I
nte
rna
t
io
na
l J
o
urna
l o
f
Adv
a
nces in Applie
d Science
s
(
I
J
AAS)
Vo
l.
9
,
No
.
3
,
Sep
tem
b
er
2
0
2
0
,
p
p
.
171
~
179
I
SS
N:
2
2
5
2
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8
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1
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: 1
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.
1
1
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9
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aa
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v
9
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.
p
p
1
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-
179
171
J
o
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e
:
h
ttp
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//ij
a
a
s
.
ia
esco
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co
m
Fault
a
na
ly
sis
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po
w
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m
usi
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m
s
co
m
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desig
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Dest
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J
o
s
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2
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De
p
a
rtme
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t
of
El
e
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tri
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a
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En
g
in
e
e
rin
g
,
Un
iv
e
rsity
of
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g
e
ria,
Nig
e
ria
2
De
p
a
rtme
n
t
of
P
e
tr
o
leu
m
En
g
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e
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rin
g
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Un
iv
e
rsity
of
U
y
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e
ria
Art
icle
I
nfo
AB
ST
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
Dec
6
,
201
9
R
ev
i
s
ed
Ma
r
4
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2
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A
cc
ep
ted
A
p
r
25
,
2
0
2
0
T
h
is
w
o
rk
p
re
s
e
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ts
a
fa
u
lt
a
n
a
ly
sis
si
m
u
latio
n
m
o
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e
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of
an
IEE
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30
b
u
s
s
y
ste
m
in
a
d
istri
b
u
t
io
n
n
e
tw
o
rk
.
T
h
is
w
o
rk
an
a
l
y
se
d
th
e
e
ff
e
c
t
of
f
a
u
lt
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t
a
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d
f
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u
lt
v
o
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a
g
e
in
a
d
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ti
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sy
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m
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c
ircu
it
b
re
a
k
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r
w
a
s
in
tro
d
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c
e
d
in
t
o
th
e
sy
ste
m
to
n
e
u
tralize
th
e
e
f
f
e
c
t
of
th
e
f
a
u
lt
.
Th
e
sy
ste
m
w
a
s
ru
n
on
a
P
S
CA
D
so
f
t
wa
re
a
n
d
re
su
lt
s
w
e
re
o
b
tain
e
d
.
T
h
e
s
y
ste
m
wa
s
m
o
n
it
o
re
d
b
a
se
d
on
t
h
e
sta
rt
ti
m
e
a
n
d
th
e
e
n
d
ti
m
e
of
th
e
f
a
u
lt
a
n
d
how
w
e
ll
th
e
c
ircu
it
b
re
a
k
e
r
re
a
c
ts
with
th
o
se
ti
m
e
s.
F
a
u
lt
o
c
c
u
rre
d
f
ro
m
0
.
1
0
0
to
0
.
3
0
0
se
c
o
n
d
s
b
e
f
o
re
it
w
a
s
re
m
o
v
e
d
.
At
th
e
ti
m
e
f
a
u
lt
wa
s
not
a
p
p
li
e
d
(i.
e
.
f
ro
m
0
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0
0
to
0
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1
0
0
a
n
d
f
ro
m
0
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3
0
0
to
0
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7
2
)
,
th
e
c
ircu
it
b
re
a
k
e
r
wa
s
c
lo
se
a
n
d
b
e
c
a
m
e
o
p
e
n
w
h
e
n
f
a
u
lt
w
a
s
a
p
p
li
e
d
so
as
to
c
u
t
o
f
f
c
u
rre
n
t
f
lo
w
th
ro
u
g
h
th
e
li
n
e
.
T
h
e
re
su
lt
o
b
tai
n
e
d
g
a
v
e
th
e
d
isru
p
ti
o
n
c
a
u
se
d
by
th
e
f
a
u
lt
a
n
d
t
h
e
q
u
ick
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sp
o
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se
of
th
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irc
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it
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re
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k
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n
e
u
tralizin
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it
.
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s
u
lt
s
g
o
tt
e
n
a
re
b
a
se
d
on
w
h
e
n
th
e
c
ircu
it
b
re
a
k
e
r
is
c
lo
se
a
n
d
no
f
a
u
lt
is
a
p
p
li
e
d
a
n
d
w
h
e
n
th
e
c
ircu
it
b
re
a
k
e
r
is
o
p
e
n
due
to
f
a
u
lt
.
F
r
o
m
th
is
w
o
rk
,
it
w
a
s
o
b
tai
n
e
d
th
a
t
c
ircu
it
b
re
a
k
e
rs
a
re
v
e
r
y
e
ss
e
n
ti
a
l
in
s
y
st
e
m
p
ro
tec
ti
o
n
a
n
d
re
li
a
b
i
li
ty
.
K
ey
w
o
r
d
s
:
C
ir
cu
it
b
r
ea
k
er
Fau
lt
c
u
r
r
en
t
Fau
lt
v
o
ltag
e
P
o
w
er
s
y
s
te
m
P
SC
AD
T
h
is
is
an
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r
th
e
CC
BY
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Am
a
n
ze
C
h
u
k
w
u
eb
u
k
a
Fo
r
tu
n
e,
Dep
ar
t
m
en
t
of
E
lectr
ical
E
n
g
i
n
ee
r
in
g
,
Un
i
v
er
s
it
y
of
Ni
g
er
ia,
Nsu
k
k
a
-
O
n
it
s
h
a
R
d
,
Nsu
k
k
a,
Nig
er
ia
.
E
m
ail:
f
o
r
tu
n
ea
m
a
n
ze
@
g
m
a
il
.
co
m
1.
I
NT
RO
D
UCT
I
O
N
Fau
lt
o
cc
u
r
r
en
ce
in
p
o
w
er
s
y
s
te
m
is
i
n
ev
itab
le.
Hen
ce
,
in
ev
er
y
p
o
w
er
s
y
s
te
m
d
esi
g
n
p
r
o
ce
d
u
r
e,
th
ese
f
au
lts
ar
e
co
n
s
id
er
ed
an
d
an
al
y
s
ed
,
t
h
eir
lik
el
ih
o
o
d
of
o
cc
u
r
r
en
ce
is
d
eter
m
i
n
ed
an
d
th
e
b
est
w
a
y
s
to
h
an
d
le
t
h
e
m
ar
e
ea
r
m
ar
k
ed
so
as
to
i
m
p
r
o
v
e
s
y
s
te
m
s
tab
ilit
y
,
r
u
g
g
ed
n
ess
,
m
ai
n
ten
an
ce
co
s
t
an
d
r
eliab
ilit
y
.
T
h
e
f
a
u
lt
an
al
y
s
is
of
a
p
o
w
er
s
y
s
te
m
is
r
eq
u
ir
ed
in
o
r
d
er
to
p
r
o
v
id
e
in
f
o
r
m
a
tio
n
f
o
r
th
e
s
elec
tio
n
of
s
w
itc
h
g
ea
r
,
cir
cu
it
b
r
ea
k
er
s
,
an
d
th
e
s
etti
n
g
of
r
ela
y
s
,
to
be
u
s
ed
in
th
e
p
o
w
er
s
y
s
te
m
s
p
r
o
tectio
n
.
A
p
o
w
er
s
y
s
te
m
is
n
o
t
s
tatic
b
u
t
c
h
a
n
g
es
d
u
r
i
n
g
o
p
er
atio
n
(
s
w
itc
h
i
n
g
on
or
of
of
g
e
n
er
ato
r
s
an
d
tr
an
s
m
is
s
io
n
li
n
es)
an
d
d
u
r
i
n
g
p
lan
n
i
n
g
o
p
er
atio
n
(
ad
d
itio
n
of
g
e
n
er
ato
r
s
an
d
tr
an
s
m
i
s
s
io
n
li
n
es).
T
h
u
s
,
f
au
lt
s
tu
d
ie
s
n
ee
d
to
be
r
o
u
tin
el
y
p
er
f
o
r
m
ed
by
u
tili
t
y
en
g
i
n
ee
r
s
[1
-
3
]
.
Fau
lt
u
s
u
all
y
o
cc
u
r
in
a
p
o
w
er
s
y
s
te
m
d
u
e
to
in
s
u
latio
n
f
ail
u
r
e,
lig
h
t
n
in
g
f
las
h
o
v
er
,
p
h
y
s
ic
al
d
am
a
g
e
or
h
u
m
an
er
r
o
r
.
T
h
ese
f
au
l
ts
m
a
y
e
ith
er
be
t
h
r
ee
-
p
h
a
s
e
in
n
atu
r
e
i
n
v
o
lv
i
n
g
all
t
h
r
ee
p
h
a
s
es
in
a
s
y
m
m
etr
ica
l
m
an
n
er
,
or
m
a
y
be
as
y
m
m
etr
i
ca
l
w
h
er
e
u
s
u
all
y
o
n
l
y
o
n
e
or
t
w
o
p
h
ase
s
m
a
y
be
in
v
o
lv
ed
.
