T
E
L
KO
M
NIK
A
, V
ol
.
16
,
No
. 5
, O
c
tob
er 20
18
,
pp
.
23
1
6
~
23
30
IS
S
N: 1
69
3
-
6
93
0
,
accr
ed
ited
F
irst
Gr
ad
e b
y K
em
en
r
istekdikti
,
Decr
ee
No: 2
1/E/
K
P
T
/20
18
DOI:
10.12928/TE
LK
OM
N
IK
A
.v
1
6
i
5
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Ab
strac
t
Th
i
s
wor
k
p
ro
p
o
s
e
s
a
m
e
th
o
d
b
a
s
e
d
o
n
a
m
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n
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l
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-
c
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v
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x
p
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a
m
m
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m
o
d
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l
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l
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th
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m
u
l
ti
s
ta
g
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tra
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m
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s
i
o
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x
p
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s
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p
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m
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ta
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m
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s
e
m
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l
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d
a
s
a
n
o
p
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m
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ti
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n
t
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l
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AC l
o
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l
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w m
o
d
e
l
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s
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d
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n
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t
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m
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e
TEP
p
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m
,
whe
re
a
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d
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c
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ta
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d
.
Fu
rth
e
rm
o
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,
th
e
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s
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th
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tra
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p
o
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m
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s
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d
d
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d
,
th
e
rm
a
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m
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t
s
a
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d
b
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s
v
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l
i
m
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s
.
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e
p
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p
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d
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c
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p
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t
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d
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a
f
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ti
m
e
f
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th
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s
t
s
y
s
t
e
m
s
.
Key
w
ords
:
m
u
l
t
i
s
t
a
g
e
tra
n
s
m
i
s
s
i
o
n
e
x
p
a
n
s
i
o
n
p
l
a
n
n
i
n
g
,
m
e
ta
-
h
e
u
ri
s
ti
c
s
,
d
i
f
fe
re
n
ti
a
l
e
v
o
l
u
ti
o
n
a
l
g
o
ri
th
m
,
AC p
o
wer
fl
o
w m
o
d
e
l
,
v
i
o
l
a
ti
o
n
c
h
e
c
k
i
n
g
,
c
o
n
s
tr
a
i
n
t
p
ro
g
ra
m
m
i
n
g
Copy
righ
t
©
2
0
1
8
Uni
v
e
rsi
t
a
s
Ahm
a
d
D
a
hl
a
n.
All
rig
ht
s
r
e
s
e
rve
d
.
1.
Int
r
o
d
u
ctio
n
T
he
f
utu
r
e
of
the
po
wer
ne
twork
i
s
to
be
a
be
tt
er
gri
d
i
n
wh
i
c
h
th
e
gr
i
d
i
s
f
l
ex
i
b
l
e
w
i
th
di
f
f
erent
s
c
en
ario
s
a
nd
r
ob
us
t
to
w
i
ths
tan
d
d
i
f
f
erent
k
i
nd
s
of
un
c
ertai
nti
es
or
di
s
t
urbanc
es
th
at
m
ay
h
ap
p
en
.
T
he
10
-
y
ea
r
s
pl
an
ni
ng
s
um
m
ar
y
w
h
i
c
h
i
s
pr
op
os
e
d
b
y
[1]
,
whi
c
h
ha
s
be
e
n
prepare
d
b
y
th
e
W
es
tern
E
l
ec
tr
i
c
i
t
y
C
oo
r
d
i
na
t
i
n
g
C
o
un
c
i
l
(
W
E
CC)
,
the
l
oa
ds
a
r
e
ex
pe
c
t
ed
to
i
nc
r
ea
s
e
14
%
be
t
wee
n
t
he
y
e
ars
of
20
17
an
d
20
2
8
.
In
ot
he
r
wor
ds
,
t
ha
t
pe
r
c
e
nta
g
e
i
s
1.2
%
c
o
m
po
un
d
a
nn
u
al
r
at
e.
O
n
the
ot
he
r
ha
n
d,
th
e
f
utu
r
e
o
f
the
ge
ne
r
at
i
o
n
un
i
ts
i
s
ex
p
ec
t
ed
to
h
av
e
an
i
m
po
r
tan
t
c
h
an
ge
f
r
om
t
he
tr
ad
i
t
i
on
al
on
es
,
s
i
nc
e
t
h
e
ad
di
t
i
on
s
of
the
n
e
w
g
en
erati
o
n
u
ni
ts
t
o
r
ep
l
ac
e
t
he
r
et
i
r
ed
o
ne
s
ar
e
r
en
e
wabl
e
un
i
ts
.
O
nl
y
th
en
the
m
an
da
t
ed
s
tat
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of
the
Ren
e
w
a
bl
e
P
ortf
ol
i
o S
tan
da
r
ds
(
RP
S
s
)
c
an
be
f
u
l
f
i
l
l
ed
.
W
i
th
s
uc
h
a
c
on
te
m
po
r
ar
y
c
ha
ng
e
,
m
an
y
i
s
s
ue
s
are
e
x
pe
c
ted
to
r
i
s
e
i
n
the
ne
ar
f
utu
r
e
of
the
po
wer
s
y
s
t
em
.
F
i
r
s
t
of
al
l
,
t
he
l
oa
d
i
nc
r
em
en
t
m
i
gh
t
c
ha
ng
e
a
nd
af
f
ec
t
the
c
o
m
po
ne
nts
of
the
p
o
w
er
f
l
o
w
i
n
th
e
ex
i
s
t
i
ng
ne
t
wor
k
.
F
urtherm
ore,
i
t
m
i
gh
t
c
au
s
e
a
p
ote
nti
al
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er
l
oa
ds
an
d
s
tab
i
l
i
t
y
prob
l
em
s
.
S
uc
h
probl
em
s
c
an
v
i
ol
a
te
the
r
e
l
i
a
bi
l
i
t
y
c
r
i
t
eria
of
th
e
s
y
s
t
em
.
S
ec
on
d,
m
os
t
of
the
r
en
e
w
a
bl
e
en
er
g
y
r
es
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r
c
es
are
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oc
at
ed
i
n
f
ar
pl
ac
es
an
d
no
t
r
e
ad
i
l
y
c
o
nn
ec
te
d
to
th
e
m
ai
n
po
wer
ne
t
wor
k
.
A
dd
i
t
i
on
a
l
tr
an
s
m
i
s
s
i
on
c
ap
ac
i
t
y
i
s
r
eq
ui
r
ed
i
n
order
t
o
c
ate
r
al
l
t
he
a
bo
v
e
probl
em
s
[2]
.
G
i
v
en
the
r
e
qu
i
r
e
d
t
as
k
i
n
T
E
P
proc
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s
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i
n
order
t
o
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n
d
th
e
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pti
m
al
pl
an
of
T
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P
ov
er
a
s
pe
c
i
f
i
e
d
h
ori
z
on
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t
e
di
o
us
a
nd
c
om
pl
ex
c
om
pu
t
ati
o
na
l
proc
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s
an
d
ex
ten
s
i
v
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pa
r
am
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r
s
are
r
eq
u
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r
ed
t
o
b
e
de
al
t
w
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t
h.
It
i
s
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m
en
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ni
n
g
th
at,
th
e
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of
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[3
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-
[
7].
Evaluation Warning : The document was created with Spire.PDF for Python.
T
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KO
M
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IS
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N: 1
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3
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AC
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Ibra
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2317
W
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a
m
m
i
ng
(
MINL
P
)
prob
l
e
m
.
Us
ua
l
l
y
,
the
MINL
P
no
n
c
on
v
ex
no
n
l
i
n
ea
r
c
o
ns
tr
ai
n
ts
are
s
ol
v
e
d
b
y
us
i
n
g
th
e
Me
ta
h
eu
r
i
s
ti
c
m
eth
od
s
,
c
on
s
i
d
erin
g
t
he
i
r
po
ten
t
i
a
l
o
f
f
i
nd
i
ng
h
i
gh
-
q
ua
l
i
t
y
s
ol
u
ti
on
s
a
nd
s
om
e
ad
v
an
t
ag
es
:
t
he
y
are
r
e
l
at
i
v
e
l
y
s
i
m
pl
e,
ab
l
e
to
m
i
x
i
nt
eg
er
an
d
n
on
-
i
n
teg
er
v
ar
i
a
b
l
es
a
nd
a
v
o
i
d
l
oc
al
op
t
i
m
a b
y
ex
p
l
or
i
ng
th
e s
tr
uc
ture of
ea
c
h
prob
l
em
wi
th
l
es
s
c
om
pu
tat
i
on
a
l
ef
f
ort [11
]
.
