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Forecasting electricity consumption: A comparison of regression
analysis, neural networks and least squares support vector machines
Fazil Kaytez
a,
⇑
, M. Cengiz Taplamacioglu
a
, Ertugrul Cam
b
, Firat Hardalac
a
a
Gazi University, Faculty of Engineering, Electrical & Electronics Engineering Department, 06750 Maltepe, Ankara, Turkey
b
Kirikkale University, Faculty of Engineering, Electrical & Electronics Engineering Department, 71450 Kirikkale, Turkey
article info
Article history:
Received 9 April 2014
Received in revised form 1 August 2014
Accepted 7 December 2014
Available online 24 December 2014
Keywords:
Electricity consumption forecasting
Regression analysis
Artificial neural network
Least square support vector machines
abstract
Accurate electricity consumption forecast has primary importance in the energy planning of the develop-
ing countries. During the last decade several new techniques are being used for electricity consumption
planning to accurately predict the future electricity consumption needs. Support vector machines (SVMs)
and least squares support vector machines (LS-SVMs) are new techniques being adopted for energy con-
sumption forecasting. In this study, the LS-SVM is implemented for the prediction of electricity energy
consumption of Turkey. In addition to the traditional regression analysis and artificial neural networks
(ANNs) are considered. In the models, gross electricity generation, installed capacity, total subscribership
and population are used as independent variables using historical data from 1970 to 2009. Forecasting
results are compared using diverse performance criteria in this study with each other. Receiver operating
characteristic (ROC) analysis is realized for determining the specificity and sensitivity of the empirical
results. The results indicate that the proposed LS-SVM model is an accurate and a quick prediction
method.
Ó2014 Elsevier Ltd. All rights reserved.
Introduction
Long term electricity consumption forecasting is the basis for
energy investment planning and plays a vital role in developing
countries for governments. Overestimation of the consumption
would lead to superfluous idle capacity which means wasted finan-
cial resources, whereas underestimation would lead the higher
operation costs for energy supplier and would cause potential
energy outages. Therefore, modeling electricity consumption with
good accuracy becomes vital in order to avoid costly mistakes.
Electricity forecasting models are developed specific to a nation
or utility depending on market conditions prevailing. Each country
has a specific consumption model to its own conditions. A few
important points need to be considered in order to model the elec-
tricity consumption accurately. First, the parameters affecting elec-
tricity consumption for the country should be well defined. Usually
historical data and the independent indicators considered to be
influential on this consumption need to be used in the model.
The second consideration is to choose a methodology suitable for
the consumption model. Traditional methods such as time series,
econometric models, regression as well as soft computing
techniques such as artificial intelligence, fuzzy logic and genetic
algorithms are being broadly used for electricity consumption fore-
casting. Ant colony optimization, particle swarm optimization and
support vector regression are emerging techniques in electricity
demand modeling. Moreover, an applied model should allow for
the next step into the future computations.
Electricity market in Turkey has a rapidly developing structure
due to industrialization, rapid urbanization and growing popula-
tion for last two decades. The average annual increase in total elec-
tricity consumption in Turkey is about 4–5%, which is far above the
average of many countries in Europe and throughout the world
[1,2]. However, energy sources in Turkey are quite scarce. Turkey’s
extensive dependence on import sources for its energy supply cre-
ates some economic and political negative effects, making author-
ities necessary to estimate future electricity consumption
accurately by using the accurate models.
Estimates of long-term energy consumption in Turkey are car-
ried out officially by the Ministry of Energy and Natural Resources
(MENR) and the Ministry of Development (MD). Official estimation
results are higher than actual consumption values in general, and
the Ministry of Energy and Natural Resources revises these results
every six months. For this reason, it is necessary to use reliable
methodologies and to develop new and alternative techniques
for the estimation of future electricity consumption in Turkey
properly.
http://dx.doi.org/10.1016/j.ijepes.2014.12.036
0142-0615/Ó2014 Elsevier Ltd. All rights reserved.
⇑
Corresponding author. Tel.: +90 312 5823349; +90 312 2311340.
E-mail addresses: fazilkaytez@hotmail.com (F. Kaytez), taplam@gazi.edu.tr
(M.C. Taplamacioglu).
