I
nte
rna
t
io
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l J
o
urna
l o
f
P
o
w
er
E
lect
ro
nics
a
nd
Driv
e
Sy
s
t
e
m
s
(
I
J
P
E
DS
)
Vo
l.
1
2
,
No
.
4
,
Dec
em
b
er
202
1
,
p
p
.
22
51
~
2
2
6
0
I
SS
N:
2088
-
8694
,
DOI
: 1
0
.
1
1
5
9
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j
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.
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1
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.i
4
.
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2251
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iv
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R
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It
is
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a
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in
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ti
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n
m
o
to
r
(IM
)
d
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s
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if
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p
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p
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th
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d
is
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late
d
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AT
LAB
/
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li
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k
fo
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m
w
it
h
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1
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lev
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l
c
a
s
c
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d
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d
H
-
b
rid
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e
i
n
v
e
rter.
K
ey
w
o
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d
s
:
C
as
c
a
d
e
d
H
-
b
r
i
d
g
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r
C
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m
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F
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t
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l
M
u
lt
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t
e
p
p
r
e
d
i
ct
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e
cu
r
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c
o
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t
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o
l
S
p
h
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d
ec
o
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r
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
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se
.
C
o
r
r
e
s
p
o
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ing
A
uth
o
r
:
P
h
u
o
n
g
Vu
Sch
o
o
l o
f
E
lectr
ical
E
n
g
i
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ee
r
i
n
g
Han
o
i U
n
iv
er
s
it
y
o
f
Scie
n
ce
an
d
T
ec
h
n
o
lo
g
y
No
.
1
,
Dai
C
o
Viet
R
o
ad
,
Hai
B
a
T
r
u
n
g
,
Ha
n
o
i,
Vietn
a
m
E
m
ail:
p
h
u
o
n
g
.
v
u
h
o
an
g
@
h
u
s
t
.
ed
u
.
v
n
1.
I
NT
RO
D
UCT
I
O
N
R
ec
en
t
l
y
,
m
u
ltil
e
v
el
i
n
v
er
ter
s
(
ML
I
)
ar
e
w
id
el
y
u
s
ed
i
n
h
i
g
h
-
p
o
w
er
in
d
u
s
tr
ial
ap
p
licatio
n
s
b
ec
au
s
e
o
f
th
ese
ad
v
a
n
ta
g
es
:
lo
w
o
u
tp
u
t
v
o
lta
g
e
d
is
to
r
tio
n
,
r
ed
u
cin
g
th
e
v
o
ltag
e
le
v
el
o
n
s
e
m
ico
n
d
u
cto
r
d
ev
ices
an
d
lo
w
er
i
n
g
t
h
e
d
u
/d
t
ch
a
n
g
i
n
g
s
p
ee
d
[
1
]
.
E
s
p
ec
ially
,
i
n
co
m
p
ar
is
o
n
w
it
h
o
th
er
ML
I
to
p
o
lo
g
ies
s
u
c
h
as
n
eu
tr
al
-
p
o
in
t
cla
m
p
ed
[
2
]
,
f
l
y
i
n
g
ca
p
a
cito
r
s
[
3
]
,
m
u
l
ti
-
m
o
d
u
lar
co
n
v
er
ter
s
(
MM
C
)
,
t
h
e
ca
s
ca
d
ed
h
-
b
r
id
g
e
(
C
HB
)
[
4
]
-
[
6
]
h
as
e
m
er
g
ed
as
a
p
r
o
m
i
n
en
t
o
n
e
f
o
r
d
r
iv
i
n
g
IM
s
y
s
t
e
m
d
u
e
to
its
h
ig
h
d
eg
r
ee
o
f
m
o
d
u
lar
it
y
,
allo
w
i
n
g
u
p
g
r
ad
e
an
d
r
ep
lace
m
e
n
t
ea
s
i
l
y
.
