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o
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o
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i
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a
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R
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L
L
s
f
o
r
s
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n
c
h
r
o
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o
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.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
5
2
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
,
Vo
l.
39
,
No
.
1
,
J
u
ly
20
25
:
23
-
32
24
T
h
e
r
is
e
in
n
o
n
lin
ea
r
lo
ad
s
an
d
R
E
S
in
teg
r
atio
n
h
as
ca
u
s
ed
u
n
b
alan
ce
d
v
o
ltag
e,
v
o
ltag
e
d
is
to
r
tio
n
,
an
d
DC
o
f
f
s
et
in
p
o
wer
lin
es,
im
p
ac
tin
g
PLL
r
esp
o
n
s
e
an
d
r
ed
u
cin
g
p
o
wer
q
u
ality
.
Ad
v
a
n
ce
d
PLL
alg
o
r
ith
m
s
u
s
in
g
g
en
er
alize
d
i
n
teg
r
ato
r
(
GI
)
f
o
r
o
r
th
o
g
o
n
al
s
ig
n
al
g
en
er
atio
n
(
OSG)
h
av
e
b
ec
o
m
e
ess
en
tial
f
o
r
s
y
n
c
h
r
o
n
izatio
n
,
o
f
f
e
r
in
g
r
esil
ien
ce
in
n
o
n
-
id
ea
l
g
r
id
v
o
l
tag
e
co
n
d
itio
n
s
.
A
co
m
p
ar
ativ
e
an
aly
s
is
o
f
OSG
b
ased
PLL
s
is
o
u
tlin
ed
in
[
1
4
]
,
s
h
o
wca
s
in
g
th
eir
e
f
f
ec
tiv
en
ess
in
m
itig
atin
g
d
iv
er
s
e
p
o
w
er
q
u
ali
ty
co
n
ce
r
n
s
.
T
o
o
b
tain
en
h
a
n
ce
d
PLL
r
e
s
p
o
n
s
e
with
ef
f
icien
t
an
d
f
aster
p
h
ase
d
etec
tio
n
,
ad
v
an
c
ed
GI
b
ased
PLL
alg
o
r
ith
m
s
as o
r
th
o
g
o
n
al
s
ig
n
al
g
en
er
ato
r
s
h
a
v
e
b
ee
n
d
ev
el
o
p
ed
[
1
5
]
-
[
2
0
]
.
T
h
o
u
g
h
d
if
f
e
r
en
t
s
o
lu
tio
n
s
f
o
r
p
o
wer
q
u
ality
is
s
u
es
th
r
o
u
g
h
PLL
lik
e
f
r
eq
u
en
cy
j
u
m
p
,
p
h
ase
ju
m
p
,
u
n
b
alan
ce
d
g
r
id
co
n
d
itio
n
s
,
s
ag
s
,
s
wells
an
d
h
ar
m
o
n
ics
p
r
es
en
t
in
g
r
id
v
o
ltag
e
ar
e
th
e
r
e,
s
till
th
er
e
is
a
r
esear
ch
g
ap
to
o
v
er
c
o
m
e
th
e
is
s
u
e
o
f
p
h
ase
est
im
atio
n
d
u
r
in
g
DC
o
f
f
s
ets
with
h
ar
m
o
n
ics
ex
is
ten
ce
in
th
e
g
r
id
v
o
ltag
e
a
n
d
h
e
n
ce
n
ee
d
s
to
b
e
b
r
id
g
ed
.
No
tab
le
s
o
l
u
tio
n
s
p
r
o
p
o
s
ed
b
y
t
h
e
r
esear
ch
er
s
in
clu
d
e
d
u
al
s
ec
o
n
d
o
r
d
er
g
en
e
r
alize
d
in
te
g
r
ato
r
p
h
ase
lo
c
k
lo
o
p
(
DSOGI
PLL
)
[
2
1
]
,
[
2
2
]
,
d
u
al
th
ir
d
o
r
d
er
g
en
er
alize
d
in
teg
r
ato
r
p
h
ase
lo
ck
lo
o
p
(
DT
OGI
PLL
)
[
2
3
]
-
[
2
5
]
a
n
d
d
u
al
m
ix
ed
s
ec
o
n
d
an
d
th
ir
d
o
r
d
er
g
e
n
er
alize
d
in
teg
r
ato
r
p
h
ase
lo
ck
l
o
o
p
(
D
MST
OGI
PLL
)
[
2
6
]
,
[
2
7
]
.
T
h
e
DSOGI
PLL
tech
n
iq
u
e
s
eg
r
eg
ates
th
e
p
o
s
itiv
e
an
d
n
eg
at
iv
e
s
eq
u
e
n
ce
co
m
p
o
n
en
ts
o
f
u
n
b
alan
ce
d
v
o
ltag
e
o
r
ig
in
atin
g
f
r
o
m
th
e
PLL
’
s
o
u
tp
u
t
f
o
r
ac
cu
r
ate
p
h
ase
esti
m
atio
n
an
d
s
y
n
ch
r
o
n
izatio
n
.
I
n
s
ce
n
ar
io
s
o
f
g
r
id
v
o
ltag
e
with
DC
o
f
f
s
et
an
d
h
a
r
m
o
n
ic
c
o
m
p
o
n
en
ts
p
r
esen
ce
,
a
s
tead
y
s
tate
er
r
o
r
ar
is
es
in
th
e
o
u
tp
u
t
o
f
DS
OGI
PLL
wh
ich
h
am
p
er
s
it’s
ef
f
ec
tiv
en
ess
in
r
o
b
u
s
t
s
y
n
ch
r
o
n
izatio
n
d
u
e
to
i
n
ac
cu
r
ac
y
in
esti
m
atio
n
.
T
h
e
ex
tr
ac
t
io
n
o
f
th
e
f
u
n
d
a
m
en
tal
g
r
id
v
o
ltag
e
co
m
p
o
n
en
t is
v
ital
f
o
r
s
y
n
ch
r
o
n
izatio
n
am
i
d
s
t
ad
v
er
s
e
co
n
d
itio
n
s
.
B
y
im
p
lem
en
tin
g
m
o
d
if
icatio
n
s
in
th
e
DSOGI
b
ased
PLL
s
,
it
'
s
p
o
s
s
ib
le
to
o
f
f
s
et
p
o
wer
q
u
ality
is
s
u
es
an
d
en
h
an
ce
PLL
p
er
f
o
r
m
an
ce
.
E
n
h
an
ci
n
g
th
e
f
ilter
'
s
o
r
d
er
to
s
h
ar
p
en
t
h
e
p
ass
b
an
d
(
r
esu
l
tin
g
in
in
cr
ea
s
ed
n
ar
r
o
wn
ess
)
f
o
r
g
r
ea
ter
atten
u
atio
n
o
f
h
ig
h
er
an
d
lo
we
r
o
r
d
er
d
o
m
in
an
t
h
ar
m
o
n
ics
an
d
n
u
ll
if
ic
atio
n
o
f
DC
o
f
f
s
et
was
f
o
u
n
d
o
u
t
to
b
e
o
n
e
o
f
th
e
p
o
s
s
ib
le
s
o
lu
tio
n
s
.
T
h
e
DT
OGI
PLL
p
r
o
p
o
s
ed
in
liter
atu
r
e
as
an
alter
n
ativ
e
m
eth
o
d
th
at
ex
h
ib
its
s
u
p
er
io
r
h
ar
m
o
n
ic
f
ilter
in
g
ca
p
ab
ilit
ies
co
m
p
ar
e
d
to
DSOGI
PLL
d
u
e
t
o
it’s
t
h
ir
d
o
r
d
er
tr
an
s
f
er
f
u
n
ctio
n
b
u
t
i
s
s
till
b
e
in
g
s
en
s
itiv
e
to
DC
o
f
f
s
ets
p
r
esen
ce
.
Fo
r
o
v
er
c
o
m
in
g
th
e
im
p
ac
t
o
f
DC
o
f
f
s
et
s
an
d
h
ar
m
o
n
ics
in
th
e
g
r
i
d
v
o
ltag
e
af
f
ec
tin
g
th
e
PLL
ac
cu
r
ac
y
in
p
h
ase
esti
m
atio
n
,
th
e
DM
STOG
I
PLL
ef
f
e
ctiv
ely
ad
d
r
ess
es
th
ese
two
is
s
u
es
in
th
e
g
r
id
with
R
E
Ss
s
y
n
ch
r
o
n
i
za
tio
n
b
u
t sti
ll h
as a
s
lo
wer
d
y
n
a
m
ic
r
esp
o
n
s
e.
T
h
e
PLL
s
m
en
tio
n
ed
a
b
o
v
e
lack
s
th
e
ca
p
ab
ilit
y
to
e
f
f
ec
tiv
el
y
tack
le
th
e
ch
allen
g
e
o
f
s
im
u
ltan
eo
u
s
ly
r
ejec
tin
g
h
ar
m
o
n
ic
v
o
ltag
e
a
n
d
DC
o
f
f
s
et
v
o
ltag
e
with
in
th
e
PLL
wh
ile
also
m
ain
t
ain
in
g
s
atis
f
ac
to
r
y
d
y
n
am
ic
ch
a
r
ac
ter
is
tics
.
