I
nte
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l J
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P
o
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lect
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Driv
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s
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(
I
J
P
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DS
)
Vo
l.
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,
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.
4
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er
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p
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.
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4
.
pp
1
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3
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-
1942
1932
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ia
e
s
jo
u
r
n
a
l.c
o
m/o
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lin
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d
ex
.
p
h
p
/I
JP
E
DS
Predic
tive Co
nt
ro
l of AC/
AC Ma
tr
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x
Conv
erte
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Siti
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a
j
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Yus
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f
1
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idi
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ha
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a
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De
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tri
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K
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w
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d
:
Ma
tr
ix
co
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v
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ter
Mo
d
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p
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ed
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co
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P
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In
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:
Sit
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Yu
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p
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cr
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[
1
]
.
A
d
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AC
/
AC
m
a
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ter
(
DM
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3
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-
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9
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1
2
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P
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C
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te
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4
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[
1
5
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[
1
6
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2
2
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d
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2
3
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d
i
s
cu
s
s
es
o
n
h
o
w
MP
C
s
c
h
e
m
e
ca
n
b
e
ap
p
lied
to
co
n
v
en
tio
n
a
l
Ma
tr
ix
C
o
n
v
er
ter
w
it
h
in
p
u
t
a
n
d
o
u
tp
u
t
lo
w
p
ass
f
ilter
s
.
T
h
e
g
o
al
o
f
t
h
e
c
o
n
tr
o
l
is
to
d
eli
v
er
h
ig
h
q
u
al
it
y
o
u
tp
u
t
v
o
lta
g
e,
g
en
er
ati
n
g
lo
w
d
is
to
r
tio
n
i
n
p
u
t
cu
r
r
en
t
s
w
it
h
u
n
it
y
p
o
w
er
f
a
cto
r
o
p
er
atio
n
.
T
h
e
co
n
tr
o
ller
u
s
e
s
a
m
o
d
el
o
f
t
h
e
s
y
s
te
m
to
p
r
ed
ict,
at
e
v
er
y
s
a
m
p
lin
g
ti
m
e
t
h
e
i
n
p
u
t
r
e
ac
ti
v
e
p
o
w
er
a
n
d
t
h
e
o
u
tp
u
t
v
o
lta
g
e
f
o
r
ea
ch
p
o
s
s
ib
le
s
w
itc
h
in
g
s
tate;
th
e
n
,
a
co
s
t
f
u
n
ct
io
n
i
s
u
s
ed
f
o
r
s
elec
ti
n
g
t
h
e
s
w
itch
in
g
s
tate
t
h
at
w
ill
b
e
ap
p
lied
in
t
h
e
n
ex
t
s
a
m
p
li
n
g
ti
m
e
o
n
th
e
b
a
s
e
o
f
m
i
n
i
m
izatio
n
o
f
r
ea
cti
v
e
p
o
w
er
an
d
o
u
tp
u
t
v
o
lta
g
e
er
r
o
r
.
T
h
is
is
ac
h
ie
v
ed
w
it
h
a
s
in
g
le
co
n
tr
o
l
lo
o
p
w
ith
o
u
t
u
s
i
n
g
a
tr
ad
itio
n
al
ca
s
ca
d
ed
co
n
tr
o
l
s
tr
u
ct
u
r
e
an
d
p
r
o
v
id
es
also
r
eg
u
lat
io
n
o
f
t
h
e
in
p
u
t
cu
r
r
en
t.
A
d
d
itio
n
all
y
,
a
f
u
ll
lo
ad
o
b
s
er
v
er
i
s
e
m
p
lo
y
ed
to
esti
m
ate
th
e
o
u
tp
u
t
c
u
r
r
en
ts
d
u
e
to
t
h
e
u
n
k
n
o
w
n
s
y
s
te
m
li
n
ea
r
lo
ad
.
Si
m
u
latio
n
r
esu
l
ts
o
b
tain
ed
in
SA
B
E
R
e
n
v
ir
o
n
m
e
n
t,
co
n
f
ir
m
th
e
e
f
f
ec
tiv
e
n
es
s
o
f
th
e
p
r
o
p
o
s
ed
s
o
lu
tio
n
,
t
h
at
m
i
n
i
m
izes
t
h
e
co
n
tr
o
l
co
m
p
l
ex
it
y
an
d
r
ed
u
ce
t
h
e
n
u
m
b
er
o
f
s
en
s
o
r
s
r
eq
u
ir
ed
f
o
r
m
ea
s
u
r
e
m
e
n
t
s
.
2.
DIRE
CT
M
AT
RIX CO
NV
E
RT
E
R
M
O
DE
L
2
.
1
.
Co
nv
er
t
er
Str
uct
ure
T
h
e
th
r
ee
-
p
h
ase
co
n
v
en
t
io
n
a
l
Dir
ec
t
Ma
tr
ix
C
o
n
v
er
ter
w
it
h
in
p
u
t
a
n
d
o
u
tp
u
t
lo
w
p
ass
f
ilter
s
co
n
s
id
er
ed
in
th
i
s
p
ap
er
is
s
h
o
w
n
i
n
Fi
g
u
r
e
1
.
Fig
u
r
e
1
.
Dir
ec
t M
atr
ix
C
o
n
v
e
r
ter
p
o
w
er
s
u
p
p
l
y
to
p
o
lo
g
y
T
h
is
Dir
ec
t
Ma
tr
ix
C
o
n
v
er
ter
co
n
s
is
ts
o
f
n
i
n
e
b
id
ir
ec
tio
n
a
l
s
w
itc
h
es
co
n
n
ec
t
in
g
d
ir
ec
tl
y
a
t
h
r
ee
-
p
h
ase
s
o
u
r
ce
to
a
th
r
ee
-
p
h
a
s
e
lo
ad
an
d
g
en
er
ati
n
g
2
7
v
alid
s
w
itc
h
i
n
g
s
tates
[
1
9
]
.
