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ale
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[
6
]
-
[
8
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.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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I
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Vo
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15
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No
.
2
,
J
u
n
e
20
26
:
535
-
545
536
T
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ex
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1
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d
m
u
ltit
ask
ass
ig
n
m
en
ts
[
3
]
,
[
1
9
]
.
T
h
is
m
eth
o
d
h
as
p
r
o
v
e
n
e
f
f
ec
tiv
e
in
o
v
er
co
m
in
g
th
e
li
m
itatio
n
s
o
f
tr
a
d
itio
n
al
o
p
ti
m
izatio
n
tech
n
i
q
u
es,
p
ar
ticu
lar
ly
in
a
d
d
r
ess
in
g
n
o
n
-
lin
ea
r
an
d
n
o
n
-
co
n
v
ex
ch
allen
g
es c
o
m
m
o
n
in
OPF p
r
o
b
lem
s
[
2
0
]
,
[
2
1
]
.
T
h
e
SO
m
eth
o
d
is
a
r
ec
en
tly
d
ev
elo
p
ed
ap
p
r
o
ac
h
f
o
r
ad
d
r
ess
in
g
th
e
OPF
p
r
o
b
lem
.
I
t
h
as
d
e
m
o
n
s
tr
ated
s
ig
n
if
ican
t
ef
f
ec
tiv
en
ess
in
o
p
tim
izin
g
v
ar
io
u
s
asp
ec
ts
o
f
p
o
wer
s
y
s
tem
s
.
Sp
ec
if
ically
,
th
e
m
eth
o
d
h
as
b
ee
n
s
h
o
wn
to
r
ed
u
ce
f
u
el
co
s
ts
,
m
in
im
ize
v
o
ltag
e
d
ev
i
atio
n
s
,
im
p
r
o
v
e
lin
e
s
tab
ilit
y
,
an
d
d
ec
r
ea
s
e
p
o
wer
lo
s
s
es
an
d
em
is
s
io
n
s
.
T
h
ese
r
esu
lt
s
wer
e
v
alid
ated
th
r
o
u
g
h
ap
p
licatio
n
o
n
th
e
s
tan
d
ar
d
3
0
-
b
u
s
test
s
y
s
tem
,
h
ig
h
lig
h
tin
g
its
p
o
ten
tial f
o
r
en
h
an
cin
g
th
e
ef
f
icien
cy
an
d
r
eliab
ilit
y
o
f
el
ec
tr
ical
g
r
id
s
[
1
]
.
Un
lik
e
m
an
y
p
r
ev
io
u
s
OPF
s
t
u
d
ies
th
at
f
o
cu
s
p
r
i
m
ar
ily
o
n
r
en
ewa
b
le
en
er
g
y
in
teg
r
atio
n
o
r
s
tan
d
ar
d
b
en
ch
m
ar
k
s
y
s
tem
s
,
th
is
s
tu
d
y
ex
p
licitly
in
v
esti
g
ates
th
e
in
teg
r
atio
n
o
f
g
as
en
g
in
e
p
o
w
er
p
lan
ts
with
in
a
p
r
ac
tical
p
o
wer
g
r
id
.
Gas
en
g
i
n
e
g
en
er
at
o
r
s
ar
e
c
h
ar
ac
ter
ize
d
b
y
f
ast
r
esp
o
n
s
e,
f
le
x
ib
le
d
is
p
atch
ca
p
ab
ilit
y
,
an
d
d
is
tin
ct
f
u
el
c
o
s
t
ch
ar
ac
ter
is
ti
cs,
wh
ich
d
ir
ec
tly
i
n
f
lu
en
ce
b
o
th
ec
o
n
o
m
ic
an
d
v
o
ltag
e
-
r
el
ated
p
er
f
o
r
m
a
n
ce
o
f
th
e
g
r
id
.
I
n
th
is
wo
r
k
,
g
as
e
n
g
i
n
e
p
o
wer
p
lan
ts
ar
e
ex
p
licitly
m
o
d
eled
i
n
th
e
OPF
f
r
a
m
ewo
r
k
u
s
in
g
c
u
s
to
m
ized
f
u
el
co
s
t
f
u
n
ctio
n
s
an
d
o
p
e
r
atio
n
al
co
n
s
tr
ain
ts
.
T
h
is
m
o
d
elin
g
ap
p
r
o
ac
h
e
n
ab
les
a
s
y
s
tem
atic
ev
alu
atio
n
o
f
th
eir
tech
n
o
-
ec
o
n
o
m
ic
im
p
ac
t
o
n
g
r
id
p
er
f
o
r
m
an
ce
.
A
tech
n
o
-
ec
o
n
o
m
ic
ass
ess
m
en
t
o
f
a
p
o
wer
g
r
id
,
f
o
llo
win
g
th
e
in
teg
r
atio
n
o
f
g
as
en
g
in
e
p
o
wer
p
lan
ts
,
is
p
er
f
o
r
m
ed
u
s
in
g
SO
to
s
o
lv
e
a
ca
s
e
-
b
ased
s
in
g
le
-
o
b
jectiv
e
OPF
p
r
o
b
lem
wh
ile
c
o
n
s
id
er
in
g
m
u
ltip
le
p
er
f
o
r
m
a
n
ce
c
r
iter
ia,
in
clu
d
i
n
g
f
u
el
co
s
t,
v
o
ltag
e
d
ev
iatio
n
,
v
o
ltag
e
s
tab
ilit
y
,
an
d
ac
tiv
e
p
o
wer
lo
s
s
m
in
im
izatio
n
.
T
h
e
m
ain
c
o
n
t
r
ib
u
tio
n
s
o
f
th
is
s
tu
d
y
a
r
e
th
r
e
ef
o
ld
:
i
)
m
o
d
elin
g
a
p
r
ac
tical
p
o
wer
g
r
id
with
g
as e
n
g
in
e
p
o
wer
p
lan
t
p
en
etr
atio
n
,
ii
)
d
esig
n
in
g
ap
p
r
o
p
r
iate
f
u
el
co
s
t
f
u
n
ctio
n
s
f
o
r
g
as
en
g
in
e
g
en
er
ato
r
s
,
an
d
iii
)
ev
alu
atin
g
g
r
id
tech
n
o
-
ec
o
n
o
m
ic
p
er
f
o
r
m
a
n
ce
u
s
in
g
th
e
SO
-
b
ased
OPF
ap
p
r
o
ac
h
.
2.
M
E
T
H
O
D
T
h
is
s
tu
d
y
em
p
lo
y
s
a
s
y
s
tem
atic
m
eth
o
d
o
lo
g
y
to
ev
al
u
ate
th
e
tech
n
o
-
ec
o
n
o
m
ic
p
er
f
o
r
m
a
n
ce
o
f
th
e
Ma
n
o
k
war
i
p
o
wer
g
r
id
af
te
r
r
ec
o
n
f
ig
u
r
ati
o
n
b
y
s
o
lv
in
g
th
e
OPF
p
r
o
b
lem
u
s
in
g
S
O
alg
o
r
ith
m
.
T
h
e
m
eth
o
d
o
l
o
g
y
co
n
s
is
ts
o
f
p
o
we
r
s
y
s
tem
m
o
d
eli
n
g
,
OPF
f
o
r
m
u
latio
n
,
im
p
lem
en
tatio
n
o
f
th
e
SO
alg
o
r
ith
m
,
an
d
s
im
u
latio
n
p
ar
am
eter
s
an
d
s
etu
p
.
2
.
1
.
P
o
wer
s
y
s
t
em
m
o
delin
g
a
nd
O
P
F
f
o
r
m
ula
t
io
n
T
h
e
Ma
n
o
k
war
i
g
r
id
was
ch
o
s
en
f
o
r
ass
ess
m
en
t
d
u
e
to
th
e
r
e
ce
n
t
in
teg
r
atio
n
o
f
two
g
as
en
g
in
e
p
o
we
r
p
lan
ts
in
to
th
e
p
o
wer
g
r
id
.
W
h
er
e
th
e
in
teg
r
atio
n
h
as
alt
er
ed
th
e
s
y
s
tem
co
n
f
ig
u
r
atio
n
.
T
h
e
s
y
s
tem
d
ata,
in
clu
d
in
g
g
en
er
ato
r
lim
its
an
d
lin
e
ca
p
ac
ities
,
wer
e
o
b
tai
n
ed
f
r
o
m
[
9
]
with
s
o
m
e
m
o
d
if
icatio
n
s
d
u
e
t
o
r
ec
o
n
f
ig
u
r
atio
n
b
y
b
y
p
ass
in
g
b
u
s
1
an
d
b
u
s
9
with
a
n
ew
lin
e
h
av
in
g
an
im
p
ed
an
ce
o
f
0
.
