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I
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6930
T
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4
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en
t
u
n
it
(
P
MU
)
.
A
co
m
p
ar
ativ
e
an
al
y
s
is
o
f
SE
in
r
ec
tan
g
u
lar
an
d
p
o
lar
co
o
r
d
in
ates
h
as
b
ee
n
p
r
o
p
o
s
ed
in
[
6
]
.
A
SE
ap
p
r
o
ac
h
f
o
r
a
d
is
t
r
ib
u
tio
n
s
y
s
te
m
co
n
s
id
er
in
g
t
h
e
co
n
d
itio
n
v
ar
iab
les,
i.e
.
,
n
o
d
e
v
o
ltag
e
an
d
an
g
le
o
f
f
ee
d
er
is
p
r
o
p
o
s
ed
in
[
7
]
.
In
[
8
]
p
r
e
s
en
t
s
ap
p
r
o
ac
h
f
o
r
th
e
im
p
le
m
en
tatio
n
o
f
r
ea
cti
v
e
p
o
w
er
an
d
/o
r
ac
tiv
e
p
o
w
er
m
ea
s
u
r
e
m
e
n
t
s
i
n
t
h
e
SE.
An
a
g
en
t
-
b
ased
ap
p
r
o
ac
h
f
o
r
d
y
n
a
m
i
c
SE
o
f
p
o
w
er
s
y
s
te
m
b
y
ta
k
in
g
th
e
ad
v
a
n
tag
e
s
o
f
h
y
b
r
id
m
ea
s
u
r
e
m
e
n
t
d
ata
is
p
r
esen
ted
in
[
9
]
.
A
h
y
b
r
id
SE
m
eth
o
d
w
it
h
g
e
n
etic
alg
o
r
ith
m
a
n
d
ce
llu
lar
co
m
p
u
tatio
n
al
n
e
t
w
o
r
k
is
p
r
o
p
o
s
ed
in
[
1
0
]
to
o
v
er
co
m
e
t
h
e
d
i
m
e
n
s
io
n
alit
y
p
r
o
b
lem
o
f
SE.
T
h
e
ap
p
licatio
n
o
f
P
SO
f
o
r
s
o
lv
i
n
g
SE
p
r
o
b
le
m
w
it
h
i
n
a
p
o
w
er
s
y
s
te
m
i
s
p
r
o
p
o
s
ed
in
[
1
1
]
.
A
n
o
n
-
iter
ati
v
e
m
et
h
o
d
w
h
ic
h
h
as
n
o
is
s
u
e
s
w
ith
co
n
v
er
g
e
n
ce
an
d
d
o
esn
'
t
n
ee
d
s
tar
tin
g
g
u
es
s
is
u
s
ed
in
[
1
2
]
f
o
r
s
o
lv
i
n
g
t
h
e
SE
p
r
o
b
le
m
.
A
r
o
b
u
s
t
an
d
r
eliab
le
least
w
i
n
s
o
r
ized
s
q
u
ar
e
est
i
m
ato
r
f
o
r
s
ta
tic
SE
is
p
r
o
p
o
s
ed
in
[
1
3
]
.
In
[
1
4
]
p
r
o
p
o
s
es
an
ex
ten
d
ed
Kal
m
a
n
f
ilter
b
ased
d
y
n
a
m
ic
SE
b
y
u
s
i
n
g
P
MU
d
ata.
A
SE
m
et
h
o
d
in
cl
u
d
in
g
eq
u
a
lit
y
co
n
s
tr
ain
t
s
to
m
o
d
el
ze
r
o
in
j
ec
tio
n
s
an
d
v
o
ltag
e
d
ep
en
d
e
n
t
lo
ad
s
i
s
p
r
o
p
o
s
ed
in
[
1
5
]
.
A
m
eth
o
d
o
lo
g
y
b
y
i
n
cl
u
d
in
g
th
e
u
n
ce
r
tai
n
t
y
i
n
SE
is
p
r
o
p
o
s
ed
in
[
1
6
]
.
A
n
o
v
er
v
ie
w
o
f
p
o
w
er
s
y
s
te
m
SE
co
n
tr
o
l
b
y
lo
ad
f
lo
w
p
r
o
g
r
a
m
in
p
u
t
d
ata
i
s
p
r
esen
ted
in
[
1
7
]
.
