I
nte
rna
t
io
na
l J
o
urna
l o
f
E
lect
rica
l a
nd
Co
m
p
ute
r
E
ng
in
ee
ring
(
I
J
E
CE
)
Vo
l.
8
,
No
.
4
,
A
u
g
u
s
t
201
8
,
p
p
.
1
9
8
5
~1
9
9
6
I
SS
N:
2
0
8
8
-
8708
,
DOI
: 1
0
.
1
1
5
9
1
/
i
j
ec
e
.
v8
i
4
.
p
p
1
9
8
5
-
1996
1985
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ia
e
s
co
r
e
.
co
m/
jo
u
r
n
a
ls
/in
d
ex
.
p
h
p
/
I
JE
C
E
Relia
bility
C
o
nst
r
a
ined
U
nit
C
o
mm
it
m
ent
C
o
nsideri
ng
t
he
E
ff
ec
t
o
f
DG
a
nd
DR
P
ro
g
ra
m
M
a
s
o
ud
Alia
kb
a
ri
1
,
P
o
uria
M
a
g
ho
uli
2
,
H
a
bib
Alla
h Aa
la
m
i
3
1
De
p
a
rtme
n
t
o
f
e
lec
tr
ica
l
e
n
g
in
e
e
rin
g
,
Isla
m
ic
A
z
a
d
U
n
iv
e
rsit
y
,
S
a
v
e
h
,
Ira
n
2
De
p
a
rtme
n
t
o
f
e
lec
tri
c
a
l
e
n
g
in
e
e
rin
g
,
S
h
a
h
e
d
U
n
iv
e
rsit
y
,
T
e
h
ra
n
,
Ira
n
3
De
p
a
rtme
n
t
o
f
e
lec
tri
c
a
l
e
n
g
in
e
e
rin
g
,
Ey
v
a
n
e
k
e
y
U
n
iv
e
rsit
y
,
Teh
ra
n
,
Ira
n
Art
icle
I
nfo
AB
ST
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
J
un
26
,
2
0
1
7
R
ev
i
s
ed
J
an
19
,
2
0
1
8
A
cc
ep
ted
J
an
26
,
2
0
1
8
Du
e
to
in
c
re
a
se
in
e
n
e
rg
y
p
rice
s
a
t
p
e
a
k
p
e
rio
d
s
a
n
d
in
c
re
a
se
in
f
u
e
l
c
o
st,
in
v
o
lv
in
g
Distrib
u
te
d
G
e
n
e
ra
ti
o
n
(DG
)
a
n
d
c
o
n
su
m
p
ti
o
n
m
a
n
a
g
e
m
e
n
t
b
y
De
m
a
n
d
Re
sp
o
n
se
(DR)
w
il
l
b
e
u
n
a
v
o
id
a
b
le
o
p
ti
o
n
s
f
o
r
o
p
ti
m
a
l
s
y
ste
m
o
p
e
ra
ti
o
n
s.
A
lso
,
w
it
h
h
ig
h
p
e
n
e
tratio
n
o
f
D
G
s
a
n
d
DR
p
ro
g
ra
m
s
in
to
p
o
w
e
r
s
y
ste
m
o
p
e
ra
ti
o
n
,
t
h
e
re
li
a
b
il
it
y
c
rit
e
rio
n
is
tak
e
n
in
t
o
a
c
c
o
u
n
t
a
s
o
n
e
o
f
th
e
m
o
st
i
m
p
o
rtan
t
c
o
n
c
e
rn
s
o
f
s
y
ste
m
o
p
e
ra
to
rs
in
m
a
n
a
g
e
m
e
n
t
o
f
p
o
w
e
r
s
y
ste
m
.
In
th
is
p
a
p
e
r,
a
Re
li
a
b
i
li
t
y
Co
n
st
ra
in
e
d
Un
it
C
o
m
m
it
m
e
n
t
(RCUC)
a
t
p
re
se
n
c
e
o
f
ti
m
e
-
b
a
s
e
d
DR
p
ro
g
ra
m
a
n
d
D
G
s
in
teg
ra
ted
w
it
h
c
o
n
v
e
n
ti
o
n
a
l
u
n
it
s
is
p
r
o
p
o
se
d
a
n
d
e
x
e
c
u
ted
t
o
re
a
c
h
a
re
li
a
b
le
a
n
d
e
c
o
n
o
m
ic
o
p
e
ra
ti
o
n
.
De
sig
n
a
ted
c
o
st
f
u
n
c
ti
o
n
h
a
s
b
e
e
n
m
in
im
i
z
e
d
c
o
n
sid
e
rin
g
re
li
a
b
il
it
y
c
o
n
stra
in
t
i
n
p
re
v
a
il
in
g
UC
f
o
r
m
u
latio
n
.
T
h
e
UC
sc
h
e
d
u
li
n
g
is
a
c
c
o
m
p
li
sh
e
d
in
sh
o
rt
-
term
so
th
a
t
th
e
re
li
a
b
il
it
y
is
m
a
in
tain
e
d
in
a
c
c
e
p
tab
le
lev
e
l.
Be
c
a
u
se
o
f
c
o
m
p
lex
n
a
tu
re
o
f
RCUC
p
ro
b
lem
a
n
d
f
u
ll
A
C
lo
a
d
f
lo
w
c
o
n
stra
in
ts,
th
e
h
y
b
rid
a
lg
o
rit
h
m
in
c
lu
d
e
d
S
im
u
late
d
A
n
n
e
a
li
n
g
(S
A
)
a
n
d
Bin
a
ry
P
a
rti
c
le
S
w
a
r
m
Op
ti
m
iz
a
ti
o
n
(B
P
S
O)
h
a
s
b
e
e
n
p
ro
p
o
se
d
t
o
o
p
ti
m
ize
th
e
p
ro
b
lem
.
Nu
m
e
ric
a
l
re
su
lt
s
d
e
m
o
n
stra
te
th
e
e
ff
e
c
ti
v
e
n
e
ss
o
f
th
e
p
ro
p
o
se
d
m
e
th
o
d
a
n
d
c
o
n
sid
e
ra
b
le
e
f
f
ica
c
y
o
f
th
e
ti
m
e
-
b
a
se
d
DR
p
ro
g
ra
m
in
re
d
u
c
i
n
g
o
p
e
ra
ti
o
n
a
l
co
sts b
y
i
m
p
le
m
e
n
ti
n
g
it
o
n
IEE
E
-
RT
S
7
9
.
K
ey
w
o
r
d
:
De
m
a
n
d
r
esp
o
n
s
e
p
r
o
g
r
a
m
Dis
tr
ib
u
ted
en
er
g
y
r
e
s
o
u
r
ce
s
O
p
er
atio
n
P
ar
ticle
s
w
ar
m
o
p
ti
m
izatio
n
R
eliab
le
an
d
e
co
n
o
m
ic
S
i
m
u
lated
a
n
n
ea
li
n
g
Un
it c
o
m
m
i
t
m
e
n
t
Co
p
y
rig
h
t
©
2
0
1
8
In
stit
u
te o
f
A
d
v
a
n
c
e
d
E
n
g
i
n
e
e
rin
g
a
n
d
S
c
ien
c
e
.
Al
l
rig
h
ts
re
se
rv
e
d
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Ma
s
o
u
d
A
lia
k
b
ar
i
,
Dep
ar
t
m
en
t o
f
E
lectr
ical
an
d
C
o
m
p
u
ter
E
n
g
in
ee
r
i
n
g
,
I
s
la
m
ic
A
za
d
u
n
i
v
er
s
it
y
,
Un
i
v
er
s
it
y
ca
m
p
u
s
,
B
lv
d
.
S
h
a
h
id
Fah
m
id
a
h
,
B
lv
d
.
Sh
a
h
id
B
eh
es
h
ti,
Sa
v
eh
,
I
r
an
.
E
m
ail:
m
.
alia
k
b
ar
i.3
6
5
@
g
m
ai
l
.
co
m
NO
M
E
NCLAT
UR
E
S
1
)
I
n
d
ices
Ho
u
r
s
co
u
n
ter
s
at
DR
a
n
d
R
C
UC
T
h
e
in
er
tial o
f
x
th
p
ar
ticle
Un
it
s
co
u
n
ter
E
lectr
icit
y
p
r
ice
in
a
th
h
o
u
r
af
t
er
DR
(
$
/MW
h
)
B
u
s
in
d
ice
s
in
L
o
ad
Flo
w
eq
u
atio
n
E
lectr
icit
y
p
r
ice
in
a
th
h
o
u
r
b
ef
o
r
e
DR
(
$
/MW
h
)
State
o
f
C
OP
T
3
)
P
a
r
am
eter
s
P
ar
ticles co
u
n
ter
in
P
SO
C
o
ld
s
tar
t
-
u
p
co
s
t o
f
u
n
it
n
I
ter
atio
n
L
o
ad
d
e
m
an
d
at
ti
m
e
t
2
)
Var
iab
les
Do
w
n
r
ate
o
f
n
th
u
n
it p
er
h
o
u
r
C
o
s
t f
u
n
ctio
n
o
f
g
e
n
er
atio
n
u
n
it n
Self
-
ela
s
ticit
y
C
o
g
n
iti
v
e
an
d
s
o
cial
lear
n
in
g
r
ates
C
r
o
s
s
ela
s
t
icit
y
o
f
th
e
d
e
m
an
d
b
et
w
ee
n
ab
th
h
o
u
r
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
8
,
No
.
