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ted
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ly
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a
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d
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ra
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ti
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a
n
d
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li
a
b
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R
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T
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W
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W
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[
̂
(
)
]
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Sin
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L
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q
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[
̂
(
)
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Sli
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SMC
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s
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‖
(
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‖
:
No
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m
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f
s
tate
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(
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Glo
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C
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(
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:
Dy
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r
o
r
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f
esti
m
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()
zt
:
States
o
f
th
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p
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t
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,
̄
:
Po
s
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co
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s
tan
ts
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J
Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
4
,
Dec
em
b
er
20
25
:
2381
-
2
3
8
8
2382
1.
I
NT
RO
D
UCT
I
O
N
T
h
e
o
p
er
atio
n
o
f
PS
is
ex
tr
e
m
ely
co
m
p
lex
d
u
e
to
t
h
e
v
ar
iab
ilit
y
o
f
lo
ad
r
eq
u
ests
an
d
r
en
ewa
b
le
g
en
er
atio
n
,
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d
esp
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th
e
ex
ch
an
g
e
o
f
elec
tr
icity
b
etwe
e
n
n
eig
h
b
o
r
in
g
a
r
ea
s
.
T
h
e
PS
co
n
tr
o
l
s
ch
em
es
a
r
e
u
s
ed
to
m
ain
tain
th
e
s
y
s
tem
in
a
s
tab
le
s
tate,
an
d
L
FC
is
an
im
p
o
r
tan
t
co
n
tr
o
l
is
s
u
e
in
wid
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ar
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PS
o
p
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atio
n
s
[
1
]
-
[
3
]
.
Am
o
n
g
co
n
tr
o
l
ap
p
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ac
h
es,
s
lid
in
g
m
o
d
e
co
n
tr
o
l
(
SMC
)
is
o
n
e
s
u
ch
well
-
k
n
o
wn
co
n
tr
o
l
p
er
f
o
r
m
an
ce
d
u
e
to
s
tu
r
d
i
n
ess
,
f
in
ite
tim
e
co
n
v
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g
en
ce
,
in
s
en
s
itiv
ity
to
p
er
tu
r
b
atio
n
s
,
an
d
u
n
ce
r
tain
ties
[
4
]
,
[
5
]
.
T
h
e
r
en
o
w
n
ed
SMC
is
a
s
p
ec
if
ic
ca
teg
o
r
y
o
f
VSC
,
wh
ich
is
th
e
n
ewe
s
t
o
n
g
o
in
g
m
o
v
em
en
t
in
m
an
y
d
if
f
er
en
t
f
ield
s
,
s
u
c
h
as
h
y
d
r
a
u
lic/air
-
f
illed
,
tr
a
n
s
m
is
s
io
n
o
f
d
ata,
s
tr
u
ctu
r
es
o
f
s
atellites
,
r
o
b
o
tic
m
a
n
ip
u
lato
r
,
an
d
esp
ec
ially
i
n
th
e
L
FC
o
f
PS
s
[
6
]
-
[
1
0
]
.
Alth
o
u
g
h
th
e
VSC
in
s
lid
in
g
m
o
d
e
h
as
n
o
tewo
r
th
y
ac
co
m
p
lis
h
m
en
ts
in
L
FC
p
r
o
b
lem
s
,
o
v
er
all,
t
h
er
e
ar
e
s
till
two
m
is
s
io
n
s
th
at
s
h
o
u
ld
b
e
u
n
r
av
eled
f
o
r
VSC
-
b
ased
L
FC
p
r
o
b
lem
s
o
f
PS
s
: T
h
is
in
clu
d
es:
i
)
Ou
tp
u
t f
ee
d
b
ac
k
: A
s
h
o
r
tco
m
in
g
o
f
th
e
cu
r
r
en
t
in
v
esti
g
atio
n
s
is
th
at
all
v
ar
iab
les
o
f
th
e
PS
s
h
av
e
to
b
e
ac
ce
s
s
ib
le.
T
h
is
is
u
n
ac
ce
p
tab
le
in
v
ar
io
u
s
p
r
ac
tic
al
p
lan
t
co
n
t
r
o
ls
.
A
n
ew
o
u
tp
u
t
f
ee
d
b
ac
k
s
lid
in
g
m
o
d
e
lo
a
d
f
r
e
q
u
en
c
y
co
n
t
r
o
ller
(
OFSMC
L
FC
)
i
s
p
r
o
p
o
s
ed
f
o
r
MRLPS
em
p
lo
y
in
g
o
n
l
y
o
u
tp
u
t
in
f
o
r
m
atio
n
;
an
d
ii
)
C
h
atter
in
g
p
h
en
o
m
en
o
n
er
a
d
icatio
n
:
A
n
e
w
OFSMC
L
FC
n
o
t
o
n
ly
p
r
o
m
is
es
th
e
en
tire
s
tead
in
ess
o
f
th
e
MRLPS
b
u
t
also
r
ed
u
ce
s
th
e
u
n
d
esira
b
le
h
ig
h
-
f
r
eq
u
en
c
y
o
s
cillatio
n
s
in
co
n
tr
o
l
in
d
icati
o
n
b
y
u
tili
zin
g
th
e
SOSMC
.
T
o
f
in
d
th
e
s
o
lu
tio
n
to
th
e
o
u
tp
u
t
f
ee
d
b
ac
k
c
o
n
tr
o
l
s
tr
ateg
y
p
r
o
b
lem
in
th
e
f
ir
s
t
task
ab
o
v
e,
a
s
ig
n
if
ica
n
t
n
u
m
b
er
o
f
s
tu
d
ies
h
av
e
b
ee
n
p
r
o
p
o
s
ed
in
L
FC
,
as
m
en
tio
n
ed
i
n
T
ab
le
1
.
T
ab
le
1
.
Su
m
m
a
r
y
o
f
k
e
y
wo
r
k
s
r
elate
d
to
th
e
f
i
r
s
t ta
s
k
o
f
n
o
tab
le
SMC
-
b
ased
L
FC
m
eth
o
d
s
R
e
f
.
S
y
st
e
ms
K
e
y
c
o
n
t
r
i
b
u
t
i
o
n
s
A
p
p
r
o
a
c
h
e
s/
t
e
c
h
n
i
q
u
e
s
Li
mi
t
a
t
i
o
n
s
[
6
]
M
i
c
r
o
g
r
i
d
s
y
st
e
m
I
mp
r
o
v
e
d
f
r
e
q
u
e
n
c
y
r
e
g
u
l
a
t
i
o
n
u
si
n
g
o
p
t
i
m
i
z
e
d
S
M
C
S
l
i
d
i
n
g
mo
d
e
c
o
n
t
r
o
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l
a
w
v
i
a
t
e
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c
h
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n
g
l
e
a
r
n
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n
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o
p
t
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mi
z
a
t
i
o
n
Tr
a
d
i
t
i
o
n
a
l
S
M
C
,
t
h
e
c
h
a
t
t
e
r
i
n
g
i
ss
u
e
r
e
m
a
i
n
s
[
7
]
M
u
l
t
i
-
r
e
g
i
o
n
p
o
w
e
r
p
l
a
n
t
w
i
t
h
t
i
me
d
e
l
a
y
s
a
n
d
p
e
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t
u
r
b
a
t
i
o
n
s
R
o
b
u
st
f
r
e
q
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e
n
c
y
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e
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u
l
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t
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o
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n
d
l
i
n
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d
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y
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n
d
p
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t
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r
b
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t
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o
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F
u
l
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-
o
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mi
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t
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o
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Tr
a
d
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t
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o
n
a
l
S
M
C
,
r
o
b
u
st
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s
s o
n
l
y
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n
t
h
e
sl
i
d
i
n
g
p
h
a
se
[
1
1
]
M
u
l
t
i
-
a
r
e
a
i
n
t
e
r
c
o
n
n
e
c
t
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A
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l
o
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d
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R
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i
r
e
s f
u
l
l
s
t
a
t
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mea
s
u
r
e
me
n
t
[
1
2
]
I
n
t
e
r
c
o
n
n
e
c
t
e
d
m
u
l
t
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-
f
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D
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t
r
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C
w
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D
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C
o
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t
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v
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f
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P
S
O
F
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l
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st
a
t
e
a
c
c
e
ssi
b
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l
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t
y
a
ssu
m
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d
[
1
3
]
I
n
t
e
r
c
o
n
n
e
c
t
e
d
p
o
w
e
r
s
y
st
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ms
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mp
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v
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d
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ma
t
o
r
-
b
a
se
d
S
M
C
I
n
t
e
g
r
a
l
S
M
C
b
a
se
d
o
n
st
a
t
e
e
st
i
mat
o
r
C
h
a
t
t
e
r
i
n
g
i
ss
u
e
r
e
m
a
i
n
s
Nev
er
th
eless
,
au
th
o
r
s
in
T
ab
l
e
1
h
av
e
u
s
ed
th
e
T
SMC
tech
n
iq
u
e
,
w
h
ich
o
n
ly
p
r
o
d
u
ce
s
th
e
wan
ted
m
o
tio
n
a
f
ter
s
lid
in
g
m
o
d
e
h
as o
cc
u
r
r
e
d
.
