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3
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I
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3
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Sep
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20
2
6
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1
1
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-
1
1
1
6
1106
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er
g
e
n
ce
o
f
p
o
wer
f
lo
w
.
T
h
e
L
B
MC
ca
n
b
e
ca
lcu
late
d
ef
f
icien
tly
u
s
in
g
o
th
e
r
tech
n
iq
u
es,
s
u
ch
as
co
n
tin
u
atio
n
p
ar
am
eter
i
z
atio
n
m
eth
o
d
s
[
6
]
.
Var
io
u
s
m
eth
o
d
o
l
o
g
ies
f
o
r
ass
es
s
in
g
L
B
MC
f
o
r
b
u
s
es
h
av
e
b
ee
n
d
o
cu
m
e
n
ted
in
th
e
ex
tan
t
liter
atu
r
e.
Am
jad
y
an
d
Vela
y
ati
[
7
]
p
r
o
p
o
s
e
a
m
eth
o
d
o
l
o
g
y
f
o
r
t
h
e
ev
alu
atio
n
o
f
t
h
e
L
B
MC.
T
h
is
p
r
o
p
o
s
ed
m
eth
o
d
d
eter
m
in
es
th
e
L
B
MC
at
th
e
p
o
in
t
o
f
v
o
ltag
e
c
o
llap
s
e
u
s
in
g
P
-
V
cu
r
v
es.
T
h
is
is
ac
h
iev
ed
b
y
co
m
b
in
in
g
th
e
p
o
we
r
f
l
o
w
co
n
tin
u
atio
n
m
eth
o
d
with
a
m
o
d
al
an
aly
s
is
o
f
th
e
lo
ad
f
lo
w
J
ac
o
b
ian
s
.
Ali
et
a
l.
[
8
]
p
r
o
p
o
s
ed
a
n
in
n
o
v
ativ
e
m
o
d
if
icatio
n
to
t
h
e
class
ic
New
to
n
–
R
ap
h
s
o
n
o
p
tim
al
lo
ad
f
lo
w
s
o
lv
er
f
o
r
ch
ar
ac
ter
i
z
in
g
th
e
s
y
s
tem
'
s
m
ax
im
u
m
lo
ad
.
T
h
is
ap
p
r
o
ac
h
s
u
p
p
lem
en
ts
th
e
s
tan
d
ar
d
p
o
wer
f
lo
w
eq
u
atio
n
s
with
two
ad
d
itio
n
al
elem
en
ts
.
Firstl
y
,
an
alg
eb
r
aic
r
ep
r
esen
tatio
n
o
f
th
e
m
ax
im
u
m
an
d
m
in
im
u
m
v
o
ltag
e
co
n
d
itio
n
s
is
in
co
r
p
o
r
ate
d
.
Se
co
n
d
ly
,
th
e
tr
a
n
s
v
er
s
ality
co
n
d
itio
n
is
im
p
o
s
ed
t
o
lim
it
th
e
s
et
o
f
s
o
lu
tio
n
s
to
th
e
b
o
u
n
d
a
r
y
o
f
th
e
s
o
lv
a
b
le
r
eg
io
n
.
I
n
th
eir
s
tu
d
y
,
Gu
p
ta
et
a
l.
[
9
]
p
r
o
p
o
s
e
a
m
eth
o
d
f
o
r
in
v
esti
g
atin
g
th
e
im
p
ac
t
o
f
in
c
r
ea
s
ed
p
h
o
to
v
o
ltaic
(
PV)
p
en
etr
atio
n
o
n
th
e
v
o
ltag
e
s
tab
ilit
y
o
f
I
E
E
E
1
4
-
b
u
s
test
s
y
s
tem
.
T
o
ac
h
iev
e
th
is
,
t
h
ey
co
n
s
id
er
th
e
m
ax
im
u
m
PV
p
en
etr
atio
n
a
n
d
th
e
s
y
s
tem
'
s
L
B
M
C
.
I
n
th
eir
ar
ticle,
Gó
m
ez
-
Qu
iles
et
a
l.
[
1
0
]
p
r
o
p
o
s
e
a
n
ew
alg
o
r
ith
m
f
o
r
id
en
tif
y
in
g
L
B
MC
in
p
o
wer
s
y
s
tem
s
.
T
h
e
alg
o
r
ith
m
in
q
u
esti
o
n
h
as
b
ee
n
d
escr
ib
ed
as
b
o
th
f
ast
an
d
s
im
p
le.
I
t
in
v
o
lv
es
th
e
im
p
lem
en
tatio
n
o
f
b
is
ec
tio
n
s
ea
r
ch
es
b
etwe
en
f
ea
s
ib
le
an
d
in
f
ea
s
ib
le
lo
ad
f
lo
w
ca
s
es.
Z
aid
an
et
a
l.
[
1
1
]
d
elin
ea
te
th
e
m
eth
o
d
o
lo
g
y
em
p
lo
y
ed
t
o
ascer
tain
th
e
L
B
MC
at
wh
ich
v
o
ltag
e
co
lla
p
s
e
o
cc
u
r
s
,
u
tili
z
in
g
th
e
co
n
tin
u
atio
n
p
o
wer
f
lo
w
tech
n
iq
u
e.
Am
a
n
et
a
l.
[
1
2
]
p
r
esen
t
a
n
ew
n
etwo
r
k
r
ec
o
n
f
i
g
u
r
atio
n
alg
o
r
it
h
m
b
ased
o
n
m
ax
im
i
z
in
g
th
e
s
y
s
tem
'
s
lo
ad
ca
p
ac
ity
.
T
h
e
v
o
ltag
e
p
r
o
f
ile
o
f
th
e
en
t
ir
e
s
y
s
tem
is
en
h
an
ce
d
in
co
m
p
ar
is
o
n
with
th
e
b
aselin
e
c
ase.
Do
n
d
ar
iy
a
an
d
Sak
r
av
d
ia
[
1
3
]
p
r
o
p
o
s
e
a
n
e
w
p
r
o
x
im
ity
in
d
icato
r
to
ass
ess
v
o
ltag
e
s
tab
ilit
y
an
d
p
r
ed
i
ct
th
e
ac
tu
al
c
r
itical
lo
ad
o
f
t
h
e
s
y
s
tem
,
as
well
as
th
e
v
o
ltag
es
at
v
ar
io
u
s
L
B
s
at
th
e
cr
itical
lo
ad
p
o
in
t.
Ach
ar
j
ee
[
1
4
]
p
r
o
p
o
s
es
a
s
im
p
le,
co
d
ed
g
en
etic
alg
o
r
it
h
m
with
r
ea
l
-
c
o
d
ed
s
ec
u
r
ity
co
n
s
tr
ain
ts
(
SC
GA)
to
id
en
tify
th
e
m
ax
i
m
u
m
lo
ad
ab
ilit
y
lim
it
(
ML
L
)
o
f
v
ar
io
u
s
I
E
E
E
s
tan
d
ar
d
test
s
y
s
tem
s
.
T
h
e
ML
L
p
r
o
b
lem
is
m
o
d
elled
as
an
o
p
tim
i
z
atio
n
p
r
o
b
lem
th
at
ta
k
es secu
r
ity
co
n
s
tr
ain
ts
in
to
ac
c
o
u
n
t.
Ma
n
o
h
aa
r
a
n
an
d
G
n
an
a
m
b
al
[
1
5
]
p
r
o
p
o
s
e
a
m
eth
o
d
o
l
o
g
ical
ap
p
r
o
ac
h
to
d
eter
m
in
in
g
th
e
m
a
x
im
u
m
p
er
m
is
s
ib
le
o
v
er
all
lo
ad
ca
p
ac
ity
.
