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Power qua
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s
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n
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ted
IEE
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-
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b
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s,
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o
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ted
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t
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t
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u
s
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sy
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c
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ro
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iza
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d
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jec
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g
re
a
c
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o
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th
e
a
n
a
l
y
sis
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u
lt
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tr
o
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c
e
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n
y
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li
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n
d
v
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g
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ro
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il
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o
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th
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k
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st
b
u
s
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o
b
se
rv
e
d
with
a
n
d
wi
th
o
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t
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S
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re
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t
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l
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e
sig
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ATLAB
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C
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Dep
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Dar
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[
1
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o
f
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it.
T
h
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[
2
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f
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b
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T
h
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m
aj
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p
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q
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s
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[
3
]
–
[
5
]
in
an
y
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s
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s
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ar
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v
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ltag
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s
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m
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r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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E
n
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I
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N:
2252
-
8
7
9
2
P
o
w
er q
u
a
lity imp
r
o
ve
men
t a
n
d
a
n
a
lysi
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o
f in
terco
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b
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s
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ystem
w
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p
h
a
s
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r
…
(
P
r
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ti K
a
b
r
a
)
53
co
m
p
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s
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x
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alter
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c
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m
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(
FAC
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d
ev
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[
6
]
–
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1
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lik
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co
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p
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(
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A
STAT
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1
1
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is
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s
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1
2
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New
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[
1
3
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h
as
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s
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in
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s
)
an
d
two
s
y
n
ch
r
o
n
o
u
s
c
o
m
p
en
s
ato
r
s
wh
ich
in
ject
r
ea
ctiv
e
p
o
wer
.
E
ac
h
b
u
s
h
as
its
o
wn
lo
a
d
co
n
n
ec
ted
with
d
if
f
er
e
n
t p
o
wer
r
atin
g
.
T
h
e
co
n
v
en
tio
n
al
STAT
C
OM
co
n
tr
o
ller
is
later
u
p
d
ated
with
v
ir
tu
al
s
y
n
ch
r
o
n
o
u
s
m
ac
h
i
n
e
co
n
tr
o
l
in
clu
d
ed
with
v
ir
tu
al
in
e
r
tia
u
p
d
atin
g
th
e
co
n
v
en
tio
n
al
ST
AT
C
OM
to
v
ir
tu
al
s
y
n
ch
r
o
n
o
u
s
m
ac
h
in
e
–
s
tatic
s
y
n
ch
r
o
n
o
u
s
co
m
p
en
s
ato
r
(
V
SM
-
STAT
C
OM
)
.
T
h
e
ef
f
ec
t
o
f
VSM
-
STAT
C
OM
to
im
p
r
o
v
e
p
o
wer
q
u
ality
o
f
s
y
s
tem
with
r
esp
ec
t
to
co
n
v
e
n
tio
n
al
STAT
C
OM
is
in
tr
o
d
u
ce
d
h
er
e
.
T
h
e
lin
e
p
ar
am
eter
s
lik
e
lin
e
r
esis
tan
ce
an
d
lin
e
r
ea
ctan
ce
b
etwe
en
d
i
f
f
er
en
t
b
u
s
es
an
d
g
en
er
ato
r
r
a
tin
g
d
ata
f
o
r
th
e
co
n
s
id
er
e
d
I
E
E
E
-
14
b
u
s
s
y
s
tem
ar
e
s
h
o
wn
in
T
a
b
le
1
a
n
d
T
a
b
le
2
r
esp
ec
tiv
ely
.
Fig
u
r
e
1.
I
E
E
E
1
4
b
u
s
s
y
s
t
em
T
ab
le
1.
B
u
s
s
y
s
tem
p
ar
am
ete
r
s
Li
n
e
N
o
.
F
r
o
m B
u
s
To
B
u
s
Li
n
e
R
e
s
i
st
a
n
c
e
(
Ω
)
Li
n
e
R
e
a
c
t
a
n
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e
(
Ω
)
1
1
2
0
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0
1
9
4
8
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9
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1
5
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5
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1
7
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5
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12
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8
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10
11
0
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2
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5
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12
13
0
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13
14
0
.
1
8
0
7
3
0
.
3
4
2
4
2
T
ab
le
2.