T
hrough
ou
t
the
pa
s
t
de
c
ad
es
,
the
r
e
ha
v
e
be
en
m
an
y
wor
k
s
propos
ed
to
s
o
l
v
e
t
h
e
T
E
P
probl
em
.
S
om
e
w
ork
s
h
av
e
be
e
n
s
i
g
ni
f
i
c
an
t
to
the
pro
bl
em
,
s
uc
h
as
:
a
hi
erar
c
hi
c
al
de
c
om
po
s
i
ti
on
a
pp
r
o
ac
h
f
o
r
op
t
i
m
al
tr
an
s
m
i
s
s
i
on
n
et
wor
k
ex
pa
ns
i
o
n
pl
a
nn
i
ng
was
i
ntrod
uc
ed
i
n
[12
]
.
A
no
t
he
r
i
m
po
r
tan
t
wor
k
w
as
propos
e
d
b
y
O
l
i
v
i
er
G
.C
at
al
.
[
13
].
A
ge
n
eral
branc
h
a
nd
bo
un
d a
l
g
orit
hm
was
us
ed
t
o o
bt
ai
n a
f
ea
s
i
b
l
e
i
nt
eg
er s
o
l
ut
i
o
n f
or eac
h
i
n
v
es
tm
en
t
s
ub
-
probl
em
.
Mo
r
eo
v
er,
an
ap
p
l
i
c
at
i
o
n
of
an
Im
prov
ed
G
en
e
ti
c
A
l
g
o
r
i
thm
(
IG
A
)
w
as
pres
e
nte
d
f
or
s
ol
v
i
n
g
t
he
T
E
P
prob
l
em
[14
].
F
urt
he
r
m
ore,
a
m
od
i
f
i
ed
P
S
O
t
ec
hn
i
qu
e
i
nc
orpor
at
i
n
g
a
no
v
el
s
w
ar
m
i
ni
ti
a
l
i
z
a
ti
o
n p
r
oc
e
du
r
e f
or s
ol
v
i
n
g t
h
e T
E
P
pr
ob
l
em
i
s
pres
en
ted
i
n
[15
].
O
ne
of
the
po
w
erf
ul
m
eta
-
he
uris
t
i
c
al
g
orit
hm
s
tha
t
ha
v
e
be
en
ut
i
l
i
z
ed
t
o
s
ol
v
e
th
e
T
E
P
probl
em
i
s
th
e D
i
f
f
erenti
al
E
v
ol
u
ti
o
n
A
l
go
r
i
t
hm
(
DE
A
)
.
T
he
DE
A
ha
s
be
e
n s
uc
c
es
s
f
ul
l
y
em
pl
o
y
e
d
to
s
ol
v
e
th
e
T
E
P
probl
em
.
F
or
i
ns
ta
nc
e,
Lu
et
a
l
.
[
16
]
pres
en
t
ed
a
d
i
f
f
erenti
al
e
v
ol
ut
i
o
n
b
as
ed
m
eth
od
f
or
po
w
er
s
y
s
tem
pl
a
nn
i
ng
pro
bl
em
.
T
he
m
eth
od
h
ad
th
e
ab
i
l
i
t
y
to
h
an
dl
e
t
he
i
nte
ge
r
v
ari
ab
l
es
an
d
n
on
-
l
i
n
ea
r
c
on
s
tr
ai
ne
d
m
ul
ti
-
ob
j
ec
ti
v
e
op
ti
m
i
z
at
i
on
prob
l
em
.
Howe
v
er,
the
ap
pro
ac
h
w
as
n
ot
r
o
bu
s
t
e
no
ug
h
d
ue
t
o
s
e
v
era
l
s
i
m
pl
i
f
i
c
ati
on
s
,
s
uc
h
as
,
i
gn
or
i
n
g
the
s
ec
urit
y
c
on
s
tr
ai
nt
a
nd
i
n
ab
i
l
i
t
y
i
n
h
an
d
l
i
n
g
t
he
un
c
ert
ai
nti
es
i
n
the
d
eregu
l
at
ed
en
v
i
r
on
m
en
t.
T
.
S
um
-
I
m
et
a
l
[1
7]
em
pl
o
y
e
d
t
he
d
i
f
f
erenti
al
ev
ol
uti
on
a
l
g
orit
hm
(
DE
A
)
as
an
o
pti
m
i
z
i
ng
to
o
l
f
or
th
e
tr
an
s
m
i
s
s
i
on
ex
pa
ns
i
o
n
p
l
a
nn
i
ng
.
H
o
w
e
v
er,
i
t
was
ap
pl
i
ed
di
r
ec
tl
y
t
o
th
e
DC
po
wer
f
l
o
w
-
ba
s
ed
m
od
el
i
n
or
de
r
t
o
f
i
n
d
a
s
o
l
ut
i
on
f
or
s
tat
i
c
a
nd
m
ul
ti
s
tag
e
(
T
E
P
)
.
T
he
m
eth
od
y
i
el
d
ac
c
ep
t
ab
l
e
r
es
ul
ts
bu
t
b
y
no
t
us
i
ng
a
n
A
C
po
w
er
f
l
o
w
m
od
el
,
th
e
DE
A
i
s
on
l
y
go
o
d
f
or
es
ti
m
ati
on
bu
t
no
t
ac
c
urate,
s
i
nc
e
r
ea
c
t
i
v
e
p
o
w
er,
s
ec
urit
y
c
r
i
teri
a
an
d
the
un
c
erta
i
nt
i
es
i
n
po
wer
s
y
s
tem
are
ne
g
l
ec
ted
.
In
order
to
c
at
er
the
m
ul
ti
-
s
tag
e
T
E
P
prob
l
em
,
a
c
on
s
i
de
r
at
i
on
of
m
ul
ti
-
ti
m
e
pe
r
i
od
s
an
d
f
i
nd
i
n
g
po
s
s
i
bl
e
s
e
qu
e
nc
es
of
tr
an
s
m
i
s
s
i
on
r
ei
nf
o
r
c
e
m
en
ts
are
r
eq
u
i
r
ed
.
H
o
wev
er,
on
l
y
a
f
ew
h
av
e c
on
s
i
de
r
ed
th
e
m
ul
t
i
-
s
tag
e
na
t
ure of
th
e T
E
P
probl
em
[1
8
-
22].
T
he
us
e
of
the
(
c
om
pl
ete
)
A
C
m
od
el
f
or
the
m
ul
ti
s
tag
e
tr
an
s
m
i
s
s
i
on
ex
pa
ns
i
on
p
l
an
ni
n
g
i
n
t
he
f
i
r
s
t
p
ha
s
e
i
s
i
nc
i
p
i
e
nt
a
nd
t
he
r
e
i
s
pr
ac
ti
c
al
l
y
n
o
tec
h
ni
c
a
l
l
i
t
erature
ab
ou
t
i
t.
In
c
o
ntras
t,
on
l
y
f
e
w
s
tu
di
es
ha
v
e
be
e
n
c
on
d
uc
ted
us
i
n
g
th
e
A
C
po
w
er
f
l
o
w
m
od
el
to
s
ol
v
e
the
s
ho
r
t
term
tr
an
s
m
i
s
s
i
on
ex
pa
ns
i
on
p
l
a
nn
i
ng
.
F
or
i
ns
tan
c
e
,
r
ef
ere
nc
e
[2
3]
us
ed
an
i
nte
r
i
or
p
oi
nt
m
eth
od
t
o
s
ol
v
e
th
e
no
n
l
i
ne
ar
progr
am
m
i
ng
probl
em
s
du
r
i
n
g
the
s
o
l
ut
i
on
s
tep
s
of
the
A
C
Lo
a
d
f
l
o
w
al
g
orit
hm
.
