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I
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8
6
9
4
A
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2343
p
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c
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ter
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with
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etwo
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s
.
T
h
e
s
u
b
ject
o
f
th
e
ar
ticle
is
th
e
p
r
o
ce
s
s
o
f
s
y
n
ch
r
o
n
izin
g
a
g
r
o
u
p
o
f
co
n
v
er
te
r
s
.
T
h
is
task
is
n
ec
ess
ar
y
f
o
r
th
e
co
o
r
d
in
ated
o
p
er
atio
n
o
f
co
n
v
er
ter
s
with
in
a
co
m
m
o
n
n
etwo
r
k
wh
en
th
e
p
o
wer
an
d
en
e
r
g
y
o
f
a
s
in
g
le
co
n
v
er
ter
ar
e
i
n
s
u
f
f
icien
t.
T
h
e
p
ap
e
r
p
r
o
p
o
s
es
a
m
eth
o
d
f
o
r
s
y
n
ch
r
o
n
izin
g
a
g
r
o
u
p
o
f
co
n
v
er
ter
s
b
ased
o
n
th
e
p
h
e
n
o
m
en
o
n
o
f
s
elf
-
s
y
n
ch
r
o
n
izatio
n
o
f
co
u
p
led
o
s
cillato
r
s
.
T
h
e
m
et
h
o
d
is
b
ased
o
n
th
e
d
escr
ip
tio
n
o
f
c
o
u
p
le
d
Ku
r
am
o
to
o
s
cillato
r
s
[
1
8
]
,
wh
ic
h
is
a
s
im
p
lifie
d
v
er
s
io
n
o
f
t
h
e
d
e
s
cr
ip
tio
n
p
r
o
p
o
s
ed
b
y
W
in
f
r
ee
[
1
9
]
,
[
2
0
]
i
n
1
9
6
7
,
as
well
as
th
e
s
tr
u
ctu
r
ed
g
r
ap
h
p
r
o
p
o
s
ed
a
n
d
s
tu
d
ied
b
y
W
iley
[
2
1
]
.
Ho
wev
e
r
,
th
e
p
r
o
p
o
s
ed
d
escr
ip
tio
n
in
tr
o
d
u
ce
s
s
ev
er
al
ch
an
g
es
th
at
s
im
p
lify
th
e
a
n
aly
s
is
b
u
t
m
a
k
e
th
e
d
escr
ip
tio
n
h
ig
h
ly
s
p
ec
ialized
.
Sectio
n
2
p
r
o
v
i
d
es
a
m
ath
em
atica
l
d
escr
ip
tio
n
o
f
th
e
s
elf
-
s
y
n
ch
r
o
n
izatio
n
m
eth
o
d
an
d
th
e
s
tep
s
to
ac
h
iev
e
it.
Sectio
n
3
im
p
lem
en
ts
th
e
p
r
o
p
o
s
ed
m
eth
o
d
f
o
r
s
y
n
ch
r
o
n
izin
g
a
g
r
o
u
p
o
f
th
r
ee
-
p
h
ase
in
v
er
ter
s
with
an
is
o
lated
n
eu
tr
al
o
p
er
at
in
g
o
n
a
co
m
m
o
n
lo
a
d
.
T
h
e
p
r
o
p
o
s
ed
s
y
n
c
h
r
o
n
izatio
n
alg
o
r
ith
m
is
also
ad
ap
ted
to
th
e
co
n
v
er
ter
with
in
d
e
p
en
d
en
t
p
h
ase
s
y
n
c
h
r
o
n
izatio
n
f
o
r
o
p
er
atio
n
u
n
d
er
asy
m
m
etr
ical
n
etwo
r
k
co
n
d
itio
n
s
d
is
cu
s
s
ed
in
th
e
p
r
e
v
io
u
s
r
esear
ch
.
2.
M
E
T
H
O
D
F
O
R
SE
L
F
-
SYN
CH
R
O
NIZ
A
T
I
O
N
O
F
A
G
RO
UP
O
F
CO
NVERT
E
RS
T
h
e
s
tu
d
y
u
tili
ze
s
th
e
p
h
en
o
m
en
o
n
o
f
s
elf
-
s
y
n
ch
r
o
n
izatio
n
t
o
ac
h
iev
e
s
y
n
c
h
r
o
n
izatio
n
o
f
c
o
n
v
er
ter
s
.
Self
-
s
y
n
ch
r
o
n
izatio
n
[
2
2
]
o
cc
u
r
s
wh
en
s
ev
er
al
ar
tific
ially
c
r
ea
ted
o
r
n
atu
r
al
o
b
jects
(
h
er
e
af
ter
r
ef
er
r
ed
to
as
n
o
d
es),
w
h
ic
h
,
in
th
e
a
b
s
en
c
e
o
f
i
n
ter
ac
tio
n
,
p
er
f
o
r
m
o
s
cillato
r
y
o
r
r
o
tatio
n
al
m
o
v
e
m
en
ts
with
d
if
f
er
e
n
t
f
r
eq
u
e
n
cies
(
an
g
u
lar
v
elo
citie
s
)
an
d
/o
r
p
h
ases
,
b
eg
in
to
m
o
v
e
with
id
en
tical,
m
u
ltip
le,
o
r
r
atio
n
ally
r
elate
d
f
r
eq
u
e
n
cies
(
an
g
u
lar
v
elo
citi
es)
u
p
o
n
t
h
e
im
p
o
s
iti
o
n
o
f
ev
en
wea
k
c
o
n
n
ec
tio
n
s
.
T
h
is
r
esu
lts
in
th
e
estab
lis
h
m
en
t o
f
ce
r
tain
p
h
ase
r
elatio
n
s
h
ip
s
b
etwe
en
th
e
o
s
cillatio
n
s
(
r
o
tatio
n
s
)
.
A
s
ig
n
if
ican
t
s
tep
to
wa
r
d
s
u
ti
lizin
g
s
elf
-
s
y
n
ch
r
o
n
izatio
n
w
as
W
in
f
r
ee
'
s
d
escr
ip
tio
n
o
f
a
s
y
s
tem
o
f
co
u
p
led
o
s
cillato
r
s
[
2
3
]
,
w
h
ich
d
escr
ib
ed
t
h
e
cir
ca
d
ian
r
h
y
t
h
m
s
o
f
p
lan
ts
an
d
an
im
als
.
θ
̇
i
=
ω
i
+
[
ε
N
∑
N
j
=
1
P
(
θ
j
)
]
R
(
θ
i
)
,
i
=
1
,
…
,
N
(
1
)
W
h
er
e
θ
i
–
th
e
p
h
ase
o
f
n
o
d
e
i,
ω
i
–
th
e
in
tr
in
s
ic
o
s
cillat
io
n
f
r
eq
u
e
n
cy
o
f
th
e
n
o
d
e,
P
an
d
R
–
p
er
io
d
ic
f
u
n
ctio
n
s
with
a
p
er
io
d
o
f
2
π
th
at
c
h
ar
ac
ter
ize
t
h
e
s
en
s
itiv
ity
an
d
m
u
t
u
al
in
f
l
u
en
ce
s
o
f
o
s
cillato
r
s
o
n
ea
c
h
o
th
er
,
N
–
th
e
n
u
m
b
er
o
f
elem
en
ts
(
n
o
d
es),
a
n
d
ε
>
0
–
t
h
e
c
o
m
m
o
n
co
u
p
lin
g
p
a
r
am
eter
.