F
u
r
th
er
m
o
r
e
,
f
o
r
th
e
ap
p
licatio
n
s
o
f
i
n
d
u
c
tio
n
m
o
to
r
d
r
i
v
es,
t
h
e
co
n
n
ec
tio
n
o
f
C
HB
-
M
L
I
w
it
h
m
u
lti
-
p
h
as
e
r
ec
tif
ier
tr
an
s
f
o
r
m
er
en
s
u
r
es
th
e
cu
r
r
en
t
d
r
aw
n
f
r
o
m
t
h
e
g
r
id
h
av
e
a
s
in
u
s
o
id
al
w
a
v
e
f
o
r
m
,
d
ec
r
ea
s
es th
e
to
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
i
n
j
ec
ted
in
to
th
e
g
r
id
.
On
t
h
e
o
th
er
h
a
n
d
,
a
co
n
s
id
er
ab
le
d
r
aw
b
ac
k
o
f
C
HB
-
M
L
I
t
h
at
p
r
o
d
u
ce
s
th
e
co
m
m
o
n
-
m
o
d
e
v
o
ltag
e
(
C
MV
)
b
et
w
ee
n
t
h
e
n
eu
tr
al
p
o
in
ts
o
f
th
e
lo
ad
a
n
d
th
e
co
n
v
er
ter
[
7
]
,
w
h
ic
h
ca
n
b
e
ca
l
cu
lated
b
y
(
1
)
an
d
illu
s
tr
ated
b
y
Fi
g
u
r
e
1
.
Du
e
t
o
th
is
C
MV
,
h
i
g
h
-
f
r
eq
u
e
n
c
y
elec
tr
o
m
ag
n
etic
i
n
ter
f
er
en
ce
(
E
MI
)
is
in
tr
o
d
u
ce
d
,
ca
u
s
i
n
g
p
r
o
b
lem
s
r
eg
ar
d
i
n
g
m
ea
s
u
r
e
m
en
t
a
n
d
s
y
s
te
m
m
o
n
it
o
r
in
g
[
8
]
.
Fu
r
th
er
m
o
r
e,
in
I
M
d
r
iv
in
g
s
y
s
te
m
,
th
e
C
MV
g
e
n
er
ates
th
e
co
m
m
o
n
-
m
o
d
e
c
u
r
r
en
t
m
ak
i
n
g
d
etr
im
en
tal
ef
f
ec
t
s
o
n
t
h
e
m
o
to
r
’
s
p
r
o
d
u
cti
v
it
y
a
n
d
en
d
u
r
an
ce
[
9
]
.
T
h
er
e
h
av
e
b
ee
n
m
a
n
y
u
n
d
er
g
o
i
n
g
r
esear
c
h
es
to
m
in
i
m
ize
t
h
e
C
MV
,
f
o
r
i
n
s
tan
ce
t
h
e
ad
d
itio
n
o
f
t
h
e
E
MI
ac
ti
v
e
o
r
p
ass
i
v
e
f
ilter
[
1
0
]
,
[
1
1
]
.
Ho
w
e
v
er
,
t
h
is
h
ar
d
w
ar
e
s
o
lu
tio
n
ca
n
lead
t
o
an
i
n
cr
ea
s
e
i
n
t
h
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
,
Vo
l.
12
,
No
.
4
,
Dec
em
b
er
202
1
:
22
51
–
22
60
2252
s
ize
an
d
co
s
t
o
f
th
e
s
y
s
te
m
.
T
h
er
ef
o
r
e
,
m
it
ig
at
io
n
o
f
C
M
V
b
ased
o
n
co
n
tr
o
l
m
et
h
o
d
ap
p
r
o
ac
h
es
lik
e
SVM
[
1
2
]
,
[
1
3
]
,
M
P
C
[
1
4
]
,
[
1
5
]
is
p
r
ef
er
r
ed
.
=
=
1
3
(
+
+
)
(
1
)
Am
o
n
g
t
h
ese
co
n
tr
o
l
m
e
th
o
d
s
,
m
u
ltis
tep
MP
C
h
as
s
i
g
n
if
ic
an
t
b
en
e
f
its
s
in
ce
it
ta
k
es
t
h
e
s
w
itch
i
n
g
n
atu
r
e
o
f
th
e
p
o
w
er
co
n
v
er
ter
.
I
t
is
also
s
h
o
w
n
t
h
at
m
u
lti
s
te
p
MP
C
ca
n
im
p
r
o
v
e
th
e
s
tead
y
-
s
tate
p
er
f
o
r
m
a
n
ce
o
f
th
e
s
y
s
te
m
b
etter
th
a
n
s
i
n
g
le
-
s
tep
MP
C
[
1
6
]
-
[
2
0
]
.
