Indonesian
J
our
nal
of
Electrical
Engineering
and
Computer
Science
V
ol.
20,
No.
2,
No
v
ember
2020,
pp.
1000
1006
ISSN:
2502-4752,
DOI:
10.11591/ijeecs.v20i2.pp1000-1006
r
1000
F
or
ecasting
f
or
smart
ener
gy:
An
accurate
and
efficient
negati
v
e
binomial
additi
v
e
model
Y
ousef-A
wwad
Daraghmi
1
,
Eman
TT
aser
Daraghmi
2
,
Motaz
Daadoo
3
,
Samer
Alsaadi
4
1,3,4
Colle
ge
of
Engineering
and
T
echnology
,
P
alestine
T
echnical
Uni
v
ersity
-
Kadoorie,
P
alestine
2
Departent
of
Applied
Computing,
P
alestine
T
echnical
Uni
v
ersity
-
Kadoorie,
P
alestine
Article
Inf
o
Article
history:
Recei
v
ed
Feb
15,
2020
Re
vised
Apr
17,
2020
Accepted
Apr
31,
2020
K
eyw
ords:
Ne
g
ati
v
e
binomial
additi
v
e
models
Nonlinearity
Ov
erdispersion
Seasonal
patterns
Short-term
load
forecasting
Smart
ener
gy
T
emporal
autocorrelation
ABSTRA
CT
Smart
ener
gy
requires
accurate
and
ef
ficient
short-term
electric
load
forecasting
to
enable
ef
ficient
ener
gy
management
and
acti
v
e
real-time
po
wer
control.
F
orecasting
accurac
y
is
influenced
by
the
characteristics
of
electrical
load
particularly
o
v
erdisper
-
sion,
nonlinearity
,
autocorrelation
and
seasonal
patterns.
Although
se
v
eral
fundamen-
tal
forecasting
methods
ha
v
e
been
proposed,
accura
te
and
ef
ficient
forecasting
meth-
ods
that
can
consider
all
electric
load
characteris
tics
are
still
needed.
Therefore,
we
propose
a
no
v
el
model
for
short-term
electric
load
forecasting.
The
model
adopts
the
ne
g
ati
v
e
binomial
additi
v
e
models
(NB
AM)
for
handling
o
v
erdispersion
and
capturing
the
nonlinearity
of
electric
load.
T
o
address
the
seasonality
,
the
daily
load
pattern
is
classified
into
high,
moderate,
and
lo
w
seasons,
and
the
autocorrelation
of
load
is
mod-
eled
separa
tely
in
each
season.
W
e
also
consider
the
ef
ficienc
y
of
forecasting
since
the
NB
AM
captures
the
beha
vior
of
predictors
by
smooth
functions
that
are
estimated
via
a
scoring
algorithm
which
has
lo
w
computational
demand.
The
proposed
NB
AM
is
applied
t
o
real-w
orld
data
set
from
Jericho
city
,
and
its
accurac
y
and
ef
ficienc
y
outper
-
form
those
of
the
other
models
used
in
this
conte
xt.
Copyright
c
2020
Insitute
of
Advanced
Engineeering
and
Science
.
All
rights
r
eserved.
Corresponding
A
uthor:
Y
ousef-A
ww
ad
Daraghmi,
Colle
ge
of
Engineering
and
T
echnology
,
P
alestine
T
echnical
Uni
v
ersity-Kadoorie,
P
alestine.
Email:
y
.a
ww
ad@ptuk.edu.ps
1.
INTR
ODUCTION
Smart
ener
gy
requires
short-term
forecasting
for
predicting
the
future
load
se
v
eral
hours
ahead
and
for
e
v
aluating
control
strate
gies
before
putting
them
in
use
[1].
Thus,
accurate
and
ef
ficient
f
o
r
ecasting
is
required
to
enable
ef
fecti
v
e
and
timely
decision
making
process.
The
accurac
y
of
the
load
forecasting
models
is
af
fected
by
electric
load
characteristics
such
as
nonlinearity
[2-5]
high
fluctuations
[5,
6],
autocorrelation
and
seasonal
patterns
[5,
7,
8].
The
high
fluctuation
in
electric
load
causes
o
v
erdispersi
o
n
e
xpressed
by
a
lar
ge
v
ariance
v
alue
that
is
clearly
lar
ger
than
the
mean
[9].
