Day ahead hourly Price Forecast in ISO New England Market using Neuro-Fuzzy Systems Alshejari, A. and Kodogiannis, V.

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1 WestmnsterResearch Day ahead hourly Prce Forecast n ISO New England Market usng Neuro-Fuzzy Systems Alshejar, A. and Kodoganns, V. Ths s a copy of the author s accepted verson of a paper subsequently to be publshed n the proceedngs of Intellgent Systems Conference 2017, London, UK, 07 to 09 Sep 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 Day ahead hourly Prce Forecast n ISO New England Market usng Neuro-Fuzzy Systems Abeer Alshejar, Vassls S. Kodoganns Faculty of Scence and Technology Unversty of Westmnster London, Unted Kngdom V.Kodoganns@westmnster.ac.uk Abstract Accurate electrcty prce forecastng s an alarmng challenge for market partcpants and managers owng to hgh volatlty of the electrcty prces. Prce forecastng s also the most mportant management goal for market partcpants snce t forms the bass of maxmzng profts. These markets are usually organzed n power pools and admnstrated by the ndependent system operator (ISO). The am of ths study s to examne the performance of asymmetrc neuro-fuzzy network models for day-ahead electrcty prce forecastng n the ISO New England market. The mplemented model has been developed wth two alternatve defuzzfcaton models. The frst model follows the Takag Sugeno Kang scheme, whle the second the tradtonal centre of average method. A clusterng scheme s employed as a pre-processng technque to fnd out the ntal set and adequate number of clusters and ultmately the number of rules n the network. Smulaton results correspondng to the mnmum and maxmum electrcty prce ndcate that the proposed network archtectures could provde a consderable mprovement for the forecastng accuracy compared to alternatve learnng-based schemes. Keywords Electrcty prce forecastng; neurofuzzy systems; neural networks; clusterng; predcton I. INTRODUCTION Durng the past two decades we have seen wdespread electrcty sector lberalzaton and deregulaton n all EU countres. Wth the ntroducton of restructurng nto the electrc power ndustry, the prce of electrcty has become the focal pont of all actvtes n the power market [1]. Electrcty prce forecastng s a challengng task and s very mportant n compettve electrcty market. The problem of electrcty prce forecastng s related yet dstnct from that of electrcty load forecastng. Although the load and the prce are correlated, ther relaton s manly non-lnear. Power load s nfluenced by the factors such as non-storablty of electrcty, consumers behavoral patterns, and seasonal changes n demand. Prce, on the other hand, s affected by those aforesad factors as well as addtonal aspects such as fnancal regulatons, compettors prcng, dynamc market factors, and varous other macro and mcro economc condtons. As a result, the prce of electrcty s a lot more volatle than the electrcty load. Interestngly, when dynamc prcng strateges are ntroduced, prces become even more volatle, where the daly average prce changes by up to 50% whle other commodtes may exhbts about 5% change [2]. Both market players and the regulators are concerned much about the prce evoluton. Market prce predcton s vtal nformaton for the producers producton arrangement and bddng strateges. There are varous methods adopted for the forecastng of future market prce. One approach to predct the market behavours s regresson. The basc dea s the usage of hstorcal prces, quantty and other nformaton such as load forecast, and temperatures to predct the market-clearng prce (MCPs). However, a smple lnear regresson model s unable to descrbe the complcated relaton between load and electrcty prces, because ther relaton s commonly dynamc and nonlnear [3]. Tradtonal ARMA models are able to fnd nherent rules of a tme seres by utlzng hstory data, but agan they do not take nto account the effect of other factors on electrcty prces. Much work has been done on electrcty prce forecastng wth the Auto Regressve Integrated Movng Average (ARIMA) method [4]. In partcular, the ARIMA method has been extended to nclude error correcton for the worse market condtons wth hgh prce volatlty [5]. Technques that are based on the wavelet transform and ARIMA model have been appled to Spansh power markets n order to mprove the accuracy of prce forecastng [6]. Due to ther smplcty and flexblty, Neural Networks (NNs) have typcally receved much attenton recently. Whle the majorty of the studes refer to day-ahead predctons, the MLP network has been utlzed n hour-ahead tme framework [7]. In order to mprove the accuracy of such methods for forecastng, dfferent technques have been combned wth NNs. A feature selecton technque, a relef algorthm, has been combned wth