Gen
e
r
ato
r
r
atin
g
d
ata
G
e
n
e
r
a
t
o
r
n
o
.
P
mi
n
(
M
W
)
P
max
(
M
W
)
1
10
1
6
0
2
20
80
3
20
50
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
11
,
No
.
1
,
Ma
r
ch
2
0
2
2
:
52
-
61
54
2.
P
H
ASO
R
M
E
ASUR
I
NG
UNIT
T
h
e
Ph
aso
r
m
ea
s
u
r
in
g
u
n
its
also
h
av
e
g
lo
b
al
p
o
s
itio
n
in
g
s
y
s
tem
(
GPS)
in
s
talled
al
o
n
g
with
p
ar
am
etr
ic
m
ea
s
u
r
in
g
,
d
ef
in
i
n
g
th
e
p
o
s
itio
n
o
f
th
e
m
ea
s
u
r
em
en
t.
T
h
e
p
h
aso
r
m
ea
s
u
r
e
m
en
t
u
n
it
s
(
PMU
s
)
p
lace
d
at
d
if
f
er
e
n
t
lo
ca
tio
n
s
g
en
er
ally
at
th
e
en
d
s
o
f
th
e
lin
e
o
r
at
d
if
f
er
en
t
b
u
s
lo
ca
tio
n
s
.
T
h
e
o
p
tim
al
p
lace
m
en
t
o
f
PMU
[
1
4
]
is
d
ec
id
e
d
b
y
d
if
f
er
e
n
t
alg
o
r
ith
m
s
lik
e
g
e
n
etic
alg
o
r
ith
m
,
p
a
r
ticle
s
war
m
o
p
tim
izatio
n
(
PS
O)
,
an
d
ar
tif
icial
b
ee
co
lo
n
y
(
AB
C
)
.
Ph
aso
r
m
ea
s
u
r
in
g
u
n
its
[
1
5
]
ar
e
th
e
d
ev
ices
wh
ich
m
ea
s
u
r
e
th
e
m
ag
n
itu
d
e,
f
r
eq
u
en
cy
an
d
p
h
ase
o
f
an
y
v
o
ltag
e
o
r
cu
r
r
en
t
o
f
a
g
r
id
s
y
s
tem
s
y
n
ch
r
o
n
ize
d
with
u
n
iv
er
s
al
tim
e
co
o
r
d
in
ate
(
U
T
C
)
.
T
h
e
m
ea
s
u
r
em
en
ts
[
1
6
]
tak
en
f
r
o
m
th
e
lo
ca
tio
n
ar
e
s
en
t
to
wid
e
ar
ea
m
ea
s
u
r
in
g
s
y
s
tem
(
W
AM
S),
wh
er
e
th
e
s
ig
n
als
a
r
e
co
m
p
ar
e
d
f
o
r
d
eter
m
in
atio
n
o
f
p
h
ase
s
h
if
t
in
th
e
an
g
le
an
d
also
v
o
ltag
e
d
r
o
p
s
.
W
ith
b
etter
m
ea
s
u
r
in
g
u
n
it’s
p
r
ec
is
e
m
e
asu
r
em
e
n
ts
[
1
7
]
a
r
e
tak
en
wh
i
ch
ar
e
h
elp
f
u
l
with
ex
ac
t
co
m
p
en
s
atio
n
v
alu
e
ca
l
cu
latio
n
s
f
o
r
im
p
r
o
v
in
g
th
e
p
o
wer
q
u
ality
.
PMUs
u
s
e
p
h
ase
lo
ck
ed
lo
o
p
(
PLL
)
,
an
alo
g
to
d
ig
ital
c
o
n
v
er
te
r
s
,
s
ig
n
al
f
ilter
s
,
an
d
GPS
m
o
d
u
les
f
o
r
s
y
n
c
h
r
o
n
izatio
n
m
ea
s
u
r
em
en
t
to
th
e
g
r
id
.
T
h
e
PLL
g
en
er
ates
t
h
e
an
g
le
at
wh
ich
th
e
v
o
ltag
e
o
r
c
u
r
r
e
n
t
is
g
en
e
r
ated
o
r
tr
an
s
m
itted
.
A
g
e
n
er
al
in
te
r
n
al
s
tr
u
ctu
r
e
o
f
PMU
ca
n
b
e
s
h
o
w
n
in
F
ig
u
r
e
2
.