Research
states
that
electric
load
fluctuation
depends
on
the
life
style,
day
time
and
location
[10,
11].
Ov
erdispersion
reduces
the
accurac
y
if
it
is
not
handled
properly
,
particularly
in
the
short-term
forecasting,
because
forecasting
methods
are
sensiti
v
e
to
the
fluctuation
[12].
In
the
meantime,
the
ef
ficienc
y
of
the
forecasting
methods
is
af
fected
by
the
data
size,
and
model’
s
time
comple
xity
that
deter
-
mines
the
time
needed
for
an
algorithm
to
produce
accurate
results
[9].
Although
se
v
eral
short
term
forecasting
models
ha
v
e
been
proposed,
o
v
erdispersion
has
not
been
appropriately
handled
i
n
these
models.
The
statistical
forecasting
models
such
as
re
gression
based
models
and
smoothing
based
models
assume
that
the
v
ariance
is
equal
to
the
mean
[4,
7,
13],
or
the
y
utilize
distrib
utions
that
ignore
the
high
v
ariations
[14,
15].
In
other
models,
the
high
v
ariance
in
time
series
is
treated
to
become
homogeneous
and
stationary
by
Box-Cox
and
dif
ferentiating
transformations
which
increase
the
computational
demand
[7].
In
the
artificial
int
elligence
based
models
(e.g.
[11,
16,
17]),
considering
the
high
v
ariation
costs
J
ournal
homepage:
http://ijeecs.iaescor
e
.com
Evaluation Warning : The document was created with Spire.PDF for Python.
Indonesian
J
Elec
Eng
&
Comp
Sci
ISSN:
2502-4752
r
1001
much
computational
time
[18].
Therefore,
this
paper
focuses
on
the
problem
of
o
v
erdispersion,
nonlinearity
and
temporal
autocorrelation
to
increase
the
accurac
y
of
forecasting
models.
Simultaneously
,
the
paper
aims
to
reduce
the
computational
demand
to
increase
the
ef
ficienc
y
of
the
forecasting
models.
This
paper
proposes
a
temporal
Ne
g
ati
v
e
Binomial
Additi
v
e
Model
(NB
AM)
to
handle
the
o
v
erdis-
persion
precisely
.
The
temporal
NB
AM
is
nonparametric
and
capture
nonlinearity
via
smoothing
functions.
T
o
address
the
autocorrelation
and
seasonality
,
the
dai
ly
load
pattern
is
classified
into
lo
w
,
moderate
and
high
seasons
in
which
the
autocorrelation
can
be
modeled
separately
.
The
proposed
model
is
ef
ficient
because
the
method
utilizes
a
lo
w-comple
xity
optimization
technique
to
estimate
the
smoothing
function.
The
proposed
model
is
tested
on
r
eal-w
orld
data
set
collected
from
Jericho
city
-
P
alestine,
and
its
results
are
compared
with
other
classical
load
forecasting
models
including
ARIMA,
ARMA,
Holt-W
inters
(HW)
and
ne
g
ati
v
e
binomial
linear
model.
The
results
sho
w
that
the
proposed
temporal
NB
AM
is
more
accurate
than
other
models
because
its
mean
absolute
percentage
error
(MAPE)
is
lo
wer
than
the
others.
Also,
the
NB
AM
is
more
ef
ficient
be-
cause
the
computational
time
needed
for
training
and
forecasting
is
lo
wer
than
the
time
of
the
other
models.
The
ne
g
ati
v
e
bi
nomial
based
models
were
successfully
applied
to
forecasting
traf
fic
data
that
is
autocorrelated,
o
v
erdispersed
and
ha
v
e
seasonal
patterns
[19-22].
2.
RESEARCH
METHOD
This
section
proposes
a
method
for
forecasting
electrical
load
which
is
nonlinear
,
o
v
erdispersed,
and
temporally
autocorrelated.
The
proposed
method
adopts
the
Generalized
Additi
v
e
Models
for
handling
non-
linearity
and
Ne
g
ati
v
e
Binomial
for
handling
o
v
erdispersion,
and
then
de
v
elops
a
temporal
model
for
handling
the
temporal
autocorrelation.
2.1.
Generalized
additi
v
e
models
(GAMs)
The
GAMs
focus
on
capturing
the
nonlinearity
by
permitting
the
correlating
v
ariables
to
ha
v
e
non-
linear
relationship
[23].
