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l J
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f
E
lect
rica
l a
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m
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ute
r
E
ng
in
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ring
(
I
J
E
CE
)
Vo
l.
8
,
No
.
1
,
Feb
r
u
ar
y
201
8
,
p
p
.
4
3
~5
1
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SS
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it
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ltag
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In
stit
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C
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A
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:
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ical
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T
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Un
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9
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m
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g
ag
ar
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@
tr
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u
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au
n
i
v
.
in
1.
I
NT
RO
D
UCT
I
O
N
R
ad
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Di
s
tr
ib
u
tio
n
s
y
s
te
m
h
a
s
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lar
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e
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u
m
b
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b
u
s
es.
So
,
it
i
s
n
o
t
p
o
s
s
ib
le
to
m
a
in
ta
in
ad
eq
u
ate
b
u
s
v
o
lta
g
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ea
ch
b
u
s
.
T
h
is
w
il
l
in
cr
ea
s
e
t
h
e
ch
a
n
ce
o
f
v
o
ltag
e
in
s
tab
ilit
y
at
th
e
b
u
s
es
[
1
]
.
I
n
cr
ea
s
e
in
lo
a
d
d
em
a
n
d
w
ill
r
ed
u
ce
th
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v
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lta
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ec
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en
d
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p
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d
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f
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le
to
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m
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th
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e
w
i
ll b
e
v
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llap
s
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[
2
]
.
Fo
r
p
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p
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p
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ati
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f
p
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y
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p
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m
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cr
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[
3
]
.
T
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m
s
tab
ilit
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d
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r
it
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,
p
lan
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in
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d
o
p
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atio
n
o
f
p
o
w
er
s
y
s
te
m
i
s
ess
e
n
t
ial
[
4
]
.
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ilit
y
a
n
al
y
s
is
m
a
y
b
e
o
f
t
w
o
f
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m
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d
d
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ic.
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n
s
tatic
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s
lo
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ased
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m
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d
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m
ai
n
b
ased
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s
p
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f
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m
ed
[
5
]
.
W
ith
th
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i
m
p
le
m
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tatio
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f
p
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m
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it
(
P
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f
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v
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s
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cr
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On
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d
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f
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b
ased
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d
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b
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ch
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m
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ab
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t v
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tab
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p
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m
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s
i
n
g
p
h
aso
r
m
ea
s
u
r
e
m
en
t u
n
it [
6
]
.
Dif
f
er
en
t
tech
n
iq
u
e
s
h
a
v
e
b
e
en
u
s
ed
f
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v
o
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g
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tab
ili
t
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al
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s
is
.
P
-
V
cu
r
v
e
an
d
Q
-
V
c
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r
v
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m
et
h
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d
[
7
-
9
]
ar
e
th
e
tr
ad
itio
n
al
m
e
th
o
d
s
o
f
v
o
ltag
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tab
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is
.
Ma
n
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d
ices
s
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SVSI
[
1
0
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L
-
in
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x
[
1
1
]
,
L
mn
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VC
P
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[
1
2
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,
in
teg
r
ated
v
o
ltag
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t
ab
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in
d
icato
r
s
[
1
3
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etc.
c
an
p
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ed
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v
o
ltag
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in
s
tab
il
it
y
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n
a
p
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.
Oth
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m
eth
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u
c
h
as
r
ad
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b
asis
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v
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s
ta
b
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n
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i
s
[
1
4
]
,
[
1
5
]
.
I
n
r
ec
en
t
y
ea
r
s
a
lo
t
o
f
w
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k
h
a
s
b
ee
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d
o
n
e
i
n
t
h
e
ar
ea
o
f
v
o
ltag
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s
tab
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t
y
.
Vo
ltag
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s
tab
ilit
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a
n
al
y
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i
s
w
a
s
d
o
n
e
b
y
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e
r
esear
ch
er
s
u
s
i
n
g
n
o
d
al
an
al
y
s
is
[
1
6
]
,
m
o
d
if
ied
d
if
f
er
en
tial
e
v
o
lu
tio
n
[
1
7
]
,
co
u
p
led
s
in
g
le
p
o
r
t
cir
cu
it
[
1
8
]
,
cir
cu
it
th
eo
r
y
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
8
,
No
.
1
,
Feb
r
u
ar
y
2
0
1
8
:
4
3
–
51
44
ap
p
r
o
ac
h
[
1
9
]
,
ca
tast
r
o
p
h
e
th
eo
r
y
[
2
0
]
,
ch
ao
tic
p
ar
ticle
s
w
ar
m
o
p
ti
m
iza
tio
n
al
g
o
r
ith
m
[
2
1
]
,
v
ec
to
r
r
eg
r
ess
io
n
m
o
d
el
[
2
2
]
etc.
A
lo
n
g
w
it
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t
h
e
o
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et
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d
s
p
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m
en
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n
it
b
ased
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ch
e
m
e
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ar
e
also
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ee
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s
ed
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n
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s
y
s
te
m
to
m
o
n
ito
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v
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s
tab
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[
2
3
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,
[
2
4
]
.
P
MU
in
s
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b
s
ta
tio
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g
iv
e
s
v
o
lta
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an
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r
en
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p
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s
in
f
o
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m
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n
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n
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m
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w
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th
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.
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t
ca
p
ab
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ata
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en
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n
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ca
n
b
e
o
b
tain
ed
.
T
h
is
p
ap
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ls
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it
h
a
n
e
w
v
o
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s
tab
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v
o
lta
g
e
s
tab
ili
t
y
co
n
d
itio
n
i
n
b
ase
ca
s
e
a
s
w
ell
as
at
m
a
x
i
m
u
m
lo
ad
in
g
co
n
d
it
io
n
co
n
s
id
er
i
n
g
d
i
f
f
er
en
t
l
in
e
t
r
ip
p
in
g
co
n
d
itio
n
.
T
h
e
d
ev
elo
p
ed
d
is
tr
ib
u
tio
n
s
y
s
te
m
s
tab
ilit
y
i
n
d
icato
r
(
DSSI)
is
test
ed
o
n
p
h
a
s
o
r
m
ea
s
u
r
e
m
e
n
t
u
n
i
t
in
co
r
p
o
r
ated
p
o
w
er
s
y
s
te
m
m
o
d
el
o
f
s
ta
n
d
ar
d
I
E
E
E
3
3
b
u
s
r
ad
ial
d
is
tr
ib
u
tio
n
s
y
s
te
m
.
T
h
e
r
esu
lt
o
f
D
SS
I
in
d
icato
r
ca
n
ac
c
u
r
atel
y
id
e
n
ti
f
y
th
e
cr
it
ical
co
n
d
itio
n
s
o
f
li
n
e
o
u
tag
e.
T
h
e
r
es
u
lt
i
s
v
er
i
f
ie
d
w
it
h
t
h
e
s
ta
n
d
ar
d
VSI
in
d
icato
r
[
2
5
]
.
T
h
e
ch
an
g
e
o
f
b
u
s
v
o
ltag
e
s
f
r
o
m
b
ase
v
alu
e
to
tr
ip
p
i
n
g
o
f
L
i
n
e
Nu
m
b
er
2
3
is
also
s
h
o
w
n
f
o
r
b
ase
lo
ad
an
d
m
a
x
i
m
u
m
lo
ad
.