4
,
A
u
g
u
s
t 2
0
1
8
:
1
9
8
5
–
1
9
9
6
1986
C
u
s
to
m
er
d
e
m
a
n
d
in
at
h
h
o
u
r
af
ter
DR
(
MW
h
)
Ho
t star
t
-
u
p
co
s
t o
f
u
n
it
n
C
u
s
to
m
er
d
e
m
a
n
d
in
at
h
h
o
u
r
b
ef
o
r
e
DR
(
MW
h
)
Min
i
m
u
m
u
p
ti
m
e
T
h
e
b
est o
b
tain
ed
v
alu
e
o
f
o
b
j
ec
tiv
e
f
u
n
c
tio
n
o
v
er
P
SO
p
r
o
ce
d
u
r
e
Min
i
m
u
m
d
o
w
n
t
i
m
e
Statu
s
o
f
u
n
it
n
at
h
o
u
r
t
Nu
m
b
er
o
f
b
u
s
es
A
cti
v
e
p
o
w
er
lo
s
s
o
f
t
h
e
s
y
s
te
m
Nu
m
b
er
o
f
g
e
n
er
ato
r
s
Ou
tp
u
t a
ctiv
e
p
o
w
er
o
f
DG
u
n
it n
at
h
o
u
r
t
Nu
m
b
er
o
f
D
G
u
n
its
Ou
tp
u
t a
ctiv
e
p
o
w
er
o
f
g
e
n
er
a
to
r
n
at
h
o
u
r
t
T
o
tal
n
u
m
b
er
o
f
p
ar
ticles
T
h
e
b
est p
r
ev
io
u
s
p
o
s
itio
n
o
f
t
h
e
x
th
p
ar
ticle
Ma
x
i
m
u
m
a
n
d
m
i
n
i
m
u
m
r
ea
ct
iv
e
p
o
w
er
g
en
er
atio
n
li
m
it o
f
u
n
it n
T
h
e
p
r
o
b
ab
ilit
y
o
f
w
o
r
s
e
a
n
s
wer
ac
ce
p
tin
g
Ma
x
i
m
u
m
a
n
d
m
i
n
i
m
u
m
r
ea
ct
iv
e
p
o
w
er
g
en
er
atio
n
DG
li
m
it o
f
u
n
it n
P
o
w
er
f
lo
w
o
n
ij
th
li
n
e
Ma
x
i
m
u
m
ap
p
ar
en
t p
o
w
er
f
lo
w
f
o
r
ij
th
lin
e
Sp
in
n
in
g
r
eser
v
e
at
h
o
u
r
t
Star
tu
p
co
s
t o
f
u
n
i
t n
at
h
o
u
r
t
Du
r
atio
n
o
f
co
n
ti
n
u
o
u
s
l
y
o
f
f
s
tate
o
f
u
n
it n
at
h
o
u
r
t
Sch
ed
u
l
in
g
p
er
io
d
Du
r
atio
n
o
f
co
n
ti
n
u
o
u
s
l
y
o
n
s
t
ate
o
f
u
n
it n
at
h
o
u
r
t
I
n
itial te
m
p
er
atu
r
e
o
f
S
A
Vo
ltag
e
m
a
g
n
it
u
d
e
at
b
u
s
j
T
h
e
s
tep
f
o
r
r
ed
u
cin
g
te
m
p
er
atu
r
e
Velo
cit
y
o
f
x
th
p
ar
ticle
in
it
th
iter
atio
n
Up
r
ate
o
f
n
th
u
n
it p
er
h
o
u
r
P
o
s
itio
n
o
f
x
th
p
ar
ticle
i
n
it
th
iter
atio
n
Ma
x
i
m
u
m
a
n
d
m
i
n
i
m
u
m
l
i
m
i
t
s
f
o
r
v
o
lta
g
e
m
ag
n
it
u
d
e
at
b
u
s
j
Ne
w
tr
ial
s
o
lu
tio
n
o
f
p
ar
ticle
Valu
e
o
f
lo
s
t lo
ad
C
u
r
r
en
t tr
ial
s
o
lu
tio
n
o
f
p
ar
ticl
e
ij
th
ar
r
ay
o
f
ad
m
itta
n
ce
m
atr
ix
Vo
ltag
e
an
g
le
o
f
b
u
s
j
S
ea
r
ch
i
n
g
i
n
te
n
s
i
f
ier
p
ar
a
m
ete
r
An
g
le
o
f
ij
th
ar
r
ay
o
f
ad
m
itta
n
ce
m
atr
i
x
Up
p
er
an
d
lo
w
er
v
o
ltag
e
a
n
g
l
e
li
m
it
s
o
f
b
u
s
j
1.
I
NT
RO
D
UCT
I
O
N
I
n
r
estru
ctu
r
ed
an
d
co
m
p
etitiv
e
en
v
ir
o
n
m
en
t,
it
is
n
ec
ess
ar
y
to
s
u
p
p
ly
th
e
elec
tr
ical
d
em
an
d
in
co
n
tin
u
o
u
s
,
r
eliab
le
an
d
ec
o
n
o
m
ic
m
an
n
er
.
Un
it
co
m
m
itm
en
t
is
o
n
e
o
f
th
e
av
ailab
le
m
ea
s
u
r
es
to
r
ea
ch
th
e
m
en
tio
n
ed
g
o
al.
I
n
UC
p
r
o
ce
d
u
r
e,
th
er
m
al
g
en
er
atin
g
u
n
its
a
r
e
s
ch
ed
u
led
to
g
en
er
ate
p
o
w
er
at
m
in
im
u
m
o
p
er
atio
n
co
s
t
s
o
th
at
all
co
n
s
tr
ain
ts
o
f
th
e
s
y
s
tem
an
d
s
p
in
n
in
g
r
eser
v
e
r
eq
u
ir
em
en
ts
ar
e
s
atis
f
ied
.
I
n
p
o
w
er
s
y
s
tem
o
p
er
atio
n
s
,
r
eliab
ilit
y
is
o
n
e
o
f
th
e
m
o
s
t
im
p
o
r
tan
t
ch
allen
g
es
w
h
ich
ca
n
n
o
t
b
e
n
eg
lecte
d
b
y
th
e
s
y
s
tem
o
p
er
ato
r
.
Hu
g
e
in
v
estm
en
t
co
s
ts
in
lar
g
e
p
o
w
er
p
lan
t
an
d
th
e
w
asted
p
o
w
er
in
th
e
f
o
r
m
o
f
p
o
w
er
lo
s
s
es
h
av
e
ca
u
s
ed
r
em
ar
k
ab
le
p
ar
ticip
atio
n
o
f
Dis
tr
ib
u
ted
E
n
er
g
y
R
eso
u
r
ce
s
(
DE
R
s
)
in
p
o
w
er
g
r
id
co
n
f
ig
u
r
atio
n
.
B
y
r
ap
id
d
ev
elo
p
m
en
t
o
f
em
er
g
in
g
n
ew
tech
n
o
lo
g
ies,
th
e
r
eliab
ilit
y
is
s
u
es
h
av
e
h
ig
h
lig
h
ted
m
o
r
e
th
an
b
ef
o
r
e.
A
lar
g
e
n
u
m
b
er
o
f
in
v
esti
g
atio
n
s
co
n
s
id
er
in
g
th
e
v
ar
iety
ty
p
e
o
f
UC
p
r
o
b
lem
h
av
e
b
ee
n
p
er
f
o
r
m
ed
.
T
h
e
s
tate
-
tr
an
s
itio
n
f
o
r
m
u
latio
n
f
o
r
th
e
u
n
it
co
m
m
itm
en
t
(
UC
)
p
r
o
b
lem
is
p
r
esen
ted
in
[
1
]
w
ith
n
ew
d
ec
is
io
n
v
ar
iab
les
i
n
s
tead
o
f
g
en
er
ato
r
’
s
o
n
/o
f
f
s
tatu
s
es
.
T
h
e
in
teg
r
atio
n
o
f
s
o
lar
en
er
g
y
r
eso
u
r
ce
s
in
to
th
e
co
n
v
en
tio
n
al
u
n
it
co
m
m
itm
en
t
is
p
r
o
p
o
s
ed
in
[
2
]
as
an
alter
n
ativ
e
en
er
g
y
r
eso
u
r
ce
s
u
s
in
g
an
t
lio
n
o
p
tim
izer
w
ith
co
n
s
id
er
atio
n
o
f
u
n
ce
r
tai
n
ties
.
I
n
[
3
]
,
th
e
UC
p
r
o
b
lem
h
as
b
ee
n
f
o
r
m
u
lated
b
y
in
teg
r
atin
g
w
in
d
p
o
w
er
g
en
er
ato
r
s
alo
n
g
w
ith
th
er
m
al
p
o
w
er
s
y
s
tem
u
s
in
g
g
r
ey
w
o
lf
o
p
tim
izatio
n
alg
o
r
ith
m
as
th
e
m
ain
o
p
tim
izatio
n
to
o
l.
A
u
th
o
r
s
in
[
4
]
f
o
cu
s
ed
o
n
s
o
lv
in
g
ef
f
icien
tly
u
n
it
co
m
m
itm
en
t
o
f
th
e
in
ter
co
n
n
ec
ted
m
u
lti
-
s
ite
C
HP
s
y
s
tem
to
co
o
r
d
in
ate
h
ea
t
an
d
p
o
w
er
p
r
o
d
u
ctio
n
in
ea
ch
s
ite
u
s
in
g
r
elax
ed
ON/OFF
s
tate
b
ased
d
y
n
am
ic
p
r
o
g
r
am
m
in
g
.
A
co
n
tin
g
en
cy
-
co
n
s
tr
ain
ed
UC
is
s
o
lv
ed
in
[
5
]
w
ith
co
n
s
id
er
in
g
a
s
et
o
f
co
n
tin
g
en
cy
p
r
o
b
ab
ilit
y
d
is
tr
ib
u
tio
n
s
I
n
s
tead
o
f
ass
ig
n
in
g
a
p
r
o
b
ab
ilit
y
esti
m
ate
f
o
r
ea
ch
co
n
tin
g
en
cy
s
ce
n
ar
io
.
C
o
n
s
id
er
in
g
th
e
w
id
esp
r
ea
d
v
ar
iety
o
f
r
eso
u
r
ce
s
in
m
icr
o
g
r
id
s
,
a
m
u
lti
o
b
j
ec
tiv
e
UC
is
ca
r
r
ied
o
u
t
in
[
6
]
to
m
in
im
ize
th
e
o
p
er
atio
n
co
s
t
an
d
C
O
2
em
is
s
io
n
.
A
u
th
o
r
s
in
[
7
]
p
r
o
p
o
s
e
an
N
-
1
s
ec
u
r
ity
co
n
s
tr
ain
ed
f
o
r
m
u
latio
n
f
o
r
SC
UC
b
ased
o
n
th
e
l
in
e
o
u
tag
e
d
is
tr
ib
u
tio
n
Facto
r
s
in
s
tead
o
f
th
e
co
n
v
en
tio
n
al
m
eth
o
d
b
ased
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
R
elia
b
ilit
y
C
o
n
s
tr
a
in
ed
Un
it C
o
mmitmen
t Co
n
s
id
er
in
g
th
e
E
ffect
o
f D
G
a
n
d
DR
…
(
Ma
s
o
u
d
A
lia
k
b
a
r
i
)
1987
o
n
I
n
j
ec
tio
n
Sen
s
itiv
ity
Facto
r
s
.
A
r
ef
o
r
m
u
latio
n
o
f
th
e
s
ce
n
ar
io
-
b
ased
tw
o
-
s
tag
e
u
n
it
co
m
m
itm
en
t
p
r
o
b
lem
u
n
d
e
r
u
n
ce
r
tain
ty
is
p
r
o
v
id
ed
i
n
[
8
]
.