In
GAMs,
a
response
v
ariable
Y
has
a
mean
v
alue
(
)
that
is
assumed
dependent
on
predictors
X
via
a
function
which
is
nonlinear
.
The
importance
of
the
GAMs
is
generalizing
the
con
v
entional
additi
v
e
models
so
that
the
response
v
ariable
can
fit
into
an
y
distrib
uti
on
from
the
e
xponential
f
amily
[23,
24].
Consequently
,
an
y
GAM
allo
ws
for
more
fle
xibility
than
parametric-based
models.
The
mean
of
Y
,
which
is
=
E
(
Y
j
X
=
x
)
can
be
link
ed
to
some
predictors
by
G
(
)
=
s
0
+
s
(
x
i
)
+
"
i
(1)
where
G
indicates
that
the
correlation
is
controlled
by
a
link
function,
and
s
0
is
the
o
v
erall
mean
or
the
intercept
of
Y
,
x
i
is
the
i
th
records
in
a
data
set,
s
(
x
i
)
is
a
smooth
function
for
the
i
th
record
of
the
predict
or
X
,
"
i
is
the
error
which
is
i
ndependent
of
the
predictors,
and
i
N
I
D
(0
;
2
)
,
and
2
is
the
v
ariance
[23,
24].
The
importance
of
the
smooth
function
is
that
it
can
beha
v
e
as
the
original
data
and
it
can
catch
nonlinearity
.
Smoothers
est
imate
the
smooth
function
by
fitting
the
data
of
a
predictor
through
de
v
eloping
a
continuous
curv
e
that
consists
of
multipl
e
sections
combined
by
knots
[23].
Each
curv
e
contains
a
total
number
of
sections
z
,
and
each
section
can
ha
v
e
an
equation
such
as
the
linear
re
gression
equation
or
the
cubic
polynomial
equation.
Each
equation
contains
a
base
function
and
coef
ficients.
Th
e
base
function
is
used
to
generate
the
model
matrix
X
n
z
,
and
the
coef
ficients
form
the
parameter
matrix
M
z
1
.
Details
on
estimating
the
base
functions
and
the
model
matrix
X
are
in
[24].
The
smoot
h
function
has
a
de
gree
of
smoothness
parameter
that
decides
the
number
of
sections
(
z
)
.
is
estimated
in
cross
v
alidation
process
such
that
the
mean
square
error
is
minimized
[23].
In
GAMs,
a
local
scori
ng
algorithm
is
used
to
computationally
esti
mate
the
smooth
functions
by
maximizes
a
lik
elihood
function
as
stated
in
[23,
24].
The
scoring
algorithm
is
chosen
carefully
so
that
the
computational
time
is
v
ery
lo
w
.
Also,
the
generalized
cross-sectional
v
alidation
is
used
for
a
v
oiding
o
v
erfitting
of
data
[24].
2.2.
Negati
v
e
binomial
additi
v
e
model
(NB
AM)
The
NB
AM
is
a
special
case
of
the
GAMs
to
o
v
ercome
its
main
limitation
which
is
only
modeling
data
of
e
xponential
distrib
ution
[25].
Besides
ha
ving
nonlinear
dependenc
y
,
the
response
v
ariable
and
the
predictors
may
follo
w
other
distrib
utions.
F
or
e
xample,
if
o
v
erdispersion
is
found
in
the
data,
i.e.
the
v
ariance
2
>
,
the
best
distrib
ution
for
describing
that
data
will
be
the
Ne
g
ati
v
e
Binomial
[12].
In
f
act,
a
NB
AM
e
xtends
the
GAM
to
treat
the
o
v
erdispersion
by
allo
wing
Y
to
ha
v
e
Ne
g
ati
v
e
Binomial
distrib
ution
[25].
The
Ne
g
ati
v
e
binomial
distrib
ution
can
accounts
for
the
high
fluctuations
in
the
data
by
permitting
the
v
ariance
2
of
Y
to
be
F
or
ecasting
for
smart
ener
gy:
An
accur
ate
and
ef
ficient
ne
gative
...
(Y
ousef-A
wwad
Dar
a
ghmi)
Evaluation Warning : The document was created with Spire.PDF for Python.
1002
r
ISSN:
2502-4752
greater
than
the
mean
as
2
=
+
'
2
where
'
is
the
o
v
erdispersion
parameter
[12].
