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ch
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ar
m
o
n
ics,
s
u
b
s
tan
tia
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lu
ctu
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s
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d
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s
ta
b
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ltag
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p
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s
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o
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s
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ts
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lead
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p
e
r
atio
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.
A
h
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d
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ically
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ag
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ip
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ap
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tr
ate
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y
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ca
n
also
m
itig
ate
h
ar
m
o
n
ics
[
1
]
-
[
5
]
.
Alth
o
u
g
h
DST
AT
C
OM
is
w
id
ely
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tili
ze
d
,
o
th
er
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ller
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ch
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p
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o
ller
s
,
h
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v
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ee
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d
ev
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.
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wev
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o
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lin
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r
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o
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o
f
ten
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u
t
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r
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th
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r
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ter
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a
r
ts
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ey
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r
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ett
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ited
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n
ag
e
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h
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co
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p
lex
ities
in
tr
o
d
u
ce
d
b
y
n
o
n
-
li
n
ea
r
lo
ad
s
[
6
]
.
T
o
m
ain
tain
s
tab
le
an
d
co
n
tr
o
lled
p
o
wer
s
y
s
tem
o
p
er
atio
n
s
,
d
is
p
atch
ce
n
ter
o
p
e
r
ato
r
s
r
eq
u
ir
e
r
ea
l
-
tim
e
s
o
lu
tio
n
s
.
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tific
ial
n
eu
r
al
n
etwo
r
k
s
(
A
NNs)
ar
e
p
ar
ticu
lar
ly
well
-
s
u
ited
f
o
r
th
is
task
,
g
iv
e
n
th
eir
a
b
ilit
y
to
r
ap
id
ly
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n
d
ac
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r
ately
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y
n
th
esize
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m
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lex
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y
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tem
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ep
r
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tatio
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s
.
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n
th
is
s
tu
d
y
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m
u
lti
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lay
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ee
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f
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r
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n
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k
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em
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lo
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ed
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ed
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th
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tr
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an
d
o
p
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atio
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al
p
a
r
am
eter
s
o
f
a
DSTA
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C
OM
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o
p
tim
izin
g
th
e
v
o
ltag
e
p
r
o
f
ile
ac
r
o
s
s
v
ar
y
in
g
lo
ad
co
n
d
itio
n
s
.
T
h
e
p
r
o
p
o
s
ed
tech
n
i
q
u
e
is
e
v
alu
ated
o
n
th
e
I
E
E
E
1
4
-
b
u
s
s
y
s
tem
,
with
r
esu
lts
d
em
o
n
s
tr
atin
g
its
s
u
p
er
io
r
p
er
f
o
r
m
an
ce
in
b
o
th
s
p
ee
d
a
n
d
ac
cu
r
ac
y
[
7
]
,
[
8
]
.
A
co
m
p
r
e
h
en
s
iv
e
r
ev
iew
o
f
t
h
e
s
m
ar
t
g
r
id
an
d
th
e
p
o
ten
tial
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.
1
4
,
No
.
2
,
J
u
n
e
20
2
5
:
449
-
4
58
450
r
o
le
o
f
AI
r
esear
ch
i
n
s
u
p
p
o
r
ti
n
g
its
v
is
io
n
was
p
r
esen
ted
in
[
9
]
.
T
o
h
ig
h
lig
h
t
AI
'
s
tech
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o
lo
g
ical
co
n
tr
ib
u
tio
n
s
to
war
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ac
h
iev
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g
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m
ar
t
g
r
id
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s
p
r
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e
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o
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jectiv
es,
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f
o
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s
o
n
two
k
ey
ar
ea
s
:
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ap
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d
y
n
am
ic
p
r
o
g
r
a
m
m
in
g
(
ADP)
-
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ased
s
m
ar
t
co
n
tr
o
l
an
d
wid
e
s
itu
atio
n
-
d
ep
e
n
d
en
t
awa
r
en
ess
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o
d
e
v
elo
p
a
n
in
tellig
en
t
p
o
wer
g
r
id
ca
p
ab
le
o
f
m
ee
ti
n
g
th
e
r
is
in
g
d
em
an
d
f
o
r
a
s
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s
tain
ab
le
g
lo
b
al
en
er
g
y
s
y
s
tem
,
ad
v
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ce
d
tim
e
o
p
tim
izatio
n
tech
n
iq
u
es,
d
is
tr
i
b
u
ted
in
tellig
en
ce
,
an
d
n
e
u
r
al
n
etwo
r
k
s
h
av
e
b
ee
n
ex
p
lo
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ed
t
o
ad
d
r
ess
co
m
p
lex
an
d
s
to
ch
asti
c
ch
allen
g
es.
A
s
tu
d
y
b
ased
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n
3
r
d
an
d
4
th
g
en
er
atio
n
p
o
we
r
s
y
s
tem
s
r
ese
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ch
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p
r
o
p
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s
ed
in
[
1
0
]
to
f
u
r
th
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r
th
is
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is
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.
B
u
ild
in
g
o
n
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ts
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u
r
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k
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ates a
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tific
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k
s
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estab
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ed
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tatio
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u
e
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o
r
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n
e
r
g
y
s
y
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tem
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o
n
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o
l.
Sp
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lly
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p
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n
R
B
FNN
-
b
ased
DSTA
T
C
O
M
to
r
eg
u
late
t
h
e
v
o
ltag
e
p
r
o
f
ile.
T
o
f
u
r
t
h
er
en
h
an
ce
s
y
s
tem
s
ta
b
ilit
y
,
we
o
p
tim
ize
th
e
r
esp
o
n
s
e
s
p
ee
d
to
in
s
tab
ilit
ies
b
y
f
in
e
-
t
u
n
in
g
th
e
g
ain
f
ac
to
r
an
d
s
ev
er
al
o
th
er
cr
itica
l
p
ar
am
eter
s
.
T
h
is
ap
p
r
o
ac
h
co
n
t
r
ib
u
tes to
th
e
d
e
v
elo
p
m
en
t
o
f
a
s
m
ar
ter
,
m
o
r
e
r
esil
ien
t p
o
wer
g
r
id
.
2.
