Electricity Price Forecasting using Asymmetric Fuzzy Neural Network Systems Alshejari, A. and Kodogiannis, Vassilis

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1 WestmnsterResearch Electrcty Prce Forecastng usng Asymmetrc Fuzzy Neural Network Systems Alshejar, A. and Kodoganns, Vassls Ths s a copy of the author s accepted verson of a paper subsequently to be publshed n the proceedngs of the 2017 Internatonal Conference on Fuzzy Systems (FUZZ-IEEE 2017). Naples, Italy 09 to 12 Jul 2017, IEEE. It s avalable onlne at: IEEE. Personal use of ths materal s permtted. Permsson from IEEE must be obtaned for all other uses, n any current or future meda, ncludng reprntng/republshng ths materal for advertsng or promotonal purposes, creatng new collectve works, for resale or redstrbuton to servers or lsts, or reuse of any copyrghted component of ths work n other works. The WestmnsterResearch onlne dgtal archve at the Unversty of Westmnster ams to make the research output of the Unversty avalable to a wder audence. Copyrght and Moral Rghts reman wth the authors and/or copyrght owners. Whlst further dstrbuton of specfc materals from wthn ths archve s forbdden, you may freely dstrbute the URL of WestmnsterResearch: (( In case of abuse or copyrght appearng wthout permsson e-mal repostory@westmnster.ac.uk

2 Electrcty Prce Forecastng usng Asymmetrc Fuzzy Neural Network Systems Abeer Alshejar, Vassls S. Kodoganns Faculty of Scence and Technology Unversty of Westmnster London, Unted Kngdom Abstract Electrcty prce forecastng s consdered as an mportant tool for energy-related utltes and power generaton ndustres. The deregulaton of power market, as well as the compettve fnancal envronment, whch have ntroduced new market players n ths feld, makes the electrcty prce forecastng problem a demandng msson. The man focus of ths paper s to nvestgate the performance of asymmetrc neuro-fuzzy network models for day-ahead electrcty prce forecastng. The proposed model has been developed from exstng Takag Sugeno Kang fuzzy systems by substtutng the IF part of fuzzy rules wth an asymmetrc Gaussan functon. In addton, a clusterng method s utlsed as a pre-processng scheme to dentfy the ntal set and adequate number of clusters and eventually the number of rules n the proposed model. The results correspondng to the mnmum and maxmum electrcty prce have ndcated that the proposed forecastng scheme could be consdered as an mproved tool for the forecastng accuracy. Keywords Electrcty prce forecastng; neurofuzzy systems; neural networks; clusterng; predcton I. INTRODUCTION Durng the past two decades, lberalzaton and deregulaton polces have been appled n energy sector n most of EU countres. Wth the ntroducton of abolshng the publc nature of electrc power ndustry, the prce of electrcty has become probably the central pont of all actvtes n ths market [1]. Electrcty prce forecastng s a challengng task and s consdered as a very mportant parameter n such compettve electrcty market. However the problem of electrcty prce forecastng s, n some ways, dfferent from that of load forecastng. Although both load and the prce are lnked, such relaton s manly non-lnear. Electrcty load s affected by parameters such as seasonal changes n energy demand, energy-savng behavor of energy consumers and manly by the fact the electrcty load s not a substtute for storablty. Prce, alternatvely, s nfluenced by the same factors as well as addtonal features such as fnancal regulatons, compettors load prcng, dynamc market factors, and other macro/mcro economc condtons. Hence, electrcty prce can be consdered as more volatle than the electrcty load. It s worth mentoned, that durng the ntroducton of dynamc prcng strateges, electrcty prces become even more volatle, where the daly average prce were changed by up to 50% whle other commodtes exhbted about 5% change [2]. Both power market players as well as ndependent operator regulators (ISO) are alarmed wth such prce evoluton. Market electrcty prce predcton s thus mportant nformaton for producers producton plannng and prce bddng strateges. Obvously, varous methods have been adopted for the forecastng of future prces. One approach for market behavour predcton s the usage of regresson methods. The fundamental dea s to utlse hstorcal electrcty prces, power load forecast as well as temperature nformaton to predct the market-clearng prce (MCPs). However, the utlsaton of such smple lnear regresson model cannot capture the complcated nonlnear dynamc relaton between load and electrcty prces [3]. Classc ARMA models on the other hand utlse hstorcal tme-seres data, but agan they fal to consder the effect of other factors on electrcty prces. Wth the presence of small number outlers, the fttng error of such model may greatly ncrease. Hence, ths defect lmts ts applcaton extensvely. Neural Network (NNs) and other ntellgent schemes have enjoyed a great applcablty n electrcty prce forecastng, whch s due to ther smple and flexble archtecture. Among exstng ntellgent schemes, generalzed regresson neural network (GRNN) ncorporated wth prncpal components analyss (PCA) have shown potental n electrcty prce forecastng [4]. Although, accordng to lterature, the majorty of appled case studes are referred to day-ahead predctons, the MLP network has been utlzed n hour-ahead tme forecastng [5]. The role of MLP s to enhance the performance of classc tme seres models (for example an ARIMA). RBF s another type of NNs that s utlzed n the case study of [6]. Ths specfc model s able to smulate complex nonlnear relatonshps, sometmes wth greater accuracy than MLP networks. Support Vector Machnes (SVMs) provde also a non-lnear mappng of the dataset nto a hgh-dmensonal space. The boundares of ths new hgh-dmensonal space are dstngushed by lnear functons. SVMs provde a global soluton to a problem unlke MLPs whch operate by mnmsng problem s objectve functon. Such nterestng characterstc has been acknowledged n many case studes related to the electrcty load and prce forecastng area [7].

3 In one of the frst applcatons utlsng fuzzy logc to electrcty prce forecastng, a combnaton of fuzzy c-means clusterng and a neural recurrent network has been consdered [8]. Another approach n electrcty prce forecastng s the use of hybrd neurofuzzy systems. An adaptve-network-based fuzzy nference system (ANFIS) has been nvestgated and results proved that such scheme s superor to MLP approaches [9]. In the majorty of electrcty prce forecastng studes, especally for the hourly prce case, only one model s normally utlzed to forecast the next 24 hourly prces. However, t s a rather dffcult task to assocate all the characterstcs of 24 dfferent hourly prces by a sngle model. Thus, the model may become under-fttng for some hourly predctons, whle at the same tme, t may become over-fttng for some others, whch eventually leads to unsatsfactory results. An obvous dsadvantage of such approach s related to the hgh complexty of the network structure (.e. a system wth 24 output nodes) n terms of tranng tme and performance. Alternatvely, a recurrent structure could provde smlar characterstcs, however n practce ts performance would be deterorated due to the feedback error accumulaton. An alternatve approach has been proposed n recent past [10] and t has been adopted also n ths paper. The core of the proposed modular forecastng system s the 24 mult-nput-sngle-output (MISO) modelng blocks. One of the advantages of the proposed modular system s ts possble use also for longrange forecastng schemes. In ths paper, neurofuzzy models are consdered to compute the forecasted prce n ISO New England market. The ISO New England market s coordnated by an ndependent system operator (ISO) ( It has been observed that although the daly load curves retan a smlar pattern, the equvalent daly prce curves are however volatle. Hence, the forecastng of Locatonal Margnal Prces (LMPs) becomes mportant as t helps the determnaton of the bddng market strateges as well as n rsk management. In ths research, the tranng/testng data set was created from the perod Both tranng and testng sets were classfed nto 24 tme seres, each one correspondng to a dfferent hour of the day. More specfcally, 600 data were allocated to tranng subset, whle 123 data for the testng one. An Asymmetrc Gaussan Fuzzy Inference Neural Network (AGFINN), utlzng a Takag Sugeno Kang (TSK) structure, has been consdered as an dentfcaton model for electrcty prce forecastng. Unlke the ANFIS system, AGFINN nvolves a clusterng component whch reduces the number of fuzzy rules, mnmzng thus the curse of dmensonalty problem. A fuzzy c-means (FCM) clusterng algorthm has been appled at the sample data n order to categorze feature vectors nto clusters. In the followng result secton, only results that correspond to hours wth the maxmum (22:00 h) and mnmum (04:00 h) electrcty prces are llustrated. The proposed modelng scheme s compared aganst ANFIS, AFLS and MLP NN forecastng schemes utlzed for the same case study n order to evaluate ts performance as an effcent predcton scheme. II. ASYMMETRIC NEUROFUZZY MODEL (AGFINN) In ths secton, the proposed Asymmetrc Gaussan Fuzzy Inference Neural Network (AGFINN) s presented an alternatve neurofuzzy modellng approach. Although AGFINN follows the classc TSK- defuzzfcaton structure, t ncludes a FCM clusterng scheme for structural / ntalzaton purposes. Although standard symmetrc Gaussan membershp functons has been utlsed wdely, AGFINN utlzes an asymmetrc functon actng as nput lngustc node. Snce the asymmetrc Gaussan membershp functon s varablty and flexblty are hgher than the standard one, t can partton nput space more effectvely [11]. In ths paper, AGFINN has been optmsed through the gradent descent learnng algorthm. The archtecture of the proposed neurofuzzy (NF) network shown n Fg 1 conssts of fve layers. Fg. 1. Structure of AGFINN system The frst three layers L 1, L 2 and L 3 correspond to IF part of fuzzy rules whereas layer L 5 contans nformaton about THEN part of these rules and perform the defuzzfcaton task. In layer L 4 a normalzaton process s performed for all rules derved from L 3. A. FCM Clusterng Algorthm Fuzzy c-means (FCM) clusterng s probably the most wellknown fuzzy unsupervsed clusterng algorthm whch s based on mnmzng an objectve functon that represents the dstance from any gven data pont to a cluster centre weghted by that data pont s membershp value. Gven n data patterns, x 1, x 2,..., x n, fuzzy clusterng parttons the data patterns nto c clusters whch centred at c. The objectve functon for FCM s defned by c n m 2 μ d, 1 c (1) = 1 j= 1 where μ s the degree of membershp of object j n cluster, m s the fuzzy weghtng exponent varyng n the range [ 1, ] and d denotes the Eucldean dstance between x j and c. The membershp μ and the cluster centres c are calculated by the followng equatons:

4 1 ( 2 ( m 1) ) c d, 1 c, 1 j n (2) k= 1 d kj μ = c n m μ j 1 x = j = n m μ j= 1 In FCM, c s updated va an nteractve procedure, usng last teraton s membershp values. Ths algorthm shfts objects between clusters untl the objectve functon cannot be decreased further. In the present study, cluster centres have been utlzed as ntal values for the centres of fuzzy membershp functons, whle the number of f then rules for AGFINN modellng s equal to the number of clusters obtaned through FCM approach. The spread values for each membershp functonσ are ntalzed accordng to (3) From the above equaton, t s obvous that the proposed MF utlzes two spreads, namely σ and rght σ left respectvely. Both of these