I
nte
rna
t
io
na
l J
o
urna
l o
f
I
nfo
rm
a
t
ics a
nd
Co
m
m
un
ica
t
io
n T
ec
hn
o
lo
g
y
(
I
J
-
I
CT
)
Vo
l.
9
,
No
.
3
,
Dec
em
b
er
2
0
2
0
,
p
p
.
1
5
0
~
15
6
I
SS
N:
2252
-
8
7
7
6
,
DOI
: 1
0
.
1
1
5
9
1
/iji
ct.
v
9
i
3
.
p
p
15
1
-
15
6
151
J
o
ur
na
l
ho
m
ep
a
g
e
:
h
ttp
:
//ij
ict.
ia
esco
r
e.
co
m
Diminutio
n of
rea
l power lo
ss
by no
v
el gento
o
peng
uin
a
lg
o
rith
m
K
a
na
g
a
s
a
ba
i Leni
n
De
p
a
rtme
n
t
o
f
EE
E
,
P
ra
sa
d
V.
P
o
tl
u
ri
S
id
d
h
a
rt
h
a
In
stit
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te o
f
Tec
h
n
o
lo
g
y
,
In
d
ia
Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
No
v
1
6
,
2
0
19
R
ev
is
ed
J
an
1
2
,
2
0
2
0
Acc
ep
ted
Feb
11
,
2
0
20
In
th
is
p
a
p
e
r
G
e
n
to
o
P
e
n
g
u
in
Al
g
o
rit
h
m
(G
P
A)
is
p
ro
p
o
se
d
to
so
l
v
e
o
p
ti
m
a
l
re
a
c
ti
v
e
p
o
we
r
p
r
o
b
lem
.
G
e
n
to
o
P
e
n
g
u
in
s
p
re
li
m
in
a
r
y
p
o
p
u
latio
n
p
o
ss
e
ss
e
s
h
e
a
t
ra
d
iatio
n
a
n
d
m
a
g
n
e
ti
z
e
s
e
a
c
h
o
th
e
r
b
y
a
b
so
rp
ti
o
n
c
o
e
fficie
n
t.
G
e
n
to
o
P
e
n
g
u
in
s
wil
l
m
o
v
e
to
wa
rd
s
fu
rth
e
r
p
e
n
g
u
in
s
w
h
ich
p
o
ss
e
ss
e
s
lo
w
c
o
st
(e
lev
a
ted
h
e
a
t
c
o
n
c
e
n
tratio
n
)
o
f
a
b
so
rp
t
io
n
.
C
o
st
is
d
e
fin
e
d
b
y
th
e
h
e
a
t
c
o
n
c
e
n
tratio
n
,
d
istan
c
e
.
G
e
n
to
o
P
e
n
g
u
in
s
p
e
n
g
u
in
a
tt
ra
c
ti
o
n
v
a
lu
e
is
c
a
lcu
late
d
b
y
th
e
a
m
o
u
n
t
o
f
h
e
a
t
p
re
v
a
il
e
d
b
e
twe
e
n
tw
o
G
e
n
to
o
p
e
n
g
u
i
n
s.
G
e
n
to
o
P
e
n
g
u
in
s h
e
a
t
ra
d
iati
o
n
is
m
e
a
su
re
d
a
s li
n
e
a
r.
Les
s h
e
a
t
is r
e
c
e
iv
e
d
in
lo
n
g
e
r
d
istan
c
e
,
in
li
t
tl
e
d
istan
c
e
,
h
u
g
e
h
e
a
t
is
re
c
e
iv
e
d
.
G
e
n
to
o
P
e
n
g
u
in
Alg
o
rit
h
m
h
a
s
b
e
e
n
tes
ted
i
n
sta
n
d
a
rd
IEE
E
5
7
b
u
s
tes
t
s
y
ste
m
a
n
d
sim
u
latio
n
re
su
lt
s
sh
o
w
t
h
e
p
ro
je
c
ted
a
lg
o
rit
h
m
re
d
u
c
e
d
t
h
e
re
a
l
p
o
we
r
lo
ss
c
o
n
sid
e
ra
b
l
y
.
K
ey
w
o
r
d
s
:
Gen
to
o
p
en
g
u
in
alg
o
r
ith
m
Op
tim
al
r
ea
ctiv
e
p
o
wer
T
r
an
s
m
is
s
io
n
lo
s
s
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Kan
ag
asab
ai
L
en
in
,
Dep
ar
tm
en
t o
f
E
E
E
,
Pra
s
ad
V.