A
n
oth
er
w
ork
i
n
[24
]
s
o
l
v
ed
th
e
T
E
P
prob
l
e
m
b
y
us
i
ng
a
di
f
f
erent
m
eth
od
;
i
t
s
tarted
wi
th
th
e s
o
l
ut
i
o
n o
f
t
he
DC
m
od
el
an
d t
he
n
r
e
i
nf
orc
i
ng
the
ex
pa
nd
e
d t
r
a
ns
m
i
s
s
i
o
n
ne
t
w
ork
us
i
n
g
ne
w
tr
a
ns
m
i
s
s
i
on
l
i
n
es
,
as
wel
l
as
r
ea
c
t
i
v
e
p
o
w
er
s
o
urc
es
.
G
en
era
l
l
y
,
pr
om
i
s
i
ng
r
es
ul
ts
h
av
e
be
en
ob
ta
i
n
ed
f
r
om
the
s
e wo
r
k
s
,
w
hi
c
h
en
c
o
urages
t
he
pl
an
n
ers
to
c
on
s
i
d
er
the
A
C
l
o
ad
f
l
o
w
i
n
s
ol
v
i
ng
t
he
m
ul
ti
s
t
ag
e
T
E
P
probl
em
. T
he
s
c
op
e o
f
t
hi
s
wor
k
ta
k
es
i
nto
ac
c
ou
nt
on
l
y
t
he
p
l
an
ni
n
g
s
tag
e.
A
l
l
t
he
g
en
era
ti
o
n
un
i
ts
are
as
s
um
ed
to
be
m
et
l
oc
al
l
y
.
T
he
op
erati
on
c
os
t
an
d
the
op
erat
i
o
n c
on
s
tr
a
i
nts
ar
e n
ot
i
nc
l
u
de
d
i
n
th
i
s
w
ork
. T
hi
s
w
ork
c
al
c
ul
ate
s
o
nl
y
t
he
c
os
t o
f
th
e
l
i
ne
s
to
be
i
ntr
od
uc
e
d
to
th
e
n
et
w
ork
.
T
he
m
aj
or
c
on
tr
i
bu
ti
o
ns
of
thi
s
p
ap
er
are
e
nu
m
erated
as
f
ol
l
o
w
s
:
a.
Us
i
ng
t
he
c
om
pl
ete
A
C
l
oa
d
f
l
o
w
m
od
el
i
n
s
ol
v
i
n
g
the
m
ul
ti
s
t
ag
e
T
E
P
pro
bl
em
,
wi
th
c
on
s
i
de
r
a
ti
o
n o
f
th
e
r
ea
c
ti
v
e p
o
wer
r
eq
u
i
r
em
en
t o
f
th
e
s
y
s
t
em
.
b.
Int
r
od
uc
i
ng
the
prop
os
ed
A
C m
od
el
an
d s
ho
wi
ng
th
e
p
erf
or
m
an
c
e o
f
DE
A
.
c.
P
r
op
os
i
ng
a
c
om
pl
ete
m
ul
ti
s
tag
e
p
l
an
ni
ng
f
r
am
ew
ork
w
hi
c
h
i
nc
l
u
de
s
th
e
o
pti
m
i
z
at
i
on
an
d
c
on
s
i
de
r
i
ng
the
v
i
ol
ati
on
c
h
ec
k
i
ng
f
or the
s
y
s
tem
al
on
g
th
e
pl
a
nn
i
ng
ho
r
i
z
o
n.
2.
M
u
lt
istag
e T
r
ansmissio
n
E
xpan
sion
P
l
ann
ing
F
o
r
mu
latio
n
T
he
c
o
m
pl
ete
A
C
po
wer
f
l
o
w
m
od
el
c
an
b
e
ap
pl
i
ed
t
o
s
ol
v
e
th
e
pro
bl
em
of
m
ul
ti
s
tag
e
tr
an
s
m
i
s
s
i
on
ex
pa
ns
i
on
p
l
a
nn
i
ng
.
T
he
i
nv
es
tm
en
t
c
os
t
of
the
p
l
an
i
s
c
on
s
i
de
r
e
d
a
s
an
ob
j
ec
t
i
v
e
f
un
c
ti
on
,
where
c
(
x
)
r
ep
r
es
en
ts
th
e
c
os
t
of
s
tag
e
t
.
T
he
tr
an
s
m
i
s
s
i
on
ex
p
an
s
i
on
i
nv
es
tm
en
t
p
l
an
i
s
ob
ta
i
n
ed
wi
th
a
r
ef
erenc
e
to
th
e
b
as
e
y
e
ar
b
ea
r
i
ng
i
n
m
i
nd
the
an
nu
a
l
r
ate
I
an
d
the
v
a
l
u
es
of
the
T
E
P
i
n
v
es
tm
en
t c
os
t i
n
the
b
as
e
y
ea
r
t
0
w
i
t
h a
ho
r
i
z
on
of
T
s
tag
es
are
as
f
ol
l
o
w
s
:
Evaluation Warning : The document was created with Spire.PDF for Python.
◼
IS
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N: 1
69
3
-
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E
L
KO
M
NIK
A
V
ol
.
16
,
No.
5,
O
c
tob
er 201
8
:
23
1
6
-
23
30
2318
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t
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c
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od
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l
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ul
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t
i
n
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i
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s
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ou
nt
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e
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i
nd
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e e
v
er
y
v
a
l
ue
of
a
n i
nv
es
tm
en
t a
t s
ta
ge
t
. T
he
ob
j
ec
t
i
v
e
f
un
c
ti
on
th
at
c
on
s
i
d
ers
the
ex
pa
ns
i
on
c
os
t
of
the
tr
an
s
m
i
s
s
i
on
ne
t
wor
k
i
s
ex
pres
s
ed
i
n
e
qu
ati
on
2
.
=
=
)
,
(
1
m
i
n
j
i
t
ij
t
ij
t
i
n
v
T
t
n
c
v
(
2)
W
h
ere
t
ij
c
r
ep
r
es
e
nts
t
he
c
i
r
c
ui
t
c
os
t
v
ec
tor
tha
t
c
a
n
be
ad
de
d
to
the
n
et
w
ork
an
d
t
ij
n
r
ep
r
es
en
ts
the
nu
m
be
r
of
t
he
ad
de
d
c
i
r
c
u
i
t’
s
v
ec
tor
f
or
s
tag
e
t
.
v
i
s
the
i
n
v
es
tm
en
t
c
os
t
of
the
ad
de
d l
i
n
es
f
or the
e
nti
r
e
pl
an
n
i
ng
ho
r
i
z
o
n.
0
)
,
,
(
=
+
−
D
G
P
P
n
V
P
(
3)
0
)
,
,
(
=
+
−
D
G
Q
Q
n
V
Q
(
4)
E
qu
ati
on
3
an
d
4
r
ep
r
es
e
nt
the
c
on
v
e
nti
on
a
l
eq
u
ati
on
s
of
A
C
po
wer
f
l
o
w
c
on
s
i
de
r
i
ng
n
,
the
n
um
be
r
of
c
i
r
c
ui
ts
(
l
i
n
es
an
d
tr
an
s
f
or
m
ers
)
,
as
v
aria
b
l
es
.
T
he
c
on
s
tr
a
i
nts
o
f
the
r
ea
l
an
d
r
ea
c
ti
v
e
po
wer
i
n
t
he
ge
n
erators
are
r
ep
r
es
en
ted
b
y
eq
ua
t
i
on
5
an
d
6
,
r
es
pe
c
ti
v
el
y
;
a
nd
7
r
ep
r
es
en
ts
th
e
v
ol
tag
e v
al
u
es
.
m
a
x
,
m
i
n
,
t
Gi
Gi
t
t
Gi
P
P
P
(
5)
m
a
x
,
m
i
n
,
t
Gi
Gi
t
t
Gi
Q
Q
Q
(
6)
m
a
x
,
m
in
,
t
t
t
Vi
i
V
Vi
(
7)
T
he
m
ax
i
m
u
m
an
d
m
i
ni
m
u
m
v
al
ue
s
of
the
c
on
s
tr
ai
nts
(
5,
6
an
d
7)
are
us
ua
l
l
y
c
on
s
i
de
r
e
d a
s
t
he
i
nt
ernat
i
on
a
l
s
tan
da
r
d
IE
C
60
0
38
s
t
ate
d,
10
5 a
nd
95
%
of
th
ei
r
no
m
i
na
l
v
a
l
ue
s
,
r
es
pe
c
ti
v
el
y
.