A
SE
ap
p
r
o
ac
h
b
y
co
n
s
id
er
in
g
th
e
m
e
a
s
u
r
ed
d
ata
o
b
tain
ed
f
r
o
m
s
y
n
c
h
r
o
n
iz
ed
an
d
u
n
s
y
n
ch
r
o
n
ized
s
en
s
o
r
s
is
pr
esen
ted
i
n
[
1
8
]
.
T
h
i
s
p
a
p
e
r
s
o
lv
e
s
th
e
S
E
p
r
o
b
l
em
o
f
p
o
w
e
r
s
y
s
t
em
as
a
c
o
n
s
t
r
a
in
e
d
n
o
n
l
in
ea
r
p
r
o
g
r
am
m
in
g
p
r
o
b
l
em
w
ith
v
a
r
i
o
u
s
c
o
n
s
t
r
a
in
t
s
an
d
b
o
u
n
d
a
r
y
l
im
i
ts
o
n
s
t
a
t
e
v
a
r
ia
b
l
e
s
.
T
h
e
o
b
je
c
t
iv
e
o
f
S
E
i
s
t
o
f
in
d
b
e
s
t
e
s
t
im
at
e
d
s
t
a
te
v
a
r
i
a
b
l
es
f
o
r
th
e
c
o
n
s
i
d
e
r
e
d
p
o
w
e
r
s
y
s
t
em
b
y
o
p
t
im
iz
in
g
a
ll
th
e
e
r
r
o
r
s
in
m
ea
s
u
r
em
en
t
s
.
T
h
is
p
r
o
b
l
em
is
s
o
lv
e
d
b
y
en
f
o
r
c
in
g
th
e
e
q
u
al
ity
a
n
d
l
im
it
c
o
n
s
t
r
a
in
ts
b
y
u
s
in
g
t
ea
ch
in
g
-
l
e
a
r
n
in
g
b
as
e
d
o
p
t
im
i
z
at
i
o
n
(
T
L
B
O
)
t
e
c
h
n
i
q
u
e
.
T
L
B
O
i
s
f
o
r
m
u
l
a
t
ed
b
y
c
o
n
s
i
d
e
r
in
g
tw
o
m
eth
o
d
s
o
f
l
e
a
r
n
in
g
(
i
.
e
.
,
t
e
a
ch
e
r
an
d
le
a
r
n
e
r
p
h
as
e
s
)
in
a
c
l
a
s
s
r
o
o
m
.
T
e
a
ch
e
r
p
h
as
e
c
o
n
s
i
s
ts
th
e
in
t
e
r
a
c
t
i
o
n
b
e
tw
ee
n
l
e
ar
n
e
r
an
d
t
e
a
ch
e
r
,
w
h
e
r
e
as
l
ea
r
n
e
r
s
p
h
as
e
c
o
n
s
i
s
t
s
t
h
e
in
t
e
r
a
ct
i
o
n
am
o
n
g
t
h
e
l
e
ar
n
e
r
s
.
Th
i
s
p
a
p
e
r
i
s
p
r
es
en
t
e
d
a
s
f
o
l
l
o
w
s
.
T
h
e
p
r
o
b
l
em
f
o
r
m
u
l
at
i
o
n
o
f
S
E
is
d
e
s
c
r
i
b
e
d
in
s
e
c
t
i
o
n
2
.
T
h
e
s
o
l
u
ti
o
n
alg
o
r
i
th
m
,
i
.
e
.
,
T
L
B
O
a
l
g
o
r
ith
m
i
s
p
r
es
en
t
e
d
i
n
s
e
ct
i
o
n
3
.
R
es
u
l
ts
an
d
d
i
s
cu
s
s
i
o
n
s
o
n
s
t
an
d
a
r
d
I
E
E
E
1
4
b
u
s
s
y
s
t
em
a
r
e
p
r
e
s
en
te
d
in
s
e
c
ti
o
n
4
.
c
o
n
c
lu
s
i
o
n
s
a
r
e
p
r
e
s
e
n
t
e
d
i
n
s
e
ct
i
o
n
5.
2.
