Energies 2011, 4, 1246-1257; doi:10.3390/en4081246 OPEN ACCESS energies ISSN 1996-1073 www.mdpi.com/journal/energies Aricle Forecasing Elecriciy Demand in Thailand wih an Arificial Neural Nework Approach Karin Kandananond Rajabha Universiy Valaya-Alongkorn, Paholyohin Rd., Klong-Luang Disric, Prahumhani 13180, Thailand; E-Mail: kandananond@homail.com; Tel.: +66-2-529-3829; Fax: +66-2-909-3036 Received: 3 May 2011; in revised form: 27 July 2011 / Acceped: 9 Augus 2011 / Published: 22 Augus 2011 Absrac: Demand planning for elecriciy consumpion is a key success facor for he developmen of any counries. However, his can only be achieved if he demand is forecased accuraely. In his research, differen forecasing mehods auoregressive inegraed moving average (ARIMA), arificial neural nework (ANN) and muliple linear regression (MLR) were uilized o formulae predicion models of he elecriciy demand in Thailand. The objecive was o compare he performance of hese hree approaches and he empirical daa used in his sudy was he hisorical daa regarding he elecriciy demand (populaion, gross domesic produc: GDP, sock index, revenue from exporing indusrial producs and elecriciy consumpion) in Thailand from 1986 o 2010. The resuls showed ha he ANN model reduced he mean absolue percenage error (MAPE) o 0.996%, while hose of ARIMA and MLR were 2.80981 and 3.2604527%, respecively. Based on hese error measures, he resuls indicaed ha he ANN approach ouperformed he ARIMA and MLR mehods in his scenario. However, he paired es indicaed ha here was no significan difference among hese mehods a α = 0.05. According o he principle of parsimony, he ARIMA and MLR models migh be preferable o he ANN one because of heir simple srucure and compeiive performance Keywords: arificial neural nework (ANN); auoregressive inegraed moving average (ARIMA); elecriciy demand; muliple linear regression (MLR)
Energies 2011, 4 1247 1. Inroducion Elecric energy is a significan driving force for economic developmen, while he accuracy of demand forecass is an imporan facor leading o he success of efficiency planning. For his reason, energy analyss need a guideline o beer choose he mos appropriae forecasing echniques in order o provide accurae forecass of elecriciy consumpion rends. The oucome of he sudy migh be used by he appropriae naional agency in Thailand (e.g., Energy Policy and Planning Office (EPPO), Minisry of Energy) as a means o develop energy policies as well as measures on energy conservaion and alernaive energy. However, here are many echniques ha conribue o he predicion of fuure elecriciy demand. In his sudy, differen forecasing echniques were uilized o forecas he elecriciy consumpion in Thailand and a comparison of hese echniques was conduced o choose he bes approach in his siuaion. The deerminaion of an appropriae forecasing model was based on hisorical daa, while he error crieria such as mean squared error (MSE) and mean absolue percenage error (MAPE) were uilized as measures o jusify he appropriae model. In addiion o minimizing he errors, one of he mos imporan condiions was ha he residual from he forecasing model had o saisfy all he assumpions or pass he model adequacy checking (normally and independenly disribued: NID). According o he lieraure, mos forecasing models were deermined from hree popular mehods, i.e., auoregressive inegraed moving average (ARIMA), arificial neural nework (ANN) and muliple linear regression (MLR) model. For ime series analysis, he auoregressive inegraed moving average (ARIMA) model is a sochasic difference equaion ha is frequenly uilized o model sochasic disurbances [1]. Some specific forms of he ARIMA model were uilized o represen auocorrelaed disurbances, e.g., auoregressive order one, ARIMA (1,0,0) or AR (1) for saionary disurbances, while an inegraed moving average, ARIMA (0,1,1) or IMA (1,1) are used o represen non-saionary disurbances, as recommended by Mongomery, Keas, Runger and Messina [2] and Box and Luceno [3]. Ediger and Akar [4] uilized boh he ARIMA and seasonal ARIMA (SARIMA) models o esimae he fuure primary energy demand of Turkey from 2005 o 2020. The ARIMA mehod was also deployed by Abdel-Aal and Al-Garni [5] o forecas monhly domesic elecric energy consumpion in he easern province of Saudi Arabia and he opimum model in his case was he firs ordered ARIMA wih a muliplicaive combinaion of seasonal and non-seasonal auoregressive pars. Zhou, Ang and