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VSI
s
h
a
v
e
b
ee
n
f
o
r
m
u
la
ted
b
ased
o
n
th
e
r
ep
r
ese
n
tatio
n
o
f
a
tr
a
n
s
m
is
s
io
n
li
n
e
in
w
h
ich
t
h
e
d
is
cr
i
m
i
n
an
t
o
f
t
h
e
v
o
ltag
e
q
u
ad
r
ati
c
eq
u
atio
n
f
o
r
m
o
s
t
o
f
th
e
li
n
es
is
s
et
to
b
e
eq
u
al
o
r
g
r
ea
ter
th
an
ze
r
o
,
to
ac
h
iev
e
v
o
lta
g
e
s
tab
ili
t
y
.
So
m
e
e
x
a
m
p
le
s
o
f
t
h
e
li
n
e
VSI
s
th
at
h
a
v
e
b
ee
n
d
ev
elo
p
ed
ar
e
th
e
L
in
e
S
tab
ilit
y
I
n
d
ex
(
L
_
m
n
)
,
f
as
t
Vo
latg
e
Stab
il
it
y
I
n
d
ex
(
FVSI)
an
d
th
e
Ne
w
Vo
lta
g
e
Stab
ilit
y
I
n
d
ex
(
NVSI
)
[
5
]
-
[
7
]
.
A
ll
th
e
V
SIs
h
av
e
t
h
eir
ad
v
a
n
t
ag
es
a
n
d
d
is
ad
v
a
n
tag
e
s
an
d
t
h
er
ef
o
r
e
it
is
n
o
t
p
r
ac
tical
to
r
ec
o
m
m
e
n
d
an
in
d
e
x
as
th
e
o
n
l
y
o
n
e
to
u
s
e.
So
m
e
in
d
ice
s
ar
e
s
u
ited
f
o
r
o
n
-
lin
e
s
t
u
d
ies
b
ec
a
u
s
e
o
f
lo
w
co
m
p
u
tatio
n
a
l
ti
m
e
b
u
t
t
h
ese
in
d
ice
s
te
n
d
to
b
e
p
o
o
r
p
r
ed
icto
r
s
o
f
p
r
o
x
i
m
it
y
to
v
o
ltag
e
co
llap
s
e.
On
t
h
e
o
t
h
er
h
a
n
d
,
s
o
m
e
i
n
d
ices
g
iv
e
ac
c
u
r
ate
m
ea
s
u
r
e
o
f
d
is
tan
ce
to
v
o
ltag
e
co
llap
s
e
b
u
t
r
eq
u
ir
e
h
i
g
h
co
m
p
u
tatio
n
al
t
i
m
e
a
n
d
m
ak
in
g
t
h
e
m
u
n
s
u
itab
le
f
o
r
o
n
li
n
e
s
t
u
d
ies
[
3
]
.
I
t
is
i
m
p
o
r
tan
t
to
n
o
te
t
h
at
all
t
h
e
ab
o
v
e
-
m
en
t
io
n
ed
i
n
d
ices
h
av
e
n
eg
lecte
d
th
e
e
f
f
ec
t
o
f
s
h
u
n
t
ad
m
itta
n
ce
s
a
n
d
r
ea
ctiv
e
p
o
w
er
in
it
s
co
m
p
u
tatio
n
to
p
r
e
d
ict
v
o
ltag
e
in
s
tab
il
it
y
[
8
]
.
T
h
e
ap
p
licati
o
n
o
f
th
e
i
n
d
ices
f
o
r
d
e
ter
m
in
i
n
g
t
h
e
v
o
lta
g
e
u
n
s
tab
le
lo
ca
tio
n
s
is
al
s
o
n
o
t
co
n
s
id
er
ed
d
u
e
to
lack
o
f
in
f
o
r
m
atio
n
o
n
r
ea
cti
v
e
p
o
w
er
tr
a
cin
g
.
R
ea
cti
v
e
p
o
w
er
f
lo
w
i
s
r
eq
u
ir
ed
to
m
ai
n
tai
n
th
e
v
o
ltag
e
to
d
eliv
er
ac
ti
v
e
p
o
w
er
th
r
o
u
g
h
tr
an
s
m
is
s
io
n
l
in
es.
D
u
e
to
t
h
e
r
estr
u
ct
u
r
in
g
o
f
p
o
w
er
s
y
s
te
m
o
p
er
atio
n
f
r
o
m
r
eg
u
lated
to
d
er
eg
u
lated
m
ar
k
et,
th
er
e
is
a
n
ee
d
to
p
r
o
v
id
e
th
e
s
er
v
ic
e
o
f
r
ea
ctiv
e
p
o
w
er
s
u
p
p
o
r
t
n
o
t
o
n
l
y
f
o
r
tr
an
s
m
i
s
s
io
n
s
y
s
te
m
p
r
icin
g
b
u
t
al
s
o
f
o
r
v
o
ltag
e
s
tab
il
it
y
co
n
tr
o
l.
