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y
h
ar
m
o
n
ics;
h
o
w
ev
er
,
t
h
e
y
s
u
f
f
er
f
r
o
m
i
m
m
u
n
it
y
a
g
ain
s
t
lo
w
o
r
d
er
h
ar
m
o
n
ics
ac
c
o
r
d
in
g
to
[
1
5
-
1
8
]
.
I
n
[
1
8
]
a
co
m
p
ar
ativ
e
ti
m
e
d
o
m
ai
n
p
er
f
o
r
m
an
ce
ev
a
lu
atio
n
o
f
ad
ap
tiv
e
tech
n
iq
u
es
;
s
u
ch
as
P
s
eu
d
o
L
i
n
ea
r
-
en
h
an
ce
d
P
L
L
(
P
L
-
E
P
L
L
)
,
SOGI
-
Fre
q
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e
n
c
y
L
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ck
ed
L
o
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p
(
SOGI
-
FLL
)
an
d
A
d
ap
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m
o
d
e
Ob
s
er
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A
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f
o
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s
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s
p
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w
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t
h
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f
f
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t
s
o
f
lo
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d
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h
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o
t r
ep
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ted
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h
is
p
ap
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ts
a
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el
s
y
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h
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izat
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o
r
it
h
m
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elies
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f
ac
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th
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t
a
P
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L
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s
y
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ch
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ized
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ta
te
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th
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ta
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et
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te
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t
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ig
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al
a
n
d
th
e
r
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ce
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i
g
n
a
l
[
1
9
]
.
T
h
u
s
,
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
,
as
s
h
o
w
n
in
F
ig
u
r
e
1
,
im
p
le
m
e
n
ts
a
f
ee
d
b
ac
k
th
at
u
s
es
th
e
esti
m
ated
p
h
ase
o
u
tp
u
t
o
b
tain
ed
f
r
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m
a
P
L
L
o
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er
t
h
e
d
u
r
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n
o
f
o
n
e
c
y
cle
o
f
t
h
e
n
o
m
i
n
al
f
r
eq
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e
n
c
y
o
f
th
e
g
r
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e.
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h
e
s
lo
p
(
esti
m
ated
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ase
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e
c
y
cle)
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d
ir
ec
tl
y
e
m
p
lo
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lcu
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ate
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d
ev
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n
i
n
th
e
f
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eq
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n
c
y
f
r
o
m
t
h
e
n
o
m
i
n
al
(
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r
in
itial)
v
alu
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f
t
h
e
g
r
id
f
r
eq
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en
c
y
.
T
h
e
am
o
u
n
t
o
f
d
ev
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n
i
n
th
e
f
r
eq
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en
c
y
is
th
e
n
u
s
ed
to
u
p
d
ate
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v
ar
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le
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an
s
p
o
r
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elay
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t
h
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Qu
ad
r
at
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e
Si
g
n
al
Ge
n
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ato
r
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QSG)
to
g
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o
r
th
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g
o
n
al
s
tatio
n
ar
y
r
e
f
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ce
f
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m
e
s
i
g
n
als o
f
th
e
g
r
id
v
o
ltag
e
(
)
.
Fig
u
r
e
1
.
M
o
d
if
ied
ti
m
e
d
ela
y
P
h
ase
L
o
c
k
ed
L
o
o
p
u
s
i
n
g
MH
DC
w
it
h
p
r
o
p
o
s
ed
tim
e
d
ela
y
ad
j
u
s
t
m
e
n
t a
t t
h
e
t
w
o
-
p
h
ase
g
en
er
ato
r
T
h
e
p
r
o
p
o
s
ed
m
et
h
o
d
s
h
o
w
ed
g
o
o
d
p
er
f
o
r
m
a
n
ce
t
h
at
’
s
ac
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u
r
ate
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d
f
a
s
t
i
n
est
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m
a
tin
g
t
h
e
p
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ase
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n
d
f
r
eq
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en
c
y
o
f
th
e
g
r
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v
o
ltag
e
s
ig
n
al.
Ho
w
e
v
er
,
th
e
p
er
f
o
r
m
an
ce
o
f
th
e
p
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o
p
o
s
ed
alg
o
r
ith
m
d
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io
r
ates
in
t
h
e
p
r
esen
ce
o
f
th
e
lo
w
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h
ar
m
o
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ic
s
d
u
e
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th
e
li
m
ited
b
an
d
w
id
t
h
P
I
c
o
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tr
o
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(
v
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ltag
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co
n
tr
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lled
o
s
cillato
r
)
in
t
h
e
P
L
L
.
I
n
o
r
d
er
to
elim
in
ate
t
h
e
ef
f
ec
t
o
f
lo
w
o
r
d
er
h
ar
m
o
n
ics,
a
Mu
lti
Har
m
o
n
ic
Dec
o
u
p
lin
g
C
el
l
(
MH
DC
)
as p
r
o
p
o
s
ed
in
[
1
7
]
,
is
i
m
p
le
m
e
n
ted
to
f
ilter
t
h
e
g
r
i
d
f
u
n
d
a
m
e
n
tal
s
i
g
n
als.
2.
Q
UAD
RAT
URE
S
I
G
NA
L
G
E
NE
RATOR
C
lar
k
e
tr
an
s
f
o
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m
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s
a
w
ell
-
k
n
o
w
n
m
e
th
o
d
u
s
ed
in
th
r
ee
p
h
ase
ap
p
licatio
n
s
to
g
e
n
er
at
e
th
e
t
w
o
o
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th
o
g
o
n
al
s
tat
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n
ar
y
r
ef
er
e
n
ce
f
r
a
m
e
v
o
lta
g
es
(
)
.
Ho
w
e
v
er
,
in
s
i
n
g
le
p
h
ase
ap
p
licatio
n
s
,
s
e
v
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p
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s
s
ib
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ies
e
x
i
s
t
f
o
r
th
e
p
h
a
s
e
g
en
er
ato
r
,
s
u
ch
a
s
a
m
et
h
o
d
u
s
i
n
g
a
lo
o
k
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u
p
tab
le,
m
et
h
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d
s
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s
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g
a
f
ir
s
t
-
o
r
d
er
an
d
a
s
ec
o
n
d
-
o
r
d
er
f
ilter
s
[
2
0
]
an
d
m
et
h
o
d
s
u
s
i
n
g
tr
an
s
p
o
r
t
d
elay
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f
T
/4
(
d
elay
o
f
q
u
ar
ter
c
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cle
o
f
f
u
n
d
a
m
en
ta
l
v
o
lta
g
e)
[
1
7
,
2
1
]
.