T
he
T
SMC
’
s
r
o
b
u
s
tn
ess
o
n
ly
h
ap
p
e
n
s
in
th
e
s
lid
i
n
g
m
o
d
e
p
er
io
d
.
T
o
ad
v
an
ce
th
e
r
o
b
u
s
tn
ess
o
f
SMC
,
th
e
au
th
o
r
s
in
th
is
s
tu
d
y
p
r
o
p
o
s
ed
a
n
o
v
el
GSMC
ap
p
r
o
ac
h
.
I
t
s
h
o
u
ld
b
e
d
is
tin
g
u
is
h
ed
th
at
GSMC
h
a
s
s
tr
o
n
g
s
tab
ilit
y
d
u
r
in
g
th
e
wh
o
le
co
n
tr
o
l
p
r
o
g
r
ess
io
n
,
b
ett
er
th
an
th
e
T
SMC
[
1
4
]
,
[
1
5
]
.
R
ec
en
tly
,
th
e
d
esig
n
o
f
th
e
L
FC
s
ch
em
e
was
s
u
g
g
ested
b
ased
o
n
ad
ap
tiv
e
GSMC
f
o
r
a
m
u
lti
-
r
eg
io
n
lin
k
ed
elec
tr
icity
s
y
s
t
em
with
im
m
ea
s
u
r
ab
le
s
tates
[
8
]
.
Ho
wev
e
r
,
m
o
s
t
o
f
th
es
e
s
tu
d
ies
n
ee
d
th
e
ac
ce
s
s
ib
ilit
y
o
f
th
e
s
tates
o
f
th
e
p
lan
t,
wh
ich
ca
n
n
o
t
b
e
w
ar
r
an
ted
i
n
p
r
ac
tice.
Pre
v
iew
s
tu
d
y
[
1
6
]
,
o
u
tp
u
t
f
ee
d
b
ac
k
s
lid
in
g
m
o
d
e
lo
a
d
f
r
eq
u
en
c
y
c
o
n
tr
o
l
law
was
p
r
o
p
o
s
ed
f
o
r
MRLPS
with
ex
t
er
n
al
p
e
r
tu
r
b
atio
n
s
.
Nev
er
th
eless
,
th
ese
s
tu
d
ies
c
o
u
ld
n
o
t
less
en
th
e
ch
atter
i
n
g
im
p
ac
t
in
th
e
in
p
u
t
s
ig
n
al.
Hig
h
-
f
r
eq
u
e
n
cy
v
ib
r
atio
n
ca
u
s
es
d
am
ag
e
o
r
w
ea
r
to
m
o
v
in
g
m
ec
h
an
ical
p
ar
ts
,
af
f
ec
ts
co
n
tr
o
l
ac
c
u
r
ac
y
,
a
n
d
ca
u
s
es
h
ig
h
h
ea
t
in
th
e
elec
tr
ical
cir
cu
it
[
1
7
]
.
T
o
d
ea
l
with
th
is
ch
atter
i
n
g
p
h
en
o
m
en
o
n
,
th
e
tech
n
i
q
u
e
o
f
h
id
i
n
g
th
e
d
is
co
n
tin
u
ity
o
f
th
e
co
n
tr
o
l sig
n
al
in
its
h
ig
h
er
d
er
iv
ativ
es
was e
x
ec
u
ted
em
p
lo
y
in
g
HOS
MC o
r
SOSM
C
.
T
h
e
HOSMC
tech
n
iq
u
e
was
elev
at
ed
b
y
L
ev
an
t
[
1
8
]
,
th
e
n
ev
en
t
u
ally
it
h
as
ev
en
tu
ally
attr
ac
ted
a
lo
t
o
f
atten
tio
n
.
I
n
ad
d
itio
n
,
t
h
e
t
h
eo
r
y
an
d
ap
p
licatio
n
o
f
t
h
e
SOSMC
ap
p
r
o
ac
h
h
a
v
e
b
ee
n
g
r
ea
tly
d
ev
elo
p
ed
in
r
ec
en
t
y
ea
r
s
.
T
h
e
id
ea
o
f
th
e
SOSMC
m
eth
o
d
o
lo
g
y
was
o
r
ig
in
ally
estab
li
s
h
ed
in
th
e
1
9
8
0
s
b
y
[
1
9
]
.
T
h
i
s
is
al
s
o
th
e
s
ec
o
n
d
m
is
s
io
n
o
f
o
u
r
s
tu
d
y
.
T
o
ac
h
i
ev
e
ch
atter
in
g
r
e
d
u
ctio
n
in
th
e
s
ec
o
n
d
task
,
th
e
r
e
ar
e
m
an
y
m
eth
o
d
s
to
m
itig
ate
th
e
ch
atter
in
g
p
h
en
o
m
en
o
n
,
as
s
h
o
wn
in
T
ab
le
2
.
T
ab
le
2
.
Su
m
m
a
r
y
o
f
th
e
m
ai
n
f
in
d
in
g
s
an
d
ass
o
ciate
d
lim
itatio
n
s
r
eg
ar
d
in
g
in
th
e
s
ec
o
n
d
m
is
s
io
n
R
e
f
.
S
y
st
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ms
K
e
y
c
o
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t
r
i
b
u
t
i
o
n
s
A
p
p
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a
c
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s/
t
e
c
h
n
i
q
u
e
s
Li
mi
t
a
t
i
o
n
s
[
2
0
]
M
u
l
t
i
-
r
e
g
i
o
n
h
y
d
r
o
p
o
w
e
r
p
l
a
n
t
s
A
d
d
r
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ss
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d
c
h
a
t
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r
i
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g
i
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LF
C
u
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g
a
d
a
p
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v
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H
O
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M
C
A
d
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p
t
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v
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n
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g
r
a
l
c
o
n
t
r
o
l
l
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g
H
O
S
M
C
S
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n
s
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t
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v
i
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t
o
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m
o
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d
d
y
n
a
mi
c
s
,
n
e
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d
s
f
u
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l
s
t
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[
2
1
]
Th
r
e
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-
r
e
g
i
o
n
p
o
w
e
r
p
l
a
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t
A
d
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p
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S
M
C
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g
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LF
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A
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C
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s
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v
i
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y
t
o
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n
a
m
i
c
s
[
2
2
]
La
r
g
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-
sca
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p
o
w
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r
p
l
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t
R
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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&
Dr
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N:
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8
6
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c
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tter
in
g
g
lo
b
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l s
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(
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2383
As
s
h
o
wn
in
T
ab
le
s
1
an
d
2
,
alth
o
u
g
h
s
ig
n
if
ican
t
p
r
o
g
r
ess
h
as
b
ee
n
m
a
d
e
in
d
esig
n
in
g
ad
v
an
ce
d
SMC
-
b
ased
L
FC
s
ch
em
es,
two
m
ajo
r
ch
allen
g
es
r
em
ain
.
First,
m
an
y
ex
is
tin
g
m
eth
o
d
s
r
eq
u
ir
e
f
u
ll
s
tate
in
f
o
r
m
atio
n
,
wh
ic
h
is
n
o
t
alw
ay
s
p
r
ac
tically
p
o
s
s
ib
le.
Seco
n
d
,
w
h
ile
v
ar
i
o
u
s
ap
p
r
o
ac
h
es
h
av
e
attem
p
ted
to
m
itig
ate
th
e
ch
atter
in
g
p
h
en
o
m
en
o
n
,
f
u
lly
elim
in
atin
g
h
i
g
h
-
f
r
e
q
u
en
c
y
o
s
cillatio
n
s
in
th
e
co
n
tr
o
l
s
ig
n
al
r
em
ain
s
d
if
f
icu
lt.
Mo
tiv
ated
b
y
th
ese
lim
itatio
n
s
,
th
is
p
ap
er
p
r
o
p
o
s
es
a
n
o
v
el
ch
atter
i
n
g
-
f
r
ee
g
lo
b
al
s
ec
o
n
d
-
o
r
d
er
s
lid
in
g
m
o
d
e
lo
ad
f
r
e
q
u
en
cy
c
o
n
tr
o
ller
(
C
GSOSML
FC
)
th
at
em
p
lo
y
s
an
o
b
s
er
v
er
-
b
ased
o
u
t
p
u
t
f
ee
d
b
ac
k
s
tr
ateg
y
to
ad
d
r
ess
b
o
th
o
f
th
ese
is
s
u
es
ef
f
ec
tiv
el
y
.
T
h
e
C
GSOSML
FC
en
s
u
r
es
g
lo
b
al
s
tab
ilit
y
o
f
th
e
MRLPS
f
r
o
m
th
e
b
eg
in
n
i
n
g
o
f
its
m
o
tio
n
wh
ile
elim
in
atin
g
h
ig
h
-
f
r
eq
u
en
cy
f
l
u
ctu
atio
n
s
in
th
e
co
n
tr
o
l
s
ig
n
al.
I
n
ad
d
itio
n
,
in
th
e
s
lid
in
g
m
o
d
e,
an
ap
p
r
o
p
r
iate
r
eq
u
i
r
em
en
t
to
asy
m
p
to
tically
allev
iate
th
e
MRL
PS
is
g
iv
en
b
y
m
ea
n
s
o
f
th
e
r
e
n
o
wn
ed
L
MI
m
eth
o
d
.
