co
p
f
)
is
n
o
t
r
ea
ch
ed
,
f
o
r
m
th
e
co
r
r
esp
o
n
d
i
n
g
b
e
n
d
er
s
cu
ts
a
n
d
r
etu
r
n
to
s
tep
1
.
I
f
t
h
e
s
co
p
f
s
o
l
u
tio
n
is
in
f
e
asib
le
an
d
th
e
m
a
x
i
m
u
m
n
u
m
b
er
o
f
i
ter
atio
n
s
is
r
ea
ch
e
d
,
lab
el
th
e
co
n
tin
g
e
n
c
y
a
s
u
n
co
n
tr
o
llab
le
.
Use
th
e
f
ea
s
ib
le
u
c
r
esu
lts
at
th
e
p
r
ev
io
u
s
iter
atio
n
a
s
th
e
f
in
al
a
n
d
g
o
to
th
e
n
e
x
t s
tep
f
o
r
th
e
ls
s
o
lu
tio
n
.
A
d
d
v
ir
t
u
al
g
e
n
er
ato
r
s
to
o
p
f
an
d
o
b
tain
th
e
l
s
s
o
lu
t
io
n
at
co
n
ti
n
g
e
n
c
y
s
tate.
3.
P
RO
B
L
E
M
F
O
R
M
UL
AT
I
O
N
3
.
1
.
UC
F
o
r
m
ula
t
io
n
T
h
e
o
b
j
ec
tiv
e
o
f
th
e
UC
p
r
o
b
le
m
is
to
d
eter
m
in
e
th
e
s
et
o
f
g
e
n
er
ati
n
g
u
n
its
w
h
i
le
m
in
i
m
ize
s
th
e
to
tal
p
r
o
d
u
ctio
n
co
s
t
o
v
er
th
e
s
ch
ed
u
lin
g
p
er
io
d
.
T
h
er
ef
o
r
e,
th
e
o
b
j
ec
tiv
e
f
u
n
ct
io
n
is
ex
p
r
e
s
s
ed
as
t
h
e
s
u
m
o
f
f
u
e
l,
s
tar
t
-
u
p
a
n
d
s
h
u
t d
o
w
n
c
o
s
ts
o
f
t
h
e
g
e
n
er
atin
g
u
n
it
s
.
T
h
e
U
C
p
r
o
b
le
m
ca
n
b
e
m
ath
e
m
atica
ll
y
f
o
r
m
u
la
ted
as [
1
7
]
:
∑
∑
{
[
(
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(
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)
]
(
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}
(
1
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Du
e
to
th
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o
p
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r
eq
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m
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m
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m
izatio
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o
f
t
h
e
o
b
j
ec
tiv
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f
u
n
ctio
n
i
s
s
u
b
j
ec
ted
to
th
e
f
o
llo
w
in
g
co
n
s
tr
ain
ts
:
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
A
P
E
I
SS
N:
2252
-
8792
I
mp
a
ct
o
f S
h
u
n
t
F
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C
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Dev
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n
S
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C
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tr
a
in
ed
Un
it C
o
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(
G.
A
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M.Ho
s
a
in
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a
jiva
r
)
25
(
a)
P
o
w
er
b
alan
ce
co
n
s
tr
ai
n
ts
∑
(
2
)
∑
(
b
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Sp
in
n
in
g
a
n
d
o
p
er
atin
g
r
eser
v
e
co
n
s
tr
ain
t
s
∑
[
]
(
3
)
∑
[
]
(
c)
Min
i
m
u
m
u
p
/d
o
w
n
ti
m
e
co
n
s
t
r
ain
ts
[
(
)
]
[
(
)
]
(
4
)
[
(
)
]
[
(
)
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(
d
)
P
o
w
er
g
e
n
er
atio
n
l
i
m
it c
o
n
s
tr
ain
ts
(
5
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(
e)
R
a
m
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Up
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w
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it
s
(
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(
(
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(
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(
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(
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(
)
(
6
)
A
l
s
o
n
o
te
th
at
P
Lh
an
d
Q
Lh
in
(
2
)
is
o
r
i
g
i
n
all
y
t
h
e
est
i
m
ated
s
y
s
te
m
lo
s
s
at
t
i
m
e
h
.
Ho
w
e
v
er
,
f
o
llo
w
in
g
t
h
e
iter
atio
n
s
b
et
w
e
en
UC
a
n
d
th
e
s
u
b
p
r
o
b
le
m
1
NC
OP
F,
th
e
es
ti
m
ated
w
ill b
e
u
p
d
ated
b
y
it
s
ex
ac
t
v
alu
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o
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tai
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ed
f
r
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m
t
h
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s
u
b
p
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lem
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f
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OP
F.
I
n
o
r
d
er
to
s
o
lv
e
UC
,
th
e
AL
R
m
et
h
o
d
is
e
m
p
lo
y
ed
f
o
r
r
elax
in
g
p
o
w
er
s
y
s
te
m
co
n
s
tr
ai
n
ts
(
2
)
,
(
3
)
.