T
h
e
m
e
th
o
d
u
s
i
n
g
th
e
f
ir
s
t
-
o
r
d
er
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s
h
o
w
s
t
h
e
s
h
o
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test
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s
ti
m
atio
n
t
i
m
e
an
d
th
e
m
e
th
o
d
u
s
in
g
t
h
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o
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d
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o
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d
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f
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s
h
o
w
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le
s
s
o
s
cilla
tio
n
[
2
0
]
.
As
d
ep
icted
in
Fi
g
u
r
e
1
,
t
h
e
g
r
id
v
o
ltag
e
(
is
s
en
s
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an
d
th
en
f
ed
to
th
e
QS
G
u
n
it
to
cr
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te
o
r
th
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s
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in
a
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t
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t
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f
C
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th
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p
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ase
s
y
s
te
m
s
.
Fi
g
u
r
e
2
(
a
)
an
d
2
(
b
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s
h
o
w
t
h
e
b
asic s
tr
u
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r
e
o
f
QSG
u
s
in
g
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ir
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,
an
d
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T
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P
L
L
P
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r
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¼
Cy
c
le
De
la
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f
L
in
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V
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l
tag
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+
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1
1
M
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r
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De
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u
p
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Ce
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A
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d
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s
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me
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o
f
t
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me
d
e
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y
to
d
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RF
tran
sf
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r
m
1
Evaluation Warning : The document was created with Spire.PDF for Python.
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u
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p
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d
(
a)
u
s
i
n
g
f
ir
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r
d
er
f
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,
(
b
)
u
s
i
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g
b
asic q
u
ar
ter
c
y
cle
d
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Giv
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n
th
a
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m
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b
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esig
n
,
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d
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g
r
id
f
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eq
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e
n
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y
(
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is
co
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s
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t
a
s
in
an
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s
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n
ar
io
,
th
e
n
th
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q
u
ad
r
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r
e
co
m
p
o
n
e
n
t
o
f
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ca
n
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g
en
er
ated
b
y
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u
ar
ter
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cle
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y
(
i.e
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⁄
,
w
h
er
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is
th
e
s
a
m
p
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g
f
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eq
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en
c
y
a
n
d
is
th
e
g
r
id
f
r
eq
u
en
c
y
)
.
As
s
h
o
w
n
i
n
Fi
g
u
r
e
1
,
th
e
o
u
t
p
u
t
o
f
th
e
t
w
o
-
p
h
a
s
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g
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ato
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is
tr
an
s
f
o
r
m
ed
in
to
th
e
s
y
n
c
h
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o
u
s
l
y
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tatin
g
r
e
f
er
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ce
f
r
a
m
e
(
S
R
F
)
v
o
ltag
es
as:
[
]
[
]
*
+
(
1
)
w
h
er
e
is
t
h
e
esti
m
ated
p
h
a
s
e
an
g
le
o
f
t
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g
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h
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P
L
L
,
ar
e
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m
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t a
n
d
q
u
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r
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co
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o
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e,
r
esp
ec
tiv
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y
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T
h
e
in
p
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t
er
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o
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n
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to
t
h
e
P
L
L
P
I
co
n
tr
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as
s
h
o
w
n
in
F
ig
u
r
e
1
is
g
i
v
e
n
as
[
2
0
,
2
1
]
:
(
2
)
w
h
er
e
,
is
t
h
e
ac
t
u
al
g
r
id
p
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ase.
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eq
.
(
2
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th
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r
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V
q
=0
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n
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V
d
=1
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g
r
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m
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,
if
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ated
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ase
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le
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th
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n
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atch
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it
h
th
e
ac
t
u
al
v
al
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e,
i.e
.
1
(
)
}
(
3
)
Ho
w
e
v
er
,
f
o
r
a
s
m
all
d
e
v
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o
n
in
f
r
o
m
ac
t
u
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v
al
u
e
o
f
t
h
e
g
r
id
p
h
ase
an
g
le
,
th
e
er
r
o
r
s
ig
n
al
in
p
u
t
o
f
th
e
P
I
co
n
tr
o
ller
is
:
(
)
∆
(
4
)
T
h
is
in
it
ial
er
r
o
r
w
il
l
b
e
r
eg
u
l
ated
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e
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L
L
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t
h
er
to
p
r
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d
u
ce
th
at
w
ill
ev
e
n
t
u
all
y
m
atc
h
th
e
ac
t
u
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g
r
id
p
h
ase
(
)
an
d
th
e
P
L
L
w
il
l
en
ter
th
e
s
y
n
ch
r
o
n
ized
s
tat
e
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d
w
ill b
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lo
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ed
.
Un
f
o
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tu
n
atel
y
,
d
u
e
to
d
ev
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ti
o
n
in
t
h
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g
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id
f
r
eq
u
e
n
c
y
f
r
o
m
n
o
m
i
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al
v
al
u
e,
an
d
t
h
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d
is
to
r
tio
n
in
th
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g
r
id
v
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lta
g
e,
t
h
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t
w
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v
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g
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al
s
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p
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d
b
y
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e
t
w
o
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p
h
a
s
e
g
en
er
ato
r
w
il
l
n
o
t
b
e
o
r
th
o
g
o
n
al.
Fo
r
ex
a
m
p
le,
if
Q
SG
is
s
et
to
p
r
o
d
u
ce
b
ased
o
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d
=
2
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k
Hz,
th
en
a
n
a
m
o
u
n
t
o
f
ti
m
e
d
ela
y
,
,
r
eq
u
ir
ed
(
to
p
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d
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ce
th
e
v
o
ltag
e
to
b
e
in
q
u
ad
r
atu
r
e
w
i
th
,
th
e
s
am
p
led
g
r
id
v
o
ltag
e)
w
i
ll
b
e
5
m
s
o
r
1
0
0
s
am
p
les.
