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14
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2
,
J
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20
25
,
p
p
.
347
~
3
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I
SS
N:
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DOI
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.
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.
pp
347
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358
347
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3
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v
7
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2
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2
4
Acc
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v
2
8
,
2
0
2
4
Th
e
p
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ica
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with
th
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l
p
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u
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r
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e
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in
to
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y
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lse
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e
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a
d
v
a
n
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e
d
m
e
terin
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fr
a
stru
c
tu
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(AMI
).
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h
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t
b
lac
k
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ify
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d
u
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sy
ste
m
a
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is.
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o
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v
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n
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te
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stim
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th
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d
a
ta
f
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th
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ti
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e
s.
Vo
lt
a
g
e
sta
b
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i
n
d
ica
to
r
(VSI)
b
a
se
d
sta
te
e
stim
a
ti
o
n
h
a
v
e
b
e
e
n
u
se
d
su
c
c
e
ss
fu
ll
y
t
o
m
a
k
e
th
e
sm
a
rt
g
rid
sy
ste
m
e
rro
r
fre
e
a
s
p
o
ss
ib
le.
VSI
m
e
th
o
d
h
a
s
b
e
e
n
u
se
d
first
t
o
fi
n
d
t
h
e
v
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l
n
e
ra
b
le
n
o
d
e
s
o
f
t
h
e
g
rid
a
fter
t
h
a
t
th
e
e
ffici
e
n
t
sta
te
e
stim
a
ti
o
n
m
e
th
o
d
i.
e
.
o
p
ti
m
a
l
we
ig
h
ted
lea
st
sq
u
a
re
(
o
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ti
m
a
l
WL
S
)
h
a
v
e
b
e
e
n
e
m
p
lo
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e
d
t
o
g
e
t
re
fin
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d
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su
lt
.
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su
lt
s
sh
o
w
th
a
t
VSI
b
a
se
d
tec
h
n
i
q
u
e
in
c
o
n
c
u
rr
e
n
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e
with
o
p
ti
m
a
l
WL
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h
a
s
p
o
ten
ti
a
l
to
e
li
m
in
a
te
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n
d
e
sira
b
le
d
a
ta
with
se
n
sib
le
lev
e
l
o
f
p
re
c
isio
n
.
K
ey
w
o
r
d
s
:
Fals
e
d
ata
in
jectio
n
Hig
h
r
is
k
ju
n
ctio
n
s
State
esti
m
atio
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Vo
ltag
e
s
tab
ilit
y
in
d
ex
W
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h
ted
least sq
u
ar
e
T
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is i
s
a
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o
p
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n
a
c
c
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ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
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n
se
.
C
o
r
r
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s
p
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A
uth
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r
:
Su
b
r
ata
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is
was
Dep
ar
tm
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f
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lectr
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g
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Neta
ji Su
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g
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C
o
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T
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C
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Gar
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Ko
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ata
-
7
0
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1
5
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en
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I
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ail:
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u
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2
8
@
g
m
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co
m
1.
I
NT
RO
D
UCT
I
O
N
Sm
ar
t
g
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id
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y
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tem
s
ar
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c
o
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b
i
n
ed
with
a
h
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g
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n
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m
b
er
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d
ev
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th
at
ar
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in
ter
c
o
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n
ec
te
d
th
r
o
u
g
h
a
co
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m
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n
icatio
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n
etwo
r
k
an
d
with
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b
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-
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ical
s
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th
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th
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u
g
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d
if
f
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ch
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n
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[
1
]
-
[
4
]
.
T
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f
alse
d
ata
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attac
k
s
(
FDI
As)
[
5
]
ar
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d
an
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o
u
s
.
T
h
e
attac
k
e
r
attac
k
s
th
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o
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th
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m
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al
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(
R
T
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d
is
tan
tly
r
etr
iev
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th
r
o
u
g
h
th
e
s
y
s
tem
[
6
]
.
F
D
I
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s
p
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b
l
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f
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h
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m
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t
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.
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m
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v
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d
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t
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s
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c
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t
r
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r
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,
w
h
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s
u
l
t
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a
t
f
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[
7
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.
I
n
2
0
1
0
co
m
p
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ter
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m
Stu
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et
ca
u
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tab
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[
8
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,
in
2
0
0
3
No
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th
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s
t
Un
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States
,
On
tar
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C
an
ad
a
,
an
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Mid
west,
h
ad
s
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a
n
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tr
ical
s
h
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td
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r
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ay
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s
[
9
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,
I
taly
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p
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ter
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1
8
h
o
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r
s
[
9
]
d
u
e
to
th
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in
s
ec
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r
e
s
m
ar
t
g
r
id
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tem
.
T
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s
af
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s
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f
th
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s
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ar
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o
d
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o
f
th
e
g
r
i
d
s
y
s
tem
with
th
e
v
o
ltag
e
s
en
s
itiv
ity
in
d
ex
m
eth
o
d
h
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b
ee
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d
is
cu
s
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th
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.
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s
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FDI
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b
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m
ea
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v
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ir
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th
r
o
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g
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th
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SC
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ar
r
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r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
14
,
No
.
2
,
J
u
n
e
20
25
:
34
7
-
3
58
348
p
h
aso
r
m
ea
s
u
r
em
en
t
u
n
its
(
PMUs)
,
wh
ich
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tes
a
m
alf
u
n
ctio
n
o
f
th
e
f
lo
w
o
f
p
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am
o
n
g
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u
s
es
o
f
th
e
n
etwo
r
k
an
d
th
e
p
o
wer
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s
er
ted
b
y
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e
b
u
s
.
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ch
em
e
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n
tr
o
d
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ce
d
b
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Hu
g
an
d
Giam
p
a
p
a
[
9
]
ca
n
id
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tify
co
n
v
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ad
d
ata,
wh
ich
was c
r
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b
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er
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ar
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n
o
t
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p
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o
f
id
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g
well
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p
la
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ed
f
alse
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ata
in
jectio
n
attac
k
s
.
So
,
th
e
attac
k
er
m
ay
in
s
er
t
a
p
ar
ticu
l
ar
attac
k
at
th
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tim
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o
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m
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r
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t a
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d
in
d
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e
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r
s
e
d
is
to
r
t th
e
co
n
s
eq
u
en
ce
s
o
f
s
tate
esti
m
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n
[
1
0
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,
[
1
1
]
.
No
wad
ay
s
,
n
etwo
r
k
attac
k
s
h
av
e
b
ec
o
m
e
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c
o
m
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d
s
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ea
k
ier
;
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e
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A
id
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tific
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ch
em
e
a
p
p
ly
in
g
W
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S
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ly
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n
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t
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e
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tify
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p
ar
ti
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lar
ly
wh
en
wh
ile
attac
k
er
is
k
n
o
wn
an
d
th
e
s
y
s
tem
in
f
o
r
m
atio
n
[
1
2
]
.
T
h
e
weig
h
ted
ex
ten
d
e
d
Kalm
an
f
ilter
(
W
E
KF)
[
1
3
]
esti
m
ates
a
r
e
s
u
p
p
o
r
ted
o
n
p
r
esen
t
q
u
an
tity
an
d
h
is
to
r
ical
in
f
o
r
m
atio
n
,
an
d
a
d
y
n
am
ic
th
r
esh
o
ld
.
Stu
d
y
in
g
o
n
co
s
t
an
d
ef
f
icien
cy
o
f
f
i
n
d
in
g
m
et
h
o
d
s
.
T
h
e
d
ea
l
o
f
FDI
A
d
ep
en
d
i
n
g
o
n
AC
a
n
d
DC
s
ta
te
esti
m
atio
n
m
eth
o
d
o
lo
g
y
,
is
v
er
y
p
o
p
u
lar
am
o
n
g
r
esear
c
h
er
s
f
o
r
s
m
ar
t
g
r
id
s
ec
u
r
ity
p
u
r
p
o
s
es
.
Ap
p
licatio
n
o
f
FDI
As
in
th
e
DC
p
r
o
to
ty
p
e
o
f
f
er
s
b
u
lk
y
r
esid
u
es
in
th
e
p
r
o
ce
s
s
o
f
th
e
AC
s
tate
esti
m
atio
n
,
wh
ich
is
im
p
r
o
v
e
d
f
o
r
d
etec
tin
g
FDI
As
[
1
4
]
.
FDI
As
ce
n
ter
ed
o
n
th
e
AC
s
tate
e
s
tim
atio
n
p
r
o
to
ty
p
e
wer
e
f
o
r
m
ed
in
[
1
5
]
to
attac
k
th
e
p
o
wer
s
u
p
p
l
y
g
r
id
s
y
s
tem
.
T
h
e
ass
ailan
t
m
ay
h
er
e
cr
ea
te
th
e
in
ac
cu
r
ate
g
r
i
d
s
tate
b
y
f
lo
w
o
f
p
o
wer
an
d
in
jectio
n
o
f
p
o
wer
q
u
an
titi
es
with
n
o
an
aly
s
i
s
o
f
th
e
cu
r
r
en
t
s
tate
o
f
a
s
y
s
tem
,
an
d
f
in
ally
v
ar
y
th
e
s
tate
esti
m
atio
n
f
r
o
m
th
e
s
af
ety
v
alu
e
as
u
n
id
e
n
tifie
d
.
W
ith
th
e
p
u
r
p
o
s
e
o
f
d
ec
r
ea
s
in
g
th
e
co
u
n
t
o
f
m
ea
s
u
r
em
en
ts
wh
en
th
e
attac
k
is
cr
e
ated
,
an
FDI
attac
k
p
r
o
to
t
y
p
e
is
en
d
o
r
s
ed
in
[
1
6
]
to
alter
t
h
e
g
r
id
p
ar
am
ete
r
s
,
a
n
d
th
is
f
in
ally
p
r
in
ci
p
als
to
a
n
im
p
r
o
v
ed
h
ar
m
o
n
izatio
n
am
o
n
g
th
e
v
a
r
iatio
n
in
s
tates o
f
th
e
g
r
id
p
l
u
s
th
e
alter
atio
n
o
f
g
r
id
p
ar
am
eter
s
.
T
h
e
attac
k
p
r
o
t
o
ty
p
ical
cr
ea
t
ed
with
n
o
n
lin
ea
r
p
h
y
s
ical
lim
its
was
o
f
f
er
ed
to
attain
th
e
s
ec
r
ete
co
n
s
eq
u
en
ce
a
n
d
e
f
f
ec
tiv
ely
e
s
ca
p
e
o
f
r
ev
ea
lin
g
[
1
7
]
.
W
ith
AC
s
tate
e
s
tim
atio
n
ar
r
an
g
em
en
ts
,
th
is
is
h
ar
d
to
in
v
ad
e
f
o
r
f
lawless
FDI
As,
a
s
well
a
s
in
s
u
f
f
icien
t
as
s
au
lts
i
n
itiate
m
o
d
if
icatio
n
s
f
o
r
th
e
p
o
s
s
ib
ilit
y
s
h
ar
in
g
o
f
m
ea
s
u
r
ed
r
esid
u
als.