Ho
w
e
v
er
,
in
[
2
1
]
m
u
lti
s
tep
m
o
d
el
p
r
ed
ictiv
e
co
n
tr
o
l
(
MP
C
)
w
i
th
C
MV
m
i
n
i
m
izat
io
n
tar
g
et
ap
p
lies
to
R
L
lo
ad
as
th
e
ca
s
e
s
tu
d
y
o
n
l
y
.
R
e
g
ar
d
in
g
I
M
d
r
iv
in
g
s
y
s
te
m
ca
s
e
s
t
u
d
y
,
i
n
[
2
2
]
,
th
e
m
u
ltis
tep
MP
C
co
n
tr
o
ller
d
o
es
n
o
t
co
n
s
id
er
C
MV
m
in
i
m
iza
tio
n
tar
g
et
s
in
ce
i
t
is
d
esig
n
ed
to
w
ar
d
o
p
tim
iz
in
g
th
e
s
w
itc
h
i
n
g
ef
f
o
r
t.
T
h
er
ef
o
r
e
,
th
is
p
ap
er
p
r
o
p
o
s
es
a
m
o
d
if
ied
m
u
lti
s
tep
MP
C
co
m
p
ar
ed
to
[
2
2
]
.
T
o
a
cc
o
u
n
t
f
o
r
C
MV
,
an
ad
d
itio
n
al
ter
m
t
h
at
p
en
ali
ze
s
th
e
C
MV
i
s
ad
d
ed
to
th
e
co
s
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n
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tio
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e
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s
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A
al
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ith
m
to
s
o
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e
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o
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ti
m
izatio
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p
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o
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m
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r
o
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m
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ap
p
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o
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u
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p
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
I
SS
N:
2088
-
8
694
Mo
d
ified
mu
ltis
tep
mo
d
el
p
r
ed
ictive
co
n
tr
o
l fo
r
th
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2253
2
.
1
.
Curre
nt
predict
iv
e
m
o
d
el
First,
t
h
e
p
h
y
s
ical
m
o
d
el
o
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t
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e
I
M
d
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ip
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el
o
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y
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HB
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ca
n
b
e
w
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itte
n
as (
2
)
:
{
(
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′
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;
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W
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e
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s
tate
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[
′
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4
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=
[
]
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et
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t
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atr
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e
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e
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s
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r
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etiza
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.
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h
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(
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ased
o
n
th
e
p
r
ed
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n
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o
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el
in
(
4
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,
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e
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n
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o
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izo
n
N>
1
ca
n
b
e
co
n
s
tr
u
cted
as (
5
)
w
ith
r
elatio
n
s
h
ip
s
i
n
(
6
)
.
(
k
)
(
(
)
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(
(
1
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.
.
.
(
(
1
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T
T
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k
k
k
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u
u
u
U
(
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2
(
k
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(
(
1
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)
(
(
2
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)
.
.
.
(
(
)
)
T
T
T
T
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k
k
k
N
Y
y
y
y
(
5
)
(
)
=
(
)
+
ϒ
(
)
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h
er
e
=
[
2
⋮
]
,
ϒ
=
[
0
⋯
0
0
⋯
0
0
⋮
⋮
⋱
⋮
⋮
−
1
−
2
⋯
]
(
6
)
2
.
2
.
Ref
er
ence
des
ig
n
B
ec
au
s
e
th
e
s
tato
r
cu
r
r
en
t
an
d
r
o
to
r
f
lu
x
s
ig
n
al
s
ar
e
s
lo
w
er
th
an
elec
tr
ical
o
n
es,
s
o
th
at
o
v
er
th
e
f
i
n
ite
p
r
ed
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n
h
o
r
izo
n
N,
th
ese
p
ar
a
m
eter
s
ar
e
as
s
u
m
ed
t
o
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e
co
n
s
tan
t.
T
h
e
o
u
tp
u
t
r
e
f
e
r
en
ce
s
eq
u
e
n
ce
f
o
r
th
e
cu
r
r
en
t c
o
n
tr
o
ller
is
d
en
o
te
d
b
y
(
7
)
.
