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I
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310
298
J
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ttp
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p
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s
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a
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SDFT
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Ac
ti
v
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p
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we
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fil
ters
a
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u
se
d
to
re
d
u
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e
c
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n
t
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a
rm
o
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ics
a
n
d
c
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e
n
sa
te
fo
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re
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c
ti
v
e
p
o
we
r
in
n
o
n
-
li
n
e
a
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a
d
s.
Th
is
p
a
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o
m
p
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s
two
a
p
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a
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s
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c
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-
fra
m
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d
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st
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sfo
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h
m
s
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p
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d
in
t
h
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stu
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y
.
T
h
e
c
o
m
p
a
riso
n
is
b
a
se
d
o
n
th
e
o
u
t
c
o
m
e
s
o
f
sim
u
latio
n
s.
F
o
r
d
iffere
n
t
l
o
a
d
c
o
n
d
it
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o
n
s,
t
h
e
re
su
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ts
a
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e
d
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y
th
e
a
p
p
ro
a
c
h
e
s
m
e
n
ti
o
n
e
d
d
iffer
g
re
a
tl
y
.
Th
e
slid
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d
isc
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te
F
o
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tra
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sfo
rm
S
DFT
a
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te
F
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tran
sfo
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-
p
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e
d
-
l
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p
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r
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DFT
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P
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is
a
p
e
rfe
c
t
m
e
th
o
d
a
ls
o
fo
r
sy
n
c
h
ro
n
izin
g
t
h
e
in
v
e
rter wit
h
a
we
a
k
n
o
isy
g
ri
d
.
K
ey
w
o
r
d
s
:
Fo
u
r
ier
tr
an
s
f
o
r
m
Ph
ase
lo
ck
lo
o
p
Po
wer
q
u
ality
Sli
d
in
g
d
is
cr
ete
Sy
n
ch
r
o
n
izatio
n
T
h
is i
s
a
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c
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ss
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rticle
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d
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r th
e
CC B
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-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
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nd
ing
A
uth
o
r
:
Mo
n
a
M.
Ma
m
d
o
u
h
Dep
ar
tm
en
t o
f
Po
wer
E
lectr
o
n
ics an
d
E
n
er
g
y
C
o
n
v
e
r
s
io
n
,
E
l
ec
tr
o
n
ics R
esear
ch
I
n
s
titu
te
C
air
o
1
2
6
2
2
,
E
g
y
p
t
E
m
ail: d
r
.
m
o
n
am
am
d
o
u
h
@
er
i
.
s
ci.
eg
1.
I
NT
RO
D
UCT
I
O
N
R
ec
en
tly
,
with
th
e
d
im
in
u
tio
n
o
f
f
o
s
s
il e
n
er
g
y
an
d
r
is
in
g
en
v
ir
o
n
m
en
tal
p
r
o
b
lem
s
,
clea
n
en
er
g
y
s
u
ch
as
p
h
o
to
v
o
ltaics
(
PVs
)
an
d
wi
n
d
tu
r
b
in
es
(
W
T
s
)
ar
e
m
o
r
e
p
o
p
u
lar
as
t
h
e
p
er
ce
n
tag
e
o
f
r
e
n
e
wab
le
en
er
g
y
a
d
d
ed
to
th
e
g
r
id
e
x
p
an
d
s
,
th
e
co
n
tr
o
l
o
f
th
em
m
u
s
t
b
e
m
o
r
e
ef
f
i
cien
t
an
d
ef
f
ec
tiv
e
[
1
]
.
Mo
s
t
g
r
id
-
tie
s
y
s
tem
s
f
o
r
ex
am
p
le,
s
h
u
n
t
ac
tiv
e
p
o
wer
f
ilter
s
(
SAPF
s
)
,
u
n
in
ter
r
u
p
ted
p
o
wer
s
u
p
p
lies
(
UPSs
)
,
an
d
f
le
x
ib
le
AC
tr
an
s
m
is
s
io
n
s
y
s
tem
s
(
FA
C
T
S
)
r
eq
u
ir
e
g
r
id
v
o
ltag
e
f
r
eq
u
e
n
cy
an
d
p
h
ase
an
g
le
to
b
e
co
n
v
en
ien
tly
co
n
n
ec
ted
to
th
e
g
r
id
(
s
y
n
ch
r
o
n
izatio
n
)
[
1
]
.
Sy
n
ch
r
o
n
izatio
n
is
v
er
y
i
m
p
o
r
tan
t
f
o
r
s
ig
n
al
p
r
o
ce
s
s
in
g
,
co
n
tr
o
l
p
u
r
p
o
s
es
,
an
d
m
o
n
ito
r
in
g
in
p
o
wer
an
d
en
er
g
y
s
y
s
tem
s
[
2
]
.
Gr
id
s
y
n
ch
r
o
n
izatio
n
is
class
i
f
ied
in
to
th
r
ee
m
eth
o
d
s
.
T
h
e
f
ir
s
t
m
eth
o
d
is
ze
r
o
-
cr
o
s
s
in
g
d
etec
tio
n
(
Z
C
D)
wh
ich
is
t
h
e
ea
s
iest
wa
y
f
o
r
d
eter
m
in
in
g
t
h
e
p
h
ase
o
f
th
e
g
r
id
v
o
ltag
e.
H
o
wev
er
,
its
p
er
f
o
r
m
a
n
ce
is
n
o
t
g
o
o
d
wh
e
n
th
e
g
r
id
v
o
ltag
e
is
d
is
to
r
ted
an
d
its
tr
ac
k
in
g
s
p
ee
d
is
s
lo
w.
T
h
e
s
ec
o
n
d
m
eth
o
d
d
ep
en
d
s
o
n
v
o
ltag
e
g
r
id
f
ilter
in
g
s
u
ch
as
Fo
u
r
ier
tr
an
s
f
o
r
m
,
Kalm
an
f
ilter
in
g
,
an
d
a
r
ctan
g
e
n
t
f
u
n
ctio
n
.
E
ac
h
ty
p
e
is
b
ased
o
n
d
if
f
er
en
t
tech
n
iq
u
e
o
f
f
ilter
in
g
[
1
]
.
I
f
t
h
e
g
r
id
v
o
ltag
e
h
as
in
ter
-
h
ar
m
o
n
ics
o
r
s
u
b
-
ha
r
m
o
n
ics,
d
is
to
r
tio
n
will
h
ap
p
en
a
n
d
s
p
ec
tr
u
m
leak
a
g
e
will
o
cc
u
r
.
T
h
e
f
ir
s
t
an
d
s
ec
o
n
d
m
eth
o
d
s
in
v
o
lv
e
co
m
p
lex
m
ath
em
atica
l
ca
lcu
latio
n
s
wh
ich
m
ay
s
lo
w
d
o
wn
th
e
s
y
s
tem
'
s
p
er
f
o
r
m
an
c
e.
T
h
e
th
ir
d
m
eth
o
d
is
p
h
ase
l
o
ck
ed
lo
o
p
or
PLL
wh
ich
is
s
im
p
le
in
im
p
lem
en
t
atio
n
an
d
p
er
f
o
r
m
s
well
u
n
d
e
r
co
m
p
lex
co
n
d
itio
n
s
.
PLL
is
class
if
ied
as
s
in
g
le
-
p
h
ase
PLL
o
r
th
r
ee
-
p
h
ase
PL
L
.
C
lar
k
an
d
Par
k
tr
a
n
s
f
o
r
m
at
io
n
s
ar
e
th
e
m
o
s
t
wid
ely
u
s
ed
ap
p
r
o
ac
h
in
th
r
ee
-
p
h
ase
PLL
.
I
n
s
in
g
le
-
p
h
ase
ca
s
es,
th
e
g
r
id
d
ata
is
lim
ited
w
h
ich
m
ak
es
th
e
p
er
f
o
r
m
an
ce
o
f
s
in
g
le
-
p
h
ase
PLL
is
ch
allen
g
in
g
.