Poh [6] improved he accuracy of elecriciy demand predicions by combining he radiional grey model GM (1,1) wih he rigonomeric residual modificaion echnique. Addiionally, Cho, Hwang and Chen [7] compared he resuls of he univariae ARIMA and he radiional regression models o forecas he shor-erm load by considering weaher-load relaionships. Anoher forecasing approach was he uilizaion of he ANN mehod o derive a predicion model. The developmen of ANN models was based on sudying he relaionship beween inpu variables and oupu variables. For applicaion in forecasing, Hsu and Chen [8] assessed he performance of ANN approach (based on hree inpus, i.e., GDP, populaion and emperaure) o forecas he regional peak load in Taiwan. The hisorical daa was he annual power load in each region from 1981 o 2000 and he performance of ANN mehod was compared wih he regression mehod. The sudy showed ha he error of ANN model was significanly lower han ha of he regression model. Moreover, Caalao, Mariano, Mendes and Ferreira [9] successfully applied he ANN for forecasing nex-week prices in
Energies 2011, 4 1248 he elecriciy marke of Spain and Sae of California shor-erm elecriciy prices. The hourly price daa of 42 days prior o he week whose prices were forecased was used as he hisorical daa. The error crierion (MAPE) of he ANN model was compared wih he one from ARIMA model and he resuls indicaed ha he ANN ouperformed he ARIMA model. Similarly, Bakirzis, Peridis, Klarzis and Alexladis [10] developed an arificial neural nework o forecas daily loads wih a lead ime of one o seven days. The seasonaliy effec from high energy usage on holidays was included in he model by uilizing he seasonal raining (raining he ANN wih he hisorical holiday daa). The muliple linear regression mehod is sill an ineresing forecasing opion because of is simpliciy. Mohamed and Bodger [11] used a muliple linear regression model o forecas he elecriciy consumpion of New Zealand where he independen variables were gross domesic produc (GDP), elecriciy price and populaion. The geneic algorihm (GA) was inegraed wih an ANN in he sudy of Azadeh, Ghaderi, Tavedian and Saberi [12] o forecas he monhly elecriciy demand in Iran. The esimaed errors (MAPE) were used as he measure of errors, while he resuls showed ha he MAPE of he proposed mehod was less han hose of regression and ime series models. Moreover, Azadeh, Ghaderi and Sohrabkhani [13] also assessed he performance of an ANN model o forecas monhly elecriciy consumpion by uilizing analysis of variance (ANOVA). Four reamens of he experimen were: acual daa, ime series, ANN and simulaion-based ANN. According o he empirical sudy, ANN was superior o he ime series and simulaion-based ANN. Hong [14] suggesed he uilizaion of a suppor vecor model (SVM) as an alernaive o an ANN for forecasing elecric consumpion. According o he empirical sudy, he performance of SVM was superior o oher mehods, regression and ANN models. Ekonomou [15] compared he abiliy o predic he Greek-long erm energy consumpion of hese hree mehods: ANN, regression and SVM. The resuls indicaed ha boh ANN and SVM were able o forecas he consumpion wih grea accuracy. Pappas, Ekonomou, Karamousanas, Chazarakis, Kasikas and Liasis [16] inroduced he uilizaion of radiional mehodology, i.e., an ARIMA model, o predic he elecriciy demand. Differen ARIMA models were seleced and he crieria (Akaike Informaion Crierion: AIC and Bayesian Informaion Crierion: BIC) were uilized o jusify he mos appropriae one. Since here are no empirical or exac rules o derive he bes forecasing model, he mos appropriae one was seleced by choosing he model wih he lowes error. Mosly, he error margins of he candidae forecasing mehods were slighly differen. Moreover, a handful of works have conribued o compare wheher here was a significan difference beween he errors from each mehod. In his research, he performance of ANN approach and he radiional mehods, i.e., ARIMA and MLR, was assessed and compared using a se of daa regarding he oal elecriciy consumpion in Thailand from 1986 o 2010. For MLR, some criical facors such as he amoun of expors and sock index which significanly affeced he consumpion were included in he forecasing model. The error (MAPE) from each mehod was calculaed and used o rank he op performer, followed by he runner-ups. Aferwards, he Wilcoxson sign rank es and paired -es were uilized o compare he errors from each pair of mehods.
