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Saif
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b
in
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am
r
i
,
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tr
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o
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s
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Un
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1
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4
]
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p
r
o
a
c
h
,
a
n
d
n
o
t
i
n
s
t
a
t
e
-
s
p
ac
e
r
e
p
r
e
s
e
n
t
a
ti
o
n
[
2
5
]
.
T
h
i
s
p
a
p
e
r
s
h
o
w
s
a
n
a
p
p
r
o
a
c
h
t
o
d
e
r
i
v
e
t
h
e
s
t
a
te
-
s
p
a
c
e
m
at
h
e
m
a
t
i
ca
l
m
o
d
e
l
o
f
m
u
l
t
i
-
a
r
e
a
m
i
c
r
o
-
g
r
i
d
n
e
t
w
o
r
k
.
T
h
e
m
o
t
iv
a
t
i
o
n
o
f
t
h
i
s
r
e
s
ea
r
c
h
w
o
r
k
is
t
o
d
e
r
i
v
e
a
n
d
d
e
t
e
r
m
i
n
e
t
h
e
e
v
a
r
a
g
e
d
y
n
a
m
i
c
a
l
b
e
h
a
v
i
o
u
r
o
f
f
r
e
q
u
e
n
c
y
n
e
t
w
o
r
k
b
y
u
s
i
n
g
s
i
m
i
l
a
r
i
t
y
t
r
a
n
s
f
o
r
m
a
t
i
o
n
a
n
d
d
e
c
o
m
p
o
s
i
t
i
o
n
a
p
p
r
o
a
c
h
.
T
h
e
p
r
o
p
o
s
e
d
m
i
c
r
o
-
g
r
i
d
m
o
d
e
l
w
a
s
v
a
l
i
d
a
t
ed
w
i
t
h
t
h
e
d
i
f
f
e
r
e
n
t
l
o
a
d
d
e
m
a
n
d
p
r
o
f
i
l
e
.
A
t
t
h
e
e
n
d
o
f
t
h
e
a
n
a
l
y
s
i
s
,
t
h
e
c
o
m
p
a
r
is
o
n
w
i
t
h
t
h
e
c
o
n
v
e
n
t
i
o
n
al
a
p
p
r
o
a
c
h
u
s
i
n
g
c
e
n
t
r
e
o
f
i
n
e
r
ti
a
(
C
O
I
)
h
a
s
b
e
e
n
m
a
d
e
.
2.
RE
S
E
ARCH
M
E
T
H
O
D
2
.
1
.
G
ener
a
t
o
r
m
o
del
T
h
e
m
ain
g
o
al
is
to
en
s
u
r
e
th
at
th
e
d
e
r
iv
ed
m
ath
em
atica
l
eq
u
atio
n
s
m
u
s
t
b
e
a
b
le
to
r
ep
r
esen
t
th
e
in
ter
co
n
n
ec
ted
,
lo
ad
s
h
ar
i
n
g
an
d
f
r
e
q
u
en
c
y
co
n
tr
o
l.
Af
ter
th
at,
o
n
e
g
en
er
at
o
r
s
y
s
tem
was d
er
iv
ed
b
y
u
s
in
g
s
ev
er
al
ap
p
r
o
x
im
atio
n
p
r
o
ce
s
s
es
to
r
ep
r
esen
t
th
eir
a
v
er
a
g
e
b
eh
av
io
r
.
Fig
u
r
e
1
s
h
o
w
th
e
in
t
er
co
n
n
ec
ted
o
f
two
ar
ea
s
o
f
m
icr
o
-
g
r
id
.
Fig
u
r
e
1
: T
h
e
in
ter
co
n
n
ec
ted
o
f
two
ar
ea
s
o
f
m
icr
o
-
g
r
id
s
n
e
two
r
k
T
h
e
s
y
s
tem
n
etwo
r
k
is
ass
u
m
ed
to
h
av
e
2
b
u
s
s
es
an
d
2
g
en
er
at
o
r
s
wh
ile
ea
ch
g
e
n
er
ato
r
is
ass
u
m
ed
t
o
b
e
eq
u
ip
p
ed
with
th
e
p
r
im
e
m
o
v
er
a
n
d
s
p
ee
d
g
o
v
e
r
n
o
r
.
T
h
e
m
o
d
el
was d
i
v
id
ed
in
to
f
o
u
r
m
ain
p
ar
ts
w
h
ich
ar
e
r
o
tatin
g
m
ass
,
p
r
im
e
m
o
v
e
r
,
s
p
ee
d
g
o
v
er
n
o
r
an
d
lo
ad
m
o
d
el.
E
ac
h
p
ar
t
was
m
o
d
eled
s
ep
ar
at
ely
an
d
a
u
g
m
en
t
e
d
all
to
g
eth
er
to
b
ec
o
m
e
o
n
e
m
o
d
el.
T
h
e
s
win
g
eq
u
atio
n
ca
n
b
e
u
s
ed
to
m
o
d
el
th
e
g
en
er
ato
r
an
d
th
e
m
icr
o
-
g
r
id
n
etwo
r
k
as sh
o
wn
i
n
(
1
)
.
T
h
is
eq
u
atio
n
d
escr
ib
es th
e
d
ev
iati
o
n
s
o
f
f
r
eq
u
e
n
cy
r
esp
o
n
s
e
in
p
er
u
n
it b
ase.
2
∆
=
∆
−
∆
(
1
)
W
h
er
e
∆
,
∆
an
d
∆
ar
e
th
e
d
ev
iat
io
n
s
o
f
m
ec
h
a
n
ical
p
o
wer
,
elec
tr
ical
lo
ad
d
em
an
d
a
n
d
f
r
e
q
u
en
cy
r
esp
ec
tiv
ely
.
is
th
e
p
er
u
n
it
in
er
tia
co
n
s
tan
t
wh
ich
r
elate
d
to
th
e
k
in
etic
en
er
g
y
at
t
h
e
s
y
n
ch
r
o
n
o
u
s
s
p
ee
d
with
r
esp
ec
t
to
g
e
n
er
ato
r
r
atin
g
.
