understanding the impacts of gdp and population in south africa's ...

Proceedings of the IASTED International Conference Modelling and Simulation (AfricaMS 2014) September 1 - 3, 2014 Gaborone, Botswana

UNDERSTANDING THE IMPACTS OF GDP AND POPULATION IN SOUTH AFRICA’S ENERGY CONSUMPTION 1*

1*

2

Oludolapo A. Olanrewaju, 2Josiah L. Munda, 3Adisa A. Jimoh

Centre for Energy and Electric Power, Tshwane University of Technology Pretoria, South Africa [email protected]

Centre for Energy and Electric Power, Tshwane University of Technology Pretoria, South Africa [email protected] 3

Electrical Engineering department, Tshwane University of Technology Pretoria, South Africa [email protected]

ABSTRACT The objective of this paper is to develop a forecast model dependent on artificial neural network (ANN) to model South Africa’s energy consumption between 2002 and 2009 based on the input factors – gross domestic product (GDP) and population. To what significance does the country’s energy consumption depend on these input factors was also successfully analyzed. The paper employs ANN to carry out these various analyses successfully. In comparison to the regression analyses, it was discovered that ANN is a better modeling technique.

for a non-linear rather than linear relationship between energy consumption and economic growth [3, 4]. South Africa is one of those countries, moving from an apartheid regime to a democratically elected regime. In this present world, with increase in the population, the need for energy is important. Understanding the relationship between energy, GDP and population is important to predict energy baseline. The use of artificial intelligence in energy studies is on the increase. Applying artificial intelligence to a system needs sufficient input and output data instead of mathematical equation [5]. The best approach to examine a country’s energy consumption is to measure the consumption based on the country’s population and GDP. This is because the country’s energy consumed is due to the growth of the nation, both economical and humanly. Olanrewaju et al. [6] have utilized ANN model for predicting the energy usage in the industrial sector of South Africa between 1993 and 2000. The study looked at energy consumption under economic activity, GDP. Their results signified intense conformity between ANN model prediction and observed values compared to linear regression model. The study of Sozen and Arcaklioglu [7] was to obtain equations based on economic indicators (gross national product – GNP and GDP) and population increase to predict the net energy consumption of Turkey using ANNs in order to determine future level of the energy consumption and make true investments in Turkey. Based on the outputs of the study, the ANN model can be used to estimate the net energy consumption from the country’s population and economic indicators with high confidence for planning future projections. Traditionally, regression analysis has been the most popular modeling technique in predicting net energy consumption [7]. But the importance of ANN approach;

KEY WORDS Energy consumption, gross domestic product, population, ANN.

1. Introduction The use of energy is critical to the economy, because almost all economic activities are connected either directly or indirectly to the consumption of energy [1]. Today, the world faces a great challenge for saving their future in terms of providing one of the most necessary requirements of humankind: energy [2]. As a nation, South Africa is no exception. An energy model to determine a nation’s energy baseline will assist future energy, especially energy planners, researchers and policy makers. It is worth noting that most previous studies are limited in scope to the applications of linear models [3]. However economic events and regime changes such as changes in economic environment, changes in energy policy and fluctuations in energy prices can cause structure changes in the pattern of energy consumption for a given time period under study [3]. This creates a room

DOI: 10.2316/P.2014.813-016

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an artificial intelligence, apart from reducing the time required, is that it is possible to make energy applications more viable and thus attractive to potential users, such as energy engineers [7]. The paper’s objective is to develop a forecast model dependent on ANN to model South Africa’s energy consumption between 2002 and 2009 based on GDP and population for energy planners and policymakers. One may judge a forecast successful if it (a) helps energy planners, (b) influence the energy policy community [8]. Wrong forecasts can lead to wrong decisions [9]. The inputs for the ANN used for this study are population and GDP, while energy consumed is the output. The influence of GDP and population on energy will also be determined as this will also assist in decision making.

2. Data Data employed were both from Statistics South Africa [10] and [11]. Table 1 presents the data for this study. Table 1 presents primary energy supply, excluding imports and electricity, including coal, crude oil, gas, hydro, nuclear, petroleum products, and renewable and waste. It should be noted that the decrease in population in the table below is due to author’s calculation which is the difference between birth-rate and death-rate within the periods of investigation.

