In
te
r
n
ation
a
l Jou
rn
al
o
f Po
we
r
Elec
tron
ic
s an
d
D
r
ive S
y
stem
(IJ
PED
S
)
V
o
l.
10, N
o.
3, S
ep 2019,
pp.
1
2
4
4
~1
2
5
4
ISSN: 2088-
8694,
DOI
:
10.11591
/ijpeds.
v10.
i
3.pp1244-1254
1
2
44
Jou
rn
a
l
h
o
me
pa
ge
:
ht
tp:
//i
a
e
score
.
com
/
j
o
u
r
na
l
s
/
i
n
d
e
x
.
p
hp/IJ
PED
S
Pow
er flow
variation base
d
on extr
eme learning m
achine
algorithm
in power system
L
a
be
d
Imen, Lab
ed
D
jame
l
Lab
o
rato
ry of
Electri
cal E
ngineer
i
n
g
,
D
e
p
artm
ent O
f
El
ectrical
Engi
neerin
g,
Un
i
vers
it
y
of
C
on
st
antin
e
1,
Al
g
e
ri
a
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
R
e
c
e
i
v
e
d
Feb
1
4
,
2
019
Re
vise
d Mar
1,
201
9
A
c
c
e
pte
d
A
pr 8,
201
9
The
m
a
in
f
o
c
us
o
f
th
is
p
aper
i
s
a
stu
d
y
t
h
at
e
m
powers
u
s
t
o
un
d
ers
t
an
d
how
the
t
e
mp
eratu
r
e
v
a
riat
ion
affects
t
h
e
trans
m
ission
l
in
e
res
i
sta
nce
an
d
as
a
resul
t
t
h
e
p
o
w
er
f
l
o
w
an
alys
is
w
ith
a
sp
ecif
i
c
end
go
al
t
o
ass
e
ss
l
oss
e
s
in
t
he
electri
cal
n
et
work
.
Th
e
p
a
per
is
c
om
p
o
s
e
d
of
t
wo
s
ect
ion
s
;
t
h
e
fi
rs
t
part
i
s
a
power
f
l
o
w
study
u
nder
n
ormal
co
ndit
i
o
ns
u
tilizi
n
g
t
h
e
neural
n
et
work
appro
ach
w
h
i
l
e
t
he
s
eco
nd
in
ves
t
i
g
ated
e
xtrem
e
l
earn
i
n
g
m
ach
in
e
a
lg
ori
t
hm
effi
cien
cy
a
n
d
e
xacti
t
u
d
e.
E
xtrem
e
l
earn
i
n
g
m
a
c
h
i
n
e
a
lg
ori
t
hm
h
as
b
ee
n
used
t
o
s
e
tt
le
s
ev
eral
c
om
p
l
icat
io
ns
i
n
po
wer
syst
em:
lo
ad
f
ore
cas
ti
ng
,
f
a
u
lt
diag
no
sis, e
co
no
m
i
c d
i
s
p
atch
, s
e
curi
ty,
tran
si
en
t st
abilit
y
;
Th
us
,
we
p
r
op
osed
to
s
t
u
dy
t
h
i
s
technique
to
f
igur
e
out
t
hi
s
s
o
rt
o
f
com
p
lex
is
su
e.
T
he
s
tu
dy
wa
s
c
o
nd
uc
te
d
fo
r
IEE
E
3
0
bu
s
te
s
t
s
ys
te
m
.
T
h
e
s
i
m
ula
t
io
n
re
su
l
t
s
a
re
expo
sed
and
ana
l
yzed
i
n
de
t
a
il
a
t
t
h
e
en
d
of
t
his
pa
p
e
r.
K
eyw
ord
s
:
C
o
ndu
ct
o
r
R
e
s
i
s
t
a
n
ce
Ex
trem
e
l
e
arning
ma
chi
n
e.
Neu
r
al
Net
wo
r
k
s
Over
head
l
i
n
e
Po
wer
F
l
o
w
Co
pyri
gh
t © 2
019 In
stit
u
t
e
of Advanced
En
gi
neeri
n
g
an
d
S
c
ien
ce.
All
rights
res
e
rv
ed.
Corres
pon
d
i
n
g
Au
th
or:
Labe
d Im
en
Lab
o
ra
tor
y
of
Elec
tric
a
l
Eng
i
n
eer
ing,
D
e
pa
rtme
nt
o
f
El
e
c
t
rica
l
Eng
i
ne
eri
ng,
U
n
i
v
ersi
ty o
f
Cons
ta
nt
ine
1,
A
lger
i
a
Em
ail:
l
a
be
d
i
me
n4
@
g
ma
i
l
.
c
o
m
1.
I
N
TR
OD
U
C
TI
O
N
El
ect
ri
c
po
we
r
sy
st
ems
a
r
e
rea
l
-t
i
m
e
en
erg
y
d
e
liv
ery
sy
st
ems.
R
ea
l
-
ti
me
m
ea
n
s
t
ha
t
po
we
r
i
s
gene
ra
ted
tr
an
spor
ted
a
nd
s
upp
l
i
ed
t
he
m
o
m
ent
w
e
t
urn
on
the
li
g
h
t
s
w
itc
h
[
1
].
E
l
e
c
t
ric
pow
er
s
y
s
t
e
m
s
a
r
e
no
t
s
t
orage
s
y
stem
s
l
i
ke
w
a
t
er
a
n
d
g
as
s
y
s
tem
s
.
Instea
d,
g
e
n
era
t
o
r
s
p
rod
u
ce
t
he
e
ne
rgy
as
t
he
d
e
m
and
cal
l
s for it [
2
, 3]
.
The
hu
ge
a
mo
un
t
of
p
ow
e
r
g
e
n
era
t
e
d
i
n
a
p
o
w
e
r
sta
t
i
o
n
(h
un
dre
d
s
o
f
M
W
)
is
t
o
be
t
r
a
nsp
o
rte
d
o
v
e
r
a
lo
ng
di
st
anc
e
(
h
und
re
d
s
o
f
k
i
lo
me
t
e
rs)
t
o
l
o
a
d
c
e
n
t
e
rs
t
o
c
a
t
er
pow
er
t
o
c
o
n
s
ume
r
s
w
ith
t
he
h
el
p
of
h
i
gh-
vo
lta
ge
t
ran
s
m
i
ss
io
n
line
in
o
rde
r
t
o
red
u
c
e
t
rans
por
ta
ti
on
l
o
s
se
s.
T
ra
nsm
i
ssi
on
an
d
distri
bu
t
i
o
n
l
o
sses
re
ac
h
a
ra
ge
o
f
4%
t
o
5%
o
f
the
to
tal
c
ons
um
p
tio
n.
T
he
h
i
g
h
e
r-vo
l
tage
t
r
a
nsmiss
i
o
n
l
i
ne
s
re
q
u
ir
e
large
r
s
t
r
u
c
tures
w
i
t
h
l
on
g
e
r
i
n
su
l
a
to
r
s
t
r
i
ng
s
in
o
rd
e
r
t
o
h
a
v
e
g
r
e
at
e
r
a
i
r
g
ap
s
and
nee
d
e
d
i
nsu
l
a
t
i
o
n.
C
o
n
d
u
ct
or
m
a
t
e
r
ia
l
(a
l
l
w
i
r
e
s
),
t
ype,
si
z
e
,
and
c
u
rre
nt
r
ati
n
g
ar
e
ke
y
fa
ctors
i
n
d
e
t
e
r
mini
n
g
t
he
pow
er
h
a
n
dl
in
g
c
a
pa
b
i
l
i
t
y
o
f
t
r
ansmiss
i
on
line
s
.
A
con
duc
t
o
r
he
ats
u
p
w
he
n
c
u
rre
nt
f
lo
w
s
t
hr
o
u
g
h
it
due
t
o
its resis
tan
c
e
,
con
d
u
ct
ors
te
nd
t
o i
n
cre
a
se t
he
ir resist
a
nce
w
i
th
a
n i
n
cre
a
se in tem
p
era
t
ur
e, ra
t
e
d
by h
o
w
m
u
ch
curr
ent
c
a
use
s
t
he
m
t
o
h
e
a
t
u
p
to
a
p
re
de
term
ine
d
a
m
o
u
n
t
o
f
de
g
re
e
s
a
bo
ve
a
mb
ien
t
t
e
m
pe
ra
tu
re
.
The
am
oun
t
of
t
em
pera
tur
e
r
ise
a
b
o
v
e
am
b
i
e
n
t
(i.e
.,
w
he
n
no
curr
ent
f
low
s
)
de
t
e
rm
ine
s
t
he
c
urr
e
nt
r
at
i
n
g
of
a
con
d
u
ct
or.
F
o
r
e
x
a
m
ple
,
w
he
n
a
c
o
n
d
u
ct
or
r
ea
ches
7
0
°
C
a
b
o
v
e
a
m
b
ie
nt
,
the
c
o
n
duc
to
r
is
s
ai
d
t
o
b
e
at
f
u
l
l
loa
d
r
atin
g
[1].
S
c
ient
is
t
s
u
sed
to
m
en
ti
o
n
t
h
e
d
y
n
am
i
c
t
h
e
rm
al
r
a
t
in
g
i
n
lite
ra
t
u
re.
Con
duc
tor
s
t
r
a
ns
p
o
rtin
g
e
n
er
g
y
in
l
ow
t
em
pera
tures
a
r
e
mor
e
e
ffic
i
e
n
t
.
F
o
r
a
n
over
h
e
a
d
t
r
a
nsmi
ss
ion
line
,
t
he
m
a
x
i
m
um
t
em
per
a
ture
i
t
sup
por
t
s
i
s
80C°
[4-6]
.
T
he
c
on
d
u
c
t
or
t
ra
n
s
mit
tin
g
70
0
a
m
pere
s
at
40C;
ca
n
t
r
a
n
spo
r
t
1
200
a
m
p
e
res
a
t
1
0C°,
w
h
ic
h im
pl
i
e
s, from
summ
er sea
so
n to w
i
n
ter
;
t
r
a
nsmiss
i
o
n
l
i
ne
c
a
pa
c
i
t
y
c
an
r
ea
ch the
d
ou
bl
e
[
4
, 6,
7].