∗
(
)
=
[
(
∗
(
+
1
)
)
(
∗
(
+
2
)
)
.
.
.
(
∗
(
+
)
)
]
∈
ℝ
2
(
7
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
,
Vo
l.
12
,
No
.
4
,
Dec
em
b
er
202
1
:
22
51
–
22
60
2254
W
h
er
e
∗
(
ℓ
)
=
[
√
2
(
)
+
2
(
)
.
(
ℓ
+
0
)
√
2
(
)
+
2
(
)
.
(
ℓ
+
0
+
2
)
]
ℓ
∈
{
+
1
;
.
.
.
;
+
}
,
0
=
(
(
)
(
)
)
is
th
e
in
itial a
n
g
le
b
et
w
ee
n
an
d
.
T
h
e
co
n
tr
o
l in
p
u
t r
ef
er
en
ce
s
e
q
u
en
ce
(
8
)
is
d
esig
n
ed
w
h
ile
c
o
n
s
id
er
in
g
a
n
u
ll
C
MV
(
=
0
)
.
∗
(
)
=
[
(
∗
(
)
)
(
∗
(
+
1
)
)
.
.
.
(
∗
(
+
−
1
)
)
]
(
8
)
W
h
er
e
∗
(
ℓ
)
=
[
1
0
−
1
2
√
3
2
3
2
−
√
3
2
]
.
(
∗
(
ℓ
)
+
(
1
+
1
−
)
∗
(
ℓ
)
−
[
1
−
1
−
−
1
−
1
−
]
′
(
)
)
2
.
3
.
Co
s
t
f
un
ct
io
n
T
o
ac
h
iev
e
th
e
d
esire
d
C
M
V
m
i
n
i
m
izatio
n
tar
g
et,
th
e
co
s
t
f
u
n
ct
io
n
(
9
)
is
m
o
d
if
ied
m
atch
u
p
to
[
2
2
]
.
I
n
ad
d
itio
n
to
o
u
tp
u
t
r
e
f
er
en
c
e
tr
ac
k
i
n
g
,
t
h
e
p
r
o
p
o
s
ed
m
et
h
o
d
w
h
ich
is
d
esi
g
n
ed
to
m
in
i
m
ize
t
h
e
C
MV
al
s
o
tr
ac
k
s
t
h
e
in
p
u
t r
ef
er
e
n
ce
s
.
(
)
=
∑
(
‖
(
ℓ
+
1
)
−
∗
(
ℓ
+
1
)
‖
2
2
+
‖
(
ℓ
)
‖
2
2
+
‖
(
ℓ
)
−
∗
(
ℓ
)
‖
2
2
)
+
−
1
=
(
9
)
I
n
(
9
)
,
(
ℓ
)
is
th
e
ca
n
d
id
ate
co
n
tr
o
l
-
in
p
u
t
th
a
t
g
en
er
ate
s
th
e
o
u
tp
u
t
c
u
r
r
en
t
p
r
ed
ictio
n
(
ℓ
+
1
)
=
(
ℓ
+
1
)
;
(
ℓ
)
=
(
ℓ
)
−
(
ℓ
−
1
)
;
is
th
e
w
ei
g
h
ti
n
g
f
ac
to
r
f
o
r
less
e
n
in
g
s
w
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tch
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g
e
f
f
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t
,
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e
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g
h
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ac
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o
r
C
MV
m
i
n
i
m
izatio
n
.
R
ep
r
esen
tat
io
n
o
f
(
9
)
in
m
a
tr
ix
f
o
r
m
ca
n
b
e
w
r
itt
en
as (
1
0
)
:
(
)
=
‖
(
)
−
∗
(
)
‖
2
2
+
‖
(
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−
(
−
1
)
‖
2
2
+
‖
(
)
−
∗
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)
‖
2
2
(
1
0
)
W
h
er
e
=
[
3
3
⋯
3
−
3
3
⋯
3
3
−
3
⋯
3
⋮
⋮
⋱
3
3
3
⋯
3
]
[
3
3
]
,
=
[
3
3
⋮
3
]
[
3
3
]
2
.
4
.