Electrical Power and Energy Systems 67 (2015) 431–438
Contents lists available at ScienceDirect
Electrical Power and Energy Systems
journal homepage: www.elsevier.com/locate/ijepes
The main objective of this manuscript is to develop an accurate
and optimal LS-SVM model and to propose applicable models for
forecasting net electricity consumption in Turkey. In recent years,
the least squares formulation of SVM, called LS-SVM has been used
in various energy research, such as forecasting, classification, and
power engineering [3–6]. The literature review reveals that the
LS-SVM technique has not been used for forecasting electricity
energy consumption previously. Therefore, this study will provide
important contributions to the literature of electricity demand
forecasting.
In the literature, there are a number of important studies on
electricity consumption and demand estimation. In these studies,
some of commonly used methods are time series models, regres-
sion models, Box–Jenkins models, econometric models, neural net-
works, ant colony optimization, genetic algorithms and statistical
learning models. Traditionally, regression analysis and time series
have been the most popular modeling techniques in electricity
consumption predicting [7–9]. The use of neural networks (NNs)
has become increasingly popular in many forecasting models.
Some researchers have proposed different models to improve the
prediction performance using neural networks [10,11]. Artificial
neural networks (ANNs) have also been used for the prediction of
electricity consumption [12–16]. The following studies were
selected from the literature in order to present the variety of the
methods. By using genetic algorithms; Ceylan and Ozturk [17] have
conducted an estimation study up to the year 2025 in Turkey’s
long-term energy demand forecasting. By using particle swarm
optimization (PSO); Unler [18] has carried out the long-term
demand forecast of Turkey up to the year 2025. By using ant colony
optimization algorithm (ACO); Toksari [19] has predicted the Tur-
key’s long-term demand under the effect of selected economic and
demographic variables. By using an optimized grey modeling;
Hamzacebi and Es [20] have forecasted the annual electricity con-
sumption in Turkey. Finally electricity consumption forecasting
and robust forecasting modeling have been proposed using the
support vector regression model [21] and singular value decompo-
sition [22].
Studies on the relationship between GDP and consumption are
increasingly common [23–26]. Karagol et al. [27] investigated the
relationship between Turkey’s GDP and electricity consumption.
They found a negative relationship through cointegration analysis
between the variables. Altinay and Karagol [28] showed that there
is a unidirectional relationship between electricity consumption
and GDP. It is a common hypothesis that energy consumption
has a positive effect on economic growth in Turkey. The reverse
of this hypothesis is controversial. Especially in Turkey, an increase
in electricity consumption is observed even in periods of low GDP.
Turkey’s yearly energy consumption was affected by the economic
crisis especially. It is difficult to predict or detect economic crises in
advance. Therefore, GDP is not used as an independent variable in
the model. This study compares mainly the accuracy in predicting
long-term electricity consumption in Turkey among three different
approaches: regression analysis, neural networks and support vec-
tor machines. When comparing accuracy in predicting electricity
energy consumption, it is found that the LS-SVM model perform
better than other models. The background of the study is described
in the following section. Methodologies and results are described
in Sections ‘Methods’ and ‘Experimental results’, respectively.
Comparative advantages of the different data analysis approaches
in application to electricity energy consumption and conclusions
of results are given in Sections ‘Results and sensitivity-specificity
analyses’ and ‘Conclusion’, respectively.
Methods
Artificial neural network approach
ANNs have been trained to overcome the restriction of the tra-
ditional methods to solve complex problems. This technique learns
from given examples by constructing an input–output mapping in
order to perform estimations. Neural networks consist of an inter-
connection of a number of neurons. There are many varieties of
connections in literature. However, this study focuses only one
type of network, which is called the multi-layer perceptron
(MLP) which is shown in Fig. 1.
ANNs use different learning algorithms. A learning algorithm is
described as a procedure that consists of adjusting the weights and
biases of a network, to minimize an error function between the
network output and sample output data for a given set of inputs
[29,30]. The backpropagation algorithm (BP) is one of many learn-
ing algorithms used to train neural networks and is widely used in
solving many practical problems. However, BP has the disadvan-
tage of slow convergence and long training time. Additionally, suc-
cess of BP algorithm depends on the user-dependent parameters
learning rate momentum constant. The Levenberg–Marquardt
(LM), scaled conjugate gradient (SCG) and Quasi-Newton algo-
rithms are faster than BP algorithm and use standard numerical
optimization methods. The Levenberg–Marquardt (LM) algorithm
is an alternative to backpropagation for use in training feedforward
neural networks based on a nonlinear optimization. LM algorithms
use an approximation of second-order derivatives of the objective
Fig. 1. MLP feed forward ANN.