The
ne
g
ati
v
e
binomial
model
for
Y
gi
v
en
predictors
X
is
additi
v
ely
fit
to
data
by
choosing
a
natural
log
link
function.
The
NB
AM
is
written
as
log
E
(
)
=
s
0
+
s
(
x
i
)
+
"
i
(2)
where
a
local
scoring
algorithm
is
used
to
train
the
smooth
function
iterati
v
ely
by
estimating
'
and
that
maximize
a
log-lik
elihood
function
e
xplained
in
[25].
2.3.
De
v
elopment
of
temporal
NB
AM
The
NB
AM
can
be
applied
to
electric
load
by
considering
the
temporal
autocorrelation
of
the
load.
First,
the
electric
load
daily
pattern
is
classified
into
three
seasons,
lo
w
,
moderate
and
high
seasons.
In
the
data
set
sho
wn
in
Figure
1,
the
seasons
are:
(1)
a
lo
w
load
season
from
02:00AM
to
10:00AM
(8
hours)
and
e
xists
in
the
early
morning
when
the
load
is
less
than
the
daily
mean;
(2)
a
high
load
season
from
06:00PM
to
01:00AM
when
the
load
is
bigger
than
the
daily
mean
(8
hours);
(3)
a
moderate
load
season
between
01:00AM-02:00AM
and
10:00AM-06:00PM(9
hours)
when
the
load
is
around
the
mean.
Each
season
will
ha
v
e
its
o
wn
forecasting
model.
The
benefit
of
this
classification
is
allo
wing
training
each
season
indi
vidually
,
remo
ving
the
outliers
and
decreasing
the
v
ariability
as
the
electric
load
is
not
fluctuating
between
the
maximum
load
v
alue
and
the
minimum
v
alue
during
a
single
season.
Second,
the
temporal
correlation
is
modelled
for
each
season.
W
e
let
y
i;t
be
the
response
v
ariable
corresponding
to
the
load
measured
from
station
i
at
time
frame
t
.
The
temporal
autocorrelation
is
considered
by
incorporating
a
one-step
lag
load
of
the
dependent
station
as
a
predictor
,
i.e.
y
i;t
1
.
Thus,
the
proposed
temporal
NB
AM
is
e
xpressed
by
ln
y
i;t
=
i
+
s
i
(
y
i;t
1
)
+
"
t
:
(3)
The
lag
v
alues
y
i;t
1
accounts
for
the
electric
load
persistence,
and
it
re
gularly
updates
the
model
with
an
y
change
of
the
data
trend.
Equation
3
is
for
accommodating
the
smooth
function
to
data
based
on
the
ne
g
ati
v
e
binomial
distrib
ution,
and
for
computing
the
model
matrix
M
and
the
parameter
matrix
P
that
are
used
in
the
forecasting
process.
The
estimation
be
gins
by
selecting
a
dependent
station,
selecting
the
season
based
on
the
time,
select-
ing
the
data
belonging
to
the
same
season
from
historical
data,
and
then
starting
the
estimation
of
the
smooth
function
of
load
for
that
station.
The
R
mg
cv
package
introduced
in
[24]
is
used
for
performing
the
analyses.
This
R
package
contains
all
libraries
needed
for
smooth
function
estimation
and
forecast
results
generation.
F
orecasting
by
GAM
models
requires
a
data
set
(data
for
the
season
of
interest),
a
model
matrix
M
and
a
model
parameter
matrix
P
which
are
computed
in
the
training
stage
[24].
Figure
1.
Single-day
electric
load
and
an
e
xample
of
the
smooth
function
for
the
load
in
Aqabat
Jaber
station
2.4.
Data
set
A
data
set
consisting
of
electrical
current
measured
e
v
ery
hour
from
15
stations
w
as
collected
in
Jericho
city
in
the
period
between
January
to
December
in
2015.
The
total
number
of
records
collected
from
Indonesian
J
Elec
Eng
&
Comp
Sci,
V
ol.
20,
No.
2,
No
v
ember
2020
:
1000
–
1006
Evaluation Warning : The document was created with Spire.PDF for Python.
Indonesian
J
Elec
Eng
&
Comp
Sci
ISSN:
2502-4752
r
1003
each
st
ation
is
4380
records.
Figure
2
illustrates
the
electric
load
pattern
for
17
consequent
days.