T
o
en
d
,
b
y
m
ath
em
atica
l e
x
am
p
le,
th
e
v
alid
ity
o
f
th
e
p
r
o
p
o
s
ed
co
n
ce
p
ts
,
tech
n
iq
u
es,
an
d
p
r
o
c
ed
u
r
es
is
s
h
o
wn
.
2.
ST
A
T
E
SP
ACE F
O
R
M
O
F
T
H
E
M
UL
T
I
-
R
E
G
I
O
N
L
I
N
K
E
D
P
O
WE
R
S
YS
T
E
M
S
I
n
th
is
p
ar
t,
th
e
MRLPS
co
n
tain
s
s
u
b
s
y
s
tem
co
n
tr
o
l
r
e
g
io
n
s
th
at
ar
e
lin
k
ed
th
r
o
u
g
h
tie
-
lin
es
[
7
]
.
Fig
u
r
e
1
illu
s
tr
ates
th
e
m
ath
e
m
atica
l
m
o
d
el
o
f
i
th
e
co
n
tr
o
l
zo
n
e
with
W
T
G,
wh
e
r
e
i
=
1
,
2
.
.
.
,
n
s
y
m
b
o
lizes
th
e
n
u
m
b
er
o
f
zo
n
es,
a
n
d
i
≠
j
.
T
h
e
m
u
lti
-
zo
n
e
elec
tr
icity
p
lan
t d
y
n
am
ics
ar
e
d
escr
ib
e
d
in
T
ab
l
e
3
.
Fig
u
r
e
1
.
B
lo
ck
d
iag
r
am
o
f
th
e
MRLPS
co
m
p
r
is
es win
d
an
d
th
er
m
al
u
n
its
T
ab
le
3
.
T
h
e
in
ter
co
n
n
ec
ted
m
u
lti
-
ar
ea
p
o
wer
s
y
s
tem
d
y
n
am
ics
[
7
]
Ex
p
r
e
ssi
o
n
/
f
o
r
mu
l
a
P
h
y
s
i
c
a
l
mea
n
i
n
g
/
e
x
p
l
a
n
a
t
i
o
n
z
̇
1i
(
t
)
=
−
1
T
Pi
z
̇
1i
(
t
)
+
K
Pi
T
Pi
z
2i
(
t
)
+
K
Pi
T
Pi
Δ
P
di
(
t
)
−
K
Pi
2
π
T
Pi
×
∑
K
s
ij
[
Δ
z
5i
(
t
)
−
Δ
z
5j
(
t
)
+
K
Pi
T
Pi
z
6i
(
t
)
]
N
i
=
1
,
j
≠
i
F
r
e
q
u
e
n
c
y
d
y
n
a
m
i
c
s
:
z
1i
(
t
)
=
Δ
f
i
(
t
)
i
s fr
e
q
u
e
n
c
y
d
e
v
i
a
t
i
o
n
i
n
a
r
e
a
i
z
̇
2i
(
t
)
=
−
1
T
Ti
z
2i
(
t
)
+
1
T
Ti
z
3i
(
t
)
G
e
n
e
r
a
t
o
r
o
u
t
p
u
t
d
y
n
a
m
i
c
s
:
z
2i
(
t
)
=
Δ
P
gi
(
t
)
i
s
d
e
v
i
a
t
i
o
n
o
f
g
e
n
e
r
a
t
o
r
o
u
t
p
u
t
p
o
w
e
r
z
̇
3i
(
t
)
=
−
1
T
Gi
R
i
z
1i
(
t
)
−
1
T
Gi
z
3i
(
t
)
−
1
T
Gi
z
4i
(
t
)
−
1
T
Gi
u
i
G
o
v
e
r
n
o
r
v
a
l
v
e
p
o
s
i
t
i
o
n
d
y
n
a
m
i
c
s
:
z
3i
(
t
)
=
Δ
X
gi
(
t
)
i
s
g
o
v
e
r
n
o
r
’
s
v
a
l
v
e
si
t
u
a
t
i
o
n
z
̇
4i
(
t
)
=
K
Ei
K
Bi
α
T
z
4i
(
t
)
+
K
E
i
α
T
2
π
∑
[
Δ
z
5i
(
t
)
−
Δ
z
5j
(
t
)
]
N
i
=
1
,
j
≠
i
I
n
t
e
g
r
a
l
c
o
n
t
r
o
l
l
e
r
o
u
t
p
u
t
d
y
n
a
mi
c
s:
z
4i
(
t
)
=
Δ
E
i
i
s
o
u
t
p
u
t
o
f
i
n
t
e
g
r
a
l
c
o
n
t
r
o
l
l
e
r
z
̇
5i
(
t
)
=
2
π
z
5i
(
t
)
R
o
t
o
r
a
n
g
l
e
d
y
n
a
mi
c
s:
z
5i
(
t
)
=
Δ
δ
i
(
t
)
i
s t
h
e
r
o
t
o
r
a
n
g
l
e
’
s a
b
e
r
r
a
t
i
o
n
z
̇
6i
(
t
)
=
α
ω
T
ω
i
z
4i
(
t
)
−
1
T
ω
i
z
6i
(
t
)
W
i
n
d
t
u
r
b
i
n
e
p
o
w
e
r
d
y
n
a
mi
c
s:
z
6i
(
t
)
=
Δ
P
ω
i
(
t
)
i
s
t
h
e
w
i
n
d
t
u
r
b
i
n
e
’
s
p
o
w
e
r
T
h
e
ter
m
s
T
Pi
,
T
Ti
,
an
d
T
ω
i
ar
e
th
e
tim
e
co
ef
f
icien
ts
o
f
th
e
p
o
wer
p
lan
t,
th
e
tu
r
b
in
e,
th
e
win
d
tu
r
b
in
e,
r
esp
ec
tiv
ely
;
T
Gi
in
d
icate
s
th
e
g
o
v
er
n
o
r
’
s
tim
e
co
n
s
tan
t,
R
i
in
d
icate
s
d
r
o
o
p
g
ain
’
s
tim
e
co
n
s
tan
t,
K
Pi
in
d
icate
s
p
o
wer
s
y
s
tem
g
ain
’
s
tim
e
co
n
s
tan
t,
K
Bi
in
d
icate
s
b
ias
f
ac
t
o
r
’
s
ti
m
e
co
n
s
tan
t,
K
Ei
in
d
icate
s
tim
e
co
n
s
tan
t
o
f
th
e
in
teg
r
al
co
n
t
r
o
ller
g
ain
.
K
s
i
j
is
th
e
tie
-
lin
e
f
ac
to
r
b
etwe
en
t
h
e
r
eg
io
n
i
an
d
j
(
i
≠
j
)
.
an
d
α
T
s
h
o
w
th
e
co
n
tr
ib
u
tio
n
co
e
f
f
icien
ts
o
f
win
d
tu
r
b
i
n
es
an
d
t
h
er
m
al
u
n
its
.
T
ab
le
4
s
h
o
ws
th
e
in
ter
co
n
n
ec
ted
elec
tr
icity
p
lan
t d
y
n
am
ics co
n
s
id
er
in
g
p
a
r
am
eter
s
o
f
u
n
ce
r
tain
ties
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J
Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
4
,
Dec
em
b
er
20
25
:
2381
-
2
3
8
8
2384
T
ab
le
4
.
State
-
s
p
ac
e
m
o
d
el
o
f
th
e
MRLPS [
7
]
Ex
p
r
e
ssi
o
n
/
f
o
r
mu
l
a
Ex
p
l
a
n
a
t
i
o
n
/
p
u
r
p
o
se
z
̇
i
(
t
)
=
A
i
z
i
(
t
)
+
∑
G
ij
N
j
=
1
,
j
≠
i
z
j
(
t
)
+
B
i
u
i
(
t
)
+
ξ
i
(
z
i
,
t
)
,
y
i
=
C
i
z
i
(
t
)
S
t
a
t
e
-
sp
a
c
e
m
o
d
e
l
o
f
t
h
e
i
t
h
p
a
r
t
i
n
M
R
LPS
w
i
t
h
d
i
s
t
u
r
b
a
n
c
e
ξ
i
(
z
i
,
t
)
.
z
i
(
t
)
=
[
Δ
f
i
(
t
)
Δ
P
gi
(
t
)
Δ
X
gi
(
t
)
Δ
E
i
Δ
δ
i
(
t
)
Δ
P
ω
i
(
t
)
]
T
D
e
f
i
n
i
t
i
o
n
o
f
t
h
e
st
a
t
e
v
e
c
t
o
r
z
i
(
t
)
.
ξ
i
(
z
i
,
t
)
=
Δ
A
i
(
z
i
,
t
)
z
i
(
t
)
+
B
i
υ
i
(
z
i
,
t
)
+
H
i
Δ
P
L
i
(
t
)
w
i
t
h
‖
ξ
i
(
z
i
,
t
)
‖
≤
D
ξ
i
S
t
r
u
c
t
u
r
e
o
f
d
i
st
u
r
b
a
n
c
e
ξ
i
(
z
i
,
t
)
.