He
n
ce
,
a
f
in
d
in
g
tech
n
iq
u
e
ap
p
ly
i
n
g
s
tatis
tical
s
tab
ilit
y
f
o
r
m
e
asu
r
ed
r
esid
u
als
is
r
ec
o
m
m
en
d
ed
in
[
1
8
]
.
E
v
en
th
o
u
g
h
th
e
tech
n
iq
u
e
m
ay
e
x
ce
llen
tly
id
en
tify
FDI
As,
th
is
m
eth
o
d
m
ay
n
o
t
d
is
co
v
er
a
n
ex
a
ct
p
o
s
itio
n
f
o
r
FDI
As.
I
n
s
m
ar
t
g
r
id
th
e
d
y
n
am
ical
p
r
o
to
ty
p
e
h
as
b
ee
n
co
n
s
id
er
ed
to
f
ig
h
t
ag
ain
s
t
FDI
As,
th
e
f
ast
attac
k
d
is
co
v
e
r
y
alg
o
r
ith
m
was
r
ec
o
m
m
en
d
e
d
in
th
e
wo
r
k
[
1
9
]
.
T
h
is
alg
o
r
ith
m
d
is
cr
im
in
ates
b
etwe
en
p
lan
n
e
d
m
o
d
if
icatio
n
s
an
d
FDI
As
v
ia
ex
am
in
in
g
ex
p
ec
ted
s
tatis
tical
p
o
s
s
es
s
io
n
s
.
I
n
s
tan
tan
eo
u
s
ly
,
th
is
tech
n
i
q
u
e
m
ay
b
e
a
b
le
to
f
in
d
o
r
r
em
o
v
e
FDI
As
with
litt
le
an
ticip
atio
n
.
I
n
t
h
e
wo
r
k
[
2
0
]
,
t
h
is
tech
n
iq
u
e
f
o
u
n
d
ed
o
n
Ku
llb
ac
k
-
L
eib
ler
d
is
tan
ce
(
KL
D)
was
u
s
ef
u
l
f
o
r
id
e
n
tify
in
g
FDI
As.
T
h
e
tech
n
iq
u
e
r
eg
u
lates
th
e
FDI
As
r
ea
lity
b
y
m
atch
in
g
d
is
s
im
ilar
ity
with
in
p
o
s
s
ib
ilit
y
d
is
tr
ib
u
tio
n
s
am
o
n
g
h
is
t
o
r
ic
an
d
p
r
ese
n
t
m
e
as
u
r
e
m
e
n
ts
.
T
h
e
t
r
o
u
b
le
o
f
th
e
i
d
e
n
ti
f
i
ca
t
io
n
m
et
h
o
d
s
ta
r
ts
w
h
e
n
it
i
n
cl
u
d
es
a
h
u
g
e
h
is
t
o
r
ic
m
ea
s
u
r
e
d
d
at
a,
as we
l
l
as f
i
n
d
in
g
e
f
f
ici
en
c
y
c
an
b
e
n
eg
o
ti
at
ed
t
o
f
i
g
h
t
t
r
a
p
e
z
o
i
d
al
a
ttac
k
s
.
A
d
is
c
o
v
e
r
y
ap
p
r
o
ac
h
g
r
o
u
n
d
e
d
o
n
PMUs
m
e
asu
r
e
d
d
a
ta
o
f
is
r
e
c
o
m
m
en
d
e
d
[
2
1
]
.
T
h
is
a
r
r
an
g
em
en
t
r
e
ce
i
v
es
t
h
e
s
tat
e
esti
m
at
es
a
c
h
ie
v
e
d
b
y
P
MU
s
,
SC
ADA,
t
h
e
n
im
p
l
em
en
ts
a
s
tab
ilit
y
c
h
e
ck
in
g
p
r
o
ce
s
s
f
o
r
id
e
n
t
if
y
i
n
g
FD
I
As
.
T
h
is
p
a
p
e
r
s
u
g
g
es
ts
a
m
et
h
o
d
f
o
r
o
p
ti
m
al
W
L
S
t
h
at
t
o
g
e
th
er
u
s
es
W
L
S
a
n
d
o
p
ti
m
al
s
a
m
p
li
n
g
m
et
h
o
d
s
.
T
h
e
o
r
g
a
n
izatio
n
o
f
p
a
p
er
is
ex
p
r
ess
ed
as
f
o
llo
ws
:
Sectio
n
2
d
ea
ls
with
th
e
o
u
tlin
e
o
f
th
e
p
r
o
b
lem
o
f
th
is
wo
r
k
f
o
r
f
i
n
d
in
g
er
r
o
r
f
r
ee
s
m
ar
t
g
r
id
.
T
h
e
ap
p
r
o
ac
h
f
o
r
f
i
n
d
in
g
v
o
ltag
e
s
tab
ilit
y
in
d
e
x
(
VSI
)
,
s
tate
e
s
tim
atio
n
m
eth
o
d
s
lik
e
AC
s
t
ate
esti
m
atio
n
id
ea
o
f
FDI
A
a
n
d
W
L
S
h
av
e
also
b
ee
n
ex
p
lain
ed
in
th
is
s
ec
tio
n
.
Sectio
n
3
o
f
th
is
wo
r
k
m
ain
ly
d
ea
ls
with
th
e
v
u
ln
e
r
ab
le
n
o
d
e
id
en
tific
atio
n
m
et
h
o
d
.
I
n
t
h
is
s
am
e
s
eg
m
en
t
th
e
esti
m
atio
n
m
eth
o
d
i.e
.
W
E
KF
wh
ich
co
u
ld
s
u
cc
ess
f
u
lly
i
d
en
tify
FDI
A
an
d
p
r
o
p
o
s
ed
m
eth
o
d
i.e
.
o
p
tim
al
W
L
S
wh
ich
s
u
p
p
o
r
ted
u
s
to
id
en
tify
th
e
FDI
A
o
f
s
m
ar
t
g
r
id
h
av
e
b
ee
n
d
is
cu
s
s
ed
.
T
h
e
s
tate
d
ev
iatio
n
p
r
o
ce
s
s
wh
ich
co
n
f
ir
m
ed
th
e
FDI
A
h
as
also
b
ee
n
ex
p
lain
e
d
in
s
ec
tio
n
3
.
I
n
s
ec
tio
n
4
,
t
h
e
p
er
f
o
r
m
a
n
ce
s
o
f
th
e
p
r
o
p
o
s
ed
s
ch
em
e
h
av
e
b
ee
n
d
escr
ib
ed
with
d
if
f
e
r
en
t
o
u
tc
o
m
es.
Sectio
n
5
s
u
m
m
ar
izes
th
e
f
in
d
in
g
s
o
f
th
e
p
r
esen
t stu
d
y
an
d
f
u
t
u
r
e
s
co
p
e
o
f
wo
r
k
.
2.
T
H
E
O
UT
L
I
NE
P
RO
B
L
E
M
AND
M
E
T
H
O
DS F
O
R
F
I
N
DING
E
RRO
R
F
R
E
E
SM
A
RT
G
RID
An
o
u
tlin
e
o
f
th
e
p
r
o
b
lem
o
f
t
h
is
wo
r
k
is
g
iv
en
i
n
th
e
f
o
llo
win
g
p
ar
a
g
r
ap
h
s
o
f
th
is
s
ec
tio
n
.
˗
T
o
im
p
r
o
v
e
th
e
s
ec
u
r
ity
s
y
s
t
em
o
f
s
m
ar
t
g
r
id
,
th
e
v
u
ln
er
a
b
le
n
o
d
es
o
f
g
r
id
s
y
s
tem
h
a
v
e
b
ee
n
d
etec
ted
with
v
o
ltag
e
s
en
s
itiv
ity
in
d
ex
(
VSI
)
m
eth
o
d
.
˗
T
h
e
f
alse
d
ata
d
etec
tio
n
tech
n
iq
u
e
is
b
ased
o
n
W
E
KF
an
d
o
p
tim
al
weig
h
ted
least
s
q
u
ar
e
(
OW
L
S)
wh
ic
h
was n
o
t p
r
ev
io
u
s
ly
u
s
ed
in
c
o
n
ju
n
ctio
n
with
d
etec
tio
n
o
f
FDI
A.
˗
T
h
e
p
r
o
p
o
s
ed
m
eth
o
d
is
als
o
ef
f
icien
t
f
o
r
d
etec
tin
g
th
e
d
y
n
am
ic
d
etec
tio
n
o
f
th
e
FDI
A
an
d
th
e
p
er
f
o
r
m
an
ce
is
v
er
y
ef
f
ec
tiv
e
h
er
e.
˗
T
h
e
p
r
o
p
o
s
ed
tech
n
iq
u
e
is
h
ig
h
ly
s
ca
lab
le
s
h
o
win
g
a
r
ea
s
o
n
ab
le
r
esu
lts
an
d
g
o
o
d
p
er
f
o
r
m
an
ce
co
m
p
ar
ed
to
ex
is
tin
g
wo
r
k
.
˗
T
h
e
r
esu
lts
o
b
tain
ed
f
r
o
m
ex
p
er
im
en
t
estab
lis
h
th
at
th
is
m
eth
o
d
o
l
o
g
y
c
o
n
tin
u
es
o
u
ts
tan
d
in
g
d
etec
tio
n
p
er
f
o
r
m
an
ce
o
f
FDI
A
h
av
in
g
v
ar
iab
le
s
tr
en
g
th
s
o
f
attac
k
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
Meth
o
d
o
lo
g
y
f
o
r
in
cisi
ve
fo
r
a
g
in
g
o
f
h
ig
h
-
r
is
k
ju
n
ctio
n
s
a
n
d
elimin
a
tio
n
o
f
i
n
jecte
d
…
(
P
o
u
la
mi
Gh
o
s
h
)
349
2
.
1
.
Vo
l
t
a
g
e
s
t
a
bil
it
y
ind
ex
I
n
th
e
d
is
tr
ib
u
tio
n
n
etwo
r
k
c
o
n
s
tan
t
v
o
ltag
e
lev
el
f
o
r
l
o
ad
e
n
d
s
id
e
is
to
b
e
m
ain
tain
ed
m
an
d
ato
r
ily
.
Dis
tr
ib
u
tio
n
o
p
er
ato
r
s
m
ain
tai
n
a
co
n
s
tan
t
v
o
ltag
e
lim
it.
Ge
n
er
ally
,
v
o
ltag
e
d
r
o
p
tak
e
p
lac
e
d
u
e
to
in
cr
ea
s
e
in
lo
ad
an
d
a
d
ec
r
ea
s
e
in
r
ea
ctiv
e
p
o
wer
.
Sp
ec
if
ic
r
esear
ch
d
et
er
m
in
es
th
e
v
o
ltag
e
s
tab
ilit
y
in
d
ex
,
w
h
ich
ca
n
b
e
ex
p
r
ess
ed
b
y
t
h
e
f
o
llo
win
g
r
el
atio
n
[
2
2
]
,
[
2
3
]
.
(
)
=
4
−
4
(
−
)
2
−
4
(
−
)
2
(
1
)
Fo
r
an
u
n
in
ter
r
u
p
ted
d
is
tr
ib
u
tio
n
s
y
s
tem
,
o
p
er
ato
r
s
n
ee
d
co
n
tr
o
l
o
n
v
ar
io
u
s
s
y
s
tem
p
ar
am
eter
s
.