Po
tlu
r
i Sid
d
h
ar
th
a
I
n
s
titu
te
o
f
T
ec
h
n
o
lo
g
y
,
Kan
u
r
u
,
Vijay
awa
d
a
,
An
d
h
r
a
Pra
d
esh
,
5
2
0
0
0
7
,
I
n
d
ia.
E
m
ail: g
k
len
in
@
g
m
ail.
co
m
1.
I
NT
RO
D
UCT
I
O
N
T
h
e
m
a
in
o
b
je
cti
v
e
o
f
o
p
t
im
a
l
r
e
ac
t
iv
e
p
o
w
er
p
r
o
b
l
em
is
t
o
m
i
n
i
m
i
ze
t
h
e
r
e
al
p
o
w
er
lo
s
s
a
n
d
b
u
s
v
o
lta
g
e
d
e
v
i
ati
o
n
.
To
til
l
d
at
e
v
ar
io
u
s
m
e
th
o
d
o
l
o
g
ies
h
as
b
ee
n
a
p
p
li
e
d
t
o
s
o
l
v
e
t
h
e
O
p
ti
m
al
R
ea
cti
v
e
P
o
we
r
p
r
o
b
l
em
.
T
h
e
k
e
y
as
p
ec
t
o
f
s
o
lv
i
n
g
R
ea
cti
v
e
P
o
w
er
p
r
o
b
le
m
is
t
o
r
e
d
u
ce
t
h
e
r
ea
l
p
o
we
r
l
o
s
s
.
Pr
ev
io
u
s
l
y
m
a
n
y
ty
p
es
o
f
m
at
h
e
m
at
ic
al
m
et
h
o
d
o
l
o
g
ies
[1
-
6
]
h
a
v
e
b
ee
n
u
til
iz
ed
to
s
o
l
v
e
t
h
e
r
e
ac
t
iv
e
p
o
w
e
r
p
r
o
b
l
em
,
b
u
t
t
h
e
y
lac
k
i
n
h
a
n
d
li
n
g
t
h
e
c
o
n
s
tr
ai
n
ts
t
o
r
ea
ch
g
l
o
b
a
l
o
p
ti
m
i
za
t
io
n
s
o
lu
ti
o
n
.
I
n
t
h
e
n
ex
t
le
v
el
v
ar
i
o
u
s
t
y
p
es
o
f
ev
o
l
u
ti
o
n
a
r
y
al
g
o
r
it
h
m
s
[
7
-
1
5
]
h
as
b
ee
n
a
p
p
li
e
d
to
s
o
l
v
e
t
h
e
r
e
ac
t
iv
e
p
o
w
er
p
r
o
b
le
m
.
T
h
is
p
ap
er
p
r
o
p
o
s
es
Gen
to
o
Pen
g
u
in
Alg
o
r
ith
m
(
GPA)
to
s
o
lv
e
o
p
tim
al
r
ea
ctiv
e
p
o
wer
p
r
o
b
lem
.
Ge
n
to
o
P
en
g
u
in
s
will
m
o
v
e
to
war
d
s
f
u
r
th
e
r
p
en
g
u
in
s
wh
i
ch
p
o
s
s
ess
es
lo
w
co
s
t
(
elev
at
ed
h
ea
t
co
n
ce
n
tr
atio
n
)
o
f
a
b
s
o
r
p
tio
n
[
1
6
]
.
Gen
to
o
Pen
g
u
in
s
p
r
elim
in
a
r
y
p
o
p
u
l
atio
n
p
o
s
s
ess
es
h
ea
t
r
ad
iatio
n
an
d
m
ag
n
etize
s
ea
ch
o
t
h
er
b
y
ab
s
o
r
p
tio
n
co
ef
f
icien
t
C
o
s
t
is
d
ef
in
ed
b
y
th
e
h
ea
t
co
n
ce
n
tr
atio
n
,
d
is
tan
ce
.
