I
nte
rna
t
io
na
l J
o
urna
l o
f
E
lect
rica
l a
nd
Co
m
p
ute
r
E
ng
in
ee
ring
(
I
J
E
CE
)
Vo
l.
11
,
No
.
2
,
A
p
r
il
2
0
2
1
,
p
p
.
9
4
5
~
9
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FACTS
a
llo
ca
tio
n
c
o
nsidering
l
o
a
ds
u
ncer
tainty
,
s
t
ea
dy
s
tate
o
pera
tion
c
o
nstra
ints,
a
nd
d
y
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ic
o
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tion
c
o
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a
ints
M
.
M
.
H
.
E
lro
by
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F
.
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ek
ha
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er
2
,
H
.
E
.
A.
T
a
la
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t
3
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.
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M
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us
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a
f
a
H
a
s
s
a
n
4
1
Ele
c
tri
c
a
l
En
g
in
e
e
rin
g
De
p
a
rtm
e
n
t,
F
a
c
u
lt
y
o
f
En
g
in
e
e
rin
g
,
A
in
S
h
a
m
s Un
iv
e
r
sit
y
,
Eg
y
p
t
2,
3
El
e
c
tri
c
a
l
En
g
in
e
e
rin
g
De
p
a
rtm
e
n
t,
F
u
tu
re
U
n
iv
e
rsity
,
Eg
y
p
t
4
El
e
c
tri
c
a
l
En
g
in
e
e
rin
g
De
p
a
rtm
e
n
t,
Ca
ir
o
Un
iv
e
rsity
,
Eg
y
p
t
Art
icle
I
nfo
AB
ST
RAC
T
A
r
ticle
his
to
r
y:
R
ec
ei
v
ed
No
v
14
,
2
0
1
9
R
ev
i
s
ed
J
u
l
11
,
20
20
A
cc
ep
ted
J
ul
27
,
2
0
20
T
h
is
stu
d
y
p
ro
p
o
se
s
a
n
a
lg
o
r
it
h
m
to
a
ll
o
c
a
te
d
if
f
e
re
n
t
t
y
p
e
s
o
f
flex
ib
le
A
C
tran
sm
issio
n
s
y
ste
m
(F
A
C
T
S
)
in
p
o
w
e
r
sy
ste
m
s.
T
h
e
m
a
in
o
b
jec
ti
v
e
o
f
th
is
stu
d
y
is
to
m
a
x
i
m
ize
p
ro
f
it
b
y
m
in
i
m
izin
g
th
e
s
y
ste
m
’s
o
p
e
ra
ti
n
g
c
o
st
in
c
lu
d
in
g
F
A
CT
S
d
e
v
ice
s
(F
Ds
)
in
sta
ll
a
ti
o
n
c
o
st
.
Dy
n
a
m
ic
a
n
d
st
e
a
d
y
sta
te
o
p
e
ra
ti
n
g
re
strictio
n
s
w
it
h
lo
a
d
s
u
n
c
e
rtain
ty
a
r
e
in
c
lu
d
e
d
in
th
e
p
ro
b
lem
f
o
r
m
u
latio
n
.
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h
e
o
v
e
ra
ll
p
ro
b
lem
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so
lv
e
d
u
sin
g
b
o
t
h
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h
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g
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rn
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g
b
a
se
d
o
p
t
im
iza
ti
o
n
(T
L
B
O)
tec
h
n
iq
u
e
f
o
r
a
tt
a
in
in
g
th
e
o
p
ti
m
a
l
a
ll
o
c
a
ti
o
n
o
f
th
e
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Ds
a
s
m
a
in
-
o
p
ti
m
iza
ti
o
n
p
r
o
b
lem
a
n
d
m
a
tp
o
w
e
r
in
terio
r
p
o
in
t
so
lv
e
r
(M
I
P
S
)
f
o
r
o
p
ti
m
a
l
p
o
w
e
r
f
lo
w
(
OP
F
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a
s
t
h
e
su
b
-
o
p
ti
m
iza
ti
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n
p
ro
b
lem
.
T
h
e
v
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li
d
a
ti
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o
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th
e
p
ro
p
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se
d
a
p
p
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a
c
h
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v
e
rif
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d
b
y
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p
p
ly
in
g
it
to
t
e
st
s
y
ste
m
o
f
5
9
-
b
u
s;
S
im
p
li
f
ied
1
4
-
g
e
n
e
ra
to
r
m
o
d
e
l
o
f
th
e
S
o
u
t
h
Eas
t
A
u
stra
li
a
n
p
o
w
e
r
s
y
ste
m
.
K
ey
w
o
r
d
s
:
F
A
C
T
S d
ev
ices
Op
ti
m
al
p
o
w
er
f
lo
w
P
o
w
er
s
y
s
te
m
m
o
d
elin
g
S
tead
y
s
tate
a
n
d
d
y
n
a
m
ic
o
p
er
atio
n
co
n
s
tr
ain
t
s
U
n
ce
r
tai
n
t
y
T
h
is i
s
a
n
o
p
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n
a
c
c
e
ss
a
rticle
u
n
d
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r th
e
CC B
Y
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SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
M.
M.
H.
E
lr
o
b
y
E
lectr
ical
E
n
g
i
n
ee
r
i
n
g
Dep
a
r
t
m
en
t,
Facu
l
t
y
o
f
E
n
g
in
ee
r
i
n
g
A
i
n
S
h
a
m
s
U
n
i
v
er
s
it
y
C
air
o
,
E
g
y
p
t
E
m
ail:
mo
u
s
ae
lr
o
b
y
@
y
a
h
o
o
.
co
m
1.
I
NT
RO
D
UCT
I
O
N
E
s
tab
lis
h
m
e
n
t
o
f
n
e
w
tr
an
s
m
is
s
io
n
-
l
in
e
s
(
T
L
s
)
i
s
ar
d
u
o
u
s
f
o
r
t
h
e
r
ea
s
o
n
s
o
f
t
h
e
e
n
v
ir
o
n
m
e
n
tal
.
C
o
n
s
eq
u
en
tl
y
,
t
h
e
T
L
s
ar
e
lo
ad
ed
n
ea
r
er
to
s
y
s
te
m
s
ec
u
r
it
y
li
m
it
s
[1
-
3]
.
T
o
en
s
u
r
e
ec
o
n
o
m
ic
a
n
d
s
ec
u
r
e
o
p
er
atio
n
,
p
r
o
p
er
ly
F
AC
T
S
d
ev
ices
(
FDs
)
allo
ca
tio
n
o
f
f
e
r
s
an
ef
f
ec
ti
v
e
m
ea
n
s
.
Du
r
i
n
g
n
o
r
m
a
l
s
tate,
t
h
e
o
b
j
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tiv
es
o
f
t
h
e
f
le
x
ib
le
AC
tr
an
s
m
is
s
io
n
s
y
s
te
m
(
F
AC
T
S
)
ca
n
b
e
r
elie
v
i
n
g
co
n
g
esti
o
n
,
in
cr
ea
s
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n
g
v
o
lta
g
e
s
tab
ilit
y
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in
cr
ea
s
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s
y
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te
m
lo
ad
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ilit
y
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d
m
i
n
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m
izi
n
g
o
p
er
atin
g
co
s
t.
D
u
r
in
g
e
m
er
g
e
n
c
y
s
tates,
t
h
e
F
A
C
T
S
ar
e
u
s
ed
to
f
ix
th
e
s
y
s
te
m
.
E
ac
h
o
f
th
e
ab
o
v
e
s
tated
o
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j
ec
tiv
es
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ein
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o
r
ce
p
o
w
er
s
y
s
te
m
p
er
f
o
r
m
a
n
ce
[4
,
5]
.
Ho
w
e
v
er
,
en
h
an
ce
m
e
n
t
i
n
o
n
e
o
b
j
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tiv
e
d
o
es
n
o
t
g
u
ar
a
n
tee
t
h
e
s
a
m
e
e
n
h
a
n
ce
m
e
n
t
i
n
o
th
er
s
.