T
he
l
i
m
i
ts
of
the
a
pp
ar
en
t
po
wer
f
l
o
ws
f
or
ea
c
h
branc
h
are
r
e
pres
en
te
d
b
y
eq
ua
ti
o
n
8
an
d
9
.
m
a
x
0
0
)
(
)
(
S
N
N
S
N
N
to
+
+
(
8)
m
a
x
0
0
)
(
)
(
S
N
N
S
N
N
fr
o
m
+
+
(
9)
T
he
c
on
s
tr
ai
nt
of
the
c
a
pa
c
i
ti
es
of
th
e
a
dd
e
d
c
i
r
c
ui
ts
i
s
r
ep
r
es
en
t
ed
b
y
(
10
)
.
N
a
nd
N0
are
d
i
a
go
n
al
m
atri
c
es
c
on
tai
n
i
n
g
v
ec
tor
n
an
d
th
e
ex
i
s
ti
n
g
c
i
r
c
u
i
ts
i
n
t
he
ba
s
e
c
as
e
of
the
ne
t
w
ork
,
r
es
pe
c
ti
v
el
y
.
n
i
s
t
he
v
ec
tor
c
on
ta
i
n
i
n
g
the
m
ax
i
m
u
m
al
l
o
w
ab
l
e
n
um
be
r
of
c
i
r
c
ui
ts
tha
t
c
an
be
ad
d
ed
.
n
t
t
n
m
a
x
,
0
(
10
)
N
N
t
ij
t
ij
1
−
(
11
)
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KO
M
NIK
A
IS
S
N: 1
69
3
-
6
93
0
◼
AC
-
B
as
e
d D
i
ffe
r
e
nti
al
E
v
o
l
uti
o
n A
l
g
orit
h
m f
or Dy
na
m
i
c
Tr
an
s
mi
s
s
i
on
…
(
Ibra
hi
m
A
l
h
am
r
o
un
i
)
2319
n
N
N
ij
ij
+
=
0
ij
(
12
)
F
r
o
m
the
a
bo
v
e
eq
u
ati
on
s
on
e
c
a
n
n
oti
c
e
th
at,
t
he
po
s
s
i
bi
l
i
t
y
of
ex
c
l
u
di
n
g
a
n
y
r
i
gh
t
of
wa
y
i
s
no
t
i
nc
l
ud
e
d.
O
n
th
e
oth
er
ha
n
d,
th
e
nu
m
be
r
of
the
ne
w
l
i
ne
s
to
b
e
ad
d
ed
i
n
the
ne
w
s
tag
e
s
ho
ul
d
b
e
i
nc
l
u
de
d
i
n
pl
an
ni
n
g
th
e
n
ex
t
s
tag
e.
T
he
el
em
en
ts
of
v
ec
tors
P
(
V
,
u,
n)
an
d
Q
(
V
, u
, n
)
are c
a
l
c
ul
a
ted
b
y
eq
u
ati
on
1
3 a
nd
1
4
, res
p
e
c
ti
v
e
l
y
.
]
s
i
n
)
(
c
o
s
)
(
[
)
,
,
(
ij
ij
ij
ij
N
j
J
i
i
n
n
V
V
n
V
P
B
G
+
=
(
13
)
]
c
o
s
)
(
s
i
n
)
(
[
)
,
,
(
ij
ij
ij
ij
N
j
J
i
i
n
n
V
V
n
V
Q
B
G
−
=
(
14
)
W
h
ere
i
,
j
r
ep
r
es
en
t
b
us
es
an
d
N
i
s
the
s
et
of
al
l
b
us
e
s
,
ij
r
ep
r
es
en
ts
th
e
c
i
r
c
ui
t
b
et
w
ee
n
bu
s
es
i
and
j
. T
he
bu
s
ad
m
i
tta
nc
e
m
atri
x
el
em
en
ts
(
G
and
B
)
are:
+
=
+
−
=
=
i
j
ij
ij
ij
ij
ij
ij
ij
ij
ij
ij
g
n
g
n
G
g
n
g
n
G
n
n
G
)
(
)
(
)
(
)
(
0
0
0
0
(
15
)
+
+
+
+
=
+
−
=
=
)
)
(
(
)
(
[
)
(
)
(
)
(
0
0
0
0
0
b
b
n
b
b
b
B
b
n
b
n
B
sh
ij
ij
ij
sh
ij
ij
i
j
sh
i
ij
ij
ij
ij
ij
ij
n
ij
n
n
B
(
16
)
W
h
ere
Ωi
r
ep
r
es
en
ts
t
he
s
e
t
of
al
l
bu
s
es
d
i
r
ec
tl
y
c
o
nn
ec
ted
t
o
bu
s
i
;
g
i
j
,
b
i
j
and
b
sh
ij
are
the
c
on
d
uc
tan
c
e,
s
us
c
ep
ta
nc
e
an
d
s
hu
nt
s
us
c
ep
ta
nc
e
of
the
tr
an
s
m
i
s
s
i
on
l
i
n
e
or
tr
an
s
f
or
m
er
ij
(
i
f
i
j
i
s
a
tr
an
s
f
or
m
er
b
sh
ij
=
0
)
,
r
es
pe
c
ti
v
e
l
y
,
an
d
bs
hi
j
i
s
the
s
h
un
t
s
us
c
ep
tan
c
e
at
b
us
i
.
Note
th
at
i
n
(
15
)
an
d
(
16
)
,
the
p
os
s
i
bi
l
i
t
y
of
a
di
f
f
erent
tr
an
s
m
i
s
s
i
on
l
i
ne
or
tr
an
s
f
orm
er
to
be
ad
de
d
i
n
pa
r
al
l
e
l
wi
th
an
ex
i
s
ti
n
g
o
n
e
i
s
c
on
s
i
de
r
e
d,
a
l
th
ou
g
h
t
he
e
qu
i
v
a
l
e
nt
c
i
r
c
u
i
t
p
a
r
am
ete
r
s
m
a
y
b
e
di
f
f
erent [
25
].
)
s
i
n
cos
(
2
ij
ij
ij
ij
j
i
g
i
j
i
f
r
o
m
ij
b
g
V
V
V
p
+
−
=
(
17
)
)
s
i
n
cos
(
2
ij
ij
ij
ij
j
i
g
i
j
j
to
ij
b
g
V
V
V
p
+
−
=
(
18
)
T
he
r
ea
l
po
wer
ge
ne
r
at
i
o
n
l
i
m
i
ts
are
r
ep
r
es
en
ted
i
n
(
17
)
a
nd
(
1
8).
W
he
r
e
P
fro
m
and
P
to
are
the
r
ea
l
p
o
w
er f
l
o
w
s
v
ec
tors
(
MV
A
)
i
n t
he
br
an
c
he
s
a
nd
t
h
ei
r
l
i
m
i
ts
.
)
(
)
(
c
o
s
s
in
2
ij
ij
ij
ij
j
i
ij
sh
ij
i
f
r
o
m
ij
b
g
V
V
b
b
V
Q
−
−
+
−
=
(
19
)
c
o
s
s
in
(
)
(
2
ij
ij
ij
ij
j
i
ij
sh
ij
j
to
ij
b
g
V
V
b
b
V
Q
−
+
+
−
=
(
20
)
T
he
eq
u
ati
on
19
an
d
20
r
e
pres
en
t
the
l
i
m
i
ts
of
th
e
r
ea
c
ti
v
e
p
o
w
er f
l
o
w
s
.
W
he
r
e
Q
fro
m
a
nd
Q
to
are
the
r
ea
c
t
i
v
e p
o
w
er f
l
o
w
s
v
e
c
tors
i
n t
h
e b
r
a
nc
he
s
i
n b
o
t
h t
erm
i
na
l
s
an
d t
h
ei
r
l
i
m
i
ts
.
Evaluation Warning : The document was created with Spire.PDF for Python.
◼
IS
S
N: 1
69
3
-
6
93
0
T
E
L
KO
M
NIK
A
V
ol
.
16
,
No.