Gen
to
o
Pen
g
u
in
s
p
r
eli
m
in
ar
y
p
o
p
u
latio
n
p
o
s
s
ess
es
h
ea
t
r
ad
iatio
n
an
d
m
ag
n
etize
s
ea
ch
o
t
h
er
b
y
ab
s
o
r
p
tio
n
co
ef
f
icien
t
Attr
ac
tio
n
is
co
m
p
leted
,
a
n
ew
-
f
an
g
led
s
o
lu
tio
n
is
esti
m
ated
f
o
r
th
at
h
ea
t
co
n
ce
n
tr
atio
n
is
m
o
d
er
n
ize
d
.
So
lu
tio
n
s
ar
e
ar
r
an
g
ed
s
eq
u
en
tially
an
d
m
o
s
t
ex
ce
llen
t
is
ch
o
s
e
n
.
Fo
r
h
ea
t
r
a
d
iatio
n
,
m
o
v
em
e
n
t,
h
ea
t
ab
s
o
r
p
tio
n
d
am
p
in
g
r
atio
is
ap
p
lied
.
Ge
n
to
o
p
en
g
u
i
n
s
p
ir
al
m
o
v
em
en
ts
th
r
o
u
g
h
o
u
t
th
e
a
b
s
o
r
p
tio
n
p
r
o
ce
d
u
r
e
ar
e
n
o
t
d
r
o
n
i
n
g
an
d
h
a
v
e
a
d
iv
er
g
e
n
ce
with
co
n
s
is
ten
t
d
is
tr
ib
u
tio
n
.
Pro
p
o
s
ed
Gen
to
o
Pen
g
u
in
Alg
o
r
ith
m
(
GPA)
h
as
b
ee
n
test
ed
in
s
tan
d
ar
d
I
E
E
E
5
7
b
u
s
test
s
y
s
tem
an
d
s
im
u
latio
n
r
esu
lts
s
h
o
w
th
e
p
r
o
jecte
d
al
g
o
r
it
h
m
r
ed
u
ce
d
th
e
r
ea
l p
o
wer
lo
s
s
ef
f
ec
tiv
ely
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
7
6
I
n
t J I
n
f
&
C
o
m
m
u
n
T
ec
h
n
o
l
,
Vo
l.
9
,
No
.
3
,
Dec
em
b
e
r
20
20
:
15
1
–
15
6
152
2.
P
RO
B
L
E
M
F
O
R
M
U
L
AT
I
O
N
R
ea
l
Po
wer
l
o
s
s
r
ed
u
ctio
n
is
m
ath
em
atica
lly
wr
itten
b
y
:
F
=
P
L
=
∑
g
k
k
∈
Nbr
(
V
i
2
+
V
j
2
−
2
V
i
V
j
c
os
θ
ij
)
(
1
)
with
r
esp
ec
t to
v
o
ltag
e
d
ev
iati
o
n
,
F
=
P
L
+
ω
v
×
Vol
ta
ge
De
via
tion
(
2
)
Vol
ta
ge
De
via
tion
=
∑
|
V
i
−
1
|
N
p
q
i
=
1
(
3
)
co
n
s
tr
ain
t
(
E
q
u
ality
)
P
G
=
P
D
+
P
L
(
4
)
co
n
s
tr
ain
ts
(
I
n
eq
u
ality
)
P
g
s
l
ack
m
i
n
≤
P
g
s
l
ac
k
≤
P
g
s
l
ack
m
ax
(
5
)
Q
gi
m
i
n
≤
Q
gi
≤
Q
gi
m
ax
,
i
∈
N
g
(
6
)
V
i
m
i
n
≤
V
i
≤
V
i
m
ax
,
i
∈
N
(
7
)
T
i
m
i
n
≤
T
i
≤
T
i
m
ax
,
i
∈
N
T
(
8
)
Q
c
m
i
n
≤
Q
c
≤
Q
C
m
ax
,
i
∈
N
C
(
9
)
3.
G
E
NT
O
O
P
E
NG
U
I
N
A
L
G
O
RIT
H
M
I
n
th
is
p
r
o
p
o
s
ed
a
p
p
r
o
ac
h
n
atu
r
e
d
ee
d
s
o
f
Gen
to
o
p
e
n
g
u
in
ar
e
im
itated
t
o
m
o
d
el
t
h
e
Gen
to
o
Pen
g
u
in
Alg
o
r
ith
m
(
GPA)
.
G
en
to
o
p
en
g
u
in
’
s
p
o
s
itio
n
an
d
co
s
t
ar
e
co
m
p
u
ted
.