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
Po
we
r
f
l
o
w
va
riat
i
on
b
a
se
d o
n
ex
tre
m
e l
e
ar
nin
g
m
a
ch
ine al
g
o
r
ithm
in
p
o
w
e
r
system
(L
ab
e
d
Im
en)
1
245
The
c
o
n
d
u
c
t
or
t
e
m
pe
rat
u
re
v
aries
i
n
t
h
e
r
ange
o
f
0
◦
t
o
6
0
◦
C
or
e
v
e
n
l
a
r
ger
,
r
e
s
ul
ti
n
g
c
han
g
es
o
f
t
h
e
li
ne
resistance [3
,
8,
9]
.
Me
a
n
w
h
il
e
,
t
h
e
r
esist
a
nce
fluc
tua
t
i
o
ns
a
re
e
xp
lic
it
l
y
t
a
k
en
i
n
t
o
ac
co
u
n
t
a
nd
c
o
u
p
l
ed
t
o
pow
e
r
f
l
o
w
ana
l
ys
is. P
o
w
e
r
flow
fluc
t
uat
i
ons
c
a
n
c
ause
vari
ous
p
he
no
m
e
na
r
ang
i
ng from
fre
q
ue
ncy
and
v
o
lta
ge s
t
a
bi
lit
y,
Therm
a
l
c
o
nti
nge
nc
y,
t
o
cri
t
ical
s
ce
nari
os
s
uc
h
as
c
o
m
po
nen
t
s
o
u
t
a
g
es
a
nd
blac
k
o
u
t
[
1
0
].
F
or
t
he
purp
o
ses
of
l
oa
d flow
de
t
erm
i
na
ti
on an
d system
sta
t
e
e
st
im
atio
n,
a
var
i
e
t
y
of me
th
o
d
s has be
en us
e
d.
The
de
v
e
l
o
p
m
e
n
t
of
t
he
se
m
et
ho
ds
i
s
m
a
i
n
l
y
l
ed
by
the
ba
s
i
c
re
qu
irem
ents
o
f
loa
d
f
l
ow
c
a
l
c
u
l
a
tio
n,
w
hic
h
ca
n be
s
umm
e
d
up as
a.
the
co
n
v
erge
nc
e
proper
ties
b.
the
com
p
u
t
in
g e
f
ficie
n
c
y
an
d
m
e
m
or
y re
qu
i
r
em
ents
c.
the
co
n
v
en
ie
nc
e
a
nd fle
x
ib
i
lit
y of t
he
i
m
p
le
m
e
ntat
i
o
n
Ma
the
m
a
tica
lly,
the
l
o
a
d
f
l
o
w
prob
lem
is
a
p
rob
l
em
o
f
solv
i
ng
a
s
y
s
t
e
m
of
non
li
ne
a
r
a
lge
b
ra
i
c
equa
t
i
o
n
s.
W
i
t
h
t
he
s
c
a
l
e
of
pow
er
s
ys
tem
con
t
i
n
ua
lly
e
x
p
an
d
i
n
g
,
the
d
i
me
nsi
o
n
o
f
l
oa
d
fl
ow
e
qua
t
i
o
n
s
n
o
w
bec
o
me
s
v
e
ry
h
ig
h,
t
h
u
s
re
se
arc
h
i
s
s
t
i
l
l
ve
ry
a
ct
ive
.
N
ew
to
n
R
a
p
hs
o
n
t
ec
h
n
i
q
ue
s
ta
nd
s
to
b
e
the
m
o
st
impor
ta
nt
a
p
p
roac
h
t
o
s
olv
e
t
he
l
oa
d
flow
.
More
ove
r
t
h
is
acc
ura
te
t
ec
hn
i
que
b
e
c
a
m
e
u
n
acc
ep
ta
b
l
e
f
o
r
re
al-
ti
m
e
e
l
e
c
t
ric
p
o
we
r
sy
s
t
em
o
pera
t
i
o
n
(
dy
na
m
i
c)
,
the
pro
b
l
e
m
s
r
e
sul
t
m
ai
nl
y
from
t
h
e
s
p
e
e
d
of
o
pera
ti
on
a
n
d
the
de
pe
nda
bil
i
t
y
(
n
o
m
iss
i
n
g
o
p
e
rat
i
o
n
s)
,
he
nce
t
h
e
in
t
r
od
uct
i
on
of
t
he
a
r
tif
i
c
i
a
l
i
n
tel
l
ig
ence
o
r
mor
e
prec
isin
g
e
x
tre
m
e
lear
ni
n
g
m
ac
hine
due
t
o
its
e
x
t
r
e
m
e
ly
f
a
s
t
tr
a
i
n
i
ng,
g
oo
d
ge
nera
liza
tio
n,
a
nd
un
i
v
ersal
appr
ox
im
at
ion
/c
lass
ifica
t
i
o
n
c
a
pa
bi
l
ity
[
11
].
I
t
has
bee
n
d
em
o
n
s
t
r
ate
d
t
o
have
e
xc
e
l
le
nt
l
ea
r
n
i
n
g
a
c
c
u
ra
cy
/spe
ed
i
n
va
ri
ous
a
p
p
lic
at
io
ns,
suc
h
a
s
fa
c
e
c
lass
i
f
ica
tio
n,
i
m
age
segm
enta
t
i
o
n
,
h
u
m
a
n
ac
t
i
o
n
r
ec
o
g
n
it
io
n,
pred
ic
ti
on,
a
n
d
func
ti
ons
a
ppr
ox
im
a
tio
n.
E
L
M
o
ffe
r
s
e
ffe
c
t
ive
s
o
l
u
t
io
n
s
f
or
t
he
e
le
ctri
c
pow
er
s
ys
tem
a
s
it
is
d
e
m
o
n
s
t
r
a
t
e
d
;
i
n
t
h
e
a
r
t
i
c
l
e
[
1
2
]
a
n
o
v
e
l
v
e
r
s
i
o
n
o
f
E
L
M
,
w
h
i
c
h
can
b
e
ap
pli
e
d
t
o
t
ra
i
n
a
s
ing
l
e
hi
d
d
e
n
l
a
y
e
r
r
e
c
u
r
r
e
n
t
n
e
u
r
a
l
n
e
tw
or
k
.
E
L
M
w
a
s
p
r
e
s
e
n
t
e
d
a
n
d
e
m
p
l
o
y
e
d
i
n
o
r
d
e
r
to
a
c
h
ie
v
e
hi
g
h
e
r
f
o
r
e
c
a
s
t
in
g
e
l
e
c
tr
ic
it
y
loa
d
a
c
c
ura
c
y
.
In
[
13]
a
ut
h
o
r
s
int
r
od
uc
ed
a
n
ELM-
b
ased
p
r
e
dic
t
o
r,
t
he
n
it
w
a
s
deve
lope
d
for
the
pow
e
r
system.
The
pr
edictor
has
been
u
sed
for
real-time
to
e
nhance
t
h
e
d
yna
mic
se
curi
ty
o
f
the
p
o
wer
sys
t
em
s.
A
r
ticle
[
1
4
]
ex
pl
ore
s
a
f
a
u
l
t
d
ia
g
n
o
s
is
m
et
h
od
for
t
h
e
ke
y
m
ech
a
n
ic
al
c
o
m
pone
n
t
s
of
t
he
w
in
d
t
u
rbi
n
e.
T
he
me
tho
d
b
a
s
e
d
on
im
pro
v
e
d
e
xt
r
e
m
e
l
ear
n
i
n
g
m
ac
h
i
ne
(
IELM)
com
b
i
n
ed
t
he
f
au
l
t
c
har
a
cte
r
isti
cs
o
f
ge
a
r
a
n
d
bea
r
i
ng
o
f
w
in
d
tur
b
i
n
e
dri
v
e
syste
m
.
A
rob
u
s
t
obser
ver
t
o
d
e
t
e
c
t
a
nd
i
so
la
te
s
e
n
s
o
rs
f
a
u
lt
in
a
v
a
r
ia
ble
spee
d
w
i
n
d
t
urbi
ne
i
s
d
i
sc
usse
d
i
n
[
15]
.
T
h
e
des
i
gne
d
a
pproac
h
w
a
s
b
a
se
d
o
n
t
he
E
LM
a
l
g
ori
t
hm
f
or
t
he
p
re
dic
t
io
n
of
u
n
k
now
n
m
odel
d
ynam
i
c
s
t
o
des
i
g
n
t
he
r
ob
us
t
n
o
n
-
l
i
nea
r
o
b
s
er
v
e
r
.
T
h
e
a
r
t
i
c
l
e
[
1
6
]
e
n
v
i
s
a
g
e
s
t
h
e
app
l
ica
t
i
o
n
of
c
ra
ziness-ba
se
d
P
S
O
to
e
n
h
a
n
c
e
t
he
p
erf
o
r
m
a
n
ce
o
f
EL
M
for
fea
t
ure
class
i
f
i
ca
ti
o
n
o
f
sin
g
l
e
a
n
d
co
mb
i
n
e
d
p
o
w
e
r
q
u
a
l
i
ty
d
is
tu
rb
a
n
c
e
s
.
Th
u
s
w
e
i
n
t
r
oduc
ed
t
hi
s f
a
st
and
a
c
c
u
rat
e
a
pp
ro
a
c
h
in
t
hi
s
pap
e
r
to
exa
m
ine
t
h
e
va
riat
io
n of
t
he
t
r
a
ns
por
ted
p
o
w
er
,
load
f
low
an
d
l
osse
s
due
t
o
the
i
n
fl
ue
nce
of
t
em
pera
ture
o
n
con
d
u
ct
or
r
esi
s
t
a
nce.
T
o
star
t
wi
th,
we
a
t
t
e
m
pt
e
d
t
o
st
udy
t
he
firs
t
pro
p
o
s
iti
on
w
h
i
c
h
i
s
the
ne
ura
l
n
e
t
w
o
r
k
The
n
f
or
f
urt
h
er
opt
imiz
a
t
i
o
n
and
i
n
t
er
ms
o
f
prec
i
s
i
on,
e
x
a
ctn
e
ss,
a
nd
profic
ienc
y
e
x
t
r
e
m
e
lear
n
i
ng
ma
chi
n
e
alg
o
ri
t
h
m
was a
p
p
lie
d t
o
a
ddr
ess the
ab
ove
p
rob
l
em
.