Hen
ce
,
th
is
p
ap
er
p
r
o
p
o
s
es
s
o
m
e
ad
v
an
ce
d
GI
b
ased
PLL
s
u
n
d
er
co
m
p
lex
g
r
i
d
co
n
d
itio
n
s
f
o
r
ac
cu
r
ately
o
b
tai
n
in
g
th
e
p
h
ase
o
f
th
e
f
u
n
d
am
e
n
tal
p
o
s
itiv
e
s
eq
u
en
ce
co
m
p
o
n
en
ts
o
f
th
e
v
o
ltag
e
with
f
astes
t
d
y
n
am
ic
r
esp
o
n
s
e
an
d
h
ig
h
er
r
o
b
u
s
tn
ess
.
Ot
h
er
s
o
lu
tio
n
s
i
n
liter
atu
r
e
in
clu
d
e
p
lacin
g
d
if
f
er
en
t
f
ilter
s
[
8
]
,
[
1
1
]
,
[
1
3
]
,
[
1
4
]
,
m
u
ltip
le
f
ilter
s
o
r
m
o
r
e
f
ilter
s
in
co
m
b
in
atio
n
to
th
e
a
f
o
r
em
en
tio
n
ed
GI
b
ased
f
ilter
s
[
1
5
]
,
[
1
6
]
,
[
1
8
]
-
[
2
0
]
,
[
2
2
]
,
[
2
4
]
b
u
t
wer
e
eith
er
in
ca
p
ab
le
o
f
r
ejec
tin
g
th
e
ef
f
ec
ts
o
f
b
o
th
th
e
is
s
u
es
o
r
e
ls
e
th
e
in
cr
ea
s
ed
s
y
s
tem
co
m
p
lex
ity
h
am
p
e
r
ed
th
e
s
y
s
tem
r
esp
o
n
s
e
f
u
r
th
er
m
o
r
e.
T
h
e
p
r
o
p
o
s
ed
PLL
s
in
th
is
p
ap
er
u
s
e
th
e
c
o
n
ce
p
t
o
f
em
p
l
o
y
m
en
t
o
f
lo
w
p
ass
f
ilter
(
L
PF
)
af
ter
th
e
GI
b
ased
ad
a
p
tiv
e
f
ilter
s
in
th
e
PLL
’
s
co
n
tr
o
l
lo
o
p
f
o
r
p
e
r
f
o
r
m
an
ce
im
p
r
o
v
em
e
n
t
w
ith
s
y
s
tem
s
i
m
p
licity
an
d
f
aster
r
esp
o
n
s
e
with
p
r
ec
is
e
p
h
ase
esti
m
atio
n
.
An
ef
f
ec
tiv
e
y
et
s
im
p
le
tech
n
iq
u
e
o
f
DC
o
f
f
s
et
elim
in
atio
n
b
ased
o
n
u
s
e
o
f
ad
ap
tiv
e
L
PF
h
as
b
ee
n
p
r
o
p
o
s
ed
to
r
em
o
v
e
th
e
DC
o
f
f
s
ets
with
h
ar
m
o
n
ics
f
r
o
m
th
e
in
p
u
t
v
o
ltag
e
s
ig
n
al
b
e
f
o
r
e
p
ass
in
g
it
o
n
to
th
e
SR
F
PLL
f
o
r
p
r
ec
is
e
p
h
ase
ex
tr
ac
tio
n
.
I
t
is
b
asically
an
ad
d
-
o
n
to
an
y
GI
b
ased
PLL
s
with
o
u
t
alter
in
g
th
e
GI
f
ilter
’
s
b
an
d
wid
th
d
esig
n
.
Un
lik
e
p
r
ev
io
u
s
m
eth
o
d
s
,
th
e
ap
p
licatio
n
o
f
th
e
p
r
o
p
o
s
ed
m
eth
o
d
f
o
r
DC
o
f
f
s
et
r
em
o
v
al
h
as
a
m
in
im
al
e
f
f
ec
t
o
n
th
e
d
y
n
am
ic
p
e
r
f
o
r
m
an
c
e
o
f
th
e
PLL
u
n
d
er
s
tu
d
y
.
T
h
e
s
u
p
er
io
r
ity
a
n
d
ef
f
ec
tiv
en
ess
o
f
th
e
p
r
o
p
o
s
ed
PLL
m
eth
o
d
s
n
am
ed
as
d
u
al
s
ec
o
n
d
o
r
d
er
g
en
e
r
alize
d
in
teg
r
ato
r
-
lo
w
p
ass
f
ilter
PLL
(
DSOGI
-
L
PF
PLL
)
,
d
u
al
th
ir
d
o
r
d
er
g
en
er
alize
d
in
teg
r
ato
r
-
lo
w
p
ass
f
ilter
PLL
(
DT
OGI
-
L
PF
PLL
)
an
d
d
u
al
m
ix
ed
s
ec
o
n
d
an
d
th
ir
d
o
r
d
er
g
en
e
r
alize
d
in
teg
r
ato
r
-
lo
w
p
ass
f
ilter
PLL
(
DM
ST
OGI
-
L
PF
PLL
)
h
as
b
ee
n
v
er
if
ie
d
b
y
th
e
s
im
u
lati
o
n
r
esu
lts
in
MA
T
L
AB
en
v
ir
o
n
m
en
t
an
d
a
p
r
o
p
er
c
o
m
p
ar
ativ
e
r
esu
lt
an
aly
s
is
.
T
h
is
p
ap
er
p
r
o
v
i
d
es
a
co
m
p
r
eh
en
s
iv
e
p
er
f
o
r
m
a
n
ce
an
aly
s
i
s
o
f
th
e
ad
v
an
ce
d
GI
b
ased
PLL
s
b
ased
o
n
th
e
en
h
an
ce
m
e
n
t
o
f
th
e
s
y
s
tem
p
er
f
o
r
m
an
ce
in
ter
m
s
o
f
s
y
s
t
em
d
y
n
am
ics
an
d
d
is
tu
r
b
an
c
e
r
ejec
tio
n
ab
ilit
ies
n
am
ed
as GI
-
L
PF
b
ased
PLL
s
with
r
esp
ec
t to
th
e
GI
b
ased
PLL
s
.
T
h
is
p
ap
er
i
s
s
tr
u
ctu
r
e
d
lik
e
t
h
is
:
s
ec
tio
n
2
p
r
esen
ts
an
Ov
er
v
iew
o
f
th
e
GI
b
ased
f
ilter
s
f
o
r
OSG
u
s
ed
b
y
th
e
SR
F
PLL
f
o
r
th
e
ac
cu
r
ate
p
h
ase
ex
tr
ac
ti
o
n
d
u
r
in
g
g
r
id
d
is
tu
r
b
an
ce
s
to
ac
h
iev
e
r
o
b
u
s
t
s
y
n
ch
r
o
n
izatio
n
.
Sectio
n
3
in
tr
o
d
u
ce
s
th
e
p
r
o
p
o
s
ed
n
o
v
el
ad
v
an
ce
d
GI
b
ased
PLL
s
with
L
PF
in
th
e
PLL
co
n
tr
o
l
lo
o
p
f
o
r
p
er
f
o
r
m
an
ce
en
h
an
ce
m
e
n
t,
f
aster
s
y
s
tem
r
e
s
p
o
n
s
e
an
d
ac
cu
r
ate
p
h
ase
esti
m
atio
n
d
u
r
in
g
g
r
id
d
is
tu
r
b
an
ce
s
with
DC
o
f
f
s
ets
an
d
h
a
r
m
o
n
ics
p
r
esen
ce
.
Sectio
n
4
co
n
d
u
cts
a
s
im
u
latio
n
b
ased
co
m
p
a
r
ativ
e
r
es
u
lt
an
aly
s
is
in
MA
T
L
A
B
e
n
v
ir
o
n
m
en
t
f
o
r
p
er
f
o
r
m
an
ce
e
v
alu
atio
n
o
f
th
e
p
r
o
p
o
s
ed
PLL
s
ag
ain
s
t
th
e
o
th
er
GI
b
ased
PLL
s
k
n
o
wn
f
o
r
th
ei
r
ex
ce
llen
t
p
er
f
o
r
m
an
ce
u
n
d
er
two
test
co
n
d
itio
n
s
wh
ich
in
c
lu
d
e
th
e
two
p
h
ase
v
o
ltag
e
s
ag
with
5
th
an
d
7
th
h
ar
m
o
n
ics
an
d
th
e
p
r
esen
ce
o
f
DC
o
f
f
s
ets
in
th
e
g
r
id
v
o
ltag
e.
Fin
ally
,
s
ec
tio
n
5
p
r
o
v
id
es
th
e
co
n
cl
u
s
io
n
im
p
li
ca
tin
g
th
e
m
o
s
t
s
u
itab
le
PLL
to
b
e
u
s
ed
f
o
r
g
r
id
with
R
E
Ss
s
y
n
ch
r
o
n
izatio
n
u
n
d
er
wea
k
g
r
id
co
n
d
itio
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4
7
5
2
A
d
va
n
ce
d
g
en
era
liz
ed
in
teg
r
a
t
o
r
b
a
s
ed
p
h
a
s
e
lo
ck
l
o
o
p
u
n
d
e
r
co
mp
lex
g
r
id
…
(
P
o
o
n
a
m
Tr
ip
a
th
y
)
25
2.
