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T
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.
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7]
v
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.
A
po
w
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m
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wo
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t
w
or
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a
s
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n in
[9
-
16
]
.
AN
N
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n
c
l
ude
s
m
a
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y c
om
po
ne
nt
s
;
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h
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Ne
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a
s
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i
g
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1
[1
7
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.
Th
i
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ac
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ear
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In
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3
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[
14]
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[1
6
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,
v
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.
In
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8
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, a
n
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N
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In
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9
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,
t
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.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-
87
08
I
nt
J
E
l
e
c
&
C
om
p
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n
g,
V
o
l
.
11
,
No
.
1,
F
e
b
r
ua
r
y
2
02
1
:
124
-
1
32
1
26
2.
TH
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EW
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E
S
T
A
BI
LI
TY
I
N
D
E
X
(
N
L
S
I_
1
)
S
t
a
t
i
c
v
o
l
t
a
g
e
s
t
a
b
i
l
i
t
y
a
n
a
l
y
s
i
s
i
n
v
o
l
v
e
s
t
h
e
d
e
t
e
r
m
i
n
a
t
i
o
n
o
f
a
s
t
a
b
i
l
i
t
y
i
n
d
i
c
a
t
o
r
s
u
c
h
a
s
P
-
V
a
nd
Q
-
V
c
u
r
ve
s
,
e
i
ge
n
va
l
ue
s
de
c
om
po
s
i
t
i
on.
T
he
s
e
i
n
d
i
cat
o
r
s
g
i
v
e a
n
ap
p
r
o
x
i
m
at
e
v
al
u
e
o
f
t
h
e d
i
s
t
an
ce o
f
t
h
e
s
y
s
t
e
m
'
s
c
u
r
r
e
n
t
o
p
e
r
a
t
i
n
g
p
o
i
n
t
t
o
v
o
l
t
a
g
e
co
l
l
ap
s
e.
S
o
m
e
o
f
t
h
es
e
i
n
d
i
cat
o
r
s
r
e
q
u
i
r
e
t
ed
i
o
u
s
an
d
d
i
f
f
i
cu
l
t
c
om
put
a
t
i
o
n,
a
nd
t
hi
s
ha
s
m
a
de
t
he
m
un
s
ui
t
a
bl
e
f
or
o
nl
i
ne
vol
t
a
ge
s
t
a
bi
l
i
t
y
a
na
l
ys
i
s
[2
1
]
.
T
he
s
ho
r
t
c
o
m
i
ngs
,
a
s
m
e
nt
i
o
ne
d e
a
r
l
i
e
r
on
,
of
s
om
e
of
t
h
e
s
e
i
ndi
c
a
t
o
r
s
,
a
r
e
o
ve
r
c
om
e
by
v
o
l
t
a
g
e
s
t
a
b
i
l
i
t
y
i
n
d
i
c
e
s
(
V
S
I
s
)
[2
2
,
2
3
]
.
O
n
e
of
s
u
c
h ind
ic
e
s
i
s
t
he
NL
S
I
_
1
pr
o
pos
e
d
i
n
[2
0
]
,
w
h
o
s
e
v
a
l
u
e
f
a
l
l
s
b
et
w
ee
n
z
er
o
an
d
o
ne
.
T
he
b
u
s
,
w
h
os
e
i
nde
x
va
l
ue
i
s
t
he
hi
ghe
s
t
i
n
t
h
e
s
y
s
t
e
m
,
i
s
l
a
be
l
l
e
d
t
he
we
a
ke
s
t
bus
i
n
t
h
e
s
y
s
t
e
m
.
T
h
e
N
L
S
I
_1
is
ob
ta
in
e
d f
r
om
t
h
e
c
o
m
b
i
n
a
t
i
o
n
o
f
t
h
e
l
i
n
e
s
t
a
b
i
l
i
t
y
i
n
d
e
x
(
L
mn
)
a
nd th
e
f
a
s
t
vol
t
a
ge
s
t
a
bi
l
i
t
y
i
n
de
x
(
F
S
V
I
)
t
hr
o
ug
h
a
bi
na
r
y
s
w
i
t
c
hi
ng
f
u
nc
t
i
on
(
σ
)
,
a
s
s
ho
w
n
i
n
(
1)
.
T
h
e v
al
u
e
o
f
t
he
s
wi
t
c
hi
n
g
f
unc
t
i
o
n
σ
i
s
de
t
e
r
m
i
ne
d
by
t
h
e
m
a
gni
t
u
de
o
f
t
he
a
n
gul
a
r
di
f
f
e
r
e
nc
e
be
t
w
e
e
n
t
he
s
e
n
di
n
g
a
n
d
r
e
c
e
i
vi
n
g e
nd
vol
t
a
ge
s
.
T
o
ex
a
m
i
n
e
w
h
e
t
h
e
r
σ
i
s
1
o
r
0
,
t
h
e
v
a
l
u
e
s
o
f
v
o
l
t
a
g
e
a
n
g
l
e
(
δ
)
c
o
m
p
u
t
e
d
f
r
o
m
t
h
e
l
o
a
d
-
fl
o
w p
ro
g
ra
m
i
s
c
o
m
p
a
re
d
w
i
t
h
a
t
h
r
e
s
h
ol
d
va
l
ue
.
(
)
(
)
1
1
s
in
4
1
_
2
2
2
1
2
≤
−
−
=
σ
σ
x
x
Z
V
Q
N
LSI
=
0
1
σ
δ
δ
≥
c
c
δ
δ
(
1)
3.
MA
T
E
R
I
A
L
S
A
ND
ME
T
H
O
DS
T
he
pr
o
pos
e
d m
e
t
ho
d
ol
o
gy
f
or
v
ol
t
a
ge
c
ol
l
a
ps
e
pr
e
di
c
t
i
on
i
s
ba
s
e
d o
n
the
a
r
t
i
f
i
c
i
a
l
n
e
u
r
a
l
n
e
t
w
o
r
k
.
T
h
e
a
i
m
o
f
t
h
i
s
i
s
t
o
p
r
e
d
i
c
t
t
h
e
p
r
o
x
i
m
i
t
y
t
o
v
o
l
t
a
g
e
i
n
s
t
a
b
i
l
i
t
y
a
n
d
r
a
n
k
t
h
e
r
e
s
u
l
t
a
n
t
v
o
l
t
a
g
e
c
o
l
l
a
p
s
e
a
c
c
or
di
n
g t
o
i
t
s
s
e
v
e
r
i
t
y
i
f
i
t
o
c
c
u
r
s
.
T
h
i
s
r
e
s
e
a
r
c
h
pa
pe
r
p
r
o
p
os
e
s
a
n onl
i
ne
v
ol
t
a
ge
s
t
a
bi
l
i
t
y
a
na
l
ys
i
s
m
o
de
l
us
i
n
g
t
he
m
ul
t
i
l
a
ye
r
pe
r
c
e
pt
r
o
n
ne
u
r
a
l
ne
t
w
o
r
k
(
ML
P
N
N
)
a
nd
a
vol
t
a
ge
s
t
a
bi
l
i
t
y
i
ndi
c
a
t
o
r
c
a
l
l
e
d
t
he
n
ew
l
i
n
e
s
t
a
b
i
l
i
t
y
i
n
d
e
x
(N
L
S
I
_
1
).