T
h
is
ap
p
r
o
ac
h
o
p
tim
i
z
es
th
e
u
tili
z
atio
n
r
ate
o
f
th
e
l
o
ad
,
t
h
er
eb
y
im
p
r
o
v
i
n
g
th
e
elec
tr
ical
s
y
s
tem
'
s
ab
ilit
y
to
m
ain
tain
an
en
er
g
y
b
alan
ce
wh
en
ad
d
itio
n
al
lo
ad
s
ar
e
ad
d
ed
o
r
in
a
n
u
n
b
alan
ce
d
s
ce
n
ar
io
.
Peq
u
en
o
d
o
s
San
to
s
et
a
l.
[
1
6
]
p
r
o
p
o
s
e
an
ap
p
r
o
ac
h
to
th
e
ass
es
s
m
en
t
o
f
co
m
p
o
s
ite
r
eliab
ilit
y
,
u
tili
zi
n
g
Mo
n
te
C
ar
lo
s
im
u
latio
n
in
co
n
ju
n
ctio
n
with
an
an
aly
s
is
o
f
m
ax
im
u
m
an
d
m
in
im
u
m
lo
ad
s
.
T
h
e
m
ax
im
u
m
lo
a
d
an
aly
s
is
,
wh
ich
is
p
r
o
p
o
s
ed
,
is
also
u
s
ed
as
p
ar
t
o
f
a
cr
o
s
s
-
en
tr
o
p
y
o
p
tim
i
z
ati
o
n
p
r
o
ce
d
u
r
e
t
o
o
p
tim
i
z
e
th
e
s
y
s
tem
'
s
s
to
ch
asti
c
p
ar
am
eter
s
.
C
h
m
ielo
wiec
et
a
l.
[
1
7
]
p
r
esen
t
th
e
r
esu
lts
o
f
ex
p
er
im
en
ts
in
v
esti
g
atin
g
th
e
u
s
e
o
f
a
m
ac
h
in
e
lear
n
in
g
ap
p
r
o
ac
h
to
esti
m
ate
n
o
d
al
lo
a
d
ca
p
ac
ity
in
p
o
wer
s
y
s
tem
s
.
T
h
ey
d
ef
i
n
e
th
e
co
n
ce
p
t
o
f
n
o
d
al
l
o
ad
ca
p
ac
ity
an
d
th
e
m
eth
o
d
o
lo
g
y
f
o
r
esti
m
atin
g
it
u
s
in
g
a
g
r
ap
h
n
eu
r
al
n
etwo
r
k
.
Ag
h
d
am
an
d
Kh
o
s
h
k
h
o
o
[
1
8
]
p
r
o
p
o
s
ed
m
eth
o
d
r
elies
s
o
lely
o
n
th
e
v
o
ltag
e
m
a
g
n
itu
d
e
an
d
th
e
p
o
wer
tr
an
s
m
itted
th
r
o
u
g
h
th
e
tar
g
et
b
u
s
.
I
t
is
an
ef
f
ec
tiv
e
to
o
l
f
o
r
esti
m
atin
g
th
e
lo
ad
ab
ilit
y
m
ar
g
i
n
.
Mo
n
d
al
et
a
l.
[
1
9
]
p
r
o
p
o
s
e
a
n
o
v
el
ap
p
r
o
ac
h
g
r
o
u
n
d
ed
in
a
m
ath
em
atica
l
m
o
d
el
th
at
ca
n
b
e
u
tili
z
ed
to
ascer
tain
th
e
m
ax
im
u
m
p
er
m
i
s
s
ib
le
lo
ad
lim
it
f
o
r
m
u
ltip
le
L
B
s
in
a
p
o
wer
s
y
s
tem
,
wh
ils
t
ac
co
u
n
tin
g
f
o
r
s
af
ety
co
n
s
tr
ain
ts
p
er
tain
in
g
to
v
o
ltag
e.
As
p
ar
t
o
f
th
eir
s
tu
d
y
,
Yad
a
v
an
d
Pal
[
2
0
]
p
r
o
p
o
s
e
a
n
ew
a
p
p
r
o
ac
h
to
d
eter
m
in
in
g
t
h
e
L
B
MC
o
f
ea
ch
L
B
.
T
h
is
ap
p
r
o
ac
h
u
s
es
a
m
o
d
if
ied
co
n
tin
u
o
u
s
p
o
wer
f
l
o
w
m
eth
o
d
to
ca
lcu
late
a
co
m
p
o
s
ite
in
d
ex
.
T
h
e
co
m
p
o
s
ite
in
d
ex
is
th
en
u
s
ed
to
class
if
y
L
B
s
an
d
id
en
tify
th
e
m
o
s
t c
r
itical
o
n
es.
So
m
e
o
f
th
e
m
eth
o
d
s
r
ef
er
e
n
ce
d
ab
o
v
e
r
eq
u
ir
e
s
ig
n
if
ica
n
t
co
m
p
u
tatio
n
al
r
eso
u
r
ce
s
.
I
n
s
o
m
e
o
f
th
e
ab
o
v
e
-
cited
r
esear
ch
,
th
e
L
B
MC
is
as
s
ess
ed
at
th
e
v
o
ltag
e
co
llap
s
e
lim
it.
Ho
wev
er
,
it
s
h
o
u
ld
b
e
n
o
te
d
th
at
a
p
er
f
o
r
m
an
ce
in
d
icato
r
m
a
y
r
e
ac
h
its
lim
it
with
in
th
e
n
etwo
r
k
with
o
u
t
ca
u
s
in
g
a
v
o
ltag
e
co
llap
s
e
in
ce
r
tain
cir
cu
m
s
tan
ce
s
.
Fo
n
s
ec
a
et
a
l.
[
2
1
]
p
r
o
p
o
s
e
an
in
n
o
v
ativ
e
ap
p
r
o
ac
h
t
o
lo
ad
ca
p
ac
ity
an
al
y
s
is
.
T
h
is
ap
p
r
o
ac
h
is
p
r
ed
icate
d
o
n
th
e
s
h
o
r
t
-
cir
cu
it
p
o
wer
at
th
e
L
B
lev
el.
T
h
is
m
eth
o
d
o
lo
g
y
f
ac
ilit
ates
th
e
d
eter
m
in
atio
n
o
f
L
B
MC,
co
n
tin
g
en
t
o
n
th
e
v
a
lu
es
o
f
a
v
o
ltag
e
s
tab
ilit
y
in
d
ex
.
So
m
e
au
th
o
r
s
h
av
e
f
o
c
u
s
ed
th
eir
wo
r
k
o
n
esti
m
atin
g
th
e
L
B
MC
at
th
e
lin
e
v
o
ltag
e
s
tab
ilit
y
lim
it
[
2
2
]
-
[
2
5
]
.
L
et
L
B
x
b
e
th
e
tar
g
e
t
L
B
f
o
r
wh
ich
t
h
e
L
B
MC
h
as
to
b
e
ass
ess
ed
.
Pre
v
io
u
s
r
e
f
er
en
ce
s
ad
o
p
t
a
n
a
p
p
r
o
ac
h
in
v
o
lv
in
g
g
r
a
d
u
ally
in
cr
ea
s
in
g
th
e
lo
ad
co
n
n
ec
ted
to
L
B
x
u
n
til
th
e
c
r
itical
s
tab
ilit
y
in
d
ex
v
alu
e
o
f
o
n
e
o
f
its
ad
jace
n
t
lin
es
(
L
B
x
AL
)
is
r
ea
ch
ed
.
W
h
en
in
cr
ea
s
in
g
th
e
l
o
ad
c
o
n
n
ec
ted
to
th
e
L
B
x
,
it
is
ass
u
m
ed
th
at
th
e
lo
a
d
s
o
n
th
e
o
th
e
r
L
B
s
in
th
e
n
etwo
r
k
will
r
em
ain
c
o
n
s
tan
t.
T
h
e
r
e
s
u
ltin
g
lo
ad
o
f
th
is
o
p
er
atio
n
th
e
n
co
r
r
esp
o
n
d
s
to
th
e
L
B
MC
o
f
L
B
x
.