2.
RESEARCH
M
E
T
H
O
D
2.1.
Neura
l
n
et
w
o
rk
s
The
ori
g
in
o
f
artific
ia
l
ne
ur
a
l
n
etw
o
rks
c
o
m
e
s
from
the
bio
l
o
g
i
ca
l
ne
ur
on
mode
l
i
n
g
t
e
s
t
by
Warr
en
Mc
Cu
lluc
h
a
n
d
W
al
ter
P
i
t
t
s.
I
ni
ti
a
lly
N
e
u
ra
l
ne
t
w
or
ks
o
b
j
ecti
v
e
w
a
s
:
p
a
tt
ern
s
r
e
c
o
g
n
itio
n
,
c
l
a
ssi
f
i
cat
io
n
th
en
it
b
ec
om
es
v
ery
inte
rest
i
ng
in
all dom
a
i
ns [1
7
]
.
2.1.
1.
N
e
u
r
on
Mod
e
l
I
ndee
d
; t
h
e
sim
p
le
a
rc
hite
ct
ure
of a
sin
gl
e
ne
ur
on w
i
th a
s
ing
l
e
lay
e
r
is com
po
sed
esse
n
t
i
a
lly
:
First, the sc
a
la
r in
pu
t
p
w
h
i
c
h
i
s
mul
t
i
pl
i
e
d
by
t
h
e
s
c
a
l
a
r
wei
ght
w
to f
orm the
pro
d
u
ct
wp
th
i
s
o
p
e
ra
ti
on
t
a
k
es
place
a
t
t
h
e i
n
t
e
gr
at
or
w
hi
c
h
i
s
o
n
e
o
f
th
e
i
m
por
tan
t
parts
o
f
t
h
e
ne
uro
n
;
t
h
e
r
e
s
ult i
s
a
ga
in
a
s
ca
la
r
a
d
de
d t
o
a
scala
r
bias
b
t
o
for
m
th
e
ne
t
i
npu
t
n.
The
result
n
i
s
t
h
en
t
ra
n
s
fo
rmed
b
y
a
t
r
a
n
sf
er
f
un
ct
i
o
n
f
w
hic
h
p
rod
u
c
e
s
t
he
n
e
u
ro
n
o
u
t
p
ut
a
.
[18,
19],
the m
ode
l
i
s
s
h
o
w
n
i
n F
i
g
u
re
1.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISS
N
:
208
8-
8
6
9
4
I
n
t
J Po
w
Elec
&
Dr
i
Sy
st,
Vo
l. 1
0
,
No
. 3
,
S
e
p
2
019
: 124
4
– 1
2
5
4
1
246
F
i
gur
e
1.
A
r
t
i
f
i
c
ial
ne
ur
o
n
m
odel
∑
,
(
1
)
2.
1.
2.
Ne
ur
al
N
et
wor
k
Learn
ing
Lea
r
ni
ng
i
s
a
pr
oc
ess
b
y
w
h
i
c
h
t
he
f
r
e
e
pa
r
a
me
t
e
r
s
f
r
o
m
a
ne
ur
a
l
ne
t
w
o
r
k
a
r
e
ada
p
te
d
,
t
hr
o
u
g
h
a
sim
u
la
ti
on
pr
o
cess
by
t
h
e
e
n
v
i
r
o
nme
n
t
in
w
h
i
ch
t
he
n
e
t
w
o
r
k
i
s
c
o
n
ta
i
n
ed
[
17,
19,
20]
T
h
e
sup
e
rvi
s
ed
a
n
d
un
sup
e
rv
is
ed
m
e
t
hod
s
a
r
e
e
sse
nti
a
ll
y
t
h
e
t
w
o
t
ype
s
of
l
ea
r
n
i
n
g
f
o
r
a
n
e
ur
al
n
e
t
w
o
r
k
.
I
n
our
c
a
s
e,
w
e
ar
e
go
in
g
to
u
s
e
t
he
s
u
p
er
v
i
se
d
lea
r
nin
g
w
he
r
e
t
he
t
r
a
i
n
i
n
g
is
c
on
tr
o
l
led
by
a
n
e
x
t
er
na
l
age
n
t
w
ho
w
a
t
c
hes
t
h
e
a
n
sw
e
r
t
h
a
t
the
ne
tw
or
k
su
pp
ose
d
t
o
ge
ne
r
a
te
f
r
om
t
he
d
e
t
e
r
m
i
ne
d
e
n
t
r
ance
.
The
s
u
pe
r
v
is
or
c
o
mpa
r
es
t
he
o
ut
put
o
f
t
h
e
ne
tw
or
k
w
i
t
h
t
he
e
xpec
t
e
d
o
ne
a
nd
de
ter
m
ines
t
he
a
m
o
u
n
t
o
f
m
odif
i
c
a
t
i
o
n
s
t
o
be
m
a
de
on
the
w
e
i
g
h
t
s
[
18,
21,
22]
.
The
su
perv
ised
l
ear
ning
can
b
e
don
e
t
h
ro
u
g
h
the
three
fo
l
l
o
win
g
P
a
r
a
digm
s:
a.
Err
o
r co
r
r
ec
t
i
o
n
l
e
a
r
ni
ng
b.
Re
in
forc
em
en
t
lea
r
ni
ng
c.
S
t
oc
ha
stic
l
ea
r
n
i
ng.
Du
ring
t
h
e
a
rtifi
c
ial
n
e
u
r
al
n
etwo
rk
t
rai
n
in
g
b
y
er
ro
r
co
rrecti
o
n
,
the
w
e
ig
h
t
s
o
f
t
he
c
om
munica
ti
on
li
n
k
s
are
a
d
ju
s
t
ed
t
r
y
i
n
g
to
m
inimi
z
e
a
fu
nc
ti
on
o
f
c
o
s
t
d
e
p
e
n
d
in
g
o
n
the
dif
f
e
r
e
nce
be
tw
ee
n
the
des
i
r
e
d
va
lue
s
a
n
d
t
he
o
b
t
a
i
ne
d
o
n
e
f
r
o
m
the
out
pu
t
ne
t
w
or
k
[1
9,
23]
.
I
t
i
s
r
e
qu
ir
ed
t
o
de
t
e
r
m
i
n
e
t
h
e
m
odif
i
ca
t
i
o
n
s
on
w
e
i
g
hts
u
s
i
ng
the
c
o
m
m
i
t
te
d
er
r
o
r
,
t
he
c
or
r
e
c
t
i
on
er
r
o
r
is
c
a
lcu
l
a
t
e
d
a
s
the
fo
l
l
ow
ing
expr
e
ssi
on
:
(
2
)
Where
:
i
s
t
he
w
eig
h
t
v
a
r
i
at
ion
of
t
he
c
on
nec
t
i
o
n
be
tw
e
e
n
t
h
e
ne
ur
on
s
j
f
r
o
m
t
h
e
a
n
t
e
r
i
o
r
l
a
y
e
r
a
n
d
t
h
e
o
u
t
p
u
t
laye
r
n
ode
k.
:
t
he
d
es
ir
ed
n
e
u
r
o
n
ou
tpu
t
.
,
and
a
r
e
t
he
out
p
u
t
va
l
u
es
p
r
oduc
e
d
i
n
the
n
e
ur
o
n
i
a
nd
k
r
esp
ect
iv
el
y
.
a
posit
i
v
e
f
a
c
t
o
r
d
enom
i
n
ate
d
t
he
l
ea
r
n
in
g
r
a
te
0
1
[
18
,
24,
25]
.
We
c
a
n
s
a
y
t
h
a
t
the
new
w
e
igh
t
i
s
pr
opor
tio
na
l
to
t
he
c
o
m
m
itt
e
d
e
r
r
o
r
p
r
o
duce
d
by
t
h
e
n
e
tw
or
k
an
d
t
h
e
a
n
sw
er
o
f
the
n
ode
j
i
n
t
h
e
pr
evi
o
us
l
a
y
er
a
s
show
n
in
t
he
f
ol
l
ow
i
n
g
f
o
r
m
ula
:
(
3
)
The
t
o
ta
l
e
r
r
o
r
is
k
now
n
a
s
t
he
m
ea
n
squar
e
d
e
r
r
o
r
expr
e
ssed
in
t
he
e
q
u
a
t
i
on
(
4
)
[
2
6,
2
7
]
:
∑∑
(
4
)
Where
:
N
is
t
he
num
be
r
of
n
eur
o
ns
i
n
t
h
e
o
u
t
p
u
t
l
a
y
e
r
a
nd
P
i
s
t
h
e
n
um
ber
of
e
xam
p
le
s
in
t
he
t
r
a
i
n
i
n
g
sam
p
le.
Nor
m
a
l
ly t
o m
i
n
i
m
i
ze this cri
teri
on fu
nc
ti
o
n
,
i
s em
pl
o
y
e
d
l
ea
rn
i
ng
r
u
le g
i
v
en by
t
h
e des
cend
i
ng
g
r
ad
ie
nt [
1
8
,
19]
.
∆
=
-
∇
E
rror
(
5
)
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
Po
we
r
f
l
o
w
va
riat
i
on
b
a
se
d o
n
ex
tre
m
e l
e
ar
nin
g
m
a
ch
ine al
g
o
r
ithm
in
p
o
w
e
r
system
(L
ab
e
d
Im
en)
1
247
If
(
t
a
k
es
a
l
it
t
l
e
v
a
l
u
e
the
le
arni
ng
proce
ss
is
m
ade
sm
oot
hly
w
h
i
ch
g
i
v
e
s
;
as
a
r
e
s
ul
t,
a
n
inc
r
em
ent
i
n
t
he
ti
m
e
o
f
con
v
e
r
gence
to
a
s
ta
b
l
e
so
lu
t
i
on.
I
n
the
ot
her
han
d
if
has
an
i
m
p
orta
nt
v
al
ue
t
h
e
s
peed
o
f
lear
ni
n
g
get
s
incr
ease
d
b
u
t
t
here
w
ill b
e
a
d
ive
r
ge
nc
e r
i
sk
a
n
d
th
i
s ca
u
ses t
h
e
i
n
sta
b
i
lit
y
of t
he
s
yste
m
[25-27].
