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2
{
(
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}
(
2
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Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
A
P
E
I
SS
N:
2252
-
8792
Op
timiz
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4
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ii)
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8792
IJ
A
P
E
Vo
l.
4
,
No
.
2
,
A
u
g
u
s
t
2
0
1
5
:
47
–
60
50
4
.
SO
L
VI
NG
E
L
D
-
UC
US
I
N
G
G
AUS
S S
E
I
DA
L
AND
DY
NAM
I
NG
P
RO
G
RAM
M
I
N
G
M
E
T
H
O
D
Op
ti
m
izatio
n
tech
n
iq
u
e
w
a
s
u
s
ed
to
s
o
lv
e
th
e
ec
o
n
o
m
ic
lo
a
d
d
is
p
atch
p
r
o
b
lem
.
I
n
t
h
is
ca
s
e,
th
e
co
s
t
f
u
n
ctio
n
f
o
r
ea
ch
g
e
n
er
ato
r
h
as
b
ee
n
ap
p
r
o
x
i
m
atel
y
r
ep
r
es
en
ted
b
y
a
s
i
n
g
le
q
u
ad
r
atic
f
u
n
ctio
n
a
n
d
is
s
o
lv
ed
u
s
i
n
g
m
at
h
e
m
a
tical
p
r
o
g
r
a
m
m
i
n
g
b
ased
o
p
ti
m
izatio
n
tech
n
iq
u
e
s
s
u
c
h
a
s
g
au
s
s
s
eid
al
m
et
h
o
d
w
h
ic
h
is
an
iter
ativ
e
al
g
o
r
ith
m
f
o
r
s
o
l
v
in
g
a
s
et
o
f
n
o
n
-
l
in
ea
r
al
g
eb
r
aic
eq
u
atio
n
.
I
t
w
a
s
o
n
e
o
f
th
e
m
eth
o
d
s
u
s
ed
in
lo
ad
f
lo
w
s
tu
d
ies
w
h
er
e
a
s
o
l
u
tio
n
o
f
v
ec
to
r
is
a
s
s
u
m
ed
a
n
d
o
n
e
o
f
t
h
e
eq
u
atio
n
s
is
u
s
ed
to
o
b
tai
n
th
e
r
ev
i
s
ed
v
alu
e
o
f
a
p
ar
ticu
lar
v
ar
iab
le
an
d
th
e
s
o
lu
t
io
n
o
f
v
ec
to
r
is
i
m
m
ed
iatel
y
u
p
d
ated
in
r
esp
ec
t
o
f
th
is
v
ar
iab
le.
T
h
e
p
r
o
ce
s
s
is
th
en
r
ep
ea
ted
f
o
r
all
th
e
v
ar
iab
le
th
er
eb
y
co
m
p
let
in
g
o
n
e
iter
atio
n
t
h
e
iter
atio
n
p
r
o
ce
s
s
i
s
r
ep
ea
ted
till
th
e
s
o
lu
ti
o
n
v
e
cto
r
co
n
v
er
g
es
w
it
h
i
n
p
r
escr
ib
ed
ac
cu
r
ac
y
.
I
n
G
A
U
SS
-
S
E
I
DE
L
alg
o
r
it
h
m
,
eq
u
atio
n
is
u
til
ized
to
f
in
d
t
h
e
f
i
n
al
b
u
s
v
o
ltag
e
s
u
s
i
n
g
s
u
cc
e
s
s
i
v
e
s
tep
o
f
iter
atio
n
s
,
w
h
er
e
[
(
∑
∑
)
]
5.
F
AULT
A
NAL
YSI
S:
Fau
lt
i
n
a
cir
cu
it
i
s
an
y
f
ail
u
r
e
w
h
ich
i
n
ter
f
er
es
w
it
h
t
h
e
n
o
r
m
al
f
lo
w
o
f
cu
r
r
en
t.
Mo
s
t
o
f
th
e
f
a
u
lt
s
o
n
th
e
p
o
w
er
s
y
s
te
m
lead
to
a
s
h
o
r
t
-
cir
cu
i
t
co
n
d
itio
n
.