O
n
t
h
e
o
th
er
h
a
n
d
,
if
t
h
er
e
is
a
d
ev
iat
io
n
i
n
t
h
e
g
r
id
f
r
eq
u
en
c
y
f
r
o
m
t
h
e
n
o
m
i
n
al
v
a
lu
e
w
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er
e
1
th
en
m
s
o
r
9
8
s
am
p
le
d
ela
y
i
s
r
eq
u
ir
ed
to
p
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o
d
u
ce
v
o
ltag
e
to
b
e
in
q
u
ad
r
atu
r
e
w
i
th
.
T
h
e
ef
f
ec
t
o
f
s
u
c
h
d
ev
iatio
n
i
n
th
e
g
r
id
f
r
eq
u
en
c
y
f
r
o
m
t
h
e
n
o
m
in
al
v
alu
e,
w
il
l th
e
n
r
es
u
lt i
n
an
er
r
o
r
in
t
h
e
t
w
o
v
o
lta
g
es i
n
q
u
ad
r
atu
r
e
as,
(
±
∆
}
(
5)
w
h
er
e
±
∆
is
th
e
p
h
a
s
e
er
r
o
r
in
t
h
e
p
h
ase
.
E
q
u
atio
n
(
2
)
is
th
e
n
m
o
d
i
f
ied
b
ased
o
n
(
5
)
an
d
th
e
ac
tu
al
er
r
o
r
s
ig
n
al
o
f
t
h
e
P
I
r
eg
u
lato
r
b
ec
o
m
es:
(
±
∆
(
)
±
1
∆
1
∆
(
+
(
6)
(
S
a
mp
l
e
r
(
(
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
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m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
Mo
d
ified
p
h
a
s
e
lo
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e
d
lo
o
p
fo
r
g
r
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co
n
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in
g
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p
h
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ter (
E
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d
R
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d
w
a
n
)
3937
E
q
u
atio
n
(
6
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h
as
th
r
ee
ter
m
s
:
th
e
f
ir
s
t
is
s
i
m
ilar
to
th
e
er
r
o
r
ter
m
s
as
in
(
4
)
,
th
e
s
ec
o
n
d
ter
m
is
a
co
n
s
ta
n
t
ter
m
th
at
w
ill
r
es
u
lt
in
a
n
er
r
o
r
in
th
e
e
s
ti
m
ated
p
h
ase
a
n
g
le
b
y
t
h
e
P
L
L
,
an
d
t
h
e
t
h
ir
d
ter
m
is
a
n
o
s
cillato
r
y
ter
m
at
t
w
i
ce
th
e
g
r
id
f
r
eq
u
en
c
y
.
T
h
e
P
I
co
n
t
r
o
ller
w
ill
r
eg
u
late
t
h
e
f
ir
s
t
t
w
o
ter
m
s
to
ze
r
o
,
h
o
w
ev
er
,
t
h
e
t
h
ir
d
ter
m
w
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ll
s
till
p
r
esen
t
o
s
cil
lato
r
y
co
m
p
o
n
en
t
i
n
t
h
e
e
s
ti
m
ated
v
ar
iab
les.
A
lo
w
b
a
n
d
w
id
t
h
P
I
co
n
tr
o
ller
in
th
e
P
L
L
w
ill
r
ed
u
ce
th
is
co
m
p
o
n
en
t,
h
o
w
ev
er
th
is
is
n
o
t
an
o
p
tio
n
s
i
n
ce
a
P
I
c
o
n
tr
o
ller
w
it
h
lo
w
er
b
an
d
w
id
t
h
w
ill
h
a
v
e
a
s
lo
w
er
d
y
n
a
m
ic
r
e
s
p
o
n
s
e.
T
h
e
d
esig
n
co
n
s
tr
ain
t
s
o
n
th
e
P
L
L
P
I
co
n
tr
o
ller
as
ad
d
r
ess
ed
in
th
e
n
e
x
t sec
tio
n
.
3.
DE
S
I
G
N
O
F
P
L
L
P
I
CO
N
T
RO
L
L
E
R
T
h
e
tr
an
s
f
er
f
u
n
ctio
n
r
elati
n
g
t
h
e
in
p
u
t a
n
d
est
i
m
a
ted
p
h
ase
o
f
P
L
L
i
s
ex
p
r
es
s
ed
as,
[
2
0
]
:
̂
(
(
(
7
)
Desig
n
i
n
g
t
h
e
P
I
co
n
tr
o
ller
f
o
r
P
L
L
i
s
a
tr
ad
e
-
o
f
f
p
r
o
ce
s
s
b
et
w
ee
n
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ilter
i
n
g
ca
p
ab
ilit
y
(
atten
u
ati
n
g
th
e
f
u
n
d
a
m
e
n
tal
f
r
eq
u
e
n
c
y
o
f
n
eg
at
iv
e
s
eq
u
en
ce
)
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d
th
e
d
y
n
a
m
ic
p
er
f
o
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m
an
ce
i
n
ter
m
s
o
f
th
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tr
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s
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n
t
ti
m
e
(
f
ast
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ac
k
in
g
)
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f
f
u
n
d
a
m
en
ta
l
f
r
eq
u
en
c
y
p
o
s
iti
v
e
s
eq
u
en
ce
.
B
o
th
r
eq
u
ir
e
m
en
ts
ca
n
’
t
b
e
m
et
s
i
m
u
lta
n
eo
u
s
l
y
.
I
n
[
2
2
]
it
is
s
h
o
w
n
th
at
t
h
e
r
ed
u
ctio
n
o
f
th
e
b
an
d
w
id
t
h
h
as
a
s
ig
n
if
ic
an
t
e
f
f
ec
t
o
n
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s
ettli
n
g
ti
m
e
(
2
%
cr
iter
ia)
o
f
th
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P
L
L
.
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th
e
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t
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h
a
n
d
,
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cr
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s
in
g
t
h
e
b
an
d
w
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t
h
w
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ll
r
es
u
lt
i
n
f
as
ter
r
es
p
o
n
s
e
b
u
t
a
t
th
e
ex
p
e
n
s
e
o
f
f
ilter
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g
(
th
e
at
ten
u
a
tio
n
)
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f
t
h
e
f
u
n
d
a
m
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n
tal
f
r
eq
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en
c
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n
eg
at
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e
s
eq
u
e
n
ce
co
m
p
o
n
en
t.