8
4
0
+
j
1
.
9
7
4
p
.
u
.
,
an
d
o
p
er
atin
g
two
g
as e
n
g
i
n
e
p
o
w
er
p
lan
ts
co
n
n
ec
ted
to
b
u
s
9
,
e
ac
h
r
ated
at
2
0
MW,
as sh
o
wn
in
r
ed
in
F
ig
u
r
e
1
.
T
h
e
s
y
s
tem
ass
ess
m
en
t i
s
d
o
n
e
in
f
o
u
r
ca
s
es wh
er
e
d
escr
ib
e
d
in
o
b
jectiv
e
f
u
n
ctio
n
as f
o
llo
ws:
C
ase
1
:
Fu
el
co
s
t
m
in
im
izatio
n
–
T
h
i
s
ca
s
e
f
o
cu
s
es
o
n
r
e
d
u
cin
g
th
e
to
tal
f
u
el
co
s
t
wh
ile
en
s
u
r
i
n
g
th
at
all
tech
n
ical
co
n
s
tr
ain
ts
,
s
u
ch
as
v
o
ltag
e
an
d
g
en
e
r
ato
r
lim
its
,
a
r
e
r
esp
ec
ted
.
C
ase
2
:
Vo
ltag
e
d
ev
iatio
n
im
p
r
o
v
e
m
en
t
–
T
h
e
g
o
al
is
to
im
p
r
o
v
e
th
e
v
o
ltag
e
p
r
o
f
ile
b
y
m
in
i
m
izin
g
th
e
d
ev
iatio
n
b
etwe
en
ac
tu
al
an
d
n
o
m
in
al
v
o
ltag
es.
C
ase
3
:
Vo
ltag
e
s
tab
ilit
y
en
h
an
ce
m
en
t
–
T
h
is
ca
s
e
aim
s
to
im
p
r
o
v
e
th
e
v
o
ltag
e
s
tab
ilit
y
o
f
th
e
g
r
id
b
y
m
in
im
izin
g
th
e
m
a
x
im
u
m
v
o
lt
ag
e
s
tab
ilit
y
in
d
ex
.
C
ase
4
:
Activ
e
p
o
wer
lo
s
s
m
in
im
izatio
n
–
T
h
e
o
b
jectiv
e
is
to
r
ed
u
ce
tr
an
s
m
is
s
io
n
lo
s
s
es in
th
e
s
y
s
t
em
,
wh
ich
co
n
tr
ib
u
tes to
in
c
r
ea
s
ed
ef
f
ici
en
cy
an
d
r
ed
u
ce
d
o
p
er
atio
n
al
co
s
ts
.
T
h
e
in
teg
r
atio
n
o
f
g
as
en
g
in
e
p
o
wer
p
la
n
ts
in
to
th
e
Ma
n
o
k
war
i
g
r
id
is
ex
p
licitly
r
ep
r
esen
ted
b
y
m
o
d
elin
g
th
e
g
as
en
g
in
e
u
n
its
as
co
n
tr
o
llab
le
g
en
er
atio
n
s
o
u
r
ce
s
with
in
th
e
OPF
f
r
am
ewo
r
k
.
T
h
ese
g
en
er
ato
r
s
ar
e
co
n
n
ec
ted
at
d
esig
n
ated
b
u
s
es
an
d
ar
e
ch
ar
ac
ter
i
ze
d
b
y
s
p
ec
if
ic
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
lim
its
,
as
well
a
s
q
u
ad
r
atic
f
u
el
co
s
t
f
u
n
ctio
n
s
r
ef
lectin
g
g
as
en
g
in
e
o
p
er
atio
n
al
b
eh
av
io
r
.
T
h
eir
d
is
p
atch
le
v
els
ar
e
tr
ea
ted
a
s
d
ec
is
io
n
v
ar
ia
b
les
in
t
h
e
o
p
tim
izatio
n
p
r
o
ce
s
s
,
allo
win
g
th
e
S
O
alg
o
r
ith
m
to
d
eter
m
i
n
e
o
p
ti
m
al
o
p
e
r
atin
g
p
o
in
ts
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
Tech
n
o
-
ec
o
n
o
mic
a
s
s
ess
men
t o
f g
a
s
en
g
i
n
e
p
o
w
er p
la
n
ts
p
e
n
etra
tio
n
…
(
A
d
el
h
a
r
d
B
en
i R
eh
ia
r
a
)
537
u
n
d
er
d
if
f
er
en
t
o
b
jectiv
e
s
ce
n
ar
io
s
.
T
h
is
m
o
d
elin
g
ap
p
r
o
ac
h
en
s
u
r
es
th
at
th
e
im
p
ac
t
o
f
g
as
en
g
in
e
p
e
n
etr
atio
n
o
n
s
y
s
tem
ec
o
n
o
m
ics an
d
tech
n
ical
p
er
f
o
r
m
an
ce
is
d
ir
ec
tly
c
ap
tu
r
ed
in
th
e
o
p
tim
izatio
n
r
es
u
lts
.
T
h
e
OPF
p
r
o
b
lem
is
f
o
r
m
u
late
d
as
a
co
n
s
tr
ain
ed
n
o
n
lin
ea
r
o
p
tim
izatio
n
p
r
o
b
lem
,
wh
e
r
e
th
e
o
b
jectiv
e
is
to
d
eter
m
in
e
t
h
e
o
p
tim
al
o
p
er
atin
g
p
o
in
t
o
f
th
e
p
o
wer
s
y
s
tem
wh
ile
s
atis
f
y
in
g
all
p
h
y
s
i
ca
l
an
d
o
p
er
atio
n
al
co
n
s
tr
ain
ts
.
T
h
e
g
e
n
er
al
OPF
f
o
r
m
u
latio
n
is
ex
p
r
ess
ed
as
th
e
m
in
im
izatio
n
o
f
an
o
b
jectiv
e
f
u
n
ctio
n
s
u
b
ject
to
eq
u
ality
an
d
in
e
q
u
ality
co
n
s
tr
ain
ts
.
E
q
u
ality
co
n
s
tr
ain
ts
r
ep
r
esen
t
th
e
p
o
wer
f
lo
w
b
alan
ce
eq
u
atio
n
s
,
en
s
u
r
in
g
th
at
g
en
er
ate
d
p
o
wer
m
ee
ts
lo
ad
d
em
a
n
d
an
d
s
y
s
tem
lo
s
s
es.
I
n
eq
u
ality
co
n
s
tr
ain
ts
e
n
f
o
r
ce
g
en
er
ato
r
o
p
er
atin
g
lim
its
,
b
u
s
v
o
ltag
e
lim
its
,
an
d
tr
an
s
m
is
s
io
n
lin
e
f
lo
w
lim
its
.
Fig
u
r
e
1
.
Sin
g
le
lin
e
d
iag
r
a
m
o
f
Ma
n
o
k
war
i g
r
id
2
.
1
.
1
.
O
bje
ct
iv
e
f
un
ct
io
n
T
h
e
o
b
jectiv
e
f
u
n
ctio
n
in
OPF
d
ef
in
es
th
e
p
o
wer
s
y
s
tem
'
s
o
p
er
atio
n
al
g
o
al,
f
o
cu
s
in
g
o
n
ec
o
n
o
m
ic
ef
f
icien
cy
,
tech
n
ical
p
er
f
o
r
m
a
n
ce
,
o
r
s
ec
u
r
ity
.
I
n
th
is
s
tu
d
y
,
o
b
jectiv
es
r
ef
lect
k
ey
ec
o
n
o
m
ic
an
d
o
p
er
atio
n
al
in
d
icato
r
s
f
o
r
g
r
i
d
s
with
g
as
en
g
in
e
p
o
we
r
p
lan
ts
.
E
ac
h
o
b
jectiv
e
is
ev
alu
ated
in
d
ep
en
d
en
tly
to
ass
ess
it
s
im
p
ac
t
o
n
s
y
s
tem
p
er
f
o
r
m
an
ce
.
T
h
e
t
o
tal
o
b
jectiv
e
f
u
n
ctio
n
J
is
to
m
in
im
ize
o
r
o
p
tim
ize
th
e
f
o
llo
win
g
co
m
p
o
n
en
ts
:
i)
Fu
el
co
s
t
m
in
im
izatio
n
:
T
h
e
e
co
n
o
m
ic
o
b
jectiv
e
to
m
in
im
iz
e
th
e
f
u
el
c
o
s
t
o
f
p
o
wer
g
en
er
a
tio
n
is
ex
p
r
ess
ed
as
(
1
)
[
1
]
,
[
9
]
,
[
1
2
]
,
[
1
4
]
,
[
2
2
]
.