W
h
e
n
s
u
c
h
a
co
n
d
itio
n
o
cc
u
r
s
,
a
h
e
av
y
cu
r
r
en
t
(
ca
lled
s
h
o
r
t
-
c
ir
cu
it
cu
r
r
e
n
t)
f
lo
w
s
t
h
r
o
u
g
h
th
e
eq
u
ip
m
e
n
t,
ca
u
s
i
n
g
co
n
s
id
er
ab
le
d
am
a
g
e
to
th
e
eq
u
ip
m
e
n
t
an
d
in
ter
r
u
p
tio
n
o
f
s
er
v
ice
to
t
h
e
co
n
s
u
m
er
s
.
T
h
e
f
a
u
lt
cu
r
r
e
n
t
th
at
f
lo
w
s
d
ep
en
d
s
o
n
t
h
e
eq
u
iv
a
len
t
T
h
ev
e
n
i
n
v
o
ltag
e,
a
n
d
th
e
eq
u
iv
ale
n
t
i
m
p
ed
an
ce
at
th
e
f
au
lt
ter
m
i
n
al
s
an
d
th
e
f
au
lt
i
m
p
ed
a
n
ce
,
as
ill
u
s
tr
ated
i
n
Fi
g
u
r
e
1.
f
TH
TH
FA
U
L
T
Z
Z
V
I
Fig
u
r
e
1
.
E
q
u
iv
ale
n
t i
m
p
ed
a
n
ce
at
th
e
f
a
u
lt ter
m
i
n
als a
n
d
th
e
f
au
l
t i
m
p
ed
an
ce
T
h
r
ee
-
p
h
ase
f
a
u
lts
ar
e
ca
lled
s
y
m
m
etr
ical
f
a
u
lt
s
w
h
ic
h
g
i
v
e
r
is
e
to
s
y
m
m
e
tr
ical
c
u
r
r
en
ts
(
i.e
.
eq
u
al
f
au
lt
cu
r
r
en
t
s
in
t
h
e
li
n
es
w
i
th
1
2
0
d
eg
r
ee
d
is
p
lace
m
e
n
t)
.
Oth
er
t
y
p
es
o
f
tr
a
n
s
m
i
s
s
io
n
-
lin
e
f
a
u
lt
s
(
lin
e
t
o
g
r
o
u
n
d
,
li
n
e
to
li
n
e
an
d
d
o
u
b
l
e
lin
e
to
g
r
o
u
n
d
f
a
u
lt
s
)
ca
u
s
e
an
i
m
b
ala
n
ce
b
et
w
ee
n
th
e
p
h
a
s
es,
an
d
s
o
t
h
e
y
ar
e
ca
lled
u
n
s
y
m
m
etr
ical
f
a
u
lt
s
.
I
n
t
h
is
p
ap
er
,
a
th
r
ee
–
p
h
ase
b
alan
ce
d
f
a
u
lt
o
cc
u
r
s
o
n
b
u
s
–
an
d
th
e
s
y
s
te
m
is
th
en
u
n
b
alan
ce
d
.
T
h
e
v
o
lta
g
e
m
ag
n
it
u
d
e
a
n
d
th
e
p
h
ase
a
n
g
l
e
at
all
t
h
e
s
y
s
te
m
b
u
s
e
s
a
r
e
c
h
an
g
ed
d
u
e
to
t
h
e
f
au
lt a
n
d
t
h
ese
v
a
lu
e
s
ar
e
th
e
n
u
p
d
ated
an
d
ar
e
u
s
ed
to
ca
r
r
y
o
u
t th
e
ec
o
n
o
m
ic
lo
ad
d
is
p
atch
an
al
y
s
is
V
TH
Z
TH
Z
F
A
U
L
T
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
A
P
E
I
SS
N:
2252
-
8792
Op
timiz
a
tio
n
o
f e
co
n
o
mic
Lo
a
d
Dis
p
a
tch
w
ith
Un
it C
o
mmit
men
t o
n
Mu
lti Ma
ch
in
e
(
R
a
n
je
et
K
u
ma
r
)
51
6.
