Ind
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g
in
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ing
and
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mp
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S
c
ienc
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V
ol
. 8
,
No.
3
,
Dec
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be
r
20
17
, p
p
.
7
7
0
~
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7
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DO
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11
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Rec
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20
17
Fau
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mp
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and
Matchi
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A
p
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L
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w
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. M
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khlis
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. K. Ra
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Copy
righ
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©
2
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1
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I
ns
titu
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Adv
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Eng
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a
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Sc
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nc
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re
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d.
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au
l
t
l
oc
ati
o
n
m
eth
od
w
as
us
ed
k
no
w
l
ed
ge
ba
s
ed
m
eth
od
.
K
no
wl
e
dg
e
B
as
ed
i
s
a
m
eth
od
ba
s
ed
on
k
no
w
l
e
dg
e,
s
uc
h
as
ge
n
eti
c
a
l
g
orit
hm
,
arti
f
i
c
i
al
n
e
ura
l
ne
t
wor
k
,
m
atc
hi
ng
ap
proac
h,
l
i
n
i
er
m
od
el
[1
3
-
1
4
],
etc
.
Ma
n
y
di
s
c
us
s
i
on
of
k
no
w
l
e
dg
e
b
as
ed
m
eth
od
w
h
i
c
h
m
en
ti
on
a
bo
ut
th
e
ac
c
urate
r
es
u
l
t
ob
ta
i
n
e
d.
B
as
ed
th
e
ad
v
an
t
ag
e
of
up
on
di
s
c
us
s
i
on
of
the
t
y
p
es
of
f
au
l
t
l
oc
ati
o
n
m
eth
od
s
,
th
i
s
pa
p
er
wi
l
l
d
i
s
c
us
s
ab
ou
t
f
au
l
t
l
oc
ati
on
m
eth
o
d
ba
s
ed
on
i
m
pe
da
nc
e
a
nd
m
atc
hi
ng
ap
proac
h
es
.
A
do
pte
d
f
r
om
i
m
pe
da
nc
e
ba
s
e
d
i
n
p
ap
e
r
[2]
an
d
m
atc
hi
ng
a
pp
r
oa
c
he
s
[13
-
14
],
t
he
ac
c
urac
y
of
bo
th
f
au
l
t
l
oc
at
i
on
m
eth
od
w
i
l
l
tes
te
d
b
y
us
i
ng
no
n
h
om
og
en
eo
u
s
di
s
tr
i
b
uti
on
n
et
wor
k
.
Co
m
pa
r
i
s
on
r
es
ul
t
f
r
o
m
bo
th
m
eth
od
wi
l
l
ob
s
erv
e
t
o
s
ho
w
s
th
e
a
dv
an
t
ag
e
a
nd
di
s
ad
v
a
na
t
ag
e
of
ea
c
h
m
eth
od
.
V
ol
tag
e s
ag
a
nd
c
urr
e
nt
s
wel
l
a
l
s
o
di
s
c
us
s
ed
i
n
th
i
s
pa
pe
r
d
ue
to
i
m
pe
da
nc
e
ba
s
e
d m
eth
od
an
d
m
atc
hi
ng
ap
pro
ac
he
s
was
ut
i
l
i
z
i
ng
v
o
l
tag
e s
ag
an
d c
u
r
r
en
t s
wel
l
p
att
ern
.
2.
V
o
lt
ag
e S
ag and
Cu
r
r
e
n
t
M
agn
it
u
d
e P
att
er
n
In
o
r
de
r
to
j
us
ti
f
y
the
us
e
of
v
ol
t
ag
e
an
d
c
urr
en
t
m
ag
ni
tud
e
i
n
l
oc
ati
ng
f
au
l
ts
,
s
tud
i
es
on
the
v
o
l
ta
ge
s
ag
m
ag
ni
tu
de
an
d
c
urr
en
t
v
ari
ati
on
f
or
di
ff
erent
l
oc
ati
on
s
w
as
c
on
d
uc
ted
.
F
or
thi
s
pu
r
po
s
e,
f
au
l
ts
are
c
r
ea
te
d
at
di
f
f
erent
no
de
s
.
T
he
pa
tte
r
n
of
v
ol
ta
ge
s
ag
a
n
d
c
urr
en
t
s
w
e
l
l
m
ag
ni
tud
e
du
e
to
T
hree
P
h
as
e t
o Gr
ou
nd
f
au
l
t a
t
no
de
3
are s
h
o
w
n
i
n F
i
gu
r
e
1
an
d Fi
g
ure 2.