1
=
∑
(
+
+
2
)
=
1
(
1
)
W
h
er
e
is
th
e
p
o
wer
g
en
er
a
ted
b
y
th
e
-
th
g
en
e
r
ato
r
a
n
d
,
,
an
d
ar
e
c
o
s
t c
o
ef
f
icien
t
s
.
ii)
Vo
ltag
e
d
ev
iatio
n
m
in
im
izati
o
n
:
T
o
im
p
r
o
v
e
th
e
v
o
ltag
e
p
r
o
f
ile,
th
e
v
o
ltag
e
d
ev
iatio
n
f
r
o
m
th
e
n
o
m
in
al
v
alu
e
at
th
e
lo
a
d
b
u
s
es is
m
in
im
ized
u
s
in
g
(
2
)
.
2
=
∑
(
+
+
2
)
=
1
+
1000
⥂
∑
|
−
1
|
=
1
(
2
)
W
h
er
e
r
ep
r
esen
ts
th
e
v
o
ltag
e
m
ag
n
itu
d
e
at
lo
ad
b
u
s
an
d
is
th
e
n
u
m
b
er
o
f
lo
ad
b
u
s
e
s
.
iii)
Vo
ltag
e
s
tab
ilit
y
en
h
an
ce
m
e
n
t
:
T
h
e
v
o
ltag
e
s
tab
ilit
y
o
f
t
h
e
s
y
s
tem
is
im
p
r
o
v
ed
b
y
m
in
im
izin
g
th
e
m
a
x
im
u
m
L
-
in
d
ex
,
wh
ich
s
er
v
es a
s
an
in
d
icato
r
o
f
s
y
s
tem
s
tab
ilit
y
.
3
=
6000
(
(
1
−
∑
=
1
)
)
=
1
,
2
,
⋯
,
(
3
)
W
h
er
e
is
th
e
s
u
b
m
atr
ix
o
f
th
e
b
u
s
ad
m
ittan
ce
m
at
r
ix
a
n
d
,
ar
e
t
h
e
v
o
ltag
e
m
ag
n
itu
d
es
at
b
u
s
es
an
d
,
r
esp
ec
tiv
el
y
.
iv
)
Activ
e
p
o
wer
lo
s
s
m
in
im
izatio
n:
T
h
e
to
tal
ac
tiv
e
p
o
wer
l
o
s
s
in
th
e
tr
an
s
m
is
s
io
n
s
y
s
tem
is
m
in
im
ized
.
4
=
∑
(
2
+
2
−
2
(
−
)
)
=
1
(
4
)
W
h
er
e
is
th
e
co
n
d
u
ctan
ce
o
f
b
r
a
n
ch
a
n
d
,
ar
e
th
e
v
o
ltag
e
an
g
les at
b
u
s
es
an
d
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
15
,
No
.
2
,
J
u
n
e
20
26
:
535
-
545
538
2
.
1
.
2
.
E
qu
a
lity
a
nd
inequ
a
lit
y
co
ns
t
ra
ints
T
h
e
OPF
p
r
o
b
lem
m
u
s
t
s
atis
f
y
eq
u
ality
an
d
in
eq
u
ality
co
n
s
tr
ain
ts
r
ep
r
esen
tin
g
p
h
y
s
ical
an
d
o
p
er
atio
n
al
lim
its
o
f
th
e
p
o
we
r
s
y
s
tem
.
T
h
ese
co
n
s
tr
ain
ts
en
s
u
r
e
b
alan
ce
d
p
o
wer
g
en
e
r
atio
n
an
d
co
n
s
u
m
p
tio
n
,
ac
ce
p
tab
le
s
y
s
tem
v
o
ltag
es,
an
d
s
af
e
tr
an
s
m
is
s
io
n
lin
e
o
p
er
at
io
n
.
Stan
d
ar
d
p
o
wer
f
lo
w
eq
u
a
tio
n
s
an
d
o
p
er
atin
g
lim
its
ar
e
ad
o
p
ted
to
m
o
d
el
r
e
al
-
wo
r
ld
s
y
s
tem
co
n
d
itio
n
s
ac
cu
r
ately
.
i)
Po
wer
f
lo
w
eq
u
atio
n
s
(
eq
u
ality
co
n
s
tr
ain
ts
):
T
h
e
p
o
wer
b
ala
n
ce
eq
u
atio
n
s
f
o
r
ac
tiv
e
an
d
r
e
ac
tiv
e
p
o
wer
at
ea
ch
b
u
s
m
u
s
t b
e
s
atis
f
ied
[
1
]
,
[
9
]
,
[
1
2
]
,
[
1
4
]
,
[
2
2
]
.
−
=
∑
(
(
+
−
)
)
=
1
(
5
)
−
=
∑
(
(
+
−
)
)
=
1
(
6
)
W
h
er
e
,
,
,
an
d
r
ep
r
esen
t
th
e
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
g
en
e
r
atio
n
an
d
d
em
a
n
d
at
b
u
s
,
an
d
an
d
ar
e
th
e
m
ag
n
itu
d
e
a
n
d
an
g
le
o
f
th
e
ad
m
ittan
ce
m
a
tr
ix
b
etwe
en
b
u
s
es
an
d
.
ii)
Sy
s
tem
o
p
er
atin
g
c
o
n
s
tr
ain
ts
(
in
eq
u
ality
co
n
s
tr
ain
ts
)
:
T
h
ese
in
clu
d
e
lim
its
o
n
g
en
er
ato
r
o
u
t
p
u
t,
b
u
s
v
o
ltag
e
,
an
d
tr
an
s
m
is
s
io
n
lin
e
ca
p
ac
ity
[
1
]
,
[
9
]
,
[
1
2
]
,
[
1
4
]
,
[
2
2
]
.
(
7
)
(
8
)
(
9
)
(1
0
)
≤
(1
1
)
W
h
er
e
min
an
d
max
ar
e
th
e
m
in
im
u
m
an
d
m
ax
im
u
m
g
e
n
er
atio
n
lim
its
,
G
min
an
d
G
max
ar
e
th
e
v
o
ltag
e
lim
its
,
an
d
max
is
th
e
th
er
m
al
lim
it o
f
th
e
tr
an
s
m
is
s
io
n
lin
e
b
etwe
en
b
u
s
es
an
d
.
2
.
2
.
Sn
a
k
e
o
ptim
iz
a
t
io
n
a
lg
o
rit
hm
f
o
r
O
P
F
T
o
s
o
lv
e
th
e
f
o
r
m
u
lated
OPF
p
r
o
b
lem
,
th
e
SO
alg
o
r
ith
m
i
s
em
p
lo
y
ed
.
SO
is
a
p
o
p
u
latio
n
-
b
ased
m
etah
eu
r
is
tic
in
s
p
ir
ed
b
y
th
e
n
atu
r
al
b
e
h
av
io
r
s
o
f
s
n
ak
es,
s
u
ch
as
f
o
o
d
s
ea
r
ch
in
g
,
c
o
m
p
e
titi
o
n
,
an
d
m
atin
g
.
T
h
ese
b
eh
av
i
o
r
s
ar
e
m
ath
em
at
ically
m
o
d
eled
to
b
alan
ce
ex
p
l
o
r
atio
n
a
n
d
e
x
p
lo
itatio
n
d
u
r
in
g
th
e
s
ea
r
ch
p
r
o
ce
s
s
,
m
ak
in
g
SO su
itab
le
f
o
r
s
o
lv
in
g
n
o
n
li
n
ea
r
an
d
n
o
n
-
co
n
v
ex
o
p
tim
izatio
n
p
r
o
b
lem
s
s
u
ch
as
OPF.
I
n
th
e
SO
-
b
ased
OPF
im
p
lem
en
tatio
n
,
ea
ch
ca
n
d
id
ate
s
o
lu
t
io
n
(
s
n
ak
e)
r
ep
r
esen
ts
a
co
m
p
lete
s
et
o
f
OPF
co
n
tr
o
l
v
ar
iab
les,
in
clu
d
i
n
g
g
e
n
er
ato
r
ac
tiv
e
p
o
wer
o
u
t
p
u
ts
,
g
en
er
at
o
r
v
o
ltag
e
m
ag
n
i
tu
d
es,
tr
an
s
f
o
r
m
e
r
tap
s
ettin
g
s
,
an
d
s
h
u
n
t
r
ea
ctiv
e
p
o
wer
co
m
p
en
s
atio
n
s
.
T
h
e
o
p
tim
izatio
n
p
r
o
ce
s
s
b
eg
in
s
b
y
r
a
n
d
o
m
ly
in
itializin
g
a
p
o
p
u
latio
n
o
f
s
n
ak
es
with
in
th
e
f
ea
s
ib
le
b
o
u
n
d
s
o
f
th
e
co
n
tr
o
l
v
ar
iab
les.