T
h
e
allo
w
ed
2
7
s
w
itc
h
in
g
s
tates
ar
e
g
e
n
er
ated
b
ased
o
n
th
e
r
estrictio
n
o
f
th
e
m
atr
i
x
co
n
v
er
ter
to
p
o
lo
g
y
;
t
h
e
lo
ad
ca
n
’
t
b
e
in
an
o
p
en
cir
cu
it
d
u
e
to
it
s
in
d
u
cti
v
e
n
a
t
u
r
e
an
d
in
p
u
t
p
h
a
s
es
ca
n
’
t
b
e
co
n
n
ec
ted
i
n
s
h
o
r
t
cir
cu
it.
T
h
e
s
w
itc
h
in
g
f
u
n
ctio
n
is
d
ef
i
n
ed
as:
=
{
1
,
0
,
(
1
)
W
h
er
e
=
1
,
2
…
9
.
B
ased
o
n
(
1
)
an
d
th
e
v
al
id
s
w
itc
h
in
g
s
tates,
t
h
e
co
n
v
er
ter
m
o
d
el
ca
n
b
e
ex
p
r
ess
ed
as f
o
llo
w
s
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
IJ
PEDS
Vo
l.
8
,
No
.
4
,
Dec
em
b
er
2
0
1
7
:
1
9
3
2
–
1
9
4
2
1934
[
]
=
[
1
2
3
4
5
6
7
8
9
]
[
]
(
2
)
[
]
=
[
1
4
7
2
5
8
3
6
9
]
[
]
(
3
)
W
h
er
e
V
f
o
an
d
ar
e
th
e
o
u
tp
u
t
v
o
ltag
e
a
n
d
th
e
o
u
tp
u
t
cu
r
r
en
t
o
f
t
h
e
co
n
v
er
ter
w
h
ils
t
V
in
an
d
ar
e
th
e
in
p
u
t v
o
lta
g
e
an
d
th
e
i
n
p
u
t c
u
r
r
en
t o
f
t
h
e
co
n
v
er
ter
.
T
h
e
in
p
u
t
L
C
f
i
lter
co
n
n
ec
ted
to
th
e
s
u
p
p
l
y
i
s
u
s
ed
to
f
il
te
r
th
e
h
i
g
h
f
r
eq
u
en
c
y
c
u
r
r
en
t
h
ar
m
o
n
ics
w
h
ile
t
h
e
o
u
tp
u
t
L
C
f
ilter
is
u
s
ed
to
r
ed
u
ce
th
e
s
w
itc
h
in
g
h
ar
m
o
n
ics
i
n
t
h
e
o
u
tp
u
t
v
o
lta
g
e
to
i
m
p
r
o
v
e
t
h
e
o
u
tp
u
t
p
o
w
er
q
u
a
lit
y
.
W
it
h
r
e
f
er
en
ce
to
Fi
g
.
1
th
e
v
ar
iab
les
,
,
,
an
d
ar
e
m
ea
s
u
r
ed
w
h
ile
an
d
ca
n
b
e
ca
lcu
lated
u
s
in
g
E
q
u
atio
n
(
2
)
an
d
(
3
)
;
th
e
lo
ad
cu
r
r
en
t
is
u
n
k
n
o
w
n
a
n
d
w
ill
b
e
p
r
ed
icted
(
)
u
s
i
n
g
an
o
b
s
er
v
er
as d
escr
ib
ed
in
s
ec
tio
n
3
.
2
C
.
2
.
2
.
F
ilte
rs
M
o
del
T
h
e
s
y
s
te
m
m
o
d
el
i
s
t
h
en
co
m
p
leted
b
y
ad
d
i
n
g
t
h
e
i
n
f
l
u
en
ce
o
f
i
n
p
u
t a
n
d
o
u
tp
u
t
f
ilter
.
T
h
e
L
C
i
n
p
u
t
f
ilter
co
n
ti
n
u
o
u
s
m
o
d
el
is
r
ep
r
esen
ted
b
y
t
h
e
f
o
llo
w
i
n
g
E
q
u
a
tio
n
s:
=
+
+
(
4
)
=
+
(
5
)
W
h
er
e,
is
th
e
in
p
u
t
f
ilter
in
d
u
cto
r
,
is
th
e
in
p
u
t
f
ilter
r
esis
to
r
an
d
is
th
e
in
p
u
t
f
ilter
ca
p
ac
ito
r
.
T
h
e
o
u
tp
u
t f
ilter
co
n
ti
n
u
o
u
s
m
o
d
el
ca
n
b
e
d
escr
ib
ed
as f
o
llo
w
s
:
=
+
+
(
6
)
=
+
(
7
)
W
h
er
e,
is
t
h
e
o
u
tp
u
t
f
ilter
i
n
d
u
cto
r
,
is
t
h
e
o
u
tp
u
t
f
i
lter
r
e
s
is
to
r
a
n
d
is
th
e
o
u
tp
u
t
f
ilter
ca
p
ac
ito
r
3.
M
O
DE
L
P
RE
DIC
T
I
V
E
CO
NT
RO
L
I
n
d
e
s
ig
n
i
n
g
t
h
i
s
clo
s
ed
lo
o
p
MP
C
co
n
tr
o
ller
,
th
e
f
o
llo
w
i
n
g
co
n
tr
o
l o
b
j
ec
tiv
es a
r
e
d
ef
in
ed
:
1)
A
chi
ev
e l
ow
d
i
s
t
or
t
i
on i
np
ut
cu
r
r
ent
s wit
h un
i
t
y
pow
e
r
f
a
ct
o
r
2)
A
chi
ev
e hi
g
h qua
l
i
t
y
cont
r
ol
of
t
he
out
put
v
ol
t
ag
e
3)
G
ene
r
a
t
e
an a
c
cur
at
e e
s
t
i
m
at
i
on of
t
he
l
o
ad c
u
r
r
ent
3.
