TELKOM
NIKA
, Vol.11, No
.11, Novemb
er 201
3, pp. 6928
~6
934
e-ISSN: 2087
-278X
6928
Re
cei
v
ed Ma
y 28, 201
3; Revi
sed
Jul
y
2
9
, 2013; Acce
pted Augu
st 9, 2013
Electricity Consumption Prediction based on
SVR with
Ant Colony Optimization
Haijiang Wang*, Shanlin Yang
Schoo
l of Man
agem
ent of He
fei Univ
ersit
y
o
f
T
e
chnolo
g
y
,
Anhu
i Hefei
23
000
9
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: ton
y
s
un8
00
@sina.c
o
m
A
b
st
r
a
ct
Accurate forec
a
sting of el
ectric loa
d
has a
l
w
a
ys
bee
n the
most i
m
p
o
rtant
i
ssues in the
electricit
y
ind
u
stry, particularly for dev
e
l
opi
ng co
untrie
s
. Due to
the various infl
ue
nces, electric
loa
d
forecastin
g
revea
l
s hig
h
ly
non
lin
ear ch
aracteristics. This paper
cre
a
te
s a system for pow
er load f
o
recasti
ng usi
n
g
supp
ort vector mach
ine a
nd
ant colo
ny opti
m
i
z
at
io
n. T
he meth
od of col
ony opti
m
i
z
a
t
io
n is employ
ed
to
process l
a
rge
amou
nt of data and
el
i
m
i
nat
e. T
he SVR mode
l w
i
th ant
colo
ny opti
m
i
z
ation is pr
op
o
s
e
d
accord
ing to t
he ch
aracterist
ics of the no
nl
ine
a
r
el
ectricity consu
m
pti
on
dat
a. T
hen AC
O-SVR mo
del
i
s
app
lie
d to
the
electricity
cons
umptio
n
pred
ic
tion
of
Ji
angs
u
prov
ince.
T
h
e
resu
lt sh
ow
s better th
an t
h
e
ANNs metho
d
and i
m
proves t
he accur
a
cy of the pred
ictio
n
.
Ke
y
w
ords
: su
pport vector re
gressi
on (SVR)
,
ant colony o
p
timi
z
a
tio
n
(ACO
)
Copy
right
©
2013 Un
ive
r
sita
s Ah
mad
Dah
l
an
. All rig
h
t
s r
ese
rved
.
1. Introduc
tion
A
ccu
rat
e
ele
c
t
r
i
c
loa
d
f
o
rec
a
st
in
g
ca
n
provide th
ose
expo
rt
oriente
d
e
c
o
nomie
s
advantag
es t
h
rou
gh
savin
g
and effici
en
tly distri
butin
g limited ene
rgy re
sou
r
ce
s. For in
accu
rate
electri
c
lo
ad f
o
re
ca
sting, it
may increa
se
operati
ng
co
sts. Fo
r exam
ple, over
esti
mation of futu
re
electri
c
loa
d
results in un
necessa
ry sp
inning
reserv
e, waste
s
lim
ited
energy reso
urce
s, even
lead
s to di
st
ribution
ineffi
cien
cy, and,
furthe
rm
o
r
e,
is n
o
t a
c
ce
pted by Inte
rnational
ene
rg
y
netwo
rks owi
ng
to exce
ss sup
p
ly.
In
co
ntra
st,
un
der
estim
a
tio
n
of lo
ad
ca
use
s
fail
ure
in
providin
g suff
icient re
se
rve
and implie
s
high cost
s in
the peaki
n
g
unit, which
discou
rag
e
a
n
y
eco
nomi
c
an
d indu
strial d
e
velopme
n
ts.
Thus, the
a
c
curacy of futu
re ele
c
tri
c
de
mand forecasting
have receive
d
growi
ng
attention,
p
a
rticularly in
the
area
s
of el
e
c
tricity load
pl
annin
g
, en
ergy
expenditu
re/cost economy
and secure o
peratio
n fi
eld
s
, in regio
nal
and natio
nal
system
s.