T
h
e
m
ea
s
u
r
in
g
f
ac
to
r
s
(
e.
g
.
cu
r
r
en
t
,
v
o
ltag
e,
an
d
n
etwo
r
k
p
o
wer
)
s
h
o
u
ld
h
av
e
er
r
o
r
-
f
r
ee
p
a
r
am
e
ter
s
.
Fo
r
th
e
er
r
o
r
-
f
r
ee
m
ea
s
u
r
em
e
n
t
s
tate
esti
m
atio
n
is
a
f
r
eq
u
en
tly
u
s
ed
to
o
l
i
n
p
o
wer
n
etwo
r
k
s
,
wh
ic
h
also
h
elp
s
to
ca
lcu
late
its
th
eo
r
etica
l v
alu
e
[
2
4
]
.
2
.
2
.
AC
s
t
a
t
e
estim
a
t
io
n
I
n
th
e
AC
g
r
id
s
y
s
tem
s
,
in
th
e
s
tate
e
s
tim
ato
r
,
th
e
p
o
wer
o
f
a
n
etwo
r
k
is
f
lo
win
g
in
th
e
f
o
r
m
o
f
a
n
o
n
lin
ea
r
f
u
n
ctio
n
o
f
p
o
wer
s
y
s
tem
p
ar
am
eter
s
o
f
s
tates
lik
e
m
ag
n
itu
d
es
o
f
v
o
ltag
e
as
well
as
an
g
les.
So
,
AC
s
tate
esti
m
atio
n
m
ay
b
e
r
ep
r
esen
ted
b
y
a
s
u
b
s
eq
u
e
n
t
n
o
n
l
in
ea
r
r
elatio
n
s
h
ip
:
−
ℎ
(
)
,
wh
en
b
ein
g
ca
lled
a
v
ec
to
r
o
f
m
ea
s
u
r
e
d
v
a
lu
es
,
an
d
wh
ich
is
s
tated
b
y
th
e
m
atr
ix
eq
u
atio
n
as
(
2
)
.
=
[
1
.
.
.
−
.
.
.
]
=
[
ℎ
1
(
1
,
2
,
.
.
.
3
)
.
.
.
ℎ
−
(
1
,
2
,
.
.
.
3
)
.
.
.
ℎ
(
1
,
2
,
.
.
.
3
)
]
+
[
1
.
.
.
−
.
.
.
]
=
ℎ
(
)
+
(
2
)
I
n
th
e
a
f
o
r
em
e
n
tio
n
ed
(
2
)
,
is
r
ep
r
esen
ted
as
a
n
o
is
e
v
ec
t
o
r
,
ex
p
r
ess
es
th
e
v
ec
to
r
o
f
n
et
wo
r
k
s
tates
(
lik
e
m
ag
n
itu
d
es
o
f
v
o
ltag
e
an
d
v
o
ltag
e
an
g
les),
h
er
e
ℎ
(
)
is
ca
lle
d
th
e
J
ac
o
b
ia
n
m
atr
ix
an
d
is
d
en
o
te
d
b
y
ℎ
wh
ich
ex
p
r
ess
es th
e
n
o
n
-
lin
ea
r
co
r
r
elatio
n
o
f
t
h
e
m
ea
s
u
r
ed
d
ata
an
d
n
etwo
r
k
p
ar
am
eter
s
o
f
s
tates,
as (
3
)
.
=
[
ℎ
1
1
ℎ
1
2
.
.
.
ℎ
1
−
1
ℎ
1
ℎ
2
1
ℎ
2
2
.
.
.
ℎ
2
−
1
ℎ
2
.
.
.
ℎ
−
1
1
ℎ
−
1
2
.
.
.
ℎ
−
1
−
1
ℎ
−
1
.
.
.
ℎ
1
ℎ
2
.
.
.
ℎ
−
1
ℎ
]
(
3
)
T
o
g
ain
ac
ce
s
s
to
a
p
ar
ticu
lar
m
ea
s
u
r
in
g
d
ev
ice,
a
h
ac
k
er
m
ay
in
tr
o
d
u
ce
an
FDI
A
,
wh
ich
i
s
alar
m
in
g
f
o
r
th
e
m
ag
n
itu
d
e
o
f
m
ea
s
u
r
e
d
d
ata.
Fo
r
r
etain
i
n
g
th
e
h
ac
k
ed
m
ea
s
u
r
em
e
n
t
co
n
ce
aled
,
m
in
im
u
m
o
n
e
o
f
th
e
s
tate
v
ar
iab
les
is
es
s
en
tial
s
h
o
u
ld
b
e
ac
tiv
e.
(
else,
er
r
o
n
e
o
u
s
v
alu
e
g
ain
ed
b
y
s
tate
esti
m
ato
r
(
1
)
will
ex
ce
e
d
th
e
o
n
s
et
,
an
d
FDI
attac
k
wil
l
b
e
id
en
tifie
d
)
[
9
]
.
T
h
e
attac
k
er
s
ar
e
o
n
ly
ab
le
to
g
ai
n
ac
ce
s
s
to
m
ea
s
u
r
in
g
d
ev
ices
b
u
t
n
o
t
o
n
s
tates
o
f
th
e
s
y
s
tem
.
T
h
e
r
ef
o
r
e
,
th
e
attac
k
er
ca
n
in
f
lu
en
ce
o
n
l
y
th
e
m
e
asu
r
ed
v
al
u
es
wh
ich
ar
e
lin
k
e
d
with
th
o
s
e
s
y
s
tem
s
tates
to
r
etain
it
u
n
tr
ac
ea
b
le
[
9
]
.
T
h
e
lin
k
b
etwe
en
t
h
e
m
e
asu
r
ed
v
al
u
es
an
d
s
tates
o
f
n
etwo
r
k
m
a
y
b
e
esta
b
lis
h
ed
f
r
o
m
a
J
ac
o
b
ian
m
atr
i
x
.
ℎ
(
i
n
(
3
)
)
.
T
h
e
AC
s
tate
esti
m
atio
n
m
eth
o
d
f
o
r
FDI
A
m
ay
b
e
r
estru
ctu
r
ed
as
d
is
cu
s
s
ed
in
[
9
]
.
‖
′
−
ℎ
(
′
)
‖
=
‖
+
−
ℎ
(
+
)
‖
=
‖
(
+
)
−
(
ℎ
(
)
ℎ
(
,
+
)
)
‖
(
4
)
W
h
er
e,
=
+
an
d
ℎ
(
)
=
ℎ
(
)
+
ℎ
(
,
+
)
,
th
e
ter
m
s
ex
p
r
ess
ed
u
s
in
g
s
u
b
s
cr
ip
t
‘
n
’
ar
e
m
ea
n
t
f
o
r
n
atu
r
al
m
ea
s
u
r
ed
v
alu
es
o
f
n
etwo
r
k
s
tates
an
d
ar
e
ex
p
r
ess
ed
ter
m
s
with
s
u
b
s
cr
ip
t
‘
a’
ar
e
attac
k
ed
m
ea
s
u
r
ed
v
alu
es o
f
th
e
n
etwo
r
k
.
I
f
th
e
FDI
attac
k
is
to
b
e
k
e
p
t u
n
tr
ac
ea
b
le
:
∥
′
−
ℎ
(
′
)
∥
=
∥
−
ℎ
(
)
∥
(
5
)
b
ut
,
f
o
r
a
n
o
r
m
al
s
itu
atio
n
∥
−
ℎ
(
)
∥
<
.
Hen
ce
,
it f
o
llo
ws th
at:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
14
,
No
.
2
,
J
u
n
e
20
25
:
34
7
-
3
58
350
‖
′
−
ℎ
(
′
)
‖
=
‖
−
ℎ
(
)
‖
=
‖
(
+
)
−
(
ℎ
(
)
ℎ
(
,
)
)
‖
(
6
)
s
o
lv
in
g
(
4
)
an
d
(
6
)
,
th
e
attac
k
v
ec
to
r
v
alu
e
,
m
ay
b
e
attain
ed
as
(
7
)
[
9
]
.
=
ℎ
(
,
+
)
−
ℎ
(
,
)
(
7
)
F
r
o
m
th
e
(
5
)
,
to
i
n
tr
o
d
u
ce
an
a
ttack
v
ec
to
r
,
th
e
h
ac
k
e
r
s
h
o
u
ld
k
n
o
w
th
e
p
er
tin
en
t sy
s
tem
s
ta
te
v
alu
es.
Hu
g
an
d
Giam
p
ap
a
[
9
]
o
b
s
er
v
ed
th
at
AC
s
tate
esti
m
atio
n
m
ay
b
e
u
s
ed
in
an
AM
I
-
d
ep
e
n
d
en
t
s
m
ar
t
g
r
id
s
f
r
am
ewo
r
k
.
T
h
e
AM
I
m
ea
s
u
r
ed
v
alu
es
ar
e
a
s
u
b
s
ec
tio
n
o
f
th
e
e
n
tire
m
ea
s
u
r
ed
v
alu
es
ex
p
r
ess
ed
in
(
2
)
.
I
f
t
h
e
h
ac
k
er
g
ai
n
s
ac
ce
s
s
to
en
tire
o
r
a
s
u
b
s
ec
tio
n
o
f
AM
I
b
ased
d
ev
ices,
e.
g
.
,
p
-
AM
I
d
ev
ices,
h
e
o
r
s
h
e
can
p
r
o
d
u
ce
a
FDI
attac
k
th
r
o
u
g
h
s
elec
tin
g
a
n
o
n
ze
r
o
att
ac
k
v
ec
to
r
a
=
{a
1
,
…,
am
}
in
th
e
m
an
n
er
s
o
th
at
th
is
attac
k
v
ec
to
r
s
at
n
o
n
-
r
ea
c
h
ab
le
d
ev
ices h
a
p
p
en
t
o
b
e
ze
r
o
(
s
o
,
ai=
0
,
wh
er
e,
i,
{AM
I
d
ev
ices})
.
Un
d
etec
tab
le
attac
k
s
ca
n
b
e
cr
ea
ted
,
a
n
d
p
o
s
s
ib
le
ac
tio
n
s
to
b
e
tak
en
ca
r
e
o
f
ar
e
d
is
cu
s
s
ed
in
th
e
r
ec
en
t
wo
r
k
s
[
9
]
,
[
2
4
]
-
[
2
7
]
.
T
h
e
FDI
attac
k
s
(
wh
er
e
th
e
atta
ck
er
’
s
o
b
jectiv
e
is
to
d
is
o
r
d
er
s
y
s
tem
f
u
n
ctio
n
)
in
AM
I
-
b
ased
d
ev
ices h
a
v
e
two
m
ain
im
p
ac
ts
.
i.
I
f
FDI
A
b
ec
o
m
es
u
n
tr
ac
ea
b
le
,
lik
e
r
esid
u
als
ar
e
a
s
m
aller
am
o
u
n
t
o
f
a
n
o
n
s
et
v
alu
e
in
a
weig
h
ted
least
s
q
u
ar
e
b
ased
esti
m
ato
r
,
n
etwo
r
k
p
a
r
am
eter
s
o
f
in
d
icate
(
e
.
g
.