I
n
o
th
er
way
,
we
ca
n
class
if
y
s
y
n
ch
r
o
n
izatio
n
m
eth
o
d
s
in
to
o
p
en
-
lo
o
p
m
et
h
o
d
s
wh
ich
h
av
e
n
o
f
ee
d
b
ac
k
s
ig
n
als
an
d
clo
s
e
-
lo
o
p
m
eth
o
d
s
wh
ich
h
av
e
f
ee
d
b
a
ck
s
ig
n
als.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
Ha
r
mo
n
ics elimin
a
tio
n
a
n
d
r
e
a
ctive
p
o
w
er c
o
mp
en
s
a
tio
n
b
a
s
ed
o
n
n
o
ve
l S
DF
T
-
P
LL
…
(
O
s
a
ma
M.
A
r
a
fa
)
299
A
clo
s
ed
lo
o
p
is
wid
ely
u
s
ed
i
n
p
o
wer
ap
p
licatio
n
s
.
C
lo
s
ed
l
o
o
p
is
class
if
ied
in
to
two
ca
teg
o
r
ies,
PLL
an
d
f
r
e
q
u
en
c
y
-
lo
ck
e
d
lo
o
p
(
F
L
L
)
.
B
o
th
ar
e
n
o
n
-
lin
ea
r
co
n
t
r
o
l
s
y
s
tem
s
.
PLL
is
u
s
ed
in
s
y
n
ch
r
o
n
o
u
s
r
ef
er
e
n
ce
f
r
am
es,
wh
er
ea
s
FLL
is
u
s
ed
in
s
tatio
n
ar
y
r
ef
er
en
ce
f
r
a
m
es
[
2
]
.
Als
o
,
we
ca
n
s
ay
th
at
PL
L
is
u
s
ed
in
p
o
wer
ap
p
licatio
n
s
b
u
t
FLL
is
em
p
l
o
y
ed
in
o
th
er
ap
p
licatio
n
s
s
u
ch
as
p
o
wer
s
y
s
tem
is
lan
d
d
e
tectio
n
[
3
]
an
d
f
lu
x
esti
m
ate
f
o
r
elec
tr
ical
m
o
to
r
c
o
n
tr
o
l
[
4
]
-
[
6
]
.
Fig
u
r
e
1
d
ep
icts
th
e
b
asic
c
o
m
p
o
n
e
n
ts
o
f
all
PLL
s
:
th
e
p
h
ase
d
etec
to
r
(
PD)
,
lo
o
p
f
ilter
(
L
F),
an
d
v
o
ltag
e
-
co
n
tr
o
lled
o
s
cillato
r
(
VC
O)
.
T
h
er
e
ar
e
n
u
m
er
o
u
s
f
o
r
m
s
o
f
PLL
s
.
A
ty
p
e
-
1
-
PLL
is
th
e
m
o
s
t b
asic ty
p
e
(
a
co
n
tr
o
l
s
y
s
tem
o
f
t
y
p
e
-
N
h
a
s
N
p
o
les
at
th
e
o
r
ig
in
in
its
o
p
en
-
lo
o
p
t
r
an
s
f
er
f
u
n
ctio
n
)
.
T
h
e
y
ar
e
ch
ar
ac
ter
ize
d
b
y
h
a
v
in
g
o
n
e
i
n
teg
r
ato
r
in
th
e
co
n
tr
o
l
lo
o
p
,
s
o
th
e
s
tab
ilit
y
m
ar
g
in
s
ar
e
h
ig
h
.
T
h
eir
m
ain
d
is
ad
v
an
tag
e
is
th
a
t
in
th
e
p
r
esen
ce
o
f
f
r
eq
u
en
cy
d
r
if
ts
,
th
ey
ca
n
n
o
t
attain
a
ze
r
o
av
er
ag
e
s
tead
y
s
tate
p
h
ase
er
r
o
r
.
T
h
is
d
is
ad
v
an
tag
e
ca
n
b
e
s
o
lv
ed
b
y
em
p
lo
y
in
g
a
q
u
asi
-
ty
p
e
PLL
with
f
ast
d
y
n
am
ic
r
esp
o
n
s
e
an
d
s
tr
o
n
g
f
ilter
in
g
ca
p
ac
ity
[
7
]
.
Go
lest
an
et
a
l.
[
7
]
d
ep
ict
a
f
ea
tu
r
e
co
m
p
a
r
is
o
n
o
f
s
y
n
ch
r
o
n
iz
atio
n
alg
o
r
ith
m
s
.
Fig
u
r
e
1
.
T
h
e
b
asic
s
ch
em
e
o
f
a
ty
p
ical
PLL
On
e
o
f
th
e
f
ir
s
t
way
s
to
e
s
tim
a
te
p
h
ase
an
g
les
was
th
e
d
is
cr
et
e
Fo
u
r
ier
tr
an
s
f
o
r
m
m
eth
o
d
(
DFT)
.
T
h
is
m
eth
o
d
p
r
o
v
id
es
a
h
ig
h
lev
el
o
f
h
ar
m
o
n
ic
r
esis
tan
ce
[
8
]
.
Sli
d
in
g
d
is
cr
ete
Fo
u
r
ier
tr
an
s
f
o
r
m
(
SDFT)
is
an
en
h
an
ce
d
v
er
s
io
n
o
f
th
e
DFT
th
at
d
eliv
er
s
o
p
tim
al
co
m
p
u
ta
tio
n
al
p
o
wer
an
d
r
e
d
u
ce
d
late
n
cy
b
y
r
ec
u
r
s
iv
ely
ap
p
ly
in
g
th
e
DFT
alg
o
r
ith
m
.
T
h
er
e
is
a
p
h
ase
s
h
if
t
b
etwe
en
th
e
ac
tu
al
g
r
i
d
an
g
le
an
d
th
e
e
s
tim
ated
an
g
le
if
th
e
SDFT
tim
e
win
d
o
w
is
n
o
t
th
e
s
am
e
as
th
e
g
r
id
p
e
r
io
d
.
So
m
e
s
o
lu
tio
n
s
f
o
r
c
o
m
p
e
n
s
atin
g
f
o
r
th
is
p
h
ase
er
r
o
r
h
av
e
b
ee
n
r
ep
o
r
ted
in
[
8
]
,
f
o
r
ex
am
p
le,
tim
e
-
v
ar
y
in
g
Po
ly
n
o
m
ial
r
eg
r
ess
io
n
an
d
Fo
u
r
ier
co
ef
f
icien
ts
.
T
h
ese
s
tr
ateg
ies,
in
r
ea
lity
,
ar
e
r
en
d
e
r
ed
with
n
o
ta
b
le
co
m
p
le
x
ity
.
T
h
e
u
n
d
esire
d
q
u
alities
o
f
th
e
SDFT
in
th
e
ca
s
e
o
f
o
f
f
-
n
o
m
in
al
f
r
eq
u
en
cy
in
clu
d
e
th
e
p
h
ase
er
r
o
r
(
wh
ich
is
a
f
u
n
ctio
n
o
f
th
e
f
r
e
q
u
en
c
y
d
ev
iatio
n
)
an
d
a
h
ig
h
-
f
r
eq
u
e
n
cy
o
s
cillatio
n
ap
p
a
r
en
t
in
th
e
m
ag
n
itu
d
e
an
d
p
h
ase
an
g
le
esti
m
atio
n
s
.
I
n
th
e
liter
atu
r
e,
th
is
h
ig
h
-
f
r
eq
u
e
n
cy
o
s
cillatio
n
is
d
e
n
o
t
ed
to
a
d
o
u
b
le
-
f
r
e
q
u
en
c
y
r
ip
p
le
,
an
d
p
o
s
t
-
p
r
o
ce
s
s
in
g
f
o
r
f
r
eq
u
en
cy
an
d
p
h
ase
an
g
le
esti
m
ates
in
th
e
o
f
f
-
n
o
m
in
al
m
o
d
e
is
p
r
o
p
o
s
ed
.
Po
s
t
-
p
r
o
ce
s
s
in
g
ca
n
b
e
d
o
n
e
with
eith
er
a
b
asic
d
ig
ita
l
av
e
r
ag
in
g
f
ilter
o
r
a
m
o
r
e
co
m
p
licated
r
esam
p
lin
g
f
ilter
[
9
]
.
