Indonesian J
ournal of Ele
c
trical Engin
eering and
Computer Sci
e
nce
Vol. 2, No. 3,
Jun
e
201
6, pp. 537 ~ 54
4
DOI: 10.115
9
1
/ijeecs.v2.i3.pp53
7-5
4
4
537
Re
cei
v
ed Ma
rch 4, 2
016;
Re
vised
Ma
y 9, 2016; Acce
pted May 2
0
, 2016
Electric Price Forecast using Interbreed Approach of
Linear Regression and SVM
Deep
ak Sain
i, Akash Sax
e
na
Dep
a
rtement o
f
Electrical Eng
i
ne
erin
g
S
w
a
m
i Kes
h
va
nan
d Institute of
T
e
chnol
og
y
Mana
geme
n
t & Gramothan, Jaip
ur, India
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: deep
ak.92
@
outlo
ok.com, akash@skit.ac.i
n
A
b
st
r
a
ct
Electricity pr
ic
e forecasti
n
g
i
s
a hy
percritic
al
iss
ue
du
e to the
invo
lve
m
e
n
t of co
nsu
m
ers
an
d
prod
ucers in electricity mar
k
ets.
Price for
e
castin
g p
l
ays
an
i
m
porta
nt role
in
pl
ann
i
ng a
nd
man
a
gin
g
econ
o
m
ic
oper
ations
rel
a
ted
w
i
th the e
l
ectri
c
al p
o
w
e
r (b
id
din
g
, tradi
ng)
and
other
d
e
ci
sions r
e
l
a
ted
w
i
t
h
loa
d
sh
ed
din
g
and
g
ener
atio
n
resch
edu
li
ng. I
t
is a
l
so
usef
u
l
for opti
m
i
z
a
t
io
n
in
el
ectrica
l
e
n
ergy tra
de. T
h
i
s
pap
er ex
plor
es
an
interbr
e
e
d
techni
qu
e b
a
s
ed o
n
S
upp
ort
Vector Mac
h
in
e (SVM) a
nd
li
near r
egr
essio
n
to
pred
ict the
day
ah
ead
el
ectric
ity pric
e
usi
ng
historic
al
data
as a r
a
w
insert
. Different 2
7
l
i
near r
egr
essio
n
mo
de
ls are for
m
e
d
to cre
a
te
initia
l fra
m
ew
o
r
k for
forecasti
ng e
ngi
ne. C
o
mp
ariso
n
of th
e perfor
m
ance
of
different forec
a
sting e
ngi
nes i
s
carried
out o
n
the b
a
sis of
error in
dices
n
a
mely Me
an S
quar
e Error (M
SE),
Sum Sq
uare
E
rror (SSE) a
n
d
other c
onv
enti
ona
l err
o
r in
dic
e
s.
A
det
ail
ed expl
anati
on of line
a
r
re
gress
i
on
system bas
ed mo
de
l
is pres
e
n
ted and
si
mu
l
a
tion
r
e
su
lt
s ex
hibit th
at the
pr
opos
ed
lear
ni
n
g
meth
od
is a
b
l
e
to forecast electricity pric
e in a
n
effective man
ner.
Ke
y
w
ords
: His
torical pric
e dat
a, line
a
r regres
sion
mo
del
, Pri
c
e F
o
recastin
g
,
Support Vector Machi
n
e
Copy
right
©
2016 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
In modern power ma
rket, price of
electr
i
c
ity plays an im
portant role.
With the
dere
gulatio
n
scen
ari
o
, i
n
crea
sing
p
opulatio
n a
n
d
ad
dition
o
f
sma
r
t g
r
id
tech
nolo
g
y, the
comp
etitive busin
ess envi
r
onment
h
a
s emerged. He
nce,
the
el
ectr
icity pri
c
e i
s
an im
porta
nt
denomi
nato
r
. Predictio
n o
f
electri
c
ity price i
s
quite
trouble
s
om
e
due to its nonlin
ear, no
n-
stationa
ry an
d volatile nat
ure. Th
ere
is an
a
c
ute n
e
ed of supe
rvised l
earning
para
d
igm
whi
c
h
not only can
predi
ct the price of the electri
c
it
y accurately but also i
s
ea
sy to impleme
n
t.