,
m
ag
n
itu
d
e
o
f
v
o
ltag
e,
an
g
le)
attain
ed
f
r
o
m
th
e
s
tate
esti
m
atio
n
m
eth
o
d
d
eliv
er
er
r
o
n
e
o
u
s
in
f
o
r
m
atio
n
[
2
8
]
.
T
h
e
er
r
o
n
eo
u
s
s
y
s
tem
co
n
d
itio
n
s
f
o
u
n
d
f
r
o
m
t
h
e
s
tate
esti
m
atio
n
m
et
h
o
d
p
r
o
d
u
ce
c
o
n
f
u
s
in
g
o
p
er
at
io
n
al
d
ec
is
io
n
s
.
T
h
ese
m
is
lead
th
e
r
ea
l
-
tim
e
an
d
p
r
o
lo
n
g
ed
r
ea
l
-
tim
e
o
p
er
a
tio
n
in
th
e
n
etwo
r
k
,
lik
e
th
e
s
o
lu
tio
n
o
f
o
p
tim
al
p
o
wer
f
lo
w
(
OPF)
o
r
v
o
lt
-
VAR
co
n
tr
o
l
(
VVC).
T
h
is
f
al
s
e
o
p
er
ativ
e
d
ec
is
io
n
will
r
ed
u
ce
th
is
s
y
s
tem
’
s
ef
f
icien
cy
,
s
tab
ilit
y
as
well,
an
d
co
n
s
eq
u
en
tly
,
t
h
is
will c
au
s
e
a
s
ig
n
if
ican
t b
lack
o
u
t.
ii.
FDI
attac
k
s
,
id
en
tifie
d
o
r
u
n
id
en
tifie
d
,
h
av
e
s
tr
aig
h
t
ef
f
ec
t
in
s
m
ar
t
g
r
id
s
et
-
u
p
.
I
n
th
ese
s
tu
d
ies,
th
e
in
f
lu
en
ce
o
f
FDI
attac
k
s
o
n
s
t
ab
ilit
y
o
f
s
y
s
tem
,
in
th
e
n
ex
t s
eg
m
en
t.
2
.
3
.
Weig
hte
d lea
s
t
s
qu
a
re
(
WL
S)
m
et
ho
d o
f
s
t
a
t
e
estima
t
io
n
State
esti
m
atio
n
in
p
o
wer
n
e
two
r
k
s
is
a
s
ig
n
if
ican
t
elem
en
t
in
p
o
wer
s
y
s
tem
e
n
er
g
y
m
an
ag
in
g
s
y
s
tem
s
.
R
em
o
te
ter
m
in
al
u
n
its
tr
an
s
m
it
f
ield
m
ea
s
u
r
em
en
t
d
ata
to
a
s
tate
esti
m
ato
r
th
r
o
u
g
h
d
ata
tr
an
s
m
is
s
io
n
s
y
s
tem
s
.
A
s
tate
esti
m
ato
r
ad
eq
u
ately
ad
j
u
s
ts
s
tate
v
ar
iab
les
o
f
th
e
p
o
wer
s
y
s
tem
b
y
r
ed
u
cin
g
th
e
s
u
m
o
f
r
esid
u
al
s
q
u
ar
es.
Few
n
o
n
-
lin
ea
r
eq
u
atio
n
s
lin
k
i
n
g
t
h
e
m
ea
s
u
r
em
en
ts
an
d
p
o
w
er
s
y
s
tem
s
tates
i.e
.
b
u
s
v
o
ltag
e,
a
n
d
p
h
ase
an
g
le
s
u
p
p
o
r
t f
o
r
th
is
m
eth
o
d
.
T
h
is
p
r
o
ce
s
s
is
th
e
f
am
o
u
s
W
L
S m
eth
o
d
.
T
h
e
p
r
elim
in
ar
y
W
L
S e
q
u
atio
n
o
f
s
tate
esti
m
atio
n
p
r
o
ce
s
s
is
g
iv
en
(
8
)
.
So
,
=
ℎ
(
)
+
(
8
)
T
h
e
v
ec
to
r
z
o
f
m
ea
s
u
r
ed
v
alu
es
is
=
[
1
2
…
]
an
d
t
h
e
v
ec
to
r
ℎℎ
=
[
ℎ
1
(
)
ℎ
2
(
)
…
ℎ
(
)
]
co
m
p
r
is
in
g
th
e
n
o
n
-
lin
ea
r
f
u
n
ctio
n
s
ℎ
(
)
is
ass
o
ciate
d
with
t
h
e
a
n
ticip
ated
v
alu
e
o
f
th
e
m
ea
s
u
r
ed
q
u
an
tity
in
s
tate
v
ec
to
r
x
h
av
in
g
n
v
ar
i
ab
les
=
[
1
2
…
]
.
An
d
is
a
v
ec
to
r
o
f
m
ea
s
u
r
em
e
n
t
er
r
o
r
s
=
[
1
2
…
]
.
T
h
e
m
ea
s
u
r
em
e
n
t
er
r
o
r
s
is
s
u
p
p
o
s
ed
t
o
f
it
th
e
s
u
b
s
eq
u
en
t
s
tatis
tical
p
r
o
p
er
ties
.
Prim
ar
ily
,
er
r
o
r
s
with
h
av
e
ze
r
o
m
ea
n
h
as
b
ee
n
ca
lcu
lated
to
f
in
d
th
e
v
o
ltag
e
s
tab
ilit
y
co
n
d
itio
n
b
y
u
s
in
g
th
e
f
o
llo
win
g
alg
o
r
ith
m
(
)
=
0
,
i
=
1
,
…
m
.
Af
ter
th
at,
er
r
o
r
s
wer
e
tak
en
as
i
n
d
ep
en
d
en
t,
(
[
]
=
0
f
o
r
I
≠
j)
,
in
s
u
ch
a
way
th
at
th
e
co
v
ar
ian
ce
m
atr
ix
is
d
iag
o
n
al.
(
)
=
(
)
=
=
{
1
2
,
2
2
.
.
.
2
}
T
h
e
o
b
jectiv
e
f
u
n
ctio
n
is
d
en
o
ted
b
y
(
9
)
.
(
)
=
∑
(
zi
-
hi
(
)
)
2
=
=
1
=
(
ℎ
(
)
)
−
1
(
−
ℎ
(
)
)
(
9
)
T
h
e
m
in
im
izatio
n
c
o
n
d
itio
n
o
f
(
9
)
is
in
d
icate
d
b
y
:
(
)
=
(
)
=
(
)
−
1
(
−
ℎ
(
)
)
=
0
wh
er
e
(
)
=
ℎ
(
)
/
.
T
h
e
T
ay
lo
r
s
er
ies ex
p
an
s
io
n
o
f
(
)
is
ex
p
r
ess
ed
as (
1
0
)
.
(
)
=
(
)
+
(
)
(
−
)
+
.
.
.
=
0
(
1
0
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
Meth
o
d
o
lo
g
y
f
o
r
in
cisi
ve
fo
r
a
g
in
g
o
f
h
ig
h
-
r
is
k
ju
n
ctio
n
s
a
n
d
elimin
a
tio
n
o
f
i
n
jecte
d
…
(
P
o
u
la
mi
Gh
o
s
h
)
351
W
h
er
e
th
e
+
1
iter
ate
is
co
r
r
elate
d
to
k
th
iter
atio
n
v
ia
:
+
1
=
−
(
)
−
1
(
)
…
(
1
1
)
an
d
(
)
is
a
g
ain
m
atr
ix
(
)
=
(
)
=
(
)
-
1
(
)
.
Her
e
,
ev
er
y
s
tep
o
f
th
e
iter
atio
n
(
)
s
atis
f
ies
(
)
=
-
1
(
−
ℎ
(
)
)
.
3.
VULN
E
RA
B
L
E
NO
DE
I
D
E
NT
I
F
I
CA
T
I
O
N
M
E
T
H
O
D
3
.
1
.
VSI
f
o
r
v
uln
er
a
ble no
d
e
identif
ica
t
io
n
I
n
r
ea
l
-
tim
e
o
p
er
atio
n
SC
AD
A
n
etwo
r
k
s
u
p
p
o
r
ts
r
u
n
n
in
g
th
e
d
ata
r
elate
d
to
th
e
co
n
s
u
m
p
tio
n
o
f
p
o
wer
to
th
e
elec
tr
ical
d
is
tr
ib
u
tio
n
o
p
er
at
o
r
.
AM
I
ass
is
tan
c
es
to
d
eliv
er
th
ese
d
ata
to
ele
ctr
ical
o
p
er
ato
r
s
.
I
f
th
e
attac
k
er
s
o
m
e
h
o
w
s
u
cc
ee
d
s
in
tack
lin
g
th
e
d
ata
a
n
d
ch
a
n
g
in
g
t
h
e
d
ata
f
o
r
p
o
wer
o
f
c
o
n
s
u
m
p
tio
n
,
h
e
ca
n
m
o
d
if
y
th
e
d
ata
o
f
AM
I
in
s
e
r
tin
g
b
ad
d
ata.
So
,
th
e
p
r
im
a
r
y
jo
b
o
f
s
m
ar
t
g
r
id
n
etwo
r
k
will
b
e
to
f
in
d
th
e
v
u
ln
er
ab
le
n
o
d
es
in
a
n
etwo
r
k
.
I
f
an
attac
k
er
s
o
m
eh
o
w
ac
ce
s
s
es
th
e
AM
I
b
ased
d
ev
ices,
o
n
e
ca
n
c
o
n
tr
o
l
t
h
e
d
ata
o
f
p
o
wer
c
o
n
s
u
m
p
tio
n
b
y
in
s
er
tin
g
w
r
o
n
g
in
f
o
r
m
ati
o
n
.
Her
e,
we
h
av
e
co
n
s
id
er
e
d
th
at
l
-
AM
I
b
ased
in
s
tr
u
m
en
ts
ar
e
attac
k
e
d
b
y
f
a
ls
e
d
ata
in
f
o
r
m
atio
n
.
So
,
th
e
attac
k
ed
v
alu
es
o
f
r
ea
l
as
wel
l
as
r
ea
ctiv
e
p
o
wer
m
ea
s
u
r
em
en
ts
,
an
d
,
ar
e
(
1
2
)
-
(
1
4
)
.
=
0
+
;
∀
{
1
,
2
,
.
.
.
}
(
1
2
)
=
0
+
;
∀
{
1
,
2
,
.
.
.
}
(
1
3
)
=
0
+
0
=
0
(
1
+
)
(
1
4
)
wh
er
e,
0
an
d
0
ar
e
th
e
co
r
r
e
ctly
m
ea
s
u
r
ed
r
ea
l
a
n
d
r
ea
ctiv
e
p
o
wer
s
o
f
i
-
th
AM
I
-
b
ased
d
ev
ices
co
r
r
esp
o
n
d
in
g
ly
.
s
y
m
b
o
lizes
m
atch
in
g
attac
k
v
ec
to
r
s
.
T
h
en
tak
in
g
=
0
,
wh
er
e
m
u
ltip
licatio
n
f
ac
to
r
o
f
ac
tu
al
d
im
e
n
s
io
n
s
,
th
e
(
8
)
m
ay
b
e
wr
itten
as (
1
1
)
.