T
h
e
p
o
p
u
latio
n
is
th
en
d
iv
id
e
d
in
to
m
ale
an
d
f
em
ale
g
r
o
u
p
s
,
an
d
t
h
e
f
itn
ess
o
f
ea
ch
s
n
a
k
e
is
ev
a
lu
ated
u
s
in
g
th
e
s
elec
ted
OPF o
b
jectiv
e
f
u
n
ctio
n
.
T
h
e
p
r
o
ce
d
u
r
e
o
f
SO
-
b
ased
O
PF
is
d
o
n
e
u
n
d
er
s
o
m
e
s
tep
s
as f
o
llo
ws
[
2
3
]
-
[
2
7
]
.
i)
Step
1
: I
n
itializatio
n
T
h
e
o
p
tim
izatio
n
p
r
o
ce
s
s
s
tar
ts
b
y
r
an
d
o
m
ly
g
en
er
ati
n
g
a
n
in
itial
p
o
p
u
latio
n
o
f
s
n
ak
es
with
in
th
e
allo
wab
le
b
o
u
n
d
s
o
f
t
h
e
OPF
co
n
tr
o
l
v
ar
iab
les
u
s
in
g
(
1
2
)
,
u
n
d
er
u
p
p
e
r
(
Ub
)
a
n
d
lo
wer
b
o
u
n
d
(
Lb
)
.
T
h
e
to
tal
p
o
p
u
latio
n
is
th
en
eq
u
ally
d
i
v
id
ed
in
to
m
ale
an
d
f
em
ale
g
r
o
u
p
s
.
E
ac
h
s
n
ak
e
is
ev
alu
a
ted
u
s
in
g
th
e
OPF
o
b
jectiv
e
f
u
n
ctio
n
to
d
eter
m
in
e
its
f
itn
ess
.
=
+
(
−
)
(
1
2
)
ii)
Step
2
: Fitn
ess
ev
alu
atio
n
T
h
e
b
est
-
p
er
f
o
r
m
in
g
s
n
ak
es
in
th
e
m
ale
(
f
best,
m
)
a
n
d
f
em
ale
(
f
be
st,
f
)
ar
e
id
e
n
tifie
d
.
T
w
o
k
ey
p
ar
am
eter
s
—
f
o
o
d
q
u
an
tity
(
Q
F
)
an
d
tem
p
e
r
atu
r
e
(
T
A
)
—
ar
e
co
m
p
u
te
d
u
s
in
g
(
1
3
)
a
n
d
(
1
4
)
.
T
h
ese
p
ar
a
m
eter
s
g
o
v
er
n
th
e
b
eh
av
io
r
al
s
tate
o
f
th
e
s
n
ak
e
p
o
p
u
latio
n
a
n
d
d
eter
m
in
e
th
e
s
u
b
s
eq
u
en
t sear
ch
s
tr
ateg
y
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
Tech
n
o
-
ec
o
n
o
mic
a
s
s
ess
men
t o
f g
a
s
en
g
i
n
e
p
o
w
er p
la
n
ts
p
e
n
etra
tio
n
…
(
A
d
el
h
a
r
d
B
en
i R
eh
ia
r
a
)
539
=
(
−
⁄
(
)
)
(
1
3
)
=
0
.
5
(
−
⁄
)
(
1
4
)
iii)
Step
3
: E
x
p
lo
r
atio
n
m
o
d
e
(
QF
<
0
.
2
5
)
W
h
en
th
e
f
o
o
d
q
u
an
tity
is
lo
w,
th
e
alg
o
r
ith
m
en
ter
s
th
e
e
x
p
lo
r
atio
n
p
h
ase.
I
n
th
is
p
h
a
s
e,
s
n
ak
e
p
o
s
itio
n
s
ar
e
u
p
d
ated
u
s
in
g
(
1
5
)
an
d
(
1
6
)
to
e
n
co
u
r
ag
e
wid
e
ex
p
lo
r
atio
n
o
f
th
e
s
ea
r
ch
s
p
ac
e
.
T
h
is
s
tep
en
h
an
ce
s
g
lo
b
al
s
ea
r
ch
ca
p
ab
ilit
y
an
d
h
elp
s
av
o
id
lo
ca
l
o
p
tim
a.
T
h
e
f
o
o
d
ac
q
u
is
itio
n
a
b
ilit
ies
o
f
m
ale
an
d
f
em
ale
(
A
m
an
d
A
f
)
,
s
n
a
k
es,
d
ef
in
e
d
in
(
1
7
)
an
d
(
1
8
)
,
r
eg
u
late
th
e
ex
p
lo
r
atio
n
p
r
o
ce
s
s
.
,
(
+
1
)
=
,
(
)
±
0
.
05
(
(
−
)
(
)
)
(
1
5
)
,
(
+
1
)
=
,
(
)
±
0
.
05
(
(
−
)
(
)
)
(
1
6
)
=
(
−
,
,
⁄
)
(
1
7
)
=
(
−
,
,
⁄
)
(
1
8
)
iv
)
Step
4
: E
x
p
lo
itatio
n
mode
(
Q
F
≥
0
.
2
5
an
d
T
A
>
0
.
6
)
I
f
s
u
f
f
icien
t
f
o
o
d
is
av
ailab
le
an
d
th
e
tem
p
er
atu
r
e
is
h
ig
h
,
th
e
alg
o
r
ith
m
s
witch
es
to
ex
p
lo
itatio
n
m
o
d
e.
I
n
th
is
m
o
d
e,
s
n
ak
es
u
p
d
ate
th
eir
p
o
s
itio
n
s
u
s
in
g
(
19
)
,
f
o
c
u
s
in
g
o
n
r
ef
in
in
g
s
o
lu
tio
n
s
ar
o
u
n
d
th
e
cu
r
r
e
n
t
b
est
ca
n
d
id
ates to
im
p
r
o
v
e
c
o
n
v
er
g
en
ce
ac
cu
r
ac
y
.
,
(
+
1
)
=
±
2
(
−
,
(
)
(
1
9
)
v)
Step
5
: M
atin
g
o
r
f
ig
h
tin
g
m
o
d
e
(
Q
F
≥
0
.
2
5
a
n
d
T
A
≤
0
.
6
)
W
h
en
th
e
tem
p
er
atu
r
e
is
lo
w,
t
h
e
alg
o
r
ith
m
p
r
o
b
ab
ilis
tically
s
elec
ts
eith
er
m
atin
g
o
r
f
i
g
h
tin
g
b
eh
a
v
io
r
.
I
n
th
e
m
atin
g
m
o
d
e
(
F
m
an
d
F
f
)
,
n
ew
o
f
f
s
p
r
in
g
s
o
lu
tio
n
s
ar
e
g
en
er
ated
u
s
in
g
(
2
0
)
an
d
(
2
1
)
,
with
f
ig
h
tin
g
ab
ilit
ies
(
M
m
an
d
M
f
)
d
ef
in
ed
i
n
(
2
2
)
an
d
(
2
3
)
.
I
f
f
i
g
h
tin
g
m
o
d
e
is
s
elec
ted
,
s
n
ak
e
p
o
s
itio
n
s
ar
e
u
p
d
ated
u
s
in
g
(2
4
)
an
d
(
2
5
)
,
wh
ile
m
atin
g
a
b
ilit
ies
ar
e
ca
lcu
lated
u
s
in
g
(
2
6
)
an
d
(
2
7
)
.
T
h
ese
b
eh
a
v
io
r
s
m
ain
tain
p
o
p
u
latio
n
d
iv
er
s
ity
an
d
b
alan
ce
ex
p
lo
r
at
io
n
an
d
ex
p
lo
itatio
n
.
,
(
+
1
)
=
,
(
)
+
2
(
(
,
−
,
(
)
(
2
0
)
,
(
+
1
)
=
,
(
)
+
2
(
(
,
−
,
(
)
(
2
1
)
=
(
−
,
⁄
)
(
2
2
)
=
(
−
,
⁄
)
(
2
3
)
,
(
+
1
)
=
,
(
)
+
2
(
(
,
(
)
−
,
(
)
)
(
2
4
)
,
(
+
1
)
=
,
(
)
+
2
(
(
,
(
)
−
,
(
)
)
(
2
5
)
=
(
−
,
,
⁄
)
(
2
6
)
=
(
−
,
,
⁄
)
(
2
7
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
15
,
No
.
2
,
J
u
n
e
20
26
:
535
-
545
540
v
i)
Step
6
: Rep
lace
m
en
t (
eg
g
-
h
at
ch
in
g
m
ec
h
an
is
m
)
Af
ter
th
e
b
eh
av
io
r
al
u
p
d
ates,
wea
k
s
n
ak
es
ar
e
id
en
tifie
d
an
d
r
ep
lace
d
with
n
ewly
g
en
e
r
ate
d
o
f
f
s
p
r
in
g
u
s
in
g
(
2
8
)
an
d
(
29
)
.