(
a)
V
ol
tag
e S
ag
Ma
g
ni
t
ud
e
at
No
de
3
(
b)
V
ol
t
ag
e S
ag
Ma
g
ni
t
ud
e
at
No
de
4
(
c
)
V
ol
tag
e
S
ag
Ma
gn
i
tud
e
at
No
de
9
(
d)
V
ol
t
ag
e S
ag
Ma
g
ni
t
ud
e
at
No
de
11
F
i
g
ure
1.
V
ol
tag
e S
ag
Ma
g
ni
tu
de
P
att
ern a
t Di
f
f
erent
Node
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N:
25
02
-
4
75
2
IJE
E
CS
V
ol
.
8
,
N
o.
3
,
Dec
em
be
r
2017
:
7
7
0
–
7
7
8
772
(
a)
Cur
r
en
t S
we
l
l
Ma
g
ni
t
ud
e
at
No
de
3
(
b
)
Curr
en
t
S
w
e
l
l
Ma
g
ni
tud
e a
t N
od
e
4
(
c
)
Curr
en
t S
wel
l
Ma
gn
i
tu
d
e a
t N
od
e
9
(
d
)
Curr
en
t
S
w
e
l
l
Ma
g
ni
tud
e a
t N
od
e
11
F
i
g
ure
2.
C
urr
en
t
S
w
e
l
l
Ma
gn
i
t
ud
e
P
att
ern
at
D
i
f
f
erent No
de
F
r
o
m
F
i
gu
r
e
1
(a
-
d)
,
i
t
c
an
be
s
ee
n
t
ha
t
th
e
v
ol
t
ag
e
s
ag
m
ag
ni
tud
e
de
c
r
ea
s
es
a
s
the
f
au
l
t
di
s
ta
nc
e
i
s
c
l
os
er
to
t
he
m
on
i
tori
n
g
no
de
.
V
ol
ta
ge
at
n
od
e
3
i
s
de
e
pe
s
t
s
ag
f
ol
l
o
wed
b
y
v
o
l
tag
e
s
ag
at
no
de
4,
no
d
e
9
an
d
n
od
e
11
.
F
or
the
c
urr
en
t
s
w
el
l
i
s
pres
en
t
ed
i
n
F
i
gu
r
e
2.
T
he
m
ag
ni
tud
e
i
nc
r
ea
s
es
,
as
t
he
f
au
l
t
di
s
ta
nc
e
i
s
c
l
os
er
to
the
m
on
i
t
orin
g
no
de
.
W
h
en
the
f
au
l
t
oc
c
ur
i
n
no
de
3,
t
he
c
urr
en
t
s
w
e
l
l
m
ag
ni
t
ud
e
ha
v
e
th
e
hi
g
he
s
t
v
al
ue
d
ue
to
no
d
e
3
i
s
the
c
l
os
es
t
no
de
.
Mo
r
e
d
i
s
tan
c
e
f
r
om
the
m
ea
s
ure
m
en
t
no
de
wi
l
l
r
ed
uc
e
c
urr
en
t
s
w
e
l
l
m
ag
ni
tud
e.
I
n
ge
ne
r
al
, t
he
LL
LG
F
ha
s
th
e
s
i
m
i
l
ar v
a
l
ue
of
v
o
l
tag
e s
a
g a
n
d c
urr
en
t s
w
e
l
l
f
or al
l
p
ha
s
es
.
3
.
M
atch
ing
A
p
p
r
o
a
ches
T
ec
h
n
iqu
e
In
order
to
a
na
l
y
s
e
t
he
f
au
l
t
di
s
t
an
c
e
b
y
us
i
n
g
m
atc
hi
ng
ap
proac
he
s
,
t
hi
s
pa
pe
r
w
as
ad
op
ted
pa
pe
r
[1
3
-
1
4
]
.
T
o
ex
p
l
ai
n
t
he
ba
s
i
c
c
on
c
ep
t
of
m
atc
hi
ng
ap
pr
oa
c
h
es
,
f
i
gu
r
e
3
i
s
r
ep
r
es
en
t
th
e
m
eth
od
.
