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r
e
g
u
lato
r
e
n
s
u
r
es
th
at
th
e
in
p
u
t
cu
r
r
en
t
tr
ac
k
s
th
e
r
ef
er
en
ce
cu
r
r
en
t
u
n
til
it
ac
h
iev
e
s
th
e
d
esire
d
lev
el.
Ho
wev
er
,
th
e
PI
co
n
tr
o
ller
wo
r
k
s
well
f
o
r
o
n
ly
DC
r
ef
er
en
ce
,
wh
ile
it
f
r
eq
u
en
tly
ca
n
'
t
b
e
ad
eq
u
ate
m
ain
tain
ed
p
e
r
f
o
r
m
an
ce
if
t
h
e
co
m
m
an
d
is
a
s
in
u
s
o
id
al
s
ig
n
al
,
s
in
ce
th
e
in
n
er
PI
co
n
tr
o
lle
r
lo
o
p
in
tr
o
d
u
ce
s
a
p
h
ase
d
elay
w
h
en
tr
ac
k
in
g
th
e
s
in
u
s
o
id
al
cu
r
r
en
t
wav
e
f
o
r
m
.
T
h
e
PR
co
n
tr
o
ller
ca
n
r
eso
lv
e
th
e
is
s
u
e,
b
u
t
th
e
d
esig
n
p
ar
am
eter
s
o
f
t
h
e
PR
co
n
tr
o
ller
ar
e
c
o
m
p
licated
to
f
it
in
v
ar
y
in
g
lin
e
f
r
eq
u
en
cy
[
1
9
]
-
[
2
1
]
.
Sev
er
al
co
n
tr
o
l
m
eth
o
d
s
a
r
e
a
p
p
lied
f
o
r
th
e
PF
C
to
im
p
r
o
v
e
th
e
co
n
v
er
ter
d
y
n
a
m
ics
,
s
u
ch
as:
s
li
d
in
g
m
o
d
e
co
n
tr
o
l
[
2
2
]
-
[
2
4
]
,
h
y
s
ter
esis
co
n
tr
o
l
[
2
5
]
,
[
2
6
]
,
f
u
zz
y
-
lo
g
ic
co
n
t
r
o
l
[
2
7
]
.
Ho
we
v
er
,
with
th
e
q
u
ick
ev
o
lu
tio
n
o
f
p
o
wer
d
ev
ices a
n
d
d
ig
ital p
r
o
ce
s
s
o
r
s
,
th
e
PI
co
n
tr
o
ller
,
s
lid
in
g
m
o
d
e
co
n
tr
o
l
,
an
d
h
y
s
ter
esis
co
n
tr
o
l f
ac
e
co
m
p
etitio
n
f
r
o
m
th
e
p
r
ed
ictiv
e
co
n
tr
o
l
s
t
r
ateg
ies
,
wh
ich
o
f
f
e
r
s
im
p
ler
in
co
n
ce
p
ts
,
ea
s
ier
im
p
lem
en
t
atio
n
,
an
d
s
u
p
er
io
r
d
y
n
am
ic
p
er
f
o
r
m
an
ce
.
B
asically
,
th
e
s
in
g
le
-
p
h
ase
T
B
B
R
h
as
h
ig
h
-
f
r
e
q
u
en
c
y
s
witch
in
g
MO
SF
E
T
s
o
n
o
n
e
leg
(
Q
1
an
d
Q
2
)
an
d
lin
e
-
f
r
eq
u
e
n
cy
s
witch
in
g
MO
SF
E
T
s
o
n
th
e
o
th
er
leg
(
S
1
an
d
S
2
)
as
s
h
o
wn
in
Fig
u
r
e
1
.
I
ts
o
p
er
atin
g
p
r
in
cip
le
d
u
r
i
n
g
b
o
th
p
o
s
itiv
e
an
d
n
eg
ativ
e
h
alf
cy
cles
o
f
th
e
AC
in
p
u
t
v
o
ltag
e
is
d
eter
m
in
ed
b
y
th
e
s
witch
in
g
s
eq
u
en
ce
.
Du
r
in
g
t
h
e
p
o
s
itiv
e
h
alf
c
y
cle,
S
2
is
th
e
co
n
tr
o
l
s
witch
an
d
S
1
is
th
e
s
y
n
ch
r
o
n
o
u
s
s
witch
;
s
im
u
ltan
eo
u
s
ly
,
Q
1
is
tu
r
n
e
d
o
n
an
d
Q
2
is
alwa
y
s
in
ac
tiv
e
.
W
h
en
s
witch
S
2
is
tu
r
n
ed
o
f
f
,
th
e
AC
s
o
u
r
ce
ch
ar
g
es
th
e
in
d
u
cto
r
wh
ile
th
e
o
u
tp
u
t
ca
p
ac
ito
r
d
is
ch
ar
g
es
th
r
o
u
g
h
t
h
e
lo
ad
to
m
ain
ta
in
a
r
eg
u
lated
v
o
ltag
e
at
th
e
o
u
tp
u
t.
W
h
en
s
witch
S
2
i
s
tu
r
n
ed
o
n
,
th
e
in
d
u
cto
r
d
is
ch
ar
g
es
th
e
s
to
r
ed
en
er
g
y
,
g
en
e
r
atin
g
a
cu
r
r
en
t
th
at
ch
ar
g
es
th
e
o
u
tp
u
t
ca
p
ac
ito
r
.
Du
r
in
g
th
e
n
e
g
ativ
e
h
alf
cy
cle,
th
e
o
p
er
atio
n
o
f
th
e
T
B
B
R
i
s
s
im
ilar
ex
ce
p
t
th
e
r
o
le
o
f
s
witch
es
is
s
wap
p
ed
,
wh
er
e
S
1
b
ec
o
m
es
th
e
m
ain
s
witch
an
d
S
2
tu
r
n
s
in
to
a
co
m
p
lem
en
tar
y
s
witch
,
m
ea
n
wh
ile
Q
2
is
tu
r
n
ed
o
n
,
leav
in
g
Q
1
in
ac
tiv
e.
As
d
escr
ib
ed
,
th
e
T
B
B
R
h
as
a
s
im
p
le
c
o
n
f
i
g
u
r
atio
n
,
a
n
d
its
o
p
er
atio
n
d
ep
en
d
s
o
n
th
e
p
o
s
s
ib
le
co
m
b
in
atio
n
s
o
f
th
e
o
n
/o
f
f
s
witch
in
g
s
tates
o
f
th
e
h
ig
h
-
f
r
eq
u
e
n
cy
s
witch
es.
Su
b
s
eq
u
en
tly
,
t
h
e
c
o
n
tr
o
l
alg
o
r
ith
m
f
o
r
T
B
B
R
ca
n
b
e
s
i
m
p
lifie
d
as
s
elec
tin
g
f
r
o
m
th
e
p
o
s
s
ib
le
s
witch
in
g
s
tates
an
a
p
p
r
o
p
r
iate
o
n
e
th
at
f
u
lf
ills
a
p
r
ed
ef
in
ed
c
o
n
d
itio
n
.
B
y
tak
in
g
in
to
ac
co
u
n
t
th
e
f
in
ite
s
et
o
f
p
o
s
s
ib
le
s
witc
h
in
g
s
tates
(
o
n
ly
2
ap
p
licab
le
s
ets),
it
is
s
u
g
g
ested
th
at
f
in
ite
co
n
tr
o
l
s
et
m
o
d
el
p
r
ed
ictiv
e
c
o
n
tr
o
l
(
FC
S
-
MPC
)
is
a
v
e
r
y
p
o
wer
f
u
l
co
n
ce
p
t
f
o
r
d
esig
n
in
g
co
n
tr
o
ll
er
s
.
T
h
e
m
ain
ad
v
an
tag
e
o
f
th
is
co
n
tr
o
l
s
tr
ateg
y
is
th
at
th
e
s
witch
in
g
s
tates
ar
e
d
ir
ec
tly
co
n
s
id
er
e
d
as
th
e
c
o
n
tr
o
l
in
p
u
t
s
o
th
at
m
o
d
u
latio
n
s
tag
es
ar
e
d
e
d
u
cted
f
r
o
m
t
h
e
o
v
e
r
all
s
y
s
tem
.