A
n
o
v
el
h
eu
r
is
tic
alg
o
r
ith
m
ca
lled
th
e
b
in
ar
y
a
r
tif
icial
s
h
ee
p
a
lg
o
r
ith
m
h
as
b
ee
n
u
s
ed
to
s
o
lv
e
th
e
UC
p
r
o
b
lem
in
[
9
]
.
I
n
[
10
]
a
n
o
v
el
b
r
an
ch
-
an
d
-
cu
t
alg
o
r
ith
m
u
s
in
g
atem
p
o
r
ally
d
ec
o
m
p
o
s
ed
b
ilev
el
s
ep
ar
atio
n
ar
ac
le
is
p
r
o
p
o
s
ed
to
s
o
lv
e
v
er
y
lar
g
e
s
ca
le
UC
p
r
o
b
lem
.
T
o
g
u
ar
an
tee
s
y
s
tem
s
ec
u
r
ity
an
d
r
eliab
ilit
y
,
au
th
o
r
s
in
[
1
1
]
h
av
e
b
ee
n
d
ev
elo
p
ed
s
u
f
f
icien
t
d
is
p
atch
ab
le
g
en
er
atio
n
an
d
tr
an
s
m
is
s
io
n
ca
p
ac
ities
to
im
p
r
o
v
e
s
y
s
tem
o
p
er
atio
n
al
p
er
f
o
r
m
an
ce
b
y
o
p
tim
izin
g
s
ch
ed
u
les
co
n
s
id
er
in
g
unc
er
tain
ty
o
f
w
in
d
p
o
w
er
.
A
u
th
o
r
s
in
[
1
2
]
h
av
e
b
ee
n
r
ec
o
m
m
en
d
ed
a
r
o
b
u
s
t
R
C
UC
at
p
r
esen
ce
o
f
m
u
ltip
le
DE
R
s
f
o
r
b
est
r
eso
u
r
ce
allo
ca
tio
n
an
d
r
eliab
ilit
y
m
ain
tain
in
g
in
a
p
r
ed
ef
in
ed
r
an
g
e.
L
ar
g
e
n
u
m
b
er
o
f
s
tu
d
ies
r
eg
ar
d
in
g
DE
R
s
m
an
ag
em
en
t
in
s
m
ar
t
g
r
id
h
as
b
ee
n
ca
r
r
ied
o
u
t
in
r
ec
en
t
y
ea
r
s
th
at
s
o
m
e
o
f
th
em
co
u
ld
b
e
b
r
ief
ly
s
u
r
v
ey
ed
as f
o
llo
w
s
.
A
m
eth
o
d
o
lo
g
y
to
o
b
tain
th
e
o
p
tim
al
lo
ca
tio
n
f
o
r
th
e
p
lace
m
en
t
o
f
m
u
ltip
le
DG
s
o
u
r
ce
s
in
a
d
is
tr
ib
u
tio
n
n
etw
o
r
k
is
p
r
o
p
o
s
ed
in
[
1
3
]
b
y
ev
alu
atin
g
a
g
lo
b
al
m
u
lti
-
o
b
j
ec
tiv
e
tech
n
ical
in
d
ex
u
s
in
g
ar
tif
icial
im
m
u
n
e
s
y
s
tem
.
T
h
e
DR
p
r
o
g
r
am
is
u
s
ed
to
o
p
tim
ize
th
e
en
er
g
y
p
r
o
f
ile
f
o
r
co
m
m
er
cial
s
ec
to
r
in
[
1
4
]
w
ith
r
ef
o
r
m
in
g
th
e
Ma
x
im
u
m
Dem
an
d
f
r
o
m
p
ea
k
zo
n
e
to
o
f
f
-
p
ea
k
zo
n
e
to
r
ed
u
ce
elec
tr
icity
co
s
t
u
s
in
g
E
v
o
lu
tio
n
ar
y
A
lg
o
r
ith
m
.
A
u
th
o
r
s
in
[
1
5
]
p
r
esen
t
th
e
u
tili
za
tio
n
o
f
d
em
an
d
r
esp
o
n
s
e
in
th
e
d
ay
-
ah
ea
d
o
p
er
atio
n
o
f
a
m
icr
o
-
g
r
id
in
th
e
p
r
esen
ce
o
f
r
en
ew
ab
le
en
er
g
y
s
o
u
r
ce
s
.
Dif
f
er
en
t
DR
p
r
o
g
r
am
s
m
o
d
elin
g
ar
e
p
r
o
p
o
s
ed
in
[
1
6
]
an
d
[
1
7
]
to
in
cr
ea
s
e
in
ef
f
icien
cy
o
f
en
er
g
y
co
n
s
u
m
p
tio
n
w
ith
m
in
im
u
m
o
p
er
atio
n
al
co
s
ts
an
d
d
esira
b
le
q
u
ality
.
T
o
th
e
b
est
o
f
o
u
r
k
n
o
w
led
g
e,
th
e
im
p
ac
t
o
f
tim
e
-
b
ased
DR
p
r
o
g
r
am
in
UC
p
r
o
ce
d
u
r
e
h
as
b
ee
n
r
ar
ely
s
tu
d
ied
an
d
in
v
esti
g
ated
.
So
,
in
th
is
p
ap
er
,
th
e
R
C
UC
is
s
ch
ed
u
led
at
p
r
esen
ce
o
f
DGs
an
d
tim
e
-
b
ased
DR
p
r
o
g
r
am
w
ith
f
u
ll
A
C
lo
ad
f
lo
w
co
n
s
tr
ain
ts
u
s
in
g
a
h
y
b
r
id
m
eth
o
d
.
T
h
e
m
ain
co
n
tr
ib
u
tio
n
o
f
th
is
p
ap
er
in
clu
d
es
in
co
r
p
o
r
atin
g
th
e
tim
e
-
b
ased
DR
p
r
o
g
r
am
in
UC
p
r
o
b
lem
an
d
u
tili
zin
g
a
h
y
b
r
id
m
eth
o
d
to
o
p
tim
ize
th
e
R
C
UC
Sch
ed
u
le.
I
n
o
r
d
er
to
illu
s
tr
ate
th
e
ef
f
ec
tiv
en
ess
o
f
th
e
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
,
it
is
ap
p
lied
to
I
E
E
E
R
eliab
ilit
y
T
est
Sy
s
tem
(
I
E
EE
-
R
T
S7
9
)
.
Fin
ally
,
a
co
m
p
ar
is
o
n
is
d
o
n
e
b
etw
ee
n
th
e
p
r
o
p
o
s
ed
o
p
tim
izatio
n
alg
o
r
ith
m
an
d
s
o
m
e
h
u
r
is
tic
alg
o
r
ith
m
s
.
T
h
e
r
em
ain
d
er
o
f
th
is
p
ap
er
is
s
tr
u
ctu
r
ed
as
f
o
llo
w
s
.
Sectio
n
2
b
r
ief
ly
d
is
cu
s
s
es
th
e
o
v
er
tu
r
e
o
f
DR
p
r
o
g
r
am
s
.
R
eliab
ilit
y
f
r
am
ew
o
r
k
s
ar
e
p
r
e
s
en
ted
in
s
ec
tio
n
3
.
Sectio
n
4
d
is
cu
s
s
es
th
e
p
r
o
p
o
s
ed
o
p
tim
izatio
n
alg
o
r
ith
m
an
d
th
e
o
b
j
ec
tiv
e
f
u
n
ctio
n
f
o
r
m
u
latio
n
.
Sectio
n
5
r
ep
r
esen
ts
th
e
n
u
m
er
ical
s
tu
d
ies
an
d
an
aly
s
is
o
f
o
b
tain
ed
an
s
w
er
s
an
d
Sectio
n
6
co
n
clu
d
es th
e
p
ap
er
.
2.
DR
P
RO
G
RAM
AND
E
CO
NO
M
I
C
M
O
DE
L
O
F
DE
M
AND
DR
p
r
o
g
r
a
m
s
ar
e
d
iv
id
ed
in
t
o
s
o
m
e
m
ain
ca
teg
o
r
ies
a
n
d
s
o
m
e
s
u
b
-
ca
teg
o
r
ies
b
a
s
ed
o
n
Fed
er
al
E
n
er
g
y
R
eg
u
lato
r
y
C
o
m
m
is
s
i
o
n
(
FER
C
)
cla
s
s
i
f
icatio
n
[
1
8
]
.
I
n
t
h
i
s
w
o
r
k
,
T
im
e
-
Of
-
Use
(
T
OU)
m
et
h
o
d
t
h
at
i
s
o
n
e
o
f
th
e
ti
m
e
-
b
ased
p
r
o
g
r
a
m
s
i
s
e
m
p
lo
y
ed
.
T
OU
ca
n
s
h
i
f
t
s
o
m
e
o
f
th
e
u
n
n
ec
es
s
ar
y
d
e
m
an
d
f
r
o
m
p
ea
k
lo
ad
p
er
io
d
to
lo
w
lo
ad
p
er
io
d
.
T
h
is
o
f
f
s
et
i
s
b
ec
au
s
e
o
f
c
u
s
to
m
e
r
’
s
d
e
m
a
n
d
s
e
n
s
iti
v
it
y
w
it
h
r
e
s
p
ec
t
to
elec
tr
icit
y
p
r
ice
ch
an
g
e
s
at
d
if
f
er
e
n
t
p
er
io
d
s
.
A
co
n
s
er
v
ati
v
e
m
o
d
el
o
f
lo
ad
h
as
b
ee
n
e
x
tr
ac
ted
as
r
esp
o
n
s
e
o
f
elas
tic
d
em
a
n
d
ag
a
in
s
t
t
h
e
p
r
ice
s
ig
n
als
e
x
p
o
u
n
d
ed
i
n
[
1
9
]
.
T
h
e
m
en
tio
n
ed
ec
o
n
o
m
ic
m
o
d
el
(
p
o
w
er
m
o
d
el)
is
co
m
p
o
s
ed
f
r
o
m
t
w
o
co
n
ce
p
t
s
,
s
in
g
le
p
er
io
d
an
d
m
u
lti
p
er
io
d
lo
ad
s
w
h
ich
ar
e
s
o
ca
lled
“self
-
ela
s
ticit
y
”
a
n
d
“
cr
o
s
s
elast
icit
y
”,
r
esp
ec
ti
v
el
y
.
T
h
e
lo
ad
s
w
it
h
s
e
lf
-
ela
s
tic
it
y
ca
n
n
o
t
s
h
i
f
t
f
r
o
m
o
n
e
p
er
io
d
to
an
o
th
er
(
e.
g
.
lig
h
ti
n
g
lo
ad
s
)
w
h
i
le
t
h
e
lo
ad
s
w
ith
cr
o
s
s
ela
s
ticit
y
ca
n
s
h
i
f
t
f
r
o
m
o
n
e
p
er
io
d
to
o
th
er
s
.