T
h
er
ef
o
r
e,
n
o
n
e
o
f
th
e
s
tated
tech
n
ical
o
b
j
ec
tiv
es
ca
n
n
o
t
b
e
ig
n
o
r
ed
in
FD
s
all
o
ca
tio
n
an
d
s
h
o
u
ld
b
e
f
o
r
m
u
la
ted
as
m
u
lti
-
o
b
j
ec
tiv
e
o
p
ti
m
izatio
n
p
r
o
b
le
m
.
A
l
m
o
s
t
al
l
cu
r
r
en
t
F
A
C
T
S
r
es
ea
r
ch
w
o
r
k
s
,
tr
y
to
i
m
p
r
o
v
e
p
o
w
er
s
y
s
te
m
s
tead
y
-
s
tate
c
h
ar
ac
ter
is
tics
.
W
h
ile
p
o
w
er
s
y
s
te
m
d
y
n
a
m
ics
s
h
o
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ld
b
e
co
n
s
id
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ed
in
th
e
m
u
lt
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-
o
b
j
ec
tiv
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o
p
t
i
m
izati
on
p
r
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b
le
m
.
Fu
r
t
h
er
m
o
r
e,
d
a
m
p
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n
g
o
f
t
h
e
in
ter
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ar
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ci
llatio
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i
s
co
n
s
id
er
ed
as
o
n
e
o
f
t
h
e
s
ig
n
i
f
i
ca
n
t
ap
p
ea
ls
to
t
h
e
elec
tr
ic
p
o
w
er
s
y
s
te
m
.
T
h
e
ad
j
u
s
t
m
e
n
t o
f
p
o
w
er
s
y
s
te
m
s
tab
i
lizer
(
P
SS
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s
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g
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o
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o
t
s
o
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n
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to
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e
th
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b
e
s
t
w
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y
to
tr
ea
t
in
ter
-
ar
ea
o
s
c
il
latio
n
s
,
as
th
e
m
o
d
es
o
f
t
h
ese
o
s
cillatio
n
ar
e
n
o
t
h
i
g
h
l
y
co
n
tr
o
llab
le
an
d
o
b
s
er
v
ab
le
f
r
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m
m
ea
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u
r
e
m
en
t
s
at
t
h
e
g
e
n
er
ati
n
g
u
n
its
[
6
]
.
Par
ticu
lar
l
y
,
F
A
C
T
S,
f
l
y
w
h
ee
l,
an
d
b
atter
y
s
to
r
a
g
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p
lay
a
n
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m
p
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t
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o
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in
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e
i
n
ter
-
ar
ea
d
a
m
p
i
n
g
o
s
cilla
tio
n
s
[
7
]
.
T
h
ese
d
ev
ices
h
a
v
e
th
e
m
er
it
to
b
e
in
s
talled
at
an
y
lo
ca
tio
n
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t
h
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p
o
w
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s
y
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te
m
,
g
r
a
n
ti
n
g
b
etter
p
er
f
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a
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ce
s
co
m
p
ar
ed
to
th
e
P
SS
,
w
h
ic
h
w
o
r
k
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
11
,
No
.
2
,
A
p
r
il 2
0
2
1
:
9
4
5
-
955
946
p
r
o
f
icien
tl
y
f
o
r
lo
ca
l
o
s
ci
llati
o
n
s
co
m
p
ar
ati
v
el
y
to
in
t
er
-
ar
ea
o
s
cillatio
n
s
.
T
o
id
en
ti
f
y
t
h
e
b
est
lo
ca
tio
n
o
f
th
ese
d
e
v
ices,
e
ig
e
n
v
al
u
e
s
e
n
s
it
iv
i
t
y
a
n
d
r
esid
u
e
al
g
o
r
ith
m
f
o
r
th
e
in
ter
-
ar
ea
m
o
d
e
is
an
al
y
ze
d
[
8
]
.
T
h
e
p
ar
ticip
atio
n
f
ac
to
r
s
a
n
d
r
esid
u
e
m
et
h
o
d
w
er
e
u
s
ed
to
d
eter
m
i
n
e
FD
s
lo
ca
tio
n
s
.
T
h
en
,
t
h
e
co
n
tr
o
ller
s
o
f
th
e
F
A
C
T
S
w
er
e
d
esi
g
n
ed
b
ased
o
n
th
eir
lo
ca
tio
n
s
[
9
]
.
I
n
[
1
0
]
,
th
e
co
n
ce
p
t
o
f
d
y
n
a
m
ic
e
n
er
g
y
b
alan
ce
w
a
s
u
s
ed
to
m
o
d
el
g
e
n
er
ato
r
o
s
cillat
io
n
s
in
d
if
f
er
en
t
ti
m
e
-
s
ca
le
s
.
I
n
[
1
1
]
,
an
ad
ap
tiv
e
co
n
tr
o
ller
u
s
i
n
g
m
o
d
el
p
r
ed
ictiv
e
co
n
tr
o
l
w
a
s
p
r
o
p
o
s
ed
.
W
ith
in
cr
ea
s
i
n
g
o
f
t
h
e
p
h
a
s
o
r
m
ea
s
u
r
e
m
e
n
t
u
n
its
,
t
h
e
C
o
n
tr
o
ller
s
o
f
t
h
e
w
id
e
-
ar
ea
h
av
e
b
ee
n
p
r
o
p
o
s
ed
to
i
m
p
r
o
v
e
d
a
m
p
i
n
g
o
f
th
e
i
n
ter
-
ar
ea
o
s
cillatio
n
s
[
6
]
.
I
n
[
1
2
]
lo
ad
-
g
en
er
atio
n
tr
ip
p
in
g
w
a
s
in
tr
o
d
u
ce
d
as a
n
ac
tiv
e
s
tr
ateg
y
f
o
r
s
u
s
tai
n
i
n
g
s
y
s
te
m
f
r
o
m
b
lac
k
o
u
t.
Fu
r
t
h
er
m
o
r
e,
v
ar
io
u
s
m
et
h
o
d
s
w
er
e
p
r
o
p
o
s
ed
f
o
r
p
o
w
er
s
y
s
te
m
o
p
ti
m
izat
io
n
co
n
s
id
er
in
g
lo
ad
s
u
n
ce
r
tai
n
tie
s
.
T
h
e
p
er
f
ec
t
m
e
th
o
d
is
th
e
Mo
n
te
C
ar
lo
s
i
m
u
latio
n
(
M
C
S).
T
h
is
m
eth
o
d
is
u
s
u
al
l
y
u
s
ed
as
s
tan
d
ar
d
m
et
h
o
d
[
1
3
]
.
I
n
[
1
4
]
,
th
e
MC
S
m
eth
o
d
f
o
r
s
iz
in
g
o
f
t
h
e
m
u
ltip
le
FDs
i
n
p
o
w
er
s
y
s
te
m
s
to
i
m
p
r
o
v
e
s
tead
y
-
s
tate
v
o
lta
g
e
p
r
o
f
ile
w
a
s
u
s
ed
.
T
o
r
ed
u
ce
th
e
co
s
t
o
f
g
en
er
atio
n
w
it
h
ta
k
in
g
in
to
ac
c
o
u
n
t
u
n
ce
r
tai
n
t
y
i
n
lo
ad
d
em
a
n
d
an
d
r
en
e
w
ab
le
s
o
u
r
ce
,
FAC
T
S
allo
ca
tio
n
w
as
s
o
lv
ed
b
y
M
C
S
i
n
co
in
cid
e
n
ce
w
it
h
d
i
f
f
er
e
n
tia
l
e
v
o
lu
tio
n
alg
o
r
it
h
m
[
1
5
]
.
T
h
e
o
r
g
an
izatio
n
o
f
t
h
is
p
ap
er
is
as
f
o
llo
w
s
:
Sec
tio
n
2
d
escr
ib
es
t
h
e
s
lo
w
co
h
er
e
n
c
y
i
n
d
ices
.
Sectio
n
3
in
tr
o
d
u
ce
s
t
h
e
p
r
o
b
ab
ilis
tic
o
p
ti
m
al
p
o
w
er
f
lo
w
(
P
OP
F).
Sectio
n
4
i
n
tr
o
d
u
ce
t
h
e
m
o
d
el
o
f
th
e
F
AC
T
S.
Sectio
n
5
p
r
esen
ts
th
e
o
p
ti
m
al
p
o
w
er
f
lo
w
.