Fig
u
r
e
2
.
Ar
c
h
itectu
r
e
o
f
PMU
T
h
e
PMUs
a
r
e
co
n
n
ec
ted
in
th
e
p
r
o
p
o
s
ed
I
E
E
E
-
1
4
b
u
s
s
y
s
tem
m
ea
s
u
r
in
g
th
e
v
o
ltag
e
m
ag
n
itu
d
e,
p
h
ases
an
d
f
r
eq
u
e
n
cies
o
f
th
e
g
r
id
s
y
s
tem
.
As
th
e
m
o
d
elin
g
is
in
s
im
u
latio
n
GPS
lo
ca
ti
o
n
is
av
o
id
ed
in
th
e
m
ea
s
u
r
em
en
t.
Fig
u
r
es
3
-
6
r
e
p
r
esen
ts
v
o
ltag
e
m
ag
n
itu
d
e,
f
r
eq
u
en
c
y
,
cu
r
r
e
n
t
m
ag
n
itu
d
e
an
d
p
h
ase
an
g
le
at
p
h
ase
A
o
f
all
th
e
1
4
b
u
s
es with
f
au
lt a
p
p
lied
o
n
t
h
e
I
E
E
E
-
1
4
b
u
s
s
y
s
tem
b
etwe
en
0
.
5
s
ec
to
0
.
5
5
s
ec
.
Fig
u
r
e
3
.
Vo
ltag
e
m
ag
n
itu
d
es
o
f
all
b
u
s
es
Fig
u
r
e
4
.
Fre
q
u
en
cies o
f
all
b
u
s
es
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
P
o
w
er q
u
a
lity imp
r
o
ve
men
t a
n
d
a
n
a
lysi
s
o
f in
terco
n
n
ec
ted
b
u
s
s
ystem
w
i
th
p
h
a
s
o
r
…
(
P
r
ee
ti K
a
b
r
a
)
55
Fig
u
r
e
5
.
C
u
r
r
e
n
t m
ag
n
itu
d
es
o
f
all
b
u
s
es
Fig
u
r
e
6
.
Ph
ase
an
g
le
at
p
h
ase
A
o
f
all
b
u
s
es
3.
VSM
-
S
T
A
T
CO
M
M
O
D
E
L
L
I
NG
T
h
e
s
y
n
ch
r
o
n
izatio
n
o
f
VSM
is
d
o
n
e
t
h
r
o
u
g
h
New
to
n
’
s
L
a
w
an
d
s
win
g
eq
u
ati
o
n
wh
ic
h
s
h
o
ws
th
e
m
o
v
em
en
ts
o
f
a
n
im
ag
in
ar
y
r
o
tatin
g
s
h
af
t
as
s
h
o
wn
in
F
ig
u
r
e
7
(
a)
wh
ic
h
co
r
r
esp
o
n
d
s
to
3
p
h
ase
co
n
v
e
r
ter
s
in
F
ig
u
r
e
7
(
b
)
.
=
ω
−
ω
(
1
)
−
−
−
(
ω
−
ω
)
wh
er
e
-
p
o
wer
an
g
le,
ω
an
d
ω
n
ar
e
d
etec
ted
f
r
e
q
u
en
c
y
an
d
g
r
id
f
r
eq
u
e
n
cy
r
esp
ec
tiv
ely
,
M
an
d
D
ar
e
v
ir
tu
a
l
an
g
u
lar
m
o
m
en
tu
m
an
d
v
ir
tu
al
d
am
p
in
g
co
ef
f
icien
t,
an
d
ar
e
d
ir
ec
t
cu
r
r
en
t
(
-
DC
)
in
p
u
t
ac
tiv
e
p
o
wer
an
d
alter
n
atin
g
cu
r
r
en
t
(
AC
)
o
u
tp
u
t a
ctiv
e
p
o
wer
o
f
t
h
e
co
n
v
e
r
ter
.
So
,
th
e
im
ag
i
n
ar
y
s
h
af
t is r
o
tatin
g
at
th
e
s
p
ee
d
ω
wh
ich
is
d
r
iv
en
b
y
an
d
b
r
a
k
ed
b
y
.
(
a)
(
b
)
Fig
u
r
e
7
.