Har
m
o
n
ics
ar
e
p
r
o
d
u
ce
d
b
y
th
e
wid
esp
r
ea
d
u
s
e
o
f
n
o
n
lin
ea
r
l
o
ad
s
lik
e
as
p
er
s
o
n
al
c
o
m
p
u
ter
s
,
v
ar
iab
le
s
p
ee
d
d
r
iv
es,
UPS
s
y
s
tem
s
,
a
n
d
o
th
er
elec
tr
o
n
ic
eq
u
ip
m
en
t
.
C
u
r
r
en
t
h
ar
m
o
n
ics
ar
e
wid
ely
u
s
ed
in
in
d
u
s
tr
ial
s
y
s
tem
s
.
Vo
ltag
e
h
ar
m
o
n
ics
in
ter
ac
t
with
s
y
s
tem
im
p
ed
a
n
ce
s
,
r
esu
ltin
g
in
c
u
r
r
en
t
h
ar
m
o
n
ics
th
at
h
a
v
e
a
s
ig
n
if
ican
t
im
p
ac
t
o
n
s
en
s
itiv
e
lo
ad
s
.
E
x
tr
ac
tio
n
o
f
h
ar
m
o
n
ic
cu
r
r
en
t
r
e
f
er
en
ce
(
E
HR
C
)
is
a
k
ey
asp
ec
t
o
f
co
n
tr
o
llin
g
s
h
u
n
t
ac
tiv
e
p
o
wer
f
ilter
s
(
SAP
Fs
)
u
s
ed
in
p
o
wer
s
y
s
tem
s
b
ec
au
s
e
an
y
er
r
o
r
in
r
ef
er
en
ce
cu
r
r
en
ts
r
esu
lts
in
er
r
o
n
eo
u
s
co
m
p
e
n
s
atio
n
.
E
x
ten
s
iv
e
r
esear
ch
o
n
E
HR
C
alg
o
r
ith
m
s
h
as
r
ec
en
tly
b
ee
n
c
o
n
d
u
cte
d
,
an
d
th
e
y
h
av
e
b
ee
n
class
if
ied
in
to
th
r
ee
m
ajo
r
g
r
o
u
p
s
:
tim
e
-
d
o
m
ain
,
f
r
eq
u
e
n
cy
-
d
o
m
ain
,
an
d
m
o
d
er
n
ap
p
r
o
ac
h
es.
Ho
wev
er
,
tim
e
-
d
o
m
ai
n
h
ar
m
o
n
ic
ex
t
r
ac
tio
n
tech
n
iq
u
es
ar
e
alwa
y
s
p
r
ev
alen
t
b
ec
au
s
e
th
ey
o
f
f
er
ea
s
y
im
p
lem
en
tatio
n
f
ea
tu
r
es
with
h
ig
h
er
s
p
ee
d
an
d
lo
wer
co
m
p
u
tin
g
o
v
er
h
ea
d
.
A
s
u
m
m
a
r
y
o
f
h
ar
m
o
n
ic
cu
r
r
en
t
ex
tr
a
ctio
n
tech
n
iq
u
es
is
illu
s
tr
ated
in
T
ab
le
1
[
1
0
]
,
[
1
1
]
.
T
ab
le
1
.
Har
m
o
n
ic
cu
r
r
en
t e
x
tr
ac
tio
n
tech
n
iq
u
es c
lass
if
icati
o
n
Tr
a
d
i
t
i
o
n
a
l
m
e
t
h
o
d
s
M
o
d
e
r
n
m
e
t
h
o
d
s
Ti
me
d
o
m
a
i
n
F
r
e
q
u
e
n
c
y
d
o
m
a
i
n
N
e
u
r
a
l
n
e
t
w
o
r
k
(
NN
)
I
n
st
a
n
t
a
n
e
o
u
s
a
c
t
i
v
e
,
r
e
a
c
t
i
v
e
p
o
w
e
r
(
PQ
)
t
h
e
o
r
y
F
o
u
r
i
e
r
s
e
r
i
e
s
A
d
a
p
t
i
v
e
n
e
u
r
a
l
n
e
t
w
o
r
k
(
ANN
)
C
r
o
ss
-
v
e
c
t
o
r
t
h
e
o
r
y
D
i
scret
e
F
o
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r
i
e
r
t
r
a
n
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o
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m
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D
F
T
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A
d
a
p
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v
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n
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n
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k
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A
D
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D
i
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c
t
me
t
h
o
d
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P
Q
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t
h
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r
y
F
a
st
F
o
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r
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r
t
r
a
n
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o
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N
e
u
r
o
-
f
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S
y
n
c
h
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C
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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N
:
2088
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
6
,
No
.
1
,
Ma
r
c
h
20
2
5
:
298
-
310
300
W
e
will f
o
cu
s
o
n
th
e
m
o
s
t c
r
u
cial
asp
ec
ts
.
Sy
n
ch
r
o
n
o
u
s
r
e
f
e
r
en
ce
f
r
a
m
e
(
SR
F
)
,
also
k
n
o
w
n
as d
-
q
in
o
th
er
d
o
cu
m
e
n
ts
an
d
p
o
wer
P
Q
th
eo
r
y
alg
o
r
ith
m
s
ar
e
th
e
m
o
s
t
co
m
m
o
n
ly
ap
p
lied
tim
e
-
d
o
m
ain
ap
p
r
o
ac
h
es
[
1
0
]
.
T
h
e
cu
r
r
en
t
g
e
n
er
ated
as
a
r
esu
lt
o
f
a
n
o
n
lin
ea
r
l
o
ad
will
h
av
e
b
o
th
f
u
n
d
am
e
n
tal
an
d
h
a
r
m
o
n
i
c
co
m
p
o
n
en
ts
.
W
h
en
a
th
r
ee
-
p
h
ase
ab
c
n
atu
r
al
f
r
a
m
e
is
tr
an
s
f
o
r
m
ed
to
a
two
-
p
h
ase
s
y
n
ch
r
o
n
o
u
s
ly
r
o
tatin
g
f
r
am
e,
t
h
e
h
a
r
m
o
n
ic
co
m
p
o
n
e
n
ts
ap
p
ea
r
as
an
AC
s
ig
n
al
w
h
ile
th
e
f
u
n
d
a
m
en
tal
c
o
m
p
o
n
e
n
t
ap
p
ea
r
s
as
a
DC
s
ig
n
al.
W
h
en
u
s
in
g
SR
F
an
d
PQ
th
eo
r
y
in
h
ar
m
o
n
ic
ex
tr
ac
tio
n
ap
p
licatio
n
s
,
th
e
p
r
ec
i
s
io
n
o
f
th
e
d
etec
ted
f
u
n
d
am
e
n
tal
co
m
p
o
n
en
t
is
cr
itical.
T
h
e
r
eq
u
is
ite
f
u
n
d
am
e
n
tal
co
m
p
o
n
e
n
ts
ar
e
f
r
eq
u
en
t
ly
attain
ed
in
b
o
th
alg
o
r
ith
m
s
b
y
em
p
lo
y
in
g
a
n
in
d
ir
ec
t
d
etec
tio
n
s
tr
ateg
y
,
i
.
e.
,
a
n
u
m
er
ical
B
u
tter
wo
r
th
-
t
y
p
e
lo
w
-
p
ass
f
ilter
(
L
PF
)
.
T
h
e
L
PF
m
eth
o
d
'
s
b
eh
av
io
r
is
ess
en
tially
d
eter
m
in
ed
b
y
th
e
u
s
ed
h
ar
m
o
n
ic
o
r
d
er
.
As
a
r
esu
lt,
th
e
n
u
m
er
ical
L
PF
m
u
s
t
b
e
m
o
d
if
ied
in
o
r
d
er
to
d
eliv
er
th
e
b
est
f
u
n
d
a
m
en
tal
co
m
p
o
n
e
n
t
d
ete
ctio
n
an
d
h
ar
m
o
n
ic
ex
tr
ac
tio
n
p
er
f
o
r
m
a
n
ce
.
I
m
p
r
o
p
er
tu
n
in
g
m
ig
h
t
ca
u
s
e
co
n
s
id
er
ab
le
tim
e
d
elay
s
an
d
d
is
to
r
tio
n
s
d
u
r
in
g
th
e
h
ar
m
o
n
ic
e
x
tr
ac
tio
n
p
r
o
ce
s
s
.