5,
O
c
tob
er 201
8
:
23
1
6
-
23
30
2320
2
2
)
)
(
(
Q
p
S
f
r
o
m
ij
f
r
o
m
ij
f
r
o
m
ij
+
=
(
21
)
2
2
)
)
(
(
Q
p
S
to
ij
to
ij
to
ij
+
=
(
22
)
T
he
l
i
m
i
ts
of
the
a
pp
ar
en
t
p
o
w
er
f
l
o
w
s
are
r
ep
r
es
e
nte
d
i
n
(
21
)
an
d
(
2
2). W
he
r
e
S
fr
om
an
d
S
to
are
the
a
pp
are
nt
po
wer
f
l
o
w
s
v
ec
tors
(
MV
A
)
i
n
the
branc
h
es
a
nd
th
ei
r
l
i
m
i
ts
.
T
he
E
l
em
en
ts
(
ij
)
of
the
v
ec
tors
of
the
P
o
wer
F
l
o
w
s
Li
m
i
t
Cons
tr
a
i
nt
i
n
t
he
br
an
c
he
s
whi
c
h
are
c
on
s
i
de
r
e
d
as
c
on
s
tr
ai
nts
i
n t
hi
s
f
orm
ul
ati
on
are
gi
v
e
n b
y
(
17
)
:
(
22
)
.
It
i
s
wor
th
m
en
ti
on
i
n
g
tha
t
,
the
m
ul
ti
s
tag
e
T
E
P
prob
l
e
m
ha
s
be
en
tr
ea
ted
d
i
f
f
erentl
y
i
n
thi
s
w
ork
c
o
m
pa
r
i
ng
to
th
e
prev
i
ou
s
w
ork
s
av
ai
l
a
bl
e
i
n
the
l
i
tera
tures
[18
-
22]
.
I
n
th
i
s
m
eth
od
,
the
ba
s
e
of
ev
er
y
s
tag
e
i
s
the
l
as
t
s
tag
e
to
po
l
og
y
an
d
the
ad
d
i
ti
on
a
l
l
i
ne
s
th
at
ha
s
b
e
en
c
on
s
i
d
ered
to
be
a
dd
e
d.
M
ore
ac
c
urat
e
an
d
c
om
prehen
s
i
v
e
pl
an
s
a
r
e
ob
ta
i
ne
d
us
i
ng
th
i
s
m
eth
o
d.
F
i
g
ure
1
i
l
l
us
tr
ate
s
an
d
s
h
o
w
s
h
o
w
thi
s
m
eth
od
i
s
no
r
m
al
l
y
d
o
ne
.
It
c
o
ns
i
d
ers
al
l
the
s
ta
ge
s
a
dd
i
ti
o
na
l
r
es
ul
ts
w
hi
c
h
af
f
ec
t
the
s
ol
uti
o
n
qu
al
i
t
y
un
l
i
k
e
the
ot
he
r
m
eth
od
s
tha
t
on
l
y
c
on
s
i
d
ers
the
orig
i
n
al
c
on
f
i
gu
r
at
i
on
as
th
e
m
ai
n b
as
e f
or al
l
the
s
t
ag
es
.
F
i
gu
r
e
1.
M
ul
t
i
s
ta
ge
T
E
P
b
as
ed
o
n d
i
f
f
erent b
as
e c
on
f
i
gu
r
at
i
o
n
T
he
t
y
pi
c
a
l
A
C
po
wer
f
l
o
w
f
or
m
ul
ati
on
c
a
n
be
f
ou
n
d
i
n
[2
0].
Dur
i
ng
the
f
orm
ul
ati
on
of
the
pr
ob
l
em
,
the
nu
m
be
r
of
c
i
r
c
ui
ts
ad
d
ed
i
n
branc
h
i
j
,
a
nd
P
G
(
th
e
r
es
i
z
i
ng
v
a
l
ue
of
the
ge
ne
r
ati
on
un
i
ts
)
are
c
on
s
i
de
r
e
d
as
the
m
os
t
i
m
po
r
t
an
t
de
c
i
s
i
o
n
v
ar
i
ab
l
es
.
T
he
r
ef
ore,
i
t
i
s
a
m
i
x
ed
i
nte
ge
r
n
on
l
i
ne
ar
pr
ob
l
em
,
w
h
ere
t
he
s
o
l
ut
i
o
n
i
nc
l
u
de
s
i
nt
eg
er
v
al
u
e
(
a
d
de
d
l
i
ne
s
)
an
d
c
on
ti
n
uo
us
v
a
l
ue
(
P
G
)
.
3.
Dif
f
er
ent
ial
E
v
o
lut
ion
A
lgo
r
it
h
m
Di
f
f
erenti
al
ev
ol
u
ti
on
i
s
a
p
o
w
erf
ul
E
A
a
l
g
orit
hm
f
or
gl
ob
a
l
op
t
i
m
i
z
at
i
on
ov
er
c
on
t
i
nu
ou
s
s
pa
c
e.
R
ec
en
t
l
y
,
t
he
DE
h
as
be
c
om
e
on
e
of
the
m
os
t
w
i
d
el
y
us
ed
e
v
o
l
ut
i
on
ar
y
al
go
r
i
thm
s
f
o
r
s
ol
v
i
ng
th
e
op
t
i
m
i
z
at
i
on
i
s
s
ue
s
[2
6
, 27
].
Di
f
f
erenti
al
ev
ol
u
ti
o
n
al
go
r
i
thm
i
s
a
pa
r
al
l
e
l
di
r
ec
t
s
e
arc
h
m
eth
od
,
w
h
i
c
h
em
pl
o
y
s
a
po
pu
l
at
i
o
n
P
of
s
i
z
e
NP
,
c
on
s
i
s
ti
ng
of
f
l
oa
ti
ng
p
oi
n
t
e
nc
od
ed
i
n
di
v
i
du
a
l
s
or
c
an
d
i
da
te
s
o
l
ut
i
on
s
.
It
s
tarts
b
y
i
ni
t
i
a
l
i
z
i
ng
th
e
p
op
u
l
at
i
on
of
th
e
c
a
nd
i
da
t
e
s
ol
ut
i
on
s
.
A
r
an
do
m
l
y
c
ho
s
en
v
a
l
ue
f
r
om
wi
th
i
n
th
ei
r
c
orr
es
p
on
d
i
n
g
f
ea
s
i
b
l
e
bo
un
ds
i
s
as
s
i
g
ne
d
f
or
al
l
the
d
ec
i
s
i
o
n
pa
r
am
ete
r
s
,
i
n
e
v
er
y
v
ec
tor
of
the
i
ni
t
i
a
l
po
p
ul
ati
o
n.
T
he
n
,
t
he
m
uta
ti
on
op
erator
ge
ne
r
at
es
m
uta
nt
v
ec
tors
b
y
pe
r
turb
i
ng
a
r
an
do
m
l
y
s
e
l
ec
ted
v
ec
tor
wi
th
th
e
di
f
f
erenc
e
of
t
w
o
ot
he
r
r
an
d
om
l
y
s
el
ec
t
ed
ve
c
tors
.
A
f
ter
w
ards
,
the
c
r
o
s
s
ov
er
proc
es
s
i
s
e
m
pl
o
y
e
d
to
he
l
p
i
nc
r
ea
s
e
t
he
d
i
v
ers
i
t
y
am
on
g
the
m
uta
nt
pa
r
am
ete
r
v
ec
tors
.
T
he
r
an
do
m
l
y
ge
n
erate
d
p
aram
ete
r
s
i
n
m
uta
ti
o
n
w
i
l
l
be
r
ep
l
ac
ed
b
y
c
ertai
n
p
aram
ete
r
s
of
the
i
nd
i
v
i
du
a
l
targ
et
v
ec
tor
to
g
en
erat
e
a
tr
i
a
l
v
ec
tor.
E
v
e
n
tua
l
l
y
,
s
el
ec
t
i
on
proc
es
s
c
o
m
pa
r
es
the
c
orr
es
po
nd
i
n
g
targ
et
v
ec
tor
an
d
the
f
i
tne
s
s
of
the
tr
i
a
l
v
e
c
tor,
an
d
the
n
c
ho
os
es
th
e
be
t
ter o
ne
s
w
h
i
c
h p
r
o
v
i
de
t
he
be
s
t s
ol
uti
o
n.