T
h
e
r
elax
ed
p
r
o
b
lem
i
s
d
ec
o
m
p
o
s
ed
i
n
to
N
s
u
b
p
r
o
b
le
m
s
f
o
r
ea
c
h
u
n
it.
D
y
n
a
m
ic
p
r
o
g
r
a
m
m
in
g
(
DP
)
in
cl
u
d
in
g
m
i
n
i
m
u
m
u
p
/d
o
w
n
ti
m
e
l
i
m
it
(
5
)
,
an
d
r
a
m
p
r
ate
li
m
its
(
6
)
is
u
s
ed
to
s
ea
r
ch
f
o
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th
e
o
p
ti
m
a
l
c
o
m
m
i
t
m
e
n
t
o
f
a
s
in
g
le
u
n
it
o
v
er
th
e
e
n
tire
s
t
u
d
y
p
er
io
d
.
L
ag
r
a
n
g
ia
n
m
u
ltip
lier
s
ar
e
u
p
d
ated
b
ased
o
n
v
io
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n
s
o
f
s
y
s
te
m
co
n
s
tr
ai
n
ts
.
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h
e
co
n
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er
g
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n
ce
cr
iter
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n
is
s
at
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f
ied
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f
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h
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d
u
a
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y
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ap
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w
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n
p
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m
al
an
d
d
u
al
s
o
lu
t
io
n
s
i
s
w
it
h
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a
g
i
v
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li
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it.
[
1
3
]
–
[
1
5
]
.
3
.
2
NCUC
/SCO
P
F
w
it
h L
o
a
d S
hedd
i
ng
B
ased
o
n
UC
r
es
u
lts
,
th
e
o
b
j
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ctiv
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f
u
n
c
tio
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(
9
)
is
to
m
i
n
i
m
i
ze
OP
F
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ter
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g
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ir
t
u
al
u
n
its
th
a
t
w
il
l
b
e
u
s
ed
if
OP
F
is
in
f
e
asib
le.
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o
n
s
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ai
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ts
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1
0
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an
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1
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r
e
p
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2
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CASE
S
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h
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hirt
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T
h
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ir
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u
s
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m
d
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ted
in
Fig
u
r
e
2
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as
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iv
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its
,
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o
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o
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s
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h
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2
4
-
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i
v
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–
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I
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esp
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tiv
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h
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9
5
an
d
1
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0
5
.
I
n
o
r
d
er
to
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
A
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8792
I
mp
a
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o
f S
h
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F
A
C
TS
Dev
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n
S
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u
r
ity
C
o
n
s
tr
a
in
ed
Un
it C
o
mmitmen
t
(
G.
A
.
M.Ho
s
a
in
i H
a
jiva
r
)
27
an
al
y
ze
th
e
e
f
f
icie
n
c
y
o
f
t
h
e
p
r
o
p
o
s
ed
m
et
h
o
d
,
th
e
f
o
llo
w
i
n
g
f
iv
e
ca
s
e
s
t
u
d
ies
w
ith
co
r
r
esp
o
n
d
in
g
co
n
s
tr
ai
n
ts
is
co
n
s
id
er
ed
:
C
ase
1
)
UC
(
w
it
h
o
u
t
n
et
w
o
r
k
co
n
s
tr
ain
ts
)
;
C
ase
2
)
NC
U
C
;
C
ase
2
_
1
)
NC
UC
w
it
h
o
u
t
SF
D.
C
ase
2
_
2
)
NC
UC
w
it
h
S
FD a
t
b
u
s
8
ad
j
u
s
t
m
e
n
t.
C
ase
2
_
3
)
NC
UC
w
it
h
S
FD a
t
b
u
s
es 7
,
8
,
2
1
an
d
3
0
ad
j
u
s
t
m
e
n
t.
C
ase
3
)
SF
D
d
ev
ice
at
b
u
s
8
ar
e
u
s
ed
to
;
C
ase
3
_
1
)
co
m
m
itted
to
m
i
n
i
m
izi
n
g
to
tal
g
e
n
er
atio
n
co
s
t.
C
ase
3
_
2
)
r
eg
u
late
r
elate
d
m
a
g
n
i
tu
d
e
v
o
lta
g
e
b
u
s
8
at
1
.
0
(
p
u
)
.
C
ase
4
)
SC
U
C
b
y
o
u
ta
g
e
o
f
li
n
e
6
–
8
(
co
n
tin
g
e
n
c
y
d
is
p
atc
h
)
;
C
ase
4
_
1
)
SC
UC
w
it
h
o
u
t SFD
.
C
ase
4
_
2
)
SC
UC
w
it
h
S
FD a
t
b
u
s
es 7
,
8
,
2
1
an
d
3
0
a
d
j
u
s
t
m
e
n
t.
Ass
u
m
e
th
e
L
S c
o
n
tr
ac
t is 5
0
0
$
/MW
h
f
o
r
ea
ch
lo
ad
.
C
ase
5
)
f
ail
u
r
e
in
u
n
it 3
(
co
n
tin
g
e
n
c
y
d
i
s
p
atch
)
;
C
ase
5
_
1
)
SC
UC
w
it
h
o
u
t SFD
.