O
VE
RVI
E
W
O
F
G
E
N
E
RA
L
I
Z
E
D
I
NT
E
G
RA
T
O
R
B
A
SE
D
F
I
L
T
E
R
S
I
n
th
e
co
n
tex
t
o
f
OSG
b
ased
f
ilter
in
g
ap
p
r
o
ac
h
f
o
r
ex
tr
ac
tin
g
th
e
s
y
n
ch
r
o
n
izin
g
s
ig
n
als
am
id
s
t
g
r
id
v
o
ltag
e
d
is
tu
r
b
an
ce
s
,
GI
b
ase
d
m
eth
o
d
s
h
o
l
d
p
r
ef
er
e
n
ce
.
A
n
o
v
e
r
v
iew
o
f
th
e
im
p
lem
e
n
tatio
n
o
f
d
if
f
er
en
t
GI
s
as
ad
ap
tiv
e
f
ilter
s
f
o
r
p
h
ase
esti
m
atio
n
in
PLL
s
h
as
b
ee
n
p
r
o
v
id
ed
i
n
th
is
s
ec
tio
n
.
Fig
u
r
es
1
-
3
illu
s
tr
ate
th
e
s
tr
u
ctu
r
es
o
f
th
e
s
tan
d
a
r
d
ize
d
s
ec
o
n
d
o
r
d
er
g
en
er
alize
d
in
teg
r
ato
r
(
SOGI
)
[
2
1
]
,
[
2
2
]
f
ilter
,
th
ir
d
o
r
d
er
g
en
er
ali
ze
d
i
n
teg
r
ato
r
(
T
OGI
)
f
ilter
[
2
3
]
-
[
2
5
]
a
n
d
m
ix
ed
s
ec
o
n
d
an
d
th
ir
d
o
r
d
er
g
en
er
alize
d
in
teg
r
at
o
r
(
MST
OGI
)
[
2
6
]
,
[
2
7
]
f
ilter
w
h
ich
s
er
v
e
as
OSG
th
r
o
u
g
h
o
u
t
th
e
PLL
’
s
p
r
e
f
i
l
t
e
r
i
n
g
s
t
a
g
e
f
o
r
a
c
c
u
r
a
t
e
p
h
a
s
e
e
x
t
r
a
c
t
i
o
n
.
I
t
g
e
n
e
r
a
t
es
t
h
e
o
r
th
o
g
o
n
a
l
s
i
g
n
a
l
s
(
′
a
n
d
′
)
a
s
f
i
l
te
r
e
d
o
u
t
p
u
t
s
o
f
a
s
t
h
e
i
n
p
u
t
s
ig
n
a
l
w
i
t
h
̂
a
n
d
k
a
s
t
h
e
es
t
i
m
a
t
e
d
f
r
e
q
u
e
n
cy
a
n
d
d
a
m
p
i
n
g
c
o
e
f
f
i
c
i
e
n
t
,
r
e
s
p
e
c
t
i
v
e
l
y
[
3
]
.
Fig
u
r
e
1
.
SOGI
OSG
f
ilter
Fig
u
r
e
2
.
T
OGI
OSG
f
ilter
Fig
u
r
e
3
.
MST
OGI
OSG
f
ilter
2
.
1
.
Seco
nd
o
rder
g
ener
a
lize
d inte
g
ra
t
o
r
T
h
e
o
p
tim
ized
g
ain
(
k
)
v
alu
e
o
f
th
e
SOGI
f
ilter
is
1
.
4
1
4
wh
ich
d
eter
m
in
es
th
e
b
an
d
wid
t
h
(
BW
)
o
f
R
(
s
)
.
A
lo
wer
ed
k
v
alu
e
en
h
a
n
ce
s
th
e
f
ilter
in
g
ca
p
ac
ity
o
f
R
(
s
)
b
u
t
in
cr
ea
s
es
d
ep
en
d
an
c
e
o
n
th
e
r
eso
n
a
n
tly
ex
tr
ac
ted
g
r
id
f
r
eq
u
e
n
cy
(
̂
)
.
C
o
n
v
er
s
ely
,
a
lo
wer
k
v
al
u
e
im
p
r
o
v
es
th
e
f
ilter
in
g
ef
f
ec
t
o
f
Q(
s
)
b
u
t
m
ay
a
f
f
ec
t
th
e
d
y
n
a
m
ic
r
esp
o
n
s
e
o
r
s
ettlin
g
tim
e.
T
h
e
tr
an
s
f
er
f
u
n
ctio
n
s
o
f
th
e
SOGI
f
ilter
ar
e
d
e
f
in
e
d
as
:
(
)
=
′
(
)
=
̂
2
+
̂
+
̂
2
(
1
)
(
)
=
′
(
)
=
̂
2
2
+
̂
+
̂
2
(
2
)
2
.
2
.
T
hird
o
rder
g
ener
a
lized
inte
g
ra
t
o
r
T
h
e
o
p
tim
ized
T
OGI
f
ilter
g
ai
n
(
1
an
d
2
)
v
alu
es
ar
e
2
.
8
2
an
d
1
.
1
ea
ch
.
T
h
e
1
p
ar
am
eter
co
n
tr
o
l
s
th
e
f
ilter
B
W
,
wh
ile
2
d
eter
m
in
es
th
e
f
ilter
’
s
d
y
n
am
ic
r
esp
o
n
s
e.
I
n
cr
ea
s
in
g
1
b
r
o
ad
e
n
s
th
e
f
ilter
’
s
b
an
d
wid
th
,
th
u
s
lo
wer
in
g
th
e
h
ar
m
o
n
ic
atten
u
atio
n
.
C
o
n
v
er
s
ely
,
an
in
cr
ea
s
ed
2
v
alu
e
r
esu
lts
in
s
lo
wer
f
ilter
’
s
r
esp
o
n
s
e
with
a
d
ec
r
ea
s
ed
o
v
er
s
h
o
o
t.
T
h
e
tr
a
n
s
f
er
f
u
n
ctio
n
s
o
f
th
e
T
OGI
f
ilter
ar
e
d
ef
in
ed
as:
(
)
=
′
(
)
=
1
̂
2
3
+
2
̂
2
+
(
1
+
1
)
̂
2
+
2
̂
3
(
3
)
(
)
=
′
(
)
=
1
̂
3
3
+
2
̂
2
+
(
1
+
1
)
̂
2
+
2
̂
3
(
4
)
2
.
3
.
M
ix
ed
s
ec
o
nd
a
nd
t
hird
o
rder
g
ener
a
lized
inte
g
ra
t
o
r
T
h
e
MST
OGI
f
ilter
is
co
n
s
tr
u
cted
with
an
ad
d
itio
n
al
c
o
m
p
o
n
en
t
in
th
e
g
e
n
er
alize
d
SOGI
to
atten
u
ate
th
e
ef
f
ec
t
o
f
th
e
DC
o
f
f
s
ets
p
r
esen
t
in
th
e
in
p
u
t
g
r
i
d
v
o
ltag
e
s
ig
n
al,
th
e
r
eb
y
p
r
o
d
u
cin
g
a
T
OGI
.
T
h
e
SOGI
an
d
T
OGI
to
g
eth
e
r
f
o
r
m
th
e
MST
OGI
ad
ap
tiv
e
f
ilte
r
wh
er
e
̂
d
en
o
tes
th
e
esti
m
ated
g
r
id
f
r
eq
u
en
cy
,
wh
ile
k
s
tan
d
s
f
o
r
th
e
g
ain
o
f
th
e
MST
OGI
f
ilter
with
an
o
p
tim
ized
v
al
u
e
as
1
.
4
1
4
.
A
lar
g
er
v
al
u
e
o
f
k
in
d
icate
s
a
f
aster
d
y
n
am
ic
r
esp
o
n
s
e
an
d
en
h
an
ce
d
s
tab
ilit
y
,
alth
o
u
g
h
at
th
e
p
o
ten
tial
co
s
t
o
f
co
m
p
r
o
m
is
ed
f
ilter
in
g
ca
p
ab
ilit
y
.
T
h
e
tr
an
s
f
er
f
u
n
ctio
n
s
o
f
th
e
MST
OGI
f
ilter
ar
e
d
ef
in
e
d
as:
(
)
=
′
(
)
=
̂
2
+
̂
+
̂
2
(
5
)
(
)
=
′
(
)
=
̂
(
̂
−
)
(
+
̂
)
(
2
+
̂
+
̂
2
)
(
6
)
3.
P
RO
P
O
SE
D
G
E
N
E
RA
L
I
Z
E
D
I
N
T
E
G
R
AT
O
R
-
L
O
W
P
ASS F
I
L
T
E
R
B
AS
E
D
P
L
L
S
T
h
e
p
r
o
p
o
s
ed
n
o
v
el
en
h
an
ce
d
g
en
er
alize
d
i
n
teg
r
ato
r
-
lo
w
p
ass
f
ilter
b
ase
d
PLL
(
GI
-
L
PF
PLL
)
,
ad
d
r
ess
es
th
e
is
s
u
es
o
f
D
C
o
f
f
s
et
an
d
h
ar
m
o
n
ics,
b
ased
o
n
th
e
GI
b
ased
PLL
s
tr
u
ctu
r
e.
