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[4
-
7]
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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Op
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187
a.
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c
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Vo
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m
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p
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in
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p
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en
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w
as
ca
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o
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t
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[
8
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b
ased
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d
ed
in
[
9
]
f
o
r
th
r
ee
d
if
f
er
e
n
t
k
i
n
d
s
o
f
lo
a
d
s
.
L
ater
o
n
,
o
th
er
an
al
y
tica
l
ap
p
r
o
ac
h
es
h
av
e
also
b
ee
n
p
r
o
p
o
s
ed
to
d
eter
m
i
n
e
o
p
tim
u
m
DG
p
lace
m
e
n
t
as
w
ell
a
s
DG
s
ize.
I
n
[
2
]
,
o
p
t
i
m
u
m
s
ize
o
f
DG
is
d
eter
m
i
n
ed
b
y
u
s
i
n
g
lo
s
s
s
en
s
iti
v
it
y
b
a
s
ed
an
al
y
tical
e
q
u
atio
n
,
w
h
er
ea
s
,
o
p
ti
m
u
m
D
G
lo
ca
tio
n
is
d
eter
m
i
n
ed
b
y
ex
ac
t
lo
s
s
eq
u
a
tio
n
.
R
ef
er
e
n
ce
[
1
0
]
co
v
er
s
t
h
e
eq
u
iv
ale
n
t
c
u
r
r
en
t
i
n
j
ec
tio
n
b
ased
ca
lcu
latio
n
o
f
lo
s
s
s
e
n
s
it
iv
i
t
y
f
ac
to
r
in
j
ec
tio
n
b
y
m
ea
n
s
o
f
t
w
o
m
atr
ix
e
s
:
B
u
s
-
I
n
j
ec
tio
n
to
B
r
an
ch
-
C
u
r
r
en
t
(
B
I
B
C
)
m
atr
i
x
an
d
B
r
an
ch
-
C
u
r
r
en
t
to
B
u
s
-
Vo
lta
g
e
(
B
C
B
V)
m
atr
i
x
.
A
co
n
v
e
n
tio
n
al
iter
ativ
e
s
ea
r
ch
al
g
o
r
ith
m
i
s
p
r
esen
ted
in
[
1
1
]
w
h
ic
h
d
ea
ls
w
it
h
OI
DG
b
ased
o
n
lo
s
s
r
ed
u
ctio
n
a
n
d
co
s
t
o
f
DG
s
ize.
Alth
o
u
g
h
t
h
i
s
m
et
h
o
d
is
s
i
m
p
le,
it
co
n
s
u
m
es
a
lo
t
o
f
ti
m
e.
R
e
f
er
e
n
ce
[
1
2
]
n
tr
o
d
u
ce
s
an
i
m
p
r
o
v
e
m
e
n
t
in
an
a
l
y
t
ical
m
et
h
o
d
f
o
r
id
e
n
ti
f
icatio
n
o
f
o
p
tim
a
l
lo
ca
tio
n
f
o
r
DG
in
s
tallatio
n
alo
n
g
w
it
h
o
p
ti
m
a
l p
o
w
er
f
ac
t
o
r
to
ac
h
iev
e
lo
s
s
r
ed
u
ctio
n
i
n
d
is
tr
ib
u
tio
n
n
et
w
o
r
k
s
.
A
l
g
o
r
ith
m
s
,
b
ased
o
n
m
u
lti
-
o
b
j
ec
tiv
es
o
p
ti
m
izatio
n
,
h
a
v
e
also
b
ee
n
p
r
o
p
o
s
ed
f
o
r
o
p
tim
u
m
DG
p
lace
m
en
t
an
d
s
izin
g
.
Me
t
h
o
d
s
b
ased
o
n
Ge
n
etic
A
l
g
o
r
ith
m
(
GA
)
ar
e
p
r
o
p
o
s
ed
in
[
1
3
-
14]
f
o
r
o
p
ti
m
izi
n
g
D
G
p
lace
m
e
n
t
an
d
s
izi
n
g
,
w
it
h
v
ar
io
u
s
o
b
j
ec
tiv
e
f
u
n
ct
io
n
s
.
R
ef
er
e
n
ce
[
1
5
]
h
as
co
m
b
in
e
d
GA
w
it
h
P
ar
ticle
S
w
ar
m
Op
ti
m
izatio
n
(
P
SO)
f
o
r
OI
DG,
s
o
lv
in
g
m
u
l
ti
-
o
b
j
ec
tiv
e
f
u
n
c
tio
n
s
th
at
i
n
clu
d
e
p
o
w
er
lo
s
s
e
s
,
v
o
ltag
e
r
eg
u
lat
io
n
a
n
d
v
o
ltag
e
s
tab
ilit
y
.
G
A
-
F
u
zz
y
ap
p
r
o
ac
h
is
u
s
e
d
in
[
1
6
]
to
o
p
ti
m
ize
lo
ca
tio
n
o
f
D
G.
Ob
j
ec
tiv
e
f
u
n
ctio
n
also
co
v
er
s
r
ed
u
ctio
n
in
p
o
w
er
s
y
s
te
m
lo
s
s
e
s
a
n
d
s
y
s
te
m
lo
a
d
in
g
a
s
w
ell
a
s
th
e
p
r
o
f
it
m
a
x
i
m
izatio
n
f
o
r
Dis
tr
ib
u
tio
n
C
o
m
p
an
ies.
A
d
y
n
a
m
ic
p
r
o
g
r
a
m
m
i
n
g
ap
p
r
o
ac
h
is
in
tr
o
d
u
ce
d
in
[
1
7
]
t
o
ascer
tain
an
o
p
tim
ized
DG
lo
ca
tio
n
t
h
at
w
o
u
ld
en
s
u
r
e
m
a
x
i
m
u
m
p
r
o
f
it.
R
e
f
er
en
ce
[
1
8
]
h
a
s
u
s
ed
An
t
C
o
lo
n
y
Sear
c
h
(
AC
S)
A
l
g
o
r
ith
m
f
o
r
r
eliab
il
it
y
b
ased
OI
DG
lo
ca
tio
n
w
i
s
e.
I
n
[
1
9
]
P
SO
alg
o
r
ith
m
i
s
i
m
p
le
m
e
n
ted
f
o
r
o
p
tim
u
m
p
lace
m
en
t
o
f
DG
wh
ile
m
i
n
i
m
izi
n
g
elec
tr
icit
y
co
s
t
f
o
r
co
n
s
u
m
er
s
.
R
ef
er
e
n
ce
[
2
0
]
h
as
u
s
ed
c
u
ck
o
o
s
ea
r
ch
al
g
o
r
ith
m
f
o
r
o
p
ti
m
u
m
DG
p
lace
m
e
n
t
to
o
b
tain
b
ett
er
v
o
ltag
e
p
r
o
f
ile
a
n
d
also
to
d
ec
r
ea
s
e
th
e
p
o
w
e
r
lo
s
s
es o
f
t
h
e
s
y
s
te
m
.
Var
io
u
s
o
t
h
er
r
esear
ch
er
s
h
a
v
e
also
co
n
s
id
er
ed
OI
DG
a
s
a
m
u
lti
-
o
b
j
ec
tiv
e
f
u
n
ctio
n
o
p
ti
m
izat
io
n
p
r
o
b
lem
.
