Forecasting and Modelling Electricity Demand Using Anfis Predictor

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1 Journal of Mathematcs and Statstcs 7 (4): 75-8, 0 ISSN Scence Publcatons Forecastng and Modellng Electrcty Demand Usng Anfs Predctor M. Mordjaou and B. Boudjema Department of Electrcal Engneerng, Faculty of Technology, Department of Physcs, Faculty of Scence, (LRPCSI Laboratory), The Unversty Skkda, Algera Abstract: Problem statement: Load forecastng plays an mportant task n power system plannng, operaton and control. It has receved an ncreasng attenton over the years by academc researchers and practtoners. Control, securty assessment, optmum plannng of power producton requred a precse short term load forecastng. Approach: Ths study tres to combne neural network and fuzzy logc for next week electrc load forecastng. The sutablty of the proposed approach s llustrated through an applcaton to electrc load consumpton data n 00 downloaded from the RTE France webste. Results: The study presents the results and evaluates them. Correspondng code was developed and used to forecast the next week load n a practcal power system and the fnal forecastng result s perfect and consstent. Concluson: The ANFIS system provdes a useful and sutable tool especally for the load forecastng. The forecastng accuracy s hgh. Key words: Electrcty demand forecastng, anfs system, tme seres analyss, approprate parameterzed, fnal forecastng, Prncpal Component Analyss (PCA) INTRODUCTION Forecastng electrc load consumpton s one of the most mportant areas n electrcal engneerng, due to ts man role for the effectveness and economcal operaton n power systems. It has become a major task for many researchers. The common approach s to analyze tme seres data of load consumpton and temperature to modellng and to explan the seres. Several load forecastng models have been used n electrc power systems for achevng accuracy. Among the models are statstcal, lnear regressons, ARMA, Box-Jenkns, flter model of Kalman. In addton, artfcal ntellgence has been ntroduced based on neural network, fuzzy logc, neuro-fuzzy system and genetc algorthm. Forecastng short, medum and long term electrc load consumpton wth artfcal neural network has receved more attenton because of ts easy mplementaton, accuracy and good performance (Abd, 009; Harun et al., 009; Senabre et al., 00; Flk and Kurban, 007; Lu and L, 006; Badran et al., 008). (James et al., 005) n ther study compare the accuracy and performance of several methods for load forecastng for lead tmes up to a day-ahead. They descrbe sx approaches: double seasonal ARMA modellng, exponental smoothng for double seasonalty, artfcal neural network, a regresson method wth Prncpal Component Analyss (PCA) and two smplstc benchmark methods usng a tme seres of hourly demand for Ro de Janero and a seres of half-hourly demand for England and Wales. They conclude that n addton to ts forecastng performance smoothng method s smplest and quckest to mplement. Espnoza et al. (007), Suykens, Belmans and De Moor used a fxed-sze least squares support vector machnes for nonlnear estmaton n NARX model for predcton the load at a gven hour by the evoluton of the load at prevous hours. They conclude that the forecastng performance assessed for dfferent load seres s satsfactory wth a mean square error less than 3% on the test data. Chen et al. (004) and all n ther study are also used support vector machne technques for med-term load forecastng by constructng models on relatve nformaton such as clmate and prevous electrc load data. They recommend the use of avalable complete nformaton for medum-term load forecastng because takng clmate factors nto account may lead to mprecse predcton and that the use of tme-seres concept may mprove the forecastng. Song et al. (005) present a new fuzzy lnear regresson method for the short term 4 hourly electrc loads forecastng of the holdays. Results shows relatvely bg load forecastng errors are sgnfcantly enhanced due to the dssmlar electrc load pattern of the specal days compared of regular weekdays. Correspondng Author: M. Mordjaou,Department of Electrcal Engneerng, Faculty of Technology The Unversty Skkda, Algera 75

