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f
E
lect
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Co
m
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I
J
E
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Vo
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15
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.
3
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J
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n
e
20
25
,
p
p
.
2726
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2
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3
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2726
J
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h
ttp
:
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ec
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O
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S
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ti
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s.
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p
la
n
ts
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re
in
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ste
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a
n
d
d
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v
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l
o
p
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d
stro
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l
y
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m
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e
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rg
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o
m
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h
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h
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th
m
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ize
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-
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P
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h
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e
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q
u
a
li
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tatio
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su
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M
ATLAB
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S
im
u
li
n
k
so
ftwa
re
.
K
ey
w
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r
d
s
:
C
ascad
in
g
H
-
B
r
id
g
e
C
o
s
t
f
u
n
ctio
n
Fin
ite
-
co
n
tr
o
l
-
s
et
m
o
d
el
p
r
ed
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co
n
tr
o
l
Mo
d
el
p
r
ed
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co
n
tr
o
l
So
lar
p
o
wer
T
h
is i
s
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n
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c
c
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ss
a
rticle
u
n
d
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r th
e
CC B
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-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
T
r
an
Hu
n
g
C
u
o
n
g
Facu
lty
o
f
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lectr
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an
d
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lectr
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n
ics E
n
g
in
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in
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T
h
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ity
VietNa
m
,
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1
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5
T
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So
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T
r
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L
iet
C
o
m
m
u
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e,
Do
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Da
Dis
tr
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Han
o
i,
Vietn
am
E
m
ail:
cu
o
n
g
th
@
tlu
.
ed
u
.
v
n
1.
I
NT
RO
D
UCT
I
O
N
T
h
e
ca
s
ca
d
ed
H
-
b
r
id
g
e
(
C
HB
)
co
n
v
e
r
ter
is
a
m
u
lti
-
lev
el
co
n
v
er
ter
co
m
m
o
n
ly
u
s
e
d
in
g
r
i
d
-
co
n
n
ec
ted
s
o
lar
p
o
wer
s
y
s
tem
s
b
ec
au
s
e
th
e
C
HB
s
tr
u
ctu
r
e
h
as
ca
p
ac
ito
r
s
o
n
ea
ch
H
-
b
r
id
g
e
th
at
ar
e
d
ir
ec
tly
co
n
n
ec
ted
t
o
th
e
s
o
lar
ce
ll
m
o
d
u
les
(
PV
)
[
1
]
–
[
3
]
.
PV
m
o
d
u
l
es
will
g
en
er
ate
a
v
o
ltag
e
lev
e
l
o
n
th
e
alter
n
atin
g
cu
r
r
en
t
(
AC
)
o
u
t
p
u
t
s
id
e
o
f
t
h
e
C
HB
co
n
v
er
ter
[
4
]
,
[
5
]
.
T
h
er
ef
o
r
e
,
th
e
C
HB
co
n
v
er
ter
ca
n
g
en
er
ate
a
lar
g
e
n
u
m
b
er
o
f
v
o
ltag
e
lev
els
o
n
t
h
e
AC
s
id
e
f
o
r
d
ir
ec
t
co
n
n
ec
tio
n
to
th
e
p
o
wer
g
r
id
with
o
u
t
t
h
e
n
ee
d
f
o
r
a
s
tep
-
u
p
tr
an
s
f
o
r
m
er
o
r
h
ar
m
o
n
ic
f
i
lter
s
o
n
th
e
o
u
t
p
u
t
s
id
e
[
6
]
.
T
h
e
m
ain
ad
v
an
tag
e
o
f
th
e
C
HB
co
n
v
er
ter
is
h
ig
h
v
o
ltag
e
o
p
er
atio
n
,
C
HB
ca
n
g
en
er
ate
s
in
u
s
o
id
al
v
o
ltag
es
f
r
o
m
s
m
aller
v
o
ltag
e
lev
els
an
d
r
e
d
u
ce
v
o
ltag
e
tr
an
s
ien
ts
o
n
s
em
ico
n
d
u
ct
o
r
v
alv
es
[
7
]
,
[
8
]
.
T
h
e
ab
o
v
e
ad
v
an
tag
es
h
elp
C
HB
b
e
b
etter
ap
p
lied
in
s
y
s
tem
s
co
n
n
ec
tin
g
r
e
n
ewa
b
le
e
n
er
g
y
s
o
u
r
ce
s
to
th
e
p
o
wer
g
r
id
.
Sev
er
al
co
n
t
r
o
l
m
eth
o
d
s
f
o
r
C
HB
h
av
e
b
ee
n
a
p
p
lied
to
C
HB
,
m
ain
ly
th
e
t
r
ad
itio
n
al
PI
co
n
t
r
o
l
m
et
h
o
d
to
c
o
n
tr
o
l
th
e
q
u
ality
o
f
cu
r
r
en
t
a
n
d
v
o
lta
g
e
o
n
th
e
AC
s
id
e
an
d
co
n
tr
o
l
th
e
f
lo
w
o
f
p
o
wer
f
r
o
m
th
e
DC
to
th
e
AC
s
id
e
[
9
]
,
[
1
0
]
.
T
h
is
m
eth
o
d
h
as
a
s
im
p
le
im
p
lem
en
tatio
n
a
n
d
q
u
ic
k
im
p
ac
t.
Ho
wev
er
,
th
is
m
eth
o
d
o
f
ten
h
as
to
b
e
c
o
m
b
in
e
d
wit
h
m
o
d
u
latio
n
s
tep
s
[
1
1
]
.
So
m
e
m
o
d
u
latio
n
m
et
h
o
d
s
h
av
e
b
e
en
co
m
m
o
n
ly
ap
p
lied
to
C
HB
s
u
ch
as
p
u
ls
e
wid
th
m
o
d
u
latio
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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&
C
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I
SS
N:
2088
-
8
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Op
timiz
in
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w
itch
in
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s
ta
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s
in
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a
cu
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t p
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co
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o
l a
lg
o
r
ith
m
fo
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…
(
A
n
Th
i H
o
a
i Th
u
A
n
h
)
2727
(
PW
M)
[
1
1
]
,
[
1
2
]
,
an
d
s
p
ac
e
v
ec
to
r
m
o
d
u
latio
n
(
SVM)
[
1
3
]
.