T
h
e
s
o
u
r
ce
o
f
m
ec
h
an
ical
p
o
wer
f
o
r
r
o
tatin
g
m
ass
is
co
m
m
o
n
ly
k
n
o
wn
as
th
e
p
r
im
e
m
o
v
er
.
T
h
e
m
o
d
el
f
o
r
p
r
im
e
m
o
v
er
is
r
elate
d
to
th
e
c
h
an
g
e
s
in
m
ec
h
a
n
ical
p
o
wer
o
u
tp
u
t
∆
to
th
e
ch
an
g
es
in
s
team
p
o
s
itio
n
∆
.
T
h
is
wo
r
k
,
u
s
ed
th
e
s
im
p
lest
p
r
im
e
m
o
v
er
m
o
d
el
wh
ich
ca
n
b
e
ap
p
r
o
x
im
ated
with
a
s
in
g
le
tim
e
co
n
s
tan
t
r
esu
ltin
g
in
th
e
f
o
llo
win
g
:
∆
=
1
(
∆
−
∆
)
(
2
)
T
h
e
s
p
ee
d
g
o
v
er
n
o
r
s
y
s
tem
∆
is
d
ep
en
d
s
o
n
th
e
elec
tr
ical
lo
ad
d
em
an
d
.
W
h
en
t
h
e
lo
ad
d
e
m
an
d
s
u
d
d
en
ly
in
c
r
ea
s
ed
,
th
e
elec
tr
i
ca
l
lo
ad
p
o
wer
e
x
ce
ed
s
th
e
m
e
ch
an
ical
p
o
wer
a
n
d
r
esu
ltin
g
t
h
e
p
o
wer
d
e
f
icien
cy
.
T
h
e
am
o
u
n
t
o
f
p
o
wer
d
ef
icie
n
cy
will
in
f
lu
en
ce
t
h
e
am
o
u
n
t
o
f
k
in
etic
en
e
r
g
y
s
to
r
e
d
in
t
h
e
r
o
tatin
g
s
y
s
tem
.
T
h
e
r
ed
u
ctio
n
in
k
i
n
etic
en
er
g
y
will
ca
u
s
e
th
e
tu
r
b
in
e
s
p
ee
d
an
d
co
n
s
eq
u
en
tly
th
e
g
en
er
at
o
r
f
r
eq
u
en
cy
to
f
all.
T
h
is
ch
an
g
e
in
s
p
ee
d
is
s
en
s
ed
b
y
th
e
tu
r
b
in
e
g
o
v
er
n
o
r
an
d
ac
t
to
ad
ju
s
t
th
e
tu
r
b
in
e
in
p
u
t
v
alv
e
to
ch
an
g
e
th
e
m
ec
h
an
ical
p
o
wer
o
u
tp
u
t
to
b
r
in
g
th
e
s
p
ee
d
to
a
n
ew
s
t
ea
d
y
-
s
tate.
T
h
e
eq
u
atio
n
wh
i
ch
d
ir
ec
tly
d
escr
ib
e
th
e
s
p
ee
d
g
o
v
er
n
o
r
b
e
h
av
io
r
is
as f
o
llo
ws
:
∆
=
1
(
∆
−
∆
−
∆
)
(
3
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6
9
3
0
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
,
Vo
l.
18
,
No
.
6
,
Dec
em
b
e
r
2
0
2
0
:
3
3
2
4
-
333
0
3326
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s
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m
c
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o
f
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t
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a
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i
g
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i
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g
a
n
d
h
e
a
t
i
n
g
l
o
a
d
s
,
a
n
d
l
o
a
d
d
e
p
e
n
d
e
n
t
t
o
f
r
e
q
u
e
n
c
y
s
u
c
h
a
s
m
o
t
o
r
l
o
a
d
s
.
T
h
e
s
e
n
s
i
t
i
v
i
t
y
o
f
s
u
c
h
l
o
a
d
s
i
s
d
e
p
e
n
d
s
o
n
t
h
e
i
r
s
p
e
e
d
-
l
o
a
d
c
h
a
r
a
c
t
e
r
i
s
t
i
c
s
a
n
d
c
a
n
b
e
a
p
p
r
o
x
i
m
a
t
e
l
y
d
e
f
i
n
e
d
b
y
:
∆
=
∆
+
∆
(
4
)
∆
is
th
e
n
o
n
-
f
r
eq
u
e
n
cy
s
en
s
itiv
e
lo
ad
ch
a
n
g
e
a
n
d
∆
is
th
e
f
r
eq
u
e
n
cy
s
en
s
itiv
e
lo
ad
c
h
an
g
e
.
is
ex
p
r
ess
ed
as p
er
ce
n
t c
h
an
g
e
in
lo
a
d
d
iv
i
d
e
b
y
p
er
ce
n
t c
h
an
g
e
i
n
f
r
e
q
u
en
cy
.
2
.
2
.
M
o
delin
g
t
he
t
wo
m
icro
-
g
rid a
re
a
2
.
2
.
1
.
T
ie
-
lin
e
m
o
del
I
n
th
is
s
ec
tio
n
,
ea
ch
m
icr
o
-
g
r
id
ar
ea
was
ass
u
m
ed
to
h
av
e
o
n
e
g
en
e
r
ato
r
m
o
d
el.
T
h
e
co
m
p
lete
m
ath
em
atica
l
eq
u
atio
n
f
o
r
two
m
icr
o
-
g
r
id
a
r
ea
tak
e
in
t
o
a
cc
o
u
n
t
th
e
i
n
f
o
r
m
atio
n
o
f
g
e
n
er
ato
r
r
o
to
r
a
n
g
le
=
.
