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r
ed
as
a
h
ar
d
task
.
I
n
[
5
]
,
[
6
]
,
th
e
to
r
q
u
e
an
d
s
tato
r
f
lu
x
er
r
o
r
s
w
i
th
r
ea
cti
v
e
p
o
w
er
m
i
n
i
m
izatio
n
w
er
e
u
s
e
d
as
th
e
th
r
ee
ter
m
s
o
f
t
h
e
q
u
a
lit
y
f
u
n
ctio
n
.
On
ce
ag
ai
n
,
it
was
o
b
s
er
v
ed
th
at
th
e
d
eter
m
in
at
io
n
o
f
w
ei
g
h
tin
g
p
a
r
a
m
eter
w
a
s
a
to
u
g
h
ta
s
k
.
T
h
e
p
r
esen
t
p
ap
er
p
r
o
p
o
s
es
a
d
esig
n
p
r
o
ce
d
u
r
e
o
f
an
o
n
lin
e
p
ar
ticle
s
w
ar
m
w
ei
g
h
ti
n
g
f
ac
to
r
o
p
ti
m
izatio
n
m
et
h
o
d
w
ell
s
u
ited
f
o
r
p
r
ed
ictiv
e
d
ir
ec
t
to
r
q
u
e
an
d
f
lu
x
co
n
tr
o
l.
A
p
r
ed
icti
v
e
FS
-
MP
C
i
s
p
r
es
en
ted
in
th
is
w
o
r
k
f
o
r
t
h
e
co
n
tr
o
l
o
f
th
e
AC
/D
C
/
AC
co
n
v
er
ter
.
I
n
th
e
p
r
o
p
o
s
ed
co
n
tr
o
l
s
tr
ate
g
y
,
th
e
f
i
n
ite
p
o
s
s
ib
le
s
w
itc
h
i
n
g
s
ta
t
es
o
f
t
h
e
AC
/D
C
/
AC
ar
e
co
n
s
id
er
ed
,
th
e
ef
f
ec
t
o
f
ea
ch
o
n
e
o
n
t
h
e
lo
ad
cu
r
r
en
t
an
d
in
p
u
t
p
o
w
er
is
e
v
al
u
ated
,
an
d
t
h
e
s
w
i
tch
i
n
g
s
tate
t
h
at
m
i
n
i
m
izes
a
q
u
alit
y
f
u
n
ctio
n
is
s
elec
ted
an
d
ap
p
li
ed
d
u
r
in
g
t
h
e
n
ex
t
s
a
m
p
lin
g
p
er
io
d
.
T
h
e
q
u
alit
y
f
u
n
ctio
n
ev
alu
a
tes
t
h
e
er
r
o
r
b
et
w
ee
n
o
r
th
o
g
o
n
al
to
r
q
u
e
a
n
d
f
lu
x
s
co
m
p
o
n
e
n
ts
p
r
ed
ictio
n
s
to
t
h
eir
co
m
p
u
ted
v
al
u
es
f
o
r
all
d
if
f
er
e
n
t
v
o
ltag
e
v
ec
to
r
s
f
o
r
t
h
e
in
v
er
t
er
,
an
d
t
h
e
r
ea
cti
v
e
p
o
w
er
er
r
o
r
f
o
r
th
e
r
ec
ti
f
ier
.
A
s
i
m
i
la
r
s
tr
ateg
y
h
as
b
ee
n
p
r
esen
ted
at
t
h
e
in
d
ir
ec
t
m
atr
i
x
co
n
v
er
ter
,
to
co
n
tr
o
l in
a
n
ea
s
y
,
a
n
i
n
t
u
iti
v
e
an
d
a
n
e
w
m
a
n
n
er
,
th
e
to
r
q
u
e
a
n
d
f
l
u
x
v
ar
iab
les
o
f
a
n
i
n
d
u
ctio
n
m
ac
h
in
e
f
ed
b
y
t
h
e
co
n
v
er
ter
w
h
ile
e
n
s
u
r
in
g
a
u
n
i
tar
y
p
o
w
e
r
f
ac
to
r
at
th
e
i
n
p
u
t
s
y
s
te
m
o
f
t
h
e
co
n
v
er
ter
.