I
n
t
h
is
p
ap
er
,
to
av
o
id
r
estate
m
e
n
t
o
f
m
o
d
eli
n
g
p
r
o
ce
d
u
r
e,
f
in
a
l
ec
o
n
o
m
ic
m
o
d
e
ls
o
f
ea
c
h
co
n
ce
p
t
(
s
el
f
an
d
cr
o
s
s
elasticit
y
)
o
f
r
esp
o
n
s
iv
e
lo
ad
s
ar
e
g
i
v
e
n
in
(
1
)
an
d
(
2
)
,
r
esp
ec
tiv
el
y
.
(
)
(1
)
(
)
(2
)
∏
(
)
(
3
)
E
ac
h
lo
ad
p
o
in
t
co
m
p
r
is
es
a
co
m
b
in
atio
n
o
f
tw
o
m
en
tio
n
ed
ty
p
e
o
f
lo
ad
s
in
th
e
p
o
w
er
s
y
s
tem
.
So
,
co
m
p
o
s
ite
p
er
io
d
elastic
lo
ad
m
o
d
el
w
h
ich
is
p
r
esen
ted
in
(
3
)
is
em
p
lo
y
ed
to
im
p
lem
en
t
th
e
T
OU
p
r
o
g
r
am
,
in
th
is
p
ap
er
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
8
,
No
.
4
,
A
u
g
u
s
t 2
0
1
8
:
1
9
8
5
–
1
9
9
6
1988
3.
R
E
L
IAB
ILIT
Y
E
V
A
L
U
A
T
IO
N
3
.
1
.
Av
a
ila
b
ility
o
f
g
ener
a
t
ing
un
it
s
I
n
o
p
er
atio
n
p
h
ase,
th
e
p
r
o
b
ab
ilit
y
o
f
g
en
er
atio
n
u
n
it
s
u
p
p
ly
in
g
ab
ilit
y
o
r
in
ab
ilit
y
is
b
ased
o
n
th
e
L
ea
d
T
im
e
(
L
T
)
.
A
t
th
is
tim
e
in
ter
v
al,
th
e
s
u
r
p
lu
s
u
n
its
ca
n
n
o
t
co
m
m
it
o
r
r
ep
lace
w
ith
co
m
m
itted
u
n
its
in
in
cr
ea
s
in
g
lo
ad
s
tate
s
o
r
lo
s
e
s
o
m
e
p
o
w
er
p
r
o
d
u
ctio
n
.
T
h
e
p
r
o
b
ab
ilit
y
o
f
s
tate
w
h
ich
th
e
g
en
er
atin
g
u
n
it
f
ails
in
L
T
in
ter
v
al
is
r
ec
o
g
n
ized
as
Ou
tag
e
R
ep
lace
m
en
t
R
ate
(
OR
R
)
o
f
ea
ch
u
n
it.
I
n
r
eliab
ilit
y
an
aly
s
is
,
ea
ch
g
en
er
atin
g
u
n
it
co
u
ld
b
e
eith
er
av
ailab
le
o
r
u
n
av
ailab
le
as
a
tw
o
s
tate
m
o
d
el
r
ep
r
esen
ted
in
Fig
u
r
e
1
.
Fig
u
r
e
1
.
T
w
o
s
tate
m
o
d
el
o
f
ea
ch
g
e
n
er
ati
n
g
u
n
it
I
f
th
e
f
ailu
r
e
an
d
r
ep
air
r
ate
is
d
is
tr
ib
u
ted
as
ex
p
o
n
en
tial
f
u
n
ctio
n
s
,
th
e
p
r
o
b
ab
ilit
y
o
f
u
n
av
ailab
ilit
y
o
f
ea
ch
u
n
it
w
ill
b
e
g
iv
en
as
(
4
)
.
(4
)
W
h
er
e,
λ
an
d
μ
ar
e
th
e
f
ailu
r
e
an
d
r
ep
air
r
ate
o
f
an
y
g
en
er
atin
g
u
n
it,
r
esp
ec
tiv
ely
.
Neg
lectin
g
th
e
r
ep
air
in
g
p
r
o
ce
d
u
r
e
in
o
p
er
atin
g
p
h
ase,
(
4
)
is
m
o
d
if
ied
as (
5
)
.
(5
)
3
.
2
.
Ca
lcula
t
io
n o
f
re
lia
bil
it
y
ind
ices
T
w
o
o
f
th
e
m
o
s
t
im
p
o
r
tan
t
in
d
ices
in
r
eliab
ilit
y
s
tu
d
ies
ar
e
lo
s
s
o
f
lo
ad
p
r
o
b
ab
ilit
y
(
L
OL
P
)
an
d
E
x
p
ec
ted
E
n
er
g
y
No
t
Su
p
p
lied
(
E
E
NS)
.
T
h
e
L
OL
P
is
th
e
s
y
s
tem
r
is
k
in
d
ex
an
d
th
e
E
E
NS
ex
p
r
ess
es
th
e
ex
p
ec
ted
en
er
g
y
th
at
w
ill
n
o
t
b
e
s
er
v
ed
b
y
p
o
w
er
s
y
s
tem
in
co
r
r
esp
o
n
d
in
g
p
er
io
d
.
I
n
th
is
p
ap
er
,
to
ca
lcu
late
th
e
r
eliab
ilit
y
in
d
ices
th
e
co
n
ce
p
t
o
f
th
e
co
n
v
o
lu
tio
n
o
f
th
e
ca
p
ac
ity
o
u
tag
e
p
r
o
b
ab
ilit
y
tab
le
(
C
OP
T
)
ex
p
o
u
n
d
ed
in
[
20
]
is
ap
p
lied
.
T
h
e
af
o
r
em
en
tio
n
ed
in
d
ices
ar
e
ca
lcu
lated
th
r
o
u
g
h
C
OP
T
as
(
6
)
-
(
9
)
.
I
n
(
6
)
-
(
8
)
,
an
d
ar
e
to
tal
ca
p
ac
ity
r
em
ain
in
g
in
s
er
v
ice
o
f
s
tate
k
o
f
C
OP
T
an
d
th
e
co
r
r
esp
o
n
d
in
g
p
r
o
b
ab
ilit
y
r
esp
ec
tiv
ely
.
{
(
6
)
∑
(
7
)
∑
(
8
)
∑
(
9
)
4.
M
E
T
H
O
DO
L
O
G
Y
T
h
e
UC
is
o
n
e
o
f
th
e
m
o
s
t
d
if
f
icu
lt
o
p
tim
izin
g
p
r
o
b
lem
s
an
d
lo
ts
o
f
co
n
s
tr
ain
ts
m
u
s
t
b
e
co
n
s
id
er
ed
.
T
h
e
m
ain
p
u
r
p
o
s
e
o
f
th
is
s
ch
ed
u
lin
g
is
m
in
im
izin
g
th
e
o
p
er
atio
n
co
s
t
d
u
r
in
g
d
is
p
atch
p
er
io
d
.
C
o
n
s
id
er
in
g
th
e
co
m
p
licatio
n
o
f
UC
p
r
o
b
lem
,
in
v
o
lv
in
g
th
e
ev
o
lu
tio
n
al
m
eth
o
d
s
in
u
n
it
s
ch
ed
u
lin
g
is
u
n
av
o
id
ab
le
esp
ec
ially
w
h
en
r
eliab
ilit
y
co
n
s
tr
ain
ts
an
d
A
C
lo
ad
f
lo
w
co
n
s
tr
ain
ts
ar
e
ad
d
r
ess
ed
.
4
.
1
.
Si
m
ula
t
ed
a
nn
ea
li
ng
Sim
u
lated
A
n
n
ea
lin
g
(
SA
)
p
r
o
p
o
s
ed
b
y
Me
tr
o
p
o
lis
at
1
9
5
7
in
o
r
d
er
to
h
an
d
le
o
p
tim
izatio
n
p
r
o
b
lem
s
w
ith
a
lar
g
e
s
ea
r
ch
in
g
s
p
ac
e
[
21
]
.
SA
at
a
co
m
m
o
n
f
o
r
m
h
as
b
ee
n
p
r
esen
ted
b
ased
o
n
th
e
s
im
ilar
ity
b
etw
ee
n
th
e
co
o
lin
g
m
o
lten
m
etal
an
d
s
o
lv
in
g
th
e
co
m
b
in
ato
r
ial
o
p
tim
izatio
n
p
r
o
b
lem
s
.
I
f
th
e
tem
p
er
atu
r
e
o
f
th
e
m
o
lten
m
etal
is
g
r
ad
u
ally
r
ed
u
ce
d
,
all
ato
m
s
ca
n
r
eg
u
late
th
em
s
elv
es
in
th
eir
lo
w
est
en
er
g
y
lev
el.
T
h
is
al
g
o
r
ith
m
ca
n
ac
ce
p
t
w
o
r
s
e
an
s
w
er
s
to
escap
e
f
r
o
m
lo
ca
l
o
p
tim
u
m
tr
ap
p
in
g
in
d
if
f
er
en
t
s
itu
atio
n
s
.
I
t
is
s
tar
ted
w
ith
an
in
itial
s
to
ch
asti
c
s
tate
an
d
b
y
a
tr
an
s
itio
n
f
r
o
m
o
n
e
s
tate
to
an
o
th
er
(
n
eig
h
b
o
r
in
g
s
tate)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
R
elia
b
ilit
y
C
o
n
s
tr
a
in
ed
Un
it C
o
mmitmen
t Co
n
s
id
er
in
g
th
e
E
ffect
o
f D
G
a
n
d
DR
…
(
Ma
s
o
u
d
A
lia
k
b
a
r
i
)
1989
g
r
ad
u
ally
m
in
im
izes
th
e
co
s
t
f
u
n
ctio
n
.
I
n
ea
ch
tr
ial,
th
e
cu
r
r
en
t
an
s
w
er
is
co
m
p
ar
ed
w
ith
p
r
ev
io
u
s
co
n
f
ig
u
r
atio
n
an
s
w
er
as (
1
0
)
.
(
1
0
)
T
h
e
v
alu
e
o
f
∆E
ca
n
b
e
eith
er
p
o
s
itiv
e,
n
eg
ativ
e
o
r
ze
r
o
.