2.
RE
S
E
ARCH
M
E
T
H
O
D
I
n
th
i
s
p
ap
er
p
h
aso
r
m
ea
s
u
r
e
m
en
t
u
n
it
(
P
MU
)
in
co
r
p
o
r
a
ted
v
o
ltag
e
s
ec
u
r
it
y
an
al
y
s
is
h
as
b
ee
n
p
er
f
o
r
m
ed
.
P
MU
is
allo
ca
ted
in
ev
er
y
b
u
s
to
g
i
v
e
b
o
th
m
ag
n
it
u
d
e
an
d
an
g
le
in
f
o
r
m
at
io
n
o
f
b
u
s
v
o
lta
g
e
an
d
cu
r
r
en
t.
Fig
u
r
e
1
s
h
o
w
s
t
h
e
f
lo
w
ch
ar
t
o
f
th
e
p
r
o
p
o
s
ed
m
et
h
o
d
.
Fig
u
r
e
1
.
Flo
w
c
h
ar
t o
f
t
h
e
p
r
o
p
o
s
ed
m
et
h
o
d
B
y
u
s
in
g
P
MU
at
ev
er
y
b
u
s
o
f
t
h
e
co
n
ce
r
n
ed
m
u
lt
i
-
b
u
s
s
y
s
te
m
t
h
e
v
o
lta
g
e
a
n
d
c
u
r
r
en
t
ca
n
b
e
m
ea
s
u
r
ed
ac
cu
r
atel
y
at
th
e
s
a
m
e
i
n
s
ta
n
t
o
f
t
i
m
e.
T
h
ese
r
ea
l
ti
m
e
d
ata
f
r
o
m
P
MU
ar
e
u
s
ed
in
t
h
e
p
r
o
p
o
s
ed
m
et
h
o
d
to
ca
lcu
la
te
t
h
e
d
is
tr
i
b
u
tio
n
s
y
s
te
m
s
tab
ilit
y
i
n
d
icat
o
r
(
DSSI)
.
T
h
en
th
is
tech
n
iq
u
e
f
i
n
d
t
h
e
v
al
u
e
o
f
DSSI
i
n
d
icato
r
f
o
r
d
if
f
er
e
n
t
c
o
n
d
itio
n
s
a
n
d
f
r
o
m
t
h
e
m
id
en
t
if
y
th
e
cr
i
tical
ca
s
e
s
.
Fro
m
t
h
e
r
esu
lt
s
th
e
v
o
lta
g
e
s
ec
u
r
it
y
an
al
y
s
is
i
s
p
er
f
o
r
m
ed
.
3.
DE
RI
VAT
I
O
N
O
F
T
H
E
P
R
O
P
O
SE
D
I
ND
E
X
F
RO
M
G
AUSS
-
S
E
I
D
E
L
E
Q
UA
T
I
O
N
Fig
u
r
e
2
d
ep
icts
a
s
i
m
p
lifie
d
t
w
o
b
u
s
n
et
w
o
r
k
w
h
er
e
s
o
u
r
ce
is
co
n
n
ec
ted
w
i
th
b
u
s
n
u
m
b
e
r
1
(
s
lack
b
u
s
)
an
d
a
lo
ad
is
co
n
n
ec
ted
to
b
u
s
n
u
m
b
er
2
(
lo
ad
b
u
s
)
.
T
o
m
ak
e
t
h
e
s
y
s
te
m
o
b
s
er
v
ab
le
in
r
esp
ec
t
to
v
o
ltag
e,
p
h
aso
r
m
ea
s
u
r
e
m
e
n
t
u
n
i
t
i
s
i
n
s
talled
in
b
o
th
t
h
e
b
u
s
es.
T
h
e
cu
r
r
e
n
t
f
lo
w
b
et
w
ee
n
b
u
s
n
u
m
b
er
1
a
n
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8708
Ga
u
s
s
-
S
eid
el
Meth
o
d
b
a
s
ed
V
o
lta
g
e
S
ec
u
r
ity
A
n
a
lysi
s
o
f D
is
tr
ib
u
tio
n
S
ystem
(
Ga
g
a
r
i D
e
b
)
45
b
u
s
n
u
m
b
er
2
is
I
.
T
h
e
lo
ad
ab
s
o
r
b
s
ap
p
ar
en
t
p
o
w
er
S
2
=
P
2
+
j
Q
2
f
r
o
m
th
e
s
y
s
te
m
.
T
w
o
b
u
s
e
s
ar
e
co
n
n
ec
ted
to
g
eth
er
b
y
i
m
p
ed
an
ce
.
Ass
u
m
in
g
s
lac
k
b
u
s
v
o
lta
g
e
e
q
u
al
to
u
n
i
t
y
,
Fig
u
r
e
2
.
P
MU
in
co
r
p
o
r
ate
d
s
im
p
li
f
ied
t
w
o
b
u
s
n
et
w
o
r
k
T
h
e
v
o
ltag
e
at
th
e
r
ec
ei
v
i
n
g
e
n
d
b
u
s
t
h
at
is
at
B
u
s
n
u
m
b
er
2
is
g
i
v
en
a
s
(
1
)
T
h
e
Gau
s
s
-
Seid
el
lo
ad
f
lo
w
E
q
u
atio
n
f
o
r
th
e
t
w
o
b
u
s
s
y
s
te
m
ca
n
b
e
w
r
itte
n
as
[
]
(
2
)
W
h
er
e,
V
1
i
s
t
h
e
v
o
ltag
e
at
b
u
s
n
u
m
b
er
1
,
V
2
is
t
h
e
v
o
ltag
e
at
B
u
s
n
u
m
b
er
2
a
n
d
Y
22
is
t
h
e
ad
m
itta
n
ce
o
f
B
u
s
n
u
m
b
er
2
.
E
q
u
atio
n
(
2
)
ca
n
b
e
w
r
itte
n
as
(
3
)
(
4
)
Fro
m
th
e
t
w
o
b
u
s
s
y
s
te
m
o
f
F
i
g
u
r
e
2
cu
r
r
en
t I
,
ca
n
b
e
w
r
itte
n
as,
(
5
)
E
q
u
atin
g
E
q
u
atio
n
(
3
)
an
d
E
q
u
atio
n
(
5
)
it c
an
b
e
w
r
i
tten
t
h
a
t,
(
6
)
T
ak
in
g
r
ea
l p
ar
t f
r
o
m
E
q
u
atio
n
(
6
)
it c
an
b
e
w
r
itte
n
as
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
8
,
No
.
