I
nte
rna
t
io
na
l J
o
urna
l o
f
Appl
ied P
o
wer
E
ng
i
neer
ing
(
I
J
AP
E
)
Vo
l.
15
,
No
.
3
,
Sep
tem
b
er
20
26
,
p
p
.
1
1
1
7
~
1
1
3
1
I
SS
N:
2252
-
8
7
9
2
,
DOI
:
1
0
.
1
1
5
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1
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.
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1
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i
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1
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1
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1
1
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1
1117
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//
ija
p
e.
ia
esco
r
e.
co
m/
Nea
r
-
z
ero
NDZ is
la
nding
det
ec
tion
for multi
-
so
urce
DG
s v
ia
hy
brid AN
FIS an
d ada
ptive fu
zzy
cla
ss
ificatio
n
M
a
da
m
a
neri
Ra
m
y
a
,
T
ha
ng
ella
m
ud
i
Dev
a
ra
j
u
D
e
p
a
r
t
me
n
t
o
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El
e
c
t
r
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c
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l
a
n
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El
e
c
t
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c
s
En
g
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e
r
i
n
g
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M
o
h
a
n
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a
b
u
U
n
i
v
e
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si
t
y
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Ti
r
u
p
a
t
i
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I
n
d
i
a
Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
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y:
R
ec
eiv
ed
Au
g
2
3
,
2
0
2
5
R
ev
is
ed
Ap
r
2
3
,
2
0
2
6
Acc
ep
ted
J
u
n
9
,
2
0
2
6
In
c
re
a
se
d
p
e
n
e
tratio
n
o
f
d
istri
b
u
t
e
d
g
e
n
e
ra
ti
o
n
(DG
)
in
c
re
a
se
s
th
e
li
k
e
li
h
o
o
d
o
f
in
a
d
v
e
rten
t
isla
n
d
i
n
g
,
in
w
h
ich
trad
it
i
o
n
a
l
a
c
ti
v
e
/p
a
ss
iv
e
a
p
p
r
o
a
c
h
e
s
a
re
p
lag
u
e
d
with
larg
e
n
o
n
-
d
e
tec
ti
o
n
z
o
n
e
s
(ND
Z)
a
n
d
p
o
we
r
-
q
u
a
li
ty
t
ra
d
e
-
o
ffs.
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is
a
rti
c
le
in
tr
o
d
u
c
e
s
a
h
y
b
rid
is
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d
i
n
g
d
e
tec
to
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th
a
t
c
o
m
b
in
e
s
a
n
a
d
a
p
ti
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e
n
e
u
ro
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f
u
z
z
y
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fe
re
n
c
e
sy
ste
m
(
AN
F
IS
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a
n
d
a
n
a
d
a
p
ti
v
e
fu
z
z
y
c
las
sifier,
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o
n
c
u
rre
n
tl
y
b
e
n
e
fit
i
n
g
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ro
m
a
c
t
iv
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fre
q
u
e
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c
y
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rift
a
n
d
ra
te
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of
-
c
h
a
n
g
e
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of
-
fre
q
u
e
n
c
y
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C
o
F
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w
h
il
e
c
o
n
su
m
in
g
m
u
lt
i
-
sig
n
a
l
fe
a
tu
re
s
—
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S
/T
HD
o
f
v
o
lt
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g
e
a
n
d
c
u
rre
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t,
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q
u
e
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y
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a
n
d
a
c
ti
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e
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c
ti
v
e
p
o
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r
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n
se
d
a
t
th
e
P
CC.
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is
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h
it
e
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t
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re
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li
m
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a
tes
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x
e
d
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th
re
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o
l
d
b
rit
t
len
e
ss
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n
d
re
d
u
c
e
s
th
e
ND
Z
to
z
e
ro
with
o
u
t
c
o
m
p
r
o
m
isin
g
p
o
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r
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u
a
li
t
y
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n
o
v
a
ti
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e
a
sp
e
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ts
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re
i)
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sta
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k
e
d
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l
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ti
m
e
sa
m
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li
n
g
a
p
p
r
o
a
c
h
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=
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m
s)
th
a
t
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p
p
li
e
s
p
e
r
-
sig
n
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l
AN
F
IS
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o
d
u
les
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n
d
a
m
a
in
d
e
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i
sio
n
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F
IS
,
ii
)
su
b
trac
ti
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e
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lu
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terin
g
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o
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ra
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z
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les
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i)
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ti
o
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o
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a
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it
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o
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to
r
w
h
e
n
q
u
e
ry
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g
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o
u
b
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l
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a
m
p
les
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ATLAB/S
imu
li
n
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e
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e
rime
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ta
ti
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o
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se
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e
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e
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g
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u
lt
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rc
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V
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in
t
e
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e
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icro
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rid
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c
l
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d
i
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o
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a
tch
e
d
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e
m
o
n
stra
tes
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st,
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o
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u
st
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p
s
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isc
o
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ti
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EE
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-
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7
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g
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e
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n
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e
s;
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e
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tu
re
a
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h
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e
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m
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imu
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l
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e
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ti
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e
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o
f
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0
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n
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re
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a
tch
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Co
m
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ra
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su
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in
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ti
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ti
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e
p
o
we
r.
T
h
ro
u
g
h
th
e
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ro
v
isio
n
o
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q
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ick
e
r,
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o
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a
li
ty
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c
o
n
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n
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g
islan
d
i
n
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d
e
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isio
n
s
with
n
e
a
r
-
z
e
ro
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Z,
th
e
tec
h
n
iq
u
e
ra
ise
s
o
p
e
ra
to
r
sa
fe
ty
a
n
d
sy
ste
m
sta
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il
it
y
,
su
p
p
o
rti
n
g
in
d
irec
tl
y
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ig
h
e
r
re
n
e
wa
b
le
h
o
stin
g
c
a
p
a
c
it
y
a
n
d
m
o
re
ro
b
u
st,
su
sta
in
a
b
le
d
i
strib
u
ti
o
n
n
e
two
rk
s.
K
ey
w
o
r
d
s
:
ANFI
S
–
f
u
zz
y
h
y
b
r
id
class
if
ier
I
s
lan
d
in
g
d
etec
tio
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Near
-
ze
r
o
n
o
n
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d
etec
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n
e
Po
wer
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q
u
ality
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p
r
o
b
in
g
PV
-
in
ter
f
ac
ed
m
icr
o
g
r
id
(
m
u
lt
i
-
s
o
u
r
ce
DG)
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Ma
d
am
an
er
i Ram
y
a
Dep
ar
tm
en
t o
f
E
lectr
ical
an
d
E
lectr
o
n
ics E
n
g
in
ee
r
i
n
g
,
M
o
h
an
B
ab
u
Un
iv
er
s
ity
T
ir
u
p
ati,
I
n
d
ia
E
m
ail:
m
u
llak
u
r
ian
u
s
h
a@
g
m
ail.
co
m
1.
I
NT
RO
D
UCT
I
O
N
T
h
e
in
cr
ea
s
in
g
p
en
etr
atio
n
o
f
d
is
tr
ib
u
ted
g
en
e
r
atio
n
(
DG)
u
n
its
s
u
ch
as
p
h
o
to
v
o
ltaic
(
PV)
s
y
s
tem
s
in
to
m
ed
iu
m
-
an
d
lo
w
-
v
o
ltag
e
n
etwo
r
k
s
h
as
s
ig
n
if
ican
tly
im
p
r
o
v
ed
e
n
er
g
y
ef
f
icien
c
y
,
r
eliab
ilit
y
,
an
d
en
v
ir
o
n
m
en
tal
s
u
s
tain
ab
ilit
y
o
f
m
o
d
e
r
n
p
o
wer
s
y
s
tem
s
[
1
]
–
[
3
]
.
As
DG
p
e
n
etr
atio
n
g
r
o
ws,
d
is
tr
ib
u
tio
n
n
e
t
w
o
r
k
s
e
v
o
l
v
e
t
o
w
a
r
d
a
c
t
i
v
e
m
i
c
r
o
g
r
i
d
s
c
a
p
a
b
l
e
o
f
o
p
e
r
a
t
i
n
g
i
n
b
o
t
h
g
r
i
d
-
c
o
n
n
e
c
t
e
d
a
n
d
i
s
l
a
n
d
e
d
m
o
d
e
s
[
4
]
.
W
h
ile
th
is
f
lex
ib
ilit
y
is
d
esira
b
le,
it
als
o
in
tr
o
d
u
ce
s
n
ew
p
r
o
tectio
n
ch
allen
g
es,
p
ar
ticu
lar
ly
th
e
r
eliab
le
d
etec
tio
n
o
f
u
n
in
ten
tio
n
al
is
lan
d
in
g
e
v
en
ts
,
in
wh
ich
a
s
ec
tio
n
o
f
th
e
g
r
i
d
c
o
n
tin
u
es
to
b
e
e
n
er
g
is
ed
b
y
l
o
c
al
DGs
af
ter
lo
s
in
g
co
n
n
ec
tio
n
with
th
e
m
ain
u
tili
ty
[
5
]
.
I
n
te
r
n
atio
n
al
s
tan
d
ar
d
s
s
u
ch
as
I
E
E
E
1
5
4
7
an
d
I
E
C
6
2
1
1
6
r
eq
u
ir
e
DG
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
1
1
7
-
1
1
3
1
1118
u
n
its
to
d
etec
t
is
lan
d
in
g
an
d
c
ea
s
e
en
er
g
is
atio
n
with
in
a
s
p
e
cif
ied
tim
e
win
d
o
w
wh
ile
m
ai
n
tain
in
g
ac
ce
p
ta
b
le
p
o
wer
q
u
ality
in
n
o
r
m
al
o
p
er
a
tio
n
[
6
]
,
[
7
]
.
C
o
n
s
eq
u
en
tly
,
is
lan
d
in
g
d
etec
tio
n
h
as
b
ec
o
m
e
a
cr
itical
s
af
ety
a
n
d
r
eliab
ilit
y
co
n
ce
r
n
in
m
u
lti
-
s
o
u
r
ce
DG
en
v
ir
o
n
m
en
ts
.
A
wid
e
r
an
g
e
o
f
is
lan
d
i
n
g
d
e
tectio
n
m
eth
o
d
s
(
I
DM
s
)
h
as
b
ee
n
r
e
p
o
r
ted
in
th
e
liter
atu
r
e
,
ty
p
ically
g
r
o
u
p
ed
in
to
p
ass
iv
e,
ac
tiv
e,
co
m
m
u
n
icatio
n
-
b
ased
,
an
d
h
y
b
r
id
ca
teg
o
r
ies
[
8
]
.
Pas
s
iv
e
m
eth
o
d
s
,
s
u
ch
as
o
v
er
/u
n
d
er
v
o
ltag
e,
o
v
er
/u
n
d
er
f
r
eq
u
en
cy
,
r
ate
-
of
-
ch
a
n
g
e
-
of
-
f
r
e
q
u
en
c
y
(
R
o
C
o
F
)
,
r
ate
-
of
-
ch
an
g
e
-
of
-
v
o
ltag
e
(
R
OC
OV)
,
an
d
v
o
ltag
e
p
h
ase
-
ju
m
p
tec
h
n
iq
u
es,
r
ely
o
n
m
o
n
ito
r
in
g
lo
ca
l
elec
tr
ical
q
u
an
ti
ties
at
th
e
p
o
i
n
t
o
f
co
m
m
o
n
c
o
u
p
lin
g
(
PC
C
)
[
9
]
,
[
1
0
]
.