P
RO
B
L
E
M
F
O
R
M
UL
AT
I
O
N
L
o
ad
f
lo
w
ca
lcu
la
tio
n
s
in
d
ee
d
ar
e
an
in
ev
itab
le
to
o
l
f
o
r
o
f
f
-
lin
e
s
t
u
d
ies
a
n
d
p
lan
n
i
n
g
ex
er
cises
,
b
u
t
in
co
m
p
lete
a
n
d
er
r
o
n
eo
u
s
m
ea
s
u
r
e
m
en
t
is
a
r
ea
l
ti
m
e
p
r
o
p
o
s
itio
n
.
So
lu
tio
n
f
o
r
s
u
ch
s
itu
a
tio
n
h
as
b
ee
n
p
r
o
v
id
ed
b
y
s
tat
ic
s
tate
e
s
ti
m
a
to
r
,
w
h
ic
h
i
g
n
o
r
es
th
e
s
lo
w
c
h
an
g
e
s
i
n
th
e
s
y
s
te
m
a
n
d
u
ti
liz
es
r
ed
u
n
d
a
n
t
s
et
o
f
m
ea
s
u
r
e
m
e
n
t
s
f
o
r
cr
o
s
s
c
h
ec
k
in
g
a
n
d
ap
p
r
o
x
i
m
ati
n
g
th
e
m
o
s
t
r
eliab
le
est
i
m
a
tes
o
f
s
y
s
te
m
s
tate
[
1
9
]
.
State
esti
m
ato
r
s
h
o
u
ld
esti
m
ate
t
h
e
s
y
s
te
m
s
tate
s
as
q
u
ick
l
y
as
p
o
s
s
ib
le,
b
u
t
co
n
v
e
n
tio
n
a
l
co
m
p
u
t
er
-
b
ased
m
et
h
o
d
s
ar
e
alm
o
s
t
r
ea
ch
in
g
a
li
m
it
i
n
ter
m
s
o
f
s
p
ee
d
.
Fig
u
r
e
1
d
ep
icts
th
e
d
escr
ip
tio
n
o
f
s
tate
es
ti
m
ato
r
/SE.
I
n
th
i
s
f
i
g
u
r
e,
m
is
n
u
m
b
er
o
f
m
ea
s
u
r
e
m
en
ts
,
n
i
s
n
u
m
b
er
o
f
s
tate
v
ar
iab
les
.
M
e
a
s
u
r
e
m
e
n
t
U
n
c
e
r
t
a
i
n
t
i
e
s
S
t
a
t
e
E
s
t
i
m
a
t
o
r
m
m
e
a
s
u
r
e
m
e
n
t
s
(
m
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n
)
n
S
t
a
t
e
V
a
r
i
a
b
l
e
s
N
e
t
w
o
r
k
P
a
r
a
m
e
t
e
r
s
Fig
u
r
e
1
.
Sch
e
m
atic
d
iag
r
a
m
o
f
s
tate
est
i
m
a
to
r
T
h
e
s
tate
v
ec
to
r
(
x
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h
a
s
v
o
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m
ag
n
it
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d
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a
n
d
a
n
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at
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s
[
2
0
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.
P
o
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h
N
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f
b
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ca
n
b
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e
x
p
r
ess
ed
as
x
=[
δ,
V]
T
w
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h
s
ize
n
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N
-
1
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s
in
g
[
2
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CO
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SI
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Po
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ased
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tech
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th
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lem
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h
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ith
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te
m
.
R
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tain
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w
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alg
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ith
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iq
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d
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ased
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alg
o
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h
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.
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NO
WL
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D
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h
is
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w
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o
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th
e
s
u
p
p
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o
f
“
W
o
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o
n
g
U
n
i
v
er
s
it
y
's
A
ca
d
e
m
ic
R
esear
ch
Fu
n
d
in
g
–
(
2019
-
2
0
2
0
)
”
.
RE
F
E
R
E
NC
E
S
[1
]
Zh
a
o
J,
e
t
a
l.