T
h
e
g
en
er
alize
d
GI
b
ased
PLL
u
tili
ze
s
two
n
u
m
b
er
s
o
f
r
esp
ec
tiv
e
GI
s
in
th
e
αβ
f
r
am
e
o
f
th
e
PLL
’
s
p
r
e
f
ilter
in
g
s
tag
e.
Hen
ce
,
th
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
5
2
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
,
Vo
l.
39
,
No
.
1
,
J
u
ly
20
25
:
23
-
32
26
GI
b
ased
PLL
s
ar
e
n
am
e
d
as
DSOGI
PLL
,
DT
OGI
PLL
an
d
DM
STOG
I
PLL
r
esp
ec
tiv
ely
.
T
h
e
p
r
o
p
o
s
ed
m
o
d
if
ied
an
d
e
n
h
an
ce
d
GI
-
L
PF
b
ased
PLL
is
s
h
o
wn
in
Fi
g
u
r
e
4
wh
ich
ca
n
b
e
n
am
e
d
as
DSO
GI
-
L
PF
PLL
,
DT
OGI
-
L
PF
PLL
an
d
DM
STOG
I
-
L
PF
PLL
r
esp
ec
tiv
ely
.
T
h
e
GI
-
L
PF
b
ased
PLL
s
u
til
i
ze
two
GI
s
an
d
two
ad
ap
tiv
e
L
PF
s
in
αβ
f
r
am
e
f
o
r
en
h
an
ce
d
an
d
ac
cu
r
ate
p
h
ase
esti
m
atio
n
.
I
n
itially
,
t
h
e
th
r
ee
p
h
ase
in
p
u
t
v
o
ltag
e
is
tr
an
s
f
o
r
m
ed
f
r
o
m
t
h
e
abc
f
r
am
e
to
th
e
αβ
f
r
am
e
u
s
in
g
th
e
C
lar
k
tr
an
s
f
o
r
m
atio
n
,
r
esu
ltin
g
in
th
e
an
d
.
Su
b
s
eq
u
en
tly
,
an
d
ar
e
f
ed
in
to
th
e
d
u
al
GI
s
,
p
r
o
d
u
cin
g
o
r
th
o
g
o
n
al
s
ig
n
als
′
,
′
,
′
an
d
′
ar
e
th
en
p
ass
ed
o
n
to
th
e
p
o
s
itiv
e
s
eq
u
e
n
ce
ca
lcu
la
tio
n
(
PS
C
)
u
n
it
to
ex
tr
ac
t
th
e
f
u
n
d
am
en
tal
f
r
eq
u
e
n
cy
p
o
s
itiv
e
s
eq
u
en
ce
(
FF
PS
)
co
m
p
o
n
en
ts
.
T
h
e
co
r
r
esp
o
n
d
in
g
FF
PS
co
m
p
o
n
e
n
ts
(
+
an
d
+
)
,
ar
e
d
er
iv
ed
th
r
o
u
g
h
th
e
in
s
tan
tan
eo
u
s
s
y
m
m
etr
ical
co
m
p
o
n
e
n
ts
(
I
SC
)
m
eth
o
d
[
2
1
]
wh
ic
h
is
cr
u
cial
f
o
r
th
e
p
r
ec
is
e
an
d
ef
f
icien
t o
p
er
atio
n
o
f
th
e
PLL
s
f
o
r
ac
cu
r
ate
p
h
as
e
esti
m
atio
n
f
o
r
s
y
n
c
h
r
o
n
izatio
n
p
u
r
p
o
s
e
:
+
=
0
.
5
(
′
−
′
)
(
7
)
+
=
0
.
5
(
′
+
′
)
(
8
)
T
h
e
GI
o
u
tp
u
ts
+
an
d
+
ar
e
th
en
in
p
u
tted
in
to
th
e
SR
F
PLL
in
s
y
n
ch
r
o
n
o
u
s
ly
r
o
tatin
g
(
dq
)
f
r
am
e
f
o
r
esti
m
atin
g
th
e
f
r
eq
u
en
cy
an
d
p
h
ase
an
g
le
o
f
th
e
u
tili
ty
g
r
id
v
o
ltag
e
i
n
ca
s
e
o
f
G
I
b
ased
PLL
s
.
T
h
e
p
r
o
p
o
s
ed
im
p
r
o
v
ed
m
o
d
el
is
co
n
s
tr
u
cted
with
th
e
em
p
lo
y
m
en
t
o
f
a
n
ad
ap
tiv
e
L
PF
af
ter
th
e
ex
tr
ac
ted
FF
PS
co
m
p
o
n
en
ts
+
an
d
+
b
y
th
e
GI
f
i
lter
p
r
io
r
to
s
en
d
i
n
g
th
e
i
n
p
u
t
s
ig
n
al
to
t
h
e
SR
F
PLL
.
No
w,
th
e
ex
tr
ac
ted
s
ig
n
als
+
+
an
d
+
+
af
ter
th
e
L
PF
ac
t
as
in
p
u
ts
f
o
r
th
e
SR
F
PLL
f
o
r
ac
cu
r
ate
p
h
ase
tr
ac
k
in
g
.
T
h
e
GI
-
L
PF
PLL
d
esig
n
ex
h
i
b
its
b
etter
f
i
lter
in
g
ca
p
ac
ity
al
o
n
g
with
e
f
f
ec
tiv
e
DC
o
f
f
s
et
elim
in
atio
n
wh
ich
r
esu
lts
in
ac
cu
r
ate
p
h
ase
tr
ac
k
in
g
.
Oth
er
s
o
lu
tio
n
s
in
liter
atu
r
e
in
cl
u
d
e
p
lacin
g
d
if
f
er
e
n
t
f
ilter
s
[
8
]
,
[
1
1
]
,
[
1
3
]
,
[
1
4
]
,
m
u
l
t
i
p
l
e
f
i
l
t
e
r
s
o
r
m
o
r
e
f
i
l
t
e
r
s
i
n
c
o
m
b
i
n
a
t
i
o
n
t
o
t
h
e
a
f
o
r
e
m
e
n
t
i
o
n
e
d
G
I
b
a
s
e
d
f
i
l
t
e
r
s
[
1
5
]
,
[
1
6
]
,
[
1
8
]
-
[
2
2
]
,
[
2
4
]
b
u
t
wer
e
eith
er
in
ca
p
a
b
le
o
f
r
ejec
tin
g
th
e
ef
f
ec
ts
o
f
b
o
th
th
e
is
s
u
es
o
r
else
th
e
in
cr
ea
s
ed
s
y
s
tem
co
m
p
lex
ity
h
am
p
er
ed
th
e
s
y
s
tem
r
esp
o
n
s
e
f
u
r
th
er
m
o
r
e.
T
h
e
p
r
o
p
o
s
ed
PLL
s
in
th
is
p
ap
er
u
s
e
th
e
c
o
n
c
e
p
t
o
f
e
m
p
l
o
y
m
e
n
t
o
f
L
P
F
a
f
t
e
r
t
h
e
G
I
b
a
s
e
d
a
d
ap
t
i
v
e
f
i
lt
e
r
s
i
n
t
h
e
P
L
L
’
s
c
o
n
t
r
o
l
l
o
o
p
f
o
r
p
e
r
f
o
r
m
a
n
c
e
i
m
p
r
o
v
e
m
e
n
t
w
it
h
s
y
s
t
e
m
s
i
m
p
l
ic
i
t
y
a
n
d
f
a
s
t
e
r
r
e
s
p
o
n
s
e
w
i
t
h
p
r
e
c
is
e
p
h
a
s
e
e
s
ti
m
a
ti
o
n
.
A
n
e
f
f
e
c
t
i
v
e
y
e
t
s
i
m
p
l
e
t
e
c
h
n
i
q
u
e
o
f
DC
o
f
f
s
e
t
e
l
i
m
i
n
a
ti
o
n
b
a
s
e
d
o
n
u
s
e
o
f
a
d
a
p
t
i
v
e
L
P
F
h
a
s
b
e
e
n
p
r
o
p
o
s
e
d
t
o
r
e
m
o
v
e
t
h
e
DC
o
f
f
s
e
t
s
w
i
t
h
h
a
r
m
o
n
i
c
s
f
r
o
m
t
h
e
i
n
p
u
t
v
o
l
t
a
g
e
s
i
g
n
a
l
b
e
f
o
r
e
p
a
s
s
i
n
g
i
t
o
n
t
o
t
h
e
S
R
F
P
L
L
f
o
r
p
r
e
c
i
s
e
p
h
a
s
e
e
x
t
r
a
c
ti
o
n
.
I
t
i
s
b
as
i
c
al
l
y
a
n
a
d
d
-
o
n
t
o
a
n
y
G
I
b
a
s
e
d
PL
L
s
w
i
t
h
o
u
t
al
te
r
i
n
g
t
h
e
G
I
f
i
lt
e
r
’
s
b
a
n
d
wi
d
t
h
d
e
s
i
g
n
.