T
he
f
au
l
t
di
s
tan
c
e
i
s
de
term
i
ne
d
b
y
as
s
um
i
ng
tha
t
the
l
en
gth
of
a
f
au
l
t
y
s
ec
ti
on
p
-
q
(
an
y
t
wo
ad
j
ac
en
t
n
od
es
of
a
s
ec
ti
on
)
c
or
r
es
po
nd
s
to
the
di
s
t
an
c
e
b
et
w
ee
n
p
oi
n
t
p
and
q
of
th
e
v
o
l
ta
ge
s
a
gs
d
ata
,
as
s
ho
w
n
i
n F
i
g
ure 3.
Evaluation Warning : The document was created with Spire.PDF for Python.
IJE
E
CS
IS
S
N:
2
50
2
-
4
75
2
F
au
l
t
Di
s
ta
nc
e I
d
en
t
i
fi
c
a
ti
o
n Us
i
n
g I
m
pe
d
an
c
e
an
d
Ma
tc
hi
ng
…
(
L
i
l
i
k
J
am
i
l
at
ul
A
w
al
i
n
)
773
F
i
gu
r
e.
3.
B
as
i
c
c
o
nc
ep
t
of
th
e f
au
l
t d
i
s
tan
c
e c
a
l
c
ul
ati
o
n
F
r
o
m
F
i
gu
r
e
3,
the
di
s
tan
c
e
be
t
w
e
en
2
no
d
es
i
s
as
s
um
ed
as
l
i
ni
er
m
od
el
of
the
s
tr
ai
gh
t
l
i
n
e.
T
he
f
au
l
t
di
s
t
an
c
e
i
s
es
ti
m
ate
d
b
y
th
e
f
au
l
t
di
s
ta
nc
e
d
F
f
r
o
m
no
de
p
.
T
he
di
s
tan
c
e
(
d
F
)
c
an
be
c
al
c
ul
a
ted
ba
s
ed
on
th
e
c
o
s
i
ne
r
u
l
e
as
f
ol
l
o
w
s
.
B
d
A
l
d
2
k
2
pq
F
/
l
e
n
g
t
h
R
e
a
l
d
F
F
d
where:
C
B
2
A
C
B
c
o
s
θ
2
2
2
1
-
BC
/
2
(
db
a
s
e
)
(
m
e
a
s
)
2
(
m
e
a
s
)
(
db
a
s
e
)
p
F
F
p
V
V
A
2
(
d
b
ase)
(
d
b
ase)
2
(
d
b
ase)
(
d
b
ase)
p
q
q
p
V
V
B
2
(
m
e
a
s
)
(
dba
s
e
)
2
(
dba
s
e
)
(
m
e
a
s
)
F
q
q
F
V
V
C
l
pq
i
s
t
he
l
en
gth
of
c
ab
l
e
/l
i
ne
f
or s
ec
ti
on
p
-
q
i
n k
m
4
.
Imp
edan
ce
B
as
ed M
eth
o
d
P
ap
er [
2
]
was
c
ho
s
en
to
r
e
pres
en
t o
ne
of
i
m
pe
da
nc
e f
au
l
t
l
oc
a
ti
o
n m
eth
od
d
ue
t
o
m
os
t
ea
r
l
y
i
m
pe
da
nc
e
f
au
l
t
l
oc
at
i
on
m
eth
od
was
propo
s
ed
i
n t
h
i
s
pa
p
er.
a
p
p
X
a
p
p
R
s
e
l
e
c
t
I
s
e
l
e
c
t
V
a
p
p
Z
s2
I
j
s1
I
0
I
k
a
I
s
e
l
e
c
t
I
2
s2
I
2
s1
I
2
sm
I
where:
1
Z
1
Z
-
0
Z
k
B
y
s
e
pa
r
at
i
ng
i
t
i
nto
r
e
al
an
d
i
m
ag
i
n
ar
y
pa
r
ts
of
E
q
ua
ti
on
7
an
d
9
,
ea
c
h
c
om
po
ne
nt
i
n
tha
t
eq
ua
ti
o
n c
a
n
be
s
u
bm
i
tte
d i
n t
he
eq
ua
t
i
on
11
. T
he
f
au
l
t
di
s
ta
nc
e i
s
ex
pr
es
s
ed
as
:
)
(
L
1
X
-
M
1
R
L
app
X
-
M
app
R
D
F
P
h
a
s
e
s
h
i
f
t
,
φ
(
r
a
d
i
a
n
)
V
o
l
t
a
g
e
s
a
g
m
a
g
n
i
t
u
d
e
,
V
(
p
.