1
,
Feb
r
u
ar
y
2
0
1
8
:
4
3
–
51
46
(
7
)
T
ak
in
g
d
er
iv
ati
v
e
o
f
b
o
th
s
id
es o
f
E
q
u
atio
n
(
7
)
w
ith
r
esp
ec
t
to
V
2
it c
an
b
e
w
r
itte
n
t
h
at,
(
8
)
Af
ter
s
i
m
p
li
f
icatio
n
E
q
u
atio
n
(
8
)
ca
n
b
e
w
r
itte
n
as,
(
9
)
A
t c
r
i
tica
l p
o
in
t o
f
v
o
lta
g
e
s
ta
b
ilit
y
,
So
,
E
q
u
atio
n
(
9
)
it c
an
b
e
w
r
it
ten
as,
So
,
cr
itical
v
o
ltag
e
at
t
h
e
r
ec
ei
v
in
g
e
n
d
o
f
th
e
eq
u
iv
ale
n
t t
w
o
b
u
s
n
et
w
o
r
k
is
w
r
itte
n
as,
(
)
(
1
0
)
Dis
tr
ib
u
tio
n
s
y
s
te
m
s
tab
ili
t
y
in
d
icato
r
(
DSSI)
ca
n
b
e
f
o
r
m
u
lated
b
y
t
h
e
d
if
f
er
en
ce
b
et
w
ee
n
t
h
e
r
ec
eiv
in
g
e
n
d
v
o
lta
g
e
o
f
t
h
e
eq
u
iv
ale
n
t
t
w
o
b
u
s
d
i
s
tr
ib
u
tio
n
s
y
s
t
e
m
at
b
ase
ca
s
e
a
n
d
cr
i
tical
v
o
ltag
e
at
t
h
e
r
ec
eiv
in
g
e
n
d
o
f
th
e
eq
u
i
v
ale
n
t t
w
o
b
u
s
d
is
tr
ib
u
tio
n
s
y
s
te
m
a
n
d
ca
n
b
e
w
r
it
ten
as
,
W
h
er
e,
V
2
is
th
e
r
ec
eiv
in
g
e
n
d
v
o
ltag
e
o
f
t
h
e
t
w
o
b
u
s
eq
u
iv
a
len
t
s
y
s
te
m
a
n
d
V
2cri
is
t
h
e
cr
itical
v
o
ltag
e
at
t
h
e
r
ec
eiv
i
n
g
en
d
o
f
th
e
s
a
m
e
s
y
s
te
m
.
So
,
at
th
e
cr
itical
p
o
in
t
o
f
v
o
ltag
e
s
ta
b
ilit
y
th
e
d
i
f
f
er
e
n
ce
b
et
w
ee
n
t
h
ese
t
w
o
w
ill
b
e
z
er
o
.
T
h
e
v
alu
e
o
f
th
e
p
r
o
p
o
s
ed
in
d
icato
r
w
ill
p
r
o
v
id
e
i
n
f
o
r
m
at
io
n
ab
o
u
t
t
h
e
v
o
ltag
e
s
tab
ilit
y
o
f
t
h
e
s
y
s
te
m
.
T
h
e
h
ig
h
er
v
al
u
e
o
f
DS
SI
in
d
icato
r
m
ea
n
s
t
h
e
s
y
s
te
m
is
les
s
s
ec
u
r
e
in
ter
m
s
o
f
v
o
ltag
e
s
tab
ilit
y
an
d
lo
w
er
v
alu
e
o
f
D
SS
I
i
n
d
icato
r
m
ea
n
s
m
o
r
e
s
ec
u
r
e
is
t
h
e
s
y
s
te
m
in
ter
m
s
o
f
v
o
lta
g
e
s
tab
ilit
y
.
4.
SI
M
UL
AT
I
O
N
A
ND
RE
SU
L
T
S
T
h
e
p
r
o
g
r
am
is
s
i
m
u
lated
in
MA
T
L
A
B
s
o
f
t
w
ar
e
an
d
th
e
d
ev
elo
p
ed
in
d
icato
r
(
DS
SI)
is
i
m
p
le
m
e
n
ted
in
s
ta
n
d
ar
d
I
E
E
E
3
3
b
u
s
r
ad
ial
d
is
tr
ib
u
tio
n
s
y
s
te
m
.
T
h
e
s
y
s
te
m
i
s
co
n
s
is
t
o
f
ac
tiv
e
p
o
wer
lo
ad
o
f
3
7
1
5
k
W
an
d
r
ea
ctiv
e
p
o
w
er
lo
ad
o
f
2
3
0
0
k
VA
.
T
h
e
w
h
o
le
s
y
s
te
m
is
r
ed
u
ce
d
i
n
to
t
w
o
b
u
s
eq
u
i
v
alen
t
n
et
w
o
r
k
.
T
h
e
r
esu
lt
o
f
DS
SI
in
d
icato
r
is
co
m
p
ar
ed
w
it
h
s
ta
n
d
ar
d
VSI
in
d
icato
r
.
T
h
e
s
i
m
u
latio
n
r
es
u
lts
ar
e
d
escr
ib
ed
in
th
e
f
o
llo
w
in
g
s
ec
t
io
n
s
.
4
.
1
.
I
dentif
ica
t
io
n a
nd
Ver
if
ica
t
io
n o
f
C
rit
ica
l
C
o
ntig
ency
C
a
s
es
C
o
n
ti
n
g
en
cie
s
ar
e
th
e
h
a
r
m
f
u
l
s
it
u
atio
n
s
o
n
p
o
w
er
s
y
s
te
m
t
h
at
m
a
y
o
cc
u
r
d
u
r
i
n
g
s
t
ea
d
y
s
tate
co
n
d
itio
n
o
f
p
o
w
er
s
y
s
te
m
.
T
h
e
co
n
ti
n
g
e
n
c
y
co
n
d
itio
n
m
a
y
b
e
o
u
tag
e
o
f
g
e
n
er
ato
r
s
o
r
tr
i
p
p
in
g
th
e
l
in
e
o
f
a
p
o
w
er
s
y
s
te
m
.
T
o
ch
ec
k
th
e
ac
cu
r
ac
y
o
f
th
e
p
r
o
p
o
s
ed
in
d
icato
r
,
DSSI
is
ca
lcu
lated
f
o
r
d
if
f
er
e
n
t
co
n
ti
n
g
e
n
t
co
n
d
itio
n
s
o
f
t
h
e
s
aid
I
E
E
E
3
3
b
u
s
r
ad
ial
d
is
tr
ib
u
tio
n
s
y
s
te
m
.
T
h
e
r
esu
lt
s
ar
e
v
er
i
f
ied
b
y
th
e
s
ta
n
d
ar
d
VSI
in
d
icato
r
.
T
ab
le
1
s
h
o
w
s
t
h
e
r
es
u
lt
s
o
f
th
e
test
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8708
Ga
u
s
s
-
S
eid
el
Meth
o
d
b
a
s
ed
V
o
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g
e
S
ec
u
r
ity
A
n
a
lysi
s
o
f D
is
tr
ib
u
tio
n
S
ystem
(
Ga
g
a
r
i D
e
b
)
47
T
ab
le
1
.