Ku
r
am
o
to
[
2
1
]
,
i
n
tu
r
n
,
s
i
m
p
lifie
d
W
in
f
r
ee
'
s
m
o
d
el
a
n
d
d
e
r
iv
ed
an
aly
tical
s
o
lu
ti
o
n
s
f
o
r
it,
s
ig
n
if
ican
tly
in
cr
ea
s
in
g
in
te
r
est in
th
e
s
elf
-
s
y
n
ch
r
o
n
izatio
n
p
h
en
o
m
e
n
o
n
.
θ
̇
i
=
ω
i
+
ε
K
N
∑
N
j
=
1
s
in
(
θ
j
−
θ
i
)
,
i
=
1
,
…
,
N
(
2
)
W
h
er
e
θ
i
–
th
e
p
h
ase
o
f
n
o
d
e
i,
s
in
(
θ
j
-
θ
i
)
–
s
in
u
s
o
id
al
f
u
n
ctio
n
th
at
c
h
ar
ac
ter
izes
th
e
co
n
n
ec
tio
n
b
etwe
en
n
o
d
es,
K
–
is
th
e
co
n
n
ec
tiv
ity
m
atr
ix
,
tak
in
g
th
e
v
alu
e
1
,
if
th
er
e
is
a
co
n
n
ec
tio
n
an
d
0
if
th
er
e
is
n
o
n
e,
a
n
d
1
/N
–
a
s
ca
lin
g
co
e
f
f
icien
t th
a
t e
n
s
u
r
es th
e
s
y
s
tem
'
s
l
im
it a
s
N→∞,
ε
–
th
e
co
m
m
o
n
co
u
p
li
n
g
p
ar
a
m
eter
.
T
h
e
p
r
in
ci
p
al
d
if
f
er
e
n
ce
s
b
et
wee
n
th
e
W
in
f
r
ee
an
d
Ku
r
am
o
to
m
o
d
els
lie
in
Ku
r
am
o
to
d
ef
in
in
g
th
e
co
u
p
lin
g
f
u
n
ctio
n
as
th
e
s
in
e
o
f
th
e
p
h
ase
d
if
f
er
en
ce
b
etwe
en
a
p
air
o
f
o
s
cillato
r
s
an
d
s
ep
ar
atin
g
th
e
weig
h
t
m
atr
ix
to
ad
ju
s
tm
en
t
m
atr
ix
a
n
d
weig
h
t
co
ef
f
icien
t,
th
u
s
g
r
ea
tly
s
im
p
lify
in
g
th
e
a
n
aly
s
is
o
f
o
s
cillatio
n
s
.
T
h
is
s
im
p
lific
atio
n
allo
wed
th
e
eq
u
atio
n
s
to
b
e
s
o
lv
ed
an
aly
tic
ally
an
d
en
a
b
led
th
e
s
tu
d
y
o
f
s
o
lu
tio
n
s
[
2
3
]
o
f
co
u
p
led
o
s
cillato
r
s
y
s
tem
s
f
o
r
o
s
cillatio
n
s
tab
ilit
y
an
d
s
elf
-
s
y
n
c
h
r
o
n
izatio
n
co
n
d
itio
n
s
.
m
o
r
eo
v
e
r
,
a
g
r
a
p
h
s
tr
u
ctu
r
e
[
2
1
]
was
p
r
o
p
o
s
ed
th
at
g
u
ar
an
tees
s
y
n
ch
r
o
n
iz
atio
n
o
f
th
e
en
tire
s
y
s
tem
wh
en
th
e
co
u
p
lin
g
co
ef
f
icien
t
ex
ce
ed
s
a
th
r
esh
o
l
d
v
alu
e.
T
h
e
co
u
p
lin
g
co
e
f
f
ici
en
t
is
co
n
s
tan
t,
an
d
th
e
K
m
at
r
ix
o
n
ly
d
ef
i
n
es
th
e
g
r
ap
h
'
s
co
n
n
ec
tiv
ity
s
tr
u
ctu
r
e,
wh
ich
,
f
o
r
a
n
etwo
r
k
o
f
s
ix
n
o
d
es,
m
ig
h
t lo
o
k
lik
e
(
3
)
.
K
=
[
0
1
1
1
0
1
1
1
0
0
1
1
1
0
1
1
1
0
0
1
1
1
0
1
1
1
0
0
1
1
1
0
1
1
1
0
]
(
3
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
4
,
Dec
em
b
er
20
25
:
2342
-
2
3
5
2
2344
T
h
e
weig
h
t
o
f
t
h
e
co
n
n
ec
tio
n
is
r
ep
r
esen
ted
b
y
a
s
ep
ar
ate
co
ef
f
icien
t,
d
en
o
ted
as
ε.
W
h
en
v
is
u
alizin
g
th
e
co
n
n
ec
tiv
ity
m
atr
ix
K
as
a
g
r
a
p
h
,
t
h
e
r
es
u
ltin
g
d
iag
r
am
is
s
h
o
wn
in
Fig
u
r
e
1
f
o
r
d
if
f
e
r
en
t
m
o
d
els:
Fig
u
r
e
1
(
a
)
th
e
m
o
d
e
l
co
r
r
esp
o
n
d
in
g
to
th
e
co
n
n
ec
tiv
ity
m
atr
ix
(
3
)
with
b
id
ir
ec
t
io
n
al
co
n
n
ec
ti
o
n
s
;
Fig
u
r
e
1
(
b
)
th
e
s
im
p
lifie
d
m
o
d
el
with
u
n
id
ir
ec
tio
n
al
c
o
n
n
e
ctio
n
s
;
Fig
u
r
e
1
(
c)
th
e
s
im
p
lifie
d
m
o
d
el
with
s
y
n
ch
r
o
n
izatio
n
to
a
r
ef
er
en
ce
o
s
cillato
r
.
(
a)
(
b
)
(
c)
Fig
u
r
e
1
.
C
o
n
n
ec
tiv
ity
g
r
a
p
h
o
f
g
en
e
r
alize
d
o
s
cillato
r
s
: (
a)
co
m
p
lete
m
o
d
el,
(
b
)
s
im
p
lifie
d
m
o
d
el,
an
d
(
c)
s
im
p
lifie
d
m
o
d
el
with
s
y
n
c
h
r
o
n
izatio
n
to
a
r
e
f
er
en
ce
o
s
cillato
r
Usi
n
g
a
tr
ig
o
n
o
m
etr
ic
f
u
n
ctio
n
in
t
h
e
m
o
d
el
d
escr
ip
tio
n
is
j
u
s
tifie
d
b
ec
au
s
e,
g
en
er
ally
,
th
e
p
h
ase
o
f
o
s
cillato
r
s
is
n
o
t
ex
p
licitly
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ce
s
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ib
le.
B
y
o
b
s
er
v
in
g
o
n
ly
th
e
o
u
tp
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t
v
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f
t
h
e
n
o
d
e,
we
o
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tain
o
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io
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ic
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ar
iab
les
f
o
r
estab
lis
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in
g
c
o
n
n
ec
tio
n
s
.