SR
F tec
h
n
iq
u
e
is
s
h
o
wn
in
Fig
u
r
e
2
.
Fig
u
r
e
2
.
d
-
q
h
ar
m
o
n
ic
d
etec
ti
o
n
tech
n
i
q
u
e
I
n
a
th
r
ee
-
p
h
ase
s
y
s
tem
,
th
e
tw
o
ap
p
r
o
ac
h
es
ca
n
c
o
n
tr
o
l
SAPF
to
r
ed
u
ce
c
u
r
r
en
t
h
ar
m
o
n
ics.
Ho
wev
er
,
SAPF
u
s
in
g
th
e
S
R
F
alg
o
r
ith
m
co
n
s
is
ten
tly
s
u
cc
ee
d
s
in
b
o
th
d
y
n
am
ic
-
s
tate
an
d
s
tead
y
-
s
tate
co
n
d
itio
n
s
.
T
h
is
is
m
ain
ly
b
ec
au
s
e
o
f
to
its
s
im
p
le
an
d
r
ap
i
d
p
r
o
ce
s
s
in
g
ch
a
r
a
cter
is
tics
,
wh
ich
r
ed
u
ce
co
m
p
u
tatio
n
al
d
elay
s
[
1
0
]
.
An
o
th
er
m
eth
o
d
is
p
r
esen
ted
in
[
1
2
]
w
h
ich
is
ca
lled
s
y
n
c
h
r
o
n
o
u
s
d
etec
tio
n
m
eth
o
d
(
SD
)
.
W
h
en
th
e
v
o
ltag
e
s
o
u
r
ce
is
co
n
s
id
er
ab
ly
im
b
ala
n
ce
d
,
c
o
n
s
id
er
ab
le
er
r
o
r
s
ca
n
ar
is
e
f
r
o
m
th
e
ca
lcu
latio
n
f
o
r
m
u
la
wh
en
u
s
in
g
th
e
PQ
th
eo
r
y
d
ir
ec
tly
.
T
h
en
,
it
is
d
if
f
icu
lt
to
ex
ec
u
te
r
ea
ctiv
e
an
d
h
ar
m
o
n
ic
cu
r
r
e
n
t
co
r
r
ec
t
io
n
ef
f
icien
tly
with
u
n
b
alan
ce
d
th
r
ee
-
p
h
ase
v
o
ltag
e
s
o
u
r
ce
s
.
T
h
e
SD
ap
p
r
o
ac
h
is
p
r
esen
ted
to
r
e
g
u
late
u
n
b
alan
ce
d
th
r
ee
-
p
h
ase
v
o
ltag
e
s
o
u
r
ce
s
.
T
h
e
eq
u
al
c
u
r
r
en
t
s
y
n
c
h
r
o
n
o
u
s
d
etec
tio
n
m
eth
o
d
is
a
v
er
y
v
alu
ab
le
n
o
tio
n
th
at
s
h
o
u
l
d
b
e
im
p
lem
en
ted
.
Har
m
o
n
ic
ex
tr
a
ctio
n
with
th
e
Fo
u
r
ier
tr
an
s
f
o
r
m
(
FT
)
is
a
co
n
v
en
ien
t
way
f
o
r
ad
ju
s
tin
g
f
o
r
ce
r
tain
h
ar
m
o
n
ic
co
m
p
o
n
en
ts
.
T
h
e
Fo
u
r
ier
tr
an
s
f
o
r
m
r
e
q
u
ir
es
o
n
e
m
o
r
e
cy
cle
o
f
v
o
ltag
e
wav
ef
o
r
m
d
ata
an
d
ass
o
ciate
d
tim
e
to
allo
w
f
o
r
d
elay
ed
h
a
r
m
o
n
ic
ca
n
ce
latio
n
[
1
3
]
.
B
ec
au
s
e
o
f
p
r
o
b
lem
s
in
th
e
PLL
an
d
p
ass
iv
e
f
ilter
s
em
p
lo
y
ed
in
th
is
tech
n
iq
u
e,
th
e
SR
F
tech
n
iq
u
e,
wh
ich
is
o
f
ten
u
s
ed
f
o
r
v
o
ltag
e
s
ag
ex
tr
ac
ti
o
n
,
d
o
es
n
o
t
r
esp
o
n
d
r
ap
id
ly
o
r
ac
cu
r
ately
to
v
o
ltag
e
h
ar
m
o
n
ics
[
1
4
]
.
R
esear
ch
e
r
s
f
r
o
m
a
v
ar
iety
o
f
s
cien
tific
ar
ea
s
,
h
o
wev
er
,
ar
e
in
v
en
tin
g
an
d
d
esig
n
in
g
ar
ti
f
icial
-
n
eu
r
al
-
n
etwo
r
k
s
(
ANN)
to
r
esp
o
n
s
e
ch
allen
g
es
in
p
atter
n
p
r
ed
ictio
n
,
o
p
tim
izatio
n
,
c
o
n
tr
o
l
a
n
d
r
ec
o
g
n
itio
n
.
ADL
I
NE
is
a
f
o
r
m
o
f
ANN
th
at
h
as
th
e
ad
v
a
n
tag
es
o
f
b
ei
n
g
ea
s
ily
d
esig
n
ed
an
d
d
ep
l
o
y
ed
t
h
r
o
u
g
h
h
ar
d
war
e
an
d
h
as b
ee
n
s
u
cc
ess
f
u
lly
ap
p
lied
to
h
a
r
m
o
n
ic
e
x
tr
ac
t
io
n
.
T
h
is
ap
p
r
o
ac
h
m
ay
esti
m
ate
th
e
h
ar
m
o
n
ic
ter
m
s
in
d
iv
id
u
ally
,
s
u
ch
as th
e
m
o
s
t d
am
ag
in
g
5
t
h
an
d
7
t
h
h
ar
m
o
n
ics
[
1
5
]
.
T
o
ad
d
r
ess
th
is
is
s
u
e,
th
e
s
u
g
g
ested
s
lid
in
g
d
is
cr
ete
Fo
u
r
ie
r
tr
an
s
f
o
r
m
-
p
h
ase
-
lo
ck
ed
-
lo
o
p
o
r
SDFT
-
PLL
is
u
s
ed
to
ex
tr
ac
t
th
e
f
u
n
d
am
e
n
tal
lo
a
d
c
u
r
r
en
t
c
o
m
p
o
n
en
t.
E
v
en
wh
en
co
n
n
ec
ted
with
a
v
a
r
iab
le
g
r
id
f
r
eq
u
en
cy
,
SDFT
-
PLL
h
as
an
ef
f
ec
tiv
e
a
b
ilit
y
to
is
o
late
th
e
DC
-
o
f
f
s
et.
T
h
is
m
et
h
o
d
ca
n
b
e
u
tili
ze
d
i
n
s
y
n
ch
r
o
n
izatio
n
ap
p
licatio
n
s
lik
e
[
1
6
]
,
as
well
as
a
h
ar
m
o
n
i
c
ex
tr
ac
tio
n
tech
n
iq
u
e
s
im
ilar
th
e
o
n
e
p
r
o
p
o
s
ed
in
th
is
p
ap
er
.
T
h
is
p
ap
e
r
'
s
co
n
tr
ib
u
tio
n
s
ca
n
b
e
s
u
m
m
ar
ized
as
f
o
llo
ws:
i)
As an
in
n
o
v
ativ
e
u
s
e
o
f
s
u
ch
a
r
eliab
le
tech
n
iq
u
e,
o
b
tain
in
g
th
e
SAPF
's
r
ef
er
en
ce
h
ar
m
o
n
ic
cu
r
r
en
t
u
s
in
g
th
e
SDFT
-
PLL
tech
n
iq
u
e
b
y
ex
tr
ac
tin
g
th
e
f
u
n
d
am
e
n
tal
lo
a
d
c
u
r
r
en
t.