Sectio
n
6
p
r
ese
n
t
s
th
e
teac
h
in
g
lear
n
i
n
g
b
ased
o
p
tim
izatio
n
(
T
L
B
O
)
.
Sectio
n
7
p
r
esen
ts
th
e
s
tate
m
e
n
t
o
f
th
e
p
r
o
b
le
m
.
Sectio
n
8
d
is
cu
s
s
e
s
th
e
ap
p
lied
ca
s
e
s
tu
d
y
.
F
in
al
l
y
,
th
e
co
n
cl
u
s
io
n
s
ar
e
ill
u
s
tr
ated
in
s
ec
tio
n
9
.
2.
T
H
E
S
L
O
W
CO
H
E
R
E
NC
Y
I
NDIC
E
S
T
h
e
in
ter
-
ar
ea
o
s
cillatio
n
s
r
e
s
u
lt
w
h
e
n
a
co
h
er
en
t
g
r
o
u
p
o
f
m
ac
h
i
n
es
s
w
i
n
g
s
a
g
ai
n
s
t
ea
ch
o
th
er
g
r
o
u
p
s
.
T
h
ese
o
s
cillatio
n
s
ar
e
r
elate
d
w
it
h
th
e
w
ea
k
T
L
s
an
d
lar
g
er
lo
ad
ed
lin
es
b
et
w
ee
n
th
e
g
r
o
u
p
s
o
f
tied
co
u
p
led
m
ac
h
i
n
es.
T
h
ese
o
s
cillatio
n
s
m
o
d
es,
if
n
o
t
p
r
o
p
er
l
y
d
a
m
p
ed
,
ca
n
lead
to
p
o
w
e
r
s
y
s
te
m
in
s
tab
ilit
y
p
r
o
d
u
cin
g
a
co
m
p
lete
b
lac
k
o
u
t.
T
h
e
o
s
cillatio
n
o
f
t
h
e
ce
n
ter
an
g
le
o
f
ea
ch
ar
ea
is
s
lo
w
er
t
h
an
th
e
o
s
cillat
io
n
s
b
et
w
ee
n
an
y
t
w
o
g
e
n
er
ato
r
s
i
n
th
e
s
a
m
e
ar
ea
.
T
h
is
p
h
en
o
m
en
o
n
o
cc
u
r
s
as
a
r
esu
lt
o
f
t
h
e
s
tr
o
n
g
tied
b
et
w
ee
n
g
en
er
ato
r
s
i
n
th
e
s
a
m
e
ar
ea
w
h
ile
b
et
w
ee
n
t
h
e
ar
ea
s
th
e
g
e
n
er
ato
r
s
ar
e
w
ea
k
tied
[
1
6
]
.
T
h
u
s
,
th
e
g
en
er
ato
r
s
i
n
th
e
s
a
m
e
ar
ea
s
in
ter
ac
t
o
n
a
“
s
h
o
r
t
-
ter
m
b
asi
s
”,
as
t
h
e
y
ar
e
co
h
er
en
t
i
n
th
e
f
a
s
t
d
y
n
a
m
ic
m
o
d
es
(
f
ast
co
h
er
en
t)
.
T
h
e
n
,
w
h
en
t
h
e
f
a
s
t
d
y
n
a
m
ics
ar
e
d
ec
a
y
ed
,
th
e
g
en
er
ato
r
s
w
i
th
d
if
f
er
e
n
t
ar
ea
s
in
ter
ac
t
o
n
a
“
lo
n
g
-
ter
m
b
asis
”,
as
th
e
y
ar
e
co
h
er
en
t
in
th
e
s
lo
w
d
y
n
a
m
ics
(
s
lo
w
co
h
er
en
t)
.
T
h
e
co
h
er
e
n
c
y
is
u
s
ed
in
th
e
d
ev
elo
p
m
en
t
o
f
p
o
w
er
s
y
s
te
m
d
y
n
a
m
ic
eq
u
iv
a
len
t
s
to
s
i
m
p
l
if
y
tr
a
n
s
ie
n
t
s
t
u
d
ies.
T
h
e
m
et
h
o
d
f
o
r
d
eter
m
i
n
i
n
g
co
h
er
en
c
y
o
f
th
e
p
o
w
er
s
y
s
te
m
is
b
ased
o
n
t
h
e
s
i
m
p
li
f
ied
m
o
d
el
w
ith
t
h
e
f
o
llo
w
in
g
as
s
u
m
p
tio
n
s
:
T
h
e
co
h
er
en
c
y
ca
n
b
e
ev
al
u
a
ted
b
ased
o
n
li
n
ea
r
ized
m
o
d
e
l,
an
d
t
h
e
co
h
er
e
n
t
ar
ea
s
ar
e
in
d
ep
en
d
en
t
o
n
a
m
o
u
n
t o
f
t
h
e
d
is
t
u
r
b
an
ce
.
T
h
e
co
h
er
en
t
ar
ea
s
ar
e
i
n
d
ep
en
d
en
t
o
f
t
h
e
g
e
n
er
ato
r
m
o
d
els
d
etail
s
.
T
h
er
ef
o
r
e,
th
e
cla
s
s
ical
g
e
n
er
ato
r
m
o
d
el
ca
n
b
e
co
n
s
id
er
ed
an
d
th
e
tu
r
b
i
n
e
-
g
o
v
er
n
o
r
an
d
ex
cit
atio
n
ca
n
b
e
ig
n
o
r
ed
.
T
o
id
en
tify
co
h
er
en
c
y
i
n
p
o
w
e
r
s
y
s
te
m
s
,
t
h
e
f
o
l
lo
w
in
g
eq
u
at
i
o
n
is
p
r
esen
ted
i
n
[
1
7
]
.
∆
δ
̈
=
M
−
1
K
∆
δ
(
1
)
w
h
er
e
M
is
th
e
d
iag
o
n
al
g
e
n
er
ato
r
in
er
tia
m
atr
ix
:
T
h
e
(
i,
j
)
elem
en
t o
f
K
h
a
s
th
e
f
o
r
m
=
(
(
−
)
−
(
−
)
)
|
(
0
,
0
)
,
≠
is
th
e
v
o
ltag
e
o
f
g
e
n
er
ato
r
i,
+
is
th
e
ad
m
itta
n
ce
b
et
w
ee
n
g
e
n
er
ato
r
an
d
.
=
−
∑
=
1
,
≠
,
for
the
dia
gon
a
l
e
l
e
me
n
ts
of
K
T
h
e
en
tr
ies
o
f
K
ar
e
t
h
e
co
ef
f
icien
ts
o
f
th
e
s
y
n
c
h
r
o
n
izi
n
g
-
to
r
q
u
e,
as
t
h
e
y
k
ee
p
t
h
e
g
e
n
er
ato
r
s
y
n
ch
r
o
n
ized
an
d
s
tab
le.
T
h
u
s
,
th
e
s
ti
f
f
n
es
s
o
f
th
e
co
n
n
ec
tio
n
s
b
et
w
ee
n
t
h
e
ar
ea
s
ar
e
r
ed
u
ce
d
,
th
e
s
lo
w
d
y
n
a
m
ics
ar
e
i
n
cr
ea
s
ed
.
T
h
e
E
ig
en
v
ec
to
r
s
o
f
−
1
s
h
o
w
s
h
ap
es
o
f
th
e
e
lectr
o
m
ec
h
an
ic
al
m
o
d
es.
I
f
g
en
er
ato
r
an
d
h
av
e
s
i
m
ilar
v
a
lu
es
o
f
th
e
E
i
g
e
n
v
ec
to
r
o
f
m
o
d
e
,
w
e
ca
n
d
ed
u
ce
t
h
at
t
h
ese
t
w
o
g
en
er
ato
r
s
ar
e
co
h
er
en
t
w
it
h
r
esp
ec
t
to
th
at
m
o
d
e
.
T
h
er
ef
o
r
e,
if
th
e
eig
en
v
ec
to
r
s
m
atr
i
x
(
Vs)
co
r
r
esp
o
n
d
to
th
e
s
m
al
l
eig
en
v
alu
e
s
o
f
−
1
,
th
en
a
s
lo
w
co
h
er
en
t
g
r
o
u
p
o
f
g
en
er
ato
r
s
h
av
e
s
i
m
ilar
r
o
w
i
n
th
e
eig
e
n
v
ec
to
r
s
m
atr
i
x
.