T
h
ese
ap
p
r
o
ac
h
es
ar
e
s
im
p
le
an
d
in
e
x
p
en
s
iv
e
b
u
t
s
u
f
f
er
f
r
o
m
lar
g
e
n
o
n
-
d
etec
tio
n
zo
n
es
(
NDZ
s
)
,
esp
ec
ially
u
n
d
er
p
o
wer
-
m
atch
e
d
co
n
d
itio
n
s
wh
er
e
lo
ad
an
d
DG
g
en
er
atio
n
ar
e
n
ea
r
ly
eq
u
al
[
1
1
]
.
Activ
e
m
eth
o
d
s
in
ten
tio
n
ally
p
er
t
u
r
b
th
e
DG
o
u
tp
u
t
—
th
r
o
u
g
h
f
r
eq
u
en
cy
d
r
if
t,
r
ea
ctiv
e
p
o
wer
v
ar
iatio
n
,
o
r
p
h
ase
d
is
tu
r
b
a
n
c
es
—
to
f
o
r
ce
o
b
s
er
v
ab
le
c
h
an
g
es
in
PC
C
v
ar
iab
les
[
1
2
]
,
[
1
3
]
.
Alth
o
u
g
h
ac
tiv
e
s
ch
em
es
ca
n
s
ig
n
if
ican
tly
r
ed
u
ce
NDZ
,
th
ey
m
ay
d
eg
r
a
d
e
p
o
wer
q
u
ality
a
n
d
in
ter
ac
t
ad
v
er
s
ely
with
o
th
er
co
n
tr
o
l
f
u
n
ctio
n
s
,
esp
ec
ially
w
h
en
m
u
ltip
le
DGs
ar
e
p
r
esen
t
[
1
4
]
.
C
o
m
m
u
n
icatio
n
-
b
ased
an
d
r
em
o
te
m
eth
o
d
s
,
in
clu
d
in
g
tr
an
s
f
er
-
t
r
ip
s
ch
em
e
s
an
d
s
y
n
ch
r
o
p
h
aso
r
-
b
ased
s
o
l
u
tio
n
s
,
o
f
f
er
h
ig
h
r
eliab
ilit
y
b
u
t r
eq
u
ir
e
d
ed
icate
d
in
f
r
astru
ctu
r
e,
h
ig
h
e
r
co
s
t,
an
d
co
m
p
lex
i
n
teg
r
atio
n
[
1
5
]
.
T
o
o
v
er
co
m
e
th
e
lim
itatio
n
s
o
f
p
u
r
el
y
p
ass
iv
e
o
r
ac
ti
v
e
ap
p
r
o
ac
h
es,
h
y
b
r
id
I
DM
s
h
av
e
b
ee
n
p
r
o
p
o
s
ed
th
at
co
m
b
in
e
m
u
ltip
le
in
d
icato
r
s
o
r
f
u
s
e
p
ass
iv
e
an
d
ac
ti
v
e
f
ea
tu
r
es
u
s
in
g
in
tellig
en
t
alg
o
r
ith
m
s
.
Fu
zz
y
lo
g
i
c
an
d
n
e
u
r
al
n
etwo
r
k
s
h
av
e
b
ee
n
u
s
ed
to
p
r
o
ce
s
s
f
ea
tu
r
es
s
u
c
h
as
v
o
ltag
e,
f
r
eq
u
e
n
cy
,
t
o
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
(
T
HD)
,
an
d
R
OC
OF
to
r
ed
u
c
e
NDZ
wh
ile
lim
itin
g
in
jecte
d
d
is
tu
r
b
an
ce
s
[
1
6
]
–
[
1
8
]
.
A
d
ap
tiv
e
n
eu
r
o
-
f
u
zz
y
in
f
er
en
ce
s
y
s
tem
s
(
ANFI
S)
an
d
o
th
er
s
o
f
t
-
co
m
p
u
tin
g
tech
n
iq
u
es
h
av
e
also
b
ee
n
ap
p
lied
t
o
ca
p
tu
r
e
n
o
n
lin
ea
r
r
elatio
n
s
h
ip
s
b
etwe
en
m
ea
s
u
r
ed
s
ig
n
als
an
d
o
p
er
atin
g
s
tates
[
1
9
]
,
[
2
0
]
.
Mo
r
e
r
ec
en
tly
,
a
d
v
an
ce
d
in
tellig
en
t
p
r
o
tectio
n
s
tr
ateg
ies,
in
clu
d
in
g
d
ee
p
-
lear
n
in
g
-
b
ased
class
if
i
er
s
an
d
o
p
tim
is
ed
n
etwo
r
k
ar
c
h
itectu
r
es,
h
av
e
b
ee
n
d
ev
elo
p
e
d
f
o
r
f
ast
an
d
r
o
b
u
s
t
f
au
lt
d
etec
tio
n
in
m
esh
ed
d
ir
ec
t
cu
r
r
en
t
(
DC
)
an
d
h
ig
h
-
v
o
l
tag
e
d
ir
ec
t
cu
r
r
en
t
(
HVDC
)
g
r
id
s
[
2
1
]
–
[
2
4
]
.
T
h
e
s
e
wo
r
k
s
d
em
o
n
s
tr
ate
th
at
in
tellig
en
t
p
r
o
tectio
n
ca
n
o
f
f
er
d
e
n
o
is
in
g
,
r
o
b
u
s
tn
ess
to
m
ea
s
u
r
em
en
t
n
o
is
e,
a
n
d
im
p
r
o
v
e
d
d
is
cr
im
in
atio
n
ca
p
a
b
ilit
y
,
b
u
t
m
an
y
m
eth
o
d
s
ar
e
tailo
r
ed
to
tr
an
s
m
is
s
io
n
-
lev
el
DC
s
y
s
tem
s
,
r
ely
o
n
lar
g
e
tr
ain
i
n
g
d
atas
ets,
o
r
im
p
o
s
e
h
ig
h
c
o
m
p
u
tatio
n
al
b
u
r
d
en
s
u
n
s
u
itab
le
f
o
r
em
b
ed
d
e
d
DG
co
n
tr
o
ller
s
.
Desp
ite
th
ese
ad
v
an
ce
s
,
s
ev
er
al
k
ey
ch
allen
g
es
r
em
ain
f
o
r
i
s
lan
d
in
g
d
etec
tio
n
in
m
u
lti
-
s
o
u
r
ce
,
PV
-
in
ter
f
ac
ed
m
icr
o
g
r
id
s
.
First,
c
o
n
v
en
tio
n
al
p
ass
iv
e
a
n
d
ac
tiv
e
s
ch
em
es
s
till
ex
h
ib
it
s
izab
le
NDZ
s
u
n
d
er
p
o
wer
-
m
atch
ed
o
r
n
ea
r
-
m
atch
e
d
co
n
d
itio
n
s
,
wh
er
e
ch
an
g
es
in
PC
C
v
o
ltag
e,
f
r
eq
u
e
n
cy
,
a
n
d
p
o
wer
f
lo
ws
ar
e
s
m
all
an
d
ea
s
ily
m
ask
e
d
b
y
n
o
r
m
al
o
p
er
atin
g
v
ar
iatio
n
s
[
1
1
]
–
[
1
4
]
.
Seco
n
d
,
m
an
y
in
tellig
en
t
an
d
f
u
zz
y
-
lo
g
ic
-
b
ased
s
ch
em
es
em
p
lo
y
f
ix
e
d
th
r
esh
o
ld
s
o
r
m
an
u
ally
d
esig
n
ed
r
u
le
b
ases
,
wh
ich
m
ay
n
o
t
g
e
n
er
alize
well
ac
r
o
s
s
d
if
f
er
en
t
l
o
ad
in
g
co
n
d
itio
n
s
,
DG
m
ix
es,
an
d
n
etwo
r
k
co
n
f
i
g
u
r
atio
n
s
[
1
6
]
,
[
1
9
]
.
T
h
ir
d
,
s
o
m
e
ex
is
tin
g
h
y
b
r
id
m
eth
o
d
s
r
ely
h
ea
v
ily
o
n
a
s
in
g
le
ty
p
e
o
f
f
ea
tu
r
e
(
e.
g
.
,
R
OC
O
F
o
r
v
o
ltag
e
T
HD)
,
m
ak
in
g
th
e
m
s
en
s
itiv
e
to
n
o
is
e
an
d
m
ea
s
u
r
em
e
n
t e
r
r
o
r
s
,
p
a
r
ticu
l
ar
ly
in
wea
k
g
r
i
d
s
.
I
n
a
d
d
iti
o
n
,
f
ew
w
o
r
k
s
ex
p
licitly
q
u
a
n
tify
th
e
r
elatio
n
s
h
ip
b
etwe
en
s
am
p
lin
g
in
ter
v
al,
s
tack
ed
d
ata
win
d
o
w,
an
d
ac
h
i
ev
ab
le
d
etec
tio
n
tim
e,
o
r
p
r
o
v
id
e
d
etailed
ANFI
S
an
d
clu
s
ter
in
g
p
ar
am
eter
s
n
ec
e
s
s
ar
y
f
o
r
r
ep
r
o
d
u
cib
ilit
y
.
Fin
ally
,
wh
ile
d
ee
p
-
lear
n
in
g
-
b
ased
p
r
o
tectio
n
m
eth
o
d
s
s
h
o
w
p
r
o
m
is
e
[
2
1
]
–
[
2
4
]
,
th
e
y
o
f
te
n
d
em
an
d
s
ig
n
if
ican
t
co
m
p
u
tatio
n
al
r
eso
u
r
ce
s
an
d
co
m
p
le
x
tr
ain
i
n
g
p
r
o
ce
s
s
es,
wh
ich
m
ay
n
o
t
b
e
p
r
ac
tical
f
o
r
r
ea
l
-
tim
e
DG
i
n
v
er
ter
s
.
T
h
ese
g
ap
s
m
o
tiv
ate
th
e
d
ev
el
o
p
m
en
t
o
f
a
h
y
b
r
id
,
c
o
m
p
u
tatio
n
ally
ef
f
icien
t,
an
d
r
ep
r
o
d
u
cib
le
I
DM
t
h
a
t
ac
h
iev
es
n
ea
r
-
ze
r
o
NDZ
with
o
u
t
c
o
m
p
r
o
m
is
in
g
p
o
wer
q
u
ality
[
2
5
]
,
[
2
6
]
.
2.
P
RO
P
O
SE
D
M
E
T
H
OD
I
n
th
is
p
a
p
er
,
we
p
r
o
p
o
s
e
a
h
y
b
r
id
ANFI
S
an
d
a
d
ap
tiv
e
f
u
zz
y
class
if
icatio
n
s
ch
em
e
f
o
r
n
ea
r
-
ze
r
o
NDZ
is
lan
d
in
g
d
etec
tio
n
in
m
u
lti
-
s
o
u
r
ce
DG
s
y
s
tem
s
in
ter
f
ac
ed
with
a
PV
p
lan
t.