H
e
r
e
,
z
i
(
t
)
a
n
d
z
j
(
t
)
a
r
e
s
ta
t
e
v
e
c
t
o
r
s
an
d
n
e
i
g
h
b
o
r
i
n
g
s
t
a
t
e
v
e
c
t
o
r
s
,
r
e
s
p
e
c
ti
v
e
l
y
;
u
i
(
t
)
i
s
t
h
e
c
o
n
t
r
o
l
s
i
g
n
a
l
;
y
i
(
t
)
i
s
t
h
e
c
o
n
t
r
o
l
l
e
d
o
u
t
p
u
t
;
a
n
d
D
ξ
i
i
s
p
o
s
i
ti
v
e
c
o
n
s
t
a
n
t
.
B
i
υ
i
(
z
i
,
t
)
a
n
d
Δ
A
i
(
z
i
,
t
)
a
r
e
t
h
e
p
e
r
t
u
r
b
a
t
i
o
n
i
n
p
u
t
s
i
g
n
a
l
a
n
d
t
h
e
u
n
c
e
r
t
a
i
n
ty
p
a
r
a
m
e
t
e
r
s
,
r
es
p
e
c
ti
v
e
l
y
.
T
h
e
p
l
a
n
t
m
a
t
r
i
c
es
A
i
,
B
i
,
G
ij
c
a
n
b
e
p
r
e
s
e
n
t
ed
a
s
:
A
i
=
[
−
1
T
Pi
−
K
Pi
T
Pi
0
0
K
Pi
2
π
T
Pi
∑
K
s
ij
N
i
=
1
j
≠
1
K
Pi
T
ω
i
0
−
1
T
Ti
1
T
Ti
0
0
0
−
1
T
Gi
R
i
0
−
1
T
Gi
−
1
T
Gi
0
0
K
Ei
K
Bi
0
0
0
K
Ei
2
π
∑
K
s
ij
N
i
=
1
j
≠
1
0
2
π
0
0
0
0
0
0
0
0
α
ω
T
ω
i
0
−
1
T
ω
i
]
,
B
i
=
[
0
0
1
T
G
i
0
0
0
]
,
G
ij
=
[
0
0
0
0
K
Ei
2
π
T
Ti
K
s
ij
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
−
K
Ei
2
π
T
Ti
K
s
ij
0
0
0
0
0
0
0
0
0
0
0
0
0
]
.
3.
M
AIN R
E
S
UL
T
S
3
.
1
.
Sli
din
g
m
o
de
wit
ho
ut
re
a
ching
ph
a
s
e
a
uto
m
a
t
ic
lo
a
d f
re
qu
ency
co
ntr
o
l desig
n
T
o
estab
lis
h
an
in
n
o
v
ativ
e
c
h
atter
-
f
r
ee
SOSMC
law
f
o
r
t
h
e
MRLPS,
a
n
o
v
el
s
tate
esti
m
ato
r
is
co
n
s
tr
u
cted
t
o
f
i
n
d
t
h
e
u
n
m
ea
s
u
r
ab
le
s
tates
o
f
t
h
e
MRLPS,
as
d
escr
ib
ed
in
T
ab
le
5
.
In
T
ab
le
5
,
z
̂
i
(
t
)
is
th
e
esti
m
ate
o
f
z
i
(
t
)
,
y
̂
i
(
t
)
is
th
e
esti
m
ate
o
f
y
i
(
t
)
,
an
d
Ξ
i
is
th
e
esti
m
ato
r
g
ain
m
atr
ix
.
No
w,
t
o
g
e
n
er
ate
a
n
o
v
el
wea
k
en
ed
-
ch
atter
i
n
g
s
in
g
le
-
p
h
ase
SOSMC
law
f
o
r
th
e
MRLPS,
a
s
in
g
le
-
p
h
ase
s
lid
in
g
m
an
if
o
ld
f
u
n
ctio
n
is
d
ef
in
ed
a
n
d
s
p
ec
if
ied
i
n
T
ab
le
6
.
I
n
T
ab
le
6
,
κ
i
is
an
y
d
iag
o
n
al
m
atr
ix
,
an
d
α
i1
an
d
α
i2
ar
e
th
e
p
o
s
itiv
e
co
n
s
tan
ts
.
F
i
,
L
i
ar
e
th
e
d
esig
n
ed
m
atr
ices.
F
i
is
s
elec
ted
to
en
s
u
r
e
th
at
is
(
F
i
B
i
)
in
v
er
tib
le.
T
h
e
d
esig
n
m
atr
ix
L
i
is
p
r
ef
er
r
ed
to
f
u
lf
ill
th
e
in
eq
u
ality
o
f
th
e
p
o
wer
p
lan
t:
Re
[
λ
i
i
i
m
ax
T
o
g
et
th
e
s
tab
ilit
y
o
f
th
e
m
u
lti
-
f
ield
lin
k
ed
elec
tr
ici
ty
p
lan
t
d
ep
icted
in
T
ab
le
4
u
p
o
n
th
e
s
p
ec
if
ied
s
lid
in
g
m
a
n
if
o
ld
in
T
ab
le
6
f
r
o
m
th
e
ze
r
o
-
attain
m
en
t
m
o
m
e
n
t
,
a
n
ew
C
GSO
SML
F
C
is
s
u
g
g
ested
as
(
1
)
.
W
h
er
e
α
i1
,
α
i2
,
φ
̄
i
ar
e
s
o
m
e
p
o
s
itiv
e
s
ca
lar
s
.
u
̇
i
(
t
)
=
−
(
α
i1
F
i
B
i
)
−
1
{
α
i1
‖
F
i
B
i
L
i
‖
‖
z
̂
̇
i
(
t
)
‖
+
∑
α
j1
‖
F
j
G
ji
‖
N
j
=
1
,
j
≠
i
‖
z
̂
̇
i
(
t
)
‖
+
α
i2
‖
F
i
Ξ
i
‖
[
‖
y
̇
i
(
t
)
‖
−
‖
y
̂
̇
i
(
t
)
‖
]
+
κ
i
‖
σ
̇
i
[
z
̂
i
(
t
)
]
‖
+
φ
̄
i
‖
ψ
i
‖
−
ε
i
2
‖
F
i
‖
‖
z
̂
i
(
0
)
‖
e
−
ε
i
t
}
s
ign
(
ψ
i
(
t
)
)
(
1
)
T
ab
le
5
.
T
h
e
s
u
g
g
ested
s
tate
e
s
tim
ato
r
f
o
r
th
e
MRLPS
Ex
p
r
e
ssi
o
n
/
f
o
r
mu
l
a
Ex
p
l
a
n
a
t
i
o
n
/
p
u
r
p
o
se
z
̂
̇
i
(
t
)
=
A
i
z
̂
i
(
t
)
+
∑
G
ij
N
j
=
1
,
j
≠
i
z
̂
j
(
t
)
+
B
i
u
i
(
t
)
+
Ξ
i
[
y
i
(
t
)
−
y
̂
i
(
t
)
]
,
y
̂
i
(
t
)
=
C
i
z
̂
i
(
t
)
O
b
serv
e
r
e
q
u
a
t
i
o
n
e
st
i
ma
t
i
n
g
t
h
e
u
n
m
e
a
s
u
r
e
d
s
t
a
t
e
s.
ϖ
i
(
t
)
=
z
i
(
t
)
−
z
̂
i
(
t
)
Est
i
m
a
t
i
o
n
e
r
r
o
r
ϖ
i
(
t
)
.
ϖ
̇
i
(
t
)
=
[
A
i
−
Ξ
i
C
i
]
ϖ
i
(
t
)
+
∑
G
ij
N
j
=
1
,
j
≠
i
ϖ
j
(
t
)
+
ξ
i
(
z
̂
i
,
t
)
D
y
n
a
mi
c
s
o
f
t
h
e
e
s
t
i
m
a
t
i
o
n
e
r
r
o
r
.
-
T
h
eo
r
em
1
.
C
o
n
s
id
er
th
e
MRLPS
s
u
b
ject
to
ex
o
g
en
o
u
s
d
is
tu
r
b
an
ce
s
as
d
escr
ib
ed
in
T
ab
le
4
.
Up
o
n
th
e
im
p
lem
en
tatio
n
o
f
t
h
e
co
n
tr
o
l
ac
t
s
p
ec
if
ied
in
(
1
)
,
th
e
s
tate
tr
ajec
to
r
ies
o
f
th
e
MRLPS
ar
e
d
r
iv
en
to
war
d
th
e
s
witch
in
g
m
an
if
o
ld
ψ
i
[
z
̂
i
(
t
)
]
=
0
im
m
ed
iately
f
r
o
m
t
h
e
in
itial
m
o
m
en
t
o
f
ac
tiv
atio
n
.
C
o
n
s
eq
u
en
t
ly
,
th
e
asy
m
p
to
tic
s
tab
ilit
y
o
f
th
e
s
y
s
tem
,
as r
ep
r
esen
ted
b
y
T
ab
le
4
,
is
en
s
u
r
ed
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
A
tten
u
a
ted
-
c
h
a
tter
in
g
g
lo
b
a
l s
ec
o
n
d
o
r
d
er sl
id
in
g
mo
d
e
lo
a
d
fr
eq
u
en
cy
…
(
P
h
a
n
-
Th
a
n
h
N
g
u
ye
n
)
2385
-
Pro
o
f
o
f
T
h
eo
r
e
m
1
.