2.2.
Ex
treme
L
e
a
r
nin
g
Ma
c
hine
E
L
M
H
u
a
n
g
et
a
l.
p
r
o
p
o
se
d
a
n
e
xt
rem
e
l
ear
ni
n
g
m
ac
hine
a
lgor
ithm
,
a
s
a
n
ew
l
e
a
rn
in
g
sc
he
me
w
orkin
g
for
si
ng
le
h
idd
e
n
l
a
yer
feed-f
orw
a
r
d
n
etw
o
r
k
s
(S
LF
N
s
)
[2
8,
29].ELM
i
s
ent
i
r
e
l
y
d
i
f
fer
e
nt
f
r
o
m
t
r
adi
tion
a
l
it
e
r
a
t
i
v
e lear
ni
ng al
gor
ithm
s
a
s
it
ran
d
o
m
l
y selec
t
s the
i
n
p
u
t
w
e
ig
hts (
)
a
n
d
bi
as
es
(
) for hid
d
e
n
n
ode
s an
d
ana
l
y
t
i
cal
l
y
c
al
cula
tes
the
o
u
t
p
u
t
w
eig
h
t
s (β) by fin
d
i
n
g the
l
eas
t squa
re
s
o
l
ut
ion.
I
n
d
o
i
ng
s
o
,
i
t
i
s
pr
ove
n
t
h
a
t
t
he
t
ra
in
i
ng
e
rror
ca
n
s
t
i
ll
be
minim
i
z
e
d
w
i
th
e
ve
n
be
tter
g
e
nera
liza
t
io
n
perform
ance
[
30].
N
o
ta
bl
y,
t
he
l
e
a
rn
i
ng
spe
e
d
o
f
E
L
M
c
a
n
b
e
t
h
o
usa
n
d
s
o
f
tim
es
f
as
ter
tha
n
t
r
a
di
t
i
o
n
a
l
f
e
e
d-
forw
a
r
d
ne
tw
o
r
k
lear
n
i
n
g
a
l
g
ori
t
hms
l
i
ke
B
P
a
l
gori
t
h
m
.
C
om
par
e
d
w
ith
c
on
ve
nt
i
ona
l
l
e
arni
ng
a
l
g
o
ri
thm
s
,
ELM
n
o
t
o
nl
y
ten
d
s
t
o
r
ea
ch
t
he
s
m
a
l
l
e
s
t
tra
i
ni
ng
e
rror
bu
t
als
o
t
o
o
b
t
a
i
n
the
sm
alle
st
n
orm
of
w
eig
h
t
s
[
2
9
,
31].
Fo
r
a
r
b
i
t
ra
ry dis
tinc
t
s
am
pl
e
s
,
where:
,
,
…
..
,
∈
(
6
)
,
,
…
.
.,
∈
(
7
)
S
t
anda
r
d
S
F
L
N
s
w
it
h
n
odes
a
nd a
c
t
i
va
t
i
o
n
f
u
n
c
t
i
on
a
re
m
a
t
hem
a
ti
c
a
l
ly
m
odele
d a
s
:
∑
.
(
8
)
1
,
…
.
,
Whe
r
e
,
,…
..
,
is the
w
e
ig
ht
v
ec
tor
con
n
e
c
tio
n
ℎ
hi
dde
n
node
a
nd
in
put
n
ode
s.
,
,…..
,
i
s
t
he
w
eig
h
t
v
ector
c
on
nec
t
i
ng
t
h
e
ℎ
)
hi
dde
n
no
de
a
nd
o
u
t
p
u
t
n
o
d
e
s
,
a
n
d
:
i
s
the t
h
re
sho
l
d
of the
ℎ
hid
den n
ode
.
.
de
no
tes
the
in
ner
prod
u
c
t
o
f
w
i
and
.
Tha
t
s
ta
nda
r
d
S
FLN
w
ith
h
idde
n
n
o
d
es
a
n
d
a
c
t
i
va
t
i
on
fu
nct
i
on
c
a
n
a
p
p
r
ox
ima
t
e
t
h
e
s
e
s
a
m
p
l
e
s
w
ith
z
e
r
o.
∑
0
(
9
)
W
h
at
mea
n
s
t
he
re
ex
i
s
t
,
s
uch
tha
t
:
∑
∑
.
(
10)
Eq
uat
i
on (10)
c
a
n
be
w
r
itt
e
n
c
ompac
t
ly
a
s
(
11)
Whe
r
e
:
…
,
…
,
…
.
…
.
⋮…
⋮
.
…
.
∗
(
12)
⋮
∗
a
nd
⋮
∗
Th
us, the
extre
me
lea
rnin
g machi
n
e
al
g
o
rit
h
m
can
b
e
summ
arize
d
as
f
o
l
lo
ws:
St
e
p
1:Ran
d
o
m
l
y
a
ssi
g
n
i
n
put
w
e
i
gh
t
and
bias
,
1
,
2
,
.
,
.
S
t
ep2
:
C
a
l
c
u
l
a
te
the
h
id
de
n
la
yer
ou
tp
u
t
m
a
t
rix H
.
St
e
p
3:
C
al
c
u
l
a
t
e
t
h
e
o
ut
p
u
t
w
e
i
ght
by
β
H
T
If
h
i
d
de
n
la
ye
r
ou
tp
u
t
m
a
t
r
i
x
is
non-s
quar
e
(
that
m
ea
ns
)
,
t
h
e
d
e
t
e
r
m
i
n
a
n
t
o
f
d
e
t
0
and
(rank
H<
)
,
i
n
l
i
n
e
a
r
a
l
g
e
b
r
a
m
a
t
r
i
x
,
i
s
a
s
s
e
s
s
e
d
a
s
a
s
i
n
g
u
l
a
r
m
a
t
r
i
x
t
ha
t
ca
nn
ot
b
e
dire
c
t
l
y
i
nver
t
e
d
[
32-
34].
β=(
H
H
)
-1
H
T
(
13)
The
i
nverse
o
f
c
a
n
n
o
t
b
e
de
te
rmine
d
i
f
i
s
not
a
f
ul
l-ra
n
k
m
atrix.
I
n
th
i
s
case,
t
he
g
e
n
era
l
i
z
ed
in
verse ma
tri
x
, k
now
n as pse
u
do
i
n
ver
s
e,
is
u
s
ed.
I
n
or
d
e
r
t
o
c
alc
u
la
te
t
he p
se
udo
i
nverse,
va
r
i
o
u
s
ap
p
roa
c
hes
Evaluation Warning : The document was created with Spire.PDF for Python.
ISS
N
:
208
8-
8
6
9
4
I
n
t
J Po
w
Elec
&
Dr
i
Sy
st,
Vo
l. 1
0
,
No
. 3
,
S
e
p
2
019
: 124
4
– 1
2
5
4
1
248
c
a
n
be
u
se
d.
T
he
m
os
t
w
i
de
ly
k
n
o
w
n
t
y
p
e
i
s
t
he
M
o
o
r
e
–P
e
n
r
o
se
p
s
eu
do
-i
nv
e
r
se
[
35
].
T
h
e
p
se
udo
-
i
nv
e
r
se
o
f
the
ma
tri
x
, n
amely
,
c
a
n
b
e
co
mp
ut
ed
v
ia
l
east
squ
a
re so
l
ut
ion
:
(
14)
Th
is
s
o
l
u
t
i
on
is
a
c
c
ur
a
t
e
as
l
on
g
as
t
he
s
qu
a
r
e
m
a
tr
ix
i
s
inver
t
i
b
l
e
.
Howeve
r,
it
is
s
in
g
u
lar
i
n
som
e
a
pp
lica
t
i
ons.
I
n
S
LF
N
,
i
t
i
s
s
in
g
u
l
a
r
in
m
ost
of
t
he
c
a
s
e
s
s
ince
t
her
e
i
s
a
ten
d
e
n
c
y
t
o
selec
t
.
In
ELM,
H
u
a
ng
e
t
a
l.
,
hav
e
s
o
l
v
e
d
th
is
p
r
o
b
l
e
m
u
sing
M
oor
e–
P
e
n
r
o
s
e
p
s
e
u
d
o
i
n
v
e
r
s
e
o
f
H
m
a
t
r
i
x
t
o
o
v
e
r
c
o
m
e
this p
roblem [32
, 3
6
,
3
7
]
.
3.
R
E
S
U
L
T
S
A
ND ANALY
S
IS
I
n
o
r
d
er
t
o
ve
r
i
f
y
t
he
p
r
o
po
sed
tw
o
a
p
pr
o
a
ches
;
EL
M
a
n
d
ne
ur
al
n
e
t
w
or
ks,
the
pa
p
e
r
st
u
dy
is
c
o
nduc
te
d
on
I
EEE
30
bus tes
t
s
y
st
e
m
s
how
n
in
F
igure
2,
i
t
c
o
mp
r
i
ses of 6
g
e
n
er
a
t
or
s,
b
us
n
umbe
r
o
n
e
(
1
)
is
c
o
n
s
i
d
er
ed
a
s
a
slack
b
us.
L
ik
e
w
i
s
e
,
2
4
loa
d
s
pow
e
r
ed
over
41
t
r
a
nsm
i
ssio
n
li
nes.
Figure
2.
S
ingle
Line
D
ia
gra
m
o
f
IEEE-30bus [38
]
3.
1.
Li
n
e
F
l
o
w So
lu
tio
n Usi
n
g
N
ew
to
n
-
Ra
ph
so
n Alg
o
r
ithm
Tab
l
e
1
dis
p
la
yed
t
h
e
line
fl
ow
r
esu
l
t
s
a
t
2
5
C
°.
I
t
is
t
he
i
n
i
t
i
a
l
st
ep
t
o
p
r
ov
id
e
,
a
c
tiv
e
and
re
ac
tiv
e
pow
e
r
a
nd
the
to
t
a
l
system
l
o
ssesThe
w
h
o
le
s
ystem
is
o
pe
r
a
ti
ng
un
d
e
r
no
rmal
c
on
di
t
i
on
s.