T
h
e
PW
M
m
eth
o
d
h
as
a
s
im
p
le
im
p
lem
en
tatio
n
b
u
t
h
as
th
e
d
is
ad
v
an
tag
e
o
f
h
av
in
g
a
lar
g
e
s
witch
in
g
f
r
e
q
u
en
cy
.
W
h
en
t
h
e
n
u
m
b
e
r
o
f
lev
els
o
f
t
h
e
C
HB
in
cr
ea
s
es,
it
also
b
ec
o
m
es
d
if
f
icu
lt
to
ap
p
ly
t
o
th
e
C
HB
an
d
ca
u
s
es
s
ig
n
if
ican
t
lo
s
s
es.
T
h
e
SVM
m
eth
o
d
ca
n
p
r
o
d
u
ce
g
o
o
d
co
n
v
er
s
io
n
q
u
al
ity
;
h
o
wev
er
,
th
is
m
eth
o
d
h
as
a
lar
g
e
an
d
co
m
p
le
x
ca
lcu
lati
o
n
v
o
lu
m
e,
s
o
it
is
n
o
t
s
u
itab
le
f
o
r
C
HB
s
with
m
an
y
v
o
ltag
e
le
v
els
[
1
4
]
.
A
p
p
ly
in
g
th
e
co
m
b
in
ed
co
n
tr
o
l
m
o
d
u
latio
n
m
eth
o
d
will
m
ak
e
th
e
co
n
tr
o
l
s
tr
u
ctu
r
e
m
o
r
e
co
m
p
licated
an
d
th
e
co
m
p
u
tin
g
v
o
lu
m
e
o
f
th
e
m
icr
o
co
n
tr
o
ller
will
in
cr
ea
s
e
[
1
5
]
,
[
1
6
]
.
W
h
en
th
e
n
u
m
b
er
o
f
lev
els
o
f
th
e
C
HB
is
r
eq
u
ir
ed
to
b
e
lar
g
e,
th
e
n
u
m
b
e
r
o
f
co
m
p
o
n
en
ts
in
th
e
s
witch
will
in
cr
ea
s
e
an
d
th
e
co
m
b
in
atio
n
o
f
s
witch
in
g
s
tates
in
a
wo
r
k
in
g
cy
cle
will
a
ls
o
in
cr
ea
s
e
m
an
y
tim
es,
wh
ich
ca
lcu
lates
c
o
n
tr
o
l
an
d
m
o
d
u
latio
n
b
ec
o
m
es
ex
tr
em
ely
co
m
p
licated
[
7
]
,
[
1
7
]
.
R
ec
en
tly
,
p
r
ed
ictiv
e
co
n
tr
o
l
h
as
attr
ac
ted
atten
tio
n
ap
p
lied
to
c
o
n
tr
o
l
s
y
s
tem
s
[
1
8
]
–
[
2
0
]
.
T
h
e
o
p
er
atin
g
p
r
in
cip
le
o
f
m
o
d
el
p
r
e
d
ictiv
e
co
n
t
r
o
l
(
MP
C
)
is
to
r
ely
o
n
th
e
b
eh
a
v
io
r
al
ch
ar
ac
ter
is
tics
o
f
th
e
co
n
tr
o
l
o
b
ject
in
th
e
p
r
esen
t
an
d
th
e
p
ast
to
p
r
e
d
ict
th
e
s
tate
o
f
th
e
o
b
ject
in
t
h
e
f
u
t
u
r
e
.
th
er
eb
y
o
r
ie
n
tin
g
wo
r
k
in
g
o
b
jects
ac
co
r
d
in
g
to
p
r
ed
ictab
le
s
tates
to
ac
h
iev
e
m
ax
im
u
m
ef
f
icien
cy
[
2
1
]
.
T
h
is
ar
ticle
wil
l
in
tr
o
d
u
ce
th
e
p
r
ed
ictiv
e
co
n
tr
o
l
m
eth
o
d
ap
p
lied
to
C
HB
to
r
e
p
lace
b
o
t
h
th
e
m
o
d
u
latio
n
an
d
co
n
tr
o
l
s
tag
es.
T
h
is
m
eth
o
d
will
ca
lcu
late
an
d
s
elec
t
ap
p
r
o
p
r
iate
s
witch
in
g
s
tates,
elim
in
ate
u
n
n
ec
ess
ar
y
s
witch
in
g
s
tates,
an
d
o
n
ly
r
eta
in
s
witch
in
g
s
tates
s
er
v
in
g
th
e
in
s
u
lated
-
g
ate
b
ip
o
lar
tr
an
s
is
to
r
(
I
GB
T
)
v
alv
e
s
witch
in
g
p
r
o
ce
s
s
.
T
h
is
m
ak
es
th
e
m
icr
o
c
o
n
tr
o
lle
r
wo
r
k
less
an
d
m
o
r
e
ef
f
icien
t
ly
.
T
h
e
ad
v
an
ta
g
es
o
f
MPC
ap
p
lied
in
th
is
m
o
d
el
ar
e
f
a
s
t
ac
tio
n
an
d
h
ig
h
f
lex
ib
ilit
y
wh
en
co
m
b
in
in
g
m
u
ltip
le
co
n
tr
o
l
o
b
jectiv
es
i
n
o
n
e
o
b
jectiv
e
f
u
n
ctio
n
t
o
ac
h
iev
e
all
co
n
tr
o
l
o
b
jectiv
es
at
th
e
s
am
e
tim
e.
T
o
im
p
lem
e
n
t
th
is
m
eth
o
d
f
o
r
C
HB
,
th
e
f
i
r
s
t
th
in
g
is
to
b
u
ild
a
m
ath
em
atica
l
m
o
d
el
o
f
C
HB
,
th
en
p
er
f
o
r
m
d
is
co
n
tin
u
ity
a
n
d
co
m
e
u
p
wi
th
a
wo
r
k
in
g
m
o
d
el
o
f
th
e
c
o
n
v
er
ter
in
t
h
e
n
e
x
t
cy
cle.