C
o
n
ti
n
g
e
n
c
y
test
r
es
u
lts
at
b
ase
lo
ad
in
g
co
n
d
itio
n
S
y
st
e
m
Co
n
f
i
g
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r
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t
i
o
n
n
u
m
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r
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y
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Fig
u
r
e
3
s
h
o
w
s
th
e
g
r
ap
h
o
f
D
SS
I
in
d
icato
r
an
d
VSI
in
d
icato
r
f
o
r
b
ase
ca
s
e
a
n
d
v
ar
io
u
s
c
o
n
tin
g
e
n
c
y
co
n
d
itio
n
s
at
b
ase
lo
ad
in
g
d
ep
icted
in
T
ab
le
1
.
(
a)
(
b)
Fig
u
r
e
3
.
P
lo
t o
f
(
a)
DSSI
an
d
(
b
)
VSI
in
d
icato
r
f
o
r
d
if
f
er
en
t
co
n
f
i
g
u
r
atio
n
s
at
b
ase
lo
ad
in
g
T
ab
le
1
an
d
Fig
u
r
e
3
clea
r
l
y
s
h
o
w
th
at
m
o
s
t
s
e
v
er
e
co
n
ti
n
g
e
n
c
y
i
s
s
y
s
te
m
co
n
f
i
g
u
r
atio
n
7
i.e
.
tr
ip
p
in
g
o
f
li
n
e
n
u
m
b
er
2
3
b
ec
au
s
e
t
h
e
v
al
u
e
o
f
th
e
DSSI
i
n
d
icato
r
is
h
i
g
h
est
in
th
i
s
ca
s
e.
P
r
o
p
o
s
ed
in
d
icato
r
,
DSSI
g
i
v
es a
cc
u
r
ate
r
esu
lt
w
h
ich
is
v
er
if
ied
b
y
t
h
e
VSI
i
n
d
i
ca
to
r
.
Af
ter
p
er
f
o
r
m
i
n
g
co
n
ti
n
g
en
c
y
test
at
b
ase
lo
ad
th
e
lo
ad
s
o
f
all
th
e
b
u
s
es
h
a
v
e
i
n
cr
ea
s
ed
s
u
cc
es
s
iv
el
y
w
it
h
an
i
n
cr
e
m
e
n
t
o
f
5
%
u
n
til
th
e
lo
ad
f
lo
w
p
r
o
g
r
a
m
f
ail
s
t
o
g
iv
e
s
o
lu
t
io
n
.
Ma
x
i
m
u
m
lo
a
d
in
g
at
w
h
ic
h
lo
ad
f
lo
w
p
r
o
g
r
a
m
r
u
n
s
is
k
n
o
w
n
as
th
e
cr
itical
lo
ad
i
n
g
o
f
th
e
s
y
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te
m
.
A
t
m
a
x
i
m
u
m
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n
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t
is
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er
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ed
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alu
ate
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h
e
ch
a
n
g
e
in
th
e
DSSI
in
d
icato
r
v
al
u
e
o
f
t
h
e
co
n
ce
r
n
ed
p
o
w
er
s
y
s
te
m
.
T
ab
le
2
s
h
o
w
s
t
h
e
r
es
u
lt o
f
co
n
ti
n
g
e
n
c
y
test
at
m
a
x
i
m
u
m
lo
ad
in
g
co
n
d
itio
n
.
T
ab
le
2
.
C
o
n
ti
n
g
e
n
c
y
test
r
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u
lts
at
m
a
x
i
m
u
m
lo
ad
in
g
co
n
d
it
io
n
S
y
st
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m
C
o
n
f
i
g
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r
a
t
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n
u
m
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st
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m C
o
n
f
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o
n
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S
I
V
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I
1
B
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se
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Fig
u
r
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4
s
h
o
w
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th
e
g
r
ap
h
o
f
D
SS
I
in
d
icato
r
an
d
VSI
in
d
icato
r
f
o
r
b
ase
ca
s
e
a
n
d
v
ar
io
u
s
c
o
n
tin
g
e
n
c
y
co
n
d
itio
n
s
at
m
a
x
i
m
u
m
lo
ad
in
g
p
o
in
t
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
8
,
No
.
1
,
Feb
r
u
ar
y
2
0
1
8
:
4
3
–
51
48
(
a)
(
b
)
Fig
u
r
e
4
.
P
lo
t o
f
(
a)
DSSI
an
d
(
b
)
VSI
in
d
icato
r
f
o
r
d
if
f
er
en
t
co
n
f
i
g
u
r
atio
n
s
at
m
a
x
i
m
u
m
lo
ad
in
g
T
ab
le
2
an
d
Fig
u
r
e
4
p
r
o
v
es
th
at
at
m
a
x
i
m
u
m
lo
ad
in
g
co
n
d
itio
n
th
e
w
o
r
s
t
s
i
tu
atio
n
is
s
y
s
te
m
co
n
f
i
g
u
r
atio
n
n
u
m
b
er
7
i.e
.
tr
ip
p
in
g
o
f
li
n
e
n
u
m
b
er
2
3
.
T
h
e
ac
cu
r
ac
y
o
f
th
e
DSSI
in
d
ica
to
r
is
ch
ec
k
ed
w
i
t
h
VSI
in
d
icato
r
.
A
t
b
ase
lo
ad
in
g
,
th
e
e
f
f
ec
ts
o
f
tr
ip
p
in
g
o
f
v
ar
io
u
s
li
n
es
a
f
f
ec
t
th
e
s
tate
o
f
t
h
e
s
y
s
te
m
a
n
d
ac
co
r
d
in
g
l
y
th
e
v
al
u
e
o
f
t
h
e
in
d
icato
r
c
h
a
n
g
e
s
f
r
o
m
b
ase
ca
s
e.
So
,
t
h
e
c
h
an
g
e
in
t
h
e
i
n
d
icato
r
v
a
lu
e
s
w
il
l
g
i
v
e
i
n
d
icatio
n
ab
o
u
t
tr
ip
p
in
g
o
f
lin
e.
W
ith
th
e
ch
a
n
g
e
in
lo
ad
d
e
m
a
n
d
,
th
e
in
d
icato
r
v
al
u
e
c
h
a
n
g
e
s
at
ev
e
r
y
co
n
ti
n
g
en
c
y
.
At
th
e
m
a
x
i
m
u
m
lo
ad
in
g
co
n
d
iti
o
n
t
h
e
v
alu
e
o
f
th
e
i
n
d
icato
r
w
il
l
b
e
d
i
f
f
er
e
n
t
f
r
o
m
t
h
e
i
n
d
i
ca
to
r
v
alu
e
s
at
b
ase
lo
ad
in
g
f
o
r
th
e
s
a
m
e
co
n
ti
n
g
e
n
cies.
Fig
u
r
e
5
d
is
p
la
y
s
th
e
ch
a
n
g
e
o
f
DSSI
i
n
d
icato
r
f
r
o
m
b
ase
lo
ad
in
g
to
m
a
x
i
m
u
m
f
o
r
d
if
f
er
e
n
t
co
n
tin
g
e
n
cies.
Fig
u
r
e
5
.
C
o
m
p
ar
is
o
n
o
f
D
SS
I
v
alu
e
at
b
ase
lo
ad
in
g
a
n
d
at
m
ax
i
m
u
m
lo
ad
in
g
Fig
u
r
e
5
s
h
o
w
s
th
at
at
m
a
x
i
m
u
m
lo
ad
in
g
co
n
d
itio
n
t
h
e
v
al
u
e
w
il
l
b
e
h
ig
h
er
t
h
an
t
h
o
s
e
o
b
tain
ed
at
b
ase
lo
ad
in
g
co
n
d
itio
n
.