parameters transform the tradtonal Gaussan functon to a more asymmetrc style whch can provde greater flexblty from the orgnal one. A schematc of the proposed MF s shown n Fg n n 2 2 ( ) uk xkj c uk k = 1 k = 1 σ = (4) These values are calculated based on the matrx U, where ts elements correspond to the fuzzy membershps of nput x k n the th cluster and have centre values obtaned agan from FCM. B. Feed-forward analyss of AGFINN The clusterng algorthm provdes the fuzzy c-partton of the sample data and practcally generates the fuzzy rules base for the AGFINN scheme. Fuzzy IF-THEN rules can be wrtten n the followng form: = q q q q IF ( x s U AND...AND x s U ) THEN ( y w w x.. w x ) (5) where U are fuzzy sets defned based on c-partton of learnng data X. The structure of the AGFINN s explaned below layer by layer: Layer 1: Ths layer s the nput layer. Nodes at ths layer smply forward the nput sgnals x 1, x 2,..., x n to L 2. Layer 2: Ths layer s the fuzzfcaton layer, and ts nodes are assocated wth the fuzzy sets used n the antecedent parts of the fuzzy rules. Each fuzzfcaton node determnes the degree to whch an nput belongs to the node s fuzzy set. The outputs of ths layer are the values of the asymmetrc Gaussan membershp functon (MF) for the nput values. 2 exp x c A = U ( x ;, ) + c left σ 2 exp x c U ( x ;, c ) rght σ 1 f a x < b where U ( x ; a, b) = 0 otherwse (6) Fg. 2. Asymmetrc membershp functon Layer 3: Ths layer s the frng strength calculaton layer. Each fuzzy rule s antecedent part has AND connecton operator, thus frng strength s calculated through the product T-norm operator. In ths case, the multplcaton has been used, and the output of ths layer has the followng form: n R = A ( x ) (7) j j Layer 4: Ths layer s the normalzaton layer. Each node n ths layer calculates the normalzed actvaton frng of each rule by: R = c R j=1 R j (8) Layer 5: Ths layer s assocated wth the defuzzfcaton part of the AGFINN. Each node at ths layer combnes the output of each node n L 4 by algebrac sum operaton after beng multpled by the output weght value f j : c O = f R (9) j=1 where j j1 1 jn n j(n 1) f w x... w x w + = represent the consequent parameters of the TSK-style defuzzfcaton scheme. The learnng algorthm of AGFINN utlses gradent descent (GD) method for optmzaton the varous network parameters. Durng the backward tranng passes, the error sgnals are calculatng from the output layer backward to the premse (.e. membershp) layers, and parameters at both defuzzfcaton and fuzzfcaton sectons are fne-tuned. j j

5 III. RESULTS & DISCUSSION Electrcty prce s a nonlnear problem wth many nput varables, ncludng past own values as well as past and forecasted values of any exogenous varables such as electrcty consumpton. To deal wth ths fact, three dfferent models have been consdered for ths study, n order to extract conclusons about the most approprate forecastng scheme. In general, hstorcal values of the parameter under study have been consdered as nput canddates for forecastng problems. In electrcty prce analyss, load factor has been consdered as the most mportant external varable. In ths study, we assume that next day s forecasted load s also avalable. There s a smlarty between prce and load parameters. Whle the load level rses, a constant ncrease of prce s observed too. A. Model A The objectve of ths frst model s to examne the smple confguraton, used by varous researchers, where electrcty prces at prevous days and hours, as well as forecasted (for the targeted hour/day) load demand are utlzed as nput varables. Thus, for electrcty prce modellng for a specfc hour () and day (j), the followng fve nput varables have been consdered: Target: Prce(,j): electrcty prce at the th hour on the (j) th day, Inputs: Prce(, j-1): prce at the th hour on the (j-1) th day, Prce(, j-2): prce at the th hour on the (j-2) th