Literatu
re su
rvey
sho
w
s that
many
r
e
se
ar
che
r
s h
a
v
e
com
e
f
o
rwa
r
d
wit
h
n
e
w
sup
e
rv
is
ed
learni
ng te
ch
nique
s, time
seri
es mod
e
li
ng techniq
u
e
s
an
d reg
r
e
s
sion
metho
d
s in orde
r to fi
nd
the price of electri
c
ity with highe
r accura
cy
. In [1]
authors empl
oyed simila
r days metho
d
to
forecast
day
ahea
d ele
c
tri
c
ity pri
c
e fo
r
PJM el
ectr
i
c
it
y markets. In
this m
e
thod
the correlatio
n
betwe
en
pri
c
e an
d lo
ad
is formul
ated
a
nd fu
rther
th
e Neu
r
al
Net
w
ork (NN) i
s
empl
oyed. T
he
statistical app
roa
c
h for inte
rval fore
casti
ng is em
ploy
ed in [2]. Foreca
sting the
predi
ction int
e
rval
is e
s
sential
for un
de
rsta
nding th
e u
n
ce
rtainty in
volved in th
e pri
c
e. Poi
n
t and i
n
terval of
predi
ction
foreca
sting i
s
p
e
rform
ed
wit
h
Fun
c
ti
on
al
Princi
pal
Co
mpone
nt An
alysis (FP
C
A
)
in
approa
ch [3]. Modified Relief Algorith
m
is employ
ed with the
hybrid ne
ural
netwo
rk by
N.
Amjady et.al. [4]. Radial Basi
s Fun
c
tion
N
eural Network (B
RF
NN) based o
n
fuzzy mea
n
s a
n
d
differential ev
olution is te
st
ed for ele
c
tri
c
ity pric
e fore
ca
sting [5]. After a ca
reful
investigatio
n of
the literature, it is concl
u
d
ed that the supervi
sed le
a
r
ning m
odel
s
namely Fee
d
Forward
Ne
ural
Network
(FF
N
N), RB
FNN and
SVM
are
empl
oye
d
a
s
reg
r
e
s
sion
ag
ents
to fore
ca
st t
h
e
electri
c
ity pri
c
e in
differe
n
t
regio
n
s. T
h
e ability of th
e neu
ral
net
works to
deal
with the
vari
able
mappin
g
pro
b
lems i
s
q
u
i
t
e good a
n
d
the re
su
lts pre
s
ente
d
i
n
previo
us
approa
che
s
are
promi
s
in
g. Howeve
r, the
computation
a
l
time and
det
ermin
a
tion
of optimal
set
o
f
parameters
for
deci
d
ing
the macro and
mi
cro
stru
cture of
the neu
ral
netwo
rks rai
s
e a
qu
estio
n
on the
reliabil
i
ty
of the app
ro
ach
e
s. T
o
a
ddre
s
s this
probl
em
, this pape
r p
r
e
s
ents lin
ear
regre
s
sion
ba
sed
approa
ch for forecastin
g the ele
c
tri
c
ity prices.
27
d
i
fferent linea
r regressio
n
model
s from
the
histori
c
al d
a
ta of electri
c
ity price are carri
ed out
to predi
ct the price of year 2
010. The dat
a for
this reg
r
e
s
sio
n
modelin
g is take
n from
Spain
Electricity markets (Iberian En
e
r
gy De
rivatives
Exchang
e) [6
]. Predictio
n
by the regre
ssi
on m
odel
s are
put fo
rward a
s
an i
nput featu
r
e
s
of
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 25
02-4
752
IJEECS
Vol.
2, No. 3, Jun
e
2016 : 537
– 544
538
Suppo
rt Vect
or Ma
chin
e (SVM). The compa
r
is
on of
the perfo
rm
ance of vari
ous
sup
e
rvi
s
ed
learni
ng mo
dels n
a
mely
FFNN, No
nlinea
r Auto Regressive
Exogenou
s (NARX
)
a
n
d
Probabilisti
c Neural Network (PNN) on
t
he
basi
s
of
error indi
ces
i
s
evaluated. T
he definition
o
f
the e
rro
r i
ndi
ce
s a
r
e
taken
from
[7]. The
rem
a
inin
g p
a
rt of thi
s
pa
per is o
r
gani
zed a
s
follows: in
se
ction
2 m
e
thodol
ogy for regre
s
sion
is
explained,
in
se
ction
3, a
h
y
brid m
odel
for
pri
c
e fo
re
cast
by SVM is explained, in section 4
sim
u
lated re
sults are exhibite
d. Section 5
summ
ari
z
e
s
the
results
in a conc
lus
i
ve form.