T
h
er
ef
o
r
e,
in
th
is
p
ap
er
th
e
p
ar
am
eter
s
o
f
th
e
P
I
c
o
n
tr
o
ller
ar
e
s
et
to
as
r
ec
o
m
m
e
n
d
ed
b
y
[
1
7
]
.
Fi
g
u
r
e
3
s
h
o
w
s
th
e
B
o
d
e
p
lo
t
o
f
t
h
e
P
I
co
n
tr
o
ller
u
s
i
n
g
t
h
e
r
ec
o
m
m
e
n
d
ed
v
a
lu
e
s
ab
o
v
e.
T
h
e
P
I
c
o
n
tr
o
ller
h
as
a
p
h
ase
m
ar
g
i
n
o
f
6
5
.
4
o
an
d
cr
o
s
s
o
v
er
f
r
e
q
u
e
n
c
y
o
f
1
0
1
r
ad
/s
w
h
ic
h
m
ee
ts
th
e
r
eq
u
ir
e
m
e
n
t
s
o
f
t
h
e
P
L
L
s
y
s
te
m
.
Fig
u
r
e
3
.
Fre
q
u
en
c
y
r
e
s
p
o
n
s
e
o
f
th
e
P
I
co
n
tr
o
ller
P
L
L
4.
M
UL
T
I
H
ARM
O
NIC DEC
O
U
P
L
I
N
G
C
E
L
L
(
M
H
DC)
T
o
r
em
o
v
e
th
e
o
s
cillatio
n
in
th
e
est
i
m
a
ted
v
ar
iab
les
(
m
ag
n
it
u
d
e
a
n
d
p
h
ase
o
f
t
h
e
g
r
id
)
ca
u
s
ed
b
y
th
e
g
r
id
lo
w
er
o
r
d
er
h
ar
m
o
n
ics,
th
e
MH
D
C
p
r
esen
ted
in
[
1
5
,
1
7
]
is
im
p
le
m
en
te
d
as
in
Fig
u
r
e
1.
T
h
e
im
p
le
m
e
n
tatio
n
o
f
t
h
e
M
HDC
is
b
a
s
ed
o
n
co
n
s
tr
u
cti
n
g
n
p
ar
allel
s
tag
es
to
b
e
eq
u
al
t
o
th
e
n
u
m
b
er
o
f
t
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e
lo
w
er
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er
h
ar
m
o
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ic
s
to
b
e
f
ilter
ed
(
n
=5
f
o
r
f
ilter
in
g
1
st
,
3
rd
,
5
th
,
7
th
,
an
d
9
th
h
ar
m
o
n
ics).
T
h
e
n
s
tag
es
w
ill
esti
m
ate
an
d
s
eg
r
eg
a
te
ea
ch
o
f
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ar
m
o
n
ic
co
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p
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e
n
ts
th
at
ex
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t
in
th
e
g
r
id
s
tatio
n
a
r
y
v
o
ltag
e
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co
m
p
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n
e
n
t
s
.
T
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is
is
d
o
n
e
b
y
th
e
m
ea
n
s
o
f
f
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t
tr
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s
f
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to
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SR
F
(
co
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it
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n
to
DC
eq
u
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v
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n
t,
t
h
u
s
t
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e
f
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in
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eq
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t
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m
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ic
co
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p
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f
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s
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.
T
h
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f
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ed
u
s
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g
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p
a
s
s
f
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ter
w
it
h
c
u
t
-
o
f
f
f
r
eq
u
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n
c
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(
)
.
T
h
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n
s
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s
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t
f
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f
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co
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v
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ted
b
ac
k
to
s
tatio
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ar
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ef
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en
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f
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a
m
e
(
t
h
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y
b
ec
o
m
e
a
t c
o
m
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n
f
r
eq
u
en
c
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,
i.e
.
f
u
n
d
a
m
e
n
tal
f
r
eq
u
e
n
c
y
)
.
T
h
e
m=n
-
1
o
u
tp
u
ts
f
r
o
m
all
s
t
ag
es,
e
x
cl
u
d
in
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f
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r
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=m
,
ar
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u
s
ed
in
a
f
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d
b
ac
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s
tag
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n
in
p
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t
to
ca
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ce
l
o
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e
all
th
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h
a
r
m
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u
s
leav
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g
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u
t
t
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esti
m
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ted
n
h
ar
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o
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ic
co
m
p
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t
as
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in
p
u
t
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r
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p
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in
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tag
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T
h
e
esti
m
ated
h
ar
m
o
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ic
co
m
p
o
n
en
t
s
in
t
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e
i
n
p
u
t si
g
n
al
is
g
i
v
en
b
y
(
8
)
.
̂
∑
*
(
+
[
(
]
*
(
+
̂
(
8
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
9
,
No
.
5
,
Octo
b
er
2
0
1
9
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3
9
3
4
-
3943
3938
w
h
er
e
̂
is
th
e
esti
m
ated
n
h
ar
m
o
n
ic
co
m
p
o
n
e
n
t
(
f
o
r
n
=1
,
3
,
5
…etc)
,
is
QSG
o
u
tp
u
t
o
b
tain
ed
f
r
o
m
th
e
g
r
id
s
ig
n
al,
(
P
ar
k
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s
tr
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s
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m
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r
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w
it
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s
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ee
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(
(
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ass
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h
e
im
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le
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e
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f
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8
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is
s
h
o
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Fi
g
u
r
e
4
f
o
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o
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w
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i
s
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DC
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ilt
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ilter
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r
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p
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9
th
h
ar
m
o
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ic,
Fi
g
.
4
ca
n
b
e
e
x
te
n
d
ed
to
an
y
h
i
g
h
er
o
r
d
er
o
f
h
ar
m
o
n
ics e
x
tr
ac
tio
n
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T
h
e
d
etailed
d
esig
n
a
n
d
an
al
y
s
i
s
o
f
M
HDC is
g
i
v
en
i
n
r
ef
er
e
n
ce
s
[
1
5
,
1
7
]
.
F
(
s
)
+
-
+
+
F
(
s
)
+
-
+
+
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(
s
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Fig
u
r
e
4
.
B
lo
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d
iag
r
a
m
o
f
M
HDC
f
o
r
n
=1
,
3
,
an
d
5
5.