,
“
P
o
w
e
r
s
y
ste
m
d
y
n
a
m
ic
st
a
te
e
sti
m
a
ti
o
n
:
m
o
ti
v
a
ti
o
n
s,
d
e
f
in
it
io
n
s,
m
e
th
o
d
o
lo
g
ies
,
a
n
d
f
u
tu
re
w
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rk
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
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n
Po
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ms
,
v
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o
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4
,
p
p
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3
1
8
8
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1
9
8
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Ju
ly
2
0
1
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.
[2
]
S
in
g
h
a
l
A
,
Ra
th
o
u
r
HK
,
e
t
a
l.
,
“
S
tate
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sti
m
a
ti
o
n
a
t
a
ll
In
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ia
lev
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l
,
”
Na
ti
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l
Po
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r
S
y
ste
ms
Co
n
fer
e
n
c
e
,
Bh
u
b
a
n
e
swa
r
,
p
p
.
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0
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.
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
K
A
T
elec
o
m
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m
p
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o
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tr
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s
ta
te
est
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u
s
in
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tea
ch
in
g
lea
r
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b
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s
e
d
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p
timiz
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tio
n
…
(
S
u
r
en
d
er R
ed
d
y
S
a
lku
ti
)
2131
[3
]
W
.
G
a
o
,
S
.
W
a
n
g
,
“
On
-
li
n
e
d
y
n
a
m
ic
sta
te
e
sti
m
a
ti
o
n
o
f
p
o
w
e
r
s
y
s
tem
s
,
”
No
rth
Ame
ric
a
n
P
o
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r
S
y
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m 2
0
1
0
,
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to
n
,
T
X
,
p
p
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1
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6
,
2
0
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0
.
[4
]
M
.
A
.
Hu
ss
e
in
a
n
d
A
.
J.
S
u
lt
a
n
,
“
En
h
a
n
c
e
m
e
n
t
o
f
S
tate
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m
a
ti
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n
P
o
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y
ste
m
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s
e
d
H
y
b
rid
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l
g
o
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h
m
,
”
2
0
1
8
1
st A
n
n
u
a
l
I
n
ter
n
a
ti
o
n
a
l
Co
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fer
e
n
c
e
o
n
I
n
f
o
rm
a
ti
o
n
a
n
d
S
c
ien
c
e
s (
Ai
CIS
)
,
F
a
ll
u
ja
h
,
Ira
q
,
p
p
.
1
6
4
-
1
6
9
,
2
0
1
8
.
[5
]
H.
T
e
b
ian
ian
a
n
d
B.
Je
y
a
su
r
y
a
,
"
D
y
n
a
m
i
c
sta
te
e
sti
m
a
ti
o
n
in
p
o
w
e
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ste
m
s
u
sin
g
Ka
lm
a
n
f
il
ter
s,"
2
0
1
3
IE
EE
El
e
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trica
l
Po
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r &
En
e
rg
y
Co
n
fer
e
n
c
e
,
p
p
.
1
-
5
,
2
0
1
3
.
[6
]
T
.
Ok
o
n
a
n
d
K.
W
il
k
o
sz
,
“
Co
m
p
a
riso
n
o
f
we
ig
h
ted
-
lea
st
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sq
u
a
re
s
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o
w
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s
y
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m
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a
ti
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n
p
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lar
a
n
d
re
c
tan
g
u
lar
c
o
o
rd
i
n
a
te
sy
ste
m
s,
”
2
0
1
0
9
th
In
ter
n
a
ti
o
n
a
l
C
o
n
fer
e
n
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o
n
E
n
v
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n
me
n
t
a
n
d
El
e
c
trica
l
En
g
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e
e
rin
g
,
p
p
.
1
4
0
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1
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3
,
2
0
1
0
.
[7
]
Y.
Yu
e
h
a
o
,
L
.
Hu
i
,
B.
W
e
i,
L
.
Zh
a
o
h
u
i,
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Ha
o
a
n
d
D.
Ya
o
h
e
n
g
,
"
A
d
istri
b
u
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n
e
tw
o
rk
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te
e
stim
a
ti
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n
m
e
th
o
d
b
a
se
d
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o
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r
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c
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rg
y
d
a
ta
a
c
q
u
isit
io
n
sy
ste
m
,
"
2
0
1
6
Ch
in
a
In
ter
n
a
ti
o
n
a
l
Co
n
fer
e
n
c
e
o
n
El
e
c
tricity
Distrib
u
ti
o
n
(
CICED)
,
p
p
.
