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I
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15
,
No
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3
,
Sep
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20
26
:
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0
2
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1
0
3
5
1024
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is
tr
ib
u
tio
n
s
y
s
tem
b
y
m
ea
n
s
o
f
a
p
o
wer
-
co
n
d
itio
n
in
g
tech
n
iq
u
e
with
a
s
u
itab
le
co
n
tr
o
l stru
ctu
r
e
f
o
r
en
er
g
y
m
an
a
g
em
en
t.
T
h
e
r
ef
o
r
e,
th
e
s
o
lar
-
PV
f
ed
DG
s
ch
em
e
is
h
ig
h
ly
d
ep
en
d
en
t
o
n
s
ig
n
if
ican
t
asp
ec
ts
s
u
ch
as
co
n
tin
u
o
u
s
p
o
we
r
s
u
p
p
o
r
t,
r
eliab
l
e
p
o
wer
co
n
tr
o
l,
g
r
ea
ter
p
o
wer
tr
an
s
f
e
r
ca
p
ac
it
y
,
an
d
well
-
co
m
p
ly
in
g
with
p
o
wer
-
q
u
ality
(
PQ)
lim
itatio
n
s
[
1
2
]
.
T
h
e
PQ
is
th
e
m
o
s
t
s
u
b
s
tan
ti
al
an
d
n
o
tab
le
k
ey
s
p
ec
if
icati
o
n
in
th
e
p
r
esen
t
u
tili
ty
-
g
r
i
d
in
teg
r
ated
d
is
tr
ib
u
tio
n
s
y
s
tem
f
o
r
d
eliv
e
r
in
g
th
e
s
tan
d
ar
d
a
n
d
q
u
ality
p
o
wer
to
en
d
-
u
s
er
c
o
n
s
u
m
er
s
,
co
m
p
ly
in
g
with
g
r
id
-
co
d
e
g
u
id
elin
es.
Du
e
to
t
h
e
p
r
esen
ce
o
f
cr
itica
l
PQ
is
s
u
es,
th
e
u
tili
ty
-
g
r
id
s
p
ec
if
icatio
n
s
lik
e
s
o
u
r
ce
v
o
ltag
e,
cu
r
r
en
t,
an
d
f
r
eq
u
e
n
cy
ar
e
p
r
o
life
r
ated
,
th
er
ef
o
r
e
af
f
ec
tin
g
th
e
en
tire
lo
ad
ap
p
ar
atu
s
h
as
b
ee
n
id
en
tifie
d
as
a
m
ajo
r
p
r
o
b
lem
.
T
h
ese
PQ
is
s
u
es
ar
e
h
ig
h
l
y
in
f
lu
en
cin
g
t
h
e
u
tili
ty
-
g
r
i
d
v
o
ltag
e
b
y
i
n
jectin
g
th
e
v
o
ltag
e
h
ar
m
o
n
ics,
v
o
ltag
e
s
ag
s
-
s
wells,
an
d
f
au
lts
,
w
h
ich
i
n
cr
ea
s
e
th
e
s
u
b
v
e
r
s
iv
e
p
o
wer
-
p
o
llu
tio
n
an
d
d
eg
r
a
d
e
th
e
o
v
er
all
f
u
n
ctio
n
in
g
o
f
en
d
-
u
s
e
r
co
n
s
u
m
er
l
o
ad
s
at
th
e
PC
C
o
f
th
e
u
tili
ty
-
g
r
id
s
y
s
tem
[
1
3
]
-
[
1
5
]
.
Mo
r
eo
v
e
r
,
th
e
g
r
id
-
is
lan
d
in
g
is
s
u
es
ar
e
also
cr
ea
tin
g
s
er
io
u
s
im
p
ac
ts
o
n
th
e
u
tili
ty
-
g
r
id
s
y
s
tem
,
wh
ich
is
in
f
lu
en
cin
g
th
e
co
n
tin
u
o
u
s
d
eliv
er
y
o
f
elec
tr
ic
p
o
wer
to
e
n
d
-
u
s
er
co
n
s
u
m
e
r
l
o
ad
s
in
lin
e
with
th
e
p
ea
k
lo
a
d
d
em
an
d
s
.