M
E
T
H
O
D
T
h
e
I
E
E
E
1
4
-
b
u
s
tr
a
n
s
m
is
s
io
n
s
y
s
tem
h
as
b
ee
n
u
s
ed
t
o
r
ep
r
esen
t
th
e
‘
Am
e
r
ican
E
lect
r
ic
Po
wer
Sy
s
tem
’
in
th
e
Mid
west
r
eg
i
o
n
o
f
th
e
USA
s
in
ce
1
9
6
2
.
Ho
wev
er
,
th
e
d
ata
o
r
ig
i
n
ally
u
s
ed
f
o
r
v
alid
atio
n
lack
ed
r
ea
l
p
o
wer
.
I
n
th
is
s
tu
d
y
,
we
em
p
lo
y
th
e
I
E
E
E
1
4
-
b
u
s
tr
an
s
m
is
s
io
n
s
y
s
tem
to
ev
alu
ate
th
e
ef
f
icien
c
y
o
f
th
e
in
tr
o
d
u
ce
d
tech
n
iq
u
e
b
y
a
n
aly
zin
g
n
etwo
r
k
g
ain
s
o
r
lo
s
s
es
th
r
o
u
g
h
th
e
in
teg
r
a
tio
n
o
f
d
is
tr
ib
u
te
d
g
en
er
ato
r
s
(
DGs)
o
f
ex
te
n
d
ab
l
e
s
izes
an
d
p
lace
s
.
Un
lik
e
p
o
wer
s
y
s
tem
s
o
f
th
e
1
9
9
0
s
,
th
e
1
4
-
b
u
s
test
s
ce
n
ar
io
d
o
es
n
o
t
im
p
o
s
e
lin
e
lim
itatio
n
s
an
d
f
ea
tu
r
es
a
r
ed
u
ce
d
v
o
ltag
e
with
wid
e
-
r
an
g
in
g
v
o
l
tag
e
ad
m
in
is
tr
atio
n
ab
ilit
ies.
Vo
ltag
e
s
tab
ili
ty
,
a
cr
itical
asp
ec
t
o
f
p
o
wer
s
y
s
tem
r
eliab
ilit
y
,
r
ef
er
s
to
th
e
g
r
id
'
s
ab
ilit
y
to
m
ain
tain
co
n
s
tan
t d
esire
d
v
o
ltag
e
m
ag
n
itu
d
es a
t a
ll b
u
s
lo
ca
tio
n
s
,
ev
e
n
in
th
e
p
r
esen
ce
o
f
d
is
tu
r
b
an
c
es [
1
1
]
.
All
p
r
o
p
o
s
e
d
b
u
s
s
p
ec
i
f
i
ca
t
io
n
s
,
i
n
cl
u
d
in
g
v
o
l
ta
g
e
a
m
p
lit
u
d
e
a
n
d
a
n
g
l
e
o
f
t
h
e
p
h
ase
,
we
r
e
tak
e
n
i
n
t
o
ac
c
o
u
n
t.
V
o
lt
ag
e
d
r
o
p
is
s
u
es
o
f
te
n
a
r
is
e
i
n
p
o
we
r
n
e
tw
o
r
k
s
b
ec
a
u
s
e
o
f
le
n
g
t
h
y
f
ee
d
er
li
n
es
,
h
i
g
h
r
ati
n
g
lo
a
d
s
a
t
th
e
n
o
d
es,
a
n
d
a
r
e
d
u
ce
d
r
ea
cta
n
c
e
-
to
-
r
esis
ta
n
c
e
X
/R
r
at
io
,
w
h
i
ch
w
ea
k
e
n
s
s
y
s
t
em
li
n
k
s
a
n
d
n
ec
ess
it
at
es
co
n
ti
n
u
o
u
s
o
b
s
e
r
v
ati
o
n
.
T
o
a
d
d
r
ess
th
is
,
a
‘
p
o
w
er
f
l
o
w
’
ass
e
s
s
m
e
n
t
is
c
o
n
d
u
c
te
d
to
i
d
en
tif
y
v
u
l
n
e
r
a
b
l
e
p
o
i
n
ts
in
th
e
n
et
wo
r
k
.
O
n
c
e
t
h
es
e
wea
k
p
o
i
n
ts
ar
e
d
et
ec
te
d
,
a
l
o
a
d
f
o
r
ec
ast
an
al
y
s
is
is
e
x
e
c
u
te
d
t
o
t
r
a
ck
p
o
w
er
co
n
s
u
m
p
t
io
n
tr
en
d
s
.
T
h
is
p
r
o
c
ess
i
n
v
o
l
v
es
m
a
n
u
all
y
ad
ju
s
ti
n
g
t
h
e
ac
ti
v
e
a
n
d
r
ea
cti
v
e
p
o
w
e
r
(
P&
Q
)
v
al
u
es
o
f
th
e
lo
ad
s
in
t
h
e
f
ee
d
e
r
s
y
s
te
m
f
o
r
a
n
a
ly
s
is
.
T
h
e
d
at
a
e
x
tr
ac
t
ed
is
t
h
en
f
e
d
i
n
t
o
t
h
e
r
a
d
i
al
b
asis
f
u
n
ct
io
n
n
e
u
r
al
n
et
wo
r
k
(
R
B
FNN
)
u
n
it,
w
h
i
c
h
is
tr
ai
n
e
d
t
o
r
e
c
o
g
n
i
ze
a
n
d
p
r
e
d
i
ct
p
o
w
er
c
o
n
s
u
m
p
t
io
n
p
att
er
n
s
b
ase
d
o
n
t
h
es
e
tr
e
n
d
s
[
1
2
]
.
Nex
t,
a
tr
ad
itio
n
al
DSTA
T
C
OM
is
in
teg
r
ated
to
th
e
d
eter
m
in
ed
wea
k
b
u
s
es,
an
d
its
im
p
ac
t
o
n
th
e
v
o
ltag
e
m
ag
n
itu
d
es
o
f
ea
ch
b
u
s
is
an
aly
ze
d
.
B
y
c
o
m
p
ar
in
g
v
o
ltag
e
m
ag
n
itu
d
es
with
an
d
with
o
u
t
th
e
DSTA
T
C
OM
,
we
a
s
s
es
s
n
etw
o
r
k
p
e
r
f
o
r
m
an
ce
u
n
d
er
b
o
th
n
o
r
m
al
an
d
f
au
lt
co
n
d
itio
n
s
.