Vir
tu
al
s
y
n
ch
r
o
n
o
u
s
m
ac
h
in
e
co
n
ce
p
t
(
a)
im
ag
in
ar
y
r
o
tatin
g
s
h
a
f
t
an
d
(
b
)
3
-
p
h
ase
co
n
v
er
te
r
T
h
e
DC
in
p
u
t
p
o
wer
is
a
co
n
tr
o
llab
le
v
ar
iab
le
an
d
r
em
ai
n
s
co
n
s
tan
t
if
co
m
m
an
d
s
ar
e
n
o
t
g
iv
en
wh
ile
with
th
e
p
o
wer
tr
a
n
s
f
er
eq
u
atio
n
th
e
ac
o
u
t
p
u
t p
o
wer
ca
n
b
e
ca
lcu
lated
.
=
(
2
)
W
h
er
e
is
a
co
n
s
tan
t
r
elativ
e
to
th
e
o
p
e
r
atin
g
c
o
n
d
itio
n
.
I
f
ω
is
g
r
ea
ter
th
an
ω
n
,
an
d
will
b
ec
o
m
e
lar
g
er
,
an
d
th
en
ω
will b
e
d
ec
r
ea
s
ed
b
y
th
e
u
n
b
alan
ce
o
f
in
p
u
t
an
d
o
u
t
p
u
t p
o
wer
,
an
d
v
ice
v
er
s
a.
I
n
th
e
s
tead
y
s
tate,
th
e
two
p
o
wer
s
will
b
e
eq
u
al
an
d
th
e
f
r
eq
u
e
n
cy
will
b
e
ev
e
n
tu
ally
th
e
g
r
id
f
r
eq
u
e
n
cy
an
d
h
e
n
ce
th
e
co
n
v
er
ter
is
s
y
n
ch
r
o
n
ized
w
ith
th
e
g
r
id
.
I
f
(
1
)
is
im
p
lem
en
ted
in
th
e
co
n
tr
o
ller
f
o
r
th
e
co
n
v
er
te
r
,
th
e
s
y
n
ch
r
o
n
izatio
n
b
eh
av
io
r
will
be
ex
ac
tly
th
e
s
am
e
with
th
e
r
o
tatin
g
s
h
af
t,
s
h
o
win
g
an
em
u
latio
n
of
s
y
n
ch
r
o
n
o
u
s
m
ac
h
in
es.
A
b
asi
c
s
tr
u
ctu
r
e
of
VSM
b
ased
co
n
tr
o
ller
is
as
s
h
o
wn
in
F
ig
u
r
e
8
.
C
o
n
tr
o
l
b
lo
ck
s
o
f
b
asic
VSM
co
n
tr
o
ller
with
o
n
ly
v
ir
tu
al
in
er
tia
p
r
esen
ted
wh
er
e
th
e
tr
an
s
f
er
f
u
n
ctio
n
Gp
la
n
t
r
ep
r
esen
ts
th
e
p
o
wer
tr
an
s
f
e.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
11
,
No
.
1
,
Ma
r
ch
2
0
2
2
:
52
-
61
56
Fig
u
r
e
8
.
C
o
n
tr
o
l b
lo
c
k
s
o
f
b
a
s
ic
VSM
co
n
tr
o
ller
W
ith
in
cr
ea
s
e
in
p
o
wer
d
em
a
n
d
an
d
co
m
p
lex
ity
o
f
th
e
g
r
i
d
s
y
s
tem
,
it
also
n
ee
d
s
to
m
a
in
tain
th
e
q
u
ality
an
d
s
tab
ilit
y
o
f
p
o
wer
s
u
p
p
ly
[
16]
.
I
n
o
r
d
er
to
d
o
th
at
d
if
f
er
en
t
p
o
wer
elec
tr
o
n
ic
d
ev
ices
[
1
7
]
ar
e
co
n
n
ec
ted
t
o
th
e
g
r
id
i
n
s
y
n
ch
r
o
n
izatio
n
with
th
e
g
r
id
v
o
ltag
e.