L
et
t
h
e
co
lu
m
n
s
o
f
ei
g
en
v
ec
t
o
r
s
m
atr
ix
b
e
n
o
r
m
alize
d
to
u
n
it
y
,
th
e
n
t
h
e
s
lo
w
-
co
h
er
en
c
y
ca
n
b
e
m
ea
s
u
r
ed
as
f
o
llo
w
s
[
1
7
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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&
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tio
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n
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ta
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ty,
s
tea
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ta
te
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tio
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a
in
ts
...
(
M.
M.
H.
E
lr
o
b
y)
947
=
/
(
|
|
|
|
)
(
2
)
w
h
er
e
an
d
ar
e
th
e
r
o
w
o
f
Vs c
o
r
r
esp
o
n
d
in
g
to
g
e
n
er
ato
r
s
an
d
,
r
esp
ec
tiv
el
y
.
I
f
g
e
n
er
ato
r
s
an
d
ar
e
p
er
f
ec
tl
y
co
h
er
e
n
t,
th
e
n
=
an
d
=
1
.
T
h
er
ef
o
r
e,
t
h
e
s
l
o
w
co
h
er
en
c
y
i
n
d
ices
(
S
C
I
)
t
h
at
m
ea
s
u
r
e
s
t
h
e
s
lo
w
co
h
er
e
n
c
y
b
et
w
ee
n
t
h
e
g
e
n
er
ato
r
s
c
an
b
e
p
r
ese
n
ted
as
f
o
llo
w
s
:
=
{
1
∑
(
1
−
1
=
2
)
,
0
≤
1
−
1
≤
0
.
05
+
2
∑
(
1
−
1
=
2
)
,
0
.
05
<
1
−
1
≤
0
.
1
+
3
∑
(
1
−
1
=
2
)
,
0
.
1
<
1
−
1
≤
2
(
3
)
w
h
er
e
n
g
i
s
th
e
n
u
m
b
er
o
f
g
en
er
ato
r
s
1
,
2
,
3
ℎ
1
<
2
<
3
3.
P
RO
B
AB
I
L
I
S
T
I
C
O
P
T
I
M
AL
P
O
WE
R
F
L
O
W
T
o
en
co
m
p
as
s
t
h
e
m
aj
o
r
it
y
o
f
p
o
s
s
ib
le
s
y
s
te
m
s
tates,
it
i
s
n
ec
ess
ar
y
to
r
u
n
th
e
d
eter
m
i
n
i
s
tic
p
o
w
er
f
lo
w
m
an
y
ti
m
e
s
at
d
if
f
er
e
n
t
o
p
er
atin
g
p
o
in
ts
.
He
n
ce
,
it
tu
r
n
s
o
u
t
th
a
t
it
i
s
ap
p
r
o
p
r
iate
to
tr
ea
t
th
e
d
eter
m
in
i
s
tic
p
o
w
er
f
lo
w
p
r
o
b
le
m
as
a
p
r
o
b
ab
ili
s
tic
p
o
w
er
f
lo
w
p
r
o
b
le
m
[
1
8
]
.
As
q
u
a
n
ti
ties
o
f
th
e
v
ar
iab
les
in
th
e
p
o
w
er
s
y
s
te
m
ar
e
tr
ea
ted
as
r
an
d
o
m
v
ar
iab
les
(
R
V
s
)
,
it
b
ec
o
m
es
ea
s
y
to
d
eter
m
i
n
e
t
h
e
r
esu
lt
s
r
an
g
e
s
o
f
th
e
p
o
w
er
f
lo
w
.
Se
v
er
al
m
et
h
o
d
s
f
o
r
P
OP
F
s
t
u
d
y
h
a
v
e
b
ee
n
d
o
n
e.
T
h
ese
m
eth
o
d
s
ca
n
b
e
d
iv
id
ed
i
n
to
t
h
r
ee
b
asic
g
r
o
u
p
s
:
ap
p
r
o
x
i
m
ate
m
e
th
o
d
s
,
MCS
m
eth
o
d
,
an
d
an
al
y
tical
m
eth
o
d
s
.
MC
S
is
a
p
r
o
ce
d
u
r
e
th
at
u
til
izes
to
s
o
lv
e
a
p
r
o
b
a
b
ilis
tic
p
r
o
b
le
m
.
I
t
is
a
s
tr
ateg
y
f
o
r
iter
ati
v
el
y
e
s
ti
m
ati
n
g
d
eter
m
i
n
is
tic
m
o
d
el.
T
h
is
s
tr
ateg
y
is
r
eg
u
lar
l
y
u
til
ized
w
h
en
t
h
e
m
o
d
el
is
n
o
n
li
n
ea
r
,
co
m
p
le
x
,
o
r
h
as
m
o
r
e
p
ar
a
m
eter
s
t
h
at
ar
e
u
n
ce
r
tai
n
.
T
h
e
d
is
ad
v
an
ta
g
e
o
f
t
h
e
M
C
S
m
et
h
o
d
is
t
h
e
h
u
g
e
n
u
m
b
er
o
f
t
h
e
r
eq
u
ir
ed
s
a
m
p
le
s
to
g
et
co
n
v
er
g
en
ce
.
Ho
w
e
v
er
,
th
e
M
C
S
tec
h
n
iq
u
e
i
s
ab
le
to
p
r
o
d
u
ce
ac
cu
r
ate
r
es
u
lts
[
1
9
]
.
T
h
e
p
o
in
t
esti
m
ate
m
eth
o
d
(
P
E
M)
is
c
u
r
r
en
tl
y
th
e
r
ep
r
esen
tativ
e
o
f
ap
p
r
o
x
i
m
ate
m
et
h
o
d
s
f
o
r
P
OP
F
ca
lcu
la
tio
n
s
.
T
h
e
P
E
M
w
a
s
u
s
ed
to
s
o
l
v
e
t
h
e
P
OP
F
[
1
8
]
,
[
2
0
]
.
T
h
e
P
E
M
lik
e
MCS
u
s
e
d
eter
m
in
i
s
tic
p
r
o
ce
d
u
r
e
to
s
o
l
v
e
P
P
s
.
Ho
w
e
v
er
,
it
r
eq
u
ir
es
a
less
co
m
p
u
tat
io
n
al
en
cu
m
b
r
an
ce
.
Mo
r
eo
v
er
,
P
E
M
o
v
er
co
m
e
t
h
e
a
w
k
w
ar
d
n
ess
ass
o
ciate
d
w
it
h
th
e
s
h
o
r
tag
e
o
f
t
y
p
ical
k
n
o
w
led
g
e
o
f
th
e
r
an
d
o
m
v
ar
iab
les,
s
in
c
e
th
ese
r
an
d
o
m
v
ar
iab
les
ar
e
ap
p
r
o
x
i
m
ated
b
y
v
ar
ian
ce
,
m
ea
n
,
k
u
r
to
s
is
,
a
n
d
s
k
e
w
n
es
s
.
T
h
er
ef
o
r
e,
a
least
d
ata
is
n
ee
d
ed
.
T
h
e
g
o
al
o
f
an
y
P
E
M
is
to
d
eter
m
i
n
e
t
h
e
m
o
m
en
t
s
o
f
th
e
f
u
n
ctio
n
th
at
is
a
f
u
n
ctio
n
o
f
r
an
d
o
m
v
ar
iab
les.
T
h
e
u
s
ed
tw
o
-
P
E
M
(
2
P
E
M)
in
[
2
1
]
is
eq
u
iv
ale
n
t
to
Ho
n
g
’
s
2
m
s
ch
e
m
e.
T
h
e
2
P
E
M
d
o
es
n
o
t
g
iv
e
ac
c
u
r
ate
r
esu
lt
s
esp
ec
iall
y
i
f
th
e
n
u
m
b
er
o
f
th
e
i
n
p
u
t
R
Vs
is
h
i
g
h
.