T
h
is
o
p
er
atio
n
is
ap
p
lied
to
ea
c
h
o
f
th
e
o
th
er
L
B
s
in
d
iv
id
u
ally
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
N
o
ve
l a
p
p
r
o
a
ch
f
o
r
a
s
s
ess
in
g
th
e
ma
ximu
m
lo
a
d
c
a
p
a
city
o
f
b
u
s
es w
ith
in
a
p
o
w
er
…
(
Mo
u
s
s
a
Go
n
d
a
)
1107
T
h
e
r
eliab
ilit
y
o
f
th
is
ap
p
r
o
ac
h
is
th
er
e
f
o
r
e
q
u
esti
o
n
a
b
le.
E
x
am
in
in
g
o
n
l
y
th
e
v
al
u
es
o
f
t
h
e
L
B
x
AL
s
tab
ilit
y
in
d
ex
co
u
ld
r
esu
lt
in
th
e
s
tab
ilit
y
in
d
e
x
o
f
a
g
iv
en
p
o
wer
s
y
s
tem
lin
e
r
ea
c
h
i
n
g
its
cr
itical
v
alu
e
b
ef
o
r
e
o
n
e
o
f
th
e
L
B
x
AL
s
tab
ilit
y
in
d
ices
r
ea
ch
es
its
cr
itical
v
alu
e.
I
n
th
is
ca
s
e,
it
ap
p
ea
r
s
th
at
th
e
L
B
MC
o
f
L
B
x
h
as
alr
ea
d
y
b
ee
n
ex
ce
e
d
ed
,
w
h
ich
is
a
s
h
o
r
tco
m
in
g
o
f
th
is
ap
p
r
o
ac
h
.
A
n
o
th
er
s
h
o
r
tco
m
in
g
o
f
th
is
ap
p
r
o
ac
h
is
th
at
s
h
o
u
ld
an
in
c
r
ea
s
e
in
lo
ad
o
cc
u
r
o
n
o
n
e
o
r
m
o
r
e
o
th
er
L
B
s
in
th
e
p
o
wer
s
y
s
tem
s
u
b
s
eq
u
en
t
to
th
e
ev
alu
atio
n
o
f
th
e
L
B
MC
f
o
r
L
B
x
,
th
e
s
tab
ilit
y
lim
it
will
b
e
ex
ce
ed
ed
,
an
d
th
e
ea
r
l
ier
ev
alu
atio
n
o
f
th
e
L
B
MC
w
ill
n
o
lo
n
g
er
b
e
v
alid
.
I
f
th
e
L
B
x
is
to
o
p
er
ate
clo
s
e
to
its
L
B
M
C
,
it
s
lo
ad
m
ar
g
in
wo
u
ld
b
e
ass
ess
ed
in
co
r
r
ec
tly
.
I
t
is
ess
en
tial
to
m
o
n
ito
r
v
o
lta
g
e
s
tab
ilit
y
in
a
p
o
wer
s
y
s
tem
.
T
h
er
ef
o
r
e,
th
e
L
B
MC
ass
es
s
m
en
t
m
u
s
t
tak
e
th
is
in
to
ac
c
o
u
n
t.
Ho
wev
er
,
in
e
x
is
tin
g
s
tu
d
ies
f
o
cu
s
in
g
o
n
th
is
is
s
u
e
[
2
2
]
-
[
2
5
]
,
t
h
e
as
s
ess
m
en
t
o
f
L
B
MC
d
o
es
n
o
t
tak
e
in
t
o
ac
co
u
n
t
t
h
e
co
m
b
in
e
d
ef
f
ec
t
o
f
in
cr
e
a
s
ed
lo
ad
s
o
n
v
o
ltag
e
s
tab
ilit
y
in
ad
d
itio
n
to
th
e
s
h
o
r
tco
m
in
g
s
p
r
e
v
io
u
s
ly
id
e
n
tifie
d
.
Ou
r
s
tu
d
y
attem
p
ts
to
ad
d
r
ess
th
ese
is
s
u
es
b
y
p
r
o
p
o
s
in
g
a
n
ew
m
eth
o
d
o
l
o
g
y
to
ass
ess
th
e
L
B
MC
o
f
ea
ch
L
B
in
a
p
o
w
er
s
y
s
tem
.
T
h
is
m
eth
o
d
o
lo
g
y
en
s
u
r
es
th
at
lo
a
d
in
cr
ea
s
es
u
p
to
a
ce
r
tain
lev
el
d
o
n
o
t
af
f
ec
t
t
h
e
p
o
wer
s
y
s
tem
'
s
o
p
er
atio
n
al
p
er
f
o
r
m
a
n
ce
,
th
u
s
g
u
ar
an
teein
g
th
e
r
eliab
ilit
y
o
f
lo
a
d
p
lan
n
i
n
g
f
o
r
ea
c
h
L
B
.
T
o
ac
h
ie
v
e
th
is
,
it
in
tr
o
d
u
ce
s
a
co
ef
f
icien
t
ca
lled
th
e
‘
g
lo
b
al
ef
f
ec
t
lo
ad
f
ac
to
r
(
GE
L
F)’
.
T
h
is
co
ef
f
icien
t
allo
ws
f
o
r
m
o
r
e
eq
u
itab
le
an
d
b
alan
ce
d
lo
ad
p
l
an
n
in
g
at
ea
ch
L
B
lev
el
b
ased
o
n
th
e
lo
ad
m
ar
g
i
n
v
alu
e
at
ea
ch
L
B
,
an
d
it
ca
n
b
e
u
p
d
ated
to
r
ef
i
n
e
th
e
p
lan
if
n
ec
ess
ar
y
.
T
h
is
m
eth
o
d
o
l
o
g
y
is
b
ased
o
n
th
e
o
p
tim
al
p
o
wer
f
lo
w
(
OPF)
b
y
New
to
n
–
R
ap
h
s
o
n
m
eth
o
d
(
N
R
m
)
co
m
b
in
ed
with
a
ch
o
s
en
p
er
f
o
r
m
an
ce
i
n
d
icat
o
r
(
PI)
.
T
h
is
ar
ticle
in
itially
u
s
es
as
th
e
PI,
th
e
co
m
p
lex
s
tab
ilit
y
in
d
ex
f
o
r
tr
an
s
m
is
s
io
n
lin
es
(
C
SIT
L
)
[
2
6
]
.
I
n
[
2
4
]
,
th
e
e
f
f
ec
tiv
en
ess
a
n
d
a
p
p
licab
ilit
y
o
f
NC
PI
ar
e
c
o
m
p
ar
ed
with
th
o
s
e
o
f
th
e
well
-
k
n
o
wn
ex
is
tin
g
i
n
d
ices
(
L
m
n
,
FVSI,
L
QP,
N
L
SI
,
an
d
VSLI
)
an
d
th
e
r
esu
lts
d
em
o
n
s
tr
ate
th
e
s
u
p
er
io
r
ity
o
f
th
e
NC
PI.
Fo
r
th
is
r
ea
s
o
n
,
in
o
r
d
e
r
to
ex
p
lo
r
e
th
e
p
o
te
n
tial
ad
v
a
n
tag
es
o
f
ch
o
o
s
in
g
a
g
i
v
en
v
o
ltag
e
s
tab
ilit
y
in
d
ex
o
v
er
an
o
th
er
,
th
e
C
SIT
L
p
e
r
f
o
r
m
an
ce
is
co
m
p
ar
ed
with
t
h
at
o
f
th
e
NC
PI.