U
n
li
k
e
p
r
e
v
i
o
u
s
m
et
h
o
d
s
,
t
h
e
a
p
p
l
i
ca
t
i
o
n
of
t
h
e
p
r
o
p
o
s
e
d
m
e
t
h
o
d
f
o
r
DC
o
f
f
s
e
t
r
e
m
o
v
a
l
h
as
a
m
i
n
i
m
a
l
e
f
f
e
c
t
o
n
t
h
e
d
y
n
a
m
i
c
p
e
r
f
o
r
m
a
n
c
e
o
f
t
h
e
P
L
L
u
n
d
e
r
s
t
u
d
y
.
T
h
e
p
r
o
p
o
s
e
d
s
i
m
p
l
e
y
e
t
e
f
f
e
ct
i
v
e
s
o
l
u
t
i
o
n
f
o
r
en
h
a
n
c
e
d
s
y
n
c
h
r
o
n
i
z
i
n
g
a
b
i
l
it
y
i
s
a
c
h
i
e
v
e
d
t
h
r
o
u
g
h
a
n
a
d
a
p
t
i
v
e
f
i
r
s
t
o
r
d
e
r
L
PF
w
h
o
s
e
c
u
t
-
o
f
f
f
r
e
q
u
e
n
c
y
(
)
h
a
s
b
e
e
n
s
e
t
t
o
a
h
i
g
h
e
r
v
a
l
u
e
f
o
r
d
i
s
tu
r
b
a
n
c
e
r
e
j
e
c
t
i
o
n
a
b
i
l
i
t
y
[
2
8
]
.
T
h
e
v
a
l
u
e
o
f
h
a
s
b
e
e
n
s
e
t
t
o
5
0
p
i
r
a
d
/
s
a
s
t
h
e
v
a
lu
e
o
f
c
u
t
-
o
f
f
f
r
e
q
u
e
n
c
y
(
)
o
f
t
h
e
L
P
F
i
s
2
5
H
z
.
T
h
e
t
r
a
n
s
f
e
r
f
u
n
c
t
i
o
n
e
x
p
r
e
s
s
i
o
n
o
f
t
h
e
u
s
e
d
L
P
F
i
s
e
x
p
r
e
s
s
e
d
a
s
f
o
l
l
o
ws
:
(
)
=
+
(
9
)
B
y
ch
o
o
s
in
g
an
o
p
tim
al
k
v
al
u
e
[
2
1
]
,
th
e
GI
-
L
PF
b
ased
P
L
L
en
s
u
r
es
en
h
a
n
ce
d
d
y
n
am
i
c
r
esp
o
n
s
e
an
d
f
ilter
in
g
ca
p
ac
ity
a
n
d
also
f
r
eq
u
en
cy
ad
a
p
tab
ilit
y
u
n
d
er
a
n
y
c
o
m
p
lex
g
r
id
c
o
n
d
it
io
n
b
y
s
en
d
in
g
th
e
ex
tr
ac
ted
g
r
i
d
f
r
e
q
u
en
c
y
̂
as
an
in
p
u
t
to
th
e
GI
f
ilter
s
lead
in
g
to
ac
c
u
r
ate
p
h
ase
an
g
le
tr
ac
k
in
g
.
T
h
e
u
p
co
m
in
g
r
esu
lt
s
ec
tio
n
will
co
n
f
ir
m
th
e
b
r
id
g
in
g
o
f
th
e
r
esear
ch
g
ap
th
r
o
u
g
h
t
h
e
s
im
u
latio
n
-
b
ased
r
esu
lts
o
f
th
e
ex
is
tin
g
GI
b
ased
PLL
s
an
d
th
e
p
r
o
p
o
s
ed
GI
-
L
PF
b
ase
d
PLL
s
s
h
o
wca
s
in
g
th
e
en
h
an
ce
d
DC
o
f
f
s
et
an
d
h
ar
m
o
n
ics
e
f
f
ec
t
atten
u
atio
n
o
f
th
e
p
r
o
p
o
s
ed
GI
-
L
PF
PLL
s
with
a
d
etailed
p
er
f
o
r
m
a
n
ce
e
v
alu
atio
n
o
f
all
th
e
PLL
s
.
T
h
e
e
f
f
icac
y
an
d
r
o
b
u
s
t
n
ess
o
f
th
e
GI
-
L
PF
PLL
s
o
v
er
th
e
GI
b
ased
PLL
s
will
b
e
v
alid
ated
in
ter
m
s
o
f
f
aster
s
y
s
tem
d
y
n
am
ic
r
esp
o
n
s
e,
p
r
ec
is
s
io
n
in
p
h
ase
tr
ac
k
in
g
alo
n
g
with
th
e
DC
o
f
f
s
et
an
d
h
ar
m
o
n
ics
r
ejec
tio
n
ab
ilit
y
to
a
v
o
id
esti
m
atio
n
er
r
o
r
s
f
o
r
a
n
en
h
an
ce
d
s
y
n
ch
r
o
n
izatio
n
u
n
d
e
r
co
m
p
lex
g
r
id
co
n
d
itio
n
.
Fig
u
r
e
4
.
Stru
ctu
r
e
o
f
GI
-
L
PF
b
ased
PLL
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4
7
5
2
A
d
va
n
ce
d
g
en
era
liz
ed
in
teg
r
a
t
o
r
b
a
s
ed
p
h
a
s
e
lo
ck
l
o
o
p
u
n
d
e
r
co
mp
lex
g
r
id
…
(
P
o
o
n
a
m
Tr
ip
a
th
y
)
27
4.
CO
M
P
ARA
T
I
V
E
R
E
SU
L
T
ANALY
SI
S A
ND
DI
SCUS
S
I
O
N
I
n
th
is
s
ec
tio
n
,
th
e
p
er
f
o
r
m
a
n
ce
o
f
th
e
p
r
o
p
o
s
ed
GI
-
L
PF
b
ased
PLL
s
(
DSOGI
-
L
PF
PLL
,
DT
OGI
-
L
PF
PLL
an
d
DM
STOG
I
-
L
PF
PLL
)
with
th
e
s
tan
d
ar
d
GI
b
ased
PLL
s
(
DSOGI
PLL
,
DT
OGI
PLL
an
d
DM
STOG
I
PLL
)
h
as
b
ee
n
e
v
alu
ated
in
th
e
MA
T
L
AB
/Si
m
u
lin
k
e
n
v
ir
o
n
m
en
t
to
a
n
aly
ze
th
eir
r
o
b
u
s
tn
ess
am
id
s
t
two
d
is
to
r
ted
g
r
id
ca
s
es.
T
h
e
o
b
jectiv
e
is
to
ch
ec
k
th
eir
r
o
b
u
s
tn
ess
in
p
h
ase
an
g
l
e
tr
ac
k
in
g
ac
cu
r
ac
y
am
id
s
t
th
e
g
r
id
d
is
tu
r
b
an
ce
s
o
cc
u
r
r
in
g
b
etwe
en
0
.
2
s
ec
o
n
d
s
an
d
0
.
4
s
ec
o
n
d
s
,
with
a
to
tal
d
u
r
atio
n
o
f
0
.
6
s
ec
o
n
d
s
.
At
0
s
ec
o
n
d
s
,
th
e
in
p
u
t
co
m
p
r
is
es
a
b
alan
ce
d
u
tili
ty
v
o
ltag
e
o
f
am
p
litu
d
e
1
p
er
u
n
it
(
p
.
u
.
)
a
n
d
g
r
id
f
r
eq
u
e
n
cy
o
f
5
0
Hz
wh
ich
is
r
ec
o
v
er
e
d
ag
ain
at
0
.
6
s
ec
o
n
d
s
.
T
h
e
in
v
esti
g
ated
two
test
ca
s
es
ar
e:
t
est
ca
s
e
1
:
A
two
p
h
ase
v
o
ltag
e
s
ag
with
5
th
an
d
7
th
h
ar
m
o
n
ics
an
d
t
est
ca
s
e
2
:
DC
o
f
f
s
et
p
r
esen
t
in
th
e
g
r
id
v
o
ltag
e.
Fo
r
all
th
e
PLL
s
tak
en
in
t
o
co
n
s
id
er
atio
n
,
t
h
e
ac
tu
al
g
r
id
f
r
eq
u
en
cy
is
1
0
0
π
r
ad
/s
,
c
o
n
s
id
e
r
in
g
ac
tu
al
g
r
i
d
f
r
eq
u
e
n
cy
as
5
0
Hz.
T
h
e
o
p
tim
ized
PI
p
ar
am
eter
s
v
alu
es
o
f
SR
F
PLL
ar
e
p
r
o
p
o
r
tio
n
al
g
ain
(
=1
8
0
)
an
d
in
teg
r
al
g
ain
(
=3
2
0
0
)
f
o
r
a
f
air
co
m
p
ar
is
o
n
am
o
n
g
all
th
e
P
L
L
s
.