I
n
th
is
m
an
n
er
,
t
h
e
m
ain
o
b
je
ctiv
e
is
n
o
t
o
n
ly
lim
ited
to
co
m
p
en
s
atio
n
o
f
s
ev
e
r
e
PQ
is
s
u
es
b
u
t
also
r
eg
u
latin
g
th
e
g
r
id
-
is
lan
d
i
n
g
is
s
u
es
b
y
em
p
lo
y
in
g
th
e
d
esira
b
le
cu
s
to
m
-
p
o
wer
tech
n
o
lo
g
y
(
C
PT)
b
y
m
an
y
p
o
wer
-
s
y
s
tem
co
n
tr
o
l
en
g
in
ee
r
s
an
d
v
ar
io
u
s
r
esear
ch
t
ea
m
s
[
1
6
]
-
[
1
9
]
.
T
h
e
C
PT
u
tili
ze
s
th
e
v
ar
io
u
s
co
m
p
en
s
atio
n
d
ev
ices
f
o
r
co
m
p
en
s
atio
n
o
f
s
ev
er
e
v
o
ltag
e
r
elev
an
t
PQ
is
s
u
es
an
d
r
esto
r
in
g
t
h
e
u
tili
ty
-
g
r
id
s
p
ec
if
icatio
n
s
as
lin
ea
r
,
f
u
n
d
a
m
en
tal
f
r
e
q
u
en
c
y
a
n
d
s
in
u
s
o
id
al
wav
e
-
s
h
ap
es,
b
alan
ce
d
s
y
s
tem
with
th
e
h
elp
o
f
r
eq
u
is
ite
id
en
tific
atio
n
an
d
cl
ass
if
icatio
n
m
eth
o
d
s
[
2
0
]
,
[
2
1
]
.
Z
h
an
g
et
al
.
[
2
0
]
ex
p
l
o
r
ed
t
h
e
v
ar
io
u
s
cu
s
to
m
-
p
o
wer
d
e
v
ices
f
o
r
e
n
h
an
ci
n
g
t
h
e
p
o
wer
q
u
ality
i
n
th
e
d
is
tr
ib
u
tio
n
n
etwo
r
k
s
b
y
em
p
lo
y
in
g
ad
v
an
ce
d
tech
n
iq
u
es.
C
h
aw
d
a
e
t
a
l
.
[
2
1
]
p
r
ese
n
te
d
t
h
e
r
o
le
a
n
d
an
al
y
ti
ca
l
o
p
e
r
at
io
n
o
f
v
a
r
i
o
u
s
cu
s
to
m
p
o
w
er
d
e
v
ic
es
f
o
r
t
h
e
m
i
ti
g
at
io
n
o
f
s
ev
er
e
PQ
is
s
u
es
in
th
e
DG
s
y
s
tem
s
.
T
h
er
e
ar
e
m
u
ltip
le
C
PT
d
ev
ices
th
at
ca
n
b
e
co
n
v
en
ien
tly
av
ailab
le
to
h
an
d
le
s
p
ec
if
ic
PQ
ch
alle
n
g
es,
r
esu
ltin
g
in
th
e
d
is
tr
ib
u
ti
o
n
s
y
s
tem
b
ein
g
s
in
u
s
o
i
d
al
in
f
o
r
m
,
ev
en
l
y
b
alan
ce
d
,
an
d
u
n
if
o
r
m
,
an
d
h
av
i
n
g
f
u
n
d
am
en
tal
ch
ar
ac
ter
is
tics
.
Swain
et
al
.
[
2
2
]
p
r
esen
ted
t
h
e
s
ig
n
if
ican
t
elim
in
atio
n
o
f
h
ar
m
o
n
ic
d
is
to
r
tio
n
s
i
n
th
e
u
ti
lity
g
r
id
an
d
also
r
eg
u
latin
g
th
e
en
er
g
y
d
em
an
d
is
s
u
es
f
o
r
im
p
r
o
v
in
g
th
e
m
icr
o
-
g
r
id
p
er
f
o
r
m
an
ce
b
y
u
s
in
g
a
s
h
u
n
t
ac
tiv
e
p
o
wer
f
ilter
o
p
e
r
ate
d
with
f
ea
s
ib
le
SHAF
co
n
tr
o
l
s
ch
em
es.