C
o
g
itat
e
th
e
ap
p
lican
t
L
y
a
p
u
n
o
v
f
u
n
ctio
n
al
as
V
[
z
̂
i
(
t
)
]
=
∑
‖
ψ
i
[
z
̂
i
(
t
)
]
‖
N
i
=
1
,
wh
er
e
d
ir
ec
t d
if
f
er
e
n
tiatio
n
o
f
V
[
z
̂
i
(
t
)
]
r
esu
lts
.
V
̇
(
t
)
≤
∑
{
α
i1
‖
F
i
B
i
L
i
‖
‖
z
̂
̇
i
(
t
)
‖
+
∑
α
j2
‖
F
j
G
ji
‖
N
j
=
1
,
j
≠
i
‖
z
̂
̇
i
(
t
)
‖
N
i
=
1
+
ψ
i
T
‖
ψ
i
‖
α
i1
F
i
B
i
u
̇
i
(
t
)
+
α
i1
‖
F
i
Ξ
i
‖
[
‖
y
̇
i
(
t
)
‖
−
‖
y
̂
̇
i
(
t
)
‖
]
−
ε
i
2
‖
F
i
‖
‖
z
̂
i
(
0
)
‖
e
−
ε
i
t
+
κ
‖
σ
̇
i
[
z
̂
i
(
t
)
]
‖
}
.
(
2
)
No
w,
b
y
s
u
b
s
titu
tin
g
th
e
o
u
tp
u
t
f
ee
d
b
ac
k
co
n
tr
o
l
s
ig
n
al
(
1
)
in
to
(
2
)
,
we
ca
n
ap
p
r
e
ciate
th
at
V
̇
[
z
̂
i
(
t
)
]
≤
−
∑
φ
̄
i
‖
ψ
i
[
z
̂
i
(
t
)
]
‖
N
i
=
1
<
0
,
φ
̄
i
>
0
.
C
o
n
s
eq
u
en
tly
,
th
e
MRLPS
’
s
s
tate
v
ar
iab
les
co
m
e
in
co
n
tact
with
th
e
s
witch
in
g
m
an
if
o
l
d
in
T
ab
le
6
f
r
o
m
th
e
ze
r
o
-
attain
m
en
t m
o
m
en
t
f
o
r
all
t
≥
0
.
T
ab
le
6
.
T
h
e
n
ew
s
in
g
le
-
p
h
ase
s
lid
in
g
m
an
if
o
l
d
f
o
r
s
u
p
p
o
r
tin
g
o
u
tp
u
t f
ee
d
b
ac
k
co
n
tr
o
ller
d
esig
n
Ex
p
r
e
ssi
o
n
/
f
o
r
mu
l
a
Ex
p
l
a
n
a
t
i
o
n
/
p
u
r
p
o
se
ψ
i
[
z
̂
i
(
t
)
]
=
σ
̇
i
[
z
̂
i
(
t
)
]
+
κ
i
σ
i
[
z
̂
i
(
t
)
]
S
i
n
g
l
e
-
p
h
a
s
e
sl
i
d
i
n
g
f
u
n
c
t
i
o
n
σ
i
[
z
̂
i
(
t
)
]
=
α
i1
F
i
z
̂
i
(
t
)
−
α
i2
F
i
∫
(
A
i
−
B
i
L
i
)
z
̂
i
t
0
(
τ
)
d
τ
−
F
i
z
̂
i
(
0
)
e
−
ε
i
t
D
e
f
i
n
i
t
i
o
n
o
f
σ
i
[
z
̂
i
(
t
)
]
σ
̇
i
=
α
i1
F
i
B
i
L
i
z
̂
i
+
∑
α
i1
F
i
G
ij
N
j
=
1
,
j
≠
i
z
̂
j
+
α
i1
F
i
B
i
u
i
+
α
i1
F
i
Ξ
i
C
i
ϖ
i
+
ε
i
F
i
z
̂
i
(
0
)
e
−
ε
i
t
F
i
r
st
d
e
r
i
v
a
t
i
v
e
o
f
σ
i
[
z
̂
i
(
t
)
]
σ
̈
i
[
z
̂
i
(
t
)
]
=
α
i1
F
i
B
i
L
i
z
̂
̇
i
+
∑
α
i1
F
i
G
ij
N
j
=
1
,
j
≠
i
z
̂
̇
j
+
α
i1
F
i
B
i
u
̇
i
+
α
i1
F
i
Ξ
i
[
y
̇
i
(
t
)
−
y
̂
̇
i
(
t
)
]
−
ε
i
2
F
i
z
̂
i
(
0
)
e
−
ε
i
t
S
e
c
o
n
d
d
e
r
i
v
a
t
i
v
e
o
f
σ
i
[
z
̂
i
(
t
)
]
,
r
e
q
u
i
r
e
d
f
o
r
S
O
S
M
C
t
e
c
h
n
i
q
u
e
ψ
̇
i
[
z
̂
i
(
t
)
]
=
α
i1
F
i
B
i
L
i
z
̂
̇
i
(
t
)
+
∑
α
i1
F
i
G
ij
N
j
=
1
,
j
≠
i
z
̂
̇
j
+
α
i1
F
i
B
i
u
̇
i
+
α
i1
F
i
Ξ
i
C
i
ϖ
̇
i
−
ε
i
2
F
i
z
̂
i
(
0
)
e
−
ε
i
t
+
κ
σ
̇
i
[
z
̂
i
(
t
)
]
Ti
me
d
e
r
i
v
a
t
i
v
e
o
f
t
h
e
sl
i
d
i
n
g
man
i
f
o
l
d
ψ
i
[
z
̂
i
(
t
)
]
3
.
2
.
St
a
bil
it
y
a
na
ly
s
is
o
f
who
le
s
y
s
t
em
in s
lid
ing
m
o
de
dy
na
m
ics
I
n
th
is
s
ec
tio
n
,
a
ap
p
r
o
p
r
iate
r
eq
u
ir
em
en
t
ex
p
r
ess
ed
in
th
e
f
o
r
m
o
f
L
M
I
is
f
o
r
m
u
lated
t
o
en
s
u
r
e
th
e
asy
m
p
to
tic
s
tab
ilit
y
o
f
th
e
M
R
L
PS
,
u
n
d
er
s
lid
in
g
m
o
d
e
c
o
n
tr
o
l.
T
o
th
is
en
d
,
we
p
r
o
ce
e
d
b
y
an
al
y
zin
g
th
e
f
o
llo
win
g
L
MI
f
o
r
m
u
latio
n
.
[
Λ
̃
i
+
∑
[
μ
j
(
G
ji
−
Γ
j
G
ji
)
T
(
G
ji
−
Γ
j
G
ji
)
+
μ
j
−
1
R
j
R
j
]
R
i
Φ
R
j
R
j
Ψ
j
0
N
j
=
1
j
≠
i
Φ
i
T
R
i
Θ
̃
i
+
∑
[
μ
̆
j
G
ji
T
Γ
j
T
Γ
j
G
ji
+
μ
̆
j
−
1
R
j
R
j
+
μ
̃
j
G
ji
T
G
ji
+
μ
̃
j
−
1
S
j
S
j
]
0
0
S
j
N
j
=
1
j
≠
i
R
j
0
−
η
̆
j
−
1
0
0
Ψ
j
T
R
j
0
0
−
η
̃
j
−
1
0
S
j
0
0
0
−
η
̃
j
−
1
]
<
0
,
(
3
)
W
h
er
e
Λ
̃
i
=
R
i
(
A
i
−
Γ
i
B
i
L
i
)
+
(
A
i
−
Γ
i
B
i
L
i
)
T
R
i
,
Θ
̃
i
=
S
i
(
A
i
−
Ξ
i
C
i
)
+
(
A
i
−
Ξ
i
C
i
)
T
S
i
,
R
i
,
S
i
ar
e
an
y
p
o
s
itiv
e
m
atr
ices,
an
d
μ
i
>
0
,
μ
̆
i
>
0
,
μ
̃
i
>
0
,
η
̆
i
>
0
,
η
̃
i
>
0
.
T
h
en
,
we
ca
n
b
u
ild
t
h
e
f
o
llo
win
g
th
e
o
r
em
:
-
T
h
eo
r
em
2
.
Su
p
p
o
s
in
g
th
at
th
e
s
u
f
f
icien
t c
o
n
d
itio
n
e
x
p
r
ess
e
d
in
th
e
L
MI
f
o
r
m
u
latio
n
(
3
)
a
d
m
its
a
f
ea
s
ib
le
s
o
lu
tio
n
R
i
>
0
,
S
i
>
0
,
an
d
th
e
s
witch
in
g
m
an
if
o
ld
is
d
em
ar
ca
ted
as
in
T
ab
le
6
.