T
ab
le
I
r
ec
ap
itu
lates
ev
a
lu
atio
n
o
f
all
th
e
PLL
s
u
n
d
er
th
e
co
n
s
id
er
e
d
test
co
n
d
itio
n
s
b
ased
o
n
s
ettlin
g
tim
e
(
d
y
n
am
ic
r
esp
o
n
s
e)
,
to
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
(
T
HD
)
o
b
tain
ed
th
r
o
u
g
h
t
h
e
f
ast f
o
u
r
ier
t
r
a
n
s
f
o
r
m
(
FFT
)
an
aly
s
is
an
d
f
r
e
q
u
en
c
y
o
v
er
s
h
o
o
t.
4
.
1
.
T
wo
ph
a
s
e
v
o
lt
a
g
e
s
a
g
wit
h 5
th
a
nd
7
th
ha
rm
o
nics
A
b
a
l
a
n
c
e
d
t
w
o
p
h
a
s
e
v
o
l
t
a
g
e
s
a
g
w
i
t
h
a
m
a
g
n
i
t
u
d
e
o
f
1
p
.
u
.
f
o
r
a
p
h
a
s
e
a
n
d
0
.
7
p
.
u
.
e
a
c
h
f
o
r
b
a
n
d
c
p
h
a
s
e
a
l
o
n
g
w
i
t
h
,
a
5
th
h
a
r
m
o
n
i
c
c
o
m
p
o
n
e
n
t
w
i
t
h
a
m
p
l
i
t
u
d
e
s
o
f
(
1
/
5
p
.
u
.
,
0
.
7
/
5
p
.
u
.
,
a
n
d
0
.
7
/
5
p
.
u
.
f
o
r
e
a
c
h
p
h
a
s
e
)
,
a
n
d
7
t
h
h
a
r
m
o
n
i
c
c
o
m
p
o
n
e
n
t
w
i
t
h
a
m
p
l
i
t
u
d
e
s
o
f
(
1
/
7
p
.
u
.
,
0
.
7
/
7
p
.
u
.
,
a
n
d
0
.
7
/
7
p
.
u
.
f
o
r
e
a
c
h
p
h
a
s
e
)
i
s
i
n
t
r
o
d
u
c
e
d
f
r
o
m
0
.
2
s
e
c
o
n
d
s
t
o
0
.
4
s
e
c
o
n
d
s
.
T
h
e
F
i
g
u
r
e
5
r
e
p
r
e
s
e
n
t
s
t
h
e
s
i
m
u
l
a
t
i
o
n
r
e
s
p
o
n
s
e
s
o
f
a
l
l
a
d
v
a
n
c
e
d
P
L
L
s
d
u
r
i
n
g
a
t
w
o
p
h
a
s
e
v
o
l
t
a
g
e
s
a
g
w
i
t
h
h
a
r
m
o
n
i
c
s
t
e
s
t
c
a
s
e
.
I
n
F
i
g
u
r
e
5
(
a
)
,
t
h
e
t
h
r
e
e
p
h
a
s
e
g
r
i
d
v
o
l
t
a
g
e
i
s
d
e
p
i
c
t
e
d
,
c
o
n
t
a
m
i
n
a
t
e
d
w
i
t
h
a
t
w
o
p
h
a
s
e
v
o
l
t
a
g
e
s
a
g
,
a
s
w
e
l
l
a
s
5
t
h
a
n
d
7
t
h
h
a
r
m
o
n
i
c
s
.
T
h
e
e
x
t
r
a
c
t
e
d
dq
o
u
t
p
u
t
s
o
f
a
l
l
t
h
e
P
L
L
s
i
n
t
h
e
dq
f
r
a
m
e
a
r
e
i
l
l
u
s
t
r
a
t
e
d
i
n
F
i
g
u
r
e
s
5
(
b
)
-
(
d
)
.
T
h
e
m
a
g
n
i
t
u
d
e
o
f
e
x
t
r
a
c
t
e
d
d
v
o
l
t
a
g
e
c
o
m
p
o
n
e
n
t
(
(
)
a
s
1
p
.
u
.
)
a
n
d
q
c
o
m
p
o
n
e
n
t
(
(
)
a
s
0
d
e
g
r
e
e
s
)
a
f
f
i
r
m
t
h
e
e
f
f
e
c
t
i
v
e
n
e
s
s
o
f
t
h
e
P
L
L
s
.
F
i
g
u
r
e
5
(
e
)
-
(
g
)
d
e
m
o
n
s
t
r
a
t
e
t
h
e
P
L
L
s
p
r
e
c
i
s
i
o
n
i
n
t
r
a
c
k
i
n
g
t
h
e
f
r
e
q
u
e
n
c
y
b
y
c
o
m
p
a
r
i
n
g
t
h
e
g
r
i
d
’
s
a
c
t
u
a
l
f
r
e
q
u
e
n
c
y
w
i
t
h
t
h
e
P
L
L
’
s
e
s
t
i
m
a
t
e
d
f
r
e
q
u
e
n
c
y
.
O
v
e
r
a
l
l
y
,
t
h
e
p
r
o
p
o
s
e
d
G
I
-
L
P
F
P
L
L
s
d
e
m
o
n
s
t
r
a
t
e
s
i
g
n
i
f
i
c
a
n
t
e
n
h
a
n
c
e
m
e
n
t
a
n
d
s
u
p
e
r
i
o
r
d
y
n
a
m
i
c
p
e
r
f
o
r
m
a
n
c
e
w
i
t
h
e
n
h
a
n
c
e
d
f
i
l
t
e
r
i
n
g
c
a
p
a
c
i
t
y
,
m
i
n
i
m
a
l
f
r
e
q
u
e
n
c
y
o
v
e
r
s
h
o
o
t
s
a
n
d
a
c
c
u
r
a
t
e
f
r
e
q
u
e
n
c
y
e
s
t
i
m
a
t
i
o
n
c
o
m
p
a
r
e
d
t
o
t
h
e
s
t
a
n
d
a
r
d
G
I
b
a
s
e
d
P
L
L
s
c
o
u
n
t
e
r
p
a
r
t
s
.
T
h
e
D
T
O
G
I
-
L
P
F
P
L
L
i
s
t
h
e
s
u
p
e
r
i
o
r
o
n
e
f
o
l
l
o
w
e
d
b
y
t
h
e
D
M
S
T
O
G
I
-
L
P
F
P
L
L
w
i
t
h
m
i
n
i
m
u
m
s
e
t
t
l
i
n
g
t
i
m
e
,
o
v
e
r
s
h
o
o
t
a
n
d
T
H
D
c
o
n
t
e
n
t
i
n
t
h
e
e
x
t
r
a
c
t
e
d
o
u
t
p
u
t
s
.
A
l
l
t
h
e
d
e
t
a
i
l
e
d
c
o
m
p
a
r
a
t
i
v
e
i
n
f
o
r
m
a
t
i
o
n
c
a
n
b
e
f
o
u
n
d
i
n
T
a
b
l
e
1
.
I
n
th
is
test
ca
s
e,
th
e
S
OGI
f
ilt
er
b
ased
PLL
s
(
DSO
GI
PLL
a
n
d
DSOGI
-
L
PF
PLL
)
s
h
o
wca
s
e
q
u
ick
est
d
y
n
am
ic
r
esp
o
n
s
e
d
u
e
to
lo
w
er
o
r
d
er
o
f
th
e
f
ilter
an
d
d
esig
n
s
im
p
licity
.
Yet,
th
ey
ex
h
ib
it
h
ig
h
s
tead
y
s
tate
r
ip
p
les
an
d
m
o
r
e
h
a
r
m
o
n
ics
c
o
n
ten
t
in
th
e
ex
tr
ac
ted
s
ig
n
als
with
T
HD
co
n
ten
t
as
3
.
3
5
%
(
DSOGI
PLL
)
an
d
0
.
0
6
%
(
DSOGI
-
L
PF
PLL
)
r
esp
ec
tiv
ely
w
h
ich
is
o
b
tain
ed
th
r
o
u
g
h
th
e
FF
T
an
aly
s
is
.
T
h
e
T
OGI
f
ilter
b
ased
PLL
s
(
DT
OGI
PLL
an
d
DT
O
GI
-
L
PF
PLL
)
s
h
o
wca
s
e
s
lo
wer
d
y
n
am
ic
r
esp
o
n
s
e
d
u
e
t
o
i
n
cr
ea
s
e
in
o
r
d
er
o
f
th
e
f
ilter
a
n
d
co
m
p
le
x
ity
.
Yet
,
th
ey
ex
h
i
b
it
m
in
im
u
m
h
ar
m
o
n
ics
co
n
te
n
t
in
th
e
e
x
tr
ac
ted
s
ig
n
als
with
T
HD
co
n
ten
t
as
1
.
3
5
%
(
DT
OGI
PL
L
)
an
d
0
.
0
4
%
(
DT
OGI
-
L
PF
PLL
)
with
least
s
tead
y
s
tate
r
ip
p
les.
T
h
e
MST
OGI
f
ilter
b
ased
PLL
s
(
DM
STOG
I
PLL
an
d
DM
STOG
I
-
L
PF
PLL
)
s
h
o
wca
s
e
s
lo
wer
d
y
n
a
m
ic
r
esp
o
n
s
e,
m
o
r
e
T
HD
co
n
ten
t
an
d
s
am
e
s
tead
y
s
tate
r
ip
p
les
a
s
th
e
SOGI
b
a
s
ed
PLL
s
b
u
t
f
aster
d
y
n
am
ic
r
esp
o
n
s
e
th
an
T
OGI
b
ased
PLL
s
.