2. Proposed
Metho
d
To d
e
velop
different
reg
r
ession
mod
e
l
s
from th
e p
a
st d
a
ta i
s
a
tediou
s
data
mining
pro
c
e
ss. In th
is se
ction
we
explain the m
e
thodol
ogy a
dopted fo
r the formation o
f
the regre
s
si
on
pattern
s. The
data from Ib
erian
sto
ck m
a
rkets a
r
e
ch
ose
n
for
carrying out the p
r
ice
predictio
n of
year 2
010. T
he ele
c
tri
c
ity pri
c
e
pattern of a ye
ar
2009, trend
of pri
c
e
on
Ne
w Yea
r
a
nd
a
workin
g day are exhibite
d in figure 1 to 3.
Figure 1. Electri
c
ity price p
a
ttern of year 2009
Figure 2. Electri
c
ity price p
a
ttern of 1-1
-
2009
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
1
16
31
46
61
76
91
106
121
136
151
166
181
196
211
226
241
256
271
286
301
316
331
346
361
Price
in
Eu
ro
hours
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
1
234
5678
9
1
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
2
0
2
1
2
2
2
3
2
4
Price
in
Euro
Hours
Evaluation Warning : The document was created with Spire.PDF for Python.
IJEECS
ISSN:
2502-4
752
Electri
c
Price Fore
ca
st usi
n
g Interbreed
Appro
a
ch of Linea
r Re
gre
ssi
on an
d SVM
(De
epa
k S)
539
Figure 3. Electri
c
ity price p
a
ttern for a worki
ng day
T
o
de
ve
lo
p th
e
r
e
gr
es
s
i
on
mod
e
l
the
c
u
rr
en
t pr
ice is co
ns
id
er
ed
b
y
the
ab
br
e
v
ia
tio
n
(DMY
H).
The
table
1
sho
w
s different va
riable
s
an
d
th
eir com
b
inati
ons. For
exa
m
ple,
de
sig
n
8
is
employed to fore
ca
st the data of
any day of 2010 of specifi
c
hou
r.
Table 1. Defi
nitions of different hi
stori
c
al pattern
s for factorial de
si
gn
1
(D-1,M,
Y
,
H
)A
(D,M-1,
Y
,
H
)B
(D,M,
Y
-1,
H
)C
2
(D-1,M,
Y
,
H
-1
)D
(D,M-1,
Y
,
H
-1
)E
(D,M,
Y
-1,
H
-1
)F
3
(D-1,M,
Y
,
H
+1)
G
(D,M-1,
Y
,
H
+1)H
(D,M,
Y
-1,
H
+1)I
4
(D-1,M,
Y
,
H
)A
(D-1,M,
Y
,
H
-1
)D
(D,M-1,
Y
,
H
-1
)E
5
(D,M,
Y
-1,
H
-1
)F
(D,M-1,
Y
,
H
-1
)E
(D-1,M,
Y
,
H
)A
6
(D,M-1,
Y
,
H
) B
(D-1,M,
Y
,
H
-1
)D
(D,M,
Y
-1,
H
-1
)F
7
(D-1,M,
Y
,
H
-1
)D
(D,M-1,
Y
,
H
)B
(D,M-1,
Y
,
H
-1
)E
8
(D,M,
Y
-1,
H
)C
(D,M-1,
Y
,
H
-1
)E
(D-1,M,
Y
,
H
-1
)D
9
(D,M,
Y
-1,
H
-1
)F
(D,M,
Y
-1,
H
)C
(D,M-1,
Y
,
H
-1
)E
10
(D-1,M,
Y
,
H
+1)
G
(D-1,M,
Y
,
H
) A
(D,M,
Y
-1,
H
+1) I
11
(D,M-1,
Y
,
H
)B
(D,M-1,
Y
,
H
+1)H
(D-1,M,
Y
,
H
+1 )
G
12
(D,M,
Y
-1,
H
)C
(D-1,M,
Y
,
H
+1)
G
(D,M-1,
Y
,
H
+1)H
13
(D-1,M,
Y
,
H
-1
)D
(D,M-1,
Y
,
H
)B
(D,M,
Y
-1,
H
) C
14
(D-1,M,
Y
,
H
)A
(D,M-1,
Y
,
H
-1
) E
(D,M-1,
Y
,
H
)B
15
(D,M,
Y
-1,
H
-1
) F
(D,M-1,
Y
,
H
)B
(D,M,
Y
-1,
H
)C
16
(D,M-1,
Y
,
H
-1
)E