DYNA
M
I
C
P
RO
G
RAM
M
I
NG
M
E
T
H
O
D
T
h
is
m
e
th
o
d
is
ap
p
licab
le
to
a
w
id
e
clas
s
o
f
p
r
o
b
lem
s
a
n
d
th
r
o
u
g
h
th
is
m
et
h
o
d
th
e
o
p
tim
u
m
co
m
b
i
n
atio
n
o
f
u
n
i
ts
to
u
s
e
w
it
h
o
u
t
ca
lc
u
lati
n
g
t
h
e
co
s
t
o
f
all
p
o
s
s
ib
le
co
m
b
in
at
io
n
s
ca
n
b
e
f
o
u
n
d
.
T
h
e
ess
e
n
ce
o
f
d
y
n
a
m
ic
p
r
o
g
r
a
m
m
i
n
g
i
s
th
at
t
h
e
p
r
o
b
lem
o
f
f
i
n
d
in
g
th
e
o
p
ti
m
u
m
o
u
tp
u
ts
o
f
th
e
v
ar
io
u
s
u
n
its
f
o
r
a
g
i
v
en
lo
ad
is
r
ep
lace
d
b
y
t
h
e
p
r
o
b
lem
o
f
f
i
n
d
in
g
t
h
e
o
p
tim
u
m
o
u
tp
u
t
s
o
f
t
h
e
v
ar
io
u
s
u
n
its
f
o
r
all
t
h
e
lo
ad
s
b
et
w
ee
n
t
h
e
m
in
i
m
u
m
a
n
d
m
ax
i
m
u
m
ca
p
ac
it
y
o
f
t
h
e
u
n
it
s
Su
p
p
o
s
e
t
h
er
e
ar
e
N
t
h
er
m
al
u
n
its
a
n
d
t
h
e
ti
m
e
h
o
r
izo
n
is
T
.
T
h
e
u
n
it
co
m
m
i
t
m
en
t
p
r
o
b
lem
is
to
d
eter
m
i
n
e
th
e
co
m
m
it
m
e
n
t
an
d
g
e
n
er
atio
n
lev
el
s
o
f
all
u
n
it
s
o
v
er
th
e
p
er
io
d
T
s
o
t
h
at
t
h
e
to
tal
g
en
er
at
io
n
co
s
t
is
m
i
n
i
m
ized
.
I
tis
f
o
r
m
u
lated
as
a
m
ix
ed
-
i
n
teg
er
o
p
tim
izatio
n
p
r
o
b
le
m
i
n
w
h
i
ch
t
h
e
g
e
n
er
ati
n
g
u
n
it
s
ar
e
ass
i
g
n
ed
p
r
io
r
it
y
d
ep
en
d
i
n
g
u
p
o
n
t
h
eir
A
F
L
C
(
Av
er
ag
e
F
u
ll
L
o
ad
C
o
s
t)
.
T
h
i
s
m
et
h
o
d
is
co
n
s
id
er
ed
to
b
e
o
n
e
o
f
th
e
s
i
m
p
lest
m
et
h
o
d
o
f
u
n
it
co
m
m
it
m
en
t
s
ch
ed
u
lin
g
.
Un
i
t
w
i
th
t
h
e
leas
t
v
alu
e
o
f
A
F
L
C
is
ass
i
g
n
ed
th
e
to
p
m
o
s
t
p
r
io
r
it
y
an
d
th
e
r
est
ac
co
r
d
in
g
to
th
e
in
cr
ea
s
i
n
g
v
alu
e
o
f
A
F
L
C
.
T
h
is
m
e
th
o
d
i
s
p
r
i
m
ar
i
l
y
b
ased
o
n
t
h
e
p
r
i
n
cip
le
t
h
at
u
n
it
w
it
h
t
h
e
lea
s
t
v
al
u
e
o
f
AFLC
s
h
o
u
ld
b
e
lo
ad
ed
to
th
e
m
a
x
i
m
u
m
le
v
el
a
n
d
th
e
u
n
i
t
w
ith
th
e
lea
s
t
v
al
u
e
s
h
o
u
ld
b
e
lig
h
tl
y
lo
ad
ed
as
th
is
m
a
y
f
etc
h
m
o
r
e
ec
o
n
o
m
ic
al
u
n
i
t c
o
m
m
it
m
e
n
t so
lu
tio
n
.