T
h
e
m
eth
o
d
co
m
b
in
es
ac
tiv
e
an
d
p
ass
iv
e
s
ig
n
atu
r
es
b
y
f
u
s
in
g
PC
C
v
o
ltag
e
an
d
cu
r
r
e
n
t
R
MS
v
alu
es,
v
o
ltag
e
an
d
cu
r
r
en
t
T
HD,
ac
tiv
e/r
ea
ctiv
e
p
o
wer
m
ea
s
u
r
em
en
ts
,
an
d
lo
w
-
m
ag
n
itu
d
e
r
ea
ctiv
e
-
cu
r
r
en
t
p
e
r
tu
r
b
atio
n
s
in
to
a
s
tack
ed
f
ea
tu
r
e
v
ec
to
r
p
r
o
ce
s
s
ed
b
y
a
m
u
lti
-
s
tag
e
ANFI
S
s
tr
u
ctu
r
e.
A
d
etailed
d
q
-
f
r
am
e
m
o
d
el
o
f
th
e
PV
-
in
ter
f
ac
ed
D
G,
in
clu
d
in
g
a
g
r
i
d
-
s
y
n
ch
r
o
n
is
ed
v
o
ltag
e
s
o
u
r
ce
c
o
n
v
er
ter
(
VSC
)
,
is
u
s
ed
to
d
er
iv
e
ex
p
licit r
elatio
n
s
h
ip
s
b
etwe
en
d
q
c
u
r
r
en
ts
a
n
d
ac
tiv
e/r
ea
ctiv
e
p
o
wer
f
lo
ws,
e
n
ab
lin
g
ac
c
u
r
ate
co
n
tr
o
l
o
f
a
s
m
all
r
ea
ctiv
e
-
p
o
wer
p
r
o
b
e
th
a
t
m
in
im
ally
af
f
ec
ts
p
o
wer
q
u
ality
.
NDZ
b
o
u
n
d
a
r
i
es
ar
e
q
u
an
titativ
ely
d
ef
in
e
d
in
ter
m
s
o
f
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
m
is
m
atch
es
an
d
f
r
eq
u
e
n
cy
co
n
s
tr
ain
ts
,
a
n
d
th
ese
a
n
aly
tical
r
esu
lts
ar
e
in
teg
r
ated
i
n
to
t
h
e
class
if
ier
d
esig
n
.
Su
b
t
r
ac
tiv
e
clu
s
ter
in
g
is
em
p
lo
y
ed
to
au
to
m
atica
lly
g
en
er
ate
f
u
zz
y
r
u
les
f
r
o
m
d
ata,
r
ed
u
cin
g
m
a
n
u
al
tu
n
in
g
ef
f
o
r
t
an
d
im
p
r
o
v
in
g
r
ep
r
o
d
u
ci
b
ilit
y
.
T
h
e
p
r
o
p
o
s
ed
s
ch
em
e
is
ev
al
u
ated
o
n
s
ev
en
r
ep
r
esen
tativ
e
o
p
er
atin
g
ca
s
es,
in
clu
d
in
g
b
o
t
h
clea
r
m
is
m
atc
h
an
d
p
o
wer
-
m
atc
h
ed
s
ce
n
ar
i
o
s
,
an
d
co
m
p
ar
ed
co
n
ce
p
tu
all
y
with
c
o
n
v
e
n
tio
n
al
R
OC
OF/
R
OC
O
V
an
d
f
u
zz
y
-
b
ased
m
eth
o
d
s
.
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
N
ea
r
-
z
ero
N
DZ isl
a
n
d
in
g
d
etec
tio
n
fo
r
mu
lti
-
s
o
u
r
ce
DGs v
ia
h
yb
r
id
A
N
F
I
S
…
(
Ma
d
a
ma
n
e
r
i R
a
mya
)
1119
3.
M
E
T
H
O
D
T
h
e
p
r
o
p
o
s
ed
n
ea
r
-
ze
r
o
NDZ
is
lan
d
in
g
d
etec
tio
n
s
ch
em
e
is
im
p
lem
en
ted
as a
h
y
b
r
id
ANFI
S with
an
ad
ap
tiv
e
f
u
zz
y
class
if
ier
o
p
e
r
atin
g
o
n
a
m
u
lti
-
s
o
u
r
ce
PV
-
in
ter
f
ac
ed
DG
s
y
s
tem
.
T
h
e
o
v
er
all
ar
ch
itectu
r
e
ex
p
lo
its
b
o
th
ac
tiv
e
an
d
p
ass
iv
e
s
ig
n
atu
r
es:
an
ac
tiv
e
f
r
eq
u
en
cy
-
d
r
if
t
m
ec
h
a
n
is
m
co
m
b
in
ed
with
R
o
C
o
F
p
r
o
b
in
g
,
an
d
a
r
ich
p
ass
iv
e
f
e
atu
r
e
s
et
co
m
p
r
is
in
g
R
MS
an
d
T
HD
o
f
v
o
ltag
e
an
d
c
u
r
r
en
t
,
s
y
s
tem
f
r
e
q
u
en
c
y
,
an
d
ac
tiv
e/r
ea
ctiv
e
p
o
wer
m
ea
s
u
r
ed
at
th
e
PC
C
.
T
h
ese
s
ig
n
als
ar
e
ac
q
u
ir
e
d
v
ia
r
elay
-
b
ased
s
en
s
in
g
at
th
e
PC
C
an
d
p
r
e
-
p
r
o
ce
s
s
ed
to
f
ee
d
a
h
ier
ar
ch
ical
ANFI
S
s
tr
u
ctu
r
e
t
h
at
r
eso
lv
es
is
lan
d
in
g
an
d
n
o
n
-
is
lan
d
in
g
ev
e
n
ts
,
esp
ec
ially
in
th
e
NDZ
,
wh
ile
m
ain
tain
in
g
p
o
wer
q
u
ality
b
y
m
i
n
im
is
in
g
p
er
tu
r
b
atio
n
s
in
r
ea
l
an
d
r
ea
ctiv
e
p
o
we
r
.
T
h
e
h
y
b
r
id
ANFI
S
–
f
u
zz
y
cla
s
s
if
ier
u
s
es
an
em
b
ed
d
e
d
ar
ti
f
icial
n
eu
r
al
n
etwo
r
k
(
ANN)
to
lear
n
co
m
p
le
x
n
o
n
lin
ea
r
m
a
p
p
in
g
s
an
d
f
u
z
zy
lo
g
ic
to
g
en
er
alis
e
in
p
u
t
p
atter
n
s
an
d
im
p
lem
en
t
lin
g
u
is
tic
r
u
le
-
b
ased
class
if
icatio
n
,
th
er
eb
y
co
m
b
in
in
g
d
ata
-
d
r
iv
en
lear
n
in
g
with
i
n
ter
p
r
etab
le
d
ec
is
io
n
lo
g
ic.
3
.
1
.
M
o
dellin
g
o
f
dis
t
ribute
d g
ener
a
t
io
n sy
s
t
em
A
m
u
lti
-
s
o
u
r
ce
DG
s
y
s
tem
is
c
o
n
s
id
er
ed
in
th
is
r
esear
ch
,
co
u
p
led
with
a
PV
s
y
s
tem
.
Fo
u
r
1
0
0
k
W
P
V
g
en
er
atio
n
u
n
its
ar
e
m
o
d
elled
,
s
o
th
at
th
e
to
tal
PV
g
en
er
atio
n
ca
p
ac
ity
r
ea
ch
es
4
0
0
k
W
.
T
h
e
eq
u
iv
alen
t
cir
cu
it
o
f
th
e
PV
s
y
s
tem
is
s
h
o
wn
i
n
Fig
u
r
e
1
(
a)
,
an
d
th
e
s
y
s
tem
is
m
o
d
elled
as
a
s
in
g
le
-
d
io
d
e
PV
ce
ll
wh
o
s
e
cu
r
r
en
t
–
v
o
ltag
e
ch
a
r
ac
ter
is
tics
d
ep
en
d
o
n
i
r
r
ad
iatio
n
an
d
tem
p
er
at
u
r
e
[
2
3
]
.
T
h
e
o
u
tp
u
t
c
u
r
r
e
n
t
o
f
th
e
PV
ce
ll
as
a
f
u
n
ctio
n
o
f
ter
m
i
n
al
v
o
ltag
e
is
ex
p
r
ess
ed
in
(
1
)
.
=
ph
−
[
e
xp
(
(
+
)
)
−
1
]
−
+
ℎ
(
1
)
W
h
er
e
ph
is
th
e
p
h
o
to
cu
r
r
en
t
(
s
h
o
r
t
-
cir
cu
it
c
u
r
r
e
n
t
d
u
e
to
s
u
n
lig
h
t)
,
is
th
e
d
io
d
e
s
atu
r
atio
n
cu
r
r
en
t,
an
d
ℎ
ar
e
th
e
s
er
ies
an
d
s
h
u
n
t
r
esis
t
an
ce
s
,
r
esp
ec
tiv
ely
,
is
th
e
v
o
lt
ag
e
ac
r
o
s
s
th
e
lo
a
d
,
is
th
e
lo
a
d
cu
r
r
e
n
t,
is
th
e
elec
tr
o
n
ch
ar
g
e
(
1
.
6
×
10
−
19
C
)
,
is
B
o
ltz
m
an
n
’
s
co
n
s
tan
t
(
1
.
38
×
10
−
23
J
/K
)
,
is
th
e
ce
ll te
m
p
er
atu
r
e,
an
d
is
th
e
d
io
d
e
id
ea
lity
f
ac
t
o
r
.
T
h
e
d
io
d
e
cu
r
r
en
t c
o
m
p
o
n
en
t
its
elf
o
b
ey
s
th
e
Sh
o
c
k
ley
e
q
u
a
tio
n
.
I
t is r
e
p
r
esen
ted
i
n
(
2
)
an
d
(
3
)
[
2
4
]
.
=
[
e
xp
(
)
−
1
]
(
2
)
pv
=
pv
pv
(
3
)
W
h
er
e
is
th
e
d
io
d
e
v
o
ltag
e
a
n
d
is
th
e
s
atu
r
atio
n
cu
r
r
e
n
t o
f
t
h
e
d
io
d
e
.
T
h
e
i
n
s
tan
tan
eo
u
s
p
o
wer
g
en
e
r
ate
d
b
y
th
e
PV
ar
r
ay
is
wr
itten
as
wh
er
e
pv
is
th
e
PV
p
o
wer
,
is
th
e
co
n
v
e
r
ter
ef
f
icie
n
cy
,
a
n
d
pv
an
d
pv
ar
e
th
e
PV te
r
m
in
al
v
o
ltag
e
an
d
cu
r
r
e
n
t,
r
esp
ec
tiv
ely
.
T
o
ex
tr
a
ct
m
ax
i
m
u
m
p
o
wer
f
r
o
m
t
h
e
PV
s
y
s
tem
u
n
d
e
r
u
n
i
f
o
r
m
ir
r
ad
ian
ce
,
a
p
e
r
tu
r
b
an
d
o
b
s
er
v
e
(
P&
O)
MPPT
tech
n
iq
u
e
is
em
p
lo
y
ed
.