Fau
lt
s
m
a
y
also
be
ca
u
s
ed
by
eith
er
s
h
o
r
t
-
cir
c
u
it
s
to
ea
r
th
or
b
et
w
ee
n
li
v
e
co
n
d
u
cto
r
s
,
or
m
a
y
be
ca
u
s
ed
by
b
r
o
k
en
co
n
d
u
cto
r
s
in
o
n
e
or
m
o
r
e
p
h
a
s
es.
So
m
et
i
m
es
s
i
m
u
lta
n
eo
u
s
f
au
l
ts
m
a
y
o
c
cu
r
i
n
v
o
l
v
i
n
g
b
o
th
s
h
o
r
t
-
cir
cu
it
f
a
u
lt
an
d
b
r
o
k
e
n
-
co
n
d
u
cto
r
f
au
l
t
(
also
k
n
o
w
n
as
o
p
en
-
cir
cu
it
f
au
lt).
B
alan
ce
d
th
r
ee
p
h
ase
f
a
u
lts
m
a
y
be
an
aly
s
ed
u
s
i
n
g
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
: 2
2
5
2
-
8814
I
n
t J
A
d
v
A
p
p
l Sci
,
Vo
l.
9
,
No
.
3
,
Sep
tem
b
er
2
0
2
0
:
1
7
1
–
1
7
9
172
an
eq
u
i
v
ale
n
t
s
i
n
g
le
-
p
h
ase
c
ir
cu
it.
W
it
h
a
s
y
m
m
etr
ical
th
r
ee
-
p
h
a
s
e
f
au
l
ts
t
h
e
u
s
e
of
s
y
m
m
etr
ical
co
m
p
o
n
e
n
t
s
h
elp
s
to
r
ed
u
ce
t
h
e
co
m
p
le
x
it
y
of
t
h
e
ca
lc
u
latio
n
s
as
t
r
an
s
m
is
s
io
n
l
in
e
s
ar
e
b
y
an
d
-
lar
g
e
s
y
m
m
etr
ica
l,
alth
o
u
g
h
th
e
f
a
u
lt
m
a
y
be
as
y
m
m
etr
ical
(
n
o
t
af
f
ec
t
in
g
t
h
e
li
n
es
t
h
e
y
o
cc
u
r
on
th
e
s
a
m
e
w
a
y
)
[
4
]
.
Du
r
in
g
t
h
e
o
p
er
atio
n
of
p
o
w
er
s
y
s
te
m
s
,
it
is
d
esira
b
le
to
s
w
i
tch
on
or
o
f
f
t
h
e
v
ar
io
u
s
cir
cu
it
s
(
e.
g
.
:
tr
an
s
m
is
s
io
n
l
in
e
s
,
d
is
tr
ib
u
to
r
s
,
g
e
n
er
ati
n
g
p
lan
t
s
etc)
u
n
d
er
b
o
th
n
o
r
m
al
a
n
d
ab
n
o
r
m
al
co
n
d
it
io
n
s
.
In
ea
r
lier
d
ay
s
,
th
is
f
u
n
ctio
n
u
s
e
d
to
be
p
er
f
o
r
m
ed
by
a
s
w
itc
h
an
d
a
f
u
s
e
p
lace
d
in
s
er
ie
s
w
i
th
t
h
e
cir
cu
it
[
5
,
6
]
.
Ho
w
e
v
er
,
s
u
c
h
m
ea
n
s
of
co
n
tr
o
l
p
r
esen
t
t
w
o
d
is
ad
v
an
tag
e
s
.
Firstl
y
,
w
h
en
a
f
u
s
e
b
lo
w
s
o
u
t,
it
tak
es
q
u
ite
s
o
m
e
ti
m
e
to
r
ep
lace
it
a
n
d
r
e
s
to
r
e
p
o
w
er
s
u
p
p
l
y
to
t
h
e
c
u
s
to
m
er
s
[
7
]
.
Seco
n
d
l
y
,
a
f
u
s
e
c
an
n
o
t
s
u
cc
es
s
f
u
ll
y
in
ter
r
u
p
t
h
ea
v
y
f
a
u
lt
cu
r
r
en
t
s
th
at
r
esu
lt
s
f
r
o
m
m
o
d
er
n
h
ig
h
v
o
lta
g
e
an
d
h
i
g
h
ca
p
ac
it
y
c
ir
cu
its
[
8
]
.
Du
e
to
th
ese
d
is
ad
v
a
n
ta
g
es,
th
e
u
s
e
of
s
w
itc
h
es
an
d
f
u
s
e
s
is
l
i
m
ited
to
lo
w
-
v
o
lta
g
e
a
n
d
s
m
al
l
ca
p
ac
it
y
c
ir
cu
it
s
w
h
er
e
f
r
eq
u
en
t
o
p
er
atio
n
s
ar
e
n
o
t
ex
p
ec
ted
e.
g
:
f
o
r
th
e
s
w
i
tch
i
n
g
a
n
d
p
r
o
tectio
n
of
d
is
tr
ib
u
tio
n
tr
a
n
s
f
o
r
m
er
s
,
lig
h
ti
n
g
cir
c
u
its
,
b
r
an
c
h
cir
cu
i
ts
of
d
is
tr
ib
u
t
io
n
li
n
es
etc.
[9
-
17]
W
ith
th
e
ad
v
an
ce
m
e
n
t
in
tech
n
o
lo
g
y
,
d
e
v
ices
t
h
at
h
an
d
le
f
au
lts
b
etter
a
n
d
also
s
w
itc
h
f
aster
,
h
av
e
b
ee
n
d
ev
elo
p
ed
.
C
ir
c
u
it
b
r
ea
k
er
s
ar
e
d
e
s
ig
n
ed
to
m
a
n
u
al
l
y
or
a
u
to
m
a
ticall
y
s
w
itc
h
h
ig
h
v
o
ltag
e,
h
i
g
h
ca
p
ac
it
y
p
o
w
er
co
m
p
o
n
en
ts
.
A
c
ir
cu
it
b
r
ea
k
er
can
m
a
k
e
or
b
r
ea
k
a
cir
cu
it
au
to
m
atica
ll
y
u
n
d
er
f
a
u
lt
co
n
d
itio
n
or
m
a
y
be
o
p
en
ed
m
an
u
all
y
or
by
r
e
m
o
te
co
n
tr
o
l
w
h
e
n
ev
er
d
esire
d
u
n
d
er
:
no
-
lo
ad
,
f
u
ll
-
lo
ad
an
d
s
h
o
r
t
-
cir
cu
i
t
co
n
d
itio
n
s
.
W
h
e
n
th
e
co
n
tact
s
of
a
cir
cu
it
b
r
ea
k
er
ar
e
s
ep
ar
ated
u
n
d
er
f
au
lt
co
n
d
itio
n
s
,
an
ar
c
is
s
tr
u
ck
b
et
w
ee
n
t
h
e
m
.
T
h
e
f
a
u
lt
c
u
r
r
en
t
is
t
h
u
s
ab
le
to
co
n
t
in
u
e
u
n
ti
l
th
e
d
i
s
ch
ar
g
e
ce
ase
s
.
T
h
e
p
r
o
d
u
ctio
n
of
ar
c
n
o
t
o
n
l
y
d
ela
y
s
cu
r
r
en
t
in
ter
r
u
p
ti
o
n
b
u
t
it
also
g
e
n
er
ates
e
n
o
r
m
o
u
s
h
ea
t
w
h
ic
h
m
a
y
ca
u
s
e
d
a
m
ag
e
to
t
h
e
s
y
s
te
m
or
to
th
e
cir
cu
it
b
r
ea
k
er
its
elf
.
T
h
er
ef
o
r
e,
th
e
m
a
in
p
r
o
b
le
m
in
a
cir
cu
it
b
r
ea
k
er
is
to
ex
ti
n
g
u
is
h
th
e
ar
c
w
it
h
i
n
th
e
s
h
o
r
tes
t
p
o
s
s
ib
le
ti
m
e
so
th
at
th
e
h
ea
t
g
en
er
ated
by
it
m
a
y
n
o
t
r
ea
ch
a
d
an
g
er
o
u
s
v
alu
e
[
1
8
]
.
C
ir
cu
it
b
r
ea
k
er
s
m
a
y
v
ar
y
in
th
e
t
y
p
e
of
m
ec
h
a
n
is
m
or
m
ater
ial
u
s
e
d
f
o
r
ar
c
q
u
en
ch
i
n
g
an
d
also
in
th
e
v
o
lta
g
e
it
ca
n
o
p
er
ate
at
s
af
el
y
;
in
s
ize
a
n
d
in
ca
p
ac
it
y
of
f
a
u
lt
cu
r
r
e
n
t
it
ca
n
w
it
h
s
ta
n
d
.