Gen
to
o
P
en
g
u
in
s
will
m
o
v
e
to
war
d
s
f
u
r
th
er
p
e
n
g
u
i
n
s
wh
ich
p
o
s
s
ess
es
lo
w
co
s
t
(
elev
ated
h
ea
t
co
n
ce
n
tr
atio
n
)
o
f
ab
s
o
r
p
tio
n
.
C
o
s
t
is
d
ef
in
ed
b
y
th
e
h
ea
t
co
n
ce
n
tr
a
tio
n
,
d
is
tan
ce
.
Attr
ac
tio
n
is
co
m
p
leted
,
a
n
ew
-
f
a
n
g
led
s
o
lu
ti
o
n
is
esti
m
ated
f
o
r
th
at
h
ea
t
c
o
n
ce
n
tr
atio
n
is
m
o
d
er
n
ized
.
So
l
u
tio
n
s
ar
e
ar
r
a
n
g
e
d
s
eq
u
e
n
tially
an
d
m
o
s
t
ex
ce
llen
t
is
ch
o
s
en
.
Fo
r
h
ea
t r
ad
iatio
n
,
m
o
v
e
m
en
t,
h
ea
t a
b
s
o
r
p
tio
n
d
am
p
in
g
r
atio
is
a
p
p
lied
.
R
u
les ar
e
f
r
am
ed
as f
o
llo
ws:
−
Gen
to
o
Pen
g
u
in
s
p
r
elim
in
ar
y
p
o
p
u
latio
n
p
o
s
s
ess
es
h
ea
t
r
ad
iatio
n
a
n
d
m
a
g
n
etize
s
ea
ch
o
th
er
b
y
ab
s
o
r
p
tio
n
c
o
ef
f
icien
t
.
−
Gen
to
o
Pen
g
u
i
n
s
b
o
d
y
s
u
r
f
ac
e
ar
ea
is
co
n
s
id
er
ed
e
q
u
ally
.
−
Gen
to
o
Pen
g
u
i
n
s
ab
s
o
r
b
c
o
m
p
lete
h
ea
t r
ad
iatio
n
−
Gen
to
o
Pen
g
u
i
n
s
h
ea
t r
ad
iatio
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is
m
ea
s
u
r
ed
as lin
ea
r
.
−
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to
o
Pen
g
u
in
s
p
e
n
g
u
i
n
attr
ac
tio
n
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alu
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is
ca
lcu
lated
b
y
th
e
am
o
u
n
t
o
f
h
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t
p
r
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aile
d
b
etwe
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n
two
Gen
to
o
p
en
g
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s
.
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ess
h
ea
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r
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er
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in
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le
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t is r
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to
o
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g
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s
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ir
al
m
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ts
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r
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r
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t d
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h
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s
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r
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en
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is
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eter
m
in
e
d
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=
2
−
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2
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1
0
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C
OM
PUT
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ON
o
f
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r
ea
k
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lated
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=
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(
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J I
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f
&
C
o
m
m
u
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T
ec
h
n
o
l
I
SS
N:
2252
-
8
7
7
6
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u
tio
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153
ca
lcu
latio
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f
f
lip
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er
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itted
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th
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ity
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lis
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with
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at
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to
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(
2
5
)
=
−
1
(
2
6
)
=
(
2
7
)
=
(
2
8
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
7
6
I
n
t J I
n
f
&
C
o
m
m
u
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T
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h
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o
l
,
Vo
l.
9
,
No
.
3
,
Dec
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b
e
r
20
20
:
15
1
–
15
6
154
th
en
th
e
co
m
p
o
n
en
ts
o
f
th
e
p
o
s
itio
n
is
o
b
tain
ed
b
y
,
=
1
{
(
1
−
)
−
1
+
−
1
}
cos
{
1
{
(
1
−
)
−
1
+
−
1
}
}
(
2
9
)
=
1
{
(
1
−
)
−
1
+
−
1
}
s
in
{
1
{
(
1
−
)
−
1
+
−
1
}
}
(
3
0
)
s
p
ir
al
m
o
v
em
en
t
o
f
Gen
to
o
p
e
n
g
u
in
s
u
m
m
e
d
with
r
an
d
o
m
v
ec
to
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an
d
m
o
v
ed
to
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ew
p
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tio
n
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y
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1
−
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{
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1
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{
(
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−
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1
+
−
1
}
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in
{
1
{
(
1
−
)
−
1
+
−
1
}
}
+
+
(
3
2
)
a.