T
h
e
se
r
esul
t
s
a
r
e
use
d
t
o
be
t
he
i
np
u
t
m
atr
i
x
f
o
r
the
neur
a
l
n
et
w
o
r
k
t
r
a
in
i
ng
pha
se.
Table
1
. Th
e
lin
e
f
l
o
w
an
d
l
o
s
ses
at T=2
5C°
i to j
P
(MW
)
Q
(MVAR
)
S
(MVA)
Lo
ss
es
(M
W
)
L
o
sse
s
(Mva
r)
i to j
P
(MW)
Q
(MVAR
)
S
(MVA)
L
o
sse
s
(MW)
Lo
ss
es
(Mva
r)
1-2
177,
77
8
-
22,
1
4
8
179,
15
2
5
,
464
10,
524
12-
1
3
0,
000
-
10,
2
9
1
1
0,
291
0
,
000
0
,
133
1-3
83,
221
5
,
127
83,
378
2
,
808
7
,
085
12
-1
4
7,
856
2
,
442
8
,
227
0
,
075
0
,
155
2-4
45,
712
2
,
705
45,
792
1
,
106
-
0,
5
1
7
12
-1
5
17,
857
6
,
947
19,
161
0
,
217
0
,
428
2-5
82,
990
1
,
703
83,
008
2
,
995
8
,
178
12
-1
6
7,
208
3
,
363
7
,
954
0
,
053
0
,
112
2-6
61,
912
-
0,
95
8
61,
920
2
,
048
2
,
264
14-
1
5
1,
582
0
,
687
1
,
724
0
,
006
0
,
005
3-4
78,
012
-
3,
15
8
78,
076
0
,
771
1
,
344
15-
1
8
6,
014
1
,
744
6
,
262
0
,
039
0
,
080
4-6
70,
126
-
17,
5
2
6
72,
282
0
,
604
1
,
179
15-
2
3
5,
001
2
,
956
5
,
810
0,
031
0
,
063
4-1
2
44,
121
14,
646
46,
489
0
,
000
4
,
685
16
-1
7
3,
654
1
,
451
3
,
932
0,
012
0
,
027
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
P
o
w
Elec
&
D
r
i
S
y
st
I
S
S
N
:
2088-
86
94
Po
wer flo
w
va
ri
at
ion b
a
se
d
o
n
extrem
e
lear
ni
n
g
m
a
c
h
i
n
e
al
g
o
rit
h
m
i
n
p
o
w
e
r
system
(
L
abe
d
I
m
e
n
)
1
249
i to j
P
(MW
)
Q
(MVAR
)
S
(MVA)
Lo
ss
es
(M
W
)
L
o
sse
s
(Mva
r)
i to j
P
(MW)
Q
(MVAR
)
S
(MVA)
L
o
sse
s
(MW)
Lo
ss
es
(Mva
r)
5-7
-
14,
2
0
5
10,
500
17,
664
0
,
151
-
1,
6
8
7
18-
1
9
2,
775
0
,
765
2
,
879
0
,
005
0
,
010
6-7
37,
523
-
1,
88
5
37,
570
0
,
367
-
0,
5
9
8
19
-2
0
-6
,
7
3
0
-
2
,
6
4
5
7,
23
1
0,
017
0
,
034
6-8
29,
528
-
3,
75
4
29,
766
0
,
103
-
0,
5
5
8
21-
2
2
-1
,
8
7
7
-
1
,
5
9
4
2,
46
2
0,
001
0
,
001
6-9
27,
693
-
7,
32
2
28,
644
0
,
000
1
,
594
22-
2
4
5,
654
2
,
788
6
,
304
0
,
043
0
,
067
6-1
0
15,
823
0
,
653
15,
836
0
,
000
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3
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0
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0
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3
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0
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2
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583
4
,
490
8
,
813
0
,
052
0
,
107
T
ota
l
l
oss
17,
599
22,244
3.
2.
The
Ne
u
r
al N
etwor
k
3.
2.
1.
T
h
e
tra
i
n
i
n
g
p
ha
se using
L
e
v
e
n
b
erg
-
M
a
r
q
u
a
r
d a
lgo
r
it
h
m
a.
The
tr
ai
n
i
n
g
a
l
gor
it
hm
i
s
Lev
e
nber
g
-
M
a
r
q
u
a
r
d
(
tr
ainlm
)
,
a
s
it
i
s
sh
ow
n
i
n
(
F
i
gur
e
3)
.
b.
The
per
f
or
m
a
nce
is
t
he
m
e
a
n
squ
a
r
e
d
er
r
o
r
(
m
se
)
(
F
igur
e
4
)
.
c.
The
co
nver
g
e
n
ce
i
s
satis
fie
d
a
t
t
=
15se
c
(
F
i
gu
r
e
3
).
d.
The
per
f
or
m
a
nce
va
l
u
e
r
e
ac
he
d
3.
15e-
19
(
F
igur
e
4)
.
I
n
t
a
b
l
e
s
1
a
n
d
2
an
d
a
l
so
(
F
i
gur
e
5)
,
it
is
e
v
i
de
n
t
t
ha
t
t
h
e
n
eur
a
l
ne
tw
or
k
ou
tpu
t
s
a
n
d
t
a
r
g
et
s
ar
e
c
o
mple
te
l
y
i
de
nt
i
c
a
l
.
The
m
a
in
s
qua
r
e
d
er
ror
r
e
ache
s
t
he
v
a
l
ue
3.
1
5
e-1
9
(
F
i
gur
e
4).
B
i
as
a
n
d
w
eig
h
ts
a
r
e
ad
j
u
st
ed
.
He
re
b
elow
w
e
can
s
e
e
c
l
e
ar
ly
t
he
n
e
u
ral
n
e
t
w
or
k
arc
h
ite
cture
a
nd
t
ra
i
n
i
n
g
ph
a
s
e
e
x
pos
ed
i
n
Fi
gu
re
s
3
,
t
h
e
pe
r
f
or
m
a
nc
e
in
F
igur
e
4
a
nd
t
h
e
r
e
gr
essi
o
n
i
n
F
i
gur
e
5
r
e
sp
ec
t
i
ve
l
y
.
F
i
gur
e
3.
N.
N ar
ch
it
ectu
re and
tr
a
i
ni
n
g
pha
se
F
i
gur
e
4.
P
e
r
f
o
r
m
a
n
ce
F
i
gur
e
5.
R
e
g
r
e
ssi
on
Ta
b
l
e2.
Line
f
low
based
o
n
a
n
eur
a
l
netw
or
k
at
2
5
C
°
i to j
P
(MW)
Q
(M
V
A
R
)
Loss
e
s
(MW
)
L
o
sse
s
(Mva
r)
i to j
P
(MW)
Q
(M
V
A
R
)
Losse
s
(MW)
Lo
ss
es
(Mva
r)
1
-
2
177,
77
8
-22,1
4
8
5,
464
10,
52
4
1
2
-
1
3
1,
705
e
-
13
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9
1
1,
421
e
-
14
0
,
133
1
-
3
83,
221
5
,
127
2
,
808
7
,
085
1
2
-
1
4
7,
856
2
,
442
0
,
075
0
,
155
2
-
4
45,
712
2
,
705
1
,
106
-
0,
51
7
1
2
-
1
5
17,
857
6
,
947
0
,
217
0
,
428
2
-
5
82,
990
1
,
703
2
,
995
8
,
178
1
2
-
1
6
7,
208
3
,
363
0
,
053
0
,
112
2
-
6
61,
912
-
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958
2
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2
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264
1
4
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1
5
1,
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0
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687
0
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0
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3
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4
78,
012
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0
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1
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1
5
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1
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0
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4
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6
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126
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2
6
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1
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2
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0
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4-
1
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44,
121
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7
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1
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2
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1
9
2,
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0
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0
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7
37,
523
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1,
885
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367
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59
8
1
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6
,
7
3
0
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645
0
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017
0
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034
6
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8
29,
528
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754
0
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103
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55
8
2
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2
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8
7
7
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594
0
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001
6
-
9
27,
693
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322
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5e
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2
2
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2
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788
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7
6-
1
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653
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7.
99
3e
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1
,
278
2
3
-
2
4
1,
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1
,
293
0
,
006
0
,
0
1
2
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
: 208
8-
869
4
Int J
P
o
w
El
e
c
&
D
ri S
yst
,
V
ol.
10,
N
o.
3
, S
e
p
2
0
1
9
:
1
2
44 –
125
4
1
250
i to j
P
(M
W
)
Q
(MVA
R
)
L
o
sse
s
(MW)
L
o
sse
s
(M
v
a
r)
i to j
P
(MW)
Q
(MVA
R
)
Lo
ss
es
(M
W
)
L
o
sse
s
(Mva
r
)
6-2
8
1
8
,
819
-
9,
61
8
0,
060
-
13,
0
8
6
24
-
2
5
-1,
3
2
5
1
,
602
0
,
008
0,
01
4
8-
2
8
-0,
5
7
5
-2,
3
7
0
8,
881e
-14
-
4,
36
8
25
-
2
6
3,
545
2
,
366
0
,
045
0,
066
9-
1
1
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2.
273e
-13
-15,
6
5
7
-
1
.
4
2
1
e
-
14
0,
462
25-
2
7
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8
7
7
-
0,
77
8
0,
026
0,
049
9-
1
0
2
7
,
693
6
,
741
0,
000
0
,
809
27-
2
8
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1
8
4
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1
5
7
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4
2
1
e
-
14
1
,
309
10
-2
0
9,
0
2
7
3,
560
0,
081
0
,
180
27
-
2
9
6,
189
1
,
668
0
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086
0,
162
10-
1
7
5,
3
7
2
4,
414
0,
014
0
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037
27-
3
0
7,
091
1
,
661
0
,
161
0,
304
10-
2
1
1
5
,
733
9
,
842
0,
110
0
,
237
29-
3
0
3,
704
0
,
606
0
,
033
0,
063
10
-2
2
7,
5
8
3
4,
490
0,
052
0
,
107
T
ot
a
l
l
oss
17,599
22,
244
The
NN
is
t
rained
a
n
d
r
eady
t
o
be
uti
l
i
zed
i
n
rea
l
time
for
re
s
i
s
tanc
e va
r
i
at
io
n R
T=30C
°
an
d R
T=05C°
.