T
h
eir
f
it
n
ess
f
u
n
c
ti
o
n
s
m
a
y
i
n
cl
u
d
e
i
m
p
r
o
v
ed
v
o
ltag
e
r
eg
u
latio
n
,
r
ed
u
ct
io
n
i
n
p
o
w
er
lo
s
s
e
s
,
an
d
v
o
ltag
e
s
tab
ilit
y
[
1
5
]
.
R
ef
er
en
ce
[
1
3
]
h
as
co
n
s
id
er
ed
co
s
t
b
e
n
ef
it
d
u
e
to
r
ed
u
ctio
n
o
f
p
o
w
er
lo
s
s
es
in
ca
s
e
o
f
DG
p
lace
m
e
n
t
in
f
it
n
ess
f
u
n
ct
io
n
a
n
d
en
s
u
r
e
th
a
t
v
o
ltag
e
p
r
o
f
ile
a
n
d
r
eliab
ilit
y
o
f
t
h
e
s
y
s
t
e
m
i
s
i
m
p
r
o
v
ed
.
I
t
h
as
b
ee
n
r
ep
o
r
ted
in
[
2
1
]
th
at
i
n
co
r
p
o
r
atio
n
o
f
D
Gs
g
i
v
es
r
i
s
e
to
t
h
e
lo
ad
ab
ilit
y
o
f
o
v
er
al
l
d
is
tr
ib
u
tio
n
n
et
w
o
r
k
.
I
n
t
h
is
p
ap
er
,
t
h
e
o
p
ti
m
al
s
i
m
u
ltan
eo
u
s
in
co
r
p
o
r
atio
n
o
f
m
u
ltip
le
DG
s
b
ased
o
n
m
ax
i
m
izatio
n
o
f
s
y
s
te
m
lo
ad
ab
ilit
y
i
s
in
v
e
s
ti
g
ated
w
h
er
e
t
h
e
m
ax
i
m
u
m
l
o
ad
ab
ilit
y
i
s
d
eter
m
i
n
ed
u
s
i
n
g
a
n
e
w
f
as
t
an
d
ac
cu
r
ate
ap
p
r
o
ac
h
.
T
h
e
o
p
tim
izatio
n
al
g
o
r
ith
m
u
s
ed
to
s
o
l
v
e
th
e
OI
DG
is
t
h
e
Vo
r
tex
S
ea
r
ch
in
g
al
g
o
r
ith
m
(
VS)
.
T
h
is
r
e
m
a
in
d
er
o
f
t
h
is
p
ap
er
is
s
tr
u
ctu
r
ed
a
s
f
o
llo
w
s
.
Sectio
n
2
p
r
esen
ts
th
e
f
o
r
m
u
latio
n
o
f
t
h
e
OI
DG
p
r
o
b
lem
.
T
h
e
o
p
tim
izatio
n
alg
o
r
ith
m
u
s
ed
in
t
h
is
p
ap
er
,
VS,
is
ex
p
lain
ed
i
n
s
ec
tio
n
3
.
Sec
tio
n
4
in
clu
d
es
t
h
e
d
is
cu
s
s
io
n
o
f
m
ai
n
r
es
u
lts
o
b
t
ain
ed
in
t
h
is
p
ap
er
.
Fin
d
i
n
g
s
o
f
th
is
p
ap
er
ar
e
co
n
clu
d
ed
in
s
ec
tio
n
5
.
2.
F
O
RM
UL
AT
I
O
N
O
F
T
H
E
O
I
DG
P
RO
B
L
E
M
E
x
p
lain
i
n
g
T
h
e
p
r
i
m
ar
y
p
u
r
p
o
s
e
o
f
OI
DG
p
r
o
b
lem
is
to
d
eter
m
i
n
e
t
h
e
o
p
ti
m
al
p
lace
m
e
n
t
a
n
d
s
ize
o
f
DG
f
o
r
i
m
p
r
o
v
ed
s
y
s
te
m
p
e
r
f
o
r
m
an
ce
.
T
h
e
OI
DG
p
r
o
b
lem
ca
n
b
e
f
o
r
m
u
la
ted
as f
o
llo
ws
[
2
2
]
:
(
)
(
1
)
(
)
(
2
)
(
)
(
3
)
[
]
(
4
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8792
I
n
t J
A
p
p
l P
o
w
er
E
n
g
,
Vo
l.
8
,
No
.
2
,
A
u
g
u
s
t 2
0
1
9
:
1
8
6
–
2
0
8
188
w
h
er
e:
(
)
is
th
e
o
b
j
ec
tiv
e
f
u
n
ct
io
n
.
x
is
t
h
e
v
ec
to
r
o
f
d
esi
g
n
v
ar
iab
les,
is
t
h
e
it
h
d
esi
g
n
v
ar
i
ab
le
an
d
r
ep
r
esen
ts
t
h
e
n
u
m
b
er
o
f
d
esig
n
v
ar
iab
les.
(
)
d
en
o
tes th
e
s
et
o
f
eq
u
alit
y
co
n
s
tr
ai
n
ts
a
n
d
is
th
e
n
u
m
b
er
o
f
eq
u
alit
y
co
n
s
tr
ai
n
ts
.
(
)
is
th
e
s
et
o
f
in
eq
u
alit
y
co
n
s
tr
ain
ts
a
n
d
is
th
e
n
u
m
b
er
o
f
i
n
eq
u
alit
y
co
n
s
tr
ain
t
s
.
Desig
n v
a
ria
bles
As
p
r
ev
io
u
s
l
y
m
e
n
tio
n
ed
,
th
i
s
p
ap
er
ai
m
s
to
ascer
tai
n
t
h
e
o
p
tim
a
l
s
ize
a
n
d
lo
ca
tio
n
o
f
DGs
to
b
e
in
s
er
ted
in
t
h
e
s
y
s
te
m
.
T
h
er
ef
o
r
e,
th
e
f
o
llo
w
i
n
g
d
esi
g
n
v
ar
ia
b
les ar
e
co
n
s
id
er
ed
.
Size
T
h
e
s
ize
o
f
DG
m
ea
n
s
t
h
e
am
o
u
n
t
o
f
p
o
w
er
g
en
er
ated
b
y
th
e
DG
u
n
it.
I
n
f
o
llo
w
in
g
s
e
ctio
n
s
,
th
e
ac
tiv
e
p
o
w
er
o
f
DG,
d
en
o
ted
b
y
,
is
co
n
s
id
er
ed
as a
d
esig
n
v
ar
iab
le
an
d
t
h
e
r
ea
ctiv
e
p
o
w
e
r
o
f
DG,
,
is
ca
lcu
lated
u
s
i
n
g
t
h
e
f
o
llo
w
i
n
g
ex
p
r
ess
io
n
:
(
(
)
)
(
5
)
T
h
e
s
ize
o
f
DG
h
as to
r
esp
ec
t
th
e
f
o
llo
w
i
n
g
co
n
s
tr
ai
n
t:
∑
∑
(
6
)
w
h
er
e:
P
F st
an
d
s
f
o
r
p
o
w
er
f
a
cto
r
.