3.
1.
G
e
n
e
r
a
t
i
on
of
t
r
ai
n
i
n
g
d
at
a
T
he
ge
ne
r
a
t
i
o
n
o
f
t
he
a
p
pr
o
pr
i
a
t
e
t
r
a
i
ni
n
g
da
t
a
i
s
of
ut
m
os
t
i
m
p
or
t
a
n
c
e
i
n
t
he
de
ve
l
opm
e
nt
a
n
d
de
pl
oy
m
e
nt
of
a
ny
m
a
c
hi
ne
l
e
a
r
ni
n
g s
ol
u
t
i
ons
.
F
o
r
ne
u
r
a
l
ne
t
w
or
ks
t
o c
o
r
r
e
c
t
l
y
p
r
e
di
c
t
t
he
o
ut
p
ut
of
a
s
ys
t
e
m
,
t
he
t
r
a
i
ni
n
g
da
t
a
us
e
d s
h
oul
d
r
e
p
r
e
s
e
nt
a
b
r
oa
d
s
pe
c
t
r
um
o
f
op
e
r
a
t
i
ng
p
oi
nt
s
of
t
he
p
r
o
bl
e
m
be
i
ng
c
on
s
i
de
r
e
d.
I
n
t
hi
s
pa
pe
r
,
a
c
o
ns
i
de
r
a
bl
e
nu
m
be
r
o
f
t
r
a
i
ni
ng
da
t
a
i
s
got
t
e
n
vi
a
o
f
f
-
l
i
n
e
p
o
w
e
r
s
y
s
t
e
m
s
i
m
u
l
a
t
i
o
n
u
s
i
n
g
t
h
e
f
o
l
l
o
w
i
n
g
p
r
o
c
e
d
u
r
e
:
−
A
r
a
n
ge
o
f
op
e
r
a
t
i
ng
p
oi
nt
s
i
s
pr
od
uc
e
d
by
va
r
yi
n
g t
he
r
e
a
c
t
i
v
e
p
ow
e
r
r
a
nd
om
l
y a
t
only
th
e
l
oa
d b
us
e
s
onl
y
f
r
om
t
he
ba
s
e
c
a
s
e
va
l
u
e
u
nt
i
l
t
he
vol
t
a
ge
c
ol
l
a
ps
e
oc
c
ur
r
e
d
.
−
F
or
e
a
c
h i
np
ut
-
out
put
pa
t
t
e
r
n ge
ne
r
a
t
e
d,
pr
e
-
c
o
nt
i
n
ge
nc
y l
i
ne
f
l
o
w
s
a
r
e
o
bt
a
i
ne
d b
y
pe
r
f
o
r
m
i
n
g
t
he
Ne
wt
o
n
R
a
phs
o
n
l
oa
d
f
l
o
w
a
na
l
ys
i
s
.
−
F
i
n
a
l
l
y
,
f
o
r
ea
ch
i
n
p
u
t
-
out
put
pa
t
t
e
r
n
,
t
he
N
L
S
I
_
1
i
s
e
va
l
ua
t
e
d
t
o
a
s
c
e
r
t
a
i
n
i
f
t
he
s
ys
t
e
m
i
s
s
t
a
bl
e
or
n
ot
.
A
t
o
t
a
l
of
342
0
inpu
t
-
out
p
ut
pa
t
t
e
r
ns
w
e
r
e
pr
o
duc
e
d
f
or
t
he
I
E
E
E
14
-
bu
s
s
y
s
te
m
a
f
te
r
u
s
ing
t
h
e ab
o
v
e p
r
o
ced
u
r
e;
t
h
at
i
s
3
8
0
s
a
m
p
l
es
p
er
l
o
ad
b
u
s
,
an
d
a t
o
t
al
of
2
9,
450
inpu
t
-
out
put
pa
t
t
e
r
n
s
w
er
e
pr
o
duc
e
d
f
or
t
he
N
NG
28
-
b
us
s
ys
t
e
m
t
ha
t
i
s
1
55
0
s
a
m
pl
e
s
pe
r
l
oa
d b
u
s
.
T
he
ge
ne
r
a
t
e
d da
t
a
s
a
m
pl
e
s
pe
r
l
oa
d
b
us
we
r
e
c
onc
a
t
e
na
t
e
d
i
n
a
n
e
xc
e
l
s
pr
e
a
ds
he
e
t
t
o
f
o
r
m
t
he
da
t
a
s
e
t
s
i
n
t
hi
s
s
t
ud
y.
3.
2.
S
el
ect
i
o
n
o
f
i
n
p
u
t
f
ea
t
u
res
I
n
p
u
t
f
eat
u
r
e s
el
ect
i
o
n
i
s
a
v
i
t
a
l
a
s
p
e
c
t
i
n
t
h
e
d
e
v
e
l
o
p
m
e
n
t
o
f
a
n
e
x
c
e
l
l
e
n
t
a
r
t
i
f
i
c
i
a
l
n
e
u
r
a
l
n
e
t
w
o
r
k
m
o
de
l
.
I
n t
hi
s
pa
pe
r
,
i
n
p
ut
f
e
a
t
ur
e
s
we
r
e
s
e
l
e
c
t
e
d ba
s
e
d
on t
he
r
e
qui
r
e
d va
r
i
a
bl
e
s
n
e
e
de
d t
o c
o
m
put
e
t
h
e N
L
S
I
_
1
,
a
s
s
een
i
n
[2
4
]
.
T
h
es
e
v
ar
i
a
b
l
es
ar
e r
eact
i
v
e
p
o
w
e
r
f
l
o
w
i
n
g
t
h
e l
i
n
e
s
(
Q
)
,
s
e
n
di
n
g e
nd
vol
t
a
ge
(V
S
)
,
i
m
p
e
d
a
n
c
e
(Z
),
l
i
n
e
re
a
c
t
a
n
c
e
(
X)
,
t
ra
n
s
m
i
s
s
i
o
n
l
i
n
e
a
n
g
l
e
(θ
),
d
e
l
t
a
(δ)
,
a
n
d
s
wi
t
c
h
i
n
g
f
u
n
c
t
i
o
n
(σ
).
3.
3.
D
at
a
n
o
r
m
al
i
z
at
i
on
T
h
i
s
r
e
s
e
a
r
c
h
w
o
r
k
u
t
i
l
i
z
e
s
t
h
e
m
i
n
-
m
a
x
d
a
t
a
n
o
r
m
a
l
i
z
a
t
i
o
n
to
im
p
r
ove
t
r
a
i
n
i
n
g
t
i
m
e
,
m
i
n
i
m
i
z
e
t
h
e s
i
ze
o
f
t
h
e i
n
p
u
t
s
p
ace,
i
n
cr
eas
e t
h
e
r
o
b
u
s
t
n
es
s
o
f
t
h
e i
m
p
l
em
en
t
ed
n
eu
r
al
n
et
w
o
r
k
s
,
a
n
d
r
e
d
u
ce
t
h
e ch
a
n
ces
o
f
e
ndi
ng up
i
n
l
o
c
a
l
o
p
t
i
m
a
[2
5
]
.