C
ase
5
_
2
)
SC
UC
w
it
h
S
FD a
t
b
u
s
es 7
,
8
,
2
1
an
d
3
0
a
d
j
u
s
t
m
e
n
t
.
Ass
u
m
e
th
e
L
S c
o
n
tr
ac
t is 5
0
0
$
/MW
h
f
o
r
ea
ch
lo
ad
.
I
n
s
o
m
e
ca
s
e
s
,
ac
co
r
d
in
g
T
ab
le
I
V,
SF
D
ar
e
co
n
s
id
er
ed
.
T
h
ese
d
ev
ice
s
ar
e
m
o
d
eled
u
s
in
g
t
h
e
p
r
o
p
o
s
ed
R
P
I
M
[
1
8
]
.
C
ase
1
)
I
n
th
is
ca
s
e,
UC
w
i
l
l
d
eter
m
i
n
e
th
e
b
ase
ca
s
e
s
c
h
ed
u
le
o
f
u
n
it
s
,
w
h
e
n
d
is
r
eg
ar
d
in
g
th
e
n
et
w
o
r
k
co
n
s
tr
ain
ts
.
T
h
e
co
m
m
it
m
e
n
t
s
ch
ed
u
le
is
s
h
o
w
n
i
n
T
ab
le
I
V
in
w
h
ic
h
1
an
d
0
r
ep
r
es
en
t
h
o
u
r
l
y
o
n
/o
f
f
s
tate
s
o
f
u
n
its
,
a
n
d
h
o
u
r
0
r
ep
r
esen
ts
t
h
e
i
n
itial
co
n
d
itio
n
.
I
n
ad
d
itio
n
,
th
e
d
ail
y
b
id
-
b
ased
g
en
er
atio
n
d
is
p
atch
co
s
t
g
i
v
e
n
in
T
ab
le
I
V
is
$
1
4
2
2
0
3
.
6
1
4
5
.
T
h
e
o
p
tim
al
g
e
n
er
atio
n
d
is
p
a
tch
g
i
v
e
n
in
T
ab
le
V.
I
n
t
h
is
ca
s
e,
t
h
e
e
co
n
o
m
ical
u
n
its
1
,
2
an
d
4
s
u
p
p
ly
th
e
b
ase
lo
ad
,
w
h
ic
h
ar
e
co
m
m
i
tted
at
th
e
e
n
tire
s
c
h
ed
u
li
n
g
h
o
r
iz
o
n
.
T
h
e
u
n
it
s
3
ar
e
co
m
m
itte
d
at
ce
r
tain
h
o
u
r
s
(
1
1
-
2
1
)
to
s
u
p
p
l
y
p
ea
k
lo
ad
an
d
to
m
i
n
i
m
ize
t
h
e
to
tal
g
e
n
er
atio
n
co
s
t.
Mo
r
e
ex
p
en
s
iv
e
u
n
it
s
4
a
n
d
5
ar
e
n
o
t
co
m
m
itted
a
t
all
h
o
u
r
s
.
C
ase
2
)
I
n
ca
s
e
2
_
1
,
th
e
i
m
p
ac
t
o
f
ac
n
e
t
w
o
r
k
co
n
s
tr
ai
n
ed
a
t
s
tead
y
s
tate
o
n
u
n
it
co
m
m
it
m
e
n
t
(
N
C
U
C
)
i
s
s
tu
d
ied
.
I
f
w
e
u
s
e
t
h
e
U
C
r
es
u
lts
in
C
a
s
e
1
f
o
r
N
C
OP
F
ca
l
cu
latio
n
s
,
m
ag
n
it
u
d
e
v
o
ltag
e
v
io
latio
n
s
w
il
l
o
cc
u
r
at
b
u
s
es
1
2
-
2
0
.
I
n
o
r
d
er
to
co
n
s
id
er
in
g
t
h
e
n
et
w
o
r
k
co
n
s
tr
ai
n
ts
,
w
e
f
in
d
t
h
at
th
e
o
th
er
UC
in
C
ase
2
_
1
.
So
,
th
e
co
m
m
it
m
en
t
s
ch
ed
u
le
is
s
h
o
w
n
in
T
ab
le
I
V
a
n
d
t
h
e
o
p
ti
m
al
g
en
er
at
io
n
d
is
p
atc
h
o
f
NC
OP
F
is
c
h
an
g
ed
as
s
h
o
w
n
in
T
ab
le
V.
T
h
e
h
ig
h
li
g
h
ted
ite
m
s
i
n
m
en
t
io
n
ed
T
ab
le
s
h
o
w
d
if
f
er
e
n
ce
s
b
et
w
ee
n
C
ase
1
a
n
d
C
a
s
e
2
_
1
.
I
n
o
r
d
er
to
m
ai
n
tai
n
in
g
th
e
m
a
g
n
it
u
d
e
v
o
lta
g
e
b
u
s
e
s
to
th
eir
li
m
its
(
0
.
9
5
≤
V
≤
1
.