I
n
v
ie
w
o
f
m
o
r
e
co
m
p
le
x
an
d
p
r
ac
tical
p
o
w
e
r
s
y
s
te
m
s
,
it
is
i
m
p
o
r
tan
t
t
o
ev
alu
ate
th
e
r
ea
cti
v
e
p
o
w
er
f
lo
w
i
n
ev
er
y
tr
an
s
m
is
s
io
n
li
n
e
an
d
d
eter
m
i
n
e
its
co
n
tr
ib
u
tio
n
to
v
o
ltag
e
s
tab
ilit
y
i
n
a
p
o
w
er
s
y
s
te
m
.
H
en
ce
,
to
d
ev
elo
p
an
ac
cu
r
ate
v
o
lta
g
e
co
llap
s
e
i
n
d
icato
r
f
o
r
d
eter
m
i
n
i
n
g
th
e
v
o
ltag
e
u
n
s
tab
le
lo
ca
tio
n
s
,
th
e
p
o
w
er
f
lo
w
tr
ac
i
n
g
p
r
in
cip
le
d
ev
elo
p
ed
b
y
B
ialek
an
d
i
m
p
r
o
v
i
s
ed
p
o
w
er
f
lo
w
tr
ac
i
n
g
m
et
h
o
d
b
y
Ni
u
et
al.
is
ap
p
lied
b
y
co
n
s
id
er
in
g
r
ea
ctiv
e
p
o
w
er
f
lo
w
i
n
t
h
is
r
esear
ch
w
o
r
k
[
9
]
-
[
1
0
]
.
T
h
is
p
ap
er
d
escr
ib
es
th
e
d
ev
elo
p
m
e
n
t
o
f
a
n
e
w
s
tab
ilit
y
in
d
ex
t
h
at
i
n
co
r
p
o
r
ates
r
ea
cti
v
e
p
o
w
er
tr
ac
in
g
co
m
p
u
tatio
n
i
n
t
h
e
i
n
d
ex
f
o
r
d
eter
m
in
in
g
t
h
e
w
ea
k
lo
ca
tio
n
s
f
r
o
m
th
e
v
o
ltag
e
in
s
tab
il
it
y
p
o
in
t
o
f
v
ie
w
.
T
h
e
p
r
o
p
o
s
ed
r
ea
ctiv
e
p
o
w
er
tr
ac
in
g
m
et
h
o
d
d
o
es
n
o
t
alter
t
h
e
n
et
w
o
r
k
s
ize
a
n
d
it
ca
n
tr
ac
e
t
h
e
r
ea
ctiv
e
p
o
w
er
f
lo
w
c
o
n
tr
ib
u
t
ed
b
y
lo
ad
b
u
s
es
i
n
a
tr
a
n
s
m
i
s
s
io
n
s
y
s
te
m
.
T
h
e
p
r
o
p
o
s
ed
r
ea
ctiv
e
p
o
w
er
tr
ac
in
g
in
d
ex
L
QP
_
L
T
is
th
e
n
co
m
p
ar
ed
w
it
h
th
e
o
t
h
er
lin
e
V
SIs s
u
ch
as t
h
e
L
m
n
,
FVSI
a
n
d
NVS
I
[
5
]
-
[
7
]
.
2.
DE
RI
VAT
I
O
N
O
F
RE
AC
T
I
VE
P
O
WE
R
T
RACK
I
N
G
I
NDEX
L
Q
P
_
L
T
L
o
ad
tr
ac
in
g
i
s
a
tas
k
f
o
r
d
eter
m
i
n
in
g
th
e
e
x
tr
ac
tio
n
o
f
p
o
w
er
b
y
lo
ad
s
an
d
is
th
e
k
e
y
p
r
in
cip
l
e
b
eh
in
d
t
h
e
d
er
iv
a
tio
n
o
f
t
h
e
r
ea
ctiv
e
p
o
w
er
tr
ac
in
g
i
n
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ex
.
L
o
ad
tr
ac
in
g
d
eter
m
in
e
s
h
o
w
m
u
c
h
lin
e
f
lo
w
an
d
g
en
er
ated
p
o
w
er
ar
e
co
n
s
u
m
e
d
b
y
a
lo
ad
[
1
1
]
-
[
1
2
]
.
T
r
ac
in
g
th
e
p
o
w
er
co
n
s
u
m
p
tio
n
b
y
an
y
lo
ad
in
a
s
y
s
te
m
ca
n
p
r
o
v
id
e
a
g
o
o
d
in
d
icatio
n
o
n
t
h
e
p
r
io
r
ity
o
f
lo
ad
to
b
e
s
h
ed
f
ir
s
t
d
u
r
in
g
a
co
n
ti
n
g
en
c
y
.
T
h
e
s
ec
tio
n
d
escr
ib
es
th
e
d
ev
elo
p
m
e
n
t
o
f
th
e
p
r
o
p
o
s
ed
r
ea
ctiv
e
p
o
w
er
t
r
ac
in
g
in
d
e
x
,
L
QP
_
L
T
f
o
r
d
et
er
m
in
in
g
t
h
e
w
ea
k
lo
ad
b
u
s
es
f
o
r
lo
ad
s
h
ed
d
in
g
p
u
r
p
o
s
e.
T
h
e
L
QP
_
L
T
in
d
ex
is
d
er
iv
ed
f
r
o
m
t
h
e
lin
e
s
tab
ilit
y
f
ac
to
r
,
L
QP
d
ev
elo
p
ed
b
y
Mo
h
a
m
ed
et
al
[
1
3
]
.