Mo
r
eo
v
er
,
it
also
h
as
f
ast
d
y
n
am
ic
r
esp
o
n
s
e,
as
well
as
ea
s
y
in
clu
s
io
n
o
f
n
o
n
lin
ea
r
ities
an
d
co
n
s
tr
ain
ts
in
th
e
d
esig
n
o
f
co
n
tr
o
ller
,
m
ak
in
g
it
p
o
p
u
lar
in
d
i
g
ital
co
n
tr
o
l
o
f
p
o
wer
co
n
v
er
te
r
s
.
B
ased
o
n
d
is
cr
ete
m
o
d
el
o
f
th
e
co
n
v
er
ter
,
th
e
FC
S
-
MPC
ev
al
u
ates
a
co
s
t
f
u
n
ctio
n
in
ac
co
r
d
an
ce
with
th
e
co
n
tr
o
l
o
b
jecti
v
es
b
y
en
u
m
e
r
atin
g
all
p
o
s
s
ib
le
co
m
b
in
atio
n
s
o
f
s
witch
in
g
s
tates
o
v
er
a
f
in
ite
h
o
r
izo
n
.
T
h
e
s
witch
in
g
s
tate
th
at
r
esu
lts
in
th
e
m
in
im
al
v
alu
e
f
o
r
th
e
c
o
s
t f
u
n
ctio
n
is
s
elec
ted
as th
e
b
est s
w
itch
in
g
s
tate
with
in
th
e
n
ex
t s
witch
in
g
cy
cle.
Fig
u
r
e
1
.
C
o
n
f
ig
u
r
atio
n
o
f
a
s
in
g
le
-
p
h
ase
to
tem
-
p
o
le
b
r
id
g
el
ess
b
o
o
s
t PFC
r
ec
tifie
r
(
T
B
B
R
)
W
h
ile
F
C
S
-
MP
C
h
as
d
em
o
n
s
tr
ated
b
en
ef
its
in
v
ar
io
u
s
p
o
wer
elec
tr
o
n
ic
ap
p
licatio
n
s
,
its
u
s
e
in
T
B
B
R
s
y
s
tem
s
r
em
ain
s
r
elativ
ely
u
n
ex
p
lo
r
ed
—
p
a
r
ticu
lar
ly
with
r
eg
ar
d
to
ad
d
r
ess
in
g
ze
r
o
-
cr
o
s
s
in
g
d
is
to
r
tio
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
A
mo
d
el
p
r
ed
ictive
co
n
tr
o
l str
a
teg
y
fo
r
en
h
a
n
ce
p
erfo
r
ma
n
c
e
o
f to
tem
-
p
o
le
P
F
C
r
ec
tifi
er
(
Le
C
h
a
u
Du
y
)
1689
an
d
m
ain
tain
in
g
s
im
p
licity
in
co
n
tr
o
l
d
esig
n
.
T
o
f
ill
th
is
r
e
s
ea
r
ch
g
ap
,
th
is
p
ap
e
r
p
r
o
p
o
s
es
a
n
o
v
el
two
-
s
tep
p
r
ed
ictio
n
h
o
r
izo
n
FC
S
-
MPC
s
tr
ateg
y
tailo
r
ed
f
o
r
th
e
T
B
B
R
.
T
h
e
m
ain
co
n
tr
ib
u
tio
n
s
o
f
th
is
wo
r
k
ar
e
as
f
o
llo
ws:
−
Dev
elo
p
m
en
t
an
d
im
p
lem
e
n
ta
tio
n
o
f
a
two
-
s
tep
h
o
r
izo
n
FC
S
-
MPC
a
lg
o
r
ith
m
th
at
elim
in
ates
th
e
n
ee
d
f
o
r
m
o
d
u
latio
n
s
tag
es,
o
f
f
er
in
g
f
a
s
ter
d
y
n
am
ic
r
esp
o
n
s
e
an
d
s
im
p
lifie
d
co
n
tr
o
l stru
ctu
r
e.
−
E
f
f
ec
tiv
e
m
itig
atio
n
o
f
ze
r
o
-
c
r
o
s
s
in
g
cu
r
r
en
t
d
is
to
r
tio
n
,
r
es
u
ltin
g
in
im
p
r
o
v
ed
p
o
wer
q
u
a
lity
an
d
clea
n
er
in
p
u
t c
u
r
r
en
t w
av
ef
o
r
m
s
.
−
E
x
p
er
im
en
tal
v
alid
atio
n
u
s
in
g
a
3
.
3
k
W
,
4
0
0
Vd
c
h
ar
d
war
e
p
r
o
to
t
y
p
e
u
n
d
er
b
o
t
h
n
o
m
in
a
l
an
d
d
is
tu
r
b
ed
g
r
id
co
n
d
itio
n
s
,
d
e
m
o
n
s
tr
atin
g
th
e
p
r
ac
tical
f
ea
s
ib
ilit
y
o
f
t
h
e
p
r
o
p
o
s
ed
m
eth
o
d
.
−
Ach
iev
em
en
t
o
f
p
o
wer
f
ac
to
r
>0
.
9
9
a
n
d
in
p
u
t
cu
r
r
en
t
T
H
D
<5
%,
f
u
lly
c
o
m
p
lian
t
with
I
E
C
-
6
1
0
0
0
-
3
-
2
C
las
s
A
s
tan
d
ar
d
s
.
T
h
is
p
ap
er
is
co
n
d
u
cted
as
f
o
l
lo
ws
:
i)
Sectio
n
2
d
is
cu
s
s
es
th
e
o
p
er
atin
g
p
r
in
ci
p
les
o
f
th
e
T
B
B
R
an
d
lim
itatio
n
s
o
f
co
n
v
en
tio
n
al
PI
-
b
ased
co
n
tr
o
ller
s
ii)
Sectio
n
3
p
r
esen
ts
th
e
p
r
o
p
o
s
ed
FC
S
-
MP
C
ap
p
r
o
ac
h
,
in
clu
d
in
g
a
m
at
h
em
atica
l
p
r
e
d
ictiv
e
m
o
d
el,
co
s
t
f
u
n
ctio
n
d
esig
n
,
an
d
th
e
o
p
tim
izatio
n
r
o
u
tin
e
;
iii)
Sectio
n
4
p
r
o
v
id
es
a
f
f
ir
m
ativ
e
s
im
u
latio
n
as
well
as
ex
p
e
r
im
en
tal
r
esu
lts
th
at
v
alid
ate
th
e
ef
f
ec
tiv
en
ess
o
f
th
e
p
r
o
p
o
s
ed
co
n
tr
o
l stra
teg
y
; a
n
d
iv
)
Fin
ally
,
s
ec
tio
n
5
c
o
n
clu
d
es th
e
p
ap
er
an
d
o
u
tlin
es f
u
tu
r
e
r
esear
ch
d
ir
ec
tio
n
s
.
2.
ANALY
SI
S O
F
CI
RCUI
T
O
P
E
RAT
I
O
N
2
.
1
.
Ana
ly
s
is
o
f
T
B
B
R
co
nv
er
t
er
T
h
is
s
ec
tio
n
an
aly
ze
s
th
e
co
n
tin
u
o
u
s
-
tim
e
o
p
er
atio
n
o
f
th
e
T
B
B
R
ac
co
r
d
in
g
to
Kir
ch
h
o
f
f
’
s
laws
d
u
r
in
g
b
o
th
p
o
s
itiv
e
an
d
n
eg
a
tiv
e
h
alf
cy
cles
as
s
h
o
wn
in
Fig
u
r
e
s
2
(
a)
an
d
2
(
b
)
,
r
esp
ec
tiv
ely
,
in
ac
co
r
d
an
c
e
with
th
e
c
o
n
tr
o
l
s
witch
es
ac
tio
n
s
to
f
o
r
m
u
late
t
h
e
f
u
tu
r
e
g
r
id
cu
r
r
en
t
p
r
ed
ictio
n
as
a
f
u
n
ctio
n
o
f
its
p
r
esen
t
an
d
p
r
e
v
io
u
s
v
al
u
es.