T
he
i
n
put
da
t
a
i
s
no
r
m
a
l
i
z
e
d be
t
we
e
n
z
e
r
o a
nd
o
ne
us
i
n
g
t
he
e
x
p
r
e
s
s
i
o
n
gi
ve
n
i
n
(
2)
.
(
)
min
m
ax
min
X
X
X
X
X
n
−
−
=
(2
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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J
E
l
e
c
&
C
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p
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n
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I
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N
:
208
8
-
87
08
V
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c
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p
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i
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c
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a
l
ne
u
r
al
n
e
t
wo
r
k
(
S
am
ue
l
I
s
aa
c
)
1
27
3.
4.
Mu
l
t
i
-
l
a
y
er
p
ercep
t
ro
n
n
eu
ra
l
n
et
w
o
r
k
(M
L
P
N
N
)
ML
P
N
Ns
a
r
e
a
ki
nd
of
f
e
e
d
-
fo
rw
a
r
d
a
r
t
i
f
i
c
i
a
l
n
e
u
r
a
l
n
e
t
w
o
r
k
s
,
w
h
i
c
h
c
o
n
s
i
s
t
s
o
f
a
t
l
e
a
s
t
t
h
r
e
e
l
a
y
er
s
:
a
n
i
n
put la
y
e
r
,
on
e
or
m
or
e
h
idd
e
n la
y
e
r
(
s
)
,
a
nd
a
n ou
t
pu
t la
y
e
r
,
a
s
s
how
n in F
igu
r
e
2
.
I
n
m
u
l
t
i
l
a
y
e
r
pe
r
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e
pt
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on
ne
u
r
a
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ks
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t
he
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ur
on
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w
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np
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ul
t
i
pl
e
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g
ht
s
a
nd
bi
a
s
e
s
c
o
n
ne
c
t
e
d
t
o e
a
c
h
ne
ur
o
n.
T
he
we
i
ght
e
d s
um
o
f
t
he
i
n
put
s
i
s
t
he
n
pa
s
s
e
d t
o
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ns
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m
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d t
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he
us
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n
f
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na
l
l
y
,
t
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out
pu
t
l
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ye
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pr
e
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nt
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p
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o
f
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ne
t
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k b
y c
ha
ngi
n
g t
he
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d
de
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ye
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a
c
t
i
va
t
i
o
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nt
o w
ha
t
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ve
r
s
c
a
l
e
t
he
o
ut
p
ut
r
e
q
u
i
r
e
d
t
o be
.
F
ig
ur
e
2.
B
as
i
c
l
ay
er
s
o
f
a
n
M
L
P
N
N
4.
R
E
S
U
L
T
S
A
ND
DI
S
C
U
S
S
I
O
N
T
h
i
s
s
e
c
t
i
o
n
p
r
e
s
e
n
t
s
t
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e
r
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s
u
l
t
s
o
b
t
a
i
n
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d
f
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m
t
h
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s
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m
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l
a
t
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o
n
s
c
a
r
r
i
e
d
o
u
t
o
n
t
h
e
I
E
E
E
1
4
-
b
u
s
s
ys
t
e
m
a
nd t
h
e
N
i
ge
r
i
a
n
28
-
bus
s
ys
t
e
m
.
F
or
b
ot
h t
e
s
t
s
y
s
t
e
m
s
,
ba
s
e
c
a
s
e
a
n
d c
o
nt
i
n
g
e
nc
y a
na
l
ys
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s
we
r
e
c
o
ndu
c
te
d,
a
n
d
A
NN
m
o
de
l
s
we
r
e
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ve
l
o
pe
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in M
A
T
L
A
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'
s
n
e
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r
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o
p
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c
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d
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v
el
o
p
ed
ar
e
a
l
s
o
gi
ve
n
a
s
f
ol
l
ows
:
4.
1.
V
ol
t
a
ge
c
ol
l
ap
s
e
p
r
e
d
i
c
t
i
on
on
i
e
e
e
14
-
bus
S
Y
S
T
EM
V
ol
t
a
ge
c
ol
l
a
p
s
e
pr
e
di
c
t
i
on
f
or
l
oa
d
b
us
e
s
i
n t
he
I
E
E
E
1
4
-
bu
s
n
e
t
w
or
k w
a
s
c
a
r
r
i
e
d o
ut
us
i
ng
an
M
L
PN
N
.
T
he
de
ve
l
ope
d
ML
P
N
N
ha
s
one
i
np
ut
l
a
ye
r
,
t
w
o
hi
dde
n
l
a
ye
r
s
,
a
n
d
a
n
o
ut
p
ut
l
a
ye
r
.
T
a
bl
e
1
s
h
o
w
s
t
h
e n
eu
r
al
ne
t
w
o
r
k
pr
e
di
c
t
i
o
n
f
or
b
as
e
cas
e
a
n
a
l
y
s
i
s
, a
n
d
fo
r
c
om
pa
r
is
o
n
pu
r
pos
e
,
t
h
e ac
t
u
al
i
n
d
ex
v
al
u
es
ar
e
a
l
s
o
g
i
v
e
n
.
F
r
o
m
t
h
e
t
a
b
l
e
,
i
t
i
s
s
e
e
n
t
h
a
t
a
l
l
t
h
e
b
u
s
e
s
a
n
d
i
n
t
e
r
c
o
n
n
e
c
t
e
d
l
i
n
e
s
i
n
t
h
e
I
E
E
E
1
4
-
bu
s
s
ys
te
m
a
r
e
s
t
a
b
l
e
;
a
s
i
ndi
c
a
t
e
d b
y a
n i
nde
x
va
l
ue
b
ei
n
g
b
e
low
T
a
bl
e
1.
Th
e
r
e
su
l
t
s
a
ls
o
s
how
t
he
ne
gl
i
gi
bl
e
e
r
r
or
b
e
t
w
e
e
n
t
h
e
a
c
t
u
a
l
w
i
t
h
t
h
e
pr
e
di
c
t
e
d
i
nde
x
v
a
l
ue
s
.
T
ab
l
e
1
.
C
o
m
p
ar
i
s
o
n
o
f
b
as
e
cas
e
act
u
al
w
i
t
h
t
h
e
p
r
e
di
c
t
e
d
i
nde
x
va
l
ue
s
Ba
se
Ca
se
F
ro
m
To
Actu
al v
alu
e*
Pr
ed
icted
v
alu
e
Erro
rs
State
1
2
0.
0279
5
0.
0279
4
0.
0000
1
Stab
le
1
5
0.
0897
1
0.
0896
8
0.
0000
3
Stab
le
2
3
0.