T
h
e
o
p
e
r
atin
g
v
o
ltag
e
o
f
th
e
PV
ar
r
ay
is
p
er
io
d
ically
p
er
tu
r
b
e
d
;
if
th
e
ex
tr
ac
ted
p
o
wer
pv
in
cr
ea
s
es
,
th
e
p
er
tu
r
b
atio
n
d
ir
ec
tio
n
is
m
ai
n
tain
ed
,
w
h
er
ea
s
if
pv
d
ec
r
ea
s
es,
th
e
d
ir
ec
tio
n
is
r
ev
er
s
ed
[
2
6
]
.
T
h
r
o
u
g
h
th
is
iter
ativ
e
p
r
o
ce
s
s
,
th
e
o
p
er
atin
g
p
o
in
t
co
n
v
er
g
es
to
war
d
th
e
m
ax
im
u
m
p
o
wer
p
o
in
t (
MPP)
,
an
d
th
e
r
esu
ltin
g
r
ef
er
en
ce
is
en
f
o
r
ce
d
b
y
th
e
d
o
wn
s
tr
ea
m
VSC
.
3
.
2
.
Vo
l
t
a
g
e
s
o
urce
co
nv
er
t
e
r
(
VSC)
I
n
th
e
p
r
o
p
o
s
ed
g
r
i
d
-
s
y
n
ch
r
o
n
i
s
ed
VSC
,
r
eg
u
latio
n
is
s
tr
u
ctu
r
ed
as
two
ca
s
ca
d
ed
lo
o
p
s
wo
r
k
in
g
in
th
e
s
y
n
ch
r
o
n
o
u
s
d
q
f
r
am
e
s
y
n
c
h
r
o
n
is
ed
to
th
e
PC
C
v
o
ltag
e
u
s
in
g
a
PLL
.
T
h
e
o
u
ter
(
s
lo
w)
lo
o
p
co
n
tr
o
ls
th
e
DC
-
lin
k
v
o
ltag
e
b
y
co
m
p
ar
in
g
th
e
s
en
s
ed
to
th
e
r
ef
e
r
en
ce
,
r
e
f
=
600
V
an
d
p
r
o
ce
s
s
in
g
th
e
er
r
o
r
t
h
r
o
u
g
h
an
an
ti
-
win
d
u
p
PI
c
o
n
tr
o
ller
wh
o
s
e
o
u
tp
u
t
is
th
e
ac
tiv
e
c
u
r
r
e
n
t
r
ef
er
e
n
ce
,
r
e
f
.
Fo
r
u
n
ity
p
o
wer
-
f
ac
to
r
(
UPF)
o
p
er
atio
n
d
u
r
i
n
g
n
o
r
m
al
c
o
n
d
itio
n
s
,
th
e
r
ea
ctiv
e
c
u
r
r
en
t
r
ef
er
en
ce
is
s
et
to
,
r
e
f
=
0
,
b
u
t
it
ca
n
b
e
b
iased
if
v
o
ltag
e
s
u
p
p
o
r
t
is
n
ee
d
ed
.
T
h
e
in
n
er
(
f
ast)
lo
o
p
e
m
p
lo
y
s
d
e
co
u
p
led
PI
c
o
n
tr
o
ller
s
p
er
ax
i
s
with
f
ee
d
-
f
o
r
war
d
o
f
th
e
g
r
id
v
o
ltag
e
an
d
cr
o
s
s
-
co
u
p
lin
g
co
m
p
en
s
atio
n
ter
m
s
±
,
wh
ich
elim
in
ates
in
d
u
ctiv
e
d
y
n
am
ics
an
d
en
h
an
ce
s
b
an
d
wid
th
.
T
h
ese
co
n
tr
o
ller
s
g
en
er
ate
co
m
m
a
n
d
ed
c
o
n
v
e
r
ter
v
o
ltag
es
an
d
,
wh
ich
a
r
e
tr
an
s
f
o
r
m
ed
b
ac
k
in
to
th
e
th
r
e
e
-
p
h
ase
s
tatio
n
ar
y
f
r
am
e
,
n
o
r
m
alis
ed
b
y
th
e
in
s
tan
tan
eo
u
s
DC
-
lin
k
v
o
ltag
e,
an
d
co
n
v
er
ted
to
th
r
ee
m
o
d
u
latin
g
s
ig
n
als
,
,
an
d
v
ia
PW
M
o
r
SVPW
M.
W
ith
th
e
d
-
ax
is
alig
n
ed
to
t
h
e
g
r
id
v
o
ltag
e,
th
e
in
s
tan
tan
e
o
u
s
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
s
ar
e
ex
p
r
ess
ed
in
d
q
c
o
o
r
d
i
n
ates.
T
h
ey
a
r
e
g
i
v
en
b
y
(
4
)
an
d
(
5
).
=
3
2
(
+
)
(
4
)
=
3
2
(
+
)
(
5
)
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
1
1
7
-
1
1
3
1
1120
W
h
er
e
,
an
d
,
ar
e
th
e
d
q
-
ax
is
c
o
m
p
o
n
e
n
ts
o
f
v
o
ltag
e
an
d
cu
r
r
en
t,
r
esp
ec
tiv
ely
.
W
h
en
th
e
d
-
ax
is
is
alig
n
ed
s
u
ch
th
at
th
e
g
r
id
v
o
lt
ag
e
lies
en
tire
ly
alo
n
g
th
e
d
-
ax
is
(
i.e
.
,
=
0
)
,
(
4
)
an
d
(
5
)
s
im
p
lify
to
(
6
)
a
n
d
(
7
)
s
h
o
w
th
at
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
a
r
e
d
ir
ec
tly
co
n
tr
o
lled
b
y
an
d
,
r
esp
ec
tiv
ely
,
wh
ich
allo
ws
th
e
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
to
co
n
tr
o
l
is
lan
d
in
g
b
eh
av
io
u
r
b
y
in
jectin
g
a
s
m
all
p
er
tu
r
b
atio
n
in
(
an
d
h
en
ce
in
r
ea
ctiv
e
p
o
wer
)
wh
ile
k
e
ep
in
g
p
o
wer
q
u
ality
with
in
ac
ce
p
tab
le
lim
its
.
=
3
2
(
6
)
=
−
3
2
(
7
)
3
.3
.
No
n
-
det
ec
t
io
n z
o
ne
T
h
e
NDZ
is
a
r
e
g
io
n
in
wh
ich
i
s
lan
d
in
g
d
etec
tio
n
ap
p
r
o
ac
h
es
ca
n
n
o
t
r
elia
b
ly
id
e
n
tify
is
lan
d
i
n
g
with
in
th
e
r
eq
u
ir
ed
tim
e,
p
ar
ticu
lar
ly
u
n
d
er
p
o
wer
-
m
atch
e
d
co
n
d
itio
n
s
b
etwe
en
DG
an
d
lo
ca
l
lo
ad
.
T
o
ch
ar
ac
ter
is
e
NDZ
,
th
e
p
o
wer
m
is
m
atch
o
f
th
e
DG
an
d
th
e
lo
ad
i
s
r
ep
r
es
en
ted
in
an
ac
tiv
e
–
r
ea
ctiv
e
co
o
r
d
in
ate
p
lan
e
.
T
h
e
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
m
is
m
atch
es a
r
e
d
ef
in
e
d
as
(
8
)
an
d
(
9
)
.
Δ
=
DG
−
L
o
a
d
(
8
)
Δ
=
DG
−
L
o
a
d
(
9
)
W
h
er
e
DG
an
d
DG
d
en
o
te
th
e
DG
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
s
,
a
n
d
L
oa
d
an
d
L
oa
d
d
en
o
te
t
h
e
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
s
o
f
th
e
lo
a
d
,
r
e
s
p
ec
tiv
ely
.
Su
itab
le
th
r
esh
o
ld
v
alu
es
f
o
r
th
e
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
w
er
m
is
m
atch
es
u
s
ed
to
d
ef
in
e
th
e
NDZ
b
o
u
n
d
ar
y
a
r
e
co
m
p
u
ted
as
(
1
0
)
an
d
(
1
1
)
.
Δ
th
=
DG
,
r
a
ted
(
1
0
)
Δ
th
=
DG
,
r
a
ted
(
1
1
)
W
h
er
e
an
d
ar
e
m
is
m
atch
c
o
e
f
f
icien
ts
th
at
en
c
o
d
e
allo
wa
b
le
p
er
ce
n
ta
g
e
d
e
v
iatio
n
s
ar
o
u
n
d
th
e
r
ated
DG
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
s
.
T
h
ese
th
r
esh
o
ld
s
,
to
g
eth
er
with
v
o
ltag
e
an
d
f
r
e
q
u
en
c
y
co
n
s
tr
ain
ts
at
th
e
PC
C
,
d
eter
m
in
e
th
e
NDZ
r
e
g
io
n
illu
s
tr
ated
in
Fig
u
r
e
1
(
b
)
.
T
h
e
v
o
ltag
e
an
d
f
r
eq
u
e
n
cy
v
al
u
es
ar
e
m
ea
s
u
r
e
d
at
th
e
PC
C
.
T
h
e
ac
tiv
e
p
o
wer
o
f
th
e
R
L
C
l
o
ad
ca
n
b
e
wr
itten
as
(
1
2
)
a
n
d
(
1
3
)
.
L
oa
d
=
P
C
C
2
(
1
2
)
L
oa
d
=
P
C
C
2
(
2
L
oa
d
−
1
2
L
oa
d
)
(
1
3
)
W
h
er
e
P
C
C
is
th
e
PC
C
v
o
ltag
e
m
ag
n
itu
d
e
an
d
is
th
e
lo
ad
r
esis
tan
ce
.
T
h
e
r
ea
ctiv
e
p
o
wer
o
f
th
e
lo
ad
is
ca
lcu
lated
as
wh
er
e
L
oa
d
is
th
e
l
o
ad
f
r
e
q
u
en
c
y
,
an
d
an
d
d
en
o
te
th
e
lo
ad
in
d
u
cta
n
ce
an
d
ca
p
ac
itan
ce
,
r
esp
ec
tiv
ely
.
T
h
e
m
is
m
atch
o
f
r
ea
ctiv
e
p
o
wer
f
o
r
NDZ
esti
m
atio
n
,
lin
k
ed
to
th
e
allo
wab
le
f
r
eq
u
e
n
cy
d
ev
iatio
n
Δ
a
ll
ow
,
is
th
en
ex
p
r
ess
ed
as
(
1
4
)
.
Δ
NDZ
=
∣
∂
L
oa
d
∂
∣
=
Δ
a
ll
ow
(
1
4
)
W
h
er
e
is
th
e
n
o
m
in
al
f
r
eq
u
en
cy
an
d
Δ
a
ll
ow
is
th
e
ad
m
is
s
ib
le
f
r
eq
u
en
c
y
r
a
n
g
e
ac
c
o
r
d
in
g
to
p
r
o
tectio
n
s
tan
d
ar
d
s
.
T
h
e
(
8
)
–
(
1
4
)
p
r
o
v
id
e
a
q
u
an
titativ
e
b
asis
f
o
r
d
ef
in
in
g
NDZ
b
o
u
n
d
ar
ies
a
n
d
f
o
r
d
esig
n
in
g
th
e
th
r
esh
o
ld
s
u
s
ed
in
th
e
p
r
o
p
o
s
e
d
ANFI
S
-
b
ased
class
if
ier
.