Fau
lt
s
ca
u
s
e
u
n
r
eliab
ilit
y
a
n
d
in
s
tab
ilit
y
in
p
o
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er
s
y
s
te
m
s
.
U
n
h
a
n
d
led
f
a
u
lts
ca
u
s
e
b
r
ea
k
d
o
w
n
of
p
o
w
er
li
n
es
an
d
e
x
p
en
s
iv
e
p
o
w
er
s
y
s
te
m
d
ev
ices
(
s
u
c
h
as
g
e
n
er
ato
r
s
,
tr
an
s
f
o
r
m
er
s
a
n
d
tr
an
s
m
i
s
s
io
n
li
n
es,
etc)
w
h
ic
h
ca
u
s
e
ec
o
n
o
m
ic
m
eltd
o
w
n
s
a
n
d
e
v
e
n
lo
s
s
of
li
v
e
s
.
D
u
r
in
g
p
o
w
er
li
n
e
m
ai
n
te
n
a
n
ce
,
it
is
s
ac
r
o
s
a
n
ct
to
be
a
b
le
to
is
o
late
th
e
p
ar
t
u
n
d
er
m
ai
n
ten
a
n
ce
f
r
o
m
ele
ctr
ical
p
o
w
er
f
o
r
th
e
s
a
f
et
y
of
th
e
p
o
w
er
lin
e
m
ai
n
ten
a
n
ce
e
n
g
i
n
ee
r
.
I
s
o
lati
o
n
of
p
o
w
er
lin
e
s
is
m
u
ch
li
k
e
s
w
itch
in
g
,
th
er
e
is
b
o
u
n
d
to
be
d
an
g
er
o
u
s
ar
cs
esp
ec
iall
y
w
h
e
n
th
e
s
w
itc
h
i
n
g
is
s
lo
w
an
d
al
s
o
w
h
e
n
th
e
ar
c
-
h
a
n
d
li
n
g
m
ec
h
an
is
m
is
n
o
t
v
er
y
e
f
f
ec
ti
v
e.
T
h
ese
ar
cs
d
am
a
g
e
th
e
s
w
itc
h
i
n
g
d
e
v
ices
w
h
en
t
h
e
y
ar
e
u
s
ed
o
v
er
s
o
m
e
p
er
io
d
of
tim
e.
T
h
e
aim
of
th
is
s
t
u
d
y
is
to
an
al
y
s
e
f
a
u
lt
in
a
p
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y
s
te
m
a
n
d
d
eter
m
i
n
e
f
a
u
lt
-
c
u
r
r
en
t
s
an
d
v
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lta
g
es
r
ela
tio
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s
h
ip
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s
i
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P
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w
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S
y
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te
m
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p
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ter
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id
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Desi
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(
P
SC
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.
T
h
e
o
b
j
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tiv
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of
th
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s
wo
r
k
ar
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to
:
-
An
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s
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f
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on
an
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ter
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E
lectr
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d
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i
cs
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n
g
in
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s
(IEEE)
s
tan
d
ar
d
30
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b
u
s
test
s
y
s
te
m
w
it
h
o
u
t
p
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tectio
n
.
-
An
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e
t
h
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o
p
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n
an
d
ch
a
r
ac
ter
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of
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P
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n
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t
h
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ef
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ap
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b
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p
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of
a
s
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d
ar
d
IEEE
b
u
s
s
y
s
te
m
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P
SC
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I
n
ter
n
atio
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al
elec
tr
ical
an
d
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tr
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n
ic
en
g
i
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s
(IEEE)
s
ta
n
d
ar
d
30
b
u
s
s
y
s
te
m
w
as
u
s
ed
in
t
h
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is
.
T
h
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y
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te
m
is
132kV
–
33
kV
s
ta
n
d
ar
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.
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lo
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p
ar
am
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w
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tab
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d
in
p
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p
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ased
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in
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d
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on
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ex
p
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f
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s
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m
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m
u
lat
io
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s
o
f
t
w
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(
P
SC
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h
e
w
o
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k
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v
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s
ar
ea
s
of
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m
p
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tatio
n
a
l
an
al
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s
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s
of
p
o
w
er
s
y
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te
m
d
ev
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on
a
tr
an
s
m
i
s
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et
w
o
r
k
,
f
au
lt
co
n
tr
o
l
alg
o
r
ith
m
s
,
a
n
d
cir
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b
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k
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o
p
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s
i
m
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in
s
o
f
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lt
a
n
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y
s
i
s
in
p
o
w
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s
y
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te
m
s
h
elp
in
t
h
e
d
eter
m
i
n
atio
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of
s
w
itc
h
es
’
ca
p
ac
ities
a
n
d
v
o
ltag
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to
be
e
m
p
lo
y
ed
in
t
h
e
p
r
o
tectio
n
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ch
e
m
e
of
p
o
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er
s
y
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te
m
s
.
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u
r
in
g
f
a
u
lt
s
v
er
y
h
ig
h
c
u
r
r
en
t
m
ag
n
it
u
d
es
h
a
v
e
to
f
lo
w
t
h
r
o
u
g
h
th
e
p
r
o
tectiv
e
s
w
itc
h
e
s
ev
en
as
t
h
e
y
atte
m
p
t
to
o
p
en
to
is
o
late
th
e
f
au
lt.
T
h
e
m
a
x
i
m
u
m
v
al
u
e
of
th
ese
c
u
r
r
en
t
s
d
ep
en
d
s
on
t
h
e
o
v
er
all
p
o
w
er
s
y
s
te
m
p
a
r
a
m
eter
s
s
u
c
h
as
to
tal
a
v
ail
ab
le
p
o
w
er
in
ea
c
h
co
m
p
o
n
e
n
t
a
n
d
th
e
v
o
ltag
e
s
.
P
r
o
tectio
n
in
p
o
w
er
s
y
s
te
m
s
is
as
i
m
p
o
r
tan
t
as
th
e
s
y
s
te
m
it
s
elf
.
Ov
er
th
e
y
ea
r
s
cir
cu
it
b
r
ea
k
er
s
h
a
v
e
b
ee
n
e
m
p
lo
y
ed
in
t
h
e
p
r
o
tec
tio
n
of
p
o
w
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li
n
es,
g
e
n
er
ato
r
s
,
tr
an
s
f
o
r
m
er
s
a
n
d
ev
er
y
o
t
h
er
co
m
p
o
n
e
n
t
of
th
e
p
o
w
er
s
y
s
te
m
.
T
h
e
m
aj
o
r
p
r
o
b
lem
s
in
p
r
o
tectio
n
ar
e
in
th
e
s
w
itc
h
in
g
on
an
d
o
f
f
of
th
ese
co
m
p
o
n
e
n
ts
.
C
ir
cu
it
b
r
ea
k
er
s
v
ar
y
in
s
u
c
h
p
ar
am
eter
s
as:
v
o
lta
g
e
(
b
ec
au
s
e
in
th
e
o
p
en
s
tate,
t
h
e
y
ar
e
lik
e
ca
p
ac
ito
r
s
th
a
t
m
u
s
t
h
a
v
e
h
ig
h
e
n
o
u
g
h
d
iele
ctr
ic
s
tr
en
g
t
h
to
w
i
th
s
tan
d
b
r
ea
k
d
o
w
n
as
a
r
es
u
lt
of
t
h
e
v
o
ltag
e
ac
r
o
s
s
it),
an
d
cu
r
r
en
t
(
b
ec
au
s
e
in
th
e
clo
s
e
d
s
tate,
th
e
y
ar
e
li
k
e
co
n
d
u
ct
o
r
s
w
h
ich
m
u
s
t
be
ab
le
to
ca
r
r
y
all
t
h
e
d
y
n
a
m
ic
cu
r
r
en
ts
of
th
e
s
y
s
te
m
)
.
T
h
e
f
o
llo
w
i
n
g
ar
e
f
au
lt
s
t
u
d
ies
a
n
d
cir
cu
it
b
r
ea
k
er
s
an
a
l
y
s
is
e
x
is
tin
g
in
li
ter
atu
r
e.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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t J
A
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p
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I
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N:
2
2
5
2
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C
o
m
p
u
ter
A
id
ed
Desi
g
n
/
E
lectr
o
m
a
g
n
etic
T
r
an
s
ien
t
s
in
clu
d
i
n
g
Dir
ec
t
C
u
r
r
en
t
(
P
SC
A
D/E
M
DT
C
)
en
v
ir
o
n
m
e
n
t.
A
cc
o
r
d
in
g
to
[
1
9
]
,
f
o
r
co
n
tr
o
lled
s
w
itc
h
i
n
g
ap
p
licatio
n
s
t
h
at
m
ai
n
l
y
o
cc
u
r
d
u
r
in
g
lo
ad
s
w
itc
h
in
g
a
n
d
f
a
u
lts
,
cir
cu
i
t
b
r
ea
k
er
s
’
c
h
ar
ac
ter
is
t
ics
p
la
y
s
an
i
m
p
o
r
tan
t
r
o
le
in
d
eter
m
i
n
in
g
th
e
i
n
s
ta
n
t
of
clo
s
in
g
an
d
o
p
en
i
n
g
.
