Int. J. Communications, Network and System Sciences, 2010, 3, 273-279
doi:10.4236/ijcns.2010.33035 blished Online March 2010 (
Copyright © 2010 SciRes. IJCNS
Short-Term Load Forecasting Using Soft
Computing Techniques
D. K. Chaturvedi1, Sinha Anand Premdayal1, Ashish Chandiok2
1Department of Electrical Engineering, D. E. I., Deemed University, Agra, India
2Department. of Electronics and Communication, B. M. A. S., Engineering College, Agra, India
Email: dkc_foe@
Received November 10, 2009; revised December 18, 2009; accepted January 21, 2010
Electric load forecasting is essential for developing a power supply strategy to improve the reliability of the
ac power line data network and provide optimal load scheduling for developing countries where the demand
is increased with high growth rate. In this paper, a short-term load forecasting realized by a generalized neu-
ron–wavelet method is proposed. The proposed method consists of wavelet transform and soft computing
technique. The wavelet transform splits up load time series into coarse and detail components to be the fea-
tures for soft computing techniques using Generalized Neurons Network (GNN). The soft computing tech-
niques forecast each component separately. The modified GNN performs better than the traditional GNN. At
the end all forecasted components is summed up to produce final forecasting load.
Keywords: Wavelet Transform, Short Term Load Forecasting, Soft Computing Techniques
1. Introduction
Short-term load forecasting (STLF) is an essential tech-
nique in power system planning, operation and control,
load management and unit commitment. Accurate load
forecasting will lead to appropriate scheduling and plan-
ning with much lower costs on the operation of power
systems [16]. Traditional load forecasting methods,
such as regression model [7] gray forecasting model [8,9]
and time series [10,11] do not consider the influence of
all kind of random disturbances into account. At recent
years artificial intelligence are introduced for load fore-
casting [1217]. Various types of artificial neural net-
work and fuzzy logic have been proposed for short term
load forecasting. They enhanced the forecasting accuracy
compared with the conventional time series method. The
ANN has the ability of self learning and non-linear ap-
proximations, but it lacks the inference common in hu-
man beings and therefore requires massive amount of
training data, which is an intensive time consuming proc-
ess. On the other hand fuzzy logic can solve uncertainty,
but traditional fuzzy system is largely dependent on the
knowledge and experiences of experts and operators, and
is difficult to obtain a satisfied forecasting result espe-
cially when the information is incomplete or insufficient.
This paper aims to find a solution to short term load
forecasting using GNN with wavelet for accurate load
forecasting results. This paper is organized as follows:
Section 2 discusses various traditional and soft comput-
ing based short term load forecasting approaches. Con-
cept of wavelet analysis required for prediction will be
discussed in Section 3 while elements of generalized
neural architecture needed will be described in Section 4.
A prediction procedure using wavelets and soft comput-
ing techniques and its application to time series of hourly
load forecasting consumption is discussed in Section 5.
Section 6 includes discussion and concluding remarks.
2. Traditional and Soft Computing Techni-
ques for Short Term Load Forecasting
2.1. Traditional Approaches
Time Series Methods
Traditional short term load forecasting relies on time
series analysis technique. In time series approach the
model is based on past load data, on the basis of this
model the forecasting of future load is done. The tech-
niques used for the analysis of linear time series load
signal are:
1) Kalman Filter Method
The kalman filter is considered as the optimal solution
to many data prediction and trend matching. The filter is
constructed as a mean square minimization which re-
quires the estimation of the covariance matrix. The role
of the filter is to extract the features from the signal and
ignore the rest part. As load data are highly non linear
and non stationary, it is difficult to estimate the covari-
ance matrix accurately [18].
2) Box Jenkins Method
This model is called as autoregressive integrated mov-
ing average model. The Box Jenkins model can be used
to represent the process as stationary or non stationary. A
stationary process is one whose statistical properties are
same over time, which means that they fluctuate over
fixed mean value. On other hand non stationary time
series have changes in levels, trends or seasonal behavior.
In Box Jenkins model the current observation is weigh-
ted average of the previous observation plus an error
term. The portion of the model involving observation is
known as autoregressive part of the model and error term
is known as moving average term. A major obstacle here
is its slow performance [19].