V
o
ltag
e
tr
en
d
s
ac
r
o
s
s
b
u
s
es
an
d
wea
k
lin
k
a
g
es
ar
e
clo
s
ely
m
o
n
ito
r
e
d
.
T
h
e
DST
AT
C
OM
is
th
en
p
lace
d
at
t
h
e
b
u
s
with
t
h
e
lo
west
v
o
ltag
e
m
ag
n
itu
d
e,
f
o
llo
wed
b
y
th
e
n
e
x
t r
o
u
n
d
o
f
v
o
ltag
e
m
a
g
n
itu
d
e
a
n
aly
s
is
.
Su
b
s
eq
u
en
tly
,
th
e
R
B
FNN
is
tr
ain
ed
u
s
in
g
o
b
s
er
v
e
d
v
o
ltag
e
v
ar
iatio
n
s
an
d
co
r
r
esp
o
n
d
in
g
n
etwo
r
k
g
ain
s
[
1
3
]
.
On
ce
tr
ain
e
d
,
th
e
R
B
FNN
i
s
in
teg
r
ated
in
to
th
e
DSTA
T
C
O
M
to
en
h
an
ce
its
co
n
tr
o
l
ca
p
ab
ilit
ies
th
r
o
u
g
h
p
r
ed
ictiv
e
f
o
r
ec
asti
n
g
.
T
h
e
o
b
tain
ed
r
esu
lts
ar
e
a
n
aly
ze
d
,
a
n
d
a
c
o
m
p
a
r
ativ
e
s
tu
d
y
is
co
n
d
u
cted
b
etwe
en
th
e
tr
ad
itio
n
al
DSTA
T
C
OM
an
d
th
e
R
B
FNN
co
n
tr
o
ller
-
b
ased
DSTA
T
C
OM
.
T
h
e
f
in
d
i
n
g
s
d
em
o
n
s
tr
ate
th
at
th
e
R
B
FNN
co
n
tr
o
ller
-
b
ased
DSTA
T
C
O
M
o
f
f
er
s
s
u
p
er
io
r
co
n
tr
o
l,
r
a
p
id
r
esp
o
n
s
e
tim
es
,
an
d
en
h
an
ce
d
s
tab
ilit
y
,
u
ltima
t
ely
co
n
tr
ib
u
tin
g
to
a
m
o
r
e
in
te
llig
en
t a
n
d
ef
f
icien
t p
o
wer
s
y
s
tem
n
etwo
r
k
.
2
.
1
.
Dis
t
ributio
n sta
t
ic
co
mp
ens
a
t
io
n (
DST
AT
CO
M
)
Fo
r
STAT
C
OM
m
o
d
u
les
d
e
p
lo
y
ed
ac
r
o
s
s
v
ar
i
o
u
s
lo
ca
ti
o
n
s
,
a
d
is
tr
ib
u
ted
a
p
p
r
o
ac
h
to
r
ea
ctiv
e
p
o
wer
(
Q)
co
m
p
e
n
s
atio
n
an
d
v
o
ltag
e
en
h
an
ce
m
en
t
ca
n
ef
f
e
ctiv
ely
ad
d
r
ess
r
ea
ctiv
e
p
o
wer
ch
allen
g
es
at
b
o
th
th
e
f
ee
d
er
an
d
d
is
tr
ib
u
tio
n
l
ev
els.
I
n
d
is
tr
ib
u
tio
n
n
etwo
r
k
s
,
th
is
m
eth
o
d
is
k
n
o
wn
as
d
is
tr
ib
u
tio
n
s
tatic
co
m
p
en
s
atio
n
(
DSTA
T
C
OM
)
.
I
n
th
e
ev
en
t
o
f
a
p
r
im
ar
y
r
e
ac
tiv
e
p
o
wer
s
o
u
r
ce
f
ailu
r
e,
DSTA
T
C
OM
h
elp
s
m
ain
tain
s
y
s
tem
s
tab
ili
ty
b
y
m
itig
atin
g
th
e
lo
s
s
o
f
r
ea
cti
v
e
s
u
p
p
o
r
t
[
1
4
]
.
DSTA
T
C
O
M
en
h
an
ce
s
p
o
wer
s
y
s
tem
ef
f
icien
cy
a
n
d
im
p
r
o
v
es
d
is
tr
ib
u
tio
n
n
etwo
r
k
r
eliab
i
lity
th
r
o
u
g
h
its
p
ar
allel
-
co
n
n
e
cted
v
o
ltag
e
s
o
u
r
ce
co
n
v
er
ter
.
B
y
p
r
o
v
id
in
g
v
o
lta
g
e
s
u
p
p
o
r
t
an
d
m
an
ag
in
g
p
o
wer
d
is
s
ip
atio
n
u
n
d
er
b
o
th
d
y
n
am
ic
an
d
s
tead
y
-
s
tate
co
n
d
itio
n
s
,
DSTA
T
C
O
Ms
p
lay
a
cr
u
cial
r
o
le
in
m
ain
tain
in
g
s
y
s
tem
p
er
f
o
r
m
an
ce
[
1
5
]
.
Key
b
e
n
ef
its
o
f
DSTA
T
C
OM
in
clu
d
e
en
h
an
ce
d
r
ea
ctiv
e
p
o
wer
s
u
p
p
o
r
t,
im
p
r
o
v
ed
v
o
ltag
e
r
eg
u
latio
n
,
r
ap
i
d
v
o
ltag
e
r
ec
o
v
er
y
,
s
tr
en
g
th
en
ed
tr
an
s
ien
t
s
tab
ilit
y
,
an
d
in
cr
ea
s
ed
o
v
er
all
s
y
s
tem
r
eliab
ilit
y
.
Ad
d
itio
n
ally
,
its
ad
ap
tab
ilit
y
co
n
tr
ib
u
tes
to
h
ig
h
er
lin
e
ca
p
ac
ity
an
d
r
ed
u
ce
d
s
y
s
tem
lo
s
s
es,
m
ak
in
g
it
an
ess
en
tial
co
m
p
o
n
e
n
t
o
f
m
o
d
er
n
p
o
wer
d
is
tr
ib
u
tio
n
n
etwo
r
k
s
[
1
6
]
.