0104
3
0.
0104
6
-
0.
00003
Stab
le
2
5
0.
0173
9
0.
0095
4
0.
0078
5
Stab
le
5
6
0.
0269
8
0.
0269
6
0.
0000
2
Stab
le
6
11
0.
1023
9
0.
1024
2
-
0.
00002
Stab
le
6
12
0.
0108
6
0.
0108
9
-
0.
00003
Stab
le
6
13
0.
0772
9
0.
0773
1
-
0.
00002
Stab
le
7
8
0.
1610
8
0.
1611
3
-
0.
00005
Stab
le
7
9
0.
0920
7
0.
0923
9
-
0.
00032
Stab
le
9
10
0.
0571
2
0.
0568
5
0.
0002
7
Stab
le
9
14
0.
0361
8
0.
0328
2
0.
0033
6
Stab
le
10
11
0.
0562
3
0.
0555
4
0.
0006
9
Stab
le
12
13
0.
0688
2
0.
0713
8
-
0.
00256
Stab
le
13
14
0.
0766
2
0.
0768
4
-
0.
00022
Stab
le
*A
dopt
e
d f
r
om
(
S
am
u
el et
al.
,
2
0
1
7
)
T
ab
l
e 2
p
r
es
e
n
t
s
t
h
e a
ct
u
al
a
n
d
p
r
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d
i
ct
ed
i
n
d
ex
v
al
u
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s
at
m
ax
i
m
u
m
r
eact
i
v
e
p
o
w
e
r
l
o
ad
i
n
g
f
o
r
eac
h
of
t
he
l
oa
d
b
us
e
s
,
a
l
o
n
g
w
i
t
h t
he
r
a
n
ki
n
g
o
f
t
he
c
o
nt
i
nge
nc
i
e
s
a
n
d
t
he
s
t
a
t
e
s
of
t
he
l
i
ne
s
ba
s
e
d
o
n
t
he
p
r
e
di
c
t
e
d i
nde
x
va
l
ue
f
r
o
m
m
o
s
t
c
r
i
t
i
c
a
l
t
o
l
e
a
s
t
c
r
i
t
i
c
a
l
.
F
r
o
m
t
h
e
t
a
b
l
e
,
t
h
e
e
r
r
o
r
w
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x
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s
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s
b
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n
t
he
a
c
t
ua
l
a
n
d
p
r
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di
c
t
e
d i
nd
e
x
va
l
ue
s
i
s
m
i
ni
m
a
l
,
w
hi
c
h
va
l
i
da
t
e
s
t
h
e
p
r
o
p
os
e
d a
p
pr
oa
c
h.
T
he
r
e
s
ul
t
s
obt
a
i
ne
d
f
r
o
m
t
he
de
ve
l
o
pe
d
ML
P
N
N
c
on
f
i
r
m
t
h
os
e
o
bt
a
i
n
e
d
b
y
[1
,
2
0
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-
87
08
I
nt
J
E
l
e
c
&
C
om
p
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n
g,
V
o
l
.
11
,
No
.
1,
F
e
b
r
ua
r
y
2
02
1
:
124
-
1
32
1
28
T
ab
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d
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a
b
i
l
i
t
y
F
ro
m
To
Actu
al v
alu
e
*
Pr
ed
icted
v
alu
e
R
an
k
**
State
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M
Var
L
o
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*
Bu
s 4
3
4
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2
1
C
r
itical
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6
1
2
4
0.
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9
0.
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5
2
C
r
itical
4
7
0.
4752
9
0.
4753
9
3
Stab
le
4
5
0.
4454
6
0.
4454
8
4
Stab
le
4
9
0.
3875
5
0.
3874
7
5
Stab
le
Bu
s 5
1
5
1.
0916
4
1.
0919
1
1
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o
llap
s
ed
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=
352.
5
5
6
0.
8805
5
0.
8805
0
2
C
r
itical
2
5
0.
8637
3
0.
8637
3
3
C
r
itical
4
5
0.
3773
7
0.
3773
9
4
Stab
le
Bu
s 7
7
8
0.
9938
4
0.
9938
8
1
C
r
itical
Q
=
165.
5
4
7
0.
7167
7
0.
7152
4
2
Str
es
s
ed
7
9
0.
1924
9
0.
1908
1
3
Stab
le
Bu
s 9
4
9
1.
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6
0.
9985
7
1
C
r
itical
Q
=
152.
5
7
9
0.
6134
4
0.
6119
2
2
Str
es
s
ed
9
10
0.
2150
9
0.
2168
4
3
Stab
le
9
14
0.
4764
4
0.
4769
7
4
Stab
le
Bu
s 1
0
10
11
0.
9564
4
0.
9585
0
1
C
r
itical
Q =
121.
8
9
10
0.
6037
7
0.
5693
4
2
Str
es
s
ed
Bu
s 1
1
6
11
0.
9269
4
0.
9270
4
1
C
r
itical
Q
=
103.
8
10
11
0.
4481
5
0.
4530
6
2
Stab
le
Bu
s 1
2
12
13
1.
0660
7
1.
0660
7
1
C
o
llap
s
ed
Q = 7
8
.
9
6
12
0.
7622
2
0.
7622
1
2
C
r
itical
Bu
s 1
3
6
13
0.
9258
5
0.
9258
3
1
C
r
itical
Q
=
151.
8
12
13
0.
6339
5
0.
6341
3
2
C
r
itical
13
14
0.
5445
3
0.
5428
7
3
C
r
itical
Bu
s 1
4
13
14
0.
9233
8
0.
9233
9
1
C
r
itical
Q = 7
4
.
6
9
14
0.
8623
2
0.
8623
3
2
C
r
itical
*A
dopt
e
d f
r
om
(
S
am
u
el et
al.
,
2
0
1
7
)
*
*
B
as
ed
o
n
th
e p
r
ed
icted
v
alu
e
T
ab
l
e 3
s
h
o
w
s
t
he
r
a
nki
n
g o
f
bu
s
e
s
i
n t
he
I
E
E
E
-
14
b
us
s
y
s
t
e
m
i
n a
s
c
e
nd
i
ng
or
de
r
f
r
o
m
w
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a
k
e
s
t
t
o
s
t
r
o
n
g
e
s
t
.
F
r
o
m
t
h
e
t
a
b
l
e
,
b
u
s
1
4
w
a
s
i
d
e
n
t
i
f
i
e
d
a
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p
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m
a
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gi
n
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f
7
4.
5 M
V
a
r
a
nd
a
pe
r
c
e
nt
a
ge
c
ha
n
ge
of
38
.
3
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i
n
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e
v
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t
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ge
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a
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ude
.
T
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ce w
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r
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i
s
t
e
d
i
n
[2
6
]
.
T
he
r
e
s
ul
t
s
ob
ta
in
e
d by
t
h
e
de
ve
l
ope
d
n
e
ur
a
l
ne
t
w
o
r
k
ar
e
i
n
a
gr
e
e
m
e
nt
wi
t
h
t
h
os
e
o
bt
a
i
ne
d
b
y
t
h
e
a
u
t
h
o
r
s
i
n
[1
,
1
3
,
1
5
,
1
8
,
1
9
,
2
7
].