T
h
is
r
ep
lace
m
en
t
m
ec
h
an
is
m
p
r
ev
en
t
s
p
r
em
atu
r
e
co
n
v
er
g
en
ce
a
n
d
en
s
u
r
es
s
u
s
tain
ed
d
iv
er
s
ity
with
in
th
e
p
o
p
u
latio
n
.
,
=
+
(
−
)
(
2
8
)
,
=
+
(
−
)
(
2
9
)
v
ii)
Step
7
: T
er
m
in
atio
n
an
d
o
u
tp
u
t
Step
s
2
–
6
ar
e
r
ep
ea
ted
u
n
til
th
e
ter
m
in
atio
n
cr
iter
io
n
is
s
atis
f
ied
,
s
u
ch
as
r
ea
ch
in
g
th
e
m
ax
im
u
m
n
u
m
b
er
o
f
iter
atio
n
s
o
r
ac
h
ie
v
in
g
co
n
v
er
g
e
n
ce
.
T
h
e
o
v
er
al
l
p
r
o
ce
d
u
r
e
o
f
th
e
s
n
ak
e
o
p
tim
izatio
n
alg
o
r
ith
m
ap
p
lied
to
th
e
OPF
p
r
o
b
lem
s
u
m
m
ar
izes
th
e
s
eq
u
en
ce
o
f
i
n
itializatio
n
,
f
itn
ess
ev
alu
atio
n
,
b
eh
av
io
r
al
m
o
d
e
s
elec
tio
n
,
s
o
lu
tio
n
u
p
d
atin
g
,
r
e
p
lace
m
en
t,
an
d
ter
m
in
atio
n
.
T
h
e
b
est
s
o
lu
tio
n
o
b
tain
ed
at
th
e
en
d
o
f
th
e
p
r
o
ce
s
s
r
ep
r
esen
ts
th
e
o
p
tim
al
OPF
s
o
lu
tio
n
f
o
r
th
e
s
elec
ted
o
b
jectiv
e.
2.
3
.
Sim
ula
t
i
o
n
pa
ra
m
e
t
er
s
a
nd
s
et
up
T
h
e
s
im
u
latio
n
s
f
o
r
th
is
s
tu
d
y
wer
e
co
n
d
u
cted
u
s
in
g
th
e
M
atp
o
wer
7
.
0
s
o
f
twar
e
p
ac
k
ag
e
,
s
p
ee
d
in
g
th
e
OPF
co
m
p
u
tatio
n
.
T
h
e
s
o
f
twar
e
was
r
u
n
o
n
an
I
n
tel
C
o
r
e
i7
-
2
6
7
7
M
C
PU
with
1
0
G
B
o
f
R
AM
,
u
n
d
er
a
W
in
d
o
ws
1
0
o
p
er
atin
g
s
y
s
tem
.
T
h
is
en
v
ir
o
n
m
e
n
t
was
s
u
f
f
ic
ien
t
to
h
a
n
d
le
th
e
co
m
p
u
tatio
n
al
d
em
an
d
s
o
f
th
e
s
im
u
latio
n
,
p
r
o
v
id
in
g
tim
ely
r
esu
lts
wh
ile
en
s
u
r
in
g
d
ata
in
te
g
r
ity
.
A
p
o
p
u
latio
n
s
ize
o
f
5
0
was
s
elec
ted
f
o
r
th
e
alg
o
r
ith
m
,
b
alan
cin
g
co
m
p
u
tatio
n
al
e
f
f
ici
en
cy
with
s
o
lu
tio
n
ac
cu
r
ac
y
.
A
m
ax
im
u
m
o
f
1
0
0
iter
atio
n
s
was
u
s
ed
to
en
s
u
r
e
th
at
th
e
alg
o
r
ith
m
h
ad
en
o
u
g
h
tim
e
to
co
n
v
er
g
e
to
a
n
o
p
tim
al
s
o
lu
tio
n
wh
ile
av
o
id
in
g
u
n
n
ec
ess
a
r
y
co
m
p
u
tatio
n
al
o
v
er
h
ea
d
.
T
h
is
co
m
b
in
atio
n
o
f
p
ar
am
eter
s
was
d
esig
n
ed
to
s
tr
ik
e
a
b
alan
ce
b
etwe
en
th
e
ex
p
lo
r
atio
n
an
d
ex
p
l
o
itatio
n
p
h
ases
o
f
th
e
SO
alg
o
r
ith
m
,
e
n
s
u
r
in
g
t
h
at
th
e
s
o
lu
tio
n
s
f
o
u
n
d
wer
e
b
o
th
g
lo
b
al
ly
o
p
tim
al
an
d
co
m
p
u
tatio
n
all
y
ef
f
icien
t.
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
3
.
1
.
Desig
n
f
uel c
o
s
t
f
un
ct
io
n
I
n
th
e
c
o
n
tex
t o
f
OPF p
r
o
b
lem
s
,
th
e
f
u
el
co
s
t f
u
n
ctio
n
p
lay
s
a
cr
u
cial
r
o
le
as th
e
p
r
im
ar
y
o
b
jectiv
e
to
b
e
m
in
im
ize
d
,
e
n
s
u
r
in
g
th
at
e
co
n
o
m
ic
ef
f
icien
c
y
is
ac
h
iev
e
d
wh
ile
s
atis
f
y
in
g
th
e
tech
n
ic
al
co
n
s
tr
ain
ts
o
f
th
e
p
o
wer
g
r
id
.
T
h
e
p
r
o
ce
s
s
o
f
d
esig
n
in
g
a
f
u
e
l
co
s
t
f
u
n
ctio
n
f
o
r
g
as
e
n
g
in
e
p
o
wer
p
lan
ts
i
n
v
o
lv
es
cr
ea
tin
g
a
m
ath
em
atica
l
m
o
d
el
th
at
ac
c
u
r
ately
r
ep
r
esen
ts
th
e
o
p
er
atio
n
al
co
s
ts
ass
o
ciate
d
with
p
o
w
er
g
en
e
r
atio
n
.
W
ith
th
e
o
p
er
atio
n
o
f
th
e
two
g
as e
n
g
in
e
p
o
wer
p
la
n
ts
in
th
e
g
r
id
o
f
Ma
n
o
k
war
i,
it is
ess
e
n
tial
t
o
f
o
r
m
u
late
th
e
f
u
el
co
s
t
f
u
n
ctio
n
o
f
th
e
p
o
wer
p
lan
ts
.
B
ased
o
n
th
e
p
r
o
v
id
e
d
d
ata
in
[
2
8
]
.
th
e
c
o
s
t
f
u
n
ctio
n
s
ca
n
b
e
d
eter
m
in
e
d
u
s
in
g
a
s
im
p
le
q
u
ad
r
atic
eq
u
a
tio
n
th
at
ac
co
u
n
ts
f
o
r
th
e
p
o
w
er
o
u
tp
u
t
an
d
f
u
el
co
n
s
u
m
p
tio
n
ch
ar
ac
ter
is
tics
o
f
th
e
p
lan
ts
,
as f
o
llo
ws:
37
=
1082.5
-
0.0627
37
+
1
−
5
37
2
38
=
2059.5
-
0.3264
38
+
3
−
5
38
2
3
.
2
.
F
uel
co
s
t
m
ini
m
iza
t
i
o
n
T
h
e
g
o
al
in
C
ase
1
was
to
m
in
im
ize
f
u
el
co
s
ts
wh
ile
m
ain
tain
in
g
ac
ce
p
tab
le
s
y
s
tem
p
er
f
o
r
m
an
ce
.
Acc
o
r
d
in
g
to
T
a
b
le
1
,
th
e
to
t
al
f
u
el
co
s
t
f
o
r
th
is
ca
s
e
was
ap
p
r
o
x
im
ately
2
.
0
0
3
m
illi
o
n
USD/h
.
T
h
is
r
esu
lt
s
h
o
ws
a
s
ig
n
if
ican
t
r
ed
u
ctio
n
i
n
o
p
er
atin
g
co
s
ts
,
d
r
i
v
en
b
y
o
p
tim
al
co
n
tr
o
l
o
v
er
ac
tiv
e
p
o
wer
g
e
n
er
atio
n
v
alu
e
s
P
1
to
P
38
,
wh
e
r
e
m
i
n
im
al
ad
j
u
s
tm
en
ts
to
p
o
wer
o
u
tp
u
ts
wer
e
ap
p
lied
.