Sp
here
deco
din
g
a
lg
o
rit
h
m
(
SDA
)
I
n
th
is
j
o
b
,
th
e
SD
A
is
ad
o
p
ted
to
s
o
lv
e
t
h
e
m
o
d
if
ied
o
p
t
i
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izatio
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o
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le
m
,
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tain
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e
i
n
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u
t
s
eq
u
en
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at
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i
n
i
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izes t
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e
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o
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t f
u
n
ctio
n
(
)
in
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etail.
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h
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m
p
u
tat
io
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al
p
r
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s
s
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ill b
e
p
r
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co
n
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.
F
u
r
th
er
d
etail
ab
o
u
t
t
h
e
SD
A
ca
n
b
e
f
o
u
n
d
in
[
1
8
]
,
[
1
9
]
.
B
y
u
s
i
n
g
(
5
)
,
th
e
co
s
t
f
u
n
ctio
n
(
1
0
)
b
ec
o
m
es:
(
)
=
(
)
(
)
+2
(
)
(
)
+
(
)
(
1
1
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W
h
er
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=
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3
(
)
=
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)
−
ϒ
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)
−
(
−
1
)
−
∗
(
)
(
)
=
[
‖
(
)
−
∗
(
)
‖
2
2
+
‖
(
−
1
)
‖
2
2
+
‖
∗
(
)
‖
2
2
]
B
y
s
o
l
v
i
n
g
=
0
,
th
e
o
p
ti
m
al
s
o
l
u
t
io
n
is
y
ie
ld
ed
in
(
1
2
)
,
w
h
ich
d
o
es
n
o
t
n
ec
ess
ar
y
b
elo
n
g
to
th
e
f
in
i
te
co
n
tr
o
l
-
i
n
p
u
t
s
et
U
.
=
−
−
1
(
)
(
1
2
)
B
ec
au
s
e
W
is
a
s
y
m
m
etr
ic
an
d
p
o
s
iti
v
e
d
ef
i
n
ite
m
atr
ix
f
o
r
,
>0
,
t
h
er
e
ex
i
s
ts
o
n
l
y
o
n
e
u
n
iq
u
e
in
v
er
t
ib
le
lo
w
er
tr
ian
g
u
lar
m
atr
ix
H
,
w
h
ic
h
ca
n
b
e
o
b
tain
ed
b
y
p
er
f
o
r
m
i
n
g
t
h
e
C
h
o
les
k
y
d
ec
o
m
p
o
s
itio
n
to
−
1
:
−
1
=
−
1
−
.
Hen
ce
,
t
h
e
m
atr
ix
w
ill
s
a
tis
f
y
t
h
e
eq
u
atio
n
:
=
.
C
o
n
s
eq
u
en
tl
y
,
th
e
co
s
t
f
u
n
ctio
n
(
1
1
)
ca
n
b
e
r
e
w
r
itte
n
as
(
1
3
)
.
Fig
u
r
e
3
ill
u
s
tr
ate
s
t
h
e
g
r
ap
h
ical
r
ep
r
esen
tatio
n
o
f
a
MP
C
p
r
o
b
lem
i
n
t
w
o
-
d
i
m
e
n
s
io
n
al
s
p
ac
e.
T
o
s
i
m
p
li
f
y
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co
n
tr
o
l
in
p
u
t
v
ec
to
r
s
r
ef
er
r
in
g
to
th
e
s
a
m
e
el
lip
s
e
w
il
l
h
a
v
e
t
h
e
s
a
m
e
co
s
t
v
al
u
e.
B
y
tr
an
s
f
o
r
m
i
n
g
th
e
co
s
t
f
u
n
ctio
n
(
1
1
)
in
to
(
1
3
)
,
th
e
o
r
ig
in
al
ellip
s
e
s
ar
e
tr
a
n
s
f
o
r
m
ed
i
n
to
cir
cle
s
.
T
h
is
p
r
o
ce
d
u
r
e
p
lay
s
an
i
m
p
o
r
tan
t r
o
le
in
SD
A
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
I
SS
N:
2088
-
8
694
Mo
d
ified
mu
ltis
tep
mo
d
el
p
r
ed
ictive
co
n
tr
o
l fo
r
th
r
ee
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h
a
s
e
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d
u
ctio
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mo
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ive
s
ystem
…
(
B
a
o
B
in
h
P
h
o
)
2255
(
)
=
‖
(
)
−
̄
(
)
‖
2
2
w
h
er
e
(
)
(
)
u
c
u
c
kk
U
H
U
(
1
3
)
H
ρ
1
ρ
2
ρ
3
U
uc
HU
uc
HU
3
HU
1
HU
2
Fig
u
r
e
3
.