2 The use of neural network for short term load forecastng provdes errors n case of speedy fluctuatons n load and temperature. To overcome ths problem, (Jan et al., 009) uses an adaptve neurofuzzy to adjust the load curves on selected smlar days whch takes nto account the effect of humdty and temperature. Results obtaned show a good predcton wth a small mean absolute percentage error. Furthermore, Neuro-fuzzy approaches have been used n short, medum and long term load forecastng (Bodyansky et al., 008; Mordjaou et al., 00). The man purpose of ths study s to develop and test a model for short term electrc load forecastng n order to cross the bypass of exstng model based on large scale of data and much tme consumng and complexty. Fg. : Comparson of a weekly profle of electrcty consumpton over the year (00) MATERIALS AND METHODS Electrc load forecastng descrpton: Electrcty s a necessary product that cannot be stored. However, to ensure safety power system, the balance between supply and demand should be respected at all tmes. Electrcty demand vares wth exogenous factors. Domestc consumpton should be known n order to provde the best means of producton necessary to meet t. Consumpton of each ste must also be known so that each provder can nject nto the network much electrcty as close as possble the consumpton of ts customers. Generally, the daly consumpton begns wth low values early n the mornng followed by mornng peak consumpton. The power demand decreases sgnfcantly towards the end of the day. It shows also that the power demand on weekend s dfferent from workday s Fg.. For dverse seasons, from Fg. and of the data under study, we can observe that the maxmum power consumpton occurs n wnter seasons but the patterns of weekly load consumpton n sprng, summer and autumn are smlar along the week except the frst two days of the week. Among the technques used by RTE for the resoluton of the supply-demand equaton s the establshment of a predcton model for next day of French consumpton. The predcton of the load curve s complcated by exogenous factors whch are: Atmospherc condtons ncludng temperature and cloudness Economc actvty Trade Offers for erasng electrc power consumpton The legal workng tme Unpredcted events and random dsturbances Fg. : Electrcty consumpton realzed n France n 00 Global energy demand ncreases wth temperature and cloudness due to the ncreased use of ar condtoners, fans, chllers, water pumps and many other electrcal equpments. For example and accordng to RTE, t s currently estmated that n wnter an average change of one degree Celsus over the entre terrtory leads to a varaton of about 450 Mega Watts (MW) of the consumpton. In summer, the varaton s of the order of 500 MW per degree. Cloudness s the ndcator of the rate of cloud cover. Hs knowledge s necessary because t has an nfluence on the use of lghtng and heatng. An average change of one unt of cloudness measurement results n consderable varaton n power consumpton (for okta the consumpton ncrease wth 650 MW n France) (INC Hebdo, 006). There are many other factors nfluencng load patterns lke geographcal condtons (rural and urban area), type of consumer (resdental, commercal and ndustral) and many other condtons and events whch can cause sudden load changes (shutdown of an ndustral operaton). 76

3 The use of bell shaped fuzzy sets s generally preferable and employed from computatonal pont of vew. It s gven by Eq. 3: µ A (x) = x c + b α (3) Fg. 3: Anfs archtecture wth two nputs and an output Adaptve Neuro-Fuzzy nference system structure: An adaptve neuro-fuzzy nference system model was used to forecast the weekly load consumpton. It s defned as a cross between an artfcal neural network and a fuzzy nference system. An adaptve network s a multlayer feed-forward network n whch each node (neuron) performs a partcular functon on ncomng sgnals. However, the Anfs network s composed of fve layers. Each layer contans some nodes descrbed by the node functon. A few layers have the same number of nodes and nodes n the same layer have smlar functons. Archtecture of ANFIS: The ANFIS s a fuzzy nference system based on the model of Takag-Sugeno and uses fve layers. To present the ANFIS archtecture, we suppose that there are two nputs and one output as ndcated n the Fg. 3, n whch a crcle ndcates a fxed node whereas a square ndcates an adaptve node. In the case of frst order usng two rules we have: Rule: If (x s A ) and (y s B ) then (f = p x + q y + r ) Rule : If (x s A ) and (y s B ) then (f = p x + q y + r ) Each ANFIS layer has specfc functons that are used n calculatng nput and output parameter sets. The functon of each layer s descrbed below (Jang, 993). Layer : In ths layer, the entre node s an adaptve node wth a node outputs gven by Eq. and : O = µ (x) =, () A where, a, b and c are the antecedent parameters of the FIS. Layer : Each node n ths layer s a fxed node labeled Π, t computes the frng strengths of the assocated rules. The output s the product of all the ncomng sgnals and can be represented by Eq. 4: O = ω = µ (x) µ (y) =, (4) A B Layer 3: All nodes n ths layer are also fxed nodes labeled N. The th node calculates the rato of the th rules frng strength to the sum of all rules frng strength. They play a normalzaton role to the frng strength from the prevous layer. The outputs of ths layer can be represented as Eq. 5: ω O = ω = =, 3 ω + ω (5) Layer 4: Every node n ths layer s an adaptve node wth a node functon Eq. 6: ( ) O = ω f = ω p x + q y + r =, (6) 4 where, ϖ s the output of layer 3 and {P, q, r }, are the consequent parameters of the FIS. Layer 5: The sngle node n ths layer s a fxed node labeled wth Σ, whch computes the overall output as the summaton of all ncomng sgnals. Hence, the overall output of the model s gven by Eq. 7: O = µ (y) = 3,4 () B where, µ A (x), µ B- (y): Any approprate parameterzed membershp functon and O : the membershp grade of fuzzy set. It specfes the degree to whch the gven nput x(y) satsfes the quantfer A. ω 5 f = ω = = ω + ω = O f (7) ANFIS learnng algorthm: There are several learnng algorthms for a Neuro-fuzzy model. The ANFIS system s generally traned by a hybrd learnng 77