0
5
)
an
d
lin
e
ca
p
ac
it
y
li
m
its
i
n
ac
c
o
r
d
an
ce
T
ab
le
I
I
,
th
e
g
en
er
ati
o
n
d
is
p
atch
o
f
th
e
ec
o
n
o
m
ical
u
n
it
s
1
,
2
,
3
an
d
4
is
ch
an
g
ed
.
T
h
e
r
elativ
el
y
ex
p
e
n
s
i
v
e
u
n
it
s
5
an
d
6
ar
e
d
is
p
atch
ed
to
s
u
p
p
l
y
th
e
s
y
s
te
m
lo
ad
s
.
A
cc
o
r
d
in
g
l
y
,
t
h
e
d
ai
l
y
co
s
t
o
f
b
id
-
b
ased
g
e
n
er
atio
n
d
is
p
atch
in
cr
ea
s
es to
$
1
6
9
5
0
5
.
1
9
.
I
n
C
ase
s
2
_
2
-
2
_
3
,
th
e
SF
D
i
n
j
ec
t
th
e
co
n
tr
o
llab
le
r
ea
ctiv
e
p
o
w
er
to
t
h
e
n
e
t
w
o
r
k
an
d
al
s
o
m
a
n
ag
e
r
ea
ctiv
e
p
o
w
er
f
lo
w
s
a
n
d
ac
co
r
d
in
g
l
y
ad
j
u
s
t
b
u
s
v
o
lta
g
e
lev
els.
T
h
e
SF
D
d
ec
r
ea
s
e
t
h
e
r
ea
ctiv
e
p
o
w
er
f
lo
w
o
n
th
e
n
et
w
o
r
k
li
n
es
a
n
d
th
er
ef
o
r
e
in
cr
ea
s
e
t
h
e
tr
an
s
f
er
ca
p
ab
ilit
y
o
f
th
e
li
n
e
s
.
I
n
ca
s
e
2_2
-
2
_
3
th
e
v
o
ltag
e
at
al
l b
u
s
es a
n
d
t
h
e
r
ea
ctiv
e
p
o
w
er
f
lo
w
at
n
et
w
o
r
k
lin
e
s
is
c
h
a
n
g
ed
b
y
t
h
e
SF
D.
I
n
ca
s
e
2
_
2
,
th
e
r
ea
cti
v
e
p
o
w
e
r
g
e
n
er
atio
n
b
y
Sh
u
n
t
F
A
C
T
S
Dev
ice
at
b
u
s
8
i
s
s
h
o
w
n
i
n
T
ab
le
VI
I
.
I
n
ca
s
e
2
_
3
,
th
e
r
ea
ctiv
e
p
o
w
er
g
en
er
atio
n
b
y
S
FD
is
s
h
o
wn
in
Fi
g
.
3
.
T
h
e
co
m
m
it
m
en
t
s
ch
ed
u
le
is
s
h
o
w
n
i
n
T
ab
le
VI
an
d
th
e
o
p
ti
m
al
g
en
er
atio
n
d
is
p
atc
h
o
f
NC
OP
F
i
s
ch
a
n
g
ed
as
s
h
o
wn
i
n
T
ab
le
VI
I
.
T
h
e
h
ig
h
li
g
h
ted
ite
m
s
in
T
ab
les
I
V,
VI
s
h
o
w
d
if
f
er
en
ce
s
b
et
w
ee
n
all
t
h
is
s
ec
tio
n
ca
s
es
co
m
p
ar
ed
to
ca
s
e
1
.
W
ith
o
u
t
th
e
SF
D
th
e
v
o
lta
g
e
d
r
o
p
o
cc
u
r
at
all
b
u
s
es
m
o
s
t
l
y
at
p
ea
k
h
o
u
r
s
.
Ho
w
e
v
er
,
th
e
r
ea
ctiv
e
p
o
w
er
in
j
ec
tio
n
to
th
e
n
et
w
o
r
k
in
cr
ea
s
es
th
e
b
u
s
v
o
lta
g
e
s
an
d
p
r
ev
en
ts
v
o
ltag
e
a
n
d
lin
e
ca
p
ac
it
y
v
io
latio
n
s
.
W
ith
o
u
t
th
e
S
h
u
n
t
F
A
C
T
S
Dev
ices,
v
o
lta
g
es
ar
e
ad
j
u
s
ted
b
y
th
e
n
eig
h
b
o
r
in
g
g
e
n
er
ati
n
g
u
n
its
.
T
h
e
r
ea
cti
v
e
p
o
w
er
g
en
e
r
atio
n
o
f
u
n
i
ts
i
s
i
n
cr
ea
s
ed
f
o
r
ad
j
u
s
tin
g
th
e
v
o
ltag
e
le
v
el
at
b
u
s
e
s
,
w
h
ich
w
o
u
ld
also
i
n
cr
ea
s
e
th
e
r
ea
ctiv
e
p
o
w
er
f
lo
w
at
n
et
w
o
r
k
lin
e
s
.