day, Prce(-1, j-1): prce at the (-1) th hour on the (j-1) th day, Prce(-2, j-1): prce at the (-2) th hour on the (j-1) th day, Load(,j): electrcty load at the th hour on the j th day, Based on ths confguraton, AGFINN model has been nvolved n forecastng the maxmum (22h) and mnmum (04h) prce respectvely. Best results were produced by ncludng 20 fuzzy rules for the case of 22h, whle 15 rules was consdered as adequate number for the case of 04h. Although the classc GD method utlzed as a learnng scheme, the tranng tme was completed n less than 1000 epochs, much faster from the equvalent tme used to tran the MLP NN. The performance of the forecastng model was determned by the root mean squared error (RMSE), the Mean absolute percentage error (MAPE) (%) and fnally and the standard error of predcton (SEP). TABLE I PERFORMANCE INDICES Statstcal ndex for AGFINN (Model A) Testng Data sets 22h 04h Root mean square error (RMSE) Mean absolute percentage error (MAPE) (%) Standard error of predcton (SEP) (%) The complete results for the hours wth mnmum and maxmum electrcty prce, are llustrated n Table I. The RMSE ndex s calculated between the desred and output values and then averaged across all data and t can be used as an estmaton of the goodness of ft of the models. It can also provde nformaton about how consstent the model would be n the long run. The MAPE term s the average absolute percent error for each tme perod or forecast mnus actual, dvded by actual. The SEP ndex s determned as the relatve devaton of the mean predcton values and t has the advantage of beng ndependent on the magntude of the measurements. Based on these ndces, the AGFINN scheme acheved a very good performance, especally for the case of maxmum prce [12]. In order to evaluate the goodness of the current performance of the proposed AGFINN scheme, a comparson aganst NN and neurofuzzy models that have been employed for the specfc datasets has been carred out. Table II provde a summary of those statstcal performances. More specfcally, the AGFINN scheme has been compared aganst a multlayer perceptron (MLP) and neurofuzzy (NF) ANFIS and AFLS systems. TABLE II PERFORMANCE INDICES COMPARISON Statstcal ndex (22h) AFLS ANFIS MLP Root mean square error (RMSE) Mean absolute percentage error (MAPE) (%) Standard error of predcton (SEP) (%) Statstcal ndex (04h) AFLS ANFIS MLP Root mean square error (RMSE) Mean absolute percentage error (MAPE) (%) Standard error of predcton (SEP) (%) The Adaptve Fuzzy Logc System (AFLS) model s a advanced MIMO NF systems whch ncorporates a novel defuzzfcaton scheme, whle dffers from conventonal fuzzy rule-table approaches that utlze the look-up table concept [13]. The AFLS scheme does not follow classc TSK s archtecture, as the number of membershps for each nput varable s drectly assocated to the number of rules, hence, the curse of dmensonalty problem s sgnfcantly reduced. The fuzzfcaton secton n AFLS s smlar to AGFINN, wth the excepton of the FCM clusterng step as well as the absence of asymmetrc MFs. Smlar to AGFINN and MLP, AFLS also utlzes the same GD learnng method for tranng. For ths specfc case study, 20 fuzzy rules for the case of 22h, and 15 rules for the case of 04h were used as a fnal confguraton. Results shown at Table II reveal that AFLS could be consdered as the closest to AGFINN n terms of performance. An MLP network was also constructed for ths case study, usng the same nput vector. After a few trals, utlzng dfferent nternal structures, a NN was mplemented wth two hdden layers (wth 20 and 8 nodes respectvely). Although AGFINN, AFLS and MLP share the same learnng tranng algorthm, the dfferent phlosophy n buldng the neurofuzzy archtecture, allowed those systems to acheve a superor performance. Fnally an ANFIS NF model has been constructed, utlsng