1
-
4
,
2
0
1
6
.
[8
]
Bra
n
d
a
li
k
R,
W
e
ll
ss
o
w
W
H
,
“
P
o
w
e
r
s
y
ste
m
sta
te
e
sti
m
a
ti
o
n
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th
e
x
ten
d
e
d
p
o
w
e
r
f
o
r
m
u
latio
n
s
,”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
Po
we
r
&
En
e
rg
y
S
y
ste
ms
,
v
o
l.
1
1
5
,
F
e
b
r
u
a
ry
2
0
2
0
.
[9
]
G
o
leijan
i
S
.
,
A
m
e
li
M
.
T
.
,
“
A
m
u
lt
i
-
a
g
e
n
t
b
a
se
d
a
p
p
ro
a
c
h
t
o
p
o
w
e
r
s
y
ste
m
d
y
n
a
m
ic
sta
te
e
stim
a
ti
o
n
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y
c
o
n
sid
e
ri
n
g
a
lg
e
b
ra
ic
a
n
d
d
y
n
a
m
ic
sta
te
v
a
riab
les
,”
El
e
c
tric
P
o
we
r
S
y
ste
ms
Res
e
a
rc
h
,
v
o
l.
1
6
3
,
p
p
.
4
7
0
-
4
8
1
,
Oc
to
b
e
r
2
0
1
8
.
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0
]
R
a
h
m
a
n
M
d
.
A
,
Ve
n
a
y
a
g
a
m
o
o
r
th
y
G
.
K
.
,
“
A
h
y
b
r
i
d
m
e
t
h
o
d
f
o
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p
o
w
e
r
sy
s
t
e
m
s
t
a
t
e
e
s
t
im
a
t
i
o
n
u
s
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n
g
Ce
l
l
u
l
a
r
C
o
m
p
u
t
a
t
i
o
n
a
l
Ne
tw
o
rk
,”
E
n
g
i
n
e
e
r
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n
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A
p
p
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t
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o
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f
A
r
t
i
f
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l
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n
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l
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g
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n
c
e
,
v
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l
.
6
4
,
p
p
.
1
4
0
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1
5
1
,
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e
p
t
e
m
b
e
r
2
0
1
7
.
[1
1
]
T
u
n
g
a
d
io
D
.
H
.
,
N
u
m
b
i
B
.
P
.
,
e
t
a
l
.
,
“
P
a
rti
c
le
sw
a
r
m
o
p
ti
m
iz
a
ti
o
n
f
o
r
p
o
w
e
r
s
y
ste
m
st
a
te
e
sti
m
a
ti
o
n
,”
Ne
u
ro
c
o
mp
u
ti
n
g
,
v
o
l
.
1
4
8
,
p
p
.
1
7
5
-
1
8
0
,
Ja
n
u
a
ry
2
0
1
5
.
[1
2
]
Jia
n
g
X
.
T
.
,
Ch
o
w
J
.
H
.
,
e
t
a
l
.
,
“
P
o
w
e
r
s
y
ste
m
sta
te
e
sti
m
a
ti
o
n
u
sin
g
a
d
irec
t
n
o
n
-
it
e
ra
ti
v
e
m
e
th
o
d
,”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
Po
we
r
&
En
e
rg
y
S
y
ste
ms
,
v
o
l.
7
3
,
p
p
.
3
6
1
-
3
6
8
,
De
c
e
m
b
e
r
2
0
1
5
.
[1
3
]
V
e
d
ik
B
.
,
Ch
a
n
d
e
l
A
.
K
.
,
“
P
o
w
e
r
sy
ste
m
sta
ti
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sta
te
e
sti
m
a
ti
o
n
u
sin
g
a
lea
st
w
in
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rize
d
sq
u
a
re
ro
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u
st
e
stim
a
to
r
,”
Ne
u
ro
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o
mp
u
ti
n
g
,
v
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l
.
2
0
7
,
p
p
.
4
5
7
-
4
6
8
,
S
e
p
tem
b
e
r
2
0
1
6
.
[1
4
]
T
e
b
ian
ian
H
.
,
Je
y
a
su
r
y
a
B
.