1.
Co
ntr
o
l St
ruct
ure
Fig
u
r
e
2
s
h
o
w
s
a
b
lo
ck
d
iag
r
a
m
o
f
th
e
p
r
o
p
o
s
ed
m
atr
i
x
co
n
v
er
ter
s
y
s
te
m
a
n
d
p
r
ed
ictiv
e
co
n
tr
o
l
i
m
p
le
m
en
ted
.
As
it
ca
n
b
e
s
ee
n
,
th
e
p
r
ed
icti
v
e
co
n
tr
o
l
c
o
n
s
is
ts
o
f
in
p
u
t
an
d
o
u
tp
u
t
p
r
ed
ictiv
e
m
o
d
els,
m
i
n
i
m
izatio
n
o
f
co
s
t f
u
n
ctio
n
an
d
s
tat
e
s
elec
t
io
n
.
T
h
e
in
p
u
t
p
r
ed
ictiv
e
m
o
d
el
i
s
b
ased
o
n
t
h
e
d
i
s
cr
etize
d
s
y
s
te
m
i
n
p
u
t
E
q
u
atio
n
s
in
cl
u
d
i
n
g
t
h
e
L
C
f
ilter
;
it
p
r
ed
icts
t
h
e
s
o
u
r
ce
cu
r
r
en
t
b
ased
also
o
n
th
e
i
n
p
u
t
c
u
r
r
en
t
o
f
th
e
m
atr
i
x
co
n
v
er
ter
w
h
ic
h
d
ep
en
d
s
o
n
th
e
o
b
s
er
v
ed
lo
ad
cu
r
r
en
t
t
h
r
o
u
g
h
t
h
e
m
atr
ix
co
n
v
er
ter
.
B
as
ed
o
n
th
e
m
ea
s
u
r
ed
v
alu
e
s
at
s
a
m
p
li
n
g
in
s
ta
n
t
k
th
is
m
o
d
el
allo
w
s
th
e
p
r
ed
ictio
n
o
f
t
h
e
i
n
p
u
t
r
ea
cti
v
e
p
o
w
e
r
at
th
e
i
n
s
ta
n
t
k
+1
,
w
h
ich
will
b
e
th
e
n
u
s
ed
to
co
n
s
tr
u
ct
t
h
e
co
s
t
f
u
n
ctio
n
g
.
T
h
e
o
u
tp
u
t
m
o
d
el
is
b
ased
o
n
th
e
o
u
tp
u
t
L
C
f
i
l
ter
,
o
n
th
e
o
b
s
er
v
ed
lo
ad
cu
r
r
en
t
an
d
o
n
th
e
m
atr
i
x
co
n
v
er
ter
o
u
tp
u
t
cu
r
r
en
t
d
ep
en
d
in
g
o
n
th
e
in
p
u
t
v
o
lta
g
e;
it
is
ab
le
to
p
r
e
d
ict
th
e
o
u
tp
u
t
v
o
ltag
e
at
t
h
e
i
n
s
ta
n
t k
+1
to
b
e
u
s
ed
in
t
h
e
co
s
t
f
u
n
ctio
n
g
.
T
h
e
co
s
t
f
u
n
ctio
n
to
b
e
m
i
n
i
m
ized
b
y
t
h
e
MP
C
i
n
cl
u
d
es
th
e
o
u
tp
u
t
v
o
lta
g
e
er
r
o
r
an
d
th
e
i
n
p
u
t
r
ea
ctiv
e
p
o
w
er
er
r
o
r
(
co
n
s
id
er
in
g
a
ze
r
o
-
r
e
f
er
en
ce
r
ea
cti
v
e
p
o
w
er
a
n
d
th
e
v
o
lta
g
e
o
u
tp
u
t r
e
f
er
en
ce
a
s
d
ictated
b
y
t
h
e
ap
p
licatio
n
s
p
ec
i
f
icatio
n
s
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PEDS
I
SS
N:
2
0
8
8
-
8
694
P
r
ed
ictive
C
o
n
tr
o
l o
f A
C
/AC
Ma
tr
ix
C
o
n
ve
r
te
r
(
S
iti Ha
ja
r
Yu
s
o
ff
)
1935
Fig
u
r
e
2
.
C
o
n
tr
o
l sch
e
m
e
o
f
Mo
d
el
P
r
e
d
ictiv
e
C
o
n
tr
o
l
A
t
ev
er
y
s
a
m
p
li
n
g
ti
m
e,
th
e
o
u
tp
u
t
s
tate
w
h
ic
h
p
r
o
d
u
ce
s
t
h
e
s
m
a
lles
t
v
al
u
e
o
f
t
h
e
co
s
t
f
u
n
ctio
n
g
i
s
s
elec
ted
f
r
o
m
th
e
2
7
p
o
s
s
ib
le
s
tates.
T
h
is
s
elec
ted
s
w
i
tch
in
g
s
tate
is
t
h
e
n
ap
p
lied
in
t
h
e
f
o
llo
w
i
n
g
s
a
m
p
l
in
g
ti
m
e
(
k
+2
)
,
g
i
v
e
n
t
h
e
co
n
tr
o
l
i
m
p
le
m
en
ta
tio
n
d
ela
y
o
f
o
n
e
s
a
m
p
li
n
g
p
er
io
d
[
2
0
]
.
Deta
iled
d
escr
ip
tio
n
o
f
th
e
p
r
ed
ictio
n
m
o
d
els an
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th
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3
.
2
.
P
re
dict
io
n M
o
dels
3
.
2
.
1
.
I
np
ut
M
o
del
A
d
is
cr
ete
ti
m
e
m
o
d
el
o
f
th
e
in
p
u
t
s
id
e
ex
p
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ess
ed
i
n
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a
s
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ate
s
p
ac
e
f
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r
m
is
d
e
v
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e
d
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m
ate
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e
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ex
t
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o
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m
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g
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h
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ts
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n
d
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o
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s
m
ea
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r
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n
t
s
at
t
h
e
k
th
s
a
m
p
li
n
g
ti
m
e.