Usi
n
g
th
e
co
n
ce
p
t
o
f
r
ed
u
cin
g
a
r
ad
ial
n
et
w
o
r
k
in
to
a
s
in
g
le
li
n
e
eq
u
iv
ale
n
t
cir
cu
i
t,
th
e
p
o
w
er
f
lo
w
i
n
a
tr
an
s
m
is
s
io
n
li
n
e
o
f
a
t
w
o
b
u
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s
y
s
te
m
is
co
n
s
i
d
er
ed
as
s
h
o
w
n
i
n
Fig
u
r
e
1
[
1
4
]
.
Fig
u
r
e
1
.
Sin
g
le
li
n
e
d
iag
r
a
m
o
f
a
t
w
o
-
b
u
s
s
y
s
te
m
B
y
ta
k
i
n
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e
i
as
th
e
r
e
f
er
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ce
n
o
d
e
an
d
letti
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g
b
e
th
e
th
e
r
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ctiv
e
p
o
w
er
en
ter
i
n
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n
o
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e
j,
th
e
f
o
llo
w
i
n
g
eq
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is
d
er
iv
ed
[
1
3
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.
,
Q
j
i
j
R
ij
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R
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Un
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(
R
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891
(
1
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T
h
u
s
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(
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R
ea
r
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an
g
in
g
(
2
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(
3
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E
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√
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T
h
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o
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l r
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e
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t b
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s
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ied
.
(
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(
)
(
5
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T
h
e
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d
itio
n
in
(
5
)
w
ill
lead
to
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a
g
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y
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o
o
ts
o
f
if
it
is
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o
t
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atis
f
ied
.
Fro
m
(
5
)
,
it
ca
n
also
b
e
o
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s
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at
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h
as
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r
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o
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d
e
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f
o
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e
r
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to
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th
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in
(
5
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is
n
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t
s
atis
f
ied
,
it
i
m
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lies
t
h
at
v
o
lta
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e
co
llap
s
e
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ce
n
ar
io
h
a
v
e
alr
ea
d
y
o
cc
u
r
ed
.
Fro
m
(
5
)
,
th
e
L
QP
in
d
ex
is
d
er
iv
ed
an
d
ex
p
r
ess
ed
as [
1
3
]
,
(
)
(
)
(
6
)
T
h
e
L
QP
i
n
d
ex
h
as
a
v
al
u
e
b
et
w
ee
n
0
to
1
.
0
an
d
t
h
at
i
f
th
e
v
al
u
e
o
f
L
QP
i
n
d
ex
i
s
clo
s
e
to
1
.
0
,
it
in
d
icate
s
p
r
o
x
i
m
it
y
to
v
o
l
ta
g
e
co
llap
s
e.
Sin
ce
r
ea
cti
v
e
p
o
w
er
f
lo
w
p
lay
s
a
cr
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cia
l
r
o
le
in
m
ain
tain
in
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a
v
o
lta
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w
it
h
i
n
a
s
tab
le
r
e
g
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,
it
i
s
i
m
p
o
r
tan
t
to
tr
ac
e
th
e
r
ea
ctiv
e
p
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w
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f
lo
w
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n
a
lin
e
th
at
w
il
l
b
e
co
n
s
u
m
ed
b
y
a
lo
ad
.
T
h
e
s
ig
n
i
f
ica
n
ce
o
f
tr
ac
in
g
r
ea
ctiv
e
p
o
w
er
f
lo
w
i
n
ev
er
y
lin
e
d
u
e
to
lo
ad
w
ill
in
f
ac
t
i
n
d
icate
w
h
ic
h
lo
ad
b
u
s
e
s
in
t
h
e
s
y
s
te
m
t
h
at
ca
u
s
e
s
h
i
g
h
est
co
n
g
e
s
tio
n
le
v
el
to
a
tr
an
s
m
is
s
io
n
li
n
e.
W
it
h
th
is
co
n
ce
p
t,
tr
ac
i
n
g
t
h
e
L
Q
P
in
d
ex
co
n
tr
ib
u
ted
b
y
a
ce
r
tain
lo
ad
in
a
s
y
s
te
m
ca
n
b
e
d
er
iv
ed
.
E
q
u
atio
n
(
4
)
h
as
s
h
o
w
n
t
h
at
r
ea
cti
v
e
p
o
w
e
r
ca
n
b
e
tr
ac
ed
in
a
lin
e
as
a
s
u
m
m
atio
n
o
f
in
d
i
v
i
d
u
al
lo
ad
co
m
p
o
n
en
ts
b
y
id
en
tify
i
n
g
t
h
e
p
o
w
er
f
r
ac
tio
n
co
n
tr
ib
u
tio
n
.
A
p
p
l
y
i
n
g
(
4
)
an
d
(
5
)
f
o
r
r
ea
ctiv
e
p
o
w
e
r
tr
ac
in
g
,
i
n
to
(
6
)
f
o
r
l
in
e
l
-
m
as
s
u
m
m
at
io
n
o
f
i
n
d
i
v
id
u
a
l
lo
ad
co
m
p
o
n
e
n
ts
,
th
e
R
ea
ct
iv
e
P
o
w
er
T
r
ac
in
g
I
n
d
ex
,
L
QP
_
L
T
is
d
er
iv
ed
.