With the
hi
gher dem
an
d for the
q
uality of wa
ter an
d the
accele
ratio
n
of the
indu
striali
z
ati
on,
the nee
d and co
ns
ump
t
ion of el
ect
r
i
c
ity are b
e
co
ming
wide
r. I
n
o
r
de
r to
m
e
e
t
the massive
requi
rem
ent
of indust
r
y, and to ma
ke the econo
my develop
smo
o
thly, it is very
importa
nt to
use
and
pro
g
ram
ele
c
tri
c
i
t
y powe
r
. As a re
sult,
we
need
to p
r
e
d
ict the
ele
c
tric
quantity, and then figure out the appoi
ntment of pro
ductio
n
plan,
thus bring o
u
t the econo
mic
and soci
al be
nefits.
Suppo
rt Vect
or Ma
chi
ne, rende
red
by Vapni
k in 1
995
[1], can
solv
e the p
heno
mena
of
'exce
ss l
earn
i
ng' with th
e prin
ciple
of minimize
the
stru
cture ri
sk. It has g
r
e
a
t gene
rali
za
tion
capability. Applying the SVR in
regressi
on analysi
s
,
we
get Support vector
regression. Since
the day of its birth, Expert
s
have
don
e
lots of wo
rk t
o
apply it int
o
many field
s
and m
odify the
model. Fo
r in
stan
ce, in p
a
per [2], the a
u
thor
use
im
mune al
go
rith
m to optimize
the pa
ramet
e
rs
of SVR model to predic
t
the us
e of elec
t
r
ic
it
y in Taiwan. In paper [6] the author blend the rough
set theo
ry a
nd the
red
u
c
tion of p
r
o
perty into
L
S
-SVR, hen
ce improving
the accu
ra
cy
of
predi
ction; P
aper [3] use
Ant Colo
ny O
p
timizati
on
to
optimize trai
ned d
a
ta an
d
spe
ed u
p
S
V
R
.
While p
ape
r [7] gets sati
sfactory results by m
odeling
poro
u
s
NiTi a
lloy with SVR. Also, the paper
[8] gets gre
a
t results by ap
plying the LS-SVR
into pre
d
iction of fina
ncial time seri
es.
In this
pape
r, we
use the
co
nsumption
of ele
c
tri
c
ity and
ma
cro
-
eco
nomy infl
uen
cing
data from 20
04 to 2009 i
n
Jian
gsu Province. By
impleme
n
ting
the ant col
ony algorith
m
to
optimize
the
para
m
eters
o
f
SVR, we
co
nstru
c
t A
C
O-
SVR. The
re
sults
sho
w
that
this m
odel,
with
highe
r accu
ra
cy of predi
ction, is su
peri
o
r
to BP-neu
ra
l network bot
h in fitting and error.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
e-ISSN:
2087
-278X
Electri
c
ity Co
nsum
ption Predictio
n ba
se
d on SVR wit
h
Ant Colon
y
Optim
i
zation (Haiji
ang
Wa
ng)
6929
2. Principle
of SVR
As
s
u
me that:
()
(
)
f
xw
x
b
(1)
()
x
is n
o
n
-
linea
r tran
sformati
on
，
which
co
nvert the
dat
aset
x
into
hi
gh di
men
s
io
n
cha
r
a
c
t
e
ri
st
ic
s sp
ac
e
F
，
w
is called weight vector
，
b
is classificatio
n
thre
shol
d. We
can se
e
()
f
x
is a line
a
r fu
nction of
()
x
。
Un
der the
prin
ci
ple of minimu
m st
ru
ct
ur
e ri
sk,
t
he d
e
si
re
d
()
f
x
sho
u
ld s
a
t
i
sf
y
:
2
1
1
()
(
,
(
)
)
2
n
ii
i
C
R
fw
L
y
f
x
N
(2)
In which
，
C
is a
positive con
s
tant. It is a comp
romi
se f
a
ctor i
n
sm
o
o
th and expe
rien
ce
error, whi
c
h i
s
also calle
d
penalty factor.