u
)
A
B
C
BC
d
k
d
F
p
q
V
q
(
d
b
a
s
e
)
(d
b
a
se)
q
φ
V
p
(
d
b
a
s
e
)
(d
b
a
se)
p
φ
V
F
(
d
b
a
s
e
)
(d
b
a
se)
F
φ
(
1)
(
2)
(
3)
(
4)
(
5
)
(
6
)
(
7)
(
8)
(
9)
(
10
)
(
11
)
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N:
25
02
-
4
75
2
IJE
E
CS
V
ol
.
8
,
N
o.
3
,
Dec
em
be
r
2017
:
7
7
0
–
7
7
8
774
where:
)
(
2
sm
I
s2
I
q
I
-
s1
I
d
I
L
)
(
2
sm
I
s1
I
q
I
-
s2
I
d
I
-
M
Va
Vc
V
s
e
l
e
c
t
(
14
)
Ia
Ic
I
s
e
l
e
c
t
(
1
5)
Ia
Ic
I
c
o
m
p
(
16
)
T
he
f
au
l
t d
i
s
tan
c
e
i
n
ea
c
h
b
us
w
as
de
term
i
ne
d
ba
s
e
d
o
n t
h
e c
a
l
c
ul
ati
on
of
th
e
v
ol
t
ag
e
an
d
c
urr
en
t
us
i
n
g
th
e
up
d
ate
d
v
o
l
ta
ge
a
nd
c
urr
en
t
b
y
us
i
ng
s
tat
i
c
i
m
pe
da
nc
e
l
oa
d
m
od
el
,
as
ad
op
ted
f
r
om
pa
pe
r
[
2
].
5
.
T
es
t
ed Net
w
o
r
k
In
order
to
a
na
l
y
z
e
th
e
i
m
pe
da
nc
e
ba
s
e
d
an
d
k
no
w
l
ed
g
e
ba
s
ed
m
eth
od
pe
r
f
or
m
an
c
es
,
a
r
ea
l
di
s
tr
i
bu
ti
on
ne
t
wor
k
,
as
s
ho
w
n
i
n
F
i
gu
r
e
4,
wh
i
c
h
b
el
on
gs
to
a
M
al
a
y
s
i
a
n
po
w
er
ut
i
l
i
t
y
c
om
pa
n
y
T
NB
,
i
s
us
e
d.
T
hi
s
ne
t
w
ork
i
s
c
on
ne
c
ted
t
o
the
grid
v
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3
1
w
hi
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om
pl
ex
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w
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pa
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c
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pe
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m
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i
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c
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ac
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urac
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n
m
atc
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ap
pro
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h.
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o
w
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v
er,
t
he
m
atc
hi
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ap
proac
h
s
ti
l
l
s
ho
w
s
the
r
ea
s
on
a
bl
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ac
c
urac
y
.
6
. Con
clus
ion
T
hi
s
pa
pe
r
ha
s
di
s
c
us
s
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c
om
pa
r
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s
on
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of
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m
pe
da
nc
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ba
s
ed
m
eth
od
an
d
m
atc
hi
ng
ap
proac
h
.
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ho
m
og
en
eo
us
di
s
tr
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b
uti
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w
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w
as
ad
op
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d
as
a
tes
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ne
t
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ol
tag
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s
ag
a
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c
urr
e
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s
wel
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p
att
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w
as
us
ed
to
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a
l
y
z
e
th
e
f
au
l
t
d
i
s
tan
c
e.
B
as
e
d
on
t
he
ob
ta
i
ne
d
r
es
ul
t,
i
t
c
an
b
e
c
on
c
l
ud
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t
ha
t
m
os
t
of
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m
pe
da
nc
e
ba
s
ed
m
eth
o
d
s
ho
w
s
m
ore
ac
c
urate
r
es
ul
t
c
om
pa
r
e
wi
th
m
atc
hi
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ap
proac
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Ho
w
e
v
er,
the
ac
c
urac
y
o
n
s
ec
ti
on
24
-
26
s
ho
w
s
tha
t
m
atc
hi
ng
ap
pr
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c
h
tec
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i
q
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ob
tai
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the
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tte
r
r
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ul
t
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om
pa
r
e
wi
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h
i
m
pe
da
nc
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s
ed
m
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.
