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I
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16
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4
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Dec
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20
25
:
2353
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o
u
s
im
p
r
o
v
e
m
en
ts
,
in
clu
d
in
g
a
d
ap
tiv
e
f
ilt
er
in
g
,
f
ee
d
f
o
r
war
d
co
m
p
en
s
atio
n
,
an
d
o
p
tim
ized
tu
n
in
g
s
tr
ateg
ies,
h
av
e
b
ee
n
p
r
o
p
o
s
ed
to
en
h
a
n
ce
its
p
er
f
o
r
m
an
ce
[
1
4
]
-
[
1
7
]
.
No
n
eth
eless
,
SR
F
-
PLL
co
n
tin
u
es
to
u
n
d
er
p
er
f
o
r
m
d
u
r
i
n
g
s
e
v
er
e
g
r
id
f
au
lts
s
u
ch
as
v
o
ltag
e
s
ag
s
an
d
s
wells,
r
esu
ltin
g
in
in
ac
cu
r
ate
s
y
n
ch
r
o
n
izatio
n
an
d
d
e
g
r
ad
ed
o
u
tp
u
t
p
o
wer
q
u
ality
[
1
8
]
,
[
1
9
]
.
T
o
o
v
er
c
o
m
e
th
ese
ch
allen
g
e
s
,
d
ig
ital
p
h
ase
-
lo
ck
ed
lo
o
p
s
(
DPLL
s
)
h
av
e
b
ee
n
d
e
v
elo
p
ed
in
th
e
d
is
cr
e
te
-
tim
e
d
o
m
ain
,
o
f
f
er
i
n
g
en
h
an
ce
d
p
r
ec
is
io
n
an
d
r
o
b
u
s
tn
ess
d
u
r
in
g
d
y
n
am
ic
g
r
id
c
o
n
d
itio
n
s
.
Alth
o
u
g
h
s
o
m
e
d
ig
ital
v
ar
ian
ts
h
av
e
b
ee
n
p
r
ev
i
o
u
s
ly
p
r
o
p
o
s
ed
,
m
a
n
y
lack
ed
p
r
ac
tical
im
p
lem
e
n
tatio
n
o
r
f
ailed
to
d
em
o
n
s
tr
ate
th
eir
a
p
p
licab
ilit
y
in
r
ea
l
-
tim
e
[
2
0
]
-
[
2
4
]
.
I
n
o
u
r
p
r
io
r
wo
r
k
[
2
5
]
,
a
DPLL
b
ased
o
n
b
ac
k
war
d
E
u
ler
ap
p
r
o
x
im
atio
n
was
im
p
lem
en
ted
a
n
d
v
alid
ated
u
n
d
er
v
ar
io
u
s
s
y
m
m
etr
ical
an
d
asy
m
m
etr
ical
f
au
lt
co
n
d
itio
n
s
.
T
h
is
d
esig
n
n
o
t
o
n
ly
im
p
r
o
v
ed
p
h
ase
tr
ac
k
in
g
b
u
t
also
s
ig
n
if
ican
tly
r
ed
u
ce
d
to
tal
h
ar
m
o
n
ic
di
s
to
r
tio
n
(
T
HD)
,
th
e
r
eb
y
en
h
an
cin
g
o
v
er
all
p
o
we
r
q
u
ality
.
Yet,
th
e
DPLL
alo
n
e
co
u
ld
n
o
t
ad
d
r
ess
v
o
ltag
e
q
u
ality
i
s
s
u
es
at
th
e
lo
ad
an
d
p
o
in
t
o
f
co
m
m
o
n
co
u
p
lin
g
(
PC
C
)
d
u
r
i
n
g
g
r
id
f
au
lts
.
Vo
ltag
e
s
ag
s
a
n
d
s
wells
p
er
s
is
ted
d
u
e
to
th
e
in
v
er
te
r
’
s
lim
ited
ca
p
ab
il
ity
in
d
y
n
am
ic
v
o
ltag
e
s
u
p
p
o
r
t.
Dy
n
am
ic
v
o
ltag
e
r
esto
r
e
r
s
(
DVRs
)
h
av
e
p
r
o
v
en
e
f
f
ec
tiv
e
i
n
r
eg
u
latin
g
v
o
ltag
e
u
n
d
er
s
u
c
h
co
n
d
itio
n
s
[
2
6
]
-
[
3
0
]
.
R
ec
en
t
s
tu
d
ies
h
ig
h
lig
h
t
t
h
at
PI
co
n
tr
o
ller
s
s
u
f
f
er
f
r
o
m
d
r
awb
ac
k
s
s
u
ch
as
d
elay
ed
r
ec
o
v
er
y
a
n
d
h
ig
h
s
en
s
itiv
ity
t
o
g
r
id
d
is
tu
r
b
an
ce
s
,
wh
ile
f
ix
ed
-
m
o
d
e
DVRs
ca
n
in
ject
u
n
n
ec
ess
ar
y
co
m
p
en
s
atin
g
v
o
ltag
e
ev
en
d
u
r
in
g
n
o
r
m
al
o
p
e
r
atin
g
co
n
d
itio
n
s
.
T
h
is
n
o
t o
n
ly
wastes
en
er
g
y
b
u
t a
ls
o
im
p
o
s
es
ad
d
itio
n
al
s
tr
ess
o
n
d
y
n
am
ic
v
o
ltag
e
r
esto
r
er
(
DVR)
co
m
p
o
n
en
ts
,
p
o
ten
tially
af
f
ec
ti
n
g
b
o
th
th
e
lo
ad
a
n
d
th
e
g
r
id
[
3
1
]
,
[
3
2
]
.
T
o
a
d
d
r
ess
th
ese
is
s
u
es,
th
e
p
r
o
p
o
s
ed
d
esi
g
n
em
p
lo
y
s
s
lid
in
g
m
o
d
e
co
n
tr
o
l
(
SMC
)
,
wh
ich
o
f
f
er
s
s
tr
o
n
g
r
o
b
u
s
tn
ess
u
n
d
er
f
ast
tr
an
s
ien
ts
,
ef
f
ec
tiv
e
o
p
er
atio
n
d
u
r
in
g
u
n
b
alan
ce
d
c
o
n
d
i
tio
n
s
,
an
d
m
in
im
al
tu
n
in
g
r
eq
u
ir
e
m
en
ts
,
th
er
e
b
y
en
h
an
cin
g
b
o
th
e
f
f
icien
cy
an
d
r
eliab
ilit
y
.
Desp
ite
th
ese
a
d
v
an
ce
m
e
n
ts
,
th
r
ee
k
ey
lim
itatio
n
s
p
er
s
is
t
in
ex
is
tin
g
ap
p
r
o
ac
h
es:
i)
SR
F
-
PLL
p
er
f
o
r
m
s
r
eliab
ly
o
n
ly
u
n
d
er
i
d
ea
l
co
n
d
itio
n
s
b
u
t
f
ails
to
s
y
n
ch
r
o
n
ize
ac
c
u
r
atel
y
d
u
r
in
g
d
is
tu
r
b
an
ce
s
;
ii)
W
h
ile
DPLL
im
p
r
o
v
es
h
ar
m
o
n
ic
s
u
p
p
r
ess
io
n
a
n
d
s
y
n
ch
r
o
n
izatio
n
u
n
d
er
f
au
lts
,
it
lack
s
v
o
ltag
e
s
u
p
p
o
r
t
c
ap
ab
ilit
y
;
an
d
iii)
DVRs
,
th
o
u
g
h
ef
f
ec
tiv
e
in
co
m
p
en
s
atin
g
f
au
lts
,
in
tr
o
d
u
ce
in
ef
f
icien
cies
wh
en
o
p
er
ated
with
o
u
t
in
tellig
en
t
co
n
tr
o
l
in
n
o
r
m
al
g
r
id
co
n
d
iti
o
n
s
.
T
o
o
v
er
c
o
m
e
th
e
ab
o
v
e
ch
al
len
g
es,
th
is
wo
r
k
p
r
esen
ts
a
n
o
v
el
h
y
b
r
id
co
n
tr
o
l
ar
ch
ite
ctu
r
e
th
at
u
n
if
ies
s
y
n
ch
r
o
n
izatio
n
an
d
in
tellig
en
t
v
o
ltag
e
r
eg
u
latio
n
wi
th
o
u
t
in
tr
o
d
u
cin
g
ad
d
itio
n
al
s
y
s
tem
co
m
p
lex
ity
.
A
p
h
ase
-
wis
e
m
o
n
ito
r
in
g
s
y
s
tem
co
n
tin
u
o
u
s
ly
ev
al
u
ates
th
e
g
r
id
co
n
d
itio
n
a
n
d
class
if
ies
it
as
eith
er
n
o
m
in
al
o
r
f
au
lted
.
B
ased
o
n
th
is
ev
a
lu
atio
n
,
th
e
f
u
zz
y
i
n
f
er
en
ce
s
y
s
tem
(
FIS)
d
y
n
a
m
ically
s
elec
ts
th
e
ap
p
r
o
p
r
iate
PLL
:
th
e
C
T
PLL
is
en
g
ag
e
d
d
u
r
i
n
g
n
o
r
m
al
g
r
id
o
p
er
atio
n
d
u
e
to
its
s
tab
le
an
d
p
r
ec
is
e
p
h
a
se
-
tr
ac
k
in
g
ca
p
ab
ilit
y
,
wh
ile
th
e
DPLL
is
ac
tiv
ated
u
n
d
er
f
au
lt
co
n
d
itio
n
s
to
en
s
u
r
e
r
o
b
u
s
t
s
y
n
ch
r
o
n
izatio
n
an
d
ef
f
ec
tiv
e
h
ar
m
o
n
ic
s
u
p
p
r
ess
io
n
.
I
n
p
ar
a
llel,
th
e
DVR
is
also
co
n
tr
o
lle
d
in
r
esp
o
n
s
e
to
th
e
r
ea
l
-
tim
e
g
r
id
class
if
icatio
n
,
in
jectin
g
co
m
p
en
s
atin
g
v
o
ltag
e
o
n
ly
wh
en
d
is
tu
r
b
an
ce
s
ar
e
d
etec
ted
,
th
u
s
av
o
id
in
g
u
n
n
ec
ess
ar
y
in
ter
v
en
tio
n
d
u
r
in
g
h
ea
lth
y
g
r
id
s
tates
an
d
m
in
im
izin
g
s
tr
ess
o
n
DVR
co
m
p
o
n
en
ts
.