Ke
ep
in
g
t
h
e
ca
p
ac
ito
r
DC
v
o
ltag
e
co
n
s
tan
t
at
its
r
ef
e
r
en
ce
v
al
u
e
th
r
o
u
g
h
o
u
t
n
o
n
-
lin
e
ar
lo
ad
in
s
tan
ce
s
;
ii)
R
eg
ar
d
less
o
f
h
o
w
n
o
n
lin
ea
r
t
h
e
lo
ad
is
,
d
eliv
er
in
g
a
b
alan
ce
d
c
u
r
r
en
t
f
r
o
m
th
e
g
r
id
wit
h
u
n
ity
p
o
wer
f
ac
to
r
a
n
d
to
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
o
r
T
HD
with
in
th
e
I
E
E
E
-
5
1
9
s
tan
d
ar
d
lim
itatio
n
s
;
an
d
iii)
Sh
o
win
g
th
e
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
ef
f
icien
c
y
b
y
co
m
p
ar
i
n
g
it
to
p
r
e
v
io
u
s
ly
p
r
esen
ted
ad
ap
tiv
e
f
ilter
in
g
tech
n
iq
u
es su
ch
as th
e
d
-
q
m
eth
o
d
.
T
h
is
p
ap
er
is
o
r
g
an
ized
as
,
s
ec
tio
n
2
d
escr
ib
es th
e
co
n
f
ig
u
r
at
io
n
o
f
th
e
SAPF
d
is
cu
s
s
in
g
in
d
etails all
its
r
elate
d
co
n
t
r
o
l
al
g
o
r
ith
m
s
,
f
o
cu
s
in
g
o
n
th
e
n
o
v
el
SDFT
-
PLL
co
n
t
r
o
l
f
o
r
th
e
s
y
n
ch
r
o
n
iza
tio
n
an
d
h
ar
m
o
n
ics
cu
r
r
en
t
e
x
tr
ac
tio
n
.
Sectio
n
3
c
o
m
p
ar
es
th
e
s
u
g
g
ested
co
n
tr
o
l
m
eth
o
d
to
t
h
e
p
r
ev
i
o
u
s
d
-
q
c
o
n
tr
o
l
m
et
h
o
d
o
lo
g
y
an
d
p
r
o
v
id
es
a
n
ev
al
u
atio
n
o
f
t
h
e
p
r
o
p
o
s
ed
s
y
s
tem
'
s
p
er
f
o
r
m
an
ce
b
ased
o
n
s
im
u
latio
n
r
esu
l
ts
.
Sectio
n
4
f
in
ally
p
r
esen
ts
th
e
co
n
clu
s
io
n
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
Ha
r
mo
n
ics elimin
a
tio
n
a
n
d
r
e
a
ctive
p
o
w
er c
o
mp
en
s
a
tio
n
b
a
s
ed
o
n
n
o
ve
l S
DF
T
-
P
LL
…
(
O
s
a
ma
M.
A
r
a
fa
)
301
2.
SH
UNT AC
T
I
VE
P
O
W
E
R
F
I
L
T
E
R
S
AP
F
CO
NF
I
G
UR
AT
I
O
N
Fig
u
r
e
3
d
e
p
icts
th
e
SAPF
'
s
b
l
o
ck
d
iag
r
am
.
T
o
ef
f
icien
tly
g
o
v
er
n
th
e
f
u
n
ctio
n
in
g
o
f
SAPF
,
i
ts
co
n
tr
o
l
s
y
s
tem
m
u
s
t b
e
b
u
ilt u
s
in
g
f
o
u
r
d
if
f
er
e
n
t ty
p
es o
f
co
n
tr
o
l a
lg
o
r
ith
m
s
,
ea
ch
o
f
w
h
ich
s
er
v
es a
s
p
ec
if
ic
p
u
r
p
o
s
e
,
as st
ated
in
th
e
f
o
llo
win
g
:
a)
E
x
tr
ac
tio
n
o
f
h
ar
m
o
n
ics alg
o
r
ith
m
T
h
e
p
r
im
ar
y
p
u
r
p
o
s
e
o
f
t
h
is
alg
o
r
ith
m
is
to
ex
tr
ac
t
h
a
r
m
o
n
ic
v
alu
es
f
r
o
m
a
h
a
r
m
o
n
ically
p
o
llu
ted
g
r
id
an
d
u
s
e
th
at
v
alu
es
to
g
en
er
ate
a
r
ef
er
en
ce
cu
r
r
en
t
s
ig
n
al
.
T
h
e
n
o
n
-
lin
ea
r
lo
a
d
cu
r
r
e
n
t
s
ig
n
a
l
is
h
an
d
led
in
th
is
way
s
o
th
at
its
h
ar
m
o
n
i
c
an
d
f
u
n
d
am
en
tal
1
elem
en
ts
ca
n
b
e
is
o
lated
.
Fo
llo
win
g
th
e
s
ep
ar
atio
n
o
f
th
e
elem
en
ts
,
ca
n
b
e
d
er
iv
ed
u
s
in
g
wh
eth
er
th
e
h
ar
m
o
n
ic
o
r
f
u
n
d
am
e
n
tal
elem
en
ts
,
ea
ch
o
f
wh
ich
h
as its
o
wn
s
et
o
f
d
e
r
iv
atio
n
s
.
T
h
is
ap
p
r
o
ac
h
is
also
k
n
o
wn
as
th
e
r
ef
er
en
ce
c
u
r
r
e
n
t
g
en
e
r
atio
n
alg
o
r
ith
m
in
s
o
m
e
p
u
b
licatio
n
s
s
in
ce
it g
en
er
ates r
ef
er
en
ce
c
u
r
r
en
t a
s
its
f
in
a
l o
u
tp
u
t.
b)
Sy
n
ch
r
o
n
izatio
n
alg
o
r
ith
m
T
h
e
p
r
im
a
r
y
r
o
le
o
f
th
is
a
p
p
r
o
ac
h
is
to
f
o
llo
w
th
e
an
g
u
lar
p
o
s
itio
n
o
f
th
e
s
o
u
r
ce
v
o
ltag
e
s
ig
n
al
an
d
th
en
co
n
s
tr
u
ct
a
p
h
ase
-
s
y
n
c
h
r
o
n
izatio
n
a
n
g
le
to
lin
k
th
e
g
e
n
er
ated
.
p
h
ase
to
th
e
r
u
n
n
in
g
p
o
wer
s
y
s
tem
p
h
ase.
T
h
er
e
ar
e
n
u
m
e
r
o
u
s
h
a
r
m
o
n
ic
ex
tr
ac
ti
o
n
m
et
h
o
d
s
d
o
n
o
t
in
clu
d
e
a
p
h
ase
tr
ac
k
in
g
co
m
p
o
n
e
n
t
an
d
in
s
tead
r
ely
s
o
lely
o
n
an
im
p
licit
s
y
n
ch
r
o
n
izatio
n
m
ec
h
an
is
m
to
p
r
o
v
id
e
an
ef
f
ec
tiv
e
s
y
n
ch
r
o
n
izati
o
n
an
g
le.
Ho
wev
er
,
s
o
m
e
h
ar
m
o
n
ic
ex
tr
ac
tio
n
tec
h
n
iq
u
es
in
h
er
it
p
h
ase
tr
ac
k
in
g
a
b
ilit
y
,
s
u
ch
as
th
e
in
s
tan
tan
eo
u
s
p
o
wer
p
-
q
t
h
eo
r
y
.