E
q
u
atio
n
s
(
4
)
an
d
(
5
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ca
n
b
e
r
e
w
r
itte
n
i
n
th
e
f
o
r
m
o
f
a
co
n
ti
n
u
o
u
s
s
tate
s
p
ac
e
m
o
d
el
as
f
o
llo
w
s
̇
(
)
=
[
0
1
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−
1
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−
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(
)
+
[
0
−
1
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1
⁄
0
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⏟
(
)
(
8
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W
h
er
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(
)
=
[
(
)
(
)
]
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d
(
)
=
[
(
)
(
)
]
(
9
)
A
d
is
cr
ete
s
tate
s
p
ac
e
m
o
d
el
ca
n
b
e
d
er
iv
ed
f
r
o
m
(
8
)
u
s
i
n
g
ze
r
o
o
r
d
er
h
o
ld
m
et
h
o
d
.
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o
n
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er
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g
a
s
a
m
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li
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g
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er
io
d
,
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e
o
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tain
:
(
+
1
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=
(
)
+
(
)
(
1
0
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h
er
e;
=
≅
[
1
3
2
4
]
(
1
1
)
=
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(
−
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0
≅
[
1
3
2
4
]
(
1
2
0
T
h
u
s
,
th
e
i
n
p
u
t c
u
r
r
en
t p
r
ed
ictio
n
ca
n
b
e
ea
s
il
y
d
er
iv
ed
as
;
(
+
1
)
=
2
(
)
+
4
(
)
+
2
(
)
+
4
(
)
(
1
3
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
IJ
PEDS
Vo
l.
8
,
No
.
4
,
Dec
em
b
er
2
0
1
7
:
1
9
3
2
–
1
9
4
2
1936
(
+
2
)
=
2
(
+
1
)
+
4
(
+
1
)
+
2
(
+
1
)
+
4
(
+
1
)
(
1
4
)
T
h
e
in
s
tan
tan
eo
u
s
r
ea
cti
v
e
in
p
u
t
p
o
w
er
ca
n
b
e
p
r
ed
icted
b
ased
o
n
th
e
p
r
ed
ictio
n
s
o
f
th
e
in
p
u
t
cu
r
r
en
t a
s
s
h
o
w
n
in
E
q
u
a
tio
n
(
1
4
)
;
(
+
2
)
=
{
(
+
2
)
̅
(
+
2
)
}
(
1
5
)
(
+
2
)
=
(
+
2
)
(
+
2
)
−
(
+
2
)
(
+
2
)
(
1
6
)
W
h
er
e
̅
is
t
h
e
co
m
p
le
x
co
n
j
u
g
ate
o
f
v
ec
to
r
w
h
il
s
t
t
h
e
s
u
b
s
c
r
ip
ts
α
a
n
d
β
r
ep
r
esen
t
t
h
e
r
ea
l
an
d
th
e
i
m
a
g
i
n
ar
y
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m
p
o
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e
n
t
s
o
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th
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ciate
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v
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to
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.
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i
n
e
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en
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y
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i
g
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als
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h
u
s
ass
u
m
i
n
g
(
)
≈
(
+
1
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(
+
2
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d
(
+
1
)
is
ca
lcu
lated
f
r
o
m
(
1
0
)
,
s
u
c
h
as:
(
+
1
)
=
1
(
)
+
3
(
)
+
1
(
)
+
3
(
)
(
1
7
)
(
+
1
)
is
d
er
iv
ed
f
r
o
m
(
3
)
w
it
h
o
n
e
s
a
m
p
lin
g
s
tep
ah
ea
d
w
h
er
e
(
+
1
)
is
b
ased
o
n
(
2
5
)
.
3
.
2
.
2
.
O
utput
M
o
del
T
h
e
co
n
tin
u
o
u
s
s
y
s
te
m
m
o
d
el
in
E
q
u
atio
n
s
(
6
)
a
n
d
(
7
)
ca
n
b
e
r
e
w
r
it
ten
i
n
t
h
e
s
tate
s
p
ac
e
f
o
r
m
a
s
f
o
llo
w
s
:
̇
(
)
=
[
−
⁄
−
1
⁄
1
⁄
0
]
⏟
(
)
+
[
1
⁄
0
0
−
1
⁄
]
⏟
(
)
(
1
8
)
W
h
er
e;
(
)
=
[
(
)
(
)
]
an
d
(
)
=
[
(
)
(
)
]
(
1
9
)
C
o
n
s
id
er
in
g
a
s
a
m
p
li
n
g
p
er
io
d
,
th
e
s
tate
s
p
ac
e
m
o
d
el
in
(
1
8
)
ca
n
b
e
d
is
cr
etize
d
:
(
+
1
)
=
(
)
+
(
)
(
2
0
)
W
h
er
e;
=
≅
[
5
7
6
8
]
(
2
1
)
=
≅
[
5
7
6
8
]
(
22)
T
h
u
s
,
th
e
o
u
tp
u
t v
o
lta
g
e
p
r
ed
ictio
n
ca
n
b
e
ea
s
il
y
d
er
iv
ed
as
f
o
llo
w
ed
;
(
+
1
)
=
8
(
)
+
6
(
)
+
6
(
)
+
8
(
)
(
2
3
)
(
+
2
)
=
8
(
+
1
)
+
6
(
+
1
)
+
6
(
+
1
)
+
8
(
+
1
)
(
2
4
)
(
+
1
)
is
ca
lcu
lated
f
r
o
m
(
2
0
)
,
s
u
ch
as:
(
+
1
)
=
5
(
)
+
7
(
)
+
5
(
)
+
7
(
)
(
2
5
)
(
+
1
)
is
d
er
iv
ed
t
h
r
o
u
g
h
(
+
1
)
in
(
1
7
)
b
ased
o
n
r
elatio
n
in
(
3
)
.