(D-1,M,
Y
,
H
+1)
G
(D,M,
Y
-1,
H
+1) I
17
(D,M,
Y
-1,
H
+1)I
(D,M,
Y
-1,
H
-1
)F
(D,M-1,
Y
,
H
+1)H
18
(D-1,M,
Y
,
H
+1)
G
(D-1,M,
Y
,
H
)A
(D,M-1,
Y
,
H
)B
19
(D,M,
Y
-1,
H
)C
(D-1,M,
Y
,
H
+1)
G
(D-1,M,
Y
,
H
)A
20
(D-1,M,
Y
,
H
)A
(D,M-1,
Y
,
H
)B
(D-1,M,
Y
,
H
-1
)D
21
(D,M-1,
Y
,
H
+1)H
(D,M,
Y
-1,
H
)C
(D-1,M,
Y
,
H
)A
22
(D-1,M,
Y
,
H
-1
)D
(D,M-1,
Y
,
H
+1)H
(D,M,
Y
-1,
H
-1
)F
23
(D,M-1,
Y
,
H
-1
)E
(D,M,
Y
-1,
H
-1
)F
(D,M-1,
Y
,
H
+1)H
24
(D,M,
Y
-1,
H
-1
) F
(D,M,
Y
-1,
H
+1)I
(D,M,
Y
-1,
H
)C
25
(D,M,
Y
-1,
H
+1)I
(D-1,M,
Y
,
H
-1
)D
(D,M-1,
Y
,
H
-1
) E
26
(D-1,M,
Y
,
H
-1
)D
(D,M-1,
Y
,
H
)C
(D,M,
Y
-1,
H
+1) I
27
(D,M,
Y
-1,
H
-1
)F
(D,M-1,
Y
,
H
+1)H
(D,M,
Y
-1,
H
)C
This de
sign
regre
s
se
s th
re
e vari
able
s
at a ti
me, th
e
d
a
ta of th
e
sa
me d
a
y, sam
e
mo
nth,
previou
s
ye
ar and
same
ho
ur
con
s
id
ered
as varia
b
le
(C),
sam
e
d
a
y, previou
s
mo
nth, sam
e
ye
ar
and
p
r
eviou
s
hour as
va
ria
b
le
(E) and previous day
, same mo
nth, same yea
r
an
d previo
us
ho
ur
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Price
in
Eu
ro
Hours
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 25
02-4
752
IJEECS
Vol.
2, No. 3, Jun
e
2016 : 537
– 544
540
as vari
able (D). Vari
able
C, E and D a
r
e empl
oyed
to predi
ct the
price of the same
day, sa
me
month, sa
me
year and
same ho
ur. S
i
milarly, in this fashion, 2
7
different li
near
reg
r
e
s
si
on
model
s a
r
e p
r
epa
re
d an
d
comp
arative analysi
s
of th
ese
patterns
is carried
out
on the
ba
sis of
Mean Squ
a
re
Error
(MSE).
The error in
predi
ction i
s
shown in figure 4.
Figure 4. Line
ar re
gre
s
sion
model for hi
st
orical ele
c
tri
c
price
It is observe
d
that pattern
10, 11 a
nd 1
9
give
lo
we
st MSE. For p
r
edictio
n
of th
e pri
c
e,
these fo
recast inputs are ut
ilized a
s
input
feature
s
of SVM.
D-
1,
M
,
Y
,
H
/A
,B
,C
D
ESI
G
N
1
D,
M
-
1,
Y
,
H
/D
,E
,F
D
ESI
G
N
2
D,
M
,
Y
-
1,
H
/G,H
,I
D
ESI
G
N
3
D,
M
,
Y
,
H-
1
/F,H
,C
DE
SI
G
N
27
S
t
and
ar
d
Mix
t
u
r
e
C
o
ns
t
r
ai
ned
M
i
x
t
ure
D
,
M
,
Y
,
H /
A
-
I
DE
S
I
G
N
Y
D
,
M
,
Y
,
H /
A
-
I
D
ESI
G
N
X
D
,
M
,
Y
,
H/
A
-
I
D
ESI
G
N
Z
Lin
ear
R
e
g
r
es
s
i
on
M
o
d
e
l
R
E
G
R
E
S
S
E
D DE
S
I
GN
S
D
,
M
-
1
,
Y
,
H
D
,
M
,
Y
-
1
,
H
D-
1,
M
,
Y
,
H
A
B
C
D
F
G
H
I
A
B
C
Figure 5. Line
ar Re
gressio
n
model for P
r
ice F
o
re
ca
sti
n
g
Figure 5 sh
ows the line
a
r reg
r
e
s
sio
n
mode
lin
g betwe
en hist
orical data sets and
formation of
different data patterns
(A
to I).