T
h
e
s
tr
u
ctu
r
e
o
f
t
h
e
p
r
esen
t
a
r
ticle
is
o
u
tlin
ed
as
f
o
llo
ws:
s
ec
tio
n
2
p
r
esen
ts
th
e
v
alid
atio
n
m
ater
ial
an
d
th
e
p
r
o
p
o
s
ed
m
et
h
o
d
o
lo
g
y
,
s
ec
tio
n
3
co
v
e
r
s
ca
s
e
s
tu
d
ies
an
d
s
im
u
latio
n
r
esu
lts
,
th
e
an
aly
s
is
o
f
r
esu
lts
an
d
d
is
cu
s
s
io
n
,
an
d
f
in
ally
,
s
ec
tio
n
4
is
in
ten
d
e
d
f
o
r
p
r
esen
ti
n
g
co
n
clu
s
io
n
s
an
d
p
er
s
p
ec
tiv
es.
2.
M
E
T
H
O
DO
L
O
G
Y
T
h
is
s
ec
tio
n
p
r
esen
ts
th
e
m
at
er
ial
u
s
ed
an
d
th
e
p
r
o
p
o
s
ed
m
eth
o
d
o
f
th
is
s
tu
d
y
.
T
h
e
m
ater
ial
u
s
ed
len
d
cr
ed
ib
ilit
y
t
o
th
e
r
esu
lts
o
b
tain
ed
u
s
in
g
t
h
is
m
eth
o
d
.
2
.
1
.
M
a
t
er
ia
l
T
h
is
n
ew
a
p
p
r
o
ac
h
was
s
im
u
lated
u
s
in
g
b
o
t
h
th
e
s
tan
d
ar
d
I
E
E
E
3
0
b
u
s
s
y
s
tem
a
n
d
a
r
ea
l
p
o
wer
tr
an
s
m
is
s
io
n
n
etwo
r
k
o
f
Nig
e
r
(
PT2
N)
,
as
illu
s
tr
ated
i
n
Fig
u
r
es
1
(
a
)
an
d
1
(
b
)
,
r
esp
ec
tiv
ely
.
T
h
e
d
ata
r
elatin
g
to
th
e
c
h
ar
ac
ter
is
tics
o
f
th
e
lin
es,
g
en
er
ato
r
s
,
an
d
b
u
s
es
ar
e
t
ak
en
f
r
o
m
[
2
7
]
f
o
r
th
e
I
E
E
E
3
0
-
b
u
s
s
y
s
tem
.
T
h
e
I
E
E
E
3
0
b
u
s
lin
es r
ated
tr
a
n
s
ited
ap
p
ar
e
n
t p
o
we
r
v
alu
es we
r
e
d
er
iv
ed
f
r
o
m
[
2
8
]
.
(
a)
(
b
)
Fig
u
r
e
1
.
Sin
g
le
-
li
n
e
d
iag
r
a
m
s
o
f
p
o
wer
s
y
s
tem
s
test
ed
: (
a)
I
E
E
E
3
0
-
b
u
s
s
y
s
tem
[
2
7
]
an
d
(
b
)
PT2
N
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
1
5
,
No
.
3
,
Sep
tem
b
er
20
2
6
:
1
1
0
5
-
1
1
1
6
1108
2
.
2
.
M
et
ho
d
Fig
u
r
e
2
p
r
esen
ts
th
e
f
lo
wch
ar
t
d
escr
ib
in
g
th
e
p
r
o
p
o
s
ed
m
eth
o
d
,
wh
ich
co
n
s
is
ts
o
f
tw
o
s
tep
s
.
As
d
escr
ib
ed
in
[
2
3
]
an
d
[
2
4
]
,
th
e
L
B
MC
ass
es
s
m
en
t
r
esu
ltin
g
f
r
o
m
a
tar
g
eted
PI
co
n
s
titu
te
s
th
e
f
ir
s
t
p
h
ase
o
f
th
e
p
r
o
p
o
s
ed
n
ew
ap
p
r
o
ac
h
.
I
f
th
e
tar
g
eted
PI
is
a
v
o
ltag
e
s
tab
ilit
y
in
d
ex
,
f
o
r
ex
am
p
le,
its
v
alu
e
is
ex
am
i
n
e
d
f
o
r
ea
ch
o
f
t
h
e
lin
es
in
th
e
p
o
wer
s
y
s
tem
.
I
n
th
is
s
tu
d
y
,
th
e
ev
alu
atio
n
is
p
er
f
o
r
m
ed
in
ap
p
ar
en
t
p
o
wer
.
I
n
th
is
ca
s
e,
th
e
L
B
MC
v
alu
e
is
r
ef
er
r
ed
to
as
th
e
'
m
ax
im
u
m
eg
o
is
tic
v
alu
e
o
f
ap
p
ar
en
t
p
o
wer
'
f
o
r
a
ta
r
g
eted
PI,
d
en
o
ted
S
max_eg_PI
.
T
h
e
ter
m
'
eg
o
is
tic'
is
u
s
ed
h
er
e
b
ec
au
s
e
t
h
e
L
B
MC
ev
alu
atio
n
d
o
es
n
o
t
tak
e
in
to
ac
co
u
n
t
th
e
co
m
b
in
ed
ef
f
ec
t
o
f
in
cr
ea
s
ed
lo
ad
s
o
n
all
L
B
s
o
n
a
tar
g
e
ted
PI.
I
t
is
as
if
th
e
L
B
f
o
r
wh
ich
th
e
L
B
MC
is
ass
es
s
ed
is
th
e
o
n
ly
o
n
e
wh
er
e
th
e
lo
ad
in
c
r
ea
s
es.
T
h
e
s
ec
o
n
d
p
h
ase
o
f
th
is
ap
p
r
o
ac
h
in
v
o
lv
es
ev
alu
atin
g
th
e
n
ew
L
B
MC
f
o
r
ea
ch
L
B
,
tak
in
g
in
to
ac
co
u
n
t
th
e
co
m
b
in
ed
ef
f
ec
t
o
f
th
e
lo
ad
s
p
r
esen
t
in
th
e
p
o
wer
s
y
s
tem
o
n
a
tar
g
eted
PI.
I
n
th
is
ca
s
e,
th
e
L
B
MC
v
alu
e
i
s
r
ef
er
r
ed
to
as
th
e
'
m
ax
im
u
m
s
o
lid
ar
y
v
alu
e
o
f
ap
p
ar
e
n
t
p
o
wer
'
,
d
en
o
ted
S
max_sol_PI
.
Her
e,
th
e
ter
m
‘
s
o
lid
ar
y
’
r
ef
er
s
to
tak
in
g
in
to
ac
co
u
n
t
th
e
co
m
b
in
e
d
ef
f
ec
t
o
f
all
lo
ad
s
in
th
e
p
o
wer
s
y
s
tem
,
g
iv
en
th
eir
in
ter
d
ep
en
d
en
ce
in
te
r
m
s
o
f
t
h
eir
co
m
b
i
n
ed
ef
f
ec
t
o
n
a
tar
g
eted
PI.
First,
d
eter
m
in
e
th
e
s
o
lid
ar
y
ap
p
a
r
en
t
p
o
wer
o
f
ea
ch
L
B
i
r
elate
d
to
th
e
tar
g
eted
PI,
d
en
o
ted
S
sol_IP
(
L
B
i)
,
u
s
in
g
(
1
)
,
wh
er
e
th
e
S
base
(
L
B
i)
co
r
r
esp
o
n
d
s
to
th
e
b
ase
ca
s
e
ap
p
ar
en
t p
o
w
er
o
f
ea
ch
L
B
i
at
th
e
tim
e
o
f
e
v
alu
atio
n
.
T
h
e
p
ar
am
eter
is
th
e
GE
L
F
r
elate
d
to
th
e
tar
g
eted
PI.
I
ts
v
alu
e
m
u
s
t
b
e
in
cr
ea
s
ed
g
r
ad
u
ally
f
r
o
m
0
u
n
til
th
e
tar
g
et
PI
r
ea
c
h
es
its
cr
itica
l
v
alu
e
(P
I
c
)
.
W
h
en
P
I
c
r
ea
ch
e
d
,
th
e
S
max_sol_PI
f
o
r
ea
ch
L
B
is
d
ed
u
ce
d
as
s
h
o
wn
b
y
(
2
)
.