As
s
h
o
wn
in
Fi
g
u
r
e
2
(
a)
,
d
u
r
i
n
g
th
e
p
o
s
i
ti
v
e
h
al
f
c
y
c
le
,
in
t
h
e
i
n
t
er
v
al
t
h
at
S
2
is
o
f
f
,
a
m
e
s
h
wit
h
t
h
e
in
d
u
ct
o
r
,
t
h
e
s
w
itc
h
S
1
,
t
h
e
s
witc
h
Q
1
,
a
n
d
th
e
g
r
i
d
v
o
lt
ag
e
s
o
u
r
ce
v
g
is
f
o
r
m
e
d
an
d
r
esu
lt
in
t
h
e
d
i
f
f
e
r
e
n
t
ial
eq
u
a
ti
o
n
,
as
(
1
)
.
=
;
=
−
1
(
1
)
C
o
n
tr
asti
n
g
ly
,
in
th
e
in
ter
v
al
th
at
S
2
is
o
n
,
th
e
cu
r
r
en
t
f
l
o
ws
th
r
o
u
g
h
t
h
e
s
witch
S
2
an
d
th
e
s
witch
Q
1
to
th
e
o
u
tp
u
t c
a
p
ac
ito
r
an
d
lo
ad
,
wh
i
ch
y
ield
s
as (
2
)
.
=
−
1
+
;
=
1
−
1
(
2
)
L
ik
ewise,
d
u
r
in
g
th
e
n
eg
ativ
e
h
alf
cy
cle
(
as
ca
n
b
e
s
ee
n
i
n
Fig
u
r
e
2
(
b
)
)
,
in
th
e
in
ter
v
a
l
th
at
S
2
i
s
o
f
f
,
th
e
cu
r
r
en
t f
lo
ws th
r
o
u
g
h
th
e
s
witch
S
1
an
d
th
e
s
witch
Q
2
to
th
e
o
u
tp
u
t c
ap
ac
ito
r
an
d
lo
ad
.
T
h
e
ex
p
r
ess
io
n
s
th
at
d
escr
ib
e
th
is
b
eh
av
i
o
r
as (
3
)
.
=
1
+
;
=
−
1
−
1
(
3
)
C
o
n
v
er
s
ely
,
in
th
e
in
ter
v
al
th
a
t
S
2
is
o
n
,
th
e
in
p
u
t
cu
r
r
en
t
f
l
o
ws
th
r
o
u
g
h
th
e
s
witch
S
2
an
d
th
e
d
io
d
e
Q
2
,
wh
ile
th
e
o
u
tp
u
t
v
o
ltag
e
is
h
eld
s
tead
y
b
y
th
e
o
u
tp
u
t
ca
p
ac
ito
r
.
T
h
is
o
p
er
atio
n
ca
n
b
e
ex
p
r
ess
ed
in
ter
m
s
o
f
(
4
)
.
=
;
=
−
1
(
4
)
Oth
er
wis
e,
ap
p
ly
in
g
f
o
r
war
d
E
u
ler
’
s
m
eth
o
d
to
th
e
cu
r
r
en
t
ch
a
n
g
e
ex
p
r
ess
io
n
an
d
v
o
ltag
e
ch
a
n
g
e
ex
p
r
ess
io
n
f
o
r
th
e
s
am
p
lin
g
ti
m
e
ts
,
th
e
d
is
cr
ete
-
tim
e
ap
p
r
o
x
im
atio
n
ca
n
b
e
o
b
tain
ed
as (
5
)
.
=
(
+
1
)
−
(
)
;
=
(
+
1
)
−
(
)
(
5
)
W
h
er
e
‘
’
r
ep
r
esen
ts
th
e
cu
r
r
e
n
t step
an
d
‘
+
1
’
r
ep
r
esen
ts
th
e
n
e
x
t step
.
2
.
2
.
Co
nv
ent
i
o
na
l P
I
co
ntr
o
l
ler
f
o
r
po
wer
f
a
c
t
o
r
co
rr
ec
t
i
o
n
A
co
n
v
en
tio
n
al
p
u
ls
e
wid
th
m
o
d
u
latio
n
(
PW
M)
alg
o
r
ith
m
was
p
r
esen
ted
f
o
r
g
en
e
r
atin
g
th
e
g
at
e
d
r
iv
in
g
s
ig
n
als
o
f
h
ig
h
f
r
eq
u
e
n
cy
s
witch
in
g
d
ev
ices.
T
h
e
c
o
n
tr
o
ller
co
n
s
is
ts
o
f
two
co
n
tr
o
l
lo
o
p
s
:
th
e
v
o
ltag
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
3
,
Sep
tem
b
er
20
25
:
168
7
-
1
70
0
1690
lo
o
p
c
o
n
tr
o
ller
wh
ic
h
r
e
g
u
late
s
th
e
o
u
tp
u
t
v
o
ltag
e
o
f
th
e
T
B
B
R
an
d
th
e
cu
r
r
e
n
t
lo
o
p
co
n
t
r
o
ller
wh
ich
m
ak
es
th
e
g
r
id
cu
r
r
en
t
wav
ef
o
r
m
t
o
b
e
i
d
en
tical
to
th
e
g
r
id
v
o
ltag
e
wav
ef
o
r
m
.
I
n
v
o
ltag
e
lo
o
p
,
t
h
e
DC
o
u
tp
u
t
v
o
ltag
e
is
attain
ed
an
d
s
u
b
tr
ac
ted
f
r
o
m
th
e
d
er
iv
e
d
DC
o
u
tp
u
t
v
o
ltag
e,
an
d
th
e
er
r
o
r
lately
p
ass
es
th
r
o
u
g
h
a
PI
co
n
tr
o
ller
to
ac
q
u
ir
e
th
e
eq
u
iv
alen
t
in
p
u
t
co
n
d
u
ctan
ce
o
f
th
e
co
n
v
er
ter
.
T
h
e
g
r
id
cu
r
r
en
t
r
ef
er
e
n
ce
i
s
g
en
er
ated
b
y
m
u
ltip
ly
in
g
th
e
eq
u
iv
alen
t in
p
u
t c
o
n
d
u
ctan
ce
with
th
e
ad
ju
s
ted
g
r
id
v
o
ltag
e
to
s
er
v
e
as th
e
in
p
u
t
o
f
cu
r
r
en
t
lo
o
p
.
I
n
th
e
cu
r
r
en
t
lo
o
p
,
a
n
o
th
er
PI
co
n
tr
o
ller
v
ar
ies
th
e
d
u
ty
cy
cle
o
f
th
e
s
w
itch
es
u
n
til
th
e
g
r
id
cu
r
r
en
t
r
ea
c
h
es
th
e
r
ef
er
en
ce
s
ig
n
al.
T
o
im
p
r
o
v
e
th
e
q
u
ality
o
f
cu
r
r
en
t
co
n
tr
o
l,
a
d
u
ty
-
r
atio
f
ee
d
f
o
r
wa
r
d
is
in
tr
o
d
u
ce
d
a
n
d
c
o
m
b
in
e
d
w
ith
th
e
o
u
tp
u
t
o
f
cu
r
r
en
t
lo
o
p
co
n
tr
o
ller
.
T
h
e
c
o
m
p
le
m
en
t
o
f
d
u
ty
-
r
atio
f
ee
d
f
o
r
war
d
allo
ws
th
e
PI
c
o
n
tr
o
ller
to
ad
a
p
t
o
n
ly
a
s
m
all
v
alu
e
o
f
in
p
u
t
cu
r
r
en
t
e
r
r
o
r
,
an
d
th
u
s
lo
w
in
p
u
t
cu
r
r
en
t
d
is
to
r
tio
n
ca
n
b
e
m
ain
tain
ed
b
y
av
o
id
an
ce
o
f
h
i
g
h
c
o
n
tr
o
ller
g
ain
.