W
h
er
e
is
r
ep
r
esen
ted
th
e
n
u
m
b
er
o
f
ar
ea
.
T
h
is
in
f
o
r
m
ati
o
n
is
im
p
o
r
tan
t
to
e
n
s
u
r
e
th
e
c
o
o
p
er
ativ
e
b
eh
av
io
r
b
et
wee
n
b
o
th
ar
ea
s
i
n
ter
m
o
f
a
m
o
u
n
t
o
f
p
o
wer
s
h
ar
in
g
o
v
e
r
th
e
tie
-
lin
e.
Du
r
in
g
n
o
r
m
al
o
p
er
atio
n
,
th
e
r
ea
l p
o
wer
tr
an
s
f
er
r
e
d
o
v
e
r
th
e
tie
lin
e
is
g
iv
en
b
y
:
=
|
|
|
|
(
5
)
W
h
e
r
e
=
+
+
a
n
d
=
−
w
h
i
l
e
a
n
d
r
e
p
r
e
s
e
n
t
t
h
e
a
r
ea
1
a
n
d
a
r
e
a
2
r
e
s
p
e
c
t
i
v
el
y
.
L
i
n
e
a
r
i
z
i
n
g
t
h
is
e
q
u
a
t
i
o
n
b
y
a
s
s
u
m
i
n
g
t
h
e
s
m
a
l
l
d
e
v
i
at
i
o
n
i
n
t
h
e
t
i
e
l
i
n
e
p
o
w
e
r
f
l
o
w
∆
12
f
r
o
m
t
h
e
n
o
m
i
n
a
l
v
a
l
u
e
:
∆
=
|
0
∆
(
6
)
=
∆
is
th
e
p
o
wer
an
g
le
at
th
e
in
it
ial
o
p
er
atin
g
an
g
le
0
=
0
−
0
an
d
it
wa
s
d
ef
in
ed
as
th
e
s
y
n
ch
r
o
n
izin
g
p
o
wer
co
ef
f
icien
t a
n
d
th
en
th
e
tie
lin
e
p
o
wer
d
e
v
iatio
n
is
tak
e
o
n
th
e
f
o
r
m
:
∆
=
(
∆
−
∆
)
(
7
)
T
h
e
d
ir
ec
tio
n
o
f
p
o
wer
f
lo
w
is
d
ictated
b
y
th
e
r
o
to
r
an
g
le
d
if
f
er
en
ce
.
As
s
h
o
wn
in
(
7
)
s
h
o
w
th
e
ex
am
p
le
o
f
p
o
wer
f
lo
ws
f
r
o
m
ar
ea
o
n
e
to
ar
ea
two
wh
en
∆
is
p
o
s
itiv
e.
As
s
h
o
wn
in
(
4
)
an
d
(
7
)
ca
n
b
e
co
m
b
in
ed
in
t
o
(
1
)
to
b
ec
o
m
e
o
n
e
c
o
m
p
lete
e
q
u
atio
n
f
o
r
r
o
tatin
g
g
e
n
er
ato
r
as f
o
llo
ws
:
∆
=
1
2
(
∆
−
(
∆
−
∆
)
−
∆
−
∆
)
(
8
)
∆
=
1
2
(
∆
−
(
∆
−
∆
)
−
∆
−
∆
)
2
.
2
.
2
.
T
ie
-
lin
e
bia
s
co
ntr
o
l
T
h
e
r
u
le
o
f
th
u
m
b
o
f
m
icr
o
-
g
r
i
d
s
y
s
tem
o
p
e
r
atio
n
c
o
n
n
ec
ted
b
etwe
en
two
ar
ea
s
is
to
en
s
u
r
e
th
e
wh
o
le
s
y
s
tem
o
p
er
atin
g
at
th
e
n
o
m
i
n
al
f
r
eq
u
e
n
cy
.
So
,
th
is
is
ab
le
to
co
n
s
id
er
th
e
a
r
ea
co
n
t
r
o
l
er
r
o
r
(
AC
E
)
wh
er
e
ea
ch
ar
ea
ten
d
s
to
r
ed
u
ce
th
e
f
r
eq
u
en
cy
e
r
r
o
r
to
ze
r
o
.
T
h
e
was
in
teg
r
ated
to
h
av
e
th
e
r
ate
o
f
ch
a
n
g
e
with
r
esp
ec
t to
tim
e
an
d
its
in
f
o
r
m
a
tio
n
is
u
s
ed
as
∆
f
o
r
c
o
m
b
in
e
with
s
p
ee
d
g
o
v
er
n
o
r
m
o
d
el
as sh
o
wn
in
(
3
)
.
∆
=
∆
=
∆
+
∆
+
∆
(
9
)
=
∆
+
∆
2
.
2
.
3
.
Sta
t
e
-
s
pa
ce
re
presenta
t
io
n
As
s
h
o
wn
in
(1
-
3
)
,
(
8
)
a
n
d
(
9
)
ca
n
b
e
wr
itten
in
to
th
e
s
tate
-
s
p
ac
e
r
ep
r
esen
tatio
n
.
Fro
m
th
e
eq
u
atio
n
d
ev
elo
p
e
d
,
ea
ch
ar
ea
will
p
r
o
v
id
e
f
iv
e
s
tate
v
ar
iab
les.
Sin
ce
it
tak
es
in
to
ac
co
u
n
t
all
th
e
i
n
f
o
r
m
atio
n
r
eq
u
ir
e
d
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
A
ve
r
a
g
e
d
yn
a
mica
l freq
u
en
cy
b
eh
a
vio
u
r
fo
r
mu
lti
-
a
r
ea
is
la
n
d
ed
micro
-
g
r
id
...