T
h
e
f
o
llo
w
i
n
g
s
ec
tio
n
s
s
h
o
w
t
h
e
d
etailed
s
tep
s
to
d
er
iv
e
L
QP
_
L
T
in
d
ex
.
T
o
s
u
cc
ess
f
u
l
l
y
o
b
tain
th
e
tr
ac
ed
L
QP
_
L
T
in
d
ex
,
th
e
r
ec
eiv
i
n
g
en
d
r
ea
ctiv
e
p
o
w
er
f
r
ac
tio
n
,
ex
tr
ac
ted
b
y
i
-
th
lo
ad
in
li
n
e
l
-
m
n
ee
d
to
b
e
q
u
a
n
ti
f
ied
.
T
o
p
er
f
o
r
m
t
h
i
s
,
t
h
e
d
o
w
n
s
tr
ea
m
lo
o
k
in
g
a
lg
o
r
it
h
m
w
h
ic
h
co
n
s
id
er
s
t
h
e
n
o
d
al
b
al
an
ce
o
u
t
f
lo
w
s
is
i
m
p
le
m
e
n
ted
.
A
p
p
l
y
in
g
t
h
is
co
n
ce
p
t
b
y
B
i
alek
,
t
h
e
to
tal
n
o
d
al
r
ea
ctiv
e
p
o
w
er
,
is
ex
p
r
es
s
ed
as [
9
]
,
∑
|
|
∑
(
7
)
w
h
er
e
is
t
h
e
s
et
o
f
n
o
d
es su
p
p
lied
d
ir
ec
tly
f
r
o
m
n
o
d
e
.
T
h
u
s
,
th
e
r
ea
ctiv
e
p
o
w
er
f
lo
win
g
o
u
t
f
r
o
m
n
o
d
e
in
th
e
r
ele
v
an
t
li
n
e
s
,
is
n
o
ted
as
.
On
th
e
o
th
er
h
an
d
,
is
t
h
e
r
ea
cti
v
e
lo
ad
at
n
o
d
e
,
is
t
h
e
r
ec
ei
v
i
n
g
e
n
d
r
ea
ctiv
e
p
o
w
er
e
x
tr
ac
ted
b
y
r
ea
ctiv
e
p
o
w
er
f
ac
tio
n
|
|
⁄
.
R
ea
r
r
an
g
i
n
g
(
7
)
,
it c
an
b
e
r
e
-
w
r
itte
n
as,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4752
I
n
d
o
n
esia
n
J
E
lec
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n
g
&
C
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m
p
Sci,
Vo
l.
12
,
No
.
3
,
Dese
m
b
er
2
0
1
8
:
8
8
9
–
8
9
8
892
∑
(
8
)
o
r
as m
u
ltip
lica
tio
n
o
f
d
o
w
n
s
t
r
ea
m
d
is
tr
ib
u
tio
n
ad
m
itta
n
ce
m
atr
i
x
[
9
]
,
(
9
)
w
h
er
e
is
t
h
e
(
d
o
w
n
s
tr
ea
m
d
is
tr
ib
u
tio
n
m
atr
ix
,
is
th
e
v
ec
to
r
o
f
n
o
d
al
th
r
o
u
g
h
r
ea
ctiv
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p
o
w
er
f
lo
w
s
a
n
d
is
th
e
v
ec
to
r
o
f
n
o
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al
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d
e
m
an
d
s
.
T
h
e
(
)
ele
m
e
n
t o
f
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n
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m
d
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tr
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m
atr
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is
eq
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al
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,
[
]
{
|
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(
1
0
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Fro
m
(
1
0
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,
if
ex
is
ts
,
t
h
e
n
=
an
d
its
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th
ele
m
en
t c
an
b
e
w
r
it
ten
as:
∑
[
]
(
1
1
)
E
q
u
atio
n
(
1
1
)
s
h
o
w
s
h
o
w
t
h
e
n
o
d
al
r
ea
ctiv
e
p
o
w
er
,
is
d
is
tr
ib
u
ted
b
et
w
ee
n
all
th
e
lo
ad
s
in
t
h
e
s
y
s
te
m
.
B
ialek
h
as
s
h
o
w
n
t
h
a
t
th
e
s
a
m
e
n
o
d
al
r
ea
ctiv
e
p
o
w
er
,
is
eq
u
al
to
th
e
s
u
m
o
f
t
h
e
lo
ad
d
em
a
n
d
at
n
o
d
e
i
an
d
all
t
h
e
o
u
t
f
lo
w
s
i
n
li
n
es
l
ea
v
i
n
g
t
h
e
n
o
d
e
[
9
]
.