Ho
wev
er
,
t
h
e
tr
ig
o
n
o
m
etr
ic
f
u
n
ctio
n
c
o
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p
licates
th
e
p
h
ase
s
y
n
ch
r
o
n
izatio
n
o
f
o
s
cillato
r
s
.
W
h
ile
g
u
ar
an
teed
f
r
eq
u
en
c
y
alig
n
m
en
t
is
ac
h
iev
ed
,
th
e
p
h
ases
o
f
o
s
cilla
tio
n
s
d
o
n
o
t
alig
n
.
I
n
s
y
n
ch
r
o
n
izin
g
ar
tific
ial
o
s
cillato
r
s
,
ad
h
er
in
g
to
th
e
co
n
s
tr
ain
t
o
f
wo
r
k
in
g
o
n
ly
with
h
ar
m
o
n
ic
s
ig
n
als
is
u
n
n
ec
ess
ar
y
,
an
d
w
e
ca
n
in
tr
o
d
u
ce
a
d
ir
ec
t
p
h
ase
co
u
p
lin
g
o
f
t
h
e
n
o
d
es.
T
h
e
s
y
s
tem
d
escr
ip
tio
n
,
in
th
is
ca
s
e,
will lo
o
k
lik
e
(
4
)
.
θ
̇
i
=
ω
i
+
ε
K
N
∑
N
j
=
1
(
θ
j
−
θ
i
)
,
i
=
1
,
…
,
N
(
4
)
Stru
ctu
r
in
g
t
h
e
co
n
n
ec
tio
n
s
r
em
ain
s
u
n
ch
a
n
g
ed
.
Fo
r
th
e
s
t
r
u
ctu
r
e
s
h
o
wn
o
n
Fig
u
r
e
1
(
a)
,
with
f
o
u
r
co
n
n
ec
tio
n
s
p
e
r
n
o
d
e
an
d
a
co
n
s
tan
t f
r
eq
u
e
n
cy
,
th
e
(
4
)
tak
es th
e
f
o
r
m
o
f
(
5
)
.
θ
̇
i
=
ω
i
+
ε
N
(
K
ij
(
θ
j
−
θ
i
)
+
K
il
(
θ
l
−
θ
i
)
+
K
ip
(
θ
p
−
θ
i
)
+
K
iq
(
θ
q
−
θ
i
)
)
(
5
)
W
h
er
e
j,
l,
p
an
d
q
-
in
d
ex
es
o
f
n
o
d
es
with
wh
ich
th
er
e
is
a
co
n
n
ec
tio
n
.
T
h
e
(
5
)
ca
n
b
e
r
ewr
itten
in
m
atr
ix
f
o
r
m
as
(
6
)
.
θ
̇
=
ω
+
ε
N
(
−
4E
+
K
)
θ
(
6
)
W
h
er
e
E
–
th
e
id
e
n
tity
m
atr
ix
.
T
h
e
r
ef
e
r
en
ce
m
o
tio
n
o
f
th
e
s
y
s
tem
is
d
escr
ib
ed
as
(
7
)
.
θ
̇
r
ef
=
ω
r
ef
,
(
7
)
S
y
n
ch
r
o
n
izatio
n
co
n
d
itio
n
wil
l lo
o
k
lik
e
(8
).
ε
N
(
−
4E
+
K
)
θ
=
0
(
8
)
C
o
n
d
itio
n
(
8
)
is
ac
h
iev
a
b
le
w
h
en
th
e
v
ec
to
r
θ
=
0
,
w
h
ich
is
n
o
t
p
er
m
is
s
ib
le
d
u
e
to
(
6
)
,
o
r
th
e
m
atr
ix
K−
4
E
is
s
in
g
u
lar
,
d
et(
K)
=
0
(
th
e
m
atr
i
x
K
p
r
o
p
o
s
ed
in
(
3
)
en
s
u
r
es
th
is
co
n
d
itio
n
)
.
Fo
r
th
e
s
tab
ilit
y
o
f
s
u
ch
a
s
y
s
tem
,
it
is
n
ec
ess
ar
y
th
at
all
eig
e
n
v
alu
es
o
f
th
e
m
atr
i
x
K−
4
E
lie
in
th
e
le
f
t
h
alf
-
p
lan
e,
ex
ce
p
t
f
o
r
o
n
e
ze
r
o
eig
en
v
alu
e,
w
h
ich
en
s
u
r
es th
e
s
in
g
u
lar
ity
o
f
t
h
e
m
atr
ix
.
Ho
wev
er
,
f
o
u
r
c
o
n
n
ec
tio
n
s
p
er
n
o
d
e
s
till
r
esu
lt
in
a
co
m
p
lex
n
etwo
r
k
s
tr
u
ctu
r
e
.
Fo
r
p
r
ac
tical
im
p
lem
e
n
tatio
n
,
f
u
r
th
e
r
s
im
p
l
if
icatio
n
is
r
eq
u
ir
e
d
.
T
h
is
n
ec
ess
itate
s
in
v
esti
g
atin
g
th
e
s
tab
ilit
y
o
f
s
tr
u
ctu
r
es
with
f
ewe
r
c
o
n
n
ec
tio
n
s
.
An
e
x
am
p
le
o
f
a
m
i
n
im
al
s
tr
u
ctu
r
e
th
at
e
n
s
u
r
es
g
r
ap
h
co
n
n
ec
ti
v
ity
is
p
r
esen
ted
o
n
d
ep
icted
as in
Fig
u
r
e
1
(
b
)
.
Fo
r
th
at
ca
s
e
,
th
e
m
atr
ix
K
is
s
in
g
u
lar
an
d
l
o
o
k
s
lik
e
(
9
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
A
p
p
r
o
a
ch
t
o
s
elf
-
s
yn
ch
r
o
n
iz
a
tio
n
o
f a
g
r
o
u
p
o
f sta
tic
p
o
w
er c
o
n
ve
r
ters
(
V
icto
r
La
vrin
o
vsk
y
)
2345
K
=
[
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
]
.
(
9
)
I
n
(
9
)
,
ea
ch
r
o
w
an
d
co
l
u
m
n
h
as
o
n
ly
o
n
e
n
o
n
-
ze
r
o
co
m
p
o
n
en
t,
wh
ic
h
is
n
o
t
o
n
th
e
d
iag
o
n
al.
T
h
e
r
esu
ltin
g
s
y
s
tem
will lo
o
k
lik
e
(
1
0
)
.
θ
̇
=
ω
+
с
(
−
E
+
K
)
θ
,
(
1
0
)
W
h
er
e
c
–
th
e
co
u
p
lin
g
p
ar
a
m
eter
o
b
tain
ed
b
y
r
ep
lacin
g
t
h
e
v
alu
e
ε/N
with
a
s
in
g
le
c
o
ef
f
icien
t,
an
d
K
is
d
escr
ib
ed
b
y
f
o
r
m
(
9
)
.
I
t
s
h
o
u
ld
b
e
n
o
te
d
th
at
if
th
e
o
s
cillatio
n
f
r
eq
u
en
cies
o
f
th
e
n
o
d
es
d
if
f
e
r
,
s
y
n
c
h
r
o
n
izatio
n
will
n
o
t
b
e
ac
h
iev
ed
.