R
ep
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tatio
n
o
f
t
h
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m
ea
n
i
n
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o
f
t
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m
a
tr
ix
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T
h
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o
p
tim
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n
tr
o
l i
n
p
u
t
f
o
r
p
r
ed
ictio
n
h
o
r
izo
n
N
ca
n
b
e
p
r
esen
ted
as (
1
4
)
:
(
)
=
[
(
)
(
+
1
)
…
(
+
−
1
)
]
(
1
4
)
No
w
,
r
ec
o
n
s
tr
u
ct
(
1
4
)
in
to
a
s
eq
u
en
ce
(
ele
m
en
t b
y
ele
m
e
n
t)
as (
1
5
)
:
=
[
1
2
…
3
]
v
ới
1
,
2
,
.
.
.
,
3
iN
(
1
5
)
Fig
u
r
e
4
d
ep
icts
th
e
ev
alu
ati
o
n
p
r
o
ce
s
s
o
f
ea
ch
elem
e
n
t
,
s
o
-
ca
lled
a
n
o
d
e,
o
f
th
e
co
n
tr
o
l
in
p
u
t
s
eq
u
en
ce
U
i
n
(
1
5
)
.
Fig
u
r
e
5
i
llu
s
tr
ates
t
h
e
f
lo
w
d
ia
g
r
a
m
o
f
SD
A
.
Fir
s
t,
an
i
n
itial
s
p
h
er
e
i
s
d
ef
i
n
ed
w
it
h
an
in
i
tial
ce
n
ter
̄
(
)
ca
lcu
lated
b
y
(
1
6
)
an
d
a
s
elec
tiv
e
i
n
itial
r
ad
iu
s
.
T
h
is
in
itial
s
p
h
er
e
s
h
o
u
l
d
b
e
s
m
al
l
en
o
u
g
h
to
co
n
tai
n
at
lea
s
t
o
n
e
s
o
l
u
tio
n
(
)
.
T
h
en
d
u
r
i
n
g
t
h
e
ev
al
u
atio
n
p
r
o
ce
s
s
,
th
e
s
ize
o
f
th
e
s
p
h
er
e
is
d
ec
r
ea
s
ed
u
n
ti
l
th
er
e
is
o
n
l
y
o
n
e
s
o
l
u
tio
n
co
n
tain
ed
i
n
it
,
an
d
th
at
is
t
h
e
o
p
ti
m
al
co
n
tr
o
l
in
p
u
t
s
eq
u
en
ce
.
E
ac
h
ti
m
e
a
n
o
d
e
is
v
is
ited
,
th
e
r
ad
iu
s
is
ca
lcu
lated
b
y
(
1
7
)
b
ef
o
r
e
ev
alu
atin
g
th
e
co
n
d
itio
n
(
1
8
)
.
I
f
v
io
lates
co
n
d
itio
n
(
1
8
)
,
th
e
n
o
d
e
w
il
l
b
e
d
is
ca
r
d
ed
an
d
it
s
f
o
llo
w
i
n
g
n
o
d
es
(
f
r
o
m
+
1
to
3
)
w
ill
b
e
d
is
ca
r
d
ed
w
it
h
o
u
t
p
er
f
o
r
m
i
n
g
an
y
co
m
p
u
tat
io
n
to
av
o
id
u
n
n
ec
es
s
ar
y
co
m
p
u
ta
tio
n
.
T
h
e
c
o
n
tr
o
l
in
p
u
t
h
a
v
in
g
th
e
s
m
alle
s
t
r
ad
iu
s
w
i
ll b
e
th
e
o
p
tim
a
l so
lu
tio
n
(
)
=
(
)
.