T
h
e
r
esu
lts
in
[
2
3
]
,
[
2
4
]
p
r
esen
ted
th
at
s
o
lar
-
PV
-
b
ased
FC
-
T
C
R
an
d
S
VC
ar
e
u
s
ed
f
o
r
co
m
p
en
s
atio
n
o
f
p
o
wer
-
d
em
an
d
s
h
o
r
tag
es,
cu
r
r
en
t
r
ele
v
an
t
PQ
co
n
ce
r
n
s
in
th
e
m
o
d
er
n
d
is
tr
ib
u
tio
n
s
y
s
tem
estab
lis
h
th
e
im
p
r
o
v
ed
p
e
r
f
o
r
m
an
ce
o
f
th
e
g
r
id
-
in
teg
r
ated
d
is
tr
ib
u
t
io
n
n
etwo
r
k
.
Ab
as
et
a
l.
[
2
5
]
ex
p
lo
r
ed
th
e
u
n
iq
u
e
p
o
we
r
-
q
u
ality
im
p
r
o
v
em
en
t
tech
n
iq
u
e
b
y
ad
o
p
tin
g
t
h
e
d
y
n
am
ic
-
v
o
ltag
e
r
esto
r
e
r
(
DVR)
f
o
r
th
e
m
itig
atio
n
o
f
s
ev
er
al
v
o
l
tag
e
-
r
elate
d
p
o
wer
-
q
u
ality
is
s
u
es.
Ku
m
ar
et
a
l.
[
2
6
]
p
r
esen
ted
t
h
e
f
ea
s
ib
le
co
m
p
en
s
atio
n
o
f
v
o
ltag
e
s
ag
s
-
s
well
co
n
ce
r
n
s
b
y
u
s
in
g
DVR,
alo
n
g
with
attain
in
g
th
e
en
h
an
ce
d
p
o
wer
-
q
u
ality
c
h
ar
ac
ter
is
tics
in
th
e
p
o
wer
-
s
y
s
tem
n
etwo
r
k
.
Acc
o
r
d
in
g
t
o
th
e
p
r
o
b
lem
i
d
en
tific
atio
n
,
th
e
DVR
is
th
e
b
est
an
d
s
u
itab
le
C
PT
d
ev
ice
f
o
r
co
m
p
en
s
atio
n
o
f
all
v
o
ltag
e
-
r
elate
d
PQ
i
s
s
u
es
b
ec
au
s
e
o
f
its
f
av
o
r
ab
le
m
er
its
s
u
ch
as
f
lex
ib
le
o
p
er
atio
n
,
co
m
p
ac
t size,
in
ex
p
e
n
s
iv
e,
an
d
r
ap
id
r
esp
o
n
s
e
to
v
o
ltag
e
-
r
el
a
ted
an
d
p
o
wer
-
r
elate
d
is
s
u
es [
2
7
]
.
T
h
e
p
r
esen
ted
s
o
lar
-
PV
DG
s
ch
em
e
d
eliv
er
s
t
h
e
r
eq
u
ir
ed
ac
tiv
e
p
o
wer
d
u
r
i
n
g
g
r
id
is
lan
d
in
g
,
alo
n
g
with
en
h
an
cin
g
th
e
v
o
ltag
e
s
tab
ilit
y
d
u
r
in
g
p
o
wer
-
q
u
alit
y
d
eter
io
r
ati
o
n
th
r
o
u
g
h
a
D
VR
n
am
ed
as
m
u
lti
-
f
u
n
ctio
n
al
d
y
n
am
ic
-
v
o
ltag
e
r
esto
r
er
(
MF
-
DVR)
d
ev
ice
with
a
f
ea
s
ib
le
co
n
tr
o
l
s
ch
em
e.
Fro
m
v
ar
io
u
s
r
ec
en
t
liter
atu
r
e
r
ev
iews,
th
e
s
y
n
ch
r
o
n
o
u
s
r
ef
er
en
ce
f
r
am
e
(
SR
F)
[
2
8
]
-
[
3
1
]
is
th
e
m
o
s
t
r
eg
u
lar
co
n
tr
o
l
s
ch
em
e
f
o
r
t
h
e
g
e
n
er
atio
n
o
f
a
v
o
ltag
e
r
ef
er
en
ce
s
ig
n
al
f
o
r
v
o
ltag
e
c
o
m
p
en
s
atio
n
is
ex
p
lo
r
ed
b
y
Sin
g
h
an
d
Sin
g
h
i
n
[
3
2
]
.