W
h
er
ea
s
(
+
1
)
is
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PEDS
I
SS
N:
2
0
8
8
-
8
694
P
r
ed
ictive
C
o
n
tr
o
l o
f A
C
/AC
Ma
tr
ix
C
o
n
ve
r
te
r
(
S
iti Ha
ja
r
Yu
s
o
ff
)
1937
o
b
tain
ed
f
r
o
m
th
e
o
b
s
er
v
er
(
3
3
)
,
as d
escr
ib
ed
in
th
e
n
ex
t
s
ec
tio
n
.
3
.
2
.
3
.
L
o
a
d Curr
ent
O
bs
er
v
er
T
h
e
u
n
k
n
o
w
n
lo
ad
cu
r
r
en
t
ca
n
b
e
esti
m
ated
u
s
in
g
a
f
u
ll
o
r
d
e
r
s
tate
o
b
s
er
v
er
.
A
s
s
u
m
in
g
t
h
e
lo
ad
cu
r
r
en
t
d
y
n
a
m
ic
s
s
lo
w
er
e
n
o
u
g
h
co
m
p
ar
ed
to
t
h
e
s
y
s
te
m
s
a
m
p
li
n
g
f
r
eq
u
e
n
c
y
,
t
h
e
lo
ad
cu
r
r
en
t
ca
n
b
e
ap
p
r
o
x
im
a
ted
as a
co
n
s
ta
n
t d
u
r
in
g
o
n
e
s
a
m
p
li
n
g
p
er
io
d
,
in
w
h
ich
:
=
0
(
2
6
)
T
ak
in
g
E
q
u
atio
n
(2
6
)
in
to
th
e
f
ilter
m
o
d
el,
th
e
d
is
cr
ete
s
tate
s
p
ac
e
f
ilter
m
o
d
el
ca
n
b
e
w
r
itten
as
in
(
2
7
)
;
̇
(
)
=
[
−
⁄
−
1
⁄
0
1
⁄
0
−
1
⁄
0
0
0
]
⏟
(
)
+
[
1
⁄
0
0
]
⏟
(
)
(
2
7
)
W
h
er
e;
(
)
=
[
(
)
(
)
(
)
]
an
d
(
)
=
[
(
)
]
(
2
8
)
B
ased
o
n
(
2
7
)
,
th
er
e
ar
e
tw
o
m
ea
s
u
r
ab
le
v
ar
iab
les:
t
h
e
f
il
te
r
cu
r
r
en
t
an
d
th
e
o
u
tp
u
t
v
o
lta
g
e
.
T
h
e
o
u
tp
u
t o
f
th
i
s
s
y
s
te
m
i
s
th
er
ef
o
r
e
d
ef
in
ed
as f
o
llo
w
s
;
(
)
=
[
1
0
0
0
1
0
]
⏟
(
)
(
2
9
)
T
h
e
f
u
ll s
tate
o
b
s
er
v
er
is
u
s
ed
to
esti
m
ate
t
h
e
s
ta
te
v
ec
to
r
th
u
s
it
s
E
q
u
atio
n
i
s
d
ef
i
n
ed
as:
̂
(
)
=
̂
(
)
+
(
)
+
(
(
)
−
̂
(
)
)
(
3
0
)
w
h
er
e
L
i
s
t
h
e
o
b
s
er
v
er
g
ai
n
s
m
atr
i
x
.
T
h
is
m
atr
ix
L
w
il
l
d
ef
i
n
e
t
h
e
o
b
s
er
v
er
d
y
n
a
m
i
cs.
I
n
th
i
s
d
esig
n
,
th
e
o
b
s
er
v
er
g
ai
n
is
c
h
o
s
en
s
o
th
e
o
b
s
er
v
er
p
o
les
p
r
o
d
u
ce
a
d
y
n
a
m
ic
s
ev
er
al
ti
m
es
f
as
ter
th
a
n
th
e
o
p
en
lo
o
p
s
y
s
te
m
d
y
n
a
m
ic
s
.
E
q
u
atio
n
(
3
0
)
ca
n
b
e
f
u
r
th
er
w
r
itten
as
:
̂
(
)
=
[
−
]
̂
+
[
]
[
]
(
3
1
)
T
h
er
ef
o
r
e,
th
e
o
b
s
er
v
er
o
u
tp
u
t
is
t
h
e
e
s
ti
m
ated
lo
ad
cu
r
r
en
t
b
ased
o
n
m
ea
s
u
r
e
m
e
n
ts
o
f
th
e
o
u
tp
u
t v
o
lta
ge
,
th
e
in
p
u
t v
o
lta
g
e
n
ee
d
ed
to
o
b
tain
V
fo
th
r
o
u
g
h
(
2
)
,
an
d
th
e
f
ilter
cu
r
r
en
t
.
C
o
n
s
id
er
in
g
a
s
a
m
p
li
n
g
p
er
io
d
,
th
e
s
tate
s
p
ac
e
m
o
d
el
in
(
3
1
)
ca
n
b
e
d
is
cr
etize
d
:
[
(
+
1
)
(
+
1
)
(
+
1
)
]
=
[
1
2
3
4
5
6
7
8
9
]
[
(
)
(
)
(
)
]
+
[
1
2
3
4
5
6
7
8
9
]
[
(
)
(
)
(
)
]
(
3
2
)
T
h
u
s
(
+
1
)
is
d
ef
in
ed
as
f
o
llo
w
s
;
(
+
1
)
=
(
7
+
8
)
(
)
+
(
8
+
9
)
(
)
+
9
(
)
+
7
(
)
(
3
3
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
IJ
PEDS
Vo
l.
8
,
No
.