T
h
is
is
ac
h
iev
ed
b
y
u
s
in
g
PLL
with
s
y
n
ch
r
o
n
o
u
s
r
ef
er
e
n
ce
f
r
a
m
e
(
SR
F)
STAT
C
OM
co
n
tr
o
l
[
1
8
]
d
ev
ices
wh
ich
im
p
r
o
v
e
th
e
p
o
wer
q
u
ality
an
d
s
tab
ilit
y
.
I
n
th
is
p
ap
er
a
STA
T
C
OM
is
in
tr
o
d
u
ce
d
with
VSM
wh
ich
m
im
ics
th
e
co
n
v
e
n
tio
n
al
s
y
n
ch
r
o
n
o
u
s
co
n
d
en
s
er
.
T
h
e
VSM
d
ev
ice
c
o
m
p
r
is
e
s
as
s
h
o
wn
in
Fig
u
r
e
9
o
f
s
tatic
p
o
wer
elec
tr
o
n
ic
s
witch
es
co
n
tr
o
lled
b
y
PLL
in
teg
r
ated
co
n
tr
o
ller
w
ith
f
ee
d
b
ac
k
f
r
o
m
th
e
g
r
id
v
o
ltag
e.
Fo
r
f
aster
a
n
d
r
o
b
u
s
t
co
n
tr
o
llin
g
d
-
q
co
m
p
o
n
en
ts
ar
e
u
s
ed
f
o
r
g
en
e
r
atio
n
o
f
r
ef
er
e
n
ce
s
ig
n
als
to
g
en
er
ate
p
u
ls
e
-
wid
th
m
o
d
u
latio
n
(
PW
M)
p
u
ls
es
f
o
r
th
e
p
o
wer
elec
tr
o
n
ic
d
ev
ic
es
co
n
n
ec
ted
in
th
e
VSM.
T
h
e
VSM
p
ar
am
eter
s
lik
e
v
ir
tu
a
l
in
er
tia
an
d
v
ir
tu
al
im
p
ed
an
ce
ar
e
im
p
lem
en
ted
f
o
r
th
e
o
p
e
r
atio
n
o
f
STAT
C
O
M
as
a
v
ar
iab
le
s
y
n
ch
r
o
n
o
u
s
co
n
d
en
s
er
d
e
v
ice.
A
STAT
C
OM
d
ev
ice
i
s
co
n
s
id
er
ed
f
o
r
r
ea
ctiv
e
p
o
we
r
in
jec
tio
n
to
im
p
r
o
v
e
p
o
wer
q
u
alit
y
of
th
e
g
r
id
.
T
h
e
cir
cu
it
to
p
o
lo
g
y
o
f
th
e
d
ev
ice
will
h
o
wev
er
b
e
th
e
s
am
e
o
n
l
y
with
th
e
ch
an
g
e
in
th
e
c
o
n
tr
o
ller
.
T
h
e
p
r
o
p
o
s
ed
co
n
tr
o
ller
o
f
th
e
VSM
-
STAT
C
OM
[
1
9
]
,
is
g
iv
en
b
elo
w
,
wi
ll b
e
les
s
s
en
s
itiv
e
to
v
ar
iatio
n
in
v
o
ltag
e
o
r
p
o
wer
d
u
e
to
n
o
n
co
n
v
en
tio
n
al
en
er
g
y
s
o
u
r
ce
s
o
r
wea
k
co
n
d
itio
n
o
f
g
r
id
an
d
also
p
r
o
v
i
d
in
g
b
et
ter
s
y
n
ch
r
o
n
izatio
n
wh
ich
r
esu
lts
in
b
etter
v
o
ltag
e
r
eg
u
latio
n
a
n
d
u
ltima
tely
im
p
r
o
v
in
g
p
o
wer
q
u
ality
o
f
th
e
s
y
s
tem
.
Fig
u
r
e
9
.
STAT
C
OM
cir
cu
it c
o
n
n
ec
ted
t
o
g
r
id
f
o
r
im
p
lem
en
tin
g
th
e
VSM
3
.
1
.
Co
nv
ent
i
o
na
l
s
t
a
t
ic
s
y
nchro
no
us
co
m
pens
a
t
o
r
co
ntr
o
l
W
e
n
ee
d
s
ix
p
u
ls
es
to
m
ak
e
th
e
v
o
ltag
e
s
o
u
r
ce
co
n
v
er
ter
(
VSC
)
o
f
th
e
STAT
C
OM
to
o
p
er
ate.