I
n
t
h
is
p
ap
er
,
w
e
i
n
v
e
s
ti
g
ate
t
h
e
p
er
f
o
r
m
a
n
ce
o
f
p
ar
ticle
s
w
a
r
m
o
p
ti
m
izatio
n
f
o
r
o
p
tim
izin
g
w
ei
g
h
ti
n
g
f
ac
to
r
p
r
o
ce
d
u
r
e
an
d
th
e
n
w
e
ca
r
r
ied
o
u
t
s
o
m
e
s
i
m
u
la
tio
n
r
esu
lts
to
v
alid
ate
th
e
p
r
o
p
o
s
ed
co
n
tr
o
l m
et
h
o
d
in
t
h
e
s
ix
t
h
s
ec
tio
n
f
o
llo
w
ed
at
last
b
y
a
g
en
er
al
co
n
cl
u
s
io
n
.
2
.
I
NDIR
E
C
T
CO
NV
E
RT
E
R
AC/DC/AC
WI
T
H
ST
O
RA
G
E
E
N
E
R
G
Y
T
h
is
p
ap
er
p
r
esen
ts
a
n
ew
co
n
tr
o
l
s
ch
em
e
f
o
r
a
r
eg
en
er
ativ
e
A
C
/DC
/A
C
co
n
v
er
ter
u
s
in
g
m
o
d
el
b
ased
P
r
ed
ictiv
e
co
n
tr
o
l.
T
h
e
co
n
tr
o
l
s
tr
ateg
y
m
in
im
izes
q
u
ality
f
u
n
ctio
n
s
,
w
h
ich
r
ep
r
esen
t
th
e
d
esire
d
b
eh
av
io
r
o
f
th
e
co
n
v
er
ter
.
T
h
e
A
C
/DC
/A
C
co
n
v
er
ter
m
o
d
el
s
h
o
w
n
in
Fig
u
r
e
1
is
co
n
s
id
er
ed
.
Fo
r
a
s
im
p
ler
an
aly
s
is
,
th
e
co
n
v
er
ter
ca
n
b
e
s
ep
ar
ated
m
ain
ly
in
r
ec
tif
ier
an
d
in
v
er
ter
s
id
es.
Fig
u
r
e
1
.
I
n
d
ir
ec
t
C
o
n
v
er
ter
(
AC
/D
C
/
AC
)
p
o
w
er
to
p
o
lo
g
y
W
ith
en
er
g
y
s
to
r
ag
e
2
.
1
.
Rec
t
if
ier
s
ide
T
h
e
r
ec
tif
ier
is
a
f
u
lly
co
n
tr
o
lled
p
o
w
er
s
w
itch
b
r
id
g
e
co
n
n
ec
ted
to
th
e
th
r
ee
-
p
h
ase
s
u
p
p
ly
v
o
ltag
es
v
s
u
s
in
g
th
e
f
ilter
in
d
u
ctan
ce
s
L
f
an
d
r
esis
tan
ce
s
R
f
.
T
h
e
in
p
u
t c
u
r
r
en
t
d
y
n
am
ics
ca
n
b
e
d
escr
ib
ed
b
y
eq
u
atio
n
:
s
f
r
e
c
s
s
f
i
R
V
V
dt
di
L
(1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8792
IJ
A
P
E
Vo
l.
4
,
No
.
3
,
Dec
em
b
er
201
5
:
1
0
4
–
1
1
7
106
w
h
er
e
i
s
is
th
e
in
p
u
t
cu
r
r
en
t
v
ec
to
r
,
V
s
is
th
e
s
u
p
p
ly
lin
e
v
o
ltag
e
an
d
V
rec
=
S
r
*V
dc
is
th
e
v
o
ltag
e
g
en
er
ated
b
y
th
e
co
n
v
er
ter
.