T
h
is
p
r
o
b
lem
ca
n
b
e
s
o
lv
ed
b
y
ad
d
in
g
an
in
teg
r
al
co
m
p
o
n
e
n
t.
I
n
th
is
ca
s
e,
th
e
s
y
s
tem
will
b
ec
o
m
e
m
o
r
e
co
m
p
lex
as (
1
1
)
.
{
θ
̇
=
ω
+
c
1
(
K
−
E
)
θ
+
c
2
x
;
x
̇
=
(
K
−
E
)
θ
,
(
1
1
)
W
h
er
e
x
–
an
ar
tific
ial
v
ar
i
ab
le,
th
e
o
u
tp
u
t
o
f
th
e
I
-
co
n
tr
o
ller
.
T
h
e
r
esu
ltin
g
m
atr
ix
o
f
th
e
d
if
f
e
r
en
tial
eq
u
atio
n
s
y
s
tem
will lo
o
k
lik
e
(
1
2
)
.
А=
[
c
1
(
K
−
E
)
c
2
E
K
−
E
0
]
(
1
2
)
T
h
e
b
lo
c
k
m
at
r
ix
(
1
2
)
with
t
h
e
ch
o
ice
o
f
m
atr
ix
K
ty
p
e
(
9
)
ca
n
en
s
u
r
e
s
y
s
tem
s
tab
ilit
y
with
th
e
ap
p
r
o
p
r
iate
ch
o
ice
o
f
co
ef
f
icien
ts
c1
an
d
c2
.
T
h
e
s
tab
ilit
y
b
o
u
n
d
ar
y
ca
n
b
e
d
ef
in
e
d
as
c2
=
2
c1
.
Fo
r
c
2
<
2
c
1
<
0
,
th
e
s
y
s
tem
h
as st
ab
le
m
o
v
em
en
ts
; in
s
u
ch
a
ca
s
e,
th
e
in
t
eg
r
ato
r
e
n
s
u
r
es f
r
eq
u
en
cy
s
y
n
ch
r
o
n
izatio
n
.
I
n
th
e
task
o
f
s
y
n
ch
r
o
n
izin
g
o
s
cillato
r
s
with
a
r
ef
er
e
n
ce
o
s
cillato
r
,
u
n
i
d
ir
ec
tio
n
al
c
o
u
p
lin
g
f
r
o
m
th
e
r
ef
er
en
ce
o
s
cillato
r
ca
n
b
e
u
s
ed
.
I
m
p
lem
en
tatio
n
ca
n
b
e
d
o
n
e
as
an
ad
d
itio
n
al
p
ar
allel
co
n
tr
o
l
lo
o
p
with
a
P
-
co
n
tr
o
ller
.
I
n
th
e
ca
s
e
o
f
d
i
f
f
er
en
t
f
r
eq
u
e
n
cies,
an
i
n
teg
r
al
co
m
p
o
n
en
t
m
u
s
t
also
b
e
i
n
tr
o
d
u
ce
d
,
wh
ich
,
with
ze
r
o
er
r
o
r
,
will p
r
o
v
id
e
c
o
n
s
tan
t c
o
r
r
ec
tiv
e
ac
tio
n
.
T
h
e
s
tr
u
ct
u
r
e
o
f
s
u
c
h
a
s
y
s
tem
is
s
h
o
wn
in
Fig
u
r
e
1
(
c)
.
Sin
ce
f
r
eq
u
en
c
y
co
r
r
ec
tio
n
i
s
also
in
tr
o
d
u
ce
d
,
th
e
co
n
d
it
io
n
o
f
eq
u
al
f
r
eq
u
en
cies
o
f
in
d
iv
id
u
al
o
s
cillato
r
s
ca
n
b
e
d
is
r
eg
a
r
d
ed
,
as
th
e
f
in
al
s
y
s
tem
ex
h
ib
its
astaticis
m
with
r
esp
ec
t
to
th
e
f
r
eq
u
e
n
cy
o
f
th
e
ex
ter
n
al
n
o
d
e.
T
h
u
s
,
th
e
p
r
o
p
o
s
ed
s
y
s
tem
h
as
th
e
f
o
llo
win
g
p
r
o
p
er
ties
:
i)
m
in
im
al
s
et
o
f
c
o
n
n
ec
tio
n
s
f
o
r
ea
ch
node
,
ii)
e
ac
h
n
o
d
e
is
an
au
to
n
o
m
o
u
s
o
s
cillato
r
,
iii)
i
n
itial
d
ev
iatio
n
s
in
p
h
ase
an
d
f
r
e
q
u
en
cy
ar
e
s
u
p
p
r
ess
ed
,
iv
)
r
eg
u
lato
r
p
a
r
am
eter
s
allo
w
ac
h
iev
in
g
th
e
d
esire
d
s
y
n
ch
r
o
n
izatio
n
d
y
n
am
ics
,
b
u
t h
a
v
e
lim
itatio
n
s
to
en
s
u
r
e
s
tab
ilit
y
.
All th
ese
co
n
d
itio
n
s
ca
n
b
e
en
s
u
r
ed
in
a
n
etwo
r
k
o
f
f
r
eq
u
e
n
cy
c
o
n
v
er
te
r
s
.
3.
SYNCH
RO
NI
Z
A
T
I
O
N
O
F
A
G
RO
UP
O
F
O
SCI
L
L
AT
O
RS TO
A
CO
M
M
O
N
L
O
A
D
T
o
en
s
u
r
e
s
y
n
c
h
r
o
n
izatio
n
o
f
th
e
o
s
cillato
r
s
,
it
is
f
ir
s
t
n
ec
ess
ar
y
to
d
e
f
in
e
t
h
e
o
s
cill
ato
r
its
elf
.
C
o
n
s
id
er
th
e
o
p
e
r
atio
n
o
f
th
e
n
etwo
r
k
b
ased
o
n
a
s
im
p
le
lin
ea
r
o
s
cillato
r
as in
(
1
3
)
.
{
θ
̇
=
ω
;
x
=
A
s
in
(
θ
)
.
(
1
3
)
A
g
r
o
u
p
o
f
s
ix
id
en
tical
lin
ea
r
o
s
cillato
r
s
wi
th
in
tr
o
d
u
ce
d
f
e
ed
b
ac
k
o
n
th
e
p
h
ase
er
r
o
r
o
f
t
h
e
n
ea
r
est o
s
cillato
r
an
d
th
e
p
h
ase
er
r
o
r
with
th
e
r
ef
er
en
ce
o
s
cillato
r
is
s
h
o
wn
i
n
Fig
u
r
e
2
.
Fo
r
th
e
s
y
n
ch
r
o
n
i
za
tio
n
ex
p
er
im
en
t,
o
n
ly
th
e
p
h
ase
er
r
o
r
with
th
e
n
ea
r
est
o
s
cillato
r
is
u
s
ed
,
an
d
f
o
r
s
y
n
ch
r
o
n
izatio
n
with
th
e
r
ef
er
en
ce
,
t
h
e
p
h
ase
er
r
o
r
with
th
e
r
ef
er
e
n
ce
is
also
u
s
ed
.