By the com
b
inatio
n
of these m
o
del
s
with
th
eir
spe
c
ific attri
butes in te
rms of day,
month,
year and h
o
u
r
, forecast
s a
r
e predi
c
ted.
The
mathemati
c
al
relation
ship
betwe
en the
s
e variable
s
is
sho
w
n in a
p
p
endix.
0
50
100
150
200
250
300
350
400
450
1
2
3
4
5
6
7
8
9
1
01
1
1
21
31
4
1
51
61
71
8
1
92
02
1
2
22
32
4
2
52
62
7
M
S
E
Linear
Regression
Models
Evaluation Warning : The document was created with Spire.PDF for Python.
IJEECS
ISSN:
2502-4
752
Electri
c
Price Fore
ca
st usi
n
g Interbreed
Appro
a
ch of Linea
r Re
gre
ssi
on an
d SVM
(De
epa
k S)
541
3. Support V
ector M
achi
n
e (SVM)
In recent ye
ars th
e appli
c
ation of SV
Ms ha
s in
creased in n
o
n
linea
r map
p
i
ng and
cla
ssifi
cation
proble
m
s d
ue to its extra ordina
ry capa
city of data matchi
ng
and re
gre
ssion.
Re
cently a
compa
r
ison of
the pe
rform
ance of
the
SVM with ot
her
releva
nt neural net
wo
rk
topologi
es h
a
s
bee
n
ca
rried o
u
t for
continge
ncy
ranki
ng
and
classificatio
n
i
n
[8]. SVMs
are
applie
d for cl
assificatio
n
o
f
power
quali
t
y events [9
], multi-dim
e
n
s
ional d
a
ta
cla
ssifi
cation
[1
0],
cla
ssifi
cation
of micro
a
rray
s [11], wind
spe
ed p
r
edi
ction [12], voltage sta
b
ility monitori
ng [1
3]
and many m
o
re [14]. The
main rea
s
on
behind this
popul
arity of the SVM as a cla
ssifie
r
is tha
t
SVM can
ha
ndle la
rge fe
ature
spa
c
e.
Structu
r
e
of
Lea
st Squa
re Suppo
rt V
e
ctor Ma
chin
e is
sho
w
n
in th
e
figure
6. In th
is p
ape
r
Radi
al Ba
sis Fun
c
tion kern
el i
s
use
d
. Th
e
ch
oice
of
RBF i
s
obviou
s
du
e
to its hig
her
accuracy. To
desi
gn th
e
SVM data of
electri
c
ity pri
c
e i
s
sub
divided
into five subsets. Cross va
lidation techn
i
que is
e
m
plo
y
ed to train, test and valid
ate the mode
l.
To train the supervi
sed le
a
r
ning m
odel e
l
ectri
c
ity price
data has b
e
en take
n for
2006
-20
09 from
the Iberia
n M
a
rket (Sp
a
in
Electri
c
ity Ma
rket
s)
and
predictio
n of th
e hou
rly load
of year 2
010
is
carrie
d out.
Supervi
sed l
earni
ng m
o
d
e
ls
use 70
% data fo
r training
and
remainin
g 3
0
% for
testing an
d validation pu
rp
ose.
Figure 6. Support Vecto
r
M
a
chi
ne
4. Results a
nd Analy
s
is
This se
ction pre
s
ent
s
the analysi
s
of
el
ectri
c
ity pri
c
e
fore
ca
st deri
v
ed by the su
pervised
learni
ng met
hod u
s
ing lin
ear regressio
n
model. To
dra
w
a fair compa
r
ison of the predi
ctio
n
perfo
rman
ce
by SVM, three
othe
r netwo
rk
s a
r
e ch
osen which
are F
F
NN,
NARX
and
Proba
bilisti
c
Neu
r
al
Net
w
o
r
k (P
NN). Th
e line
a
r re
gre
ssi
on
model
con
s
i
s
ts
of 2
7
different d
e
s
ign
sets of me
rg
e histo
r
i
c
al
data of Spai
n ele
c
tr
i
c
ity price ma
rket. This
mod
e
l
provid
es th
ree
resultant o
p
timal de
sign
sets which a
r
e
less e
r
roneo
us a
nd
give a
n
eno
rmo
u
s
relation b
e
twe
e
n
raw his
t
orical ins
e
rts
to predic
ted data set.