L
o
ca
t
io
n
L
o
ca
tio
n
o
f
DG
m
ea
n
s
th
e
o
p
ti
m
al
b
u
s
to
in
s
er
t
th
e
DG
u
n
i
t.
T
h
e
lo
ca
tio
n
o
r
p
o
s
itio
n
o
f
DG
h
as
to
r
esp
ec
t th
e
f
o
llo
w
i
n
g
co
n
s
tr
ai
n
t:
(
7
)
w
h
er
e:
is
th
e
n
u
m
b
er
o
f
b
u
s
es
.
Fu
r
t
h
er
m
o
r
e,
if
t
h
er
e
ar
e
m
o
r
e
t
h
an
o
n
e
o
f
DG
u
n
i
t,
th
e
f
o
llo
w
i
n
g
co
n
s
tr
ai
n
t
h
as
to
b
e
r
esp
ec
ted
also
:
(
8
)
P
o
w
er
f
a
ct
o
r
I
n
s
o
m
e
o
f
t
h
e
i
n
v
e
s
ti
g
ated
c
ases
o
f
t
h
is
p
ap
er
,
th
e
P
F
o
f
th
e
D
G
u
n
i
t
is
i
m
p
o
s
ed
an
d
i
n
s
o
m
e
o
f
th
e
m
th
e
P
F is
co
n
s
id
er
ed
as a
d
esig
n
v
ar
iab
le
an
d
it h
a
s
to
b
e
d
eter
m
i
n
ed
.
O
bje
ct
iv
e
f
un
ct
io
n
Her
e,
th
e
m
ai
n
o
b
j
ec
tiv
e
f
u
n
ct
io
n
is
s
y
s
te
m
m
a
x
i
m
u
m
lo
ad
ab
ilit
y
.
M
a
x
i
m
u
m
lo
a
da
bil
it
y
Dif
f
er
en
t
d
ef
i
n
itio
n
s
an
d
d
i
f
f
e
r
en
t
ter
m
i
n
o
lo
g
ies
o
f
lo
ad
ab
ilit
y
a
n
d
m
a
x
i
m
u
m
lo
ad
ab
ilit
y
h
av
e
b
ee
n
r
ep
o
r
ted
in
[
2
3
-
28]
.
T
h
ese
d
ef
in
itio
n
s
v
ar
y
i
n
ter
m
s
o
f
co
n
s
t
r
ain
ts
,
s
tab
ilit
y
o
f
s
y
s
te
m
an
d
th
e
r
ep
r
esen
tatio
n
o
f
lo
ad
ab
ilit
y
.
Ma
x
i
m
u
m
lo
ad
ab
ilit
y
o
r
m
ax
i
m
u
m
lo
ad
i
n
g
m
ar
g
i
n
i
s
u
s
ed
to
r
ef
er
m
ax
i
m
u
m
p
o
w
er
lo
ad
th
at
co
u
l
d
lo
ad
th
e
s
y
s
te
m
to
t
h
e
p
o
i
n
t
o
f
i
n
s
tab
ilit
y
f
r
o
m
t
h
e
b
a
s
e
lo
a
d
.
Ma
x
i
m
u
m
lo
ad
ab
ilit
y
o
f
t
h
e
s
y
s
te
m
i
n
d
icate
s
h
o
w
m
u
c
h
t
h
e
s
y
s
te
m
m
u
s
t
b
e
s
tr
ess
ed
in
o
r
d
er
to
r
ea
ch
t
h
e
i
n
s
tab
ili
t
y
.
V
o
lta
g
e
in
s
ta
b
ilit
y
is
co
n
s
id
er
ed
a
cr
u
cial
p
ar
am
e
ter
th
r
o
u
g
h
o
u
t
th
is
p
ap
er
,
th
u
s
t
h
e
m
a
x
i
m
u
m
lo
ad
ab
ilit
y
o
f
th
e
s
y
s
te
m
ca
n
b
e
d
ef
in
ed
as
th
e
m
ax
i
m
u
m
in
cr
ea
s
e
i
n
p
o
w
er
s
y
s
te
m
lo
ad
f
r
o
m
t
h
e
b
ase
lo
ad
till
th
e
p
o
in
t
w
h
er
e
v
o
lta
g
e
c
o
llap
s
es.
Ma
x
i
m
u
m
lo
ad
ab
ilit
y
o
f
th
e
s
y
s
te
m
r
ep
r
esen
t
s
t
h
e
lo
ad
in
g
f
ac
to
r
i
n
m
u
ltip
le
o
f
b
ase
ca
s
e
lo
ad
till
t
h
e
p
o
in
t
o
f
v
o
lta
g
e
co
llap
s
e
an
d
r
ep
r
esen
ted
w
i
th
th
e
v
ar
iab
le
λ
m
ax
.
T
h
e
m
ax
i
m
u
m
lo
ad
ab
ilit
y
o
f
t
h
e
s
y
s
te
m
ca
n
also
b
e
r
ef
er
r
ed
as o
r
Vo
ltag
e
Stab
ilit
y
Ma
r
g
i
n
(
VSM)
o
r
Vo
ltag
e
Stab
ilit
y
L
i
m
it (
VS
L
)
.
P
ro
po
s
ed
a
pp
ro
a
ch
I
n
t
h
is
p
ap
er
,
a
n
e
w
ap
p
r
o
ac
h
f
o
r
ca
lc
u
lati
n
g
is
p
r
o
p
o
s
ed
.
T
h
is
ap
p
r
o
ac
h
is
m
u
c
h
f
a
s
ter
th
a
n
th
e
cla
s
s
ica
l
o
n
e
p
r
o
p
o
s
ed
an
d
i
m
p
le
m
en
ted
i
n
[
2
1
]
.
T
h
e
f
lo
w
ch
ar
t
o
f
th
e
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
is
g
i
v
en
i
n
Fig
u
r
e
1
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
A
P
E
I
SS
N:
2252
-
8792
Op
tima
l in
co
r
p
o
r
a
tio
n
o
f m
u
ltip
le
d
is
tr
ib
u
ted
g
en
era
tio
n
u
n
i
ts
b
a
s
ed
o
n
a
n
ew s
ystem…
(
Y
.
La
tr
ec
h
e
)
189
Fig
u
r
e
1
.
Flo
w
c
h
ar
t f
o
r
th
e
ca
l
cu
latio
n
o
f
.
T
o
f
in
d
th
e
m
a
x
i
m
u
m
lo
ad
ab
ilit
y
i.e
.
,
o
n
ea
ch
b
u
s
,
b
o
th
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
w
e
r
ar
e
in
cr
ea
s
ed
u
s
in
g
t
h
e
f
o
llo
w
i
n
g
:
(
9
)
(
1
0
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8792
I
n
t J
A
p
p
l P
o
w
er
E
n
g
,
Vo
l.
8
,
No
.
2
,
A
u
g
u
s
t 2
0
1
9
:
1
8
6
–
2
0
8
190
w
h
er
e:
an
d
ar
e
th
e
in
itial
ac
tiv
e
an
d
r
ea
c
tiv
e
p
o
w
er
s
o
f
co
m
b
in
ed
lo
ad
s
,
r
esp
ec
tiv
el
y
.