T
h
e
p
u
ls
es
to
th
is
co
n
v
er
ter
a
r
e
f
e
d
in
s
y
n
ch
r
o
n
izatio
n
t
o
th
e
g
r
id
with
PC
C
v
o
ltag
e
f
ee
d
b
ac
k
.
T
h
e
c
o
n
tr
o
ller
o
f
th
e
co
n
v
e
n
tio
n
al
STAT
C
OM
[
2
0
]
ca
n
b
e
s
ee
n
in
F
ig
u
r
e
1
0
.
Fig
u
r
e
1
0
.
C
o
n
v
en
tio
n
al
ST
AT
C
OM
co
n
tr
o
l
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
P
o
w
er q
u
a
lity imp
r
o
ve
men
t a
n
d
a
n
a
lysi
s
o
f in
terco
n
n
ec
ted
b
u
s
s
ystem
w
i
th
p
h
a
s
o
r
…
(
P
r
ee
ti K
a
b
r
a
)
57
3
.
2
.
V
irt
ua
l sy
nchro
no
us
ma
chine
–
s
t
a
t
ic
s
y
nchro
no
us
c
o
m
pens
a
t
o
r
co
ntr
o
l
I
n
VSM
-
STAT
C
OM
co
n
tr
o
l
f
o
r
f
aster
an
d
r
o
b
u
s
t
co
n
t
r
o
llin
g
d
-
q
co
m
p
o
n
en
ts
[
2
1
]
an
d
f
o
r
m
u
lti
-
o
b
jectiv
e
p
lace
m
en
t
o
f
STAT
C
OM
[
2
2
]
ar
e
u
s
ed
f
o
r
g
en
er
atio
n
o
f
r
ef
er
e
n
ce
s
ig
n
als
to
g
en
er
ate
PW
M
[
2
3
]
(
p
u
ls
e
wid
th
m
o
d
u
latio
n
)
p
u
ls
es
f
o
r
th
e
p
o
wer
elec
tr
o
n
ic
d
e
v
ices
co
n
n
ec
ted
in
th
e
VSM.
Fo
r
im
p
lem
en
tin
g
th
e
VSM
p
ar
am
eter
s
[
2
4
]
lik
e
v
ir
tu
al
in
e
r
tia
an
d
v
ir
t
u
al
i
m
p
ed
an
ce
ar
e
c
o
n
s
id
er
ed
f
o
r
th
e
o
p
e
r
atio
n
o
f
th
e
d
ev
ice.
Fo
r
r
ea
ctiv
e
p
o
wer
in
j
ec
tio
n
in
to
th
e
g
r
id
a
STAT
C
OM
d
ev
ice
is
co
n
s
id
er
ed
.
T
h
e
cir
cu
it
to
p
o
l
o
g
y
o
f
th
e
d
ev
ice
will
h
o
we
v
er
b
e
th
e
s
am
e
o
n
ly
with
c
h
an
g
e
in
th
e
co
n
tr
o
ller
.
T
h
e
p
r
o
p
o
s
ed
co
n
tr
o
ller
o
f
th
e
VSM
-
STAT
C
OM
[
2
5
]
is
s
h
o
wn
in
F
ig
u
r
e
11
.
Fig
u
r
e
11
.
C
o
n
tr
o
ller
o
f
VSM
-
STAT
C
OM
d
ev
ice
4.
VSM
CO
N
T
RO
L
B
L
O
CK
S
Op
er
atio
n
o
f
th
e
s
y
s
tem
is
b
ec
o
m
in
g
less
s
tab
le
d
u
e
to
an
in
cr
ea
s
in
g
p
r
o
p
o
r
tio
n
o
f
n
o
n
-
s
y
n
ch
r
o
n
o
u
s
g
en
er
atio
n
a
n
d
n
o
n
c
o
n
v
e
n
tio
n
al
en
er
g
y
s
o
u
r
ce
s
o
p
er
ate
at
m
ax
im
u
m
p
o
wer
p
o
in
t
tr
ac
k
in
g
(
MPPT)
m
o
d
e
.