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KO
M
NIK
A
IS
S
N: 1
69
3
-
6
93
0
◼
AC
-
B
as
e
d D
i
ffe
r
e
nti
al
E
v
o
l
uti
o
n A
l
g
orit
h
m f
or Dy
na
m
i
c
Tr
an
s
mi
s
s
i
on
…
(
Ibra
hi
m
A
l
h
am
r
o
un
i
)
2321
Di
f
f
erenti
al
e
v
ol
ut
i
on
al
go
r
i
thm
ha
s
m
an
y
s
tr
at
eg
i
es
tha
t
c
an
be
em
pl
o
y
e
d
f
or
the
op
ti
m
i
z
at
i
o
n
pu
r
po
s
e.
T
he
r
e
are
f
i
v
e
v
ar
i
at
i
on
s
,
as
or
i
gi
na
l
l
y
prop
os
ed
b
y
S
torn
i
n
[
26
],
w
h
i
c
h
are c
om
m
on
l
y
us
ed
to
s
o
l
v
e t
he
T
E
P
pro
bl
em
.
4.
A
p
p
lic
atio
n
o
f
DE
A
in
M
u
lt
istag
e
T
r
ansmissi
o
n
E
xpan
sion
P
lanin
g
B
as
ed
o
n
A
C
L
o
ad F
low
4
.1.
P
r
o
b
l
em
O
p
t
imiz
atio
n
and
Co
n
t
r
o
l P
ar
amet
e
r
s
S
ett
ing
A
n
i
m
po
r
tan
t
f
ac
tor
tha
t
s
tr
on
g
l
y
af
f
ec
ts
the
c
on
v
erg
en
c
e
an
d
the
q
ua
l
i
t
y
of
the
s
ol
uti
o
ns
of
DE
A
i
s
c
ho
os
i
n
g
th
e
c
o
ntrol
pa
r
am
ete
r
s
v
a
l
ue
s
.
S
t
orn
an
d
P
r
i
c
e
[
26
]
ha
d
d
es
c
r
i
be
d
ho
w
to
c
ho
os
e
s
ui
t
ab
l
e
c
on
tr
o
l
p
a
r
am
ete
r
s
o
f
Np,
F
an
d
C
R.
T
o
m
en
ti
on
s
om
e,
f
or
Np,
i
t
m
us
t
be
be
t
w
e
en
5*
D
an
d
1
0*
D
bu
t
i
t
m
us
t
no
t
be
l
es
s
tha
n
4
*
D
to
m
a
k
e
s
ure
tha
t
DE
A
wi
l
l
ha
v
e
t
he
en
ou
gh
m
utu
al
l
y
d
i
f
f
erent
v
ec
tors
.
T
he
y
a
l
s
o
r
ec
om
m
e
nd
ed
t
ha
t
F
=
0.5
a
nd
CR
to
be
1
or
0.9
to
get
f
as
ter
c
on
v
erg
en
c
e.
T
he
D
E
A
proc
ed
ure
f
or
op
t
i
m
i
z
i
ng
the
T
E
P
pr
ob
l
em
i
s
i
l
l
us
tr
ate
d
i
n
F
i
gu
r
e
2.
F
i
gu
r
e
2.
Im
pl
em
en
tat
i
o
n
f
l
o
w
d
i
ag
r
am
Evaluation Warning : The document was created with Spire.PDF for Python.
◼
IS
S
N: 1
69
3
-
6
93
0
T
E
L
KO
M
NIK
A
V
ol
.
16
,
No.
5,
O
c
tob
er 201
8
:
23
1
6
-
23
30
2322
T
he
propos
ed
D
E
A
proc
ed
ure
to
s
ol
v
e
the
m
ul
ti
s
tag
e
T
E
P
prob
l
em
s
tarts
wi
th
c
h
ec
k
i
ng
the
d
ata
of
m
i
ni
m
u
m
an
d
m
ax
i
m
u
m
s
i
z
es
of
the
n
et
w
ork
,
s
uc
h
as
po
w
er
g
en
erat
i
o
n,
l
oa
d
de
m
an
d
an
d
t
he
tr
a
ns
m
i
s
s
i
on
l
i
ne
s
.
A
h
ori
z
on
of
ti
m
e
s
tag
e
p
l
an
ni
ng
(
T
)
an
d
an
an
nu
al
i
nt
eres
t
r
ate
v
al
ue
(
I)
.
T
he
l
o
wer
an
d
u
pp
er
bo
u
nd
s
of
the
i
ni
ti
a
l
p
op
u
l
at
i
o
n
(
x
j
m
i
n
an
d
x
j
m
ax
)
are
de
f
i
ne
d
.
DE
A
i
s
v
er
y
s
en
s
i
ti
v
e
r
eg
ar
di
n
g
the
c
on
tr
ol
pa
r
am
ete
r
s
,
a
go
o
d
c
ho
i
c
e
f
or
the
m
;
gu
ara
nte
e
a
f
as
ter
c
on
v
er
ge
nc
e
an
d
g
oo
d
r
es
ul
ts
.
T
he
a
l
g
orit
hm
c
on
ti
nu
es
b
y
i
n
i
ti
al
i
z
i
n
g
t
he
po
pu
l
at
i
o
n
of
i
n
di
v
i
du
a
l
s
an
d
ev
al
ua
t
i
ng
the
f
i
tn
es
s
f
un
c
ti
on
,
f
ol
l
o
wed
b
y
c
he
c
k
i
ng
the
c
on
s
tr
ai
nts
.
N
ex
t
i
s
the
op
ti
m
i
z
ati
on
s
tep
,
w
he
r
e
G
=
1
an
d
ap
p
l
y
i
n
g
m
uta
ti
on
,
c
r
os
s
ov
er
an
d
s
el
ec
ti
on
t
o
ge
ne
r
at
e
th
e
ne
w
i
nd
i
v
i
d
ua
l
s
.
T
he
n,
t
he
f
i
tne
s
s
f
un
c
ti
o
n
i
s
e
v
a
l
ua
te
d
an
d
th
e
al
g
orit
hm
c
he
c
k
s
i
f
the
r
e
i
s
an
y
v
i
ol
ati
on
of
the
A
C
l
oa
d
f
l
ow
c
on
s
tr
a
i
nts
.
I
n
c
as
e
of
an
y
v
i
ol
ati
on
r
eg
i
s
tere
d,
t
he
o
bta
i
n
ed
s
o
l
uti
o
n
i
s
c
o
ns
i
d
ered
i
nf
ea
s
i
b
l
e
a
nd
the
s
el
ec
t
ed
v
a
l
ue
s
of
the
c
on
tr
o
l
pa
r
am
ete
r
s
s
ho
ul
d
b
e
c
ha
ng
e
d.
T
he
proc
ed
ur
e
s
top
s
when
the
pr
ed
ef
i
n
ed
c
on
v
erg
en
c
e
c
r
i
teri
on
i
s
ob
t
ai
ne
d
or
t
he
m
a
x
i
m
u
m
nu
m
be
r
of
ge
ne
r
ati
o
n
i
s
r
ea
c
h
ed
.
O
the
r
wi
s
e
,
the
a
l
go
r
i
th
m
r
ep
ea
ts
t
he
o
pti
m
i
z
at
i
o
n
pr
oc
es
s
an
d
wi
l
l
c
on
t
i
nu
e
s
e
arc
hi
ng
.
T
he
op
t
i
m
i
z
a
ti
o
n
s
tep
f
or
f
i
nd
i
n
g
t
he
be
s
t
s
ol
u
ti
o
n
i
s
r
e
pe
a
te
d
u
nti
l
the
m
ax
i
m
u
m
nu
m
b
er
of
g
en
erat
i
o
ns
(
G
m
ax
)
i
s
r
ea
c
he
d
.
T
he
propos
e
d
tec
hn
i
q
ue
c
an
b
e
i
m
pl
em
en
ted
w
i
t
h
v
ario
u
s
s
y
s
tem
s
.
It
c
an
be
f
urthe
r
i
m
pl
e
m
en
ted
f
or a prac
ti
c
al
s
y
s
tem
s
i
nc
e i
t d
ea
l
s
w
i
t
h a
l
l
t
he
as
pe
c
ts
of
th
e rea
l
w
or
l
d
ne
t
wor
k
s
.
4
.2.
Fit
n
e
ss
Fu
n
ctio
n
C
al
culat
ion
A
f
ter
ge
ne
r
ati
ng
t
he
i
ni
t
i
a
l
po
pu
l
at
i
o
n,
e
ac
h
i
nd
i
v
i
du
al
wi
l
l
c
on
t
ai
n
i
n
teg
er
v
al
u
ed
Ni
j
an
d
c
on
ti
n
uo
us
v
a
l
u
ed
P
G
.