So
,
th
e
S
FD
co
u
ld
r
ed
u
ce
t
h
e
ac
ti
v
e
a
n
d
r
ea
ctiv
e
p
o
w
er
d
is
p
atc
h
o
f
u
n
it
s
,
d
ec
r
ea
s
e
r
ea
ctiv
e
p
o
w
er
li
n
e
f
lo
w
s
,
b
u
s
v
o
lta
g
e
s
u
p
p
o
r
t
an
d
m
in
i
m
ize
t
h
e
to
tal
g
e
n
er
atio
n
co
s
t.
I
n
t
h
e
w
h
o
le
ca
s
e
s
ar
e
m
en
tio
n
ed
,
ca
s
e
2
_
3
h
as
t
h
e
m
i
n
i
m
u
m
to
tal
g
e
n
er
atio
n
co
s
t
a
n
d
le
s
s
co
m
m
itted
m
o
r
e
ex
p
e
n
s
i
v
e
u
n
it
s
.
T
h
er
ef
o
r
d
is
tr
ib
u
ted
SF
D
i
n
lo
ad
b
u
s
es
is
b
etter
ch
o
ice
f
o
r
p
o
w
er
s
y
s
t
e
m
p
lan
n
i
n
g
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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:
2
2
5
2
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8792
IJ
A
P
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Vo
l.
5
,
No
.
1
,
A
p
r
il
2
0
1
6
:
22
–
39
28
C
ase
3
)
I
n
t
h
ese
ca
s
e
s
(
3
_
1
an
d
3
_
2
)
,
NC
UC
w
ill
d
eter
m
i
n
e
s
c
h
ed
u
le
o
f
u
n
it
s
w
h
e
n
S
FD
is
co
m
m
i
tted
to
m
i
n
i
m
izi
n
g
to
tal
g
e
n
er
atio
n
co
s
t
(
ca
s
e
3
_
1
)
an
d
r
eg
u
late
r
elate
d
b
u
s
v
o
ltag
e
at
1
p
u
.
T
h
e
co
m
m
i
t
m
e
n
t
s
ch
ed
u
le
is
s
h
o
wn
in
T
ab
le
VI
I
I
an
d
ac
tiv
e
p
o
w
er
g
en
er
atio
n
d
is
p
atch
i
n
T
ab
le
I
X.
I
t
is
clea
r
th
at
w
h
e
n
t
h
e
SF
D
co
m
m
itted
to
r
eg
u
la
tin
g
co
r
r
es
p
o
n
d
in
g
b
u
s
v
o
lta
g
e
is
le
s
s
ef
f
ec
tiv
e
o
n
m
i
n
i
m
izi
n
g
co
s
t
f
u
n
ct
io
n
.
T
h
er
ef
o
r
e,
it
is
d
esira
b
le
th
ese
co
n
tr
o
llab
le
d
ev
ices
s
h
o
u
ld
b
e
ad
ju
s
t
b
ased
o
n
NC
UC
p
la
n
n
in
g
.
I
f
co
n
t
i
n
g
e
n
c
y
i
s
o
cc
u
r
r
ed
,
th
e
SC
U
C
d
eter
m
i
n
es
t
h
e
s
et
tin
g
o
f
SF
D.
T
h
e
ca
p
ac
i
t
y
o
f
t
h
is
eq
u
ip
m
e
n
t
s
h
o
u
ld
b
e
d
eter
m
i
n
ed
b
ased
o
n
lo
n
g
-
ter
m
p
lan
n
i
n
g
.
T
h
e
r
ea
ct
iv
e
p
o
w
er
g
en
er
atio
n
b
y
S
FD
i
s
s
h
o
w
n
in
T
ab
le
I
X.
T
h
e
h
i
g
h
li
g
h
ted
ite
m
s
in
T
ab
les
VI
I
I
s
h
o
w
d
if
f
er
en
ce
s
b
et
w
ee
n
all
th
is
s
ec
t
io
n
ca
s
e
s
co
m
p
ar
ed
to
ca
s
e
1
.
C
ase
4
)
T
h
e
o
u
tag
e
o
f
li
n
e
6
–
8
,
b
ased
o
n
r
esu
lt
s
o
f
N
C
U
C
,
w
ill
ca
u
s
e
t
h
e
li
n
e
ca
p
ac
ity
6
-
2
8
,
8
-
2
8
,
2
1
-
2
4
an
d
2
2
-
2
4
o
u
t
o
f
p
er
m
is
s
ib
le
r
an
g
e.
T
h
e
ad
d
itio
n
o
f
B
en
d
er
s
cu
ts
to
t
h
e
S
C
OP
F
f
o
r
a
p
r
ev
en
ti
v
e
d
is
p
atch
co
n
tr
o
l
w
ill
p
r
o
v
id
e
a
f
ea
s
ib
le
d
is
p
atc
h
s
o
l
u
tio
n
.
T
h
en
B
en
d
er
s
c
u
ts
to
U
C
f
o
r
m
o
d
if
y
i
n
g
th
e
U
C
/
SC
OP
F
s
o
lu
tio
n
ar
e
g
en
er
ated
.
I
n
T
ab
le
X
t
h
e
m
o
d
if
ied
U
C
s
o
lu
tio
n
is
g
i
v
e
n
.