On
e
o
f
th
e
m
o
s
t
im
p
o
r
tan
t
p
r
o
b
lem
s
in
n
o
n
co
n
v
en
tio
n
al
en
e
r
g
y
s
o
u
r
ce
s
(
NC
E
S)
an
d
s
m
ar
t
g
r
id
in
teg
r
atio
n
is
h
o
w
to
s
y
n
c
h
r
o
n
ize
in
v
e
r
ter
s
with
g
r
id
.
M
o
r
e
co
n
v
er
t
o
r
-
b
as
ed
tech
n
o
l
o
g
ies
ar
e
c
o
n
n
ec
tin
g
to
th
e
s
y
s
tem
an
d
th
er
e
is
in
cr
ea
s
ed
n
ee
d
o
f
im
m
ed
iate
r
ea
ctiv
e
s
u
p
p
o
r
t
d
u
r
in
g
a
d
is
tu
r
b
an
ce
an
d
im
m
ed
iat
ely
af
t
er
o
th
er
wis
e
it
lead
s
to
in
cr
ea
s
ed
r
is
k
o
f
co
m
b
in
ed
v
o
ltag
e
an
d
f
r
e
q
u
en
c
y
e
v
en
ts
.
T
h
e
VSM
-
STAT
C
OM
p
r
o
p
o
s
ed
in
th
is
p
ap
er
h
as
v
ir
tu
al
b
a
ck
E
MF
e
,
v
ir
tu
al
in
er
tia
M
,
an
d
v
ir
tu
al
im
p
ed
an
ce
R
+jX
L
ap
p
lied
in
th
e
co
n
tr
o
ller
as
v
ar
iab
le
s
y
n
ch
r
o
n
o
u
s
co
n
d
e
n
s
er
.
STA
T
C
OM
co
n
s
id
er
in
g
v
ir
tu
al
in
er
tia,
with
o
u
t
lo
s
in
g
s
y
n
ch
r
o
n
izatio
n
,
will
n
atu
r
ally
s
y
n
ch
r
o
n
ize
with
th
e
g
r
id
p
er
f
ec
tly
i
n
ca
s
e
o
f
an
y
ch
an
g
e
in
th
e
f
r
e
q
u
en
c
y
.
Vir
tu
al
im
p
ed
an
ce
n
o
t
o
n
ly
m
in
im
izes
th
e
h
ar
m
o
n
ic
s
d
u
e
to
th
e
co
n
v
er
ter
its
elf
b
u
t
also
r
ejec
t
th
at
f
r
o
m
th
e
s
y
s
tem
en
s
u
r
in
g
im
m
u
n
ity
u
n
d
er
h
ar
m
o
n
ic
co
n
d
itio
n
s
an
d
a
s
y
m
m
etr
ical
f
au
lts
co
n
d
itio
n
.
VSM
-
b
ased
STAT
C
OM
will
b
e
less
s
en
s
itiv
e
to
p
o
wer
o
r
v
o
ltag
e
f
lu
ctu
atio
n
in
d
u
ce
d
b
y
NC
E
S
[
1
6
]
o
r
th
e
g
r
id
it
s
elf
,
r
esu
ltin
g
in
b
etter
s
y
n
ch
r
o
n
izatio
n
p
er
f
o
r
m
an
ce
an
d
f
u
r
t
h
er
wh
ich
r
esu
l
ts
in
a
b
etter
v
o
lta
g
e
r
eg
u
latio
n
an
d
s
tab
ilit
y
o
f
s
y
s
tem
th
an
th
e
co
n
v
en
tio
n
al
STAT
C
OM
co
n
tr
o
lled
in
th
e
d
-
q
f
r
am
e.
VSM
co
n
tr
o
ller
h
as
co
n
tr
o
l
b
l
o
ck
s
,
as
s
h
o
wn
in
F
ig
u
r
e
1
2
i
n
th
e
u
p
p
er
m
id
d
le
with
v
ir
tu
al
in
er
tia
M
an
d
v
ir
tu
al
d
am
p
in
g
c
o
ef
f
icien
t
D
an
d
p
r
o
v
id
in
g
t
h
e
p
h
ase
θ
o
f
th
e
b
a
ck
E
MF,
wh
ich
s
y
n
ch
r
o
n
izes
with
th
e
g
r
id
in
th
e
s
tead
y
s
tate
with
a
p
h
ase
d
if
f
e
r
en
ce
k
n
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I
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[
2
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(
d
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