4
.
2
.
E
f
f
ec
t
o
f
Co
nting
ency
o
n
B
us
V
o
lt
a
g
es
Vo
ltag
e
m
ag
n
it
u
d
es a
t d
i
f
f
er
e
n
t b
u
s
es is
a
ls
o
ch
a
n
g
es d
u
e
to
co
n
tin
g
e
n
c
y
.
Fi
g
u
r
e
6
co
m
p
ar
es th
e
b
u
s
v
o
ltag
e
s
f
o
r
b
ase
ca
s
e
an
d
f
o
r
tr
ip
p
in
g
o
f
L
i
n
e
n
u
m
b
er
2
3
at
b
ase
lo
ad
in
g
.
F
ig
u
r
e
6
s
h
o
w
s
t
h
at
f
o
r
b
ase
d
ata
an
d
f
o
r
tr
ip
p
in
g
o
f
lin
e
n
u
m
b
er
2
3
th
er
e
is
a
s
m
a
ll
ch
a
n
g
e
i
n
b
u
s
v
o
ltag
e
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8708
Ga
u
s
s
-
S
eid
el
Meth
o
d
b
a
s
ed
V
o
lta
g
e
S
ec
u
r
ity
A
n
a
lysi
s
o
f D
is
tr
ib
u
tio
n
S
ystem
(
Ga
g
a
r
i D
e
b
)
49
A
t
t
h
e
p
o
in
t
o
f
m
a
x
i
m
u
m
lo
ad
in
g
t
h
e
s
y
s
te
m
i
s
m
o
r
e
p
r
o
n
e
to
v
o
ltag
e
in
s
tab
ilit
y
a
n
d
th
e
b
u
s
v
o
ltag
e
s
m
a
y
b
e
less
t
h
a
n
th
e
allo
w
ab
le
li
m
it.
So
,
it
is
es
s
en
tia
l
to
ch
ec
k
t
h
e
b
u
s
v
o
lta
g
es
at
t
h
is
s
tag
e
o
f
p
o
w
er
s
y
s
te
m
.
W
it
h
t
h
e
in
cr
ea
s
e
in
lo
ad
in
g
t
h
e
b
u
s
v
o
ltag
e
s
w
il
l d
ec
r
ea
s
e.
Fig
u
r
e
7
s
h
o
w
s
t
h
e
b
u
s
v
o
lta
g
es
at
m
ax
i
m
u
m
lo
ad
in
g
f
o
r
all
th
e
b
u
s
es
o
f
t
h
e
co
n
ce
r
n
ed
d
i
s
tr
ib
u
tio
n
s
y
s
te
m
f
o
r
b
ase
d
ata
an
d
f
o
r
o
u
tag
e
o
f
li
n
e
n
u
m
b
er
2
3
.
Fig
u
r
e
6
.
C
o
m
p
ar
is
o
n
o
f
o
r
i
g
i
n
al
b
u
s
v
o
lta
g
es a
n
d
b
u
s
v
o
lta
g
es
f
o
r
o
u
tag
e
o
f
li
n
e
n
u
m
b
er
2
3
at
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ase
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ad
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u
r
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.
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o
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p
ar
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o
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a
l b
u
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u
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s
h
o
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ata
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at
m
ax
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m
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m
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ad
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g
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er
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m
all.
5.
CO
NCL
U
SI
O
N
B
y
ap
p
l
y
in
g
t
h
e
p
r
o
p
o
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ed
in
d
icato
r
th
e
cr
itical
co
n
tin
g
e
n
c
y
ca
s
e
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o
f
th
e
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y
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te
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ca
n
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id
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ied
v
er
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s
il
y
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h
ich
i
s
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er
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b
y
t
h
e
s
ta
n
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ar
d
VSI
in
d
i
ca
to
r
.
A
t
m
ax
i
m
u
m
lo
ad
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t
h
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ec
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r
it
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tate
ca
n
b
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u
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ip
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itio
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f
th
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u
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ar
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ate
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ilit
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r
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y
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te
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th
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u
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er
to
p
r
ed
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ct
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n
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g
en
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y
ca
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es.
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,
it
w
ill b
e
p
o
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tectio
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.
RE
F
E
R
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NC
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S
[1
]
S
u
y
a
n
to
,
C.
Ra
h
m
a
d
h
a
n
i,
O.
P
e
n
a
n
g
sa
n
g
a
n
d
A
.
S
o
e
p
rij
a
n
t
o
,
"
P
o
w
e
r
F
lo
w
De
v
e
lo
p
m
e
n
t
Ba
se
d
o
n
th
e
M
o
d
if
ied
Ba
c
k
wa
rd
-
F
o
rw
a
rd
f
o
r
V
o
lt
a
g
e
P
r
o
f
il
e
I
m
p
ro
v
e
m
e
n
t
o
f
Distrib
u
t
io
n
S
y
ste
m
,"
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
Co
m
p
u
ter
E
n
g
i
n
e
e
rin
g
,
v
o
l.
6
,
No
.
5
,
p
p
.
2
0
0
5
-
2
0
1
4
,
2
0
1
6
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2
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8
8
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8708
I
n
t J
E
lec
&
C
o
m
p
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n
g
,
Vo
l.
8
,
No
.
1
,
Feb
r
u
ar
y
2
0
1
8
:
4
3
–
51
50
[2
]
K.
M
istry
a
n
d
R.
Ro
y
,
"
En
h
a
n
c
e
m
e
n
t
o
f
v
o
lt
a
g
e
st
a
b
il
it
y
In
d
e
x
o
f
Distrib
u
ti
o
n
S
y
ste
m
b
y
Ne
t
w
o
rk
Re
c
o
n
f
ig
u
ra
ti
o
n
In
c
lu
d
in
g
S
tatic
L
o
a
d
M
o
d
e
l
a
n
d
Da
il
y
L
o
a
d
Cu
rv
e
,"
in
2
0
1
1
IEE
E
PE
S
I
n
n
o
v
a
ti
v
e
S
ma
rt
Gr
id
T
e
c
h
n
o
l
o
g
ies
-
In
d
i
a
,
2
0
1
1
.
[3
]
P
.
P
a
v
it
h
re
n
,
R.
R.
Ra
m
a
n
,
P
.
N
a
ir
a
n
d
K.Nit
h
iy
a
n
a
n
,
"
V
o
lt
a
g
e
S
tab
il
it
y
A
n
a
l
y
sis
a
n
d
S
tab
il
it
y
I
m
p
ro
v
e
m
e
n
t
o
f
P
o
w
e
r
S
y
ste
m
,"
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
C
o
mp
u
ter
En
g
i
n
e
e
rin
g
,
v
o
l.
5
,
N
o
.
2
,
p
p
.
1
8
9
-
1
9
7
,
2
0
1
5
.
[4
]
T
.
Zab
a
io
u
,
L
.
A
.