3) Regression Model
The regression method is widely used statistical tech-
nique for load forecasting. This model forms a relation-
ship between load consumptions done in past hour as a
linear combination to estimate the current load. A large
data is required to obtain correct results, but it requires
large computation time.
4) Spectral Expansion Technique
This method is based on Fourier series. The load data
is considered as a periodic signal. Periodic signal can be
represented as harmonic summation of sinusoids. In the
same way electrical load signal is represented as summa-
tion of sinusoids with different frequency. The drawback
of this method is that electrical load is not perfect peri-
odic. It is a non stationary and non linear signal with
abrupt variations caused due to weather changes. This
phenomenon results in the variation of high frequency
component which may not be represented as periodic
spectrum. This method is not suitable and also requires
complex equation and large computation time.
2.2. Soft Computing Approach
Soft computing is based on approximate models working
on approximate reasoning and functional approximation.
The basic objective of this method is to exploit the tol-
erance for imprecision, uncertainty and partial truth to
achieve tractability, robustness, low solution cost and
best results for real time problems.
1) Artificial Neural Networks (ANN)
An artificial neural network is an efficient information
processing system to perform non-linear modeling and
adaptation. It is based on training the system with past
and current load data as input and output respectively.
The ANN learns from experience and generalizes from
previous examples to new ones. It is able to forecast
more efficiently the load as the load pattern are non lin-
ear and ANN is capable to catch trends more accurately
than conventional methods.
2) Rule Based Expert Systems
An expert system is a logical program implemented on
computer, to act as a knowledge expert. This means that
program has an ability to reason, explain and have its
knowledge base improved as more information becomes
available to it. The load-forecast model can be built us-
ing the knowledge about the load forecast domain from
an expert in the field. The knowledge engineer extracts
this knowledge from the load domain. This knowledge is
represented as facts and rules using the first predicate
logic to represent the facts and IF-THEN production
rules. Some of the rules do not change over time, some
changes very slowly; while others change continuously
and hence are to be updated from time to time [20].
3) Fuzzy Systems
Fuzzy sets are good in specialization, fuzzy sets are
able to represent and manipulate electrical load pattern
which possesses non-statistical uncertainty. Fuzzy sets
are a generalization of conventional set theory that was
introduced as a new way to represent vagueness in the
data with the help of linguistic variable. It introduces
vagueness (with the aim of reducing complexity) by
eliminating the sharp boundary between the members of
the class from nonmembers [21,22].
These approaches are based on specific problems and
may represent randomness in convergence or even can
diverge. The above mentioned approaches use either reg-
ression, frequency component or mean component or the
peak component to predict the load. The prediction of the
load depends upon both time and frequency component
which varies dynamically. In this paper, an attempt is
made to predict electrical load that combines the above
mentioned features using generalized neurons and wave-
3. Elements of Wavelet Analysis
Wavelet analysis is a refinement of Fourier analysis [9
15,23–29] which has been used for prediction of time
series of oil, meteorological pollution, wind speed, rain-
fall etc. [28,29]. In this section some important vaults
relevant to our work have been described. The underly-
ing mathematical structure for wavelet bases of a func-
tion space is a multi-scale decomposition of a signal,
known as multi-resolution or multi-scale analysis. It is
called the heart of wavelet analysis. Let L2(R) be the
space of all signals with finite energy. A family {Vj} of
subspaces of L2(R) is called a multi resolution analysis of
this space if
Copyright © 2010 SciRes. IJCNS
1) intersection of all Vj, j = 1, 2, 3, ...... be non-empty,
that is j
2)This family is dense in L2(R), that is, = L2(R)
3) f (x) V
j if and only if f (2x) V
j + 1  
4) V1V2 ..... Vj V
j + 1
 
There is a function preferably with compact support of
such that translates
(x k) k Z, span a space V0. A
finer space Vj is spanned by the integer translates of the
scaled functions for the space Vj and we have scaling
()(2 1)
xa x
 (1)
with appropriate coefficient ak, kZ.