I
n
teg
r
atin
g
DSTA
T
C
OM
with
an
en
er
g
y
s
to
r
ag
e
s
y
s
tem
(
E
SS
)
f
u
r
th
er
en
h
an
ce
s
its
f
le
x
ib
ilit
y
an
d
v
o
ltag
e
s
u
p
p
o
r
t
ca
p
ab
ilit
ies,
lev
er
ag
in
g
th
e
b
en
ef
its
o
f
f
lex
ib
le
AC
tr
an
s
m
i
s
s
io
n
s
y
s
tem
s
(
FAC
T
S)
d
ev
ices.
Ad
d
itio
n
ally
,
s
u
p
er
c
o
n
d
u
ctin
g
m
ag
n
etic
en
e
r
g
y
s
to
r
a
g
e
(
SME
S)
in
co
m
b
in
atio
n
with
DSTA
T
C
OM
ca
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
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l Po
wer
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n
g
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SS
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8
7
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o
lta
g
e
p
r
o
file e
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a
n
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men
t i
n
g
r
id
s
ystem
u
s
in
g
ex
p
ert s
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em
(
G.
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a
th
is
h
Go
u
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)
451
im
p
r
o
v
e
tr
a
n
s
m
is
s
io
n
ca
p
ac
ity
.
W
ith
th
e
ca
p
ab
ilit
y
to
b
o
th
ab
s
o
r
b
an
d
s
u
p
p
ly
P&
Q,
DSTA
T
C
OM
o
p
er
ates in
f
o
u
r
q
u
a
d
r
an
ts
.
B
ey
o
n
d
v
o
ltag
e
r
eg
u
latio
n
,
it
ca
n
m
o
d
if
y
s
y
s
tem
p
h
ase
an
g
les
a
n
d
s
er
ies
im
p
ed
an
ce
,
en
a
b
lin
g
tr
an
s
m
is
s
io
n
lin
es
to
f
u
n
ctio
n
clo
s
er
to
th
er
m
al
lim
its
wh
ile
m
in
im
izin
g
lin
e
lo
s
s
es
[
1
7
]
.
DSTA
T
C
OM
tech
n
o
lo
g
y
is
ap
p
licab
le
ac
r
o
s
s
u
ltra
-
h
ig
h
-
v
o
ltag
e
(
UHV)
,
e
x
tr
a
-
h
ig
h
-
v
o
ltag
e
(
E
HV)
,
an
d
h
ig
h
-
v
o
ltag
e
(
HV)
f
ee
d
er
s
y
s
tem
s
.
Fu
n
d
am
en
tally
,
DSTA
T
C
OM
an
d
o
th
er
F
AC
T
S
d
ev
ices
s
h
ar
e
s
im
ilar
d
esig
n
p
r
in
cip
les
an
d
f
u
n
ctio
n
alities
,
m
ak
in
g
th
em
e
s
s
en
tial c
o
m
p
o
n
en
ts
f
o
r
m
o
d
e
r
n
p
o
wer
s
y
s
tem
s
tab
ilit
y
an
d
ef
f
icien
cy
.
2
.
2
.
Su
pp
o
rt
v
ec
t
o
r
ma
chine (
SVM
)
SVMs
o
b
jectiv
e
to
in
cr
ea
s
e
th
e
m
ar
g
in
ac
r
o
s
s
th
e
d
iv
i
d
in
g
h
y
p
e
r
p
lan
e
a
n
d
th
e
d
ata
p
o
in
ts
wh
ile
r
ed
u
cin
g
th
e
u
p
p
e
r
b
o
u
n
d
o
f
s
im
p
lific
atio
n
er
r
o
r
s
.
I
n
m
o
s
t
o
f
ca
s
es,
th
e
h
y
p
er
p
lan
e
f
o
r
d
ata
ca
talo
g
in
g
is
d
eter
m
in
ed
b
y
s
elec
tin
g
a
s
u
b
s
et
o
f
s
u
p
p
o
r
t v
ec
to
r
s
f
r
o
m
t
h
e
tr
ain
in
g
s
et
o
f
in
p
u
t.
B
y
em
p
lo
y
in
g
th
e
s
tr
u
ctu
r
al
r
is
k
m
in
im
izatio
n
(
SR
M)
p
r
in
cip
le,
SVMs
d
ec
r
ea
s
e
s
im
p
l
if
icatio
n
er
r
o
r
s
o
n
test
d
atasets
.
SR
M
en
h
an
ce
s
class
s
ep
ar
atio
n
b
y
m
ap
p
in
g
d
ata
n
o
n
-
lin
ea
r
ly
in
t
o
a
h
ig
h
-
d
im
en
s
io
n
al
s
p
ac
e,
wh
e
r
e
a
s
im
p
ler
m
o
d
el
is
ch
o
s
en
f
o
r
a
g
i
v
en
tr
ain
in
g
m
o
d
el,
en
s
u
r
in
g
th
at
th
e
d
ec
is
io
n
lim
it
in
th
e
tr
an
s
f
o
r
m
ed
s
p
ac
e
r
em
ain
s
lin
ea
r
[
1
8
]
.
Alter
n
ativ
ely
,
SVM
k
e
r
n
els
ca
n
n
o
n
-
lin
ea
r
ly
ad
ju
s
t
t
h
e
‘
in
p
u
t
s
p
ac
e’
to
a
‘
h
ig
h
er
-
d
im
en
s
io
n
al
s
p
ac
e’
,
en
ab
lin
g
m
o
r
e
ef
f
ec
tiv
e
class
if
icatio
n
.
A
k
er
n
el
f
u
n
ctio
n
,
K
(
y
i,y
)
is
p
r
o
p
o
s
ed
u
s
in
g
s
u
p
p
o
r
t
v
ec
to
r
s
‘
y
i’
f
r
o
m
th
e
test
d
ata
an
d
an
in
p
u
t
v
ec
to
r
‘
y
’
.