T
h
en
,
th
e
MRLPS
s
u
b
jecte
d
to
ex
o
g
en
o
u
s
p
er
tu
r
b
atio
n
s
,
as
d
escr
ib
ed
b
y
T
ab
le
4
,
is
asy
m
p
to
tically
s
tab
le
wh
en
th
e
s
y
s
tem
tr
ajec
to
r
ies ev
o
lv
e
o
n
th
e
s
lid
i
n
g
m
an
if
o
ld
ψ
i
[
z
̂
i
(
t
)
]
=
0
.
-
Pro
o
f
o
f
T
h
e
o
r
em
2
.
B
ased
o
n
th
e
d
ef
in
ed
s
witch
in
g
m
an
i
f
o
ld
ψ
i
[
z
̂
i
(
t
)
]
=
ψ
̇
i
[
z
̂
i
(
t
)
]
=
0
,
th
e
eq
u
iv
alen
t
co
n
tr
o
l la
w
ca
n
b
e
d
e
r
iv
ed
a
n
d
ex
p
r
ess
ed
as
(
4
)
.
u
i
eq
(
t
)
=
−
(
α
i1
F
i
B
i
)
−
1
{
α
i1
F
i
B
i
L
i
z
̂
i
+
∑
α
i2
F
i
G
ij
N
j
=
1
,
j
≠
i
z
̂
j
+
α
i1
F
i
Ξ
i
[
y
i
(
t
)
−
y
̂
i
(
t
)
]
+
ε
i
F
i
z
̂
i
(
0
)
e
−
ε
i
t
}
(
4)
No
w,
we
s
u
b
s
titu
te
th
e
v
alu
e
o
f
u
i
eq
(
t
)
in
to
t
h
e
f
ir
s
t
e
q
u
atio
n
o
f
t
h
e
MRIPS
’
s
s
tate
s
p
ac
e
m
o
d
e
l
in
T
ab
le
4
an
d
s
im
p
lify
as
(
5
)
.
z
̇
i
(
t
)
=
[
A
i
−
Γ
i
B
i
L
i
]
z
i
+
Φ
i
ϖ
i
+
[
∑
G
ij
N
j
=
1
,
j
≠
i
−
∑
Γ
i
G
ij
N
j
=
1
,
j
≠
i
]
z
j
+
∑
Γ
i
G
ij
N
j
=
1
,
j
≠
i
ϖ
j
+
ξ
i
+
Ψ
i
e
−
ε
i
t
(
5
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J
Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
4
,
Dec
em
b
er
20
25
:
2381
-
2
3
8
8
2386
W
h
er
e
Φ
i
=
α
i1
B
i
(
α
i1
F
i
B
i
)
−
1
F
i
B
i
L
i
−
α
i1
B
i
(
α
i1
F
i
B
i
)
−
1
F
i
Ξ
i
C
i
,
Γ
i
=
α
i1
B
i
(
α
i1
F
i
B
i
)
−
1
F
i
an
d
Ψ
i
=
−
ε
i
B
i
×
(
α
i1
F
i
B
i
)
−
1
F
i
z
̂
i
(
0
)
.
No
w,
to
co
n
f
ir
m
th
e
s
tead
in
ess
o
f
th
e
MRL
PS
d
y
n
am
ic,
we
d
elib
er
ate
th
e
L
y
ap
u
n
o
v
p
o
s
itiv
e
d
ef
in
itio
n
f
u
n
ctio
n
V
[
z
i
(
t
)
,
ϖ
j
(
t
)
]
=
∑
[
z
j
(
t
)
ϖ
j
(
t
)
]
T
[
R
i
0
0
S
i
]
[
z
j
(
t
)
ϖ
j
(
t
)
]
N
i
=
1
,
wh
er
e
R
i
>
0
an
d
S
i
>
0
s
ati
s
f
y
th
e
L
MI
(
3
)
f
o
r
i
=
1
,
2
,
.
.
.
,
L
.
T
h
en
,
tak
in
g
th
e
d
er
iv
ativ
e
o
f
tim
e,
co
m
b
in
in
g
(
5
)
an
d
th
e
d
y
n
am
ics
o
f
th
e
esti
m
atio
n
er
r
o
r
in
T
ab
le
5
,
an
d
b
y
m
ea
n
s
o
f
L
e
m
m
a
3
o
f
wo
r
k
[
2
3
]
an
d
L
em
m
a
o
f
s
tu
d
y
[
2
4
]
,
we
h
av
e
V
̇
[
z
i
(
t
)
,
ϖ
j
(
t
)
]
≤
[
z
i
ϖ
i
]
T
∑
[
Λ
̃
i
+
∑
[
μ
j
(
G
ji
−
Γ
j
G
ji
)
T
(
G
ji
−
Γ
j
G
ji
)
+
μ
j
−
1
R
j
R
j
]
+
η
̆
j
R
j
R
j
+
η
̃
j
R
j
Ψ
j
Ψ
j
T
R
j
N
j
=
1
j
≠
i
R
i
Φ
Φ
i
T
R
i
Θ
̃
i
+
∑
[
μ
̆
j
G
ji
T
Γ
j
T
Γ
j
G
ji
+
μ
̆
j
−
1
R
j
R
j
+
μ
̃
j
G
ji
T
G
j
i
+
μ
̃
j
−
1
S
j
S
j
]
N
j
=
1
j
≠
i
+
η
j
S
j
S
j
]
N
i
=
1
×
[
z
i
(
t
)
ϖ
i
(
t
)
]
T
+
∑
[
γ
̃
i
θ
i
2
+
λ
i
(
t
)
]
N
i
=
1
(
6
)
W
h
er
e
Λ
̃
i
=
R
i
(
A
i
−
Γ
i
B
i
L
i
)
+
(
A
i
−
Γ
i
B
i
L
i
)
T
R
i
,
Θ
̃
i
=
S
i
(
A
i
−
Ξ
i
C
i
)
+
(
A
i
−
Ξ
i
C
i
)
T
S
i
,
γ
̃
i
=
η
j
−
1
+
η
̆
j
−
1
,
θ
i
(
t
)
=
‖
ξ
j
(
z
i
,
t
)
‖
,
an
d
λ
i
(
t
)
=
η
̃
j
−
1
(
e
−
ε
i
t
)
T
e
−
ε
i
t
.
T
h
en
,
em
p
lo
y
in
g
well
-
k
n
o
wn
L
M
I
ap
p
r
o
ac
h
[
2
5
]
t
o
in
eq
u
ality
(
3
)
,
we
attain
Ξ
̆
i
=
−
[
Λ
̃
i
+
∑
[
μ
j
(
G
ji
−
Γ
j
G
ji
)
T
(
G
ji
−
Γ
j
G
ji
)
+
μ
j
−
1
R
j
R
j
]
+
η
̆
j
R
j
R
j
+
η
̃
j
R
j
Ψ
j
Ψ
j
T
R
j
N
j
=
1
,
j
≠
i
R
i
Φ
Φ
i
T
R
i
Θ
̃
i
+
∑
[
μ
̆
j
G
ji
T
Γ
j
T
Γ
j
G
ji
+
μ
̆
j
−
1
R
j
R
j
+
μ
̃
j
G
ji
T
G
ji
+
μ
̃
j
−
1
S
j
S
j
]
N
j
=
1
,
j
≠
i
+
η
j
S
j
S
j
]
>
0
(
7
)
B
ased
o
n
(
6
)
an
d
(
7
)
,
it
ca
n
b
e
s
ee
n
th
at
V
≤
∑
[
−
λ
m
in
N
i
=
1
̇
(
Ξ
i
)
|
|
ẑ
i
(
t
)
|
|
2
+
γ
i
θ
i
2
+
λ
i
(
t
)
]
,
wh
en
th
e
te
r
m
λ
i
(
t
)
will
ten
d
to
ze
r
o
in
th
e
in
f
in
it
y
tim
e.
W
e
ca
n
b
e
r
ep
r
esen
te
d
as
V
̇
≤
∑
[
−
λ
(
Ξ
̆
i
)
‖
z
̂
i
(
t
)
‖
2
̃
i
i
2
m
i
n
[
]
]
N
∑
i
=
1
wh
er
e
th
e
co
n
s
tan
t
v
alu
e
γ
̃
i
θ
i
(
t
)
=
γ
̃
i
‖
ξ
j
(
z
i
,
t
)
‖
an
d
t
h
e
eig
e
n
v
alu
e
λ
m
in
(
Ξ
i
)
>
0
.
Hen
ce
,
V
̇
<
0
is
d
er
iv
e
d
with
|
|
ẑ
i
(
t
)
|
|
>
√
γ
i
θ
i
2
∕
λ
m
i
n
(
Ξ
i
)
wh
ich
s
h
o
ws th
at
th
e
MRLPS
is
asy
m
p
to
tically
s
tab
le.
4.
SI
M
UL
A
T
I
O
N
R
E
S
UL
T
S
I
n
th
is
s
ec
tio
n
,
th
e
p
ar
am
ete
r
s
o
f
a
th
r
ee
-
r
eg
io
n
lin
k
e
d
e
lectr
icity
p
lan
t
with
W
T
Gs,
wh
ich
ar
e
item
ized
in
[
7
]
,
is
s
im
u
lated
b
y
MA
T
L
AB
s
o
f
twar
e
to
v
alid
ate
th
e
f
ea
s
ib
le
s
o
lu
tio
n
o
f
th
e
s
u
g
g
ested
L
FC
ap
p
r
o
ac
h
.