B
u
t,
th
e
r
eg
u
lar
SR
F
co
n
tr
o
l
s
ch
em
e
h
as
s
u
b
s
tan
tial
p
r
o
b
lem
s
id
en
tifie
d
an
d
is
also
n
o
t
r
ec
o
m
m
en
d
e
d
d
u
e
to
tech
n
ical
lim
itatio
n
s
s
u
ch
as
s
o
p
h
is
ticated
tr
an
s
f
o
r
m
atio
n
s
an
d
m
ath
e
m
atica
l
ca
lcu
latio
n
s
,
h
ig
h
tr
an
s
ien
t
d
elay
in
th
e
r
ef
e
r
en
ce
s
ig
n
al,
w
h
ich
d
eg
r
ad
es th
e
co
m
p
en
s
atio
n
p
e
r
f
o
r
m
a
n
ce
an
d
ef
f
icien
cy
.
T
h
e
s
e
cr
itical
tech
n
ical
lim
itatio
n
s
in
th
e
r
eg
u
lar
SR
F
co
n
tr
o
l
s
ch
em
e
h
a
v
e
b
ee
n
eli
m
in
ated
b
y
p
r
o
p
o
s
in
g
th
e
n
o
v
el
m
o
d
i
f
ied
v
o
ltag
e
v
ec
to
r
r
ef
er
en
ce
(
MV
VR
)
co
n
tr
o
l
s
ch
em
e.
T
h
e
p
r
o
p
o
s
ed
MV
VR
co
n
tr
o
ller
p
er
f
ec
tly
p
r
o
d
u
ce
s
th
e
u
n
iq
u
e
r
ef
er
e
n
ce
v
o
ltag
e
s
ig
n
als
f
o
r
d
eliv
er
in
g
a
f
ea
s
ib
le
s
witch
in
g
p
atter
n
to
th
e
MF
-
DVR
d
e
v
ice.
I
n
th
is
wo
r
k
,
th
e
d
esig
n
an
d
p
er
f
o
r
m
an
ce
o
f
th
e
p
r
o
p
o
s
ed
MV
VR
-
co
n
tr
o
lled
s
o
lar
-
PV
-
f
ed
MF
-
DVR
h
av
e
b
ee
n
v
er
i
f
ied
u
n
d
er
e
n
h
an
ci
n
g
p
o
wer
-
q
u
ality
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en
t
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u
r
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.
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ter
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ter
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ase
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u
r
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atio
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,
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ts
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e
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atio
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d
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ated
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o
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m
m
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n
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ito
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dc.
s
)
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n
er
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y
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n
DG
m
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e,
an
y
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is
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d
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s
u
es
ar
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etec
te
d
,
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e
n
th
e
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y
s
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ir
ec
tly
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m
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C
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t
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ter
alo
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I
NC
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MPPT
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n
tr
o
ller
f
o
r
r
eg
u
latin
g
th
e
s
o
lar
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PV
p
o
wer
u
n
d
er
v
ar
y
in
g
co
n
d
itio
n
s
.
T
h
e
e
n
er
g
y
g
e
n
er
ated
f
r
o
m
s
o
lar
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PV
h
as
b
ee
n
d
ir
ec
tly
d
eliv
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ed
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d
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lev
el
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n
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m
e
r
s
f
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r
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tiv
e
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eg
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n
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er
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is
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m
o
d
e
b
y
u
s
in
g
th
e
av
aila
b
le
VSC
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th
e
MF
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d
ev
ice.
T
h
is
p
r
o
p
o
s
ed
DG
s
y
s
tem
r
ed
u
ce
s
th
e
u
tili
za
tio
n
o
f
a
n
ad
d
itio
n
al
i
n
v
er
ter
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n
v
er
ter
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o
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el
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o
r
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s
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g
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d
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is
s
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th
e
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is
tr
i
b
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tio
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tem
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wh
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elp
s
to
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u
ce
th
e
in
itial
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s
t,
o
cc
u
p
an
cy
,
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d
s
ize
o
f
th
e
co
m
p
en
s
atio
n
d
ev
ice.
T
h
is
ca
n
b
e
attain
ed
b
y
tr
an
s
itio
n
VSC
o
f
MF
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a
s
a
g
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fo
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m
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e
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to
r
eg
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late
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e
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ed
u
tili
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ar
ac
ter
is
tics
,
en
s
u
r
in
g
th
e
s
t
ab
le
v
o
ltag
e
an
d
p
o
wer
s
u
p
p
o
r
t to
en
d
-
u
s
er
c
o
n
s
u
m
er
lo
ad
s
with
r
esp
ec
t to
lo
ad
d
em
an
d
.