T
h
is
u
n
if
ied
,
a
d
ap
tiv
e
f
r
am
ew
o
r
k
en
h
an
ce
s
o
v
er
all
s
y
s
tem
p
er
f
o
r
m
an
ce
b
y
en
s
u
r
in
g
ac
c
u
r
ate
s
y
n
ch
r
o
n
izati
o
n
,
im
p
r
o
v
ed
p
o
wer
q
u
ality
at
b
o
th
th
e
p
o
in
t
o
f
co
m
m
o
n
c
o
u
p
lin
g
an
d
th
e
l
o
ad
,
a
n
d
r
e
d
u
ce
d
h
ar
d
war
e
an
d
c
o
n
tr
o
l c
o
m
p
le
x
ity
.
T
h
e
r
est
o
f
t
h
is
p
ap
e
r
is
o
r
g
an
ized
as
f
o
llo
ws
:
i)
Sectio
n
2
d
etails
th
e
p
r
o
p
o
s
ed
m
et
h
o
d
o
lo
g
y
,
in
clu
d
in
g
th
e
m
ath
e
m
atica
l
im
p
lem
en
tat
io
n
o
f
th
e
DVR,
th
e
f
u
zz
y
in
f
e
r
en
ce
s
y
s
tem
(
FI
S)
f
o
r
a
d
ap
tiv
e
PL
L
s
witch
in
g
,
an
d
th
e
p
h
ase
-
wis
e
v
o
ltag
e
m
o
n
ito
r
i
n
g
lo
g
ic
;
ii)
Sectio
n
3
d
escr
ib
es
th
e
co
m
p
lete
s
y
s
tem
ar
ch
itectu
r
e
an
d
th
e
im
p
lem
e
n
tatio
n
in
MA
T
L
AB
S
im
u
lin
k
o
f
th
e
1
0
0
-
k
W
g
r
id
-
tied
PV
s
y
s
tem
,
it
s
co
n
tr
o
l
f
r
am
ewo
r
k
,
an
d
t
h
e
in
teg
r
at
ed
o
p
er
atio
n
o
f
DVR
with
ad
ap
tiv
e
PLL
s
elec
tio
n
;
iii)
Sectio
n
4
p
r
esen
ts
s
im
u
latio
n
r
esu
lts
an
d
d
is
cu
s
s
i
o
n
f
o
r
s
y
m
m
etr
ical
an
d
asy
m
m
etr
ical
s
ag
/s
well
co
n
d
itio
n
s
ac
r
o
s
s
th
r
ee
co
n
tr
o
l
ca
s
es
,
DPLL
-
o
n
ly
,
DVR
wit
h
DPLL
,
an
d
th
e
p
r
o
p
o
s
ed
DVR
with
FIS
-
b
ased
ad
ap
tiv
e
PLL
s
witch
in
g
—
ev
alu
atin
g
v
o
ltag
e
r
esto
r
atio
n
,
h
ar
m
o
n
ic
p
er
f
o
r
m
an
ce
,
an
d
r
ec
o
v
er
y
tim
e
;
an
d
iv
)
Secti
o
n
5
c
o
n
clu
d
es
th
e
wo
r
k
with
k
e
y
f
in
d
i
n
g
s
an
d
o
u
tlin
es d
ir
ec
tio
n
s
f
o
r
f
u
tu
r
e
r
esear
ch
.
2.
M
E
T
H
O
DO
L
O
G
Y
T
h
e
m
ath
em
atica
l
f
o
r
m
u
latio
n
s
o
f
th
e
co
r
e
s
u
b
s
y
s
tem
s
co
n
s
titu
tin
g
th
e
p
r
o
p
o
s
ed
FIS
-
b
ased
DVR
co
n
tr
o
l stra
teg
y
a
r
e
d
etailed
in
th
is
s
ec
tio
n
.
2
.
1
.
Dy
na
m
ic
v
o
lt
a
g
e
re
s
t
o
r
er
(
DVR)
T
h
e
DVR,
a
s
er
ies
v
o
ltag
e
in
jectio
n
d
ev
ice
,
is
u
s
ed
in
th
is
wo
r
k
to
m
itig
ate
v
o
lta
g
e
f
lu
ct
u
atio
n
s
at
th
e
p
o
i
n
t
o
f
c
o
m
m
o
n
c
o
u
p
lin
g
(
PC
C
)
.
I
n
th
e
p
r
o
p
o
s
ed
s
y
s
tem
,
th
e
DVR
o
p
er
ates
u
n
d
e
r
a
v
o
ltag
e
in
jectio
n
s
tr
ateg
y
r
eg
u
lated
b
y
a
r
o
b
u
s
t
s
lid
in
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m
o
d
e
co
n
tr
o
ller
(
S
MC)
im
p
lem
en
ted
in
th
e
s
y
n
ch
r
o
n
o
u
s
r
ef
er
en
ce
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
F
u
z
z
y
lo
g
ic
-
b
a
s
ed
a
d
a
p
tive
P
LL
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w
itch
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g
s
tr
a
teg
y
fo
r
…
(
R
.
S
r
ila
ksh
mi
)
2355
f
r
am
e
(
d
q
-
f
r
am
e)
.
T
h
e
DVR’s
p
r
im
ar
y
o
b
jectiv
e
is
to
en
s
u
r
e
lo
ad
-
s
id
e
v
o
ltag
e
s
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ilit
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d
u
r
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g
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o
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s
y
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m
etr
ical
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d
asy
m
m
etr
ical
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d
is
tu
r
b
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ce
s
.
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h
e
m
ea
s
u
r
ed
th
r
ee
-
p
h
ase
g
r
i
d
v
o
ltag
es
V
abc
(
t)
at
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PC
C
ar
e
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ir
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t
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n
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er
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it
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p
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.
)
va
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es u
s
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g
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e
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ase
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ase
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as e
x
p
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ess
ed
in
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1
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(
)
=
(
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T
h
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n
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n
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ig
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als
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e
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er
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[
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=
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[
(
−
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(
+
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in
−
s
in
(
−
2
3
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−
s
in
(
+
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3
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1
2
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2
1
2
]
⌈
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(
2
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T
h
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p
er
-
u
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it
v
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a
r
e
tr
an
s
f
o
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ed
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to
th
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y
n
c
h
r
o
n
o
u
s
r
e
f
er
en
ce
f
r
am
e
u
s
in
g
th
e
Par
k
tr
an
s
f
o
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m
atio
n
,
as
s
h
o
wn
in
(
2
)
[
3
3
]
.
T
h
e
tr
an
s
f
o
r
m
atio
n
an
g
le
θ
is
d
er
iv
ed
f
r
o
m
eith
er
th
e
d
ig
ital
PLL
(
DPLL
)
o
r
C
T
PLL
,
d
ep
en
d
i
n
g
o
n
th
e
c
o
n
d
itio
n
-
b
ased
s
witch
in
g
lo
g
ic
g
o
v
er
n
e
d
b
y
th
e
f
u
zz
y
in
f
e
r
en
ce
s
y
s
tem
(
FIS)
.
2
.
1
.
1
.
SM
C
-
b
a
s
ed
DVR
c
o
nt
ro
l
T
h
e
SMC
tr
ac
k
s
th
e
er
r
o
r
b
e
twee
n
th
e
r
ef
e
r
en
ce
a
n
d
ac
tu
al
d
q
-
f
r
am
e
v
o
ltag
es.
T
h
e
er
r
o
r
an
d
its
d
er
iv
ativ
e
ar
e
d
ef
in
e
d
in
(
3
)
.
(
)
=
−
,
̇
(
)
=
(
)
(
3)
Un
lik
e
tr
ad
itio
n
al
SMC
s
th
at
u
s
e
d
is
co
n
tin
u
o
u
s
s
ig
n
f
u
n
ct
io
n
s
,
th
is
wo
r
k
em
p
lo
y
s
a
s
atu
r
atio
n
f
u
n
ctio
n
t
o
r
ed
u
ce
ch
atter
i
n
g
an
d
im
p
r
o
v
e
co
n
v
er
g
en
ce
,
as sh
o
w
n
in
th
e
eq
u
atio
n
,
w
h
ich
is
k
n
o
w
n
as
th
e
co
n
tr
o
l
l
aw
(
4
)
:
(
)
=
(
(
)
)
(4
)
wh
er
e
(
)
=
(
(
)
,
̇
(
)
)
.
T
h
is
ap
p
r
o
ac
h
e
n
s
u
r
es
a
s
m
o
o
th
tr
an
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itio
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o
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th
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n
tr
o
l
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ig
n
al
with
in
b
o
u
n
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ed
lim
its
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m
ak
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g
it
well
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s
u
ited
f
o
r
p
o
wer
elec
tr
o
n
ic
co
n
v
er
ter
s
an
d
en
h
a
n
cin
g
s
y
s
tem
lo
n
g
ev
ity
a
n
d
co
n
tr
o
l
p
r
ec
is
io
n
.
T
h
e
f
in
al
co
n
tr
o
l
s
ig
n
al
is
th
en
tr
an
s
f
o
r
m
ed
b
ac
k
to
th
e
AB
C
f
r
am
e
a
n
d
a
p
p
lied
t
h
r
o
u
g
h
th
e
DVR
in
v
er
ter
to
in
ject
th
e
ap
p
r
o
p
r
iate
co
m
p
en
s
atin
g
v
o
ltag
e
at
th
e
PC
C
[
3
4
]
.
2
.
1
.
2
.
DVR
s
izing
T
h
e
DVR’s p
o
wer
r
atin
g
a
n
d
en
er
g
y
r
eq
u
ir
e
m
en
ts
ar
e
d
eter
m
in
ed
u
s
in
g
(
5
)
a
n
d
(
6
)
:
=
√
3
∗
,
∗
(5
)
=
∫
(
)
∗
(
)
2
1
(6
)
wh
er
e
,
=
(
)
−
(
)
.
T
h
ese
eq
u
atio
n
s
g
u
id
e
th
e
d
esig
n
o
f
DVR
ca
p
ac
ity
to
en
s
u
r
e
ef
f
ec
tiv
e
co
m
p
en
s
atio
n
d
u
r
in
g
g
r
i
d
d
is
tu
r
b
an
ce
s
.
2
.
2
.
F
uzzy
lo
g
ic
-
ba
s
ed
a
da
pt
iv
e
P
L
L
s
wit
ch
ing
m
ec
ha
nis
m
T
o
en
h
an
ce
s
y
n
c
h
r
o
n
izatio
n
d
u
r
in
g
g
r
id
d
is
tu
r
b
a
n
ce
s
wh
ile
en
s
u
r
in
g
co
n
t
r
o
l
s
im
p
licity
in
n
o
r
m
al
co
n
d
itio
n
s
,
an
ad
ap
tiv
e
PLL
s
witch
in
g
s
tr
ateg
y
is
im
p
lem
en
ted
u
s
in
g
a
Ma
m
d
a
n
i
-
ty
p
e
f
u
z
zy
in
f
er
en
c
e
s
y
s
tem
(
FIS)
.