An
ex
p
licit sy
n
ch
r
o
n
izatio
n
al
g
o
r
ith
m
m
i
g
h
t b
e
o
m
itted
in
t
h
is
s
ce
n
ar
io
.
c)
C
ap
ac
ito
r
v
o
ltag
e
r
e
g
u
latio
n
a
lg
o
r
ith
m
T
h
e
f
u
n
d
am
en
tal
r
o
le
o
f
th
e
c
ap
ac
ito
r
v
o
ltag
e
DC
r
eg
u
latio
n
alg
o
r
ith
m
is
to
esti
m
ate
th
e
am
o
u
n
t
o
f
dc
-
lin
k
c
h
ar
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r
r
en
t
n
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SAPF
to
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k
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o
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s
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e
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esire
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alu
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n
g
a
v
o
ltag
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c
o
n
tr
o
l
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o
p
a
n
d
eith
er
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r
o
p
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n
al
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in
teg
r
al
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o
r
f
u
zz
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o
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tr
o
l
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FL
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p
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o
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im
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r
r
en
t c
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o
l a
lg
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ith
m
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ith
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ith
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ith
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t
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u
latio
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SP
W
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,
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tr
o
l
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d
s
p
ac
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ec
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PW
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o
f
co
m
m
o
n
ap
p
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o
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t
h
is
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eth
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h
e
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o
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r
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t
r
o
l
alg
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m
s
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k
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k
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clo
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ed
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with
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ig
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s
er
v
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d
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etu
r
n
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e
co
m
p
ar
ed
with
th
e
i
n
ten
d
ed
u
n
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t
h
e
m
e
asu
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u
tp
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r
o
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ce
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v
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f
r
o
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ted
with
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ter
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u
p
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s
s
u
ch
as
d
y
n
am
ic
co
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itio
n
s
,
t
h
e
alg
o
r
ith
m
s
h
av
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n
d
e
m
o
n
s
tr
ated
in
p
r
ac
tice
to
b
e
ca
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ab
le
o
f
r
esp
o
n
d
in
g
f
ast
in
o
r
d
er
t
o
r
etu
r
n
th
e
m
o
n
ito
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ed
o
u
tp
u
t
to
its
d
esire
d
s
h
ap
e
[
1
7
]
.
T
h
e
f
o
u
r
alg
o
r
ith
m
s
em
p
lo
y
ed
in
th
is
s
tu
d
y
will b
e
th
o
r
o
u
g
h
ly
d
etailed
in
th
e
f
o
llo
win
g
s
ec
tio
n
s
.
Fig
u
r
e
3
.
B
lo
ck
d
iag
r
am
o
f
a
s
h
u
n
t A
PF
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
6
,
No
.
1
,
Ma
r
c
h
20
2
5
:
298
-
310
302
2
.
1
.
M
a
t
hem
a
t
ica
l
a
na
ly
s
is
o
f
SDFT
m
et
ho
d
f
o
r
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rm
o
nic
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t
ra
ct
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n
a
l
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niza
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T
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ar
m
o
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ic
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tr
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o
r
ith
m
an
d
th
e
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y
n
ch
r
o
n
izatio
n
a
lg
o
r
ith
m
is
d
is
cu
s
s
ed
in
th
is
s
e
ctio
n
.
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h
e
FT
co
n
ce
p
t
is
r
ev
is
ited
in
th
is
s
tu
d
y
,
wh
ich
e
m
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lo
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s
a
tim
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d
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m
ain
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aly
s
is
to
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aly
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th
e
u
n
d
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le
q
u
alities
ass
o
ciate
d
with
o
f
f
-
n
o
m
i
n
al
g
r
id
f
r
e
q
u
en
c
y
.
T
h
e
FT
f
o
r
m
u
lat
io
n
in
a
s
lid
in
g
m
o
d
e
is
e
x
p
lo
r
ed
in
len
g
th
in
[
9
]
,
as
is
th
e
m
ath
em
atica
l
an
aly
s
is
f
o
r
esti
m
atin
g
p
h
ase
an
d
m
ag
n
itu
d
e
er
r
o
r
s
u
n
d
e
r
o
f
f
-
n
o
m
in
al
f
r
e
q
u
en
c
y
co
n
d
itio
n
s
.
T
h
e
m
ai
n
ad
v
an
t
ag
e
o
f
th
e
im
p
lem
e
n
tatio
n
d
escr
ib
ed
in
[
9
]
is
th
e
ca
n
ce
ll
atio
n
o
f
th
e
d
o
u
b
le
f
r
eq
u
e
n
cy
o
s
cillatio
n
b
y
ad
d
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g
to
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th
e
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in
e
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o
m
p
o
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o
f
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e
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r
ee
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h
ases
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d
th
e
c
o
s
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e
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m
p
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en
ts
.
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o
,
th
e
v
ar
iab
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win
d
o
w
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g
th
an
d
th
e
co
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tin
u
o
u
s
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s
tm
en
t
o
f
th
e
win
d
o
w
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g
th
to
th
e
in
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u
t
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m
ak
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th
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o
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ith
m
f
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ll
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a
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e
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iatio
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a
n
d
en
a
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les
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g
en
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o
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ate
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ase
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g
le,
f
r
eq
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e
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cy
,
a
n
d
m
ag
n
itu
d
e
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f
o
r
m
atio
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o
f
th
e
in
p
u
t
th
r
ee
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h
ase
s
ig
n
al.
Fig
u
r
e
s
4
an
d
5
o
u
tlin
e
th
e
m
ai
n
m
ath
em
atica
l m
an
ip
u
latio
n
s
o
f
th
e
alg
o
r
ith
m
.
W
e
o
p
ted
SDFT
-
PLL
tech
n
iq
u
e
f
o
r
ex
tr
ac
tin
g
th
e
f
u
n
d
am
en
t
al
lo
ad
b
ec
a
u
s
e
t
h
is
tech
n
iq
u
e
is
f
ast
an
d
ac
cu
r
ate;
it
in
v
o
lv
es
th
e
ca
n
ce
llatio
n
o
f
th
e
d
o
u
b
le
f
r
eq
u
en
cy
o
s
cillatio
n
th
at
ca
n
b
e
f
o
u
n
d
in
ty
p
ical
im
p
lem
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tatio
n
o
f
s
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in
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d
is
cr
ete
Fo
u
r
ier
tr
an
s
f
o
r
m
.
T
h
e
PLL
co
m
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o
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en
t
also
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r
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v
i
d
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ad
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tab
ilit
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to
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e
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ich
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f
o
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d
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k
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r
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s
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o
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ed
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e
d
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tr
ib
u
ted
e
n
er
g
y
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r
ce
s
.
On
ce
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e
f
u
n
d
am
e
n
tal
lo
ad
cu
r
r
e
n
t
is
f
o
u
n
t,
th
e
h
ar
m
o
n
ic
r
ef
er
en
ce
ca
n
b
e
ea
s
ily
o
b
tain
ed
an
d
also
th
e
d
is
p
lace
m
en
t
an
g
le
f
o
r
co
n
tr
o
llin
g
r
ea
ctiv
e
p
o
wer
in
jectio
n
.
Fig
u
r
e
4
.
SDFT
-
PLL
b
ased
f
u
n
d
am
en
tal
lo
a
d
cu
r
r
en
t e
x
tr
ac
t
io
n
Fig
u
r
e
5
.
SDFT
an
aly
ze
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
Ha
r
mo
n
ics elimin
a
tio
n
a
n
d
r
e
a
ctive
p
o
w
er c
o
mp
en
s
a
tio
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a
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l S
DF
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LL
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(
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s
a
ma
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A
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fa
)
303
2
.
2
.
Alg
o
rit
hm
f
o
r
co
ntr
o
llin
g
t
h
e
v
o
lt
a
g
e
o
f
a
DC
-
lin
k
ca
pa
ci
t
o
r
Sh
u
n
t
PI
o
r
a
f
u
zz
y
l
o
g
ic
co
n
tr
o
ller
(
FLC)
ca
n
g
o
v
er
n
th
e
d
y
n
am
ic
r
esp
o
n
s
e
o
f
th
e
ac
tiv
e
p
o
wer
f
ilter
(
APF
)
.
I
n
r
ec
e
n
t
tr
en
d
s
,
ar
tif
icial
in
tellig
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tech
n
o
lo
g
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s
s
u
ch
as
ar
tific
ial
n
eu
r
al
n
e
two
r
k
s
an
d
g
en
etic
alg
o
r
ith
m
s
ar
e
b
ein
g
ap
p
lied
.
Ar
tific
ial
I
n
tellig
en
ce
h
as
m
ad
e
s
ig
n
if
ican
t
im
p
r
o
v
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e
n
ts
in
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tr
ical
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d
elec
tr
o
n
ic
en
g
in
ee
r
in
g
with
m
an
y
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licatio
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s
in
m
o
tio
n
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tr
o
l
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d
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o
wer
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tr
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n
ics.
T
h
e
ac
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ac
t.
o
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th
e
DC
s
id
e
ca
p
ac
ito
r
i
s
m
e
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d
co
m
p
a
r
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to
a
r
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e
r
en
ce
v
o
ltag
e
(
)
.