Similar
ly
,
wh
en
an
y
v
o
ltag
e
-
r
elev
an
t
is
s
u
es
s
u
ch
as
v
o
ltag
e
h
ar
m
o
n
ics,
v
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e
s
ag
s
,
s
well
s
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o
r
f
au
lts
h
av
e
o
cc
u
r
r
e
d
,
af
f
ec
tin
g
th
e
o
v
er
all
f
u
n
ctio
n
in
g
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f
en
d
-
u
s
er
co
n
s
u
m
er
lo
ad
s
at
th
e
PC
C
o
f
th
e
u
tili
ty
-
g
r
id
s
y
s
tem
d
u
e
to
s
u
b
v
er
s
iv
e
p
o
wer
-
p
o
llu
tio
n
,
d
is
co
n
tin
u
o
u
s
p
o
wer
-
f
lo
w.
I
n
th
is
m
o
d
e,
th
e
VSC
o
f
MF
-
D
VR
tr
an
s
itio
n
s
in
to
PQ
en
h
a
n
ce
m
en
t
m
o
d
e
f
o
r
co
m
p
en
s
atio
n
o
f
all
v
o
ltag
e
-
r
elev
an
t
PQ
is
s
u
es,
as
an
in
-
p
h
ase
v
o
ltag
e
co
m
p
en
s
atio
n
p
r
i
n
cip
l
e
th
at
in
jects
th
e
r
eq
u
is
ite
co
m
p
en
s
atio
n
v
o
lta
g
e
o
f
V
Cse.
abc
(
V)
in
to
th
e
PC
C
o
f
th
e
d
is
tr
ib
u
tio
n
s
y
s
tem
.
T
h
e
in
jecte
d
v
o
ltag
e
r
esto
r
es
th
e
u
tili
ty
-
g
r
id
s
p
ec
if
icatio
n
s
as
lin
ea
r
,
f
u
n
d
am
en
tal
f
r
eq
u
e
n
cy
,
a
n
d
s
in
u
s
o
id
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wav
e
s
h
ap
es,
a
b
alan
ce
d
s
y
s
tem
,
an
d
s
o
o
n
.
T
h
e
i
n
jecte
d
v
o
ltag
e
is
v
ar
ied
b
ased
o
n
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.
15
,
No
.
3
,
Sep
tem
b
er
20
26
:
1
0
2
3
-
1
0
3
5
1026
th
e
ty
p
e
o
f
v
o
ltag
e
is
s
u
es
b
y
s
en
s
in
g
th
r
o
u
g
h
d
etec
tio
n
d
ev
ice
s
,
an
d
th
e
p
r
esen
ted
n
o
tch
es
d
u
r
in
g
co
m
p
e
n
s
atio
n
ar
e
elim
in
ated
b
y
u
s
in
g
L
C
L
f
ilter
s
,
wh
ich
h
elp
to
co
n
tin
u
o
u
s
ly
lo
ad
v
o
ltag
e
r
eg
u
latio
n
in
th
e
d
is
tr
ib
u
tio
n
s
y
s
tem
.
I
t
is
n
o
ted
th
at,
as
p
er
I
E
E
E
/I
E
C
r
eg
u
latio
n
s
,
th
e
p
r
o
p
o
s
ed
MF
-
DVR
d
ev
ice
h
as
b
ee
n
r
ec
o
g
n
ized
f
o
r
DG
o
p
er
atio
n
s
an
d
co
m
p
en
s
a
tio
n
o
f
v
o
ltag
e
-
r
elate
d
is
s
u
es
in
a
u
tili
ty
-
g
r
i
d
in
teg
r
ate
d
d
is
tr
ib
u
tio
n
s
y
s
tem
b
y
em
p
lo
y
in
g
a
n
ewly
p
r
o
p
o
s
ed
MV
VR
co
n
tr
o
l sch
em
e.
3.
P
RO
P
O
SE
D
M
V
VR
CO
NT
RO
L
SCH
E
M
E
T
h
e
b
lo
ck
d
iag
r
am
o
f
th
e
n
ew
ly
p
r
o
p
o
s
ed
MV
VR
co
n
tr
o
l
s
ch
em
e
f
o
r
th
e
MF
-
DVR
d
ev
ice
is
s
h
o
wn
in
Fig
u
r
e
2
.