T
h
e
s
ch
em
atic
d
iag
r
am
o
f
v
o
ltag
e
-
cu
r
r
en
t lo
o
p
PW
M
co
n
tr
o
ller
i
n
clu
d
in
g
d
u
ty
-
r
atio
f
ee
d
f
o
r
wa
r
d
is
p
r
esen
ted
in
Fig
u
r
e
3
.
(
a)
(
b
)
Fig
u
r
e
2
.
C
u
r
r
e
n
t f
lo
ws in
T
B
B
R
d
u
r
in
g
(
a)
p
o
s
itiv
e
h
alf
cy
cle
an
d
(
b
)
n
e
g
ativ
e
h
alf
c
y
cle
Fig
u
r
e
3
.
C
o
n
tr
o
l d
iag
r
am
o
f
v
o
ltag
e
-
cu
r
r
e
n
t lo
o
p
PW
M
co
n
tr
o
ller
f
o
r
T
B
B
R
3.
P
RO
P
O
SE
D
F
CS
-
M
P
C
F
O
R
P
O
WE
R
F
AC
T
O
R
CO
R
RE
C
T
I
O
N
T
h
e
p
r
o
p
o
s
ed
PF
C
co
n
tr
o
l
d
iag
r
am
f
o
r
T
B
B
R
is
s
h
o
wn
in
Fig
u
r
e
4
.
An
FC
S
-
MPC
s
ch
em
e
is
em
p
lo
y
ed
t
o
g
en
er
ate
th
e
d
r
iv
i
n
g
s
ig
n
als f
o
r
h
ig
h
-
f
r
e
q
u
en
c
y
s
witch
es.
B
y
s
elec
tin
g
a
p
r
o
p
e
r
co
s
t f
u
n
ctio
n
,
t
h
e
o
u
tp
u
t
v
o
ltag
e
V
o
ca
n
b
e
r
eg
u
lated
,
an
d
th
e
p
o
wer
f
ac
to
r
co
r
r
ec
tio
n
o
f
th
e
in
p
u
t
cu
r
r
en
t
i
L
ca
n
b
e
r
ea
lized
.
FC
S
-
MP
C
o
f
f
er
s
p
r
ec
is
e
an
d
d
y
n
am
ic
co
n
tr
o
l
o
f
th
e
h
ig
h
-
f
r
eq
u
en
c
y
s
witch
es,
allo
win
g
f
o
r
f
ast
r
esp
o
n
s
e
to
lo
ad
ch
an
g
es
an
d
g
r
id
d
is
tu
r
b
an
ce
s
,
wh
ich
en
s
u
r
es
ef
f
icien
t
p
o
wer
co
n
v
er
s
io
n
an
d
m
in
im
izes
en
er
g
y
lo
s
s
es.
B
esid
es,
th
e
co
n
d
u
ct
tim
e
o
f
th
e
lin
e
-
f
r
eq
u
e
n
cy
s
witch
es
is
d
eter
m
in
ed
b
y
a
ze
r
o
cr
o
s
s
in
g
d
etec
tio
n
(
Z
C
D)
s
ch
em
e,
wh
er
e
th
e
g
r
id
v
o
ltag
e
is
s
am
p
led
an
d
e
v
alu
ated
to
g
e
n
er
ate
t
h
e
s
witch
g
atin
g
s
ig
n
als.
B
y
en
s
u
r
in
g
p
r
o
p
er
s
y
n
ch
r
o
n
izatio
n
with
t
h
e
g
r
id
f
r
e
q
u
en
c
y
,
Z
C
D
m
in
i
m
izes
th
e
r
is
k
o
f
m
alf
u
n
ctio
n
an
d
p
o
wer
q
u
ality
is
s
u
es.
T
h
e
d
etailed
im
p
lem
en
tatio
n
o
f
th
e
FC
S
-
MPC
will b
e
illu
s
tr
ated
in
th
e
f
o
llo
win
g
:
3
.
1
.
P
re
dict
iv
e
curr
ent
m
o
d
el
T
h
e
p
r
e
d
icted
g
r
id
cu
r
r
e
n
t in
t
h
e
in
s
tan
t ‘
+
1
’
with
r
esp
ec
t to
th
e
p
o
s
itiv
e
h
alf
cy
cle
is
as (
6
)
,
(
+
1
)
=
(
)
−
2
(
)
+
(
)
,
2
∈
{
0
,
1
}
(
6
)
a
n
d
,
f
o
r
th
e
n
eg
ativ
e
h
alf
cy
cl
e,
th
e
p
r
e
d
icted
in
d
u
cto
r
c
u
r
r
e
n
t is
as (
7
)
.
(
+
1
)
=
(
)
+
2
(
)
+
(
)
,
2
∈
{
0
,
1
}
(
7
)
I
n
th
e
s
am
e
m
a
n
n
er
,
t
h
e
p
r
e
d
i
cted
g
r
id
c
u
r
r
en
t i
n
th
e
in
s
tan
t
‘
+
2
’
ca
n
b
e
o
b
tain
e
d
as
(
8
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
A
mo
d
el
p
r
ed
ictive
co
n
tr
o
l str
a
teg
y
fo
r
en
h
a
n
ce
p
erfo
r
ma
n
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e
o
f to
tem
-
p
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le
P
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ec
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er
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h
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(
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−
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(
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Wi
th
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(
+
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(
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(
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an
d
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(
+
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(
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3
.
2
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Ref
er
ence
curr
ent
estima
t
io
n
As
m
en
tio
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ed
p
r
ev
io
u
s
ly
,
t
h
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co
n
tr
o
l
alg
o
r
ith
m
f
o
r
T
B
B
R
s
h
o
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ld
d
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iv
e
th
e
g
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id
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r
r
e
n
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p
er
f
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tly
in
p
h
ase
with
th
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g
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v
o
ltag
e
s
o
th
at
t
h
e
m
a
x
im
u
m
p
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wer
tr
an
s
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er
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n
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e
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ea
lized
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ity
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A
p
p
l
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g
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m
s
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as
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s
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e
o
f
m
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i
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it
y
,
t
h
e
g
r
i
d
c
u
r
r
e
n
t
r
e
f
e
r
e
n
c
e
c
a
n
b
e
e
s
t
a
b
l
i
s
h
e
d
as
(
1
1
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.
=
2
(
1
1
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W
h
er
e
is
th
e
d
esire
d
DC
o
u
t
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t
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d
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th
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m
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al
r
m
s
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e
o
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th
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T
r
an
s
f
o
r
m
in
g
in
to
d
is
cr
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o
r
m
,
(
1
1
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ca
n
b
e
r
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itten
as (
1
2
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(
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=
2
(
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(
1
2
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Ob
v
io
u
s
ly
,
t
h
e
g
r
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c
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r
r
en
t
r
e
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r
l
y
s
ca
le
d
to
t
h
e
ch
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n
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e
o
f
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u
tp
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t
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er
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d
in
h
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en
tly
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s
ted
r
e
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d
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g
th
e
o
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atin
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e
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v
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t
h
e
wav
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m
o
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th
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g
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t
r
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s
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o
r
r
esp
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n
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th
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v
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r
m
o
f
th
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g
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s
is
ten
tly
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As
th
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g
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s
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d
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t
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o
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n
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to
b
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u
t
in
to
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f
ec
t,
in
wh
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th
e
g
r
id
c
u
r
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n
t
r
ef
er
en
ce
ex
clu
s
iv
ely
k
ee
p
s
tr
ac
k
o
f
th
e
f
u
n
d
am
en
ta
l
h
ar
m
o
n
ic
o
f
th
e
g
r
i
d
v
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ltag
e
.
T
h
en
,
th
e
g
r
id
cu
r
r
en
t
r
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e
r
e
n
ce
ca
n
ca
r
r
y
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n
a
tr
u
e
s
in
u
s
o
id
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ef
o
r
m
d
esp
ite
th
e
d
is
to
r
tio
n
in
th
e
elec
tr
ic
p
o
wer
lin
e.
3
.
3
.