[
_
(
1
)
_
(
2
)
⋮
_
(
)
]
=
[
b
as
e
(
1
)
b
as
e
(
2
)
⋮
b
as
e
(
)
]
+
[
m
ax
_
_
(
1
)
−
b
as
e
(
1
)
m
ax
_
_
(
2
)
−
b
as
e
(
2
)
⋮
m
ax
_
_
(
)
−
b
as
e
(
)
]
(
1
)
[
_
_
(
1
)
_
_
(
2
)
⋮
_
_
(
)
]
=
[
(
1
)
(
2
)
⋮
(
)
]
+
(
|
=
)
[
_
_
(
1
)
−
(
1
)
_
_
(
2
)
−
(
2
)
⋮
_
_
(
)
−
(
)
]
(
2
)
Fig
u
r
e
2
.
Flo
wch
ar
t
o
f
th
e
p
r
o
p
o
s
ed
m
eth
o
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
N
o
ve
l a
p
p
r
o
a
ch
f
o
r
a
s
s
ess
in
g
th
e
ma
ximu
m
lo
a
d
c
a
p
a
city
o
f
b
u
s
es w
ith
in
a
p
o
w
er
…
(
Mo
u
s
s
a
Go
n
d
a
)
1109
On
ce
th
e
S
max_sol_PI
h
as
b
ee
n
ev
alu
ated
f
o
r
ea
ch
o
f
th
e
L
B
s
,
th
e
r
esu
ltin
g
s
o
lid
ar
y
lo
ad
m
ar
g
in
_
ca
n
b
e
d
eter
m
in
ed
u
s
in
g
(
3
)
.
T
h
e
im
p
o
r
ta
n
t
asp
ec
t
to
n
o
te
with
S
max_sol_PI
i
s
th
at,
ev
en
th
o
u
g
h
GE
L
F
ap
p
ea
r
s
as
th
e
l
o
ad
f
ac
to
r
u
s
ed
b
y
o
th
e
r
ex
is
tin
g
s
tu
d
ies,
ta
k
in
g
in
t
o
ac
co
u
n
t
th
e
g
ap
b
et
wee
n
S
max_sol_PI
an
d
S
base
is
th
e
n
ew
co
n
s
id
er
atio
n
.
Mo
r
eo
v
er
,
it
is
th
is
c
o
n
s
id
er
atio
n
o
f
th
e
g
a
p
b
etwe
en
S
max
_eg_PI
an
d
S
base
t
h
at
ju
s
tifie
s
th
e
‘
s
o
lid
ar
y
’
q
u
alif
i
er
attr
ib
u
ted
to
S
max_sol_PI
,
b
ec
au
s
e
th
e
g
r
ea
ter
th
is
g
ap
is
f
o
r
a
g
iv
en
L
B
,
th
e
g
r
ea
ter
its
L
M
sol_PI
,
an
d
th
e
s
m
aller
it is
,
th
e
lo
wer
its
L
M
sol_P
I
.
B
ased
o
n
a
s
im
p
le
tr
an
s
p
o
r
t
li
n
e
m
o
d
el
(
s
ee
Fig
u
r
e
3
)
,
t
h
e
C
SIT
L
s
tab
ilit
y
in
d
ex
an
d
its
m
o
d
u
le
ar
e
ex
p
r
ess
ed
b
y
(
4
)
a
n
d
(
5
)
,
r
esp
ec
tiv
ely
.
Similar
ly
,
th
e
NC
PI
f
o
r
m
u
latio
n
(
6
)
is
d
e
r
iv
ed
f
r
o
m
th
is
m
o
d
el.
_
=
_
_
(
)
−
(
)
(
3
)
=
4
2
(
2
(
−
)
+
2
(
−
)
)
(
4
)
|
|
=
4
2
√
(
2
(
−
)
)
2
+
(
2
(
−
)
)
2
<
1
(
5
)
=
4
2
2
(
4
2
2
2
+
|
|
)
<
1
ℎ
=
√
2
+
2
(
6
)
Fig
u
r
e
3
.
Simp
le
tr
a
n
s
p
o
r
t lin
e
m
o
d
el
3.
CASE
S
T
UD
I
E
S AN
D
S
I
M
UL
A
T
I
O
N
R
E
SU
L
T
S
3
.
1
.
E
v
a
lua
t
i
o
n o
f
Sm
a
x
_
s
o
l
:
ca
s
e
o
f
t
he
I
E
E
E
3
0
bu
s
s
y
s
t
em
I
n
th
is
ca
s
e
s
tu
d
y
,
th
e
ap
p
ar
e
n
t
p
o
wer
s
S
max_eg_PI
an
d
S
max_sol_
PI
ar
e
ev
alu
ated
at
ea
ch
L
B
an
d
th
e
lo
ad
m
ar
g
in
s
L
M
sol_CSITL
an
d
L
M
so
l_NCPI
ar
e
d
ed
u
ce
d
.
T
h
e
GE
L
F
o
b
tain
ed
b
y
tak
in
g
C
SIT
L
as
m
o
n
ito
r
ed
PI,
is
=
0
.
075
,
an
d
th
at
o
b
tain
ed
b
y
tak
in
g
NC
PI
as
th
e
PI
to
m
o
n
ito
r
,
=
0
.
1554
.
T
h
e
s
im
u
latio
n
r
esu
lts
o
b
tain
ed
ar
e
p
r
esen
ted
in
T
ab
le
1
.
T
h
ese
r
esu
lts
o
b
tai
n
ed
r
e
v
ea
l
th
at
th
e
v
alu
e
o
f
S
max_eg_PI
o
r
S
max_sol_PI
v
ar
ies
d
ep
en
d
in
g
o
n
t
h
e
PI
m
o
n
ito
r
ed
d
u
r
in
g
t
h
e
ev
alu
at
io
n
,
ev
e
n
f
o
r
th
e
s
am
e
b
u
s
.
T
h
is
ca
n
b
e
s
ee
n
b
y
lo
o
k
in
g
at
L
B
3
:
th
e
v
alu
e
o
f
S
max_eg_CSITL
o
b
tain
ed
is
1
1
3
M
VA,
wh
ich
is
s
ig
n
i
f
ican
tly
l
o
wer
th
an
th
e
v
alu
e
o
f
S
max_eg_NCPI
(
4
7
6
MV
A)
.
Ho
wev
er
,
th
is
d
if
f
er
e
n
ce
is
less
s
i
g
n
if
ican
t
f
o
r
th
e
s
am
e
L
B
b
e
twee
n
S
max_sol_CSIT
L
an
d
S
max_sol_NCPI
,
as
illu
s
tr
ated
b
y
Fig
u
r
e
4
.
As
ca
n
b
e
s
ee
n
f
r
o
m
T
ab
le
1
,
th
e
v
alu
es
o
f
S
max_sol_CSITL
an
d
S
max_sol_NCPI
ar
e
r
esp
ec
tiv
ely
1
0
.
9
6
MV
A
an
d
7
6
.
2
4
MV
A.
T
h
e
v
alu
es
o
f
S
max_eg_NCPI
an
d
S
max_sol_NCPI
ar
e
r
esp
ec
tiv
ely
h
ig
h
er
t
h
an
th
o
s
e
o
f
S
max_eg_CSITL
an
d
S
max_sol_CS
IT
L
at
ea
ch
L
B
.
At
th
e
lev
el
o
f
ea
ch
L
B
,
th
e
r
esu
lts
o
b
tain
ed
f
o
r
L
M
sol_CSITL
an
d
L
M
sol_NCPI
s
h
o
w
s
ig
n
if
ican
t
d
if
f
er
en
ce
s
b
etwe
en
th
ese
two
s
ta
b
ilit
y
in
d
ices.
T
h
e
f
in
d
in
g
s
f
r
o
m
T
ab
le
1
in
d
icat
e
th
at
th
e
lo
west
L
M
sol_CSITL
v
alu
e
is
r
ec
o
r
d
e
d
at
L
B
2
6
(
2
.