3
.
4
.
P
r
o
po
s
ed
ANF
I
S
–
a
da
ptiv
e
f
uzzy
cla
s
s
if
ier
f
o
r
is
la
nd
ing
det
ec
t
io
n
As
d
is
cu
s
s
ed
in
p
r
ev
io
u
s
s
ec
ti
o
n
s
,
th
e
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
in
ten
d
s
to
ac
cu
r
ately
d
etec
t
is
lan
d
in
g
ev
e
n
with
in
th
e
NDZ
.
T
h
e
s
ch
em
at
ic
o
f
th
e
h
y
b
r
id
m
eth
o
d
is
s
h
o
wn
in
Fig
u
r
e
1
(
c)
.
A
p
o
wer
m
eter
m
ea
s
u
r
es
th
e
r
ea
ctiv
e
p
o
wer
o
f
th
e
PV
s
y
s
te
m
PV
,
th
e
lo
ad
L
oa
d
,
an
d
t
h
e
g
r
id
Gr
i
d
at
th
e
PC
C
.
I
n
ad
d
itio
n
,
th
e
R
MS
v
alu
es
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
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wer
E
n
g
I
SS
N:
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-
8
7
9
2
N
ea
r
-
z
ero
N
DZ isl
a
n
d
in
g
d
etec
tio
n
fo
r
mu
lti
-
s
o
u
r
ce
DGs v
ia
h
yb
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id
A
N
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S
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(
Ma
d
a
ma
n
e
r
i R
a
mya
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1121
o
f
v
o
ltag
e
a
n
d
cu
r
r
en
t
(
R
MS
an
d
R
MS
)
an
d
th
e
T
HD
v
alu
es
o
f
v
o
ltag
e
an
d
cu
r
r
e
n
t
(
T
HD
an
d
T
HD
)
ar
e
co
n
tin
u
o
u
s
ly
m
o
n
ito
r
e
d
.
T
h
es
e
s
ig
n
als
f
o
r
m
th
e
p
r
im
ar
y
in
p
u
ts
to
th
e
h
y
b
r
id
ANFI
S
–
ad
ap
t
iv
e
f
u
zz
y
class
if
ier
,
wh
ich
r
ed
u
ce
s
NDZ
with
o
u
t d
eg
r
ad
in
g
p
o
wer
q
u
ality
.
(
a)
(
b
)
(
c)
Fig
u
r
e
1
.
C
o
m
p
o
n
en
ts
o
f
th
e
p
r
o
p
o
s
ed
PV isl
an
d
in
g
d
etec
tio
n
s
y
s
tem
: (
a)
eq
u
i
v
alen
t c
ir
cu
i
t o
f
th
e
PV
s
y
s
tem
,
(
b
)
n
o
n
-
d
etec
tio
n
zo
n
e
(
NDZ
)
o
f
is
lan
d
in
g
,
an
d
(
c)
s
ch
em
atic
r
ep
r
esen
tatio
n
o
f
th
e
p
r
o
p
o
s
ed
h
y
b
r
id
ap
p
r
o
ac
h
T
h
e
g
r
id
s
y
s
tem
co
n
tain
s
two
cir
cu
it
b
r
ea
k
er
s
(
C
B
s
)
:
o
n
e
to
s
ep
ar
ate
th
e
DG
an
d
p
r
ev
e
n
t
ex
ce
s
s
iv
e
p
o
wer
in
jectio
n
in
to
th
e
u
p
s
tr
e
am
g
r
id
,
an
d
th
e
o
th
e
r
to
tr
ip
u
n
d
er
f
au
lt c
o
n
d
itio
n
s
.
T
h
e
s
tan
d
ar
d
tr
ip
p
in
g
tim
e
o
f
C
B
s
u
n
d
er
is
lan
d
in
g
an
d
f
a
u
lt
co
n
d
itio
n
s
i
s
less
th
an
0
.
1
s
.
I
n
p
u
t
s
ig
n
als
o
b
tain
ed
f
r
o
m
t
h
e
PC
C
ar
e
s
u
p
p
lied
to
th
e
DG
b
r
ea
k
er
lo
g
ic.
ANFI
S
u
s
es
th
e
in
p
u
t
s
ig
n
als
an
d
a
s
tack
o
f
eig
h
t
r
ec
e
n
t
s
am
p
les
p
e
r
s
ig
n
al
to
g
en
er
ate
a
f
u
zz
y
in
f
er
e
n
ce
s
y
s
tem
(
FIS)
v
ia
s
u
b
tr
ac
tiv
e
clu
s
ter
in
g
,
wh
ich
m
ap
s
in
p
u
t
–
o
u
tp
u
t
r
elatio
n
s
h
ip
s
an
d
au
to
m
atica
lly
d
e
r
iv
es
I
F
–
T
H
E
N
r
u
les.
T
o
r
e
d
u
ce
c
o
m
p
u
tatio
n
al
lo
ad
,
ea
ch
s
ig
n
al
is
p
r
o
ce
s
s
ed
with
its
o
wn
ANFI
S
m
o
d
u
le;
th
eir
o
u
tp
u
ts
ar
e
th
en
s
tack
ed
an
d
u
s
ed
as
i
n
p
u
ts
to
th
e
m
ain
d
ec
is
io
n
ANFI
S,
as
d
ep
icted
in
Fig
u
r
e
2
(
a)
.
T
h
e
e
f
f
ec
tiv
en
ess
o
f
th
e
ANFI
S
-
b
ased
d
etec
to
r
d
ep
en
d
s
o
n
th
e
s
am
p
lin
g
in
ter
v
al,
th
e
n
u
m
b
e
r
o
f
s
am
p
led
s
ig
n
als,
an
d
th
e
n
u
m
b
er
o
f
s
am
p
les
p
e
r
s
ig
n
al.
E
a
ch
s
ig
n
al
is
s
am
p
led
at
=
0
.
005
s
,
e
v
er
y
n
ew
s
am
p
le
is
ad
d
ed
to
th
e
d
ata
s
tack
at
th
is
in
ter
v
al.
Fo
r
a
s
tack
o
f
s
am
p
les,
th
e
m
in
im
u
m
a
n
d
id
ea
l
tim
e
f
o
r
is
lan
d
in
g
d
etec
tio
n
a
r
e
(
1
5
)
an
d
(
1
6
)
.
de
t,
mi
n
=
(
1
5
)
L
o
a
d
=
√
L
oa
d
2
+
L
oa
d
2
(
1
6
)
Fo
r
=
8
an
d
=
0
.
005
s
,
th
is
g
iv
es
de
t,
mi
n
=
0
.
04
s
,
en
s
u
r
in
g
f
ast d
etec
tio
n
.
T
h
e
to
tal
lo
ad
p
o
wer
c
o
n
s
u
m
p
tio
n
,
co
m
b
in
i
n
g
ac
tiv
e
an
d
r
ea
ctiv
e
co
m
p
o
n
e
n
ts
,
is
ex
p
r
ess
ed
as
wh
er
e
L
oa
d
is
th
e
ap
p
ar
en
t
p
o
wer
o
f
th
e
lo
ad
.
T
h
e
ANFI
S
–
f
u
zz
y
class
if
ier
p
r
o
ce
s
s
es
all
th
ese
in
p
u
t
s
to
p
r
o
v
id
e
a
s
in
g
le
o
u
tp
u
t
in
d
icatin
g
wh
et
h
er
is
lan
d
in
g
is
p
r
esen
t,
wh
il
e
also
m
itig
atin
g
p
o
wer
-
q
u
ality
d
is
tu
r
b
an
ce
s
b
y
en
f
o
r
cin
g
o
p
tim
al
th
r
esh
o
ld
v
alu
es
f
o
r
ea
ch
in
p
u
t.
T
h
e
o
v
e
r
all
p
r
o
ce
s
s
f
lo
w
is
illu
s
tr
ated
i
n
Fig
u
r
e
2
(
b
)
.
T
h
e
d
ec
is
io
n
lo
g
ic
o
p
er
ates
as
f
o
llo
ws.
I
n
n
o
r
m
al
g
r
id
-
co
n
n
ec
ted
o
p
er
atio
n
,
Gr
id
s
u
p
p
lies
o
r
ab
s
o
r
b
s
r
ea
ctiv
e
p
o
wer
s
u
ch
th
at
th
e
DG
an
d
g
r
id
r
em
ain
s
y
n
ch
r
o
n
is
ed
a
n
d
th
e
VSC
o
p
er
ates
n
ea
r
u
n
ity
p
o
wer
f
ac
to
r
(
≈
0
)
.
Af
ter
an
u
p
s
tr
ea
m
d
is
co
n
n
ec
tio
n
,
th
e
s
y
s
tem
m
o
n
ito
r
s
th
e
r
elativ
e
m
ag
n
itu
d
es
o
f
Gr
id
,
PV
,
an
d
L
oa
d
.
I
f
Gr
id
is
s
m
all
o
r
ze
r
o
wh
ile
PV
an
d
L
oa
d
r
em
ain
s
ig
n
if
ican
t,
th
e
s
y
s
tem
tr
e
ats
th
is
as
a
p
o
ten
tial
is
lan
d
in
g
ev
en
t
an
d
r
elies o
n
th
e
lear
n
e
d
ANFI
S r
u
les an
d
s
y
n
ch
r
o
n
is
atio
n
s
tatu
s
to
co
n
f
ir
m
is
lan
d
i
n
g
.
T
o
en
h
an
ce
o
b
s
er
v
a
b
ilit
y
n
ea
r
th
e
NDZ
,
th
e
co
n
tr
o
ller
in
je
cts
a
s
m
all
r
ea
ctiv
e
cu
r
r
e
n
t
p
er
tu
r
b
atio
n
Δ
co
r
r
esp
o
n
d
i
n
g
to
a
tem
p
o
r
a
r
y
p
o
wer
-
f
ac
to
r
s
h
if
t
to
0
.
9
5
,
ap
p
lied
f
o
r
a
s
h
o
r
t
in
ter
v
al
(
e.
g
.
,
3
m
s
)
.
T
h
is
alter
s
th
e
PV
r
ea
ctiv
e
p
o
wer
wh
ile
m
in
im
ally
af
f
ec
tin
g
p
o
wer
q
u
ality
.
I
f
th
e
r
esu
ltin
g
ch
an
g
e
in
PV
d
o
es
n
o
t
p
r
o
p
a
g
ate
to
Gr
id
.
T
h
e
s
y
s
tem
in
f
er
s
th
at
th
e
DG
i
s
i
s
lan
d
ed
; if
a
clea
r
ch
an
g
e
in
Gr
id
is
o
b
s
er
v
ed
,
th
e
g
r
id
is
s
till
co
n
n
ec
ted
,
an
d
n
o
is
lan
d
in
g
is
d
ec
lar
ed
.
I
n
p
ar
allel,
th
e
R
MS
an
d
T
HD
v
alu
es
o
f
v
o
ltag
e
an
d
cu
r
r
en
t
,
p
ar
ticu
lar
ly
T
HD
,
ar
e
u
s
ed
to
d
is
tin
g
u
is
h
is
lan
d
in
g
p
h
en
o
m
en
a
f
r
o
m
o
th
er
g
r
id
d
is
tu
r
b
an
ce
s
.