A
n
A
C
l
oa
d f
l
o
w
c
a
l
c
u
l
at
i
on
s
i
s
pe
r
f
or
m
ed
f
or ev
er
y
i
nd
i
v
i
d
ua
l
.
G
en
eral
l
y
,
the
f
i
tn
es
s
f
un
c
ti
o
n
i
s
em
pl
o
y
e
d
f
or
f
i
nd
i
ng
th
e
be
s
t
s
ol
ut
i
o
n
t
ha
t
s
ati
s
f
i
es
a
l
l
th
e
c
on
s
tr
ai
nts
b
y
c
he
c
k
i
ng
f
or
v
i
ol
a
ti
o
ns
.
In
order
to
r
ep
r
es
e
nt
th
e
v
i
ol
ati
on
s
of
the
e
qu
a
l
i
t
y
a
nd
i
ne
q
ua
l
i
t
y
c
on
s
tr
ai
nts
,
pe
n
al
t
y
f
un
c
ti
o
ns
are ap
pl
i
e
d i
n t
h
e f
i
tne
s
s
f
un
c
ti
on
as
f
ol
l
o
w
s
:
P
W
P
W
OF
FF
s
t
a
g
e
s
t
a
g
e
PF
2
2
1
1
*
*
+
+
=
(
2
3)
W
h
ere
F
F
an
d
O
F
are
th
e
f
i
tne
s
s
f
un
c
ti
on
an
d
ob
j
ec
t
i
v
e
f
un
c
ti
on
of
th
e
T
E
P
pr
ob
l
em
,
r
es
pe
c
ti
v
el
y
,
a
nd
P
1
a
nd
P
2
are
t
he
e
qu
a
l
i
t
y
a
nd
i
ne
q
ua
l
i
t
y
c
on
s
tr
a
i
nt
pe
n
al
t
y
f
un
c
ti
o
ns
,
r
es
pe
c
ti
v
el
y
.
P
F
i
s
the
P
en
al
t
y
F
ac
tor
f
or
the
v
i
o
l
at
i
o
n
of
a
c
on
s
tr
ai
nt
whi
c
h
i
s
s
et
to
10
0
00
i
n
thi
s
wor
k
.
W
1
an
d
W
2
are
pe
n
al
t
y
we
i
gh
t
i
n
g
f
ac
tors
,
whi
c
h
are
s
et
t
o
1.
0
i
n
th
i
s
w
ork
.
T
he
m
od
i
f
i
c
ati
on
s
of
the
N
e
w
ton
R
ap
hs
on
A
C
po
wer
f
l
ow
m
od
el
to
s
o
l
v
e
th
e
m
ul
ti
s
tag
e
T
E
P
probl
em
an
d c
he
c
k
th
e c
on
s
tr
ai
nts
v
i
o
l
at
i
o
ns
are as
f
ol
l
o
w
s
:
=
=
)
,
(
1
m
i
n
j
i
t
ij
t
ij
t
i
n
v
T
t
n
c
v
(
24
)
+
+
+
+
+
=
V
V
V
V
V
V
P
n
n
S
t
o
S
t
o
S
f
r
o
m
S
f
r
o
m
QG
QG
PG
PG
V
V
2
(
25
)
0
1
=
P
(
26
)
where
:
−
−
=
M
i
n
Gi
Gi
M
i
n
Gi
Gi
M
a
x
Gi
Gi
M
a
x
Gi
Gi
M
a
x
Gi
Gi
M
i
n
Gi
QG
Q
Q
if
Q
Q
Q
Q
if
Q
Q
Q
Q
Q
if
V
0
(
27
)
−
−
=
V
V
V
V
V
M
i
n
M
i
n
M
a
x
M
a
x
M
a
x
M
i
n
V
V
if
V
V
if
V
Vi
Vi
Vi
if
0
(
28
)
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KO
M
NIK
A
IS
S
N: 1
69
3
-
6
93
0
◼
AC
-
B
as
e
d D
i
ffe
r
e
nti
al
E
v
o
l
uti
o
n A
l
g
orit
h
m f
or Dy
na
m
i
c
Tr
an
s
mi
s
s
i
on
…
(
Ibra
hi
m
A
l
h
am
r
o
un
i
)
2323
−
−
=
M
i
n
Gi
Gi
M
i
n
Gi
Gi
M
a
x
Gi
Gi
M
a
x
Gi
Gi
M
a
x
Gi
Gi
M
i
n
Gi
PG
P
P
if
P
P
P
P
if
P
P
P
P
P
if
V
0
(
29
−
−
=
0
0
0
0
n
if
n
n
if
n
n
if
n
n
n
V
M
a
x
M
a
x
M
a
x
n
(
30
)
+
+
+
−
+
+
+
=
m
a
x
0
0
m
a
x
0
0
m
a
x
0
0
)
(
)
(
)
(
)
(
)
(
)
(
0
S
N
N
S
N
N
if
S
N
N
S
N
N
S
N
N
S
N
N
if
fr
o
m
fr
o
m
fr
o
m
S
fr
o
m
V
(
31
)
+
+
+
−
+
+
+
=
m
a
x
0
0
m
a
x
0
0
m
a
x
0
0
)
(
)
(
)
(
)
(
)
(
)
(
0
S
N
N
S
N
N
if
S
N
N
S
t
o
N
N
S
N
N
S
N
N
if
to
to
S
to
V
(
32
)
T
he
v
a
l
ue
of
P
2
ex
pres
s
e
s
the
s
um
m
ati
on
of
th
e
v
i
ol
at
i
o
n
i
n
e
v
er
y
c
on
s
tr
a
i
nt.
T
he
c
on
s
tan
t
h
as
t
he
s
am
e
v
a
l
ue
of
F (
m
uta
ti
on
f
ac
tor)
.
A
no
th
er a
dv
an
ta
ge
of
us
i
ng
t
he
di
f
f
erenti
a
l
ev
o
l
ut
i
o
n
a
l
go
r
i
thm
i
s
tha
t,
i
t
c
an
ev
en
s
t
art
w
i
t
h
i
m
po
s
s
i
bl
e
s
o
l
ut
i
o
n.
In
order
t
o
f
i
nd
the
f
i
t
ne
s
s
f
un
c
ti
on
f
or the
al
l
s
ta
ge
s
, a
s
i
m
pl
e d
eri
v
at
i
on
s
ho
u
l
d
b
e m
ad
e a
s
f
ol
l
o
wi
n
g:
OF
FF
V
io
s
t
a
g
e
s
t
a
g
e
s
t
a
g
e
PF
−
=
(
33
)
Vi
o
Vi
o
Vi
o
s
ta
g
e
T
s
ta
g
e
T
t
s
ta
g
e
v
i
o
l
a
t
i
o
n
+
+
=
=
2
1
1
(
34
)
T
o
en
s
ure
tha
t
t
he
ob
t
ai
ne
d
s
o
l
ut
i
on
i
s
f
ea
s
i
b
l
e,
th
e
t
ota
l
v
i
ol
a
ti
o
n
i
n
th
i
s
eq
u
ati
o
n
m
us
t
eq
ua
l
t
o 0
. O
t
he
r
wi
s
e t
h
e p
aram
ete
r
s
s
ho
ul
d b
e c
ha
ng
ed
to
f
i
nd
t
he
o
pti
m
al
s
ol
uti
on
.
=
−
=
T
t
T
s
ta
g
e
to
t
a
l
OF
OF
t
i
n
v
1
1
.
(
35
)
V
io
OF
FF
t
o
t
a
l
t
o
t
a
l
t
o
t
a
l
PF
+
=
(
36
)
T
he
v
i
ol
at
i
on
of
ev
er
y
s
ta
g
e
an
d
t
he
tot
al
v
i
ol
a
ti
on
c
a
n
be
ob
tai
ne
d
b
y
(
3
3)
an
d
(
34
)
,
r
es
pe
c
ti
v
el
y
.
E
q
ua
t
i
on
35
e
x
pres
s
es
the
tot
al
v
al
u
e
of
the
o
bj
ec
ti
v
e
f
un
c
ti
on
of
th
e
thre
e
s
tag
es
an
d
th
e
tot
al
f
i
tne
s
s
f
u
nc
ti
o
n
i
s
ob
ta
i
n
ed
b
y
eq
ua
t
i
on
3
6
.