is called a scal-
ing function or father wavelet. The mother wavelet
is obtained by building linear combinations of
. Fur-
ther more
should be orthogonal, that is,
()() 0k,l,l,kZ
  (2)
These two conditions given by (1) and (2) leads to
conditions on coefficients bk which characterize a mother
wavelet as a linear combination of the scaled and dilated
father wavelets:
()= (2)
Haar, Daubechies and Coefmann are some well known
Haar wavelet (Haar mother wavalet) denoted by ψ is
given by
1,01 2
()= 1,12<1
0,<0, >1
Can be obtained from the father wavelet
1, 01
()= 0,0, 1
In this case coefficients ak in (1) are a0 = a1 = 1 and ak
= 0 for k 0, 1. The Haar wavelets is defined as a linear
combination of scaled father wavelets
(x) =
(2x) –
(2x – 1) which means that coefficients bk in (3) are b0 =
1, b1 = –1 and bk = 0 otherwise, Haar wavelets can be
interpreted as Daubechie’s wavelet of order 1 with two
coefficients. In general Daubechies’ wavelets of order N
are not given analytically but described by 2N coeffi-
cients. The higher N, the smoother the corresponding
Daubechies’ wavelets are (the smoothness is around 0-2N
for greater N). Daubechies’ wavelets are constructed in
a way such that they give rise to orthogonal wavelet
bases. It may be verified that orthogonality of translates
, requires that
a = 2 and = 2.
It is quite clear that in the higher case the scaled, trans-
lated and normalized versions of are denoted by
jk tx
With orthogonal wavelet the set {
j, k | j, k
is an orthogonal wavelet basis. A function f can be rep-
resented as
j,k j,kj,k
=c (, c< f >)
The Discrete Wavelet Transform (DWT) corresponds
to the mapping f cj,k. DWT provides a mechanism to
represent a data or time series f in terms of coefficients
that are associated with particular scales [24,26,27] and
therefore is regarded as a family of effective instrument
for signal analysis. The decomposition of a given signal f
into different scales of resolution is obtained by the ap-
plication of the DWT to f. In real application, we only
use a small number of levels j in our decomposition (for
instance j = 4 corresponds to a fairly good level wavelet
decomposition of f).
The first step of DWT corresponds to the mapping f to
its wavelet coefficients and from these coefficients two
components are received namely a smooth version, nam-
ed approximation and a second component that corre-
sponds to the deviations or the so-called details of the
signal. A decomposition of f into a low frequency part a,
and a high frequency part d, is represented by f = a1 + d1.
The same procedure is performed on a1 in order to obtain
decomposition in finer scales: a1 = a2 + d2. A recursive
decomposition for the low frequency parts follows the
directions that are illustrated in Figure 1.
The resulting low frequency parts a1, a2, ..... an are ap-
proximations of f, and the high frequency parts d1, d2, .....
dn contain the details of f. This diagram illustrates a
wavelet decomposition into N levels and corresponds to
123 1
 
In practical applications, such decomposition is ob-
tained by using a specific wavelet. Several families of
wavelets have proven to be especially useful in various
applications. They differ with respect to orthogonality,
smoothness and other related properties such as vanish-
ing moments or size of the support.
Figure 1. Wavelet decomposition in form of coarse and de-
tail coeffici e nts.
opyright © 2010 SciRes. IJCNS
4. Neuro Theory of Generalized Neuron
The following steps are involved in the training of a
summation type generalized neuron as shown in Figure 2.
4.1. Forward Calculations
Step 1: The output of thepart of the summation type
generalized neuron is 1
where _iio
netW XX
Step 2: The output of the part of the summation type
generalized neuron is
ppi net
ii o
pinetW XX
Step 3: The output of the summation type generalized
neuron can be written as
*(1 )*
4.2. Reverse Calculation
Step 4: After calculating the output of the summation
Input, Xi
Outpu t, Op k
Output, O pk
Figure 2. Learning algorithm of a summation type general-
ized neuron.
neural network, it is compared with the
Then, the uared error for
patterns is
type generalized neuron in the forward pass, as in the
desired output to find the error. Using back-propagation
algorithm the summation type GN is trained to minimize
the error. In this step, the output of the single flexible
summation type generalized neuron is compared with the
desired output to get error for the ith set of inputs:
Error ()
EYO (12)
sum-sq convergence of all the
A multiplication factor of
plify the calculations.