I
n
th
is
ca
s
e,
P1
r
em
ai
n
ed
n
ea
r
ze
r
o
,
wh
ile
P
37
an
d
P
38
wer
e
s
ig
n
if
ican
tly
h
ig
h
er
,
r
ef
lectin
g
th
e
ef
f
icien
t
u
s
e
o
f
d
if
f
e
r
en
t
g
en
er
a
tio
n
u
n
its
to
k
ee
p
co
s
ts
lo
w.
T
h
is
ac
h
iev
em
en
t
is
v
alid
ated
in
[
9
]
,
wh
e
r
e
th
e
o
th
er
p
o
we
r
p
lan
ts
wo
r
k
at
m
a
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m
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ile
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e
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est
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led
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1
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R
eg
ar
d
in
g
th
e
v
o
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p
r
o
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ile
in
Fig
u
r
e
2
,
C
ase
1
r
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lted
in
r
elativ
ely
s
tab
le
v
o
ltag
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ac
r
o
s
s
all
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with
m
o
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es
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er
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ig
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est
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,
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ich
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ile
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im
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h
iev
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s
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m
e
m
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o
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v
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d
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p
s
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r
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ed
,
esp
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at
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e
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d
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Ho
wev
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alu
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r
em
ain
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with
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ac
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p
tab
le
o
p
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in
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th
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s
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s
tem
'
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r
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d
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ity
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th
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ce
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was
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elativ
ely
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ig
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at
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h
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s
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i
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ad
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o
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t
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izat
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ateg
ies,
wh
er
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y
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te
m
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n
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ig
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m
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s
ts
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er
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im
al
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Ho
we
v
er
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h
e
f
o
cu
s
o
n
f
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el
c
o
s
t
m
in
im
izatio
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e
n
s
u
r
es
th
at
t
h
e
f
in
an
cial
b
en
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its
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u
tweig
h
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e
s
m
all
in
cr
ea
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e
in
p
o
wer
lo
s
s
es a
n
d
th
e
v
o
ltag
e
d
ev
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n
o
b
s
er
v
ed
i
n
s
o
m
e
p
a
r
ts
o
f
th
e
s
y
s
tem
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
Tech
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ess
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t o
f g
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(
A
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eh
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r
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)
541
T
ab
le
1
.
Var
iab
les ch
a
n
g
e
in
e
ac
h
ca
s
e
V
a
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i
a
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l
e
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a
se
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se
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se
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a
se
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Fig
u
r
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2
.
Vo
ltag
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p
r
o
f
ile
in
ea
ch
ca
s
e
3
.
3
.
Vo
l
t
a
g
e
dev
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t
io
n im
pr
o
v
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I
n
C
ase
2
,
th
e
p
r
im
ar
y
f
o
c
u
s
was
o
n
im
p
r
o
v
i
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th
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v
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lta
g
e
d
ev
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n
(
VD)
ac
r
o
s
s
th
e
n
etwo
r
k
.
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o
r
d
in
g
to
T
ab
le
1
,
t
h
is
s
tr
ateg
y
y
ield
e
d
th
e
l
o
west
VD
v
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o
f
0
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5
5
7
7
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u
.
,
a
s
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n
if
ica
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t
im
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t
o
v
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ase
1
’
s
0
.
9
1
9
3
p
.
u
.
T
h
e
o
p
tim
izatio
n
in
th
is
ca
s
e
r
esu
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in
m
u
ch
m
o
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e
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n
i
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m
v
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p
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f
iles
ac
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s
all
b
u
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as
s
ee
n
in
Fig
u
r
e
2
.
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h
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lar
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m
1
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o
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r
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d
at
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h
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v
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9
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m
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d
is
tr
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.
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wev
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im
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m
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h
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t
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1
4
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7
m
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o
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USD/h
,
wh
ich
r
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lects
th
e
ad
d
itio
n
al
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ts
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ato
r
o
u
tp
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ts
to
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h
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ce
v
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iles
.
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n
th
is
ca
s
e,
th
e
p
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we
r
o
u
tp
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ts
P
1
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o
P
38
s
h
o
w
s
ig
n
if
ica
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t
v
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r
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n
,
esp
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ially
in
P
1
,
wh
ich
in
cr
ea
s
ed
f
r
o
m
n
ea
r
ly
z
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o
in
C
ase
1
to
6
.
0
6
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h
is
in
d
icate
s
th
at
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tili
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an
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ate
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em
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Fu
r
th
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m
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e
,
th
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ac
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p
o
we
r
lo
s
s
es
in
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s
e
in
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atica
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to
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2
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4
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8
MW,
in
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th
at
th
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ad
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ig
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l
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es
to
m
ain
tain
th
e
v
o
ltag
e
p
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f
ile
im
p
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e
m
en
t.
T
h
is
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ad
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o
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f
h
ig
h
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h
ts
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alan
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in
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s
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ilit
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ig
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d
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ex
p
en
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T
h
e
r
esu
lt
is
th
e
s
am
e
as in
[
1
]
,
[
1
4
]
,
[
2
2
]
,
wh
e
r
e
th
e
VD
is
lo
wer
,
th
e
f
u
el
co
s
t i
s
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d
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ce
d
,
a
n
d
th
e
p
o
wer
l
o
s
s
is
h
ig
h
er
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
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E
n
g
,
Vo
l.
15
,
No
.
2
,
J
u
n
e
20
26
:
535
-
545
542
3
.
4
.
Vo
l
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a
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it
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enha
ncem
ent
Vo
ltag
e
s
tab
ilit
y
en
h
an
ce
m
en
t
was
th
e
k
ey
o
b
jectiv
e
in
C
ase
3
,
wh
er
e
th
e
s
y
s
tem
aim
ed
t
o
im
p
r
o
v
e
lo
n
g
-
ter
m
v
o
ltag
e
s
tab
ilit
y
ac
r
o
s
s
all
b
u
s
es.
Acc
o
r
d
in
g
t
o
T
ab
le
1
,
th
e
L
max
in
d
ex
,
wh
ich
r
ep
r
esen
ts
th
e
m
ax
im
u
m
lo
ad
a
b
ilit
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lim
it,
was
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ed
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ce
d
to
0
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0
2
0
0
p
.
u
.
,
th
e
lo
west
am
o
n
g
all
ca
s
e
s
,
i
n
d
icatin
g
a
n
o
tab
l
e
im
p
r
o
v
em
e
n
t
in
v
o
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e
s
tab
ilit
y
.
T
h
is
lo
wer
L
max
m
ea
n
s
th
at
th
e
s
y
s
tem
co
u
ld
h
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le
m
o
r
e
lo
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u
t
f
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g
in
s
tab
ilit
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,
a
cr
itical
f
ac
to
r
f
o
r
p
r
ev
en
tin
g
v
o
ltag
e
co
llap
s
e
u
n
d
er
s
tr
ess
ed
co
n
d
itio
n
s
.
I
n
ter
m
s
o
f
th
e
v
o
ltag
e
p
r
o
f
il
e,
g
iv
en
in
Fig
u
r
e
2
,
C
ase
3
m
ain
tain
ed
r
elativ
ely
h
ig
h
v
o
l
tag
e
lev
els
ac
r
o
s
s
th
e
n
etwo
r
k
,
with
m
o
s
t
b
u
s
es
h
av
in
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v
o
ltag
es
clo
s
e
to
1
.
0
5
p
.
u
.
T
h
e
o
n
ly
n
o
tab
le
d
ip
o
cc
u
r
r
e
d
at
b
u
s
3
0
,
wh
er
e
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e
v
o
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e
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c
h
ed
0
.
9
9
4
2
3
p
.
u
.
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s
ti
ll
with
in
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c
ep
tab
le
b
o
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n
d
s
.
T
h
is
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s
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g
g
ests
th
at
v
o
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e
s
tab
ilit
y
was
ac
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iev
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with
o
u
t
ca
u
s
in
g
s
ig
n
if
ican
t
d
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s
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wh
ich
is
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er
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h
is
f
in
d
in
g
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alid
ate
d
in
[
1
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,
[
9
]
,
[
1
2
]
,
wh
er
e
v
o
lta
g
e
d
ev
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n
is
in
cr
e
ased
wh
en
L
max
is
lo
wer
.
T
h
e
f
o
cu
s
o
n
v
o
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e
s
tab
ilit
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ca
m
e
at
a
h
ig
h
er
co
s
t
o
f
2
.
7
0
8
8
m
illi
o
n
USD/h
an
d
in
cr
ea
s
ed
p
o
wer
lo
s
s
es
(
1
.
1
3
1
6
MW)
co
m
p
ar
ed
to
C
ase
1
b
u
t
lo
wer
th
an
C
ase
2
.