P
RO
P
O
SE
D
M
O
DIFIE
D
T
I
M
E
DE
L
AY
P
L
L
(
M
T
DP
L
L
)
T
h
e
co
n
s
tr
ain
t
s
o
n
t
h
e
P
I
co
n
tr
o
ller
s
et
a
g
o
o
d
r
ec
o
m
m
en
d
at
io
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f
o
r
th
e
b
an
d
w
id
t
h
to
tack
le
th
e
tr
ad
eo
f
f
b
et
w
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n
s
p
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d
o
f
r
esp
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n
s
e
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d
f
il
ter
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g
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is
t
o
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tio
n
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u
e
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ig
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o
r
d
er
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ar
m
o
n
ic
s
in
t
h
e
g
r
id
v
o
ltag
e.
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w
e
v
er
,
a
s
lo
w
d
r
if
t
o
r
v
ar
iatio
n
i
n
th
e
s
u
p
p
l
y
f
r
e
q
u
en
c
y
f
r
o
m
n
o
m
i
n
al
v
a
lu
e,
a
n
d
th
e
p
r
ese
n
ce
o
f
lo
w
er
o
r
d
er
h
ar
m
o
n
ics
i
n
th
e
g
r
id
w
il
l
r
esu
l
t
u
n
f
o
r
t
u
n
ate
l
y
i
n
o
s
cillato
r
y
ter
m
s
at
t
w
ice
t
h
e
s
u
p
p
l
y
f
r
eq
u
en
c
y
,
an
d
t
h
e
h
ar
m
o
n
ic
co
n
ten
t
will
s
t
ill
b
e
o
b
s
er
v
ed
in
t
h
e
esti
m
ated
v
ar
iab
le
s
.
T
h
is
w
i
ll
h
a
v
e
s
i
g
n
if
ica
n
t
d
eter
io
r
atin
g
e
f
f
ec
ts
o
n
th
e
in
s
tan
ta
n
eo
u
s
v
alu
e
o
f
t
h
e
e
s
ti
m
ated
an
g
u
lar
f
r
eq
u
en
c
y
a
n
d
a
m
p
lit
u
d
e
o
f
t
h
e
g
r
id
an
d
co
n
s
eq
u
e
n
tl
y
o
n
t
h
e
p
o
w
e
r
q
u
alit
y
o
f
g
r
id
-
tied
i
n
v
er
ter
a
s
d
is
cu
s
s
ed
in
[
1
7
]
.
A
m
o
d
i
f
ied
ti
m
e
d
ela
y
al
g
o
r
it
h
m
i
s
p
r
o
p
o
s
ed
in
th
is
p
ap
er
to
ad
j
u
s
t
th
e
in
it
ial
ti
m
e
d
ela
y
(
1
/4
cy
cle
o
f
th
e
g
r
id
)
p
er
io
d
ically
,
ev
e
r
y
o
n
e
c
y
cle
o
f
th
e
g
r
id
.
T
h
e
ad
j
u
s
t
m
e
n
t
p
r
o
p
o
s
ed
as
in
Fig
u
r
e
3
d
ep
en
d
s
o
n
t
h
e
s
a
m
p
li
n
g
f
r
eq
u
en
c
y
o
f
t
h
e
p
r
o
ce
s
s
o
r
an
d
an
in
itia
l
v
a
lu
e
o
f
t
h
e
g
r
id
f
r
eq
u
en
c
y
.
T
h
e
m
o
d
if
ied
ti
m
e
d
ela
y
(
±
)
is
allo
w
ed
to
eit
h
er
a
s
i
n
g
le
in
cr
e
m
e
n
t
o
r
d
ec
r
em
en
t
e
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er
y
s
in
g
le
c
y
cle
o
f
t
h
e
g
r
id
to
ad
j
u
s
t th
e
ti
m
e
d
ela
y
u
s
ed
b
y
t
h
e
t
w
o
-
p
h
ase
g
en
er
ato
r
to
p
r
o
d
u
ce
(
)
.
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r
ex
a
m
p
le,
a
s
y
s
te
m
(
e.
g
.
i
n
v
er
ter
)
t
h
at
o
p
er
ates
at
P
W
M
o
f
2
0
k
Hz
s
w
i
tch
in
g
f
r
eq
u
e
n
c
y
w
o
u
ld
r
eq
u
ir
e
a
m
in
i
m
u
m
o
f
2
0
k
Hz
s
a
m
p
li
n
g
f
r
eq
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en
c
y
,
i.e
.
a
g
r
i
d
o
p
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atin
g
at
5
0
Hz
w
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ld
b
e
s
a
m
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led
4
0
0
ti
m
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s
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e
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y
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le.
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h
u
s
,
a
q
u
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ter
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cle
ti
m
e
d
ela
y
(
5
m
s
)
w
ill tr
a
n
s
late
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n
to
a
d
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y
o
f
1
0
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a
m
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les.
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m
m
ed
iate
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ter
th
e
f
ir
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t
c
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cle
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4
0
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am
p
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o
f
t
h
e
g
r
id
v
o
ltag
e
t
h
e
esti
m
ated
p
h
ase
1
̂
is
lo
ad
ed
(
s
to
r
ed
)
an
d
th
en
an
o
th
er
4
0
0
s
a
m
p
les
la
ter
an
o
th
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v
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lu
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i
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led
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̂
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id
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g
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t
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T
=
0
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0
2
s
)
,
w
ill
g
i
v
e
th
e
esti
m
ated
f
r
eq
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e
n
c
y
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∆
̂
∆
b
y
t
h
e
P
L
L
.
T
h
e
d
ev
iatio
n
o
r
e
r
r
o
r
in
th
e
f
r
eq
u
en
c
y
̂
ca
n
b
e
u
s
ed
to
ad
j
u
s
t
t
h
e
q
u
ar
ter
ti
m
e
d
ela
y
(
n
u
m
b
er
o
f
s
a
m
p
les)
±
w
h
er
e
an
d
∆
∆
.
T
h
e
ad
j
u
s
t
m
e
n
t
∆
is
r
o
u
n
d
ed
to
a
n
i
n
teg
er
v
al
u
e
w
h
ic
h
w
il
l
b
e
u
s
ed
to
ad
j
u
s
t
th
e
in
itial ti
m
e
d
ela
y
t
h
at
co
r
r
esp
o
n
d
s
to
n
o
m
i
n
al
g
r
id
f
r
eq
u
en
c
y
.