T
h
is
m
ec
h
an
is
m
d
y
n
a
m
ically
s
elec
ts
b
etwe
en
a
co
n
v
en
tio
n
al
SR
F
-
b
ased
PLL
(
C
T
PLL
)
an
d
a
d
ig
ital
PLL
(
DPLL
)
b
ased
o
n
r
ea
l
-
ti
m
e
f
au
lt m
o
n
ito
r
in
g
.
2
.
2
.
1
.
Rea
l
-
t
i
m
e
f
a
ult
det
ec
t
i
o
n lo
g
ic
A
t
h
r
e
e
-
p
h
a
s
e
v
o
l
t
a
g
e
m
o
n
i
t
o
r
i
n
g
u
n
i
t
(
F
i
g
u
r
e
1
)
c
o
m
p
u
t
e
s
R
M
S
v
a
l
u
es
o
f
V
a
,
V
b
,
a
n
d
V
c
.
T
h
e
n
c
o
m
p
a
r
e
s
w
i
t
h
t
h
e
t
h
r
e
s
h
o
l
d
o
f
±
1
0
%
o
f
t
h
e
n
o
m
i
n
a
l
v
a
l
u
e
,
a
n
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e
a
c
h
p
h
a
s
e
i
s
a
s
s
i
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n
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d
a
f
a
u
l
t
s
t
at
u
s
b
a
s
e
d
o
n
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e
v
i
a
t
i
o
n
t
h
r
e
s
h
o
l
d
s
:
i
)
0
:
n
o
f
a
u
l
t
d
e
t
e
c
t
e
d
(
v
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t
a
g
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t
h
i
n
n
o
m
i
n
a
l
l
i
m
i
ts
)
,
i
i
)
0
.
5
:
l
i
k
e
ly
f
a
u
l
t
o
r
p
r
e
-
f
a
u
l
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
:
2353
-
2
3
6
8
2356
b
e
h
a
v
i
o
r
(
m
i
n
o
r
d
e
v
i
a
ti
o
n
)
,
a
n
d
i
i
i
)
1
:
C
o
n
f
i
r
m
e
d
f
a
u
lt
(
s
i
g
n
if
i
c
a
n
t
v
o
l
ta
g
e
s
a
g
o
r
s
w
el
l
.
T
h
e
s
e
d
is
c
r
et
e
v
al
u
e
s
a
l
l
o
w
t
h
e
s
y
s
t
e
m
t
o
d
e
t
ec
t
b
o
t
h
n
o
r
m
a
l
a
n
d
f
a
u
l
t
(
s
y
m
m
e
t
r
ic
a
l
o
r
a
s
y
m
m
e
t
r
i
c
al
f
a
u
l
ts
,
s
a
g
o
r
S
w
e
ll
)
e
f
f
e
c
ti
v
e
l
y
.
Fig
u
r
e
1
.
Ph
ase
-
w
is
e
R
MS
v
o
ltag
e
m
o
n
ito
r
i
n
g
an
d
f
u
zz
y
lo
g
ic
-
b
ased
ad
ap
tiv
e
PLL
s
witch
i
n
g
ar
ch
itectu
r
e
2
.
2
.
2
.
Switc
hin
g
m
ec
ha
nis
m
T
h
e
FIS
(
Fig
u
r
e
2
)
ac
ce
p
t
s
th
r
ee
in
p
u
ts
(
p
h
ase
f
au
lt
s
tatu
s
es)
an
d
p
r
o
d
u
ce
s
tw
o
o
u
t
p
u
ts
:
C
T
PLL
_
m
o
d
e
an
d
DPLL
_
m
o
d
e.
E
ac
h
in
p
u
t u
s
es th
r
ee
tr
a
p
e
zo
id
al
m
em
b
er
s
h
i
p
f
u
n
ctio
n
s
(
Fig
u
r
e
3
(
a)
)
,
wh
ile
o
u
tp
u
ts
f
o
llo
w
a
th
r
ee
-
lev
el
f
u
zz
y
s
tr
u
ctu
r
e:
o
f
f
,
p
ar
tial,
an
d
o
n
(
Fig
u
r
e
3
(
b
)
)
.
T
h
e
FIS
r
u
le
b
ase
in
ter
p
r
ets
all
p
o
s
s
ib
le
co
m
b
in
atio
n
s
o
f
th
e
t
h
r
ee
in
p
u
t p
h
ases
(
3
^
3
=
2
7
c
o
m
b
in
atio
n
s
)
.
Ho
wev
er
,
f
o
r
s
y
s
tem
s
im
p
licity
an
d
r
elev
an
ce
,
o
n
ly
s
elec
ted
m
ea
n
i
n
g
f
u
l r
u
les ar
e
im
p
lem
e
n
ted
,
s
u
ch
as:
−
No
Fau
lt (
0
)
: CTPLL
r
em
ain
s
f
u
lly
ON,
DPLL
r
em
ain
s
f
u
lly
OFF
;
−
Fau
lt (
1
)
: CTPLL
r
am
p
s
d
o
wn
to
OFF,
DPLL
r
am
p
s
u
p
to
O
N
; a
n
d
−
L
ik
ely
Fau
lt
(
0
.
5
)
:
B
o
th
PLL
s
ar
e
p
ar
tially
ac
tiv
e
f
o
r
a
s
h
o
r
t
tr
an
s
itio
n
p
er
i
o
d
.
C
T
PLL
s
tar
ts
r
am
p
in
g
d
o
wn
wh
ile
DPLL
s
tar
ts
r
am
p
in
g
u
p
.
T
h
is
r
u
le
-
b
ased
lo
g
ic
en
s
u
r
es
th
at
th
e
DPLL
is
ac
tiv
a
ted
o
n
ly
wh
en
n
ec
ess
ar
y
,
o
p
tim
izin
g
co
m
p
u
tatio
n
al
ef
f
icien
cy
.
T
h
e
p
r
o
p
o
s
ed
co
n
tr
o
l
f
r
am
ewo
r
k
h
as
b
ee
n
d
esig
n
ed
with
m
in
i
m
al
co
m
p
u
tatio
n
al
o
v
er
h
ea
d
.
DVR
s
izin
g
is
b
ased
o
n
s
tan
d
ar
d
p
er
-
u
n
it
v
o
ltag
e
in
jectio
n
ca
lcu
latio
n
s
,
av
o
id
in
g
iter
ativ
e
o
p
tim
izatio
n
r
o
u
tin
es.
T
h
e
p
h
ase
-
wis
e
m
o
n
ito
r
in
g
lo
g
ic
an
d
FIS
-
b
ased
s
witch
in
g
r
eq
u
ir
e
o
n
ly
s
im
p
le
R
MS
vol
tag
e
ev
alu
atio
n
s
an
d
tr
a
p
e
zo
id
al
m
em
b
er
s
h
ip
e
v
alu
atio
n
s
p
er
c
o
n
tr
o
l
cy
cle,
wh
ich
a
r
e
co
m
p
u
tatio
n
ally
lig
h
t
f
o
r
m
o
d
er
n
DSP
o
r
FP
GA
co
n
tr
o
ller
s
.
As
s
u
ch
,
th
e
ad
ap
tiv
e
PLL
s
witch
in
g
an
d
DVR
o
p
er
atio
n
ca
n
b
e
ex
ec
u
ted
in
r
ea
l tim
e
with
o
u
t i
n
cr
ea
s
in
g
h
ar
d
war
e
r
e
q
u
ir
em
e
n
ts
o
r
co
m
p
r
o
m
is
in
g
s
y
s
tem
r
esp
o
n
s
e
s
p
ee
d
.
Fig
u
r
e
2
.
Fu
zz
y
in
f
er
e
n
ce
s
y
s
tem
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
F
u
z
z
y
lo
g
ic
-
b
a
s
ed
a
d
a
p
tive
P
LL
s
w
itch
in
g
s
tr
a
teg
y
fo
r
…
(
R
.
S
r
ila
ksh
mi
)
2357
(
a)
(
b
)
Fig
u
r
e
3
.
Me
m
b
er
s
h
ip
f
u
n
ctio
n
s
p
lo
t: (
a)
in
p
u
t v
a
r
iab
le
“Ph
aseA”
an
d
(
b
)
o
u
tp
u
t v
ar
iab
le
“DPL
L
_
Mo
d
e”
2
.
3
.
O
v
er
v
iew
o
f
ph
a
s
e
-
lo
cked
lo
o
p
(
P
L
L
)
s
t
ruct
ures
T
h
is
wo
r
k
em
p
lo
y
s
a
d
u
al
-
PL
L
s
y
n
ch
r
o
n
izatio
n
ap
p
r
o
ac
h
c
o
n
s
is
tin
g
o
f
a
co
n
v
en
tio
n
al
s
y
n
ch
r
o
n
o
u
s
r
ef
er
en
ce
f
r
am
e
p
h
ase
-
lo
ck
e
d
l
o
o
p
(
C
T
PLL
)
an
d
a
d
ig
ital
p
h
ase
-
lo
ck
ed
lo
o
p
(
DPLL
)
,
wh
o
s
e
o
p
er
atio
n
s
ar
e
ad
ap
tiv
ely
co
n
t
r
o
lled
b
ased
o
n
r
ea
l
-
tim
e
g
r
id
co
n
d
itio
n
s
.
T
h
e
co
m
p
lete
d
esig
n
,
m
at
h
e
m
atica
l
f
o
r
m
u
latio
n
,
an
d
im
p
lem
e
n
tatio
n
d
etails
o
f
b
o
th
C
T
PLL
an
d
DPLL
h
av
e
b
ee
n
e
x
ten
s
iv
ely
d
is
cu
s
s
ed
an
d
v
alid
ate
d
in
o
u
r
ea
r
lier
wo
r
k
[
2
5
]
.
T
h
er
e
f
o
r
e,
o
n
ly
a
co
n
cise
o
v
er
v
iew
is
p
r
esen
ted
h
er
e
to
co
n
te
x
tu
ali
ze
th
eir
r
o
le
in
th
e
p
r
o
p
o
s
ed
h
y
b
r
id
co
n
tr
o
l
s
tr
ateg
y
.
T
h
e
C
T
PLL
,
g
r
o
u
n
d
ed
i
n
th
e
s
y
n
ch
r
o
n
o
u
s
r
ef
er
en
ce
f
r
am
e
th
eo
r
y
,
u
s
es
Par
k
tr
an
s
f
o
r
m
atio
n
f
o
r
p
h
ase
d
etec
tio
n
an
d
o
p
er
ates
r
eliab
ly
u
n
d
er
b
alan
ce
d
,
s
tead
y
-
s
tate
g
r
id
co
n
d
itio
n
s
.