Si
m
ilar
l
y
,
an
d
r
ep
r
esen
t th
e
n
e
w
ac
tiv
e
a
n
d
r
ea
ctiv
e
p
o
w
er
s
(
lo
ad
s
)
,
r
esp
ec
tiv
el
y
an
d
is
th
e
lo
ad
in
g
f
ac
to
r
.
Ho
w
e
v
er
,
in
s
tead
o
f
k
ee
p
in
c
r
ea
s
in
g
u
s
i
n
g
a
s
m
al
s
tep
as
in
th
e
clas
s
ical
ap
p
r
o
ac
h
[
2
1
]
,
h
er
e
w
e
s
tar
t
f
r
o
m
a
n
in
itia
l
in
ter
v
al
[
a,
b
]
,
th
en
is
ca
lcu
latd
as
th
e
m
id
p
o
in
t
o
f
t
h
is
i
n
ter
v
al.
Af
te
r
th
at,
P
an
d
Q
ar
e
in
cr
ea
s
ed
u
s
i
n
g
eq
u
at
io
n
s
(
9
)
an
d
(
1
0
)
.
T
h
e
p
o
w
er
f
lo
w
e
q
u
atio
n
s
ar
e
s
o
l
v
ed
,
i
f
it
is
s
u
cc
es
s
f
u
l
th
e
n
e
w
in
ter
v
a
l
w
ill
b
e
[
a,
]
o
th
er
w
i
s
e
th
e
n
e
w
in
ter
v
al
w
ill
b
e
[
,
b
]
.
T
h
is
p
r
o
ce
s
s
is
co
n
tin
u
ed
u
n
t
il
th
e
in
ter
v
al
[
a,
b
]
b
ec
o
m
es s
m
alle
r
t
h
an
a
p
r
ed
ef
in
ed
to
ler
an
ce
(
).
Co
m
pa
ra
t
iv
e
s
t
ud
y
I
n
o
r
d
er
to
s
h
o
w
th
e
s
p
ee
d
an
d
ef
f
icien
c
y
o
f
t
h
e
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
co
m
p
ar
ed
to
t
h
e
o
n
e
p
r
o
p
o
s
ed
in
[
2
1
]
,
s
ev
er
al
test
s
h
av
e
b
ee
n
ac
h
iev
ed
as
s
h
o
w
n
in
T
ab
le
1
.
I
n
th
is
tab
le,
th
e
an
d
th
e
ti
m
e
tak
e
n
to
co
m
p
u
te
t
h
e
ar
e
r
ep
o
r
ted
.
I
t
ca
n
b
e
n
o
ticed
f
r
o
m
T
ab
le
1
th
at,
th
e
is
th
e
s
a
m
e
u
s
in
g
b
o
th
ap
p
r
o
ac
h
es
f
o
r
all
ca
s
es,
h
o
w
ev
er
,
t
h
er
e
i
s
a
h
u
g
e
ti
m
e
d
if
f
er
e
n
ce
b
et
w
ee
n
b
o
th
ap
p
r
o
ac
h
es.
Fo
r
i
n
s
ta
n
ce
f
o
r
t
h
e
1
0
-
b
u
s
r
ad
ial
s
y
s
te
m
th
e
ti
m
e
h
as
b
ee
n
r
ed
u
ce
d
b
y
9
4
.
6
4
%,
f
o
r
th
e
6
9
-
b
u
s
r
ad
ial
s
y
s
te
m
t
h
e
ti
m
e
h
as
b
ee
n
r
ed
u
ce
d
b
y
9
9
.
1
4
%
an
d
f
o
r
th
e
1
18
-
b
u
s
r
ad
ial
s
y
s
te
m
t
h
e
ti
m
e
h
a
s
b
ee
n
r
ed
u
ce
d
b
y
9
9
.
0
7
% u
s
i
n
g
t
h
e
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
co
m
p
ar
ed
to
th
e
o
n
e
p
r
o
p
o
s
ed
in
[
2
1
]
.
Mo
r
eo
v
er
,
it
is
w
o
r
th
m
e
n
tio
n
in
g
th
a
t,
th
is
t
i
m
e
h
a
s
b
ee
n
co
m
p
u
ted
f
o
r
o
n
e
s
i
m
u
lat
io
n
,
t
h
er
ef
o
r
e,
if
th
is
s
i
m
u
latio
n
i
s
r
ep
ea
ted
a
t
h
o
u
s
a
n
d
t
i
m
e
s
a
s
w
h
e
n
s
o
l
v
i
n
g
t
h
e
OI
DG
p
r
o
b
lem
t
h
e
g
ai
n
i
n
ti
m
e
b
ec
o
m
e
s
ex
tr
e
m
e
l
y
i
m
p
o
r
tan
t.
T
ab
le
1
.
C
o
m
p
ar
is
o
n
o
f
th
e
P
r
o
p
o
s
ed
A
p
p
r
o
ac
h
w
it
h
th
e
C
la
s
s
ical
O
n
e
T
e
st
s
y
st
e
m
C
l
a
ssi
c
a
l
a
p
p
r
o
a
c
h
P
r
o
p
o
se
d
a
p
p
r
o
a
c
h
T
i
me
(
s)
T
i
me
(
s)
10
-
b
u
s ra
d
i
a
l
sy
st
e
m
[
2
9
]
2
.
0
6
4
1
.
6
9
8
2
.
0
6
3
0
.
0
9
1
16
-
b
u
s ra
d
i
a
l
sy
st
e
m
[
2
1
]
7
.
5
5
0
7
.
8
5
2
7
.
5
4
9
0
.
1
1
0
33
-
b
u
s ra
d
i
a
l
sy
st
e
m
[
3
0
]
3
.
4
0
7
9
.
6
4
8
3
.
4
0
6
0
.
1
2
5
69
-
b
u
s ra
d
i
a
l
sy
st
e
m
[
3
1
]
3
.
2
1
0
2
8
.
8
1
3
3
.
2
1
0
0
.
2
4
5
85
-
b
u
s ra
d
i
a
l
sy
st
e
m
[
3
2
]
2
.
5
9
9
3
1
.
9
5
8
2
.
5
9
9
0
.
3
2
6
1
1
8
-
b
u
s
r
a
d
i
a
l
sy
st
e
m
[
3
3
]
2
.
4
6
5
4
6
.
9
3
3
2
.
4
6
4
0
.
4
3
8
Co
ns
t
ra
ints
Fo
r
OI
DG,
b
o
th
eq
u
alit
y
a
n
d
in
eq
u
alit
y
co
n
s
tr
ain
ts
ar
e
p
r
esen
t
in
p
r
o
b
le
m
f
o
r
m
u
latio
n
.