T
h
is
in
d
icate
s
th
at
wh
ile
th
e
s
y
s
tem
p
r
io
r
itized
lo
n
g
-
ter
m
v
o
ltag
e
s
tab
ilit
y
,
it
s
till
m
an
ag
ed
to
m
ain
tain
r
ea
s
o
n
ab
le
p
o
wer
lo
s
s
lev
els,
b
ala
n
cin
g
s
tab
ilit
y
an
d
ef
f
icien
cy
ef
f
ec
ti
v
ely
.
T
h
e
im
p
r
o
v
em
e
n
t
in
s
tab
ilit
y
is
cr
u
cial
f
o
r
s
y
s
tem
r
eliab
ilit
y
,
esp
ec
ially
u
n
d
er
v
ar
y
in
g
lo
ad
co
n
d
itio
n
s
.
3
.
5
.
Act
i
v
e
po
wer
lo
s
s
deprec
ia
t
io
n
R
ed
u
cin
g
lo
s
s
es
is
cr
u
cial
f
o
r
im
p
r
o
v
in
g
th
e
o
v
er
all
ef
f
icie
n
cy
o
f
t
h
e
p
o
wer
g
r
id
an
d
en
s
u
r
in
g
th
at
m
o
r
e
o
f
t
h
e
g
en
e
r
ated
p
o
wer
r
ea
ch
es
co
n
s
u
m
er
s
.
I
n
C
ase
4
,
t
h
e
s
y
s
tem
aim
ed
to
m
in
im
ize
ac
tiv
e
p
o
wer
lo
s
s
es.
T
h
is
ef
f
o
r
t
led
to
th
e
lo
west
p
o
wer
lo
s
s
am
o
n
g
a
ll
ca
s
es,
wit
h
a
v
alu
e
o
f
0
.
3
4
2
3
MW,
as
in
d
icate
d
in
T
ab
le
1
.
B
y
m
in
im
izin
g
th
ese
lo
s
s
es,
th
e
s
y
s
tem
im
p
r
o
v
e
d
o
v
er
all
e
f
f
icien
cy
,
r
e
d
u
cin
g
waste
in
en
er
g
y
tr
a
n
s
m
is
s
io
n
.
T
h
is
ac
h
iev
em
en
t
r
e
f
lects
th
e
ef
f
ec
tiv
en
ess
o
f
o
p
tim
ized
d
i
s
p
atch
s
tr
ateg
ies,
p
ar
ticu
la
r
ly
in
th
e
ad
ju
s
tm
en
ts
m
ad
e
to
th
e
p
o
wer
o
u
t
p
u
ts
P
1
to
P
38
,
wh
ich
wer
e
k
ep
t
r
elativ
ely
lo
w,
ex
ce
p
t
f
o
r
P
1
at
2
2
.
8
7
4
MW.
Sin
ce
P
1
is
clo
s
e
to
th
e
lo
ad
b
u
s
o
f
b
u
s
3
1
-
3
5
,
th
e
o
u
tp
u
t
o
f
th
e
o
th
e
r
p
o
w
er
p
lan
t
b
eh
i
n
d
th
e
r
ea
cta
n
ce
m
ig
h
t
b
e
m
in
im
ized
as sam
e
in
[
9
]
.
T
h
e
v
o
ltag
e
p
r
o
f
ile
in
C
ase
4
,
p
r
esen
ted
in
Fig
u
r
e
2
,
s
h
o
ws
a
s
tab
le
s
y
s
tem
with
m
in
im
al
v
o
ltag
e
d
ev
iatio
n
.
Mo
s
t
b
u
s
es
m
ain
tain
ed
a
v
o
ltag
e
clo
s
e
to
1
.
0
4
p
.
u
.
,
ex
ce
p
t
f
o
r
a
s
lig
h
t d
r
o
p
at
b
u
s
3
0
(
0
.
9
9
4
2
p
.
u
.
)
.
T
h
ese
r
esu
lts
in
d
icate
th
at
p
o
wer
lo
s
s
m
in
im
iz
atio
n
d
id
n
o
t
co
m
e
at
th
e
ex
p
en
s
e
o
f
v
o
ltag
e
s
tab
ilit
y
,
s
h
o
wca
s
in
g
th
e
ef
f
icien
cy
o
f
th
e
s
y
s
tem
in
m
an
ag
in
g
b
o
th
o
b
jectiv
es
s
im
u
ltan
eo
u
s
ly
.
Ho
wev
er
,
th
is
im
p
r
o
v
em
e
n
t
in
p
o
wer
lo
s
s
r
ed
u
ctio
n
ca
m
e
at
th
e
h
ig
h
est
o
p
er
atio
n
al
co
s
t,
r
ea
ch
in
g
2
.
9
2
1
3
m
illi
o
n
USD/
h
.
T
h
is
r
ef
lects
th
e
ty
p
ical
tr
ad
e
-
o
f
f
wh
er
e
m
in
im
izin
g
lo
s
s
es
o
f
ten
r
eq
u
ir
es
h
ig
h
er
i
n
v
estme
n
t
in
r
eso
u
r
ce
s
an
d
c
o
n
tr
o
l
m
ec
h
a
n
is
m
s
.
W
h
ile
th
e
co
s
t
was
s
u
b
s
tan
ti
al,
th
e
b
en
ef
it
o
f
r
ed
u
cin
g
en
er
g
y
waste
ca
n
ju
s
tify
th
e
ex
p
en
s
e,
esp
ec
ially
i
n
s
y
s
tem
s
wh
er
e
p
o
wer
lo
s
s
es r
ep
r
esen
t a
s
ig
n
if
ican
t o
p
er
atio
n
al
ch
allen
g
e.
3
.
6
.
Ass
ess
m
ent
s
um
m
a
ry
E
ac
h
o
f
th
e
f
o
u
r
ca
s
es
p
r
esen
ted
d
if
f
er
en
t
tr
a
d
e
-
o
f
f
s
b
etwe
en
co
s
t,
v
o
ltag
e
s
tab
ilit
y
,
v
o
ltag
e
d
ev
iatio
n
,
an
d
p
o
wer
lo
s
s
es.
I
n
C
ase
1
,
th
e
f
o
cu
s
was
o
n
m
in
im
izin
g
f
u
el
co
s
ts
,
r
esu
ltin
g
in
r
elativ
ely
s
tab
le
v
o
ltag
e
p
r
o
f
iles
b
u
t
h
ig
h
er
p
o
wer
lo
s
s
es.
C
ase
2
a
im
ed
to
im
p
r
o
v
e
v
o
ltag
e
d
ev
iatio
n
,
ac
h
iev
in
g
b
etter
v
o
ltag
e
u
n
if
o
r
m
ity
at
th
e
ex
p
en
s
e
o
f
h
ig
h
er
co
s
ts
an
d
p
o
wer
lo
s
s
es.
C
ase
3
em
p
h
asized
v
o
ltag
e
s
tab
ilit
y
,
lead
in
g
to
im
p
r
o
v
e
d
s
y
s
tem
r
eliab
ilit
y
,
t
h
o
u
g
h
with
a
m
o
d
er
ate
in
cr
ea
s
e
in
co
s
ts
an
d
p
o
wer
lo
s
s
es.
C
ase
4
,
f
o
cu
s
ed
o
n
m
in
im
izin
g
ac
tiv
e
p
o
wer
lo
s
s
es,
ac
h
iev
ed
th
e
b
est p
er
f
o
r
m
a
n
ce
in
ter
m
s
o
f
ef
f
icien
cy
b
u
t i
n
cu
r
r
e
d
th
e
h
ig
h
est
o
p
er
atio
n
al
c
o
s
ts
.
T
h
e
v
o
ltag
e
p
r
o
f
ile
r
em
ai
n
ed
s
tab
le
an
d
th
e
s
y
s
tem
was a
b
le
to
m
in
im
ize
lo
s
s
es.
E
ac
h
ca
s
e
d
em
o
n
s
tr
ates
a
u
n
iq
u
e
a
p
p
r
o
ac
h
to
o
p
tim
izin
g
d
if
f
er
en
t
asp
ec
ts
o
f
p
o
wer
s
y
s
tem
p
er
f
o
r
m
an
ce
,
h
ig
h
lig
h
tin
g
th
e
b
alan
ce
b
etwe
en
o
p
er
atio
n
al
c
o
s
ts
,
s
y
s
tem
r
eliab
ilit
y
,
an
d
ef
f
icien
cy
.
Ho
wev
e
r
,
th
e
r
esu
lts
s
h
o
w
th
at
th
er
e
is
n
o
o
n
e
-
s
ize
-
f
its
-
all
s
o
lu
t
io
n
,
an
d
ea
ch
o
p
tim
izatio
n
g
o
al
h
as
its
b
en
ef
its
an
d
d
r
awb
ac
k
s
.