=
0
+
0
=
0
(
1
5
)
W
h
er
e
=
1
+
.
Similar
ly
:
=
0
(
1
6
)
in
(
1
5
)
is
attac
k
d
eg
r
ee
ex
p
r
ess
ed
with
an
y
r
ea
l
n
u
m
b
e
r
.
T
h
e
VSI
f
o
r
a
n
o
d
e
i
n
th
e
s
m
ar
t
g
r
id
is
ex
p
r
ess
ed
with
(
1
)
.
Acc
o
r
d
in
g
to
t
h
e
ex
p
lan
atio
n
o
f
VSI
,
r
ea
l
p
o
wer
an
d
r
ea
ctiv
e
p
o
wer
at
r
t
h
n
o
d
e
m
ay
b
e
ex
p
r
ess
ed
u
n
d
e
r
r
eg
u
lar
o
p
e
r
ativ
e
s
tate
in
th
is
way
:
=
∑
0
∀
+
(
)
0
+
∑
∀
(
1
7
)
=
∑
0
∀
+
(
)
0
+
∑
∀
(
1
8
)
wh
er
e,
0
an
d
0
ar
e
th
e
r
ea
l
p
o
wer
an
d
r
ea
ctiv
e
p
o
wer
o
f
th
e
lo
ad
s
o
f
p
o
wer
c
o
n
s
u
m
er
s
,
co
r
r
esp
o
n
d
in
g
ly
.
(
)
an
d
(
)
ar
e
r
ea
l
an
d
r
ea
ctiv
e
p
o
wer
lo
ad
s
o
f
th
e
r
th
en
e
r
g
y
co
n
s
u
m
er
s
,
co
r
r
esp
o
n
d
in
g
ly
.
an
d
ar
e
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
lo
s
s
es
o
f
th
e
d
iv
is
io
n
s
co
r
r
esp
o
n
d
in
g
ly
.
I
n
th
e
a
b
o
v
e
eq
u
at
io
n
s
,
an
d
s
ig
n
if
y
en
tire
b
u
s
es a
n
d
b
r
an
c
h
es c
o
r
r
esp
o
n
d
in
g
ly
,
b
ey
o
n
d
n
o
d
e
‘
r
’
wh
en
VSI
h
as b
ee
n
c
o
m
p
u
ted
.
L
et
u
s
co
n
s
id
er
‘
r
’
r
ep
r
esen
ts
an
AM
I
m
ea
s
u
r
ed
q
u
a
n
tity
n
o
d
e
wh
ich
is
u
n
d
er
th
e
attac
k
er
,
th
e
(
1
3
)
an
d
(
1
4
)
m
a
y
b
e
c
h
an
g
e
d
u
tili
zin
g
(
1
1
)
an
d
(
1
2
)
as f
o
llo
ws:
=
∑
0
∀
+
(
)
0
+
∑
∀
(
1
9
)
=
∑
0
∀
+
(
)
0
+
∑
∀
(
2
0
)
an
d
will
ch
an
g
e,
if
ch
an
g
es
,
an
d
it
will
in
f
lu
e
n
ce
o
n
VSI
in
d
ex
s
h
o
w
n
in
(
1
)
.
Fr
o
m
th
e
(
1
9
)
an
d
(
2
0
)
,
a
n
y
in
s
er
tio
n
o
f
f
alse
d
ata
will
m
o
d
if
y
th
e
v
alu
e
o
f
an
d
,
wh
ich
s
tar
ts
ag
ain
to
r
ed
u
c
e
th
e
v
alu
e
o
f
VSI
o
b
s
er
v
ed
in
(
1
)
.
At
th
e
n
etwo
r
k
d
is
tr
ib
u
tio
n
en
d
,
R
/X
r
atio
is
v
er
y
h
ig
h
[
2
9
]
.
A
lo
w
am
o
u
n
t
o
f
VSI
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
14
,
No
.
2
,
J
u
n
e
20
25
:
34
7
-
3
58
352
in
d
icate
s
a
f
ailu
r
e
o
f
v
o
ltag
e
o
f
th
e
s
y
s
tem
.
Hen
ce
,
th
e
g
r
id
o
p
er
ativ
es
wo
u
ld
m
ain
tain
th
e
s
y
s
tem
wi
th
in
th
e
s
tab
ilit
y
b
o
u
n
d
a
r
y
.
Fro
m
(
1
)
,
VSI
d
e
p
en
d
s
o
n
r
esis
tan
ce
R
an
d
in
d
u
ctan
ce
X
o
f
th
e
p
o
wer
g
r
id
.
So
,
th
e
eq
u
al
v
alu
e
o
f
λ
(
m
ea
n
s
s
am
e
q
u
an
tity
o
f
f
alse
d
ata
in
s
er
tio
n
)
at
v
ar
io
u
s
n
o
d
es,
th
e
v
alu
es
o
f
VSI
s
h
o
u
ld
d
if
f
er
s
u
b
ject
t
o
ch
an
g
es
o
f
th
e
v
alu
es
o
f
R
a
n
d
X
o
f
th
e
d
o
wn
r
iv
er
b
r
a
n
ch
e
s
o
f
d
i
f
f
er
en
t
n
o
d
es
wh
ile
th
e
y
ar
e
attac
k
ed
.
T
h
e
f
o
llo
win
g
s
eg
m
e
n
t
d
escr
ib
es
th
e
co
n
n
ec
tio
n
o
f
VSI
an
d
F
DI
attac
k
.
As
s
co
p
e
o
f
t
h
is
p
ap
er
,
VSI
h
as
b
ee
n
u
tili
ze
d
f
o
r
s
ea
r
ch
in
g
o
f
v
u
ln
er
ab
le
n
o
d
es
in
I
E
E
E
1
4
b
u
s
to
p
o
lo
g
y
(
Fig
u
r
e
1
)
as
ex
p
er
im
en
tal
n
etwo
r
k
.
Fig
u
r
e
2
s
h
o
ws th
e
v
u
ln
er
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s
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k
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Fig
u
r
e
1
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Fig
u
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e
2
.
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h
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v
u
l
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er
ab
le
n
o
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e
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etec
ted
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th
e
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le
n
etwo
r
k
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
Meth
o
d
o
lo
g
y
f
o
r
in
cisi
ve
fo
r
a
g
in
g
o
f
h
ig
h
-
r
is
k
ju
n
ctio
n
s
a
n
d
elimin
a
tio
n
o
f
i
n
jecte
d
…
(
P
o
u
la
mi
Gh
o
s
h
)
353
3
.
2
.
E
s
t
im
a
t
io
n m
e
t
ho
ds
f
o
r
identif
ica
t
io
n o
f
F
DIA
3
.
2
.
1
.
WE
K
F
ba
s
ed
m
ea
s
urem
ent
Hu
et
a
l.
[
1
3
]
tr
ied
to
s
im
p
li
f
y
th
e
E
KF
[
3
0
]
to
o
u
ts
tan
d
i
n
g
esti
m
atio
n
r
esu
lt
in
th
e
p
r
esen
ce
o
f
FDI
As
in
th
e
n
etwo
r
k
.
W
E
KF
m
eth
o
d
ad
ap
tiv
ely
r
e
d
u
ce
s
th
e
g
ain
v
alu
e
o
f
f
ilter
o
f
E
KF
with
th
e
ex
p
ec
tatio
n
,
w
h
ich
ce
r
tifie
s
th
e
h
ar
m
e
d
m
ea
s
u
r
e
d
v
al
u
es
f
o
r
h
av
in
g
a
s
m
aller
weig
h
t
f
o
r
t
h
e
s
tate
esti
m
atio
n
tech
n
iq
u
e.
T
h
e
weig
h
ts
f
o
r
ese
en
,
ex
p
e
cted
m
ea
s
u
r
e
d
v
alu
es
h
av
e
s
ee
n
to
b
e
en
lar
g
e
d
.
T
h
e
b
o
n
d
am
o
n
g
t
h
e
weig
h
t
m
atr
ix
o
f
th
e
m
ea
s
u
r
ed
v
alu
es
an
d
th
e
c
o
v
ar
ian
ce
m
atr
ix
R
o
f
th
e
m
ea
s
u
r
ed
n
o
i
s
e
is
=
−
1
.
T
h
e
weig
h
t m
atr
ix
o
f
m
ea
s
u
r
e
d
v
alu
es is
ex
p
r
ess
ed
as (
2
1
)
.
(
)
−
1
=
−
1
∗
|
−
ℎ
(
|
=
1
̂
)
|
(
2
1
)
T
h
e
p
er
f
o
r
m
an
ce
o
f
s
tate
esti
m
atio
n
ca
n
b
e
s
u
cc
ess
f
u
lly
ex
p
lain
ed
b
ec
a
u
s
e
with
th
e
in
cr
em
en
t
in
attac
k
s
tr
en
g
th
,
th
e
tec
h
n
iq
u
e
co
u
ld
r
estra
in
s
u
cc
ess
f
u
lly
th
e
attac
k
.
W
h
en
th
e
p
r
ed
icted
esti
m
ated
m
ea
s
u
r
em
en
t
ℎ
(
|
−
1
̂
)
d
iv
er
g
es
m
ea
n
in
g
f
u
lly
f
r
o
m
th
e
p
r
esen
t
m
ea
s
u
r
em
en
t
,
th
e
en
h
an
ce
m
en
t
in
p
r
ed
icted
r
em
ain
in
g
v
ec
to
r
cr
ea
tes
th
e
n
o
is
e
d
u
e
to
m
ea
s
u
r
em
en
t
wh
ich
u
ltima
tely
r
ed
u
c
es
th
e
Kalm
an
g
ain
.
Sli
g
h
t
d
if
f
er
en
ce
s
am
o
n
g
th
e
f
o
r
ec
asted
an
d
p
r
esen
t
m
e
asu
r
em
en
ts
d
ir
ec
t
to
s
m
all
f
lu
ctu
atio
n
s
in
th
e
m
ea
s
u
r
em
en
t
n
o
is
e.
T
h
is
d
ir
ec
ts
to
s
m
all
v
ar
iatio
n
s
in
Kalm
an
g
ain
an
d
f
in
ally
t
o
s
m
all
v
ar
iatio
n
s
in
p
r
ed
ictab
le
v
alu
es.
I
n
th
e
p
r
esen
ce
o
f
FDI
As,
th
e
W
E
KF
ca
n
r
estra
in
th
e
co
n
s
eq
u
en
c
es
o
f
attac
k
s
in
a
n
im
p
r
o
v
e
d
m
an
n
er
,
e
v
en
tu
ally
r
aisi
n
g
th
e
m
is
m
atch
b
etwe
en
th
e
W
E
KF a
n
d
o
p
tim
al
W
L
S e
s
tim
atio
n
.
3.
3
.
O
ptim
a
l WLS
3.
3
.
1
.
A
weig
hte
d lea
s
t
-
s
qu
a
re
s
a
pp
ro
x
im
a
t
io
n
I
n
th
is
r
esear
ch
p
ap
er
,
we
s
tar
t
with
th
e
d
is
cr
ete
n
o
r
m
leas
t
-
s
q
u
ar
es
m
eth
o
d
.