T
h
e
T
HD
co
n
ten
t
in
th
e
ex
tr
ac
ted
s
ig
n
als
as
4
.
2
5
%
(
DM
STOG
I
PLL
)
a
n
d
0
.
2
3
%
(
DM
STOG
I
-
L
PF
PLL
)
r
esp
ec
tiv
ely
ar
e
o
b
tain
ed
th
r
o
u
g
h
th
e
FF
T
a
n
aly
s
is
.
Ov
er
ally
,
th
e
p
r
o
p
o
s
ed
m
eth
o
d
s
ex
h
ib
it
r
o
u
g
h
ly
f
aster
d
y
n
am
ic
r
esp
o
n
s
e
o
r
r
esp
o
n
s
iv
en
ess
in
ter
m
s
o
f
s
ettlin
g
tim
e
an
d
b
etter
h
ar
m
o
n
ics
f
ilter
in
g
ab
ilit
y
th
an
th
e
s
tan
d
a
r
d
GI
b
ased
PLL
s
.
T
h
is
m
ar
k
s
a
s
ig
n
if
ican
t
en
h
an
ce
m
e
n
t.
Ad
d
iti
o
n
ally
,
it
b
o
asts
th
e
lo
west f
r
eq
u
en
cy
o
v
er
s
h
o
o
t.
Her
e,
th
e
DT
OGI
-
L
PF
PLL
ac
ts
as th
e
s
u
p
er
io
r
o
n
e
f
o
llo
wed
b
y
th
e
DM
STOG
I
-
L
PF
PLL
.
Fu
r
th
er
in
f
o
r
m
atio
n
ca
n
b
e
f
o
u
n
d
in
T
a
b
le
1
.
4
.
2
.
DC
o
f
f
s
et
present
in t
he
g
rid v
o
lt
a
g
e
F
r
o
m
0
.
2
s
e
c
o
n
d
s
t
o
0
.
4
s
e
c
o
n
d
s
,
a
D
C
o
f
f
s
et
i
s
i
n
j
ec
t
e
d
o
f
m
a
g
n
i
t
u
d
e
s
o
f
0
.
2
p
.
u
.
(
p
h
a
s
e
a
)
,
0
.
1
p
.
u
.
(
p
h
a
s
e
b
)
,
a
n
d
-
0
.
2
p
.
u
.
(
p
h
a
s
e
c
)
i
n
t
h
e
i
n
p
u
t
a
b
c
g
r
i
d
v
o
l
t
a
g
e
.
T
h
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I
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p
Sci
,
Vo
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39
,
No
.
1
,
J
u
ly
20
25
:
23
-
32
28
(
a)
(
b
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(
c)
(
d
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e)
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(
g
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Fig
u
r
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5
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latio
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s
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v
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29
Un
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test
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th
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s
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f
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ased
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t
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y
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ase
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ch
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o
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izatio
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.
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h
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s
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it
is
ev
id
en
t
th
at
SOGI
b
ased
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s
(
DSOGI
P
L
L
an
d
DSOGI
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L
PF
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)
an
d
T
OGI
b
ased
PL
L
s
(
DT
OGI
PLL
an
d
DT
OGI
-
L
PF
PLL
)
ex
h
ib
it
s
tead
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tate
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cillatio
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s
in
r
esp
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s
e
to
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f
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h
e
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L
PF
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d
is
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lay
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n
ill
f
r
eq
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en
c
y
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v
e
r
s
h
o
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t
as
0
Hz
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d
a
f
aster
r
esp
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n
s
e
o
r
a
s
ettlin
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e
with
in
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cle.
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ile,
th
e
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d
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a
f
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s
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e
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ar
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e
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L
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n
co
n
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o
th
t
h
e
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a
n
d
T
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ilter
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ased
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ail
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ate
in
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ac
k
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th
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g
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id
f
r
eq
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d
p
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ase
wh
en
th
e
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f
f
s
et
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p
r
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in
th
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t
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ig
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h
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ilter
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p
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o
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icac
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ase
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ac
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et
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p
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m
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with
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esp
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e,
m
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u
m
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t,
a
cc
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ate
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aster
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ase
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atio
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d
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is
e
s
y
n
ch
r
o
n
izatio
n
.
(
a)
(
b
)
(
c)
(
d
)
(
e)
(f)
(
g
)
Fig
u
r
e
6
.
Simu
latio
n
r
esp
o
n
s
e
s
o
f
all
ad
v
an
ce
d
PLL
s
d
u
r
i
n
g
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o
f
f
s
et
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g
r
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o
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e
:
(
a)
p
o
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ted
g
r
id
v
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e
in
abc
f
r
am
e
,
(
b
)
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an
d
DSOGI
-
L
PF
PLL
s
r
esp
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n
s
e
in
dq
f
r
a
m
e
,
(
c)
DT
OGI
an
d
DT
OGI
-
L
PF
PLL
s
r
esp
o
n
s
e
in
dq
f
r
am
e
,
(
d
)
DM
STOG
I
an
d
DM
STOG
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-
L
PF
PLL
s
r
esp
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s
e
in
dq
f
r
a
m
e
,
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n
d
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ated
f
r
eq
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en
c
y
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m
p
ar
is
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n
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f
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an
d
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L
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PLL
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(f)
a
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al
an
d
esti
m
ated
f
r
eq
u
en
cy
co
m
p
ar
is
o
n
o
f
DT
OGI
an
d
D
T
OGI
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L
PF
PLL
,
an
d
(
g
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Actu
al
an
d
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ated
f
r
eq
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m
p
ar
is
o
n
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f
DM
STOG
I
an
d
DM
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I
-
L
PF
PLL
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
5
2
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
,
Vo
l.
39
,
No
.
1
,
J
u
ly
20
25
:
23
-
32
30
5.
CO
NCLU
SI
O
N
T
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is
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ap
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ased
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n
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an
d
th
e
DC
o
f
f
s
ets
p
r
esen
t
in
th
e
g
r
i
d
v
o
ltag
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.
T
h
e
p
r
o
p
o
s
ed
GI
-
L
PF
PLL
s
(
DSOGI
-
L
PF
PLL
,
DT
OGI
-
L
PF
PLL
an
d
DM
STOG
I
-
L
PF
P
LL
)
d
em
o
n
s
tr
ate
s
u
p
er
io
r
d
y
n
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ic
p
er
f
o
r
m
a
n
ce
with
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n
h
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ce
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f
ilter
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g
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p
ac
ity
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m
in
im
al
f
r
e
q
u
en
cy
o
v
er
s
h
o
o
ts
an
d
ac
cu
r
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te
f
r
eq
u
en
cy
esti
m
atio
n
co
m
p
ar
ed
to
th
e
s
tan
d
ar
d
GI
b
ased
PLL
s
(
DSOGI
PLL
,
DT
OGI
PLL
an
d
DM
STOG
I
PLL
)
.
I
t
is
o
b
s
er
v
ed
th
at
u
n
d
e
r
two
p
h
ase
v
o
ltag
e
s
ag
with
5
th
a
n
d
7
th
h
ar
m
o
n
ics,
th
e
d
y
n
am
ic
r
esp
o
n
s
e
a
n
d
T
HD
co
n
te
n
t
o
f
ex
tr
ac
te
d
s
ig
n
als
th
r
o
u
g
h
FF
T
an
aly
s
is
d
eter
m
in
e
th
e
f
ilter
in
g
ef
f
icien
cy
o
f
DT
OGI
-
L
PF
PLL
as
th
e
s
u
p
er
io
r
o
n
e
f
o
llo
wed
b
y
th
e
DM
STOG
I
-
L
PF
PLL
.
On
th
e
o
th
er
h
an
d
,
th
e
DM
STOG
I
-
L
PF
PLL
d
em
o
n
s
tr
ates
s
tr
o
n
g
est
p
er
f
o
r
m
an
ce
in
th
e
p
r
esen
ce
o
f
DC
o
f
f
s
et.
T
h
e
p
r
o
p
o
s
ed
GI
-
L
PF
b
ased
PLL
s
en
h
an
ce
th
e
s
tan
d
ar
d
GI
b
ased
PLL
s
p
er
f
o
r
m
an
ce
i
n
ter
m
s
o
f
im
p
r
o
v
e
d
d
y
n
am
ic
r
esp
o
n
s
e,
h
ar
m
o
n
ics
f
ilter
in
g
an
d
p
r
ec
is
e
p
h
ase
tr
ac
k
in
g
.
C
o
n
s
eq
u
en
tly
,
it
i
s
in
f
er
r
ed
f
o
r
m
th
e
s
im
u
latio
n
r
esu
lts
-
b
ased
an
aly
s
is
ca
r
r
ied
o
u
t
in
MA
T
L
AB
f
o
r
co
m
p
ar
is
o
n
th
at
am
o
n
g
all
th
e
PLL
s
,
th
e
p
r
o
p
o
s
ed
DM
STOG
I
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L
PF
PLL
ex
h
ib
its
s
u
p
er
i
o
r
p
er
f
o
r
m
an
ce
u
n
d
er
th
e
two
test
ca
s
es
with
two
p
h
ase
v
o
ltag
e
s
ag
with
5
th
an
d
7
th
h
ar
m
o
n
ics
an
d
DC
o
f
f
s
et
r
ejec
tio
n
ca
p
a
b
ilit
ies,
en
h
an
ce
d
p
h
ase
tr
ac
k
in
g
a
n
d
d
y
n
am
ic
r
esp
o
n
s
e.