T
h
e
cu
r
r
en
t
T
HD
is
esti
m
ated
as
(
1
7
)
.
T
HD
=
h,
r
ms
1
,
r
ms
×
100
%
(
1
7
)
W
h
er
e
h,
r
ms
is
th
e
R
MS
v
alu
e
o
f
all
cu
r
r
e
n
t
h
ar
m
o
n
ic
c
o
m
p
o
n
en
ts
(
ex
clu
d
i
n
g
t
h
e
f
u
n
d
am
e
n
tal)
a
n
d
1
,
r
ms
is
th
e
R
MS
v
alu
e
o
f
th
e
f
u
n
d
am
e
n
t
al
cu
r
r
en
t.
I
f
T
HD
ex
ce
ed
s
its
allo
wab
le
lim
it
(
e.
g
.
,
5
%),
th
e
h
y
b
r
id
ANFI
S
r
ein
f
o
r
ce
s
th
e
is
lan
d
in
g
d
ec
is
i
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
1
1
7
-
1
1
3
1
1122
(
a)
(
b
)
Fig
u
r
e
2
.
Pro
p
o
s
ed
a
p
p
r
o
ac
h
:
(
a)
d
ata
s
tack
an
d
(
b
)
h
y
b
r
id
A
NFI
S f
lo
wch
ar
t
3
.
4
.
1
.
Ada
ptiv
e
neuro
-
f
uzzy
i
nfe
re
nce
s
y
s
t
em
(
ANF
I
S)
–
a
da
ptiv
e
f
uzzy
cla
s
s
if
ier
T
h
e
ANFI
S
co
m
b
in
es
n
eu
r
al
n
etwo
r
k
s
an
d
f
u
zz
y
lo
g
ic
f
o
r
m
o
d
ellin
g
n
o
n
lin
ea
r
r
elatio
n
s
h
ip
s
in
DG
s
y
s
tem
s
.
T
h
e
ad
ap
tiv
e
FIS
ca
n
lear
n
an
d
ad
ju
s
t
m
em
b
er
s
h
i
p
-
f
u
n
cti
o
n
p
ar
am
eter
s
an
d
r
u
l
e
co
n
s
eq
u
en
ts
f
r
o
m
tr
ain
in
g
d
ata
u
s
in
g
g
r
ad
ie
n
t
-
d
e
s
ce
n
t
o
p
tim
is
atio
n
(
e.
g
.
,
b
ac
k
p
r
o
p
ag
atio
n
)
,
t
h
er
eb
y
m
in
im
is
in
g
th
e
er
r
o
r
b
etwe
en
p
r
ed
icted
an
d
ac
tu
al
o
u
tp
u
ts
.
ANFI
S
is
p
ar
ticu
lar
ly
well
-
s
u
ited
f
o
r
r
ea
l
-
tim
e
an
al
y
s
is
b
ec
au
s
e
it
ca
n
o
p
er
ate
d
ir
ec
tly
o
n
m
ea
s
u
r
e
d
in
p
u
t
d
at
a,
to
ler
ate
p
a
r
am
eter
v
ar
iab
ilit
y
,
an
d
ap
p
r
o
x
im
ate
n
o
n
lin
ea
r
d
ec
is
io
n
b
o
u
n
d
a
r
ies.
T
h
e
wo
r
k
in
g
p
r
in
cip
le
o
f
th
e
p
r
o
p
o
s
ed
ANFI
S
–
ad
ap
tiv
e
f
u
zz
y
class
if
ier
is
a
s
f
o
llo
ws:
i)
f
u
zz
if
icatio
n
m
ap
s
cr
is
p
in
p
u
ts
(
PV
,
Gr
id
,
L
oa
d
,
R
MS
,
R
MS
,
T
HD
,
T
HD
)
to
f
u
zz
y
s
ets;
i
i)
a
r
u
le
b
ase
o
f
f
u
zz
y
I
F
–
T
HE
N
s
tatem
en
ts
r
elate
s
in
p
u
t
lin
g
u
is
tic
ter
m
s
to
o
u
tp
u
t
ter
m
s
(
“I
s
lan
d
i
n
g
”,
“Distu
r
b
an
ce
”)
;
iii)
f
u
zz
y
in
f
er
en
ce
co
m
p
u
tes
th
e
f
ir
in
g
s
tr
en
g
th
o
f
ea
ch
r
u
le
b
ased
o
n
th
e
f
u
zz
if
ied
in
p
u
ts
;
iv
)
r
u
le
ag
g
r
eg
atio
n
co
m
b
in
es
th
e
ac
tiv
ated
r
u
le
o
u
t
p
u
ts
in
to
an
o
v
er
all
f
u
zz
y
r
esp
o
n
s
e;
an
d
v
)
d
ef
u
zz
if
icatio
n
co
n
v
er
ts
th
is
f
u
zz
y
r
esp
o
n
s
e
in
to
a
c
r
is
p
o
u
t
p
u
t
in
d
icatin
g
t
h
e
is
lan
d
in
g
d
ec
is
io
n
.
I
n
th
e
p
r
o
p
o
s
ed
m
eth
o
d
,
m
em
b
er
s
h
ip
-
f
u
n
ctio
n
s
h
a
p
es
an
d
r
u
le
co
n
s
eq
u
en
ts
ar
e
tu
n
ed
au
t
o
m
atica
lly
v
ia
ANFI
S
tr
ain
in
g
,
an
d
,
a
f
ter
a
tr
ial
-
a
n
d
-
e
r
r
o
r
co
m
p
ar
is
o
n
,
Gau
s
s
ian
m
em
b
er
s
h
ip
f
u
n
ctio
n
s
ar
e
ad
o
p
ted
.
T
h
e
m
em
b
er
s
h
ip
f
u
n
ct
io
n
s
f
o
r
th
e
th
r
ee
p
r
in
cip
al
r
e
ac
tiv
e
-
p
o
wer
in
p
u
ts
1
=
PV
,
2
=
Gr
id
,
3
=
L
oa
d
ar
e
s
h
o
wn
in
Fig
u
r
e
3
.
T
h
e
cl
ass
if
ier
o
u
tp
u
ts
two
d
ec
is
io
n
v
ar
iab
les
1
an
d
2
,
r
ep
r
esen
tin
g
th
e
d
eg
r
ee
s
o
f
b
elief
in
“
is
lan
d
in
g
”
an
d
“
d
is
tu
r
b
an
ce
”,
r
esp
ec
tiv
ely
;
th
e
f
in
a
l
b
in
ar
y
d
ec
is
io
n
is
o
b
tain
ed
b
y
co
m
p
a
r
in
g
1
an
d
2
an
d
e
n
f
o
r
ci
n
g
s
y
n
c
h
r
o
n
is
atio
n
co
n
s
tr
ain
ts
.
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
N
ea
r
-
z
ero
N
DZ isl
a
n
d
in
g
d
etec
tio
n
fo
r
mu
lti
-
s
o
u
r
ce
DGs v
ia
h
yb
r
id
A
N
F
I
S
…
(
Ma
d
a
ma
n
e
r
i R
a
mya
)
1123
(
a)
(
b
)
(
c)
Fig
u
r
e
3
.
Me
m
b
er
s
h
ip
f
u
n
ctio
n
s
f
o
r
th
e
ANFI
S
:
(
a)
m
e
m
b
er
s
h
ip
f
u
n
ctio
n
f
o
r
th
e
PV sy
s
tem
,
(
b
)
m
em
b
er
s
h
i
p
f
u
n
ctio
n
f
o
r
t
h
e
g
r
i
d
s
y
s
tem
,
a
n
d
(
c)
m
em
b
er
s
h
i
p
f
u
n
ctio
n
f
o
r
th
e
lo
ad
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
h
e
p
e
r
f
o
r
m
an
ce
o
f
th
e
h
y
b
r
id
ANFI
S
-
b
ased
is
lan
d
in
g
d
et
ec
tio
n
ap
p
r
o
ac
h
with
a
n
a
d
ap
tiv
e
f
u
zz
y
class
if
ier
was
ev
alu
ated
in
MA
T
L
AB
/Si
m
u
lin
k
u
s
in
g
a
d
et
ailed
m
o
d
el
o
f
th
e
m
u
lti
-
s
o
u
r
c
e
PV
-
in
ter
f
ac
ed
DG
s
y
s
tem
.
T
h
e
ANFI
S
p
ar
am
eter
s
an
d
co
n
tr
o
ller
g
ain
s
wer
e
tu
n
ed
to
o
b
tain
r
o
b
u
s
t
b
eh
a
v
io
u
r
ac
r
o
s
s
a
wid
e
o
p
er
atin
g
r
an
g
e
.
C
o
m
p
lian
ce
with
I
E
E
E
-
1
5
4
7
was
en
f
o
r
ce
d
b
y
co
n
s
tr
ain
in
g
th
e
PC
C
v
o
ltag
e
to
0
.
9
–
1
.
1
p
.
u
.
,
th
e
f
r
e
q
u
en
c
y
to
5
9
.
5
–
6
0
.
1
5
H
z,
an
d
th
e
m
ax
im
u
m
is
lan
d
in
g
d
etec
tio
n
tim
e
t
o
less
th
an
1
s
,
as
s
u
m
m
a
r
is
ed
in
T
ab
le
1
.
T
h
ese
s
tan
d
ar
d
lim
its
p
r
o
v
id
e
th
e
b
en
ch
m
a
r
k
a
g
ain
s
t
wh
ich
th
e
d
etec
tio
n
s
p
ee
d
an
d
p
o
wer
-
q
u
alit
y
im
p
ac
t o
f
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
ar
e
ass
ess
ed
.
T
o
co
v
er
b
o
t
h
m
is
m
atch
ed
an
d
p
o
wer
-
m
at
ch
ed
co
n
d
itio
n
s
,
th
e
s
im
u
latio
n
s
etu
p
was
ex
a
m
in
e
d
u
n
d
er
s
ev
en
ca
s
es:
C
ase
1
(
p
o
wer
m
is
m
atch
b
etwe
en
t
h
e
DG
an
d
th
e
lo
ad
)
,
C
ase
2
(
NDZ
p
o
wer
-
m
atch
ed
co
n
d
itio
n
)
,
an
d
C
ases
3
–
7
(
ac
t
iv
e
-
p
o
wer
lev
els r
an
g
in
g
f
r
o
m
2
0
k
W
to
6
0
0
k
W
,
with
th
e
DG
r
atin
g
u
n
ch
an
g
ed
)
.
T
ab
le
1
.
Stan
d
a
r
d
I
E
E
E
1
5
4
7
p
ar
am
eter
s
f
o
r
an
ti
-
is
lan
d
in
g
t
ec
h
n
iq
u
e
P
a
r
a
me
t
e
r
s
S
t
a
n
d
a
r
d
v
a
l
u
e
s
V
o
l
t
a
g
e
r
a
n
g
e
9
0
%
<
V
<
1
1
0
%
F
r
e
q
u
e
n
c
y
r
a
n
g
e
5
9
.
5
<
f
<
6
0
.
1
5
Th
e
ma
x
i
mu
m
t
i
me
f
o
r
d
e
t
e
c
t
i
n
g
i
sl
a
n
d
i
n
g
< 1
se
c
4
.1
.