,
“
Dy
n
a
m
i
c
sta
te
e
sti
m
a
ti
o
n
in
p
o
w
e
r
sy
ste
m
s:
M
o
d
e
li
n
g
,
a
n
d
c
h
a
ll
e
n
g
e
s
,”
El
e
c
tric
Po
we
r S
y
ste
ms
Res
e
a
rc
h
,
v
o
l.
1
2
1
,
p
p
.
1
0
9
-
1
1
4
,
A
p
ril
2
0
1
5
.
[1
5
]
Ka
b
iri
M
.
,
e
t
a
l.
,
“
En
h
a
n
c
in
g
p
o
w
e
r
s
y
ste
m
sta
te
e
sti
m
a
ti
o
n
b
y
in
c
o
rp
o
ra
ti
n
g
e
q
u
a
li
ty
c
o
n
stra
in
ts
o
f
v
o
lt
a
g
e
d
e
p
e
n
d
e
n
t
lo
a
d
s
a
n
d
z
e
ro
i
n
jec
ti
o
n
s
,”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
Po
we
r
&
En
e
rg
y
S
y
s
tem
s
,
v
o
l.
9
9
,
p
p
.
6
5
9
-
6
7
1
,
Ju
ly
2
0
1
8
.
[1
6
]
A
.
K.
A
l
-
Oth
m
a
n
a
n
d
M
.
R.
Irv
i
n
g
,
“
Un
c
e
rtain
ty
m
o
d
e
ll
in
g
in
p
o
w
e
r
s
y
ste
m
st
a
te
e
sti
m
a
ti
o
n
,
”
IE
E
Pro
c
e
e
d
in
g
s
Ge
n
e
ra
ti
o
n
,
T
ra
n
sm
issio
n
a
n
d
Di
strib
u
ti
o
n
,
v
o
l.
1
5
2
,
n
o
.
2
,
p
p
.
2
3
3
-
2
3
9
,
M
a
rc
h
2
0
0
5
.
[1
7
]
G
u
lati
A
.
,
G
u
lati
N
.
,
S
o
lan
k
i
S
.
K
.
,
“
Ov
e
r
v
ie
w
o
f
S
tate
Esti
m
a
ti
o
n
T
e
c
h
n
iq
u
e
f
o
r
P
o
w
e
r
S
y
ste
m
Co
n
tr
o
l
,”
IOS
R
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
El
e
c
tro
n
ics
En
g
in
e
e
rin
g
,
v
o
l
.
8
,
n
o
.
5
,
p
p
.
5
1
-
5
5
,
De
c
e
m
b
e
r
2
0
1
3
.
[1
8
]
M
a
n
o
u
sa
k
is
N
.
M
.
,
Ko
rre
s
G
.
N
.
,
“
A
h
y
b
rid
p
o
w
e
r
s
y
ste
m
sta
te
e
s
ti
m
a
to
r
u
sin
g
s
y
n
c
h
ro
n
ize
d
a
n
d
u
n
sy
n
c
h
ro
n
ize
d
se
n
so
rs
,”
In
ter
n
a
ti
o
n
a
l
T
ra
n
sa
c
ti
o
n
s
o
n
E
lec
trica
l
En
e
r
g
y
S
y
ste
ms
,
v
o
l.
2
8
,
n
o
.
8
,
A
p
ril
2
0
1
8
.
[1
9
]
P
.
Ba
rto
l
o
m
e
y
a
n
d
S
.
S
e
m
e
n
e
n
k
o
,
“
S
u
p
e
r
-
a
c
c
e
lera
ted
p
o
w
e
r
s
y
st
e
m
s
p
o
w
e
r
f
lo
w
a
n
d
sta
te
e
sti
m
a
t
io
n
c
a
lcu
lati
o
n
s
w
it
h
in
th
e
W
A
M
S
e
n
v
iro
n
m
e
n
t,
”
2
0
1
7
1
4
th
In
ter
n
a
ti
o
n
a
l
Co
n
fer
e
n
c
e
o
n
En
g
in
e
e
rin
g
o
f
M
o
d
e
rn
E
lec
tric
S
y
ste
ms
(
EM
ES
)
,
p
p
.
5
5
-
5
8
,
2
0
1
7
.