Star
t
b.
E
n
g
en
d
e
r
p
r
elim
in
a
r
y
p
o
p
u
latio
n
ar
r
a
y
o
f
Gen
to
o
p
en
g
u
in
c.
E
n
g
en
d
e
r
th
e
p
o
s
itio
n
o
f
ea
ch
Gen
to
o
p
en
g
u
in
d.
E
n
g
en
d
e
r
th
e
c
o
s
t o
f
ea
ch
Ge
n
to
o
p
en
g
u
in
e.
Fin
d
o
u
t th
e
p
r
elim
in
ar
y
h
ea
t
ab
s
o
r
p
tio
n
c
o
ef
f
icien
t
f.
Fo
r
I
t=1
to
Ma
x
im
u
m
I
te
r
atio
n
d
o
g.
E
n
g
en
d
e
r
th
e
r
e
p
licate
r
ep
r
o
d
u
ctio
n
o
f
p
o
p
u
latio
n
a
r
r
ay
;
h.
Fo
r
i=1
to
n
p
o
p
u
latio
n
d
o
i.
Fo
r
j=1
to
n
p
o
p
u
latio
n
d
o
j.
if
co
s
tj <
co
s
ti; th
en
k.
C
o
m
p
u
te
th
e
h
ea
t
r
ad
iatio
n
v
a
lu
e
b
y
=
∙
∙
∙
4
l.
C
o
m
p
u
te
th
e
attr
ac
tiv
en
ess
v
a
lu
e
b
y
=
∙
∙
∙
4
∙
−
m.
C
o
m
p
u
t
e
th
e
co
o
r
d
in
ate
d
s
p
ir
al
m
o
v
em
en
t
v
alu
e
b
y
=
1
{
(
1
−
)
−
1
+
−
1
}
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{
1
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(
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+
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+
−
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}
s
in
{
1
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(
1
−
)
−
1
+
−
1
}
}
n.
Fin
d
o
u
t n
ew
-
f
an
g
led
p
o
s
itio
n
b
y
,
=
1
{
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in
{
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+
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}
+
+
o.
E
s
tim
ate
n
ew
-
f
an
g
led
s
o
lu
tio
n
s
;
p.
E
n
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J I
n
f
&
C
o
m
m
u
n
T
ec
h
n
o
l
I
SS
N:
2252
-
8
7
7
6
Dimin
u
tio
n
o
f rea
l p
o
w
er lo
s
s
b
y
n
o
ve
l
g
en
to
o
p
en
g
u
in
a
lg
o
r
ith
m
(
K
a
n
a
g
a
s
a
b
a
i Len
in
)
155
q.
Ar
r
an
g
e
an
d
d
is
co
v
e
r
m
o
s
t e
x
ce
llen
t so
lu
tio
n
;
r.
Mo
d
er
n
ize
th
e
h
ea
t r
ad
iatio
n
v
alu
e
(
d
r
o
p
o
f
f
co
n
d
itio
n
)
;
s.
Mo
d
er
n
ize
th
e
m
u
tatio
n
c
o
ef
f
i
cien
t (
d
r
o
p
o
f
f
co
n
d
itio
n
)
;
t.
Mo
d
er
n
ize
th
e
h
ea
t a
b
s
o
r
p
tio
n
co
ef
f
icien
t (
e
n
h
an
ce
d
m
o
d
e)
;
u.
E
n
d
4.
SI
M
UL
A
T
I
O
N
ST
U
DY
Pro
p
o
s
ed
Gen
t
o
o
Pen
g
u
in
Al
g
o
r
ith
m
(
GPA)
h
as
b
ee
n
test
ed
,
in
I
E
E
E
5
7
B
u
s
s
y
s
tem
[
1
7
]
.
T
ab
le
1
s
h
o
ws
th
e
co
n
s
tr
ain
ts
o
f
co
n
tr
o
l
v
a
r
iab
les,
T
ab
le
2
s
h
o
ws
th
e
lim
its
o
f
r
ea
ctiv
e
p
o
wer
g
en
er
at
o
r
s
an
d
co
m
p
ar
is
o
n
r
esu
lts
ar
e
p
r
esen
t
ed
in
T
ab
le
3
.