6 32 fuzzy rules. As the number of MFs n AGFINN s equal to the numbers of rules, ths archtecture has advantages over the classc ANFIS model. The ncreased number of Gaussan membershp functons ncreases the localzaton of the nput sgnal whle n the same tme mantans the requred number of rules at low level. B. Model B Research has ndcated that current hour electrcty prce shows a hgh correlaton wth those of hour h-24 and h-168, a fact that ndcates some daly and weekly perodcty. The objectve of ths model s to nvestgate ths specfc ssue. No exogenous nput varables are consdered n ths specfc case study. Thus, for electrcty prce modelng for a specfc hour () and day (j), the followng sx nput varables have been consdered: Target: Prce(,j): electrcty prce at the th hour on the (j) th day, Inputs: Prce(, j-1): prce at the th hour on the (j-1) th day, Prce(, j-2): prce at the th hour on the (j-2) th day, Prce(, j-3): prce at the th hour on the (j-3) th day, Prce(, j-7): prce at the th hour on the (j-7) th day, Prce(-1, j-1): prce at the (-1) th hour on the (j-1) th day, Prce(-2, j-1): prce at the (-2) th hour on the (j-1) th day, The complete results for the hours wth mnmum and maxmum electrcty prce, for the AGFINN case are llustrated n Table III. The nformaton related to weekly perodcty ndeed resulted n an mproved forecastng performance compared to Model A. Best results were produced by ncludng 25 fuzzy rules for the case of 22h, whle 20 rules were adequate for the case of 04h. All statstcal performance ndces were mproved at ths case study, compared to Model A. Ths was due to the expanson of nput varables vector by addng addtonal past electrcty prces on the same hour. In fact, the assumpton that electrcty prces contan a perodcty effect was verfed by ths smulaton. TABLE III PERFORMANCE INDICES Statstcal ndex for AGFINN (Model B) Testng Data sets 22h 04h Root mean square error (RMSE) Mean absolute percentage error (MAPE) (%) Standard error of predcton (SEP) (%) Results shown at Table IV llustrate results from alternatve methods. For ths case study, an AFLS model was constructed wth 25 rules for the case of 22h, whle 20 rules were used for the case of 04h. The MLP NN retaned the same network confguraton, whle under these condtons, ANFIS performed satsfactory, ts performance however was acheved wth a hgh computatonal cost, by utlzng two membershp functons for each nput varables and 64 fuzzy rules. ANFIS s a classc representatve of TSK-based neurofuzzy systems. Its man drawback s that the number of fuzzy rules ncreases exponentally wth respect to the number of nputs n. TABLE IV PERFORMANCE INDICES COMPARISON Statstcal ndex (22h) AFLS ANFIS MLP Root mean square error (RMSE) Mean absolute percentage error (MAPE) (%) Standard error of predcton (SEP) (%) Statstcal ndex (04h) AFLS ANFIS MLP Root mean square error (RMSE) Mean absolute percentage error (MAPE) (%) Standard error of predcton (SEP) (%) C. Model C The objectve of ths model s to expand Model B, by addng the exogenous nput of the forecasted electrcty load. Thus, for electrcty prce modelng for a specfc hour () and day (j), the followng seven nput varables have been consdered: Target: Prce(,j): electrcty prce at the th hour on the (j) th day, Inputs: Prce(, j-1): prce at the th hour on the (j-1) th day, Prce(, j-2): prce at the th hour on the (j-2) th day, Prce(, j-3): prce at the th hour on the (j-3) th day, Prce(, j-7): prce at the th hour on the (j-7) th day, Prce(-1, j-1): prce at the (-1) th hour on the (j-1) th day, Prce(-2, j-1): prce at the (-2) th hour on the (j-1) th day, Load(,j): electrcty load at the th hour on the j th day, The complete results for the hours wth mnmum and maxmum electrcty prce, for the AGFINN case are llustrated n Table V. The nformaton related to weekly perodcty as well as the exogenous load parameter ndeed resulted n an mproved forecastng performance compared to prevous case studes. TABLE V PERFORMANCE INDICES Statstcal ndex for AGFINN (Model C) Testng Data sets 22h 04h Root mean square error (RMSE) Mean absolute percentage error (MAPE) (%) Standard error of predcton (SEP) (%) Best results were produced by ncludng 25 fuzzy rules for the case of 22h, whle 20 rules were consdered adequate for