(,
(
)
)
ii
Ly
f
x
is loss function. Usu
a
ll
y, we let the
loss
function b
e
the
non-se
nsiti
v
e loss fun
c
ti
on, whi
c
h me
ans for
1,
2
,
,
in
，
0,
(
)
(,
(
)
)
(
,
(
)
)
()
,
ii
ii
ii
ii
yf
x
Ly
f
x
L
y
f
x
yf
x
ot
he
r
s
(3)
Thus, the
ab
ove reg
r
e
s
si
on solving p
r
oble
m
be
co
mes the
opti
m
ization
pro
b
lem a
s
follows
:
2
**
1
1
mi
n
(
,
,
)
(
)
2
n
ii
i
i
i
Rw
w
C
(4)
*
*
()
..
(
)
,0
,
1
,
2
,
,
ii
i
ii
i
ii
yf
x
st
f
x
y
in
In orde
r to sol
v
e (4), we d
e
fine Lag
ran
ge
function:
2
**
1
*
11
*
11
1
(,
,
,
,
,
,
,
)
(
)
2
((
)
)
(
(
)
)
n
ii
i
i
i
i
i
i
i
nn
ii
i
i
i
i
i
i
ii
nn
ii
ii
ii
Lw
b
w
C
yw
x
b
w
x
b
y
(5)
For
partial
de
rivative of
*
(
,
,
,
,,,,
)
ii
i
i
i
i
Lw
b
variabl
e
w
，
b
，
i
，
*
i
，
by letting th
e
result be z
e
ro, we get:
11
1
(
)
()
(
)
()
0
nn
n
ii
i
i
i
i
i
ii
i
L
wx
x
w
x
w
(6)
11
0
nn
ii
ii
L
b
(7)
0
ii
i
L
C
(8)
*
0
ii
i
L
C
(9)
Evaluation Warning : The document was created with Spire.PDF for Python.
e-ISSN: 2
087-278X
TELKOM
NIKA
Vol. 11, No
. 11, Novemb
er 201
3: 692
8 – 6934
6930
Thro
ugh ta
kin
g
(6)~(9) to (5
)
，
while at the s
a
me time
ass
u
ming that k
e
rnel func
tion
(,
)
(
)
(
)
ij
i
j
K
xx
x
x
，
and
cha
ngi
ng theo
ptimization
pro
b
le
m into its o
w
n a
n
tithesi
s
probl
em, we
have:
11
1
1
1
ma
x
(
)
(
)
(
)
(
)
(
,
)
2
nn
n
n
ii
i
i
i
i
i
j
j
i
j
ii
i
j
yK
x
x
11
0
..
,
[
0,
],
1
,
2,
,
nn
ii
ii
ii
st
Ci
n
(10)
To solve qu
a
d
ratic p
r
o
g
ra
mming (1
0)
，
11
()
(
)
(
)
()
(
)
(
,
)
nn
ii
i
i
i
i
ii
f
x
x
xb
K
x
xb
(11)
In which,
1
()
(
)
n
ii
i
i
wx
(12)
Due
to kernel
functio
n
[1]
of sati
sfying
Mercer, thi
s
mean
s
co
rre
spondi
ng to
a
grou
p of
dot p
r
odu
ct i
n
hig
h
dim
e
n
s
ion
spa
c
e.
What
we
hav
e to
kno
w
is the
spe
c
ific fu
nction
that m
eets
this co
ndition.
Then we ca
n get
the reg
r
e
ssi
on
fun
c
tio
n
()
f
x
even thou
gh we h
a
ve n
o
idea
of spe
c
ific
formulatio
n of
()
x
. Here
we let the kernel fun
c
tion be radia
l
basi
s
functio
n
,
2
2
(,
)
e
x
p
(
)
ii
Kx
x
x
x
(13)
3. ACO
for F
eatur
e Selec
t
ion
The a
n
t col
o
ny optimization alg
o
rithm
(ACO
)
p
r
ovid
es a
n
alte
rna
t
ive feature
selectio
n
tool inspi
r
ed
by the behavior of ant
s in finding path
s
from the colo
ny to food. Real ants exhi
bit
strong ability to find the
shortest
routes f
r
om
the
colony to food usin
g a
way of depositing
pheromo
ne
a
s
they
travel.