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i
s
p
os
s
i
b
l
e
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to
s
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t
i
on
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2
6
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s
the
s
h
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t
s
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ti
on
i
n
the
l
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d
i
s
ta
nc
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f
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the
m
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s
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m
en
t
no
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e.
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o,
i
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wi
l
l
c
on
tr
i
b
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th
e
un
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qu
e
p
att
ern
of
v
ol
tag
e
s
ag
an
d
c
urr
en
t
s
w
e
l
l
whi
c
h
i
m
pa
c
t
to
the
be
tte
r
ac
c
urac
y
f
or
m
atc
hi
ng
ap
proac
he
s
.
Ho
we
v
er,
f
or
i
m
pe
d
an
c
e
ba
s
ed
m
eth
od
w
i
l
l
c
on
tr
i
bu
te
to
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m
pe
da
nc
e
l
i
ne
v
al
u
es
w
h
i
c
h
ef
f
ec
t
to
the
ac
c
urac
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of
f
au
l
t
di
s
tan
c
e
c
a
l
c
ul
ati
on
.
In
g
en
eral
,
th
e
be
tt
er
ac
c
urac
y
f
a
ul
t
d
i
s
tan
c
e
w
as
ge
ne
r
at
ed
b
y
i
m
pe
da
nc
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ba
s
ed
m
eth
od
c
om
pa
r
e
w
i
t
h
m
atc
hi
ng
ap
proac
h
es
.
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o
w
e
v
er,
m
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c
hi
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ap
pr
oa
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he
s
s
ti
l
l
s
h
o
w
s
the
r
ea
s
o
na
bl
e
ac
c
urac
y
.
Refe
ren
c
e
s
[1
]
Fo
rc
e
,
U.
-
C.
P.
S.
O
.
T
.,
A
b
r
a
h
a
m
,
S.,
e
t
a
l
.
Fi
n
a
l
R
e
p
o
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o
n
th
e
Au
g
u
s
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1
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2
0
0
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a
c
k
o
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Uni
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ta
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n
d
Can
a
d
a
:
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u
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n
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Rec
o
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d
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ti
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s
:
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-
Can
a
d
a
P
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O
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ta
g
e
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s
k
Fo
rc
e
.
2
0
0
4
.
[2
]
A.
A.
G
i
rg
i
s
,
C.
M
.
Fa
l
l
o
n
,
a
n
d
D.
L
.
L
u
b
k
e
m
a
n
.
A
fa
u
l
t
l
o
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ti
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te
c
h
n
i
q
u
e
fo
r
ru
ra
l
d
i
s
tri
b
u
ti
o
n
fe
e
d
e
r
s
.
IEEE
Tra
n
s
.
In
d
.
Ap
p
l
.
1993
;
29
(
6
)
Nov
. /
De
c
:
1
1
7
0
–
1175
.
[3
]
J
u
n
Z
h
u
,
D.L
.
L
u
b
k
e
m
a
n
,
A.
A
G
i
rg
i
s
.
A
u
to
m
a
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fa
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t
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o
n
fe
e
d
e
rs
.
Po
wer
De
l
i
v
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r
y
,
IEEE
Tr
a
n
s
a
c
t
i
o
n
s
o
n
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;
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)
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;
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0
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-
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.
[4
]
M
.
M
.
Sa
h
a
,
J
.
Iz
y
k
o
w
s
k
i
,
E
.
Ros
o
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o
w
s
k
i
,
B.
Ka
s
z
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.
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n
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w
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c
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u
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d
l
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.
Po
wer
Del
i
v
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ry
,
IEEE
Tra
n
s
a
c
t
i
o
n
s
o
n
.
1
9
9
9
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3
)
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9
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[5
]
Se
u
n
g
-
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m
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.
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Tra
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s
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)
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D.
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Res
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Bre
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a
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o
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Po
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e
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s
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2
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.G.
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,
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.
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.R.S.
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Tra
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s
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m
s
.
Po
wer
Del
i
v
e
r
y
,
IEEE
Tra
n
s
a
c
ti
o
n
s
o
n
.
2004
;
1
(1
)
J
a
n
:,
35
-
41.
[1
0
]
J
.
Hora
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.
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