E
qu
a
lity
co
ns
t
ra
ints
∑
(
)
(
1
1
)
∑
(
)
(
1
2
)
w
h
er
e;
is
g
e
n
er
ato
r
ac
tiv
e
p
o
w
er
o
u
tp
u
t a
t b
u
s
is
g
e
n
er
ato
r
r
ea
ctiv
e
p
o
w
er
o
u
tp
u
t a
t b
u
s
is
ac
tiv
e
p
o
w
er
d
e
m
an
d
at
b
u
s
is
r
ea
ctiv
e
p
o
w
er
d
e
m
a
n
d
at
b
u
s
is
v
o
lta
g
e
o
f
b
u
s
;
is
p
h
ase
v
o
ltag
e
an
g
le
at
b
u
s
is
to
tal
n
u
m
b
er
o
f
b
r
an
c
h
es i
n
th
e
g
i
v
e
n
r
ad
ial
d
is
tr
ib
u
tio
n
s
y
s
te
m
.
N
r
ep
r
esen
ts
to
tal
n
u
m
b
er
o
f
b
u
s
e
s
in
g
i
v
en
r
ad
ial
d
is
tr
ib
u
t
io
n
s
y
s
te
m
I
nequ
a
lity
co
ns
t
ra
ints
Vo
lt
a
g
e
li
m
it
s
T
h
e
n
o
d
al
v
o
lta
g
es
m
u
s
t
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e
co
n
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ain
ed
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et
w
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n
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eir
m
i
n
i
m
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m
a
n
d
m
a
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i
m
u
m
li
m
its
.
T
h
er
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o
r
e,
v
o
ltag
e
li
m
i
ts
co
n
s
tr
ain
t c
a
n
b
e
f
o
r
m
u
lated
as f
o
llo
w
s
:
(
1
3
)
T
her
m
a
l li
m
it
P
o
w
er
f
lo
w
t
h
r
o
u
g
h
a
n
y
d
is
t
r
ib
u
tio
n
f
ee
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er
m
u
s
t
co
m
p
l
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w
it
h
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e
t
h
er
m
al
ca
p
ac
it
y
o
f
th
e
li
n
e.
T
h
er
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o
r
e,
th
e
th
er
m
al
li
m
i
t c
o
n
s
tr
ain
ts
ca
n
b
e
f
o
r
m
u
lated
as f
o
llo
w
s
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
A
P
E
I
SS
N:
2252
-
8792
Op
tima
l in
co
r
p
o
r
a
tio
n
o
f m
u
ltip
le
d
is
tr
ib
u
ted
g
en
era
tio
n
u
n
i
ts
b
a
s
ed
o
n
a
n
ew s
ystem…
(
Y
.
La
tr
ec
h
e
)
191
|
|
|
|
(
1
4
)
w
h
er
e:
is
th
e
ap
p
ar
en
t p
o
w
er
at
b
r
an
ch
an
d
is
th
e
m
a
x
i
m
u
m
ap
p
ar
en
t p
o
w
er
at
b
r
an
ch
.
M
a
x
i
m
u
m
ca
pa
cit
y
T
h
e
m
a
x
i
m
u
m
ca
p
ac
it
y
o
f
D
Gs
th
at
ca
n
b
e
in
s
talled
in
th
e
n
et
w
o
r
k
is
r
estricte
d
b
y
DG
p
en
etr
atio
n
lev
el
(
)
.
T
h
er
ef
o
r
e,
th
er
e
is
a
ca
p
ac
it
y
co
n
s
tr
ain
t
at
u
n
it
y
p
o
w
er
f
ac
to
r
o
f
D
G
g
e
n
er
ati
n
g
p
o
w
er
t
h
at
is
g
iv
e
n
b
y
f
o
llo
w
i
n
g
e
x
p
r
e
s
s
io
n
:
(
)
(
1
5
)
I
f
b
o
th
ac
ti
v
e
an
d
r
ea
cti
v
e
p
o
w
er
s
ar
e
b
ei
n
g
g
e
n
er
ated
b
y
DG,
th
e
n
t
h
e
p
r
ec
ed
en
t
eq
u
at
io
n
ca
n
b
e
m
o
d
i
f
ied
as:
(
)
(
1
6
)
w
h
er
e
is
th
e
to
tal
n
u
m
b
er
o
f
DG
u
n
its
i
n
co
r
p
o
r
ated
in
th
e
p
o
w
er
s
y
s
te
m
;
r
ep
r
esen
ts
m
ax
i
m
u
m
p
en
etr
atio
n
lev
el
as
a
p
er
ce
n
t
ag
e
o
f
p
ea
k
lo
ad
o
f
th
e
s
y
s
te
m
;
an
d
ar
e
d
en
o
tin
g
to
tal
ac
t
iv
e
p
o
w
er
lo
ad
an
d
to
tal
ap
p
ar
en
t p
o
w
er
lo
ad
o
f
th
e
s
y
s
te
m
,
r
esp
ec
tiv
el
y
.
Co
ns
t
ra
ints ha
nd
l
ing
pro
ce
d
ure
I
t
is
w
o
r
th
to
m
e
n
tio
n
t
h
at
th
e
i
n
eq
u
ali
t
y
co
n
s
tr
ai
n
t
s
ar
e
tak
e
n
i
n
to
ac
co
u
n
t
u
s
i
n
g
t
h
e
p
en
alt
y
m
et
h
o
d
.
I
n
t
h
i
s
m
et
h
o
d
a
p
en
alt
y
ter
m
i
s
ad
d
ed
to
t
h
e
p
r
i
m
ar
y
o
b
j
ec
tiv
e
f
u
n
ctio
n
w
h
ic
h
co
n
s
i
s
ts
o
f
m
u
ltip
l
y
in
g
a
p
en
alt
y
p
ar
a
m
e
ter
b
y
a
p
e
n
alt
y
f
ac
to
r
.
T
h
e
p
en
alt
y
p
ar
a
m
eter
is
a
m
ea
s
u
r
e
o
f
h
o
w
m
u
c
h
th
e
co
n
s
tr
ain
ts
ar
e
v
io
lated
,
if
th
er
e
is
n
o
v
io
latio
n
th
is
p
ar
a
m
ete
r
is
n
u
ll.
T
h
is
m
et
h
o
d
h
a
s
b
ee
n
i
m
p
le
m
e
n
ted
a
n
d
u
s
ed
b
y
t
h
e
VS a
l
g
o
r
it
h
m
to
h
an
d
le
in
eq
u
a
lit
y
co
n
s
tr
ai
n
ts
.
E
v
a
lua
t
io
n ind
ices
T
h
e
ev
alu
atio
n
o
f
t
h
e
OI
DG
o
n
s
y
s
te
m
p
er
f
o
r
m
a
n
ce
i
s
p
er
f
o
r
m
ed
u
s
i
n
g
t
h
e
f
o
llo
w
i
n
g
in
d
i
ce
s
w
h
er
e
th
e
s
u
b
s
cr
ip
t
(
0
)
r
e
p
r
esen
ts
v
a
lu
es
b
ef
o
r
e
th
e
i
n
co
r
p
o
r
atio
n
o
f
DG
an
d
th
e
s
u
b
s
cr
ip
t
DG
r
ep
r
esen
ts
t
h
e
v
al
u
es
ca
lcu
lated
af
ter
t
h
e
i
n
co
r
p
o
r
ati
o
n
o
f
DG
[
2
1
]
.
