A Meta-Heuristics Based Input Variable Selection Technique for Hybrid Electrical Energy Demand Prediction Models

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1 A Mea-Heurisics Based Inpu Variable Selecion Technique for Hybrid Elecrical Energy Demand Predicion Models Badar ul Islam Perumal allagownden Zuhairi Baharudin Masood Rehman Absrac Elecrical energy demand forecasing plays a pivoal role as a decision suppor ool in he modern power indusry. The focus of he paper is o propose a hybrid approach for he selecion of he mos influenial inpu variables for he raining and esing of neural nework based hybrid models. The combined influence of he geneic algorihm and correlaion analysis are used in his echnique. The significance of he seleced inpu variable vecors is sudied o analyze heir effecs on he predicion process. Anoher objecive of he sudy is o develop and compare he predicion models for elecrical energy demand of one day-ahead. These models are developed by inegraing mulilayer percepron neural nework and evoluionary opimizaion echniques. Geneic algorihm and simulaed annealing echniques are used o opimize he conrol parameers of he neural nework. The resuls show ha he neural nework opimized wih geneic algorihm and rained wih an opimally and inelligenly seleced inpu vecor conaining hisorical load and meeorological variables produced he bes predicion accuracy. Keywords - arificial neural nework; mean absolue percenage error; geneic algorihm; simulaed annealing; correlaion analysis I. ITRODUCTIO Elecrical energy demand forecasing is indispensible for he cos effecive, secure and reliable operaion of he power sysems [1, ]. Shor erm load forecas (STLF) of one dayahead faciliaes muliple power sysem operaions, for insance, scheduling of fuel purchase, mainenance of equipmen, adjusmen of ariff and conrac assessmens []. Arificial neural nework (A) is an arificial inelligence based echnique, which provides much beer performance as compared o previously implemened mehod for STLF [3]. This is because of he powerful capabiliy of A o map and memorize he non-linear relaions beween he inpu and he oupu variables during he raining process. The performance of A based models depends upon many facors, such as, neural nework archiecure, ype of raining algorihm, selecion of inpu variables and iniial values of economic variables using hi and rial mehods for heir selecion [8-10]. However some researchers implemened compuaional inelligence in he daa selecion process [11, 1]. In his paper, he imporan issues relaed o he bes inpu variable selecion for A based STLF models are synapic weighs [4]. Among he ohers, he selecion of mos influenial inpu variables and choice of raining echnique have a criical impac on he forecas resuls. Many evoluionary search echniques have been implemened o opimize he raining inpu vecors and conrol parameer of he neural neworks for STLF applicaion. Mos of hese effors emphasize on he correlaion analysis of he daa, however some of he researchers also focused on he combinaion of mahemaical formulaion o resor he derived variables by squaring, averaging, adding or differencing he daa sequences o deermine he suiable inpu variables [5, 6]. Because of heir linear and inconsisen approach, hese mehods are unable o rack he unusual and brisk variaions occurring in he real ime inpu daa, [7]. Many inpu variables have been used for he A based STLF, such as a hisorical load, meeorological variables and addressed. A new echnique is proposed ha inegraes he geneic algorihm (GA) and correlaion coefficien mehods o esablish he supremacy of he cerain inpu variables over he ohers. The opimally seleced inpu variable vecors (IVs) are used o rain he A based hybrid models using GA and simulaed annealing (SA). The analysis of he resuls DOI /IJSSST.a ISS: x online, prin