I
f
th
e
n
ew
o
b
tain
ed
s
o
lu
tio
n
is
b
etter
th
an
th
e
cu
r
r
en
t
o
n
e
(
n
eg
ativ
e
v
alu
e
o
f
∆E
)
,
it
w
ill
b
e
ac
ce
p
ted
an
d
o
th
er
w
is
e
(
ze
r
o
o
r
p
o
s
itiv
e
v
alu
e
o
f
∆E
)
th
e
ac
ce
p
tan
ce
is
p
er
f
o
r
m
ed
b
ased
o
n
a
p
r
o
b
ab
ilit
y
g
iv
en
b
y
B
o
ltzm
an
n
d
is
tr
ib
u
tio
n
as f
o
llo
w
s
:
(
1
1
)
{
(
1
2
)
4
.
2
.
B
ina
ry
pa
rt
icle
s
wa
r
m
o
pti
m
i
za
t
io
n
B
in
ar
y
P
ar
ticle
Sw
ar
m
Op
tim
izatio
n
(
B
P
SO)
is
an
in
tellig
en
t
p
o
p
u
latio
n
-
b
ased
alg
o
r
ith
m
w
h
ich
ca
n
s
ea
r
ch
th
e
d
is
cr
ete
s
p
ac
e
to
s
o
lv
e
o
p
tim
izatio
n
p
r
o
b
lem
s
.
Dec
is
io
n
v
ar
iab
les
in
th
is
m
eth
o
d
ar
e
“
0
”
o
r
“
1
”
b
its
o
f
a
b
in
ar
y
s
tr
in
g
.
Sev
er
al
v
er
s
io
n
o
f
th
is
alg
o
r
ith
m
b
ased
o
n
th
e
p
r
o
b
lem
m
o
d
ality
h
as
b
ee
n
ex
ten
d
ed
.
A
n
im
p
r
o
v
ed
v
er
s
io
n
o
f
b
in
ar
y
P
SO
alg
o
r
ith
m
h
as
b
ee
n
u
tili
ze
d
in
th
is
p
ap
er
ex
p
o
u
n
d
ed
in
[
22
]
.
I
n
an
y
iter
at
io
n
th
e
p
o
s
itio
n
o
f
p
ar
ticle
is
u
p
d
ated
as f
o
llo
w
s
:
(
1
3
)
̅
(
)
(
)
(
1
4
)
(
1
5
)
(
1
6
)
E
q
u
atio
n
(
1
4
)
s
h
o
w
s
th
e
v
e
lo
city
u
p
d
atin
g
p
r
o
ce
d
u
r
e
at
it
th
iter
atio
n
b
ased
o
n
th
e
p
r
ev
io
u
s
iter
atio
n
.
I
t
s
h
o
u
ld
b
e
n
o
ted
h
er
e
th
at
p
ar
am
eter
p
la
y
s
an
im
p
o
r
tan
t
r
o
le
in
th
e
alg
o
r
ith
m
p
r
o
g
r
ess
.
I
n
p
r
im
ar
y
iter
atio
n
s
,
th
e
v
alu
e
o
f
in
er
tial
p
r
o
b
ab
ilit
y
is
h
ig
h
an
d
th
e
alg
o
r
ith
m
ex
p
lo
r
es
th
e
s
ea
r
ch
s
p
ac
e.
Gr
ad
u
ally
,
b
y
in
cr
ea
s
in
g
th
e
n
u
m
b
er
o
f
iter
atio
n
s
an
d
d
ec
r
ea
s
in
g
th
e
v
alu
e,
th
e
ex
p
lo
r
at
io
n
is
co
n
v
er
ted
to
ex
p
lo
it
th
e
s
ea
r
ch
s
p
ac
e
w
ith
s
m
all
ch
an
g
es
in
v
ar
iab
les.
4
.
3
.
O
pti
m
iza
t
io
n
pro
ce
du
re
I
n
s
p
ite
o
f
th
e
ex
ce
llen
t
ca
p
ab
ilit
ies
o
f
P
SO
alg
o
r
ith
m
s
in
ex
p
lo
r
in
g
th
e
f
ea
s
ib
le
r
eg
io
n
an
d
f
ast
co
n
v
er
g
en
ce
,
th
er
e
is
a
co
n
s
id
er
ab
le
p
r
o
b
ab
ilit
y
f
o
r
tr
ap
p
in
g
in
lo
ca
l
o
p
tim
u
m
s
in
alg
o
r
ith
m
.
T
h
is
d
ef
ec
t
h
as
b
ee
n
s
o
m
ew
h
at
elim
in
ated
w
ith
SA
m
eth
o
d
b
y
d
ef
in
in
g
a
p
r
o
b
ab
ilit
y
f
o
r
ac
ce
p
tin
g
th
e
w
o
r
s
e
s
o
lu
tio
n
s
.
I
f
th
is
ad
v
an
tag
e
is
s
y
n
th
esized
in
to
P
SO
s
tr
u
ctu
r
e,
th
e
lo
o
s
in
g
in
f
o
r
m
atio
n
o
n
lo
ca
l
o
p
tim
u
m
s
is
d
ec
eler
ated
w
h
ile
th
e
p
er
f
o
r
m
an
ce
is
in
cr
ea
s
ed
.
I
n
th
is
r
eg
ar
d
,
an
im
p
r
o
v
ed
v
er
s
io
n
o
f
b
in
ar
y
P
SO
alg
o
r
ith
m
r
ec
o
m
m
en
d
ed
in
[
22
]
is
tak
en
in
to
co
n
s
id
er
atio
n
as
m
ain
alg
o
r
ith
m
.
T
h
e
B
P
SO
is
u
p
d
ated
in
tw
o
s
tag
es
th
at
s
o
ca
lled
“
p
er
s
o
n
al
b
est
u
p
d
ate”
an
d
“
Glo
b
al
b
est
u
p
d
ate”
.
I
n
th
is
p
ap
er
,
th
e
p
er
s
o
n
al
b
est
u
p
d
ate
p
r
o
ce
d
u
r
e
o
f
ea
ch
p
ar
ticle
is
d
o
n
e
b
ased
o
n
SA
alg
o
r
ith
m
at
an
y
iter
atio
n
.
A
s
,
if
n
ew
o
b
tain
ed
s
o
lu
tio
n
o
f
p
ar
ticle
at
it
th
iter
atio
n
w
as
b
etter
th
an
o
f
its
cu
r
r
en
t
p
er
s
o
n
al
b
est
th
en
th
e
s
o
lu
tio
n
is
ac
ce
p
ted
as
p
er
s
o
n
al
b
est
(
p
er
s
o
n
al
b
est
u
p
d
atin
g
)
an
d
o
th
er
w
is
e
th
e
ac
ce
p
tan
ce
o
f
s
o
lu
tio
n
as
p
er
s
o
n
al
b
est
is
d
o
n
e
b
ased
o
n
p
r
o
b
ab
ilit
y
g
iv
en
b
y
(
1
0
)
.
A
ls
o
,
th
e
g
lo
b
al
b
est
is
n
o
r
m
ally
u
p
d
ated
at
an
y
iter
atio
n
an
d
it
is
co
n
s
id
er
ed
as
f
in
al
s
o
lu
tio
n
at
last
iter
atio
n
ev
en
tu
ally
.
T
h
is
co
m
b
in
atio
n
ass
u
r
es
th
e
ac
ce
ler
atio
n
in
co
n
v
er
g
en
ce
an
d
in
cr
ea
s
es
th
e
ab
ilit
y
in
d
ee
p
s
ea
r
ch
p
r
o
ce
s
s
.
I
n
th
is
p
ap
er
,
a
h
y
b
r
id
SA
an
d
B
P
SO
is
p
r
o
p
o
s
ed
f
o
r
co
m
b
in
in
g
ca
p
ab
ilit
ies
o
f
th
ese
m
eth
o
d
s
an
d
elim
in
atin
g
th
eir
w
ea
k
n
ess
es.
T
h
e
f
lo
w
ch
ar
t
o
f
th
e
p
r
o
p
o
s
ed
h
y
b
r
id
alg
o
r
ith
m
is
illu
s
tr
ated
in
Fig
u
r
e
2
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
8
,
No
.
4
,
A
u
g
u
s
t 2
0
1
8
:
1
9
8
5
–
1
9
9
6
1990
S
t
a
r
t
I
n
i
t
i
a
l
i
z
i
n
g
t
h
e
p
a
r
t
i
c
l
e
s
a
n
d
s
e
t
p
a
r
a
m
e
t
e
r
s
o
f
S
A
a
l
g
o
r
i
t
h
m
I
t
=
1
x
=
1
B
i
n
a
r
y
s
t
r
i
n
g
p
r
o
d
u
c
i
n
g
b
a
s
e
d
o
n
(
1
3
)
a
n
d
(
1
4
)
a
n
d
m
o
d
i
f
y
i
n
g
b
a
s
e
d
o
n
M
U
T
&
M
D
T
E
v
a
l
u
a
t
i
o
n
o
f
C
o
s
t
F
u
n
c
t
i
o
n
a
n
d
c
a
l
c
u
l
a
t
i
o
n
o
f
Δ
E
Δ
E
=
(
X
j
-
X
i
)
/
X
i
x
≤
P
a
m
a
x
A
c
c
e
p
t
a
n
c
e
o
f
p
o
s
i
t
i
o
n
o
f
x
-
t
h
P
a
r
t
i
c
l
e
a
s
p
e
r
s
o
n
a
l
B
e
s
t
Δ
E
≤
0
A
c
c
e
p
t
a
n
c
e
o
f
p
o
s
i
t
i
o
n
o
f
x
-
t
h
P
a
r
t
i
c
l
e
a
s
p
e
r
s
o
n
a
l
B
e
s
t
W
i
t
h
P
r
o
b
a
b
i
l
i
t
y
e
x
p
(
-
Δ
E
/
T
e
m
p
)
≥
U
(
0
,
1
)
U
p
d
a
t
e
t
h
e
G
l
o
b
a
l
B
e
s
t
i
n
i
t
-
t
h
i
t
e
r
a
t
i
o
n
I
t
≤
M
a
x
I
t
I
t
=
i
t
+
1
x
=
x
+
1
Y
e
s
N
o
P
r
i
n
t
r
e
s
u
l
t
s
Y
e
s
Y
e
s
N
o
N
o
R
e
d
u
c
t
i
o
n
o
f
t
e
m
p
e
r
a
t
u
r
e
b
a
s
e
d
o
n
(
1
2
)
X
j
<
G
l
o
b
a
l
B
e
s
t
Y
e
s
N
o
E
E
N
S
<
E
m
a
x
A
l
l
o
c
a
t
i
o
n
t
h
e
a
v
e
r
a
g
e
o
f
a
l
l
b
u
s
e
s
L
M
P
a
s
V
O
L
L
A
l
l
o
c
a
t
i
o
n
a
l
a
r
g
e
p
e
n
a
l
t
y
t
o
c
o
s
t
o
f
r
e
l
i
a
b
i
l
i
t
y
t
=
1
t
<
T
t
=
t
+
1
Y
e
s
N
o
Y
e
s
N
o
P
e
r
s
o
n
a
l
B
e
s
t
U
p
d
a
t
e
B
a
s
e
d
o
n
S
A
G
l
o
b
a
l
B
e
s
t
U
p
d
a
t
e
N
o
r
m
a
l
l
y
Fig
u
r
e
2
.