I
ts
ad
v
an
t
ag
es
in
clu
d
e
lo
w
co
m
p
u
tatio
n
al
co
m
p
le
x
ity
an
d
f
a
s
t
s
tead
y
-
s
tate
r
e
s
p
o
n
s
e,
m
ak
in
g
it
s
u
itab
le
f
o
r
d
ep
lo
y
m
e
n
t d
u
r
in
g
n
o
r
m
al
g
r
i
d
o
p
er
atio
n
to
c
o
n
s
er
v
e
r
eso
u
r
ce
s
an
d
m
ain
tain
s
y
s
tem
s
tab
ilit
y
.
T
h
e
DPLL
,
in
co
n
tr
ast,
is
d
ev
elo
p
ed
u
s
in
g
a
d
is
cr
ete
-
tim
e
b
ac
k
war
d
E
u
ler
a
p
p
r
o
x
im
atio
n
tech
n
iq
u
e
to
en
h
an
ce
s
y
n
ch
r
o
n
izatio
n
ac
cu
r
ac
y
u
n
d
er
d
is
to
r
ted
an
d
f
au
lted
g
r
id
s
ce
n
ar
io
s
.
As
d
em
o
n
s
tr
ated
in
[
2
5
]
,
th
is
s
tr
u
ctu
r
e
p
r
o
v
id
es
s
u
p
er
io
r
d
y
n
am
ic
p
er
f
o
r
m
an
ce
,
r
ed
u
ce
s
h
ar
m
o
n
ic
d
is
to
r
tio
n
s
ig
n
i
f
ican
tly
,
an
d
im
p
r
o
v
e
s
s
y
s
tem
s
ta
b
ilit
y
with
o
u
t
in
cr
ea
s
in
g
co
n
tr
o
l
c
o
m
p
lex
ity
.
T
h
e
DPLL
ac
h
iev
ed
n
o
ta
b
le
r
ed
u
ctio
n
s
in
T
HD
an
d
in
ter
-
h
ar
m
o
n
ic
e
f
f
ec
ts
,
alo
n
g
with
a
n
ea
r
-
u
n
ity
p
o
wer
f
ac
to
r
,
v
alid
atin
g
its
r
o
b
u
s
tn
ess
an
d
co
m
p
u
tatio
n
al
ef
f
icien
cy
.
I
n
th
e
c
u
r
r
e
n
t
s
y
s
tem
,
th
ese
two
PLL
s
ar
e
n
o
t
o
p
er
ate
d
co
n
cu
r
r
e
n
tly
.
I
n
s
tead
,
th
eir
e
n
g
ag
em
en
t
is
d
eter
m
in
ed
b
y
a
p
h
ase
-
wis
e
m
o
n
ito
r
in
g
lo
g
ic
an
d
f
u
zz
y
in
f
er
en
ce
s
y
s
tem
th
at
ass
es
s
es
t
h
e
v
o
ltag
e
co
n
d
itio
n
o
f
ea
ch
p
h
ase.
C
T
PLL
is
en
g
ag
ed
u
n
d
e
r
n
o
m
i
n
al
g
r
id
co
n
d
itio
n
s
,
wh
ile
th
e
DPLL
is
s
elec
tiv
ely
ac
tiv
ated
wh
en
f
a
u
lt
s
ig
n
atu
r
es
a
r
e
d
et
ec
ted
.
T
h
is
a
d
ap
tiv
e
c
o
n
f
i
g
u
r
atio
n
en
s
u
r
es
p
r
ec
is
e
s
y
n
c
h
r
o
n
izatio
n
,
e
n
h
an
ce
d
h
ar
m
o
n
ic
r
esil
ien
ce
,
a
n
d
o
p
ti
m
al
co
n
tr
o
l
p
e
r
f
o
r
m
an
ce
ac
r
o
s
s
v
ar
y
in
g
g
r
id
d
is
tu
r
b
a
n
ce
s
,
with
o
u
t
alter
in
g
th
e
co
r
e
o
p
e
r
atio
n
o
f
eith
er
PLL
.
3.
SYST
E
M
DE
SCRI
P
T
I
O
N
T
h
e
p
r
o
p
o
s
ed
co
n
tr
o
l
ar
ch
itectu
r
e
b
u
ild
s
u
p
o
n
th
e
v
alid
ated
1
0
0
k
W
g
r
id
-
tied
s
o
lar
PV
s
y
s
tem
p
r
esen
ted
in
[
2
5
]
,
wh
ich
in
c
lu
d
es
a
s
in
g
le
-
d
io
d
e
m
o
d
el
-
b
ased
PV
ar
r
ay
,
a
b
o
o
s
t
co
n
v
er
ter
f
o
r
DC
-
lin
k
r
eg
u
latio
n
,
a
v
o
ltag
e
-
s
o
u
r
ce
in
v
er
ter
(
VSI
)
with
an
L
C
f
ilter
,
an
d
d
u
al
s
y
n
ch
r
o
n
izatio
n
s
ch
em
es u
s
in
g
C
T
PLL
an
d
DPLL
.
T
h
at
f
o
u
n
d
atio
n
a
l
s
y
s
tem
o
p
er
atin
g
u
n
d
er
a
v
o
ltag
e
-
co
n
tr
o
lled
in
v
e
r
ter
s
tr
a
teg
y
d
em
o
n
s
tr
ated
r
eliab
le
p
h
ase
tr
ac
k
in
g
an
d
p
o
wer
q
u
ality
u
n
d
er
v
ar
y
in
g
ir
r
a
d
ian
ce
,
lo
ad
,
an
d
f
au
lt c
o
n
d
iti
o
n
s
.
I
n
th
is
ex
ten
d
ed
wo
r
k
,
a
DVR
with
a
1
5
k
VA
p
o
wer
r
atin
g
i
s
in
teg
r
ated
in
s
er
ies
b
etwe
en
th
e
u
tili
ty
g
r
id
a
n
d
th
e
p
o
in
t
o
f
co
m
m
o
n
co
u
p
lin
g
(
PC
C
)
to
ad
d
r
ess
v
o
ltag
e
d
is
tu
r
b
a
n
ce
s
.
Ad
d
iti
o
n
ally
,
a
n
a
d
ap
tiv
e
s
y
n
ch
r
o
n
izatio
n
lay
e
r
is
i
n
tr
o
d
u
ce
d
to
e
n
ab
le
r
ea
l
-
tim
e
P
L
L
s
witch
in
g
t
h
r
o
u
g
h
a
f
u
zz
y
in
f
e
r
en
ce
s
y
s
tem
(
FIS)
,
as
s
h
o
wn
in
Fig
u
r
e
4
,
s
ig
n
if
ican
tly
en
h
an
cin
g
r
esp
o
n
s
e
f
lex
ib
ilit
y
with
o
u
t
in
cr
ea
s
in
g
s
y
s
tem
co
m
p
lex
ity
.
A
p
h
ase
-
wis
e
m
o
n
ito
r
in
g
u
n
it
a
n
aly
s
es
R
MS
g
r
id
v
o
ltag
e
o
v
e
r
tim
e,
d
is
ca
r
d
i
n
g
in
itial
t
r
an
s
ien
ts
an
d
class
if
y
in
g
ea
ch
p
h
ase
as
h
ea
lth
y
(
0
)
,
p
r
e
-
f
au
lt
(
0
.
5
)
,
o
r
f
au
lted
(
1
)
.
T
h
e
“p
r
e
-
f
au
lt”
s
tate
(
0
.
5
)
e
n
ab
les
a
s
m
o
o
th
r
am
p
e
d
tr
an
s
itio
n
,
wh
er
e
th
e
o
u
tg
o
i
n
g
PLL
g
r
ad
u
ally
d
is
en
g
ag
es
wh
ile
th
e
in
co
m
i
n
g
PLL
g
r
a
d
u
ally
tak
es
o
v
er
.
T
h
is
av
o
id
s
ab
r
u
p
t
co
n
tr
o
l
m
o
d
e
ch
a
n
g
es
an
d
m
in
im
izes tr
an
s
ien
t d
is
tu
r
b
an
c
es d
u
r
in
g
s
witch
in
g
.
T
h
ese
s
ev
er
ity
in
d
ices
ar
e
f
ed
in
to
a
Ma
m
d
an
i
-
ty
p
e
FIS,
wh
ich
g
o
v
e
r
n
s
th
e
PLL
s
elec
tio
n
lo
g
ic
—
ac
tiv
atin
g
C
T
PLL
d
u
r
in
g
s
tab
le
co
n
d
itio
n
s
,
DPLL
wh
en
d
is
tu
r
b
an
ce
s
ar
e
d
etec
ted
,
an
d
p
a
r
tial
o
v
er
lap
in
p
r
e
-
f
au
lt c
o
n
d
itio
n
s
to
en
s
u
r
e
a
s
ea
m
less
s
wi
tch
o
v
er
.
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
:
2353
-
2
3
6
8
2358
T
h
e
s
elec
ted
PLL
g
o
v
er
n
s
th
e
g
en
er
atio
n
o
f
Vab
c
r
ef
er
en
ce
s
ig
n
als
u
s
ed
f
o
r
PW
M
-
b
ased
VSI
co
n
tr
o
l.
T
h
e
DVR
o
p
er
ates
in
in
jectio
n
m
o
d
e,
s
u
p
p
ly
in
g
co
r
r
ec
tiv
e
v
o
ltag
es
to
m
ain
tain
s
tab
le
lo
ad
an
d
PC
C
v
o
ltag
e
d
u
r
in
g
g
r
id
f
au
lts
,
wh
ile
r
em
ain
in
g
in
ac
tiv
e
d
u
r
in
g
h
ea
lth
y
g
r
i
d
o
p
e
r
atio
n
.
T
h
is
en
tire
s
etu
p
is
m
o
d
eled
a
n
d
s
im
u
lated
u
s
in
g
MA
T
L
AB
/
S
im
u
lin
k
as sh
o
wn
in
Fig
u
r
e
5
(
s
ee
Ap
p
en
d
ix
)
.
Sy
s
tem
p
er
f
o
r
m
an
ce
is
test
ed
u
n
d
er
m
u
ltip
le
g
r
id
f
au
lt
s
ce
n
ar
io
s
,
in
clu
d
in
g
b
ala
n
ce
d
an
d
u
n
b
alan
ce
d
v
o
ltag
e
s
ag
s
an
d
s
well
s
in
tr
o
d
u
ce
d
at
s
p
ec
if
ic
tim
e
in
s
tan
ce
s
.
T
h
e
p
r
o
p
o
s
ed
FIS
-
d
r
iv
en
PLL
ad
ap
tatio
n
is
ev
alu
ated
b
ased
o
n
its
ab
ilit
y
to
r
esto
r
e
th
e
PC
C
v
o
ltag
e,
r
ed
u
ce
to
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
(
T
HD)
,
s
u
p
p
r
es
s
in
ter
-
h
ar
m
o
n
ic
co
m
p
o
n
en
ts
,
an
d
m
ain
tain
a
u
n
ity
p
o
wer
f
ac
to
r
at
th
e
lo
a
d
s
id
e.