4
,
Dec
em
b
er
2
0
1
7
:
1
9
3
2
–
1
9
4
2
1938
3
.
2
.
4
.
Co
s
t
F
un
ct
io
n
T
h
e
b
lo
ck
d
iag
r
am
o
f
th
e
p
r
o
p
o
s
ed
co
n
tr
o
l
s
ch
e
m
e
is
s
h
o
w
n
in
Fi
g
u
r
e
2
.
T
h
e
m
ea
s
u
r
e
d
v
ar
iab
les
,
,
,
an
d
an
d
th
e
e
s
ti
m
ated
lo
ad
cu
r
r
en
t
ar
e
f
ee
d
in
to
t
h
e
p
r
ed
ictiv
e
m
o
d
el
w
h
ic
h
is
t
h
e
n
u
s
ed
to
ca
lcu
late
t
h
e
p
r
ed
ictio
n
s
(
+
2
)
an
d
(
+
2
)
as in
(
1
6
)
an
d
(
2
4
)
.
As
s
tated
ea
r
lier
,
t
h
e
co
n
tr
o
l
o
b
j
ec
tiv
es
ar
e
to
p
r
o
d
u
ce
a
r
eg
u
lated
an
d
s
in
u
s
o
id
al
o
u
tp
u
t
v
o
ltag
e
an
d
to
g
en
er
ate
a
lo
w
h
ar
m
o
n
ic
d
is
to
r
tio
n
in
p
u
t
cu
r
r
e
n
t
to
g
et
h
er
w
it
h
u
n
it
y
i
n
p
u
t
p
o
w
er
f
ac
to
r
o
p
er
atio
n
.
T
h
e
in
p
u
t
s
id
e
o
b
j
ec
tiv
es
ca
n
b
e
ac
h
iev
ed
b
y
m
i
n
i
m
izi
n
g
t
h
e
p
r
ed
icted
r
ea
ctiv
e
p
o
w
er
g
i
v
e
n
i
n
E
q
u
atio
n
(
1
6
)
co
n
s
id
er
in
g
a
ze
r
o
r
ef
er
en
ce
as sh
o
w
n
i
n
(
3
5
)
.
∆
[
+
2
]
=
|
∗
[
+
2
]
−
[
+
2
]
|
(
3
4
)
W
h
er
e;
∗
[
+
2
]
=
0
(
3
5
)
Th
u
s
E
q
u
atio
n
(
3
4
)
is
r
e
w
r
itte
n
as;
∆
[
+
2
]
=
|
[
+
2
]
|
(
3
6
)
T
h
e
o
u
tp
u
t
s
id
e
o
b
j
ec
tiv
e
ca
n
b
e
ac
h
ie
v
ed
b
y
m
i
n
i
m
izi
n
g
t
h
e
er
r
o
r
b
et
w
ee
n
th
e
o
u
tp
u
t
v
o
ltag
e
r
ef
er
en
ce
∗
(
+
2
)
an
d
th
e
r
esp
ec
tiv
e
p
r
ed
icted
v
alu
e
(
+
2
)
as
f
o
llo
w
s
;
∆
[
+
2
]
=
∗
[
+
2
]
−
[
+
2
]
(
3
7
)
T
h
e
r
esu
ltin
g
co
s
t
f
u
n
ctio
n
g
th
at
in
cl
u
d
es
b
o
th
o
b
j
ec
tiv
es,
is
o
b
tain
ed
b
y
ad
d
in
g
(
3
6
)
an
d
(
3
7
)
.
T
h
u
s
;
(
+
2
)
=
|
[
+
2
]
|
+
∆
[
+
2
]
(
3
8
)
W
h
er
e
λ
is
a
w
ei
g
h
ti
n
g
f
ac
to
r
.
T
h
e
w
eig
h
ti
n
g
f
ac
to
r
is
s
ele
cted
b
ased
o
n
th
e
T
HD
o
f
th
e
in
p
u
t
a
n
d
o
u
tp
u
t
c
u
r
r
en
t
a
s
p
r
ese
n
ted
in
[
9
]
.
Fu
r
th
er
tec
h
n
iq
u
es
o
f
s
el
ec
tin
g
t
h
e
w
ei
g
h
ti
n
g
f
ac
to
r
s
a
r
e
d
escr
ib
ed
in
[
21
]
an
d
ca
n
ev
e
n
t
u
all
y
b
e
u
s
ed
.
A
v
al
u
e
o
f
g
=0
g
i
v
es
p
er
f
ec
t
o
u
tp
u
t
v
o
lta
g
e
tr
ac
k
in
g
an
d
u
n
it
y
p
o
w
er
f
ac
to
r
at
th
e
i
n
p
u
t
s
id
e.
T
h
is
co
s
t
f
u
n
ctio
n
g
i
s
ev
al
u
ated
f
o
r
ev
er
y
p
o
s
s
ib
le
s
w
itc
h
i
n
g
s
tat
e:
th
e
s
tate
a
m
o
n
g
1
…
27
(
+
2
)
th
at
m
i
n
i
m
izes
g
is
s
e
lecte
d
an
d
ap
p
lied
at
th
e
Dir
ec
t
M
atr
ix
C
o
n
v
er
ter
o
u
tp
u
t
in
t
h
e
k
+2
s
a
m
p
li
n
g
p
er
io
d
.
4.
S
I
M
UL
AT
I
O
N
A
ND
E
XP
E
RIM
E
NT
AL
R
E
S
UL
T
S
I
n
o
r
d
er
to
an
al
y
s
e
t
h
e
e
f
f
ec
ti
v
en
e
s
s
o
f
t
h
e
p
r
o
p
o
s
ed
m
et
h
o
d
,
th
e
p
r
ed
ictiv
e
co
n
tr
o
l
s
tr
ate
g
y
a
n
d
t
h
e
o
b
s
er
v
er
alg
o
r
ith
m
ar
e
s
i
m
u
l
ated
.