T
h
e
co
m
m
o
n
f
o
r
m
o
f
th
e
d
is
cr
ete
n
o
r
m
is
s
h
o
wn
in
(
2
2
)
.
‖
‖
≔
(
1
∑
=
1
|
(
)
|
2
)
(
2
2
)
T
h
e
ab
o
v
e
eq
u
atio
n
will
b
e
u
s
ed
n
o
w
f
o
r
th
e
weig
h
ted
l
ea
s
t
-
s
q
u
ar
es
esti
m
ato
r
.
Her
e
,
s
am
p
lin
g
m
ea
s
u
r
e
d
v
alu
e
µ
,
u
s
u
ally
v
ar
ies f
r
o
m
h
as b
ee
n
ap
p
lied
a
n
d
ca
n
b
e
wr
it
ten
as
(
2
3
)
.
µ
=
(
2
3
)
H
er
e
is
co
n
s
id
er
ed
as
p
o
s
itiv
e
f
u
n
ctio
n
d
escr
ib
e
d
u
n
iv
e
r
s
ally
o
n
X.
So
−
1
=
1
,
an
d
we
h
er
e
r
ef
l
ec
t
weig
h
ted
least
-
s
q
u
ar
e
m
eth
o
d
wh
er
e
weig
h
ts
h
av
e
b
ee
n
co
n
s
id
er
ed
as
f
o
llo
ws:
=
(
)
.
Her
e
we
s
elec
t
th
e
n
o
r
m
s
o
t
h
at,
th
e
n
o
r
m
‖
‖
ap
p
r
o
ac
h
es
‖
‖
as
n
im
p
r
o
v
es.
W
h
en
µ
=
an
d
≡
1
in
d
icate
s
s
tan
d
ar
d
least
-
s
q
u
ar
es
m
eth
o
d
ev
alu
ated
b
y
T
h
eo
r
em
1
.
1
.
I
t
is
to
b
e
n
o
ted
th
at
v
ar
y
in
g
th
e
s
am
p
lin
g
v
alu
es
ar
e
a
u
s
u
al
p
r
ac
tice
s
ch
em
e
f
o
r
d
ec
r
ea
s
in
g
th
e
d
if
f
er
e
n
ce
in
Mo
n
te
C
ar
lo
m
eth
o
d
s
,
wh
ic
h
i
n
clu
d
es im
p
o
r
ta
n
ce
s
am
p
lin
g
.
d
en
o
tes
2
(
,
)
o
r
th
o
n
o
r
m
al
b
asis
o
f
an
d
with
th
is
an
in
tr
o
d
u
ctio
n
o
f
n
ew
f
u
n
ctio
n
c
an
b
e
m
en
tio
n
ed
as (
2
4
)
.
→
,
(
)
:
=
∑
(
)
|
(
)
|
2
=
1
(
2
4
)
W
h
ich
is
d
ep
en
d
en
t
o
n
,
,
an
d
.
,
=
,
(
,
,
)
≔
‖
,
‖
∞
(
2
5
)
I
t
is
to
b
e
n
o
ticed
th
at,
as
√
ar
e
an
2
(
,
µ
)
o
r
th
o
n
o
r
m
al
b
asis
o
f
√
wh
er
e
s
p
ac
e
c
o
n
s
is
ts
o
f
f
u
n
ctio
n
s
√
with
g
∈
,
we
o
b
tain
∫
,
µ
=
an
d
th
u
s
,
≥
.
3.
3
.
2
.
O
ptim
a
l sa
m
pli
ng
T
h
eo
r
em
2
.
1
in
lea
d
s
th
e
s
tu
d
y
with
u
s
u
al
way
aim
in
g
f
o
r
o
p
tim
al
s
am
p
lin
g
s
ch
em
e
f
o
r
weig
h
ted
least
-
s
q
u
ar
e
m
eth
o
d
.
L
et
u
s
co
n
s
id
er
:
≔
=
∑
|
|
2
=
1
(
26
)
f
o
r
an
y
v
alu
e
o
f
,
o
n
e
m
ay
test
o
u
t th
at
:
µ
≔
(
2
7
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
14
,
No
.
2
,
J
u
n
e
20
25
:
34
7
-
3
58
354
is
th
e
p
r
o
b
ab
ilit
y
m
ea
s
u
r
e
o
n
as
∫
=
.
Fu
r
th
er
m
o
r
e,
f
o
r
th
e
s
p
ec
if
ic
ch
o
ice
,
=
=
.
T
h
er
ef
o
r
e
:
,
=
.
(
2
8
)
th
u
s
,
we
co
n
clu
d
e
th
at
r
esu
l
t
is
s
u
b
s
eq
u
en
t
r
esu
lt
o
f
ab
o
v
e
t
h
eo
r
em
.
T
h
is
t
h
eo
r
em
d
is
p
lay
s
th
at
ab
o
v
e
s
elec
tio
n
o
f
an
d
µ
p
er
m
its
f
o
r
attain
in
g
n
ea
r
est
-
o
p
tim
al
esti
m
ates
wh
ich
r
e
d
u
ce
s
weig
h
te
d
least
-
s
q
u
ar
es
esti
m
ato
r
,
b
elo
w
n
o
m
in
al
co
n
d
itio
n
wh
ich
s
elec
ts
s
o
th
at
it b
ec
o
m
es
least o
f
o
r
d
er
(
)
.
3.
4
.
I
dentif
ica
t
io
n pro
ce
s
s
wit
h sta
t
e
dev
ia
t
io
n
T
h
e
p
o
wer
f
lo
w
ca
lcu
latio
n
o
f
p
o
we
r
s
y
s
tem
is
e
x
ec
u
ted
f
o
r
k
,
an
d
ca
lcu
lated
r
esu
lt
is
in
clu
d
ed
f
o
r
d
ev
iatio
n
e
r
r
o
r
f
o
ll
o
win
g
Ga
u
s
s
ian
d
is
tr
ib
u
tio
n
wh
ic
h
is
t
h
e
m
ea
s
u
r
em
e
n
t
s
y
s
tem
.
At
th
is
co
n
d
itio
n
two
n
u
m
b
er
s
o
f
s
tate
esti
m
atio
n
ap
p
r
o
ac
h
es
o
f
f
er
ed
a
b
o
v
e
ar
e
a
p
p
lied
to
ev
alu
ate
th
e
s
y
s
tem
s
tate.
Prim
ar
ily
,
f
o
r
co
m
p
ar
in
g
th
e
d
e
v
iatio
n
s
am
o
n
g
two
esti
m
ates th
e
co
n
s
is
ten
cy
test
is
ap
p
lied
.
T
h
e
f
o
r
m
u
la
is
g
iv
en
by
(
2
9
)
.
ˆ
−
ˆ
2
≤
(
2
9
)
H
er
e
ˆ
an
d
ˆ
s
y
m
b
o
lizes
th
e
f
o
r
e
ca
s
t state
e
s
tim
ates u
s
in
g
o
p
tim
al
W
L
S a
n
d
W
E
KF r
esp
ec
ti
v
ely
.
T
h
e
co
n
s
is
ten
cy
ch
ec
k
th
r
esh
o
ld
i
s
ex
p
r
ess
ed
with
.
T
h
e
v
alu
e
o
f
is
f
ix
ed
b
y
m
ea
s
u
r
em
en
t
e
r
r
o
r
as
well
a
s
co
r
r
ec
tn
ess
o
f
s
tate
esti
m
atio
n
o
u
tco
m
e.
As
f
o
r
ec
asted
v
al
u
e
is
d
esig
n
e
d
b
y
m
ea
n
s
o
f
Ho
lt’s
two
p
a
r
am
ete
r
ap
p
r
o
ac
h
,
u
n
e
x
p
ec
ted
d
e
v
iatio
n
s
in
g
en
er
ato
r
an
d
lo
a
d
a
r
e
n
o
t
ac
ce
p
ted
in
s
y
s
tem
.
Fo
r
r
em
o
v
in
g
f
alse
id
en
tific
atio
n
s
d
u
e
to
s
u
d
d
en
ch
an
g
e
in
g
en
er
ato
r
o
u
tp
u
t
o
r
ch
an
g
es
in
lo
ad
,
th
e
r
esid
u
es
f
r
o
m
th
e
ca
lcu
lated
esti
m
ates a
n
d
th
e
o
r
ig
in
al
m
ea
s
u
r
ed
v
alu
e
a
r
e
en
s
u
r
e
d
.
T
h
e
tech
n
iq
u
e
o
f
r
esid
u
al
test
is
g
iv
en
b
y
(
3
0
)
.
−
ℎ
(
ˆ
)
2
≤
(
3
0
)
H
er
e
ℎ
(
ˆ
)
ca
n
b
e
e
x
p
r
ess
ed
as
esti
m
ated
m
ea
s
u
r
e
d
v
alu
e
f
o
u
n
d
f
r
o
m
t
h
e
o
p
tim
al
W
L
S;
th
e
id
e
n
tific
atio
n
th
r
esh
o
ld
o
f
b
ad
d
ata
is
,
an
d
to
ler
an
ce
er
r
o
r
o
f
th
e
c
h
i
-
s
q
u
ar
e
d
is
tr
ib
u
tio
n
d
ec
id
es
th
e
r
esu
lt
also
.
I
f
th
e
p
o
wer
g
r
id
is
attac
k
ed
with
FDI
A,
th
e
test
r
esu
lt
s
r
eg
ar
d
in
g
co
n
s
is
ten
cy
o
f
th
e
s
tate
esti
m
atio
n
ac
h
iev
ed
th
r
o
u
g
h
th
ese
two
esti
m
atio
n
ap
p
r
o
ac
h
es
W
E
KF
an
d
o
p
ti
m
al
W
L
S
ar
e
m
u
ch
h
ig
h
er
t
h
an
th
e
t
h
r
esh
o
ld
v
alu
es.
I
t
en
s
u
r
es
t
h
e
p
r
esen
c
e
o
f
FDI
As.
Ultim
ately
,
th
e
f
o
r
ec
ast
esti
m
ate
v
alu
es
o
b
tain
ed
ap
p
ly
in
g
W
E
KF
ar
e
u
n
d
e
r
g
o
n
e
th
r
o
u
g
h
r
esid
u
a
l te
s
ts
to
d
eter
m
in
e
th
e
p
r
esen
ce
o
f
FDI
As.
I
f
th
e
th
r
esh
o
ld
v
alu
e
o
f
t
h
e
o
p
tim
al
W
L
S
test
i
s
les
s
er
th
an
th
e
o
u
tco
m
e
o
f
r
esid
u
al
test
,
th
e
p
r
e
s
en
ce
o
f
FDI
A
is
s
u
r
e
in
th
e
s
y
s
tem
.
C
o
n
v
er
s
ely
,
if
th
r
esh
o
ld
o
f
c
h
i
-
s
q
u
ar
e
test
is
g
r
ea
ter
th
an
o
u
tco
m
e
o
f
a
r
esid
u
al
test
,
th
en
th
e
c
o
n
s
is
ten
cy
test
r
esu
lt
is
in
ter
r
u
p
ted
,
last
ly
it is
d
eter
m
in
ed
th
at
th
e
s
y
s
tem
is
attac
k
-
f
r
ee
.