2 show ha hybrid model based on A and GA rained wih he opimally seleced IV which conains load and merological variables produced beer forecas accuracy as compared o oher IVs. II. DATA AALYSIS AD PRE-PROCESSIG The hisorical daa of he Sae of Vicoria and ew Souh Wales of Ausralia are used in he experimenaion. A comprehensive correlaion analysis is conduced o sudy he maximum relevance of he inpu variables wih load demand [7]. The resuls of he analysis are shown in Table I. All he inpu variables are normalized/scaled beween 0 and 1, before applying hem o he models [13]. TABLE I. CORRELATIO AALYSIS RESULTS Inpu Variables Correlaion Same ime in he previous day load L(h-4) Same day and ime in previous week load L(h-168) Same ime, wo days earlier load L(h-48) 0.80 Same day, wo hours earlier load L(H-) Same ime, previous day emperaure T(h-4) Same ime, previous week emperaure T(h-168) III. RESEARCH METHODOLOGY The framework of he research aciviies are menioned in he following seps. Apply a hybrid scheme based on he GA and correlaion mehod for he selecion of mos appropriae inpu variables for he raining of simulaion models. The hybrid muli-layer percepron (MLP) models are developed and validaed, where he iniial parameers are opimized by GA and SA for one day ahead elecrical energy demand predicion using he seleced inpu variables. Compare he forecass and acual energy demand of he opimized models wih and wihou using opimally seleced IVs. A. Selecion of forecas model inpus The firs sep in he developmen of he GA is o define a chromosome. A fixed lengh chromosome equal o 8 is implemened in he design. The value of each genome in he defined chromosome is he index of inpu variables. These chromosomes correspond o he possible soluions in he selecion process. Once he individual chromosome is defined, an iniial populaion S conaining n number of chromosomes are generaed. The finess funcion is developed ha maximizes he correlaion coefficien and minimizes he mean square error (MSE) beween acual and forecas load. The defined finess funcion is called (mxrmne), maximum correlaion value and minimum error (see equaion. 3). Mean square error (equaion. ) is used as a performance index in his case. The roulee wheel selecion mehod wih a single poin crossover and mulipoin muaion is implemened in his echnique. The muaion operaor is defined as given in equaion 4. This operaor complemens he values in he genome o avoid from he local minima [14]. In he firs sep of his geneic-based algorihm, he chromosome lengh and index of inpu variables are defined. Real coded GA is implemened wih a fixed lengh chromosome i.e. 8 and he value of each genome in a paricular chromosome is he index of he inpu variable. In he second sep, he GA is used for he selecions of he final daa se on he basis of defined finess funcion. The crossover and muaion raes are seleced as 0.8 and 0.1 respecively. The process flow diagram of he proposed mehod is shown in Fig. 1. mu Q, k,qk K Q (1) k () err (A P ) 1 1 max R, min err Q, p x, p.r(x ) i Q xi Q (A P) (3) i ò R finness funcion (4) 1 err where, Q is a subse of inpu variables, R is he correlaion value and p is arge class of he predicion variable. A and P are he acual and prediced load values. Whereas, k is muaion poin and K is he lengh of inpu dimension. A se of inpu variables is iniially generaed conaining hisorical load of differen ime inervals, meeorological variables and dae/ime indicaors. The se is hen splied ino wo subses conaining hisorical load relaed variables and meeorological variables respecievely. The proposed selecion process in implemened on he original se and he subses. Consequenly, hree opimally seleced inpu variable vecors IV1, IV and IV3 are reurned, conaining combinaion of load and meerological variables, load relaed variables and meeorological variables, respecievly. The opimized inpu variable vecor IV1 is composed of; day and ime indicaors; dry bulb emperaure of he same ime in he previous day T(w, d, h), dew poin of he same ime in he previous day D(w,d-1,h), elecrical load of he same ime in he previous day L(w, d-1, h), load of same day and ime in he previous week L(w-1, d, h), load of he previous day minus one hours L (w, d, h-1) and load of he previous day minus wo hours L (w, d, h-). B. Developmen of opimized models As menioned previously, he performance of MLP neural nework models depends on is free parameers, and choice of he raining algorihm. The opimizaion algorihms including GA and SA are developed o une he crucial parameers of he nework via minimizing raining errors and DOI /IJSSST.a ISS: x online, prin