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e
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i
g
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er
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e
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h
e
i
m
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le
m
e
n
tat
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t
h
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ti
m
e
d
elay
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s
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g
Si
m
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li
n
k
i
s
s
h
o
w
n
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Fi
g
u
r
e
5
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Fig
u
r
e
5
.
Si
m
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li
n
k
b
lo
ck
d
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g
r
a
m
o
f
ti
m
e
d
ela
y
ad
j
u
s
t
m
en
t
6.
RE
SU
L
T
S
A
ND
AN
AL
Y
SI
S
T
h
e
s
i
m
u
la
tio
n
r
es
u
lts
f
o
r
co
n
v
e
n
tio
n
al
P
L
L
an
d
th
e
MT
DP
L
L
s
y
s
te
m
s
ar
e
g
iv
e
n
i
n
th
is
s
ec
t
io
n
.
SIM
UL
I
NK
/M
A
T
L
A
B
is
u
s
e
d
in
th
is
s
tu
d
y
w
it
h
f
o
llo
w
in
g
s
i
m
u
latio
n
Mo
d
el
C
o
n
f
i
g
u
r
atio
n
p
ar
a
m
eter
s
:
So
lv
er
:
Fix
ed
s
tep
au
to
m
atic
s
o
lv
er
w
it
h
f
i
x
ed
s
tep
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ize
o
f
1
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s
a
m
p
lin
g
f
r
eq
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e
n
c
y
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I
n
itial
s
i
m
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la
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n
i
s
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r
r
ied
o
u
t
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n
v
e
s
ti
g
ate
t
h
e
ab
ilit
y
o
f
th
e
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r
o
p
o
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ed
MT
D
P
L
L
to
a
d
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u
s
t
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e
d
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y
w
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e
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th
e
s
u
p
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l
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i
s
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iall
y
a
t
4
9
Hz
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d
5
1
Hz.
R
esu
lt
s
in
Fi
g
u
r
e
6
(
a
)
,
6(
b
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an
d
6
(
c
)
r
esp
ec
tiv
el
y
,
s
h
o
w
t
h
e
t
i
m
e
d
ela
y
ad
j
u
s
t
m
e
n
t,
t
h
e
ti
m
e
d
ela
y
t
h
at
co
r
r
esp
o
n
d
s
to
4
9
Hz,
an
d
p
h
a
s
e
a
n
g
le
o
f
t
h
e
g
r
id
.
R
es
u
lt
s
in
Fi
g
u
r
e
7
s
h
o
w
MT
DP
L
L
o
p
er
atio
n
f
o
r
g
r
id
in
itial
f
r
eq
u
en
c
y
5
1
Hz.
T
h
e
r
esu
l
ts
s
h
o
w
th
at
t
h
e
MT
DP
L
L
w
a
s
ab
le
to
tr
ac
k
a
n
d
d
etec
t
th
e
g
r
id
p
h
a
s
e
an
g
le
a
f
ter
4
c
y
cles
(
0
.
0
8
s
ec
)
in
ca
s
e
o
f
4
9
Hz,
an
d
o
n
e
c
y
c
le
(
0
.
0
2
s
ec
)
w
h
e
n
th
e
g
r
id
at
5
1
Hz.
T
h
e
o
s
cillatio
n
in
t
h
e
esti
m
ated
v
ar
iab
le
w
er
e
eli
m
i
n
ated
in
th
e
ca
s
e
o
f
th
e
MT
DP
L
L
w
h
e
n
co
m
p
ar
ed
w
ith
t
h
e
co
n
v
e
n
tio
n
al
P
L
L
(
im
p
le
m
e
n
ted
w
i
th
a
lo
w
p
a
s
s
f
i
lter
th
at
h
a
s
a
cu
to
f
f
f
r
eq
u
en
c
y
f
ix
ed
at
w
h
ic
h
co
r
r
esp
o
n
d
s
to
n
o
m
i
n
al
g
r
id
f
r
eq
u
en
c
y
).
(
a)
(
b
)
(
c)
Fig
u
r
e
6
.
R
esp
o
n
s
e
o
f
co
n
v
e
n
t
io
n
al
P
L
L
an
d
MT
DP
L
L
w
h
e
n
g
r
id
is
i
n
itial
l
y
at
4
9
Hz
(
a)
(
b
)
(
c)
Fig
u
r
e
7
.
R
esp
o
n
s
e
o
f
co
n
v
e
n
t
io
n
al
P
L
L
an
d
MT
DP
L
L
w
h
e
n
g
r
id
is
i
n
itial
l
y
at
5
1
Hz
Sa
mp
l
i
n
g
o
f
T
h
e
t
a
O
n
e
cyc
l
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I
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lec
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p
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g
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Vo
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9
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5
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9
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9
3
4
-
3943
3942
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ap
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licatio
n
o
f
P
L
L
i
n
s
y
n
ch
r
o
n
izatio
n
o
f
s
in
g
le
-
p
h
a
s
e
g
r
id
-
tied
in
v
er
te
r
.
T
h
e
p
r
o
p
o
s
ed
tech
n
iq
u
e
u
s
es
t
h
e
s
lo
p
o
f
th
e
p
h
ase
a
n
g
le
(
g
e
n
er
ated
b
y
co
n
v
e
n
tio
n
al
P
L
L
)
to
m
o
d
if
y
a
tr
an
s
p
o
r
t
d
elay
ti
m
e
i
n
a
Qu
ad
r
atu
r
e
Sig
n
al
Ge
n
er
ato
r
u
n
it.
T
h
e
ac
cu
r
ac
y
i
n
esti
m
ati
n
g
t
h
e
p
h
ase
o
f
t
h
e
g
r
id
v
o
ltag
e
r
esu
l
ted
in
ca
n
ce
ll
i
n
g
t
h
e
o
s
cillatio
n
an
d
an
y
s
te
ad
y
s
tate
er
r
o
r
s
in
th
e
e
s
ti
m
ated
S
R
F
v
o
lta
g
es.
T
h
is
w
ill
in
tu
r
n
e
n
h
a
n
ce
t
h
e
ef
f
i
cie
n
c
y
o
f
a
g
r
id
t
ied
-
i
n
v
er
ter
.