Ca
s
e
1
:
P
o
wer
m
is
m
a
t
c
h bet
wee
n DG
a
nd
lo
a
d (
no
rm
a
l c
a
s
e)
I
n
C
ase
1
,
th
e
lo
ad
co
n
s
u
m
es 1
0
0
k
W
an
d
4
0
k
VAr
.
At
=
0
.
4
s
,
th
e
cir
cu
it
b
r
ea
k
er
d
is
co
n
n
ec
ts
th
e
g
r
id
,
a
n
d
th
e
p
r
o
p
o
s
ed
d
etec
to
r
is
ev
al
u
ated
u
n
d
e
r
th
is
cle
ar
p
o
we
r
-
m
is
m
atch
c
o
n
d
itio
n
.
T
h
e
ev
o
l
u
tio
n
o
f
r
ea
ctiv
e
p
o
wer
f
o
r
t
h
e
g
r
i
d
,
P
V
g
en
er
ato
r
,
an
d
lo
ad
is
s
h
o
wn
in
Fig
u
r
e
4
(
a)
.
B
ef
o
r
e
d
is
co
n
n
ec
tio
n
,
th
e
g
r
id
s
u
p
p
lies
th
e
r
ea
ctiv
e
d
em
an
d
an
d
h
en
ce
Gr
i
d
is
p
o
s
itiv
e,
wh
ile
t
h
e
co
n
v
er
te
r
o
p
er
ates
with
≈
0
,
s
o
PV
is
n
eg
lig
ib
le.
Af
ter
th
e
b
r
ea
k
er
o
p
en
s
at
0
.
4
s
,
Gr
i
d
r
ap
id
ly
d
r
o
p
s
to
war
d
s
ze
r
o
,
in
d
icatin
g
th
at
th
e
g
r
id
is
n
o
lo
n
g
er
s
u
p
p
o
r
tin
g
th
e
l
o
ad
,
w
h
er
ea
s
th
e
lo
ad
'
s
r
ea
ctiv
e
p
o
wer
L
oa
d
b
ec
o
m
es
u
n
b
alan
ce
d
,
an
d
th
e
PV
u
n
i
t
b
eg
in
s
to
s
u
p
p
ly
it,
ca
u
s
in
g
PV
t
o
in
cr
ea
s
e.
T
h
e
h
y
b
r
id
ANFI
S
r
ec
o
g
n
is
es
th
is
p
atter
n
—
lo
s
s
o
f
g
r
id
r
ea
ctiv
e
p
o
wer
b
u
t
s
u
s
tain
ed
PV
an
d
lo
ad
r
ea
ctiv
e
p
o
wer
s
with
ac
tiv
e
s
y
n
ch
r
o
n
is
atio
n
s
till
p
r
esen
t
—
as
an
u
n
am
b
ig
u
o
u
s
is
lan
d
in
g
s
ig
n
atu
r
e
a
n
d
in
s
tan
t
ly
f
lag
s
is
lan
d
in
g
at
ap
p
r
o
x
im
a
tely
0
.
4
s
.
T
h
is
b
e
h
av
io
u
r
s
atis
f
ies
th
e
I
E
E
E
-
1
5
4
7
d
etec
tio
n
-
tim
e
r
e
q
u
ir
em
e
n
t
wi
th
a
s
u
b
s
tan
tial
m
a
r
g
in
an
d
co
n
f
ir
m
s
th
at,
u
n
d
er
clea
r
m
is
m
atch
co
n
d
itio
n
s
,
th
e
p
r
o
p
o
s
ed
m
eth
o
d
ca
n
r
ely
p
u
r
ely
o
n
r
ea
ctiv
e
-
p
o
wer
tr
ajec
to
r
ies with
o
u
t r
eq
u
ir
i
n
g
ad
d
itio
n
al
p
r
o
b
in
g
.
4
.2
.
Ca
s
e
2
:
P
o
wer
m
a
t
ch
bet
wee
n DG
a
nd
lo
a
d (
NDZ ca
s
e)
C
ase
2
i
s
d
esig
n
ed
to
em
u
late
a
class
ica
l
NDZ
:
th
e
lo
ad
is
a
d
ju
s
ted
to
4
0
0
k
W
at
u
n
ity
p
o
wer
f
ac
to
r
(
0
k
VAr
)
,
ef
f
ec
tiv
ely
m
atch
in
g
th
e
DG
r
atin
g
.
Un
d
er
s
u
ch
a
p
o
wer
-
m
atc
h
ed
co
n
d
itio
n
,
c
o
n
v
en
tio
n
al
p
ass
iv
e
m
eth
o
d
s
s
tr
u
g
g
le
b
ec
au
s
e
b
o
th
v
o
ltag
e
an
d
f
r
eq
u
e
n
cy
r
em
ain
with
in
ac
ce
p
tab
le
lim
its
,
an
d
t
h
e
n
et
p
o
wer
f
lo
ws
ap
p
ea
r
u
n
c
h
an
g
e
d
.
T
h
e
s
im
u
lated
r
ea
ctiv
e
-
p
o
wer
b
e
h
av
io
u
r
f
o
r
DG,
lo
ad
,
an
d
g
r
id
in
th
is
NDZ
s
ce
n
ar
io
is
illu
s
tr
ated
in
Fig
u
r
e
4
(
b
)
.
Af
t
er
th
e
g
r
id
is
d
is
co
n
n
ec
ted
at
0
.
4
s
,
PV
an
d
L
o
a
d
r
em
ain
n
ea
r
ly
b
alan
ce
d
an
d
Gr
id
s
tay
s
s
m
all,
s
o
th
e
in
s
tan
tan
eo
u
s
p
atter
n
alo
n
e
is
n
o
t su
f
f
icien
t to
d
is
cr
im
in
ate
is
lan
d
in
g
.
T
o
r
eso
lv
e
th
is
am
b
ig
u
ity
,
t
h
e
co
n
t
r
o
ller
in
jects
a
v
er
y
s
m
all
r
ea
ctiv
e
-
cu
r
r
e
n
t
p
e
r
tu
r
b
atio
n
b
y
tem
p
o
r
ar
ily
s
h
if
tin
g
t
h
e
p
o
wer
f
ac
to
r
to
ab
o
u
t
0
.
9
5
a
n
d
m
o
n
i
to
r
in
g
th
e
r
esp
o
n
s
e.
I
f
th
e
p
er
t
u
r
b
atio
n
lead
s
to
a
co
r
r
esp
o
n
d
in
g
ch
a
n
g
e
in
Gr
id
,
th
e
s
y
s
tem
in
f
er
s
th
at
th
e
g
r
id
is
s
till
co
n
n
ec
ted
;
if
Gr
id
r
em
ain
s
u
n
ch
an
g
e
d
wh
ile
PV
an
d
L
oa
d
ch
an
g
e,
th
e
n
is
lan
d
in
g
is
d
ec
lar
ed
.
Simu
latio
n
r
esu
lts
co
n
f
ir
m
th
at
th
is
lo
w
-
m
ag
n
itu
d
e
,
s
h
o
r
t
-
d
u
r
ati
o
n
p
r
o
b
e
i
n
C
ase
2
allo
ws
th
e
h
y
b
r
id
ANFI
S
to
d
etec
t
th
e
is
lan
d
ed
co
n
d
itio
n
q
u
ick
ly
an
d
r
eliab
ly
,
wh
ile
k
ee
p
in
g
t
h
e
PC
C
v
o
ltag
e,
f
r
eq
u
en
cy
,
an
d
h
ar
m
o
n
ic
d
i
s
to
r
tio
n
with
in
th
e
lim
its
o
f
T
a
b
le
1
.
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
1
1
7
-
1
1
3
1
1124
(
a)
(
b
)
Fig
u
r
e
4
.
Simu
latio
n
r
esu
lts
o
f
th
e
DG
–
lo
ad
p
o
wer
r
elatio
n
s
h
ip
: (
a)
p
o
wer
m
is
m
atch
in
C
ase
1
an
d
(
b
)
p
o
wer
m
atch
in
C
ase
2
4
.
3
.
Ca
s
e
3
:
L
o
a
d a
ct
i
v
e
po
wer
2
0
k
W
(
po
wer
m
a
t
ched
wit
h DG
)
I
n
C
ase
3
,
th
e
ac
tiv
e
p
o
wer
o
f
th
e
lo
ad
is
r
e
d
u
ce
d
to
2
0
k
W
with
th
e
DG
s
till
ca
p
ab
le
o
f
s
u
p
p
ly
in
g
th
e
s
am
e
p
o
wer
,
r
e
p
r
esen
tin
g
an
o
t
h
er
s
u
b
tle
NDZ
-
lik
e
c
o
n
d
itio
n
.
T
h
e
s
y
s
tem
r
esp
o
n
s
es
ar
e
d
ep
i
cted
in
Fig
u
r
e
5
(
a)
,
wh
ich
p
r
esen
ts
th
e
r
ea
ctiv
e
-
p
o
wer
b
eh
av
io
u
r
,
an
d
in
Fig
u
r
e
5
(
b
)
,
wh
ich
s
h
o
ws
th
e
co
r
r
esp
o
n
d
in
g
v
o
ltag
e
an
d
cu
r
r
en
t
wav
e
f
o
r
m
s
.
Her
e
,
th
e
g
r
id
s
u
p
p
lies
th
e
s
m
all
r
ea
ctiv
e
d
em
an
d
b
ef
o
r
e
d
is
co
n
n
ec
ti
o
n
,
b
u
t
a
f
ter
0
.
4
s
,
th
e
b
r
ea
k
er
o
p
en
s
,
a
n
d
th
e
DG
co
n
tin
u
es
to
f
ee
d
th
e
lo
ad
.
B
ec
a
u
s
e
th
e
a
b
s
o
lu
te
le
v
els
o
f
r
ea
c
tiv
e
p
o
wer
ar
e
lo
w,
th
e
ch
an
g
es
in
Gr
id
an
d
PV
ar
e
m
o
d
est,
an
d
ac
tiv
e
p
o
wer
r
em
ai
n
s
n
ea
r
ly
co
n
s
tan
t,
m
ak
in
g
p
u
r
e
p
o
wer
-
m
is
m
atch
cr
iter
ia
u
n
r
eliab
le.
Mo
r
e
im
p
o
r
tan
tly
,
th
e
r
e
is
alm
o
s
t n
o
ch
an
g
e
i
n
,
s
o
a
c
o
n
v
e
n
tio
n
al
s
ch
em
e
th
a
t
m
o
n
ito
r
s
o
n
l
y
an
d
wo
u
ld
f
ail
to
d
etec
t th
e
is
lan
d
.
T
h
e
h
y
b
r
id
m
eth
o
d
o
v
e
r
co
m
e
s
th
is
lim
itatio
n
b
y
also
an
aly
s
in
g
th
e
h
ar
m
o
n
ic
c
o
n
ten
t
o
f
t
h
e
cu
r
r
e
n
t.
Fig
u
r
e
6
(
a)
s
h
o
ws
th
at
s
o
o
n
a
f
ter
d
is
co
n
n
ec
tio
n
,
th
e
c
u
r
r
en
t
wav
ef
o
r
m
b
ec
o
m
es
n
o
ticea
b
l
y
d
is
to
r
ted
,
an
d
th
e
cu
r
r
en
t
T
HD
T
HD
ex
ce
ed
s
th
e
5
%
s
tan
d
ar
d
lim
it.