T
h
e
p
r
im
ar
y
o
b
jec
tiv
e
o
f
SVMs
is
to
m
in
im
ize
s
o
r
tin
g
er
r
o
r
s
b
y
co
n
s
tr
u
ctin
g
o
p
tim
al
f
in
alize
d
f
u
n
ctio
n
s
th
at
ac
cu
r
ately
p
r
ed
ict
an
d
ca
teg
o
r
ize
h
id
d
e
n
in
p
u
ts
in
to
s
ep
ar
ate
g
r
o
u
p
s
.
I
n
o
u
r
ap
p
r
o
ac
h
,
we
u
tili
ze
SVMs
to
ac
h
iev
e
th
is
g
o
al.
T
h
e
r
esu
ltin
g
SVM
f
u
n
c
tio
n
ex
h
ib
its
s
tr
o
n
g
g
en
er
aliza
tio
n
ca
p
ab
ilit
ies,
r
ed
u
cin
g
o
v
er
s
h
o
o
t
wh
ile
id
en
tify
in
g
a
well
-
o
r
ien
ted
,
m
ax
im
ized
-
m
ar
g
in
h
y
p
er
p
lan
e.
T
h
e
m
ath
em
atica
l
ex
p
r
ess
io
n
f
o
r
th
e
o
p
tim
al
s
ep
ar
atin
g
h
y
p
e
r
p
lan
e
is
f
o
r
m
u
lated
an
d
s
o
lv
ed
u
s
in
g
MA
T
L
AB
SVM
to
o
ls
(
1
)
.
∗
.
+
∗
=
0
(
1
)
I
t
m
in
im
izes
m
is
class
if
icatio
n
er
r
o
r
s
wh
ile
m
ax
im
izin
g
t
h
e
m
ar
g
i
n
.
T
h
e
(
2
)
d
ef
in
es
th
e
o
p
tim
al
weig
h
t
v
ec
to
r
∗
.
∗
=
∑
∗
=
1
∗
(
2
)
W
h
er
e
1
*
=
(
1
*
,
2
*
,
3
*
……
……
N
*
)
,
yi
with
*
>0
ar
e
th
e
p
o
in
ts
o
f
s
u
p
p
o
r
t
v
ec
to
r
.
T
h
e
(
3
)
ca
n
b
e
u
tili
ze
d
to
s
ep
ar
ate
a
n
o
v
el
d
at
a
v
ec
to
r
y
.
=
(
(
)
)
(
3
)
Her
e,
f(
y)
is
th
e
o
p
tim
u
m
d
eter
m
in
ed
b
o
u
n
d
a
r
y
wh
ich
n
ee
d
f
r
o
m
s
am
p
les
o
f
th
e
tr
a
in
in
g
v
ar
iab
le
s
et
ex
p
r
ess
ed
in
(
4
)
.
(
)
=
∗
.
+
∗
(
4
)
Her
e
is
an
o
th
er
way
t
o
s
tate
th
e
ab
o
v
e
e
q
u
atio
n
:
(
)
=
(
∑
∗
)
+
∗
=
1
(
5
)
n
ex
t,
th
e
s
ets
o
f
tr
ain
in
g
is
u
tili
ze
d
to
d
eter
m
in
e
th
e
class
z
∈
{−
1
,
1
}
o
f
‘
y
’
b
y
co
m
p
u
tin
g
th
e
d
o
t
p
r
o
d
u
ct
am
i
d
th
e
tr
ain
ed
d
ata
an
d
th
e
s
u
p
p
o
r
t
v
ec
to
r
[
1
9
]
.
Fo
r
lin
ea
r
ly
s
ep
ar
ab
le
d
ata,
a
d
iv
id
in
g
h
y
p
er
p
l
an
e
ca
n
b
e
u
tili
ze
d
f
o
r
class
if
icatio
n
.
T
h
o
u
g
h
,
in
r
ea
l
-
wo
r
ld
s
ce
n
ar
io
s
,
d
ata
is
o
f
ten
n
o
n
-
s
ep
ar
a
b
le
an
d
n
o
n
-
lin
ea
r
,
r
e
q
u
ir
in
g
k
er
n
el
f
u
n
ctio
n
s
f
o
r
ef
f
ec
tiv
e
m
ap
p
in
g
.
T
h
is
ar
ch
itectu
r
e
allo
ws f
o
r
v
ar
i
o
u
s
ty
p
es o
f
d
ata
s
ep
ar
atio
n
.
3.
RADIA
L
B
A
SI
S F
UNCT
I
O
N
NE
URA
L
N
E
T
WO
RK
Fig
u
r
e
1
illu
s
tr
ates
a
b
ac
k
p
r
o
p
ag
atio
n
n
etwo
r
k
s
tr
u
ctu
r
e
w
ith
a
s
in
g
le
h
id
d
en
la
y
er
,
wh
ich
f
o
r
m
s
th
e
co
r
e
o
f
a
R
B
FNN.
C
o
n
f
er
r
in
g
t
o
s
u
r
v
e
y
f
i
n
d
in
g
s
i
n
[
2
0
]
,
R
B
FNN
is
th
e
u
tm
o
s
t
ef
f
ec
tiv
e
an
d
r
eliab
le
n
etwo
r
k
f
o
r
o
r
g
an
izatio
n
task
s
.
E
ac
h
h
id
d
en
lay
er
co
n
s
is
ts
o
f
ce
n
tr
o
id
s
an
d
a
s
m
o
o
th
in
g
f
ac
to
r
.
T
y
p
ically
,
n
eu
r
o
n
s
ca
lcu
late
th
e
d
is
tan
ce
b
etwe
en
th
e
in
p
u
t
an
d
t
h
e
ce
n
tr
o
id
s
,
p
r
o
d
u
cin
g
r
esu
lts
th
at
s
u
r
v
ey
a
d
is
tan
ce
-
d
ep
en
d
en
t,
r
a
d
ially
b
alan
ce
d
p
atter
n
.
As th
e
in
p
u
t a
p
p
r
o
ac
h
es th
e
ce
n
tr
o
id
v
alu
e,
t
h
e
o
u
tp
u
t b
ec
o
m
es
m
o
r
e
r
o
b
u
s
t.
T
h
e
m
ap
p
i
n
g
f
u
n
ctio
n
,
ca
n
b
e
g
en
er
ally
g
iv
en
as (
6
)
.
(
)
=
∑
=
1
[
(
−
)
/
]
(
6
)
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.