Energies 2011, 4 1249 2. Hisorical Daa Elecriciy consumpion (GWh) is influenced by many facors: populaion, gross domesic produc (GDP), sock index (SET index) and oal revenue from exporing indusrial producs (expor). The hisorical daa se regarding hese facors was colleced annually from 1986 o 2010 and is shown in Table 1. I was uilized as a basis o deermine a forecasing model for fuure elecriciy demand. Table 1. Energy Daa of Thailand from 1986 o 2010. Year Populaion GDP SET Index Expor (million bah) Elecriciy Consumpion (GWh) 1986 52511000 1257177 207.2 364017.25 10162.7 1987 53427000 1376847 284.94 455991.43 11319.4 1988 54326000 1559804 386.73 462426.83 11942.38 1989 55214000 1749952 879.19 562426.76 14328.1 1990 55839000 1945372 612.86 683946.13 16717.23 1991 56574000 2111862 711.36 725448.79 19406.02 1992 57294000 2282572 893.42 824643.29 21641.01 1993 58010000 2470908 1682.85 940862.59 24321.28 1994 58713000 2692973 1360.09 1137601.65 27758.43 1995 59401000 2941736 1280.81 1153489 31870.37 1996 60003000 3115338 831.57 1153894.61 34607.29 1997 60602000 3072615 372.69 1492331.29 36981.24 1998 61201000 2749684 355.81 1854500.09 35154.99 1999 61806000 2871980 481.92 1871544.78 36275.13 2000 62236000 3008401 269.19 2378191.26 39546.26 2001 62836000 3073601 303.85 2454987.54 41658.51 2002 63419000 3237042 356.48 2506442.96 44805.66 2003 63982000 3468166 772.15 2857191.85 48293.79 2004 64531000 3688189 668.1 3361360.69 50810.54 2005 65099000 3858019 713.73 3897247.1 53894.12 2006 65574000 4054504 679.84 4305406.71 56994.75 2007 66041000 4259026 858.1 4691207.01 59436.12 2008 66482000 4364833 449.96 5149902.76 60266.29 2009 66903000 4263139 734.54 4619810.05 59401.92 2010 67209942.8 4595809 1032.76 5476766.65 60315.04 Source: Bank of Thailand, Deparmen of Expor Promoion, Energy Policy and Planning Office (EPPO) and Sock Exchange of Thailand. 3. Daa Analysis The daa analysis was performed using hree mehodologies, ARIMA, ANN and MLR.
Energies 2011, 4 1250 3.1. ARIMA Model The general form of he ARIMA model is shown in Equaion (1): Δ dy = μ + φ Δ Y + φ Δ Y +... + φ Δ Y + a θ a 1... θ a 1 d 1 2 d 2 p d p 1 q q (1) The order of an ARIMA model is normally idenified in he form of (p, d, q), where p indicaes he order of he auoregressive par, while d is for he amoun of difference and q for he order of he moving average par. The elecriciy demand ime series was ploed in Figure 1 in order o sudy he daa srucure before deermining he appropriae ARIMA model. The plo showed ha here was a consan growh rae of rend as ime increased. However, no seasonaliy migh exis in his case since here was no repeaed paern over ime. Therefore, his se of daa was no saionary and had a rend. Figure 1. Time series plo of elecriciy demand. 60000 Time Series Plo of GWh 50000 40000 GWh 30000 20000 10000 2 4 6 8 10 12 14 Index 16 18 20 22 24 The concree assumpion of non-saionary daa was suppored by considering he correlogram of he demand (Figure 2) and i signified ha he daa was highly correlaed a lag 1 and 2. Figure 2. Correlogram of elecriciy demand. Auocorrelaion Funcion for GWh (wih 5% significance limis for he auocorrelaions) Auocorrelaion 1.0 0.8 0.6 0.4 0.2 0.0-0.2-0.4-0.6-0.8-1.0 1 2 3 Lag 4 5 6
Energies 2011, 4 1251 Therefore, since he correlaion was embedded in he daa, he ARIMA model was an ineresing choice uilized o explain he daa srucure. A saisical package, SaGraphics Cenurion version 14, was deployed o deermine an ARIMA model and four differen models were seleced by he package based on heir MAPEs (Table 2). The resuls indicaed ha he mos appropriae ARIMA model o forecas he demand was ARIMA (0,2,2). Equaion (1) was rewrien as: Table 2. Four differen ARIMA models. Model MAPE ARIMA (0,2,2) 2.80981 ARIMA (1,2,1) 3.02891 ARIMA (1,1,0) 3.34578 ARIMA (0,2,0) 3.30197 φ ( = θ a where d B )(1 B) X ( B) p φ ( B) = 1+ φ1 B +... + φ pb and q θ ( B) = 