Table 1: Data used for the study Year

GDP at 2005 constant price (R millions)

Population

Primary energy in Terajoules

2002 (Period 1)

1236270

1167622

8647126

2003 (Period 2)

1273129

1162612

8728384

2004 (Period 3)

1330390

1153924

7804789

2005 (Period 4)

1401067

1143062

7949201

2006 (Period 5)

1478492

1131306

7742673

2007 (Period 6)

1561076

1116931

7538066

2008 (Period 7)

1619738

1103281

6874635

2009 (Period 8)

1597860

1090567

6683347

3. Methodology

takes the form

y = a0 + a1 x1 + a2 x2 ....an xn

, and the

∧

The ANN method based on a multilayer perceptron model is employed for this study. The objective functional chosen for this problem is the mean square error (MSE) between the outputs from the neural network (observed energy consumption) and the target values (the predicted energy consumption). As the inputs are applied to the network, the network output is compared to the target. The architecture of this network consists of three layers namely the input, hidden and output layer, with each layer having one or more neurons, in addition to bias neurons connected to the hidden and output layers. The computational procedure of the network is given as:

Yi = f (∑ wij xij )

error

ei

is equal to

yi − yi , the variation between the a0 , a1 ,...an are the

actual and fitted values. Where

x1 , x2 ,...xn

regression coefficients and are the independent variables considered. Mean absolute percentage error (MAPE) and coefficient of correlation which are yardsticks of accuracy in a fitted series value in statistics were used for comparing the prediction performances of the models. MAPE usually expresses accuracy as a percentage

1 N MAPE = Ai

(1)

i

where Yj is the output of node j, ƒ(.) the transfer function, wij the connection weight between node j and node i in the lower layer and xi the input signal from the node i in the lower layer [12]. Comparing artificial network analyses to regression analyses; the regression equation

N

∑| i =1

Ai − Pi | X 100% Ai

where is the observed (Actual) value and predicted value.

133

(2)

Pi

is the

3.1 Network Design using MATLAB

With Imp (i) indicating the comparative significance of factor i; n representing hidden nodes’ number; x represents hidden node’s index number; CWih(x) signifies connectivity weight between input factor i and hidden node x; CWho(x) signifies weight between hidden node x and the output node. This section quantifies the driving factors, liable to the South Africa’s energy consumption between the periods of 2002 and 2009. Input 1 represents GDP and input 2 represents population.

Newff is a Matlab code which creates a feed-forward backpropagation network. This was used to calculate a precise function of the MLP neural network. The number of hidden neurons was determined by comparing the performance of different cross-validated networks, with 1 – 12 hidden neurons, and choosing the number that produced the greatest network performance. This resulted in a network with two input neurons (GDP and population), five hidden neurons and a single output neuron (primary energy consumption). The five hidden neurons process the inputs via connection weights and links the inputs to the output layer. In the analyses, network parameters of learning rate and momentum were set at 0.05 and 0.7, respectively. A variable learning rate with momentum (trainlm) as the network’s training function, and tansig as activation functions for all layers was used. The data used by the network must be scaled for the network to be effectual. In theory the inputs to the network can be any value. However, scaling values to the same order of magnitude (generally in the range 0 to 1 or -1 to 1) enables the network to learn relationships more quickly [13]. In this paper, the data were scaled to the range -1 to 1 to ensure a consistent scaling regime for input and output. Half of the data was used to train the network; those are for years 2002, 2004, 2006 and 2008. Data for the years 2003 and 2007 were used for testing and data for years 2005 and 2009 for validation. The Matlab code for the design is given in appendix section.

Table 2: Connection weight approach Hidden 1

Hidden 2

Hidden 3

Hidden 4

Hidden 5

Input 1

-2.8206

-0.6695

2.3620

1.7921

3.6704

Input 2

1.4634

-3.6151

2.4999

3.0804

0.6324

0.5581

-1.1889

X Output

0.6529

0.2133

-0.6170 =

Input 1

-1.84156

-0.1428

-1.45735

1.00017

-4.3637

Input 2

0.95545

-0.7711

-1.54243

1.71917

-0.7518

5

input x = ∑ Hidden

3.2 Regression Analysis using MATLAB

y =1

Matlab program was written for the regression analysis. The Matlab code is given at the appendix section. This leads to the following equation: y = -215.1524x105 + 0.154x105x1 + 25.6160x105x2

3.3 Determining the significance of the input factors The method for assessing and evaluating the variable components in the neural network in our investigation is the connection weight approach. The method adds the product of the weight of the connection from input neuron to the hidden neurons with the weight of the connection from the hidden neurons to the output neurons for all input parameters [14, 15]. As the sum of the connection weights gets larger, the more the significance of the parameter linked to the input neuron. Table 1 shows the greenhouse gas variables. The comparative significance of input factor i is estimated along the ensuing equation [15]: Imp (i) = ∑nx=1(CWih(x) CWho(x))

Significance

Rank

Input 1(GDP)

-6.8052

2

Input 2(Population)