ACO
mimi
c t
h
is
ant
see
k
i
ng foo
d
p
hen
omeno
n to
yield the
sho
r
test
path (whi
ch
mean
s the sy
stem of interests h
a
s
co
n
v
erged to a
single solution
).Differe
nt eq
ually
sho
r
test
path
s
can
exi
s
t. An ACO
al
g
o
rithm
ca
n
b
e
ge
ne
rally
applie
d to
a
n
y co
mbin
atorial
probl
em a
s
far as it is po
ssi
b
le to define:
Firstly, the problem
can b
e
described i
n
a set of no
des a
nd ed
g
e
s bet
wee
n
node
s to
form a graph.
So the probl
em can b
e
se
en ea
s
ily to find the main p
r
oble
m
and o
v
erco
me it.
Secondly, heuristi
c desirability
of paths: it is a suitable heu
risti
c
m
easure
whi
c
h can find
better path
s
from on
e no
d
e
to every other
con
n
e
c
te
d node, a
nd i
t
can be d
e
scrib
ed in a g
r
aph
details.
Thirdly, con
s
tructio
n
of
sol
u
tions: a
fea
s
ib
le and co
mplete soluti
on
of
the
fo
rmulated
inter-cell l
a
yout probl
em i
s
con
s
id
ere
d
a
s
a p
e
rm
ut
ation of man
u
fa
cturin
g cells.
Each p
a
rt of t
h
is
solutio
n
is termed
state. In
the o
p
timum
pro
c
e
s
s,
each
ant initiall
y assi
gns a cell to location 1
then assig
n
s
anothe
r cell t
o
locatio
n
2 a
nd so o
n
till a complete
sol
u
tion is obtai
ned.
Fourthly, ph
e
r
omo
ne u
pda
ting rul
e
: first
l
y,
it is the a
r
ea ph
eromon
e upd
ating
ru
le, the
effect is to make the de
si
rability of edges chan
ge dynamically in orde
r to shuff
l
e the tour. The
node
s i
n
o
n
e
ants tou
r
will
be
ch
osen
with a lo
we
r
probability in
b
u
ilding
othe
r
ants to
urs. A
s
a
con
s
e
que
nce
,
ants will
favor th
e expl
oration of
edg
e
s
n
o
t yet visit
ed a
nd
preve
n
t co
nverging
to
a comm
on pa
th.
Next, go to
gl
obal u
pdatin
g
rule, thi
s
p
r
o
c
e
s
s
is pe
rformed
afte
r
all ants have co
mpleted
their tou
r
s.
T
herefo
r
e, o
n
l
y
the glob
ally best
ant
that
found th
e b
e
st
solution
u
p
to the
cu
rrent
iteration of the algorith
m
is permitted to depo
sit phe
ro
mone.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
e-ISSN:
2087
-278X
Electri
c
ity Co
nsum
ption Predictio
n ba
se
d on SVR wit
h
Ant Colon
y
Optim
i
zation (Haiji
ang
Wa
ng)
6931
Fifthly, probabilisti
c tran
sition rule: the rule
dete
r
mine
s the
prob
ability of an ant
traversing
fro
m
on
e
n
ode
in the graph
to the
next.
The heu
risti
c
desirability of traversal a
n
d
edge p
herom
one level
s
is
combi
ned to form t
he so-ca
lled pro
babili
stic tran
sition rule.
Figure 1. ACO-SVR Fo
re
casting Process
4. Modeling and Predicti
on
4.1. Data
Ch
oosing and
Pre-dispo
s
in
g
In this p
ape
r, we
choo
se the influ
e
n
cin
g
facto
r
s data a
nd t
he ove
r
all e
l
ectri
c
ity
con
s
um
ption
of Jiang
su P
r
ovince from
Jan
uary 2
0
0
4
to Octob
e
r 2009. And
we
con
s
ide
r
the
data of Janu
ary 2004 to July 2009 to be the trai
ned
sets, thu
s
co
nstru
c
t ACO
-
SVR model. We
think the data
from Augu
st to Octobe
r 20
09 are the te
st sets.