I
n
Fig
u
r
e
2
,
th
e
co
u
p
lin
g
co
ef
f
icien
t ε
is
d
en
o
ted
as K
.
Fo
r
th
e
an
al
y
s
is
o
f
th
e
p
r
o
p
o
s
ed
m
eth
o
d
,
a
m
o
d
el
o
f
s
ix
o
s
cillato
r
s
was
b
u
ilt,
co
r
r
esp
o
n
d
in
g
to
th
e
g
r
ap
h
p
r
esen
ted
in
Fig
u
r
e
1
(
b
)
.
T
h
e
r
esu
lt
o
f
s
y
n
c
h
r
o
n
izatio
n
is
s
h
o
wn
in
Fig
u
r
e
3
.
I
n
t
h
e
s
y
n
ch
r
o
n
izatio
n
p
r
o
ce
s
s
,
ea
ch
o
s
cillato
r
h
as
d
i
f
f
er
en
t
in
tr
in
s
ic
f
r
e
q
u
en
cies,
r
an
d
o
m
ly
g
e
n
er
ated
in
t
h
e
r
a
n
g
e
o
f
4
5
t
o
5
5
Hz,
an
d
in
itial
p
h
ases
with
a
r
an
d
o
m
d
is
tr
ib
u
tio
n
in
th
e
r
an
g
e
o
f
0
to
2
π.
As
s
ee
n
in
Fig
u
r
e
3
,
th
e
p
h
ases
o
f
th
e
o
s
cillato
r
s
co
n
v
er
g
e
an
d
n
o
f
u
r
th
er
d
iv
er
g
en
ce
o
cc
u
r
s
,
allo
win
g
f
o
r
s
ea
m
less
s
y
n
ch
r
o
n
izatio
n
r
eg
a
r
d
less
o
f
th
e
s
witch
in
g
d
y
n
a
m
ics o
f
th
e
eq
u
ip
m
en
t.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
4
,
Dec
em
b
er
20
25
:
2342
-
2
3
5
2
2346
T
o
v
e
r
if
y
th
e
s
tab
ilit
y
o
f
t
h
e
s
y
n
ch
r
o
n
ize
d
s
tate,
th
e
s
y
n
c
h
r
o
n
izatio
n
tim
e
f
o
r
a
g
r
o
u
p
o
f
s
ix
n
o
d
es
was
ch
ec
k
ed
.
T
h
e
v
alu
e
o
f
ε
v
ar
ies
f
r
o
m
0
.
1
to
1
5
,
with
1
0
ex
p
er
im
en
ts
p
er
f
o
r
m
ed
f
o
r
ea
ch
v
alu
e.
A
PI
co
n
tr
o
ller
is
u
s
ed
f
o
r
s
y
n
ch
r
o
n
izatio
n
with
th
e
c
o
m
m
o
n
r
e
f
er
en
ce
,
b
ased
o
n
th
e
p
h
ase
er
r
o
r
o
f
th
e
n
o
d
e
with
th
e
r
ef
er
en
ce
,
with
co
ef
f
icien
t
s
o
f
1
an
d
2
5
,
r
esp
ec
tiv
ely
.
T
h
e
r
esu
lts
with
d
if
f
er
en
t
co
n
d
i
tio
n
s
ar
e
s
h
o
wn
in
Fig
u
r
e
4
.
Fig
u
r
e
4
(
a)
illu
s
tr
a
te
s
y
n
ch
r
o
n
izatio
n
o
f
n
o
d
es
with
a
s
p
r
ea
d
o
f
2
π
with
th
e
lin
ea
r
co
n
n
ec
tio
n
.
Fig
u
r
e
4
(
b
)
illu
s
tr
ates
d
y
n
am
i
c
o
f
n
o
d
es
f
o
r
th
e
f
r
eq
u
en
cy
s
p
r
ea
d
o
f
±
5
%
an
d
a
r
an
d
o
m
i
n
itial
p
h
ase
f
r
o
m
0
to
2
π
an
d
co
n
n
ec
ted
as
in
Ku
r
am
o
to
m
o
d
el.
Fig
u
r
e
4
(
c)
d
ep
icts
n
o
d
es
d
y
n
am
ic
f
o
r
an
in
itial
p
h
ase
s
p
r
ea
d
o
f
π
with
th
e
lin
ea
r
in
ter
co
n
n
ec
ti
o
n
s
an
d
eq
u
al
o
s
cillato
r
f
r
e
q
u
en
cies.
Po
in
ts
with
a
tim
e
o
f
3
0
s
o
n
th
e
g
r
ap
h
s
co
r
r
esp
o
n
d
to
a
lac
k
o
f
p
h
ase
s
y
n
ch
r
o
n
izatio
n
.
Fig
u
r
e
2
.
Stru
ctu
r
al
m
o
d
el
with
o
s
cillato
r
s
Fig
u
r
e
3
.
Ph
ase
d
is
cr
ep
a
n
cy
g
r
ap
h
d
u
r
in
g
th
e
s
y
n
c
h
r
o
n
izatio
n
p
r
o
ce
s
s
o
f
s
ix
o
s
cillato
r
s
to
th
e
r
ef
er
e
n
ce
(
a)
(
b
)
(
c)
Fig
u
r
e
4
.
Stab
ilit
y
v
e
r
if
icatio
n
o
f
s
y
n
ch
r
o
n
izatio
n
: (
a)
lin
ea
r
co
n
n
ec
tio
n
s
with
in
itial p
h
ase
s
p
r
ea
d
2
π,
(
b
)
Ku
r
a
m
o
to
with
f
r
eq
u
e
n
cy
an
d
p
h
ase
s
p
r
ea
d
,
an
d
(
c)
lin
e
ar
with
s
am
e
f
r
eq
u
en
cy
a
n
d
π
p
h
ase
s
p
r
ea
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
A
p
p
r
o
a
ch
t
o
s
elf
-
s
yn
ch
r
o
n
iz
a
tio
n
o
f a
g
r
o
u
p
o
f sta
tic
p
o
w
er c
o
n
ve
r
ters
(
V
icto
r
La
vrin
o
vsk
y
)
2347
As
s
h
o
wn
in
Fig
u
r
e
4
(
c)
,
if
th
e
in
itial
s
ig
n
o
f
th
e
o
u
tp
u
t
v
ar
iab
le
is
th
e
s
am
e
f
o
r
all
o
s
cill
ato
r
s
(
th
e
in
itial
p
h
ase
s
p
r
ea
d
is
f
r
o
m
0
to
π)
,
s
y
n
c
h
r
o
n
izatio
n
is
ac
h
iev
ed
in
f
i
n
ite
tim
e
with
a
r
e
lativ
e
ac
cu
r
ac
y
o
f
0
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1
6
%
f
o
r
lin
ea
r
in
ter
co
n
n
e
ctio
n
s
with
f
i
x
ed
o
s
cillato
r
f
r
eq
u
en
cies.