Li
ne
f
l
o
w
re
su
l
t
s
u
s
i
n
g
t
h
e
n
e
ur
al
n
e
t
w
o
r
k
a
pp
r
o
ach
a
r
e
e
xp
ose
d
i
n
Tabl
e
3
fo
r
th
e
t
w
o
re
sis
t
an
ce
Va
l
u
es
R
T
=
30C
°
an
d
R
T
=
05C°.
Ta
b
l
e
3.
Line
flow
us
i
ng t
h
e
tr
aine
d ne
ura
l
n
e
t
w
o
rk i
n r
eal
tim
e
(T=
3
0
C
° a
nd T
=
5C° )
i to j
R
(
pu)
30C
°
P
(MW)
Q
(MV
a
r)
L
o
ss
(MW)
L
o
ss
(Mva
r)
R
(
pu)
05C
°
P
(MW)
Q
(MVa
r)
Loss
(MW)
L
o
ss
(M
v
a
r)
1-
2
0.
0195
178,
01
0
-23,
3
1
2
5,
593
10,
591
0
,
0177
176,
84
0
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501
4,
960
10,
273
1-
3
0,
0460
83,
370
4
,
788
2,
871
7
,
119
0
,
0416
82,
639
6
,
479
2
,
561
6
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961
2-
4
0,
0581
45,
709
2
,
525
1,
127
-
0,
52
0
0,
0525
45,
719
3
,
432
1
,
024
-
0
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07
2-
5
0,
0481
83,
105
1
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320
3,
061
8
,
208
0
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0435
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543
3
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2
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738
8
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6
0,
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909
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2
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087
2
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61,
918
0
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1
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2,
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4
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099
-
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53
1
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1
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350
0
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0121
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678
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8
2
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703
1
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6
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138
-
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0
1
8
0,
618
1
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0
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0109
70,
080
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564
0
,
5
49
1
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147
4- 12
0,
0000
44,
155
14,
58
1
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4
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689
0
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000
43,
989
14,
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1
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1
5
5
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72
0
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2
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14,
395
9
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0
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1
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4
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7
0,
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485
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1,
0
1
0
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1
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94
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8
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531
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0
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4290
0
,
0610
17,
783
7
,
002
0
,
199
0
,
426
12
-
1
6
0,
0963
7
,
220
3
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346
0
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055
0
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1130
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7
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3
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0
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0,
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14- 1
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1
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0
,
719
0
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0
,
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15- 1
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0,
1093
6
,
0180
1
,
732
0
0,
0400
0
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0800
0
,
0908
6
,
001
1
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794
0
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036
0
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079
15- 2
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0,
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5
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0
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1
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0
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6,
740
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9
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0,
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620
2
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0
3
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1
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781
1
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282
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0060
0
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1
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1
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333
0
,
0
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24
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0,
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7
9
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0,
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0
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0
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1007
-
4,
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0,
7
3
3
0,
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0
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050
27- 2
8
0,
0000
-
18,
1
7
3
-4,
1
6
9
2,
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e
-
14
1
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3090
0
,
2952
-
18,
227
-
4,
1
1
0
-7
,
2
7
0
e
-
11
1
,
312
27
-
2
9
0,
2240
6
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192
1
,
668
0,
0880
0
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1620
0
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000
6
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179
1
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0
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079
0
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27- 3
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0,
3264
7
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094
1
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7
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1
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660
0
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1
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302
29- 3
0
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3
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704
0
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606
0,
0340
0
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0630
0
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2211
-
3,
669
-
0,
5
4
2
0,
031
0
,
063
T
ota
l
l
osse
s
17,
985
22,
407
T
ota
l
l
osse
s
16,
079
21,
641
3.3.
Ex
treme lea
r
ning
m
a
c
h
i
ne
a
lg
o
r
ithm
3.3.
1.
Tr
ain
i
n
g
-v
a
lid
ation
an
d
te
s
t
The
EL
M
tra
i
nin
g
-
va
lida
t
i
o
n
a
n
d
t
e
st
p
roc
e
ss
is
e
xp
ose
d
i
n
F
i
g
ure
6,
t
h
e
p
e
r
form
anc
e
in
F
ig
ur
e
7,
a
nd
t
h
e
regr
ession
i
n
Fig
ure
8
respec
t
i
ve
ly.
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
Po
we
r
f
l
o
w
va
riat
i
on
b
a
se
d o
n
ex
tre
m
e l
e
ar
nin
g
m
a
ch
ine al
g
o
r
ithm
in
p
o
w
e
r
system
(L
ab
e
d
Im
en)
1
251
F
i
gure
6. Tr
a
in
ing
an
d
Test
in
g
Tim
e
F
i
gure
7.
P
e
rfor
m
a
n
ce
F
i
gure
8.
Regr
e
ssi
o
n
Tab
l
e
4 il
lus
t
ra
t
e
s ELM tra
i
n
i
ng p
h
a
s
e pa
ra
m
e
ter
s
.
Tab
l
e
4.
ELM
t
rai
n
i
n
g phas
e
par
am
eters
E
x
treme
l
e
a
r
n
i
ng mac
h
in
e
Value
s
T
r
a
i
ning
ti
m
e
(s)
0,
0469
Te
sting time
(
s)
0,
0000
T
r
a
i
ning
pe
r
f
orm
a
nc
e
3,
666e
-25
Te
sti
ng
p
e
rf
orm
a
n
c
e
8,
248e
-27
ELM m
ode
l is bu
i
lt
a
n
d
r
ea
dy
to be
use
d
in
rea
l
t
i
m
e.
Tab
l
e
5
sh
ow
s
the
l
i
n
e
fl
ow
r
e
s
ults
p
ro
v
i
de
d
b
y
t
he
ELM
t
raine
d
m
ode
l
for
the
tw
o
resis
t
ance
v
a
r
ia
ti
o
n
:
R
T
=
30C
°
an
d
R
T
=
05C°
Tabl
e 5
.
Li
n
e
fl
o
w
b
a
s
e
d
on
Ex
t
r
eme l
e
arn
i
ng
ma
c
h
i
n
e
al
gori
t
h
m
i
n
r
ea
l tim
e (T=3
0
C
°
and T
=
5C
°
)
i to j
R
(
pu)
30
C
°
P
(M
W
)
Q
(
M
V
a
r)
L
o
ss
(M
W
)
L
o
ss
(Mva
r)
R
(
pu)
05C
°
P
(MW)
Q
(MV
a
r)
Loss
(MW)
L
o
ss
(Mva
r)
1-2
0,
0195
178,
010
-
23,
3
1
2
5,
593
10,
591
0
0,
0177
176,
84
0
-17,
5
0
1
4
,
960
10,
273
1-3
0,
0460
83,
37
0
4,
788
2,
871
7,
1190
0
,
0416
82,
639
6
,
479
2
,
561
6,
961
2-4
0,
0581
45,
70
9
2,
525
1,
127
-0,
5
2
00
0,
0525
45,
719
3
,
432
1
,
024
-
0,
50
7
2-5
0,
0481
83,
10
5
1,
320
3,
061
8,
2080
0
,
0435
82,
543
3
,
232
2
,
738
8,
069
2-6
0,
0592
61,
90
9
-1,
2
6
2
2,
087
2,
2630
0
,
0535
61,
918
0
,
268
1
,
890
2
,
270
3-4
0,
0134
78,
09
9
-3,
5
3
1
0,
788
1,
3500
0
,
0121
77,
678
-
1,
68
2
0,
70
3
1,
320
4-6
0,
0121
70,
13
8
-18,
0
1
8
0,
618
1,
1880
0
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0109
70,
080
-
15,
5
64
0,
549
1
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147
4-
1
2
0,
0000
44,
15
5
14,
58
1
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7
7
41e
-12
4
,
6890
0
,
000
43,
989
14,
90
1
1,
885e
-13
4,
669
5-7
0,
0468
-
14,
1
5
5
10,
72
0,
156
-1,
6
8
20
0,
0424
-
14,
3
9
5
9,
613
0
,
1
33
-
1,
70
4
6-7
0,
0272
37,
48
5
-2,
1
0
2
0,
374
-0,
6
0
00
0,
0246
37,
669
-
1,
01
0
0,
3
41
-
0,
59
4
6-8
0,
0122
29,
53
1
-4,
2
5
4
0,
106
-0,
5
5
60
0,
0110
29,
520
-
1,
76
3
0,
0
94
-
0,
56
3
6-9
0,
0000
27,
69
3
-7,
3
4
1
-2,
5
2
7
e
-
13
1,
5950
0
,
0000
27,
690
-
7,
24
9
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1
,
1
7
5
e
-
13
1
,
590
6-
1
0
0,
0000
15,
82
2
0,
651
-4,
9
3
2
e
-
14
1,
2790
0
,
0000
15,
823
0
,
658
-
1,
77
9e
-
1
4
1,
277
6-
2
8
0,
0172
18,
80
9
-9,
6
8
6
0,
061
-13,
0
8
2
0
0
,
0155
18,
857
-
9,
34
8
0
,
055
-
13,
1
0
2
8-
2
8
0,
0648
-
0,
57
5
-2,
2
8
6
-3,
5
3
3
e
-
14
-4,
3
6
80
0,
0586
-
0,
57
4
-2,
7
02
2
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8
e
-
1
2
-
4
,3
71
9-
1
0
0,
0000
27,
69
3
6,
772
-2,
6
2
9
e
-
13
0,
8100
0
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0000
27,
690
6
,
617
-
1
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8
4
8
e
-
14
0
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8060
9-
1
1
0,
0000
-
3,
38
8e
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-15,
7
0
8
-3,
0
2
4
e
-
14
0,
4650
0
,
0000
2
,
698e
-
13
-15,
4
56
-
2
,
7
3
3
e
-
13
0
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449
10 -1
7
0,
0330
5
,
361
0
4,
431
0,
015
0,
0370
0
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0862
5
,
415
4
,
347
0
,
0
1
3
0,
037
10-
2
0
0,
0954
9
,
027
0
3,
572
0
0,
0820
0,
1810
0
,
0298
9
,
029
3
,
509
0
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074
0
,
180
10-
2
1
0,
0354
15,
7410
9
,
843
0
0,
1120
0,
2370
0
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0320
15,
701
9
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837
0,
101
0
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236
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2
0,
0741
7
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587
0
4,
488
0
0,
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0,
1070
0
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7
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568
4
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499
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0
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106
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435
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1
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1.