1
4
MV
A)
an
d
th
e
h
ig
h
est
at
L
B
1
0
(
1
7
.
0
3
MV
A
)
.
Fu
r
th
er
m
o
r
e,
th
e
lo
west
L
M
sol_NCPI
v
alu
e
is
r
ec
o
r
d
ed
at
th
e
s
am
e
L
B
2
6
(
5
.
1
MV
A)
,
wh
ile
th
e
h
ig
h
est
is
r
ec
o
r
d
e
d
at
L
B
3
(
7
3
.
5
5
MV
A)
.
Acc
o
r
d
in
g
to
th
e
C
SIT
L
an
d
th
e
NC
PI,
th
e
wea
k
est
an
d
m
o
s
t
p
o
wer
f
u
l
L
B
s
ar
e
p
r
esen
ted
as
s
u
ch
(
b
u
s
2
6
a
n
d
b
u
s
1
0
,
r
esp
ec
tiv
ely
)
.
On
e
m
ig
h
t
n
atu
r
ally
ass
u
m
e
th
at
o
n
e
o
f
th
e
two
in
d
ices
is
m
o
r
e
r
eliab
le,
s
in
ce
t
h
e
im
p
ac
t
o
n
s
tab
ilit
y
s
h
o
u
ld
b
e
th
e
s
am
e
f
o
r
th
e
s
am
e
L
B
.
Do
es
th
e
f
ac
t
th
at
L
M
sol_NCPI
is
h
ig
h
er
th
an
L
M
s
ol_CSITL
at
ea
ch
L
B
lev
el
im
p
l
y
th
at
NC
PI
is
m
o
r
e
r
eliab
le
th
an
C
SIT
L
f
o
r
ass
e
s
s
in
g
L
B
M
C
?
T
h
e
id
ea
b
eh
in
d
th
e
S
max_sol_PI
as
s
es
s
m
en
t
is
to
d
eter
m
in
e
th
e
m
ax
im
u
m
l
o
ad
t
h
at
ca
n
b
e
a
p
p
lied
s
im
u
ltan
eo
u
s
ly
to
ea
ch
L
B
o
f
th
e
p
o
wer
s
y
s
tem
at
th
e
PI
cr
iticality
lim
it.
Ho
wev
er
,
th
is
m
u
s
t n
o
t
h
av
e
a
n
ad
v
er
s
e
ef
f
ec
t o
n
th
e
s
y
s
tem
's o
th
er
p
er
f
o
r
m
a
n
ce
s
.
I
n
o
r
d
er
to
ev
al
u
ate
th
e
ef
f
ec
tiv
en
ess
o
f
th
e
two
in
d
ices
u
s
ed
in
th
is
s
tu
d
y
,
th
e
im
p
ac
t
o
f
s
im
u
ltan
eo
u
s
ly
ap
p
ly
in
g
S
max_sol_CSITL
an
d
th
e
n
S
max_sol_NCPI
o
n
th
e
b
u
s
v
o
ltag
e
p
r
o
f
ile
an
d
t
h
e
ap
p
ar
en
t
p
o
wer
tr
an
s
m
itted
th
r
o
u
g
h
lin
es
in
th
e
I
E
E
E
3
0
-
b
u
s
s
y
s
tem
is
an
aly
s
ed
.
T
h
e
r
esu
lts
o
b
tain
e
d
ar
e
p
r
esen
ted
in
Fig
u
r
es
5
(
a
)
a
n
d
5
(
b
)
.
As
d
e
m
o
n
s
tr
ated
in
Fig
u
r
e
5
(
a
)
,
th
e
ap
p
licatio
n
o
f
S
max_sol_NCPI
o
n
ea
ch
L
B
r
esu
lts
in
th
e
co
llap
s
e
o
f
t
h
e
v
o
ltag
e
o
f
th
e
m
ajo
r
ity
o
f
b
u
s
es.
C
o
n
v
er
s
ely
,
th
e
a
p
p
licatio
n
o
f
S
max_sol_CSITL
o
n
ea
c
h
L
B
r
esu
lts
in
a
m
a
r
g
in
al
alter
atio
n
to
th
e
b
u
s
v
o
ltag
e
p
r
o
f
ile.
Fig
u
r
e
5
(
b
)
s
h
o
ws
th
at,
u
n
lik
e
th
e
a
p
p
licatio
n
o
f
S
max_sol_CSITL
to
ea
ch
L
B
,
th
e
p
o
wer
tr
an
s
m
itted
th
r
o
u
g
h
th
e
l
in
es
r
esu
ltin
g
f
r
o
m
th
e
ap
p
lica
tio
n
o
f
S
max_sol_NCPI
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
1
5
,
No
.
3
,
Sep
tem
b
er
20
2
6
:
1
1
0
5
-
1
1
1
6
1110
to
ea
ch
L
B
is
g
r
ea
ter
t
h
an
t
h
e
n
o
m
in
al
t
r
an
s
m
is
s
io
n
ca
p
ac
ity
o
f
th
e
lin
es.
Ap
p
ly
in
g
S
max_sol_CSITL
h
as
a
m
ar
g
in
al
im
p
ac
t
o
n
b
o
th
th
e
b
u
s
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t
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m
itted
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r
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u
g
h
th
e
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C
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n
v
er
s
ely
,
th
e
im
p
ac
t
o
f
a
p
p
ly
in
g
S
max_sol_NCPI
to
th
ese
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o
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er
atio
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al
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er
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is
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ig
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le
1
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V
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L
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m
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I
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V
A
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m
a
x_s
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T
L
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a
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6
Fig
u
r
e
4
.
Ma
x
im
u
m
lo
a
d
ca
p
a
cities (
S
max_sol_
CSITL
an
d
S
max_so
l_NCPI
)
an
d
lo
ad
m
ar
g
in
s
(
L
M
so
l_CSITL
an
d
L
M
sol_NCPI
)
o
f
th
e
L
B
s
(
a)
(
b
)
Fig
u
r
e
5
.
I
ll
u
s
tr
atio
n
o
f
t
h
e
im
p
ac
t o
f
ap
p
ly
in
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th
e
S
base
,
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e
S
max_sol_CSITL
,
an
d
th
en
th
e
S
max_sol_NCPI
to
ea
ch
L
B
in
th
e
I
E
E
E
3
0
-
b
u
s
s
y
s
tem
o
n
:
(
a)
th
e
v
o
ltag
e
p
r
o
f
ile
an
d
(
b
)
th
e
tr
an
s
ited
p
o
wer
b
y
t
h
e
lin
es
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
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l Po
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E
n
g
I
SS
N:
2252
-
8
7
9
2
N
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ess
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Go
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1218
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128
.
T
h
e
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im
u
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T
ab
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2
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itio
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er
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en
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as
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ig
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7
9
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,
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ig
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,
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d
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max_sol_NCPI
v
alu
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1
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MV
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6
6
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8
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7
3
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4
6
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A
,
r
esp
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tiv
ely
)
.
L
B
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1
h
as
th
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ig
h
est
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M
sol_CSITL
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d
L
M
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v
alu
es
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8
.
6
9
an
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1
2
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4
9
MV
A,
r
esp
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tiv
ely
)
,
wh
ile
L
B
3
4
h
as
th
e
lo
west
(
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9
1
a
n
d
0
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9
2
,
r
esp
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tiv
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.
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e
r
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o
f
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e
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d
y
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e
illu
s
tr
ated
in
Fig
u
r
e
6
.
As
in
th
e
p
r
ev
io
u
s
ca
s
e
s
tu
d
y
,
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e
im
p
ac
t
o
f
s
im
u
ltan
e
o
u
s
ly
ap
p
l
y
in
g
S
max_sol_CSITL
an
d
th
en
S
max_sol_NCPI
o
n
th
e
b
u
s
v
o
ltag
e
p
r
o
f
ile
a
n
d
th
e
ap
p
ar
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n
t
p
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we
r
tr
an
s
m
itted
th
r
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h
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is
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aly
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ed
.