Co
s
t
f
un
ct
io
n a
nd
o
ptim
iza
t
io
n a
pp
ro
a
ch
T
h
e
two
-
s
tep
p
r
ed
ictio
n
FC
S
-
MPC
s
tr
ateg
y
p
r
ed
icts
th
e
b
eh
av
io
r
o
f
th
e
T
B
B
R
o
n
th
e
n
ex
t
two
s
am
p
lin
g
in
ter
v
als
with
two
p
r
im
ar
y
o
b
jectiv
es:
i)
ac
cu
r
ate
tr
ac
k
in
g
o
f
th
e
r
e
f
er
en
ce
g
r
id
c
u
r
r
en
t
f
o
r
p
o
wer
f
ac
to
r
co
r
r
ec
tio
n
an
d
o
u
tp
u
t
v
o
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e
r
eg
u
latio
n
,
an
d
ii)
m
in
im
izatio
n
o
f
g
r
id
cu
r
r
en
t
h
a
r
m
o
n
ics
to
im
p
r
o
v
e
p
o
wer
q
u
ality
.
T
o
ac
h
iev
e
t
h
ese
o
b
jectiv
es,
t
h
e
c
o
s
t
f
u
n
ctio
n
ass
o
ciate
d
with
th
e
tw
o
-
s
tep
p
r
ed
ictio
n
is
ex
p
r
ess
ed
as (
1
3
)
.
=
∑
[
(
+
)
−
(
+
)
]
2
2
=
1
+
[
(
+
)
−
(
+
−
1
)
]
2
(
1
3
)
Fig
u
r
e
4
.
Pro
p
o
s
ed
PF
C
co
n
tr
o
l b
lo
ck
d
iag
r
am
o
f
T
B
B
R
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
3
,
Sep
tem
b
er
20
25
:
168
7
-
1
70
0
1692
T
h
e
f
ir
s
t
ter
m
,
wh
ich
m
in
im
izes
th
e
er
r
o
r
b
etwe
en
th
e
p
r
ed
icted
g
r
id
cu
r
r
en
t
(
+
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an
d
its
r
ef
er
en
ce
(
+
)
,
en
s
u
r
es
th
at
th
e
c
o
n
v
er
ter
d
eliv
er
s
th
e
r
eq
u
ir
ed
p
o
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t
o
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eg
u
late
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e
o
u
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t
v
o
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e
p
r
o
p
er
l
y
.
W
ith
o
u
t
th
is
ter
m
,
th
e
g
r
id
cu
r
r
e
n
t
wo
u
ld
n
o
t
f
o
ll
o
w
th
e
d
esire
d
tr
ajec
to
r
y
,
lea
d
in
g
to
p
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o
r
v
o
ltag
e
r
eg
u
latio
n
.
T
h
e
s
ec
o
n
d
ter
m
p
en
alize
s
r
ap
id
v
ar
iatio
n
s
in
th
e
g
r
id
cu
r
r
e
n
t,
r
ed
u
cin
g
h
i
g
h
-
f
r
eq
u
en
cy
h
ar
m
o
n
ics
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d
en
s
u
r
in
g
a
s
m
o
o
th
wav
ef
o
r
m
.
W
ith
o
u
t
th
is
ter
m
,
th
e
c
o
n
tr
o
ller
m
ay
ag
g
r
ess
iv
ely
s
w
itch
s
tates,
ca
u
s
in
g
h
ig
h
T
HD
an
d
in
s
tab
ilit
y
in
p
o
wer
d
eliv
er
y
.
B
y
co
m
b
in
in
g
b
o
th
te
r
m
s
,
th
e
co
s
t
f
u
n
ctio
n
en
ab
les
a
well
-
r
eg
u
lated
o
u
t
p
u
t
v
o
ltag
e
wh
il
e
m
ain
tain
in
g
a
lo
w
-
d
is
to
r
tio
n
g
r
id
cu
r
r
e
n
t.
T
h
e
s
eq
u
en
ce
m
in
im
izin
g
th
e
co
s
t
f
u
n
ctio
n
is
s
elec
ted
an
d
em
p
lo
y
ed
in
th
e
T
B
B
R
d
u
r
in
g
th
e
n
ex
t sam
p
lin
g
in
ter
v
al.
T
h
e
weig
h
tin
g
f
ac
to
r
in
th
e
c
o
s
t
f
u
n
ctio
n
o
f
FC
S
-
MPC
p
la
y
s
a
cr
u
cial
r
o
le
in
b
alan
cin
g
cu
r
r
en
t
tr
ac
k
in
g
ac
cu
r
ac
y
an
d
h
ar
m
o
n
ic
m
in
im
izatio
n
,
d
i
r
ec
tly
in
f
lu
en
cin
g
o
u
tp
u
t
v
o
ltag
e
r
eg
u
latio
n
an
d
p
o
we
r
q
u
ality
.
I
ts
tu
n
in
g
is
ess
en
tial,
as
an
o
v
e
r
ly
s
m
all
lead
s
to
f
ast
b
u
t
n
o
is
y
cu
r
r
en
t
tr
ac
k
in
g
with
h
ig
h
T
HD,
wh
ile
an
e
x
ce
s
s
iv
ely
lar
g
e
r
esu
lts
in
a
s
m
o
o
t
h
er
c
u
r
r
en
t
b
u
t
s
lo
wer
r
esp
o
n
s
e
to
l
o
ad
c
h
a
n
g
es.
A
p
r
ac
tical
ap
p
r
o
ac
h
to
esti
m
atin
g
is
g
iv
en
b
y
th
e
f
o
r
m
u
la
=
,
wh
er
e
(
g
r
id
in
d
u
ctan
ce
)
a
f
f
ec
ts
n
atu
r
al
cu
r
r
en
t
s
m
o
o
th
in
g
,
(
s
am
p
lin
g
tim
e)
d
eter
m
in
es
co
n
tr
o
l
r
ea
ctio
n
s
p
ee
d
,
an
d
(
o
u
tp
u
t
v
o
ltag
e)
in
f
lu
en
ce
s
p
o
we
r
tr
an
s
f
er
s
tab
ilit
y
.
T
h
e
em
p
ir
ical
f
ac
to
r
(
ty
p
ically
b
etwe
e
n
0
.
1
a
n
d
1
)
is
ad
ju
s
ted
th
r
o
u
g
h
s
im
u
latio
n
a
n
d
ex
p
er
im
en
tal
v
alid
atio
n
to
ac
h
iev
e
an
o
p
tim
al
tr
a
d
e
-
o
f
f
.
Hig
h
er
n
atu
r
ally
s
m
o
o
th
s
c
u
r
r
en
t
,
allo
win
g
a
lo
wer
,
wh
er
ea
s
s
h
o
r
ter
im
p
r
o
v
es
c
o
n
tr
o
l
ac
cu
r
ac
y
,
r
e
d
u
cin
g
th
e
n
ee
d
f
o
r
ad
d
itio
n
al
s
m
o
o
t
h
in
g
.
A
h
ig
h
e
r
in
cr
ea
s
es
p
o
wer
f
lu
ctu
atio
n
s
,
n
ec
ess
itatin
g
a
lar
g
er
f
o
r
b
etter
s
tab
ilit
y
.
A
well
-
o
p
tim
ized
en
s
u
r
es
lo
w
T
HD,
f
ast o
u
tp
u
t v
o
ltag
e
s
tab
i
lizatio
n
,
an
d
c
o
m
p
lian
ce
with
p
o
wer
q
u
ality
s
tan
d
ar
d
s
.
C
u
r
r
en
t
r
ef
er
e
n
ce
s
at
f
u
tu
r
e
ti
m
e
s
tep
s
‘
+
1
’
an
d
‘
+
2
’
,
wh
ich
is
ad
ap
ted
f
r
o
m
(
1
1
)
,
ca
n
b
e
d
er
iv
ed
b
y
ex
t
r
ap
o
latin
g
f
r
o
m
p
ast an
d
p
r
esen
t
r
ef
er
en
ce
v
al
u
es a
n
d
f
in
ally
s
h
o
w
u
p
in
(1
4
)
an
d
(
1
5
).