Flo
w
c
h
ar
t o
f
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
4
.
4
.
O
bje
ct
iv
e
f
un
ct
io
n a
nd
co
ns
t
ra
ints
So
m
e
o
f
in
v
o
lv
ed
co
n
s
tr
ain
ts
in
R
C
UC
im
p
lem
en
tin
g
ar
e
p
r
esen
ted
in
th
is
s
ec
tio
n
.
Fu
el
co
s
t
o
f
ea
ch
th
er
m
al
u
n
it
is
a
s
ec
o
n
d
o
r
d
er
f
u
n
ctio
n
o
f
its
g
en
er
ated
p
o
w
er
w
h
ich
is
ex
p
r
ess
ed
as
f
o
llo
w
s
:
(
1
7
)
I
n
(
1
7
)
,
,
an
d
ar
e
f
u
el
co
s
t
co
ef
f
icien
ts
.
T
h
e
o
b
j
ec
tiv
e
f
u
n
ctio
n
o
f
UC
p
r
o
b
lem
in
th
e
p
r
esen
ce
o
f
DG
u
n
its
an
d
DR
p
r
o
g
r
am
w
ith
th
e
aim
o
f
d
ec
r
ea
s
in
g
o
p
er
atio
n
an
d
r
eliab
ilit
y
co
s
t
is
f
o
r
m
u
lated
as
(
1
8
)
.
T
h
e
m
en
tio
n
ed
o
b
j
ec
tiv
e
f
u
n
ctio
n
co
n
s
is
ts
o
f
tw
o
ter
m
s
.
T
h
e
f
ir
s
t
ter
m
r
ep
r
esen
ts
f
u
el
co
s
t
o
f
co
n
v
en
tio
n
a
l
an
d
DG
u
n
its
to
g
eth
er
w
ith
s
tar
tin
g
u
p
co
s
t
to
m
ee
t
th
e
d
em
an
d
.
T
h
e
h
o
u
r
ly
co
s
t
o
f
E
E
NS
h
as
b
ee
n
s
h
o
w
n
in
s
ec
o
n
d
ter
m
.
T
h
e
d
ev
elo
p
ed
o
b
j
ec
tiv
e
f
u
n
ctio
n
in
(
1
8
)
is
s
u
b
j
ec
ted
to
s
o
m
e
co
n
s
tr
ain
ts
as f
o
llo
w
s
:
∑
∑
[
(
)
]
(
1
8
)
E
q
u
atio
n
(
1
9
)
is
th
e
r
eliab
ilit
y
co
n
s
tr
ain
t
an
d
its
co
s
t
is
o
b
tain
ed
b
y
(
2
0
)
.
T
h
e
p
o
w
er
b
alan
ce
an
d
s
p
in
n
in
g
r
eser
v
e
co
n
s
tr
ain
ts
ar
e
r
ep
r
esen
ted
in
(
2
1
)
an
d
(
2
2
)
.
T
h
e
co
n
s
tr
ain
ts
(
2
3
)
-
(
2
8
)
en
s
u
r
e
th
e
p
r
o
p
er
o
p
er
atio
n
o
f
g
en
er
atio
n
u
n
its
co
n
s
id
er
in
g
th
e
p
o
w
er
f
lo
w
lim
its
.
Star
tu
p
co
s
t
ca
n
b
e
ev
alu
ated
b
ased
o
n
(
2
9
)
an
d
also
it
ca
n
b
e
co
n
s
id
er
ed
as
a
co
n
s
tan
t
v
alu
e
f
o
r
ea
ch
g
en
er
atio
n
u
n
it.
C
o
n
s
tr
ain
ts
o
n
m
in
im
u
m
u
p
tim
e,
m
in
im
u
m
d
o
w
n
tim
e
an
d
r
am
p
r
ates
o
f
g
en
er
atio
n
u
n
its
ar
e
g
iv
en
th
r
o
u
g
h
(
3
0
)
-
(
3
3
)
,
r
esp
ec
tiv
ely
.
Netw
o
r
k
s
ec
u
r
ity
co
n
s
tr
ain
ts
ar
e
r
ep
r
esen
ted
in
(
3
4
)
an
d
(
3
5
)
.
(
1
9
)
(
2
0
)
∑
(
2
1
)
∑
(
2
2
)
∑
|
|
(
2
3
)
∑
|
|
(
2
4
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
R
elia
b
ilit
y
C
o
n
s
tr
a
in
ed
Un
it C
o
mmitmen
t Co
n
s
id
er
in
g
th
e
E
ffect
o
f D
G
a
n
d
DR
…
(
Ma
s
o
u
d
A
lia
k
b
a
r
i
)
1991
(
2
5
)
(
2
6
)
(
2
7
)
(2
8
)
{
(
2
9
)
W
h
er
e
(
)
(
)
(
3
0
)
(
)
(
)
(
3
1
)
(
3
2
)
(
3
3
)
(
3
4
)
|
|
(
3
5
)
4.
N
UM
E
RICAL
S
T
UD
Y
T
h
e
R
C
UC
in
co
r
p
o
r
ated
w
ith
DGs
an
d
DR
im
p
lem
en
tatio
n
is
ca
r
r
ied
o
u
t
o
v
er
th
e
IEEE
-
R
T
S7
9
[
23
]
.
I
t
is
ass
u
m
ed
th
at
th
r
ee
2
5
MW
s
m
all
s
ca
le
g
as
tu
r
b
in
es
as
DGs
ar
e
lo
ca
ted
in
3
,
9
,
an
d
1
0
b
u
s
es.
T
h
e
h
o
u
r
ly
A
C
o
p
tim
al
p
o
w
er
f
lo
w
(
A
C
OP
F)
is
p
er
f
o
r
m
ed
u
tili
zin
g
MA
T
P
OW
E
R
to
o
lb
o
x
in
MA
T
L
A
B
s
o
f
tw
ar
e
to
d
is
tr
ib
u
te
th
e
g
en
er
ated
p
o
w
er
co
n
s
id
er
in
g
th
e
n
etw
o
r
k
co
n
s
tr
ain
ts
[
2
4
]
.
T
h
e
MA
T
P
OW
E
R
to
o
lb
o
x
em
p
lo
y
s
MA
T
L
A
B
I
n
ter
io
r
P
o
in
t
So
lv
er
(
MI
P
S)
f
o
r
A
C
OP
F.
T
h
e
s
p
ec
if
icatio
n
s
o
f
DGs
f
o
r
o
p
er
atio
n
co
s
t
an
d
r
eliab
ilit
y
ass
ess
m
en
t
is
ex
tr
ac
ted
f
r
o
m
[
1
4
]
.
A
ls
o
,
th
e
co
m
m
o
n
in
f
o
r
m
atio
n
r
elate
d
to
co
n
v
en
tio
n
al
u
n
its
in
UC
p
r
o
b
le
m
(
e.
g
.
s
tar
tin
g
u
p
an
d
s
h
u
ttin
g
d
o
w
n
co
s
ts
,
r
am
p
r
ate
an
d
etc.
)
h
av
e
b
ee
n
ex
tr
ac
ted
f
r
o
m
[
2
5
]
.
T
h
e
m
in
im
u
m
s
p
in
n
in
g
r
eser
v
e
r
eq
u
ir
em
en
t
is
ass
u
m
ed
to
b
e
1
0
%
o
f
h
o
u
r
ly
d
em
an
d
.
DR
p
r
o
g
r
am
s
ar
e
also
in
v
esti
g
ated
b
ased
o
n
T
OU
m
o
d
el
w
h
ich
is
o
n
e
o
f
th
e
tim
e
-
ba
s
ed
DR
p
r
o
g
r
am
s
.
I
n
o
r
d
er
to
im
p
lem
en
t
T
OU
p
r
o
g
r
am
,
a
ty
p
ical
lo
ad
cu
r
v
e
h
as
b
ee
n
ex
tr
ac
ted
f
r
o
m
[
1
9
]
an
d
w
er
e
n
o
r
m
alize
d
b
ased
o
n
p
ea
k
h
o
u
r
lo
ad
(
2
6
7
0
MW
)
in
th
is
ca
s
e
s
tu
d
y
.
T
h
e
lo
ad
cu
r
v
e
is
d
iv
id
ed
in
to
th
r
ee
in
ter
v
als:
lo
w
lo
ad
p
er
io
d
(
0
2
:0
0
to
0
9
:0
0
)
,
o
f
f
-
p
ea
k
p
er
io
d
(
1
0
:0
0
to
1
9
:0
0
)
an
d
p
ea
k
p
er
io
d
(
2
0
:0
0
to
0
1
:0
0
)
.
T
h
e
elasticity
o
f
th
e
lo
ad
s
is
s
h
o
w
n
in
T
ab
le
1
w
h
ich
is
o
r
ig
in
ally
tak
en
f
r
o
m
[
1
9
].
T
ab
le
1
.
T
h
e
E
last
icit
y
o
f
L
o
a
d
s
f
o
r
DR
I
m
p
le
m
en
tin
g
P
e
a
k
Off
-
P
e
a
k
L
o
w
-
P
e
a
k
P
e
a
k
-
0
.
2
0
.
0
1
6
0
.
0
1
2
Off
-
P
e
a
k
0
.
0
0
6
-
0
.
2
0
.
0
1
L
o
w
-
P
e
a
k
0
.
0
0
8
0
.
0
1
-
0
.
2
T
w
o
s
ce
n
ar
io
s
ar
e
d
is
cu
s
s
ed
in
n
u
m
er
ical
s
tu
d
ies.
I
n
th
e
f
ir
s
t
s
ce
n
ar
io
,
o
p
er
atio
n
w
ith
o
u
t
DGs
an
d
DR
p
r
o
g
r
am
is
p
r
esen
ted
.
T
h
en
,
th
e
n
ew
lo
ad
cu
r
v
e
is
o
b
tain
ed
b
y
T
OU
im
p
lem
en
tin
g
o
n
m
ain
lo
ad
cu
r
v
e
at
an
y
b
u
s
u
s
in
g
f
ir
s
t
s
ce
n
ar
io
L
o
ca
l
Ma
r
g
in
al
P
r
ices
(
L
MP
s
)
.