0.5 has been taken to sim-
Step 5: Reverse pass for modifying the connection
1) Weight associated with the1and 2 part of the
summation type Generalized Neu is:
()( 1)Wk WkW
 (14)
where ()
 (1)Wk
and ()
ts associated withe inputs of th2) Weigh the
of the summation type Generalized Neuron are:
()( 1)
ii i
Wk WkW
 (15)
where (1
ij i
 
 
and (1)*
s associated with the input of the part of
the summation type generalized Neuron are:
3) Weight
()( 1)
ii i
Wk WkW
 (16)
ij i
where )
 
 
and (1) * (2*_) *
Mcomentum factor for better convergene.
by expe
d NeuronWavelet Approach
sed to predict the electrical load. In this approach, Dau-
Learning rate.
from 0 to 1 and is determine of these factors is
. Generalize5
The Generalized NeuronWavelet approach has be
bechies wavelets Db8 have been applied in the decom-
position for the give data pattern. There are four wavelet
coefficients are used. All these wavelet coefficients are
time dependent (the first three wavelet coefficients from
Copyright © 2010 SciRes. IJCNS
d1 to d3 and the coarse approximation a3. These coeffi-
cients are illustrated in the Figure 3. We observe the
substantial difference of variability of the signals at dif-
ferent levels. The higher is the wavelet level, the lower
variation of the coefficients and easier prediction of them.
Our main idea is to substrate the prediction task of the
original time series of high variability by the prediction
of its wavelet coefficients on different levels of lower
variability’s, and then using Equation (4) for final pre-
diction of the power load at any time instant n. Since
most of the wavelet coefficients are of lower variability
we expect the increase of the total prediction accuracy.
The wavelet tool available in Matlab is used for the
process of wavelet decomposition of the time series rep
senting average of the power load data for 120 hours.
This step involves several different families of wavelets
and a detailed comparison of their performance. In our
case, The Daubechies wavelets of order 8 are performed.
Three level wavelet decomposition of the given time
series XN = f : is performed
addd (17)
The smooth part of f is stored in a3
ferent levels are captured by d, d,
, and details on dif-
d. Consequently a
1 2 3
composition of the time series in three different scales
is obtained. Figure 4 illustrates the decomposition of the
original signals. The forecasting procedure methodology
explained in Section 4 is used to predict the next value.
The basic idea is to use the wavelet transforms and pre-
dict the data by soft computing techniques for individual
coefficients of wavelet transform represented by a3, d1,
d2, d3. The input to the architecture to predict the wavelet
coefficients is explained in Figure 5.
Figure 4. Mechanism for forecasting Procedure.
Figure 5. Actual and pr edicted training output using gener
alized neuron model (GNN).
load at an instant (i) is given
The total predicted power
ififififi   (18)
. Results and Discussions
ollected for 120 hours
om Gujarat system and normalized them in the range
The electric load data have been c
01. The Daubechies wavelet Db8 is used for decompo-
sition and the wavelet coefficients d1d3 and a3 have
been calculated. The trend of coefficients has been used
for GN training and predicting the wavelet coefficients
for future loads. So wavelet is used to extract the feature
coefficients from data and then GN is implemented to
predict the trend of the wavelet coefficient. The results of
GN and actual load have been compared and shown in
Figure 3. Wavelet decomposition of hour load data into
wavelet coeff ic ient.
opyright © 2010 SciRes. IJCNS
Figures 5 and 6. The root means square error for training
and testing results are .1127 and .1152 mega watts (MW)
as in Table 1. When using generalized neuron and wave-
let conjunction model, training each coefficient and
combining to get the predicted output, a very high im-
provement is obtained in both training and testing results
as shown in Figures 7 and 8. The root means square er-
ror for training and testing data are .0554 and .0763 re-
spectively as in Table 1. The improvement in the results
shows that accuracy of forecasting increases in the com-
bined model and can give correct output for short term
load forecasting.
Figure 6. Actual and predicted testing output using gee
alized neuron model (GNN).
GNN Wavelet
pe Min. Error
Max. Error
n r
Table 1. Comparison between GNN and
GNN (training) 0.10009520.3663 0.1127
GNNW(training) 0.002184 0.1706 0.0554
GNN(testing) 0.1306 0.2094 0.1152
G NNW(testing) 0.00462 0.1913 0.0673
Figure 8. Actual and predicted testing output using gene
alized neuron wavelet model (GNNW).
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