4.
RE
SU
L
T
S
AND
D
I
SCU
SS
I
O
N
Fo
r
ex
p
er
im
e
n
tal
p
u
r
p
o
s
e
M
AT
L
AB
R
2
0
1
8
b
h
as
b
ee
n
s
e
lecte
d
f
o
r
s
im
u
latio
n
a
n
d
a
n
a
ly
s
is
.
T
h
e
p
o
wer
f
lo
w
o
f
th
e
n
etwo
r
k
was
ev
alu
ated
ap
p
ly
in
g
s
ig
n
i
f
ican
t
d
ata
o
b
tain
ed
b
y
MA
T
POW
E
R
7
.
1
p
o
wer
s
im
u
latio
n
p
latf
o
r
m
.
I
n
th
is
ex
p
er
im
en
t,
Gau
s
s
ian
n
o
is
e
h
a
s
b
ee
n
in
clu
d
ed
in
p
o
wer
f
lo
w
r
esu
lts
.
Her
e
th
e
m
ea
n
v
alu
e
is
s
elec
ted
0
a
n
d
t
h
e
v
ar
ian
ce
o
f
0
.
0
1
0
.
I
n
th
e
r
e
s
u
lt
s
ec
tio
n
,
th
e
o
u
tco
m
e
r
eg
a
r
d
in
g
id
e
n
tific
atio
n
o
f
p
r
o
jecte
d
m
eth
o
d
h
as
b
ee
n
estab
lis
h
ed
f
r
o
m
th
e
s
im
u
l
atio
n
r
esu
lts
.
Acc
o
r
d
in
g
to
th
e
p
r
o
p
o
s
ed
s
ch
em
e,
attac
k
v
ec
to
r
h
as
b
ee
n
in
jecte
d
as
FDI
A
in
I
E
E
E
-
1
4
b
u
s
n
etwo
r
k
.
Firstl
y
,
t
h
e
FDI
A
n
o
d
es
ar
e
d
etec
ted
b
y
VSI
m
eth
o
d
.
Seco
n
d
l
y
af
ter
FDI
A
in
s
m
ar
t
g
r
id
th
e
s
tate
esti
m
atio
n
r
esu
lts
ap
p
ly
in
g
W
E
KF,
an
d
p
r
o
p
o
s
ed
m
eth
o
d
(
o
p
tim
al
W
L
S)
h
av
e
b
ee
n
co
m
p
ar
ed
.
L
astl
y
,
th
e
p
r
esen
ce
o
f
FDI
A
h
as
b
ee
n
d
eter
m
in
ed
b
y
th
e
p
r
o
p
o
s
ed
id
en
tific
atio
n
a
p
p
r
o
a
ch
in
I
E
E
E
-
1
4
b
u
s
s
y
s
tem
.
T
h
e
VSI
in
d
ex
m
eth
o
d
was
ap
p
lied
in
I
E
E
E
-
1
4
b
u
s
s
y
s
tem
with
in
jecte
d
f
alse
d
ata
in
s
o
m
e
n
o
d
es.
T
h
e
ex
p
er
im
e
n
tal
r
esu
lt
with
VSI
is
s
h
o
wn
in
T
ab
le
1
.
T
h
e
VSI
h
as
ef
f
icien
tly
d
etec
ted
th
e
v
u
ln
er
ab
le
n
o
d
es.
T
ab
le
2
(
co
lu
m
n
1
)
s
h
o
ws
al
l
th
e
m
eter
m
ea
s
u
r
em
en
ts
(
tak
en
as
b
ef
o
r
e
attac
k
)
alo
n
g
with
th
e
esti
m
ates
g
en
er
ated
b
y
W
E
KF
an
d
p
r
o
p
o
s
ed
m
eth
o
d
.
Fig
u
r
e
3
illu
s
tr
ates
th
e
ex
p
er
im
e
n
tal
r
es
u
lts
f
o
r
th
e
v
o
ltag
e
m
ag
n
itu
d
e
o
f
I
E
E
E
-
1
4
b
u
s
s
y
s
tem
.
T
h
e
cu
r
v
es
in
d
icate
v
o
lt
ag
e
m
a
g
n
itu
d
es
f
o
r
th
e
d
if
f
e
r
e
n
t
m
eth
o
d
s
o
f
s
tate
esti
m
atio
n
with
th
e
p
r
o
p
o
s
ed
s
ch
em
e.
T
h
e
p
r
o
p
o
s
ed
s
c
h
em
e
estab
lis
h
es
a
v
er
y
g
o
o
d
,
esti
m
ated
v
alu
e
co
m
p
ar
ed
t
o
th
e
o
th
er
m
et
h
o
d
s
.
T
ab
le
3
ex
p
lain
s
d
ata
(
v
o
lt
ag
e
p
h
ase)
wh
ich
wer
e
o
b
tain
ed
b
y
all
th
e
m
eter
m
ea
s
u
r
em
en
ts
(
tak
en
as
b
ef
o
r
e
attac
k
)
alo
n
g
with
th
e
esti
m
atin
g
m
eth
o
d
s
wh
ich
ar
e
g
en
e
r
ated
b
y
W
E
KF
an
d
p
r
o
p
o
s
ed
m
eth
o
d
.
Fig
u
r
e
4
illu
s
tr
ates
th
e
ex
p
er
im
e
n
tal
r
esu
lts
f
o
r
th
e
v
o
ltag
e
p
h
ase
o
f
I
E
E
E
-
1
4
b
u
s
s
y
s
tem
.
T
h
e
cu
r
v
es
s
p
ec
if
y
v
o
ltag
e
p
h
ases
f
o
r
th
e
d
if
f
e
r
en
t
m
eth
o
d
s
o
f
s
tate
esti
m
atio
n
with
th
e
p
r
o
p
o
s
ed
s
ch
em
e
wh
ich
estab
lis
h
es a
v
er
y
g
o
o
d
,
esti
m
ated
v
alu
e
th
an
t
h
e
o
th
er
m
eth
o
d
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
Meth
o
d
o
lo
g
y
f
o
r
in
cisi
ve
fo
r
a
g
in
g
o
f
h
ig
h
-
r
is
k
ju
n
ctio
n
s
a
n
d
elimin
a
tio
n
o
f
i
n
jecte
d
…
(
P
o
u
la
mi
Gh
o
s
h
)
355
T
ab
le
1
.
Vu
ln
e
r
ab
le
n
o
d
e
d
etec
tio
n
u
s
in
g
VSI
B
u
s
N
o
.
V
S
I
S
t
a
b
i
l
i
t
y
s
t
a
t
u
s
B
u
s
N
o
.
V
S
I
S
t
a
b
i
l
i
t
y
s
t
a
t
u
s
1
1
.
0
0
0
0
S
t
a
b
l
e
8
1
.
0
0
0
0
S
t
a
b
l
e
2
-
5
4
.
1
9
4
2
V
u
l
n
e
r
a
b
l
e
9
-
9
7
.
5
1
9
9
V
u
l
n
e
r
a
b
l
e
3
1
.
0
0
0
0
S
t
a
b
l
e
10
1
.
0
0
0
0
S
t
a
b
l
e
4
-
2
3
.
8
9
7
3
V
u
l
n
e
r
a
b
l
e
11
1
.
0
0
0
0
S
t
a
b
l
e
5
-
2
2
.
1
3
5
0
V
u
l
n
e
r
a
b
l
e
12
-
8
.
2
8
9
4
V
u
l
n
e
r
a
b
l
e
6
-
4
2
.
1
5
9
3
V
u
l
n
e
r
a
b
l
e
13
-
7
6
.
7
2
2
4
V
u
l
n
e
r
a
b
l
e
7
1
.
0
0
0
0
S
t
a
b
l
e
14
-
9
8
.
1
8
5
6
V
u
l
n
e
r
a
b
l
e
T
ab
le
2
.
C
o
m
p
a
r
is
o
n
tab
le
f
o
r
v
o
ltag
e
m
ag
n
itu
d
e
o
f
W
E
KF a
n
d
th
e
p
r
o
p
o
s
ed
m
eth
o
d
af
ter
FDI
B
u
s
N
o
.
M
e
a
su
r
e
d
v
a
l
u
e
i
n
P
.
U
M
e
t
h
o
d
o
l
o
g
y
u
se
d
B
u
s
N
o
.
M
e
a
su
r
e
d
v
a
l
u
e
i
n
P
.
U
M
e
t
h
o
d
o
l
o
g
y
u
se
d
B
e
f
o
r
e
F
D
I
A
f
t
e
r
F
D
I
W
EK
F
[
1
3
]
P
r
o
p
o
se
d
met
h
o
d
B
e
f
o
r
e
F
D
I
A
f
t
e
r
F
D
I
W
EK
F
[
1
3
]
P
r
o
p
o
se
d
met
h
o
d
1
1
.
0
6
8
1
.
2
1
3
4
1
.
1
5
1
.
0
7
8
1
.
0
2
8
7
1
.
1
3
4
7
1
.
0
6
1
.
0
2
3
2
0
.
9
8
9
9
1
.
0
9
5
9
1
.
0
8
0
.
9
9
9
0
.
9
7
6
3
1
.
0
8
8
1
.
0
7
0
.
9
7
6
3
0
.
9
5
1
8
1
.
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4
5
1
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5
0
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9
6
10
0
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9
7
5
8
1
.
0
8
7
3
1
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0
7
0
.
9
7
9
4
0
.
9
5
7
9
1
.
0
7
1
6
1
.
0
6
1
0
.
9
5
8
11
0
.
9
9
3
2
1
.
1
0
2
5
1
.
1
0
.
9
8
5
0
.
9
6
1
5
1
.
0
7
4
9
1
.
0
6
0
.
9
6
12
1
.
0
0
0
9
1
.
1
0
9
1
1
.
1
1
.
0
0
1
6
1
.
0
1
8
5
1
.
1
2
5
1
.
1
1
5
1
.
0
1
9
13
0
.
9
9
4
1
.
1
0
2
8
1
.
1
1
.
0
3
7
0
.
9
9
1
9
1
.
1
0
2
8
1
.
1
1
.
0
1
14
0
.
9
6
4
7
1
.
0
7
7
2
1
.
0
5
0
.
9
7
T
ab
le
3
.
C
o
m
p
a
r
is
o
n
tab
le
f
o
r
v
o
ltag
e
p
h
ase
o
f
W
E
KF a
n
d
t
h
e
p
r
o
p
o
s
ed
m
et
h
o
d
a
f
ter
FDI
B
u
s
N
o
.
M
e
a
su
r
e
d
v
a
l
u
e
i
n
d
e
g
r
e
e
M
e
t
h
o
d
o
l
o
g
y
u
se
d
B
u
s
N
o
.
M
e
a
su
r
e
d
v
a
l
u
e
i
n
d
e
g
r
e
e
M
e
t
h
o
d
o
l
o
g
y
u
se
d
B
e
f
o
r
e
F
D
I
A
f
t
e
r
F
D
I
W
EK
F
[
1
3
]
P
r
o
p
o
se
d
met
h
o
d
B
e
f
o
r
e
F
D
I
A
f
t
e
r
F
D
I
W
EK
F
[
1
3
]
P
r
o
p
o
se
d
M
e
t
h
o
d
1
0
0
0
0
8
-
1
3
.