Mean
while, in
orde
r to elimi
nate of dime
n
s
i
on i
n
fluen
ce
, we ap
ply the stan
dard 0-1, that
is:
*
mi
n
ma
x
m
i
n
xx
x
x
x
(14)
So the ne
w d
a
ta set
s
a
r
e a
ll in
[0
,
1
]
，
and th
e
data sets al
so eliminate th
e diversity un
its,
whi
c
h interfe
r
e the re
sults.
As the
er
ro
r
of non
-sen
sitive loss fu
ncti
on i
s
too
sm
all, even th
ou
gh it
can
en
h
ance
the accuracy
of trained model, it red
u
ce
s ge
neral
ization ability
.
On the con
t
rary, if
is too
bigge
r, the co
nstru
c
ted
mo
del ha
rdly ca
n depi
ct
the
chang
e of ele
c
tricity quantity. After repeat
ed
experim
ent, we d
e
fine
to 0.01. It can bot
h gua
rante
e
the fitting accura
cy and th
e
gene
rali
zatio
n
ability of model.
4.2. Result o
f
Regr
essio
n
Forecas
ting
of the Mod
e
l
Due to
ele
c
tri
c
ity con
s
u
m
p
t
ion tren
ds fl
uctuate
by inf
l
uen
cing fa
ct
ors.
Thu
s
we
cho
o
se
the influen
ci
ng facto
r
s in
clud
e Averag
e Month
Te
mperature
(A
MT), Social
Retail Sale
s of
Con
s
um
er G
ood
s
(SRS
CC), In
du
st
ry I
n
crea
sing
V
a
lue
(IIV),
Co
nsum
er
Pri
c
e
Index (CPI) and
Gro
s
s Value
of Export-Imp
o
rt (GVEI
). Hence, we
sele
ct five infl
uen
cing fa
ctors a
s
input va
riab
le.
Con
s
id
erin
g there
ha
s mul
t
icolline
a
rity betwe
en t
he
influen
cing fa
ctors. Thi
s
p
aper
use LS
to
extract th
e m
a
in
comp
one
nt variabl
e. Fi
nally, we
can
get the
mai
n
influen
cin
g
i
n
clu
de AMT,
IIV
and GVEI. As the erro
r
of
non-se
nsitive
loss fun
c
tion
is t
oo sm
all, even though it can e
nha
nce
the accuracy
of trained mo
del, and it ca
n redu
ce
g
e
n
e
rali
zation a
b
ility. On the contra
ry, if
is
too bigg
er, th
e co
nstructe
d
model h
a
rdly
can
depi
ct
th
e ch
ang
e of electri
c
ity co
n
s
umptio
n. After
repe
ated exp
e
rime
nt, we
define
to 0.01. It can both guarantee t
he fitting accura
cy and th
e
gene
rali
zatio
n
ability of m
odel.
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4.3. Experiment Study
In this su
b-
section,
we co
nstru
c
t an
d a
nalyze the
experim
ent of the propo
se
d model in
this pap
er u
s
ing matlab to
ols
，
the p
r
e
d
ictive re
sult o
f
regre
s
sion f
o
re
ca
sting u
s
ing ACO
-
SVR
forecastin
g m
odel is
sho
w
e
d
in Figure 2.
Figure 2. The
Compa
r
i
s
on
of Fore
ca
stin
g Re
sult
Beside
s, we
give out the reg
r
e
s
sion
fitting result
s an
d Rel
a
tive Erro
rs
(RE) from
Novemb
er 2
0
07 to July 20
09, the pre
d
i
c
tion result
s
and rel
a
tive errors from A
ugu
st to Octo
ber
2009. It is sh
owe
d
in the Table 4.
Table 1. The
Fitting Regre
ssi
on an
d Rel
a
tive Errors
Month
Actual
Value
The fitted
values Value
Relative
Error
2007.11
247.42
247.6876
0.08%
2007.12
265.77
251.3041
-5.82%
2008.01
262.59
237.8942
-9.41%
2008.02
202.29
224.3234
7.91%
2008.03
266.58
264.6345
-0.73%
2008.04
256.19
258.1616
0.77%
2008.05
265.68
267.5671
0.71%
2008.06
260.4
269.3890
3.42%
2008.07
314.72
299.1235
-4.97%
2008.08
297.54
277.5878
-6.61%
2008.09
265.34
263.3123
-0.73%
2008.10
245.21
254.6784
3.93%
2008.11
233.35
235.1435
0.81%
2008.12
250.74
241.1235
-3.59%
2009.01
214.96
230.4677
7.01%
2009.02
221.54
223.1236
0.85%
2009.03
265.87
260.7899
-1.84%
2009.04
252.39
251.1234
-0.36%
2009.05
263.95
270.1237
2.37%
2009.06
287.78
285.1279
-0.68%
2009.07
319.54
317.6724
-0.58%
Whe
r
e the
relative error
is
ˆ
()
ii
i
RE
y
y
y
，
i
y
is the real value
，
ˆ
i
y
is the predi
cted
value.