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e
r
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e
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r
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ted
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Fig
u
r
es
7
an
d
8
.
T
h
e
r
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lts
s
h
o
w
th
at
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l
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in
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S
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to
ea
ch
o
f
th
e
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B
s
p
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v
e
d
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o
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e
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ap
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ly
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g
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max_sol_NCPI
.
Ap
p
ly
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g
S
max_sol_CSITL
o
n
ly
d
e
g
r
ad
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e
v
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p
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L
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,
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lo
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co
n
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ast,
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e
a
p
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licatio
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led
to
a
s
ig
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ican
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t b
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,
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er
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ely
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ar
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r
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tain
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2
.
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ca
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e
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u
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r
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)
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l
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ol
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IT
L
(
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ol
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1
0
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1
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1
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.
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0
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5
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.
2
4
2
.
2
8
0
.
6
9
0
.
6
9
LB
3
9
0
.
8
9
9
.
4
0
1
0
.
0
0
1
.
9
3
2
.
0
6
1
.
0
4
1
.
1
1
LB
4
1
1
3
.
6
9
4
0
.
7
0
7
9
.
0
0
1
6
.
9
8
2
2
.
0
5
3
.
2
9
7
.
9
5
LB
4
5
1
.
7
8
1
7
.
3
0
1
7
.
2
5
3
.
6
7
3
.
7
6
1
.
8
9
1
.
8
8
LB
4
6
1
2
.
1
1
3
9
.
5
8
8
8
.
6
0
1
5
.
4
6
2
1
.
9
0
3
.
3
5
9
.
3
2
LB
4
7
1
6
.
6
9
4
5
.
2
5
9
6
.
8
0
2
0
.
1
7
2
6
.
9
4
3
.
4
8
9
.
7
6
Fig
u
r
e
6
.
Ma
x
im
u
m
lo
a
d
ca
p
a
cities (
S
max_sol_
CSITL
an
d
S
max_so
l_NCPI
)
an
d
lo
ad
m
ar
g
in
s
(
LM
so
l_CSITL
an
d
LM
sol_NCPI
)
o
f
th
e
L
B
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
1
5
,
No
.
3
,
Sep
tem
b
er
20
2
6
:
1
1
0
5
-
1
1
1
6
1112
Fig
u
r
e
7
.
I
ll
u
s
tr
atio
n
o
f
t
h
e
im
p
ac
t o
f
ap
p
ly
in
g
th
e
S
base
,
th
e
S
max_sol_CSITL
,
an
d
th
en
th
e
S
max_sol_NCPI
to
ea
ch
L
B
in
th
e
PT2
N
o
n
th
e
v
o
ltag
e
p
r
o
f
ile
Fig
u
r
e
8
.
I
ll
u
s
tr
atio
n
o
f
t
h
e
im
p
ac
t o
f
ap
p
ly
in
g
th
e
S
base
,
th
e
S
max_sol_CSITL
an
d
th
en
th
e
S
max_sol_NCPI
to
ea
ch
L
B
in
th
e
PT2
N
o
n
th
e
tr
an
s
ited
p
o
wer
b
y
t
h
e
lin
es
4.
ANALY
SI
S O
F
R
E
SU
L
T
S
AND
DIS
CUSS
I
O
N
Sin
ce
th
e
p
r
o
p
o
s
ed
L
B
MC
ev
alu
atio
n
m
eth
o
d
ta
k
es
in
to
ac
c
o
u
n
t
th
e
co
m
b
in
ed
ef
f
ec
t
o
f
th
e
in
cr
ea
s
e
in
th
e
lo
ad
o
f
ea
ch
L
B
,
v
a
r
iatio
n
s
in
th
ese
lo
ad
s
will
n
o
t
h
av
e
an
im
m
e
d
iate
im
p
ac
t
o
n
th
e
S
max_sol_PI
af
ter
ev
alu
atio
n
,
u
n
less
th
e
p
o
wer
s
y
s
tem
is
clo
s
e
to
it
s
ca
p
ac
ity
lim
it.
T
h
is
d
ep
en
d
s
o
n
th
e
tar
g
et
PI
b
ein
g
m
o
n
ito
r
ed
.
T
h
is
m
eth
o
d
is
in
n
o
v
ativ
e
b
ec
au
s
e
it
d
o
es
n
o
t
r
eq
u
ir
e
m
o
n
ito
r
in
g
th
e
d
y
n
am
i
cs
o
f
lo
ad
ch
an
g
es
o
n
ea
c
h
b
u
s
.
Pro
v
id
ed
th
at
th
e
S
max_sol_PI
o
f
a
b
u
s
is
n
o
t
e
x
ce
ed
ed
,
t
h
e
PI
will
n
o
t
d
eg
r
a
d
e.
As
th
e
av
ailab
le
lo
ad
m
ar
g
in
f
o
r
ea
ch
L
B
is
k
n
o
wn
,
it
is
p
o
s
s
ib
le
to
m
o
n
ito
r
th
e
r
is
k
o
f
ex
ce
ed
i
n
g
S
max_sol_PI
.
Pro
v
id
e
d
th
e
lo
a
d
in
cr
ea
s
e
f
o
r
ea
ch
L
B
r
e
m
ain
s
with
in
its
m
ar
g
in
,
r
e
g
ar
d
less
o
f
th
e
d
y
n
am
ics
o
f
th
is
in
c
r
ea
s
e,
th
e
PI
in
q
u
esti
o
n
will
n
o
t
d
eter
io
r
ate.
Ho
wev
e
r
,
all
o
f
th
is
d
ep
e
n
d
s
o
n
h
o
w
r
el
iab
le
th
e
PI
is
.
T
h
is
m
eth
o
d
is
p
ar
ticu
lar
ly
u
s
ef
u
l
f
o
r
th
e
p
o
wer
s
y
s
tem
s
o
p
er
at
in
g
clo
s
e
to
th
eir
ca
p
ac
ity
lim
its
,
as
i
t
en
ab
les
at
-
r
is
k
PIs
to
b
e
m
o
n
ito
r
ed
b
y
d
eter
m
in
in
g
th
e
S
max_sol_PI
an
d
L
M
sol_PI
o
f
ea
ch
L
B
r
elativ
e
t
o
ea
ch
tar
g
eted
P
I
.
On
ce
th
ese
v
alu
es
ar
e
k
n
o
wn
,
it is
s
im
p
ly
a
m
atter
o
f
m
o
n
ito
r
in
g
th
em
t
o
p
r
e
d
ict
th
e
d
e
g
r
a
d
atio
n
tr
en
d
o
f
th
e
tar
g
ete
d
P
I
s
.
T
h
is
m
eth
o
d
en
ab
les
L
B
s
to
b
e
ch
a
r
ac
ter
i
z
ed
as
eith
e
r
c
lo
s
e
to
o
r
d
is
tan
t
f
r
o
m
th
eir
S
max_sol_PI
,
d
ep
en
d
i
n
g
o
n
th
e
r
esu
lts
o
b
tai
n
ed
.
T
h
is
p
r
o
x
i
m
ity
is
r
elativ
e
.
Fo
r
in
s
tan
ce
,
i
n
th
e
I
E
E
E
3
0
b
u
s
s
y
s
tem
,
L
B
2
6
h
as
a
L
M
sol_CSITL
o
f
2
.
1
4
MV
A,
r
ep
r
esen
tin
g
5
1
.
0
7
%
o
f
its
S
base
(
4
.
1
9
MV
A)
.
T
h
er
e
f
o
r
e,
if
th
is
b
u
s
is
lo
ca
te
d
in
an
ar
ea
wh
er
e
th
e
lo
a
d
ev
o
l
u
tio
n
d
y
n
am
ics
ar
e
co
r
r
elate
d
with
S
base
(
r
u
r
al
ar
ea
)
,
it
is
n
o
t
th
e
b
u
s
clo
s
est
to
its
S
max_sol_CS
ITL
.