T
h
e
ef
f
ec
ti
v
e
o
p
e
r
atio
n
an
d
r
o
b
u
s
t
p
e
r
f
o
r
m
an
ce
o
f
th
e
p
r
o
p
o
s
ed
MF
-
DVR
d
ev
ice
r
ely
o
n
a
s
u
itab
le
r
ef
er
en
ce
co
n
tr
o
l
s
ch
em
e.
T
h
e
p
r
o
p
o
s
ed
MV
VR
co
n
tr
o
l
s
ch
e
m
e
is
b
est
s
u
ited
f
o
r
th
e
ex
tr
ac
tio
n
o
f
v
o
ltag
e
v
ec
to
r
r
e
f
er
en
ce
s
ig
n
als
am
o
n
g
th
e
tr
ad
itio
n
al
SR
F
co
n
tr
o
lle
r
r
ep
o
r
ted
in
[
2
8
]
.
T
h
e
g
en
e
r
at
ed
r
ef
er
e
n
ce
s
ig
n
al
h
as
a
f
ast
d
y
n
a
m
ic
r
esp
o
n
s
e
d
u
e
to
lo
w
tr
a
n
s
ien
t
d
elay
,
s
im
p
le
tr
an
s
f
o
r
m
atio
n
s
,
a
n
d
m
ath
e
m
atica
l
ca
lcu
latio
n
s
,
an
d
im
p
r
o
v
es
th
e
c
o
m
p
en
s
ati
o
n
ef
f
icien
cy
an
d
p
er
f
o
r
m
a
n
c
e.
T
h
is
v
o
ltag
e
v
ec
to
r
r
ef
er
e
n
ce
s
ig
n
al
u
tili
ze
s
th
e
u
n
it
-
v
ec
to
r
tem
p
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en
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ates
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en
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itiv
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ed
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ce
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e
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c
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lex
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n
it
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s
ig
n
als ar
e
ex
tr
ac
ted
as p
h
ase
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g
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d
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ates o
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l
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as d
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∆
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{
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3
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.
2
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2
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Fig
u
r
e
2
.
B
lo
ck
d
iag
r
am
o
f
n
e
wly
p
r
o
p
o
s
ed
MV
VR
co
n
tr
o
l
s
ch
em
e
f
o
r
MF
-
DVR
d
ev
ice
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
A n
o
ve
l MV
V
R
co
n
tr
o
lled
s
o
la
r
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P
V
fed
MF
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1027
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n
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t
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ig
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ep
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h
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ig
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tr
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On
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(
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(
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5
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h
e
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en
e
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ated
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lar
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o
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r
o
m
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lar
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PV sy
s
tem
u
n
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r
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A)
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A)
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Fig
u
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3
s
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m
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ce
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er
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Fig
u
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3
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a)
illu
s
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ates
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u
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3
(
b
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s
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ates
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e
I
–
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ter
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tics
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e
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ated
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ter
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h
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ax
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ith
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le
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n
o
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s
o
lar
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y
s
tem
wo
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k
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g
o
n
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s
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s
s
ib
le
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r
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e
s
lo
p
es o
f
s
o
lar
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PV v
o
ltag
e
V
pv.
dg
an
d
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u
r
r
en
t I
pv
.
dg
,
it m
ay
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e
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er
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ig
h
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o
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t
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o
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itiv
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ativ
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e
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ax
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m
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t
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d
/o
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ze
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e
at
m
ax
im
u
m
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ea
k
p
o
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n
t
is
d
escr
ib
ed
as
(
7
)
.
∆
I
pv
∆
V
pv
=
-
I
pv
V
pv
;
a
t MP
P
∆
I
pv
∆
V
pv
<
-
I
pv
V
pv
;
r
ig
h
t o
f MP
P
∆
I
pv
∆
V
pv
>
-
I
pv
V
pv
;
left o
f MP
P
}
(
7
)
Fro
m
th
e
r
esu
ltan
t
n
o
n
-
c
o
m
p
l
ex
u
n
it
v
ec
to
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ig
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als
(
.
)
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d
t
h
e
r
ef
e
r
en
ce
v
o
ltag
e
m
ag
n
itu
d
e
(
.
∗
)
ar
e
m
u
ltip
lied
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o
r
g
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e
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atio
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o
f
f
in
al
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er
e
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ce
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to
r
s
ig
n
al
(
.
∗
)
to
VSC
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MF
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it is
d
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(
8
)
.
.
∗
=
.
∗
×
.
.
∗
=
.
∗
×
.
.
∗
=
.
∗
×
.