[2
0
]
E.
G
h
a
h
re
m
a
n
i
a
n
d
I.
Ka
m
wa
,
“
L
o
c
a
l
a
n
d
W
id
e
-
A
re
a
P
M
U
-
Ba
se
d
De
c
e
n
tralize
d
D
y
n
a
m
i
c
S
tate
Esti
m
a
ti
o
n
i
n
M
u
lt
i
-
M
a
c
h
in
e
P
o
w
e
r
S
y
ste
m
s,”
in
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Po
we
r S
y
ste
ms
,
v
o
l.
3
1
,
n
o
.
1
,
p
p
.
5
4
7
-
5
6
2
,
Ja
n
.
2
0
1
6
.
[2
1
]
H.
Kh
a
z
ra
j,
F
.
F
a
ria
d
a
S
il
v
a
a
n
d
C.
L
.
Ba
k
,
“
A
p
e
r
f
o
rm
a
n
c
e
c
o
m
p
a
riso
n
b
e
tw
e
e
n
e
x
t
e
n
d
e
d
Ka
l
m
a
n
F
il
ter
a
n
d
u
n
sc
e
n
ted
Ka
lm
a
n
F
il
ter
in
p
o
w
e
r
s
y
st
e
m
d
y
n
a
m
ic
sta
te
e
sti
m
a
ti
o
n
,
”
2
0
1
6
5
1
st
I
n
ter
n
a
ti
o
n
a
l
Un
i
v
e
rs
it
ies
Po
we
r
En
g
i
n
e
e
rin
g
C
o
n
fer
e
n
c
e
(
UPEC)
,
p
p
.
1
-
6
,
2
0
1
6
.
[2
2
]
W
a
n
g
X
,
Zh
a
o
J,
e
t
a
l
.
,
“
F
a
st
ro
b
u
st
p
o
w
e
r
s
y
ste
m
d
y
n
a
m
ic
sta
te
e
sti
m
a
ti
o
n
u
sin
g
m
o
d
e
l
t
ra
n
sf
o
r
m
a
ti
o
n
,
”
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
E
lec
trica
l
Po
we
r
&
En
e
rg
y
S
y
ste
ms
,
v
o
l.
1
1
4
,
Ja
n
u
a
ry
2
0
2
0
.
[2
3
]
S
c
h
m
id
t
F
.
,
A
l
m
e
id
a
M
.
C
.
,
“
A
th
e
o
re
ti
c
a
l
f
ra
m
e
w
o
rk
f
o
r
q
u
a
li
tat
iv
e
p
ro
b
lem
s
in
p
o
w
e
r
s
y
ste
m
st
a
te
e
sti
m
a
ti
o
n
,”
El
e
c
tric P
o
we
r S
y
ste
ms
Res
e
a
rc
h
,
v
o
l.
1
5
4
,
p
p
.
5
2
8
-
5
3
7
,
Ja
n
u
a
ry
2
0
1
8
.
[2
4
]
Ch
e
n
T
.
,
“
Ro
b
u
st
sta
te
e
stim
a
ti
o
n
f
o
r
p
o
w
e
r
s
y
ste
m
s
v
i
a
m
o
v
in
g
h
o
rizo
n
stra
teg
y
,”
S
u
sta
in
a
b
le
E
n
e
rg
y
,
Gr
id
s
a
n
d
Ne
two
rk
s
,
v
o
l.
1
0
,
p
p
.
4
6
-
5
4
,
J
u
n
e
2
0
1
7
.
[2
5
]
Ch
e
n
T
.
,
F
o
o
Y
.
S
.
E
.
,
e
t
a
l.
,
“
Distrib
u
te
d
S
tate
Esti
m
a
ti
o
n
Us
in
g
a
M
o
d
if
ied
P
a
rti
ti
o
n
e
d
M
o
v
in
g
Ho
rizo
n
S
trate
g
y
f
o
r
P
o
w
e
r
S
y
ste
m
s
,”
S
e
n
so
rs
,
v
o
l.
1
7
,
n
o
.
1
0
,
2
0
1
7
.