C
o
n
v
er
s
ely
,
i
f
we
co
n
s
id
er
L
B
7
,
its
L
M
sol_CSITL
is
5
.
0
1
MV
A,
r
ep
r
esen
tin
g
1
9
.
8
%
o
f
its
S
base
(
2
5
.
2
7
MV
A)
.
I
f
it
is
lo
ca
ted
i
n
an
ar
ea
wh
er
e
l
o
ad
ev
o
lu
tio
n
d
y
n
a
m
ics
ar
e
also
co
r
r
elate
d
with
S
base
(
e.
g
.
an
u
r
b
an
a
r
ea
)
,
th
e
n
it is
clo
s
er
to
its
S
max_sol_
CSITL
th
an
B
2
6
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
N
o
ve
l a
p
p
r
o
a
ch
f
o
r
a
s
s
ess
in
g
th
e
ma
ximu
m
lo
a
d
c
a
p
a
city
o
f
b
u
s
es w
ith
in
a
p
o
w
er
…
(
Mo
u
s
s
a
Go
n
d
a
)
1113
W
ith
r
eg
ar
d
to
th
e
r
esu
lts
o
b
t
ain
ed
,
o
b
s
er
v
atio
n
o
f
t
h
e
lo
ad
m
ar
g
in
s
at
th
e
v
ar
io
u
s
L
B
s
r
ev
ea
ls
th
at
th
e
L
B
s
in
t
h
e
I
E
E
E
3
0
b
u
s
s
y
s
tem
ar
e
lo
ca
ted
f
u
r
th
er
f
r
o
m
th
eir
m
ax
im
u
m
S
max_sol_CSITL
th
an
th
o
s
e
i
n
th
e
T
P2
N.
I
t
is
n
o
tewo
r
th
y
th
at
t
h
e
v
o
ltag
e
p
r
o
f
ile
r
esu
ltin
g
f
r
o
m
th
e
ap
p
licatio
n
o
f
S
max_sol_CSITL
f
o
r
ea
c
h
L
B
p
r
o
v
es
t
o
b
e
m
o
r
e
e
f
f
ec
tiv
e
f
o
r
I
E
E
E
3
0
-
b
u
s
s
y
s
tem
b
u
s
es
th
an
f
o
r
T
P2
N
E
HV
b
u
s
es.
T
h
is
is
n
o
t
th
e
ca
s
e
wh
en
S
max_sol_NCPI
is
ap
p
lied
f
o
r
ea
ch
L
B
,
wh
eth
e
r
in
th
e
I
E
E
E
3
0
-
b
u
s
s
y
s
tem
o
r
in
T
P2
N,
wh
ich
ca
u
s
es
a
v
er
y
s
ig
n
if
ican
t
co
llap
s
e
in
b
u
s
v
o
ltag
e.
T
h
e
r
esu
lts
also
r
ev
ea
l
th
at,
u
n
lik
e
ap
p
ly
in
g
S
max_sol_NCPI
f
o
r
ea
ch
L
B
,
ap
p
ly
in
g
S
max_sol_CSITL
f
o
r
ea
ch
L
B
d
id
n
o
t
ca
u
s
e
an
y
lin
e
o
v
er
lo
ad
f
o
r
eith
e
r
s
y
s
tem
,
esp
e
cially
f
o
r
t
h
e
I
E
E
E
30
-
b
u
s
s
y
s
tem
.
5.
CO
NCLU
SI
O
N
T
h
is
ar
ticle
in
tr
o
d
u
ce
s
a
n
o
v
e
l
m
eth
o
d
f
o
r
ass
ess
in
g
th
e
m
a
x
im
u
m
lo
a
d
ca
p
ac
ity
o
f
b
u
s
es
with
in
a
p
o
wer
s
y
s
tem
.
T
h
e
r
elev
an
ce
o
f
th
is
ap
p
r
o
ac
h
was
ass
e
s
s
ed
th
r
o
u
g
h
s
im
u
latio
n
s
o
f
th
e
I
E
E
E
3
0
-
b
u
s
s
y
s
tem
an
d
a
r
ea
l
n
etwo
r
k
(
PT
2
N)
.
Un
lik
e
o
th
er
ex
is
tin
g
m
eth
o
d
s
,
th
is
ap
p
r
o
ac
h
is
s
im
p
le
to
im
p
lem
en
t.
I
t
m
ak
es
it
p
o
s
s
ib
le
to
ass
e
s
s
th
e
lik
elih
o
o
d
o
f
an
in
cr
ea
s
e
in
lo
ad
o
n
a
b
u
s
af
f
ec
tin
g
a
p
o
wer
s
y
s
tem
p
er
f
o
r
m
a
n
ce
in
d
ex
o
v
er
a
g
iv
e
n
p
er
io
d
,
b
ased
o
n
th
e
av
ailab
le
lo
ad
m
ar
g
i
n
(
L
M
sol_PI
)
.
T
h
is
is
b
ec
au
s
e
it
en
a
b
les
th
e
L
M
sol_PI
to
b
e
d
eter
m
in
ed
f
o
r
ea
ch
lo
a
d
ed
b
u
s
.
Pro
v
i
d
ed
th
e
lo
ad
o
n
ea
ch
o
f
th
ese
b
u
s
es
r
em
ai
n
s
with
in
L
M
sol_PI
,
S
max_sol_PI
r
em
ain
s
v
alid
.
T
h
is
en
ab
les
th
e
lo
a
d
t
o
b
e
p
lan
n
ed
ac
co
r
d
i
n
g
t
o
a
g
iv
e
n
p
e
r
f
o
r
m
an
ce
o
b
jectiv
e,
with
th
e
tim
e
h
o
r
izo
n
d
ep
en
d
in
g
o
n
th
e
L
M
sol_PI
an
d
th
e
lo
ad
ev
o
lu
tio
n
d
y
n
am
ics
at
ea
ch
lo
ad
ed
b
u
s
.
T
h
is
m
eth
o
d
is
u
s
ef
u
l
f
o
r
m
o
n
ito
r
in
g
p
o
w
er
s
y
s
tem
wh
o
s
e
b
u
s
es
ar
e
cl
o
s
e
to
th
eir
m
ax
im
u
m
lo
ad
c
ap
ac
ity
r
elativ
e
to
a
tar
g
et
PI.
I
t
in
v
o
lv
es
u
p
d
atin
g
th
e
GE
L
F
p
ar
am
eter
(
)
at
a
p
p
r
o
p
r
iate
in
ter
v
als.
T
h
e
in
te
g
r
atio
n
o
f
t
h
is
p
ar
am
eter
with
co
n
tem
p
o
r
ar
y
ar
tific
ial
in
tellig
en
ce
tec
h
n
iq
u
es
h
as
th
e
p
o
ten
tial
to
en
h
an
ce
th
e
ef
f
icac
y
o
f
a
g
iv
en
PI
p
r
ed
ictio
n
d
eter
io
r
ati
o
n
with
in
a
p
o
wer
s
y
s
tem
co
n
t
ex
t.
F
UNDING
I
NF
O
R
M
A
T
I
O
N
Au
th
o
r
s
s
tate
n
o
f
u
n
d
in
g
in
v
o
lv
ed
.
AUTHO
R
CO
NT
RI
B
UT
I
O
NS ST
A
T
E
M
E
N
T
T
h
is
jo
u
r
n
al
u
s
es
th
e
C
o
n
tr
ib
u
to
r
R
o
les
T
ax
o
n
o
m
y
(
C
R
ed
iT)
to
r
ec
o
g
n
ize
in
d
iv
id
u
al
au
th
o
r
co
n
tr
ib
u
tio
n
s
,
r
ed
u
ce
au
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