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wev
er
,
with
a
lar
g
er
s
p
r
ea
d
an
d
d
if
f
er
en
t
f
r
eq
u
en
cies
as
s
h
o
w
n
in
Fig
u
r
e
4
(
a)
in
lin
ea
r
i
n
te
r
co
n
n
ec
ted
n
et,
s
tatic
s
tates
with
eq
u
al
f
r
eq
u
en
cy
b
u
t
d
if
f
er
e
n
t
p
h
ases
,
d
is
tr
ib
u
ted
ac
r
o
s
s
s
tab
le
lev
els
o
f
2
π/N,
wh
er
e
N
is
th
e
n
u
m
b
er
o
f
o
s
cillato
r
s
,
ca
n
ar
is
e.
I
f
th
e
in
itial
s
ig
n
is
d
if
f
er
en
t
(
th
e
in
itial
p
h
ase
s
p
r
ea
d
is
f
r
o
m
−π
to
π
)
,
p
r
ec
is
e
s
y
n
ch
r
o
n
izatio
n
with
an
ac
cu
r
ac
y
o
f
0
.
1
6
%
d
o
es
n
o
t
o
cc
u
r
i
n
s
o
m
e
ca
s
es.
E
v
e
n
r
elax
in
g
th
e
c
r
iter
io
n
to
1
%,
u
n
s
y
n
ch
r
o
n
ized
o
s
cillato
r
s
r
em
ain
.
I
n
th
e
Ku
r
am
o
to
s
y
s
tem
,
as
s
h
o
wn
in
Fig
u
r
e
4
(
b
)
,
s
y
n
ch
r
o
n
izatio
n
is
en
s
u
r
ed
at
a
n
y
co
u
p
lin
g
c
o
ef
f
icien
t
v
alu
e,
w
ith
an
o
p
tim
al
v
alu
e
at
wh
ich
s
y
n
ch
r
o
n
izatio
n
o
cc
u
r
s
f
aster
,
an
d
with
f
u
r
th
e
r
g
r
o
wth
,
th
e
s
y
n
ch
r
o
n
izatio
n
ti
m
e
o
n
ly
i
n
cr
ea
s
es.
T
h
u
s
,
w
e
h
a
v
e
d
e
v
e
l
o
p
e
d
a
t
o
o
l
f
o
r
s
y
n
c
h
r
o
n
i
z
i
n
g
m
a
n
y
i
d
e
n
t
i
c
a
l
o
s
c
i
l
l
a
t
o
r
s
.
N
e
x
t
,
i
t
i
s
n
e
c
e
s
s
a
r
y
t
o
v
e
r
i
f
y
s
y
n
c
h
r
o
n
i
z
a
t
i
o
n
w
i
t
h
i
n
s
t
a
t
i
c
c
o
n
v
e
r
t
e
r
s
.
T
o
c
h
e
c
k
t
h
i
s
,
a
c
i
r
c
u
i
t
c
o
n
s
i
s
t
i
n
g
o
f
s
i
x
t
h
r
e
e
-
p
h
a
s
e
a
u
t
o
n
o
m
o
u
s
v
o
l
t
a
g
e
i
n
v
e
r
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e
r
s
w
i
t
h
a
n
i
s
o
l
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t
e
d
n
e
u
t
r
a
l
w
a
s
s
t
u
d
i
e
d
,
a
s
s
h
o
w
n
i
n
F
i
g
u
r
e
5
.
I
n
i
t
,
a
t
h
r
e
e
-
p
h
a
s
e
s
c
a
l
a
r
p
u
l
s
e
-
w
i
d
t
h
m
o
d
u
l
a
t
i
o
n
(
P
W
M
)
g
e
n
e
r
a
t
o
r
a
n
d
a
t
w
o
-
l
e
v
e
l
i
n
v
e
r
t
e
r
o
p
e
r
a
t
i
n
g
f
r
o
m
a
D
C
s
o
u
r
c
e
w
e
r
e
a
d
d
e
d
t
o
e
a
c
h
o
s
c
i
l
l
a
t
o
r
.
Simu
latio
n
r
esu
lts
f
o
r
a
g
r
o
u
p
o
f
s
ix
in
v
er
ter
s
o
p
er
atin
g
o
n
a
co
m
m
o
n
lo
ad
with
o
s
cillato
r
s
s
ettin
g
th
e
r
ef
er
en
ce
v
o
ltag
e
as
in
(
7
)
ar
e
s
h
o
wn
in
Fig
u
r
e
6
.
I
n
t
h
e
s
im
u
latio
n
,
th
e
DC
lin
k
v
o
ltag
e
was
s
et
to
5
3
0
V,
th
e
in
v
er
ter
o
u
tp
u
t
f
ilter
was
p
u
r
ely
in
d
u
ctiv
e
at
1
m
H,
an
d
th
e
lo
ad
was
an
ac
tiv
e
-
in
d
u
ctiv
e
co
m
b
in
atio
n
o
f
0
.
1
m
H
an
d
3
Oh
m
s
.
Fo
r
illu
s
tr
atio
n
o
f
th
e
s
y
n
ch
r
o
n
izatio
n
p
r
o
ce
s
s
,
Fig
u
r
e
6
s
h
o
ws
s
y
n
ch
r
o
n
o
u
s
g
r
ap
h
s
f
r
o
m
to
p
to
b
o
tto
m
:
th
e
cu
r
r
e
n
t
th
r
o
u
g
h
th
e
in
v
er
ter
p
h
ase
d
u
r
in
g
u
n
s
y
n
ch
r
o
n
ized
PW
M
o
p
e
r
atio
n
an
d
th
e
r
ef
er
en
ce
s
ig
n
al
o
f
th
e
PW
M
g
en
er
ato
r
s
.
T
h
e
PW
M
f
r
eq
u
en
cies
f
o
r
th
e
in
v
er
ter
s
d
u
r
in
g
u
n
s
y
n
c
h
r
o
n
ized
m
o
d
u
latio
n
wer
e
s
et
f
r
o
m
3
t
o
5
.
5
k
Hz
with
a
s
tep
o
f
5
0
0
Hz.
Un
s
y
n
ch
r
o
n
ized
PW
M
f
r
eq
u
en
cies
i
n
cr
ea
s
e
cu
r
r
en
t
r
ip
p
le,
b
u
t
d
o
n
o
t
af
f
ec
t
s
y
n
ch
r
o
n
izatio
n
.
At
th
e
b
eg
in
n
in
g
(
u
p
to
~0
.
1
s
)
s
y
n
c
h
r
o
n
izatio
n
o
cc
u
r
s
b
etwe
en
th
e
in
v
er
ter
s
u
n
til
th
e
p
h
ase
d
if
f
er
en
ce
is
less
th
an
1
0
-
5
r
ad
ian
s
.
Af
ter
r
ea
ch
in
g
s
u
ch
a
m
is
m
atch
,
th
e
in
v
er
ter
is
co
n
n
ec
ted
to
th
e
n
e
two
r
k
.
Fig
u
r
e
5
.
Stru
ctu
r
al
d
iag
r
am
o
f
th
e
s
tu
d
ied
s
y
s
tem
Fig
u
r
e
6
.
Simu
latio
n
o
f
i
n
v
er
t
er
s
y
n
ch
r
o
n
izatio
n
P
r
e
v
i
o
u
s
l
y
i
n
[
2
4
]
,
a
n
u
n
i
n
t
e
r
r
u
p
t
i
b
l
e
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r
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u
p
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(
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PS
)
wa
s
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o
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e
r
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o
r
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p
e
r
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tw
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t
em
s
.