T
h
e
in
p
u
t
cu
r
r
en
t v
ec
to
r
is
r
elate
d
to
th
e
p
h
ase
cu
r
r
en
ts
b
y
th
e
eq
u
atio
n
:
sC
sB
sA
s
i
a
ai
i
i
2
3
2
W
h
er
e
3
2
e
a
(2
)
S
r
is
t
h
e
s
w
itc
h
i
n
g
s
tate
v
ec
to
r
f
o
r
th
e
r
ec
tif
ier
a
n
d
is
d
ef
i
n
ed
as
:
rC
rB
rA
r
S
a
aS
S
S
2
3
2
(
3
)
w
h
er
e
S
rA
,
S
r
B
an
d
S
r
C
ar
e
th
e
s
w
itc
h
i
n
g
s
tate
s
o
f
ea
ch
r
ec
ti
f
ie
r
leg
,
a
s
s
h
o
w
n
i
n
Fi
g
.
1
,
an
d
tak
e
th
e
v
al
u
e
o
f
0
if
S
x
is
o
f
f
,
o
r
1
if
S
x
is
o
n
.
2
.
2
.
I
nv
er
t
er
s
ide
Fo
r
a
t
w
o
lev
el
v
o
lta
g
e
s
o
u
r
c
e
in
v
er
ter
f
ee
d
i
n
g
a
s
y
m
m
etr
i
ca
l
th
r
ee
-
p
h
ase
i
n
d
u
ctio
n
m
o
t
o
r
g
iv
e
n
i
n
f
i
g
u
r
e
2
,
ea
ch
leg
i
s
co
m
p
o
s
e
d
o
f
t
w
o
b
y
-
d
ir
ec
tio
n
al
s
w
itc
h
es
(
S
i1
,
S
i2
i=a
,
b
,
c
)
w
h
er
e
a
,
b
,
c
th
e
th
r
ee
p
h
ases
.
T
h
e
s
w
itc
h
i
n
g
s
tates
S
d
eter
m
i
n
ed
b
y
g
ati
n
g
s
i
g
n
a
ls
ar
e
g
i
v
e
n
in
a
v
ec
to
r
ial
f
o
r
m
a
s
f
o
llo
ws:
ic
ib
ia
i
S
a
aS
S
S
2
3
2
(4
)
T
h
e
v
o
ltag
e
V
inv
i
s
li
n
k
ed
to
th
e
in
v
er
ter
s
w
i
tch
in
g
s
tate
S
i
:
V
inv
=
S
i
V
dc
.
Fig
u
r
e
2
.
T
w
o
lev
el
s
o
u
r
ce
in
v
er
ter
w
it
h
d
if
f
er
en
t
v
o
lta
g
e
v
e
cto
r
s
2
.
3
.
M
ini
m
iza
t
io
n o
f
co
s
t
f
un
ct
io
n
2
.
3
.
1
.
C
o
ntr
o
l o
f
t
he
inv
er
t
er
s
ide
T
h
e
co
n
tr
o
l
o
f
th
e
i
n
v
er
ter
s
id
e
is
s
i
m
ila
r
to
t
h
e
s
c
h
e
m
e
p
r
e
s
en
ted
i
n
[
7
]
.
T
h
e
ef
f
ec
t
o
f
ea
ch
p
o
s
s
ib
le
v
o
ltag
e
v
ec
to
r
,
g
en
er
ated
b
y
th
e
in
v
er
ter
,
o
n
th
e
b
eh
a
v
io
r
o
f
th
e
lo
ad
cu
r
r
en
t
is
e
v
al
u
at
ed
u
s
in
g
a
q
u
alit
y
f
u
n
ctio
n
G
i
.
T
h
e
v
o
lta
g
e
v
ec
to
r
th
at
m
in
i
m
izes
t
h
is
f
u
n
ctio
n
is
s
elec
ted
a
n
d
ap
p
lied
d
u
r
in
g
th
e
n
ex
t
s
a
m
p
l
in
g
p
er
io
d
[8
]
[
1
4
]
as
ca
n
b
e
s
h
o
wn
i
n
f
ig
.