T
h
e
f
in
d
in
g
s
s
h
ed
lig
h
t
o
n
t
h
e
p
er
f
o
r
m
a
n
ce
ac
co
m
p
lis
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m
en
t
o
f
GI
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L
PF
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ased
PLL
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n
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er
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io
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is
tu
r
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ce
co
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tio
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m
ak
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th
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o
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g
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F
UNDING
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DATA AV
AI
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AB
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ticle
[
an
d
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r
its
s
u
p
p
lem
en
tar
y
m
ater
ials
]
.
RE
F
E
R
E
NC
E
S
[
1
]
K
.
Z
e
b
e
t
a
l
.
,
“
A
c
o
mp
r
e
h
e
n
s
i
v
e
r
e
v
i
e
w
o
n
i
n
v
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r
t
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r
t
o
p
o
l
o
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s
a
n
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c
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n
t
r
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l
st
r
a
t
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s
f
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n
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c
t
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d
p
h
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t
o
v
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t
a
i
c
s
y
st
e
m,
”
Re
n
e
w
a
b
l
e
a
n
d
S
u
st
a
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n
a
b
l
e
En
e
rg
y
R
e
v
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e
w
s
,
v
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l
.
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p
p
.
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j
.
r
ser.
2
0
1
8
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0
6
.
0
5
3
.
[
2
]
P
.
G
a
w
h
a
d
e
a
n
d
A
.
O
j
h
a
,
“
R
e
c
e
n
t
a
d
v
a
n
c
e
s
i
n
s
y
n
c
h
r
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z
a
t
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n
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q
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s
f
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g
r
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d
-
t
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d
P
V
sy
s
t
e
m
:
A
r
e
v
i
e
w
,
”
En
e
r
g
y
Re
p
o
r
t
s
,
v
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l
.
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p
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[
3
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S
.
G
o
l
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s
t
a
n
,
A
.
A
k
h
a
v
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n
,
J.
M
.
G
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e
r
o
,
A
.
M
.
A
b
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s
o
r
r
a
h
,
M
.
J.
H
.
R
a
w
a
,
a
n
d
J.
C
.
V
a
s
q
u
e
z
,
“
I
n
-
l
o
o
p
f
i
l
t
e
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s
a
n
d
p
r
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f
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l
t
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n
p
h
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se
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l
o
c
k
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d
l
o
o
p
sy
s
t
e
ms
:
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q
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i
v
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l
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t
o
r
d
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f
f
e
r
e
n
t
s
o
l
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t
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n
s
?
,
”
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EE
E
I
n
d
u
s
t
ri
a
l
E
l
e
c
t
r
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s
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e
,
v
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.
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.
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p
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I
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2
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1
.
3
1
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1
6
5
2
.
[
4
]
S
.
G
o
l
e
st
a
n
,
J.
M
.
G
u
e
r
r
e
r
o
,
M
.
J
.
H
.
R
a
w
a
,
A
.
M
.
A
b
u
so
r
r
a
h
,
a
n
d
Y
.
A
l
-
T
u
r
k
i
,
“
F
r
e
q
u
e
n
c
y
-
l
o
c
k
e
d
l
o
o
p
s
i
n
e
l
e
c
t
r
i
c
a
l
p
o
w
e
r
a
n
d
e
n
e
r
g
y
s
y
s
t
e
ms
:
e
q
u
i
v
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l
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n
t
o
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d
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f
f
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n
t
t
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s
e
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l
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k
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d
l
o
o
p
s
?
,
”
I
EE
E
I
n
d
u
st
r
i
a
l
El
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c
t
ro
n
i
c
s
M
a
g
a
z
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e
,
v
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l
.
1
5
,
n
o
.
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,
p
p
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5
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–
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4
,
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c
.
2
0
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,
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:
1
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0
9
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2
0
2
1
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3
0
5
4
5
8
0
.
[
5
]
Y
.
H
u
a
n
g
e
t
a
l
.
,
“
I
mp
a
c
t
s
o
f
p
h
a
s
e
-
l
o
c
k
e
d
l
o
o
p
d
y
n
a
mi
c
o
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t
h
e
st
a
b
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D
C
-
l
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k
v
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l
t
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g
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c
o
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t
r
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l
i
n
v
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l
t
a
g
e
so
u
r
c
e
c
o
n
v
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r
t
e
r
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n
t
e
g
r
a
t
e
d
t
o
w
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a
k
g
r
i
d
,
”
I
EE
E
J
o
u
r
n
a
l
o
n
Em
e
rg
i
n
g
a
n
d
S
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l
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c
t
e
d
T
o
p
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c
s
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n
C
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t
s
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d
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m
s
,
v
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.
1
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1
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.
[
6
]
Z.
-
X
.
Z
o
u
a
n
d
M
.
Li
serr
e
,
“
M
o
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-
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l
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t
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f
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c
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d
c
o
n
v
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r
t
e
r
s
,
”
I
E
EE
T
ra
n
s
a
c
t
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o
n
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E
n
e
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2
9
3
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4
2
5
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
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J
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n
g
&
C
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m
p
Sci
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N:
2502
-
4
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5
2
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d
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d
g
en
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liz
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r
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id
…
(
P
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Tr
ip
a
th
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)
31
[
7
]
J.
X
u
e
t
a
l
.
,
“
O
v
e
r
v
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e
w
o
f
S
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I
-
b
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s
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n
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p
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P
h
.
D.
d
e
g
re
e
in
El
e
c
tri
c
a
l
E
n
g
i
n
e
e
rin
g
i
n
2
0
1
8
fr
o
m
KIIT
Un
i
v
e
rsity
,
Bh
u
b
a
n
e
sw
a
r,
In
d
ia.
S
h
e
is
wo
rk
i
n
g
a
s
a
ss
o
c
iate
p
ro
fe
ss
o
r
in
S
c
h
o
o
l
o
f
El
e
c
tri
c
a
l
En
g
i
n
e
e
rin
g
,
KIIT
Un
iv
e
rsity
,
B
h
u
b
a
n
e
sw
a
r,
In
d
ia.
He
r
re
se
a
rc
h
a
re
a
in
c
lu
d
e
s
p
o
we
r
q
u
a
li
ty
e
n
h
a
n
c
e
m
e
n
t,
p
o
we
r
e
lec
tro
n
ics
a
n
d
d
ri
v
e
s
,
d
e
sig
n
,
a
n
a
l
y
sis
a
n
d
a
p
p
li
c
a
ti
o
n
s
o
f
a
c
ti
v
e
a
n
d
p
a
ss
iv
e
fil
ters
f
o
r
h
ig
h
p
o
we
r
a
p
p
li
c
a
ti
o
n
s,
a
n
d
g
rid
sy
n
c
h
ro
n
isa
ti
o
n
tec
h
n
i
q
u
e
s.
Sh
e
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
b
m
isra
fe
l@k
ii
t.
a
c
.
in
.
Dr
.
By
a
m
a
k
e
sh
Na
y
a
k
re
c
e
iv
e
d
h
is
M
a
ste
r
De
g
re
e
in
El
e
c
tr
ica
l
En
g
in
e
e
rin
g
fro
m
In
st
it
u
te
o
f
Tec
h
n
o
l
o
g
y
,
Ba
n
a
ra
s
Hin
d
u
Un
i
v
e
rsity
(IT
-
BHU
),
In
d
ia
a
n
d
P
h
.
D.
d
e
g
re
e
in
El
e
c
tri
c
a
l
En
g
i
n
e
e
rin
g
fr
o
m
KIIT
Un
iv
e
rsity
,
Bh
u
b
a
n
e
sw
a
r,
In
d
ia
.
He
is
c
u
rre
n
tl
y
wo
r
k
in
g
a
s
De
a
n
,
S
c
h
o
o
l
o
f
El
e
c
tri
c
a
l
E
n
g
i
n
e
e
rin
g
,
KIIT
Un
i
v
e
rsity
,
Bh
u
b
a
n
e
sw
a
r,
In
d
ia
.
His
re
se
a
rc
h
in
tere
st
in
c
lu
d
e
s
re
n
e
wa
b
le
e
n
e
rg
y
,
p
o
we
r
e
lec
tro
n
ics
a
n
d
e
lec
tri
c
a
l
d
riv
e
s
a
n
d
a
p
p
li
c
a
ti
o
n
o
f
P
IC
M
icro
c
o
n
tro
ll
e
rs
in
sp
e
c
ial
d
riv
e
a
p
p
li
c
a
ti
o
n
s,
h
y
b
rid
v
e
h
icle
a
n
d
m
u
lt
i
lev
e
l
in
v
e
rters
.
He
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
e
lec
tri
c
b
k
n
1
1
@
g
m
a
il
.
c
o
m
.
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