3 validaion errors. In his paper, we choose back-propagaion (BP) as a raining algorihm. In his process an iniial populaion (p) of 30 chromosomes is creaed and he number of ieraions (ier) is se o 100. The finess funcion is defined which is he minimum mean square error (MSE) beween he acual and forecas values of MLP. The MLP is rained and esed for he raining daa and MSE and finess [f(p(ier)] is calculaed for he curren ieraion. The GA operaors crossover and muaion are applied on he seleced pairs in he populaion and a new populaion is generaed and esed on he basis of he finess funcion in he nex ieraion (ier=ier+1). The eliism mehod of selecion is used wih he crossover and muaion rae of 0.8 and 0.1 respecively. error. In his way, he forecas error is periodically reduced afer every ieraion. The iniial values of he criical conrol parameers for GA and SA are summarized in Table II. TABLE II. IITIAL PARAMETERS OF EMPLOYED OPTIMIZATIO ALGORITHMS GA Parameers SA Parameers Populaion size 30 Populaion size 30 Crossover rae 0.8 Minimum Temperaure 0.00 Muaion rae 0.1 Maximum Temperaure umber of ieraions 100 Sep size (ΔT) 0.98 ormal disribuion (σ) 0.5 C. Performance Analysis To analyze he performance and accuracy of hybrid predicion models on he basis of IV1, IV and IV3, roo mean square error (RMSE), mean absolue percenage error (MAPE), mean square error (MSE) and mean absolue error (MAE) are used. These performance evaluaion measures can be compued as follows: 1 RMSE ( A P ) 1 1 A P MAPE 100% A (5) (6) 1 1 ( ) (7) 1 1 (8) 1 MSE A P MAE A P Figure 1. Flow diagram for inpu variable selecion echnique. The opimizaion process of he simulaed annealing algorihm sars wih generaing an iniial soluion (rank marix) R aken as he curren saring soluion. Then a neighbor (rank marix) R* of (rank marix) R is generaed and he difference Δ=F(R * ) F(R) in he objecive funcion values of boh schedules is calculaed. If Δ < 0, he neighbor R* is acceped as he new saring soluion in he nex ieraion since i has a beer funcion value. If he objecive funcion value does no decrease (i.e. Δ 0), he generaed neighbor may also be acceped wih a probabiliy exp( Δ/E), where E is a conrol parameer called where, A and P are he acual and prediced values a ime poin. The MAPE is considered as a benchmark performance index due o is sable performance ha resolves he inconsisency problem in he predicion resuls [10]. IV. RESULTS AD DISCUSSIO The hybrid models are applied o predic he elecrical energy demand. As he predicion ime horizon is one dayahead (wih 30 minue inerval), so he oal numbers of observaions would be fory-eigh. The opimally seleced inpu variable vecors IV1, IV and IV3 are used for he raining and esing of he hybrid models. The predicion resuls of he opimized hybrid models MLP-GA and MLP-SA are compared on he basis DOI /IJSSST.a ISS: x online, prin

4 of MSE, MAE, MAPE and RMSE. These resuls are depiced in Fig., Fig. 3 and Table III. The hybrid model based on GA has shown beer performance as compared o he SA based model for one day-ahead load demand forecass. The bes forecasing performance is observed by using he hisorical load and weaher variables relaed inpu vecor IV1. The MAPE using IV1 for MPL-GA and MLP-SA are observed 1.75% and 1.91%, respecively. TABLE III. Forecas Techniques MLP-GA OE DAY-AHEAD FORECAST RESULTS OF OPTIMIZED MODELS BASED O IPUT VECTORS Opimized inpu variable Performance Index vecors MAE MSE MAPE RMSE Load & Weaher (IV1) Load Relaed (IV) Weaher Relaed (IV3) MLP-SA Load & Weaher (IV1) Load Relaed (IV) Weaher Relaed (IV3) The comparaive analysis of MLP-GA wih ha of he MLP-SA reveals ha, he GA par has improved performance han he SA par. Figure. One day-ahead forecas resuls based on IV1 o IV3 for MLP-GA Figure 3. One day-ahead forecas resuls based on IV1 o IV3 for MLP-SA model. The improved percenage of he MAPE from IV1 o IV3 is observed as; 0.6%, 0.4% and 0.03%, respecively. On he oher hand, IV3 generaed high forecas error because of he weak correlaion of he meeorological inpu variables wih he load demand. The use of load relaed variables (IV) produced reasonable accuracy which is slighly lesser ha he resuls shown by implemening IV1. V. COCLUSIO This paper proposed a hybrid mehod o idenify and selec he bes inpu variables for A based forecas models. In his echnique, he combined effec of minimum MSE and maximum value of correlaion coefficien are used o develop a finess funcion of GA for he selecion of mos influenial IV in STLF. In his way, hree inpu vecors, including, load relaed (IV3), merological relaed (IV) and a combined vecor of hese wo ypes of variables (IV1) are seleced. These opimally seleced inpu vecors are deployed in he raining and esing processes of MLP- GA and MLP-SA models and he resuls are analysed. These resuls show ha he performance of opimized MLP model wih GA using IV1 ouperformed all oher models and inpu vecors used in his research. The obained resuls show ha he research has provided a suiable echnique for he selecion of bes inpu variables for he A based hybrid load demand predicion models. ACKOWLEDGMET The auhors would like o hank and appreciae he suppor of Universiy Technology PETROAS for providing he funding under he gran number (URIF 0153AA-B13) o conduc his research. DOI /IJSSST.a ISS: x online, prin

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