NNs, whle partcle swarm optmzaton has been used for NN tranng [8-9]. K-Means clusterng method has been used to fnd clusters for the number of neural networks. The wavelet and NN models have been ftted together for greater prce forecastng accuracy [10]. RBF s another type of NNs that s utlzed n the work of [11]. An RBF network ncludes a hdden and an output layer. Ths type of NNs s able to smulate complex relatonshps underlyng the data and can adapt fast to possble changes of these relatonshps. Support Vector Machnes (SVMs) provde a nonlnear mappng of the orgnal data nto hgh dmensonal space. The boundares of the new space are demarcated usng lnear functon. SVMs provde a global soluton to a problem unlke MLPs who can operate wthn local mnma of ther objectve functon. Ths fact has been also recognzed n many research studes related to the load and prce forecastng area 1 P age

3 [12]. Genetc algorthms, n combnaton wth LSSVM (Least Square Support Vector Machne), have been proposed. It has been proven that the forecastng s more accurate than the orgnal SVM forecastng [13]. One of the frst applcatons of fuzzy logc to electrcty prce forecastng was performed by Hong [14], who utlze fuzzy c-means for classfyng hstorcal data nto three clusters (peak, medum and off-peak), and then employ a recurrent network for forecastng. Another approach n prce forecastng s the synergetc operaton of Fuzzy Logc (FL) and NNs. Ths part of the lterature can be further classfed nto two categores: Studes that utlze FL and NN n the same system (.e. neuro-fuzzy systems lke ANFIS) and the studes where FL and NN are separated forecasters that are combned nto a two-part forecaster. An adaptve-network-based fuzzy nference system (ANFIS) has been nvestgated and results proved that such scheme s superor to MLP approaches [15]. In most of the prce forecastng case studes, especally n the hourly prce forecastng utlzng learnng-based algorthms, only one model s bult to forecast the 24 hourly prces of the next day. However, t s a rather dffcult task to assocate all the characterstcs of 24 dfferent hourly prces by one sngle model. Thus, the model may become under-fttng for some hourly prces; but at the same tme, t may become over-fttng for some others, whch leads to unsatsfactory results. An obvous dsadvantage of ths approach however 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, n theory, 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 [16] 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) modellng blocks. One of the flexbltes of the proposed module system s ts possble use also for long-range 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 power demand curves havng smlar pattern, but the daly prce curves are however volatle. Therefore, forecastng of Locatonal Margnal Prces (LMPs) become more mportant as t helps market partcpants not only to determne the bddng strateges of ther generators, but also n rsk management. In ths work, 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. Two Asymmetrc Gaussan Fuzzy Inference Neural Networks (AGFINN) utlzng a Takag Sugeno Kang (TSK) and a centre of average defuzzfcaton structures respectvely have been consdered as dentfcaton models for electrcty prce forecastng. Unlke the ANFIS system, AGFINN ncludes a clusterng component whch reduces the number of fuzzy rules, mnmzng thus the curse of dmensonalty problem. A fuzzy c-means (FCM) clusterng algorthm s appled for the sample data n order to organze feature vectors nto clusters such that ponts wthn a cluster are closer to each other than vectors belongng to dfferent 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 modellng scheme s compared aganst ANFIS, AFLS, Wavelet network (WNN) 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 In ths secton, the proposed Asymmetrc Gaussan Fuzzy Inference Neural Network (AGFINN) concept s presented as an alternatve neurofuzzy modellng approach. Intally, AGFINN has been mplemented as a MIMO neurofuzzy (NF) network whch ncorporates a clusterng pre-processng stage. The archtecture of the proposed scheme shown n Fg 1 ncludes also a FCM clusterng scheme for structural / ntalzaton purposes. In spte of the extensve use of the standard symmetrc Gaussan membershp functons, AGFINN utlzes an asymmetrc functon actng as nput lngustc node. Snce the asymmetrc Gaussan membershp functon s varablty and flexblty are hgher than the tradtonal one, t can partton nput space more effectvely [17]. In ths paper, AGFINN has been optmzed through the gradent descent learnng algorthm, whle centre average (CA) defuzzfer has been used as defuzzfcaton method. Ths technque s more effcent n terms of mplementaton compared to the tradtonal, for fuzzy logc systems, centrod of area approach [18]. Fg. 1. Structure of AGFINN-CA system Many neuro-fuzzy schemes are followng the TSK defuzzfcaton style, where only one output s enabled. ANFIS s a well-known representatve of TSK-based neurofuzzy systems. However, ANFIS s man lmtaton s the exponental growth of rules subjected to the number of nput varables. Generally, TSK-based models allow us to model nonlnear behavour wth relatvely fast tranng speed. Thus, t would be nterestng to nvestgate a TSK-based verson for 2 P age