Act
iv
e
lo
s
s
es r
educt
io
n in
de
x
T
h
e
A
cti
v
e
L
o
s
s
es
R
ed
u
ct
io
n
(
AL
R
)
i
n
d
ex
i
s
b
e
g
iv
e
n
b
y
:
(
1
7
)
w
h
er
e:
T
h
e
ac
tiv
e
p
o
w
er
lo
s
s
e
s
ar
e
s
et
as f
o
llo
w
s
:
∑
|
|
(
1
8
)
w
h
er
e:
is
th
e
r
esis
ta
n
ce
o
f
b
r
an
ch
k
,
r
ep
r
esen
ts
th
e
cu
r
r
e
n
t
p
ass
in
g
th
r
o
u
g
h
b
r
an
ch
an
d
d
en
o
tes
t
h
e
to
tal
n
u
m
b
er
o
f
b
r
an
ch
e
s
.
Rea
ct
iv
e
lo
s
s
es r
educt
io
n in
dex
T
h
e
R
ea
ctiv
e
L
o
s
s
e
s
R
ed
u
c
tio
n
(
R
L
R
)
i
n
d
ex
i
s
g
i
v
en
b
y
:
(
1
9
)
Sy
s
t
e
m
lo
a
da
bil
it
y
i
m
pro
v
em
e
nt
ind
e
x
T
h
e
s
y
s
te
m
lo
ad
ab
ilit
y
i
m
p
r
o
v
e
m
en
t (
SL
I
)
i
n
d
ex
is
g
i
v
en
b
y
:
(
2
0
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8792
I
n
t J
A
p
p
l P
o
w
er
E
n
g
,
Vo
l.
8
,
No
.
2
,
A
u
g
u
s
t 2
0
1
9
:
1
8
6
–
2
0
8
192
Vo
lt
a
g
e
pro
f
ile
im
pro
v
e
m
e
n
t
ind
ex
T
h
e
v
o
ltag
e
p
r
o
f
ile
i
m
p
r
o
v
e
m
en
t (
VP
I
)
in
d
ex
is
g
iv
e
n
b
y
:
(
2
1
)
W
h
er
e
th
e
v
o
lta
g
e
p
r
o
f
ile
is
d
ef
i
n
ed
as f
o
llo
w
s
:
∑
(
)
(
2
2
)
W
h
er
e
is
th
e
r
ated
v
o
lta
g
e
(
tak
en
a
s
1
p
.
u
.
in
th
i
s
p
ap
er
)
.
Vo
lt
a
g
e
s
t
a
bil
it
y
enha
nce
m
e
nt
ind
ex
T
h
e
v
o
ltag
e
s
tab
ilit
y
e
n
h
a
n
ce
m
en
t in
d
e
x
(
VSI
M)
is
as
f
o
llo
w
s
:
(
2
3
)
an
d
v
o
ltag
e
s
tab
ilit
y
in
d
e
x
(
V
SI)
w
ill b
e
ex
p
r
es
s
ed
as
[
3
4
]
:
(
(
)
)
(
2
4
)
w
h
er
e
SI
o
f
n
o
d
e
is
g
iv
e
n
b
y
:
(
)
|
|
[
(
)
(
)
]
|
|
[
(
)
(
)
]
(
2
5
)
w
h
er
e
is
th
e
v
o
ltag
e
o
f
b
u
s
m
i,
(
)
is
to
tal
r
ea
l
p
o
w
er
lo
ad
f
ed
th
r
o
u
g
h
b
u
s
n
i,
(
)
is
to
tal
r
ea
ctiv
e
p
o
w
er
lo
ad
f
ed
th
r
o
u
g
h
b
u
s
n
i,
is
th
e
r
esi
s
ta
n
c
e
o
f
b
r
an
ch
I
,
is
th
e
r
ea
cta
n
ce
o
f
b
r
an
ch
i.
Nu
m
ber
o
f
bu
s
es v
io
la
t
ing
v
o
lt
a
g
e
lim
it
Nu
m
b
er
o
f
b
u
s
es
v
io
lati
n
g
v
o
ltag
e
l
i
m
i
t
(
NB
VV)
,
as
i
n
d
ica
ted
b
y
its
n
a
m
e,
co
u
n
t
s
t
h
e
n
u
m
b
er
s
o
f
b
u
s
s
e
s
w
h
er
e
v
o
ltag
e
li
m
it
s
(
u
p
p
er
o
f
lo
w
er
li
m
it
s
)
ar
e
n
o
t r
esp
ec
ted
.
3.
O
P
T
I
M
I
Z
AT
I
O
N
AL
G
O
R
I
T
H
M
T
h
e
VS
alg
o
r
ith
m
is
a
s
in
g
le
-
s
o
l
u
tio
n
b
ased
m
eta
h
eu
r
i
s
t
ic
th
at
e
v
o
lv
es
to
o
p
ti
m
alit
y
u
s
i
n
g
a
g
en
er
atio
n
a
n
d
a
r
ep
lace
m
en
t
p
r
o
ce
d
u
r
e.
I
n
th
e
g
e
n
er
atio
n
p
h
ase
N
ca
n
d
id
ate
s
o
l
u
tio
n
s
ar
e
g
e
n
er
ated
i
n
s
id
e
a
r
ad
iu
s
ar
o
u
n
d
t
h
e
b
est
s
o
l
u
tio
n
u
s
i
n
g
a
s
p
ec
i
f
ied
p
r
o
c
ed
u
r
e
an
d
,
in
t
h
e
r
ep
lace
m
e
n
t,
p
h
ase
a
s
o
lu
tio
n
r
ep
lace
s
th
e
cu
r
r
en
t
b
est
s
o
lu
tio
n
.
T
h
i
s
p
r
o
ce
s
s
is
r
ep
ea
ted
u
n
til
a
t
er
m
in
a
tio
n
cr
iter
io
n
i
s
m
et.
I
t
is
r
ep
o
r
ted
in
[
3
5
]
th
at
t
h
e
VS
h
as
e
x
ce
lle
n
t
p
er
f
o
r
m
a
n
ce
f
o
r
th
e
o
p
ti
m
iza
tio
n
o
f
m
at
h
e
m
atica
l
f
u
n
ct
io
n
s
.
I
n
th
is
p
ap
er
is
u
s
ed
as
th
e
o
p
ti
m
izat
io
n
al
g
o
r
ith
m
f
o
r
s
o
l
v
i
n
g
t
h
e
OI
DG
p
r
o
b
le
m
.
Alg
o
rit
h
m
des
cr
iptio
n
T
h
e
f
lo
w
c
h
ar
t
o
f
t
h
e
VS
a
lg
o
r
ith
m
is
s
k
etch
ed
i
n
F
ig
u
r
e
1
.
T
h
e
m
ai
n
s
tep
s
o
f
t
h
e
V
S
al
g
o
r
ith
m
ar
e
ex
p
lain
ed
b
elo
w
:
Ste
p 1
:
in
t
h
e
i
n
itiali
s
atio
n
p
h
ase,
f
ir
s
t th
e
ce
n
tr
e
o
f
th
e
s
ea
r
ch
s
p
ac
e
is
s
elec
ted
as
th
e
f
ir
s
t
g
en
er
ated
s
o
lu
tio
n
.