Table 2. Co
m
pari
s
on of the
Netwo
r
k T
o
p
o
logie
s
Error Indices
FFNN
N
A
R
X
Probabili
stic
SVM
Mean Square
Err
o
r
0.0062
0.0059
0.4049
0.0009
Root Mean Squ
a
r
e Erro
r
0.0878
0.0768
0.6300
0.030
Mean Absolute Error
0.0605
0.0585
0.6233
0.0155
Sum of Square
d
Error
4.5396
4.3743
301.24
0.6765
Sum of Absolute Error
55.027
43.49
463.70
11.5680
Followi
ng poi
nts are
emerged from tabl
e 2:
a.
After careful observation
s
it is con
c
lud
e
d
t
hat SVM has lo
w value
s
of errors th
at advocate
the efficacy o
f
the propo
se
d approa
ch i
n
the predi
cti
on of the ele
c
tri
c
ity price.
These erro
rs
are plotted in
figure 7 an
d 8. The obviou
s
ch
oice fo
r solving this foreca
sting p
r
ob
lem is SVM
due to lower
values of erro
rs.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 25
02-4
752
IJEECS
Vol.
2, No. 3, Jun
e
2016 : 537
– 544
542
Figure 7. Non
linear Auto
Regre
s
sive Exogen
ou
s (NA
R
X) Error
Figure 8. Support Vecto
r
M
a
chi
ne Error
b.
The erro
r indi
ce
s are
sho
w
n in figure 9 and 10.
It is also
con
c
lud
ed that PNN i
s
not a good
choi
ce fo
r predictio
n of the ele
c
tricity p
r
ice. In
thi
s
p
a
rticul
ar
pro
b
l
e
m, this topol
ogy not only
gives a
wea
k
perfo
rman
ce
of the pre
d
iction task
but also req
u
ire
s
high comp
uta
t
ional
time.
The p
r
edi
ctio
n of ele
c
tricit
y price i
s
a
critical task h
e
n
ce, a
n
y app
roa
c
h
whi
c
h requires
high
comp
utationa
l time is not suitable for p
r
e
d
iction.
Figure 9. Mean ab
solute E
rro
r for p
r
edi
ction model
s
0
100
20
0
30
0
40
0
50
0
60
0
70
0
-0.
4
-0.
2
0
0.
2
0.
4
0.
6
Ho
u
r
s
E
rro
r f
o
r
NA
RX
0
100
20
0
30
0
40
0
50
0
60
0
70
0
-0.
3
-0.
2
-0.
1
0
0.
1
0.
2
H
our
s
i
n
m
o
nt
h
E
r
ro
r i
n
pr
edi
c
t
i
o
n
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
FFNN
N
ARX
P
robabilistic
S
VM
Mean
Absolute
Error
Evaluation Warning : The document was created with Spire.PDF for Python.
IJEECS
ISSN:
2502-4
752
Electri
c
Price Fore
ca
st usi
n
g Interbreed
Appro
a
ch of Linea
r
Re
gre
ssi
on an
d SVM
(De
epa
k S)
543
Figure 10. Ro
ot Mean Squ
a
red Erro
r for predi
c
tion m
odel
s
c.
These sim
u
la
tion results show a futuri
st
ic solu
tio
n
for different se
ctions of a com
p
lex powe
r
system
netwo
rk. T
he e
r
ror
plots of
Ja
nu
ary mont
h
of
2010
predicti
on is sh
own i
n
figure 10, it
is ob
se
rved
that FFNN
a
nd NA
RX perform
s
marginally well
and show al
most same
respon
se in term
s of predi
ction erro
rs. The lo
wer val
ues a
r
e ob
se
rved in the predictio
n by
SVM. This sho
w
s the
efficacy of this
supe
rvised lea
r
nin
g
model ove
r
rest of th
e
conve
n
tional topologi
es.
5. Conclusio
n
In the compe
t
itive business scena
rio, a
n
accu
rate predictio
n of the electri
c
ity price i
s
inevitable. El
ectri
c
ity as a
comm
odity can’t be
st
o
r
e
d
and
sto
c
kpi
l
ed. Trading
of ele
c
tricity
has
come i
n
pra
c
tice i
n
the
rec
ent years.
This p
ape
r p
r
esents
a
straight forward
approa
ch fo
r
establi
s
hi
ng different
re
gression
mo
del
s between hi
stori
c
al data
sets
to the p
r
edicte
d
data
sets.