Fig
u
r
e
1
s
h
o
ws th
e
co
m
p
ar
is
o
n
o
f
R
ea
l
Po
wer
L
o
s
s
an
d
Fig
u
r
e
2
I
n
d
icate
ab
o
u
t th
e
R
ea
l p
o
wer
lo
s
s
r
ed
u
ctio
n
in
p
er
ce
n
tag
e
.
Tab
le 1
.
C
o
n
stra
i
n
ts o
f
c
o
n
tro
l
v
a
riab
les
V
a
r
i
a
b
l
e
s t
y
p
e
M
i
n
i
m
u
m
v
a
l
u
e
(
P
U
)
M
a
x
i
m
u
m
v
a
l
u
e
(
P
U
)
I
EEE
5
7
B
u
s
G
e
n
e
r
a
t
o
r
V
o
l
t
a
g
e
0
.
9
5
1
.
1
Tr
a
n
sf
o
r
mer T
a
p
o
.
9
1
.
1
V
A
R
S
o
u
r
c
e
0
0
.
2
0
Tab
le 2
.
Co
n
stra
i
n
s o
f
re
a
c
ti
v
e
p
o
we
r
g
e
n
e
ra
to
rs
V
a
r
i
a
b
l
e
s
Q
M
i
n
i
mu
m
(
P
U
)
Q
M
a
x
i
mu
m
(
P
U
)
I
EEE
5
7
B
u
s
1
-
1
4
0
2
0
0
2
-
17
50
3
-
10
60
6
-
8
25
8
-
1
4
0
2
0
0
9
-
3
9
12
-
1
5
0
1
5
5
Tab
le 3
.
S
imu
lati
o
n
re
su
lt
s o
f
IE
EE
−
5
7
sy
ste
m
C
o
n
t
r
o
l
v
a
r
i
a
b
l
e
s
B
a
se
c
a
se
M
P
S
O
[
1
8
]
P
S
O
[
1
8
]
C
G
A
[
1
8
]
A
G
A
[
1
8
]
G
P
A
V
G
1
1
.
0
4
0
1
.
0
9
3
1
.
0
8
3
0
.
9
6
8
1
.
0
2
7
1
.
0
2
4
V
G
2
1
.
0
1
0
1
.
0
8
6
1
.
0
7
1
1
.
0
4
9
1
.
0
1
1
1
.
0
2
7
V
G
3
0
.
9
8
5
1
.
0
5
6
1
.
0
5
5
1
.
0
5
6
1
.
0
3
3
1
.
0
2
9
V
G
6
0
.
9
8
0
1
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0
3
8
1
.
0
3
6
0
.
9
8
7
1
.
0
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1
1
.
0
1
7
V
G
8
1
.
0
0
5
1
.
0
6
6
1
.
0
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1
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2
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1
.
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2
8
V
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9
0
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9
8
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1
1
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0
2
3
V
G
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1
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1
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R
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P
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0
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To
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N
R
*
-
N
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p
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r
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e
d
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
7
6
I
n
t J I
n
f
&
C
o
m
m
u
n
T
ec
h
n
o
l
,
Vo
l.
9
,
No
.
3
,
Dec
em
b
e
r
20
20
:
15
1
–
15
6
156
F
ig
u
re
1
.
C
o
m
p
a
riso
n
o
f
re
a
l
p
o
we
r
lo
ss
F
ig
u
re
2
.
Re
a
l
p
o
we
r
l
o
ss
re
d
u
c
ti
o
n
i
n
p
e
rc
e
n
tag
e
5.
CO
NCLU
SI
O
N
Gen
to
o
Pen
g
u
in
Alg
o
r
ith
m
(
GPA)
s
u
cc
es
s
f
u
lly
s
o
lv
ed
th
e
o
p
tim
al
r
ea
ctiv
e
p
o
wer
p
r
o
b
le
m
.
Gen
to
o
Pen
g
u
in
s
p
en
g
u
in
attr
ac
tio
n
v
alu
e
is
ca
lcu
lated
b
y
th
e
a
m
o
u
n
t
o
f
h
ea
t
p
r
e
v
ailed
b
et
wee
n
two
Gen
to
o
p
en
g
u
i
n
s
.
L
ess
h
ea
t
is
r
ec
eiv
ed
in
lo
n
g
e
r
d
is
tan
ce
,
in
litt
le
d
is
tan
ce
,
h
u
g
e
h
ea
t
is
r
ec
ei
v
ed
.