T
ab
l
e
3
.
B
us
r
a
nki
ng
i
n
t
he
I
E
E
E
1
4
-
bu
s
sy
st
e
m
L
oa
d B
us
N
o
F
ro
m
To
Q
m
ax
Pr
ed
icted
v
alu
e
R
a
nki
ng
14
13
14
74.
6
0.
9233
9
1
12
12
13
78.
9
1.
0660
7
2
11
6
11
103.
8
0.
9270
4
3
10
10
11
121.
8
0.
9585
0
4
13
6
13
151.
8
0.
9258
3
5
9
4
9
152.
5
0.
9985
7
6
7
7
8
165.
5
0.
9938
8
7
5
1
5
352.
5
1.
0919
1
8
4
3
4
361
0.
9473
2
9
I
t w
a
s
a
ls
o
o
bs
e
r
v
e
d
t
h
a
t
b
u
s
e
s
w
i
t
h
m
a
n
y
i
n
t
e
r
c
o
n
n
e
c
t
e
d
l
i
n
e
s
t
e
n
d
t
o
h
a
v
e
h
i
g
h
e
r
r
e
a
c
t
i
v
e
p
o
w
e
r
m
a
r
gi
ns
a
n
d t
hi
s
i
s
be
c
a
us
e
,
wi
t
h
m
o
r
e
l
i
n
e
s
,
a
n
y i
nc
r
e
a
s
e
i
n r
e
a
c
t
i
ve
p
ow
e
r
c
a
n
be
a
pp
o
r
t
i
one
d a
m
on
gs
t
t
h
e
l
i
n
e
s
[
1,
19,
2
0]
.
W
i
t
h
t
he
de
ve
l
ope
d
ne
ur
a
l
ne
t
wo
r
k
m
o
de
l
,
b
e
i
n
g
pr
opo
s
e
d in t
h
is
p
a
p
e
r
,
a
n R
-
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al
u
e o
f
0.
99
7
45 a
n
d a
n M
S
E
v
a
l
ue
o
f
2.
1
82
4
15
×
10
−
5
w
er
e
ob
t
a
i
n
e
d
a
f
t
e
r
c
r
o
s
s
-
va
l
i
da
t
i
on
w
a
s
c
a
r
r
i
e
d
out
t
o
s
ol
ve
t
he
i
nhe
r
e
nt
s
t
a
bi
l
i
t
y
pr
obl
e
m
f
a
c
e
d
b
y
A
N
N
.
W
he
n
c
o
m
pa
r
e
d
wi
t
h
t
h
e
r
e
s
ul
t
s
o
bt
a
i
n
e
d
i
n
[1
9
]
,
t
he
pr
o
pos
e
d
a
pp
r
oa
c
h
wa
s
f
ou
n
d
t
o
be
s
up
e
r
i
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i
n
t
e
r
m
s
o
f
be
t
t
e
r
a
c
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ur
a
c
y
a
nd
ge
ne
r
a
l
i
z
a
t
i
on
of
t
he
d
e
ve
l
o
p
e
d
m
o
d
el
.
4.
2.
V
ol
t
a
ge
c
ol
l
ap
s
e
p
r
e
d
i
c
t
i
on
on
N
N
G
28
-
b
u
s
sy
st
e
m
V
ol
t
a
ge
c
ol
l
a
p
s
e
pr
e
di
c
t
i
o
n f
or
l
oa
d
b
us
e
s
i
n
t
he
N
N
G
3
3
0k
V
28
-
bus
ne
t
w
o
r
k
w
a
s
c
a
r
r
i
e
d o
ut
us
in
g
a
n ML
P
N
N
.
Th
e
de
ve
l
ope
d
ML
P
N
N
ha
s
o
ne
i
n
p
ut
l
a
ye
r
,
t
hr
e
e
hi
d
de
n l
a
ye
r
s
,
a
nd t
he
out
put
l
a
ye
r
.
T
ab
l
e
4
pr
e
s
e
nt
s
t
he
p
r
e
di
c
t
e
d
i
nd
e
x
va
l
ue
s
us
i
n
g
t
h
e
de
ve
l
o
pe
d
M
L
P
N
N
m
o
de
l
fo
r
b
as
e
ca
s
e
an
a
l
y
s
i
s
,
an
d
t
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act
u
al
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nde
x
va
l
ue
s
a
r
e
a
l
s
o
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h
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n
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or
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om
pa
r
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s
o
n
.
It
i
s
o
b
s
e
rv
e
d
fr
o
m
T
ab
l
e
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,
t
h
at
al
l
t
h
e
b
u
s
e
s
an
d
i
n
t
e
r
co
n
n
ect
ed
l
i
n
e
s
i
n
t
h
e
n
e
t
w
o
r
k
a
r
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s
t
a
b
l
e
,
as
i
n
d
i
cat
ed
b
y
t
h
e
i
n
d
ex
v
al
u
es
t
h
at
ar
e
be
l
ow
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
E
l
e
c
&
C
om
p
E
n
g
I
S
S
N
:
208
8
-
87
08
V
o
l
t
a
g
e
c
o
l
l
a
p
s
e
p
r
e
d
i
c
t
i
o
n
u
s
i
n
g
a
r
t
i
f
i
c
i
a
l
ne
u
r
al
n
e
t
wo
r
k
(
S
am
ue
l
I
s
aa
c
)
1
29
T
ab
l
e
4
.
C
o
m
p
ar
i
s
o
n
o
f
b
as
e
cas
e
act
u
al
w
i
t
h
t
h
e
p
r
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di
c
t
e
d
i
nde
x
va
l
ue
s
Ba
se
Ca
se
F
ro
m
To
Actu
al v
alu
e*
Pr
ed
icted
v
alu
e
Erro
rs
State
3
1
0.
0341
2
0.
0322
9
0.
0018
4
Stab
le
4
5
0.
0560
8
0.
0551
3
0.
0009
5
Stab
le
1
5
0.
2160
2
0.
2158
4
0.
0001
8
Stab
le
5
8
0.
3479
7
0.
3478
1
0.
0001
7
Stab
le
5
9
0.
1373
7
0.
1372
9
0.
0000
8
Stab
le
5
10
0.
0815
5
0.
0806
5
0.
0009
0
Stab
le
6
8
0.
0229
1
0.
0229
6
-
0.
00004
Stab
le
2
8
0.
1260
3
0.
1266
2
-
0.
00059
Stab
le
2
7
0.
0122
0
0.
0124
2
-
0.
00022
Stab
le
7
24
0.
0155
7
0.
0155
6
0.
0000
1
Stab
le
8
14
0.
1876
9
0.
1884
9
-
0.
00080
Stab
le
8
10
0.
1684
7
0.
1686
3
-
0.
00016
Stab
le
8
24
0.
1568
7
0.