(
8
)
Fin
ally
,
th
e
g
en
er
ated
r
ef
er
e
n
ce
v
o
ltag
e
v
ec
to
r
s
ig
n
al
is
f
o
r
war
d
ed
to
s
in
u
s
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id
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u
lti
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ca
r
r
ier
p
u
ls
e
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wid
th
m
o
d
u
latio
n
(
SMC
-
PW
M)
with
ce
r
tai
n
tr
ian
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lar
m
u
lti
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r
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ier
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ig
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als
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ce
th
e
f
ea
s
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le
s
witch
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g
s
tates
to
VS
C
o
f
MF
-
DVR
d
ev
ice
f
o
r
b
o
th
D
G
o
p
er
atio
n
s
an
d
all
PQ
en
h
an
ce
m
en
t
m
o
d
es.
T
h
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.
15
,
No
.
3
,
Sep
tem
b
er
20
26
:
1
0
2
3
-
1
0
3
5
1028
p
u
ls
atio
n
in
d
e
x
o
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t
h
e
VSC
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f
MF
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to
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atica
lly
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et
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u
r
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o
m
p
en
s
atio
n
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as
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o
n
th
e
r
ef
e
r
en
ce
v
o
ltag
e
g
e
n
er
ated
b
y
t
h
e
p
r
o
p
o
s
ed
MV
VR
co
n
tr
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l
s
ch
em
e,
an
d
th
e
s
witch
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g
o
r
ca
r
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ier
f
r
eq
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en
cy
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s
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ted
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o
d
d
m
u
ltip
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tili
ty
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g
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ly
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ic
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etter
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ilter
s
ize,
an
d
lo
w
r
ip
p
le
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n
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t.
T
h
e
f
ea
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le
s
witch
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g
s
tates
h
elp
to
o
p
er
at
e
th
e
VSC
o
f
MF
-
DVR
as
d
ir
ec
t
v
o
ltag
e
in
jectio
n
,
wh
ich
r
esto
r
es
th
e
u
tili
ty
-
g
r
id
s
p
ec
if
icatio
n
s
in
th
e
d
is
tr
ib
u
tio
n
s
y
s
tem
as
lin
ea
r
,
f
u
n
d
a
m
e
n
tal
f
r
eq
u
e
n
cy
,
an
d
s
in
u
s
o
id
al
wav
e
s
h
ap
es,
a
b
al
an
ce
d
s
y
s
tem
,
an
d
s
o
o
n
.
T
h
e
s
ch
em
atic
m
o
d
el
d
ia
g
r
am
o
f
th
e
n
ewly
p
r
o
p
o
s
ed
MV
VR
-
co
n
tr
o
lled
MF
-
DVR
d
ev
ice
f
o
r
DG
o
p
er
atio
n
s
a
n
d
PQ
en
h
an
ce
m
e
n
t
in
th
e
u
ti
lity
-
g
r
id
i
n
teg
r
ated
d
is
tr
ib
u
tio
n
s
y
s
tem
is
d
ep
icted
in
Fig
u
r
e
4
.
(
a)
(
d
)
Fig
u
r
e
3
.
So
lar
-
PV
p
er
f
o
r
m
an
ce
:
(
a)
PV
ch
ar
ac
ter
is
tic
s
an
d
(
b
)
I
V
c
h
ar
ac
ter
is
tics
Fig
u
r
e
4
.
Sch
em
atic
m
o
d
el
d
ia
g
r
am
o
f
n
ewly
p
r
o
p
o
s
ed
MV
VR
co
n
tr
o
lled
s
o
lar
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e
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✓
✓
Du
r
g
am
R
ajab
ab
u
✓
✓
✓
✓
✓
✓
✓
✓
✓
Md
Mu
jah
id
I
r
f
an
✓
✓
✓
✓
✓
✓
✓
✓
✓
✓
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
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g
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n
a
l
D
r
a
f
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E
:
W
r
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t
i
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-
R
e
v
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&
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
E
NT
Au
th
o
r
s
s
tate
n
o
co
n
f
lict o
f
in
t
er
est.
DATA AV
AI
L
AB
I
L
I
T
Y
Data
av
ailab
ilit
y
is
n
o
t a
p
p
lica
b
le
to
th
is
p
ap
er
as n
o
n
ew
d
at
a
wer
e
cr
ea
ted
o
r
an
aly
ze
d
in
t
h
is
s
tu
d
y
.
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