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7
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433
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1135
7
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2
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474
0
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0
69
0
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155
12 -1
5
0,
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17,
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6
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933
0
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0,
4290
0
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17,
783
7
,
002
0,
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0
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426
12 -1
6
0,
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7
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0
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0
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0,
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0
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6
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1
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794
0
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036
0
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079
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0,
1019
5
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013
0
2,
946
0
0,
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0,
0630
0
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0922
4
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957
2
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996
0
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029
0
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063
16 -1
7
0,
0840
3
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666
0
1,
434
0
0,
0120
0,
0270
0
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0759
3
,
609
1
,
518
0
,
011
0
,
027
18-
1
9
0,
0651
2
,
778
0
0,
752
0
0,
0050
0,
0100
0
,
0589
2
,
765
0
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815
0
,
005
0
,
010
19 -2
0
0,
0346
-
6,
72
70
-
2,
65
80
0
,
0170
0,
0340
0
,
0313
-
6,
74
0
-2,
5
9
5
0,
016
0
,
034
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
: 208
8-
869
4
Int J
P
o
w
El
e
c
&
D
ri S
yst
,
V
ol.
10,
N
o.
3
, S
e
p
2
0
1
9
:
1
2
44 –
125
4
1
252
i to j
R
(
pu)
30
C
°
P
(M
W
)
Q
(
M
V
a
r)
L
o
ss
(M
W
)
L
o
ss
(Mva
r)
R
(
pu)
05C
°
P
(MW)
Q
(MV
a
r)
Loss
(MW)
L
o
ss
(Mva
r)
21-
2
2
0,
0118
-
1,
87
10
-
1,
59
30
0
,
0010
0,
0001
0
,
0106
-
1,
89
9
-1,
5
9
9
0,
001
0
,
0001
22-
2
4
0,
1172
5
,
662
0
2,
787
0
0,
0440
0,
0670
0
,
1060
5
,
620
2
,
793
0
,
039
0
,
066
23-
2
4
0,
1345
1
,
781
0
1,
282
0
0,
0060
0,
0120
0
,
1217
1
,
728
1
,
333
0
,
005
0
,
012
24 -2
5
0,
1921
-
1,
30
70
1
,
590
0
0,
0060
0,
0130
-
1,
39
70
1
,
648
-
1,
32
1
0
,
008
0
,
015
25 -2
6
0,
2593
3
,
545
0
2,
367
0
0,
0400
0,
0670
0
,
2345
3
,
541
2
,
366
0
,
041
0
,
066
25-
2
7
0,
1114
-
4,
86
00
-
0,
79
00
0
,
0320
0,
0490
0
,
1007
-
4,
94
5
-0,
7
3
3
0,
024
0
,
050
27-
2
8
0,
0000
-
18,
1
7
3
-4,
1
6
9
0
0,
0120
1,
3090
0
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2952
-
18,
2
2
7
-4,
1
1
0
-
5,
21
6e
-
1
4
1,
312
27 -2
9
0,
2240
6
,
192
0
1,
668
0
0,
0050
0,
1620
0
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0000
6
,
179
1
,
666
0
,
079
0
,
161
27-
3
0
0,
3264
7
,
094
0
1,
662
0
0,
0170
0,
3040
0
,
2026
7
,
079
1
,
660
0
,
148
0
,
302
29-
3
0
0,
2445
3
,
704
0
0,
606
0
0,
0340
0,
0630
0
,
2211
-
3,
66
9
-0,
5
4
2
0,
031
0
,
063
T
ota
l
l
osse
s
17,
9850
22,
407
0
T
o
t
a
l
los
s
e
s
16,
079
21,
641
3.4.
Di
scussion of
results
3.4.
1.
Neura
l
netw
o
rk
s
Th
is
case
s
t
ud
y
dem
ons
trate
s
t
he
a
p
p
lica
t
ion
a
n
d
prac
tic
a
l
b
ene
fi
ts
o
f
the
ne
ural
n
e
t
w
o
rk
w
ith
bac
kpr
o
p
a
g
at
i
on,
a
s
i
t
i
s
in
t
r
oduc
e
d
h
ere
to
s
olve
a
n
on
l
i
n
ear
prob
lem
w
h
ic
h
is
t
h
e
v
a
r
i
a
ti
o
n
o
f
the
c
o
nd
uc
tor
resista
n
ce
d
ue
t
o
the
tem
p
e
r
ature
fl
uc
tua
t
i
ons
a
n
d
its
i
n
f
l
u
e
n
c
e
on
the
p
o
w
e
r
flow
a
nd
los
s
es
c
h
a
nge
s;
attem
p
ti
ng
to
o
ptim
i
z
e
the
t
i
me
of
si
m
u
la
t
i
o
n
.
Th
e
Ne
wton
r
a
p
h
s
on
m
e
t
ho
d
g
e
n
e
rat
e
d
th
e
d
a
t
a
set
to
b
e
use
d
f
o
r
t
h
e
trai
ni
n
g
p
a
t
t
e
rn
s
p
r
oce
s
s.
T
he
in
put
m
a
t
r
i
x
i
s
c
om
p
o
se
d
o
f
;
lin
e
re
si
s
t
a
n
ce
(
R),
loa
d
d
em
and
(
P
D
),
(
Q
D
)
(rea
l
a
nd
r
e
a
c
ti
ve
pow
e
r
),
bus
vo
lta
ge
m
agn
i
t
ude
(
V
i
).
T
he
n
eura
l
ne
tw
or
k
m
o
d
e
l
de
ve
lo
pe
d
for
IEEE
3
0
b
u
s
t
e
s
t
w
a
s
trai
ne
d
to
p
rov
i
de
pow
er
s
ys
tem
val
u
es
w
hic
h
a
r
e
pow
er
g
ener
a
tio
n
(r
eal
a
nd
r
eac
ti
ve
pow
er)(P
g
),
(
Q
g
)
and
s
y
stem
l
osses
(P
ij
),
(Q
ij
)(r
eal
a
nd r
eac
tive
)
.
T
h
e
t
r
a
i
n
i
n
g
p
h
a
s
e
t
o
o
k
1
5
s
t
o
m
e
e
t
t
h
e
c
o
n
v
e
r
g
e
n
c
e
(
F
i
g
u
r
e
3
)
,
t
he
p
e
r
for
m
a
n
ce
r
eac
hed
t
h
e
best
v
al
u
e
3.15e
-
19
a
t
1
5
s
(
F
i
gure
4).
The
ne
tw
ork
p
a
ra
me
ters
a
r
e
a
dj
us
te
d
(
bias
a
nd
w
e
i
g
ht
s)
a
nd
i
t
i
s
rea
d
y
to
b
e
ut
iliz
e
d
i
n re
al time
(
f
or the
t
w
o
di
f
fere
n
t
v
a
l
ue
s of tem
per
a
t
u
r
e
:
T1
=
30
C°
a
nd T2
=
0
5C°
)
.
The
c
o
nd
uc
tor
'
s
r
e
sista
n
ce
in
cre
a
ses
as
its
t
em
per
a
ture
i
nc
re
as
e
s
a
n
d
s
o
l
o
s
s
e
s
,
d
u
e
t
o
;
e
i
t
h
e
r
t
h
e
curr
ent
loa
d
o
r
the
w
e
at
her
con
d
iti
on
s.
R
e
s
ults sh
o
w
n
i
n
(Table
3
)
a
r
e
ac
q
u
i
r
e
d
i
n
mi
l
l
i
s
econ
d
s
(n
eu
ral
netw
ork resu
l
t
s
)
.
The obje
c
t
ive
of
w
ork is t
o
m
i
nim
i
ze
t
i
m
e b
y
u
t
il
i
z
ing the
ne
ural
ne
t
w
o
rk for
s
uc
h ch
a
n
g
i
ng
of
t
em
per
a
ture.
Als
o
t
o
as
sess
th
e
g
e
n
e
ra
t
e
d
po
we
rs
a
nd
l
osse
s
du
ring
t
h
e
2
4
hou
rs
p
er
d
a
y
a
nd
t
h
r
o
ugh
t
he
ent
i
re
y
ear
wit
hin
mil
l
i
se
co
n
d
s.
3.4.
2.
Ex
t
r
e
m
e
l
e
a
r
ni
n
g
m
a
c
hi
ne
Mo
st
o
f
our
e
ffort
has
foc
u
se
d
on
Ex
trem
e
l
e
a
r
ning
m
a
c
h
ine
a
l
g
o
r
i
t
h
m
i
n
t
h
i
s
pa
pe
r.
E
ven
for
EL
M
the
s
i
mu
lat
i
o
n
proce
s
s
c
o
n
t
a
i
ni
ng
tw
o
s
t
eps
;
t
he
t
rai
n
i
ng-
val
i
d
at
ion
a
nd
t
h
e
tes
t
p
hase.
The
da
t
a
se
t
i
s
rand
om
ly
p
art
i
t
i
o
ned
i
n
to
t
w
o
n
o
n
-
o
v
e
rlap
p
e
d
se
t
s
,
t
o
f
orm
t
h
e
i
n
p
u
t
train
i
ng
-
v
al
i
d
at
i
o
n
m
a
tr
ix
a
nd
the
te
st
one.
T
h
e
in
put
m
a
t
r
i
x
is c
om
p
o
se
d o
f
line
r
e
s
i
s
t
anc
e
R
,
loa
d
d
e
ma
nd
(
re
al
a
n
d
r
e
a
c
ti
v
e
powe
r
)
(P
D
),
(
Q
D
),
bus
vo
lta
ge m
ag
n
i
t
ude (V
i
). The target
matrix
i
s containi
ng p
o
w
er
ge
n
era
t
i
o
n
(
r
ea
l
and r
eactive power))
(
P
g
),
(
Q
g
)
and
s
y
s
t
em
l
os
ses
(r
eal
a
nd
rea
c
tive
)
(
P
ij
),
(
Q
ij
)
.