1564
6
0.
0004
0
Stab
le
9
10
0.
1387
1
0.
1387
3
-
0.
00001
Stab
le
15
21
0.
3091
3
0.
3083
4
0.
0007
9
Stab
le
10
17
0.
0624
7
0.
0619
0
0.
0005
8
Stab
le
11
12
0.
1481
4
0.
1481
7
-
0.
00004
Stab
le
12
14
0.
1547
8
0.
1541
6
0.
0006
2
Stab
le
13
14
0.
1804
8
0.
1805
3
-
0.
00005
Stab
le
16
19
0.
2675
7
0.
2672
4
0.
0003
3
Stab
le
17
18
0.
0108
5
0.
0109
9
-
0.
00014
Stab
le
17
23
0.
1889
0
0.
1890
4
-
0.
00014
Stab
le
17
21
0.
0523
7
0.
0514
1
0.
0009
5
Stab
le
19
20
0.
1244
7
0.
1245
3
-
0.
00006
Stab
le
20
22
0.
4181
8
0.
4180
9
0.
0000
9
Stab
le
20
23
0.
3039
4
0.
3036
4
0.
0003
0
Stab
le
23
26
0.
1438
8
0.
1431
0
0.
0007
7
Stab
le
12
25
0.
2550
9
0.
2550
7
0.
0000
2
Stab
le
19
25
0.
0308
6
0.
0310
3
-
0.
00017
Stab
le
25
27
0.
2162
7
0.
2167
0
-
0.
00043
Stab
le
5
28
0.
2062
6
0.
2063
2
-
0.
00006
Stab
le
*A
dopt
e
d f
r
om
(
S
am
u
el et
al.
,
2
0
1
9
)
T
ab
l
e
5
(
s
e
e
i
n
a
p
pe
nd
ix)
p
r
es
en
t
s
t
h
e
a
c
t
u
a
l
w
i
t
h
t
h
e
p
r
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d
i
ct
ed
i
n
d
e
x
v
al
u
es
at
m
ax
i
m
u
m
r
eact
i
v
e
po
w
e
r
l
oa
di
n
g
f
o
r
e
a
c
h
of
t
he
l
oa
d
bus
e
s
.
T
he
r
e
s
ul
t
s
o
bt
a
i
ne
d
i
n
di
c
a
t
e
t
he
a
bi
l
i
t
y o
f
t
h
e
p
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p
os
e
d
a
p
pr
oa
c
h
t
o pr
e
di
c
t
vol
t
a
ge
c
ol
l
a
ps
e
i
n m
o
r
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co
m
p
l
ex
t
es
t
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et
w
o
r
k
s
.
T
h
es
e
r
es
u
l
t
s
ar
e
v
al
i
d
at
ed
b
y
t
h
o
s
e
o
b
t
ai
n
e
d
i
n
[
1,
28
]
.
T
a
b
l
e
6
s
ho
ws
t
he
r
a
nki
ng
o
f
b
us
e
s
i
n
t
he
NN
G
-
28
b
us
s
ys
t
e
m
i
n
a
s
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e
n
di
n
g
o
r
de
r
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r
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m
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ke
s
t
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r
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n
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e
s
t
.
F
r
o
m
t
h
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t
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b
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e
,
b
u
s
1
6
w
a
s
i
d
e
n
t
i
f
i
e
d
a
s
t
h
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w
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a
k
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t
b
u
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i
n
t
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s
y
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m
w
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t
h
a
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e
a
c
t
i
v
e
p
o
w
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r
m
a
r
gi
n
of
1
3
9.
5
MV
a
r
a
n
d a
pe
r
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e
nt
a
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e
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ha
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g
e
of
3
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06
%
i
n
t
h
e
v
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l
t
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m
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gni
t
u
de
a
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i
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t
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e
s
t
h
e
c
r
i
t
e
r
i
o
n
l
i
s
t
e
d
i
n
[2
6
]
.
T
he
r
e
s
ul
t
s
o
bt
a
i
ne
d
by
t
h
e
p
r
o
p
os
e
d a
p
pr
oa
c
h a
gr
e
e
s
w
i
t
h
t
h
os
e
o
bt
a
i
ne
d
i
n
[
1,
28
]
.
A
n
R
-
va
l
ue
o
f
0.
99
8
9 a
n
d a
n
MS
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va
l
ue
o
f
1.
25
2
7
×
10
−
7
w
er
e o
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t
ai
n
ed
u
s
i
ng
t
he
de
ve
l
o
pe
d
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eu
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et
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k
m
o
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el
a
f
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er
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s
s
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.
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ab
l
e
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.
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us
r
a
nki
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s
s
ys
te
m
L
oa
d B
us
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o
F
ro
m
To
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ax
Pr
ed
icted
v
alu
e
R
a
nki
ng
16
16
19
139.
5
1.
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2
1
15
15
21
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9
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9882
2
2
22
20
22
202.
6
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9858
0
3
19
16
19
232.
5
1.
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6
6
8
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8
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5
13
13
14
384.
5
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0
6
20
20
23
418.
9
0.
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0
7
25
12
25
462.
7
0.
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1
8
26
23
26
632
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7
9
14
8
14
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3
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0
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9
9
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32
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3
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5
0.
9989
0
18
17
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5639.
2
0.
9819
2
19
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-
87
08
I
nt
J
E
l
e
c
&
C
om
p
E
n
g,
V
o
l
.
11
,
No
.
1,
F
e
b
r
ua
r
y
2
02
1
:
124
-
1
32
1
30
5.
C
O
N
CL
U
S
I
O
N
T
hi
s
pa
pe
r
p
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e
s
e
nt
e
d
a
n
A
N
N
-
ba
s
e
d
o
nl
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ne
vol
t
a
ge
c
ol
l
a
p
s
e
pr
e
di
c
t
i
on
u
s
i
ng
t
he
Ne
w
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i
n
e
S
t
a
b
i
l
i
t
y
I
n
de
x (
NL
S
I
_
1)
.
S
i
m
ul
a
t
i
o
n
s
w
e
r
e
c
a
r
r
i
e
d
out
on t
he
I
E
E
E
1
4
-
b
u
s s
y
st
e
m
,
a
nd
the
N
ig
e
r
ia
n
330
kV
,
th
e
28
-
bu
s
s
y
s
t
em
an
d
t
he
r
e
s
ul
t
s
i
ndi
c
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To
Actu
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*
Pr
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v
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R
an
k
**
State
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M
Var
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Bu
s 3
3
1
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C
r
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5
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s 4
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5
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9
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5
28
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1
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Q =
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9
1
5
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1
0.
9108
5
3
C
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ed
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8
1.
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1.
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2
C
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10
0.
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6
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9
4
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4
5
0.
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9
0.
0809
49
5
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9
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2
6
Stab
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Bu
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6
8
0.
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C
r
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8
Bu
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7
24
0.
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0.
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1
C
r
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Q
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2565.
9
2
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7166
75
2
C
r
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Bu
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8
24
0.