432 F. Kaytez et al. / Electrical Power and Energy Systems 67 (2015) 431–438
function so that better convergence behavior can be obtained.
Moreover, this method provides a better parameter change vector
than gradient descent technique. Scaled conjugate gradient (SCG)
uses second order information from neural network and avoids a
time consumption line-search. Quasi-Newton algorithms build up
curvature information at each iteration to formulate a quadratic
problem. LM, SCG and Quasi-Newton algorithms resolve the some
disadvantages of BP mentioned above [30–32]. ANNs are designed
according to their connection architecture, learning algorithm,
number of hidden layer, number of nodes in a hidden layer and
transfer function. Also, these design criteria affect the performance
of ANNs [33,34].
Least squares support vector machine (LS-SVM)
LS-SVM is a alteration of the standard SVM and was improved by
Suykens et al. [35]. The LS-SVM uses the least squares loss function
to construct the optimization problem based on equality constraints.
The least squares loss function entails only the solution of a linear
equation series instead of the long and computationally difficult
quadratic programing in the
e
-insensitive loss function of the origi-
nal support vector machines. LS-SVM is generally used for the opti-
mal control, classification and regression problems [35,36].
In this section, the LS-SVM for regression is introduced briefly,
called LS-SVR. The LS-SVR technique is to approximate an obscure
function by using given a sample of a training data series x
i
;y
i
fg
l
i¼1
.
The regression function can be formulated as feature space
representation:
y¼fðxÞ¼w
T
u
ðxÞþbð1Þ
where the x2R
n
,y2Rand
u
(): R
n
!R
nh
is the mapping to the
high dimensional feature space. The optimization problem of LS-
SVM is given as:
min J
1
ðw;b;eÞ¼1
2w
T
wþ1
2CX
l
i¼1
e
2
i
ð2Þ
subjective to y
i
¼w
T
u
ðx
i
Þþbþe
i
;i¼1;2;...lð3Þ
where e¼ðe
1
;e
2
;...e
l
Þ2R
l
introduce the Lagrangian function as
L
1
ðw;b;e;
a
Þ¼J
1
ðw;b;eÞþX
l
i¼1
a
i
ðy
i
w
T
u
ðx
i
Þbe
i
Þð4Þ
where a¼ða
1
;a
2
;...;a
l
Þ2Rare the Lagrange multipliers, which
can be positive or negative in LS-SVM formulation. The conditions
for optimality are
@L
1
@w
¼0!w¼X
l
i¼1
a
i
u
ðx
i
Þ;
@L
1
@b
¼0!X
l
i¼1
a
i
¼0;
@L
1
@e
i
¼0!e
i
¼
1
C
a
i
;
@L
1
@
a
i
¼0!y
i
¼w
T
u
ðx
i
Þþbþe
i
;
ð5Þ
For i¼1;2;3...l
k(x
i
,x
j
) indicates a Kernel function whose value equals the inner
product of x
i
and x
j
vectors in the feature space
u
(x
i
) and
u
(x
j
).
kðx
i
;x
j
Þ¼
u
ðx
i
Þ
T
u
ðx
j
Þð6Þ
The basic features of a Kernel function are derived from Mer-
cer’s theorem [37]. Applicable Kernel functions must satisfy Mer-
cer’s conditions [37,38]. This study uses the radial basis function
(RBF), the linear function and the polynomial function as Kernel
functions, as shown below:
kðx
i
;x
j
Þ¼expð x
i
x
j
2
=
r
2
ÞðRBFÞ
kðx
i
;x
j
Þ¼x
T
j
x
i
ðLinearÞ
kðx
i
;x
j
Þ¼ðtþx
T
j
x
i
Þ
d
ðpolynomialÞ
ð7Þ
Mercer’s condition is valid for all
r
values in the radial basis
function case and positive tvalues in the polynomial function case
[37]. Therefore, we can indicate K=(k
ij
)
lxl
,k
ij
=k(x
i
,x
j
) and Vas
V= diag(1/C,1/C,...,1/C), thus LS-SVM regression model (LS-SVR)
can be defined as:
A1
1
T
0
a
b
¼y
0
;ð8Þ
where A=K+V. The regression model in Eq. (1) is found by solving
Eq. (9). The fitting function namely the output of LS-SVM regression
is:
fðxÞ¼X
l
i¼1
a
i
Kðx;x
i
Þþbð9Þ
where
a
i
and bare the solutions to the linear system. Although the
selections of the Kernel function K(x
i
,x
j
) in LS-SVM are the identical
as those in standard SVM, more emphasis has been put on the force-
ful RBF Kernel. Note that in the case of RBF kernels, LS-SVM has only
two additional tuning parameters (C,
r
), which is lesser than for a
standard support vector regressor [35–40].