Fin
ally
,
an
o
b
jectiv
e
f
u
n
ctio
n
is
u
s
ed
to
o
p
tim
ize
th
e
co
n
tr
o
l
v
ar
ia
b
les
an
d
s
elec
t
th
e
o
p
tim
al
v
alv
e
-
s
witch
in
g
s
tates
f
o
r
th
ese
c
o
n
t
r
o
l
v
ar
ia
b
les.
T
o
d
em
o
n
s
tr
ate
th
e
o
p
e
r
atio
n
o
f
t
h
e
co
n
tr
o
l
s
y
s
tem
,
ex
p
er
im
e
n
ts
wer
e
s
im
u
lated
o
n
MA
T
L
AB
/Si
m
u
lin
k
s
o
f
twar
e.
T
h
e
g
o
al
o
f
th
is
is
th
at
th
e
cu
r
r
en
t,
v
o
ltag
e
an
d
p
o
wer
v
alu
es
f
o
llo
w
th
e
p
r
eset
d
esir
ed
v
alu
es,
th
e
ca
p
ac
ito
r
s
o
s
ci
llate
with
in
th
e
allo
wab
le
v
al
u
es.
T
h
e
f
o
llo
win
g
s
ec
tio
n
2
will
p
r
esen
t
th
e
co
n
t
in
u
o
u
s
tim
e
m
o
d
el
an
d
th
e
f
u
t
u
r
e
p
r
e
d
ictio
n
m
o
d
el
o
f
th
e
c
o
n
v
er
ter
.
Sectio
n
3
will
p
r
esen
t
th
e
p
r
ed
ictiv
e
co
n
tr
o
l
alg
o
r
ith
m
s
f
o
r
th
e
cu
r
r
e
n
t
o
f
th
e
C
HB
co
n
v
er
ter
.
T
h
e
s
im
u
latio
n
r
esu
lts
an
d
th
eir
e
v
alu
atio
n
will b
e
p
r
esen
ted
in
s
ec
tio
n
4
.
2.
P
RE
DIC
T
I
O
N
M
O
D
E
L
O
F
T
H
RE
E
-
P
H
ASE
CH
B
CO
NVER
T
E
R
T
h
e
s
tr
u
ctu
r
e
o
f
t
h
e
s
ev
en
-
lev
el
th
r
ee
-
p
h
ase
C
HB
co
n
v
er
ter
is
b
u
ilt
f
r
o
m
th
r
ee
H
-
b
r
id
g
es
co
n
n
ec
ted
in
s
er
ies
o
n
ea
c
h
p
h
ase
as
s
h
o
wn
in
Fig
u
r
e
1
.
E
ac
h
H
-
b
r
id
g
e
in
clu
d
es
4
I
GB
T
s
em
ico
n
d
u
ct
o
r
v
alv
es
co
n
n
ec
ted
ac
c
o
r
d
i
n
g
to
t
h
e
b
r
id
g
e
d
iag
r
a
m
,
th
e
p
o
wer
s
o
u
r
ce
o
f
ea
ch
H
-
b
r
id
g
e
is
tak
en
f
r
o
m
th
e
DC
s
o
u
r
ce
g
e
n
e
r
a
t
e
d
b
y
P
V
p
a
n
e
l
s
.
B
y
o
p
e
n
i
n
g
a
n
d
c
l
o
s
i
n
g
t
h
e
v
a
l
v
e
p
a
i
r
s
(
S
1
,
S
2
)
a
n
d
(
S
3
,
S
4
)
,
t
h
r
e
e
o
u
t
p
u
t
v
o
l
t
a
g
e
l
e
v
e
l
s
o
f
t
h
e
H
b
r
i
d
g
e
w
i
l
l
b
e
c
r
e
a
t
e
d
+V
dc
,
0
,
-
V
dc
,
c
o
r
r
e
s
p
o
n
d
i
n
g
t
o
t
h
e
o
p
e
n
a
n
d
c
l
o
s
e
d
s
t
a
t
e
s
o
f
“
0
”
a
n
d
“
1
”
.
Acc
o
r
d
in
g
to
Fig
u
r
e
1
,
th
e
m
ath
em
atica
l
eq
u
atio
n
o
f
th
e
th
r
ee
-
p
h
ase
C
HB
co
n
v
er
ter
at
tim
e
t
wh
en
co
n
n
ec
ted
t
o
th
e
g
r
id
is
s
h
o
wn
as (
1
)
.
_
(
)
=
(
)
+
(
)
+
(
)
=
,
,
(1
)
w
h
er
e
_
(
)
is
th
e
o
u
tp
u
t
v
o
ltag
e
v
alu
e
o
f
th
e
C
HB
,
(
)
is
th
e
g
r
id
v
o
ltag
e
a
n
d
is
the
in
duc
t
or
c
urr
e
n
t
.
E
ac
h
v
o
ltag
e
(
)
can
tak
e
o
n
o
n
e
o
f
s
ev
en
v
o
ltag
e
le
v
els
*
(
,
1
,
.
.
.
,
0
,
.
.
.
,
)
dc
V
n
n
n
−
−
+
T
h
ese
v
o
ltag
e
lev
els ar
e
ca
lled
s
tate
lev
els.
T
h
e
State
lev
el
ca
n
b
e
e
x
p
r
ess
ed
as (
2
)
.
(
)
=
.
(
)
{
,
1
,
.
.
.
,
0
,
.
.
.
,
}
lj
v
n
n
n
-
Î
-+
(
2
)
E
q
u
atio
n
(
1
)
ca
n
also
b
e
e
x
p
r
ess
ed
as
a
v
ec
to
r
eq
u
atio
n
i
n
th
e
αβ
co
o
r
d
in
ate
s
y
s
tem
t
h
r
o
u
g
h
th
e
C
lar
k
tr
an
s
f
o
r
m
atio
n
as (
3
)
.