3
.
T
h
e
q
u
alit
y
f
u
n
cti
o
n
to
b
e
m
i
n
i
m
ized
f
o
r
t
h
e
i
n
v
er
ter
th
e
tr
ac
k
i
n
g
er
r
o
r
b
etw
ee
n
r
e
f
er
en
ce
an
d
p
r
ed
icted
m
ea
s
u
r
ed
to
r
q
u
e,
s
tato
r
f
l
u
x
,
w
h
ic
h
i
s
e
x
p
r
es
s
ed
in
o
r
th
o
g
o
n
al
co
o
r
d
in
ates a
s
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
A
P
E
I
SS
N:
2252
-
8792
P
r
ed
ictive
C
o
n
tr
o
l fe
d
b
y
a
n
I
n
d
ir
ec
t Co
n
ve
r
ter w
i
th
a
n
d
w
ith
o
u
t e
n
erg
y
s
to
r
a
g
e
…
(
Za
ka
r
ia
La
mmo
u
ch
i
)
107
2
2
*
2
2
*
1
1
1
1
n
s
s
n
e
e
i
k
k
T
k
T
k
T
G
(5
)
w
h
er
e
T
n
an
d
n
ar
e
th
e
n
o
m
i
n
al
to
r
q
u
e
an
d
n
o
m
in
al
s
tato
r
f
l
u
x
v
al
u
es,
an
d
,,
ar
e
th
e
w
ei
g
h
t
co
ef
f
icie
n
t
s
w
h
ich
d
en
o
te
s
th
e
p
r
io
r
ity
in
t
h
e
co
n
tr
o
l.
Fig
u
r
e
3
.
Selectio
n
o
f
t
h
e
o
p
tim
al
v
o
lta
g
e
v
ec
to
r
f
o
r
C
o
s
t f
u
n
ctio
n
o
p
ti
m
i
za
tio
n
i
n
a
t
w
o
-
l
ev
el
Vo
ltag
e
s
o
u
r
ce
i
n
v
er
ter
w
it
h
F
S
-
MP
C
co
n
tr
o
l
2
.
3
.
2
.
Co
ntr
o
l
o
f
t
he
re
ct
if
ier
s
ide
T
h
e
p
u
r
p
o
s
e
o
f
th
e
r
ec
tif
ier
co
n
tr
o
l
is
th
e
p
o
s
s
ib
ilit
y
to
co
n
tr
o
l
th
e
d
is
p
lace
m
en
t
f
ac
to
r
in
th
e
s
u
p
p
ly
v
o
ltag
e
s
id
e
b
y
m
in
i
m
izin
g
th
e
in
p
u
t
r
ea
ctiv
e
p
o
w
er
(
f
ig
.
4
.
a)
.
I
n
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k
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ased
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I
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N
:
2
2
5
2
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8792
IJ
A
P
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4
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3
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Dec
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5
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108
(
a)
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ith
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Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
A
P
E
I
SS
N:
2252
-
8792
P
r
ed
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109
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ased
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0
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1
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ased
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u
r
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8792
IJ
A
P
E
Vo
l.
4
,
No
.
3
,
Dec
em
b
er
201
5
:
1
0
4
–
1
1
7
110
Fo
r
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ch
v
o
ltag
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to
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co
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n
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tag
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[
9
].
T
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ter
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[
11]
.
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h
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d
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v
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[
v
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]
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d
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h
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i
rC
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v
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ier
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T
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Fig
u
r
e
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.
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n
d
ir
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tr
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o
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ter
(
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MC)
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.
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ec
tif
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tag
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9
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if
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t p
o
s
s
ib
le
s
w
itch
in
g
s
tates
r
esp
ec
tiv
ely
[
9
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
A
P
E
I
SS
N:
2252
-
8792
P
r
ed
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[
5
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as c
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ig
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r
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h
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q
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ated
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u
r
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On
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8792
IJ
A
P
E
Vo
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4
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No
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Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
A
P
E
I
SS
N:
2252
-
8792
P
r
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C
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