T
h
e
v
alu
e
o
f
AFLC is
ca
lc
u
lat
ed
as f
o
llo
w
s
:
(
)
(
)
Fo
llo
w
i
n
g
s
tep
s
ar
e
f
o
llo
w
ed
f
o
r
h
av
in
g
u
n
i
t c
o
m
m
it
m
e
n
t th
r
o
u
g
h
P
r
io
r
ity
L
i
s
t M
eth
o
d
–
-
A
cc
o
r
d
in
g
to
th
e
A
F
L
C
v
al
u
e,
ar
r
an
g
e
ea
c
h
g
e
n
er
ato
r
in
in
cr
ea
s
i
n
g
o
r
d
er
o
f
th
e
ir
AF
L
C
v
al
u
es.
Ge
n
er
ato
r
w
it
h
lea
s
t v
al
u
e
is
g
i
v
en
t
h
e
h
i
g
h
e
s
t p
r
io
r
it
y
.
-
No
w
ac
co
r
d
in
g
to
th
e
to
tal
d
em
a
n
d
„
D
‟
,
s
elec
t
h
o
w
m
an
y
g
e
n
er
ato
r
s
r
eq
u
ir
ed
to
f
etch
th
e
g
i
v
en
d
e
m
a
n
d
i.e
.
∑
o
f
h
o
w
m
a
n
y
g
en
er
ato
r
s
f
r
o
m
to
p
ar
e
g
iv
in
g
t
h
e
r
eq
u
ir
ed
De
m
an
d
.
-
I
f
n
u
m
b
er
„
n
‟
co
m
es o
u
t to
b
e
o
n
e,
th
an
e
n
tire
g
e
n
er
atio
n
f
r
o
m
t
h
at
p
r
io
r
it
y
1
u
n
it.
-
I
f
„
n
‟
co
m
es
o
u
t
to
b
e
t
w
o
,
th
a
n
t
h
r
o
u
g
h
ex
h
a
u
s
ti
v
e
te
ch
n
iq
u
e
c
h
ec
k
in
g
w
h
ic
h
co
m
b
in
at
io
n
o
f
p
o
w
er
d
is
tr
ib
u
tio
n
b
et
w
ee
n
th
e
t
w
o
u
n
its
i
s
f
e
tch
i
n
g
th
e
m
o
s
t o
p
ti
m
ized
r
esu
lt.
-
I
f
„
n
‟
i
s
co
m
i
n
g
g
r
ea
ter
t
h
an
t
w
o
,
t
h
an
all
th
e
g
en
er
ato
r
s
f
r
o
m
1
to
(
n
-
2
)
w
ill
b
e
lo
ad
ed
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ter
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th
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e
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b
et
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h
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n
iq
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,
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i
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t
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ai
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w
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X
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x
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r
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t
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it
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th
e
g
o
al
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f
y
in
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o
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estab
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h
i
n
g
th
e
ac
c
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y
o
f
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o
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s
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n
th
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s
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t
h
e
s
i
m
u
latio
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e
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l
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f
t
h
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p
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o
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ed
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y
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r
ith
m
s
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ize
t
h
e
E
co
n
o
m
ic
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o
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Dis
p
atch
(
E
L
D)
an
d
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n
it
C
o
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m
it
m
e
n
t
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UC
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i
s
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s
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.
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ai
n
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o
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ith
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m
.
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d
al
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ith
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ated
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h
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ata
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th
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li
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atr
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I
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8792
IJ
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Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
A
P
E
I
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N:
2252
-
8792
Op
timiz
a
tio
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Lo
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Dis
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tch
w
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Un
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Mu
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ch
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e
(
R
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K
u
ma
r
)
53
T
ab
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3
.
Gen
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w
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r
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it
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.
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