H
o
w
e
v
er
,
at
h
o
u
r
s
1
-
2
4
,
b
ec
au
s
e
o
f
b
u
s
v
o
ltag
e
a
n
d
m
en
tio
n
ed
lin
e
ca
p
ac
ity
li
m
i
ts
,
i
f
all
o
f
th
e
u
n
it
s
i
s
co
m
m
i
tted
s
till
ca
n
n
o
t
s
ati
s
f
y
th
e
n
et
w
o
r
k
co
n
s
tr
ai
n
ts
.
T
h
u
s
,
v
ir
tu
al
g
e
n
er
ato
r
ar
e
ad
d
e
d
at
lo
ad
b
u
s
8
f
o
r
lo
ad
cu
r
tail
m
en
t.
A
s
a
r
esu
lt,
ce
r
ta
in
a
m
o
u
n
t
o
f
lo
ad
is
cu
r
tai
led
at
v
io
lated
h
o
u
r
s
(
1
-
2
4
)
.
Desp
ite
L
S
co
s
t,
th
e
d
ail
y
b
id
-
b
ased
d
is
p
atch
co
s
t
is
m
o
r
e
in
cr
ea
s
ed
.
T
h
e
n
e
w
g
e
n
er
atio
n
d
is
p
atch
i
n
SC
OP
F i
s
ill
u
s
tr
ated
i
n
T
ab
le
XI
.
I
n
ca
s
e
4
_
2
,
th
e
co
n
s
id
er
in
g
o
f
SF
D
in
th
e
n
et
w
o
r
k
h
a
s
c
au
s
ed
t
h
at
m
ag
n
it
u
d
e
v
o
ltag
e
o
f
th
e
b
u
s
e
s
ar
e
n
o
t
o
u
t
o
f
r
an
g
e.
B
u
t
b
e
ca
u
s
e
o
f
li
n
e
ca
p
ac
it
y
l
i
m
i
ts
o
r
n
et
w
o
r
k
co
n
g
es
tio
n
i
n
t
h
is
ca
s
e,
th
e
SF
D
d
o
es
n
o
t
h
elp
to
p
r
ev
en
t
lo
ad
cu
r
tail
m
e
n
t
at
h
o
u
r
s
8
-
2
4
.
T
h
e
h
ig
h
li
g
h
ted
ite
m
s
in
T
ab
les
X
s
h
o
w
d
if
f
er
en
ce
s
b
et
w
ee
n
all
t
h
is
s
ec
t
io
n
ca
s
es
co
m
p
ar
ed
to
ca
s
e
1
.
I
n
ca
s
e
4
_
2
,
B
ec
au
s
e
o
f
en
tire
r
ea
ctiv
e
p
o
w
er
in
j
ec
tio
n
co
n
tr
o
l
lin
g
an
d
r
ea
ctiv
e
p
o
w
er
f
lo
w
m
an
a
g
i
n
g
in
n
et
w
o
r
k
,
t
h
e
SF
D
ar
e
th
e
b
est
o
p
tio
n
in
o
p
ti
m
izi
n
g
co
s
t,
less
lo
ad
cu
r
tail
m
e
n
t
a
n
d
m
ai
n
tai
n
in
g
n
et
w
o
r
k
s
ec
u
r
it
y
.
I
t
is
clea
r
with
d
i
s
tr
ib
u
ted
SF
D
in
n
e
t
w
o
r
k
a
n
d
s
u
p
p
o
r
tin
g
o
f
a
ll
b
u
s
v
o
ltag
es
h
a
s
th
e
b
etter
r
esu
lt
i
n
N
C
UC
/SC
UC
p
r
o
b
lem
s
.
T
h
e
r
ea
ctiv
e
p
o
w
er
g
e
n
er
atio
n
b
y
SF
D
i
s
s
h
o
w
n
i
n
Fi
g
.
4
.
C
ase
5
)
I
n
ca
s
e
s
5
_
1
-
5
_
2
,
th
e
g
en
er
ati
n
g
u
n
it
2
o
u
t
o
f
s
er
v
ic
e.
A
cc
o
r
d
in
g
to
th
e
NC
U
C
r
es
u
lts
,
u
n
it
3
f
a
ils
t
o
s
u
p
p
l
y
lo
ad
s
at
h
o
u
r
s
1
th
r
o
u
g
h
2
4
.
T
h
u
s
,
t
h
e
SC
OP
F
s
o
lu
tio
n
f
o
r
th
is
co
n
tin
g
e
n
c
y
will
r
eq
u
ir
e
B
en
d
er
s
cu
t
f
o
r
r
ec
o
m
p
u
tin
g
UC
.
T
h
e
co
m
m
it
m
e
n
t
s
ch
ed
u
l
e
is
s
h
o
w
n
i
n
T
ab
le
XI
I
an
d
ac
tiv
e
p
o
w
er
g
en
er
atio
n
d
is
p
atc
h
i
n
T
ab
le
XI
I
I
.
T
h
e
h
ig
h
li
g
h
ted
ite
m
s
i
n
T
ab
les
XI
I
s
h
o
w
d
i
f
f
er
en
ce
s
b
et
w
ee
n
all
th
is
s
ec
t
io
n
ca
s
es
co
m
p
ar
ed
to
ca
s
e
1
.