Hen
ce
,
t
h
e
r
ea
cti
v
e
p
o
w
er
o
u
tf
lo
w
i
n
li
n
e
f
r
o
m
n
o
d
e
i
ca
n
b
e
ca
lcu
lated
u
s
i
n
g
th
e
p
r
o
p
o
r
tio
n
al
s
h
ar
i
n
g
p
r
in
cip
le
s
h
o
w
n
as,
|
|
(
|
|
)
∑
[
]
(
1
2
)
Fro
m
h
er
e,
t
h
e
tr
ac
ed
r
ea
cti
v
e
p
o
w
er
allo
ca
tio
n
to
ea
ch
lin
e
d
u
e
a
p
ar
ticu
lar
lo
ad
co
m
p
o
n
en
t
i
s
i
m
p
le
m
e
n
ted
in
to
th
e
L
QP
in
d
e
x
an
d
n
a
m
ed
as
.
ca
n
n
o
w
b
e
w
r
it
ten
as
:
(
1
3
)
E
x
p
an
d
in
g
(
1
3
)
to
in
co
r
p
o
r
ate
th
e
tr
ac
ed
r
ea
cti
v
e
p
o
w
er
tr
ac
in
g
co
n
tr
ib
u
ted
b
y
lo
ad
co
m
p
o
n
en
t
s
i
n
i
n
d
iv
id
u
al
lin
e
,
th
e
f
o
llo
w
in
g
is
d
er
iv
ed
.
(
)
(
)
(
)
(
1
4
)
Fin
all
y
,
th
e
to
tal
tr
ac
ed
L
QP
_
L
T
o
f
lin
e
l
-
m
d
u
e
to
th
e
i
-
th
lo
ad
o
f
r
ea
ctiv
e
p
o
w
er
,
is
g
en
er
alis
ed
an
d
w
r
itte
n
as
f
o
llo
w
s
,
[
∑
]
(
1
5
)
w
h
er
e,
:
n
u
m
b
er
o
f
lo
ad
s
o
r
r
ea
ctiv
e
p
o
w
er
s
i
n
k
s
i
n
th
e
s
y
s
te
m
:
r
ec
eiv
in
g
e
n
d
r
ea
ctiv
e
p
o
w
er
c
o
n
tr
ib
u
ted
b
y
th
e
i
-
t
h
lo
ad
o
r
r
ea
ctiv
e
s
i
n
k
in
l
in
e
l
-
m
:
r
ec
eiv
in
g
e
n
d
r
ea
ctiv
e
p
o
w
er
f
r
ac
tio
n
in
li
n
e
l
–
m
:
lin
e
r
ea
ctan
ce
:
s
en
d
i
n
g
e
n
d
v
o
lta
g
e
in
p
.
u
.
:
s
en
d
i
n
g
e
n
d
r
ea
l p
o
w
er
an
d
3.
RE
AC
T
I
V
E
P
O
WE
R
T
RA
CIN
G
AL
G
O
R
I
T
H
M
A
r
ea
cti
v
e
p
o
w
er
tr
ac
i
n
g
al
g
o
r
ith
m
i
s
d
ev
elo
p
ed
in
M
A
T
L
A
B
to
ca
lcu
late
t
h
e
p
r
o
p
o
s
ed
r
ea
ctiv
e
p
o
w
er
tr
ac
in
g
i
n
d
ex
,
L
QP
_
L
T
an
d
r
an
k
in
g
t
h
e
i
n
d
ex
f
o
r
id
en
ti
f
y
i
n
g
t
h
e
w
ea
k
li
n
es
i
n
a
p
o
w
er
s
y
s
te
m
.
T
h
e
o
v
er
all
i
m
p
le
m
e
n
tatio
n
s
t
ep
s
o
f
th
e
r
ea
cti
v
e
p
o
w
er
tr
ac
i
n
g
al
g
o
r
ith
m
ar
e
d
escr
ib
ed
as f
o
llo
w
s
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esia
n
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4752
R
ea
ctive
P
o
w
er Tr
a
cin
g
I
n
d
ex
LQP_
LT
fo
r
V
o
lta
g
e
Un
s
ta
b
le
Lo
a
d
B
u
s
I
d
en
tifi
ca
tio
n
…
(
R
en
u
g
a
V
era
yia
h
)
893
Step
1
:
I
n
p
u
t d
ata
o
f
th
e
te
s
t p
o
w
er
s
y
s
te
m
.
Step
2
:
Ob
tain
t
h
e
b
ase
ca
s
e
p
o
w
er
f
lo
w
s
o
lu
tio
n
f
o
r
th
e
p
o
w
er
s
y
s
te
m
u
s
i
n
g
t
h
e
MA
T
L
A
B
b
ased
MA
T
P
OW
E
R
lo
ad
f
lo
w
p
r
o
g
r
a
m
.
Step
3
:
A
p
p
l
y
a
d
is
tu
r
b
an
ce
ev
en
t,
s
u
c
h
as
s
i
n
g
le
li
n
e
o
u
tag
e,
d
o
u
b
le
lin
e
o
u
tag
e
w
i
th
an
d
w
it
h
o
u
t
lo
ad
in
cr
ea
s
e
i
n
th
e
s
y
s
te
m
.
Step
4
:
C
alc
u
late
n
e
w
r
ea
cti
v
e
p
o
w
er
i
n
ea
c
h
l
in
e
at
b
o
th
s
en
d
i
n
g
an
d
r
ec
ei
v
i
n
g
en
d
b
u
s
es
d
u
e
to
r
ea
cti
v
e
p
o
w
er
g
e
n
e
r
ated
b
y
s
h
u
n
t
ad
m
itta
n
ce
,
co
n
n
ec
ted
to
ea
ch
b
u
s
.