1 θ1 B... θq B. Le β 1 = ( φ1,..., φ p, θ1,..., θq ). The amoun of p and q as well as β 1 in he ARIMA (p, 0, q) model: φ ( B ) X = θ ( B) b were calculaed by a Box Jenkins mehod and AIC crierion d p where b = ( 1 B) a. Aferwards, le ˆ q φ = 1+ φ1 B +... + φ p B, ˆ( θ B) = 1 ˆ θ B... ˆ 1 θqb and Z { ˆ( B)} 1 d = θ ˆ( φ B) Y, he parameer of ARIMA (0,d,0) model: ( 1 B ) Z = a was esimaed by n 1 1 1 applying he log Gaussian likelihood funcion as: l( d ) = ln 2π ln R Z R Z where 2 2 2 R = Covariance marix of Z ( Z 1,..., Z ). The ARIMA (0,2,2) model coefficiens are given in Table 3. = Table 3. Coefficiens of ARIMA (0,2,2). Parameer Esimae MA(1) 0.434155 MA(2) 0.488944 Afer he model was derived, he correlogram in Figure 3 was used o verify wheher he residual was correlaed or no. According o he correlogram, he correlaions of each lag were no significan because hey were sill in he confidence inerval. Figure 3. Correlogram of he residual. 1.6 Auocorrelaions.2 -.2 -.6-1 2 4 6 8 lag
Energies 2011, 4 1252 3.2. Arificial Neural Nework Basically, he neural archiecure consiss of hree or more layers i.e., inpu layer, oupu layer and hidden layer, as shown in Figure 4. Figure 4. The archiecure of a neural nework. The funcion of his nework was described as follows: Y j = f ( i wij X ij ) (2) where Y j is he oupu of node j, f (.) is he ransfer funcion, w ij he connecion weigh beween node j and node i in he lower layer and X ij is he inpu signal from he node i in he lower layer o node j. As shown in Equaion (2), he nework was a biased weighed sum of he inpus and passed he acivaion level hrough a ransfer funcion o produce he oupu. The unis of a nework were arranged in he form of layered feedforward srucure. In conclusion, any neural nework was inerpreed as a form of inpu-oupu model wih he weighs and free parameers of he model. For daa analysis, he same se of daa was divided ino 25 cases wih four inpu variables: populaion, SET index, GDP and Expor, while he oupu variable was GWh. Two of he mos popular neural nework archiecures, mulilayer perceprons (MLP) and radial basis funcion (RBF), were uilized for he regression purpose. Normally, he ANN srucure is based on he MLP archiecure in which he number of layers and number of unis in each layer are seleced while he weighs of neworks and hresholds are se so as o minimize he predicion error. For RBF, is neworks have a saic Gaussian funcion as he nonlineariy for he hidden layer elemens. The advanage of he RBF nework was ha i esablishes he inpu o oupu map using local approximaors which require few weighs. For his reason, he neworks were rained exremely fas and required fewer raining samples. In his research, he amoun of neworks used o rain was se a 200 while he op performing five neworks were reained and shown in Table 4. STATISTICA version 8 was deployed o analyze he daa and he resuls are illusraed in Figure 5. The resuls poined ou ha he MLP nework ouperformed RBF when he number of hidden layers ranged from 5 o 10. The hidden neuron
Energies 2011, 4 1253 acivaion funcions of he reained five neworks were ideniy (he acivaion of he neuron was passed on direcly as he oupu), Gaussian, Exponenial and Logisic while he angen hyperbolic (anh) and ideniy funcions were assigned o he oupu neuron acivaion funcions. Moreover, he raining algorihm of he MLP nework employed o build he models was he Broyden-Flecher-Goldfarb-Shanno (BFGS) algorihm wih he number of cycles used o rain he model ranging from 11 o 116 cycles. According o he MAPE in Table 4, MLP (4,6,1) model had he lowes error among all oher models. Table 4. Differen neural neworks and heir MAPEs. Model MAPE MLP (4,10,1) 2.770 RBF (4,6,1) 3.033 MLP (4,8,1) 2.598 MLP (4,6,1) 0.996 MLP (4,5,1) 3.2938 Figure 5. The ANN analysis resuls. Due o Figure 6, he plo beween errors and fied values showed ha he daa was randomly scaered along he cener line and here was no developed paern like a funnel shape so he residual was uncorrelaed wih zero mean and consan variance. Figure 6. Residuals vs. fied plo. GWh (Residuals) 4000 3500 3000 2500 2000 1500 1000 500 0-500 -1000-1500 -2000-2500 -3000-3500 -4000-4500 -5000 5000 10000 15000 Samples: T rain, Tes 20000 25000 30000 35000 40000 45000 50000 GWh (Oupu) 55000 60000 65000 70000 1.MLP 4-10-1 2.RBF 4-6-1 3.MLP 4-8-1 4.MLP 4-6-1 5.MLP 4-5-1