Before
the
analyses
start,
the
in
v
alid
records
such
as
missing
v
alues,
ne
g
ati
v
e
v
alues
and
zero
v
alues
in
the
data
set
were
treated.
The
number
of
the
these
records
is
less
than
(2%)
per
day
which
is
v
ery
small
and
does
not
reduce
the
forecasting
accurac
y
.
Figure
2.
The
load
o
v
er
17
days
from
13/No
v/2015
to
29/No
v/2015
in
Aqabat
Jaber
station
The
electric
loads
of
the
selected
st
attions
during
17
days
are
represented
by
time
series.
Figure
2
illustrates
an
e
xample
of
the
load
time
serie
s
during
17
days,
while
Figure
1
illustrates
the
load
time
series
during
a
single
day
.
The
figures
demonstrate
that
the
load
data
ha
v
e
c
yclic
seasonal
patterns
that
are
repeated
e
v
ery
day
.
Also,tThe
electric
load
illustrated
in
Figure
2
and
1
is
temporally
autocorrelated,
that
is,
the
v
alue
of
the
load
at
an
y
moment
depends
on
the
pre
vious
one.
The
electric
load
has
o
v
erdispersion
because
the
v
ariance
of
the
load
at
each
station
is
lar
ger
than
the
mean
as
sho
wn
in
T
able
1.
The
table
sho
ws
the
mean,
the
v
ariance
and
the
dispersion
v
alues
for
three
stations
during
t
he
lo
w
,
moderate
and
high
seasons.
Ov
erdispersion
e
xists
in
the
data
if
the
dispersion
v
alue
which
is
”the
Pearson
statis
tic
(
2
)
di
vided
by
the
de
grees
of
freedom
is
lar
ger
than
one”
[12].
In
the
data
set,
all
loads
are
o
v
erdispersed
as
the
corresponding
dispersion
v
alues
sho
wn
in
T
able
1
are
lar
ger
than
one.
The
aforementioned
characteristics
are
common
among
electrical
netw
orks
loca
lly
and
globally
.
The
o
v
erdispersion
of
the
load
refers
to
the
v
ariations
in
the
consumption
of
electric
ener
gy
within
the
seasonal
daily
patterns.
The
v
ariations
depend
on
the
place
in
the
city
(urban,
industry
,
mark
et),
changing
conditions
of
weather
,
time
of
the
day
,
and
life
style.
T
able
1.
The
statistical
measures
of
four
stations
during
the
four
load
seasons
Area
Aqabat
Jaber
Sea
le
v
el
1
Sea
le
v
el
2
Sea
le
v
el
3
for
high
season
153.0
149.2
87.3
205.9
2
for
high
season
168.1
181.4
127.7
327.5
dispersion
for
high
season
2.4
2.3
2.5
2.8
for
moderate
season
125.7
127.6
68.3
189.3
2
for
moderate
season
143.1
155.3
98.0
242.6
dispersion
for
moderate
season
2.7
2.8
1.9
1.9
for
lo
w
season
101.8
97.8
46.1
151.4
2
for
lo
w
season
117.2
152.6
77.3
197.0
dispersion
for
lo
w
season
1.9
2.5
1.7
2.0
3.
RESUL
T
AND
DISCUSSION
This
section
sho
ws
the
results
of
the
proposed
method
whic
h
is
the
temporal
NB
AM.
The
s
ection
firstly
sho
ws
ho
w
the
method
is
trained,
and
then
sho
ws
its
accurac
y
and
ef
ficienc
y
.
F
or
ecasting
for
smart
ener
gy:
An
accur
ate
and
ef
ficient
ne
gative
...
(Y
ousef-A
wwad
Dar
a
ghmi)
Evaluation Warning : The document was created with Spire.PDF for Python.
1004
r
ISSN:
2502-4752
3.1.
T
raining
of
the
pr
oposed
temporal
NB
AM
The
proposed
NB
AM
is
trained
for
the
four
stations
in
the
data
set,
and
ten-months
data
collected
from
January-2015
to
October
-2015
are
used.
The
proposed
model
is
trained
separately
for
each
load
season
such
that
the
complete
data
set
is
di
vided
to
three
data
sets
including
a
set
for
daily
lo
w
season
of
eight
hours
length,
a
set
for
daily
moderate
season
of
se
v
en
hours
length,
and
a
set
for
daily
high
season
of
nine
hours
length.