T
h
e
p
r
o
p
o
s
ed
tech
n
iq
u
e
w
h
en
co
m
b
i
n
ed
with
M
u
lti
Har
m
o
n
ic
Dec
o
u
p
l
in
g
C
ell
s
p
r
o
v
id
es
ex
ce
lle
n
t
ac
cu
r
ac
y
an
d
f
ast
co
n
v
er
g
e
n
ce
ev
e
n
i
n
th
e
p
r
esen
ce
o
f
s
e
v
er
g
r
id
d
is
t
u
r
b
an
ce
s
(
lo
w
er
o
r
d
er
h
ar
m
o
n
ic
s
,
f
r
eq
u
en
c
y
j
u
m
p
,
p
h
ase
j
u
m
p
an
d
v
o
ltag
e
s
a
g
)
.
ACK
NO
WL
E
D
G
E
M
E
NT
S
T
h
e
r
esear
ch
er
s
ar
e
g
r
ate
f
u
l
t
o
th
e
A
p
p
lied
Scien
ce
P
r
iv
ate
Un
i
v
er
s
it
y
Am
m
an
,
J
o
r
d
an
f
o
r
th
e
f
u
l
l
f
i
n
an
cia
l
s
u
p
p
o
r
t g
r
ated
to
th
is
r
esear
ch
p
r
o
j
ec
t
RE
F
E
R
E
NC
E
S
[1
]
K.
Ca
b
a
n
a
,
e
t
a
l.
,
“
V
o
lt
a
g
e
se
n
s
it
iv
it
y
a
n
a
l
y
sis
to
d
e
ter
m
in
e
th
e
o
p
ti
m
a
l
in
teg
ra
ti
o
n
o
f
d
istri
b
u
ted
g
e
n
e
ra
ti
o
n
i
n
d
istri
b
u
ti
o
n
sy
ste
m
s,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
Co
mp
u
ter
En
g
in
e
e
rin
g
(
IJ
ECE
)
,
v
o
l.
9
,
p
p
.
5
5
-
6
5
,
2
0
1
9
.
[2
]
R
.
S
.
R
.
S
a
n
k
a
r,
e
t
a
l.
,
“
A
d
a
p
ti
v
e
F
u
z
z
y
P
I
Cu
rre
n
t
C
o
n
tr
o
l
o
f
G
ri
d
In
tera
c
t
P
V
In
v
e
rter
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
El
e
c
trica
l
a
n
d
C
o
mp
u
ter
En
g
in
e
e
rin
g
(
IJ
ECE
)
,
v
o
l.
8
,
p
p
.
4
7
2
-
4
8
2
,
2
0
1
8
.
[3
]
J
.
R.
Did
a
t,
e
t
a
l.
,
“
M
o
d
e
li
n
g
a
n
d
e
x
p
e
ri
m
e
n
tal
tes
ti
n
g
o
f
a
g
rid
-
c
o
n
n
e
c
ted
sm
a
ll
W
in
d
En
e
rg
y
Co
n
v
e
rsio
n
S
y
ste
m
,
”
EW
EC
2
0
0
6
,
A
th
e
n
s,
G
re
e
c
e
,
2
0
0
6
.
[4
]
Y
.
L
o
n
g
,
a
n
d
Y
.
S
u
n
,
“
A
Ne
w
P
L
L
S
i
m
u
latio
n
V
a
li
d
a
ti
o
n
f
o
r
T
h
re
e
-
p
h
a
se
G
rid
u
n
d
e
r
H
e
a
v
y
Disto
rted
Co
n
d
it
io
n
s,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
On
li
n
e
a
n
d
Bi
o
me
d
ica
l
E
n
g
i
n
e
e
rin
g
(
iJO
E)
,
"
M
ES
I
2
0
1
4
,
"
v
o
l.
11
,
2
0
1
5
.
[5
]
N.
Ja
a
la
m
,
e
t
a
l.
,
“
A
c
o
m
p
re
h
e
n
siv
e
re
v
ie
w
o
f
s
y
n
c
h
ro
n
iza
ti
o
n
m
e
th
o
d
s
f
o
r
g
rid
-
c
o
n
n
e
c
ted
c
o
n
v
e
rters
o
f
re
n
e
wa
b
le
e
n
e
rg
y
so
u
rc
e
,
”
Ren
e
wa
b
le a
n
d
S
u
sta
i
n
a
b
le E
n
e
rg
y
Rev
iews
,
v
o
l.
5
9
,
p
p
.
1
4
7
1
-
1
4
8
1
,
Ju
n
2
0
1
6
.
[6
]
B.
P
.
M
c
G
ra
th
,
e
t
a
l.
,
“
P
o
w
e
r
c
o
n
v
e
rter
li
n
e
s
y
n
c
h
ro
n
iza
ti
o
n
u
sin
g
a
d
isc
re
te
f
o
u
rier
tran
sf
o
r
m
(D
F
T
)
b
a
se
d
o
n
a
v
a
riab
le sa
m
p
le rate
,
”
IEE
E
T
ra
n
s P
o
we
r E
lec
tro
n
.
,
v
o
l.
20
,
p
p
.
8
7
7
-
8
8
4
.
,
2
0
0
5
.
[7
]
M
.
S
.
Re
z
a
,
e
t
a
l.
,
“
A
c
c
u
ra
te
e
stim
a
ti
o
n
o
f
sin
g
le
-
p
h
a
se
g
rid
v
o
lt
a
g
e
p
a
ra
m
e
ters
u
n
d
e
r
d
ist
o
rted
c
o
n
d
it
i
o
n
s
,
”
IEE
E
T
ra
n
s.
Po
we
r De
l
.,
v
o
l
.
2
9
,
p
p
.
7
4
-
8
0
,
F
e
b
2
0
1
4
.
[8
]
K.
De
Bra
b
a
n
d
e
re
,
e
t
a
l.
,
“
De
sig
n
a
n
d
o
p
e
ra
ti
o
n
o
f
a
p
h
a
se
-
lo
c
k
e
d
lo
o
p
w
it
h
Ka
lm
a
n
e
stim
a
to
r
-
b
a
se
d
f
il
ter
f
o
r
sin
g
le
-
p
h
a
se
a
p
p
li
c
a
ti
o
n
s,
”
Pr
o
c
.
IEE
E
IECON/IE
CON
,
p
p
.
5
2
5
-
5
3
0
,
No
v
2
0
0
6
.
[9
]
Y
.