0
1
2
3
4
5
6
1970
1972
1974
1976
1978
1980
1982
1984
1986
1988
1990
1992
1994
1996
1998
2000
2002
2004
2006
2008
Observed values of indicators x10000
Years
Net electricity consumption (TWh) Total subscribership (Million)
Population(Million) Gross electricity generation(TWh)
Installed capacity(GW)
Fig. 2. Turkey’s historical net electricity consumption and corresponding indicators.
F. Kaytez et al. / Electrical Power and Energy Systems 67 (2015) 431–438 433
Experimental results
Data sets
All the analyses in this study installed capacity (IC), gross elec-
tricity generation (GEG), population (P), and total subscribership
(TS) data were selected as independent variables (shown in
Fig. 2). The Turkish Electricity Transmission Company (TEIAS) sta-
tistical database was used for Turkey’s total IC and GEG data [41–
43], and the Turkish Statistical Institute (TIE) database was used for
P data [44]. Both the number of subscribers and the net electricity
consumption values for Turkey were taken from Turkish Electricity
Distribution Company (TEDAS) and other private electricity distri-
bution companies [45]. The data used for Turkey’s electricity con-
sumption modeling spans the years from 1970 to 2009 that
corresponds to the most up to date data available at the time this
research was performed. The total number of subscribers and pop-
ulation data are not reliable for Turkey, especially before 1970.
Since the census of population was performed every five years dur-
ing 1970–2010 in Turkey, the values of some years are not avail-
able in TIE records. The interpolation method was used to find
these missing values. In all prediction models, 2/3 of the input data
were used for training, and 1/3 of them were used for testing. Data
from 2010 and 2011 were used for validation purposes. Turkey’s
net consumption data for the 2012 and 2013 are not in the official
reports yet.
Performance criterion
Maximum error (MaxError), mean absolute percentage error
(MAPE), mean square error (MSE), root mean square error (RMSE)
and sum square error (SSE) are used as performance measures in
our model comparison. Performance criteria are defined as;
MaxError ¼max y
f
y
r
ð10Þ
MAPEð%Þ¼100xP
N
k¼1
y
r
y
f
y
r
Nð11Þ
MSE ¼1
NX
N
k¼1
ðy
r
y
f
Þ
2
ð12Þ
RMSE ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
P
N
k¼1
ðy
r
y
f
Þ
2
N
sð13Þ
SSE ¼X
N
k¼1
ðy
r
y
f
Þ
2
ð14Þ
where y
r
denotes the realized consumption values, y
f
shows the
forecasted values for kth year and Nshows number of years.
The square of Pearson product-moment correlation coefficient
(R
2
) is an important tool in determining the degree of linear corre-
lation of variables in regression analysis. It is also known as the
correlation coefficient. The adjusted-R
2
is a modified version of
R
2
that has been adjusted for the number of predictors in the model
and should always be used with models with more than one pre-
dictor variable. R
2
and adjusted R
2
are defined as follows
respectively:
R
2
¼SSR
SST ¼1SSE
SST ð15Þ
Adjusted R
2
¼1n1
np
SSE
SST ð16Þ
where SSR is the sum of squared regression, SST is the sum of
squared total, SSE is the sum of squared error, pis the number of
regression coefficients and n is the number of observations. R
2
and MSE were used to evaluate the prediction capability of pro-
posed models.
Multi linear regression (MLR) analysis
In this part, Turkey’s electricity consumption has been modeled
with the multiple linear regression model. This model can be sum-
marized as:
Model :y¼a
1
x
1
þb
2
x
2
þc
3
x
3
þd
4
x
4
þf
where yrepresents the estimated electricity consumption; a
1
,b
2
,c
3,
d
4
and fvalues are the regression coefficients. The xvalues indicate
the four independent variables used as the predictors of y(x
1
: IC, x
2
:
GEG, x
3
: P and x
4
: TS). Certain statistical results such as R
2
, Adjusted
R
2
and F-test were used for the validation. The regression coeffi-
cients were obtained by computer-aided solution of the regression
equation, are shown in Table 1.