Usi
n
g
th
e
f
u
l
l
s
ch
e
m
at
i
c
m
o
d
el
o
f
th
e
s
y
s
te
m
,
all
s
i
m
u
latio
n
s
ar
e
d
o
n
e
u
n
d
er
b
a
lan
ce
d
th
r
ee
p
h
a
s
e
s
u
p
p
ly
v
o
ltag
e
s
an
d
b
alan
ce
d
th
r
ee
p
h
ase
R
L
lo
ad
.
I
t
h
as
to
b
e
n
o
ticed
th
at
i
n
th
e
s
i
m
u
lat
io
n
s
,
th
e
ap
p
licatio
n
o
f
t
h
e
n
ex
t
s
w
i
tch
in
g
s
tate
i
s
i
n
s
ta
n
ta
n
eo
u
s
,
s
o
n
o
d
ela
y
co
m
p
e
n
s
atio
n
is
u
s
ed
th
r
o
u
g
h
o
u
t th
e
m
o
d
elli
n
g
.
I
n
p
u
t
an
d
o
u
tp
u
t
f
u
n
d
am
en
tal
f
r
eq
u
en
cy
is
ch
o
s
en
at
5
0
Hz
an
d
th
e
o
u
tp
u
t
v
o
ltag
e
is
co
n
tr
o
lled
at
4
2
V.
Fig
u
r
e
3
s
h
o
w
s
th
e
s
im
u
latio
n
r
esu
lts
f
o
r
s
o
u
r
ce
cu
r
r
en
t
an
d
v
o
ltag
e
in
o
n
e
in
p
u
t
p
h
ase.
I
t
is
p
o
s
s
ib
le
to
n
o
tice
th
at
u
n
ity
p
o
w
er
f
ac
to
r
an
d
q
u
asi
s
in
u
s
o
id
al
s
o
u
r
ce
cu
r
r
en
ts
ar
e
o
b
tain
ed
.
T
h
e
in
p
u
t
cu
r
r
en
t
is
s
in
u
s
o
id
al
an
d
in
p
h
ase
w
ith
th
e
s
u
p
p
ly
v
o
ltag
e,
w
h
ich
co
n
f
ir
m
th
e
co
n
tr
o
l
o
f
th
e
in
p
u
t
p
o
w
er
f
ac
to
r
(
P
F)
is
ac
h
iev
ed
.
Fig
u
r
e
4
s
h
o
w
s
th
e
s
p
ec
tr
u
m
an
aly
s
is
o
f
th
e
in
p
u
t
p
h
ase
cu
r
r
en
t.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PEDS
I
SS
N:
2
0
8
8
-
8
694
P
r
ed
ictive
C
o
n
tr
o
l o
f A
C
/AC
Ma
tr
ix
C
o
n
ve
r
te
r
(
S
iti Ha
ja
r
Yu
s
o
ff
)
1939
Fig
u
r
e
3
.
I
n
p
u
t c
u
r
r
en
t a
n
d
v
o
l
ta
g
e
(
⁄
)
d
u
r
in
g
s
tead
y
s
tate
o
p
er
atio
n
w
it
h
r
ea
ctiv
e
p
o
w
er
m
i
n
i
m
izatio
n
Fig
u
r
e
4
.
Har
m
o
n
ic
s
p
ec
tr
a
o
f
in
p
u
t c
u
r
r
en
t 8
0
µs
(T
s
)
,
T
HD=
8
%
Fig
u
r
e
5
s
h
o
w
s
a
v
o
ltag
e
s
tep
ch
an
g
e
in
am
p
litu
d
e
o
f
th
e
r
ef
er
en
ce
v
o
ltag
e
(
∗
)
f
r
o
m
2
0
V
to
4
2
V.
A
s
ex
p
ec
ted
,
th
e
o
u
tp
u
t
v
o
ltag
e
(
V
o
)
h
as a
g
o
o
d
tr
ac
k
in
g
an
d
f
o
llo
w
in
g
th
e
r
ef
er
en
ce
v
o
ltag
e
(
∗
)
.
M
e
a
s
u
r
e
d
E
s
t
i
m
a
t
e
d
Fig
u
r
e
5
.
A
s
tep
-
i
n
o
u
tp
u
t r
e
f
e
r
en
ce
v
o
lta
g
e
Fig
u
r
e
6
.
Ob
s
er
v
er
lo
ad
cu
r
r
en
t e
s
ti
m
at
io
n
an
d
t
h
e
m
ea
s
u
r
ed
lo
ad
cu
r
r
en
t
Fig
u
r
e
1
.
Me
asu
r
ed
an
d
esti
m
ated
o
u
tp
u
t c
u
r
r
en
t
f
o
r
r
esis
ti
v
e
-
i
n
d
u
cti
v
e
lo
ad
s
tep
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
IJ
PEDS
Vo
l.
8
,
No
.
4
,
Dec
em
b
er
2
0
1
7
:
1
9
3
2
–
1
9
4
2
1940
Fig
u
r
e
6
ill
u
s
tr
ate
s
t
h
e
es
ti
m
ated
o
b
s
er
v
er
lo
ad
cu
r
r
en
t
c
o
m
p
ar
ed
to
t
h
e
m
ea
s
u
r
ed
lo
ad
cu
r
r
en
t
d
u
r
in
g
s
tead
y
s
tate.
T
h
e
r
e
s
u
lt
d
e
m
o
n
s
tr
ati
n
g
t
h
e
e
x
ce
l
len
t
o
b
s
er
v
er
tr
ac
k
in
g
ca
p
a
b
ilit
ies,
w
it
h
g
o
o
d
esti
m
atio
n
an
d
f
a
s
t
d
y
n
a
m
ic
r
esp
o
n
s
e.