F
i
g
u
r
e
4
.
C
o
m
p
l
e
t
e
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y
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t
e
m
a
r
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i
t
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u
r
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o
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i
d
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t
i
e
d
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V
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y
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t
e
m
w
i
t
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D
V
R
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n
d
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I
S
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b
a
s
e
d
a
d
a
p
t
i
v
e
P
L
L
s
w
i
t
c
h
i
n
g
4.
SI
M
UL
A
T
I
O
N
R
E
SU
L
T
S
AND
DIS
CU
SS
I
O
N:
VO
L
T
AG
E
R
E
G
UL
A
T
I
O
N
UN
DE
R
G
RID
F
AULT
S
T
h
i
s
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ec
t
i
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r
e
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e
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t
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h
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im
u
l
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t
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l
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u
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o
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s
,
s
y
m
m
e
t
r
i
c
a
l
s
w
e
ll
a
n
d
a
s
y
m
m
e
t
r
ic
a
l
s
a
g
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h
e
s
e
t
w
o
c
a
s
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a
r
e
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el
e
c
te
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t
t
h
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o
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t
b
al
a
n
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e
d
a
n
d
m
o
s
t
c
r
i
t
i
ca
l
s
c
e
n
a
r
i
o
s
,
r
es
p
e
c
ti
v
e
l
y
.
Si
m
u
l
a
ti
o
n
s
a
r
e
c
a
r
r
i
e
d
o
u
t
ac
r
o
s
s
t
h
r
e
e
p
r
o
g
r
e
s
s
i
v
e
c
o
n
f
i
g
u
r
a
t
i
o
n
s
:
i
)
C
as
e
1
:
D
P
L
L
-
b
as
e
d
s
y
n
c
h
r
o
n
i
z
a
t
i
o
n
(
N
o
D
VR
)
,
i
i
)
C
as
e
2
:
D
P
L
L
w
i
t
h
DV
R
co
m
p
e
n
s
a
ti
o
n
,
a
n
d
i
i
i
)
C
a
s
e
3
:
D
P
L
L
+
DV
R
wi
t
h
F
I
S
-
b
a
s
e
d
a
d
a
p
t
i
v
e
PL
L
s
w
it
c
h
i
n
g
.
4
.
1
.
Ca
s
e
1
:
DP
L
L
-
ba
s
ed
s
y
nchro
niza
t
io
n wit
ho
ut
DVR
Fig
u
r
e
6
illu
s
tr
ates
th
e
s
y
s
tem
p
er
f
o
r
m
an
ce
wh
e
n
o
n
l
y
th
e
d
ig
ital
p
h
ase
-
lo
ck
ed
lo
o
p
(
DPL
L
)
is
u
s
ed
f
o
r
g
r
id
s
y
n
ch
r
o
n
izatio
n
,
with
o
u
t a
n
y
DVR
-
b
ased
v
o
ltag
e
c
o
m
p
en
s
atio
n
.
−
Fig
u
r
e
6
(
a
)
p
r
esen
ts
th
e
g
r
id
a
n
d
PC
C
v
o
ltag
e
wav
e
f
o
r
m
s
u
n
d
er
two
g
r
i
d
f
a
u
lt
co
n
d
itio
n
s
:
a
s
y
m
m
etr
ical
s
well
(
2
0
%
in
cr
ea
s
e
in
all
th
r
ee
p
h
ases
)
an
d
an
asy
m
m
etr
i
ca
l
s
ag
(
2
0
%
d
r
o
p
in
Ph
ase
A
o
n
ly
)
.
I
n
b
o
th
ca
s
es,
th
e
d
is
tu
r
b
an
ce
s
at
th
e
g
r
id
lev
el
ar
e
d
ir
ec
tly
r
ef
lecte
d
at
th
e
P
C
C
,
lead
in
g
to
elev
ated
v
o
ltag
es
d
u
r
in
g
s
well
an
d
im
b
alan
ce
d
v
o
ltag
es d
u
r
in
g
s
ag
.
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
F
u
z
z
y
lo
g
ic
-
b
a
s
ed
a
d
a
p
tive
P
LL
s
w
itch
in
g
s
tr
a
teg
y
fo
r
…
(
R
.
S
r
ila
ksh
mi
)
2359
−
Fig
u
r
e
6
(
b
)
s
h
o
ws
th
e
v
o
ltag
e
an
d
cu
r
r
en
t
r
esp
o
n
s
es
o
f
a
n
o
n
lin
ea
r
lo
ad
u
n
d
er
th
e
s
am
e
f
au
lt
co
n
d
itio
n
s
.
T
h
e
v
o
ltag
e
s
wells
ca
u
s
e
o
v
e
r
v
o
ltag
e
s
tr
ess
at
th
e
lo
ad
ter
m
in
als,
wh
ile
th
e
asy
m
m
etr
ic
al
s
ag
lead
s
to
d
is
to
r
ted
v
o
ltag
e
wa
v
ef
o
r
m
s
an
d
im
b
alan
ce
in
cu
r
r
en
t m
a
g
n
i
tu
d
es a
cr
o
s
s
p
h
ases
.
−
Fig
u
r
e
6
(
c
)
d
is
p
lay
s
t
h
e
r
esp
o
n
s
e
o
f
a
r
e
g
u
lar
R
L
lo
ad
.
Similar
to
th
e
n
o
n
lin
ea
r
ca
s
e,
th
e
v
o
ltag
e
an
d
cu
r
r
en
t
wav
ef
o
r
m
s
d
ev
iate
f
r
o
m
th
eir
id
ea
l
s
in
u
s
o
id
al
s
h
ap
e.
Un
d
er
asy
m
m
etr
ical
s
ag
,
u
n
b
al
an
ce
d
cu
r
r
en
t
f
lo
w
is
o
b
s
er
v
ed
d
u
e
to
p
h
ase
v
o
ltag
e
d
is
p
ar
ity
,
a
n
d
u
n
d
er
s
y
m
m
etr
ical
s
well,
o
v
er
v
o
ltag
e
af
f
ec
ts
cu
r
r
e
n
t
am
p
litu
d
e
u
n
if
o
r
m
l
y
.
(
a)
(
b
)
(
c)
Fig
u
r
e
6
.
V
o
ltag
e
(
V)
a
n
d
c
u
r
r
en
t (
A)
wav
ef
o
r
m
s
u
n
d
er
s
y
m
m
etr
ical
s
well
an
d
asy
m
m
etr
ical
s
ag
co
n
d
itio
n
s
with
o
u
t D
VR
c
o
m
p
en
s
atio
n
: (
a)
g
r
id
a
n
d
PC
C
v
o
ltag
es
,
(
b
)
n
o
n
lin
ea
r
l
o
ad
v
o
ltag
es a
n
d
c
u
r
r
en
ts
,
an
d
(
c)
R
L
lo
ad
v
o
ltag
es a
n
d
c
u
r
r
en
ts
4
.
1
.
1
.
I
m
pa
ct
o
n
lo
a
d c
urre
nt
a
nd
po
wer
qu
a
lity
T
h
e
d
i
s
t
o
r
t
i
o
n
i
n
v
o
l
t
a
g
e
d
i
r
e
c
t
l
y
a
f
f
e
c
t
s
t
h
e
l
o
a
d
c
u
r
r
e
n
t
p
r
o
f
i
l
e
s
.
N
o
n
l
i
n
e
a
r
l
o
a
d
c
u
r
r
e
n
ts
s
h
o
w
a
n
i
n
c
r
e
a
s
e
i
n
h
a
r
m
o
n
i
c
c
o
n
t
e
n
t
an
d
u
n
b
a
l
a
n
c
e
d
b
e
h
a
v
i
o
r
u
n
d
e
r
a
s
y
m
m
e
t
r
i
ca
l
s
a
g
,
as
i
l
l
u
s
t
r
a
te
d
i
n
Fi
g
u
r
e
s
5
(
b
)
a
n
d
5
(
c
)
.
R
L
l
o
a
d
c
u
r
r
e
n
t
a
l
s
o
d
e
v
i
a
t
e
s
f
r
o
m
i
t
s
e
x
p
e
c
t
e
d
s
i
n
u
s
o
i
d
a
l
p
r
o
f
i
l
e
d
u
e
t
o
t
h
e
v
o
l
t
a
g
e
a
s
y
m
m
e
t
r
y
.
T
h
i
s
n
o
t
o
n
l
y
r
e
d
u
c
e
s
p
o
w
e
r
t
r
a
n
s
f
e
r
e
f
f
i
c
i
e
n
c
y
b
u
t
a
ls
o
c
r
e
a
te
s
s
t
r
es
s
in
p
o
w
e
r
e
l
e
c
t
r
o
n
i
c
d
e
v
i
ce
s
.
T
h
e
s
e
r
e
s
u
lt
s
c
o
n
f
i
r
m
t
h
at
w
h
i
l
e
DP
L
L
m
a
i
n
t
ai
n
s
s
y
n
c
h
r
o
n
iz
a
t
i
o
n
,
i
t
a
l
o
n
e
c
a
n
n
o
t
r
e
g
u
l
ate
v
o
l
t
a
g
e
a
n
o
m
a
l
i
e
s
a
t
t
h
e
PC
C
o
r
p
r
e
v
e
n
t
t
h
e
i
r
i
m
p
a
ct
o
n
d
o
w
n
s
t
r
ea
m
l
o
a
d
s
.
B
o
t
h
l
o
a
d
t
y
p
es
e
x
h
i
b
i
t
v
o
l
t
a
g
e
d
i
s
t
o
r
t
i
o
n
a
n
d
c
u
r
r
e
n
t
i
m
b
a
l
a
n
c
e
u
n
d
e
r
f
au
l
t
c
o
n
d
i
t
i
o
n
s
,
u
n
d
e
r
li
n
i
n
g
t
h
e
n
e
e
d
f
o
r
d
e
d
i
c
a
t
e
d
v
o
l
t
a
g
e
c
o
m
p
e
n
s
a
t
i
o
n
s
u
p
p
o
r
t
.
4
.
2
.
Ca
s
e
2
:
DVR
co
m
pens
a
t
io
n w
it
h
DP
L
L
-
ba
s
ed
s
y
nc
h
ro
niza
t
io
n
Fig
u
r
e
7
illu
s
tr
ates
th
e
s
y
s
te
m
r
esp
o
n
s
e
u
n
d
e
r
th
e
s
am
e
g
r
id
f
au
lt
co
n
d
itio
n
s
—
s
y
m
m
etr
ical
s
well
an
d
asy
m
m
etr
ical
s
ag
—
b
u
t
n
o
w
with
a
DVR
in
teg
r
ated
,
o
p
er
atin
g
alo
n
g
s
id
e
th
e
DPLL
-
b
ased
s
y
n
ch
r
o
n
izatio
n
s
tr
ateg
y
.