-
n
n
-
n
n
-
n
n
-
n
-
n
n
n
-
n
n
u
1
u
2
u
3
N
-
1
u
3
N
U
p
d
a
t
e
U
o
p
t
,
ρ
o
p
t
ρ
o
p
t
=
ρ
i
n
i
(
:
N
o
d
e
i
s v
i
si
t
e
d
,
:
N
o
d
e
i
s
d
i
sc
a
r
d
e
d
,
:
N
o
d
e
i
s
d
i
s
c
a
r
d
e
d
w
i
t
h
o
u
t
p
e
r
f
o
r
mi
n
g
a
n
y
c
o
mp
u
t
a
t
i
o
n
)
Fig
u
r
e
4
.
A
tr
ee
-
d
ia
g
r
a
m
o
f
th
e
co
n
tr
o
l in
p
u
t seq
u
en
ce
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
,
Vo
l.
12
,
No
.
4
,
Dec
em
b
er
202
1
:
22
51
–
22
60
2256
N
N
S
t
a
r
t
U
uc
(
k
)
,
H
,
ρ
p
a
s
t
=
ρ
i
n
i
,
i
=
0
,
c
0
=
0
,
ρ
0
=
0
,
u
(
k
-
1
)
i
=
i
+
1
,
U
i
=
-
n
+
c
0
I
f
-
n
≤
U
i
≤
n
i
=
i
-
2
I
f
i
≥
0
a
p
p
l
y
U
o
p
t
(
k
)
E
n
d
ρ
i
=(
H
[
i
,
1
:
i
]
U
[
1
:
i
]
-
U
uc
[
i
]
)
2
+
ρ
i
-
1
Y
c
0
=
U
i
+
1
+
n
+
1
I
f
ρ
i
<
ρ
p
a
s
t
If
i
=
3
N
Y
Y
U
p
d
a
t
e
U
o
p
t
(
k
)=
U
,
ρ
p
a
s
t
=
ρ
i
c
0
=
0
N
i
=
i
-
1
,
c
0
=
c
0
+
1
Y
N
Fig
u
r
e
5
.
SDA
f
lo
w
d
iag
r
a
m
[
2
0
]
̄
(
)
=
(
−
−
)
(
)
(
1
6
)
=
|
|
[
.
.
.
]
⏟
[
,
:
]
[
.
.
.
]
⏟
[
:
]
−
̄
,
⏟
̄
[
]
|
|
+
−
(1
7
)
C
o
n
d
itio
n
:
≤
(
1
8
)
2.
5.
S
w
it
ching
s
t
a
t
e
t
a
ble
W
h
en
t
h
e
o
p
ti
m
al
s
o
lu
tio
n
(
)
is
o
b
tain
ed
,
o
n
l
y
th
e
f
ir
s
t
ele
m
e
n
t
(
)
is
e
m
p
lo
y
ed
to
t
h
e
f
i
n
d
th
e
s
w
itc
h
in
g
s
tates
f
o
r
t
h
e
i
n
v
er
ter
.
No
tice
t
h
at
(
)
is
t
h
e
p
h
ase
v
o
lta
g
e
lev
e
ls
.
T
ab
le
1
s
h
o
w
s
th
e
s
w
itc
h
in
g
s
tates
s
e
lectio
n
s
tr
ateg
y
c
lear
l
y
.
I
n
T
ab
le
1
,
v
ar
iab
le
r
ep
r
esen
t
th
e
p
h
ase
s
,
t
h
e
in
d
e
x
n
o
tatio
n
d
en
o
tes
th
e
p
o
s
itio
n
-
n
u
m
b
er
o
f
a
H
-
b
r
id
g
e
i
n
p
h
ase,
i
s
th
e
v
o
ltag
e
le
v
el
o
f
p
h
ase,
is
t
h
e
v
o
ltag
e
le
v
el
o
f
t
h
e
H
-
b
r
id
g
e
in
p
h
ase,
ar
e
th
e
s
w
i
tch
i
n
g
s
tate
s
o
f
v
al
v
e
1
an
d
3
o
f
th
e
H
-
b
r
id
g
e
in
p
h
ase.
Fi
g
u
r
e
1
illu
s
tr
ates
th
is
s
w
itc
h
in
g
s
tate
s
elec
tio
n
s
tr
ate
g
y
.
T
ab
le
1
.