E
q
u
atio
n
s
(
1
6
)
an
d
(
1
7
)
ar
e
u
s
ed
to
o
b
tain
th
e
n
e
w
r
ea
ct
iv
e
p
o
w
er
in
j
ec
tio
n
s
co
n
s
id
er
in
g
th
e
s
h
u
n
t a
d
m
it
tan
ce
s
.
Fig
u
r
e
2
.
I
m
p
le
m
e
n
tatio
n
s
tep
s
o
f
L
QP
_
L
T
in
d
ex
co
m
p
u
tat
i
o
n
(
1
6
)
(
1
7
)
Step
5
:
C
o
m
p
lete
th
e
π
m
o
d
el
n
et
w
o
r
k
b
y
co
n
s
id
er
in
g
th
e
f
o
llo
w
i
n
g
ca
lc
u
latio
n
s
.
T
h
e
n
et
w
o
r
k
i
s
n
o
w
co
n
s
id
er
ed
as
lo
s
s
le
s
s
s
i
n
ce
th
e
s
h
u
n
t
ad
m
i
ttan
ce
s
h
a
s
b
ee
n
attr
ib
u
ted
to
s
en
d
i
n
g
e
n
d
b
u
s
e
s
as
s
h
o
w
n
i
n
Step
4
.
a)
C
alcu
late
th
e
r
ea
cti
v
e
p
o
w
er
g
en
er
atio
n
at
ea
c
h
b
u
s
t
h
at
is
eq
u
al
to
to
tal
g
en
er
ated
p
o
w
er
an
d
attr
ib
u
ted
s
h
u
n
t a
d
m
it
tan
ce
s
.
In
p
u
t
te
st
p
o
w
e
r
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2
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d
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Vo
l.
12
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No
.
3
,
Dese
m
b
er
2
0
1
8
:
8
8
9
–
8
9
8
894
(
1
8
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2
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2
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6
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th
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(
1
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1
2
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.
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d
(
1
5
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.
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1
0
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k
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ith
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Fi
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2
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4.
T
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L
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T
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f
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ac
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ex
,
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d
eter
m
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t
h
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w
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b
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a
p
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m
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s
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m
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ices,
n
a
m
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FV
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L
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n
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NVSI
[
5
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-
[
7
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th
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E
5
7
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M
A
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R
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is
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ex
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k
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th
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d
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x
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d
t
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v
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r
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.
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d
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cr
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th
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m
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la
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s
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n
d
ices,
FVSI,
L
m
n
a
n
d
NVSI
.
T
h
e
lin
e
s
tab
ilit
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i
n
d
ex
,
k
n
o
w
n
a
s
L
m
n
is
e
x
p
r
ess
ed
a
s
[
5
]
,
[
|
|
]
(
2
2
)
w
h
er
e
X
is
t
h
e
li
n
e
r
ea
ctan
ce
,
Q
r
is
th
e
r
ea
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v
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p
o
w
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th
e
r
ec
eiv
in
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n
d
,
V
s
is
th
e
s
e
n
d
in
g
e
n
d
v
o
lta
g
e,
i
s
lin
e
i
m
p
ed
an
ce
a
n
g
le
an
d
i
s
th
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a
n
g
le
d
i
f
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er
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n
ce
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et
w
ee
n
t
h
e
s
u
p
p
l
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v
o
ltag
e
a
n
d
t
h
e
r
ec
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in
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v
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L
m
n
is
u
s
ed
f
o
r
p
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ed
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g
v
o
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e
in
s
tab
ilit
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s
u
c
h
th
at
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m
n
i
s
le
s
s
th
a
n
1
.
0
0
,
th
e
p
o
w
er
s
y
s
te
m
is
co
n
s
id
er
ed
s
tab
le,
o
th
er
w
i
s
e
t
h
e
s
y
s
te
m
is
u
n
s
tab
le.
T
h
e
FV
SI
is
ex
p
r
ess
ed
as [
6
]
,
(
2
3
)
w
h
er
e
Z
is
th
e
li
n
e
i
m
p
ed
an
ce
,
X
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th
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li
n
e
r
ea
ctan
ce
,
Q
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th
e
r
ea
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p
o
w
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f
lo
w
a
t
th
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ec
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in
g
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n
d
an
d
V
s
is
th
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s
e
n
d
in
g
en
d
v
o
lta
g
e.
T
h
e
li
n
e
t
h
at
g
i
v
es
i
n
d
ex
v
al
u
e
clo
s
e
to
1
.
0
0
w
ill
b
e
t
h
e
m
o
s
t
cr
itical
li
n
e
a
n
d
m
a
y
lead
to
s
y
s
te
m
w
id
e
v
o
lta
g
e
in
s
tab
ilit
y
.
T
h
e
NVSI
[
7
]
is
ex
p
r
ess
ed
as,
√
(
2
4
)
w
h
er
e
X
is
t
h
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l
in
e
r
ea
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n
ce
,
Q
r
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h
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r
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v
e
p
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w
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v
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en
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a
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d
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h
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s
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n
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g
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d
v
o
ltag
e.