(
Mo
h
d
S
a
ifu
z
a
m
b
in
Ja
mri
)
3327
f
o
r
two
ar
ea
s
in
ter
co
n
n
ec
tio
n
,
th
e
to
tal
s
tate
v
ar
iab
les will
b
e
co
m
e
ten
.
T
h
e
s
y
s
tem
ca
n
b
e
r
ep
r
esen
ted
in
s
tate
s
p
ac
e
as f
o
llo
ws
:
̇
=
+
(
1
0
)
T
h
e
m
atr
ix
an
d
is
ar
r
an
g
ed
a
s
s
h
o
wn
in
(
1
1
)
an
d
(
1
2
)
.
=
[
−
1
2
1
⁄
0
−
2
1
⁄
2
1
⁄
1
2
1
⁄
0
0
0
0
0
0
−
2
2
2
⁄
2
2
⁄
−
2
2
⁄
0
1
2
1
⁄
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
−
1
1
⁄
0
1
1
⁄
0
0
0
0
0
0
0
0
−
1
2
⁄
0
1
2
⁄
0
0
−
1
1
1
⁄
0
0
0
0
0
−
1
1
⁄
0
1
1
⁄
0
0
−
1
2
2
⁄
0
0
0
0
0
−
1
2
⁄
0
2
2
⁄
−
1
0
−
0
0
0
0
0
0
0
−
2
−
0
0
0
0
0
0
]
(
1
1
)
=
[
−
1
2
1
−
1
2
2
0
0
0
.
.
.
.
.
.
0
]
(
1
10
)
(
1
2
)
2
.
2
.
4
.
An a
v
er
a
g
e
beha
v
io
r
I
n
th
is
s
ec
tio
n
,
an
av
er
ag
e
b
eh
av
io
r
was
d
eter
m
in
ed
b
y
u
s
in
g
s
im
ilar
ity
tr
an
s
f
o
r
m
atio
n
m
eth
o
d
.
T
h
e
n
ew
s
tate
v
ar
iab
les ar
e
in
t
r
o
d
u
ce
d
wh
ich
d
escr
ib
ed
th
e
p
lu
s
-
m
in
u
s
av
er
ag
e
b
eh
a
v
io
r
as
f
o
llo
ws
:
=
1
2
1
+
1
2
2
(
1
3
)
=
1
2
1
−
1
2
2
(
1
4
)
is
th
e
n
ew
s
tate
v
ar
iab
les
wh
ile
is
th
e
g
en
er
ato
r
s
t
ate
v
ar
iab
l
e.
T
h
is
eq
u
atio
n
wo
u
ld
g
en
er
at
e
th
e
tr
an
s
f
o
r
m
atio
n
m
atr
ix
wh
i
ch
wo
u
ld
b
e
u
s
ed
to
g
en
er
ate
th
e
n
ew
v
ec
to
r
m
atr
ix
.
A
s
y
s
te
m
in
p
r
ev
io
u
s
s
ec
tio
n
ca
n
b
e
tr
an
s
f
o
r
m
ed
to
a
s
im
ilar
s
y
s
tem
,
̇
=
−
1
+
(
1
5
)
is
th
e
tr
an
s
f
o
r
m
atio
n
m
atr
ix
wh
er
e
th
e
co
lu
m
n
s
ar
e
th
e
co
o
r
d
in
ates
o
f
t
h
e
b
asis
v
ec
to
r
s
o
f
th
e
n
ew
s
tate
v
ec
to
r
s
s
p
ac
e.
3.
SI
M
UL
A
T
I
O
N
SE
T
UP
Ar
ea
1
a
n
d
a
r
ea
2
ar
e
ass
u
m
ed
to
h
a
v
e
d
i
f
f
er
en
t
p
ar
am
eter
s
a
s
s
h
o
wn
in
T
a
b
le
1
s
o
th
at
th
ei
r
b
eh
a
v
io
r
to
war
d
s
an
y
lo
a
d
ch
a
n
g
e
is
n
o
t id
en
tical.
T
ab
le
1
.
Par
am
eter
o
f
two
a
r
e
a
m
icr
o
-
g
r
id
A
r
e
a
1
2
S
p
e
e
d
r
e
g
u
l
a
t
i
o
n
,
R
0
.
0
5
0
.
0
6
2
5
F
r
e
q
u
e
n
c
y
-
se
n
si
t
i
v
i
t
y
,
D
0
.
6
0
.
9
I
n
e
r
t
i
a
c
o
n
s
t
a
n
t
,
H
5
4
G
o
v
e
r
n
o
r
t
i
me
c
o
n
s
t
a
n
t
,
0
.
2
0
.
3
Tu
r
b
i
n
e
t
i
m
e
c
o
n
st
a
n
t
,
0
.
5
0
.
6
I
n
t
e
g
r
a
t
o
r
g
a
i
n
,
K
i
=
0
.
3
B
y
u
t
i
li
z
i
n
g
t
h
e
m
a
t
r
i
x
as
s
h
o
wn
i
n
s
e
c
t
i
o
n
2
.
3
a
n
d
2
.
4
,
t
h
e
n
s
u
b
s
t
i
t
u
te
t
h
e
p
a
r
a
m
e
t
e
r
s
i
n
T
a
b
l
e
1
,
t
h
e
s
t
a
te
-
s
p
a
c
e
r
e
p
r
e
s
e
n
t
a
ti
o
n
i
s
c
o
m
p
o
s
e
d
a
n
d
t
r
a
n
s
f
o
r
m
e
d
i
n
t
o
p
l
u
s
-
m
i
n
u
s
av
e
r
a
g
i
n
g
m
o
d
e
l
a
s
f
o
l
l
o
ws
:
[
]
=
[
−
0
.
0862
1
0
−
76
.