T
h
e
er
r
o
r
=
(
)
−
.
is
u
s
ed
as
an
in
p
u
t
to
PI
c
o
n
tr
o
ller
.
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a
d
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atel
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cted
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s
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al.
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t
-
o
f
f
f
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eq
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o
f
th
e
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PF
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is
5
0
Hz,
wh
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to
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u
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ig
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e
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co
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n
en
ts
wh
ile
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win
g
j
u
s
t
f
u
n
d
am
e
n
tal
co
m
p
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n
en
ts
.
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h
e
lin
k
DC
v
o
ltag
e
ca
n
b
e
k
ep
t
co
n
s
tan
t
at
its
r
ef
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en
ce
v
alu
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b
y
lo
s
s
es c
alcu
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th
e
cir
cu
it u
s
in
g
(
1
)
.
=
(
−
.
)
+
∫
(
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(
1
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W
h
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e
is
th
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p
r
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p
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tio
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n
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g
o
v
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th
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s
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n
tr
o
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ile
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i
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teg
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e
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tr
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ller
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ates
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in
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cu
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s
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t
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eg
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u
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en
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t.
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ir
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en
ce
co
m
p
en
s
atin
g
cu
r
r
en
ts
,
m
u
ltip
ly
th
e
p
ea
k
v
alu
e
o
f
th
e
cu
r
r
en
t
(
I
max
)
b
y
th
e
u
n
it
s
in
e
v
ec
to
r
s
in
p
h
ase
with
th
e
r
el
ated
s
o
u
r
ce
v
o
ltag
es.
T
h
ese
esti
m
ated
r
ef
er
en
ce
cu
r
r
en
ts
(
I
sa*
,
I
sb*
,
I
sc*
)
ar
e
ad
d
ed
to
th
e
h
ar
m
o
n
ics
elim
in
atio
n
r
ef
er
e
n
ce
cu
r
r
e
n
ts
.
T
h
e
d
etec
ted
cu
r
r
en
ts
wer
e
th
en
co
m
p
ar
ed
to
r
ea
l c
u
r
r
en
ts
(
I
sa
, I
sb
,
I
sc
)
at
a
h
y
s
ter
esis
b
an
d
,
y
ield
in
g
th
e
APF s
ig
n
als o
f
g
atin
g
[
1
8
]
-
[
2
2
]
.
2
.
3
.
Curre
nt
co
ntr
o
l a
lg
o
rit
hm
(
p
uls
e
wi
dth
m
o
du
la
t
io
n
(
P
WM
)
t
ec
hn
iq
ue)
T
h
e
v
o
ltag
e
s
o
u
r
ce
in
v
er
ter
(
VSI
)
p
r
o
d
u
ce
s
a
th
r
ee
-
p
h
ase
v
o
ltag
e
s
o
u
r
ce
with
v
ar
iab
le
am
p
litu
d
e,
f
r
eq
u
e
n
cy
,
a
n
d
p
h
ase.
T
h
e
V
SI
is
s
et
to
en
s
u
r
e
th
at
th
e
in
v
er
ter
'
s
o
u
tp
u
t
cu
r
r
en
ts
ar
e
f
o
r
ce
d
to
f
o
llo
w
th
eir
p
r
ed
eter
m
in
e
d
r
e
f
er
en
ce
cu
r
r
e
n
ts
.
T
h
e
b
asic
id
ea
is
b
ased
o
n
a
c
o
m
p
ar
is
o
n
o
f
th
e
r
ea
l
an
d
r
ef
e
r
en
ce
c
u
r
r
e
n
ts
p
r
o
d
u
ce
d
b
y
d
if
f
e
r
en
t
ex
tr
ac
ti
o
n
tech
n
iq
u
es.
VSI
in
v
er
ter
s
ca
n
b
e
co
n
tr
o
lled
in
a
v
ar
iety
o
f
way
s
,
in
clu
d
i
n
g
h
y
s
ter
esis
cu
r
r
en
t
co
n
t
r
o
l,
s
in
u
s
o
id
al
p
u
ls
e
wid
th
m
o
d
u
latio
n
an
d
s
p
ac
e
v
ec
to
r
PW
M
co
n
t
r
o
l
(
SVPW
M)
th
at
u
s
ed
in
th
is
p
ap
er
.
Ma
n
y
SVPW
M
d
esig
n
s
h
av
e
b
ee
n
ex
te
n
s
iv
ely
s
tu
d
ied
i
n
th
e
liter
atu
r
e.
E
ac
h
m
o
d
u
latio
n
s
tr
ateg
y
is
d
esig
n
ed
to
r
ed
u
ce
s
witch
in
g
lo
s
s
es,
b
o
o
s
t
b
u
s
u
s
a
g
e,
r
ed
u
ce
h
a
r
m
o
n
ic
co
n
ten
t,
a
n
d
m
ain
tain
p
r
ec
is
e
co
n
tr
o
l
[
2
3
]
-
[
2
5
]
.
I
n
th
e
p
r
o
p
o
s
ed
e
x
tr
ac
tio
n
alg
o
r
ith
m
,
th
er
e
a
r
e
two
m
o
d
es
o
f
r
ef
er
en
ce
c
u
r
r
e
n
t
ca
lcu
latio
n
.
Fig
u
r
e
6
s
h
o
ws
a
Mo
d
e
1
s
elec
to
r
f
o
r
ac
tiv
atin
g
/d
ea
ctiv
ati
n
g
h
a
r
m
o
n
ic
ca
n
ce
llatio
n
an
d
a
M
o
d
e
2
s
elec
to
r
f
o
r
ac
tiv
atin
g
/d
ea
ctiv
atin
g
r
ea
ctiv
e
p
o
wer
co
m
p
e
n
s
atio
n
.
Fig
u
r
e
7
d
ep
icts
th
e
p
r
o
p
o
s
ed
s
y
s
tem
'
s
in
v
er
ter
g
atin
g
co
n
tr
o
l
b
l
o
ck
d
ia
g
r
am
.
T
h
is
s
y
s
tem
co
n
s
is
ts
o
f
a
th
r
ee
-
p
h
ase
s
o
u
r
ce
v
o
ltag
e
lin
k
ed
to
a
th
y
r
is
to
r
co
n
v
er
ter
t
h
at
p
o
wer
s
a
DC
m
o
to
r
.
T
h
e
SAPF
is
a
VSI
with
s
ix
-
s
witch
es
h
av
in
g
th
e
co
m
b
i
n
atio
n
o
f
b
o
th
co
m
p
en
s
atin
g
an
d
f
ilter
in
g
co
m
p
o
n
en
t.
T
h
is
ac
tiv
e
f
ilter
is
ca
p
ab
le
o
f
d
etec
tin
g
h
ar
m
o
n
ic
cu
r
r
en
ts
an
d
ca
n
ce
lin
g
th
em
b
y
in
jectin
g
co
m
p
en
s
atin
g
c
u
r
r
e
n
t.
As
a
r
es
u
lt,
th
e
cu
r
r
en
t
f
lo
ws
as
a
s
in
e
wav
e
o
f
f
u
n
d
am
en
tal
f
r
eq
u
en
c
y
.
T
h
e
PI
co
n
tr
o
ller
is
u
s
ed
to
k
ee
p
t
h
e
DC
v
o
ltag
e
co
n
s
tan
t.
Fig
u
r
e
6
.
Mo
d
e
1
/ M
o
d
e
2
s
elec
to
r
b
lo
ck
d
iag
r
a
m
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
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-
8
6
9
4
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l.
1
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No
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1
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Ma
r
c
h
20
2
5
:
298
-
310
304
I
h
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SV
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``
S
w
i
t
c
h
i
n
g
s
i
g
n
a
l
s
S1
S3
S5
S2
S4
S6
1
M
ode
S
i
gn
al
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y
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t
r
e
s
i
s
b
a
n
d
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α
β
to
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u
t
y
a
b
c
Fig
u
r
e
7
.
I
n
v
er
te
r
g
atin
g
co
n
tr
o
l b
lo
ck
d
iag
r
am
f
o
r
t
h
e
p
r
o
p
o
s
ed
s
y
s
tem
3.