T
h
en
,
th
e
i
n
itial r
ad
i
u
s
i
s
co
m
p
u
ted
u
s
i
n
g
t
h
e
f
o
llo
w
i
n
g
ex
p
r
ess
io
n
:
(
)
(
26
)
w
h
er
e:
is
th
e
in
v
er
s
e
in
co
m
p
lete
g
a
m
m
a
f
u
n
ctio
n
an
d
is
th
e
i
n
itial
s
tan
d
ar
d
d
is
tr
ib
u
tio
n
ca
lc
u
lated
as
f
o
llo
w
s
:
(
)
(
)
(
1
7
)
w
h
er
e:
is
th
e
u
p
p
er
b
o
u
n
d
o
f
d
esig
n
v
ar
iab
les,
is
th
e
lo
w
er
b
o
u
n
d
o
f
th
e
d
esig
n
v
ar
iab
les
,
is
a
r
an
d
o
m
v
ar
iab
le
a
n
d
is
th
e
s
h
ap
e
p
ar
a
m
eter
s
elec
ted
as
1
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
A
P
E
I
SS
N:
2252
-
8792
Op
tima
l in
co
r
p
o
r
a
tio
n
o
f m
u
ltip
le
d
is
tr
ib
u
ted
g
en
era
tio
n
u
n
i
ts
b
a
s
ed
o
n
a
n
ew s
ystem…
(
Y
.
La
tr
ec
h
e
)
193
Af
ter
th
a
t,
th
e
b
est
s
o
l
u
tio
n
a
n
d
f
it
n
es
s
o
b
tain
ed
s
o
f
ar
r
ef
e
r
r
ed
to
as
g
best
an
d
S
best
,
r
esp
ec
tiv
el
y
ar
e
in
itial
ized
w
i
th
t
h
e
f
ir
s
t so
l
u
ti
o
n
g
e
n
er
ated
.
Ste
p
2
:
in
th
i
s
s
tep
N
ca
n
d
id
ate
s
o
lu
tio
n
s
(
w
it
h
N
th
e
s
ize
o
f
s
o
l
u
tio
n
s
)
ar
e
g
en
er
a
ted
in
th
e
n
eig
h
b
o
r
h
o
o
d
o
f
g
best
u
s
i
n
g
a
Gau
s
s
ian
d
is
tr
ib
u
tio
n
w
h
er
e
th
is
n
ei
g
h
b
o
r
h
o
o
d
is
ch
ar
ac
ter
ized
w
it
h
th
e
f
o
llo
w
in
g
r
ad
iu
s
:
(
)
(
28
)
w
h
er
e
th
e
s
h
ap
e
p
ar
a
m
eter
is
d
ec
r
ea
s
ed
u
s
in
g
t
h
e
f
o
llo
w
i
n
g
ex
p
r
ess
io
n
:
(
29
)
w
h
er
e
is
iter
atio
n
n
u
m
b
er
an
d
is
th
e
m
ax
i
m
u
m
n
u
m
b
er
o
f
i
t
er
atio
n
s
.
I
t is
w
o
r
t
h
to
m
e
n
tio
n
h
er
e
t
h
a
t; t
h
is
r
ad
iu
s
is
o
f
p
ar
a
m
o
u
n
t
i
m
p
o
r
ta
n
ce
i
n
th
e
co
n
v
er
g
e
n
ce
o
f
t
h
e
VS
alg
o
r
ith
m
.
Fo
r
a
g
i
v
en
o
p
ti
m
i
za
tio
n
p
r
o
b
lem
,
t
h
is
r
ad
iu
s
is
i
n
itialized
w
it
h
a
h
ig
h
v
alu
e
(
a
s
in
eq
u
at
io
n
(
1
)
)
in
o
r
d
er
to
p
r
o
m
o
te
t
h
e
e
x
p
lo
r
atio
n
p
h
a
s
e
i
n
th
e
f
ir
s
t
iter
atio
n
s
an
d
t
h
en
it
is
d
ec
r
ea
s
ed
alo
n
g
w
it
h
th
e
n
u
m
b
er
o
f
iter
atio
n
s
i
n
cr
ea
s
es
i
n
o
r
d
er
to
p
r
o
m
o
te
th
e
ex
p
lo
itatio
n
p
h
ase.
I
t
is
r
ep
o
r
ted
in
[
3
5
]
th
at
u
n
til
a
ce
r
tai
n
n
u
m
b
er
o
f
iter
atio
n
s
is
r
ea
ch
e
d
,
th
e
r
ad
iu
s
v
ar
ies
ap
p
r
o
x
im
atel
y
lin
ea
r
l
y
an
d
th
e
n
it
d
ec
r
ea
s
es
s
i
g
n
i
f
ica
n
tl
y
.
T
h
is
b
eh
av
io
r
allo
w
s
to
h
a
v
e
a
g
o
o
d
b
alan
ce
b
et
w
ee
n
e
x
p
lo
r
atio
n
an
d
ex
p
lo
itatio
n
p
h
ase
s
.
Ste
p
3
:
in
th
e
p
r
ev
io
u
s
s
tep
s
o
m
e
o
f
t
h
e
g
e
n
er
ated
s
o
lu
t
io
n
s
m
a
y
la
y
o
u
t
s
id
e
th
e
s
ea
r
ch
s
p
ac
e,
th
er
ef
o
r
e
th
e
y
h
av
e
to
b
e
b
r
o
u
g
h
t b
ac
k
in
s
id
e
th
e
s
ea
r
c
h
s
p
a
ce
u
s
i
n
g
t
h
e
f
o
ll
o
w
in
g
ex
p
r
es
s
io
n
:
{
(
)
(
)
(
30
)
Ste
p
4
:
in
th
is
s
tep
t
h
e
g
en
er
a
ted
s
o
lu
tio
n
s
ar
e
e
v
al
u
ated
i
n
o
r
d
er
to
ca
lcu
late
th
e
ir
f
itn
e
s
s
‟
s
,
t
h
e
b
e
s
t
s
o
lu
tio
n
a
m
o
n
g
th
e
m
i
s
id
en
ti
f
ied
an
d
n
o
ted
as
g
best_New
a
n
d
S
best_New
.
T
h
en
,
i
f
S
best_New
i
s
f
o
u
n
d
to
b
e
b
etter
th
an
S
best
,
th
er
e
f
o
r
e
g
best
a
n
d
S
best
ar
e
u
p
d
ated
.
Ste
p 5
:
in
th
i
s
s
tep
th
e
r
ad
iu
s
i
s
u
p
d
ated
u
s
i
n
g
eq
u
atio
n
(
28
)
.
Ste
p
6
:
f
i
n
all
y
,
if
t
h
e
n
u
m
b
er
o
f
iter
atio
n
s
ex
ce
ed
s
th
e
p
r
o
ce
s
s
is
s
to
p
p
ed
an
d
g
best
a
n
d
S
b
est
ar
e
d
is
p
lay
ed
o
th
er
w
i
s
e
th
e
p
r
o
ce
s
s
is
r
ep
ea
ted
f
r
o
m
Ste
p 2
.
T
h
e
VS
alg
o
r
ith
m
as
it
is
p
r
o
p
o
s
ed
in
is
[
3
5
]
d
o
es
n
o
t
h
an
d
le
d
is
cr
ete
o
r
in
teg
er
d
esig
n
v
ar
iab
les.