1
4
,
No
.
2
,
J
u
n
e
20
2
5
:
449
-
4
58
452
Her
e
‘
’
is
r
ad
ial
s
y
m
m
etr
ical
k
er
n
el
f
u
n
ctio
n
wh
ich
is
c
alcu
lated
u
s
in
g
Z
k
er
n
el
u
n
i
ts
.
Fu
n
d
am
en
tal
ex
p
o
n
e
n
tial f
u
n
ctio
n
s
o
f
o
n
e
o
f
R
B
F
's is
g
iv
en
as (
7
)
.
(
)
=
e
xp
(
−
∑
[
(
−
)
/
]
2
)
(
7
)
T
h
e
s
p
r
ea
d
p
a
r
am
eter
(
)
,
co
n
s
tan
t
(
β)
,
a
n
d
ce
n
tr
o
id
(
)
m
u
s
t
b
e
ch
o
s
en
d
e
p
en
d
e
n
t
o
n
th
e
tr
ain
in
g
d
ataset
[
2
1
]
.
T
h
e
ef
f
ec
tiv
en
ess
o
f
DSTA
T
C
OM
s
in
th
e
p
o
wer
g
r
id
d
e
p
en
d
s
o
n
th
eir
n
u
m
b
er
,
p
lace
m
e
n
t,
an
d
ca
p
ac
ity
,
wh
eth
er
d
ep
lo
y
ed
i
n
d
ep
en
d
en
tly
o
r
in
ag
g
r
eg
ati
o
n
with
a
d
y
n
a
m
ic
s
o
u
r
ce
.
D
STAT
C
OM
p
lay
s
a
cr
itical
r
o
le
in
e
n
h
an
ci
n
g
g
r
id
p
er
f
o
r
m
an
ce
.
N
u
m
er
o
u
s
s
tu
d
i
es
h
av
e
ex
p
lo
r
ed
o
p
tim
al
p
lac
em
en
t
s
tr
ateg
ies
f
o
r
FAC
T
S
d
ev
ices,
in
clu
d
in
g
D
STAT
C
OM
,
to
m
ax
im
ize
p
o
wer
s
y
s
tem
ef
f
icien
cy
.
Po
ten
t
ial
in
s
tallatio
n
s
ites
in
clu
d
e
b
o
th
th
e
co
n
s
u
m
er
s
id
e
d
is
tr
ib
u
tio
n
an
d
th
e
f
ee
d
er
s
id
e
lev
els.
DSTA
T
C
OM
s
ca
n
b
e
d
ep
lo
y
e
d
eith
er
ce
n
tr
ally
in
a
s
in
g
le
lo
ca
tio
n
o
r
d
is
tr
ib
u
ted
ac
r
o
s
s
m
u
ltip
le
s
ites
f
o
r
im
p
r
o
v
ed
p
er
f
o
r
m
an
ce
.
Fig
u
r
e
1
.
Ar
c
h
itectu
r
e
o
f
NN
3
.
1
.
P
SAT
m
o
dellin
g
o
f
I
E
E
E
1
4
bu
s
s
y
s
t
em
Var
iab
le
lo
ad
s
wer
e
in
tr
o
d
u
ce
d
to
ex
am
in
e
t
h
e
s
y
s
tem
'
s
r
es
p
o
n
s
e.
C
ap
ac
ito
r
b
a
n
k
s
ar
e
in
co
r
p
o
r
ated
to
co
u
n
ter
ac
t
th
e
in
itial
v
o
ltag
e
d
r
o
p
tr
ig
g
er
ed
b
y
th
e
v
ar
i
ab
le
h
ea
v
y
lo
ad
s
.
PS
AT
to
o
ls
wer
e
em
p
lo
y
ed
to
f
ac
ilit
ate
to
p
r
esen
t
o
f
wav
ef
o
r
m
p
lo
ttin
g
in
g
r
a
p
h
ical
f
o
r
m
at
an
d
f
o
r
an
aly
s
is
.
B
y
ch
o
o
s
in
g
ap
p
r
o
p
r
iate
ch
o
ices,
r
esp
o
n
s
es
f
r
o
m
th
e
lo
west
an
d
h
ig
h
est
v
o
ltag
e
b
u
s
es,
am
o
n
g
o
t
h
er
s
,
wer
e
o
b
tain
ed
[
2
2
]
.
T
h
e
to
o
lb
ar
’
s
lib
r
ar
y
f
u
n
ctio
n
s
e
n
a
b
led
th
e
cr
ea
tio
n
o
f
d
is
tu
r
b
an
ce
s
with
in
th
e
s
y
s
tem
,
allo
win
g
f
o
r
m
o
d
if
icatio
n
s
to
in
d
iv
i
d
u
al
f
au
lt p
ar
am
eter
s
as
n
ee
d
ed
.
T
o
f
u
r
th
er
ass
ess
s
y
s
tem
p
er
f
o
r
m
an
ce
an
d
e
n
h
an
ce
its
in
tellig
en
ce
,
a
f
au
lt
co
n
d
itio
n
—
s
p
ec
if
ically
a
‘
lin
e
-
to
-
g
r
o
u
n
d
(L
-
G)
’
f
a
u
lt
o
n
b
u
s
1
was
in
tr
o
d
u
ce
d
.
T
h
e
f
au
lt
is
o
cc
u
r
r
e
d
at
t
=
0
s
ec
o
n
d
s
an
d
was
r
em
o
v
ed
at
2
s
ec
o
n
d
s
.
T
h
e
b
u
s
s
y
s
tem
was
th
en
r
ed
esig
n
ed
an
d
s
im
u
lated
u
s
in
g
PS
AT
s
o
f
twar
e
[
2
3
]
.
Vo
ltag
e
p
r
o
f
ile
s
ac
r
o
s
s
all
b
u
s
es
was
an
aly
ze
d
to
ev
alu
ate
s
y
s
tem
s
tab
ilit
y
.
Fig
u
r
es
2
a
n
d
3
p
r
esen
t th
e
I
E
E
E
1
4
-
b
u
s
s
y
s
tem
’
s
s
in
g
le
-
lin
e
d
iag
r
am
an
d
P
SAT
m
o
d
el,
r
esp
ec
tiv
ely
.