T
h
er
ef
o
r
e,
it
is
n
o
t
s
u
itab
le
f
o
r
p
o
w
er
s
y
s
te
m
o
f
ac
t
u
al
s
ize.
Ho
w
e
v
er
,
th
e
2
m
+1
s
c
h
e
m
e
is
b
etter
th
an
th
e
2
m
s
ch
e
m
e
b
ec
au
s
e
it
ta
k
e
in
to
co
n
s
id
er
atio
n
t
h
e
k
u
r
to
s
is
o
f
th
e
in
p
u
t
R
V
s
w
h
i
le
o
n
l
y
o
n
e
ev
alu
atio
n
o
f
th
e
f
u
n
ctio
n
is
ad
d
ed
[
1
8
]
.
T
h
er
ef
o
r
e,
in
th
is
p
ap
er
,
th
e
s
ch
e
m
e
2
m
+1
i
s
u
s
ed
to
s
o
lv
e
th
e
P
O
P
F p
r
o
b
lem
.
3
.
1
.
+
Sche
m
e
T
h
is
s
ch
e
m
e
r
eq
u
ir
es
2
+
1
ev
alu
a
tio
n
o
f
th
e
f
u
n
ct
io
n
.
C
o
n
s
eq
u
en
tl
y
,
t
h
e
w
e
ig
h
ts
a
n
d
s
tan
d
a
r
d
lo
ca
tio
n
s
ar
e
[
1
8
]
:
.
=
+
,
=
1
,
2
,
3
,
=
,
3
2
+
(
−
1
)
3
−
√
,
4
−
3
4
2
,
3
=
1
,
2
,
3
=
0
(
4
)
.
=
(
−
1
)
3
−
,
(
,
1
−
,
2
)
=
1
,
2
.
3
=
1
−
1
(
,
4
−
2
,
3
)
(
5
)
w
h
er
e
.
is
th
e
lo
ca
tio
n
s
o
f
t
h
e
in
p
u
t r
an
d
o
m
v
ar
iab
le
,
is
th
e
s
ta
n
d
ar
d
lo
ca
tio
n
,
1
,
ar
e
th
e
s
tan
d
ar
d
d
ev
iatio
n
a
n
d
m
ea
n
o
f
t
h
e
i
n
p
u
t r
an
d
o
m
v
a
r
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le
,
,
4
,
3
ar
e
th
e
k
u
r
to
s
is
a
n
d
s
k
e
w
n
e
s
s
o
f
th
e
i
n
p
u
t r
an
d
o
m
v
ar
iab
le
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
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8
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I
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&
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.
is
w
e
ig
h
t
s
o
f
th
e
lo
ca
tio
n
s
.
Fro
m
(
4
)
,
s
ettin
g
,
3
=
0
y
ield
s
.
3
=
an
d
s
o
,
o
f
th
e
lo
ca
tio
n
s
ar
e
th
e
s
a
m
e
(
1
,
2
,
…
,
,
.
.
.
,
)
p
o
in
t.
T
h
er
ef
o
r
e,
it
is
s
u
f
f
ici
en
t
to
r
u
n
o
n
e
ev
alu
at
io
n
o
f
th
e
p
r
o
b
ab
ilit
y
f
u
n
ctio
n
at
th
is
lo
ca
tio
n
,
g
i
v
e
n
th
at
co
r
r
es
p
o
n
d
in
g
w
ei
g
h
t
0
as f
o
llo
w
s
:
w
0
=
1
−
∑
1
m
(
λ
l
,
4
−
λ
l
2
,
3
)
m
l
=
1
(
6
)
Fu
r
t
h
er
m
o
r
e,
(
4
)
s
h
o
w
s
th
a
t
th
is
s
c
h
e
m
e
g
i
v
e
n
o
n
-
r
ea
l
lo
ca
tio
n
s
w
h
e
n
,
4
−
3
4
2
,
3
is
n
e
g
ati
v
e
v
al
u
e
.
Ho
w
e
v
er
,
in
p
o
w
er
s
y
s
te
m
p
r
o
b
lem
s
th
e
p
r
o
b
ab
ilit
y
d
is
tr
ib
u
tio
n
s
ar
e
u
s
u
all
y
u
til
ized
to
b
in
o
m
ia
l,
u
n
if
o
r
m
,
o
r
n
o
r
m
al
m
o
d
el,
th
er
e
f
o
r
e
th
e
l
o
ca
tio
n
s
ar
e
p
er
m
a
n
en
tl
y
r
ea
l
v
alu
e
s
.
T
o
s
o
lv
e
th
e
P
OP
F
p
r
o
b
lem
b
y
2
m
+1
s
ch
e
m
e,
th
e
p
o
w
er
f
lo
w
i
n
p
u
t
d
ata
ar
e
m
o
d
eled
as
r
an
d
o
m
v
ar
iab
les,
t
h
en
t
h
e
lo
ca
tio
n
s
a
n
d
w
ei
g
h
ts
ar
e
co
m
p
u
ted
u
s
i
n
g
(
4
)
an
d
(
5
)
.
T
h
e
s
o
lu
tio
n
o
f
t
h
e
P
OP
F
p
r
o
b
lem
is
p
r
ese
n
ted
in
[
1
8
]
w
h
er
e
th
e
id
ea
ca
n
b
e
ex
p
lain
ed
u
s
i
n
g
t
h
e
(
7
)
:
(
)
=
∑
∑
.
(
(
,
)
)
2
=
1
=
1
+
0
0
,
(
7
)
w
h
er
e
(
,
)
is
o
u
tp
u
t
o
f
t
h
e
p
r
o
b
ab
ilit
y
f
u
n
ctio
n
r
elate
d
to
th
e
k
th
co
n
ce
n
tr
atio
n
(
1
,
2
,
…
,
,
,
…
,
)
o
f
th
e
in
p
u
t r
a
n
d
o
m
v
ar
iab
le
is
m
o
m
en
t
s
o
f
t
h
e
o
u
tp
u
t
0
is
o
u
tp
u
t
o
f
th
e
p
r
o
b
ab
ilit
y
f
u
n
ct
io
n
r
elate
d
to
th
e
k
th
co
n
ce
n
tr
atio
n
(
1
,
2
,
…
,
…
,
)
o
f
th
e
in
p
u
t
r
an
d
o
m
v
ar
iab
le
T
h
e
g
r
o
s
s
n
u
m
b
er
o
f
d
eter
m
i
n
is
t
ic
o
p
ti
m
al
p
o
w
er
f
lo
w
(
O
P
F
)
to
b
e
r
u
n
r
el
ies
o
n
th
e
co
n
ce
n
tr
at
io
n
s
ch
e
m
es.
T
h
e
(
,
)
0
ar
e
u
s
ed
to
ev
alu
ate
th
e
r
a
w
m
o
m
e
n
ts
o
f
th
e
f
u
n
ct
io
n
o
u
tp
u
t.
T
h
e
alg
o
r
ith
m
w
il
l
en
d
s
w
h
e
n
all
co
n
ce
n
tr
atio
n
s
o
f
th
e
all
in
p
u
t
R
V
s
ar
e
co
n
s
id
er
ed
.
T
h
en
,
th
e
ev
alu
ated
r
a
w
m
o
m
e
n
ts
o
f
t
h
e
f
u
n
ctio
n
o
u
tp
u
t
w
ill b
e
u
s
ed
to
ca
lcu
late
t
h
e
r
eq
u
ir
ed
s
tatis
t
ic
al
in
f
o
r
m
atio
n
u
s
in
g
(
7
)
.
4.
F
ACTS
m
o
de
l
FDs
tech
n
o
lo
g
y
in
cl
u
d
es
a
g
r
o
u
p
o
f
co
n
tr
o
ller
s
th
at
p
r
o
v
id
e
a
p
o
s
s
ib
ilit
y
o
f
co
n
tr
o
ll
in
g
p
o
w
er
s
y
s
te
m
p
ar
a
m
eter
s
,
a
n
d
it
ca
n
b
e
co
n
n
ec
ted
to
a
p
o
w
er
s
y
s
te
m
i
n
v
ar
io
u
s
m
e
th
o
d
s
,
s
u
c
h
as
in
s
h
u
n
t,
s
er
ie
s
,
o
r
a
co
m
b
i
n
atio
n
o
f
s
h
u
n
t a
n
d
s
e
r
ies
[
2
2
]
.