T
h
e
k
e
y
p
ar
a
m
eter
s
th
at
ca
n
af
f
ec
t
t
h
e
ac
cu
r
ac
y
of
cir
cu
it
b
r
ea
k
er
s
w
i
tch
i
n
g
in
s
ta
n
t
s
ar
e:
a.
Op
er
atin
g
ti
m
e
of
p
h
y
s
ical
co
n
tacts
of
cir
cu
it
b
r
ea
k
er
b.
R
ate
of
d
ec
a
y
of
d
ielec
tr
ic
s
tr
en
g
t
h
(
R
DDS)
c.
R
ate
of
r
is
e
of
d
ielec
tr
ic
s
tr
en
g
th
(
R
R
D
S)
d.
A
r
ci
n
g
t
i
m
e
F
a
u
lt
a
n
a
lysi
s
of
th
e
1
5
0
kV
S
o
u
th
S
u
l
a
w
esi
tr
a
n
s
mi
s
s
io
n
s
yst
em
u
s
in
g
P
S
C
A
D/E
MT
DC
In
th
e
w
o
r
k
of
[
2
0
]
,
s
h
o
r
t
cir
cu
it
f
a
u
lt
w
a
s
co
n
s
id
er
ed
as
o
n
e
of
th
e
c
h
ar
ac
ter
is
tic
s
of
tr
an
s
ie
n
t
d
is
tu
r
b
an
ce
s
in
elec
tr
ic
p
o
w
e
r
s
y
s
te
m
s
t
h
at
m
u
s
t
be
ad
d
r
ess
ed
by
s
a
f
et
y
eq
u
ip
m
en
t
s
.
It
d
e
m
o
n
s
tr
ates
t
h
at
th
e
i
n
cr
ea
s
e
in
o
cc
u
r
r
en
ce
of
s
h
o
r
t
cir
c
u
it
g
e
n
er
ates
lar
g
e
e
lectr
ical
cu
r
r
e
n
ts
a
n
d
at
a
v
er
y
lo
w
v
o
lta
g
e.
T
h
i
s
r
esear
ch
clai
m
s
to
ad
d
r
ess
t
h
e
s
i
m
u
latio
n
of
s
h
o
r
t
cir
cu
it
in
ter
r
u
p
tio
n
in
a
1
5
0
k
V
tr
an
s
m
is
s
io
n
lin
e.
T
h
e
m
et
h
o
d
is
u
s
ed
to
p
er
f
o
r
m
th
e
s
i
m
u
latio
n
w
i
th
t
h
e
h
el
p
of
P
SC
A
D
/
E
MT
DC
an
d
P
W
S
(
P
o
w
er
W
o
r
ld
Si
m
u
lato
r
)
s
o
f
t
w
ar
e’
s
to
o
b
tai
n
th
e
c
h
ar
ac
ter
is
tic
of
cu
r
r
en
t
an
d
v
o
ltag
e
on
th
e
1
5
0
k
V
tr
a
n
s
m
i
s
s
io
n
n
et
w
o
r
k
in
So
u
th
S
u
la
w
e
s
i.
It
ex
a
m
i
n
e
s
th
e
c
h
an
g
es
in
c
u
r
r
en
t
an
d
v
o
ltag
e
d
u
r
i
n
g
s
h
o
r
t
cir
cu
it
f
a
u
lt
w
it
h
or
w
i
th
o
u
t
f
au
lt
i
m
p
ed
a
n
ce
an
d
f
a
u
lt
lo
ca
tio
n
d
is
ta
n
ce
.
A
n
a
lysi
s
of
r
esea
r
ch
and
d
ev
el
o
p
men
t
tr
en
d
s
in
va
c
u
u
m
circu
it b
r
ea
ke
r
s
A
cc
o
r
d
in
g
to
[
2
1
]
,
s
ev
er
al
co
m
p
a
n
ie
s
in
t
h
e
b
eg
in
n
i
n
g
of
th
e
t
w
e
n
tiet
h
ce
n
tu
r
y
,
n
o
tab
l
y
Gen
er
al
E
lectr
ic
an
d
W
esti
n
g
h
o
u
s
e
in
t
h
e
Un
ited
States
,
in
v
este
d
s
ig
n
i
f
ican
t
R
&
D
m
a
n
p
o
w
e
r
an
d
f
i
n
an
ce
s
i
n
to
b
u
ild
in
g
th
e
k
n
o
w
led
g
e
a
n
d
ex
p
er
tis
e
in
v
ac
u
u
m
ar
cs,
v
a
cu
u
m
co
n
tac
ts
,
an
d
v
ac
u
u
m
in
ter
r
u
p
ter
s
.
T
h
ese
ef
f
o
r
t
s
r
es
u
lted
in
s
u
cc
es
s
f
u
l
d
ep
lo
y
m
e
n
t
of
co
m
m
er
cial
v
ac
u
u
m
cir
c
u
it
b
r
ea
k
er
s
f
o
r
m
ed
iu
m
v
o
lta
g
e
d
is
tr
ib
u
tio
n
s
y
s
te
m
s
.
T
h
e
co
m
p
an
ies
w
er
e
also
v
er
y
e
n
t
h
u
s
i
asti
c
to
co
n
ti
n
u
e
th
e
m
ai
n
r
es
ea
r
ch
in
e
x
te
n
d
in
g
th
e
ap
p
licab
ilit
y
of
v
ac
u
u
m
i
n
to
h
ig
h
er
v
o
ltag
e,
s
u
b
-
tr
an
s
m
i
s
s
io
n
a
n
d
tr
an
s
m
is
s
io
n
s
y
s
te
m
s
.
So
o
n
th
e
y
w
er
e
to
be
f
ac
ed
w
it
h
b
i
g
d
is
ap
p
o
in
t
m
e
n
t.
It
t
u
r
n
s
out
t
h
at
t
h
e
v
ac
u
u
m
in
ter
r
u
p
ter
s
ar
e
n
o
t
ea
s
il
y
s
ca
lab
le
to
h
ig
h
er
v
o
ltag
e
s
.
P
ar
ticu
lar
l
y
,
t
h
e
e
le
ctr
ic
f
ie
ld
b
r
ea
k
d
o
w
n
b
et
w
ee
n
t
w
o
co
n
tact
s
in
v
ac
u
u
m
is
n
o
t
p
r
o
p
o
r
tio
n
al
to
th
e
co
n
tact
d
is
tan
ce
.
A
lt
h
o
u
g
h
a
0
.
5
mm
co
n
tac
t
g
ap
can
with
s
tan
d
ap
p
r
o
x
i
m
atel
y
15
k
V
,
th
e
g
ap
of
50
mm
w
il
l
n
o
t
h
a
n
d
le
1500
k
V,
or
1
.
5
MV
.
T
h
e
s
ca
lin
g
la
w
is
n
o
t
lin
ea
r
an
d
o
th
er
p
h
y
s
ical
p
r
o
ce
s
s
es
s
tan
d
on
th
e
w
a
y
of
u
s
i
n
g
lo
n
g
co
n
tact
g
ap
s
f
o
r
h
i
g
h
er
v
o
lta
g
es.
T
h
e
in
itial
ex
ci
te
m
e
n
t
d
i
m
in
i
s
h
ed
an
d
t
h
e
v
ac
u
u
m
s
w
itc
h
p
r
o
d
u
ctio
n
co
m
p
a
n
ies
co
n
ce
n
tr
ated
on
th
e
d
is
tr
ib
u
tio
n
p
r
o
d
u
cts
w
i
th
ad
d
itio
n
al
ap
p
licatio
n
s
of
lo
w
v
o
ltag
e
v
ac
u
u
m
co
n
ta
cto
r
s
.
T
o
d
ay
o
n
l
y
a
h
an
d
f
u
l
of
co
m
p
an
ie
s
m
a
in
tain
p
r
o
d
u
ctio
n
li
n
e
of
co
m
m
er
cial
v
ac
u
u
m
s
w
it
c
h
i
n
g
p
r
o
d
u
cts
ab
o
v
e
36
kV
p
r
im
ar
il
y
by
e
m
p
lo
y
in
g
a
s
er
i
es
co
m
b
i
n
atio
n
of
i
n
ter
r
u
p
ter
s
each
r
ated
in
t
h
e
15
-
36
kV
r
an
g
e.
T
h
is
s
it
u
atio
n
m
i
g
h
t
be
ch
a
n
g
i
n
g
.