Fig
u
r
e
3
p
r
esen
ts
th
e
in
tr
o
d
u
c
ed
DSTA
T
C
OM
to
p
o
lo
g
y
,
wh
ich
is
b
ased
o
n
th
e
R
B
FNN
tech
n
iq
u
e.
T
h
e
v
o
ltag
e
p
r
o
f
ile
v
ar
iatio
n
s
an
d
r
esp
o
n
s
e
g
ain
s
o
b
tai
n
ed
f
r
o
m
a
tr
a
d
itio
n
al
co
n
tr
o
ller
s
e
r
v
e
as
in
p
u
ts
to
th
e
R
B
FNN.
Du
r
in
g
d
ata
an
aly
s
is
,
th
e
R
B
FN
N
m
o
d
u
le
allo
ca
tes
8
5
%
o
f
th
e
in
p
u
t
d
ata
f
o
r
p
r
o
ce
s
s
in
g
an
d
1
5
%
f
o
r
t
u
n
in
g
an
d
test
in
g
.
T
h
e
s
y
s
tem
ad
o
p
ts
th
e
b
ac
k
-
p
r
o
p
a
g
atio
n
alg
o
r
ith
m
f
o
r
th
e
tr
ain
in
g
,
en
ab
lin
g
it
to
ad
ap
t
ef
f
ec
tiv
ely
to
n
ew
o
r
u
n
k
n
o
wn
v
o
ltag
e
p
r
o
f
iles
an
d
g
ain
v
a
r
i
atio
n
s
[
2
4
]
.
T
h
e
R
B
FN
N
co
n
tr
o
ller
-
b
ase
d
DSTA
T
C
OM
i
s
d
esig
n
ed
in
MA
T
L
AB
to
s
im
u
late
an
L
-
G
f
au
lt
d
is
tu
r
b
an
ce
at
b
u
s
1
2
.
T
h
e
f
a
u
lt
o
cc
u
r
s
at
t
=
0
s
ec
o
n
d
s
a
n
d
is
clea
r
ed
a
f
ter
2
s
ec
o
n
d
s
.
R
esu
lts
in
d
icate
th
at
th
e
p
o
we
r
s
y
s
tem
i
n
co
r
p
o
r
atin
g
th
e
R
B
FNN
co
n
tr
o
ller
-
b
ase
d
DSTA
T
C
OM
r
esto
r
es
th
e
v
o
ltag
e
p
r
o
f
ile
m
o
r
e
r
ap
id
ly
th
an
a
tr
ad
itio
n
ally
c
o
n
tr
o
lled
b
u
s
s
y
s
tem
.
Ad
d
itio
n
ally
,
s
y
s
tem
s
tab
ilit
y
is
ef
f
icie
n
tly
s
u
s
tain
ed
ev
en
d
u
r
in
g
m
u
ltip
le
d
is
tu
r
b
an
ce
s
to
th
e
s
y
s
tem
.
T
o
d
em
o
n
s
tr
ate
th
e
en
h
an
ce
d
p
er
f
o
r
m
a
n
c
e
o
f
th
e
in
tellig
en
t
s
y
s
tem
,
th
e
v
o
ltag
e
m
ag
n
itu
d
es
o
f
t
h
e
3
lo
w
-
v
o
ltag
e
b
u
s
es
d
u
r
in
g
t
h
e
f
a
u
lt
ar
e
co
m
p
ar
ed
f
o
r
b
o
t
h
th
e
tr
ad
itio
n
ally
co
n
tr
o
lled
DSTA
T
C
OM
an
d
th
e
R
B
FNN
co
n
tr
o
ller
-
b
ased
DSTA
T
C
OM
.
T
h
is
co
m
p
ar
is
o
n
h
ig
h
lig
h
ts
th
e
im
p
r
o
v
ed
ef
f
ici
en
cy
an
d
ad
ap
ta
b
ilit
y
o
f
th
e
b
u
s
s
y
s
tem
ac
h
iev
ed
th
r
o
u
g
h
ar
tific
ial
in
tellig
en
ce
in
teg
r
atio
n
[
2
5
]
.
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
V
o
lta
g
e
p
r
o
file e
n
h
a
n
ce
men
t i
n
g
r
id
s
ystem
u
s
in
g
ex
p
ert s
yst
em
(
G.
S
a
th
is
h
Go
u
d
)
453
Fig
u
r
e
2
.
I
E
E
E
1
4
b
u
s
s
y
s
tem
Fig
u
r
e
3
.
I
E
E
E
1
4
b
u
s
s
y
s
tem
PS
AT
m
o
d
el
B
u
s
1
4
B
u
s
1
3
B
u
s
1
2
B
u
s
1
1
B
u
s
1
0
B
u
s
0
9
B
u
s
0
8
B
u
s
0
7
B
u
s
0
6
B
u
s
0
5
B
u
s
0
4
B
u
s
0
3
B
u
s
0
2
B
u
s
0
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.
1
4
,
No
.
2
,
J
u
n
e
20
2
5
:
449
-
4
58
454
4.
RE
SU
L
T
AND
DI
SCUS
SI
O
N
T
h
e
o
b
s
er
v
e
d
o
s
cillatio
n
s
ar
e
a
r
esu
lt
o
f
th
e
v
ar
iab
le
lo
ad
i
n
g
ch
ar
ac
ter
is
tics
.
I
n
itial
d
ec
lin
e
in
th
e
v
o
ltag
e
m
ag
n
itu
d
e
is
attr
ib
u
ted
to
th
e
i
n
h
er
e
n
t
n
at
u
r
e
o
f
d
y
n
am
ic
lo
ad
in
g
.
As
p
r
es
en
ted
,
t
h
e
v
o
ltag
e
m
ag
n
itu
d
e
h
as
f
allen
b
elo
w
1
p
er
u
n
it
(
p
.
u
.
)
,
class
if
y
in
g
th
e
m
as
wea
k
er
ce
lls
.
T
h
ese
wea
k
er
ce
lls
ar
e
h
ig
h
ly
s
en
s
itiv
e
to
d
is
tu
r
b
an
ce
s
,
an
d
an
y
d
is
r
u
p
ti
o
n
ca
n
lead
to
s
y
s
t
em
in
s
tab
ilit
y
.