SI
M
UL
A
T
I
O
N
R
E
S
UL
T
S
AND
DIS
CUSS
I
O
NS
Simu
latio
n
s
u
s
in
g
MA
T
L
AB
/
Simu
lin
k
p
r
o
g
r
am
v
er
if
y
t
h
e
n
ew
ap
p
r
o
ac
h
'
s
p
er
f
o
r
m
a
n
ce
i
n
a
v
ar
iety
o
f
o
p
er
atio
n
al
s
ce
n
ar
io
s
.
T
h
e
p
ar
am
eter
s
o
f
th
e
s
y
s
tem
lis
ted
i
n
T
ab
le
2
ar
e
u
s
ed
.
T
h
e
o
v
e
r
all
s
im
u
latio
n
s
y
s
tem
is
s
h
o
wn
in
Fig
u
r
e
8
.
T
h
e
ch
ar
g
in
g
r
esis
tan
ce
is
u
s
ed
to
ch
ar
g
e
th
e
ca
p
ac
ito
r
f
o
r
its
in
itial
ch
ar
g
e.
T
h
e
s
y
s
tem
is
p
o
wer
ed
b
y
th
r
ee
-
p
h
ase
b
alan
ce
d
v
o
ltag
e
s
o
u
r
ce
s
th
at
f
ee
d
a
th
r
ee
-
p
h
ase
th
y
r
is
to
r
co
n
v
er
t
er
co
u
p
led
to
a
DC
m
o
to
r
.
T
h
e
co
u
p
lin
g
ci
r
cu
it
d
ep
icted
in
Fig
u
r
e
9
co
n
n
ec
ts
t
h
e
f
ilter
to
th
e
p
o
in
t
o
f
c
o
m
m
o
n
co
u
p
lin
g
(
PC
C
)
.
T
h
e
s
im
u
latio
n
is
d
iv
id
e
d
in
t
o
th
r
ee
s
ce
n
ar
io
s
.
T
h
e
f
ir
s
t
s
ce
n
ar
io
i
n
clu
d
es
SAPF
d
ea
cti
v
ated
.
T
h
e
s
ec
o
n
d
s
ce
n
ar
io
in
v
o
l
v
es
u
tili
zin
g
t
h
e
d
-
q
alg
o
r
ith
m
to
ac
tiv
ate
SAPF
f
o
r
h
ar
m
o
n
ics
elim
in
atio
n
an
d
r
ea
ctiv
e
p
o
wer
co
m
p
en
s
atio
n
.
T
h
e
th
i
r
d
s
ce
n
ar
i
o
is
SAPF
ac
tiv
ated
f
o
r
h
ar
m
o
n
ics
elim
in
atio
n
an
d
r
ea
ctiv
e
p
o
wer
co
m
p
en
s
atio
n
u
s
in
g
t
h
e
n
o
v
el
SDFT
alg
o
r
ith
m
.
B
o
th
alg
o
r
ith
m
s
ar
e
co
m
p
er
ed
to
v
alid
ated
t
h
e
n
o
v
el
alg
o
r
ith
m
.
T
h
e
s
im
u
latio
n
tim
e
s
tep
is
elec
ted
s
o
s
m
all
th
at
a
PW
M
cy
cle
(
1
0
0
u
s
)
ca
n
b
e
p
o
p
u
lated
with
ap
p
r
o
x
im
ately
1
0
0
-
tim
e
s
tep
to
en
ab
le
s
u
f
f
icien
t
PW
M
r
eso
lu
tio
n
b
ein
g
ca
p
tu
r
ed
in
t
o
s
y
s
tem
d
y
n
am
ics.
T
h
e
p
er
io
d
ic
tim
e
o
f
th
e
co
n
tr
o
l
lo
o
p
s
(
1
0
0
u
s
)
an
d
th
e
s
am
p
lin
g
r
ate
o
f
th
e
f
ee
d
b
ac
k
an
alo
g
m
ea
s
u
r
em
en
ts
(
1
0
k
Hz)
is
s
elec
ted
to
b
e
s
u
itab
le
to
th
e
ex
ec
u
tio
n
s
p
ee
d
s
o
f
k
n
o
wn
DSP
n
o
r
m
ally
u
s
ed
f
o
r
s
u
ch
ap
p
licatio
n
s
(
1
0
0
u
s
)
an
d
f
o
r
th
eir
A/D
co
n
v
er
te
r
s
s
p
e
ed
.
T
h
e
s
im
u
latio
n
m
o
d
e
is
d
is
cr
ete
with
f
ix
ed
s
tep
(
1
u
s
)
to
m
im
ic
th
e
r
ea
l
s
y
s
tem
with
DSP
co
n
tr
o
ller
s
.
T
h
e
co
u
p
lin
g
in
d
u
ct
o
r
s
h
o
u
ld
b
e
s
ized
s
u
ch
th
at
th
e
h
ar
m
o
n
i
c
co
m
p
o
n
en
t
o
f
th
e
co
m
p
en
s
atio
n
c
u
r
r
en
t a
t th
e
s
witch
in
g
f
r
eq
u
en
cy
s
h
o
u
ld
n
o
t
ex
ce
ed
5
% o
f
th
e
f
u
n
d
am
e
n
ta
l o
f
th
e
lo
ad
cu
r
r
e
n
t
to
lim
it th
e
h
ig
h
f
r
eq
u
en
c
y
r
ip
p
le
in
th
e
s
o
u
r
ce
r
esu
ltan
t c
u
r
r
en
t.
T
h
e
d
c
v
o
ltag
e
s
h
o
u
ld
b
e
ad
ju
s
ted
s
o
th
at:
Vd
c/2
-
Vac
(
p
ea
k
)
>m
ax
im
u
m
r
ate
o
f
ch
a
n
g
e
o
f
lo
ad
cu
r
r
e
n
t
*
co
u
p
lin
g
f
ilter
in
d
u
ctan
ce
Acc
o
r
d
in
g
t
o
th
e
ch
o
ices m
ad
e
h
er
e:
Vd
c/2
=
4
5
0
/2
=
2
2
5
,
Vac
p
ea
k
=
2
0
8
,
th
en
Vd
c/2
-
Vac
p
e
ak
=
225
-
2
0
8
=
1
7
v
o
lt.
T
h
e
L
couplin
g
=
2e
-
3
,
th
en
m
ax
im
u
m
r
ate
o
f
ch
an
g
e
o
f
lo
ad
cu
r
r
en
t
s
h
o
u
ld
n
o
t
ex
ce
e
d
(
1
/2
e
-
3
)
*
17
=
1
7
*
5
0
0
=
8
.
5
K
A/s
.
I
f
lo
ad
c
u
r
r
e
n
t
was
f
o
u
n
d
to
h
av
e
h
ig
h
er
r
ate
o
f
ch
an
g
e,
c
o
n
s
id
er
in
cr
ea
s
in
g
t
h
e
in
d
u
ctan
ce
o
f
th
e
r
ec
tifie
r
s
m
o
o
th
er
in
d
u
ctan
ce
to
s
lo
w
it
d
o
wn
.
T
h
e
ca
p
ac
ito
r
v
alu
e
o
f
th
e
DC
lin
k
s
h
o
u
l
d
b
e
s
ized
s
u
ch
th
at
th
e
r
ip
p
le
v
o
ltag
e
is
with
in
2
%
o
f
th
e
DC
v
o
ltag
e
Vr
ip
p
le
=
Vm
ax
-
Vim
,
Vr
ip
p
le/Vd
c<
2
%.
W
e
u
s
e
th
e
PID
co
n
tr
o
ller
an
d
n
o
t
PI
as,
a
PI
co
n
tr
o
ller
is
u
s
ed
s
in
ce
th
e
D
co
m
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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&
Dr
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t
I
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N:
2088
-
8
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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N
:
2088
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8
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
Ha
r
mo
n
ics elimin
a
tio
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a
n
d
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e
a
ctive
p
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mp
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s
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DF
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…
(
O
s
a
ma
M.
A
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a
fa
)
307
3
.
3
.
T
hird
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ce
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rio
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ct
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t
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DF
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ith
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f
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ller
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r
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k
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l
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th
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s
am
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p
r
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s
lo
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itio
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s
.
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PID
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tr
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ll
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a
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ar
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0
0
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1
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im
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ar
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2
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