W
h
ils
t,
t
h
e
m
ea
s
u
r
ed
lo
ad
cu
r
r
en
t
a
n
d
t
h
e
es
ti
m
ate
d
lo
ad
cu
r
r
en
t
f
o
r
a
lo
ad
s
tep
is
ap
p
lied
to
o
n
e
p
h
ase
o
f
th
e
lo
ad
is
s
h
o
w
n
i
n
F
i
g
u
r
e
7
f
o
r
li
n
ea
r
lo
ad
.
T
h
is
lo
ad
s
tep
is
ap
p
lied
at
ti
m
e
0
.
2
s
.
T
h
e
esti
m
ated
lo
ad
cu
r
r
en
t
g
i
v
es
a
g
o
o
d
r
esp
o
n
s
e
in
a
q
u
ick
lo
ad
ch
an
g
e
co
n
d
itio
n
.
I
t
co
n
clu
d
es
th
at
t
h
e
o
b
s
er
v
er
lo
ad
s
cu
r
r
en
t
esti
m
a
tio
n
s
h
o
w
f
a
s
t d
y
n
a
m
ic
r
esp
o
n
s
e
d
u
r
in
g
t
h
is
tr
a
n
s
ie
n
t
ev
en
t.
Fig
u
r
e
8
.
E
x
p
er
i
m
en
t
al
s
et
u
p
o
f
a
Dir
ec
t A
C
/
AC
Ma
tr
i
x
C
o
n
v
er
ter
E
x
p
er
i
m
e
n
tal
s
etu
p
o
f
t
h
i
s
w
o
r
k
is
s
h
o
w
n
in
Fi
g
u
r
e
8
ab
o
v
e
.
R
es
u
lt
s
f
o
r
a
s
tep
c
h
a
n
g
e
in
v
o
ltag
e
a
m
p
lit
u
d
e
r
ef
er
en
ce
(
∗
)
f
r
o
m
2
0
V
to
4
2
V
is
s
h
o
w
n
i
n
Fi
g
u
r
e
9
.
I
t
ca
n
b
e
s
ee
n
th
at
th
e
o
u
tp
u
t
v
o
lta
g
e
(
V
o
)
ex
h
ib
its
g
o
o
d
d
y
n
a
m
ic
tr
ac
k
in
g
ev
e
n
w
ith
s
u
d
d
en
r
ef
er
en
ce
ch
an
g
e.
Fig
u
r
e
9
(
a)
s
h
o
w
s
th
e
o
u
tp
u
t
v
o
ltag
e
p
h
ase
a
d
u
r
in
g
a
r
e
f
er
en
ce
s
tep
c
h
a
n
g
e
a
t
ti
m
e
-
0
.
0
2
0
s
w
h
il
s
t
Fig
u
r
e
9
(
b
)
s
h
o
w
s
al
l
th
r
ee
p
h
a
s
es
o
f
th
e
o
u
tp
u
t v
o
lta
g
es
a
,
b
an
d
c
d
u
r
in
g
a
r
ef
er
en
ce
s
tep
ch
a
n
g
e
at
ti
m
e
-
0
.
0
2
0
s
.
Fig
u
r
e
9
.
A
s
tep
-
i
n
o
u
tp
u
t r
e
f
e
r
en
ce
v
o
lta
g
e
f
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[
1
]
Katsis
,
D.
W
.
,
P
.
W
.
;
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lar
e,
J
.
C
.
;
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m
p
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2
0
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4
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.
2
3
5
5
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2359
[
2
]
W
h
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ler
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P
.
W
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R
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.
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,
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288
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3
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9
–
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.
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.
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–
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5
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.
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.
,
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.
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2
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–
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6
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S.,
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.
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.
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.
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7
]
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Y.
D.
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a.
S.K.
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[
8
]
M.
L
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,
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W
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Tr
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.
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0
1
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5
7
(
1
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)
: p
.
3
3
8
5
–
3394.
[
9
]
S.
Ko
u
r
o
,
P
.
C
.
,
R
.
Var
g
as,
U.
A
m
m
an
n
,
an
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J
.
R
o
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6
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1
0
]
J
.
R
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2
0
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.
5
4
(
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.
4
9
5
-
503.
[
1
1
]
P
.
C
o
r
tes,
M.
P
.
K.
,
R
.
M.
Ken
n
el,
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E
.
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,
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.
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.
2
0
0
8
.
5
5
(
1
2
)
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.
4
3
1
2
-
4324.
[
1
2
]
P
.
Z
an
ch
e
tta,
J
.
C
.
,
P
.
W
h
ee
ler
,
D.
Katsis
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B
lan
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,
L
.
E
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p
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y
2
0
0
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.
5
5
(
1
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: p
.
2
0
9
-
217.
[
1
3
]
C
o
r
tes,
P
.
O.
,
G.
;
Yu
z,
J
.
I
.
;
R
o
d
r
ig
u
ez
,
J
.
;
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q
u
ez
,
S.
;
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n
q
u
elo
,
L
.
G.
,
“
Mo
d
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ed
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tr
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I
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s
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s
,
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2
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0
9
5
6
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.
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8
7
5
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1883
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1
4
]
C
o
r
t
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,
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.
W
.
,
A.
;
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.
;
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ez
,
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.
;
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b
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-
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,
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;,
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7
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.
2
6
9
1
-
2699
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1
5
]
R
.
Var
g
as,
J
.
R
.
,
U.
A
m
m
an
n
,
an
d
P
.
W
.
W
h
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Tr
a
n
s
.
I
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d
.
E
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.
,
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.
2
0
0
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.
5
5
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1
2
)
:
p
.
4
3
6
2
–
4371.
[
1
6
]
R
iv
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a,
M.
R
.
,
C
.
; Ro
d
r
;
g
u
ez
,
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.
; W
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ler
,
P
.
; B
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,
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.
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E
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s
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s
,
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2
0
1
1
.
2
6
(
1
0
)
: p
.
2
7
9
4
-
2803
[
1
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