I
n
th
e
s
ec
o
n
d
s
ce
n
ar
io
,
DGs
an
d
co
n
v
en
tio
n
al
u
n
its
ar
e
co
m
m
itted
in
R
C
UC
at
p
r
esen
ce
o
f
n
ew
lo
ad
cu
r
v
e
all
o
v
er
th
e
n
etw
o
r
k
.
T
h
e
b
ase
p
r
ices
at
ea
ch
lo
ad
b
u
s
ar
e
eq
u
al
to
av
er
ag
e
L
MP
s
f
o
r
2
4
h
o
u
r
s
d
er
iv
ed
f
r
o
m
OP
F
in
th
e
f
ir
s
t
s
ce
n
ar
io
.
T
h
e
r
atio
o
f
elec
tr
icity
p
r
ices
h
as
b
ee
n
co
n
s
id
er
ed
o
n
e
h
alf
o
f
b
ase
p
r
ices
in
lo
w
lo
ad
p
er
io
d
,
eq
u
al
to
b
ase
p
r
ices
in
o
f
f
-
p
ea
k
an
d
eq
u
al
to
o
n
e
an
d
a
h
alf
tim
es
o
f
th
e
b
ase
p
r
ices
at
p
ea
k
p
er
io
d
[
2
6
]
.
P
ar
ticip
a
tio
n
p
o
ten
tial
f
o
r
DR
im
p
lem
en
tatio
n
is
ass
u
m
ed
to
b
e
2
0
%
at
an
y
lo
ad
p
o
in
t.
T
h
e
ac
ce
p
tab
le
lev
el
o
f
r
eliab
ilit
y
is
a
p
r
ed
ef
in
ed
p
er
ce
n
tag
e
o
f
co
n
s
u
m
p
tio
n
en
er
g
y
w
h
ich
th
e
m
ax
im
u
m
allo
w
ab
le
v
alu
e
h
as
b
ee
n
co
n
s
id
er
ed
to
b
e
0
.
1
%
o
f
d
aily
co
n
s
u
m
ed
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
8
,
No
.
4
,
A
u
g
u
s
t 2
0
1
8
:
1
9
8
5
–
1
9
9
6
1992
en
er
g
y
in
t
h
is
s
tu
d
y
.
T
h
e
r
eliab
ilit
y
ev
alu
atin
g
is
b
ased
o
n
HL
-
I
.
T
h
e
r
eliab
ilit
y
co
n
s
tr
ain
t
is
ap
p
lied
to
ea
ch
f
ea
s
ib
le
s
o
lu
tio
n
o
f
p
ar
ticles as f
o
llo
w
s
:
I
f
E
E
NS
Tot
<E
m
ax
,
th
e
co
s
t o
f
r
eliab
ilit
y
is
ca
lcu
lated
b
ased
o
n
av
er
ag
e
o
f
all
b
u
s
es
L
MP
s
at
an
y
h
o
u
r
.
I
f
E
E
NS
T
ot
>E
m
ax
,
th
e
tr
ial
s
o
lu
tio
n
p
r
o
v
id
es
an
u
n
d
esire
d
lev
el
o
f
r
eliab
ilit
y
an
d
a
f
ix
ed
lar
g
e
p
en
alty
is
allo
ca
ted
to
r
eliab
ilit
y
co
s
t in
th
e
s
ec
o
n
d
ter
m
o
f
th
e
co
s
t
f
u
n
ctio
n
.
Fin
al
s
o
lu
tio
n
is
ch
o
s
en
th
r
o
u
g
h
s
ev
er
al
tr
ials
co
n
s
id
er
in
g
th
e
s
to
ch
asti
c
in
h
er
en
t
b
eh
av
io
r
o
f
ev
o
lu
tio
n
ar
y
alg
o
r
ith
m
.
P
ar
am
eter
s
s
ettin
g
o
f
p
r
o
p
o
s
ed
alg
o
r
ith
m
h
av
e
b
ee
n
d
eter
m
in
ed
b
ased
o
n
tr
ials
w
h
ich
ar
e
p
r
esen
ted
in
T
ab
le
2
.
T
h
e
o
p
tim
al
o
p
er
atio
n
o
f
D
G
u
n
its
an
d
d
em
an
d
v
ar
iatio
n
s
d
u
e
to
T
OU
im
p
lem
en
tatio
n
ar
e
p
r
esen
ted
in
Fig
u
r
e
3
.
T
ab
le
2
.
Settin
g
P
ar
a
m
eter
s
f
o
r
P
r
o
p
o
s
ed
A
lg
o
r
ith
m
0
.
0
5
0
.
9
5
2
0
0
40
0
.
9
8
10
0
.
2
A
s
it
ca
n
b
e
s
ee
n
in
Fig
u
r
e
3
,
th
e
p
r
ice
s
ig
n
als
f
r
o
m
T
OU
ca
n
co
n
s
id
er
ab
ly
alter
th
e
d
em
an
d
an
d
r
ed
u
ce
th
e
p
ea
k
d
em
an
d
b
y
1
8
6
MW
.
T
h
e
h
o
u
r
ly
DGs
p
ar
ticip
atio
n
is
o
b
tain
ed
b
y
p
r
o
p
o
s
ed
h
y
b
r
id
alg
o
r
ith
m
d
ec
is
io
n
b
esid
e
o
th
er
co
n
v
en
tio
n
al
u
n
its
.
W
ith
in
cr
ea
s
e
in
lo
ad
at
p
ea
k
p
er
io
d
,
DGs
p
ar
ticip
atio
n
is
in
cr
ea
s
ed
an
d
in
j
ec
ted
p
o
w
er
b
y
s
m
all
n
o
n
-
ex
p
en
s
iv
e
u
n
its
af
f
ec
ts
th
e
m
o
s
t
s
ig
n
if
ican
t
o
p
er
atio
n
al
in
d
ices.
Hen
ce
,
an
ex
ten
s
iv
e
n
u
m
er
ical
co
m
p
ar
is
o
n
h
as
b
ee
n
p
r
esen
ted
in
T
ab
le
3
w
h
ile
th
e
lead
tim
e
w
as
f
ix
ed
at
4
h
.
W
ith
in
cr
ea
s
e
in
p
o
w
er
in
j
ec
tio
n
s
b
y
DGs,
d
e
-
co
m
m
itti
n
g
ex
p
en
s
iv
e
g
en
er
ato
r
s
an
d
alter
in
g
d
em
an
d
p
r
o
f
ile,
r
elief
o
f
tr
an
s
m
is
s
io
n
ca
p
ac
ity
an
d
d
ec
r
ea
s
e
o
f
o
p
er
atio
n
al
co
s
ts
co
u
ld
b
e
ac
h
iev
ed
s
im
u
ltan
eo
u
s
ly
.
T
h
e
T
OU
im
p
lem
en
tatio
n
ca
n
r
en
d
er
s
o
m
e
d
em
an
d
f
r
o
m
p
ea
k
lo
ad
p
er
io
d
to
lo
w
lo
ad
p
er
io
d
to
p
r
ev
en
t
lo
ad
s
h
ed
d
in
g
an
d
s
y
s
tem
v
o
ltag
e
co
llap
s
e
w
h
en
th
e
p
o
w
er
s
y
s
tem
r
eliab
ilit
y
is
j
eo
p
ar
d
ized
.
T
h
e
in
itial
lo
ad
f
o
r
ec
asti
n
g
an
d
th
e
lo
ad
cu
r
v
e
af
ter
ap
p
ly
in
g
T
OU
h
av
e
b
ee
n
s
h
o
w
n
in
Fig
u
r
e
4
.
T
h
e
o
p
tim
al
u
n
it
co
m
m
itm
en
t
s
ch
ed
u
lin
g
r
esu
lts
f
o
r
b
o
th
s
ce
n
ar
io
ar
e
s
h
o
w
n
in
T
ab
le
4
an
d
T
ab
le
5.
Fig
u
r
e
3
.
T
h
e
in
j
ec
ted
p
o
w
er
b
y
DGs
an
d
th
e
ch
an
g
e
d
em
an
d
d
u
e
to
T
OU
f
o
r
L
T
=
4
h
Fig
u
r
e
4
.
L
o
ad
cu
r
v
e
b
ef
o
r
e
an
d
af
ter
T
OU
i
m
p
le
m
e
n
ti
n
g
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
R
elia
b
ilit
y
C
o
n
s
tr
a
in
ed
Un
it C
o
mmitmen
t Co
n
s
id
er
in
g
th
e
E
ffect
o
f D
G
a
n
d
DR
…
(
Ma
s
o
u
d
A
lia
k
b
a
r
i
)
1993
T
ab
le
4
.
Op
tim
al
U
n
it C
o
m
m
i
t
m
e
n
t Sc
h
ed
u
le
R
es
u
lts
w
i
th
o
u
t D
G
&
DR
U
n
i
t
/
h
o
u
r
1
2
3
4
5
6
7
8
9
1
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
2
0
2
1
2
2
2
3
2
4
U
1
&
U
2
U3
U4
U
5
&
U
6
U7
U8
U9
U
1
0
U
1
1
U
1
2
U
1
3
U
1
4
U
1
5
~
U
1
9
U
2
0
~
U
2
3
U
2
4
U
2
5
U
2
6
T
ab
le
5
.
Op
tim
al
U
n
it C
o
m
m
i
t
m
e
n
t Sc
h
ed
u
le
R
es
u
lts
w
i
th
DG
&
D
R
U
n
i
t
/
h
o
u
r
1
2
3
4
5
6
7
8
9
1
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
2
0
2
1
2
2
2
3
2
4
U
1
~
U
2
U3
U4
U
5
~
U
6
U7
U8
U9
U
1
0
U
1
1
U
1
2
U
1
3
U
1
4
U
1
5
~
U
1
9
U
2
0
~
U
2
6
D
G
1
D
G
2
D
G
3
A
ch
iev
in
g
a
b
etter
lev
el
o
f
r
eliab
ilit
y
r
eq
u
ir
es
th
e
co
m
m
itm
en
t
o
f
m
o
r
e
u
n
its
an
d
th
is
in
cr
ea
s
es
th
e
R
C
UC
co
s
t
in
d
is
p
atch
p
er
io
d
.
Ho
w
ev
er
r
esu
lts
o
f
T
ab
le
3
s
h
o
w
s
th
at
a
b
etter
r
eliab
ilit
y
in
d
ex
ca
n
b
e
o
b
tain
ed
w
ith
lo
w
er
o
p
er
atio
n
al
co
s
ts
b
y
o
p
tim
al
s
ch
e
d
u
lin
g
o
f
g
en
er
atio
n
u
n
its
.