Therefore,
each
load
season
will
ha
v
e
a
dif
ferent
forecasting
model.
The
result
of
the
training
process
is
described
in
T
able
2
and
Figure
1.
As
sho
wn
in
T
able
2,
the
three
load
seasons
ha
v
e
significant
load
autocorrelation
because
the
P-
v
alue
is
smaller
than
the
significance
le
v
el.
In
our
analyses,
the
statistical
confidence
interv
al
is
95%
and
the
significance
le
v
el
is
5%,
similar
to
[10].
T
able
2
sho
ws
the
main
statistical
output
of
the
NB
AM
when
Aqabat
Jaber
is
the
response
v
ariable.
The
use
of
the
Ne
g
ati
v
e
Binomial
is
justified
because
the
v
alues
of
'
are
greater
than
zero
as
sho
wn
in
T
able
2.
Also,
the
smooth
function
for
the
data
in
Aqabat
Jaber
station
is
plotted
in
Figure
1.
The
NB
AM
describes
the
real
data
with
tin
y
dif
ferences
which
moti
v
ates
us
to
use
this
model
for
forecasting.
T
able
2.
The
main
outputs
of
the
NB
AMs
for
the
Aqabat
Jaber
station
lo
w
season
Moderate
season
high
season
autocorrelation
P-v
alue
7
10
14
2
10
14
5
10
14
Intercept
(
)
3.45
4.57
2.39
o
v
erdipsersion
'
3.63
2.33
3.18
data
size
n
2432
2128
2736
z
41
38
33
size
of
M
2432
41
2128
38
2736
33
3.2.
F
or
ecasting
accuracy
The
NB
AM
utilizes
the
R
mg
cv
package
mainly
the
pr
edict
function.Tthe
proposed
NB
AM
is
e
v
alu-
ated
during
each
load
season
using
the
models
generated
in
the
training
stage.
The
smooth
functions
obtained
from
the
training
stage
based
on
the
coef
ficients
sho
wn
in
T
able
2
is
used
to
produce
the
Aqabat
Jaber
forecasts
for
multiple
steps
ahead,
ranging
from
one
hour
to
24
hours.
The
models
used
for
comparison
are
trained
as
in
[9].
These
models
are
classical
forecasting
models
and
the
y
are
widely
used
in
in
this
field.
The
models
are:
the
temporal
NBLM
[9],
the
Holt-W
int
ers
(HW)
[26],
Auto
Re
gressi
v
e
Inte
grated
Mo
ving
A
v
erage
(ARIMA)
[14],
and
the
Auto
Re
gressi
v
e
Mo
ving
A
v
erage
(ARMA)
method
as
in
[7].
A
single
season
for
the
HW
,
the
ARMA
and
the
ARIMA
models
is
used
because
the
y
are
c
yclic-based
models
and
need
a
repeated
pattern.
The
Mean
Absolute
Percentage
Error
(MAPE)
is
calculated
to
compare
the
accurac
y
of
the
models
forecasting
results,
similar
to
[3,
10].
T
able
3
sho
ws
the
MAPE
v
alues
of
the
fi
v
e
models
for
the
selected
stations
during
the
three
load
seasons
for
a
ten-hours
horizon.
T
o
sho
w
the
accurac
y
of
the
NB
AM,
the
results
of
the
models
during
the
high
load
season
are
also
presented
in
Figure
3.
T
able
3.
The
MAPE
v
alues
of
dif
ferent
models
for
three
electric
stations
during
the
three
load
seasons
load
MAPE
%
MAPE
%
MAPE
%
season
Method
Aqabat
Jaber
sea
le
v
el
1
seas
le
v
el
2
NB
AM
0.88
1.09
0.83
Lo
w
T
emporal
NBLM
1.51
1.72
1.39
Load
HW
3.17
3.62
3.49
Season
ARMA
2.36
3.12
2.97
ARIMA
6.27
5.09
4.24
NB
AM
2.38
1.97
2.11
Moderate
T
emporal
NBLM
3.57
1.95
2.77
Load
HW
5.24
3.29
4.33
Season
ARMA
4.77
2.83
3.91
ARIMA
6.79
4.65
5.18
NB
AM
3.35
1.61
1.24
High
T
emporal
NBLM
4.62
2.12
2.61
Load
HW
5.87
3.68
4.36
Season
ARMA
5.29
3.63
3.61
ARIMA
7.19
5.95
5.98
Indonesian
J
Elec
Eng
&
Comp
Sci,
V
ol.