B
y
co
m
p
ar
i
s
o
n
o
p
ti
m
al
g
e
n
er
atio
n
d
is
p
atc
h
i
n
T
ab
les
VI
I
a
n
d
XI
I
I
,
it
is
clea
r
t
h
at
t
h
e
e
x
p
en
s
iv
e
u
n
it
s
3
,
5
an
d
6
r
ep
lace
s
u
n
i
t
2
to
s
u
p
p
l
y
m
o
r
e
lo
ad
s
.
I
n
ca
s
e
5
_
2
,
b
y
ec
o
n
o
m
ic
ad
j
u
s
ti
n
g
o
f
SF
D
in
th
e
n
et
w
o
r
k
h
as c
a
u
s
ed
th
a
t
m
a
g
n
it
u
d
e
v
o
lta
g
e
o
f
t
h
e
b
u
s
es a
r
e
n
o
t
o
u
t o
f
r
an
g
e.
T
h
e
r
ea
ctiv
e
p
o
w
er
g
e
n
er
atio
n
b
y
SF
D
i
s
s
h
o
w
n
in
Fig
.
5
.
5.
CO
NCLU
SI
O
NS
T
h
e
NC
UC
/
SC
U
C
r
es
u
lt
s
o
f
n
u
m
er
ical
te
s
ts
s
h
o
w
t
h
e
e
f
f
ec
ti
v
en
e
s
s
o
f
th
e
p
r
o
p
o
s
ed
m
et
h
o
d
f
o
r
m
i
n
i
m
izi
n
g
b
id
b
ased
g
e
n
er
at
io
n
co
s
t
a
n
d
m
ai
n
tai
n
n
et
w
o
r
k
s
ec
u
r
it
y
i
n
s
tead
y
s
tate
a
n
d
co
n
ti
n
g
e
n
c
y
.
T
h
e
p
r
o
p
o
s
ed
m
et
h
o
d
co
u
ld
s
o
lv
e
b
o
th
NC
UC
a
n
d
SC
U
C
m
o
d
u
les
b
ased
o
n
ac
co
n
s
tr
ain
t
s
an
d
ad
v
ice
a
g
o
o
d
s
et
o
f
co
r
r
ec
tiv
e
an
d
p
r
ev
en
ti
v
e
c
o
n
tr
o
l p
r
o
to
c
o
l f
o
r
th
e
s
ec
u
r
e
an
d
ec
o
n
o
m
ical
o
p
er
atio
n
o
f
p
o
w
er
s
y
s
te
m
s
.
I
m
p
ac
t
o
f
SF
D
ad
j
u
s
t
m
e
n
t
was
in
v
esti
g
ated
i
n
to
th
e
NC
U
C
/S
C
UC
w
i
th
AC
n
e
t
w
o
r
k
co
n
s
tr
ai
n
ts
at
s
tead
y
s
tate
a
n
d
co
n
ti
n
g
e
n
c
y
.
T
o
en
h
an
ce
t
h
e
p
r
o
p
o
s
ed
A
C
s
o
lu
t
io
n
o
f
S
C
U
C
,
Sh
u
n
t
F
AC
T
S
d
ev
ices
w
er
e
co
n
s
id
er
ed
.
A
R
P
I
M
w
as
u
s
ed
to
m
o
d
el
t
h
e
ef
f
ec
t
o
f
SF
D
in
t
h
e
AC
p
o
w
er
f
lo
w
,
u
s
in
g
r
ea
ct
iv
e
p
o
w
er
in
j
ec
tio
n
s
to
s
y
s
te
m
lo
ad
b
u
s
es.
W
e
co
n
clu
d
ed
th
at
th
e
in
co
r
p
o
r
atio
n
o
f
SF
D
w
o
u
ld
e
n
h
a
n
ce
th
e
h
o
u
r
l
y
SC
U
C
s
o
lu
tio
n
w
h
en
co
n
s
id
er
in
g
b
u
s
v
o
ltag
e
a
n
d
lin
e
ca
p
ac
it
y
co
n
s
tr
ain
t
s
.
I
f
th
e
SF
D
w
i
th
th
e
s
u
f
f
icie
n
t
ca
p
ac
it
y
at
f
u
l
l
lo
ad
ce
n
ter
s
to
b
e
in
s
talled
a
n
d
u
ti
lized
,
m
o
r
e
ef
f
ec
tiv
e
i
n
th
e
s
h
o
r
t
-
ter
m
p
o
w
er
s
y
s
t
e
m
p
lan
n
in
g
w
ill
y
ield
.
Dis
t
r
ib
u
ted
f
ast
co
n
tr
o
llab
le
s
h
u
n
t
r
ea
ctiv
e
p
o
w
er
r
eso
u
r
ce
s
w
il
l
r
eg
u
late
b
u
s
v
o
ltag
e,
less
r
ea
ctiv
e
p
o
w
er
f
lo
w
a
n
d
r
ed
u
ce
lo
s
s
es
in
th
e
p
o
w
er
s
y
s
te
m
.