De
ss
a
in
t
a
n
d
I.
Ka
m
w
a
,
"
P
re
v
e
n
ti
v
e
Co
n
tro
l
A
p
p
ro
a
c
h
f
o
r
Vo
lt
a
g
e
S
tab
il
it
y
Im
p
r
o
v
e
m
e
n
t
Us
in
g
V
o
l
tag
e
S
tab
il
it
y
Co
n
stra
in
e
d
Op
ti
m
a
l
P
o
w
e
r
F
lo
w
Ba
se
d
o
n
S
tatic
L
in
e
V
o
lt
a
g
e
S
tab
il
it
y
In
d
ice
s
,
"
IET
Ge
n
e
ra
ti
o
n
,
T
ra
n
sm
issio
n
&
Distrib
u
ti
o
n
,
v
o
l.
8
,
Iss
.
5
,
p
p
.
9
2
4
-
9
3
4
,
2
0
1
4
.
[5
]
H.
Kh
o
s
h
k
h
o
o
a
n
d
S
.
M
.
S
h
a
h
rt
a
sh
,
"
F
a
st
On
li
n
e
Dy
n
a
m
i
c
V
o
lt
a
g
e
In
sta
b
il
it
y
P
re
d
icti
o
n
a
n
d
Vo
lt
a
g
e
S
tab
il
it
y
Clas
sif
ic
a
ti
o
n
,
"
IET
Ge
n
e
ra
t
io
n
,
T
ra
n
sm
issio
n
&
Distrib
u
ti
o
n
,
v
o
l.
8
,
Iss
.
5
,
p
p
.
9
5
7
-
9
6
5
,
2
0
1
4
.
[6
]
I.
R.
P
o
r
d
a
n
jan
i,
Y.
W
a
n
g
a
n
d
W
.
X
u
,
"
Id
e
n
t
if
ica
ti
o
n
o
f
Crit
ica
l
Co
m
p
o
n
e
n
ts
f
o
r
Vo
lt
a
g
e
S
tab
il
it
y
A
ss
e
ss
m
e
n
t
Us
in
g
Ch
a
n
n
e
l
Co
m
p
o
n
e
n
ts
T
ra
n
sf
o
rm
,"
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
S
ma
rt
Gr
id
,
v
o
l.
4
,
No
.
2
,
p
p
.
1
1
2
2
-
1
1
3
2
,
Ju
n
e
2
0
1
3
.
[7
]
M
.
A
.
Ak
h
e
r,
"
V
o
lt
a
g
e
S
tab
il
it
y
A
n
a
l
y
si
s
o
f
Un
b
a
lan
c
e
d
Distrib
u
ti
o
n
S
y
ste
m
s
u
sin
g
Ba
c
k
wa
rd
/F
o
rw
a
rd
S
w
e
e
p
L
o
a
d
F
lo
w
A
n
a
l
y
sis
M
e
th
o
d
w
it
h
S
e
c
a
n
t
P
re
d
icto
r
,
"
IET
Ge
n
e
ra
ti
o
n
,
T
r
a
n
sm
issio
n
&
Distrib
u
ti
o
n
,
v
o
l
.
7
,
Iss
.
3
,
p
p
.
3
0
9
-
3
1
7
,
2
0
1
3
.
[8
]
K.
Ka
w
a
b
e
a
n
d
K.
T
a
n
a
k
a
,
"
A
n
a
ly
ti
c
a
l
M
e
th
o
d
f
o
r
S
h
o
rt
-
T
e
rm
V
o
lt
a
g
e
S
tab
il
it
y
Us
in
g
th
e
S
tab
il
it
y
Bo
u
n
d
a
ry
in
th
e
P
-
V
P
la
n
e
,"
IEE
E
T
ra
n
sa
c
ti
o
n
s o
n
P
o
we
r S
y
ste
ms
,
v
o
l.
2
9
,
No
.
6
,
p
p
.
3
0
4
1
-
3
0
4
7
,
2
0
1
4
.
[9
]
S
.
Ko
n
a
r,
D.
Ch
a
tt
e
rjee
a
n
d
S
.
P
a
tra,
"
V
-
Q S
e
n
siti
v
it
y
-
b
a
se
d
In
d
e
x
f
o
r
As
se
ss
m
e
n
t
o
f
D
y
n
a
m
i
c
V
o
lt
a
g
e
S
tab
il
it
y
o
f
P
o
w
e
r
S
y
ste
m
s
,
"
IET
Ge
n
e
ra
ti
o
n
,
T
ra
n
sm
issio
n
&
Distrib
u
ti
o
n
,
v
o
l
.
9
,
Iss
.
7
,
p
p
.
6
7
7
-
6
8
5
,
2
0
1
5
.
[1
0
]
S
.
P
.
L
o
n
d
o
n
o
,
L
.
F
.
Ro
d
rig
u
e
z
a
n
d
G
.
Oliv
a
r,
"
A
S
im
p
li
f
ied
V
o
lt
a
g
e
S
tab
il
it
y
In
d
e
x
(S
V
S
I)
,"
El
e
c
trica
l
Po
we
r
a
n
d
En
e
rg
y
S
y
ste
ms
,
v
o
l.
6
3
,
p
p
.
8
0
6
-
8
1
3
,
2
0
1
4
.
[1
1
]
T
.
A
.
V
.
Ra
m
a
n
d
K.M
.
Ha
n
e
e
s
h
,
"
V
o
lt
a
g
e
S
ta
b
il
it
y
An
a
lys
is
Us
in
g
L
-
in
d
e
x
Un
d
e
r
Va
rio
u
s
T
ra
n
sf
o
rm
e
r
T
a
p
Ch
a
n
g
e
r
S
e
tt
i
n
g
s,
"
i
n
2
0
1
6
I
n
tern
a
ti
o
n
a
l
Co
n
f
e
re
n
c
e
o
n
Circu
it
,
P
o
w
e
r
a
n
d
Co
m
p
u
ti
n
g
T
e
c
h
n
o
l
o
g
ies
(ICCP
CT
)
,
M
a
rc
h
2
0
1
6
.
[1
2
]
M
.
Cu
p
e
ll
i
,
C.
D.
Ca
rd
e
t
a
n
d
A
.
M
o
n
t
i,
"
V
o
lt
a
g
e
S
t
a
b
i
li
ty
In
d
ice
s
Co
mp
a
riso
n
o
n
th
e
IEE
E
-
3
9
B
u
s
S
y
ste
m
u
sin
g
RT
DS
,
"
in
2
0
1
2
I
EE
E
I
n
tern
a
ti
o
n
a
l
Co
n
f
e
re
n
c
e
o
n
P
o
w
e
r
S
y
ste
m
T
e
c
h
n
o
lo
g
y
(P
OW
ERCON)
,
p
p
.
1
-
6
,
N
o
v
e
m
b
e
r,
2
0
1
2
.
[1
3
]
K.
Ch
a
k
ra
b
o
rty
,
A
.
Ch
a
k
ra
b
a
rti
a
n
d
A
.