Construction and analysis of ANN
The success of ANN applications is closely related to the
approaches and experiences applied. There are numerous struc-
tural parameters that affect the behavior of an ANN system. Deter-
mining the most appropriate parameters for each problem
constitutes a problem itself, and their selection is extremely
important.
In our study, a multilayer feed-forward back-propagation neu-
ral network model was used for the estimation of net electricity
consumption in Turkey. The four independent parameters ana-
lyzed in the previous section represent inputs to our ANN model,
and the electricity consumption represents the output. Normaliza-
tion of ANN inputs to a certain range is required in order to make
the activation function identify the inputs at the minimum and
maximum range of the data set (see Table 2). Although there are
various normalization techniques, their common characteristic is
to convert the data sets to desired levels by using a scaling factor.
In all of the analyses conducted in this study, each set of input and
output values is scaled into the [1, 1] range according to Eq. (17).
X
new
¼2Xx
min
x
max
x
min
1ð17Þ
The MATLAB
Ò
neural network toolbox was used to train the
developed network models [46]. In this part of the study, different
ANN models were designed and tested. The successful models are
summarized in Table 3. For present investigation, 5 different back-
propagation learning algorithms, 5 different transfer functions, 1–6
hidden layers, and all possible combinations of 2–70 neurons at
Table 1
Model regression coefficients and R
2
value.
Linear model a
1
b
2
c
3
d
4
f
Coefficients 0.417 0.585 0.567 1.427 16.248
R
2
= 99.83%, adjusted-R
2
= 99.70%, MSE = 6.45, F-value = 1961.92.
Table 2
Values for normalization.
Indicators X
min
X
max
Installed capacity 2.235 56.38
Gross electricity generation 8.623 315
Total subscribership 4.43 39.34
Population 35.32 78.83
Net electricity consumption 7.31 310
434 F. Kaytez et al. / Electrical Power and Energy Systems 67 (2015) 431–438
each hidden layer are tried with higher period (epoch) numbers.
Among these models, the fastest model having the best generaliza-
tion capability and the lowest error rate is selected as Turkey’s
electricity consumption model. This model has two hidden layers
10 and 9 neurons at each hidden layer, respectively. However, it
has the Levenberg Marquardt algorithm as the learning algorithm
and a transfer function group of the type linear–tangent sig-
moid–linear between the layers. The learning rate and momentum
coefficient were selected as 0.1 and 0.9 respectively. In the training
phase, the mean square error (MSE) is minimized to the final value
of 3.29 within 43 epochs. The test error is MSE 3.31, which is an
acceptable level.
LS-SVM analysis
Both the use of the LS-SVM model for regression and its theoret-
ical foundations was previously discussed in Section ‘Least squares
support vector machine (LS-SVM)’. Although LS-SVM is a new for-
mulation of the standard SVM, it has advantages such as fast con-
vergence, high sensitivity, and simple computation in comparison
to the standard SVM [35]. However, it is quite difficult to select
appropriate parameters for LS-SVM because there are no theoreti-
cal methods for doing so, which is a critical process in the accuracy
of the regression. Optimization techniques should be utilized in
order to manage this process properly. The LS-SVM training algo-
rithm also applied in this study is defined as in Table 4. MATLAB
Ò
was used for implementing, training and the analysis of the
algorithm.
As in the ANN analysis, the input and output data are normal-
ized into the [1 +1] range by Eq. (15). In the experiment, the
radial basis function (RBF) kernel with
r
2
bandwidth is used
because it tends to achieve better performance than other kernel
functions. No major variations occurred in the upper and lower
values of the [30–200] and [0.1–1.9] ranges of the Cand
r
2
param-
eters respectively, and the trainers with the lowest error rate
occurred in this range. In determining the kernel bandwidth,
r
2
and margin Care set to 0.3 and 50 respectively. The lowest mean
square error (MSE) of 0.169 is reached at these values of
r
2
and
C. The curve in Fig. 3 shows the rate of change in the error value
of
r
2
.
Results and sensitivity–specificity analyses
In the present study, the training and test sets are prepared in
the same way in order to compare the performances of the MLR,
ANN, and LS-SVM models objectively. First, the regression coeffi-
cients are found by forming the multiple linear regression model
with four independent variables in Section ‘Multi linear regression
(MLR) analysis’. The validity of the proposed regression model is
checked by reliability indicators such as R
2
, adjusted R
2
, MSE and
F-test. Second, to create an ANN suitable for the present problem
and to have a good generalization capability, different network
configurations are designed with different learning algorithms.