[2
6
]
S
h
a
h
i
d
e
h
p
o
u
r
M
,
M
a
rw
a
li
M
,
“
Ro
le
o
f
F
u
z
z
y
S
e
ts
in
P
o
w
e
r
S
y
ste
m
S
tate
Esti
m
a
ti
o
n
,”
In
ter
n
a
t
i
o
n
a
l
J
o
u
rn
a
l
o
f
Eme
rg
in
g
El
e
c
tric P
o
we
r S
y
ste
ms
,
v
o
l.
1
,
n
o
.
1
,
2
0
0
4
.
[2
7
]
I.
A
k
in
g
e
n
e
y
e
J.
W
u
a
n
d
J.
Ya
n
g
,
“
Op
ti
m
u
m
P
M
U
p
lac
e
m
e
n
t
f
o
r
p
o
w
e
r
s
y
ste
m
sta
t
e
e
sti
m
a
ti
o
n
,
”
2
0
1
7
IEE
E
Po
we
r
&
En
e
rg
y
S
o
c
iety
Ge
n
e
ra
l
M
e
e
ti
n
g
,
p
p
.
1
-
5
,
2
0
1
7
.
[2
8
]
Kh
a
n
Z
.
,
Ra
z
a
li
R
.
B
.
,
e
t
a
l
.
,
“
S
tate
e
stim
a
ti
o
n
o
f
th
e
p
o
w
e
r
s
y
ste
m
u
sin
g
ro
b
u
st
e
stim
a
to
r
,”
AIP
Co
n
fer
e
n
c
e
Pro
c
e
e
d
in
g
s
,
2
0
1
6
.
[2
9
]
Bo
u
c
h
e
k
a
ra
H
.
R
.
E
.
H
.
,
A
b
id
o
M
.
A
.
,
e
t
a
l
.
,
“
Op
ti
m
a
l
p
o
w
e
r
f
lo
w
u
sin
g
T
e
a
c
h
in
g
-
L
e
a
rn
in
g
-
Ba
se
d
Op
ti
m
iza
ti
o
n
tec
h
n
iq
u
e
,”
El
e
c
tric P
o
we
r S
y
ste
ms
Res
e
a
rc
h
,
v
o
l.
1
1
4
,
p
p
.
49
-
5
9
,
S
e
p
tem
b
e
r
2
0
1
4
.
[3
0
]
G
il
l
HS,
Kh
e
h
ra
BS
,
e
t
a
l
.
,
“
T
e
a
c
h
in
g
-
lea
rn
in
g
-
b
a
se
d
o
p
t
im
iz
a
ti
o
n
a
lg
o
rit
h
m
to
m
in
i
m
ize
c
r
o
ss
e
n
tro
p
y
f
o
r
se
lec
ti
n
g
m
u
lt
il
e
v
e
l
th
re
sh
o
l
d
v
a
lu
e
s
,”
Eg
y
p
ti
a
n
In
f
o
rm
a
ti
c
s J
o
u
rn
a
l
.
v
o
l
.
2
0
,
n
o
.
1
,
p
p
.
1
1
-
2
5
,
M
a
rc
h
2
0
1
9
.
[3
1
]
R.
R.
Nu
c
e
ra
a
n
d
M
.
L
.
G
il
les
,
“
A
b
lo
c
k
e
d
sp
a
rs
e
m
a
tri
x
f
o
r
m
u
latio
n
f
o
r
th
e
so
lu
t
io
n
o
f
e
q
u
a
li
ty
-
c
o
n
stra
in
e
d
sta
te
e
sti
m
a
ti
o
n
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Po
we
r
S
y
ste
ms
,
v
o
l.
6
,
n
o
.
1
,
p
p
.
2
1
4
-
2
2
4
,
F
e
b
.
1
9
9
1
.
[3
2
]
Ro
g
é
rio
M
.
,
A
n
to
n
i
o
S
.
C
.
,
e
t
a
l.
,
“
In
f
o
rm
a
ti
o
n
T
h
e
o
re
ti
c
G
e
n
e
ra
li
z
e
d
S
tate
Esti
m
a
ti
o
n
i
n
p
o
w
e
r
s
y
ste
m
s
,”
El
e
c
tric
Po
we
r S
y
ste
ms
Res
e
a
rc
h
,
v
o
l.
1
8
2
,
M
a
y
2
0
2
0
.
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