6650
−
18
.
75
0
.
0263
0
0
−
23
.
3350
−
1
.
85
0
0
0
0
0
0
0
0
0
0
0
.
1125
0
−
1
.
8350
0
0
−
0
.
0125
0
−
0
.
1650
0
0
0
0
1
.
8350
−
4
.
1650
0
0
0
0
.
1650
−
0
.
8350
0
0
0
0
1
.
25
0
0
0
0
0
.
25
0
0
.
0263
0
0
−
23
.
3350
−
1
.
85
−
0
.
0862
1
0
−
76
.
6650
−
18
.
75
0
.
05
0
0
0
0
−
0
.
45
0
0
0
−
4
−
0
.
0125
0
−
0
.
1650
0
0
0
.
1125
0
−
1
.
8350
0
0
0
0
0
.
1650
−
0
.
8350
0
0
0
1
.
8350
−
4
.
1650
0
0
0
0
0
.
25
0
0
0
0
1
.
25
0
]
(
1
6
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6
9
3
0
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
,
Vo
l.
18
,
No
.
6
,
Dec
em
b
e
r
2
0
2
0
:
3
3
2
4
-
333
0
3328
T
h
is
is
th
e
s
tate
-
s
p
ac
e
r
ep
r
esen
tatio
n
f
o
r
d
escr
ib
in
g
th
e
a
v
er
ag
e
b
eh
a
v
io
r
o
f
two
ar
ea
s
s
y
s
tem
.
I
t
ca
n
b
e
s
ee
n
th
at
th
e
s
tate
v
ec
to
r
s
o
f
th
e
eq
u
atio
n
ar
e
d
i
v
id
ed
in
to
two
p
ar
titi
o
n
s
wh
ich
r
elate
d
to
th
e
p
lu
s
-
m
in
u
s
av
er
ag
e.
I
n
o
r
d
er
to
g
et
an
a
v
e
r
ag
e
b
eh
a
v
io
r
o
f
th
e
wh
o
le
n
et
wo
r
k
,
it is
p
o
s
s
ib
le
to
r
ed
u
ce
th
e
s
y
s
tem
o
r
d
er
b
y
o
n
ly
ta
k
in
g
th
e
u
p
p
e
r
h
alf
o
f
t
h
e
s
tate
v
ec
to
r
s
an
d
s
tate
m
atr
ix
an
d
ig
n
o
r
e
th
e
m
in
u
s
a
v
er
a
g
e
m
o
d
el
e
q
u
atio
n
s
at
th
e
lo
wer
h
alf
o
f
s
tate
v
ec
to
r
s
.
T
h
e
p
r
o
p
o
s
ed
m
o
d
el
was
tes
ted
u
n
d
er
two
co
n
d
itio
n
s
wh
ic
h
ar
e
s
in
g
le
s
u
d
d
en
lo
ad
ch
an
g
e
in
ar
ea
1
with
0
.
2
p
er
u
n
it
d
ev
iati
o
n
.
T
h
e
eq
u
atio
n
is
r
ed
u
ce
d
as f
o
llo
w
:
=
̇
+
=
[
−
0
.
0862
1
0
−
76
.
6650
−
18
.
75
0
0
0
0
0
0
.
1125
0
−
1
.
8350
0
0
0
0
1
.
8350
−
4
.
1650
0
0
0
0
1
.
25
0
]
(
1
7
)
=
[
−
0
.
05
0
0
0
0
]
(
1
8
)
4.
RE
SU
L
T
S AN
D
AN
AL
Y
SI
S
4
.
1
.
Sim
ula
t
i
o
n
re
s
ults f
o
r
f
re
qu
ency
dy
na
m
ica
l beha
v
io
r
Fig
u
r
e
2
s
h
o
ws
th
e
d
e
v
iatio
n
s
o
f
p
er
u
n
it
f
r
e
q
u
en
cy
d
y
n
a
m
ical
r
esp
o
n
s
e
u
n
d
e
r
l
o
ad
ch
an
g
e
in
a
r
ea
1
r
esp
ec
tiv
ely
.
Fro
m
th
e
o
b
s
er
v
atio
n
s
,
th
e
f
r
eq
u
en
cy
d
e
v
iatio
n
in
ar
ea
1
g
iv
es m
o
r
e
o
s
cillatio
n
s
co
m
p
ar
e
t
o
ar
ea
2
s
in
ce
th
e
s
u
d
d
e
n
lo
ad
ch
a
n
g
e
is
h
ig
h
ly
d
o
m
in
an
t
in
a
r
ea
1
.
T
h
e
m
icr
o
-
g
r
id
s
y
s
tem
in
ar
e
a
2
g
iv
es
a
b
ac
k
-
u
p
r
o
le
to
t
h
e
m
icr
o
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g
r
i
d
s
y
s
tem
i
n
ar
ea
1
.
I
t
clea
r
ly
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e
s
ee
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t
h
a
t
ar
ea
2
o
n
ly
co
n
t
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te
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l
am
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u
n
t
o
f
p
o
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u
r
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g
t
h
e
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ir
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t
m
o
m
en
t
o
f
lo
ad
ch
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g
e
b
ec
au
s
e
o
f
s
m
all
f
r
eq
u
en
cy
d
ev
iatio
n
s
.
T
h
is
p
h
e
n
o
m
en
o
n
h
a
p
p
en
e
d
d
u
e
to
th
e
p
o
wer
f
lo
w
s
h
ar
in
g
b
etwe
en
two
ar
ea
s
th
r
o
u
g
h
t
h
e
tie
-
lin
e.
Sin
ce
th
e
m
o
d
el
c
o
n
s
id
er
ed
th
e
AC
E
,
th
e
s
y
s
tem
f
r
eq
u
en
cy
o
f
ea
ch
ar
ea
will
g
o
b
ac
k
to
th
e
n
o
m
in
al
af
ter
s
ev
er
al
s
ec
o
n
d
.