4
.
1
.
T
hy
risto
r
co
ntr
o
lled ser
ies ca
pa
cit
o
r
T
h
e
T
C
SC
ca
n
b
e
c
o
n
s
id
er
ed
as
co
n
tr
o
lled
r
ea
ctan
ce
in
s
er
ies
w
ith
t
h
e
tr
a
n
s
s
i
m
is
s
io
n
li
n
e
.
T
h
e
m
ai
n
o
b
j
ec
tiv
e
o
f
th
is
d
ev
ice
is
to
co
m
p
en
s
ate
i
m
p
ed
a
n
ce
o
f
th
e
T
L
.
T
h
is
co
m
p
en
s
atio
n
o
f
th
e
i
m
p
ed
an
ce
ca
n
p
r
o
v
id
e
a
co
n
tr
o
l
t
h
e
p
o
w
er
f
lo
w
.
T
h
is
i
n
cr
ea
s
es
th
e
s
y
s
te
m
lo
ad
ab
ilit
y
a
n
d
i
n
cr
ea
s
e
s
t
h
e
d
a
m
p
i
n
g
o
f
t
h
e
in
ter
ar
ea
o
s
cillatio
n
,
an
d
also
p
r
o
v
id
es a
ch
an
ce
to
q
u
ick
l
y
a
d
j
u
s
t p
o
w
er
f
lo
w
i
n
r
esp
o
n
s
e
t
o
th
e
co
n
ti
n
g
en
cie
s
th
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a
s
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a
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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On
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ter
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s
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h
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s
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A
B
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1
7
b
[
2
5
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.
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P
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s
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ited
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s
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.
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I
SS
N
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2
0
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b
ased
tech
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iq
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s
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p
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to
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lo
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h
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p
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th
e
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L
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s
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litt
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’
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el.
I
n
t
h
is
p
h
ase,
th
e
s
tu
d
e
n
t
w
ill co
m
e
to
k
n
o
w
n
e
w
i
n
f
o
r
m
atio
n
by
s
el
f
-
s
t
u
d
y
i
n
g
.
I
n
th
is
p
h
a
s
e,
s
t
u
d
en
t
u
p
d
atin
g
i
s
g
i
v
e
n
:
R
an
d
o
m
l
y
,
s
elec
t t
w
o
s
t
u
d
en
ts
Si an
d
Sj
w
h
er
e
i
≠
j
,
=
,
+
(
−
)
(
)
<
(
)
,
=
,
+
(
−
)
(
)
≥
(
)
(
1
8
)
I
f
,
g
iv
es
b
etter
s
o
lu
tio
n
th
an
S
o
ld
,
i
th
en
,
ac
ce
p
t
it
o
th
er
w
is
e
k
ee
p
as
it
is
.
T
h
e
alg
o
r
ith
m
w
ill
co
n
tin
u
e
u
n
t
il th
e
ab
o
r
t c
o
n
d
itio
n
i
s
m
e
t.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
F
A
C
TS
a
llo
ca
tio
n
co
n
s
id
erin
g
lo
a
d
s
u
n
ce
r
ta
in
ty,
s
tea
d
y
s
ta
te
o
p
era
tio
n
c
o
n
s
tr
a
in
ts
...
(
M.
M.
H.
E
lr
o
b
y)
951
7.
P
RO
B
L
E
M
ST
AT
E
M
E
NT
T
h
e
allo
ca
tio
n
o
f
th
e
ST
A
T
C
OM
an
d
T
C
S
C
is
ex
p
r
es
s
ed
as
a
m
i
x
ed
c
o
n
ti
n
u
e
s
-
d
is
cr
ete
p
r
o
b
lem
.
T
h
e
f
lo
w
ch
ar
t
o
f
t
h
e
p
lan
n
ed
alg
o
r
ith
m
is
s
h
o
w
n
i
n
F
ig
u
r
e
1
.
T
h
e
o
v
er
all
p
r
o
b
lem
i
s
f
o
r
m
u
lated
as
t
w
o
lev
els.
I
n
t
h
e
f
ir
s
t
lev
el,
th
e
T
L
B
O
s
ea
r
ch
e
s
o
f
lo
ca
tio
n
an
d
r
atin
g
o
f
t
h
e
FDs
t
h
en
t
h
e
r
esu
lt
o
f
th
e
f
ir
s
t
le
v
el
is
p
ass
ed
in
to
th
e
s
ec
o
n
d
lev
el
.
I
n
t
h
e
s
ec
o
n
d
le
v
el,
t
h
e
p
r
o
b
le
m
i
s
d
i
v
id
ed
in
to
t
w
o
b
r
an
c
h
es.
T
h
e
f
ir
s
t b
r
an
c
h
(
th
e
r
ig
h
t
b
r
an
ch
)
,
th
e
T
L
B
O
s
ea
r
ch
es
o
f
t
h
e
lo
ad
s
b
et
w
ee
n
th
e
u
p
p
er
an
d
lo
w
er
v
a
lu
e
t
h
at
r
etu
r
n
m
a
x
v
al
u
e
o
f
th
e
OP
F v
io
lat
io
n
li
m
it
s
(
i.e
.
th
e
w
o
r
s
t c
ase
o
f
th
e
s
y
s
te
m
v
io
latio
n
li
m
i
ts
)
ac
co
r
d
in
g
to
t
h
e
(
1
9
)
:
E
cm
ax
=
ma
x
{
W
1
(
Pgc
+
Q
gc
+
Ic
+
Vc
)
+
W
2
SCI
}
(
1
9
)
T
h
e
s
ec
o
n
d
b
r
an
ch
(
th
e
lef
t
b
r
an
ch
)
u
s
es
2
P
E
M
an
d
OP
F
f
o
r
th
e
ev
alu
at
io
n
o
f
t
h
e
ex
p
e
cted
v
alu
e
(
i.e
.
m
o
m
e
n
t
o
n
e
(
7
)
)
o
f
g
e
n
er
atio
n
co
s
t
(
)
.
T
h
en
th
e
w
o
r
s
t
ca
s
e
o
f
t
h
e
co
n
s
tr
ain
t
s
E
cm
ax
an
d
ar
e
r
etu
r
n
ed
to
th
e
f
ir
s
t le
v
el
t
o
b
e
co
n
s
id
er
in
th
e
o
b
j
ec
tiv
e
f
u
n
ctio
n
as
f
o
llo
w
s
:
F
m
i
n
=
min
{
W
3
(
+
C
h
)
+
W
4
E
cm
a
x
}
(
2
0
)
I
t
ca
n
b
e
co
n
clu
d
ed
th
at
t
h
e
alg
o
r
ith
m
s
ea
r
c
h
es
o
f
t
h
e
b
es
t
lo
ca
tio
n
s
an
d
r
ati
n
g
s
o
f
t
h
e
FDs
t
h
at
m
in
i
m
ize
g
en
er
atio
n
an
d
FD
s
co
s
t f
o
r
al
l p
o
s
s
ib
le
lo
ad
s
an
d
m
i
n
i
m
ize
th
e
w
o
r
s
t
-
ca
s
e
o
f
t
h
e
s
y
s
te
m
v
io
latio
n
li
m
its
.
8.
CASE
S
T
UD
Y
T
h
e
ef
f
ec
ti
v
en
e
s
s
o
f
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
is
d
e
m
o
n
s
tr
ate
d
o
n
th
e
I
E
E
E
1
4
-
Gen
er
ato
r
t
est
s
y
s
te
m
.
T
h
e
d
ata
o
f
th
is
p
o
w
er
s
y
s
te
m
s
ar
e
av
ailab
le
in
[
2
7
]
.
A
ll
FD
s
ar
e
r
em
o
v
ed
f
r
o
m
s
y
s
te
m
t
h
en
it
co
n
s
id
er
ed
as
a
b
ase
ca
s
e.
T
h
e
s
tatis
tical
d
ata
f
o
r
th
is
s
y
s
te
m
is
id
en
t
if
i
ed
b
ef
o
r
eh
an
d
.