T
h
er
ef
o
r
e,
f
o
r
th
e
p
u
r
p
o
s
e
o
f
th
e
OI
DG
p
r
o
b
le
m
w
e
h
a
v
e
a
d
d
ed
s
o
m
e
m
o
d
if
ica
tio
n
s
o
n
t
h
e
i
n
itial
v
er
s
io
n
o
f
th
e
VS a
l
g
o
r
ith
m
to
c
o
p
e
w
it
h
th
is
i
s
s
u
e.
4.
RE
SU
L
T
AND
DI
SCUS
SI
O
N
P
r
o
v
id
e
I
n
th
is
p
ap
er
,
6
2
ca
s
e
s
tu
d
ie
s
h
a
v
e
b
ee
n
i
n
v
esti
g
a
ted
u
s
i
n
g
2
te
s
t
s
y
s
te
m
s
.
Mo
r
e
d
etails
ab
o
u
t te
s
t s
y
s
te
m
s
a
n
d
in
v
es
ti
g
ated
ca
s
es a
r
e
g
i
v
e
n
in
t
h
e
f
o
llo
w
i
n
g
t
w
o
s
u
b
s
ec
tio
n
s
.
T
est
s
y
s
t
e
m
s
I
n
th
i
s
p
ap
er
,
tw
o
test
s
y
s
te
m
s
ar
e
co
n
s
id
er
ed
:
3
3
-
b
u
s
an
d
6
9
-
b
u
s
R
T
S
.
T
h
e
m
ai
n
ch
ar
ac
ter
is
tics
o
f
th
ese
s
y
s
te
m
s
ar
e
g
i
v
en
i
n
T
ab
le
2
.
Mo
r
eo
v
er
,
th
e
s
in
g
le
li
n
e
d
iag
r
a
m
s
o
f
f
ir
s
t
a
n
d
s
ec
o
n
d
test
s
y
s
te
m
s
ar
e
s
h
o
w
n
in
F
ig
u
r
e
3
an
d
Fig
u
r
e
4
,
r
esp
ec
tiv
el
y
.
T
ab
le
2
.
T
h
e
M
ain
C
h
ar
ac
ter
i
s
tics
o
f
t
h
e
I
n
v
esti
g
ated
T
est Sy
s
te
m
s
S
y
st
e
m
33
-
b
u
s R
T
S
69
-
b
u
s R
T
S
S
y
st
e
m C
h
a
r
a
c
t
e
r
i
st
i
c
s
D
a
t
a
i
s g
i
v
e
n
i
n
[
3
0
]
D
a
t
a
i
s g
i
v
e
n
i
n
[
3
1
]
B
u
se
s
33
69
B
r
a
n
c
h
e
s
32
68
T
o
t
a
l
a
c
t
i
v
e
l
o
a
d
(
M
W
)
3
.
7
1
5
0
3
.
8
0
2
1
T
o
t
a
l
r
e
a
c
t
i
v
e
l
o
a
d
(
M
v
a
r
)
2
.
3
0
0
0
2
.
6
9
4
5
P
l
o
ss (M
W
)
0
.
2
1
1
0
0
.
2
2
5
0
Q
l
o
ss (M
v
a
r
)
0
.
1
4
3
0
0
.
1
0
2
1
3
.
4
0
6
5
3
.
2
1
0
2
V
S
I
1
1
VP
0
.
1
3
3
8
0
.
0
9
9
3
V
max
1
.
1
1
.
1
V
m
i
n
0
.
9
5
0
.
9
5
S
max
(
M
V
A
)
5
5
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
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8792
I
n
t J
A
p
p
l P
o
w
er
E
n
g
,
Vo
l.
8
,
No
.
2
,
A
u
g
u
s
t 2
0
1
9
:
1
8
6
–
2
0
8
194
Fig
u
r
e
2
.
Flo
w
c
h
ar
t o
f
t
h
e
v
s
alg
o
r
ith
m
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
A
P
E
I
SS
N:
2252
-
8792
Op
tima
l in
co
r
p
o
r
a
tio
n
o
f m
u
ltip
le
d
is
tr
ib
u
ted
g
en
era
tio
n
u
n
i
ts
b
a
s
ed
o
n
a
n
ew s
ystem…
(
Y
.
La
tr
ec
h
e
)
195
Fig
u
r
e
3
.
Sin
g
le
li
n
e
d
iag
r
a
m
o
f
th
e
3
3
-
b
u
s
R
T
S
Fig
u
r
e
4
.
Sin
g
le
li
n
e
d
iag
r
a
m
o
f
th
e
6
9
-
b
u
s
R
T
S
DG
t
y
pe
s
Ma
in
l
y
,
th
er
e
ar
e
f
o
u
r
d
i
f
f
er
e
n
t c
ateg
o
r
ies o
f
DG
s
co
n
s
id
er
e
d
in
liter
atu
r
e
as r
ep
o
r
ted
in
[
2
4
]
.
C
ateg
o
r
y
1
: D
G
s
u
p
p
lies
ac
ti
v
e
p
o
w
er
o
n
l
y
,
e.
g
.
s
o
lar
s
y
s
te
m
.
C
at
eg
o
r
y
2
: D
G
s
u
p
p
lies
r
ea
ct
iv
e
p
o
w
er
o
n
l
y
,
e.
g
.
s
y
n
ch
r
o
n
o
u
s
co
m
p
en
s
ato
r
s
.
C
ateg
o
r
y
3
: D
G
s
u
p
p
lies
ac
ti
v
e
p
o
w
er
b
u
t c
o
n
s
u
m
es r
ea
ctiv
e
p
o
w
er
,
e.
g
.
i
n
d
u
ctio
n
g
e
n
er
a
to
r
.
C
ateg
o
r
y
4
: D
G
s
u
p
p
lies
b
o
th
ac
tiv
e
an
d
r
ea
cti
v
e
p
o
w
er
e.
g
.
s
y
n
ch
r
o
n
o
u
s
g
en
er
ato
r
.
I
n
th
i
s
w
o
r
k
,
w
h
er
e
th
e
P
F
is
co
n
s
id
er
ed
as
u
n
it
y
th
e
D
G
u
n
i
ts
ar
e
co
n
s
id
er
ed
f
r
o
m
T
y
p
e
1
w
h
ils
t
w
h
e
n
th
e
P
F
is
co
n
s
id
er
ed
as
a
d
esig
n
v
ar
iab
le
t
h
e
DG
u
n
it
s
ar
e
co
n
s
id
er
ed
as
ac
tiv
e
-
r
ea
ctiv
e
p
o
w
er
s
o
u
r
ce
s
(
i.e
.
T
y
p
e
4
)
.
I
nv
estig
a
t
ed
ca
s
es
As p
r
ev
io
u
s
l
y
m
e
n
tio
n
ed
,
in
t
h
is
p
ap
er
,
6
2
ca
s
e
s
tu
d
ies ar
e
in
v
e
s
ti
g
ated
as s
h
o
w
n
i
n
T
ab
le
3
.
Evaluation Warning : The document was created with Spire.PDF for Python.