T
h
e
av
er
ag
e
f
r
e
q
u
en
cy
r
esp
o
n
s
e
f
o
r
th
e
wh
o
le
n
etwo
r
k
ca
n
b
e
s
ee
n
in
Fig
u
r
e
3
.
Fig
u
r
e
2
.
Dy
n
am
ical
f
r
e
q
u
en
c
y
r
esp
o
n
s
es f
o
r
ea
ch
ar
ea
n
etwo
r
k
s
Fig
u
r
e
3
.
An
av
er
ag
e
f
r
eq
u
en
c
y
d
ev
iatio
n
o
f
th
e
wh
o
le
n
etwo
r
k
.
4
.
2
.
Co
m
pa
riso
n wit
h c
o
nv
e
t
io
na
l a
pp
ro
a
ch
T
h
e
co
n
v
en
tio
n
al
ap
p
r
o
ac
h
b
a
s
ically
o
n
ly
u
tili
ze
s
th
e
i
n
f
o
r
m
atio
n
o
f
in
er
tia
c
o
n
s
tan
t
an
d
f
r
eq
u
en
cy
d
ev
iatio
n
s
in
ea
ch
a
r
ea
to
f
o
r
m
an
eq
u
atio
n
ca
lled
as th
e
ce
n
ter
o
f
i
n
er
tia
(
C
OI
)
f
r
e
q
u
en
c
y
.
∆
=
∑
=
1
,
2
.
.
∑
=
1
,
2
.
.
(
1
9
)
Fig
u
r
e
4
s
h
o
ws
th
e
r
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lts
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m
p
ar
is
o
n
b
etwe
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r
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p
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ed
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s
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d
el
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d
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p
r
o
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h
as
s
h
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in
(
1
9
)
.
T
h
e
r
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lt
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h
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ws
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p
r
o
p
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ield
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th
e
s
im
ilar
s
h
ap
e
lik
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th
e
co
n
v
e
n
tio
n
al.
Ho
wev
e
r
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t
h
e
p
r
o
p
o
s
ed
m
eth
o
d
g
i
v
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le
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s
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n
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d
g
o
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s
tead
y
-
s
tate
f
aster
co
m
p
ar
e
d
to
C
OI
m
eth
o
d
.
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Un
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f
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Ma
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NC
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S
[1
]
Z.
S
h
u
a
i
,
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t
a
l
.
,
“
M
icro
g
rid
sta
b
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y
:
c
las
sifica
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a
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Rev
iews
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v
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p
.
1
6
7
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a
y
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6
.
[2
]
W.
Xu
d
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g
,
e
t
a
l.
,
“
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t
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3
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6
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[3
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.
C
h
e
n
g
,
L.
Zh
a
o
a
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X.
Jia
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g
,
“
Dy
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[
4
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,
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p
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3
,
2017.
[5
]
N
.
B
.
S
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l
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a
l
.
,
“
F
r
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,
”
2018
I
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.
[
6
]
M
.
N
.
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.
1
3
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.
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]
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N.
A.
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k
a
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e
t
a
l
.
,
“
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icro
g
r
id
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l
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,
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w.
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.
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Rev
.
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l.
7
1
,
p
p
.
1
6
1
-
1
6
9
,
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a
y
2
0
1
7
.
[8
]
M
.
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e
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ra
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,
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l
.
,
“
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c
o
n
tro
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th
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m
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-
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o
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a
n
d
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d
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m
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d
e
s,”
El
e
c
tr
ic
Po
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r S
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.
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2
,
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5
.
[9
]
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m
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S
.
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u
,
“
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S
’
1
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),
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.
1
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3
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2
0
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1
0
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.
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1
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.
[1
1
]
C.
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,
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.
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g
,
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Ha
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,
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.
Qin
a
n
d
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Jia
,
“
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re
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n
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p
.
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[1
2
]
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.
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l
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.
,
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)
,
K
o
l
l
a
m
,
p
p
.
1
8
2
-
1
8
6
,
2015
.
[1
3
]
J.
A.
P
.
L
o
p
e
s,
A.
M
a
d
u
re
ira,
N.
G
il
,
a
n
d
F
.
Re
se
n
d
e
,
“
Op
e
ra
ti
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n
o
f
m
u
lt
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-
m
icro
g
r
id
s.”
Bo
o
k
C
h
a
p
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:M
icr
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ri
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s:
Arc
h
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p
p
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1
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5
-
2
0
5
,
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m
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1
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.
[1
4
]
A.
Us
m
a
n
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n
d
B.
Div
a
k
a
r,
“
S
imu
latio
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st
u
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.
2
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r
2
0
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5
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.
A.
Je
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i
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.
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id
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Ab
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5
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-
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a
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.
[1
6
]
K.
Ah
m
e
d
M
.
,
“
Ne
u
ra
l
p
re
d
ictiv
e
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o
n
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sy
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n
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ms
En
g
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1
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4
9
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8
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1
7
]
P
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a
De
v
i
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.
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.
9
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2
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6
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7
4
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2
0
1
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.
[1
8
]
Z.
S
h
u
a
i
,
e
t
a
l.
,
“
Op
ti
m
a
l
p
o
we
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s
h
a
rin
g
fo
r
m
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ri
d
wit
h
m
u
lt
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d
istri
b
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e
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ra
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o
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a
En
g
.
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l.
6
4
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o
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4
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p
p
.
5
4
6
-
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5
1
,
2
0
1
3
.
[1
9
]
H.
M
a
sru
r,
e
t
a
l
.