In
t
h
i
s
w
o
r
k
,
it
w
a
s
s
tated
t
h
at
in
la
s
t
s
e
v
er
al
y
ea
r
s
of
ad
v
an
ce
s
,
p
r
o
v
is
io
n
h
a
s
b
ee
n
m
ad
e
on
m
o
r
e
u
n
d
er
s
tan
d
i
n
g
of
th
e
p
r
ac
tical
is
s
u
e
s
ass
o
ciate
d
w
it
h
v
ac
u
u
m
s
w
itc
h
g
ea
r
.
A
l
s
o
,
th
e
ec
o
n
o
m
ic
s
of
t
h
e
v
ac
u
u
m
i
n
ter
r
u
p
ter
m
an
u
f
ac
t
u
r
in
g
c
h
an
g
ed
d
r
a
m
atica
l
l
y
,
t
h
e
d
ev
ice
s
b
ein
g
less
ex
p
e
n
s
i
v
e,
s
m
a
ller
,
an
d
m
o
r
e
e
f
f
icie
n
t.
T
h
e
w
o
r
k
also
s
tated
t
h
at
tr
ad
itio
n
al
b
o
u
n
d
ar
y
b
et
w
ee
n
th
e
ap
p
licatio
n
s
of
S
u
lp
h
u
r
He
x
aFl
u
o
r
id
e
(
SF
6
)
an
d
v
ac
u
u
m
tech
n
o
lo
g
ies
is
ch
a
n
g
in
g
a
n
d
th
e
r
ec
en
t
i
n
q
u
ir
ie
s
of
t
h
e
en
v
ir
o
n
m
e
n
tal
i
m
p
ac
t
of
SF6
al
s
o
p
la
y
a
r
o
le
in
t
h
is
p
r
o
ce
s
s
.
A
ll
s
aid
,
th
e
v
ac
u
u
m
s
w
itc
h
g
ea
r
is
a
m
at
u
r
e
tech
n
o
lo
g
y
a
n
d
s
till
an
ac
ti
v
e
i
n
d
u
s
tr
y
w
i
th
d
y
n
a
m
icall
y
i
n
cr
ea
s
i
n
g
s
h
ar
es
of
t
h
e
w
o
r
ld
m
ar
k
e
ts
,
p
r
o
d
u
ctio
n
v
o
lu
m
es,
a
n
d
m
o
r
e
ef
f
ic
ien
t,
s
m
a
ller
an
d
b
etter
p
r
o
d
u
cts.
Dyn
a
mic
s
imu
la
tio
n
of
a
v
a
cu
u
m
s
w
itch
w
ith
P
S
C
A
D
T
h
e
w
o
r
k
of
[
2
2
]
s
h
o
w
s
th
at
t
h
e
s
w
itc
h
in
g
b
eh
av
io
u
r
of
t
h
e
v
ac
u
u
m
cir
c
u
it
b
r
ea
k
er
is
d
if
f
er
en
t
f
r
o
m
th
at
of
o
th
er
cir
cu
it
b
r
ea
k
er
s
w
h
e
n
th
e
e
f
f
ec
t
s
of
c
u
r
r
en
t
ch
o
p
p
in
g
,
d
ielec
tr
ic
s
tr
en
g
th
of
v
ac
u
u
m
g
ap
,
th
e
ar
c
v
o
ltag
e,
t
h
e
q
u
e
n
ch
i
n
g
ca
p
ab
ilit
y
of
h
ig
h
f
r
eq
u
en
c
y
cu
r
r
en
ts
,
v
ir
t
u
al
c
u
r
r
en
t
ch
o
p
p
i
n
g
a
n
d
p
r
estrik
es.
T
h
e
w
o
r
k
d
e
m
o
n
s
tr
ated
t
h
e
a
b
o
v
e
b
eh
av
io
u
r
s
in
s
i
m
u
latio
n
u
s
i
n
g
P
SC
AD.
T
h
e
Vac
u
m
m
C
ir
cu
it
B
r
ea
k
er
(
VC
B
)
m
o
d
el
d
ev
elo
p
ed
in
th
is
p
ap
er
u
s
es
th
e
v
ar
iab
le
r
esis
to
r
ap
p
r
o
ac
h
r
ep
r
esen
tin
g
f
r
eq
u
en
tl
y
s
w
itc
h
i
n
g
in
d
u
cta
n
ce
s
an
d
ca
p
ac
ita
n
ce
s
.
It
also
me
n
tio
n
s
t
h
at
t
h
e
o
t
h
er
ap
p
r
o
ac
h
to
m
o
d
elli
n
g
a
VC
B
is
by
u
s
i
n
g
an
id
ea
l
cir
cu
it
b
r
ea
k
er
w
h
ic
h
is
s
w
itch
ed
on
/
o
f
f
af
ter
d
if
f
er
en
t
cr
iter
ia
h
av
e
b
ee
n
ch
ec
k
ed
.
T
h
is
w
o
r
k
also
in
v
e
s
ti
g
ates
t
h
e
s
tr
e
s
s
on
a
V
C
B
an
d
t
h
e
e
n
er
g
y
in
t
h
e
v
ac
u
u
m
tu
b
e:
as
c
u
r
r
en
t
t
h
r
o
u
g
h
a
VC
B
is
f
lo
w
i
n
g
f
r
o
m
m
o
m
e
n
t
of
co
n
tact
s
ep
ar
atio
n
u
n
til
n
e
x
t
ze
r
o
cr
o
s
s
in
g
,
to
g
et
h
er
w
it
h
t
h
e
ar
c
v
o
ltag
e,
th
e
e
n
er
g
y
co
n
v
er
s
io
n
is
v
er
y
h
ig
h
,
d
ep
en
d
en
t
on
th
e
m
o
m
e
n
t
of
co
n
tact
s
ep
ar
atio
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
: 2
2
5
2
-
8814
I
n
t J
A
d
v
A
p
p
l Sci
,
Vo
l.
9
,
No
.
3
,
Sep
tem
b
er
2
0
2
0
:
1
7
1
–
1
7
9
174
2.
RE
S
E
ARCH
M
E
T
H
O
D
2
.
1
.
M
e
t
ho
ds
e
m
plo
y
ed
in
t
he
a
n
a
ly
s
is
s
i
m
u
la
t
io
n
T
h
is
r
esear
ch
a
n
al
y
s
i
s
u
s
es
P
SC
A
D
to
s
i
m
u
late
f
a
u
lt
co
n
d
i
tio
n
s
of
a
s
tan
d
ar
d
IEEE
30
-
B
u
s
s
y
s
te
m
u
s
i
n
g
t
h
e
tr
an
s
m
is
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io
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l
in
e
m
o
d
el
lin
e
B
er
g
er
o
n
of
P
SC
A
D
w
h
ic
h
h
as
a
g
r
ap
h
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l
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s
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ter
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ac
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MT
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lat
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n
tr
o
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s
i
m
u
l
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e
n
g
i
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e
[
2
3
]
.
P
SC
A
D
e
n
ab
les
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s
er
s
to
b
u
ild
a
cir
c
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it
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ch
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at
ic,
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u
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s
i
m
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lat
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s
,
an
d
a
n
al
y
s
e
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,
m
a
n
ag
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d
ata
in
a
f
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te
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ated
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r
ap
h
ical
en
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o
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m
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t,
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o
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eter
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te
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ar
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s
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s
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m
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latio
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r
u
n
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d
can
o
b
tain
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m
m
ed
iate
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lt
s
[
2
4
,
2
5
]
.
P
SC
A
D
co
m
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s
w
it
h
a
lib
r
ar
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m
o
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v
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p
r
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d
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ested
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g
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r
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ass
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tr
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f
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tio
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s
a
n
d
m
o
r
e
co
m
p
lex
m
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u
c
h
as
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tr
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ac
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AC
T
S
d
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an
s
m
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s
s
io
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li
n
es,
tr
an
s
f
o
r
m
er
s
a
n
d
ca
b
les.
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MT
DC
(
E
lectr
o
m
a
g
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et
ic
T
r
an
s
ien
t,
I
n
cl
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in
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D
C
)
p
r
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p
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s
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d
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if
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er
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t
ial
eq
u
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in
ti
m
e
d
o
m
ai
n
.
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h
e
s
o
lu
tio
n
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ca
lcu
lated
b
ased
on
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x
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ti
m
e
s
tep
,
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th
e
p
r
o
g
r
a
m
s
tr
u
ct
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r
e
allo
w
s
f
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th
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ep
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tat
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n
tr
o
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s
y
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te
m
.
T
h
e
VC
B
m
o
d
el
u
s
ed
in
th
i
s
w
o
r
k
is
w
r
itte
n
in
FO
R
T
R
AN7
7
co
d
e.
It
is
p
o
s
s
ib
le
to
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te
o
w
n
m
o
d
el
s
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te
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ate
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h
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m
in
to
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ar
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of
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if
t
h
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n
o
t
alr
ea
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v
ailab
le.