Fu
r
t
h
er
m
o
r
e,
th
e
u
s
e
o
f
m
a
x
i
m
u
m
ca
p
ac
it
y
o
f
th
e
tr
an
s
m
i
s
s
io
n
s
y
s
te
m
w
ill
b
e
p
r
o
v
id
ed
.
Me
an
w
h
i
le,
ec
o
n
o
m
ic
d
i
s
p
atch
o
f
lo
ad
b
et
w
ee
n
p
o
w
er
p
lan
t
s
ca
n
p
r
o
v
id
e.
W
ith
t
u
r
n
o
f
f
m
o
r
e
ex
p
e
n
s
i
v
e
u
n
i
ts
in
lo
w
a
n
d
m
ed
iu
m
d
e
m
an
d
h
o
u
r
s
,
t
h
e
t
o
tal
p
r
o
d
u
ctio
n
co
s
t
d
ec
r
ea
s
es.
Mo
r
e
ex
p
en
s
i
v
e
u
n
i
ts
m
a
y
b
e
u
s
ed
in
ter
m
s
o
f
n
et
w
o
r
k
e
m
er
g
en
c
y
ev
e
n
t
if
n
ee
d
ed
to
m
ai
n
tai
n
n
et
w
o
r
k
s
ec
u
r
it
y
.
T
h
er
ef
o
r
e
p
r
o
p
er
o
p
er
atio
n
o
f
th
is
eq
u
ip
m
e
n
t in
t
h
e
S
C
U
C
is
n
ec
ess
ar
y
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
A
P
E
I
SS
N:
2252
-
8792
I
mp
a
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o
f S
h
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F
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Dev
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ed
Un
it C
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(
G.
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M.Ho
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a
in
i H
a
jiva
r
)
29
U
C
(
W
i
t
h
o
u
t
N
e
t
w
o
r
k
C
o
n
st
r
a
i
n
t
s
)
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p
t
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m
a
l
sc
h
e
d
u
l
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o
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u
n
i
t
s
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o
u
r
l
y
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e
t
w
o
r
k
C
h
e
c
k
(
B
a
s
e
c
a
s
e
)
N
C
O
P
F
B
Y
S
h
u
n
t
F
A
C
T
S
d
e
v
i
c
e
s
t
u
n
n
i
n
g
F
e
a
si
b
l
e
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i
o
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a
t
i
o
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L
a
s
t
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o
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i
n
g
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o
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r
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w
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h
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h
u
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d
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s
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F
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si
b
l
e
(
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l
a
t
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M
a
x
I
t
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r
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e
n
d
M
a
s
t
e
r
P
r
o
b
l
e
m
S
u
b
p
r
o
b
l
e
m
1
(
N
C
O
P
F
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u
b
p
r
o
b
l
e
m
2
(
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P
F
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a
x
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t
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r
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o
a
d
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h
e
d
d
i
n
g
(
S
t
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y
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t
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t
e
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a
d
S
h
e
d
d
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n
g
(
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t
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n
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y
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e
s
No
Y
e
s
C
u
t
Y
e
s
No
Y
e
s
No
Y
e
s
No
Fig
u
r
e
1
.
Flo
w
c
h
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f
S
C
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it
h
S
h
u
n
t F
A
C
T
S De
v
ices
f
o
r
r
ea
ctiv
e
p
o
w
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m
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ag
e
m
e
n
t
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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IJ
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39
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Fig
u
r
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h
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m
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ab
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Un
it Da
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n
i
t
N
o
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1
2
3
4
5
6
B
u
s
N
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1
2
13
22
23
27
U
n
i
t
C
o
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t
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o
e
f
f
i
c
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e
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t
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a
(
M
B
t
u
)
1
5
0
1
8
0
1
2
5
2
0
0
90
75
b
(
M
B
t
u
/
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W
h
)
30
2
0
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3
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.
3
1
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c
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0
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P
m
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(
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W
)
10
10
10
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10
10
P
max
(
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)
90
80
70
80
90
90
Q
m
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n
(
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v
a
r
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-
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max
(
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v
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r
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70
60
50
60
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t
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30
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(
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n
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M
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p
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M
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D
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me
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R
a
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p
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(
M
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)
50
40
30
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20
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R
a
m
p
D
o
w
n
R
a
t
e
(
M
W
/
h
)
60
45
25
50
25
40
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
A
P
E
I
SS
N:
2252
-
8792
I
mp
a
ct
o
f S
h
u
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t
F
A
C
TS
Dev
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n
S
ec
u
r
ity
C
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n
s
tr
a
in
ed
Un
it C
o
mmitmen
t
(
G.
A
.
M.Ho
s
a
in
i H
a
jiva
r
)
31
T
ab
le
2.
T
r
an
s
m
is
s
io
n
L
i
n
e
D
ata
L
i
n
e
N
o
.
F
r
o
m
B
u
s
To
B
u
s
R
(
p
u
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(
p
u
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B
(
p
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)
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t
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n
e
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.
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r
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m
B
u
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To
B
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(
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15
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T
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3
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Data
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