3
9
-
1
1
.
3
9
-
1
4
.
3
9
-
1
3
.
1
2
-
4
.
9
7
-
4
.
8
6
-
4
.
9
-
4
.
9
2
9
-
1
4
.
9
1
-
1
2
.
9
1
-
1
5
.
9
1
-
1
4
.
6
2
3
-
1
2
.
7
5
-
1
2
.
8
9
-
1
2
.
8
-
1
2
.
7
3
10
-
1
5
.
4
-
1
3
.
4
-
1
6
.
4
-
1
5
.
1
1
4
-
1
0
.
3
-
8
.
3
-
1
1
.
3
-
1
0
.
0
1
11
-
1
4
.
9
-
1
2
.
9
-
1
5
.
9
-
1
4
.
6
1
5
-
8
.
7
6
-
6
.
7
6
-
9
.
7
6
-
8
.
4
7
12
-
1
5
.
7
-
1
3
.
7
-
1
6
.
7
-
1
5
.
4
1
6
-
1
4
.
5
-
1
2
.
5
-
1
5
.
5
-
1
4
.
2
1
13
-
1
5
.
5
-
1
3
.
5
-
1
6
.
5
-
1
5
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2
1
7
-
1
3
.
3
-
1
1
.
3
-
1
4
.
3
-
1
3
.
0
1
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-
1
6
.
0
8
-
1
4
.
0
8
-
1
7
.
0
8
-
1
5
.
7
9
Fig
u
r
e
3
.
C
o
m
p
a
r
is
o
n
o
f
v
o
lta
g
e
am
p
litu
d
e
at
ea
c
h
b
u
s
b
ef
o
r
e
an
d
af
ter
FDI
attac
k
4
.
1
.
Co
m
pa
riso
n o
f
RM
SE
v
a
lues
f
o
r
diff
er
ent
m
et
ho
ds
T
h
e
p
ap
e
r
also
ap
p
lies
th
e
r
o
o
t
m
ea
n
s
q
u
ar
e
er
r
o
r
(
R
MSE
)
f
o
r
d
eter
m
in
i
n
g
th
e
esti
m
ato
r
s
-
W
L
S,
W
E
KF
an
d
o
p
tim
al
W
L
S
p
er
f
o
r
m
an
ce
.
T
h
e
R
MSE
is
also
u
s
ed
h
er
e
to
f
in
d
t
h
e
s
tr
en
g
t
h
o
f
s
tate
esti
m
atio
n
wh
ile
W
L
S,
W
E
K
F
as
well
as
o
p
tim
al
W
L
S
ar
e
u
n
d
er
FDI
A
attac
k
.
T
h
e
R
MSE
co
m
p
u
tes
th
e
esti
m
atio
n
er
r
o
r
f
o
r
W
L
S,
W
E
KF
an
d
o
p
tim
al
W
L
S
e
s
tim
ato
r
s
b
y
m
ea
n
s
o
f
d
ev
iatio
n
b
etwe
en
an
ticip
ated
esti
m
atio
n
an
d
th
e
r
ea
l
v
alu
e.
T
h
e
a
n
ticip
ated
esti
m
ated
v
alu
e
f
o
r
b
u
s
v
o
ltag
e
is
m
atch
ed
with
r
ea
l
v
alu
e
wh
ile
n
etwo
r
k
is
attac
k
ed
.
C
o
m
p
u
tatio
n
o
f
R
MSE
m
ay
b
e
p
e
r
f
o
r
m
ed
with
th
e
f
o
llo
win
g
eq
u
atio
n
.
T
h
e
R
MSE
co
m
p
u
ted
b
y
esti
m
ated
er
r
o
r
o
f
ev
er
y
b
u
s
h
as
b
ee
n
cited
in
T
ab
le
4
.
Fr
o
m
T
ab
le
4
,
R
MSE
o
b
tain
e
d
b
y
o
p
tim
al
W
L
S
esti
m
atio
n
is
ex
p
r
ess
iv
ely
lo
w
er
co
m
p
ar
ed
to
R
MSE
o
f
th
e
W
E
KF
esti
m
atio
n
.
So
,
in
p
r
es
en
ce
o
f
FDI
A,
th
e
o
p
tim
al
W
L
S p
r
esen
ts
en
h
an
c
ed
p
er
f
o
r
m
an
ce
f
o
r
esti
m
atio
n
th
an
th
e
W
E
KF a
n
d
W
L
S.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
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n
g
,
Vo
l.
14
,
No
.
2
,
J
u
n
e
20
25
:
34
7
-
3
58
356
=
√
1
∑
(
̂
−
)
2
=
1
(
3
1
)
Her
e
d
en
o
tes
th
e
b
u
s
n
u
m
b
er
s
;
̂
d
en
o
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an
ticip
ated
esti
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ated
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u
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h
e
esti
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ate
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th
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ltag
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p
ar
am
eter
f
o
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v
er
y
ar
e
s
h
o
wn
in
T
a
b
le
5
.
T
h
ese
d
ata
o
f
v
o
ltag
e
v
alu
es
h
av
e
b
ee
n
tak
en
wh
ile
th
e
s
m
ar
t
g
r
id
is
u
n
d
er
attac
k
.
I
n
T
ab
le
5
,
t
h
e
esti
m
ate
er
r
o
r
o
f
o
p
tim
al
W
L
S
is
f
o
u
n
d
to
b
e
m
in
im
al
wh
e
n
g
r
id
is
u
n
d
er
th
e
in
jectio
n
o
f
f
alse
d
ata
s
tate.
So
o
p
tim
al
W
L
S
s
h
o
ws
an
im
p
r
o
v
em
en
t
f
o
r
esti
m
atio
n
p
er
f
o
r
m
an
ce
o
v
er
W
E
KF
wh
ile
s
m
ar
t
g
r
id
f
ac
ed
attac
k
b
y
F
DI
A.
T
h
e
co
lu
m
n
o
f
p
r
o
p
o
s
ed
m
eth
o
d
in
T
a
b
le
5
an
d
T
a
b
le
5
u
s
in
g
o
p
tim
al
W
L
S
s
h
o
ws
v
er
y
g
o
o
d
r
esu
lts
a
s
o
p
tim
al
weig
h
t
least
m
eth
o
d
u
s
es
s
elec
tio
n
o
f
w
an
d
µ
wh
ich
p
er
m
its
th
e
u
s
er
f
o
r
attain
i
n
g
n
ea
r
est
o
p
tim
al
esti
m
ates
o
f
ab
r
id
g
ed
weig
h
t
ed
least
-
s
q
u
ar
es
esti
m
ato
r
.
Her
e
th
e
m
in
im
u
m
co
n
d
itio
n
is
th
at
is
m
in
im
al
f
o
r
th
e
o
r
d
er
(
)
.
Fig
u
r
e
4
.
C
o
m
p
a
r
is
o
n
o
f
v
o
lta
g
e
p
h
ase
an
g
les at
ea
ch
b
u
s
b
e
f
o
r
e
an
d
af
ter
FDI
attac
k
T
ab
le
4
.
R
MSE
o
f
v
o
ltag
e
am
p
litu
d
e
A
l
g
o
r
i
t
h
m
R
M
S
E
W
LS
0
.
1
0
9
4
W
EK
F
[
1
3
]
0
.
0
0
5
4
O
p
t
i
mal
W
LS
0
.
0
0
0
3
8
T
ab
le
5
.
E
s
tim
ated
er
r
o
r
o
f
W
L
S,
W
E
KF,
an
d
p
r
o
p
o
s
ed
o
p
ti
m
al
W
L
S a
n
d
p
r
o
p
o
s
ed
m
eth
o
d
B
u
s
N
o
.
W
LS me
t
h
o
d
(
R
M
S
E)
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EK
F
[
1
3
]
(
R
M
S
E)
P
r
o
p
o
se
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m
e
t
h
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d
(
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M
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u
s
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o
.
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LS me
t
h
o
d
(
R
M
S
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[
1
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]
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P
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(
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1
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1
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1
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.
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1
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1
1
.
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4
×
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2
3
.
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×
1
0
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3
6
.
4
6
×
1
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6
7
1
0
.
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0
×
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5
.
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4
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1
1
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1
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4
.
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×
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0
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×
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1
1
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5
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6
5.
CO
NCLU
SI
O
N
T
h
is
p
ap
er
r
ec
o
m
m
en
d
s
a
tech
n
iq
u
e
b
ased
o
n
VSI
i
n
d
ex
a
n
d
s
tate
d
ev
iatio
n
to
e
f
f
icien
t
ly
id
en
tify
an
d
p
in
p
o
in
t
th
e
FDI
A.
T
o
p
in
p
o
in
t
th
e
FDI
A
th
e
VSI
i
n
d
ex
alg
o
r
ith
m
h
as
b
ee
n
im
p
lem
en
ted
.
Usi
n
g
a
d
is
cr
ete
o
p
tim
al
s
am
p
lin
g
weig
h
tin
g
f
u
n
ctio
n
to
t
h
e
o
r
t
h
o
d
o
x
W
L
S
m
eth
o
d
,
t
h
e
d
etec
tio
n
p
er
f
o
r
m
an
ce
d
u
e
to
th
e
FDI
A
attac
k
is
b
lo
ck
ed
ef
f
icien
tly
.
T
h
e
c
o
n
s
is
ten
cy
test
f
o
r
W
L
S,
W
E
KF
a
s
wel
l
as
o
p
tim
al
W
L
S
esti
m
atio
n
wer
e
ex
ec
u
ted
t
o
p
r
im
ar
ily
d
ec
id
e
th
e
p
r
esen
ce
o
f
f
alse
d
ata
in
jectio
n
attac
k
with
in
n
etwo
r
k
.
W
ith
th
e
in
ten
tio
n
o
f
d
r
o
p
p
in
g
th
is
v
alu
e
f
o
r
er
r
o
r
f
in
d
in
g
r
ate
,
r
esid
u
al
test
wa
s
also
ex
ec
u
ted
.
Fo
r
r
ed
u
ci
n
g
th
e
r
ed
u
n
d
an
cy
o
f
th
e
n
etwo
r
k
,
e
f
f
icien
t
ch
i
-
s
q
u
ar
e
test
h
as
b
e
en
ex
ec
u
ted
.
Ultim
ately
,
th
e
e
x
p
er
im
en
tal
r
esu
lts
estab
lis
h
th
e
o
u
ts
tan
d
in
g
en
ac
tm
en
t
o
f
p
r
o
p
o
s
ed
s
ch
em
e
to
id
en
tify
FDI
A.
As
f
u
tu
r
e
wo
r
k
,
d
iv
e
r
s
e
FDI
A
o
f
s
m
ar
t g
r
id
n
etwo
r
k
,
lik
e
tim
e
s
y
n
ch
r
o
n
izatio
n
attac
k
as we
ll a
s
in
ter
ce
p
tio
n
attac
k
s
ca
n
b
e
co
n
s
id
er
ed
.
Evaluation Warning : The document was created with Spire.PDF for Python.