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TELKOM
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e-ISSN:
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Electri
c
ity Co
nsum
ption Predictio
n ba
se
d on SVR wit
h
Ant Colon
y
Optim
i
zation (Haiji
ang
Wa
ng)
6933
From the re
sult of Table
1, ACO-SVR lead
s
to a s
a
tis
f
ac
tory res
u
lt of elec
tric
ity
con
s
um
ption
from Aug
u
st t
o
Octo
be
r 20
09, and th
e
relative errors confin
es i
n
1
0
%. More
ove
r
,
the relative errors
of las
t
tw
o months a
r
e
confin
es to 5
%
.
In ord
e
r to
a
s
sess th
e rationality of the
model
is
pro
posed in
this pape
r.
We
compa
r
e
the ACO-SVR model with t
he PSO-SV
R
mod
e
l an
d
LS-SVR
，
the
analysi
s
result is sho
w
ed
as
Figure 3.
Figure 3. Rel
a
tive Error
Compa
r
ison wi
th other Fo
re
ca
sting Meth
od (
0.
01
,
3
K
)
Whe
r
e:
2
1
1
ˆ
()
n
ii
i
M
SE
y
y
n
；
2
2
1
22
11
ˆˆ
((
)
(
)
)
ˆ
ˆ
()
(
)
n
ii
i
nn
ii
ii
yy
y
y
R
y
yy
y
，
i
y
is the actual
value
，
ˆ
i
y
is the predi
ctive value
，
1
1
n
i
i
yy
n
，
1
1
ˆˆ
n
i
i
yy
n
.
M
SE
measures th
e deviation o
f
predi
ctive
value fro
m
the actu
al valu
e. The
M
SE
is
smalle
r sho
w
s that deviati
on deg
re
e is
smalle
r,
and
the pre
d
ictive
pre
c
isi
on of
the fore
ca
sting
model is m
o
re accurate.
5. Conclusio
n
The re
sea
r
ch
of this paper is base
d
on SVR
to const
r
uct mo
del a
nd pre
d
ict. We solve
the proble
m
s of
pickin
g
paramete
r
s.
We
u
s
e
th
e pa
rtial
swarm
optimiza
t
ion to find
out
approximate
optimal valu
e
and
at the
same time
, u
s
e the
cro
s
s v
a
lidation to
l
o
we
r p
r
edi
ct
e
d
errors and
construct ACO-SVR
mo
de
l. By doing this, on on
e hand, SVR can solve the
non-
linear, big vol
a
tility proble
m
. On the other ha
nd,
the
param
eters
cho
o
si
ng pro
b
lems
can al
so be
solved by pa
rtial swa
r
m op
timization. From the final
result, we
can
dra
w
a co
ncl
u
sio
n
confid
e
n
tly
that the mode
l we build, wit
h
highe
r accu
racy, is
supe
rior to BP-neu
ral network
Ackn
o
w
l
e
dg
ements
This
work wa
s pa
rtially su
pporte
d by the Nation
al Natural Sci
e
n
c
e Foun
dation
of China
Grant
No. 7
1101
041
an
d No.710
710
45, National
863
Proj
ect
Grant
No.
2011AA0
5A1
16,
Found
ation
o
f
High
er S
c
h
ool O
u
tstan
d
i
ng Tal
ents No. 201
2SQRL009
and
Na
tional Innovat
ive
Experiment P
r
og
ram No. 11103
5954. T
han
ks for the
help.
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ces
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：
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ger. 19
95.
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