De
,
"
In
teg
r
a
ted
V
o
lt
a
g
e
S
tab
il
it
y
In
d
ica
to
r
Ba
se
d
As
se
s
s
m
e
n
t
o
f
V
o
lt
a
g
e
S
tab
il
it
y
in
a
P
o
w
e
r
S
y
ste
m
a
n
d
A
p
p
li
c
a
ti
o
n
o
f
A
NN
,"
I
ra
n
ia
n
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
C
o
mp
u
t
e
r
En
g
in
e
e
rin
g
,
v
o
l.
1
0
,
No
.
2
,
p
p
.
8
5
-
9
2
,
2
0
1
1
.
[1
4
]
A
.
De
,
K.
Ch
a
k
ra
b
o
rty
a
n
d
A
.
Ch
a
k
ra
b
a
rti
,
"
Clas
sif
i
c
a
ti
o
n
P
o
w
e
r
S
y
st
e
m
V
o
lt
a
g
e
S
tab
il
i
ty
Co
n
d
it
i
o
n
s
u
si
n
g
Ko
h
o
n
e
n
’s
S
e
lf
o
rg
a
n
isin
g
F
e
a
tu
re
M
a
p
a
n
d
L
e
a
rn
in
g
V
e
c
to
r
Qu
a
n
ti
sa
ti
o
n
,"
Eu
ro
p
e
a
n
T
ra
n
sa
c
ti
o
n
s
o
n
El
e
c
trica
l
Po
we
r
,
v
o
l.
2
2
,
p
p
.
4
1
2
-
4
2
0
,
2
0
1
2
.
[1
5
]
K.
Ch
a
k
ra
b
o
rti
,
A
.
De
a
n
d
A
.
C
h
a
k
ra
b
a
rti
,
"
A
ss
e
ss
m
e
n
t
o
f
V
o
lt
a
g
e
S
e
c
u
rit
y
in
a
M
u
lt
i
-
b
u
s
P
o
w
e
r
S
y
ste
m
Us
in
g
A
rti
f
icia
l
N
e
u
ra
l
Ne
t
w
o
rk
a
n
d
Vo
lt
a
g
e
S
tab
il
it
y
In
d
ica
to
rs
,"
J
o
u
rn
a
l
o
f
El
e
c
trica
l
S
y
ste
ms
,
v
o
l.
6
-
4
,
p
p
.
5
1
7
-
5
2
9
,
2
0
1
0
.
[1
6
]
D.H.A
.
L
e
e
,
"
V
o
lt
a
g
e
S
tab
il
it
y
A
ss
e
s
s
m
e
n
t
Us
in
g
Eq
u
iv
a
len
t
No
d
a
l
A
n
a
l
y
sis
,"
IEE
E
T
ra
n
sa
c
t
io
n
s
o
n
Po
we
r
S
y
ste
ms
,
v
o
l.
3
1
,
N
o
.
1
,
p
p
.
4
5
4
-
4
6
3
,
Ja
n
u
a
ry
2
0
1
6
.
[1
7
]
C.
M
.
S
e
lv
i
a
n
d
K.G
n
a
n
a
m
b
a
l,
"
Po
we
r
S
y
ste
m
Vo
lt
a
g
e
S
ta
b
il
it
y
A
n
a
l
y
sis u
sin
g
M
o
d
if
ied
Diff
e
re
n
ti
a
l
Evo
lu
ti
o
n
,
"
in
In
tern
a
ti
o
n
a
l
C
o
n
f
e
re
n
c
e
o
n
Co
m
p
u
ter,
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o
m
m
u
n
ica
ti
o
n
a
n
d
E
lec
tri
c
a
l
T
e
c
h
n
o
l
o
g
y
-
ICCCE
T
2
0
1
1
,
M
a
rc
h
,
2
0
1
1
.
[1
8
]
Y.
W
a
n
g
,
I.
R.
P
o
r
d
a
n
ja
n
i,
W
.
L
i,
W
.
X
u
,
T
.
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e
n
,
E.
V
a
a
h
e
d
i
a
n
d
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.
G
u
rn
e
y
,
"
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o
lt
a
g
e
S
tab
il
i
ty
M
o
n
it
o
ri
n
g
Ba
se
d
o
n
th
e
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n
c
e
p
t
o
f
Co
u
p
led
S
in
g
le
-
P
o
rt
Circu
it
,"
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Po
we
r
S
y
ste
ms
,
v
o
l.
2
6
,
No
.
4
,
p
p
.
2
1
5
4
-
2
1
6
3
,
N
o
v
e
m
b
e
r
2
0
1
1
.
[1
9
]
S
.
Ch
it
ra
a
n
d
N.
De
v
a
ra
jan
,
"
Cir
c
u
it
T
h
e
o
ry
A
p
p
ro
a
c
h
f
o
r
V
o
lt
a
g
e
S
tab
il
it
y
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se
ss
m
e
n
t
o
f
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c
o
n
f
ig
u
re
d
P
o
w
e
r
Ne
tw
o
rk
,"
IET
Circ
u
it
s,
De
v
ice
s a
n
d
S
y
ste
ms
,
v
o
l.
8
,
Iss
.
6
,
p
p
.
4
3
5
-
4
4
1
,
2
0
1
4
.
[2
0
]
G
.
A
.
M
a
h
m
o
u
d
,
"
Vo
lt
a
g
e
S
tab
il
it
y
A
n
a
l
y
sis
o
f
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d
ial
Distrib
u
t
io
n
Ne
tw
o
rk
s
u
sin
g
Ca
tas
tro
p
h
e
T
h
e
o
ry
,
"
IET
Ge
n
e
ra
ti
o
n
,
T
ra
n
sm
issio
n
&
Distrib
u
ti
o
n
,
v
o
l.
6
,
Iss
.
7
,
p
p
.
6
1
2
-
6
1
8
,
2
0
1
2
.
[2
1
]
L
.
Ku
ru
,
A
.
Oz
tu
rk
,
E.
Ku
ru
a
n
d
O.
Ka
n
d
a
ra
,
"
De
ter
m
in
a
ti
o
n
o
f
V
o
l
tag
e
S
tab
il
it
y
Bo
u
n
d
a
ry
V
a
lu
e
s
in
El
e
c
tri
c
a
l
P
o
w
e
r
S
y
st
e
m
s
b
y
u
sin
g
th
e
C
h
a
o
ti
c
P
a
rti
c
le
S
w
a
r
m
Op
ti
m
iza
ti
o
n
A
lg
o
rit
h
m
,"
El
e
c
trica
l
Po
we
r
a
n
d
En
e
rg
y
sy
ste
ms
,
v
o
l.
6
4
,
p
p
.
8
7
3
-
8
7
9
,
2
0
1
5
.
[2
2
]
M
.
V.
S
u
g
a
n
y
a
d
e
v
i
a
n
d
C.
K.
Ba
b
u
lal,
"
S
u
p
p
o
rt
V
e
c
to
r
Re
g
re
ss
io
n
M
o
d
e
l
f
o
r
th
e
P
re
d
ictio
n
o
f
L
o
d
a
b
il
it
y
M
a
rg
in
o
f
a
P
o
w
e
r
S
y
ste
m
,"
Ap
p
li
e
d
S
o
f
t
Co
mp
u
ti
n
g
,
v
o
l.