T
h
e
a
l
g
o
r
i
t
h
m
s
e
e
m
s
t
o
b
e
v
e
r
y
f
a
s
t
,
i
t
a
c
h
i
e
v
e
s
t
h
e
h
i
g
h
e
s
t
ac
cura
cy 1
0
-2
7
(Fi
g
u
r
e
1
3
)
a
nd
fa
s
t
e
st
t
ra
inin
g
ti
me
:
0
.
0469
(S) an
d
a
l
so
te
s
ti
n
g
t
ime
0(S
)
(
fig
u
re
12).
In
o
rder
t
o
further
verif
y
t
he
v
al
idi
t
y
o
f
th
e impro
v
e
d
b
ui
lt
m
ode
l,
a
nd
t
h
e
gene
ra
liza
t
i
o
n;
t
w
o
ex
t
rem
e
v
al
ues
of
t
he
re
s
i
s
ta
nc
e 30
C° a
n
d
05
C
a
re
intro
d
u
c
e
d
, r
esult
s
a
re
di
s
p
l
a
yed i
n
T
able 4.
Ac
cordi
n
g
to
ELM
b
ase
d
p
o
w
er
f
low,
w
e
est
i
ma
ted
t
o
m
a
t
c
h
r
esu
l
t
s
o
ffe
r
e
d
b
y
t
he
n
e
u
r
a
l
ne
tw
or
k
w
ith
f
urt
h
er
o
p
timiz
a
t
i
on
i
n
t
i
m
e
and
m
o
re
e
xac
t
i
t
u
d
e
(Ta
b
le
5
)
.
It
i
s
e
v
i
d
ent
tha
t
t
he
r
egress
ion
accuracy
o
f
ELM a
lg
ori
t
h
m
i
s
superior
t
o
the N
N
.
Losses at:
T=
2
5
C
°
are
17,
599
M
W
,
22,24
4
M
v
a
r.
T=
3
0
C
°
are
17,
985
M
W
,
22,
40
7 M
v
ar.
T=
0
5
C
°
are
16,
79M
W, 21,
6
4
1
M
va
r.
Ma
the
m
a
tic
a
lly
l
osse
s
a
r
e
c
o
ve
red
by
th
e
p
l
ant
c
o
nnec
t
e
d
t
o
t
h
e
s
lac
k
b
us
(
sla
c
k
nu
m
b
er
one
1
),
but
in
t
he
r
eal
i
n
t
e
r
c
o
n
n
ecte
d
p
o
w
er
s
yste
m;
t
h
e
s
l
a
c
k
bus
g
e
n
era
t
o
r
is
n
ot
a
lw
ays
a
si
n
g
l
e
e
q
u
iva
l
e
n
t
m
a
chi
n
e
loca
te
d
i
n
a
c
on
tro
l
a
rea
,
l
osse
s
c
a
n
be
i
nt
e
r
prete
d
a
s
e
x
c
h
an
g
e
s
a
nd
p
o
w
e
r
tra
n
sact
i
ons
a
cros
s
mult
i-are
a
syste
m
s.
T
hi
s
m
a
y
im
pose
an
a
dd
it
io
na
l
opera
t
i
ng
c
o
st.
The
pric
e
incre
a
ses
a
s
w
ell
as
t
he
s
l
ack
b
us
pro
duc
t
i
o
n
i
ncre
ases.
ELM
m
ak
es
a
n
i
m
p
r
ov
e
m
e
n
t
i
n
t
h
e
e
l
e
ct
ri
cal
s
y
s
t
e
m
re
sp
ons
e;
t
h
e
gri
d
pa
ram
e
ter
s
c
a
n
b
e
pr
eve
n
t
e
d
in
sta
n
tl
y
at
a
n
y
m
ome
n
t
,
a
nd
t
he
p
la
nt
s
ge
n
e
r
a
tion
ca
n
be
r
e
s
ch
ed
ule
d
t
o
m
e
e
t
l
oad
de
m
a
nd
(in
a
d
d
i
t
i
o
n
t
o
lo
sse
s
)
,
t
o
m
a
in
t
a
in
pow
er
s
ys
tem
sec
u
rit
y
,
t
o
a
v
o
i
d
c
o
n
tin
ge
nc
ie
s
and
loa
d
s
he
d
d
in
g
(vo
l
t
a
ge
d
rop,
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
Po
we
r
f
l
o
w
va
riat
i
on
b
a
se
d o
n
ex
tre
m
e l
e
ar
nin
g
m
a
ch
ine al
g
o
r
ithm
in
p
o
w
e
r
system
(L
ab
e
d
Im
en)
1
253
fre
que
nc
y
fluc
tua
t
io
n),
to
p
r
e
ve
n
t
s
ystem
vi
o
l
at
i
ons
a
n
d
over
l
o
a
d
s,
t
o
pre
d
i
c
t
the
e
f
fe
ct
o
f
o
u
ta
ge
s
a
nd
t
o
minim
i
z
e
t
he
fue
l
co
ns
um
pti
o
n.
A
d
d
iti
ona
l
l
y
,
ELM
c
ou
l
d
l
i
k
e
w
ise
be
e
x
t
e
n
ded
t
o
m
a
k
e
u
s
e
of
a
l
a
r
g
e
s
c
a
l
e
d
a
t
a
b
a
s
e
,
(
W
i
t
h
i
n
[
0
5
3
0
]
C
°
)
,
ca
use
i
t
is a
l
r
eady
tra
i
ne
d,
and
a
lso for
m
o
re adva
nc
e
d
c
ompl
ic
a
tio
ns i
n p
o
w
e
r system
.
Tabl
e
6
li
st
s
the
mean
c
o
m
p
a
ri
son
result
s
o
f
ANN
an
d
ELM.
E
xt
re
me
L
e
a
rn
in
g
M
achin
e
s
(
ELM
s
)
are
very
c
on
t
r
overs
ial
a
n
d
v
e
r
y
f
ast
ma
ch
i
n
e
lea
r
n
i
ng
m
o
del
s
t
h
a
t
p
e
r
f
o
r
m
v
e
r
y
w
e
l
l
.
E
L
M
r
e
s
u
l
t
s
a
r
e
b
e
t
t
e
r
tha
n
A
N
N
, due
t
o t
h
e
a
b
ili
t
y
o
f the e
x
ce
lle
nt gener
a
liza
t
io
n pe
rform
a
nc
e a
nd the lear
n
i
n
g
speed wh
i
ch c
an be
th
ousa
nds
o
f t
i
m
es fa
s
t
e
r
t
h
a
n
tradi
ti
o
n
a
l
ne
u
r
a
l netw
or
ks.
Tabl
e 6
.
C
o
m
p
a
r
i
s
on
N
e
u
r
a
l
n
e
t
w
ork
Extre
m
e
l
e
a
r
ning
m
a
chin
e
T
r
a
i
ning
ti
m
e
(s)
15
0
,
0469
T
e
sting
tim
e
(
s)
/
0
,
0000
T
r
a
i
ning
pe
r
f
orm
a
nc
e
3,
15e
-
1
9
3,
666e
-25
Te
sti
n
g
pe
r
f
orm
a
n
c
e
/
8,
248e
-27
4.
CO
NC
L
U
S
I
O
N
P
o
wer
s
y
stem
s
ecurity
requires
sy
s
t
e
m
m
o
n
i
t
o
r
i
n
g
i
n
r
e
a
l
t
i
m
e
,
w
h
er
e
th
e
da
ta
base
i
s
c
ont
in
u
o
u
s
l
y
up
da
ted.
T
hi
s
pape
r
in
ves
t
iga
t
ed
t
he
i
mpa
c
t
of
t
he
t
em
p
e
ra
ture
var
i
at
i
on
o
n
ove
r
h
ea
d
p
o
w
e
r
l
i
ne
s.
T
h
i
s
in
flue
nce
on
th
e
con
d
u
c
t
or
's
r
esis
tance
ca
nn
ot
b
e
ne
glec
te
d.
W
e
n
o
t
i
c
e
d
d
i
f
f
e
r
e
n
t
v
a
r
i
a
t
i
o
n
s
o
n
t
h
e
b
e
h
a
v
i
o
r
of
t
he
ele
c
t
rica
l
gri
d
, nota
b
ly
:
the
system
l
os
ses,
the
g
ener
at
ed pow
e
r
s,
a
nd
the
li
n
e
f
l
ow
.
We i
n
t
ro
duc
e
d
Ex
trem
e
lear
ning al
g
o
rit
h
m
to
s
olve
t
his
pr
ob
lem
.
Th
e
b
a
si
c
ANN
mo
d
e
l
i
zati
o
n
(feed
forw
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d
ba
c
k
p
ro
paga
tio
n)
s
e
e
m
s
t
o
be
a
p
p
ro
pria
t
e
f
or
t
he
a
p
p
l
i
cati
o
n
I
EEE
30
B
u
s
s
y
s
t
em
;
but
i
n
term
s
of
ac
cura
cy
a
nd
exac
t
i
t
ude
o
f
re
su
l
t
s
o
f
f
e
r
e
d
b
y
E
L
M
(
t
h
e
t
i
m
i
n
g
m
i
n
i
m
i
z
a
tio
n
,
p
erf
o
rma
n
ce
),
w
e
c
a
n
s
ay
ec
onom
ic
o
b
j
e
c
t
i
v
es
a
re
r
ea
l
i
ze
d
(t
he
o
p
t
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m
iza
t
i
o
n
i
n
t
i
m
e
,
fue
l
co
ns
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m
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i
o
n
an
d
t
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e
duct
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on
of
t
h
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cos
t
)
;
ELM sta
n
d
s t
o
be
the
mos
t
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ifte
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versi
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f
th
e a
r
tific
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tel
l
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g
e
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ni
q
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es
REFE
RENCES
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.
B
.
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t
e
v
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n
a
n
d
M
.
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.
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l
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a
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a
r
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,
“Elect
ri
c
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t
em
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,
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C
on
d
u
cto
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T
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p
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r
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tu
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I
m
p
act
on
S
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d
o
pe
ra
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r Flow
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