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r
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v
a
lu
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les
s
t
h
an
1
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0
0
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th
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s
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te
m
i
s
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id
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p
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f
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f
t
h
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L
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ase
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th
e
f
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llo
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s
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tio
n
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esia
n
J
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lec
E
n
g
&
C
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m
p
Sci
I
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N:
2502
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4752
R
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895
4
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Co
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a
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,
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d
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e
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d
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as
th
e
w
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k
lo
ad
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u
s
.
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h
e
1
0
cr
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lin
es
f
o
r
th
e
test
s
y
s
te
m
ar
e
s
h
o
w
n
in
T
ab
le
3
.
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v
alu
atio
n
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n
t
h
e
in
d
e
x
p
er
f
o
r
m
a
n
ce
f
o
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th
e
s
y
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te
m
s
h
o
w
s
t
h
at
L
m
n
a
n
d
NV
S
I
in
d
ex
i
n
d
icate
d
b
u
s
1
6
as
th
e
w
ea
k
es
t
b
u
s
,
w
h
ile
L
QP
_
L
T
in
d
ex
tr
ac
ed
b
u
s
3
1
a
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e
w
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k
est
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u
s
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n
d
th
e
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i
n
d
ex
in
d
icate
d
b
u
s
4
9
as
th
e
w
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k
e
s
t
b
u
s
.
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b
s
eq
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en
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k
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n
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r
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r
th
e
w
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k
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ad
b
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v
ar
ies
f
o
r
all
th
e
in
d
ices.
T
h
e
FVSI
in
d
ex
in
d
icate
d
lin
e
co
n
n
ec
tin
g
f
r
o
m
b
u
s
1
3
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o
b
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s
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m
o
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t
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icate
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lt
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,
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MN
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v
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d
if
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t
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t
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t
th
er
e
ar
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s
i
m
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h
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v
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x
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r
m
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r
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a
m
p
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L
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in
d
ice
s
c
o
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s
id
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ls
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a
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s
h
o
w
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r
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te
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Fig
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3
1
Evaluation Warning : The document was created with Spire.PDF for Python.
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h
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to
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T
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at
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n
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it
ical
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e
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T
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e
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r
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e
p
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a
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.
RE
F
E
R
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NC
E
S
[1
]
Zam
a
n
i
M
K,
M
u
sirin
I,
Om
a
r
M
S
,
S
u
l
im
a
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a
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i
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Ba
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c
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f
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r
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tab
il
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ty
Im
p
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v
e
m
e
n
t.
In
d
o
n
e
sia
n
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o
u
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a
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o
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2
0
1
8
;
9
(
1
):
1
2
3
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1
3
0
.
[2
]
No
r
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,
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O
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In
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A
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f
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Us
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M
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In
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2
0
1
6
;
3
(3
):
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5
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2
.
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Bu
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∑
∑
1
13
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7
33
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4752
I
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d
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J
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12
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No
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3
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Dese
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2
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8
:
8
8
9
–
8
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8
898
[3
]
M
o
d
a
rre
si
J,
G
h
o
li
p
o
u
r
E.
A
Co
m
p
re
h
e
n
s
iv
e
Re
v
ie
w
o
f
th
e
V
o
lt
a
g
e
S
tab
il
it
y
In
d
ice
s.
Ren
e
wa
b
le
a
n
d
S
u
st
a
in
a
b
le
En
e
rg
y
Rev
iews
.
2
0
1
6
;
6
3
:
1
-
1
2
.
[4
]
Be
rizz
i
A
.
T
h
e
Ita
li
a
n
2
0
0
3
Bl
a
c
k
o
u
t
.
IEE
E
P
o
w
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r
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g
in
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rin
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S
o
c
iet
y
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n
e
ra
l
M
e
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ti
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g
.
D
e
n
v
e
r.
2
0
0
4
;
2
:
1
6
7
3
-
1
6
7
9
.
[5
]
M
o
g
h
a
v
v
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m
i
M
,
O
m
a
r
F
M
.
1
9
9
7
.
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w
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f
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d
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lt
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g
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ta
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ty
Co
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it
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o
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in
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m
.
P
r
o
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g
s o
f
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I
n
tern
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ti
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l
Co
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P
o
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in
g
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p
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re
.
1
9
9
7
;
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2
3
-
2
2
1
.
[6
]
M
u
sirin
I,
A
b
d
u
l
Ra
h
m
a
n
T
K.
E
stim
a
ti
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g
M
a
x
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m
u
m
L
o
a
d
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b
il
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f
o
r
W
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a
k
Bu
s
Id
e
n
ti
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ti
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n
Us
in
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V
S
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EE
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Po
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g
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rin
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Rev
iew
.
2
0
0
2
;
2
2
(
1
1
)
:
5
0
-
5
2
.
[7
]
Ka
n
im
o
z
h
i
R,
S
e
lv
i
K.
A
No
v
e
l
L
in
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S
tab
il
it
y
In
d
e
x
f
o
r
V
o
lt
a
g
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S
tab
il
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y
A
n
a
l
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sis
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d
Co
n
ti
n
g
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c
y
R
a
n
k
in
g
in
P
o
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ste
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s u
sin
g
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u
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Ba
se
d
L
o
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d
F
l
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J
o
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rn
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El
e
c
tric
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l
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n
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g
T
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h
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g
y
.