Note
t
ha
t,
i
f
the
r
e
i
s
no
v
i
ol
ati
on
at
t
he
pl
a
nn
i
ng
s
tag
e
the
r
e
wi
l
l
b
e
no
ne
e
d
to
pe
r
f
orm
the
T
E
P
proc
es
s
s
i
nc
e
al
l
the
c
on
s
tr
ai
nts
are
s
ati
s
f
i
ed
a
nd
s
y
s
t
em
i
s
w
or
k
i
ng
ad
eq
ua
t
el
y
.
5.
T
es
t
s a
n
d
Re
sult
s
T
he
pl
an
c
on
s
i
s
ts
of
three
pl
an
ni
ng
s
tag
es
P
1,
P
2
a
nd
P
3
.
T
he
P
1
s
tag
e
i
s
th
e
f
i
r
s
t
s
tag
e
w
h
i
c
h
i
s
the
pe
r
i
od
f
r
om
20
17
un
t
i
l
2
02
0
an
d
2
0
17
i
s
the
ba
s
e
y
e
ar
f
or
thi
s
s
tag
e.
T
he
P
2
s
tag
e
i
s
t
he
pe
r
i
od
f
r
om
20
20
un
t
i
l
20
24
an
d
2
02
0
i
s
t
he
ba
s
e
y
e
ar f
or th
e s
ec
on
d s
tag
e.
T
he
P
3
s
tag
e
i
s
t
he
pe
r
i
od
f
r
o
m
20
24
un
t
i
l
2
02
7
a
nd
20
24
i
s
the
b
as
e
y
e
ar
f
or
the
th
i
r
d
s
tag
e
.
I
n
t
hi
s
pa
pe
r
,
th
e
to
tal
tr
an
s
m
i
s
s
i
on
ex
pa
ns
i
o
n
i
n
v
es
tm
en
t
pl
an
i
s
ob
t
ai
ne
d
w
i
th
r
ef
eren
c
e
to
t
he
ba
s
e
y
e
ar
2
01
4
an
d
the
an
n
ua
l
i
nte
r
es
t
r
ate
v
a
l
u
e
I=
10
%.
T
he
m
ax
i
m
u
m
nu
m
be
r
of
l
i
ne
s
al
l
o
wed
to
be
a
dd
e
d
i
n
p
aral
l
e
l
w
i
th
t
h
e
ex
i
s
ti
ng
l
i
ne
s
i
n
th
i
s
s
tud
y
i
s
f
ou
r
l
i
n
es
i
n
ea
c
h
bran
c
h.
Note
tha
t,
i
f
the
r
e
i
s
no
v
i
o
l
at
i
o
n
at
th
e
i
ni
ti
a
l
p
l
an
ni
n
g
s
tag
e
t
h
ere
wi
l
l
be
n
o
ne
e
d
to
pe
r
f
or
m
the
T
E
P
proc
es
s
s
i
nc
e
al
l
th
e
c
on
s
tr
ai
nts
ar
e
s
ati
s
f
i
ed
an
d
the
s
y
s
t
em
i
s
w
ork
i
ng
ad
e
qu
a
t
el
y
.
O
th
erw
i
s
e,
the
m
eth
od
a
tte
m
pts
to
ob
t
ai
n
the
f
ea
s
i
bl
e a
n
d t
h
en
th
e o
pt
i
m
u
m
s
ol
uti
on
.
Evaluation Warning : The document was created with Spire.PDF for Python.
◼
IS
S
N: 1
69
3
-
6
93
0
T
E
L
KO
M
NIK
A
V
ol
.
16
,
No.
5,
O
c
tob
er 201
8
:
23
1
6
-
23
30
2324
5.1
.
I
E
E
E
24
-
Bu
s
S
ys
t
em
T
he
IE
E
E
2
4
b
us
s
y
s
tem
i
s
us
ed
i
n
t
hi
s
wor
k
to
tes
t
t
he
pro
po
s
ed
m
eth
od
o
l
og
y
f
or
the
m
ul
ti
s
tag
e
T
E
P
prob
l
em
.
T
he
s
y
s
tem
ha
s
33
ge
ne
r
at
o
r
s
c
on
ne
c
ted
at
10
bu
s
s
es
an
d
21
l
oa
ds
.
T
he
l
i
n
e
i
n
v
es
tm
en
t
c
os
t
an
d
the
s
y
s
tem
de
ta
i
l
s
c
a
n
be
f
ou
nd
i
n
[
20
].
T
h
e
to
tal
l
o
ad
of
thi
s
s
y
s
t
em
i
s
28
50
M
W
.
T
he
propos
ed
m
eth
od
h
as
s
ho
w
n
i
ts
ab
i
l
i
t
y
i
n
o
bta
i
ni
ng
g
oo
d
r
es
ul
ts
an
d
h
i
g
h
qu
a
l
i
t
y
s
ol
ut
i
on
s
.
A
l
l
D
E
A
m
od
es
ob
ta
i
ne
d
c
om
pe
ti
ti
v
e
a
nd
p
r
om
i
s
i
ng
r
es
ul
ts
;
DE
A
m
od
e
3
ha
s
f
ou
nd
the
b
es
t
to
po
l
og
y
f
or
the
e
x
pa
ns
i
o
n
p
l
an
w
i
t
h
t
he
l
ea
s
t
i
n
v
es
tm
en
t
c
os
t.
In
ad
di
t
i
on
,
F
i
gu
r
es
(
3)
an
d
(
4)
s
ho
w
the
be
s
t
ob
t
a
i
ne
d
o
bj
ec
ti
v
e
f
un
c
ti
on
an
d
f
i
tne
s
s
f
un
c
ti
on
b
as
ed
on
DE
A
m
od
e
3.
F
urtherm
ore,
the
r
e
i
s
no
v
i
ol
at
i
o
n
r
eg
i
s
t
ered
a
nd
a
l
l
th
e
c
on
s
tr
ai
n
ts
are
s
ati
s
f
i
ed
.
T
ab
l
e
1
s
ho
w
s
the
a
dd
i
ti
on
a
l
l
i
n
es
to
be
a
dd
ed
to
t
he
s
y
s
t
em
a
l
on
g
t
he
p
l
an
ni
ng
h
ori
z
on
an
d
th
e
r
el
a
ted
i
n
i
t
i
al
c
os
t o
f
th
e e
x
pa
ns
i
o
n b
ef
or
e c
on
s
i
d
erin
g t
h
e d
i
s
c
ou
nt
f
ac
tors
du
e t
o t
h
e i
ns
ta
l
l
a
ti
o
n d
e
l
a
y
.
T
ab
l
e 1
.
T
he
E
x
pa
ns
i
on
In
v
es
tm
en
t Cos
t Cal
c
u
l
at
i
on
of
IE
E
E
24
-
bu
s
T
es
t S
y
s
tem
P
lan
n
ing
s
t
a
g
e
A
d
d
it
ion
a
l
li
n
e
s
I
n
v
e
s
t
men
t
C
o
s
t
,
(
M
U
S
$
)
S
t
a
g
e
P
1
n
1
-
2
=
1
,
n
6
-
10
=
1
,
n
17
-
18
=1
a
n
d
n
20
-
23
=
1
69
S
t
a
g
e
P
2
n
3
-
9
=
1
a
n
d
n
17
-
18
=
1
,
n
6
-
7
=
1
,
n
10
-
12
=
1
,
n
14
-
23
=1
a
n
d
n
4
-
9
=
1
264
S
t
a
g
e
P
3
n
1
-
2
=
1
,
n
9
-
12
=1
,
n
5
-
10
=
1
,
n
2
-
8
=
1
,
n
11
-
14
=
1
,
n
16
-
23
=
1
a
n
d
n
8
-
9
=
1
324
T
he
ad
d
i
ti
on
a
l
tr
a
ns
m
i
s
s
i
on
l
i
ne
s
de
t
erm
i
ne
d
b
y
t
h
e
pro
po
s
ed
DE
A
m
eth
od
us
i
n
g
m
od
e 3
are as
f
ol
l
o
w
s
:
S
tag
e
P
1
:
n1
-
2
=
1,
n6
-
10
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