[
]
=
[
2
3
0
−
1
3
1
√
3
−
1
3
−
1
√
3
]
[
]
(3
)
w
h
er
e
a
,
b
,
c
a
r
e
th
e
v
alu
es
r
ep
r
esen
tin
g
t
h
e
v
o
ltag
e
o
r
c
u
r
r
en
t
o
f
th
e
a
b
c
co
o
r
d
in
ate
s
y
s
tem
.
α
,
β
a
r
e
th
e
v
ec
to
r
v
a
r
iab
les
af
ter
a
,
b
,
c
a
r
e
tr
an
s
f
o
r
m
ed
f
r
o
m
th
e
a
,
b
,
c
co
o
r
d
in
ate
s
y
s
tem
to
th
e
αβ
co
o
r
d
in
ate
s
y
s
tem
.
T
h
en
(
1
)
ca
n
b
e
d
escr
ib
e
d
as (
4
)
.
,
+
,
+
_
,
=
,
(
4
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
3
,
J
u
n
e
20
25
:
2
7
2
6
-
2
7
3
4
2728
w
h
er
e
,
ar
e
v
o
ltag
e
v
ec
to
r
s
an
d
,
ar
e
lo
a
d
cu
r
r
en
t v
ec
to
r
s
.
PV
L
a
R
a
V
dc
+
_
o
i
a
v
aO
v
ga
S
3
S
4
S
1
S
2
L
b
L
c
R
b
R
c
v
bO
v
cO
v
gb
v
gc
i
b
i
c
PV
PV
PV
PV
PV
PV
PV
PV
PV
N
Fig
u
r
e
1
.
C
HB
co
n
v
er
ter
s
tr
u
c
tu
r
e
with
th
r
ee
p
h
ases
an
d
s
ev
en
lev
els
T
h
e
im
p
lem
en
tatio
n
o
f
th
e
M
PC
co
n
tr
o
l
m
eth
o
d
will
b
e
b
a
s
ed
o
n
th
e
d
is
co
n
tin
u
o
u
s
m
o
d
el,
s
o
th
e
m
ath
em
atica
l
m
o
d
el
(
1
)
in
t
h
e
co
n
tin
u
o
u
s
d
o
m
ain
o
f
C
HB
m
u
s
t
b
e
d
is
co
n
tin
u
o
u
s
.
T
h
e
r
e
ar
e
m
an
y
d
if
f
e
r
en
t
d
is
co
n
tin
u
ity
m
eth
o
d
s
with
d
i
f
f
er
en
t
ac
cu
r
ac
y
[
2
2
]
,
[
2
3
]
.
H
o
wev
er
,
if
th
e
in
ter
r
u
p
tio
n
p
er
io
d
is
s
m
all
en
o
u
g
h
,
E
u
ler
’
s
f
o
r
war
d
m
eth
o
d
ca
n
b
e
ap
p
lied
in
th
is
ca
s
e
d
u
e
to
i
ts
s
im
p
le
im
p
lem
en
tatio
n
[
2
4
]
,
[
2
5
]
,
wh
ich
u
s
es
th
e
f
ir
s
t d
er
iv
ativ
e
a
p
p
r
o
x
im
at
ed
in
th
e
f
o
r
m
g
en
er
al
as (
5
)
.
=
(
+
1
)
−
(
)
(
5
)
Her
e
T
s
is
th
e
s
am
p
lin
g
tim
e
,
(
+
1
)
và
(
)
is
th
e
v
alu
e
o
f
th
e
co
n
tr
o
l v
ar
iab
les
in
th
e
n
ex
t
s
am
p
lin
g
p
er
io
d
an
d
th
e
cu
r
r
en
t
s
tate.
E
q
u
atio
n
(
1
)
is
d
is
co
n
tin
u
o
u
s
b
y
E
u
l
er
'
s
f
o
r
war
d
m
et
h
o
d
,
th
e
n
th
e
p
r
e
d
icted
e
q
u
atio
n
f
o
r
g
r
id
-
co
n
n
ec
ted
c
u
r
r
e
n
t w
ill b
e
as (
6
)
.
(
+
1
)
=
(
1
−
)
(
)
+
1
[
_
(
)
−
(
)
]
(
6
)
I
n
f
er
r
e
d
:
(
+
1
)
=
(
1
−
)
(
)
+
[
_
(
)
−
(
)
]
(
7
)
Fro
m
(
7
)
,
we
ca
n
wr
ite
th
e
d
is
co
n
tin
u
o
u
s
s
tate
eq
u
atio
n
as (
8
)
.
(
+
1
)
=
(
)
+
(
)
+
(
)
(
8
)
I
n
th
er
e:
(
)
=
[
(
)
(
)
(
)
]
;
(
)
=
[
(
)
(
)
(
)
]
;
(
)
=
[
(
)
(
)
(
)
]
;
=
[
1
−
0
0
1
−
]
;
=
3
[
2
−
1
−
1
−
1
2
−
1
]
;
=
−
[
1
0
0
1
]
E
q
u
atio
n
(
7
)
is
wr
itten
as (
9
)
i
n
th
e
α
β co
o
r
d
in
ate
s
y
s
tem
as:
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:
2088
-
8
7
0
8
Op
timiz
in
g
s
w
itch
in
g
s
ta
tes u
s
in
g
a
cu
r
r
en
t p
r
ed
ictive
co
n
tr
o
l a
lg
o
r
ith
m
fo
r
…
(
A
n
Th
i H
o
a
i Th
u
A
n
h
)
2729
_
(
+
1
)
=
(
1
−
)
_
(
)
+
[
_
(
)
−
_
(
)
]
(
9
)
3.