P
ar
am
eter
izatio
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of
th
e
V
C
B
is
d
o
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e
by
f
il
lin
g
t
h
e
in
p
u
t
m
ask
.
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h
er
s
i
m
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la
tio
n
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o
f
t
w
ar
e
m
ig
h
t
h
av
e
o
t
h
er
m
ea
n
s
of
p
r
ese
n
tin
g
t
h
ese.
2
.
2
.
VCB
m
o
del
T
h
e
VC
B
in
th
is
p
ap
er
is
m
o
d
eled
by
a
v
ar
iab
le
r
esis
ta
n
ce
,
th
is
is
i
m
p
o
r
tan
t
f
o
r
co
n
s
id
er
i
n
g
t
h
e
ar
c
v
o
ltag
e.
I
n
p
u
t
p
ar
a
m
eter
s
ar
e:
v
o
lta
g
e,
c
u
r
r
en
t
a
n
d
s
w
itch
in
g
co
m
m
a
n
d
.
T
h
e
o
u
tp
u
t
p
ar
a
m
eter
is
t
h
e
v
al
u
e
of
r
esis
ta
n
ce
.
Fu
r
t
h
er
m
o
r
e,
t
h
er
e
ar
e
s
ev
er
al
p
ar
a
m
eter
s
w
h
ic
h
can
be
ad
m
itted
by
th
e
i
n
p
u
t
m
as
k
as
s
h
o
w
n
in
T
ab
le
1
.
T
ab
le
1
.
I
n
p
u
t
m
a
s
k
of
VC
B
C
o
n
f
i
g
u
r
a
t
i
o
n
M
a
x
i
m
u
m
V
o
l
t
a
g
e
[
k
V
]
60
[
k
V
]
M
e
t
a
l
v
a
p
o
u
r
a
r
c
v
o
l
t
a
g
e
[
V
]
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[
V
]
R
e
si
st
a
n
c
e
(
c
l
o
se
d
)
[
o
h
m
]
80e
-
6
[
o
h
m
]
R
e
si
st
a
n
c
e
(
o
p
e
n
)
[
o
h
m
]
1
0
0
e
6
[
o
h
m
]
F
r
e
q
u
e
n
c
y
[
H
z
]
60
[
H
z
]
S
l
o
p
e
of
d
i
e
l
e
c
t
r
i
c
r
e
c
o
v
e
r
y
[
k
V
/
ms
]
30
[
k
V
/
µ
s
]
I
n
i
t
i
a
l
v
a
l
u
e
of
d
i
e
l
e
c
t
r
i
c
s
t
r
e
n
g
t
h
[
k
V
]
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[
k
V
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l
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p
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of
d
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l
e
c
t
r
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c
st
r
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n
g
t
h
[
k
V
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µ
s]
50
[
k
V
/
µ
s
]
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n
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t
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a
l
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l
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of
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s
t
sr
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h
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k
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k
V
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u
r
r
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t
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c
h
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b
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t
y
[
A
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µ
s]
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µ
s
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e,
elec
tr
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ar
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ar
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c
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ta
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clo
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d
o
p
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p
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ax
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m
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m
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d
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al
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v
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ch
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h
e
ar
c
v
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is
m
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eled
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a
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t
v
al
u
e
in
o
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er
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im
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li
f
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th
e
m
o
d
el.
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h
e
co
r
r
esp
o
n
d
in
g
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alu
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of
r
esis
ta
n
ce
is
ca
lcu
late
d
by
(
1
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r
=
V
arc
/I
VCB
(
1
)
B
o
th
d
ielec
tr
ic
r
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er
y
m
ec
h
an
is
m
s
ar
e
m
o
d
eled
u
s
i
n
g
(
2
)
.
V
contact
(
t)
=
30
k
V/
m
s
.
t
(
e
f
f
ec
ti
v
e
o
n
l
y
at
m
o
m
en
t
of
co
n
tact
s
ep
ar
atio
n
)
V
dielectric
(
t)
=
50
k
V/µs.t
(
ef
f
ec
t
iv
e
at
cu
r
r
en
t
s
ep
ar
atio
n
)
Gen
er
all
y
,
V
=
a.
x
(
2
)
W
h
er
e:
x
=
co
n
tacts
d
is
tan
ce
a
=
s
lo
p
e
of
di
-
elec
tr
ic
T
h
ese
v
alu
e
s
ar
e
li
m
i
ted
by
th
e
m
a
x
i
m
u
m
v
o
lta
g
e
of
V
C
B
(
6
0
k
V)
.
T
h
e
clo
s
in
g
of
c
o
n
tacts
is
m
o
d
eled
by
60
kV
–
V
contact
.
A
f
u
n
ctio
n
ch
ec
k
s
d
i/d
t
of
c
u
r
r
en
t
at
ev
er
y
ze
r
o
cr
o
s
s
i
n
g
to
co
n
s
id
er
th
e
c
u
r
r
en
t
q
u
en
c
h
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g
ca
p
ab
ilit
y
of
th
e
v
ac
u
u
m
s
p
ac
e.
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h
e
v
alu
e
i
s
s
et
to
a
m
a
x
i
m
u
m
of
80
A
/
µs.
If
th
i
s
v
al
u
e
is
ex
ce
ed
ed
,
cu
r
r
en
t
w
ill
go
on
f
l
o
w
i
n
g
ti
ll
th
e
n
e
x
t
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r
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en
t
ze
r
o
.
T
h
is
VC
B
m
o
d
el
w
il
l
be
e
m
p
l
o
y
ed
in
th
e
s
ta
n
d
ar
d
IEEE
30
b
u
s
s
y
s
te
m
f
o
r
f
a
u
lt
s
t
u
d
ies.
T
h
e
m
o
d
el
b
lo
ck
is
as
s
h
o
w
n
in
Fi
g
u
r
e
1
an
d
th
e
lab
el
“
B
R
K”
r
ep
r
esen
ts
t
h
e
co
n
tr
o
l
s
ig
n
al
as
s
h
o
wn
in
Fi
g
u
r
e
2
.
Her
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
A
d
v
A
p
p
l Sci
I
SS
N:
2
2
5
2
-
8814
F
a
u
lt a
n
a
lysi
s
in
p
o
w
er sys
te
m
u
s
in
g
p
o
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tems c
o
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ter a
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ma
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h
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u
r
e
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h
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Fig
u
r
e
2
.
T
h
e
VC
B
m
o
d
el
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lo
ck
2
.
3
.
T
he
f
a
ult
m
o
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le
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s
h
o
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t
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f
a
u
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b
lo
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in
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SC
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D
lib
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ar
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s
ed
to
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h
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f
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m
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ab
le
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h
e
f
au
lt
m
as
k
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h
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h
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a
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a
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Ty
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I
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
: 2
2
5
2
-
8814
I
n
t J
A
d
v
A
p
p
l Sci
,
Vo
l.
9
,
No
.
3
,
Sep
tem
b
er
2
0
2
0
:
1
7
1
–
1
7
9
178
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ip
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t
d
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ctio
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h
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r
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er
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m
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lt
y
s
y
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te
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w
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h
p
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tectio
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.
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id
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l
VC
B
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ld
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av
e
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u
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ed
n
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g
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o
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h
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en
t
h
e
f
a
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e
atte
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t
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y
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h
e
V
C
B
to
is
o
late
it
w
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s
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ted
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th
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n
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ich
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tio
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m
e
d
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ic
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er
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t
h
e
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.
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h
is
s
a
m
e
t
h
i
n
g
h
ap
p
en
s
w
h
en
th
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VC
B
i
s
de
-
en
er
g
ized
af
ter
th
e
f
a
u
lt r
e
m
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e
f
a
u
lt s
ig
n
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g
i
v
e
n
in
Fig
u
r
e
1
3
.
Fig
u
r
e
12
.
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u
s
Vo
ltag
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at
th
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in
s
ta
n
t
of
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a
u
lt
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n
d
f
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lt
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m
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al
Fig
u
r
e
13.
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h
e
f
au
l
t
s
i
g
n
al
4.
CO
NCLU
SI
O
N
E
v
er
y
d
ev
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o
b
e
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s
Ne
w
to
n
’
s
f
ir
s
t
la
w
of
m
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d
t
h
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V
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m
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ab
le
co
n
tact
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ar
e
n
o
t
ex
ce
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tio
n
s
.
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d
er
h
ea
v
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s
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ch
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its
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n
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it
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ts
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ates
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ar
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n
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t
r
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w
h
ich
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t
s
up
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h
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n
tact
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.
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f
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l
t
is
n
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r
ly
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m
e
n
ts
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u
c
h
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it
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a
m
a
g
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l
d
be
d
o
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e
on
th
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y
s
te
m
w
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l
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tast
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o
p
h
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d
ex
tr
e
m
e
l
y
d
an
g
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o
u
s
,
b
u
t
also
co
s
tl
y
.