(
+
1
)
=
2
(
+
1
)
=
2
[
3
(
)
−
3
(
−
1
)
+
(
−
2
)
]
(1
4
)
(
+
2
)
=
2
(
+
2
)
=
2
[
6
(
)
−
8
(
−
1
)
+
3
(
−
2
)
]
(1
5
)
Du
e
to
a
v
er
y
s
m
all
p
r
ed
ictio
n
h
o
r
izo
n
o
f
FC
S
-
MPC
(
N
=
2
)
as
well
as
ad
m
is
s
ib
le
s
witch
in
g
s
tates
(
S
=
2
)
,
th
e
ex
h
a
u
s
tiv
e
s
ea
r
ch
is
a
u
s
ef
u
l
m
eth
o
d
to
s
o
lv
e
t
h
e
m
in
im
izatio
n
p
r
o
b
lem
ex
p
o
s
ed
b
y
(
1
3
)
.
T
h
is
m
eth
o
d
e
n
u
m
er
ates
all
p
o
s
s
ib
le
s
o
lu
tio
n
s
ets
an
d
ch
ec
k
s
ea
ch
o
n
e
to
s
ee
if
it
s
atis
f
ies
th
e
p
r
o
b
lem
'
s
co
n
d
itio
n
s
.
T
h
e
o
n
e
with
th
e
s
m
allest
co
s
t
is
ch
o
s
en
as
th
e
co
n
tr
o
l
in
p
u
t.
Fo
r
ev
e
r
y
tim
e
-
s
tep
,
th
e
alg
o
r
ith
m
o
b
ey
s
th
e
f
o
llo
win
g
s
tep
s
:
i)
Dete
r
m
in
e
all
p
o
s
s
ib
le
s
witch
in
g
s
tates
o
v
er
th
e
p
r
e
d
ictio
n
h
o
r
izo
n
;
ii)
Fo
r
ea
ch
o
f
th
ese
s
witch
in
g
s
tates,
co
m
p
u
te
th
e
p
r
e
d
icted
g
r
id
cu
r
r
e
n
t
ac
co
r
d
in
g
to
(
6
)
-
(
9
)
an
d
th
e
p
r
ed
icted
g
r
id
cu
r
r
en
t
r
ef
e
r
en
ce
ac
co
r
d
in
g
to
(
1
4
)
an
d
(1
5
)
;
iii)
Fo
r
ea
ch
s
witch
in
g
s
tate,
co
m
p
u
te
th
e
co
s
t
J
ac
co
r
d
in
g
to
(
1
3
)
;
an
d
iv
)
C
h
o
o
s
e
th
e
s
witch
in
g
s
tate
wh
ich
m
in
im
izes
th
e
co
s
t
an
d
ap
p
ly
to
th
e
T
B
B
R
.
T
h
e
p
r
o
ce
d
u
r
e
f
o
r
s
elec
tin
g
th
e
o
p
tim
al
s
witch
in
g
s
eq
u
e
n
ce
is
s
u
m
m
ar
ized
i
n
Fig
u
r
e
5
.
3
.
4
.
Ana
ly
s
is
a
nd
cha
lleng
es
o
f
F
CS
-
M
P
C
Un
lik
e
co
n
v
en
tio
n
al
li
n
ea
r
c
o
n
tr
o
ller
s
,
FC
S
-
MPC
is
in
h
er
en
tly
n
o
n
lin
ea
r
a
n
d
o
p
er
ates
in
a
d
is
cr
ete
-
tim
e
d
o
m
ain
,
m
ak
i
n
g
s
tab
ilit
y
an
aly
s
is
m
o
r
e
co
m
p
le
x
.
Ho
w
ev
er
,
s
tab
ilit
y
ca
n
b
e
ass
ess
ed
th
r
o
u
g
h
L
y
ap
u
n
o
v
-
b
ased
m
eth
o
d
s
,
wh
er
e
a
L
y
ap
u
n
o
v
ca
n
d
i
d
ate
f
u
n
ctio
n
was
s
elec
ted
b
ased
o
n
th
e
d
ev
iatio
n
o
f
th
e
s
tate
f
r
o
m
its
r
ef
er
en
ce
,
as in
(
1
6
)
.
(
)
=
1
2
(
(
)
−
,
(
)
)
2
(
1
6
)
T
h
e
d
if
f
e
r
en
ce
in
t
h
e
L
y
a
p
u
n
o
v
f
u
n
ctio
n
b
etwe
en
two
s
u
cc
ess
iv
e
tim
e
s
tep
s
is
as (
1
7
)
.
∆
=
(
+
1
)
−
(
)
(
1
7
)
Su
b
s
titu
tin
g
(
+
1
)
f
r
o
m
th
e
s
y
s
tem
eq
u
atio
n
,
as (
1
8
)
.
∆
=
1
2
(
(
+
1
)
−
,
(
+
1
)
)
2
−
1
2
(
(
)
−
,
(
)
)
2
(
1
8
)
FC
S
-
MP
C
s
elec
ts
th
e
co
n
tr
o
l
ac
tio
n
th
at
p
r
o
d
u
ce
s
th
e
s
m
allest
p
r
ed
icted
er
r
o
r
in
f
u
tu
r
e
s
tates,
en
s
u
r
in
g
th
at
th
e
d
ev
iatio
n
f
r
o
m
th
e
r
ef
e
r
en
ce
is
r
ed
u
ce
d
in
ea
ch
s
tep
.
I
t
f
o
llo
ws th
at,
as sh
o
wn
in
(
1
9
)
a
n
d
(
2
0
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
A
mo
d
el
p
r
ed
ictive
co
n
tr
o
l str
a
teg
y
fo
r
en
h
a
n
ce
p
erfo
r
ma
n
c
e
o
f to
tem
-
p
o
le
P
F
C
r
ec
tifi
er
(
Le
C
h
a
u
Du
y
)
1693
|
(
+
1
)
−
,
(
+
1
)
|
<
|
(
)
−
,
(
)
|
(
1
9
)
W
h
ich
im
p
lies
as (
2
0
)
.
∆
=
(
+
1
)
−
(
)
<
0
(
2
0
)
T
h
u
s
,
th
e
L
y
ap
u
n
o
v
f
u
n
ctio
n
is
m
o
n
o
to
n
ically
d
ec
r
ea
s
in
g
,
p
r
o
v
in
g
asy
m
p
to
tic
s
tab
ilit
y
.
T
h
e
weig
h
tin
g
f
ac
to
r
h
elp
s
in
e
n
s
u
r
in
g
a
s
m
o
o
th
c
u
r
r
en
t
r
esp
o
n
s
e,
f
u
r
th
e
r
p
r
ev
e
n
tin
g
in
s
tab
ilit
y
.
T
o
f
u
r
th
er
e
n
h
an
ce
s
tab
ilit
y
,
ad
ap
tiv
e
t
u
n
in
g
o
f
ca
n
b
e
im
p
lem
en
ted
,
wh
er
e
its
v
alu
e
is
ad
ju
s
ted
d
y
n
am
ically
b
ased
o
n
s
y
s
tem
co
n
d
itio
n
s
.
Ad
d
itio
n
ally
,
im
p
l
em
en
tin
g
co
n
s
tr
ain
t
h
an
d
lin
g
(
s
u
ch
as
cu
r
r
en
t
lim
its
)
en
s
u
r
e
s
th
at
th
e
co
n
tr
o
ller
d
o
es n
o
t d
r
iv
e
th
e
s
y
s
tem
in
to
u
n
s
tab
le
r
eg
io
n
s
.
T
h
e
im
p
lem
en
tatio
n
o
f
FC
S
-
MPC
im
p
o
s
es
s
ig
n
if
ican
t
co
m
p
u
tatio
n
al
r
e
q
u
ir
em
e
n
ts
d
u
e
to
th
e
n
ee
d
f
o
r
r
ea
l
-
tim
e
c
u
r
r
en
t
p
r
ed
ictio
n
,
co
s
t
f
u
n
ctio
n
ev
alu
atio
n
,
a
n
d
o
p
tim
al
s
witch
in
g
s
tate
s
elec
tio
n
with
in
ea
ch
co
n
tr
o
l
cy
cle.