T
h
e
e
x
ter
n
al
d
is
tu
r
b
an
ce
s
o
f
th
e
th
r
ee
r
eg
io
n
s
ar
e
r
esp
ec
tiv
ely
s
u
p
p
o
s
ed
as
ξ
1
=
0
.
04
,
ξ
2
=
0
.
022
,
ξ
1
=
0
.
06
.
T
h
e
o
b
tain
e
d
r
esu
lts
o
f
th
ese
elec
tr
icity
p
lan
ts
ar
e
ex
em
p
lifi
ed
in
Fig
u
r
e
2
.
-
R
em
ar
k
T
h
e
p
er
f
o
r
m
an
ce
o
f
th
e
p
r
o
p
o
s
ed
C
GS
OSML
F
C
(
1
)
in
th
e
MRLPS
in
teg
r
ated
with
W
T
G
s
is
s
h
o
wn
in
Fig
u
r
e
2
.
I
n
Fig
u
r
e
2
(
a)
,
th
e
f
r
eq
u
en
c
y
d
ev
iatio
n
s
Δ
f
₁,
Δ
f
₂,
an
d
Δ
f
₃
r
esp
o
n
d
r
a
p
id
ly
im
m
ed
iately
af
ter
th
e
in
itial
d
is
tu
r
b
an
ce
.
Alth
o
u
g
h
s
lig
h
t
o
s
cillatio
n
s
o
cc
u
r
with
i
n
th
e
f
ir
s
t
0
-
2
s
ec
o
n
d
s
,
all
f
r
eq
u
en
c
y
cu
r
v
es
o
f
th
r
ee
ar
ea
s
co
n
v
er
g
e
to
a
s
tab
le
v
alu
e
in
3
,
5
s
ec
o
n
d
s
,
with
u
n
d
er
s
h
o
o
t
ar
e
−1
,
2
×
1
0
−3
(
p
u
MW)
an
d
−1
.
7
×
10
−3
(
p
u
MW).
Fig
u
r
e
2
(
b
)
s
h
o
ws
th
e
co
n
tr
o
l
s
ig
n
als
f
o
r
t
h
e
th
r
ee
ar
ea
s
.
I
t
is
r
em
ar
k
ab
l
e
th
at
th
e
p
r
o
p
o
s
ed
m
eth
o
d
ex
h
ib
its
n
o
ch
atter
in
g
an
d
d
o
es
n
o
t
r
eq
u
i
r
e
ac
ce
s
s
to
th
e
s
tate
v
ar
iab
les
o
f
th
e
MRLPS,
wh
ich
is
a
clea
r
ad
v
a
n
tag
e
o
v
er
r
ec
e
n
t
s
tu
d
ies
[
6
]
-
[
8
]
.
T
h
is
v
er
if
ies
th
at
th
e
s
u
g
g
ested
C
GSOSML
F
C
(
1
)
s
u
cc
ess
f
u
lly
d
is
m
is
s
e
s
u
n
d
esira
b
le
h
ig
h
-
f
r
eq
u
en
cy
s
witch
in
g
.
Fig
u
r
e
2
(
c)
p
lo
ts
th
e
s
witch
in
g
s
u
r
f
ac
e
s
o
f
th
e
th
r
ee
ar
ea
s
r
ap
id
ly
co
n
v
er
g
in
g
to
ze
r
o
wit
h
o
u
t
o
s
cillatio
n
s
f
r
o
m
th
e
in
iti
al
in
s
tan
t
o
f
s
y
s
tem
m
o
tio
n
.
I
t
ca
n
b
e
s
tated
th
at
th
e
en
h
an
ce
d
r
o
b
u
s
tn
ess
an
d
th
e
an
ticip
ated
d
y
n
am
ic
r
esp
o
n
s
e
o
f
th
e
MRLPS
ar
e
co
n
q
u
er
ed
b
y
s
ac
k
in
g
th
e
r
ea
ch
in
g
p
h
ase
in
th
e
T
SMC
a
p
p
r
o
ac
h
,
th
at
h
as c
o
n
d
en
s
ed
t
h
e
r
estrictio
n
s
r
eq
u
ir
ed
in
o
th
e
r
s
tu
d
ies [
1
3
]
,
[
1
6
]
,
[
2
1
]
,
[
2
2
]
.
Fig
u
r
e
2
(
d
)
d
em
o
n
s
tr
ates
th
at
th
e
ar
ea
co
n
tr
o
l
er
r
o
r
s
d
ec
lin
e
q
u
ick
ly
an
d
a
p
p
r
o
ac
h
ze
r
o
with
in
ap
p
r
o
x
im
ately
3
s
ec
o
n
d
s
,
r
e
f
l
ec
tin
g
p
r
ec
is
e
f
r
eq
u
e
n
cy
an
d
p
o
wer
r
eg
u
latio
n
.
Ov
er
all,
th
e
s
im
u
latio
n
r
esu
lts
p
r
o
v
e
t
h
at
th
e
C
GSOSML
F
C
(
1
)
n
o
t
o
n
ly
p
r
o
v
id
es
h
ig
h
-
p
er
f
o
r
m
an
ce
f
r
e
q
u
en
c
y
r
eg
u
latio
n
with
f
ast
r
esp
o
n
s
e,
g
lo
b
al
s
y
s
tem
s
tab
ilit
y
,
an
d
s
m
all
s
tead
y
-
s
tate
er
r
o
r
,
b
u
t a
ls
o
c
o
m
p
letely
elim
in
at
es c
h
atter
in
g
.
Fro
m
ab
o
v
e
o
b
tain
ed
ac
h
iev
e
m
en
ts
,
th
e
an
ticip
ated
m
eth
o
d
d
o
es
n
o
t
n
ec
ess
ar
ily
th
e
ac
ce
s
s
ib
ilit
y
o
f
th
e
s
tate
v
ar
iab
les.
W
e
ca
n
c
o
n
clu
d
e
th
at
th
e
p
r
o
p
o
s
ed
m
e
th
o
d
n
o
t
o
n
ly
ef
f
icien
tly
s
o
lv
es
th
e
s
tab
ilizatio
n
p
r
o
b
lem
b
u
t
also
r
e
d
u
ce
s
th
e
ch
atter
in
g
f
o
r
th
e
MRLPS
in
t
eg
r
ated
with
W
T
Gs.
Su
b
s
eq
u
en
tly
,
th
is
tech
n
iq
u
e
is
h
ig
h
ly
ap
p
r
ec
iated
an
d
m
o
r
e
r
ea
lis
tic,
s
in
ce
it c
an
b
e
ea
s
ily
in
s
tig
ated
in
p
r
ac
tical
s
y
s
tem
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
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4
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tten
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ted
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c
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tter
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g
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l s
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o
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id
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e
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en
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…
(
P
h
a
n
-
Th
a
n
h
N
g
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ye
n
)
2387
(
a)
(
b
)
(
c)
(
d
)
Fig
u
r
e
2
.
T
im
e
h
is
to
r
y
o
f
(
a)
th
e
f
r
eq
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en
cy
ab
er
r
atio
n
s
,
(
b
)
th
e
lo
ad
f
r
eq
u
e
n
cy
c
o
n
tr
o
ller
s
,
(
c)
th
e
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in
g
le
-
p
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ase
s
lid
in
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s
u
r
f
ac
es,
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d
(
d
)
th
e
a
r
ea
co
n
t
r
o
l
er
r
o
r
o
f
th
r
ee
-
ar
ea
p
o
wer
p
la
n
ts
with
W
T
Gs
5.
CO
NCLU
SI
O
N
I
n
th
is
p
ap
er
,
a
n
ew
ch
atter
in
g
-
f
r
ee
g
l
o
b
al
s
ec
o
n
d
o
r
d
er
s
lid
in
g
m
o
d
e
lo
ad
f
r
eq
u
en
cy
co
n
tr
o
ller
(
C
GSOS
ML
FC
)
h
as
b
ee
n
d
ev
elo
p
ed
f
o
r
m
u
lti
-
r
e
g
io
n
lin
k
e
d
p
o
wer
s
y
s
tem
s
(
MRLPS)
s
u
b
jecte
d
to
ex
te
r
n
al
p
er
tu
r
b
atio
n
s
.
T
o
r
eso
lv
e
th
e
u
n
m
ea
s
u
r
ab
le
s
tate
v
ar
iab
les
p
r
o
b
lem
,
a
n
o
v
el
o
b
s
er
v
er
h
a
s
b
ee
n
p
r
o
jecte
d
f
o
r
g
u
ess
in
g
th
e
u
n
m
ea
s
u
r
ab
le
s
t
ate
v
ar
iab
les.
A
n
ewly
f
o
r
m
u
lated
o
n
e
-
p
h
ase
s
witch
in
g
m
a
n
if
o
ld
f
u
n
ctio
n
h
as
b
ee
n
s
y
s
tem
atica
lly
f
o
r
m
u
lated
f
o
r
SMC
s
u
ch
th
at
all
s
tates
tr
ajec
to
r
ies
o
f
th
e
s
y
s
tem
b
e
g
in
at
th
e
s
u
r
f
ac
e
at
an
in
itial
tim
e
m
o
m
en
t
wh
i
ch
m
ak
es
it
h
ig
h
ly
r
o
b
u
s
t
f
o
r
ap
p
licatio
n
s
.