Dep
e
n
d
in
g
o
n
th
e
p
r
io
r
ities
o
f
a
p
o
wer
s
y
s
tem
,
o
p
er
at
o
r
s
ca
n
c
h
o
o
s
e
t
h
e
ap
p
r
o
p
r
iate
s
tr
ateg
y
to
m
in
im
ize
co
s
ts
,
im
p
r
o
v
e
v
o
ltag
e
p
er
f
o
r
m
an
ce
,
o
r
r
e
d
u
ce
lo
s
s
es,
k
ee
p
in
g
in
m
in
d
th
e
as
s
o
ciate
d
tr
ad
e
-
o
f
f
s
.
Fro
m
a
s
y
s
tem
-
lev
el
p
er
s
p
ec
tiv
e,
th
e
r
esu
lts
in
d
icate
th
at
t
h
e
in
clu
s
io
n
o
f
g
as
en
g
in
e
p
o
wer
p
lan
ts
p
lay
s
a
s
ig
n
if
ican
t
r
o
le
in
en
h
an
cin
g
g
r
id
f
lex
ib
ilit
y
an
d
o
p
e
r
atio
n
al
p
er
f
o
r
m
an
ce
.
C
o
m
p
ar
e
d
to
tr
ad
itio
n
al
g
en
er
atio
n
d
is
p
atch
,
g
as
en
g
in
e
u
n
its
p
r
o
v
id
e
ef
f
ec
tiv
e
s
u
p
p
o
r
t
f
o
r
v
o
ltag
e
r
eg
u
latio
n
a
n
d
l
o
s
s
r
ed
u
ctio
n
d
u
e
t
o
th
ei
r
p
r
o
x
im
ity
to
lo
a
d
ce
n
ter
s
an
d
ad
ju
s
tab
le
o
u
tp
u
t
ca
p
ab
ilit
y
.
T
h
e
r
elativ
e
p
er
f
o
r
m
an
ce
im
p
r
o
v
em
en
ts
o
b
s
er
v
e
d
ac
r
o
s
s
th
e
f
o
u
r
ca
s
es
h
ig
h
lig
h
t
th
at
g
as
en
g
in
e
p
en
etr
atio
n
,
w
h
en
o
p
tim
ally
d
is
p
atch
ed
u
s
in
g
th
e
SO
-
b
ased
OPF
ap
p
r
o
ac
h
,
co
n
t
r
ib
u
tes
n
o
t
o
n
l
y
to
ec
o
n
o
m
ic
b
en
e
f
its
b
u
t
also
to
im
p
r
o
v
e
d
v
o
ltag
e
s
tab
ili
ty
an
d
tr
an
s
m
is
s
io
n
ef
f
icien
cy
.
I
n
ad
d
itio
n
t
o
ab
s
o
lu
te
p
er
f
o
r
m
an
ce
ev
al
u
atio
n
,
a
r
elativ
e
a
n
aly
s
is
is
p
er
f
o
r
m
e
d
to
co
n
tex
tu
alize
th
e
ef
f
ec
tiv
en
ess
o
f
th
e
p
r
o
p
o
s
ed
s
n
ak
e
o
p
tim
izatio
n
(
SO)
-
b
as
ed
OPF
ap
p
r
o
ac
h
.
Acr
o
s
s
th
e
f
o
u
r
ca
s
es,
th
e
SO
alg
o
r
ith
m
d
em
o
n
s
tr
ates
a
co
n
s
is
ten
t
tr
ad
e
-
o
f
f
b
etwe
en
ec
o
n
o
m
ic
an
d
tech
n
ical
o
b
jectiv
es.
C
ase
2
ac
h
iev
es
a
3
9
.
3
%
r
e
d
u
ctio
n
in
v
o
ltag
e
d
ev
iatio
n
co
m
p
ar
ed
to
C
ase
1
,
at
th
e
ex
p
en
s
e
o
f
in
cr
ea
s
ed
f
u
el
co
s
t
an
d
p
o
wer
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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n
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8
7
9
2
Tech
n
o
-
ec
o
n
o
mic
a
s
s
ess
men
t o
f g
a
s
en
g
i
n
e
p
o
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er p
la
n
ts
p
e
n
etra
tio
n
…
(
A
d
el
h
a
r
d
B
en
i R
eh
ia
r
a
)
543
lo
s
s
es.
C
a
s
e
3
f
u
r
th
er
im
p
r
o
v
e
s
v
o
ltag
e
s
tab
ilit
y
b
y
a
p
p
r
o
x
im
ately
6
2
.
6
%
r
elativ
e
to
C
ase
2
with
m
o
d
er
ate
co
s
t
in
cr
ea
s
es.
Mo
r
eo
v
er
,
C
ase
4
attain
s
a
9
6
.
7
%
r
ed
u
ctio
n
in
ac
tiv
e
p
o
wer
l
o
s
s
es
co
m
p
ar
ed
to
C
ase
1
,
h
ig
h
lig
h
tin
g
th
e
s
tr
o
n
g
ca
p
ab
ilit
y
o
f
SO in
lo
s
s
m
in
im
izatio
n
.
Fro
m
a
m
eth
o
d
o
lo
g
ical
p
er
s
p
e
ctiv
e,
th
e
r
esu
lts
ar
e
co
m
p
etiti
v
e
with
o
th
er
m
eta
-
h
eu
r
is
tic
-
b
ased
OPF
ap
p
r
o
ac
h
es,
s
u
ch
as
PS
O,
g
r
ey
wo
lf
o
p
tim
izer
,
an
d
teac
h
in
g
–
lear
n
in
g
-
b
ased
o
p
tim
izatio
n
[
1
2
]
,
[
1
5
]
,
[
1
7
]
,
[
2
2
]
.
Alth
o
u
g
h
d
ir
ec
t
n
u
m
er
ical
co
m
p
ar
is
o
n
is
co
n
s
tr
ain
e
d
b
y
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if
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er
en
ce
s
in
s
y
s
tem
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n
f
ig
u
r
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s
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d
o
b
jectiv
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th
e
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el
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t,
v
o
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a
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s
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p
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in
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liter
at
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r
e.
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h
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n
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ir
m
s
th
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r
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ased
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CO
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in
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o
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u
tili
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f
r
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h
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alg
o
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ith
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im
p
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ac
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s
k
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er
f
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m
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ce
m
etr
ics.
T
h
e
ass
ess
m
en
t
f
o
cu
s
ed
o
n
f
o
u
r
cr
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l
o
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m
in
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f
u
el
co
s
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cin
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SO
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m
d
em
o
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it
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ef
f
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tiv
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in
o
p
tim
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t
h
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g
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’
s
o
p
er
atio
n
al
ef
f
icien
c
y
wh
ile
ad
d
r
ess
in
g
b
o
th
ec
o
n
o
m
ic
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n
d
tech
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ch
allen
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teg
r
a
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o
f
g
as e
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p
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p
lan
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s
.
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lts
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ly
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ate
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im
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m
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f
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Ma
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h
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t
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p
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led
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ticea
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p
r
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f
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t
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el
co
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t
m
in
im
izatio
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iev
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th
r
o
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g
h
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lan
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to
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o
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o
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r
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th
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th
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o
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ac
r
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tan
tially
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th
e
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v
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o
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ir
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ig
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ax
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y
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wer
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im
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to
0
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3
4
2
3
MW,
r
ef
lectin
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in
cr
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o
u
t
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y
th
e
p
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g
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in
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in
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atin
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s
ec
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n
o
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ic
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u
tco
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u
t a
ls
o
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ig
n
if
ic
an
tly
im
p
r
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v
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e
tech
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s
tab
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d
ef
f
icien
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f
th
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s
y
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tem
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l,
th
e
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tu
d
y
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ir
m
s
th
at
g
as
en
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o
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lan
ts
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r
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l
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in
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o
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lex
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ec
o
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o
m
ically
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icien
t
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at
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eso
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if
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tly
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n
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o
t
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tech
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ical
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m
an
ce
o
f
p
r
ac
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p
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g
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ch
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lan
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o
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ce
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n
d
er
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ig
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d
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i
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el
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.
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r
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ay
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o
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p
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m
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o
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ac
tical
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m
ar
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Dep
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tm
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Un
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Pap
u
a
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Un
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s
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ab
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s
ig
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ts
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n
d
ex
p
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tis
e,
wh
ich
s
ig
n
if
ican
tly
co
n
tr
ib
u
ted
to
th
e
s
u
cc
ess
o
f
t
h
is
r
esear
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.
F
UNDING
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NF
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Au
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AUTHO
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C
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to
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tio
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s
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r
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au
th
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s
h
ip
d
is
p
u
tes,
an
d
f
ac
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co
llab
o
r
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n
.
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