Un
lik
e
tr
ad
itio
n
al
co
n
tr
o
ller
s
s
u
ch
as
PI
o
r
PR
co
n
tr
o
ller
s
,
wh
ich
r
ely
o
n
s
im
p
le
alg
eb
r
aic
ca
lcu
latio
n
s
,
FC
S
-
M
PC
r
eq
u
i
r
es
s
o
lv
in
g
d
is
cr
ete
-
tim
e
s
y
s
t
em
eq
u
atio
n
s
an
d
ev
alu
atin
g
m
u
ltip
le
s
witch
in
g
s
ce
n
ar
io
s
at
ea
ch
tim
e
s
tep
.
T
h
e
co
m
p
u
tatio
n
al
b
u
r
d
en
i
n
cr
ea
s
es
with
th
e
p
r
ed
ictio
n
h
o
r
izo
n
an
d
th
e
n
u
m
b
e
r
o
f
s
witch
in
g
s
tates
co
n
s
id
er
e
d
.
I
n
th
is
s
tu
d
y
,
a
two
-
s
tep
p
r
e
d
ictio
n
h
o
r
izo
n
with
two
p
o
s
s
ib
le
s
witch
in
g
s
tates
p
er
s
tep
r
esu
lts
in
an
ac
ce
p
tab
le
co
m
p
u
tatio
n
tim
e.
T
o
m
ee
t
th
ese
d
em
an
d
s
,
h
ig
h
-
s
p
ee
d
d
ig
ital
s
ig
n
al
p
r
o
ce
s
s
o
r
s
(
DSPs
)
o
r
f
ield
-
p
r
o
g
r
am
m
ab
le
g
ate
ar
r
a
y
s
(
FP
GAs)
ar
e
o
f
ten
r
eq
u
ir
e
d
.
T
h
e
s
am
p
lin
g
tim
e
d
eter
m
in
es
th
e
m
ax
im
u
m
all
o
wab
le
co
m
p
u
tatio
n
tim
e
p
e
r
cy
cle
s
o
th
at
if
th
e
e
x
ec
u
tio
n
tim
e
ex
ce
ed
s
th
is
lim
it,
th
e
co
n
tr
o
ller
will f
ail
to
u
p
d
ate
s
witch
in
g
s
tates
in
r
ea
l tim
e,
lead
in
g
to
p
er
f
o
r
m
an
ce
d
eg
r
ad
atio
n
.
On
c
e
s
ettled
,
FC
S
-
MP
C
p
r
o
v
id
es
ab
ilit
y
to
d
ir
ec
tly
o
p
tim
ize
s
witch
in
g
d
ec
is
io
n
s
with
o
u
t
r
eq
u
ir
in
g
a
m
o
d
u
latio
n
s
tag
e,
o
f
f
er
in
g
s
u
p
er
i
o
r
d
y
n
am
ic
r
esp
o
n
s
e
an
d
p
o
wer
f
ac
to
r
c
o
r
r
ec
tio
n
.
Fig
u
r
e
5
.
T
h
e
p
r
o
ce
d
u
r
e
f
o
r
th
e
ex
h
au
s
tiv
e
s
ea
r
ch
o
p
tim
izatio
n
ap
p
r
o
ac
h
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
4
.
1
.
Sim
ula
t
i
o
n
r
esu
lt
s
T
o
v
alid
ate
th
e
th
e
o
r
etica
l a
n
a
ly
s
is
,
a
3
.
3
k
W
T
B
B
R
h
as b
ee
n
d
esig
n
ed
u
s
in
g
PS
I
M®
,
wh
er
e
th
e
k
ey
p
ar
am
eter
s
o
f
th
e
co
n
v
er
ter
a
r
e
lis
ted
in
T
ab
le
1
.
T
h
e
co
r
r
esp
o
n
d
in
g
g
atin
g
s
ig
n
als
o
f
a
ll
ac
tiv
e
s
witch
e
s
d
u
r
in
g
o
n
e
g
r
id
c
y
cle
ar
e
d
is
p
lay
ed
in
Fig
u
r
e
6
.
Fig
u
r
e
7
s
h
o
ws
th
e
s
tead
y
-
s
tate
wav
ef
o
r
m
o
f
th
e
g
r
i
d
-
s
id
e
cu
r
r
en
t
an
d
g
r
id
-
s
id
e
v
o
ltag
e
at
f
u
ll
lo
ad
with
th
e
im
p
lem
e
n
tatio
n
o
f
th
e
FC
S
-
MPC
m
eth
o
d
.
I
t
i
n
d
icate
s
th
at
th
e
T
B
B
R
ac
h
iev
es
a
h
ig
h
-
p
o
wer
f
ac
to
r
o
f
ar
o
u
n
d
0
.
9
9
with
a
l
o
w
in
p
u
t
c
u
r
r
e
n
t
T
HD
o
f
2
.
6
7
%
ap
p
r
o
x
im
ately
.
4
.
2
.
E
x
perim
ent
a
l r
esu
lt
s
T
o
v
e
r
if
y
th
e
t
h
eo
r
etica
l
r
esu
lts
o
f
th
e
s
y
s
tem
,
s
o
m
e
ex
p
er
i
m
en
ts
wer
e
c
o
n
d
u
cted
u
s
in
g
t
h
e
3
.
3
k
W
to
tem
-
p
o
le
b
r
id
g
eless
b
o
o
s
t
PF
C
co
n
v
er
ter
p
r
o
to
ty
p
e
.
T
h
e
k
ey
p
ar
am
eter
s
o
f
th
is
p
r
o
t
o
ty
p
e
a
r
e
s
h
o
wn
in
T
ab
le
2
.
Par
am
eter
s
u
s
ed
i
n
th
e
ex
p
er
im
en
t
h
ad
a
s
lig
h
t
t
o
ler
an
ce
d
u
r
i
n
g
th
e
o
p
er
atio
n
,
an
d
th
e
o
p
tim
al
tu
n
in
g
v
alu
e
λ
p
ac
h
iev
ed
th
r
o
u
g
h
th
e
s
im
u
latio
n
was r
ec
alcu
l
ated
an
d
a
p
p
lied
to
t
h
e
ex
p
e
r
i
m
en
t.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
3
,
Sep
tem
b
er
20
25
:
168
7
-
1
70
0
1694
Fig
u
r
e
8
illu
s
tr
ates
th
e
e
n
tir
e
s
tr
u
ctu
r
e
o
f
th
e
p
r
o
p
o
s
ed
to
tem
-
p
o
le
PF
C
r
ec
tifie
r
s
y
s
tem
.
T
h
e
T
MS3
2
0
F2
8
3
7
9
D
DSP
co
llects
v
o
ltag
e
an
d
cu
r
r
en
t
s
ig
n
als
v
ia
ADCs
,
p
r
o
ce
s
s
es
th
em
th
r
o
u
g
h
a
p
r
e
d
ictiv
e
m
o
d
el
an
d
c
o
s
t
f
u
n
ctio
n
m
in
im
izatio
n
,
an
d
g
e
n
er
ates
o
p
ti
m
ized
s
witch
in
g
s
tates
f
o
r
t
h
e
d
r
i
v
er
b
o
ar
d
to
ac
h
iev
e
h
ig
h
p
o
we
r
q
u
ality
.
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h
e
co
m
p
u
tatio
n
tim
e
f
o
r
th
e
p
r
o
p
o
s
ed
m
eth
o
d
is
1
2
.
2
u
s
.
All
elec
tr
ical
r
esp
o
n
s
es
wer
e
o
b
s
er
v
ed
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d
ev
alu
ated
b
y
a
d
ig
ital
o
s
cill
o
s
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p
e
(
Sig
len
t
SDS2
1
0
4
X
Plu
s
)
to
p
er
ce
iv
e
th
e
o
v
er
all
s
y
s
tem
’
s
p
er
f
o
r
m
an
ce
in
r
ea
lity
.