M
O
DE
L
P
RE
DIC
T
I
O
N
CO
NT
RO
L
F
O
R
T
H
E
CUR
RE
NT
O
F
T
H
E
CH
B
CO
NVE
RT
E
R
I
n
th
is
p
ap
er
,
th
e
Fin
ite
-
co
n
t
r
o
l
-
s
et
-
m
o
d
el
p
r
ed
ictiv
e
co
n
tr
o
l
(
FC
S
-
MPC
)
p
r
ed
ictiv
e
co
n
tr
o
l
m
eth
o
d
is
p
r
esen
ted
to
lim
it
th
e
n
u
m
b
er
o
f
m
icr
o
co
n
tr
o
ller
ca
lcu
la
tio
n
s
an
d
r
ed
u
ce
s
ig
n
al
d
elay
to
t
h
e
lo
west
lev
el
with
th
e
f
astes
t r
esp
o
n
s
e
s
p
ee
d
.
T
h
is
m
o
d
el
is
ap
p
lied
to
C
HB
in
clu
d
in
g
7
v
o
ltag
e
lev
els.
T
h
is
m
eth
o
d
h
as th
e
ch
ar
ac
ter
is
tic
o
f
ca
lcu
latin
g
s
tates
at
a
f
u
tu
r
e
tim
e
a
n
d
elim
in
atin
g
u
n
n
ec
ess
ar
y
s
tates,
k
e
ep
in
g
o
n
ly
s
u
itab
le
s
tates
to
o
p
tim
ize
th
e
o
b
jectiv
e
f
u
n
ctio
n
.
T
h
is
will select
th
e
o
p
tim
al
v
alv
e
clo
s
in
g
s
tates c
o
r
r
esp
o
n
d
in
g
to
th
e
o
b
jectiv
e
f
u
n
ctio
n
to
ap
p
ly
at
p
r
esen
t.
T
h
er
ef
o
r
e,
it
will
b
e
n
ec
ess
ar
y
to
f
in
d
a
cu
r
r
en
t
th
a
t
m
ee
ts
th
e
co
n
tr
o
l
r
eq
u
ir
em
e
n
ts
.
I
n
th
e
f
o
llo
win
g
cy
cles,
th
e
p
r
o
ce
s
s
is
r
ep
ea
ted
m
an
y
tim
es,
m
ea
n
in
g
th
e
alg
o
r
ith
m
alwa
y
s
ca
lcu
lates th
e
f
u
tu
r
e
c
o
n
tr
o
l
v
alu
e
in
ad
v
a
n
ce
an
d
ap
p
lies
it
to
th
e
p
r
esen
t tim
e.
3
.
1
.
O
pera
t
ing
princip
le
o
f
F
CS
-
M
P
C
f
o
r
CH
B
co
nv
er
t
er
C
o
n
s
id
er
a
m
u
ltil
ev
el
C
H
B
c
o
n
v
er
ter
,
with
th
e
n
u
m
b
er
o
f
H
-
b
r
id
g
es
o
n
ea
ch
p
h
ase
b
ein
g
N.
T
h
en
th
e
n
u
m
b
er
o
f
lev
els
M
c
r
e
ated
is
M
=
2
N
+1
.
T
h
e
n
u
m
b
er
o
f
s
witch
in
g
s
tate
co
m
b
i
n
atio
n
s
o
f
C
HB
is
K
M
=
M
3
.
W
ith
a
lar
g
e
n
u
m
b
er
o
f
tr
an
s
itio
n
s
tates,
th
e
co
n
tr
o
ller
'
s
s
ig
n
al
p
r
o
ce
s
s
in
g
s
p
ee
d
will
b
ec
o
m
e
s
lo
wer
an
d
th
e
s
ig
n
al
r
esp
o
n
s
e
tim
e
will
b
e
lo
n
g
er
.
As
t
h
e
n
u
m
b
e
r
o
f
lev
els o
f
th
e
co
n
v
er
ter
in
cr
ea
s
es,
th
e
n
u
m
b
er
o
f
s
tates
to
b
e
co
n
v
er
ted
in
cr
ea
s
es
ex
p
o
n
en
tially
.
T
h
er
e
f
o
r
e,
th
e
ca
lcu
latio
n
p
r
ess
u
r
e
o
f
t
h
e
co
n
tr
o
ller
i
n
th
e
s
am
e
s
am
p
le
ex
tr
ac
tio
n
tim
e
is
v
er
y
la
r
g
e.
T
h
er
ef
o
r
e,
th
e
FC
S
-
MP
C
m
eth
o
d
will
o
p
tim
ize
th
e
ca
lcu
latio
n
s
tates
an
d
s
elec
t
o
n
ly
th
e
ap
p
r
o
p
r
iate
s
tates
b
ef
o
r
e
e
n
ter
i
n
g
s
ig
n
al
p
r
o
ce
s
s
in
g
.
Fig
u
r
e
2
s
h
o
ws
th
e
C
HB
co
n
v
er
ter
co
n
tr
o
l stru
ctu
r
e
u
s
in
g
th
e
FC
S
-
MPC
co
n
tr
o
l m
eth
o
d
.
S
abc
1
H
B
1
H
B
2
H
B
3
R
L
F
C
S
-
M
P
C
S
abc
2
S
abc
3
i
abc
v
g
_
abc
N
O
a
,
b
,
c
v
g
_
α
β
G
r
i
d
abc
α
β
i
α
β
i
*
α
β
PV
PV
PV
Fig
u
r
e
2
.
Prin
cip
le
d
iag
r
am
o
f
MPC
co
n
tr
o
l m
eth
o
d
f
o
r
C
HB
T
h
e
p
r
o
p
o
s
ed
FC
S
-
MPC
m
e
th
o
d
h
er
e
is
u
s
ed
to
p
r
e
d
ict
th
e
g
r
id
cu
r
r
en
t
b
eh
av
io
r
,
wh
ich
will
co
r
r
esp
o
n
d
to
th
e
s
tep
-
wis
e
o
u
tp
u
t
v
o
ltag
e
o
f
th
e
C
HB
co
n
v
er
ter
with
th
e
p
r
in
cip
le
o
f
p
r
ed
ictin
g
th
e
n
ex
t
cy
cles
o
f
t
h
e
cu
r
r
en
t,
wh
ich
is
s
h
o
wn
i
n
Fig
u
r
e
3
.