2
0
1
3
.
8
(4
):
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9
4
-
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0
3
.
[8
]
L
i
S
.
S
e
n
siti
v
it
y
M
o
d
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l
o
f
L
In
d
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x
f
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tea
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o
lt
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tab
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o
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in
d
P
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r
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y
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m
s
w
it
h
Do
u
b
ly
F
e
d
In
d
u
c
ti
o
n
G
e
n
e
ra
to
rs.
El
e
c
trica
l
Po
we
r Co
mp
o
n
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n
ts
a
n
d
S
y
ste
ms
.
2
0
1
6
;
4
4
(
1
8
)
:
2
0
1
7
-
2
0
2
4
.
[9
]
Biale
k
J.
T
ra
c
in
g
th
e
f
lo
w
o
f
El
e
c
tri
c
it
y
.
IEE
E
Pro
c
e
e
d
i
n
g
s
-
G
e
n
e
ra
ti
o
n
,
T
r
a
n
sm
issio
n
a
n
d
Dis
trib
u
ti
o
n
.
1
9
9
6
;
1
4
3
(4
):
3
1
3
-
3
2
0
.
[1
0
]
Niu
R,
Zen
g
Y,
Ch
e
n
g
M
,
Wan
g
X
.
S
tu
d
y
o
n
L
o
a
d
S
h
e
d
d
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n
g
M
o
d
e
l
b
a
se
d
o
n
Imp
r
o
v
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d
Po
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r
Fl
o
w
T
ra
c
in
g
M
e
th
o
d
i
n
P
o
we
r
S
y
ste
m
Ri
sk
Asse
ss
me
n
t
.
4
th
I
n
tern
a
ti
o
n
a
l
Co
n
f
e
re
n
c
e
o
n
El
e
c
tri
c
Util
i
t
y
D
e
re
g
u
latio
n
,
Re
stru
c
tu
rin
g
a
n
d
P
o
w
e
r
Tec
h
n
o
l
o
g
ies
(DRP
T
).
S
h
a
n
d
o
n
g
.
2
0
1
1
;
4
5
-
5
0
.
[1
1
]
Zu
lk
if
f
li
AH
,
M
u
sirin
I.
Op
ti
m
a
l
F
u
z
z
y
In
fe
re
n
c
e
S
y
ste
m
I
n
c
o
rp
o
ra
ted
w
it
h
S
tab
il
i
ty
In
d
e
x
T
r
a
c
in
g
:
A
n
A
p
p
li
c
a
ti
o
n
f
o
r
Ef
f
e
c
ti
v
e
L
o
a
d
S
h
e
d
d
i
n
g
.
Exp
e
rt
S
y
ste
ms
wit
h
A
p
p
li
c
a
ti
o
n
s
.
2
0
1
4
;
4
1
(4
):
1
0
9
5
-
1
1
0
3
.
[1
2
]
Zam
a
n
i
M
K,
M
u
siri
n
I,
Ha
ss
a
n
H,
S
h
a
a
y
a
S
A
,
S
u
laim
a
n
S
I,
G
h
a
n
i
NA
,
S
u
li
m
a
n
S
I.
A
c
ti
v
e
a
n
d
Re
a
c
ti
v
e
P
o
w
e
r
S
c
h
e
d
u
l
in
g
Op
t
im
iza
ti
o
n
u
sin
g
F
iref
l
y
A
lg
o
rit
h
m
to
Im
p
ro
v
e
V
o
lt
a
g
e
S
tab
il
it
y
Un
d
e
r
L
o
a
d
De
m
a
n
d
V
a
riatio
n
.
In
d
o
n
e
sia
n
J
o
u
rn
a
l
o
f
El
e
c
trica
l
En
g
i
n
e
e
rin
g
a
n
d
C
o
mp
u
ter
S
c
ien
c
e
.
2
0
1
8
;
9
(2
)
:
3
6
5
-
3
7
2
.
[1
3
]
M
o
h
a
m
e
d
A
,
Ja
s
m
o
n
G
B,
Yu
so
ff
S
.
A
S
tatic
V
o
lt
a
g
e
Co
ll
a
p
se
In
d
ica
to
r
u
sin
g
L
in
e
S
tab
il
it
y
In
d
ica
to
rs.
J
o
u
rn
a
l
o
f
In
d
u
stria
l
T
e
c
h
n
o
lo
g
y
.
1
9
8
9
;
7
(1
)
:
7
3
-
8
5
.
[1
4
]
J
a
s
m
o
n
G
B,
Lee
L
HCC.
Dist
rib
u
ti
o
n
Ne
tw
o
rk
Re
d
u
c
ti
o
n
f
o
r
Vo
lt
a
g
e
S
tab
il
it
y
A
n
a
l
y
sis
a
n
d
L
o
a
d
f
lo
w
Ca
lcu
latio
n
s.
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
Po
we
r a
n
d
En
e
rg
y
S
y
ste
ms
.
1
9
9
1
;
1
3
(1
):
9
-
13.
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