-0.3907

1

4. Results and Discussions Computer codes for ANN-MLP model and regression were developed in Matlab Software (version 2010a). The MLP-model was trained until the best performance was achieved. In order to test and validate the model, a statistical test (the correlation coefficient R2) between the observed and the predicted primary energy consumption data using the MLP network was carried out. From the simulation carried out, it was found that better performance was delivered by the MLP-model according

(3)

134

to the correlation coefficient between both sets of data (observed and predicted). The obtained R2 is 0.9405, higher than the corresponding regression model of 0.9119, even though they are both good prediction models for the analyses. MAPE for the ANN-MLP model also confirmed its superiority to the regression analysis. MAPE for ANNMLP model is 0.0019, less than the regression of 0.0240. Regression analysis is a likely confirmation approach to ANN between the predicted and observed primary energy consumption values. The analysis should lead to a line y =a +bx with a correlation coefficient R2. A perfect prediction gives b = 1and R2 = 1.

90

E n e rg y C o n s u m p tio n

80

75

70

65 1

4

5

6

7

8

Figure 3: Regression analysis between the predicted and actual energy consumption.

6

5. Conclusion actual predicted

Examining a country’s energy consumption and the effects of its factors will help build a sustainable nation. As such, modeling plays a pivoted role in this regard. Establishing accurately the relationship between South Africa’s energy consumption, GDP and population; ANN model was employed, comparing it to its regression counterpart. The observed annual energy consumption and the predicted MLP-ANN energy consumption was validated using regression analysis. The result of the statistical measure: coefficient of correlation and MAPE suggest that ANN model provides accurate results than the traditional regression model. Another important outcome of the analyses suggests that behavioral policies should be promoted to help shape the country’s energy sector in a sustainable manner.

8.5 E n e r g y o n s u m p tio n

3

Figure 2: Comparison between actual and predicted energy consumption using regression analysis.

x 10

8

7.5

7

6.5 1

2

Periods

With the ANN conducted, it gives an appropriate prediction with b=1 and R2= 0.9990. It should be noted that b is 1 and R2 can be approximated to 1 respectively. Figures 1 and 2 demonstrate the prediction results of both models, while Figure 3 confirms the regression analysis on the ANN-MLP model for its validation. In our study, ANN model has been employed to predict South Africa’s primary energy consumption. This study gives a realistic result where energy is concerned because of the population factor considered as opposed to the study of Sozen, A. and E. Arcaklioglu (2007) where it’s only the GDP that was considered. Policy and decision making towards a country’s energy consumption requires awareness to the degree of significance of the comparative causal factors. With regard to the outcome of the ANN employed, the country’s population has more effect on the energy consumed in comparison to the country’s GDP. This result would give a clue to policymakers on behavioral policies that can assist to shape the country’s energy sector. 9

predicted actual

85

2

3

4

5

6

7

8

Periods

Figure 1: Comparison between actual and predicted energy consumption using MLP-ANN model.

135

sst=norm(t-mean(t))^2 ssr=sst-sse rsquared=ssr/sst net.iw{1,1} net.lw{2,1}

Appendix ANN Matlab code p= [1236270 1273129 1330390 1401067 1478492 1561076 1619738 1597860; 1167622 1162612 1153924 1143062 1131306 1116931 1103281 1090567]; t= [8647126 8728384 7804789 794201 7742673 7538066 6874635 6683347]; [pn,minp,maxp,tn,mint,maxt] = premnmx(p,t); iitst = 2:4:Q; iival = 4:4:Q; iitr = [1:4:Q 3:4:Q]; val.P = pn(:,iival); val.T = tn(:,iival); test.P = pn(:,iitst); test.T = tn(:,iitst); ptr =pn(:,iitr); ttr = tn(:,iitr); net = newff(minmax(ptr),[5 1],{'tansig' 'tansig'},'trainlm'); net.trainParam.show=50; net.trainParam.lr=0.05; net.trainParam.mc=0.7; [net,tr]=train(net,ptr,ttr,[],[],val,test); an=sim(net,pn); a = postmnmx(an,mint,maxt); error=(t-a) sse=norm(error)^2

Regression Matlab code y= [8647126 8728384 7804789 7949201 7742673 7538066 6874635 6683347]'; x1=[1236270 1273129 1330390 1561076 1619738 1597860]'; x2=[1167622 1162612 1153924 1116931 1103281 1090567]'; X=[ones(size(x1)) x1 x2]; a=X\y Y=X*a Err=(y-Y) sse=norm(Err)^2 sst=norm(y-mean(y))^2 ssr=sst-sse rsquared=ssr/sst

1401067

1478492

1143062

1131306

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