These mo
del
s a
r
e te
sted
and the
finest model
s a
r
e
taken fo
r the
predi
ction. P
r
edicte
d
outp
u
t
s
are em
ploye
d
as an in
pu
t features to
SVM and th
e forecastin
g
of hourly electri
c
ity price
is
carrie
d out. It is observed
that the prop
ose
d
me
thod
is efficient and ca
n be a benefi
c
ial too
l
at
energy man
ageme
n
t ce
nter. To est
ablish the e
fficacy of the prop
osed approa
ch a fair
comp
ari
s
o
n
betwe
en the
perfo
rman
ce
s of netwo
rk
s
are
ca
rrie
d o
u
t. Long term fore
ca
stin
g of
electri
c
ity pri
c
e by this method lie
s in the scope of th
e future.
Referen
ces
[1]
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al, T
Senj
yu,
N Ur
as
aki, T
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dia
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r
ans
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The
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e
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i
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ta Mi
tta
l
an
d
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s
h
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ax
en
a
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“Lay
e
r
R
e
cu
rre
n
t
N
e
u
r
a
l
N
e
t
w
ork ba
se
d
Po
w
e
r Syste
m
L
oad
Forecasting”.
T
e
leko
monik
a
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nesi
a
n
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ourn
a
l
of
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trical En
gi
neer
ing. T
E
LKO
M
NIKA
. 201
5:
16(3): 42
3 – 43
0.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
FFNN
N
ARX
P
robabilistic
S
VM
RMSE
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 25
02-4
752
IJEECS
Vol.
2, No. 3, Jun
e
2016 : 537
– 544
544
[8]
Bhan
u Prata
p
Soni, Ak
ash
Saxen
a
a
n
d
Vikas Gu
pta.
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u
a
r
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pport v
e
c
t
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ne
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oach for c
ontin
ge
nc
y
c
l
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n
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a
rge p
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r s
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neer
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g
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Yon
g
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Bho
w
mik, F
M
agn
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ctiv
e Po
w
e
r
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y cl
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ng W
a
v
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t T
r
ansform
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ort Vector Machi
nes
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th Appl
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ł
a
w
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y
g
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Kra
w
cz
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cha
ł
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ź
ni
a
k
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l
t
i
d
i
m
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l
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i
t
h
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a
l d
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stan
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ker
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i
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[11]
M Kumar, S
K
u
mar
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Cl
assificati
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us
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ng M
a
p
Re
du
ce b
a
se
d pr
ox
imal s
u
p
port
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a
c
h
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w
l. Bas
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y
st
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[12]
Xi
ao
bin
g
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ng
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ang
jie
Li
u, Ruife
ng S
h
i,
K
w
a
n
g
Y L
ee,
W
i
nd sp
ee
d
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usi
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g red
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ce
d
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th
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e
ctio
n.
Neuro co
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[13]
KS Sajan, Vish
al Kumar, Barj
eev T
y
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g
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pport
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e for on-li
n
e
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e stabi
lit
y mo
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ng”.
Internatio
na
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a
l of Elect
r
ical Pow
e
r &
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m
s
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15; 73
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208.
[14]
F
eng Lv, F
e
n
gni
ng Ka
ng,
Hao S
un. T
he Pr
ed
ictive
Method
of Po
w
e
r L
oad B
a
sed o
n
SVM.
T
e
leko
monik
a
Indo
nesi
an Jo
u
r
nal of Electric
al Eng
i
ne
eri
n
g
.
2014; 1
2
(4): 3
068-
307
7.
A
p
pe
ndix
DESIG
N
S
REG
R
ESSI
O
N
E
Q
U
A
TIONS
DESGIN 1.
R = -4783 + 77
.8
A + 81.0 B + 17
6.1 C - 1.
296 A*
B - 2.82 A*C -
2.
96 B*C+ 0.0472
A*B*C
DESGIN 2.
R = -1109 + 17
.8
D + 17.8 E + 31.
2 F - 0.2
69 D*E -
0.471 D*F
- 0.47
8 E*F+ 0.0072 D
*
E*F
DESGIN 3.
R = -1891 + 34
.5
G + 34.1
H + 74.
2 I - 0.599
G*H
-
1.31 G*I
- 1.32 H
*
I+ 0.0231 G*
H*I
DESGIN 4.
R = 5565 - 8
9
.1
A - 92.7 D
- 91.8
E + 1.50 A*D + 1
.
47 A*E + 1.56 D
*
E- 0.0249 A*D*
E
DESGIN 5.
R = -3145 + 10
2
F + 51.7 E + 51.
6 A - 1.66
F*E -
1.63 F*A - 0.
829
E*A + 0.0264 F*
E*A
DESGIN 6.
R = -1326 + 23
.5
B + 23.8 D + 37.
9 F - 0.4
01 B*D -
0.65 B*F - 0
.
658
D*F + 0.0112 B*
D*F
DESGIN 7.