According to the results obtained in Section ‘Construction and
analysis of ANN’, the network structure given in the fourth row
of Table 3 is taken as a reference. Finally, an LS-SVM consumption
Table 3
Training data of the ANN model.
No. Structure Backpropagation learning algorithm Transfer function (%) Training error (MSE) Testing error (MSE) Epochs
1 4/10/9/1 Resilient Back. Tansig–tansig–purelin 3.35 3.44 163
2 4/10/9/1 Levenberg Marq. Tansig–tansig–purelin 3.32 3.37 34
3 4/10/9/1 Gradient descent Tansig–tansig–purelin 4.12 4.18 89
4 4/10/9/1 Levenberg Marq. Purelin–tansig–purelin 3.08 3.29 43
5 4/10/5/1 Resilient Back. Purelin–purelin–purelin 3.97 4.03 159
6 4/10/5/1 Levenberg Marq. Purelin–purelin–purelin 4.37 4.31 51
7 4/10/5/1 Gradient descent Purelin–purelin–purelin 3.71 3.77 319
8 4/5/5/1 Gradient descent Tansig–tansig–purelin 4.61 4.53 164
9 4/5/5/1 Levenberg Marq. Tansig–tansig–purelin 3.70 3.64 12
10 4/5/5/1 Resilient Back. Tansig–tansig–purelin 3.37 3.32 166
11 4/10/1 Levenberg Marq. Tansig–purelin 3.77 3.75 27
12 4/10/1 Gradient descent Purelin–purelin 4.20 4.25 87
Table 4
Main steps of LS-SVM algorithms.
Step 1. Initialization: solve LS-SVM problem (4) (or solve 9) and set the
solution LS-SVM model as w
(0)
and b
(0)
Step 1. Generate
r
2
and Cvalues
Step 1. Training
Step 1. Simulation
Step 1. Performance calculation
Step 1. Store if it is better than the previous parameter and go to Step 2.
Otherwise go to Step 2 again
Step 1. Stop condition: stop processing steps after 1000 epochs. And use
the best solution in Step 8
Step 1. Output: set new w=w
(k)
and b=b
(k)
and output the regressor Eq.
(2)
0
0,05
0,1
0,15
0,2
0,25
0,1 0,3 0,5 0,7 1 1,3 1,6 1,9
MSE (Mean Square Error)
σ2
C=50
Fig. 3. Simulated relation between
r
2
and MSE.
Table 5
Model results.
Performance criteria Training Test
MLR ANN LS-SVM MLR ANN LS-SVM
MAPE (%) 4.01 4.86 0.876 3.34 1.19 1.004
MaxError 7.62 3.03 1.05 8.25 5.92 4.4
MSE 6.06 3.08 0.1699 6.45 3.3 2.06
RMSE 2.46 1.76 0.412 2.54 1.82 1.435
SSE 163.69 83.19 4.59 83.79 42.85 26.782
R-squared (%) 99.72 99.89 99.99 99.76 99.88 99.98
F. Kaytez et al. / Electrical Power and Energy Systems 67 (2015) 431–438 435
forecasting model is set up to examine the sensitivity of the LS-
SVM algorithm in Section ‘LS-SVM analysis’. Optimization tech-
niques are used for the selection of appropriate parameters for this
model.
The performance results obtained at the end of training and test-
ing procedures on the MLR, ANN, and LS-SVM models are shown in
Table 5. Considering all the results in this table, although the MAPE
value, which is a reliable performance criterion in the literature,
give successful results in the training of ANN and LS-SVM models
such as 0.91% and 0.88% respectively. The test errors of the models
are observed as a little higher and had closer values. Despite these
two models, the training and test error rates of the MLR analysis are
observed to be quite high in all of the performance criteria. The
comparison between the test results of the models and actual val-
ues are shown in the bar chart in Fig. 4. Although these three mod-
els that have been analyzed in this study gave quite successful
estimations between 1975 and 1987, it can be said that all three
failed in 2008. However, the error rates of ANN and LS-SVM algo-
rithms have close oscillations in most of the test data.