T
h
e
FC
S
-
MPC
is
im
p
lem
en
ted
at
a
s
am
p
lin
g
in
ter
v
al
T
s
at
k
,
with
th
e
m
ea
s
u
r
ed
cu
r
r
en
t
co
n
tr
o
l
v
ar
ia
b
le
i(
k)
.
As
th
e
s
i
g
n
al
is
s
am
p
led
at
ea
ch
tim
e
p
o
in
t,
th
e
o
b
jectiv
e
f
u
n
ctio
n
p
e
r
f
o
r
m
s
th
e
task
o
f
ca
lcu
latin
g
all
p
o
s
s
ib
le
s
wi
tch
in
g
s
tates
f
o
r
th
e
cy
cle
at
tim
e
k+1
b
ased
o
n
th
e
cu
r
r
en
t
s
tate
at
tim
e
k
.
T
h
en
,
t
h
e
o
p
tim
al
s
tates
will
b
e
s
elec
ted
to
clo
s
e
th
e
v
alv
e
o
f
th
e
C
HB
.
T
h
ese
s
elec
ted
v
alv
e
-
s
witch
in
g
s
tates
will
k
ee
p
th
e
o
u
tp
u
t
cu
r
r
en
t
v
alu
e
o
n
th
e
AC
s
id
e
s
tab
le
ac
co
r
d
in
g
to
th
e
s
et
cu
r
r
en
t
v
alu
e
o
f
i
*
(
k+1
)
.
T
h
e
alg
o
r
ith
m
will
o
p
tim
ally
ca
lcu
late
th
e
o
b
jectiv
e
f
u
n
ctio
n
s
o
th
at
th
e
d
if
f
e
r
en
ce
b
etwe
en
i(
k)
an
d
i
*
(
k+1
)
is
s
m
allest.
T
h
e
co
n
tin
u
in
g
p
r
o
ce
s
s
is
ca
r
r
ied
o
u
t f
o
r
th
e
n
ex
t sam
p
lin
g
c
y
cl
es
k+2
,
k+3
...
E
q
u
atio
n
(
9
)
r
e
p
r
esen
ts
th
e
s
tate
cu
r
r
e
n
t
p
r
ed
ictio
n
b
ased
o
n
th
e
d
is
cr
ete
m
o
d
el
o
f
th
e
s
y
s
tem
an
d
it
is
u
s
ed
in
th
e
co
n
tr
o
ller
to
p
r
ed
ict
th
e
f
u
tu
r
e
v
alu
e
o
f
th
e
AC
cu
r
r
en
t.
T
h
e
o
b
jectiv
e
f
u
n
ctio
n
th
at
p
er
f
o
r
m
s
o
p
tim
ally
b
etwe
en
i(
k
)
an
d
i
*
(
k+1
)
is
s
h
o
wn
in
(
1
0
)
.
(
+
1
)
=
|
∗
(
+
1
)
−
(
+
1
)
|
2
+
|
∗
(
+
1
)
−
(
+
1
)
|
2
(
1
0
)
Her
e
,
∗
(
+
1
)
is
th
e
p
r
e
d
icted
c
u
r
r
en
t
at
th
e
k+1
wo
r
k
in
g
cy
cle
in
th
e
αβ
c
o
o
r
d
in
ate
s
y
s
tem
.
T
h
e
ab
o
v
e
ca
lcu
latio
n
is
r
ep
ea
ted
in
ea
ch
s
am
p
lin
g
cy
cle.
Ass
u
m
in
g
th
e
s
am
p
lin
g
tim
e
T
s
is
s
m
all
en
o
u
g
h
,
th
e
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
3
,
J
u
n
e
20
25
:
2
7
2
6
-
2
7
3
4
2730
,
∗
(
+
1
)
≈
,
∗
(
)
,
T
h
is
m
ea
n
s
th
at
th
e
ap
p
lied
cu
r
r
en
t
v
alu
e
d
o
es
n
o
t
ch
an
g
e
in
th
e
en
tire
p
r
ed
ictio
n
d
o
m
ain
a
n
d
th
e
o
b
jectiv
e
f
u
n
c
tio
n
(
1
0
)
is
r
ewr
itten
as f
o
llo
w
s
(
1
1
)
.
(
+
1
)
=
|
∗
(
)
−
(
+
1
)
|
2
+
|
∗
(
)
−
(
+
1
)
|
2
(1
1
)
T
h
e
co
s
t
f
u
n
ctio
n
(
1
1
)
at
ti
m
e
k+1
is
ev
alu
ated
f
o
r
ea
c
h
s
tate
co
r
r
esp
o
n
d
i
n
g
to
alte
r
n
atin
g
cu
r
r
en
t
an
d
m
in
im
izes it
to
s
elec
t a
n
d
ap
p
l
y
to
tim
e
k
.
t
(
k
)
t
(
k
+
1
)
t
(
k
-
1
)
t
(
k
+
2
)
t
(
k
+
3
)
0
i
(
k
)
i
(
k
+
1
)
i
(
k
)
i
*
(
k
)
i
t
i
*
(
k
)
Fig
u
r
e
3
.
Mo
d
el
to
p
r
ed
ict
alte
r
n
atin
g
cu
r
r
en
t
u
s
in
g
th
e
FC
S
-
MPC
m
eth
o
d
3
.
2
.
Appl
y
F
CS
-
M
P
C
t
o
a
C
H
B
co
nv
er
t
er
wit
h sev
en
v
o
lt
a
g
e
lev
els
W
ith
th
e
C
H
B
co
n
v
er
ter
as
s
h
o
wn
in
Fig
u
r
e
1
,
it
ca
n
g
en
e
r
ate
7
o
u
tp
u
t
v
o
ltag
e
lev
els
(
i.e
.
M
=
7
)
.
T
h
en
,
K
M
=
M
3
=
343
is
th
e
to
ta
l
n
u
m
b
er
o
f
v
o
ltag
e
s
tates
o
n
th
e
th
r
ee
p
h
ases
o
f
th
e
C
HB
.