20,
No.
2,
No
v
ember
2020
:
1000
–
1006
Evaluation Warning : The document was created with Spire.PDF for Python.
Indonesian
J
Elec
Eng
&
Comp
Sci
ISSN:
2502-4752
r
1005
Figure
3.
The
forecasting
of
load
for
10-hours
horizon
during
the
high
load
season
in
Aqabat
Jaber
station
The
MAPE
v
alues
of
the
NB
AM
are
less
than
those
of
the
temporal
NBLM,
the
HW
,
the
ARMA
and
the
ARIMA
which
concludes
that
the
NB
AM
is
more
accurate
than
the
others.
Also,
Figure
3
emphasizes
that
the
NB
AM
has
better
accurac
y
than
the
other
models.
The
temporal
NBLM
handles
the
o
v
erdispersion
b
ut
its
structure
contains
a
re
gression
which
incorporates
fe
w
correlating
hours
from
the
r
ecent
past.
On
the
contrary
,
the
NB
AM
captures
the
entir
e
trend
and
pattern
because
its
structure
contains
a
smooth
function
that
beha
v
es
e
xactly
the
same
as
the
real
data.
W
e
find
that
the
smooth
function
of
the
NB
AM
performs
better
than
the
temporal
correlation
with
the
pre
vious
fi
v
e
hours
as
in
NBLM.
Classifying
the
load
into
three
dif
ferent
seasons,
the
v
ariance
is
ensured
to
be
lo
wer
than
the
v
ariance
of
the
entire
daily
season,
as
in
T
able
1.
Thus,
the
forecast
accurac
y
is
increased.
3.3.
F
or
ecasting
efficiency
T
o
measure
the
ef
ficienc
y
of
the
proposed
NB
AM,
the
computational
time
during
the
training
and
forecasting
stages
is
recorded.
More
focus
is
gi
v
en
to
the
high
load
season
since
this
season
has
the
lar
gest
data
size
which
is
2736.
As
in
[9],
the
model
is
tested
on
Intel
CPU
of
2.8
GHz,
64-bit
operating
system
and
16GB
RAM.
The
NB
AM
is
found
f
aster
than
the
ot
her
models
during
training
for
producing
the
smooth
functions,
and
during
the
forecasting,
as
presented
in
T
able
4.
The
NB
AM
ef
ficienc
y
also
outperforms
the
other
models
during
the
forecasting
and
the
training
stages.
The
reason
behind
the
lo
w
computational
time
is
that
the
smooth
function
is
optimized
using
re
gression
spli
ne
where
each
section
coef
ficie
nts
are
comput
ed
by
minimi
zing
the
mean
square
error
.
T
able
4.
The
computation
time
of
the
models
during
the
training
and
forecasting
stages
Model
T
raining
(sec)
F
orecasting
(sec)
NB
AM
1.69
0.08
NBLM
2.124
0.26
ARMA
5.94
3.19
ARIMA
6.82
4.78
HW
6.38
0.86
4.
CONCLUSION
Nonlinearity
,
o
v
erdispersion,
temporal
autocorrelation
and
seasonality
are
important
characteristics
of
El
ectrical
load.
These
characteristics
ha
v
e
dramatic
ef
fect
on
the
forecasti
ng
accurac
y
and
ef
ficienc
y
,
and
the
y
requires
careful
handling
during
de
v
eloping
a
forecasting
model.
Therefore,
this
paper
adopted
the
NB
AM
because
of
its
ability
to
handle
nonlinearity
and
o
v
erdispersion.
A
temporal
NB
AM
w
as
deri
v
ed
by
allo
wing
the
current
elec
trical
load
to
autocorrelate
with
pre
vious
loads.
Also,
In
the
proposed
model,
the
seasonal
patterns
of
the
electric
load
is
classified
into
lo
w
,
moderate
and
high
load
patterns.
The
future
w
ork
will
include
applying
the
de
v
eloped
NB
AM
to
a
real
time
electrical
load
monitoring
system
in
P
alestine.
F
or
ecasting
for
smart
ener
gy:
An
accur
ate
and
ef
ficient
ne
gative
...
(Y
ousef-A
wwad
Dar
a
ghmi)
Evaluation Warning : The document was created with Spire.PDF for Python.
1006
r
ISSN:
2502-4752
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