4 AGFINN and explore any possble mprovement aganst ANFIS. Smlarly to prevous AGFINN-CA scheme, AGFINN-TSK has been bult around fve layers, utlsng the same learnng tranng algorthm. The archtecture for AGFINN-TSK s shown n Fg 2.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. cannot be decreased further. The result s a set of clusters that are as compact and well-separated as possble. In the present study, cluster centres have been utlzed as ntal values for the centres of Gaussan membershp functons, whle the number of f then rules for AGFINN modellng s equal to the number of clusters obtaned through FCM clusterng approach. The spread values for each membershp functonσ are ntalzed accordng to 1 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 th the cluster and have centre values obtaned agan from FCM. Fg. 2. Structure of AGFINN-TSK system A. FCM Clusterng Algorthm Fuzzy c-means (FCM) clusterng s the most promnent 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,..., xn fuzzy clusterng means parttonng 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) where = 1 j= 1 µ s the degree of membershp of object j n cluster, m s the 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: 1 ( 2 ( m 1 )) c d µ =, 1 c, 1 j n (2) k= 1 d kj c n m µ j 1 x = j = n m µ j= 1 FCM clusterng s an nteractve procedure whch updates c usng the last teraton s membershp values. Ths algorthm moves objects between clusters untl the objectve functon (3) B. Feed-forward analyss of AGFINN The clusterng algorthm gves the fuzzy c-partton of the sample data. Ths result helps us to generate fuzzy rules base for AGFINN schemes. Fuzzy IF-THEN rules can be wrtten n the followng form: IF ( x s U AND...AND x s U ) THEN ( y= w + wx wx ) (5) 1 1 q q q q where U are fuzzy sets defned based on c-partton of learnng data X. The structure of AGFINN schemes s explaned below layer by layer: Layer 1: Ths layer s smply the nput layer. Nodes n ths layer pass on the nput sgnals x1, x2,..., x n to L 2. Layer 2: Ths layer s the fuzzfcaton layer, and ts nodes represent the fuzzy sets used n the antecedent parts of the fuzzy rules. A fuzzfcaton node receves an nput and determnes the degree to whch ths nput belongs to n 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 ) (6) rght σ 1 f a x < b where U ( x ; a, b) = 0 otherwse From the above equaton, t s obvous that the proposed MF utlzes two spreads, namely and left σ rght σ 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 P age

5 Fg. 3. Structure of AGFINN-TSK system Layer 3: Ths layer s the frng strength calculaton layer. Snce each fuzzy rule s antecedent part has AND connecton operator, the frng strengths are calculated usng 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 Layer 5: Ths layer s related to the defuzzfcaton /output 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 or w : c j j j j= 1 j= 1 R j (8) O = w R ( CA) or O = f R ( TSK ) (9) where f j = w j1x w jn xn + w j(n + 1) represent the consequent parameters of the TSK-style defuzzfcaton scheme. The learnng algorthm of AGFINN nvolves the use of the gradent descent (GD) method to optmze 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. III. RESULTS & DISCUSSION Electrcty prce s a nonlnear functon of many nput varables, ncludng ther past values as well as past and forecasted values of any exogenous varables such as load consumpton. To deal wth ths fact, three dfferent models c have been consdered for ths study, n order to extract safe conclusons about the forecastng approach that needs to be followed for the specfc dataset. In the majorty of forecastng problems, hstorcal values of the parameter under study have always been consdered as nput canddates. In electrcty prce analyss, the most nfluental external varable s consdered to be the load. In ths study, we assume that next day s forecasted load s avalable. There s an analogy between prce and load values. Whle the load level rses, a constant ncrease of prce s also observed. A. Model A The objectve of ths model s to examne a 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 Inputs: Prce(, j-1): prce at the th hour on the (j-1) th Prce(, j-2): prce at the th hour on the (j-2) th Prce(-1, j-1): prce at the (-1) th hour on the (j- 1) th Prce(-2, j-1): prce at the (-2) th hour on the (j- 1) th Load(,j): electrcty load at the th hour on the j th Based on ths confguraton, AGFINN models have 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 were adequate for the case of 04h. Although the classc gradent 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 neural network. 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). Statstcal ndex for AGFINN (Model A) TABLE I PERFORMANCE INDICES Testng Datasets (TSK) Testng Data sets (CA) 22h 04h 22h 04h Root mean square error (RMSE) Standard error of predcton (SEP) P age