Fro
m
th
is
,
we
ca
n
k
n
o
w
th
at
th
e
n
u
m
b
er
o
f
v
o
lta
g
e
v
alu
es
(
)
th
at
n
ee
d
to
b
e
ca
lcu
lated
is
3
4
3
,
s
o
in
ea
ch
s
am
p
lin
g
p
er
io
d
T
s
,
th
e
o
b
jectiv
e
f
u
n
ctio
n
n
ee
d
s
to
b
e
ca
lc
u
lated
ac
co
r
d
in
g
to
(
1
1
)
.
T
h
e
n
u
m
b
er
o
f
tu
r
n
s
i
s
3
4
3
t
o
ap
p
ly
f
o
r
s
ev
en
-
lev
el
C
HB
.
T
h
e
o
b
jectiv
e
f
u
n
ctio
n
(
1
2
)
is
u
s
ed
to
d
eter
m
in
e
th
e
o
p
tim
al
wo
r
k
i
n
g
s
tate
o
f
th
e
cu
r
r
en
t,
th
er
eb
y
s
elec
tin
g
t
h
e
ap
p
r
o
p
r
i
ate
s
witch
in
g
s
tate
o
f
th
e
c
o
n
v
er
ter
.
T
h
e
alg
o
r
ith
m
f
lo
w
c
h
ar
t
f
o
r
im
p
lem
en
tin
g
th
e
m
eth
o
d
is
s
h
o
wn
in
Fig
u
r
e
4
.
C
al
c
ul
at
e
t
he
c
os
t
f
unc
t
i
on J
(
k
+
1
)
ac
c
or
di
ng t
o e
qua
t
i
on
(
11
)
No
Y
e
s
Y
e
s
No
C
hoo
s
e
t
he
opt
i
m
al
s
w
i
t
c
hi
ng s
t
at
e
P
e
r
f
or
m
s
w
i
t
c
hi
ng
o
f
val
v
e
s
S
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P
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r
f
or
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m
e
as
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v
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i
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<
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m
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and J
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:
343
i
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α
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onv
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al
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ul
at
e
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gj
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ac
c
or
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ng t
o e
qua
t
i
on
(
9
)
Fig
u
r
e
4
.
Alg
o
r
ith
m
f
l
o
w
ch
ar
t to
im
p
lem
en
t FC
S
-
MPC
f
o
r
C
HB
co
n
v
er
ter
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:
2088
-
8
7
0
8
Op
timiz
in
g
s
w
itch
in
g
s
ta
tes u
s
in
g
a
cu
r
r
en
t p
r
ed
ictive
co
n
tr
o
l a
lg
o
r
ith
m
fo
r
…
(
A
n
Th
i H
o
a
i Th
u
A
n
h
)
2731
T
h
e
p
r
o
ce
s
s
to
elim
in
ate
th
e
in
ap
p
r
o
p
r
iate
s
witch
in
g
s
tate
is
s
elec
ted
in
a
s
h
o
r
t
tim
e
th
a
n
k
s
to
th
e
co
n
tr
o
ller
'
s
q
u
ick
p
r
o
ce
s
s
in
g
b
ased
o
n
t
h
e
p
r
o
g
r
am
m
in
g
al
g
o
r
ith
m
in
Fig
u
r
e
4
.
T
h
is
p
r
o
ce
s
s
is
s
m
al
l
en
o
u
g
h
n
o
t
to
af
f
ec
t
C
HB
's
ac
tiv
itie
s
.
W
ith
a
s
in
u
s
o
id
al
r
ef
er
e
n
ce
cu
r
r
en
t,
th
e
H
-
b
r
id
g
es
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er
f
o
r
m
v
alv
e
s
witch
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g
with
o
p
tim
al
w
o
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k
in
g
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d
will
cr
ea
te
a
s
tep
p
e
d
o
u
tp
u
t
v
o
ltag
e
with
7
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co
r
r
esp
o
n
d
in
g
to
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n
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tin
g
th
r
ee
H
-
b
r
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s
er
ies
o
n
ea
ch
p
h
ase
o
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th
e
C
HB
co
n
v
er
ter
.
Ho
wev
e
r
,
as
th
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n
u
m
b
e
r
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f
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els
in
cr
ea
s
es,
p
r
o
g
r
am
m
in
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g
r
am
s
m
u
s
t
p
er
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m
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lc
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latio
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e
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o
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n
t
o
f
ca
lcu
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s
in
a
s
m
all
s
am
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lin
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h
at
ca
n
m
ak
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r
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s
s
in
g
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d
g
en
er
ati
n
g
th
e
o
u
tp
u
t sig
n
al
ta
k
e
a
lo
n
g
tim
e.
4.
S
I
M
UL
AT
I
O
N
O
F
C
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RR
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N
T
P
R
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D
I
C
T
I
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C
O
NT
RO
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M
E
T
H
O
D
F
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R
T
H
RE
E
-
P
H
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SE
C
H
B
Simu
late
th
e
C
HB
co
n
v
er
ter
u
s
in
g
th
e
FC
S
-
MPC
co
n
tr
o
l
m
eth
o
d
with
t
h
e
p
ar
am
eter
s
g
iv
en
in
T
ab
le
1
.
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h
e
s
im
u
latio
n
m
o
d
el
is
im
p
lem
en
ted
o
n
MA
T
L
AB
/SIM
UL
I
NK
s
o
f
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e.
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h
e
s
im
u
latio
n
r
esu
lts
ar
e
p
er
f
o
r
m
ed
f
r
o
m
th
e
tim
e
t
h
e
co
n
v
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ter
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tar
ts
wo
r
k
in
g
to
0
.
1
s
an
d
a
r
e
s
h
o
wn
i
n
Fig
u
r
es
5
to
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.
T
ab
le
1
.
Simu
latio
n
p
ar
am
eter
s
P
a
r
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me
t
e
r
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l
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e
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n
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t
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n
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d
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t
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r
e
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r
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Hz
Fig
u
r
e
5
s
h
o
ws
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e
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cu
r
r
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n
t
r
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lts
o
n
all
th
r
ee
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h
ases
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th
e
C
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n
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ter
.