9992
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9806
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1
C
r
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Q =
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8
0.
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2
C
r
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8
10
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4
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8
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6
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8
Bu
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0
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17
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1
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r
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8
10
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3
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2
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r
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C
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*A
dopt
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d f
r
om
(
S
am
u
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al.
,
2
0
1
9
)
*
*
B
as
ed
o
n
th
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ed
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v
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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J
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1
31
R
EF
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E
N
C
ES
[1]
I.
A
.
S
a
m
ue
l
,
"
A
N
e
w
V
ol
t
a
ge
S
t
a
bi
l
i
t
y Ind
e
x
F
or P
re
di
c
t
i
ng
V
ol
t
a
ge
Col
l
a
ps
e
In E
l
e
c
t
ri
c
a
l
P
ow
e
r S
ys
t
e
m
Ne
t
wo
rks
,
"
Cov
e
nant
U
ni
v
e
r
s
i
t
y
,
2017
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[2]
P
.
T
.
S
on
a
nd
N
.
V
oropa
i
,
"
T
he
M
a
j
or
O
ut
a
g
e
i
n
S
out
h
V
i
e
t
na
m
i
n
2013 :
T
he
N
a
t
ure
of
Bl
a
c
kout
,
S
e
c
ur
i
t
y
M
e
a
s
ure
s
a
nd S
t
ra
t
e
gy
of
N
a
t
i
on
a
l
P
ow
e
r S
ys
t
e
m
M
ode
rni
z
a
t
i
on,
"
Int
e
r
nat
i
onal
C
onf
e
r
e
nc
e
on
P
r
obl
e
m
o
f
Cr
i
tic
a
l
S
t
ru
c
t
u
re
s,
p
p.
17
7
-
182,
2015
.
[3]
O
.
P
.
V
e
l
oz
a
a
n
d F
.
S
a
nt
a
m
a
ri
a
,
"
A
na
l
ys
i
s
of
m
a
j
or
bl
a
c
kout
s
fr
om
2003
t
o
201
5:
C
l
a
s
s
i
fi
c
a
t
i
on
of
i
n
c
i
d
e
nt
s
a
n
d
r
ev
i
ew
o
f
m
ai
n
c
au
s
es
,"
T
h
e E
l
ec
t
r
i
ci
t
y Jo
u
r
n
a
l
,
vo
l
.
2
9,
n
o.
7,
p
p.
4
2
-
49,
2016
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[4]
Y
. K
. Wu
, S
. M
.
C
h
an
g
,
an
d
Y
.
L
.
H
u,
"
L
i
t
e
ra
t
ur
e
Re
vi
e
w
of P
o
w
e
r S
ys
t
e
m
Bl
a
c
kout
s
,
"
E
n
er
g
y
P
r
o
ced
i
a,
vol
.
1
41,
pp.
428
-
431
,
20
17.
[5]
B.
L
i
u
,
B.
Z
hou
,
D
.
J
i
a
ng,
Z
.
Y
u
,
X
.
Y
a
ng,
a
nd
X
.
M
a
,
"
D
i
s
t
ri
b
ut
e
d
A
c
c
o
m
m
od
a
t
io
n
f
o
r
D
is
tr
ib
u
te
d
G
e
n
e
r
a
tio
n
-
F
rom
t
he
V
i
e
w
of P
ow
e
r S
ys
t
e
m
Bl
a
c
kou
t
s
,
"
A
dv
anc
e
s
i
n G
r
e
e
n
E
ne
r
gy
S
y
s
t
e
m
s
and Sm
ar
t
G
r
i
d.
Spr
i
nge
r
,
Si
ngapor
e
,
vo
l
.
925,
pp
.
236
-
24
6,
2018
.
[6]
H
. H
aes
A
l
h
el
o
u
, M
.
H
am
ed
an
i
-
G
ol
s
ha
n,
T
.
N
j
e
nda
,
a
nd
P
.
S
i
a
no,
"
A
S
urv
e
y
on P
ow
e
r S
ys
t
e
m
B
l
a
c
kou
t
a
n
d
Ca
s
c
a
di
ng
E
v
e
nt
s
:
Re
s
e
a
r
c
h M
ot
i
va
t
i
ons
a
nd Ch
a
l
l
e
nge
s
,
"
E
n
er
g
i
es
,
vol
.
12,
no.
4
,
2019.
[7]
P
.
K
undur,
"
Po
w
e
r S
ys
t
e
m
S
t
a
bi
l
i
t
y A
nd Con
t
rol
,
"
M
c
Gra
w
-
H
ill,
I
n
c
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1994.
[8]
S
.
S
a
hu,
S
.
Re
d
dy,
a
nd S
.
K
um
a
r,
"
N
e
w
V
ol
t
a
g
e
S
t
a
bi
l
i
t
y Ind
e
x
(N
V
S
I) for V
ol
t
a
ge
S
t
a
bi
l
i
t
y A
na
l
ys
i
s
i
n P
ow
e
r
S
y
s
te
m,
"
I
n
t
.
J.
E
l
e
ct
r
.
E
l
ect
r
o
n
.
E
n
g
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R
es
.,
vol
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[9]
M
.
Be
i
ra
gh
i
a
nd
A
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Ra
nj
b
a
r,
"
O
nl
i
ne
V
ol
t
a
g
e
S
e
c
uri
t
y A
s
s
e
s
s
m
e
nt
Ba
s
e
d on
W
i
de
-
A
r
e
a M
ea
s
u
r
em
en
t
s
,"
I
E
E
E
T
r
ans
.
P
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el
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v.
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[10]
J
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Re
n
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W
.
Q
i
n
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X
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a
n,
a
nd P
.
W
a
ng
,
"
V
ol
t
a
ge
s
t
a
bi
l
i
t
y
a
na
l
ys
i
s
ba
s
e
d
on a
da
p
t
i
ve
fuz
z
y l
ogi
c
c
ons
i
d
e
ri
ng
lo
a
d
f
lu
c
tu
a
tio
n
,
"
IE
E
E
Int
e
r
nat
i
onal
Conf
e
r
e
nc
e
on P
ow
e
r S
y
st
e
m T
e
c
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n
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WE
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CO
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Co
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P
re
di
c
t
i
on By
N
e
uro
-
F
uz
z
y (
A
N
F
IS
)
S
c
he
m
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,
"
I
n
t
. J
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B
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ag
i
, "
G
en
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t
i
c
a
l
gori
t
h
m
-
ba
s
e
d
s
upport
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c
t
or
m
a
c
h
i
ne
for onl
i
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vol
t
a
ge
s
t
a
b
i
l
i
t
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m
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ori
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"
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.
J.