R = -2201 + 32
.6
D + 32.3 B + 36.
6 E - 0.458
D*B -
0.529 D*E - 0
.
52
2 B*E + 0.00745
D*B*E
DESGIN 8.
R = -2794 + 10
0.
4 C + 44.1 E + 5
0
.3 D - 1.
57 C*E
- 1.77 C*D
- 0.77
6 E*D + 0.0275
C*E*D
DESGIN 9.
R = -1704 + 60
.2
F + 58.1 C + 2
8
.
8
E - 1.95
F*C -
0.971 F*E -
0.95
C*E + 0.0315 F*
C*E
DESGIN 1
0
.
R = 4008 - 6
7
.0
G - 61
.8 A - 14
6.
6 I + 1.049
G*A + 2.51 G*I + 2.2
6
A*I - 0.0387
G*A
*
I
DESGIN 1
1
.
R = -3564 + 74
.7
B + 45.3 H + 60.
7 G -
1.008 B*H
-
1.249 B*G
- 0.7
59 H*G + 0.
0169
B*H*G
DESGIN 1
2
.
R = -1740 + 61
.3
C + 30.6
G + 30.
7 H - 1.04
0 C*
G
- 1.06 C*H
- 0.52
0 G*H + 0.0
180
C*G*H
DESGIN 1
3
.
R = -4595 + 81
.0
D + 78.4 B + 16
6.7 C - 1.
362 D*
B - 2.89 D*C
- 2.
82 B*C + 0.0489
D*B*C
DESGIN 1
4
.
R = -4755 + 77
.5
A + 83.6 E + 71.
5 B - 1.344 A*E -
1.153 A*B - 1.25
3 E*B + 0.0202
A*E*B
DESGIN 1
5
.
R = 248 + 0.8 F
-
2.9 B - 4.6
C - 0.
013 F*B - 0.
08 F
*
C+ 0.069 B*C +
0.0014 F*B*C
DESGIN 1
6
.
R = -1380 + 21
.9
E + 24.8 H + 51
I - 0.374 E*H
- 0.
79 E*I - 0.87
H*I + 0.0135 E*H*I
DESGIN 1
7
.
R = 3779 - 1
32.8
I - 112.1
F - 65
.4
H + 3.98 I*F + 2.
334 I*H + 1.983
F*H- 0.0
702 I*F*
H
DESGIN 1
8
.
R = 1324 - 6
.
8 G - 35.8 A -
24.5 B
+ 0.374 G*A + 0
.
18 G*B + 0.64
3
A*B- 0.0071
G*A
*
B
DESGIN 1
9
.
R = 2658 - 8
6
.7
C - 46.2
G -
40.4
A + 1.563 C*G + 1.320 C*A + 0.7
19 G*A- 0
.
0238
C*G*A
DESGIN 2
0
.
R = 1324 - 3
5
.8
A - 24.5 B -
6.8
D + 0.64 A*B + 0
.
374 A*D + 0.18
B*D- 0.0071 A*B
*
D
DESGIN 2
1
.
R = -2240 + 39
.7
H + 82.9 C + 38.
9 A - 1.44 H*
C -
0.668 H*A - 1.
39
5 C*A+ 0.0242 H
*
C*A
DESGIN 2
2
.
R = 725 - 8.
8 D -
12.9 H -
26.8 F
+ 0.174 D*H + 0.
368 D*F + 0.5
05
H*F- 0.0
070 D*H
*
F
DESGIN 2
3
.
R = 907 - 11
.2 E
- 28.8 F
- 15.8
H
+ 0.40 E*F + 0.2
13 E*H + 0.53 F*
H- 0.007
4 E*F*H
DESGIN 2
4
.
R = 643 - 8.
8 F -
20.8 I - 31.
0 C +
0.355 F*I + 0.6
2
6
F*C + 1.092 I*
C- 0.023
0 F*I*C
DESGIN 2
5
.
R = -1575 + 60
I
+ 24.9 D + 24.6
E - 0.91 I*D
- 0.9
1
I*E - 0.372
D*E + 0.0137 I*D*E
DESGIN 2
6
.
R = 991 - 11
.4 D
- 16.3 C
- 47 I +
0.205 D*C + 0.6
1
D*I + 0.81 C*I
-
0.0106 D*C*I
DESGIN 2
7
.
R = 2012 - 5
7
.4
F - 34.1
H - 5
7
.9
C + 1.007 F*
H + 1.68 F*C + 1.0
1
3
H*C - 0.02
96 F*
H*C
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