T
h
e
im
p
r
o
v
em
en
t
o
f
co
n
s
id
er
ed
r
eliab
ilit
y
in
d
ex
(
E
E
NS)
d
em
o
n
s
tr
ates
th
e
ap
p
licab
ilit
y
an
d
u
s
ef
u
ln
ess
o
f
co
m
b
in
in
g
th
e
DGs
an
d
DR
p
r
o
g
r
am
an
d
p
r
o
p
o
s
ed
alg
o
r
ith
m
.
L
ea
d
tim
e
is
an
o
th
er
p
ar
am
eter
th
at
af
f
ec
ts
th
e
r
eliab
ilit
y
in
d
ices
.
T
h
e
L
OL
P
in
d
ex
f
o
r
d
if
f
er
en
t
am
o
u
n
t
o
f
lead
tim
e
h
as
b
ee
n
p
r
esen
ted
in
Fig
u
r
e
5
.
T
h
is
in
d
ex
in
d
icate
s
th
e
p
r
o
b
ab
ilit
y
o
f
s
tate
th
at
th
e
av
ailab
le
g
en
er
atio
n
alo
n
g
w
ith
s
p
in
n
in
g
r
eser
v
e
is
n
o
t
ab
le
to
m
ee
t
th
e
s
y
s
tem
lo
ad
an
d
s
atis
f
y
th
e
co
n
s
tr
ain
ts
.
T
ab
le
3
.
C
o
m
p
ar
is
o
n
b
et
w
ee
n
Sev
er
al
Op
er
atio
n
al
P
ar
a
m
eter
s
(
L
T
=4
h
)
O
p
e
r
a
t
i
o
n
a
l
P
a
r
a
me
t
e
r
s
W
i
t
h
D
G
&
D
R
W
i
t
h
o
u
t
D
G
&
D
R
T
o
t
a
l
c
o
st
o
f
R
C
U
C
(
$
)
9
6
3
,
1
4
5
.
9
7
1
,
0
4
3
,
8
0
6
.
9
4
S
t
a
r
t
U
p
C
o
st
(
$
)
2
3
,
0
0
0
2
8
,
5
0
0
C
o
st
o
f
c
o
n
v
e
n
t
i
o
n
a
l
u
n
i
t
s (
$
)
9
1
3
,
7
6
8
.
2
8
1
,
0
1
1
,
0
3
8
.
8
7
C
o
st
o
f
D
G
s ($
)
2
5
,
3
0
9
.
5
3
0
C
o
st
o
f
r
e
l
i
a
b
i
l
i
t
y
(
$
)
1
,
0
6
8
.
1
6
4
,
2
6
8
.
0
7
O
p
e
r
a
t
i
o
n
C
o
st
r
e
d
u
c
i
n
g
d
u
e
t
o
T
O
U
(
$
)
5
2
,
3
5
1
.
4
4
0
T
r
a
n
smissi
o
n
N
e
t
w
o
r
k
C
o
n
g
e
st
i
o
n
a
t
p
e
a
k
h
o
u
r
(
M
W
)
3
,
4
1
3
.
7
3
3
,
6
0
7
.
4
A
c
t
i
v
e
p
o
w
e
r
L
o
ss (M
W
)
8
4
6
.
0
1
8
3
0
.
6
4
L
o
a
d
F
a
c
t
o
r
(
%)
9
1
.
5
7
8
4
.
6
1
EEN
S
(
M
W
h
/
d
a
y
)
2
4
.
0
9
2
8
.
3
1
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
8
,
No
.
4
,
A
u
g
u
s
t 2
0
1
8
:
1
9
8
5
–
1
9
9
6
1994
Fig
u
r
e
5
d
ep
icts
th
at
th
e
lead
tim
e
ca
n
af
f
ec
t
th
e
s
o
lu
tio
n
o
f
UC
p
r
o
b
lem
.
T
h
e
ch
an
g
e
in
lead
tim
e
r
esu
lts
in
ch
an
g
e
o
f
g
en
er
atin
g
u
n
it
u
n
av
ailab
ilit
y
an
d
th
is
is
s
u
e
ca
u
s
es
an
in
cr
ea
s
e
o
r
d
ec
r
ea
s
e
in
n
u
m
b
er
o
f
co
m
m
itted
u
n
its
to
p
r
o
v
id
e
th
e
s
am
e
r
eliab
ilit
y
lev
el.
I
n
o
r
d
er
to
d
em
o
n
s
tr
ate
th
e
ef
f
ec
t
o
f
lead
tim
e
v
ar
iatio
n
s
,
Fig
u
r
e
6
an
d
Fig
u
r
e
7
illu
s
tr
ate
th
e
to
tal
co
m
m
itted
ca
p
ac
ity
o
f
ea
ch
lo
ad
cu
r
v
e
s
h
o
w
n
in
Fig
u
r
e
4
w
h
ile
th
e
lead
tim
e
is
v
ar
ied
f
r
o
m
4
to
8
h
.
I
t
ca
n
b
e
s
ee
n
th
at
th
e
r
eq
u
ir
ed
s
p
in
n
in
g
r
eser
v
e
g
r
o
w
s
w
ith
in
cr
ea
s
e
in
co
m
m
itted
ca
p
ac
ity
to
ac
h
iev
e
th
e
s
am
e
d
esire
d
lev
el
o
f
r
eliab
ilit
y
.
Fig
u
r
e
5
.
L
O
L
P
at
ea
c
h
h
o
u
r
o
v
er
th
e
d
is
p
atc
h
p
er
io
d
Fig
u
r
e
6
.
E
x
p
ec
ted
in
itial lo
ad
an
d
to
tal
co
m
m
i
tted
ca
p
ac
it
y
at
ea
ch
h
o
u
r
f
o
r
t
w
o
v
alu
e
s
o
f
lead
ti
m
e
T
o
v
alid
ate
th
e
co
m
p
u
tatio
n
al
ef
f
icien
cy
o
f
th
e
p
r
o
p
o
s
ed
h
y
b
r
id
m
eth
o
d
,
th
e
s
am
e
f
o
r
m
u
latio
n
is
s
o
lv
ed
u
s
in
g
b
in
ar
y
r
ea
l
co
d
ed
f
ir
ef
ly
(
B
R
C
FF
)
alg
o
r
ith
m
an
d
n
o
v
el
ad
ap
tiv
e
q
u
an
tu
m
-
in
s
p
ir
ed
b
in
ar
y
g
r
av
itatio
n
al
s
ea
r
ch
(
QB
GSA
)
alg
o
r
ith
m
.
T
h
e
co
n
s
id
er
ed
alg
o
r
ith
m
s
h
av
e
th
e
ab
ilit
y
f
o
r
s
ea
r
ch
in
lar
g
e
s
p
ac
e
w
ith
f
ast
co
n
v
er
g
en
ce
r
ate.
A
m
o
r
e
d
etailed
d
escr
ip
tio
n
o
f
th
is
alg
o
r
ith
m
s
,
in
clu
d
in
g
f
o
r
m
u
latin
g
an
d
f
lo
w
ch
ar
t
o
f
o
p
tim
izin
g
p
r
o
ce
d
u
r
e
ca
n
b
e
f
o
u
n
d
in
[
2
7
]
an
d
[
2
8
]
.
Fig
u
r
e
8
d
ep
icts
co
m
p
ar
is
o
n
b
etw
ee
n
p
r
o
p
o
s
ed
o
p
tim
izatio
n
m
eth
o
d
,
QB
GSA
,
B
P
SO
an
d
B
R
C
FF
b
ased
o
n
R
C
UC
f
o
r
m
u
latio
n
to
ass
ess
h
o
w
s
ea
r
ch
in
g
th
e
s
p
ac
e
o
f
p
r
o
b
lem
.
Hig
h
g
ap
b
etw
ee
n
co
n
v
er
g
en
ce
p
o
in
ts
o
f
alg
o
r
ith
m
s
r
ev
ea
l
th
e
p
o
w
er
f
u
ln
ess
o
f
th
e
p
r
o
p
o
s
ed
m
eth
o
d
ag
ain
s
t
o
th
er
o
n
es.
C
o
n
s
id
er
in
g
th
e
o
b
tain
ed
r
esu
lts
p
r
o
p
o
s
ed
alg
o
r
itm
p
r
o
v
id
es
th
e
b
est
o
p
tim
al
s
o
lu
tio
n
in
ter
m
s
o
f
co
m
p
u
tatio
n
s
p
ee
d
an
d
ac
cu
r
ac
y
co
m
p
ar
ed
w
ith
o
th
er
s
.
T
h
e
o
b
j
ec
tiv
e
o
f
th
is
co
m
p
ar
is
o
n
is
to
s
elec
t
th
e
m
o
s
t
ap
p
r
o
p
r
iate
o
p
tim
izatio
n
tech
n
iq
u
e
f
o
r
s
o
lv
in
g
th
e
UC
p
r
o
b
lem
in
f
u
tu
r
e
r
esear
ch
.
Fig
u
r
e
7
.
L
o
ad
cu
r
v
e
af
ter
T
O
U
an
d
to
tal
co
m
m
itted
ca
p
ac
it
y
at
ea
ch
h
o
u
r
f
o
r
t
w
o
v
alu
e
s
o
f
lead
ti
m
e
Fig
u
r
e
8
.
C
o
n
v
er
g
en
ce
c
h
ar
ac
t
er
is
tics
o
f
p
r
o
p
o
s
ed
m
et
h
o
d
,
QB
GSA
,
B
P
SO a
n
d
B
R
C
FF
(
L
T
=4
h
)
5.
CO
NCLU
SI
O
N
I
n
th
is
p
ap
er
,
a
n
ew
ap
p
r
o
ac
h
w
h
ich
is
a
co
m
b
in
atio
n
o
f
tw
o
h
eu
r
is
tic
alg
o
r
ith
m
s
w
as
p
r
esen
ted
to
s
o
lv
e
th
e
UC
p
r
o
b
lem
at
p
r
esen
ce
o
f
DGs
an
d
DR
p
r
o
g
r
am
s
w
ith
r
eliab
ilit
y
an
d
A
C
p
o
w
er
f
lo
w
co
n
s
tr
ain
ts
.
T
h
e
en
f
o
r
ce
m
en
t
o
f
r
eliab
ilit
y
co
n
s
tr
ain
t
d
eter
m
in
es
t
h
e
s
p
ec
if
ic
lev
el
o
f
g
en
er
atio
n
an
d
co
m
m
itted
ca
p
ac
ity
Evaluation Warning : The document was created with Spire.PDF for Python.