,
“
Au
t
o
m
a
ti
c
G
e
n
e
ra
ti
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Co
n
tro
l
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f
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re
a
p
o
w
e
r
sy
ste
m
with
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p
ti
m
ize
d
g
a
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p
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ra
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e
ters
,
”
2
n
d
In
t.
C
o
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El
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E
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In
f
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2
0
1
5
,
p
p
.
2
1
–
2
3
,
M
a
y
2
0
1
5
.
[2
0
]
A.
P
rit
a
m
,
e
t
a
l
.
,
“
Au
t
o
m
a
ti
c
g
e
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e
ra
ti
o
n
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o
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tr
o
l
stu
d
y
in
two
a
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re
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e
a
t
th
e
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a
l
p
o
we
r
sy
ste
m
a
u
t
o
m
a
ti
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g
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n
e
ra
ti
o
n
c
o
n
tro
l
stu
d
y
in
tw
o
a
re
a
re
h
e
a
t
th
e
rm
a
l
p
o
we
r
sy
ste
m
,”
IOP
Co
n
fer
e
n
c
e
S
e
rie
s:
M
a
ter
ia
ls
S
c
ien
c
e
a
n
d
En
g
i
n
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e
rin
g
,
v
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l.
2
2
5
,
n
o
.
1
,
2
0
1
7
.
[2
1
]
A.
M
e
z
o
u
a
ri,
e
t
a
l.
,
“
A
n
e
w
p
h
o
t
o
v
o
lt
a
ic
e
n
e
rg
y
s
h
a
rin
g
sy
ste
m
b
e
twe
e
n
h
o
m
e
s
in
sta
n
d
a
lo
n
e
a
re
a
s
.
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
C
o
mp
u
t
e
r E
n
g
i
n
e
e
rin
g
(IJ
ECE
)
,
v
o
l
o
l.
8
,
n
o
.
6
,
p
p
.
4
8
5
5
-
4
8
6
2
,
De
c
e
m
b
e
r
2
0
1
8
.
[2
2
]
G
.
K.
Ve
n
a
y
a
g
a
m
o
o
rt
h
y
,
e
t
a
l.
,
“
Tie
-
li
n
e
b
ias
c
o
n
tro
l
a
n
d
o
sc
il
lati
o
n
s
wit
h
v
a
riab
le
g
e
n
e
ra
ti
o
n
i
n
a
two
-
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re
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p
o
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sy
ste
m
,
”
7
th
I
n
ter
n
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ti
o
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l
Co
n
fer
e
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e
o
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I
n
fo
rm
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ti
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n
d
Au
to
ma
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n
fo
r
S
u
st
a
in
a
b
i
li
ty
,
C
o
lo
m
b
o
,
p
p
.
1
-
6
,
2
0
1
4
.
[2
3
]
C.
Ch
e
n
,
K.
Z
h
a
n
g
,
K.
Y
u
a
n
,
a
n
d
X.
Ten
g
,
“
Ti
e
-
Li
n
e
b
ias
c
o
n
tr
o
l
a
p
p
li
c
a
b
il
i
ty
to
l
o
a
d
fre
q
u
e
n
c
y
c
o
n
tro
l
fo
r
m
u
lt
i
-
a
re
a
in
terc
o
n
n
e
c
ted
p
o
we
r
sy
ste
m
s o
f
c
o
m
p
le
x
to
p
o
lo
g
y
,”
E
n
e
rg
ies
,
v
o
l.
1
0
,
n
o
.
1
,
Ja
n
u
a
ry
2
0
1
7
.
[2
4
]
D.
K.
S
a
m
b
a
ri
y
a
a
n
d
V.
Na
th
,
“
A
p
p
li
c
a
ti
o
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o
f
NA
RM
A
L2
c
o
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tro
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ler
fo
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fre
q
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e
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y
c
o
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m
u
lt
i
-
a
re
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p
o
we
r
sy
ste
m
,
”
2
0
1
6
1
0
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h
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n
ter
n
a
ti
o
n
a
l
Co
n
fer
e
n
c
e
o
n
In
telli
g
e
n
t
S
y
ste
ms
a
n
d
Co
n
tro
l
(I
S
CO)
,
C
o
imb
a
to
re
,
p
p
.
1
-
7
,
2
0
1
6
.
[2
5
]
J.
Zh
a
o
,
Y.
Tan
g
a
n
d
V.
Terz
ij
a
,
“
Ro
b
u
st
o
n
li
n
e
e
stim
a
ti
o
n
o
f
p
o
we
r
sy
ste
m
c
e
n
ter
o
f
in
e
rti
a
fre
q
u
e
n
c
y
,
”
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
4
,
n
o
.
1
,
pp.
8
2
1
-
8
2
5
,
Ja
n
u
a
ry
.
2
0
1
9
.
B
I
O
G
RAP
H
I
E
S
O
F
AUTH
O
RS
M.
S
a
if
u
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a
m
J
a
m
r
i
wa
s
b
o
r
n
i
n
Oc
to
b
e
r
1
9
8
4
.
He
re
c
e
iv
e
d
h
is
b
a
c
h
e
lo
r
d
e
g
re
e
in
El
e
c
tri
c
a
l
En
g
i
n
e
e
rin
g
(
P
o
we
r
El
e
c
tro
n
ics
&
Driv
e
s)
fro
m
Un
iv
e
rsiti
Te
k
n
i
k
a
l
M
a
lay
sia
M
e
lak
a
,
M
a
lay
sia
in
2
0
0
7
a
n
d
re
c
e
iv
e
d
th
e
M
a
ste
r
De
g
re
e
in
El
e
c
tri
c
a
l
P
o
we
r
E
n
g
i
n
e
e
rin
g
fro
m
Un
iv
e
rsiti
Tek
n
o
l
o
g
i
M
a
lay
sia
in
2
0
0
9
.