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t
is
th
er
ef
o
r
e,
ex
tr
e
m
el
y
i
m
p
o
r
ta
n
t
to
p
er
f
o
r
m
f
au
l
t
s
tu
d
ie
s
on
ev
er
y
p
o
w
er
s
y
s
t
e
m
,
in
o
r
d
er
to
d
eter
m
in
e
t
h
e
r
atin
g
s
of
t
h
e
r
esp
ec
tiv
e
p
r
o
tectiv
e
ele
m
e
n
ts
e
m
p
lo
y
ed
.
T
h
e
im
p
o
r
tan
ce
of
C
B
s
in
p
o
w
er
s
y
s
te
m
s
is
ex
t
r
e
m
el
y
i
m
p
o
r
tan
t
an
d
th
e
VC
B
in
p
ar
ticu
lar
h
as
a
v
er
y
g
o
o
d
f
a
u
lt
er
r
o
r
clea
r
in
g
ca
p
ab
ilit
ies,
ea
s
e
of
i
n
s
tal
latio
n
a
n
d
en
v
ir
o
n
m
e
n
tall
y
f
r
ien
d
l
y
.
C
o
n
ce
r
n
ed
in
d
u
s
tr
ies
s
h
o
u
ld
p
io
n
ee
r
r
es
ea
r
ch
p
r
o
g
r
am
s
in
t
h
e
ar
ea
of
d
ev
elo
p
m
en
t
of
h
i
g
h
v
o
lt
ag
e
VC
B
s
in
o
u
r
in
s
t
itu
tio
n
s
a
n
d
r
esear
ch
ce
n
t
er
s
.
E
v
er
y
co
m
p
o
n
en
t
of
o
u
r
p
o
w
er
s
y
s
te
m
s
h
o
u
ld
be
p
r
o
tecte
d
f
r
o
m
f
atal
an
d
to
tal
f
ail
u
r
es
u
s
u
all
y
ca
u
s
ed
by
f
au
lts
a
n
d
ac
cid
en
ts
on
t
h
e
tr
a
n
s
m
is
s
io
n
an
d
d
i
s
tr
i
b
u
tio
n
s
ec
tio
n
s
.
To
p
r
o
tect
f
ailu
r
e
s
in
o
u
r
n
atio
n
al
g
r
id
,
p
o
w
er
s
y
s
te
m
p
r
o
tectio
n
e
n
g
i
n
ee
r
s
s
h
o
u
ld
be
e
m
p
lo
y
ed
to
e
x
a
m
in
e
an
d
p
er
f
o
r
m
ad
eq
u
ate
f
a
u
lt
s
tu
d
y
on
th
e
s
y
s
te
m
.
RE
F
E
R
E
NC
E
S
[1
]
L.
X
in
g
p
i
n
g
,
Distrib
u
ti
o
n
tr
a
n
sf
o
rm
e
rs
h
e
a
lt
h
c
o
n
d
i
ti
o
n
mo
n
it
o
rin
g
a
n
d
e
v
a
lu
a
ti
o
n
me
th
o
d
s
,
Ch
o
n
g
q
in
g
,
2
0
1
3
.
[2
]
S
tate
G
rid
,
Q
-
GDW
1
1
1
9
0
-
2
0
1
4
h
ig
h
o
v
e
rlo
a
d
c
a
p
a
c
it
y
o
f
r
u
ra
l
p
o
we
r
d
istrib
u
ti
o
n
tra
n
sf
o
rm
e
rs
tec
h
n
ica
l
g
u
i
d
e
li
n
e
,
C
h
i
n
a
El
e
c
tri
c
P
o
w
e
r
P
re
ss
,
Be
ij
in
g
,
2
0
1
4
.
[3
]
IEE
E
S
t
a
n
d
a
r
d
C5
7
.
9
1
-
1
9
9
5
IEE
E
Gu
id
e
fo
r
L
o
a
d
i
n
g
M
in
e
ra
l
-
Oil
-
Imm
e
rs
e
d
T
ra
n
sfo
rm
e
rs
.
[4
]
G.
S
w
if
t,
Z.
Zh
a
n
g
,
“A
d
iffere
n
t
a
p
p
ro
a
c
h
to
tran
sf
o
rm
e
r.
th
e
rm
a
l
m
o
d
e
li
n
g
”,
IEE
E
T
ra
n
s
m
issio
n
a
n
d
Distri
b
u
t
io
n
Co
n
f
e
re
n
c
e
,
Ne
w
Orle
a
n
s,
A
p
r
1
9
9
9
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
A
d
v
A
p
p
l Sci
I
SS
N:
2
2
5
2
-
8814
F
a
u
lt a
n
a
lysi
s
in
p
o
w
er sys
te
m
u
s
in
g
p
o
w
er sys
tems c
o
mp
u
ter a
id
ed
d
esig
n
(
A
ma
n
z
e
C
h
u
kwu
eb
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ka
F
o
r
tu
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e
)
179
[5
]
IEC
(In
ter
n
a
ti
o
n
a
l
El
e
c
tro
tec
h
n
i
c
a
l
Co
m
m
issio
n
)
S
tan
d
a
rd
3
5
4
S
e
c
o
n
d
E
d
it
i
o
n
,
1
9
9
1
-
09,
L
o
a
d
in
g
g
u
i
d
e
fo
r
o
il
-
imme
rs
e
d
p
o
we
r
tra
n
sf
o
rm
e
rs
,
p
p
.
1
4
3
-
1
4
5
,
1
9
9
1
.
[6
]
M.
Kla
se
n
-
M
e
m
m
e
r
a
n
d
H.
Hirsc
h
m
a
n
n
,
“
L
iq
u
id
c
ry
sta
l
m
a
teria
l
s
f
o
r
d
e
v
ice
s
”,
IN
J.
Ch
e
n
,
W.
Cra
n
to
n
a
n
d
M
Fi
h
n
(
e
d
s.)
“
Ha
n
d
b
o
o
k
of
Vi
rt
u
a
l
Disp
la
y
T
e
c
h
n
o
lo
g
y
”,
S
p
ri
n
g
e
r
-
V
e
rlag
Be
rli
n
He
id
e
l
b
e
rg
,
2
0
1
2
.
[7
]
J.
J.
G
ra
in
g
e
r
a
n
d
W.
D.
S
tev
e
n
so
n
,
P
o
we
r
sy
ste
m a
n
d
a
n
a
l
y
sis
,
T
a
ta
Mc
-
G
ra
w
-
Hill
,
2
0
0
5
.
[8
]
E.
A
c
h
a
.
,
V.
Ag
e
li
d
is,
O.
A
n
a
y
a
-
L
a
ra
,
T.
M
il
ler,
Po
we
r
e
lec
tro
n
ic
c
o
n
tro
l
in
e
lec
trica
l
sy
ste
ms
,
Ne
w
n
e
ss
P
o
w
e
r
En
g
in
e
e
rin
g
S
e
ries
2
0
0
2
.
[9
]
S
a
d
o
h
J
,
P
h
D
,
“
T
h
e
sis
on
p
o
w
e
r
s
y
ste
m
p
ro
tec
ti
o
n
:
in
v
e
stig
a
ti
o
n
of
s
y
st
e
m
p
ro
tec
ti
o
n
sc
h
e
m
e
s
on
th
e
3
3
0
KV
of
Nig
e
ria
tran
s
m
issio
n
n
e
tw
o
rk
,
”
Un
iv
e
rsity
of
Be
n
in
,
Be
n
i
n
Cit
y
,
2
0
0
6
.
[1
0
]
L
.
P
.
S
in
g
h
,
Ad
v
a
n
c
e
d
p
o
we
r
sy
ste
m
a
n
a
lys
is
a
n
d
d
y
n
a
mic
s
,
W
il
e
y
,
Ne
w
Yo
rk
,
1
9
8
3
.
[1
1
]
A
n
d
e
rso
n
,
P
a
u
l
M
,
An
a
lys
is
of
fa
u
lt
e
d
p
o
we
r
sy
ste
ms
,
Io
w
a
S
tate
P
re
ss
,
Am
e
s,
1
9
7
3
.
[1
2
]
H.E
.
Br
o
w
n
a
n
d
C.
E.
P
e
rso
n
,
“
S
h
o
rt
c
ircu
it
stu
d
ies
of
larg
e
s
y
ste
m
s
by
th
e
im
p
e
d
a
n
c
e
m
a
tri
x
m
e
th
o
d
,
”
Pro
c
.
PICA
,
p
p.
3
3
5
,
1
9
6
7
.
[1
3
]
S.
Ba
k
a
n
a
g
a
ri,
A.
M
a
h
e
sh
Ku
m
a
r
,
M.
Ch
e
e
n
y
a
,
“
T
h
re
e
p
h
a
se
f
a
u
lt
a
n
a
ly
sis
w
it
h
a
u
to
re
se
t
f
o
r
tem
p
o
ra
ry
f
a
u
lt
a
n
d
tri
p
f
o
r
p
e
rm
a
n
e
n
t
f
a
u
lt
,
”
In
t.