Ho
we
v
e
r
,
i
t
is
o
n
l
y
v
ali
d
t
o
p
e
r
f
o
r
m
s
u
c
h
l
i
n
e
ar
iza
ti
o
n
wh
e
n
th
e
p
h
ase
d
ev
i
ati
o
n
is
l
ess
t
h
a
n
π/
6
.
Al
s
o
,
th
is
a
p
p
r
o
a
ch
to
s
y
n
c
h
r
o
n
i
za
ti
o
n
is
w
ell
-
s
u
it
e
d
f
o
r
i
m
p
le
m
e
n
ta
ti
o
n
in
v
i
r
t
u
al
o
s
cill
at
o
r
co
n
tr
o
l
m
et
h
o
d
s
,
alt
h
o
u
g
h
i
t
h
as
lim
i
tat
io
n
s
.
W
i
th
a
la
r
g
e
p
h
ase
d
e
v
ia
ti
o
n
i
n
a
g
r
o
u
p
o
f
o
s
ci
lla
to
r
s
,
s
i
m
p
l
y
in
tr
o
d
u
ci
n
g
t
h
e
v
o
lta
g
e
o
f
t
h
e
n
ea
r
est
n
o
d
e
is
n
o
t
e
n
o
u
g
h
.
An
e
x
p
e
r
i
m
e
n
t
wit
h
a
p
h
ase
d
e
v
i
ati
o
n
i
n
t
h
e
r
a
n
g
e
o
f
2
π
s
h
o
we
d
t
h
a
t
th
e
o
r
d
e
r
p
a
r
a
m
e
te
r
m
a
y
n
o
t
s
ta
b
i
liz
e
i
n
s
y
n
ch
r
o
n
i
ze
d
s
t
at
es.
T
h
e
p
r
o
p
o
s
e
d
s
y
n
c
h
r
o
n
i
za
t
io
n
m
et
h
o
d
ill
u
s
t
r
ates
wh
y
co
n
v
e
r
t
er
s
wi
th
v
i
r
t
u
al
o
s
ci
lla
to
r
c
o
n
tr
o
l
a
r
e
s
y
n
c
h
r
o
n
i
zi
n
g
a
n
d
w
h
y
th
e
y
m
ay
n
o
t
.
I
n
th
e
c
o
n
te
x
t
o
f
c
o
n
v
er
t
er
t
ec
h
n
o
lo
g
y
,
t
h
e
u
s
e
o
f
a
P
L
L
t
o
r
ec
o
v
e
r
th
e
p
h
ase
o
f
th
e
g
r
i
d
o
r
n
ei
g
h
b
o
r
i
n
g
c
o
n
v
e
r
t
er
is
s
t
a
n
d
ar
d
.
T
h
e
in
tr
o
d
u
ce
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
4
,
Dec
em
b
er
20
25
:
2342
-
2
3
5
2
2350
s
im
p
li
f
ic
ati
o
n
is
,
f
i
r
s
t
,
eq
u
i
v
a
len
t
f
o
r
s
m
a
ll
d
ev
iati
o
n
s
s
in
c
e
f
o
r
x
<
π
/6
,
s
in
(
x
)
=
x
.
S
e
co
n
d
,
f
o
r
c
o
n
v
e
r
te
r
tec
h
n
o
lo
g
y
,
d
et
e
r
m
i
n
i
n
g
t
h
e
p
h
as
e
o
f
a
s
i
g
n
a
l is
a
s
o
l
v
a
b
l
e
t
a
s
k
an
d
is
u
s
e
d
i
n
m
o
s
t
c
o
n
t
r
o
l
s
y
s
te
m
s
.
T
h
is
ar
ticle
d
id
n
o
t
ad
d
r
ess
is
s
u
es
o
f
lo
ad
d
is
tr
ib
u
tio
n
an
d
r
e
ac
tiv
e
p
o
wer
g
en
e
r
atio
n
th
ese
ar
e
f
u
tu
r
e
wo
r
k
s
th
at
will
b
e
b
ased
o
n
t
h
e
v
ir
tu
a
l
o
s
cillato
r
co
n
tr
o
l
tech
n
iq
u
e.
A
co
n
tin
u
atio
n
o
f
th
e
wo
r
k
in
v
o
lv
es
th
e
elim
in
atio
n
o
f
c
o
o
r
d
i
n
ate
tr
an
s
f
o
r
m
atio
n
an
d
a
s
h
if
t
to
war
d
s
ar
tific
ial
o
s
cillato
r
s
an
d
r
eso
n
an
t
r
e
g
u
lato
r
s
to
cr
ea
te
d
is
tr
ib
u
ted
co
n
tr
o
l
o
f
m
o
d
u
lar
m
u
ltil
ev
el
b
atter
y
e
n
er
g
y
s
to
r
ag
e
s
y
s
tem
in
a
n
o
n
s
y
m
m
etr
ical
g
r
id
.
Fu
r
th
er
d
ev
el
o
p
m
en
t
o
f
th
e
p
r
o
p
o
s
ed
wo
r
k
in
clu
d
es
s
ev
er
al
task
s
:
i)
C
r
ea
tin
g
n
o
n
lin
ea
r
f
e
ed
b
ac
k
co
m
p
atib
le
with
co
m
m
o
n
n
o
n
lin
ea
r
K
u
r
am
o
to
m
o
d
el
b
ased
o
n
s
ec
o
n
d
o
r
d
e
r
g
e
n
er
alize
d
in
t
eg
r
ato
r
t
o
en
s
u
r
e
s
y
n
ch
r
o
n
izatio
n
with
an
y
s
tar
tin
g
p
h
ase
d
ev
iatio
n
;
ii)
M
o
d
if
y
in
g
d
is
p
atch
in
g
to
d
is
ab
lin
g
an
d
en
ab
lin
g
co
n
v
er
ter
in
g
r
o
u
p
an
d
co
m
p
e
n
s
ated
p
h
ase
lo
ad
d
ev
iatio
n
;
a
n
d
iii)
M
ak
in
g
in
d
ep
en
d
e
n
t
p
h
ase
co
n
tr
o
l
b
ased
o
n
s
ec
o
n
d
o
r
d
e
r
g
e
n
er
alize
d
in
teg
r
ato
r
with
f
r
eq
u
e
n
cy
ad
a
p
ta
tio
n
to
o
p
er
a
te
in
n
o
n
s
y
m
m
etr
ical
g
r
id
s
tates.
T
h
e
p
r
esen
ted
wo
r
k
s
h
o
ws
th
a
t
th
e
lin
ea
r
ize
d
Ku
r
a
m
o
to
m
o
d
el
allo
ws
s
y
n
ch
r
o
n
izatio
n
o
f
o
s
cillatin
g
s
y
s
tem
s
.
Ho
wev
er
,
it
i
s
o
n
ly
v
alid
to
p
er
f
o
r
m
s
u
ch
lin
ea
r
izatio
n
wh
en
th
e
p
h
ase
d
ev
iatio
n
is
less
th
an
π/6
.