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h
e
r
e
s
u
lts
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h
o
w
th
at
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e
cu
r
r
en
t
s
h
ap
e
is
s
in
u
s
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d
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er
e
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n
o
tr
an
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ien
t
wh
en
th
e
cu
r
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t
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o
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atin
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s
tead
ily
,
th
ese
r
esu
lts
m
ee
t
th
e
p
o
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q
u
ality
r
eq
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ir
em
e
n
ts
wh
en
th
e
co
n
v
er
ter
is
co
n
n
ec
ted
to
th
e
g
r
id
.
T
h
e
AC
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r
r
en
t
o
f
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h
ase
a
is
s
h
o
wn
in
Fig
u
r
e
6
,
wh
ich
s
h
o
ws
th
at
th
e
cu
r
r
en
t
f
o
llo
ws
th
e
r
ef
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en
ce
cu
r
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n
t
an
d
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er
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ast
r
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ter
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0
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h
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th
at
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e
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e
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er
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g
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ir
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t c
y
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n
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t v
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e
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5
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ase
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h
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n
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ec
ted
t
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g
r
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Fig
u
r
e
6
.
Gr
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co
n
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en
t
o
f
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ase
a
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i
m
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s
(
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i
m
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(
s
)
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t
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ga
i
gb
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Fig
u
r
e
7
.
Vo
ltag
e
at
th
e
o
u
tp
u
t
o
f
p
h
ase
A
o
f
th
e
co
n
v
er
ter
Fig
u
r
e
8
.
AC
v
o
ltag
e
o
f
th
e
C
HB
co
n
v
er
ter
in
jecte
d
in
to
th
e
g
r
i
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
3
,
J
u
n
e
20
25
:
2
7
2
6
-
2
7
3
4
2732
T
h
e
o
u
tp
u
t
v
o
ltag
e
o
f
p
h
ase
a
is
s
h
o
wn
in
Fig
u
r
e
7
,
wh
ich
is
th
e
o
u
tp
u
t
v
o
ltag
e
o
f
th
e
co
n
tr
o
ller
.
T
h
e
r
esu
lts
s
h
o
w
th
at
th
er
e
ar
e
s
ev
en
lev
els o
f
o
u
tp
u
t v
o
ltag
e
,
th
e
lev
els ar
e
v
er
y
clea
r
an
d
th
er
e
is
n
o
co
n
f
lict
b
etwe
en
th
e
lev
els.
Fig
u
r
e
8
s
h
o
ws
th
e
v
o
ltag
e
p
atter
n
o
n
th
e
AC
s
id
e
o
n
all
th
r
ee
p
h
ases
o
f
th
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co
n
v
er
ter
to
s
u
p
p
ly
t
h
e
p
o
wer
g
r
id
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I
t
s
h
o
w
s
th
at
th
e
co
n
v
er
ter
o
p
e
r
ates
well
an
d
s
tab
ly
in
th
e
f
ir
s
t
wo
r
k
in
g
cy
cle.
Per
f
o
r
m
Fo
u
r
ier
an
aly
s
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o
f
th
e
v
o
ltag
e
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g
u
p
to
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e
2
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h
ar
m
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ic,
i
n
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ter
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als
o
f
0
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1
s
as
s
h
o
wn
in
Fig
u
r
e
9
.
T
h
e
T
HD
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alu
e
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f
t
h
e
v
o
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e
af
ter
a
n
aly
s
is
,
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g
et
th
e
r
e
s
u
lt
o
f
T
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4
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i
n
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ich
th
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e
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v
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ew
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ig
h
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o
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h
ar
m
o
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ics
with
lar
g
e
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litu
d
e,
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ly
s
h
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ws
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e
a
d
v
an
ta
g
e
o
f
t
h
e
C
HB
m
u
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lev
el
co
n
v
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ter
wh
en
c
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g
d
ig
ital
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n
ce
llatio
n
.
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a
n
tify
th
e
s
witch
in
g
s
tate
f
o
r
th
e
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cu
it
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d
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ie
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e
g
o
al
o
f
o
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tim
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s
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n
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r
r
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q
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ality
t
h
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r
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ch
th
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d
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h
is
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n
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r
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r
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ac
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0
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d
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l
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5
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H
D
=
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.
64
%
Fig
u
r
e
9
.
Fo
u
r
ier
an
al
y
s
is
r
esu
lts
o
f
v
o
ltag
e
v
g
5.
CO
NCLU
SI
O
N
T
h
is
ar
ticle
p
r
esen
ts
a
p
r
ed
ictiv
e
co
n
tr
o
l
m
eth
o
d
f
o
r
C
HB
c
o
n
v
er
ter
s
.
Fro
m
t
h
e
r
eq
u
ir
e
m
en
ts
o
f
th
e
AC
s
id
e
o
u
tp
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t
p
ar
am
eter
s
o
f
th
e
C
HB
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n
v
er
ter
,
th
e
FC
S
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MPC
co
n
tr
o
l
m
eth
o
d
is
b
u
ilt
to
p
r
ed
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th
e
f
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t
u
r
e
cu
r
r
en
t
v
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e,
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n
d
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NC
E
S
[
1
]
C
.
L
a
mn
a
t
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,
D
.
C
h
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mi
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[
2
]
J.
A
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s
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N
.
O
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3
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M
.
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[
5
]
J.
L.
S
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6
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M
.
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.
,
“
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o
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[
7
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B
.
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,
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s
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strial
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h
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f
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c
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lt
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g
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n
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T
h
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y
L
o
i
Un
iv
e
rsity
s
(TL
U).
His
c
u
rre
n
t
in
tere
sts
in
c
lu
d
e
p
o
we
r
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tro
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c
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tri
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to
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d
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c
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n
v
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rt
e
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tri
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it
y
fro
m
re
n
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wa
b
le
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rg
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so
u
rc
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s
to
t
h
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g
r
id
,
sa
v
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n
g
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y
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ti
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p
p
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d
f
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rid
a
n
d
tran
s
p
o
rtati
o
n
.
He
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
c
u
o
n
g
th
@
tl
u
.
e
d
u
.
v
n
.
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