6 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. In order to evaluate the goodness of the current performance of the proposed AGFINN schemes, a comparson aganst NN, WNN and neurofuzzy models that have been employed for the specfc datasets has been carred out. Table II provdes a summary of those statstcal performances. More specfcally, AGFINN schemes have been compared aganst a multlayer perceptron (MLP), wavelet NN and neurofuzzy (NF) ANFIS and AFLS systems. TABLE II PERFORMANCE INDICES COMPARISON Statstcal ndex (22h) AFLS ANFIS WNN MLP Root mean square error (RMSE) Mean absolute percentage error (MAPE) Standard error of predcton (SEP) Statstcal ndex (04h) AFLS ANFIS WNN MLP Root mean square error (RMSE) Mean absolute percentage error (MAPE) Standard error of predcton (SEP) The Adaptve Fuzzy Logc System (AFLS) model s an advanced MIMO NF systems whch ncludes a prototype defuzzfcaton scheme, whle dffers from conventonal fuzzy rule-table approaches that utlze the look-up table concept [19]. The AFLS scheme does not follow 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 component n AFLS s smlar to AGFINN, wth the excepton of the FCM clusterng step as well as the absence of asymmetrc MFs. 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-CA 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. An ANFIS NF model has been constructed, utlsng 32 fuzzy rules. As the number of MFs n AGFINNs s equal to the numbers of rules, the proposed archtecture has advantages over the classc ANFIS model. An nterestng fndng from ths smulaton s related to the performance of WNN, whch outperformed ANFIS for the case of 22h. More specfcally, 20 Morlet wavelet functons were utlsed n the constructon of WNN [20]. 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 daly and weekly perodcty. The objectve of ths model s to nvestgate ths ssue. No exogenous nput varables are consdered n ths specfc case study. Thus, for electrcty prce modellng for a specfc hour () and day (j), the followng sx nput varables have been consdered: Target: Inputs: Prce(,j): electrcty prce at the th hour on the (j) th Prce(, j-1): prce at the th hour on the (j-1) th Prce(, j-2): prce at the th hour on the (j-2) th Prce(, j-3): prce at the th hour on the (j-3) th Prce(, j-7): prce at the th hour on the (j-7) th Prce(-1, j-1): prce at the (-1) th hour on the (j-1) th Prce(-2, j-1): prce at the (-2) th hour on the (j-1) th 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. Statstcal ndex for AGFINN (Model B) TABLE III PERFORMANCE INDICES Testng Datasets (TSK) Testng Data sets (CA) 22h 04h 22h 04h Root mean square error (RMSE) Standard error of predcton (SEP) All statstcal performance ndces were mproved at ths case study, compared to Model A. Ths was due to the expanson of 5 P age

7 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. 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. TABLE IV PERFORMANCE INDICES COMPARISON Statstcal ndex (22h) AFLS ANFIS WNN MLP Root mean square error (RMSE) Mean absolute percentage error (MAPE) Standard error of predcton (SEP) Statstcal ndex (04h) AFLS ANFIS WNN MLP Root mean square error (RMSE) Mean absolute percentage error (MAPE) Standard error of predcton (SEP) ANFIS s a classc representatve of TSK-based neuro-fuzzy systems. Generally, n ths type of models, an nput space s dvded nto K 1 K 2... K n fuzzy subspaces, where K, = 12,,..,n s the number of fuzzy subsets for the th nput varable. As one fuzzy rule s normally assgned for each one of these subspaces, ther man drawback s that the number of fuzzy rules ncreases exponentally wth respect to the number of nputs n. Results from ths case study, ndcate that may ANFIS scheme s not a sutable dentfcaton model for cases wth large nput vectors. The WNN however, reveal a remarkable robustness aganst ANFIS, resultng n a smlar performance wth only 20 wavelet MFs. 