De
p
en
d
in
g
o
n
th
e
en
v
ir
o
n
m
en
t
its
h
as
b
ee
n
ass
u
m
ed
th
at
g
en
t
o
o
p
e
n
g
u
in
is
in
th
er
m
al
eq
u
ilib
r
iu
m
.
Pro
p
o
s
ed
Ge
n
to
o
Pen
g
u
in
Alg
o
r
ith
m
(
GPA)
h
a
s
b
ee
n
test
ed
in
s
tan
d
ar
d
I
E
E
E
5
7
b
u
s
test
s
y
s
tem
an
d
s
im
u
latio
n
r
esu
lts
s
h
o
w
th
e
p
r
o
jecte
d
alg
o
r
ith
m
r
ed
u
c
ed
th
e
r
ea
l
p
o
wer
l
o
s
s
ef
f
icien
tly
.
An
d
r
ed
u
ctio
n
o
f
r
ea
l
p
o
wer
lo
s
s
v
alu
e
is
2
6
.
7
6
%
w
h
e
n
c
o
m
p
a
re
d
to
th
e
b
a
se
v
a
lu
e
.
RE
F
E
R
E
NC
E
S
[
1
]
K.
Y.
Lee
,
“
F
u
e
l
-
c
o
st
m
in
imis
a
ti
o
n
f
o
r
b
o
t
h
re
a
l
a
n
d
re
a
c
ti
v
e
-
p
o
we
r
d
is
p
a
tch
e
s,”
Pro
c
e
e
d
in
g
s
Ge
n
e
ra
ti
o
n
,
T
ra
n
sm
issio
n
a
n
d
Distrib
u
ti
o
n
C
o
n
fer
e
n
c
e
,
v
o
l
.
1
3
1
,
n
o
.
3
,
p
p
.
8
5
-
9
3
,
1
9
8
4
.
[
2
]
Ao
k
i,
K.,
A.
Nis
h
ik
o
ri
a
n
d
R
.
T.
Yo
k
o
y
a
m
a
,
“
Co
n
stra
in
e
d
l
o
a
d
fl
o
w
u
sin
g
re
c
u
rsiv
e
q
u
a
d
ra
t
ic
p
r
o
g
r
a
m
m
in
g
,
”
IEE
E
T
.
Po
we
r
S
y
st
.,
v
o
l
.
2
,
n
o
.
1
,
p
p
.
8
-
16
,
1
9
8
7
.
[
3
]
Kirsc
h
e
n
,
D.S
.
a
n
d
H.
P
.
Va
n
M
e
e
tere
n
,
“
M
W/
v
o
l
tag
e
c
o
n
tr
o
l
in
a
li
n
e
a
r
p
ro
g
ra
m
m
in
g
b
a
se
d
o
p
ti
m
a
l
p
o
we
r
flo
w
,”
IEE
E
T
.
Po
we
r
S
y
st
,
v
o
l.
3
,
n
o
.
2
,
p
p
.
4
8
1
-
4
8
9
.
1
9
8
8
.
[
4
]
Li
u
,
W.
H.E
.
,
A.D.
P
a
p
a
lex
o
p
o
u
l
o
s
a
n
d
W.
F
.
Ti
n
n
e
y
,
“
Disc
re
te
s
h
u
n
t
c
o
n
tr
o
ls
i
n
a
Ne
wto
n
o
p
ti
m
a
l
p
o
we
r
flo
w
,”
IEE
E
T
.
Po
we
r
S
y
st
,
v
o
l.
7
,
n
o
.
4
,
p
p
.
1
5
0
9
-
1
5
1
8
,
1
9
9
2
.
[
5
]
V.
H.
Qu
i
n
tan
a
a
n
d
M
.
S
a
n
to
s
-
Nie
to
,
“
Re
a
c
ti
v
e
-
p
o
we
r
d
isp
a
tch
b
y
s
u
c
c
e
ss
iv
e
q
u
a
d
ra
ti
c
p
ro
g
ra
m
m
in
g
,
”
IE
EE
T
ra
n
sa
c
ti
o
n
s
o
n
En
e
rg
y
C
o
n
v
e
rs
i
o
n
,
v
o
l.
4
,
n
o
.
3
,
p
p
.
4
2
5
-
4
3
5
,
1
9
8
9
.
[
6
]
V.
d
e
S
o
u
sa
,
E.