L
iu
,
e
t
a
l
.
,
“
S
ig
n
a
l
F
re
q
u
e
n
c
y
Esti
m
a
ti
o
n
Ba
se
d
o
n
Ka
l
m
a
n
F
il
terin
g
M
e
th
o
d
,
”
W
e
b
o
f
C
o
n
fer
e
n
c
e
s,
In
ter
n
a
t
io
n
a
l
C
o
n
fer
e
n
c
e
o
n
C
o
mp
u
ter
a
n
d
Au
to
ma
t
io
n
E
n
g
i
n
e
e
rin
g
(
ICCAE
2
0
1
6
)
,
v
o
l.
5
6
,
2
0
1
6
.
[1
0
]
S
.
G
o
les
tan
,
e
t
a
l.
,
“
A
n
a
d
a
p
ti
v
e
lea
st
-
e
rro
r
sq
u
a
re
s
f
il
ter
-
b
a
se
d
p
h
a
se
-
lo
c
k
e
d
lo
o
p
f
o
r
s
y
n
c
h
ro
n
iza
ti
o
n
a
n
d
sig
n
a
l
d
e
c
o
m
p
o
siti
o
n
p
u
rp
o
se
s,
”
IEE
E
T
ra
n
s.
I
n
d
.
El
e
c
tro
n
.
,
v
o
l
.
6
4
,
p
p
.
3
3
6
-
3
4
6
,
Ja
n
2
0
1
7
.
[1
1
]
W
.
Da
i,
e
t
a
l.
,
“
A
P
L
L
Co
n
tro
l
B
a
se
d
o
n
A
lg
o
rit
h
m
o
f
BP
Ne
u
ra
l
Ne
tw
o
rk
,
”
CI
M
S
A
2
0
0
9
,
p
p
.
9
7
-
1
0
1
,
M
a
y
2
0
0
9
.
[1
2
]
M
.
K.
G
h
a
rte
m
a
n
i
a
n
d
M
.
R.
Ira
v
a
n
i,
“
A
m
e
th
o
d
f
o
r
s
y
n
c
h
ro
n
iza
ti
o
n
o
f
p
o
w
e
r
e
le
c
tro
n
ic co
n
v
e
rters
in
p
o
ll
u
ted
a
n
d
v
a
riab
le f
r
e
q
u
e
n
c
y
e
n
v
iro
n
m
e
n
ts,
”
IEE
E
T
ra
n
s.
P
o
we
r S
y
ste
ms
,
v
o
l.
1
9
,
p
p
.
1
2
6
3
-
1
2
7
0
,
2
0
0
4
.
[1
3
]
M
.
Cio
b
o
taru
,
e
t
a
l.
,
“
A
n
e
w
si
n
g
le
-
p
h
a
se
P
L
L
stru
c
tu
re
b
a
se
d
o
n
se
c
o
n
d
o
rd
e
r
g
e
n
e
ra
li
z
e
d
in
teg
ra
to
r
,
”
Po
we
r
El
e
c
tro
n
ics
S
p
e
c
ia
li
sts C
o
n
fer
e
n
c
e
2
0
0
6
.
P
ES
C
'
0
6
.
3
7
th
I
EE
E,
2
0
0
6
.
[1
4
]
Y.
Ya
n
g
,
e
t
a
l.
,
“
Be
n
c
h
m
a
rk
in
g
o
f
p
h
a
se
lo
c
k
e
d
lo
o
p
b
a
se
d
sy
n
c
h
ro
n
iza
ti
o
n
tec
h
n
i
q
u
e
s
f
o
r
g
rid
-
c
o
n
n
e
c
ted
in
v
e
rter
s
y
ste
m
s,
”
2
0
1
5
9
th
In
ter
n
a
ti
o
n
a
l
Co
n
fer
e
n
c
e
o
n
P
o
we
r
El
e
c
tro
n
ics
a
n
d
ECCE
Asi
a
(
ICPE
-
ECCE
Asia
)
,
p
p
.
2
1
6
7
-
2
1
7
4
,
2
0
1
5
.
[1
5
]
L
.
Ha
d
ji
d
e
m
e
tri
o
u
,
e
t
a
l
.,
“
A
S
y
n
c
h
ro
n
iza
ti
o
n
M
e
th
o
d
f
o
r
S
i
n
g
le
-
P
h
a
se
G
rid
-
T
i
e
d
In
v
e
rters
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Po
we
r E
lec
tro
n
ics
,
v
o
l
.
31
,
p
p
.
2
1
3
9
-
2
1
4
9
,
2
0
1
6
.
[1
6
]
F
.
X
iao
,
e
t
a
l.
,
“
A
No
v
e
l
Op
e
n
-
lo
o
p
F
re
q
u
e
n
c
y
Esti
m
a
ti
o
n
M
e
th
o
d
f
o
r
S
in
g
le
-
P
h
a
se
G
rid
S
y
n
c
h
ro
n
iza
ti
o
n
u
n
d
e
r
Disto
rted
C
o
n
d
it
i
o
n
s,
”
IEE
E
J
o
u
rn
a
l
o
f
Eme
r
g
in
g
a
n
d
S
e
lec
ted
T
o
p
ics
in
P
o
we
r E
lec
tro
n
ics
,
v
o
l
.
5
,
S
e
p
2
0
1
7
.
[1
7
]
L
.
Ha
d
ji
d
e
m
e
tri
o
u
,
e
t
a
l.
,
“
A
S
y
n
c
h
ro
n
iza
ti
o
n
S
c
h
e
m
e
f
o
r
S
in
g
le
-
P
h
a
se
G
rid
-
T
ied
In
v
e
rters
u
n
d
e
r
Ha
rm
o
n
ic
Disto
rti
o
n
a
n
d
G
rid
Distu
r
b
a
n
c
e
s,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Po
we
r E
l
e
c
tro
n
ics
,
v
o
l.
32,
p
p
.
2
7
8
4
-
2
7
9
3
,
2
0
1
7
.
[1
8
]
H.
A
h
m
e
d
,
e
t
a
l.
,
“
F
a
st
Esti
m
a
ti
o
n
o
f
P
h
a
se
a
n
d
F
re
q
u
e
n
c
y
f
o
r
S
in
g
le
P
h
a
se
G
rid
S
ig
n
a
l,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
In
d
u
stria
l
El
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