Fo
r
s
im
p
lici
t
y
,
th
e
v
alu
e
s
o
f
th
e
s
k
e
w
n
es
s
,
s
ta
n
d
ar
d
d
ev
iatio
n
,
an
d
k
u
r
to
s
i
s
f
o
r
ea
ch
lo
ad
b
u
s
ar
e
s
et
o
n
1
5
%,
0
.
3
0
4
1
,
an
d
2
.
5
3
9
2
,
r
esp
ec
tiv
el
y
.
I
n
ad
d
itio
n
,
th
e
m
ea
n
,
t
h
e
lo
w
er
,
an
d
u
p
p
er
f
o
r
ea
ch
lo
ad
b
u
s
ar
e
co
n
s
id
er
ed
0
.
8
,
0
.
6
,
an
d
1
.
1
o
f
th
e
h
ea
v
y
ca
s
e
r
esp
ec
ti
v
el
y
.
T
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
is
u
s
ed
to
allo
ca
te
f
o
u
r
ST
A
T
C
OM
an
d
f
o
u
r
T
C
SC
d
ev
ices
i
n
t
h
e
test
s
y
s
te
m
.
T
h
e
alg
o
r
ith
m
d
e
s
cr
ib
ed
in
se
cti
o
n
7
w
as
u
s
ed
to
ca
lcu
late
t
h
e
lo
ca
tio
n
s
a
n
d
r
ati
n
g
o
f
th
e
FDs
.
T
h
e
r
ig
h
t
b
r
an
ch
i
n
th
e
s
ec
o
n
d
lev
el
o
f
t
h
e
Fig
u
r
e
1
w
as
u
s
ed
to
in
v
esti
g
ate
th
e
w
o
r
s
t
ca
s
e
o
f
th
e
s
y
s
te
m
v
io
latio
n
li
m
it
s
in
th
e
ca
s
e
o
f
t
h
e
ab
s
en
ce
o
f
FD
s
.
T
h
en
t
h
e
r
es
u
lt
s
o
f
t
h
ese
t
w
o
c
ases
(
i.e
.
w
it
h
an
d
w
it
h
o
u
t FDs)
ar
e
s
h
o
w
n
i
n
T
ab
le
1
.
T
h
e
lef
t b
r
an
ch
i
n
th
e
s
e
co
n
d
lev
el
o
f
t
h
e
Fi
g
u
r
e
1
w
as
u
s
ed
to
in
v
esti
g
ate
th
e
ex
p
ec
ted
g
en
er
atio
n
co
s
t
(
)
in
th
e
ca
s
e
o
f
t
h
e
ab
s
en
ce
o
f
FDs
.
T
h
en
th
e
r
es
u
l
t
s
o
f
t
h
ese
t
wo
ca
s
es
(
i.e
.
w
i
th
a
n
d
w
ith
o
u
t
F
Ds)
ar
e
s
h
o
w
n
i
n
T
ab
le
2
.
I
n
ad
d
itio
n
,
T
a
b
le
3
s
h
o
w
s
t
h
e
r
e
s
u
lt
s
o
f
t
h
e
F
AC
T
S
lo
ca
tio
n
an
d
r
atin
g
.
T
h
e
Fi
g
u
r
e
2
s
h
o
w
s
t
h
e
co
n
v
er
g
e
n
c
e
cu
r
v
e
o
f
t
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
.
F
ig
u
r
e
3
to
Fig
u
r
e
5
s
h
o
w
b
u
s
es
v
o
lta
g
e
a
n
d
li
n
es
f
lo
w
f
o
r
t
h
e
w
o
r
s
t
ca
s
e
o
f
t
h
e
s
y
s
te
m
v
io
latio
n
li
m
it
s
i
n
t
h
e
ca
s
e
o
f
t
h
e
p
r
esen
ce
an
d
ab
s
e
n
ce
o
f
F
Ds.
B
ased
o
n
th
e
r
esu
lts
o
f
t
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
,
th
e
FD
s
s
h
o
w
n
i
n
T
ab
le
3
ar
e
u
s
ed
in
t
h
e
Si
m
u
li
n
k
m
o
d
el
to
p
er
f
o
r
m
t
i
m
e
-
d
o
m
ai
n
s
i
m
u
lati
o
n
test
as
f
o
llo
w
s
:
a.
C
o
n
ti
n
g
en
c
y
ca
s
e
:
A
t
h
r
ee
-
p
h
ase
f
au
l
t
i
s
o
cc
u
r
r
ed
at
t
h
e
en
d
o
f
li
n
e
4
0
9
-
4
1
1
n
ea
r
b
u
s
4
1
1
at
ti
m
e
=1
.
T
h
e
f
au
lt
w
as
c
lear
ed
af
ter
0
.
1
s
.
T
h
e
Fig
u
r
e
6
an
d
Fi
g
u
r
e
7
s
h
o
w
t
h
e
s
i
m
u
latio
n
r
es
u
lts
o
f
all
g
e
n
er
ato
r
s
f
r
eq
u
en
c
ies o
f
t
h
e
co
n
ti
n
g
en
c
y
ca
s
e
f
o
r
w
it
h
o
u
t
FDs
a
n
d
w
i
th
FD
s
ca
s
es.
b.
R
e
m
ar
k
s
:
As
ex
p
ec
ted
,
th
e
to
tal
ex
p
ec
ted
co
s
t
(
G
ex
p
c
)
an
d
C
o
n
s
tr
ain
ts
d
ev
i
atio
n
ar
e
s
m
a
ll
in
th
e
ca
s
e
w
it
h
FDs
th
a
n
ca
s
e
w
ith
o
u
t FD
s
.
I
t
is
o
b
v
io
u
s
t
h
at
t
h
e
s
y
s
te
m
o
p
er
ate
w
ith
o
u
t
co
n
s
id
er
in
g
FDs
f
ail
to
m
ai
n
tai
n
t
h
e
i
n
ter
-
ar
ea
o
s
cillatio
n
w
h
e
n
it
is
s
u
b
j
ec
ted
to
th
is
co
n
ti
n
g
e
n
c
y
.
Ho
w
e
v
er
,
w
h
e
n
F
Ds ar
e
co
n
s
id
er
ed
,
th
e
i
n
ter
-
ar
ea
o
s
cillatio
n
ca
n
b
e
s
u
cc
ess
f
u
ll
y
d
a
m
p
ed
.
T
h
is
d
e
m
o
n
s
tr
ated
th
at
t
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
co
u
ld
s
u
c
ce
s
s
f
u
l
l
y
h
an
d
l
e
co
n
tin
g
e
n
cies a
n
d
r
ed
u
ce
to
ta
l c
o
s
t.
T
ab
le
1
.
T
h
e
w
o
r
s
t
ca
s
e
o
f
th
e
s
y
s
te
m
co
n
s
tr
ai
n
ts
v
io
latio
n
l
i
m
it
s
Pgc
Q
gc
Vc
Ic
S
C
I
W
i
t
h
o
u
t
F
D
s
0
0
0
.
4
3
0
.
2
3
0
.
5
6
W
i
t
h
F
D
s
0
0
0
0
0
.
1
T
ab
le
2
.
T
h
e
ex
p
ec
ted
g
en
er
atio
n
co
s
t
W
i
t
h
o
u
t
F
D
s
W
i
t
h
F
D
s
M
e
t
h
o
d
O
P
F
g
c
e
x
p
e
c
t
e
d
O
P
F
g
c
e
x
p
e
c
t
e
d
+
Ch
2
P
E
M
8
5
3
3
8
5
.
6
8
0
2
1
8
5
.
6
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
11
,
No
.
2
,
A
p
r
il 2
0
2
1
:
9
4
5
-
955
952
T
ab
le
3
.
FA
C
T
Ss
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.
R
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NC
E
S
[1
]
M
.
V
.
Ra
o
,
e
t
a
l.
,
“
A
v
a
il
a
b
le
tran
sf
e
r
c
a
p
a
b
il
it
y
e
v
a
lu
a
ti
o
n
a
n
d
e
n
h
a
n
c
e
m
e
n
t
u
sin
g
v
a
rio
u
s
F
A
CT
S
c
o
n
tro
ll
e
rs:
S
p
e
c
ial
f
o
c
u
s o
n
sy
st
e
m
se
c
u
rit
y
,
”
Ai
n
S
h
a
ms
En
g
in
e
e
rin
g
J
o
u
rn
a
l
,
v
o
l.