Energies 2011, 4 1254 3.3. Muliple Linear Regression The general form of a muliple regression model was shown as follows: yi = β 0 + β1 + β2x2i +... + βk + εi (3) where y i is he dependen variable, x.i is he independen variable, β i is he regression coefficien of x.i and ε i is he random error. In order o consruc he regression model, he independen variables (x.i ) were populaion, SET index, GDP and Expor, while he dependen variable (y i ) was GWh. In order o esimae he coefficiens of he model, he prediced response was shown in Equaion (4): y ˆ i = b + b1 + b2 x 2 i +... + bk The residuals beween he observed and prediced responses were: 0 (4) i = yi y ˆ i = yi b0 b1 b2 x 2 i... bk ε (5) The sum square of residuals (SSE) was: 2 SSE = ( yi b0 b1 b2 x2i... bk ) i (6) Then, aking he parial derivaive of SSE wih respec o each b i and le i equal o zero. This yielded Equaion (7): b0 b0 b0n + + b1 + b1 b1 x1 + b 2 i + b2 2 +... + bk 1 x k x2i +... + bk ki = yi x2i +... + b = yi (7) xk 1, i + bk 2 = yi n is he number of pairs (x 1, y 1 ),, (x n, y n ). The coefficiens b 0, b1, b2,..., bk were obained by solving Equaion (7). As a resul, he regression equaion was compued as follows: GWh = 91411 + 0.00170 populaion + 0.00794 GDP 2.57 SET Index + 0.00114 Expor Figure 7. The normal probabiliy plo of residuals. 2.5 Normal Probabiliy Plo of Residuals 2.0 1.5 Expeced Normal Value 1.0 0.5 0.0-0.5-1.0-1.5-2.0-2.5-3000 -2000-1000 0 1000 2000 3000 Residuals
Energies 2011, 4 1255 Afer he regression equaion was derived, he model adequacy checking was performed. The normal probabiliy plo in Figure 7 shows ha he daa poins randomly formed a sraigh line so he errors were normally disribued. Afer he model was fied o he daa, he calculaed error (MAPE) was 3.2604527. 4. Resuls The errors from he above hree mehods are compared in Table 5. The resuls showed ha he error minimizaion capabiliy of he ANN model (0.996%) ouperformed he oher wo approaches (2.80981% and 3.2604527%, respecively). However, he performance of ANN model was compared wih hose of he ARIMA and MLR models by uilizing wo dependen samples ess. Therefore, he Wilcoxson signed-rank es and paired -es were performed o assess he significan difference of he errors from hese pairs: ANN:MLR and ANN:ARIMA. Table 5. The comparison of errors from he hree mehods. Model MAPE ARIMA (0,2,2) 2.80981 MLP (4,6,1) 0.996 MLR 3.2604527 The resuls of he Wilcoxson signed-rank es in Table 6 showed ha here was no significan difference beween he errors of ANN-MLR and ANN-ARIMA since heir p-values (0.819095 and 0.784289 respecively) were much higher han 0.05. Due o Table 7, he paired -es indicaed he same resuls as he ones from signed-rank es. Table 6. Wilcoxson signed-rank es for each pair of forecasing mehods. Pairs of Mehods p-value ANN-MLR 0.819095 ANN-ARIMA 0.784289 Table 7. Paired -es for each pair of forecasing mehods. Pairs of Mehods p-value ANN-MLR 0.785697 ANN-ARIMA 0.927594 5. Discussion Alhough he arificial neural nework has he bes performance in his sudy (considering is MAPE solely), he mached pair ess did no indicae ha here is a difference beween he errors of each mehod. For his reason, he boom line is ha he decision should no depend on only one crierion o judge which mehod is he mos appropriae one in each scenario. The criical issue in developing an ANN model is ha is compuaion ime is much higher han he oher wo because of is sophisicaed archiecure.