(
a
)
(
b
)
(
c
)
(
a
)
(
b
)
(
c
)
(
a
)
(
b
)
(
c
)
(
a
)
(
b
)
(
c
)
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
:
2353
-
2
3
6
8
2360
i)
Fig
u
r
e
7
(
a)
: G
r
i
d
,
PC
C
,
an
d
in
jecte
d
v
o
ltag
es
Un
d
er
s
y
m
m
etr
ical
s
well,
th
e
DVR
o
p
er
ates
in
v
o
ltag
e
in
je
ctio
n
m
o
d
e
,
in
tr
o
d
u
cin
g
a
co
m
p
en
s
atin
g
n
eg
ativ
e
v
o
ltag
e
(
V
_
in
jecte
d
)
p
r
ec
is
ely
d
u
r
in
g
th
e
o
v
er
v
o
ltag
e
in
ter
v
al.
As
a
r
esu
lt,
th
e
PC
C
v
o
ltag
e
is
r
eg
u
lated
clo
s
e
t
o
its
n
o
m
in
a
l
m
ag
n
itu
d
e,
ev
e
n
th
o
u
g
h
th
e
g
r
id
r
em
ain
s
in
an
o
v
er
v
o
l
tag
e
s
tate.
Du
r
in
g
asy
m
m
etr
ical
s
ag
,
th
e
DVR
s
elec
tiv
ely
in
jects
v
o
ltag
e
in
t
h
e
af
f
ec
ted
p
h
ase
(
Ph
ase
A)
,
ef
f
ec
tiv
ely
r
esto
r
in
g
PC
C
v
o
ltag
e
s
y
m
m
etr
y
.
T
h
e
wav
ef
o
r
m
s
h
o
ws
tim
ely
an
d
p
h
ase
-
s
p
e
cif
ic
V_
in
jecte
d
ac
tio
n
,
en
s
u
r
in
g
th
at
th
e
v
o
ltag
e
im
b
alan
ce
d
o
es n
o
t p
r
o
p
ag
ate
d
o
wn
s
tr
ea
m
.
ii)
Fig
u
r
e
7
(
b
)
: N
o
n
lin
ea
r
lo
ad
v
o
ltag
e
an
d
cu
r
r
en
t r
esp
o
n
s
e
Fo
r
b
o
th
s
well
an
d
s
ag
co
n
d
itio
n
s
,
th
e
n
o
n
lin
ea
r
lo
ad
v
o
ltag
es
m
ain
tain
th
eir
s
in
u
s
o
id
al
s
h
ap
e
an
d
n
o
m
in
al
R
MS
v
alu
e.
T
h
e
cu
r
r
en
t
wav
ef
o
r
m
s
ex
h
ib
it
m
in
i
m
al
d
is
to
r
tio
n
co
m
p
ar
ed
to
t
h
e
u
n
r
eg
u
lated
ca
s
e,
r
ef
lectin
g
r
e
d
u
ce
d
h
ar
m
o
n
ic
i
m
p
ac
t
d
u
e
to
s
tab
ilized
i
n
p
u
t
v
o
ltag
es
at
th
e
PC
C
.
T
h
is
d
em
o
n
s
tr
ates
th
at
th
e
DVR,
ev
en
with
ju
s
t D
PLL
co
n
tr
o
l,
s
ig
n
if
ican
tly
e
n
h
an
c
e
s
v
o
ltag
e
q
u
ality
f
o
r
n
o
n
lin
ea
r
lo
ad
s
.
iii)
Fig
u
r
e
7
(
c)
: RL
lo
a
d
v
o
ltag
e
a
n
d
cu
r
r
en
t r
esp
o
n
s
e
R
L
lo
ad
v
o
ltag
es
r
em
ain
u
n
if
o
r
m
a
n
d
u
n
d
is
to
r
ted
,
clo
s
ely
f
o
llo
win
g
t
h
e
r
e
g
u
lated
PC
C
wav
ef
o
r
m
.
L
o
ad
cu
r
r
e
n
ts
r
ec
o
v
er
th
eir
s
in
u
s
o
id
al
n
atu
r
e
an
d
p
h
ase
s
y
m
m
etr
y
,
in
d
ica
tin
g
th
at
th
e
p
o
wer
f
lo
w
b
alan
ce
is
r
esto
r
ed
.
C
o
m
p
a
r
ed
to
th
e
p
r
e
v
io
u
s
ca
s
e
(
Fig
u
r
e
6
)
,
th
is
h
ig
h
lig
h
ts
th
e
v
o
ltag
e
s
tab
ilizatio
n
ca
p
ab
ilit
y
o
f
t
h
e
DVR
ac
r
o
s
s
b
o
th
lin
ea
r
a
n
d
n
o
n
lin
ea
r
lo
ad
ty
p
es.
W
h
ile
th
e
DPLL
-
b
ased
s
y
n
ch
r
o
n
izatio
n
co
u
p
led
with
DVR
co
m
p
e
n
s
atio
n
im
p
r
o
v
es
PC
C
v
o
ltag
e
r
eg
u
latio
n
an
d
r
esto
r
es
wav
ef
o
r
m
s
y
m
m
etr
y
u
n
d
e
r
b
o
th
s
y
m
m
etr
ical
s
well
an
d
asy
m
m
etr
ical
s
ag
co
n
d
itio
n
s
,
ce
r
tain
lim
itatio
n
s
p
er
s
is
t.
No
tab
ly
,
th
e
DVR
co
n
tin
u
es
to
in
ject
co
m
p
en
s
atin
g
v
o
lta
g
e
—
u
p
to
5
0
V
—
ev
en
d
u
r
in
g
n
o
r
m
al
g
r
id
c
o
n
d
itio
n
s
,
wh
ich
is
u
n
d
esira
b
le.
T
h
is
u
n
n
ec
ess
ar
y
in
jectio
n
ca
n
d
is
r
u
p
t
p
o
wer
f
lo
w,
in
d
u
ce
lo
s
s
es,
an
d
ac
ce
ler
ate
wea
r
o
f
DVR
co
m
p
o
n
en
ts
.
Hen
ce
,
a
m
o
r
e
in
tellig
en
t
co
n
tr
o
l
m
ec
h
an
is
m
is
n
ee
d
ed
—
o
n
e
th
at
d
is
cr
im
in
ates
b
etwe
en
f
au
lt
an
d
h
ea
lth
y
s
tates
in
r
ea
l
tim
e.
T
h
is
s
ets
t
h
e
s
tag
e
f
o
r
t
h
e
FIS
-
b
ased
ad
ap
tiv
e
s
witch
in
g
s
tr
ateg
y
,
d
is
cu
s
s
ed
n
ex
t,
w
h
ich
en
h
an
ce
s
s
elec
tiv
ity
an
d
o
p
ti
m
izes D
VR
o
p
er
atio
n
b
ased
o
n
ac
tu
al
g
r
id
co
n
d
itio
n
s
.
(
a)
(
b
)
(
c)
Fig
u
r
e
7
.
V
o
ltag
e
(
V)
a
n
d
c
u
r
r
en
t (
A)
wav
ef
o
r
m
s
u
n
d
er
s
y
m
m
etr
ical
s
well
an
d
asy
m
m
etr
ical
s
ag
co
n
d
itio
n
s
with
DVR C
o
m
p
en
s
atio
n
: (
a)
g
r
id
an
d
PC
C
v
o
ltag
es
,
(
b
)
n
o
n
lin
ea
r
lo
ad
v
o
ltag
es a
n
d
cu
r
r
en
ts
,
an
d
(
c)
R
L
lo
ad
v
o
ltag
es a
n
d
c
u
r
r
en
ts
(a)
(b)
(c
)
(a)
(b)
(c
)
(a)
(b)
(c
)
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
F
u
z
z
y
lo
g
ic
-
b
a
s
ed
a
d
a
p
tive
P
LL
s
w
itch
in
g
s
tr
a
teg
y
fo
r
…
(
R
.
S
r
ila
ksh
mi
)
2361
4
.
3
.
Ca
s
e
3
:
P
er
f
o
rma
nce
wit
h F
I
S
-
ba
s
ed
a
da
ptiv
e
P
L
L
a
nd
D
VR
Fig
u
r
e
8
illu
s
tr
ates
th
e
v
o
ltag
e
an
d
cu
r
r
en
t
r
esp
o
n
s
e
o
f
th
e
s
y
s
tem
u
n
d
er
s
y
m
m
etr
ical
s
well
an
d
asy
m
m
etr
ical
s
ag
s
ce
n
ar
io
s
w
h
en
th
e
p
r
o
p
o
s
ed
f
u
z
zy
lo
g
ic
-
b
ased
ad
ap
tiv
e
PLL
m
ec
h
an
is
m
is
in
teg
r
ated
with
DVR
co
n
tr
o
l.
C
o
m
p
ar
ed
to
th
e
DVR
-
o
n
ly
ca
s
e,
th
is
co
n
f
ig
u
r
atio
n
d
em
o
n
s
tr
ates
m
ar
k
e
d
im
p
r
o
v
em
en
t
i
n
v
o
ltag
e
r
eg
u
latio
n
p
r
ec
is
io
n
,
cu
r
r
en
t
wav
ef
o
r
m
b
alan
ce
,
an
d
s
y
s
tem
r
esp
o
n
s
iv
en
ess
.
No
tab
ly
,
th
e
DVR
in
jectio
n
is
n
o
w
lim
ited
to
~5
–
6
V
d
u
r
in
g
s
tead
y
-
s
tate,
av
o
id
in
g
u
n
n
ec
ess
ar
y
ac
tio
n
d
u
r
in
g
h
ea
lth
y
g
r
id
co
n
d
itio
n
s
.
T
h
is
d
ir
ec
tly
ad
d
r
ess
es
th
e
o
v
er
co
m
p
en
s
atio
n
o
b
s
er
v
ed
ea
r
lier
,
p
r
eser
v
in
g
g
r
id
s
tab
ilit
y
an
d
r
ed
u
cin
g
DVR
s
witch
in
g
ef
f
o
r
t
an
d
c
o
m
p
o
n
en
t
s
tr
ess
.
All
th
r
ee
p
h
ases
at
th
e
PC
C
ex
h
ib
it
b
etter
s
in
u
s
o
id
al
s
y
m
m
etr
y
,
a
n
d
b
o
th
n
o
n
lin
ea
r
an
d
R
L
lo
a
d
c
u
r
r
en
ts
s
h
o
w
h
ig
h
wa
v
ef
o
r
m
q
u
ality
with
m
in
im
al
d
is
to
r
tio
n
,
ev
en
u
n
d
er
u
n
b
alan
ce
d
co
n
d
i
tio
n
s
.