Ba
p
ti
sta
,
a
n
d
G
.
d
a
Co
sta
,
“
Op
ti
m
a
l
re
a
c
ti
v
e
p
o
we
r
flo
w
v
ia
th
e
m
o
d
ifi
e
d
b
a
rrier
Lag
ra
n
g
ian
fu
n
c
ti
o
n
a
p
p
r
o
a
c
h
,
”
El
e
c
tric P
o
w
e
r S
y
ste
ms
Res
e
a
rc
h
,
v
o
l.
8
4
,
n
o
.
1
,
p
p
.
1
5
9
-
1
6
4
,
2
0
1
2
.
[
7
]
Y.
Li
,
X.
Li
,
a
n
d
Z.
Li
,
“
Re
a
c
ti
v
e
p
o
we
r
o
p
ti
m
iza
ti
o
n
u
si
n
g
h
y
b
rid
CABC
-
DE
a
lg
o
rit
h
m
,
”
El
e
c
tric
Po
we
r
Co
mp
o
n
e
n
ts
a
n
d
S
y
ste
ms
,
v
o
l.
4
5
,
n
o
.
9
,
p
p
.
9
8
0
-
9
8
9
,
2
0
1
7
.
[
8
]
S
.
M
o
u
a
ss
a
,
T.
Bo
u
k
t
ir,
a
n
d
A.
S
a
lh
i,
“
An
t
li
o
n
o
p
ti
m
ize
r
fo
r
so
lv
in
g
o
p
ti
m
a
l
re
a
c
ti
v
e
p
o
we
r
d
isp
a
tch
p
ro
b
lem
in
p
o
we
r
sy
ste
m
s,”
En
g
in
e
e
rin
g
S
c
i
e
n
c
e
a
n
d
T
e
c
h
n
o
lo
g
y
,
a
n
I
n
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
,
v
o
l
.
2
0
,
n
o
.
3
,
p
p
.
8
8
5
-
8
9
5
,
2
0
1
7
.
[
9
]
J.
Din
g
,
Q
.
Zh
a
n
g
,
a
n
d
Y.
M
a
,
“
Op
ti
m
a
l
re
a
c
ti
v
e
p
o
we
r
d
is
p
a
tch
b
a
se
d
o
n
th
e
CS
-
P
S
O
a
lg
o
rit
h
m
,
”
in
Pro
c
e
e
d
in
g
s
o
f
t
h
e
1
3
th
C
o
n
fer
e
n
c
e
o
n
I
n
d
u
stria
l
El
e
c
tro
n
ics
a
n
d
Ap
p
li
c
a
ti
o
n
s
(
ICIEA
),
IEE
E
,
W
u
h
a
n
,
Ch
in
a
,
2
0
1
8
.
[
1
0
]
K.
Ab
a
c
i
a
n
d
V.
Ya
m
a
ç
li
,
“
Op
ti
m
a
l
re
a
c
ti
v
e
-
p
o
we
r
d
isp
a
tch
u
sin
g
d
iffere
n
ti
a
l
se
a
rc
h
a
lg
o
rit
h
m
,
”
El
e
c
trica
l
En
g
i
n
e
e
rin
g
,
v
o
l.
9
9
,
n
o
.
1
,
p
p
.
2
1
3
–
2
2
5
,
2
0
1
7
.
[
1
1
]
J.
Din
g
,
Q.
Zh
a
n
g
a
n
d
Y.
M
a
,
“
Op
ti
m
a
l
re
a
c
ti
v
e
p
o
we
r
d
is
p
a
tch
b
a
se
d
o
n
th
e
CS
-
P
S
O
a
lg
o
rit
h
m
,
”
2
0
1
8
1
3
t
h
IEE
E
Co
n
fer
e
n
c
e
o
n
In
d
u
stri
a
l
El
e
c
tro
n
ics
a
n
d
A
p
p
li
c
a
ti
o
n
s (ICIE
A)
,
W
u
h
a
n
,
p
p
.
1
1
7
2
-
1
1
7
6
,
2
0
1
8
.
[
1
2
]
Th
a
n
g
Tr
u
n
g
Ng
u
y
e
n
,
Die
u
Ng
o
c
Vo
,
Ha
i
Va
n
Tran
,
a
n
d
Le
Va
n
Da
i,
“
Op
ti
m
a
l
Disp
a
tch
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