He
is
c
u
rre
n
tl
y
wo
r
k
e
d
wi
th
t
h
e
Un
iv
e
rsiti
Tek
n
ik
a
l
M
a
lay
sia
M
e
lak
a
(UTe
M
)
a
s
a
l
e
c
tu
re
r
a
n
d
b
e
lo
n
g
s
to
Ce
n
tre
fo
r
Ro
b
o
t
ics
a
n
d
In
d
u
stria
l
Au
to
m
a
ti
o
n
(Ce
RIA)
g
r
o
u
p
.
His
in
tere
st
is
in
p
o
we
r
sy
ste
m
stu
d
y
a
n
d
m
icro
-
g
rid
in
c
l
u
d
i
n
g
lo
a
d
fre
q
u
e
n
c
y
c
o
n
tr
o
l
(LF
C)
a
n
d
re
n
e
wa
b
le
e
n
e
rg
y
in
teg
ra
ti
o
n
.
H
e
is
c
u
rre
n
tl
y
p
e
rsu
in
g
th
e
P
h
D i
n
Un
i
v
e
rsity
Tek
n
i
n
a
l
M
a
la
y
sia
M
e
lak
a
u
n
d
e
r
F
a
c
u
lt
y
o
f
E
lec
tri
c
a
l
En
g
i
n
e
e
rin
g
.
Mu
h
a
m
m
a
d
Niz
a
m
K
a
m
a
r
u
d
i
n
wa
s
b
o
r
n
in
S
e
lan
g
o
r,
M
a
la
y
sia
.
He
re
c
e
iv
e
d
th
e
B.
E
n
g
(Ho
n
s.)
El
e
c
tri
c
a
l
fr
o
m
th
e
Un
i
v
e
rsiti
Tek
n
o
lo
g
i
M
ARA
,
M
a
lay
s
ian
in
2
0
0
2
,
a
n
d
M
.
S
c
in
Au
to
m
a
ti
o
n
a
n
d
C
o
n
tr
o
l
fro
m
t
h
e
Un
iv
e
rsit
y
o
f
Ne
wc
a
stle
Up
o
n
Ty
n
e
,
Un
it
e
d
Kin
g
d
o
m
i
n
2
0
0
7
.
He
re
c
e
iv
e
d
th
e
D
o
c
to
r
o
f
P
h
il
o
so
p
h
y
i
n
El
e
c
tri
c
a
l
E
n
g
i
n
e
e
rin
g
fr
o
m
th
e
U
n
iv
e
rsiti
Tek
n
o
lo
g
i
M
a
la
y
sia
in
2
0
1
5
.
He
is
c
u
rre
n
tl
y
wit
h
t
h
e
Un
iv
e
rsiti
T
e
k
n
ik
a
l
M
a
lay
sia
M
e
lak
a
(UTe
M
).
He
is
th
e
m
e
m
b
e
r
o
f
th
e
Bo
a
rd
o
f
En
g
i
n
e
e
rs,
M
a
lay
sia
a
n
d
I
n
stit
u
te
o
f
E
n
g
in
e
e
rs,
M
a
lay
sia
.
His
re
se
a
rc
h
in
tere
sts
i
n
c
lu
d
e
n
o
n
li
n
e
a
r
c
o
n
tro
ls
a
n
d
ro
b
u
st
c
o
n
tro
l
sy
ste
m
s.
Be
fo
re
jo
in
i
n
g
UTe
M
,
h
e
wo
r
k
e
d
a
s
a
Tec
h
n
ica
l
En
g
i
n
e
e
r
a
t
th
e
m
a
g
n
e
tr
o
n
d
e
p
a
rtme
n
t
o
f
S
a
m
su
n
g
El
e
c
tro
n
ics
M
a
lay
sia
.
Mo
h
d
Lu
q
m
a
n
M
o
h
d
J
a
m
i
l
re
c
e
iv
e
d
B.
E
n
g
.
d
e
g
re
e
fro
m
th
e
U
n
i
v
e
rsiti
Tek
n
o
lo
g
i
M
ARA
,
S
h
a
h
Ala
m
,
M
a
lay
sia
,
in
2
0
0
0
,
M
.
S
c
.
d
e
g
re
e
fr
o
m
Un
iv
e
rist
y
o
f
Ne
wc
a
stle u
p
o
n
Ty
n
e
,
U.K.
,
in
2
0
0
3
,
a
n
d
P
h
.
D.
d
e
g
re
e
fro
m
Th
e
Un
iv
e
rsit
y
o
f
S
h
e
ffield
,
S
h
e
ffield
,
U.K.,
i
n
2
0
1
1
,
a
ll
i
n
e
lec
tri
c
a
l
e
n
g
in
e
e
rin
g
.
He
is
c
u
rr
e
n
tl
y
a
n
a
c
a
d
e
m
icia
n
i
n
F
a
c
u
lt
y
o
f
El
e
c
tri
c
a
l
En
g
in
e
e
rin
g
,
Un
iv
e
rsity
Te
k
n
i
k
a
l
M
a
lay
sia
M
e
lak
a
,
M
e
lak
a
,
M
a
lay
sia
.
He
is
a
lso
a
n
a
c
ti
v
e
re
se
a
rc
h
e
r
in
P
o
we
r
El
e
c
tro
n
ics
a
n
d
Driv
e
s
Re
se
a
rc
h
G
ro
u
p
(P
EDG
)
th
a
t
e
sta
b
li
sh
e
d
u
n
d
e
r
t
h
e
sa
m
e
fa
c
u
lt
y
.
.
His
re
se
a
rc
h
in
tere
sts
in
c
l
u
d
e
th
e
d
e
sig
n
,
c
o
n
tro
l
a
n
d
a
n
a
ly
sis
o
f
p
e
rm
a
n
e
n
t
-
m
a
g
n
e
t
m
a
c
h
in
e
s.
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