T
h
e
FIS
ef
f
ec
tiv
ely
en
ab
les
f
ast
PLL
s
witch
in
g
,
en
s
u
r
in
g
th
at
DPLL
is
in
v
o
k
e
d
o
n
l
y
d
u
r
in
g
ac
tu
al
f
au
lts
,
allo
win
g
C
T
PLL
to
h
an
d
le
n
o
m
in
al
c
o
n
d
itio
n
s
ef
f
icien
tly
.
Fig
u
r
e
8.
V
o
ltag
e
(
V)
a
n
d
c
u
r
r
en
t (
A)
wav
ef
o
r
m
s
u
n
d
er
s
y
m
m
etr
ical
s
well
an
d
asy
m
m
etr
ical
s
ag
co
n
d
itio
n
s
,
FIS
-
b
ased
ad
ap
tiv
e
PLL
an
d
DVR:
g
r
id
an
d
PC
C
v
o
ltag
es
Sm
aller
d
ev
iatio
n
s
in
d
icate
h
ig
h
er
r
esto
r
atio
n
ac
c
u
r
ac
y
an
d
b
etter
v
o
ltag
e
p
r
o
f
ile
r
eg
u
l
atio
n
.
Fo
r
in
s
tan
ce
,
p
ar
am
eter
s
s
u
ch
as
VPC
C
an
d
VR
L
lo
ad
ap
p
r
o
ac
h
in
g
3
3
8
.
7
V
clo
s
ely
r
ef
lec
t
id
ea
l
s
tead
y
-
s
tate
o
p
er
atio
n
.
Similar
ly
,
in
v
e
r
ter
an
d
PC
C
cu
r
r
en
t
v
al
u
es
co
n
v
er
g
in
g
to
war
d
s
th
eir
n
o
m
i
n
al
r
ef
er
en
ce
s
I
PC
C
=2
0
4
.
6
A,
I
R
L
lo
ad
=
1
0
0
.
3
A
c
o
n
f
ir
m
im
p
r
o
v
ed
cu
r
r
en
t
s
y
m
m
etr
y
a
n
d
r
ed
u
ce
d
d
is
to
r
tio
n
.
T
h
e
r
ec
o
v
er
y
tim
e
r
o
w
p
r
o
v
id
es
th
e
m
ea
s
u
r
ed
d
e
lay
f
r
o
m
f
au
lt
i
n
ce
p
tio
n
to
f
u
ll
v
o
ltag
e
r
esto
r
atio
n
;
lo
wer
v
al
u
es
r
ep
r
esen
t
f
aster
co
m
p
en
s
atio
n
r
esp
o
n
s
e.
T
h
is
co
m
b
in
ed
co
m
p
ar
is
o
n
o
f
m
ag
n
itu
d
e
ac
cu
r
ac
y
an
d
r
ec
o
v
er
y
s
p
ee
d
o
f
f
er
s
a
q
u
an
titativ
e
b
asis
f
o
r
ass
es
s
in
g
an
d
r
an
k
i
n
g
th
e
th
r
ee
co
n
tr
o
l
s
tr
ateg
ies.
A
s
u
m
m
ar
y
o
f
v
o
ltag
e
r
esto
r
atio
n
ac
cu
r
ac
y
an
d
r
ec
o
v
er
y
tim
e
f
o
r
ea
ch
ca
s
e
is
p
r
esen
ted
in
T
ab
le
1
.
T
h
e
“
I
d
e
a
l
V
al
u
e
s
”
c
o
l
u
m
n
l
is
t
s
t
h
e
n
o
m
i
n
a
l
r
e
f
e
r
e
n
c
e
v
a
l
u
es
f
o
r
e
a
c
h
p
a
r
a
m
e
t
e
r
u
n
d
e
r
p
e
r
f
e
c
t
o
p
e
r
a
t
i
n
g
c
o
n
d
i
t
i
o
n
s
,
s
e
r
v
i
n
g
as
t
h
e
b
e
n
c
h
m
a
r
k
f
o
r
c
o
m
p
a
r
i
s
o
n
.
A
ll
m
e
as
u
r
e
d
v
o
l
ta
g
e
s
a
n
d
c
u
r
r
e
n
ts
f
r
o
m
t
h
e
t
h
r
e
e
c
o
n
f
i
g
u
r
a
t
i
o
n
s
,
D
P
L
L
-
o
n
l
y
,
D
VR
+
D
P
L
L
,
a
n
d
DVR
+
D
PL
L
+
F
I
S
a
r
e
e
v
a
l
u
at
e
d
a
g
a
i
n
s
t
t
h
e
s
e
n
o
m
i
n
a
l
v
a
l
u
es
.
4
.
4
.
T
o
t
a
l
ha
rmo
ni
c
dis
t
o
rt
io
n
(
T
H
D)
a
na
ly
s
is
T
o
ass
ess
th
e
im
p
ac
t
o
f
DVR
an
d
ad
ap
ti
v
e
PLL
s
witch
in
g
o
n
h
ar
m
o
n
ic
p
er
f
o
r
m
a
n
ce
,
a
d
e
tailed
to
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
(
T
HD)
an
aly
s
is
is
ca
r
r
ied
o
u
t a
cr
o
s
s
th
r
ee
co
n
f
ig
u
r
atio
n
s
:
i)
B
ase
s
y
s
tem
: D
PLL
o
n
ly
(
n
o
DVR,
n
o
FIS)
ii)
E
n
h
an
ce
d
s
y
s
tem
: D
PLL
+
DVR (
with
o
u
t FI
S)
iii)
Pro
p
o
s
ed
ad
a
p
tiv
e
s
y
s
tem
: D
VR
with
FIS
-
b
ased
C
T
PLL
/D
PLL
s
witch
in
g
T
h
e
T
HD
is
e
v
alu
ated
f
o
r
in
v
er
ter
cu
r
r
en
t,
n
o
n
lin
ea
r
l
o
ad
c
u
r
r
en
t,
an
d
PC
C
cu
r
r
en
t
u
n
d
er
s
y
m
m
etr
ical
s
well
an
d
asy
m
m
etr
ical
s
ag
co
n
d
iti
o
n
s
.
T
h
e
an
al
y
s
is
u
s
es
a
2
-
cy
cle
win
d
o
w
d
u
r
in
g
f
au
lt
in
ter
v
als,
co
m
p
lem
en
ted
b
y
1
0
-
cy
cle
win
d
o
ws b
ef
o
r
e
a
n
d
af
ter
t
h
e
d
is
tu
r
b
a
n
ce
to
o
b
s
er
v
e
r
ec
o
v
er
y
b
eh
av
i
o
r
.
Ob
s
er
v
atio
n
s
:
i)
C
ase
1
:
T
h
e
DPLL
-
o
n
ly
s
y
s
t
em
ex
h
ib
its
s
ig
n
if
ican
t
T
HD
in
n
o
n
lin
ea
r
lo
a
d
cu
r
r
en
t
an
d
PC
C
cu
r
r
en
t
,
esp
ec
ially
d
u
r
in
g
g
r
id
v
o
ltag
e
d
is
tu
r
b
an
ce
s
.
T
h
is
is
d
u
e
to
th
e
in
ab
ilit
y
to
c
o
r
r
ec
t
th
e
g
r
id
v
o
ltag
e
a
n
d
p
h
ase,
lead
in
g
t
o
d
is
to
r
tio
n
p
r
o
p
ag
atio
n
f
r
o
m
th
e
in
v
er
ter
s
id
e.
ii)
C
ase
2
:
I
n
tr
o
d
u
cin
g
a
DVR
with
DPLL
co
n
tr
o
l
r
ed
u
ce
s
T
HD
b
y
in
jectin
g
co
m
p
en
s
atin
g
v
o
ltag
e
d
u
r
i
n
g
d
is
tu
r
b
an
ce
p
er
io
d
s
.
Ho
wev
er
,
d
u
r
in
g
n
o
m
in
al
co
n
d
itio
n
s
,
r
esid
u
al
DVR
ac
tiv
ity
an
d
D
PLL
esti
m
atio
n
d
elay
s
ca
u
s
e
m
in
o
r
h
ar
m
o
n
ic
i
n
jectio
n
,
s
lig
h
tly
af
f
e
ctin
g
in
v
er
ter
-
s
id
e
cu
r
r
e
n
t q
u
ality
.
iii)
C
ase
3
:
T
h
e
DVR
+
FIS
ad
ap
tiv
e
s
y
s
tem
d
eliv
er
s
th
e
b
es
t
p
er
f
o
r
m
a
n
ce
ac
r
o
s
s
all
m
etr
ics.
T
h
e
FIS
s
elec
tiv
ely
ac
tiv
ates
DPLL
o
n
ly
d
u
r
in
g
d
is
tu
r
b
ed
in
ter
v
als
an
d
s
witch
es
b
ac
k
t
o
C
T
PLL
d
u
r
in
g
n
o
r
m
al
o
p
er
atio
n
.
T
h
is
s
tr
ateg
y
m
in
im
izes
u
n
n
ec
ess
ar
y
s
witch
in
g
an
d
h
ar
m
o
n
ic
d
is
to
r
tio
n
d
u
r
i
n
g
s
tead
y
-
s
tate,
wh
ile
s
till
en
s
u
r
in
g
r
o
b
u
s
t c
o
m
p
en
s
atio
n
d
u
r
in
g
f
au
lts
.
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
:
2353
-
2
3
6
8
2362
T
ab
le
1
.
C
o
m
p
ar
ativ
e
a
n
aly
s
is
o
f
v
o
ltag
e
(
V)
,
c
u
r
r
en
t
(
A)
,
a
n
d
r
ec
o
v
er
y
tim
e
(
m
s
ec
)
p
e
r
f
o
r
m
an
ce
u
n
d
er
g
r
id
f
au
lt c
o
n
d
itio
n
s
Param
et
e
rs
V
n
o
n
-
l
i
n
e
ar
In
o
n
-
l
i
n
e
ar
V
p
cc
Ip
cc
V
i
n
v
e
rt
e
r
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i
n
v
e
rt
e
r
V
g
r
i
d
I
g
r
i
d
V
i
n
j
e
ct
e
d
V
R
L
l
oa
d
I
RL
l
o
a
d
Rec
o
v
er
y
t
i
me
2
0
%
Sy
m
me
t
ri
c
Sw
e
l
l
D
P
L
L
4
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6
.
4
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4
4
0
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4
0
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6
4
0
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8
5
n
i
l
4
0
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2
NA
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+
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V
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3
2
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1
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3
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ms
e
c
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3
6
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3
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3
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e
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A
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y
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t
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Sag
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4
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6
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n
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l
4
0
6
1
2
0
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2
NA
D
P
L
L
+
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V
R
3
3
8
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7
1
8
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3
4
3
3
3
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e
c
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5
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9
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m
me
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0
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NA
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+
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3
3
6
.