Fig
u
r
es
9
(
a)
an
d
9
(
b
)
s
h
o
ws
th
e
s
tead
y
-
s
tate
o
p
er
atin
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ig
n
als
o
f
th
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o
n
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ter
,
i
n
clu
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n
g
o
u
tp
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t
v
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(
C
h
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el
1
)
,
g
r
id
v
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e
(
C
h
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2
)
a
n
d
g
r
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d
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r
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(
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h
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)
,
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ated
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th
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ad
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d
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0
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,
r
esp
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ely
in
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s
e
o
f
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0
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m
s
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0
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in
p
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t
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o
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e.
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t
ca
n
b
e
s
ee
n
th
a
t
th
e
ze
r
o
-
cr
o
s
s
in
g
cu
r
r
en
t
d
is
to
r
tio
n
is
m
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s
tly
d
i
s
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r
ed
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d
t
h
e
g
r
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r
r
en
t
ca
n
b
e
well
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ch
r
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ized
wi
th
th
e
g
r
id
v
o
ltag
e.
Ho
wev
er
,
th
e
g
r
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v
o
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e
co
n
tain
s
s
o
m
e
h
a
r
m
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ic
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m
p
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,
s
u
ch
th
at
th
e
p
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f
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was
m
ea
s
u
r
e
d
to
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e
0
.
9
9
2
.
T
h
e
p
o
wer
f
ac
t
o
r
is
o
b
tain
ed
at
0
.
9
8
4
s
in
ce
o
p
er
at
io
n
at
a
lig
h
ter
lo
ad
as
s
h
o
wn
in
Fig
u
r
e
9
(
b
)
.
T
h
e
o
u
tp
u
t
v
o
ltag
e
is
r
eg
u
lated
at
4
0
0
V
with
a
d
ec
en
t f
lu
ct
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atio
n
.
Fig
u
r
e
1
0
(
a)
illu
s
tr
ates
th
e
s
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y
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s
tate
o
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atin
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ig
n
als
o
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th
e
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o
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v
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ter
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p
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y
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/5
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H
z
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d
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r
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at
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ated
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wer
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ad
o
f
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Ω
.
T
h
e
in
p
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t c
u
r
r
en
t is
ca
r
r
ied
o
u
t
in
p
h
ase
with
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e
in
p
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t
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s
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ch
th
at
th
e
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wer
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ac
to
r
ca
n
ac
h
iev
e
th
e
v
alu
e
o
f
0
.
9
9
5
.
I
t
is
co
n
clu
d
e
d
th
at
th
e
FC
S
-
M
PC
m
eth
o
d
s
h
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ws
a
g
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o
d
p
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wer
f
ac
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r
o
f
well
ab
o
v
e
0
.
9
9
at
f
u
l
l
p
o
wer
r
eg
ar
d
less
th
e
lev
el
o
f
g
r
id
v
o
ltag
e.
T
h
e
o
u
tp
u
t
v
o
ltag
e
o
f
4
0
0
V
is
well
-
r
eg
u
lated
with
ac
ce
p
tab
le
DC
-
lin
k
v
o
ltag
e
r
ip
p
le.
Fig
u
r
e
1
0
(
b
)
d
em
o
n
s
tr
ates
th
e
s
tead
y
-
s
tate
o
p
er
atin
g
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ig
n
als
o
f
th
e
co
n
v
er
ter
s
u
p
p
lied
b
y
r
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tial
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es
o
f
2
2
0
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m
s
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0
Hz
an
d
wo
r
k
ed
at
h
alf
o
f
r
ate
d
p
o
wer
with
a
r
esis
tiv
e
lo
ad
o
f
1
0
0
Ω
.
B
y
cu
ttin
g
th
e
p
o
wer
lo
ad
d
o
w
n
to
5
0
%,
it
s
m
o
o
th
s
o
u
t
th
e
DC
-
lin
k
v
o
ltag
e
r
ip
p
le
s
o
th
at
th
e
o
u
t
p
u
t
wav
ef
o
r
m
th
e
n
b
ec
o
m
es
q
u
ite
f
lat.
T
h
e
g
r
id
-
s
id
e
p
o
wer
f
ac
to
r
at
5
0
%
lo
ad
co
n
d
itio
n
was
m
ea
s
u
r
e
d
to
b
e
0
.
9
8
8
.
T
h
is
r
esu
lt
s
h
o
ws
th
at
th
e
p
o
wer
f
ac
to
r
th
r
esh
o
ld
r
em
ai
n
s
th
e
s
am
e
eith
er
wh
en
t
h
e
co
n
v
er
ter
wo
r
k
s
a
t
f
u
ll
p
o
we
r
lo
ad
o
r
wh
en
it r
u
n
s
at
h
alf
p
o
wer
lo
a
d
,
wh
ich
in
d
icate
s
th
e
b
en
ef
it
o
f
u
s
in
g
FC
S
-
MPC
m
eth
o
d
.
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ab
le
1
.
Par
am
eter
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s
ed
f
o
r
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latio
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r
a
me
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o
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u
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u
r
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m
s
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Evaluation Warning : The document was created with Spire.PDF for Python.
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h
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e
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ad
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5
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d
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b
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1
0
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Fig
u
r
e
1
1
d
is
p
lay
s
th
e
in
p
u
t
c
u
r
r
en
t
T
HD
a
n
aly
s
is
with
th
e
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MP
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m
eth
o
d
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er
e
t
h
e
co
n
v
e
r
ter
o
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ates
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2
2
0
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m
s
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0
Hz
in
p
u
t
an
d
f
u
ll
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ad
c
o
n
d
itio
n
.
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v
io
u
s
ly
,
th
e
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litu
d
e
o
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a
p
ar
ticu
lar
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ar
m
o
n
ic
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r
r
en
t
s
atis
f
ies
it
s
co
r
r
esp
o
n
d
in
g
r
eq
u
i
r
em
en
t
p
r
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e
d
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th
e
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6
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0
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2
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lass
A
s
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d
ar
d
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h
e
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ar
m
o
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ic
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tio
n
o
f
th
e
in
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t
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r
r
en
t
is
s
m
aller
th
an
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A
s
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g
e
f
r
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h
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to
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u
ll
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ad
u
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in
g
a
r
esis
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e
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ad
is
illu
s
tr
ated
in
Fig
u
r
e
1
2
.
T
h
e
wav
ef
o
r
m
s
o
f
t
h
e
in
p
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t v
o
ltag
e
an
d
cu
r
r
e
n
t,
as we
ll a
s
th
e
o
u
tp
u
t
v
o
ltag
e,
co
n
f
ir
m
th
at
th
e
o
u
tp
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t
v
o
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e
r
em
ain
s
tig
h
tly
r
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g
u
lated
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r
o
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g
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o
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t
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ly
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s
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h
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d
b
r
ief
d
i
p
(
5
%~2
0
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.
T
h
ese
r
esu
lts
h
ig
h
lig
h
t
th
e
co
n
v
er
ter
’
s
f
ast
d
y
n
am
ic
r
esp
o
n
s
e
an
d
s
tr
o
n
g
co
n
tr
o
l
p
er
f
o
r
m
an
ce
u
n
d
er
s
u
d
d
en
lo
a
d
v
ar
iatio
n
s
.
As
s
h
o
wn
in
Fig
u
r
e
1
3
,
th
e
e
f
f
icien
cy
o
f
th
e
im
p
lem
e
n
ted
PF
C
cir
cu
it
h
as
b
ee
n
m
ea
s
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r
ed
ac
r
o
s
s
a
wid
e
r
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g
e
o
f
lo
a
d
p
o
wer
lev
els,
f
r
o
m
0
.
3
k
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to
3
.
3
k
W
.
T
h
e
r
esu
lts
d
em
o
n
s
tr
ate
th
at
th
e
cir
cu
it
m
ain
tain
s
h
ig
h
ef
f
icien
cy
th
r
o
u
g
h
o
u
t
th
e
en
tire
o
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atin
g
r
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g
e,
with
a
m
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im
u
m
ef
f
icien
cy
o
f
9
2
.
1
5
%
at
l
ig
h
t
lo
ad
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d
a
m
ax
im
u
m
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f
icien
cy
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f
9
8
.
8
2
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at
f
u
ll
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ad
.
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h
is
tr
en
d
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