2
4
,
p
p
.
3
0
4
-
3
1
5
,
2
0
1
4
.
[2
3
]
C.
Zh
e
n
g
,
V
.
M
a
lb
a
sa
a
n
d
M
.
Ke
z
u
n
o
v
ic,
"
Re
g
r
e
ss
io
n
T
re
e
f
o
r
S
tab
il
it
y
M
a
rg
in
P
re
d
ictio
n
u
sin
g
S
y
n
c
h
ro
p
h
a
so
r
M
e
a
su
re
m
e
n
ts
,"
IEE
E
T
ra
n
sa
c
ti
o
n
s o
n
Po
we
r
S
y
ste
ms
,
v
o
l.
2
8
,
N
o
.
2
,
p
p
.
1
9
7
8
-
1
9
8
7
,
M
a
y
2
0
1
3
.
[2
4
]
J.H.
L
iu
a
n
d
C.
C.
C
h
u
,
"
W
id
e
-
A
re
a
M
e
a
su
re
m
e
n
t
–
Ba
se
d
V
o
lt
a
g
e
S
tab
il
it
y
In
d
ica
to
rs
b
y
M
o
d
if
ied
Co
u
p
le
d
S
in
g
le
-
P
o
r
t
M
o
d
e
ls
,"
IEE
E
T
ra
n
s
a
c
ti
o
n
s o
n
P
o
we
r S
y
ste
ms
,
v
o
l.
2
9
,
No
.
2
,
p
p
.
7
5
6
-
7
6
4
,
M
a
rc
h
2
0
1
4
.
[2
5
]
S
.
M
.
S
.
Hu
ss
a
in
a
n
d
N.
V
isa
li
,
"
Id
e
n
ti
f
ica
ti
o
n
o
f
Wea
k
Bu
se
s
u
sin
g
V
o
lt
a
g
e
S
tab
il
it
y
In
d
ica
to
r
a
n
d
it
s
V
o
lt
a
g
e
P
r
o
f
il
e
I
m
p
ro
v
e
m
e
n
t
b
y
u
sin
g
DST
AT
COM
in
Ra
d
ial
Distrib
u
ti
o
n
S
y
ste
m
s
,"
IOS
R
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
El
e
c
tro
n
ics
En
g
in
e
e
rin
g
(
IOS
RJE
EE
)
,
v
o
l.
2
,
Iss
u
e
4
,
p
p
.
1
7
-
23
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8708
Ga
u
s
s
-
S
eid
el
Meth
o
d
b
a
s
ed
V
o
lta
g
e
S
ec
u
r
ity
A
n
a
lysi
s
o
f D
is
tr
ib
u
tio
n
S
ystem
(
Ga
g
a
r
i D
e
b
)
51
B
I
O
G
RAP
H
I
E
S
O
F
AUTH
O
RS
G
a
g
a
r
i
D
e
b
w
a
s
b
o
rn
in
T
rip
u
ra
o
n
F
e
b
ru
a
ry
2
4
,
1
9
8
2
.
S
h
e
h
a
s
c
o
m
p
lete
d
h
e
r
B.
E
in
El
e
c
tri
c
a
l
En
g
in
e
e
rin
g
f
ro
m
T
rip
u
ra
En
g
in
e
e
rin
g
Co
ll
e
g
e
(n
o
w
NI
T
,
A
g
a
rtal
a
)
in
2
0
0
4
.
S
h
e
h
a
s
c
o
m
p
lete
d
h
e
r
M
.
T
e
c
h
in
E
lec
tri
c
a
l
En
g
in
e
e
rin
g
f
ro
m
T
rip
u
ra
Un
iv
e
rsity
(
A
Ce
n
tral
Un
iv
e
rsity
)
in
th
e
y
e
a
r
2
0
0
8
.
S
h
e
is
p
re
se
n
tl
y
w
o
rk
in
g
a
s
a
n
A
ss
istan
t
P
r
o
f
e
ss
o
r
in
De
p
a
rtme
n
t
o
f
El
e
c
tri
c
a
l
En
g
in
e
e
rin
g
in
T
rip
u
ra
Un
iv
e
rsity
(
A
Ce
n
tral
Un
iv
e
rsit
y
).
He
r
re
s
e
a
rc
h
a
re
a
is
P
o
w
e
r
S
y
ste
m
.
S
h
e
is
c
u
rre
n
tl
y
p
u
rsu
i
n
g
P
h
.
D
d
e
g
re
e
f
ro
m
N
a
ti
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n
a
l
In
stit
u
te
o
f
T
e
c
h
n
o
l
o
g
y
,
Ag
a
rt
a
la,
T
rip
u
ra
,
In
d
ia.
K
a
b
ir
C
h
a
k
r
a
b
o
r
ty
w
a
s
b
o
rn
in
Dh
a
rm
a
n
a
g
a
r
,
T
rip
u
ra
,
In
d
ia,
o
n
A
u
g
u
st
5
,
1
9
7
8
.
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is
A
s
sista
n
t
P
r
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f
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in
th
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d
e
p
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rtm
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o
f
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tri
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a
l
En
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g
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t
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rip
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ra
In
stit
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o
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c
h
n
o
lo
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y
,
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rsin
g
a
rh
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T
rip
u
ra
,
In
d
ia.
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h
o
l
d
s
a
B.
S
c
.
P
h
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sic
s
(Ho
n
s.)
f
ro
m
A
s
sa
m
Un
iv
e
rsit
y
,
a
n
d
B.
Tec
h
a
n
d
M
.
Tec
h
in
El
e
c
tri
c
a
l
En
g
in
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rin
g
f
ro
m
th
e
Un
iv
e
rsit
y
o
f
Ca
lcu
tt
a
.
He
c
o
m
p
lete
d
h
is
P
h
D
in
2
0
1
3
f
ro
m
In
d
ian
In
stit
u
te
o
f
En
g
in
e
e
rin
g
S
c
ien
c
e
a
n
d
T
e
c
h
n
o
lo
g
y
(IIE
S
T
),
S
h
ib
p
u
r,
(F
o
rm
e
rl
y
B
e
n
g
a
l
En
g
in
e
e
rin
g
a
n
d
S
c
ien
c
e
Un
iv
e
rsit
y
,
S
h
ib
p
u
r
,
)
W
e
st
Be
n
g
a
l,
In
d
ia.
He
h
a
s
1
2
y
e
a
r
s
o
f
tea
c
h
in
g
a
n
d
6
y
e
a
rs
o
f
r
e
se
a
r
c
h
e
x
p
e
rien
c
e
.
He
h
a
s
p
u
b
li
sh
e
d
se
v
e
r
a
l
p
a
p
e
rs i
n
i
n
tern
a
ti
o
n
a
l
a
n
d
n
a
ti
o
n
a
l
jo
u
rn
a
ls
a
n
d
c
o
n
f
e
re
n
c
e
p
ro
c
e
e
d
in
g
s an
d
a
b
o
o
k
.
Evaluation Warning : The document was created with Spire.PDF for Python.