3
1
8
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5
1
3
3
9
.
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4
4
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8
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.
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6
6
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1
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3
3
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.
4
9
9
.
0
7
0
.
0
5
ms
e
c
D
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L
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+
D
V
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+
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3
3
6
.
5
1
8
.
3
2
3
3
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.
9
2
0
1
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5
4
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y
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r
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c
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2
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i
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2
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+
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3
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9
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2
2
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+
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5
.
9
1
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1
3
3
5
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7
2
0
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3
4
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2
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4
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9
6
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0
5
3
3
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4
9
9
.
0
3
n
o
d
e
l
a
y
Id
ea
l
V
al
u
e
s
3
3
8
.
7
1
8
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6
5
3
3
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7
2
0
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.
6
4
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5
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9
2
n
i
l
3
3
8
.
8
1
0
0
.
3
-
4
.
4
.
1
.
H
a
r
m
o
n
ic
a
n
a
l
y
sis u
n
d
e
r
a
sy
m
m
e
tr
ic sw
e
ll
a
n
d
sa
g
fa
u
lts
T
ab
le
2
p
r
esen
ts
th
e
h
a
r
m
o
n
i
c
p
er
f
o
r
m
a
n
ce
o
f
t
h
e
s
y
s
tem
u
n
d
er
2
0
%
s
y
m
m
etr
ic
s
well
an
d
s
ag
co
n
d
itio
n
s
,
in
clu
d
in
g
DC
co
m
p
o
n
e
n
ts
,
f
u
n
d
am
e
n
tal
R
MS/p
ea
k
v
alu
es,
an
d
T
HD
f
o
r
in
v
er
ter
cu
r
r
en
t,
n
o
n
lin
ea
r
l
o
ad
cu
r
r
en
t,
an
d
P
C
C
cu
r
r
en
t.
T
h
e
r
esu
lts
co
m
p
ar
e
th
r
ee
co
n
tr
o
l
c
o
n
f
ig
u
r
atio
n
s
:
i)
B
ase
Sy
s
tem
:
DPLL
o
n
ly
(
n
o
DVR,
n
o
FIS)
;
ii)
E
n
h
an
ce
d
s
y
s
tem
:
DPLL
+
DVR
(
with
o
u
t
FIS)
;
an
d
iii)
Pro
p
o
s
ed
ad
a
p
tiv
e
s
y
s
t
em
: D
VR
w
ith
FIS
-
b
ased
C
T
PLL
/DPLL
s
witch
in
g
.
T
ab
le
2
.
T
h
e
p
er
f
o
r
m
a
n
ce
o
f
h
ar
m
o
n
ic
an
al
y
s
is
o
f
in
v
er
ter
,
PC
C
,
an
d
lo
ad
cu
r
r
en
ts
u
n
d
e
r
s
y
m
m
etr
ical
f
au
lts
(
s
well
an
d
s
ag
)
H
a
r
mo
n
i
c
a
n
a
l
y
s
i
s
d
u
r
i
n
g
sy
m
met
r
i
c
sw
e
l
l
a
n
d
sa
g
f
a
u
l
t
s
P
a
r
a
me
t
e
r
s
D
C
c
o
m
p
o
n
e
n
t
F
u
n
d
a
m
e
n
t
a
l
(
p
e
a
k
)
F
u
n
d
a
m
e
n
t
a
l
(
r
ms)
%T
H
D
F
a
u
l
t
c
u
r
r
e
n
t
c
o
m
p
o
n
e
n
t
C
a
se
C
a
se
C
a
se
C
a
se
C
a
se
C
a
se
C
a
se
C
a
se
C
a
se
C
a
se
C
a
se
C
a
se
1
2
3
1
2
3
1
2
3
1
2
3
2
0
%
S
y
mm
e
t
r
i
c
S
w
e
l
l
I
i
n
v
e
r
t
e
r
0
.
0
6
7
3
2
0
.
7
0
7
9
0
.
5
6
5
8
1
6
2
.
2
1
9
5
.
6
1
9
6
.
1
1
1
4
.
7
1
3
8
.
3
1
3
8
.
6
3
.
9
1
1
.
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2
1
.
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1
I
n
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n
l
i
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e
a
r
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o
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d
0
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0
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2
4
5
0
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0
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7
0
.
0
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2
6
2
4
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1
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S
y
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e
t
r
i
c
S
a
g
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i
n
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e
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t
e
r
3
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a
r
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a
d
0
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4
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p
c
c
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.
6
2
0
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7
2
2
0
.
5
8
1
1
2
4
7
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6
1
9
8
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3
1
9
7
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8
1
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5
.
1
1
4
0
.
2
1
3
9
.
9
3
.
8
2
.
9
7
2
.
5
T
h
e
p
r
o
p
o
s
ed
FIS
-
b
ased
SMC
DVR
(
C
ase
3
)
d
em
o
n
s
tr
ates
s
ig
n
if
ican
t
T
HD
r
ed
u
ctio
n
c
o
m
p
ar
ed
t
o
b
o
th
th
e
u
n
co
m
p
e
n
s
ated
s
y
s
tem
(
C
ase
1
)
an
d
th
e
co
n
v
en
tio
n
al
DVR
(
C
a
s
e
2
)
.
Un
d
er
2
0
%
s
y
m
m
etr
ic
s
well,
in
v
er
ter
cu
r
r
e
n
t
T
HD
d
ec
r
ea
s
ed
b
y
5
6
.
2
6
%
r
elativ
e
to
C
ase
1
an
d
b
y
6
.
0
4
%
o
v
er
C
ase
2
,
wh
ile
PC
C
cu
r
r
en
t
T
HD
im
p
r
o
v
ed
b
y
3
5
.
0
8
%
an
d
1
5
.
1
4
%,
r
esp
ec
tiv
ely
.
Similar
tr
en
d
s
wer
e
o
b
s
er
v
ed
f
o
r
2
0
%
s
y
m
m
etr
ic
s
ag
,
with
in
v
er
ter
cu
r
r
en
t
T
HD
r
e
d
u
ctio
n
s
o
f
4
3
.
3
8
%
an
d
3
.
9
3
%,
an
d
PC
C
cu
r
r
en
t
r
ed
u
ctio
n
s
o
f
3
5
.
5
7
%
an
d
1
5
.
8
2
%.
T
h
ese
r
esu
lts
co
n
f
ir
m
th
e
p
r
o
p
o
s
ed
c
o
n
tr
o
ller
’
s
ab
ilit
y
to
d
eliv
er
s
u
b
s
tan
tial
ad
d
itio
n
al
h
ar
m
o
n
ic
m
itig
atio
n
b
ey
o
n
d
t
h
at
o
f
a
s
tan
d
ar
d
DVR.
Fu
n
d
am
en
tal
R
MS
an
d
p
ea
k
cu
r
r
e
n
t
v
al
u
es
ar
e
m
ain
tain
ed
clo
s
e
to
n
o
m
in
al
in
all
F
I
S
-
ass
is
te
d
ca
s
es,
en
s
u
r
in
g
v
o
ltag
e
s
tab
ilit
y
wh
ile
m
in
im
izin
g
u
n
n
ec
es
s
ar
y
DVR
ac
tiv
ity
.
T
h
is
co
n
f
ir
m
s
th
at
ad
a
p
tiv
e
PLL
s
witch
in
g
im
p
r
o
v
es
h
a
r
m
o
n
ic
s
u
p
p
r
ess
io
n
a
n
d
v
o
ltag
e
r
eg
u
latio
n
s
im
u
ltan
eo
u
s
ly
.
Fig
u
r
e
9
illu
s
tr
ates
th
e
T
HD
r
ed
u
ctio
n
f
o
r
all
ca
s
es,
s
h
o
win
g
th
at
th
e
p
r
o
p
o
s
ed
FIS
-
b
ased
co
n
tr
o
l
o
u
tp
e
r
f
o
r
m
s
b
o
th
DPLL
-
o
n
ly
an
d
DVR
-
o
n
ly
s
y
s
tem
s
ac
r
o
s
s
all
m
ea
s
u
r
ed
p
o
in
ts
.
4
.
4
.
2
.
H
a
r
m
o
n
ic a
n
a
l
y
sis u
n
d
e
r
a
sy
m
m
e
tr
ic sw
e
ll
a
n
d
sa
g
fa
u
lts
T
ab
le
3
s
u
m
m
ar
izes
th
e
ab
s
o
l
u
te
T
HD
v
al
u
es
u
n
d
er
asy
m
m
etr
ic
s
well
an
d
s
ag
c
o
n
d
itio
n
s
f
o
r
ea
ch
p
h
ase.
Fo
r
a
2
0
%
asy
m
m
etr
ic
s
well
(
Ph
ase
A)
,
th
e
p
r
o
p
o
s
ed
FIS
-
b
ased
SMC
DV
R
(
C
a
s
e
3
)
r
ed
u
ce
d
in
v
e
r
ter
cu
r
r
en
t
T
HD
b
y
2
6
.
7
3
%
co
m
p
ar
ed
to
th
e
u
n
co
m
p
en
s
ated
s
y
s
tem
(
C
ase
1
)
an
d
b
y
1
3
.
4
2
%
o
v
er
th
e
co
n
v
en
tio
n
al
DVR (
C
ase
2
)
.
PC
C
cu
r
r
en
t T
HD
im
p
r
o
v
e
d
b
y
2
5
.
9
9
% a
n
d
1
1
.
3
7
%,
r
esp
ec
tiv
ely
.
I
n
th
e
2
0
%
asy
m
m
etr
i
c
s
ag
s
ce
n
ar
io
,
in
v
er
ter
cu
r
r
en
t
T
HD
r
ed
u
ctio
n
s
wer
e
9
.
4
9
%
an
d
1
4
.
7
7
%
co
m
p
ar
ed
to
C
ases
1
an
d
2
,
wh
ile
PC
C
cu
r
r
en
t
T
HD
d
ec
r
ea
s
ed
b
y
7
.
5
6
%
a
n
d
1
1
.
1
5
%,
r
esp
ec
tiv
ely
.
No
n
lin
ea
r
lo
ad
cu
r
r
en
t
T
HD
ch
an
g
es
wer
e
m
in
im
al
ac
r
o
s
s
ca
s
es,
in
d
icatin
g
th
at
th
e
p
r
im
ar
y
b
e
n
ef
it
o
f
th
e
p
r
o
p
o
s
ed
co
n
tr
o
ller
is
in
m
itig
atin
g
g
r
id
-
s
id
e
a
n
d
in
v
e
r
ter
h
ar
m
o
n
ics
u
n
d
er
u
n
b
alan
ce
d
f
au
lt
co
n
d
itio
n
s
.
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