T
h
e
n
o
v
el
C
GSOS
ML
FC
i
s
s
y
s
tem
atica
lly
d
esig
n
ed
to
s
u
p
p
r
ess
h
ig
h
-
f
r
eq
u
en
cy
c
h
atter
in
g
p
h
e
n
o
m
e
n
a
an
d
t
o
r
o
b
u
s
tly
s
tab
ilize
th
e
MRLPS
u
n
d
er
th
e
in
f
lu
e
n
ce
o
f
ex
ter
n
al
p
er
t
u
r
b
atio
n
s
.
Fu
r
th
er
m
o
r
e,
th
e
s
tead
in
ess
o
f
th
e
MRLPS
is
p
r
o
m
is
ed
v
ia
th
e
L
MI
m
eth
o
d
wh
ich
is
ex
tr
ac
ted
b
ased
o
n
L
y
a
p
u
n
o
v
s
tead
in
ess
th
eo
r
y
.
Ultim
atel
y
,
th
e
ex
p
er
im
e
n
tal
r
ep
licatio
n
s
ar
e
a
p
p
lied
to
a
th
r
ee
-
ar
ea
in
ter
co
n
n
ec
ted
p
o
w
er
n
etwo
r
k
to
v
alid
ate
t
h
e
en
h
an
ce
d
u
s
ef
u
ln
ess
o
f
th
e
p
lan
n
e
d
co
n
tr
o
ller
i
n
s
u
p
p
r
ess
in
g
ch
atter
in
g
an
d
o
u
tp
er
f
o
r
m
i
n
g
e
x
is
tin
g
s
lid
in
g
m
o
d
e
c
o
n
tr
o
l
m
eth
o
d
o
l
o
g
ies.
I
n
f
u
tu
r
e
wo
r
k
,
we
will
e
x
am
in
e
th
e
r
o
b
u
s
tn
ess
o
f
th
e
p
r
o
p
o
s
ed
a
p
p
r
o
ac
h
with
c
o
m
p
lex
p
o
wer
s
y
s
tem
s
,
in
clu
d
in
g
v
ar
i
o
u
s
r
en
ewa
b
le
e
n
er
g
y
s
o
u
r
ce
s
an
d
en
er
g
y
s
to
r
a
g
e
s
y
s
tem
s
.
F
UNDING
I
NF
O
R
M
A
T
I
O
N
T
h
is
r
esear
ch
was
s
u
p
p
o
r
ted
b
y
H
o
C
h
i
Min
h
C
ity
Un
iv
er
s
ity
o
f
T
ec
h
n
o
lo
g
y
an
d
E
d
u
ca
tio
n
,
Ho
C
h
i M
in
h
C
ity
,
Vietn
am
u
n
d
er
g
r
an
t n
u
m
b
er
T
2
0
2
5
-
1
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9
.
AUTHO
R
CO
NT
RI
B
UT
I
O
NS ST
A
T
E
M
E
N
T
T
h
is
jo
u
r
n
al
u
s
es
th
e
C
o
n
tr
ib
u
to
r
R
o
les
T
ax
o
n
o
m
y
(
C
R
ed
iT)
to
r
ec
o
g
n
ize
in
d
iv
id
u
al
au
th
o
r
co
n
tr
ib
u
tio
n
s
,
r
ed
u
ce
au
th
o
r
s
h
ip
d
is
p
u
tes,
an
d
f
ac
ilit
ate
co
llab
o
r
atio
n
.
Na
m
e
o
f
Aut
ho
r
C
M
So
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I
R
D
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Vi
Su
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an
-
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h
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h
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u
y
en
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o
n
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r
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g
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u
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en
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C
:
C
o
n
c
e
p
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a
t
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n
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:
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e
t
h
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:
So
f
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:
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l
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t
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Fo
r
mal
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n
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s
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:
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n
v
e
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ac
h
au
th
o
r
in
th
is
wo
r
k
ag
r
ee
s
to
d
ec
lar
e
th
at
we
h
a
v
e
n
o
c
o
n
f
lict o
f
i
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ter
est.
DATA AV
AI
L
AB
I
L
I
TY
D
a
t
a
a
v
a
il
a
b
i
li
t
y
is
n
o
t
a
p
p
l
i
ca
b
l
e
t
o
t
h
is
p
a
p
e
r
a
s
n
o
n
e
w
d
at
a
w
e
r
e
c
r
e
a
t
e
d
o
r
a
n
al
y
z
e
d
i
n
t
h
is
s
t
u
d
y
.
RE
F
E
R
E
NC
E
S
[
1
]
C.
-
T.
N
g
u
y
e
n
,
C
.
Tr
o
n
g
H
i
e
n
,
a
n
d
V
.
-
D
.
P
h
a
n
,
“
O
b
s
e
r
v
e
r
-
b
a
s
e
d
s
i
n
g
l
e
p
h
a
se
r
o
b
u
st
n
e
ss
l
o
a
d
f
r
e
q
u
e
n
c
y
sl
i
d
i
n
g
mo
d
e
c
o
n
t
r
o
l
l
e
r
f
o
r
mu
l
t
i
-
a
r
e
a
i
n
t
e
r
c
o
n
n
e
c
t
e
d
p
o
w
e
r
s
y
st
e
ms,
”
B
u
l
l
e
t
i
n
o
f
E
l
e
c
t
ri
c
a
l
E
n
g
i
n
e
e
ri
n
g
a
n
d
I
n
f
o
rm
a
t
i
c
s
,
v
o
l
.
1
3
,
n
o
.
5
,
p
p
.
3
1
4
7
–
3
1
5
4
,
O
c
t
.
2
0
2
4
,
d
o
i
:
1
0
.
1
1
5
9
1
/
e
e
i
.
v
1
3
i
5
.
7
8
9
3
.
[
2
]
H
.
B
e
v
r
a
n
i
,
R
o
b
u
s
t
p
o
w
e
r
s
y
s
t
e
m
f
r
e
q
u
e
n
c
y
c
o
n
t
r
o
l
.
C
h
a
m
:
S
p
r
i
n
g
e
r
I
n
t
e
r
n
a
t
i
o
n
a
l
P
u
b
l
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s
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i
n
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,
2
0
1
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.
d
o
i
:
1
0
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1
0
0
7
/
9
7
8
-
3
-
3
1
9
-
0
7
2
7
8
-
4.
[
3
]
P
.
K
u
n
d
u
r
,
Po
w
e
r
sys
t
e
m
s
t
a
b
i
l
i
t
y
a
n
d
c
o
n
t
r
o
l
.
M
c
G
r
a
w
-
H
i
l
l
,
1
9
9
4
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J
Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
4
,
Dec
em
b
er
20
25
:
2381
-
2
3
8
8
2388
[
4
]
J.
Y
.
H
u
n
g
,
W
.
G
a
o
,
a
n
d
J.
C
.
H
u
n
g
,
“
V
a
r
i
a
b
l
e
st
r
u
c
t
u
r
e
c
o
n
t
r
o
l
:
a
s
u
r
v
e
y
,
”
I
EEE
T
r
a
n
s
a
c
t
i
o
n
s o
n
I
n
d
u
s
t
ri
a
l
El
e
c
t
r
o
n
i
c
s
,
v
o
l
.
4
0
,
n
o
.
1
,
p
p
.
2
–
2
2
,
1
9
9
3
,
d
o
i
:
1
0
.
1
1
0
9
/
4
1
.
1
8
4
8
1
7
.
[
5
]
Y.
-
W
.
Ts
a
i
a
n
d
C
.
-
T.
N
g
u
y
e
n
,
“
V
a
r
i
a
b
l
e
s
t
r
u
c
t
u
r
e
c
o
n
t
r
o
l
f
o
r
mi
sma
t
c
h
e
d
u
n
c
e
r
t
a
i
n
s
y
st
e
ms
u
si
n
g
o
u
t
p
u
t
v
a
r
i
a
b
l
e
s
w
i
t
h
f
i
n
i
t
e
-
t
i
m
e
c
o
n
v
e
r
g
e
n
c
e
,
”
J
o
u
r
n
a
l
o
f
t
h
e
C
h
i
n
e
s
e
I
n
s
t
i
t
u
t
e
o
f
E
n
g
i
n
e
e
rs
,
v
o
l
.
4
3
,
n
o
.
5
,
Ju
l
.
2
0
2
0
,
d
o
i
:
1
0
.
1
0
8
0
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0
2
5
3
3
8
3
9
.
2
0
2
0
.
1
7
5
1
7
2
0
.
[
6
]
A
.
D
e
v
,
B
.
M
o
n
d
a
l
,
V
.
K
.
V
e
r
m
a
,
a
n
d
V
.
K
u
mar,
“
Te
a
c
h
i
n
g
l
e
a
r
n
i
n
g
o
p
t
i
mi
z
a
t
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o
n
-
b
a
s
e
d
s
l
i
d
i
n
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m
o
d
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