7 the case of 04h. Fgures 3 and 4 llustrate the testng performances for mnmum and maxmum electrcty prce forecastng usng Model C. IV. CONCLUSIONS An approach s proposed n ths paper for short-term electrcty prces forecastng, based on an asymmetrc neurofuzzy dentfcaton model. The applcaton of the proposed approach to electrcty prces forecastng on the ISO New England market s novel n terms of network archtecture and forecastng performance. The effectveness of ths approach has been thoroughly assessed by comparng t wth alternatve neural or neurofuzzy technques, va three case studes. Future research ncludes the ncorporaton n the modelng process addtonal exogenous parameters. Fg. 3. Forecastng for Electrcty Prce at 22:00, (AGFINN-Model C) Fg. 4. Forecastng for Electrcty Prce at 04:00, (AGFINN-Model C) Smlarly, to prevous case studes, AFLS, ANFIS and MLP NN have been appled to ths specfc case study and ther performances are presented at Table VI. ANFIS s performance was acheved however wth a huge computatonal cost, by utlzng 128 fuzzy rules. TABLE VI PERFORMANCE INDICES COMPARISON Statstcal ndex (22h) AFLS ANFIS MLP Root mean square error (RMSE) REFERENCES [1] A.J. Conejo, J. Contreras, R. Espínola, M.A. Plazas, Forecastng electrcty prces for a day-ahead pool-based electrc energy market, Int. J Forecastng, Vol. 21, No. 3, pp , [2] F. Zel, R. Stenert, S. Husmann, Effcent modelng and forecastng of electrcty spot prces, Energy Econ, Vol. 47, pp , [3] C.J. Cuaresma, J. Hlouskova, S. Kossmeer, M. Oberstener, Forecastng electrcty spot-prces usng lnear unvarate tme-seres models, Appled Energy, Vol. 77, pp , [4] S. Anbazhagan, N. Kumarappan, Day-ahead deregulated electrcty market prce classfcaton usng neural network nput featured by DCT, Int. J. Electr. Power Energy Syst., Vol. 37, pp , [5] R. Gareta, L.M. Romeo, A. Gl, Forecastng of electrcty prces wth neural networks, Energy Converson Management, Vol. 47, , [6] Z. Yun, Z. Quan, S. Caxn, L. Shaolan, L. Yumng, S. Yang, RBF neural network and ANFIS-based short-term load forecastng approach n real-tme prce envronment, IEEE Trans Power Systems, Vo. 23, No. 3, pp , [7] A. Mohamed, M.E El-Hawary, Md-term electrcty prce forecastng usng SVM, 2016 IEEE Canadan Conference on Electrcal and Computer Engneerng, 2016, Artcle number [8] Y.-Y. Hong, C.-Y. Hsao, Locatonal margnal prce forecastng n deregulated electrcty markets usng artfcal ntellgence, IEE Proceedngs: Generaton, Transmsson and Dstrbuton, Vol. 149, No. 5, pp , [9] J.P. Catalao, H.M. Pousnho, V.M. Mendes, Hybrd wavelet-pso- ANFIS approach for short-term electrcty prces forecastng, IEEE Trans Power Systems, Vol.26, No. 1, pp , [10] V.S. Kodoganns, M. Amna, I. Petrounas, A clusterng-based fuzzy-wavelet neural network model for short-term load forecastng, Int. Journal of Neural Systems, Vol. 23, No. 5, 2013 [11] I. Rojas, H. Pomares, F.J. Fernandez, A new methodology to obtan fuzzy systems autonomously from tranng data, IEEE conf. Fuzzy System, Vol. 1, pp , [12] V.S. Kodoganns, T. Pachds, E. Kontogann, An ntellgent based decson support system for the detecton of meat spolage, Eng. Appl. of Artfcal Intellgence, Vol. 34, pp , [13] V.S. Kodoganns, A. Alshejar, An adaptve neuro-fuzzy dentfcaton model for the detecton of meat spolage, Appled Soft Computng, Vol. 23, pp , Mean absolute percentage error (MAPE) (%) Standard error of predcton (SEP) (%) Statstcal ndex (04h) AFLS ANFIS MLP Root mean square error (RMSE) Mean absolute percentage error (MAPE) (%) Standard error of predcton (SEP) (%)