J
o
u
rn
a
l
of
E
n
g
in
e
e
rin
g
R
e
se
a
rc
h
and
A
p
p
li
c
a
ti
o
n
s
,
vol
.
3,
n
o
.
6,
pp.
1
0
8
2
-
1
0
8
6
,
2
0
1
3
.
[1
4
]
G.
V
lad
im
ir,
El
e
c
trica
l
re
la
y
s
p
ri
n
c
ip
le
a
n
d
a
p
p
l
ica
ti
o
n
s
,
T
a
y
lo
r
a
n
d
f
ra
n
c
is
g
ro
u
p
p
u
b
li
c
a
ti
o
n
,
2
0
0
6
.
[1
5
]
D.
M
iro
sla
v
,
F
a
u
lt
a
n
a
lys
is i
n
p
o
we
r sy
ste
ms
b
y
u
sin
g
t
h
e
fo
rte
sc
u
e
me
th
o
d
,
T
ES
LA
In
stit
u
te,
2
0
0
9
.
[1
6
]
J.
Zh
u
.
“
A
n
a
l
y
sis
of
tran
s
m
issio
n
s
y
ste
m
f
a
u
lt
s
th
e
p
h
a
se
do
m
a
in
,
”
T
e
x
a
s
A
&
M
Un
iv
e
rsit
y
.
M
a
ste
r
Th
e
sis,
2
0
0
4
.
[1
7
]
M.
A
lek
sa
n
d
a
r,
“
A
n
a
l
y
sis
of
a
s
y
m
m
e
tri
c
a
l
f
a
u
lt
s
in
p
o
w
e
r
s
y
ste
m
s
u
sin
g
d
y
n
a
m
ic
p
h
a
so
rs
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
on
Po
we
r
S
y
ste
ms
,
v
o
l.
15
,
n
o
.
3
,
p
p
.
1
0
6
2
-
1
0
6
8
,
2
0
0
0
.
[1
8
]
V.
G
a
m
it
,
e
t
a
l
,
“
F
a
u
lt
a
n
a
ly
sis
on
t
h
re
e
p
h
a
se
s
y
ste
m
by
a
u
to
re
c
lo
sin
g
m
e
c
h
a
n
is
m
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
of
Res
e
a
rc
h
in
E
n
g
i
n
e
e
rin
g
a
n
d
T
e
c
h
n
o
lo
g
,
v
o
l
.
4,
n
o
.
5,
p
p
.
2
9
2
-
2
9
8
,
2
0
1
5
.
[1
9
]
T.
M
u
sh
iri
a
n
d
C.
M
b
o
h
w
a
,
“
R
e
se
a
rc
h
on
th
e
u
se
of
M
A
TL
AB
in
th
e
m
o
d
e
li
n
g
of
3
-
p
h
a
se
p
o
w
e
r
s
y
ste
m
s
,
”
Pro
c
e
e
d
in
g
s
of
t
h
e
W
o
rld
Co
n
g
re
ss
on
E
n
g
i
n
e
e
rin
g
(
W
CE
2
0
1
5
)
,
v
o
l.
1
,
2
0
1
5
.
[2
0
]
C.
V
ij
a
y
a
T
h
a
ra
n
i,
e
t
a
l
,
“
M
A
T
LA
B
b
a
se
d
sim
u
latio
n
s
m
o
d
e
l
f
o
r
t
h
re
e
p
h
a
se
s
p
o
w
e
r
s
y
ste
m
n
e
t
w
o
rk
,
”
In
t
.
J
o
u
rn
a
l
fo
r
Res
e
a
rc
h
in
Ap
p
li
e
d
S
c
ien
c
e
&
En
g
in
e
e
rin
g
T
e
c
h
n
o
lo
g
y
,
v
o
l
.
4
,
no
.
1
1
,
p
p
.
5
0
2
-
5
0
9
,
2
0
1
6
.
[2
1
]
A.
A
d
l
y
,
M.
Ch
rist
o
p
h
e
r,
G.
F
a
ll
o
n
,
L.
Da
v
id
,
"A
f
a
u
lt
lo
c
a
ti
o
n
tec
h
n
iq
u
e
f
o
r
ru
ra
l
d
istri
b
u
ti
o
n
f
e
e
d
e
rs,"
IEE
E
tra
n
sa
c
ti
o
n
on
In
d
u
stry
A
p
p
l
ica
ti
o
n
,
v
o
l.
2
9
,
n
o
.
6
,
p
p
.
1
1
7
0
-
1
1
7
5
,
1
9
9
3
.
[2
2
]
N.
Am
j
a
d
y
,
“
De
si
g
n
a
n
d
im
p
li
m
e
n
tatio
n
of
a
f
a
u
lt
d
iag
n
o
sis
s
y
ste
m
f
o
r
tran
s
m
issin
a
n
d
su
b
tran
sm
issio
n
n
e
tw
o
rk
s”
,
IEE
E
p
a
p
e
r
on
tr
a
n
miss
i
o
n
&
d
istrib
u
ti
o
n
c
o
n
.
Exp
.,
v
o
l.
2,
pp
.
69
-
7
0
4
,
2
0
0
3
.
[2
3
]
J.A
.
Ha
ll
u
d
a
y
,
C.
H.
S
h
i
h
,
“
Re
so
n
e
n
t
o
v
e
rv
o
lt
a
g
e
p
h
e
n
o
m
e
n
a
c
o
u
se
d
by
tran
sm
is
sio
n
li
n
e
f
a
u
lt
,
”
IEE
E
tra
n
s.
Po
we
r
a
p
p
a
ra
t
u
s
&
s
y
ste
m
,
v
o
l.
1
0
4
,
n
o
.
9
,
pp.
2
5
3
1
-
2
5
3
9
,
1
9
8
5
.
[2
4
]
D.
C.
Yu
,
D.
Ch
e
n
,
S.
Ra
m
a
s
a
m
y
a
n
d
D.
G.
F
li
n
n
,
“
A
w
in
d
o
w
s
b
a
se
d
g
ra
p
h
ica
l
p
a
c
k
a
g
e
f
o
r
s
y
m
m
e
tri
c
a
l
c
o
m
p
o
n
e
n
ts
a
n
a
ly
sis
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
on
Po
we
r
S
y
ste
ms
,
v
o
l.
10
,
n
o
.
4,
p
p
.
1
7
4
2
-
1
7
4
9
,
1
9
9
5
.
[2
5
]
M.
Yu
e
n
Ch
o
w
,
S.
L
e
ro
y
,
“A
n
o
v
e
l
a
p
p
ro
a
c
h
f
o
r
d
istri
b
u
ti
o
n
fa
u
lt
a
n
a
l
y
sis
,
”
IEE
E
T
ra
n
sa
c
t
io
n
s
on
P
o
we
r
De
li
v
e
ry
,
v
o
l
.
8
,
n
o
.
4
,
pp.
1
8
8
2
-
1
8
8
9
,
1
9
9
3
.
B
I
O
G
RAP
H
I
E
S
OF
AUTH
O
RS
F
o
rtu
n
e
Ch
u
k
w
u
e
b
u
k
a
Am
a
n
z
e
is
a
g
ra
d
u
a
te
re
se
a
r
c
h
e
r
a
t
th
e
De
p
a
rtm
e
n
t
o
f
El
e
c
tri
c
a
l
En
g
in
e
e
rin
g
,
Un
iv
e
rsity
o
f
Nig
e
ri
a
,
Ns
u
k
k
a
in
En
u
g
u
S
tate
Nig
e
ria.
His
re
se
a
rc
h
in
tere
sts
a
re
in
P
o
w
e
r
S
y
te
m
s,
P
o
w
e
r
El
e
c
tro
n
ics
a
n
d
C
o
n
tr
o
l
S
y
ste
m
s E
n
g
in
e
e
rin
g
.
De
stin
y
Jo
sia
h
Am
a
n
z
e
is
a
g
ra
d
u
a
te
re
se
a
rc
h
e
r
w
h
o
h
a
s
a
f
lair
f
o
r
En
e
rg
y
s
y
ste
m
s
a
n
d
e
ff
ici
e
n
t
u
ti
li
z
a
ti
o
n
o
f
En
e
rg
y
.
His
re
s
e
a
rc
h
a
p
p
r
o
a
c
h
is
a
im
e
d
a
t
se
e
k
in
g
a
lt
e
rn
a
ti
v
e
s
to
a
lrea
d
y
e
x
isti
n
g
e
n
e
rg
y
so
u
rc
e
s a
n
d
e
ff
icie
n
t
u
se
o
f
c
u
rre
n
t
e
n
e
rg
y
so
u
rc
e
s to
in
c
re
a
se
p
ro
d
u
c
ti
v
it
y
.
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