T
h
e
ANFI
S
–
f
u
zz
y
class
if
ier
,
wh
ich
h
as
b
ee
n
tr
ain
ed
o
n
co
m
b
in
ed
R
MS
an
d
T
HD
f
ea
t
u
r
es,
in
ter
p
r
ets
th
is
s
u
s
tain
ed
in
cr
ea
s
e
in
T
HD
(
to
g
eth
er
with
s
m
a
ll
ch
an
g
es
in
R
MS
v
o
ltag
e
an
d
cu
r
r
en
t)
as
an
is
lan
d
in
g
s
ig
n
at
u
r
e
d
is
tin
ct
f
r
o
m
o
r
d
in
a
r
y
d
is
tu
r
b
an
ce
s
.
As
a
r
esu
lt,
ev
en
th
o
u
g
h
tr
ad
itio
n
al
p
o
wer
in
d
i
ce
s
r
em
ain
in
c
o
n
clu
s
iv
e,
th
e
p
r
o
p
o
s
ed
d
etec
to
r
co
r
r
ec
tly
id
en
tifie
s
is
lan
d
in
g
in
C
ase
3
w
ith
in
a
f
r
ac
tio
n
o
f
a
s
ec
o
n
d
af
te
r
th
e
g
r
id
is
d
is
co
n
n
ec
ted
.
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
N
ea
r
-
z
ero
N
DZ isl
a
n
d
in
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d
etec
tio
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mu
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DGs v
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yb
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id
A
N
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I
S
…
(
Ma
d
a
ma
n
e
r
i R
a
mya
)
1125
(
a)
(
b
)
Fig
u
r
e
5
.
Simu
latio
n
r
esu
lts
u
n
d
er
C
ase
3
: (
a)
DG
–
lo
a
d
p
o
wer
m
atch
an
d
(
b
)
s
y
s
tem
v
o
lta
g
e
an
d
c
u
r
r
e
n
t
r
esp
o
n
s
es
4
.
4
.
Ca
s
e
4
:
L
o
a
d a
ct
i
v
e
po
wer
4
0
0
k
W
(
po
wer
ma
t
che
d wit
h DG
)
C
ase
4
ag
ain
co
n
s
id
er
s
a
4
0
0
k
W
lo
ad
with
ze
r
o
r
ea
ctiv
e
p
o
wer
,
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u
t
th
e
em
p
h
asis
h
er
e
is
o
n
t
h
e
d
y
n
am
ic
r
esp
o
n
s
e
an
d
d
etec
ti
o
n
tim
in
g
.
T
h
e
s
im
u
latio
n
o
u
t
co
m
es
f
o
r
th
e
p
o
wer
m
atch
b
e
twee
n
lo
ad
an
d
DG
a
r
e
s
h
o
w
n
i
n
F
i
g
u
r
e
6
(
b
)
,
w
h
i
le
F
i
g
u
r
e
7
(
a
)
p
r
es
e
n
ts
t
h
e
a
s
s
o
c
i
a
t
e
d
v
o
lt
a
g
e
a
n
d
c
u
r
r
e
n
t
w
a
v
e
f
o
r
m
s
f
o
r
C
a
s
e
4
.
W
h
en
th
e
cir
cu
it
b
r
ea
k
er
o
p
en
s
at
0
.
4
s
,
a
s
m
all
m
is
m
atch
b
et
wee
n
DG
an
d
g
r
id
p
o
wer
ap
p
e
ar
s
,
an
d
Gr
id
d
r
o
p
s
to
ze
r
o
wh
ile
PV
an
d
L
oa
d
ad
ju
s
t
to
m
ain
tain
p
o
wer
b
alan
ce
with
in
th
e
is
lan
d
.
T
h
e
h
y
b
r
id
ANFI
S
tak
es
ad
v
an
tag
e
o
f
th
is
s
m
all,
b
u
t
d
e
tecta
b
le,
m
is
m
atch
alo
n
g
with
tr
an
s
ien
t
d
ev
iatio
n
s
in
R
MS
q
u
an
titi
es.
Alth
o
u
g
h
th
e
u
n
d
e
r
ly
in
g
s
y
s
tem
ex
h
ib
it
s
a
s
h
o
r
t
d
elay
ass
o
ciate
d
with
th
e
r
eb
al
a
n
cin
g
o
f
p
o
wer
f
l
o
ws,
th
e
p
r
o
p
o
s
ed
d
etec
to
r
s
till
id
en
tifie
s
th
e
is
lan
d
at
ap
p
r
o
x
im
ately
0
.
4
s
,
ess
en
tially
tr
ac
k
in
g
th
e
b
r
ea
k
er
a
ctio
n
an
d
a
v
o
id
in
g
th
e
p
o
wer
-
q
u
ality
is
s
u
es th
at
wo
u
ld
ar
is
e
f
r
o
m
a
lo
n
g
er
d
etec
tio
n
d
elay
.
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
1
1
7
-
1
1
3
1
1126
(
a)
(
b
)
Fig
u
r
e
6
.
Simu
latio
n
r
esu
lts
u
n
d
er
C
ases
3
an
d
4
:
(
a)
is
lan
d
i
n
g
co
n
d
itio
n
id
e
n
tifie
d
in
C
ase
3
an
d
(
b
)
DG
–
lo
ad
p
o
wer
m
atch
in
C
ase
4
4
.
5
.
Ca
s
e
5
:
L
o
a
d a
ct
i
v
e
po
wer
1
5
0
k
W
(
po
wer
ma
t
che
d wit
h DG
)
I
n
C
ase
5
,
th
e
lo
ad
co
n
s
u
m
es
1
5
0
k
W
wh
ile
th
e
DG
r
atin
g
r
em
ain
s
u
n
ch
a
n
g
ed
.
T
h
e
lo
ad
is
d
is
co
n
n
ec
ted
at
0
.
4
s
,
an
d
th
e
s
im
u
latio
n
r
esu
lts
ar
e
p
lo
tted
in
Fig
u
r
e
7
(
b
)
(
p
o
wer
m
atch
b
et
wee
n
lo
ad
an
d
DG)
an
d
Fig
u
r
e
8
(
a)
(
v
o
ltag
e
a
n
d
c
u
r
r
en
t
r
esp
o
n
s
e
with
is
lan
d
d
e
tectio
n
)
.
T
h
e
p
o
wer
tr
ac
es
in
Fig
u
r
e
7
(
b
)
in
d
icate
th
at,
d
esp
ite
th
e
d
is
co
n
n
ec
tio
n
,
th
e
g
r
id
c
o
n
tin
u
es
to
ap
p
ea
r
s
y
n
ch
r
o
n
is
ed
,
an
d
th
er
e
ar
e
n
o
s
ig
n
if
ican
t
ch
an
g
es
in
Gr
id
r
.
C
o
n
s
eq
u
en
tly
,
a
p
u
r
ely
p
o
wer
-
b
ased
d
etec
to
r
wo
u
ld
n
o
t
r
ec
o
g
n
is
e
th
e
is
lan
d
in
g
co
n
d
itio
n
.
Ho
wev
er
,
th
e
c
u
r
r
en
t
wa
v
ef
o
r
m
s
in
Fig
u
r
e
8
(
a
)
ex
h
ib
it
n
o
tic
ea
b
le
f
lu
ctu
atio
n
s
af
ter
0
.
4
s
,
a
n
d
th
e
h
y
b
r
i
d
ANFI
S
u
s
es
th
ese
f
lu
ctu
atio
n
s
ca
p
tu
r
e
d
v
ia
cu
r
r
en
t
R
MS
an
d
T
H
D
f
ea
tu
r
es
to
class
if
y
th
e
ev
en
t
c
o
r
r
ec
tly
.
Acc
o
r
d
in
g
to
th
e
s
im
u
latio
n
d
ata,
th
e
is
la
n
d
in
g
co
n
d
itio
n
in
C
ase
5
is
d
etec
ted
b
etwe
en
0
.
4
an
d
0
.
5
s
,
with
o
n
ly
a
s
m
al
l
d
elay
r
elativ
e
to
t
h
e
b
r
ea
k
er
o
p
er
atio
n
,
a
n
d
s
till
well
with
in
th
e
<
1
s
r
eq
u
ir
em
en
t.
4
.
6
.
Ca
s
e
6
:
L
o
a
d a
ct
i
v
e
po
wer
3
0
5
k
W
(
po
wer
ma
t
che
d wit
h DG
)
C
ase
6
f
u
r
th
er
in
cr
ea
s
es
th
e
a
ctiv
e
lo
ad
t
o
3
0
5
k
W
wh
ile
k
ee
p
in
g
th
e
DG
r
atin
g
co
n
s
tan
t,
th
er
eb
y
cr
ea
tin
g
a
n
ea
r
-
m
atch
ed
h
i
g
h
-
p
o
wer
co
n
d
itio
n
.
T
h
e
p
o
wer
-
f
l
o
w
b
eh
av
io
u
r
f
o
r
th
is
ca
s
e
is
s
h
o
wn
in
Fig
u
r
e
8
(
b
)
,
an
d
th
e
co
r
r
esp
o
n
d
i
n
g
v
o
ltag
e
an
d
cu
r
r
e
n
t
r
esp
o
n
s
es
ar
e
g
iv
en
in
Fig
u
r
e
9
(
a
)
.
Af
ter
th
e
lo
a
d
is
d
is
co
n
n
ec
ted
at
0
.
4
s
,
th
e
g
r
id
'
s
r
ea
ctiv
e
p
o
wer
Gr
id
f
alls
to
ze
r
o
,
co
n
f
ir
m
in
g
th
at
t
h
e
g
r
id
is
n
o
lo
n
g
e
r
s
h
ar
i
n
g
r
ea
ctiv
e
s
u
p
p
o
r
t,
wh
ile
th
e
lo
ad
co
n
tin
u
es
to
b
e
s
u
p
p
lied
b
y
th
e
PV
u
n
it.
T
h
e
tex
tu
al
an
aly
s
is
in
th
e
m
an
u
s
cr
ip
t
n
o
tes
th
at
th
is
s
ce
n
ar
io
lead
s
to
a
m
o
d
est
tim
e
d
elay
b
ef
o
r
e
tr
ad
itio
n
al
in
d
ic
es
w
o
u
ld
r
eliab
ly
in
d
icate
is
la
n
d
in
g
.
No
n
eth
eless
,
Fig
u
r
e
9
(
a)
d
em
o
n
s
tr
ates
th
at
th
e
h
y
b
r
id
ANFI
S
ap
p
r
o
ac
h
r
ec
o
g
n
is
es
th
e
r
esu
ltin
g
s
ig
n
al
f
lu
ctu
atio
n
s
an
d
d
etec
ts
th
e
is
lan
d
in
g
co
n
d
itio
n
v
er
y
q
u
ic
k
ly
,
ef
f
ec
tiv
ely
at
0
.
4
s
,
th
u
s
co
m
p
en
s
atin
g
f
o
r
t
h
e
in
h
er
e
n
t
d
elay
i
n
p
o
wer
-
f
lo
w
r
eb
alan
cin
g
.
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