E
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ec
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. P
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S
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n
i
, an
d
V
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u
p
t
a,
"
V
o
l
t
ag
e s
t
ab
i
l
i
t
y
as
s
es
s
m
e
n
t
u
s
i
n
g
ar
t
i
f
i
ci
a
l
n
eu
r
al
n
et
w
o
r
k
,"
IE
E
MA
E
ngi
n
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e
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Inf
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Con
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a
di
a
l
ba
s
i
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func
t
i
on ne
t
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y
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es
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m
en
t
t
hrough
t
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ul
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i
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ay
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eed
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a
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e
ura
l
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e
t
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e
ne
ra
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i
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d
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ont
ro
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t
e
m
of
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re
c
t
c
urr
e
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t
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r
dri
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r,
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Int
e
r
nat
i
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our
nal
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f
E
l
e
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t
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i
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put
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ngi
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s
t
i
m
at
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o
n
o
f
v
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l
t
a
g
e
s
t
a
b
i
l
i
t
y
i
n
d
ex
f
o
r
p
o
w
er
s
y
s
t
e
m
em
p
l
o
y
i
n
g
a
r
t
i
f
i
ci
al
n
e
ur
a
l
ne
t
w
or
k t
e
c
h
n
i
que
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nd T
C
S
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pl
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e
ur
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pu
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g
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s
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ili
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s
e
s
s
me
n
t in
p
o
w
e
r
s
y
s
te
ms
u
s
in
g
A
r
tif
i
c
ia
l N
e
u
r
a
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N
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e
l
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P
re
d
i
c
t
i
on
of V
ol
t
a
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Col
l
a
ps
e
i
n
E
l
e
c
t
r
i
c
a
l
P
ow
e
r S
ys
t
e
m
N
e
t
w
orks
us
i
ng
a
N
e
w
V
ol
t
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t
a
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om
bi
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t
a
t
i
c
a
nd
dyna
m
i
c
a
n
a
l
y
s
i
s
of vol
t
a
ge
c
ol
l
a
ps
e
i
n
vol
t
a
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s
ta
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ili
ty
a
s
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e
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s
me
n
t,
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P
r
oc
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IE
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E
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owe
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E
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um
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Ra
m
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re
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A
na
l
ys
i
s
of V
ol
ta
g
e
S
t
a
b
ili
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U
s
in
g
L
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Inde
x M
e
t
hod
I.
Int
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t
i
on II
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F
unda
m
e
nt
a
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:
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i
ngl
e
G
e
n
e
ra
t
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ag
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ect
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C
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i
n
e V
o
l
t
ag
e
S
ta
b
il
ity
I
n
d
ic
e
s
unde
r S
i
ngl
e
L
i
ne
O
ut
a
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Cond
i
t
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In
t
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In
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R
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ua
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i
on
for
V
ol
t
a
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S
ta
b
ili
t
y
Indi
c
e
s
i
n P
ow
e
r
S
ys
t
e
m
U
s
i
ng A
rt
i
fi
c
i
a
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h
e
E
f
f
ec
t
o
f
D
at
a
P
r
e
-
pro
c
e
s
s
i
ng on O
pt
i
m
i
z
e
d
T
ra
i
ni
ng
of
A
rt
i
fi
c
i
a
l
N
e
ura
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N
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t
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z
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Z
a
r
e
,
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Re
vi
e
w
a
nd
S
i
m
ul
a
t
i
o
n of
S
t
a
t
i
c
Indi
c
e
s
i
n
D
e
t
e
c
t
i
on
of P
ro
x
imi
ty
To
V
ol
t
a
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Col
l
a
ps
e
,
"
D
e
te
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tio
n
o
f
Pr
o
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it
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Vo
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C
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lla
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,
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003
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a
gde
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hkum
a
r,
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S
i
m
ul
a
t
i
on
t
e
c
hni
q
ue
for
vol
t
a
ge
s
t
a
bi
l
i
t
y A
na
l
ys
i
s
a
nd c
on
t
i
nge
n
c
y ra
nki
ng
i
n
pow
e
r
sy
st
e
m
s,
"
Int
e
r
nat
i
ona
l
J
our
nal
of
R
e
c
e
nt
T
r
e
nds
i
n E
ng
i
ne
e
r
i
n
g,
v
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l
. 2
, n
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l
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A.
I
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A
de
ki
t
a
n,
a
n
d F
.
A
.
A
gbe
t
uy
i
,
"
P
ow
e
r s
ys
t
e
m
vol
t
a
g
e
c
ol
l
a
ps
e
pre
di
c
t
i
on us
i
ng
a
ne
w
l
i
n
e
s
t
a
bi
l
i
t
y i
nde
x (N
L
S
I
-
1):
A
c
a
s
e
s
t
udy
of t
he
330
-
kV
N
i
ge
ri
a
n N
a
t
i
on
a
l
G
ri
d,
"
Int
e
r
nat
i
o
nal
J
our
nal
of
E
l
e
c
t
r
i
c
al
and
Co
m
put
e
r
E
ngi
n
e
e
r
i
ng (IJ
E
CE
)
,
vol
.
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Evaluation Warning : The document was created with Spire.PDF for Python.
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p
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o
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.
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,
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e
b
r
ua
r
y
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02
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:
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l
a
t
i
on o
f dyna
m
i
c
a
l
s
ys
t
e
m
s
.
K
a
t
e
nde
Jame
s
i
s
a
P
rofe
s
s
or
of E
l
e
c
t
ri
c
a
l
E
n
gi
ne
e
r
i
ng
a
nd
a
l
e
c
t
ur
e
r i
n
t
he
D
e
pa
rt
m
e
nt
of
E
l
e
c
t
ri
c
a
l
a
nd
Com
put
e
r
E
ngi
ne
e
ri
ng
,
N
a
m
i
b
i
a
U
ni
v
e
rs
i
t
y
of S
c
i
e
n
c
e
a
nd
T
e
c
hnol
ogy,
Wi
n
d
h
o
ek
, N
am
i
b
i
a
. H
i
s
r
es
ear
ch
ar
e
as
i
n
c
l
u
d
e
r
obot
i
c
s
a
nd a
ut
om
a
t
i
on
,
po
w
e
r s
ys
t
e
m
a
nd
c
ont
rol
,
m
od
e
l
l
i
ng a
nd
s
i
m
ul
a
t
i
o
n of dyna
m
i
c
a
l
s
ys
t
e
m
s
,
a
nd
r
e
ne
w
a
bl
e
e
ne
rgy
.
Awo
so
p
e
Cl
a
u
d
i
u
s
is
a
P
rofe
s
s
o
r of
E
l
e
c
t
ri
c
a
l
E
ngi
ne
e
r
i
ng a
nd
a
l
e
c
t
ure
r i
n
t
h
e
D
e
pa
rt
m
e
nt
o
f
E
l
e
c
t
ri
c
a
l
&
Inf
orm
a
t
i
on
E
ng
i
n
e
e
ri
ng
,
Cov
e
na
n
t
U
ni
ve
rs
i
t
y
,
O
t
a
.
H
i
s
r
es
ear
ch
ar
e
as
i
n
c
l
u
d
e
P
ow
e
r s
ys
t
e
m
r
e
l
i
a
bi
l
i
t
y
,
op
e
ra
t
i
on a
nd
m
a
i
nt
e
n
a
nc
e
.
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