Sw
itch
in
g
s
tate
s
elec
t
io
n
s
tr
ateg
y
(
,
1
;
,
3
)
1
(
1
,
1
;
1
,
3
)
2
(
2
,
1
;
2
,
3
)
3
(
3
,
1
;
3
,
3
)
4
(
4
,
1
;
4
,
3
)
5
(
5
,
1
;
5
,
3
)
+5
1
(
1
;
0
)
1
(
1
;
0
)
1
(
1
;
0
)
1
(
1
;
0
)
1
(
1
;
0
)
+4
1
(
1
;
0
)
1
(
1
;
0
)
1
(
1
;
0
)
1
(
1
;
0
)
0
(
0
;
0
)
+3
1
(
1
;
0
)
1
(
1
;
0
)
1
(
1
;
0
)
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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w
E
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&
Dr
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S
y
s
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I
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N:
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63
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
,
Vo
l.
12
,
No
.
4
,
Dec
em
b
er
202
1
:
22
51
–
22
60
2258
Fig
u
r
e
7
.
Gr
ap
h
s
o
f
s
tato
r
cu
r
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ts
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co
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m
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m
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d
e
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u
r
e
8
.
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f
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t T
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s
w
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CO
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u
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MP
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f
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v
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t
wo
m
a
in
co
n
tr
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u
tio
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s
:
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ir
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t
h
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f
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MV
w
h
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etain
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Ou
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Natio
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Un
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it
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C
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in
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r
i
n
g
(
NUCE
)
n
u
m
b
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ed
30
-
2
0
2
1
/KHXD
-
TĐ
.
RE
F
E
R
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NC
E
S
[1
]
K.
Dh
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e
sh
k
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r,
C.
S
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]
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[4
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T
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n
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,
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.
Vu
,
a
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,
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sim
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ter
n
a
ti
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J
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u
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l
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ics
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d
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ms
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IJ
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L
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.
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g
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a
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.
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rd
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latio
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IEE
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Veh
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P
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Ho
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.
W
e
i,
N.
Zarg
a
ri,
B.
W
u
,
a
n
d
S
.
Rizz
o
,
“
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m
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a
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m
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Rec
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2
0
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4
IEE
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In
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stry
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]
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C
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,
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-
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a
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d
J.
Ch
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u
,
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ti
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,
”
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[9
]
I.
S
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o
,
N.
B.
Be
lay
n
e
h
n
,
C.
P
a
r
k
,
a
n
d
J.
Kim
,
“
A
S
tu
d
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f
Co
m
m
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M
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d
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l
tag
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ra
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latio
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d
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io
n
S
trate
g
ies
o
n
M
M
C
S
y
ste
m
,
”
2
0
1
8
IEE
E
En
e
rg
y
Co
n
v
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d
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(
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0
]
J.
Ka
laise
lv
i
a
n
d
S
.
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ri
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s,
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ss
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m
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In
ter
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Co
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2
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7
.
[1
1
]
H.
Ak
a
g
i,
H.
Ha
se
g
a
wa
,
a
n
d
T
.
Do
u
m
o
to
,
“
De
sig
n
a
n
d
p
e
rf
o
rm
a
n
c
e
o
f
a
p
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s
siv
e
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f
il
ter
f
o
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u
se
w
it
h
a
v
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lt
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g
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so
u
rc
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in
v
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a
v
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u
so
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tp
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m
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-
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,
”
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E
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ra
n
sa
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ti
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Po
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2
]
H.
T
ru
o
n
g
,
C.
M
a
i,
C.
Ng
u
y
e
n
,
a
n
d
P
.
Vu
,
“
M
o
d
if
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S
p
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c
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V
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t
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lati
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sc
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In
v
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w
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th
Op
e
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-
Circu
it
P
o
w
e
r
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ll
s,”
J
o
u
rn
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6
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2
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4
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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N
:
2
0
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694
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
,
Vo
l.
12
,
No
.
4
,
Dec
em
b
er
202
1
:
22
51
–
22
60
2260
[2
5
]
A
.
K.
A
li
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n
d
R.
G
.
Om
a
r,
“
F
i
n
it
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t
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c
o
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y
w
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o
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ter
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ti
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l
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trica
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n
d
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s p
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m
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le
c
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m
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in
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d
riv
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.
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