Energies 2011, 4 1256 Moreover, is accuracy migh be jeopardized from overfiing because of he limied number of available raining cases. Anoher imporan issue is ha i is quie difficul for praciioners o uilize and inerpre an ANN model. On he oher hand, he grea advanage of using he ARIMA model is ha i only needs he informaion regarding one variable o build a model. However, i will ake ime o choose he opimal coefficiens, especially if he saisical package used lacks he capabiliy of searching for he righ coefficien. For MLR, alhough is accuracy is he lowes among all proposed mehods, he algorihm is he simples one. Addiionally, i uses less calculaion ime o generae he regression model han he oher wo mehods. As a resul, users need o evaluae he rade-off beween forecasing accuracy and limiaion of he mehod before swiching from radiional mehods o ANN. This is an ineresing issue since he imporan aspec of he forecasing is he principle of parsimony. If all models are equal, simple models will be preferred o complex models. For his reason, boh ARIMA and MLR migh be preferred o he ANN model since he srucure of boh mehods is simpler han he one of ANN. 6. Conclusions Three mehodologies, ARIMA, ANN and MLR, were deployed o forecas he elecriciy demand in Thailand based on he hisorical daa from 1986 o 2010. For he ARIMA approach, he resuls indicaed ha he ARIMA (0,2,2) was he bes model o fi he hisorical daa while he mulilayer perceprons (MLP) mehod was seleced o use as he archiecure for he ANN model. Four facors, i.e., amoun of populaion, sock exchange index, GDP and amoun of expor were uilized o consruc a MLR model. Alhough he resuls based on he error measuremen showed ha ANN model was superior o oher approaches, paired ess poined ou ha here was no significan difference among hese errors. As a resul, oher facors should be uilized o deermine he mos appropriae model. References 1. Box, G.E.P.; Jenkins, G.M. Time Series Analysis: Forecasing and Conrol; Holden-Day: San Francisco, CA, USA, 1970; pp. 5 10. 2. Mongomery, D.C.; Keas, J.B.; Runger, G.C.; Messina, W.S. Inegraing saisical process conrol and engineering process conrol. J. Qual. Technol. 1994, 26, 79 87. 3. Box, G.E.P.; Luceno, A. Saisical Conrol by Monioring and Feedback Adjusmen; John Wiley & Sons: New York, NY, USA, 1997. 4. Ediger, V.S.; Akar, S. ARIMA forecasing of primary energy demand by fuel in Turkey. Energy Policy 2007, 35, 1701 1708. 5. Abdel-Aal, R.E.; Al-Garni, A.Z. Forecasing monhly elecric energy consumpion in easern saudi arabia using univariae ime-series analysis. Energy 1997, 22, 1059 1069. 6. Zhou, P.; Ang, B.W.; Poh, K.L. A rigonomery grey predicion approach o forecasing elecriciy demand. Energy 2006, 31, 2839 2847. 7. Cho, M.Y.; Hwang, J.C.; Chen, C.S. Cusomer Shor Term Load Forecasing by Using ARIMA Transfer Funcion Model. In Proceedings of he Inernaional Conference on Energy Managemen and Power Delivery, EMPD 95, Singapore, 20 23 November 1995; pp. 317 322.
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