Fig
u
r
e
4
illu
s
tr
ates
th
e
m
ag
n
itu
d
e
o
f
b
u
s
v
o
ltag
es
f
o
r
b
u
s
e
s
4
,
5
,
an
d
1
4
,
s
h
o
win
g
v
alu
e
s
d
r
o
p
p
in
g
b
elo
w
1
p
.
u
.
I
d
en
tif
y
in
g
wea
k
lin
k
s
in
t
h
e
n
etwo
r
k
is
v
it
al
f
o
r
m
ai
n
tain
in
g
th
e
s
y
s
tem
s
tab
ilit
y
in
th
ese
co
n
d
itio
n
s
.
T
h
ese
v
u
ln
er
a
b
le
p
o
in
ts
ar
e
co
n
tin
u
o
u
s
ly
m
o
n
it
o
r
ed
to
e
n
s
u
r
e
th
ey
r
em
ain
u
n
d
er
co
n
tr
o
l,
th
er
e
b
y
p
r
ev
en
tin
g
p
o
te
n
tial n
etwo
r
k
-
wid
e
m
alf
u
n
ctio
n
s
o
r
o
u
tag
es.
T
h
e
PI
r
eg
u
lato
r
h
as
a
s
ig
n
if
i
ca
n
t
p
ar
t
in
d
eter
m
in
in
g
th
e
p
r
o
p
o
r
ti
o
n
al
g
ain
(
K
p
)
,
in
teg
r
al
g
ain
(
Ki)
,
g
ain
s
o
f
AC
an
d
DC
co
n
tr
o
lle
r
s
,
an
d
th
e
d
am
p
i
n
g
co
n
tr
o
ller
.
As
p
er
th
e
s
im
u
latio
n
r
esu
lts
,
it
is
o
b
s
er
v
ed
th
at
th
er
e
is
an
im
p
r
o
v
em
en
t
i
n
t
h
e
v
o
ltag
e
m
ag
n
itu
d
es
o
f
3
lo
w
v
o
ltag
es
b
u
s
es.
No
tab
ly
,
th
e
3
b
u
s
es
v
o
ltag
e
m
ag
n
itu
d
es
wer
e
m
ain
tain
e
d
n
ea
r
to
1
p
.
u
.
T
h
e
v
o
ltag
e
g
o
es
lo
w
in
th
ese
b
u
s
es
ar
e
ef
f
e
ctiv
ely
in
cr
ea
s
ed
b
y
in
teg
r
atin
g
th
e
DSTA
T
C
OM
,
as illu
s
tr
ated
in
Fig
u
r
es 5
th
r
o
u
g
h
1
1
.
Fig
u
r
e
4
.
B
u
s
es with
lo
west v
o
ltag
e
(
a)
(
b
)
Fig
u
r
e
5
.
V
o
lta
g
e
m
a
g
n
it
u
d
e
c
o
m
p
ar
is
o
n
wit
h
a
n
d
w
it
h
o
u
t
D
-
STA
T
C
OM
i
n
p
er
u
n
it
at
(
a
)
b
u
s
1
a
n
d
(
b
)
b
u
s
2
(
a)
(
b
)
Fig
u
r
e
6
.
V
o
lta
g
e
m
a
g
n
it
u
d
e
c
o
m
p
ar
is
o
n
wit
h
a
n
d
w
it
h
o
u
t
D
-
STA
T
C
OM
i
n
p
er
u
n
it
at
(
a
)
b
u
s
3
a
n
d
(
b
)
b
u
s
4
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
V
o
lta
g
e
p
r
o
file e
n
h
a
n
ce
men
t i
n
g
r
id
s
ystem
u
s
in
g
ex
p
ert s
yst
em
(
G.
S
a
th
is
h
Go
u
d
)
455
(
a)
(
b
)
Fig
u
r
e
7
.
V
o
ltag
e
m
ag
n
itu
d
e
c
o
m
p
ar
is
o
n
with
a
n
d
with
o
u
t D
-
STAT
C
OM
in
p
er
u
n
it
at
(
a)
b
u
s
5
an
d
(
b
)
b
u
s
6
(
a)
(
b
)
Fig
u
r
e
8
.
V
o
ltag
e
m
ag
n
itu
d
e
c
o
m
p
ar
is
o
n
with
a
n
d
with
o
u
t D
-
STAT
C
OM
in
p
er
u
n
it
at
(
a)
b
u
s
7
an
d
(
b
)
b
u
s
8
(
a)
(
b
)
Fig
u
r
e
9
.
V
o
ltag
e
m
ag
n
itu
d
e
c
o
m
p
ar
is
o
n
with
a
n
d
with
o
u
t D
-
STAT
C
OM
in
p
er
u
n
it
at
(
a)
b
u
s
9
an
d
(
b
)
b
u
s
1
0
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.
1
4
,
No
.
2
,
J
u
n
e
20
2
5
:
449
-
4
58
456
(
a)
(
b
)
Fig
u
r
e
1
0
.
V
o
ltag
e
m
ag
n
itu
d
e
co
m
p
ar
is
o
n
with
a
n
d
with
o
u
t
D
-
STAT
C
OM
in
p
er
u
n
it
at
(
a)
b
u
s
1
1
an
d
(
b
)
b
u
s
1
2
(
a)
(
b
)
Fig
u
r
e
1
1
.
V
o
ltag
e
m
ag
n
itu
d
e
co
m
p
ar
is
o
n
with
a
n
d
with
o
u
t
D
-
STAT
C
OM
in
p
er
u
n
it
at
(
a)
b
u
s
1
3
an
d
(
b
)
b
u
s
1
4
5.
CO
NCLU
SI
O
N
T
h
is
s
tu
d
y
em
p
h
asized
th
e
i
m
p
o
r
tan
ce
o
f
m
ai
n
tain
in
g
a
co
n
s
tan
t
v
o
ltag
e
p
r
o
f
ile
an
d
ex
p
lo
r
e
d
v
ar
io
u
s
asp
ec
ts
r
elate
d
to
v
o
ltag
e
s
tab
ilit
y
.
I
t
d
elv
ed
in
to
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RE
F
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NC
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S
[
1
]
P
.
K
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.
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.
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u
mar,
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P
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6
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