The results obtained above may not be sufficient to check the
validity of the model. The forecast performances of the designed
models are measured by their proximity to actual electricity con-
sumption. Testing the sensitivity and specificity of the models, par-
ticularly on the test data is very important. The sensitivity and
specificity levels of the analysis results are compared using an
ROC analysis method based on statistics. ROC analysis provides
the means to select the most appropriate model and to eliminate
the independent suboptimal area in the class distribution prob-
lems. In this study, ROC analysis is applied to the net electricity
consumption of Turkey depicted in Fig. 2. The confusion matrix
required for the ROC analysis are created by defining a specific
limit range at the upper and lower levels of the actual consumption
curve, and by labeling the estimations inside this range as class-1
and outside of this range as class-0. In the analysis, 1% of the lower
and upper bound ranges are determined on the consumption curve
(Fig. 5). The classifications and confusion matrices are created for
the MLR, ANN, and LS-SVM models, and then the ROC curves of
the models are plotted by calculating the sensitivity and specificity
values (Fig. 6).
The sensitivity and specificity values obtained in the analysis
and the area values calculated according to the ROC curves in
Fig. 6 are shown in Table 6. According to these results, the LS-
SVM model had a sensitivity 99.9% higher than the other two mod-
els. In addition, in the specificity analysis, it is observed that the LS-
SVM and ANN models have better results, whereas the MLR model
has a lower specificity value of 66.67%. Likewise, for the area under
the ROC curves, the LS-SVM algorithm has a larger area than both
the MLR and ANN algorithms by 7.13% and 2.78% respectively. The
classifying characteristics of LS-SVM model is better than other
two models.
0
20
40
60
80
100
120
140
160
180
Actual MLR ANN LS-SVM
Consumption (TWh)
Years
1972 1975 1978 1981 1984 1987 1990 1993 1996 1999 2002 2005 2008
Fig. 4. Comparing test results of MLR, ANN and LS-SVM.
Actual 9,53 13,49 18,93 22,03 27,64 36,7 46,82 59,2 74,2 91,2 102,95 130,26 161,95
MLR pppnnpppnpnnn
ANN ppppppppnpnnn
LS-SVMpppppppppppnn
Fig. 5. Classification of the consumption change curve for confusion matrix.
436 F. Kaytez et al. / Electrical Power and Energy Systems 67 (2015) 431–438
Conclusion
Electricity generation, transmission and distribution facilities
require an investment of billions of dollars. Therefore, forecasting
electricity consumption is very important for the investors and
companies. Adequate capacity planning requires accurate forecasts
of the future demand variations and timing of electricity demand.
In official 2008 reports for Turkey [47], gross electricity con-
sumption was estimated as 216,992 GW h in 2009, whereas actual
2009 consumption was 194,080 GW h. This 11.81% error is not
acceptable difference in energy sector. Accurate consumption
models are needed immediately in Turkey. For this purpose, in this
manuscript, The LS-SVM model is recommended for alternative
and successful estimation of electricity consumption of Turkey.
The LS-SVM model has resulted in absolute training and testing
errors of 0.876% and 1.004% respectively, which is more successful
than the other two models. Also, the success of the ANN model in
the training and testing processes is close to that of the LS-SVM
model. However, ANN’s lack of convergence to the actual value
in some of the test data reduces the success rate in comparison
to LS-SVM. This is also clearly seen in the sensitivity and specificity
analysis. The test results are not within acceptable limits in a tra-
ditional regression analysis and have a higher error rate. Especially,
for the year 2010, which was used for validation purposes, the LS-
SVM model achieved more successful results than the MLR and
ANN models by 1.70% and 0.88% respectively.
The analyzed results indicate that the LS-SVM model can be
used effectively for Turkey’s long-term net electricity consumption
forecast. In addition, a successfully trained ANN model is a
powerful forecasting tool as well. Therefore, the recommendations
Fig. 6. ROC curves of the model result with (a) ANN, (b) LS-SVM and (c) MLR.
Table 6
Results of the statistically (ROC) analysis.
Sensitivity (%) Specificity (%) Region under the curve (%)
MLR 85.71 66.67 92.86
ANN 88.89 99.8 100 97.22
LS-SVM 99.9 100 99.9 100 99.9 100
F. Kaytez et al. / Electrical Power and Energy Systems 67 (2015) 431–438 437
presented in this article are useful for policy makers and energy
planners.
Acknowledgement
The authors are grateful for the support provided for the
present work by the Ministry of Energy and Natural Resources of
Turkey (MENR), TURKSTAT, TETC, TEDC.
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