7
,
n
o
.
1
,
p
p
.
1
9
1
-
2
0
7
,
2
0
1
6
.
[2
]
S
.
Da
w
n
,
e
t
a
l.
,
“
A
n
a
p
p
ro
a
c
h
fo
r
s
y
ste
m
ris
k
a
ss
e
ss
m
e
n
t
a
n
d
m
it
ig
a
ti
o
n
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y
o
p
ti
m
a
l
o
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e
ra
ti
o
n
o
f
w
in
d
f
a
r
m
a
n
d
F
A
C
T
S
d
e
v
ice
s
in
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c
e
n
tralize
d
c
o
m
p
e
ti
ti
v
e
p
o
we
r
m
a
rk
e
t,
”
IEE
E
T
ra
n
s
a
c
ti
o
n
s
o
n
S
u
sta
i
n
a
b
le
E
n
e
rg
y
,
v
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l.
1
0
,
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o
.
3
,
p
p
.
1
0
5
4
-
1
0
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5
,
2
0
1
9
.
[3
]
A
.
Co
lme
n
a
r
-
S
a
n
to
s,
e
t
a
l
.
,
“
Dis
tri
b
u
te
d
g
e
n
e
ra
ti
o
n
:
A
re
v
ie
w
o
f
f
a
c
to
rs
th
a
t
c
a
n
c
o
n
tri
b
u
te
m
o
st
to
a
c
h
iev
e
a
sc
e
n
a
rio
o
f
D
G
u
n
it
s
e
m
b
e
d
d
e
d
in
th
e
n
e
w
d
istri
b
u
t
io
n
n
e
tw
o
rk
s,”
Ren
e
w
a
b
le
a
n
d
S
u
st
a
i
n
a
b
le
En
e
rg
y
Rev
iew
,
v
o
l.
5
9
,
p
p
.
1
1
3
0
-
1
1
4
8
,
2
0
1
6
.
[4
]
B.
V
.
Ku
m
a
r
a
n
d
N.
V
.
S
rik
a
n
th
,
“
A
h
y
b
rid
a
p
p
ro
a
c
h
f
o
r
o
p
ti
m
a
l
lo
c
a
ti
o
n
a
n
d
c
a
p
a
c
it
y
o
f
UP
F
C
t
o
im
p
ro
v
e
th
e
d
y
n
a
m
ic sta
b
il
it
y
o
f
th
e
p
o
w
e
r
s
y
ste
m
,
”
Ap
p
l
ied
S
o
ft
C
o
mp
u
t
in
g
,
v
o
l.
5
2
,
p
p
.
9
7
4
-
9
8
6
,
2
0
1
7
.
[5
]
A
.
El
m
it
w
a
ll
y
,
e
t
a
l.
,
“
L
o
n
g
-
ter
m
e
c
o
n
o
m
ic
m
o
d
e
l
f
o
r
a
ll
o
c
a
ti
o
n
o
f
F
A
C
T
S
d
e
v
i
c
e
s
in
re
stru
c
tu
re
d
p
o
w
e
r
s
y
ste
m
s
in
teg
ra
ti
n
g
w
in
d
g
e
n
e
ra
ti
o
n
,
”
IE
T
Ge
n
e
r
a
ti
o
n
,
T
r
a
n
sm
issio
n
a
n
d
D
istrib
u
ti
o
n
,
v
o
l.
1
0
,
n
o
.
1
,
p
p
.
1
9
-
3
0
,
2
0
1
6
.
[6
]
W
.
Ya
o
,
e
t
a
l.
,
“
W
id
e
-
A
re
a
Da
m
p
in
g
Co
n
tr
o
ll
e
r
f
o
r
P
o
w
e
r
S
y
ste
m
In
tera
re
a
Os
c
il
latio
n
s:
A
N
e
t
wo
rk
e
d
P
re
d
ictiv
e
Co
n
tr
o
l
A
p
p
ro
a
c
h
,
”
IEE
E
T
ra
n
s
a
c
ti
o
n
s
o
n
C
o
n
tr
o
l
S
y
st
e
ms
T
e
c
h
n
o
l
ogy
,
v
o
l.
2
3
,
n
o
.
1
,
p
p
.
2
7
-
3
6
,
2
0
1
4
.
[7
]
L
.
Ya
z
d
a
n
i
a
n
d
M
.
R.
A
g
h
a
m
o
h
a
m
m
a
d
i,
“
Da
m
p
in
g
in
ter
-
a
re
a
o
sc
il
latio
n
b
y
g
e
n
e
ra
ti
o
n
re
sc
h
e
d
u
li
n
g
b
a
se
d
o
n
w
id
e
-
a
re
a
m
e
a
su
re
m
e
n
t
in
f
o
r
m
a
t
io
n
,
”
In
t
e
rn
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
E
lec
tr
ica
l
Po
we
r
and
En
e
rg
y
S
y
st
e
ms
,
v
o
l.
6
7
,
p
p
.
1
3
8
-
1
5
1
,
2
0
1
5
.
[8
]
M
.
M
a
n
d
o
u
r
,
e
t
a
l.
,
“
Da
m
p
in
g
o
f
P
o
w
e
r
S
y
ste
m
s Os
c
il
latio
n
s u
sin
g
F
A
C
T
S
P
o
w
e
r
Os
c
il
latio
n
Da
m
p
e
r
–
De
sig
n
a
n
d
P
e
rf
o
rm
a
n
c
e
A
n
a
l
y
sis
D
a
m
p
in
g
o
f
P
o
w
e
r
S
y
ste
m
s
Os
c
il
latio
n
s
u
sin
g
F
A
C
T
S
P
o
w
e
r
Os
c
il
latio
n
Da
m
p
e
r
–
De
sig
n
a
n
d
P
e
rf
o
rm
a
n
c
e
A
n
a
l
y
sis,”
1
6
th
In
t
e
rn
a
ti
o
n
a
l
M
id
d
le
-
Ea
st
P
o
we
r
S
y
st
em
Co
n
f
e
re
n
c
e
(
M
EP
C
ON’2
0
1
4
)
A
in
S
h
a
m
s Un
iv
.
Ca
iro
,
Eg
y
p
t,
2
0
1
4
,
p
p
.
1
-
8.
[9
]
W
.
Ya
o
,
e
t
a
l.
,
“
W
id
e
-
a
re
a
d
a
m
p
in
g
c
o
n
tro
ll
e
r
o
f
F
a
c
ts
d
e
v
ice
s
f
o
r
in
ter
-
a
re
a
o
sc
il
latio
n
s
c
o
n
si
d
e
rin
g
c
o
m
m
u
n
ica
ti
o
n
t
im
e
d
e
la
y
s,”
IEE
E
T
ra
n
s
a
c
ti
o
n
s o
n
P
o
we
r S
y
st
em
,
v
o
l.
2
9
,
n
o
.
1
,
p
p
.
3
1
8
-
3
2
9
,
2
0
1
4
.
[1
0
]
K.
N.
S
tan
to
n
,
“
Dy
n
a
m
ic
e
n
e
rg
y
b
a
lan
c
e
stu
d
ies
f
o
r
sim
u
latio
n
o
f
p
o
w
e
r
-
f
r
e
q
u
e
n
c
y
tran
sie
n
ts,”
IEE
E
T
ra
n
s
a
c
ti
o
n
s
on
P
o
we
r A
p
p
a
r
a
tu
s
a
n
d
S
y
st
e
ms
,
v
o
l.
P
A
S
-
9
1
,
n
o
.
1
,
p
p
.
1
1
0
-
1
1
7
,
1
9
7
2
.
[1
1
]
H.
Ye
a
n
d
Y.
L
iu
,
“
De
sig
n
o
f
m
o
d
e
l
p
re
d
ictiv
e
c
o
n
tro
ll
e
rs
f
o
r
a
d
a
p
ti
v
e
d
a
m
p
in
g
o
f
in
ter
-
a
re
a
o
sc
il
latio
n
s,”
In
t
e
rn
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
E
lec
tr
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