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 modellng 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 Inputs: Prce(, j-1): prce at the th hour on the (j-1) th Prce(, j-2): prce at the th hour on the (j-2) th Prce(, j-3): prce at the th hour on the (j-3) th Prce(, j-7): prce at the th hour on the (j-7) th Prce(-1, j-1): prce at the (-1) th hour on the (j- 1) th Prce(-2, j-1): prce at the (-2) th hour on the (j- 1) th Load(,j): electrcty load at the th hour on the j th The complete results for the hours wth mnmum and maxmum electrcty prce, for the AGFINN case are llustrated n Table V. TABLE V PERFORMANCE INDICES Statstcal ndex for AGFINN (Model C) Testng Data sets (TSK) Testng Data sets (CA) 22h 04h 22h 04h Root mean square error (RMSE) Standard error of predcton (SEP) The nformaton related to weekly perodcty as well as the exogenous load parameter resulted n an mproved forecastng performance compared to prevous case studes. Best AGFINN 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 Models A and B. 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 also by ths smulaton. TABLE VI. PERFORMANCE INDICES COMPARISON Statstcal ndex (22h) AFLS ANFIS WNN MLP Root mean square error (RMSE) Standard error of predcton (SEP) Statstcal ndex (04h) AFLS ANFIS WNN MLP Root mean square error (RMSE) Standard error of predcton (SEP) Smlarly, to prevous case study, AFLS, ANFIS, WNN 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. It seems the only comparable method to AGFINN s the AFLS scheme. Even WNN approach outperformed ANFIS n ths specfc case study, revealng ANFIS s defcences. 6 P age

8 Fgures 4 and 5 llustrate the testng performances for mnmum and maxmum electrcty prce forecastng usng Model C, usng AGFINN-TSK scheme. Fg. 4. Forecastng for Electrcty Prce at 22:00, (AGFINN-Model C) Comparson of the proposed two AGFINN-based models ndcates that TSK verson s far superor to model utlsng CA defuzzfcaton scheme. AFGINN-TSK has also advantages over AFLS as well as TSK-based schemes lke ANFIS. Fg. 5. Forecastng for Electrcty Prce at 04:00, (AGFINN-Model C) IV. CONCLUSIONS An approach s proposed n ths paper for short-term electrcty prces forecastng, based on an asymmetrc neuro-fuzzy dentfcaton model. The applcaton of the proposed approach to electrcty prces forecastng on the 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 modellng process addtonal exogenous parameters, as well as the adopton of recursve least squares algorthm for the optmzaton of the consequent component at AGFINN-TSK model. REFERENCES 1. Conejo A.J., Contreras J., Espínola R., Plazas M.A., Forecastng electrcty prces for a day-ahead pool-based electrc energy market, Int. J Forecastng 21(3), , Zel F., Stenert R., Husmann S. Effcent modelng and forecastng of electrcty spot prces, Energy Econ 47, , Cuaresma C.J., Hlouskova J., Kossmeer S., Oberstener M., Forecastng electrcty spot-prces usng lnear unvarate tmeseres models, Appled Energy 77, , Zhou M., Yan Z., N Y.X., L G. and Ne Y. Electrcty Prce Forecastng wth Confdence-nterval Estmaton through an Extended ARIMA Approach, IEE Proc.- Gener. Tansm. Dstrb. 153(2), , Contreras J., Espnola R., Nogales F.J., Conejo A.J., ARIMA Models to Predct Next-Day Electrcty Prces, Power Engneerng Revew, IEEE 22(9), 57 87, Conejo A.J., Plazas M.A., Espnola R., Molna A.B., Day- Ahead Electrcty Prce Forecastng Usng the Wavelet Transform and ARIMA Models, IEEE Transactons on Power Systems 20(2), , Anbazhagan S., Kumarappan N. Day-ahead deregulated electrcty market prce classfcaton usng neural network nput featured by DCT, Int. J. Electr. Power Energy Syst. 37, , Amjady N., Daraeepour A. Day-ahead Electrcty Prce Forecastng Usng the Relef Algorthm and Neural Networks, 5th Internatonal Conference on European Electrcty Market, Lsbon, 1-7, Srnvasan D., Yong F.C., Lew A.C., Electrcty Prce Forecastng Usng Evolved Neural Networks, Inter. Conference on Intellgent Systems Applcatons to Power Systems, Ngata, 1-7, Xan Z., X-Fan W., Fang-Hua C., Bn Y., and Hao-Yong C., Short- Term Electrcty Prce Forecastng Based on Perod- Decoupled Prce Sequence, Proceedngs of the CSEE, 25(15), 1-6, Yun Z., Quan Z., Caxn S., Shaolan L., Yumng L., Yang S., RBF neural network and ANFIS-based short-term load forecastng approach n real-tme prce envronment, IEEE Trans Power Systems 23(3), , Mohamed A., El-Hawary M.E., Md-term electrcty prce forecastng usng SVM, 2016 IEEE Canadan Conference on Electrcal and Computer Engneerng, 2016, No Mahjoob M.J., Abdollahzade M., and Zarrnghalam R., GA based Optmzed LSSVM Forecastng of Short Term Electrcty Prce n Compettve Power Markets, 3rd IEEE Conference on Industral Electroncs and Applcatons, Sngapore, 73 78, Hong Y.-Y., Hsao C.-Y. Locatonal margnal prce forecastng n deregulated electrcty markets usng artfcal ntellgence, IEE Proceedngs: Generaton, Transmsson and Dstrbuton, 149(5), , Catalao J.P., Pousnho H.M., Mendes V.M., Hybrd wavelet- PSO-ANFIS approach for short-term electrcty prces forecastng, EEE Trans Power Systems, 26(1), , P age

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