Als
o
,
th
is
ap
p
r
o
ac
h
to
s
y
n
ch
r
o
n
izatio
n
is
well
s
u
ited
f
o
r
im
p
lem
en
tatio
n
in
v
ir
tu
al
o
s
cillato
r
co
n
tr
o
l
m
et
h
o
d
s
,
alth
o
u
g
h
it
h
as
lim
itatio
n
s
.
W
ith
a
lar
g
e
p
h
ase
d
ev
iatio
n
in
a
g
r
o
u
p
o
f
o
s
cillato
r
s
,
s
im
p
ly
in
tr
o
d
u
cin
g
th
e
v
o
ltag
e
o
f
th
e
n
ea
r
est
n
o
d
e
is
n
o
t
en
o
u
g
h
.
An
ex
p
e
r
i
m
en
t
with
a
p
h
ase
d
ev
iatio
n
in
th
e
r
an
g
e
o
f
2
π
s
h
o
we
d
th
at
th
e
o
r
d
e
r
p
ar
a
m
eter
m
ay
n
o
t stab
ilize
in
s
y
n
ch
r
o
n
ized
s
tates.
5.
CO
NCLU
SI
O
N
T
h
e
s
tu
d
y
in
v
esti
g
ates
an
d
im
p
lem
en
ts
s
y
n
ch
r
o
n
izatio
n
alg
o
r
ith
m
s
f
o
r
a
g
r
o
u
p
o
f
o
s
cillato
r
s
am
o
n
g
th
em
s
elv
es
an
d
with
an
ex
ter
n
al
g
r
id
,
u
s
in
g
co
m
p
u
ter
m
o
d
els.
T
h
e
s
y
n
ch
r
o
n
izatio
n
p
r
o
ce
s
s
in
a
s
y
m
m
etr
ical
g
r
id
is
d
em
o
n
s
tr
ated
with
s
ix
in
v
er
ter
s
o
p
er
atin
g
o
n
a
co
m
m
o
n
lo
a
d
.
Fo
r
an
asy
m
m
etr
ical
g
r
id
,
th
e
s
y
n
ch
r
o
n
izatio
n
o
f
f
o
u
r
th
r
ee
-
p
h
ase
f
o
u
r
-
wir
e
co
n
v
er
ter
s
o
p
er
atin
g
i
n
in
v
er
ter
m
o
d
e
o
n
a
co
m
m
o
n
l
o
ad
is
co
n
s
id
er
ed
.
On
e
o
f
th
e
s
ig
n
i
f
ican
t
ch
allen
g
es
in
in
teg
r
atin
g
s
o
u
r
ce
s
,
s
to
r
ag
e
u
n
its
,
an
d
co
n
s
u
m
er
s
in
to
a
u
n
if
ied
g
r
id
with
in
a
m
icr
o
g
r
id
is
th
e
s
y
n
ch
r
o
n
izatio
n
p
r
o
b
lem
,
wh
ich
c
u
r
r
en
tly
r
e
q
u
ir
es
a
co
m
p
lex
s
y
n
ch
r
o
n
izatio
n
p
r
o
ce
d
u
r
e.
T
h
er
ef
o
r
e
,
th
e
s
tu
d
y
p
r
o
p
o
s
es
an
ap
p
r
o
ac
h
to
s
y
n
ch
r
o
n
izati
o
n
th
at
en
s
u
r
es
t
h
e
s
elf
-
s
y
n
ch
r
o
n
izatio
n
o
f
d
ev
ice
s
b
ef
o
r
e
th
ey
ar
e
co
n
n
ec
ted
to
th
e
g
r
id
.
T
h
e
r
esear
ch
r
esu
lts
h
av
e
b
ee
n
u
s
ed
to
d
esig
n
a
p
r
o
to
ty
p
e
o
f
UPS b
ased
o
n
a
g
r
id
-
f
o
r
m
in
g
in
v
er
ter
with
a
n
o
m
in
al
a
p
p
ar
en
t
p
o
we
r
o
f
1
0
k
VA.
F
UNDING
I
NF
O
R
M
A
T
I
O
N
T
h
e
r
esear
ch
p
r
esen
ted
in
th
is
ar
ticle
wa
s
co
n
d
u
cted
as
p
ar
t
o
f
th
e
R
&
D
p
r
o
ject
"
Dev
el
o
p
m
en
t
o
f
d
ig
ital
s
tr
u
ctu
r
es
an
d
h
ar
d
war
e
an
d
s
o
f
twar
e
f
o
r
is
o
lated
p
o
wer
s
y
s
tem
s
with
s
ca
lab
le
e
n
er
g
y
s
to
r
ag
e
(
SP
-
4
/2
0
2
4
/
1
,
Prio
r
ity
2
0
3
0
)
".
R
eg
is
tr
atio
n
n
u
m
b
er
:
1
2
4
0
9
1
7
0
0
0
1
4
-
5.
AUTHO
R
CO
NT
RI
B
UT
I
O
NS ST
A
T
E
M
E
N
T
T
h
is
jo
u
r
n
al
u
s
es
th
e
C
o
n
tr
ib
u
to
r
R
o
les
T
ax
o
n
o
m
y
(
C
R
ed
iT)
to
r
ec
o
g
n
ize
in
d
iv
id
u
al
au
th
o
r
co
n
tr
ib
u
tio
n
s
,
r
ed
u
ce
au
th
o
r
s
h
ip
d
is
p
u
tes,
an
d
f
ac
ilit
ate
co
llab
o
r
atio
n
.
Na
m
e
o
f
Aut
ho
r
C
M
So
Va
Fo
I
R
D
O
E
Vi
Su
P
Fu
Victo
r
L
av
r
in
o
v
s
k
y
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
Nik
ita
Do
b
r
o
s
k
o
k
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
Vale
r
y
B
u
ly
ch
ev
✓
✓
✓
✓
✓
✓
✓
R
u
s
lan
Mig
r
an
o
v
✓
✓
✓
✓
✓
✓
✓
Yu
r
iy
Yu
Per
ev
alo
v
✓
✓
✓
✓
✓
✓
An
astas
ia
Sto
tck
aia
✓
✓
✓
✓
✓
C
:
C
o
n
c
e
p
t
u
a
l
i
z
a
t
i
o
n
M
:
M
e
t
h
o
d
o
l
o
g
y
So
:
So
f
t
w
a
r
e
Va
:
Va
l
i
d
a
t
i
o
n
Fo
:
Fo
r
mal
a
n
a
l
y
s
i
s
I
:
I
n
v
e
s
t
i
g
a
t
i
o
n
R
:
R
e
so
u
r
c
e
s
D
:
D
a
t
a
C
u
r
a
t
i
o
n
O
:
W
r
i
t
i
n
g
-
O
r
i
g
i
n
a
l
D
r
a
f
t
E
:
W
r
i
t
i
n
g
-
R
e
v
i
e
w
&
E
d
i
t
i
n
g
Vi
:
Vi
su
a
l
i
z
a
t
i
o
n
Su
:
Su
p
e
r
v
i
s
i
o
n
P
:
P
r
o
j
e
c
t
a
d
mi
n
i
st
r
a
t
i
o
n
Fu
:
Fu
n
d
i
n
g
a
c
q
u
i
si
t
i
o
n
CO
NF
L
I
C
T
O
F
I
N
T
E
R
E
S
T
ST
A
T
E
M
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