4 algorthm proposed by Jang. Ths algorthm combnng the least squares method and the gradent descent method. The role of tranng algorthm s tunng all the modfable parameters to make the ANFIS output match the tranng data. In the forward pass the algorthm uses least-squares method to optmze the consequent parameters. Once the optmal consequent parameters are found, the backward pass start. However, n ths stage the hybrd algorthm use a gradent descent method for updatng and adjustng optmally the premse parameters correspondng to the fuzzy sets n the nput. The system output s calculated by usng the consequent parameters calculated n the forward pass. Table summarzes the algorthm for adjustng the rules of the ANFIS system. (a) RESULTS In ths study, an ANFIS model based on both ANN and FL has been developed to predct electrc load. The nput varables consst of the tmes seres half hour weekly load data rearranged n mult nput sngle output. For the gven weekly data ponts Neuro- Fuzzy predctor s supposed to work wth twelve nputs and one output only. The nputs are drectly extracted from the data sets. Here, the weekly load data s used. There are 336 data samples (y (t), u (t)), from t = to t = 336 correspondng of half hourly load for a week. Fgure 4 shows the correspondng structure of nput vectors and output. Wth ths dea, the sample ahead s forecasted by usng past samples. Pror to the learnng phase and predcton of weekly electrc load, we used nput vectors canddate to ANFIS (y (t ) for = :5 and u (t j ) for j = : 7) converted from the orgnal data contanng 336 pars. Table : Two passes n the hybrd learnng algorthm for ANFIS Forward pass Backward pass Premse parameters Fxed Gradent descent Consequent parameters Least squares estmator Fxed Sgnals Node outputs Error sgnals (b) (c) (d) Fg. 4: Input and output vectors to ANFIS Fg. 5: Intal and fnal membershp functons: (a) Intal on x (b) Intal on y (c) Adjusted membershp functon on x (d) Adjusted membershp functon on y 78

5 Frstly, we suppose that there are two nputs of ANFIS and we have to create 35 ANFIS models wth dfferent nput combnatons and then select the one wth mnmum error n tranng phase. Results obtaned after several attempts to choose the number and type of membershp functons used. Results obtaned after several attempts to choose the number and type of membershp functons used wth respect to tranng error for one epoch was the model [y (t) u (t-7)]. The frst 50% of data pars selected was used for tranng and the remanng data pars for checkng. The data concerns the actve power consumpton of France realzed n 00. The fnal and the ntal membershp s functons on x and are llustrated by Fg. 5. The model developed was tested several tmes usng dfferent number of rules and membershp functons. Fnally the best results are obtaned by four bell shaped membershp functons and sxteen rules. The performance of the forecast model was evaluated and the results are as shown n Fg. 9 and 0 for day and 3 day respectvely. DISCUSSION The graphcal representaton of the comparson between the desred weekly load values and the ANFIS predcted values s presented n Fg. 6. Results clearly show the excellent tranng as well as predcton performance. The tranng error; checkng error and the step-sze progress are llustrated n Fg. 7 and 8. The ntal step sze s defned to 0.0. The step sze decrease rate s.5 and the step sze ncrease rate s.5. The tranng error goal s set to 0. Fg. 8: Step szes Fg. 6: Comparson of load seres wthn a week realzed and predcted Fg. 9: Load forecasted for day (48 ponts) Fg. 7: Comparng the tranng and checkng errors Fg. 0: Load forecasted for 3 day (44 ponts) 79

6 Fg. : Anfs surface Table : Anfs structure Number of nodes 53 Number of lnear parameters 48 Number of nonlnear parameters 4 Total number of parameters 7 Number of tranng data pars 68 Number of checkng data pars 63 Number of fuzzy rules 6 The parameters of the system for next half hour load forecastng are as mentoned n Table. The structure of ANFIS used contans a total of 7 fttng parameters, of whch 4 are nonlnear and 48 are lnear and the Anfs surface s shown n Fg., t s cut off at the maxmum and the mnmum of the desredoutput. CONCLUSION Ths study presents an applcaton of neurofuzzy model wth a hgh forecastng accuracy that depends on prevous weekly load data. The results obtaned show that the ANFIS approach can accurately predct weekly load consumpton and the performance of the proposed model s not affected by rapd fluctuatons n power demand whch s the man drawback of neural networks models. REFERENCES Abd, M.K., 009. Electrcty load forecastng based on framelet neural network technque. Am. J. Appled Sc., 6: DOI: /ajassp Badran, I., H. El-Zayyat and G. Halasa, 008. Shortterm and medum-term load forecastng for Jordan's power system. Am. J. Appled Sc., 5: DOI: /ajassp J. Math. & Stat., 7 (4): 75-8, 0 80 Bodyansky, Y., S. Popov and T. Rybalchenko, 008. Multlayer neuro-fuzzy network for short term electrc load forecastng. Lecture Notes Comput. Sc., 500: DOI: 0.007/ _34 Chen., B.J., C. Mng-We and L. Chh-Jen, 004. Load forecastng usng support vector machnes: A study on EUNITE competton 00. IEEE Trans. Power Syst., 4: DOI: 0.09/TPWRS Espnoza, M., J.A.K. Suykens, R. Belmans and B. De Moor, 007. Electrc load forecastng. IEEE Ctrl. Syst., 7: DOI: 0.09/MCS Flk, U.B. and M. Kurban, 007. A new Approach for the Short-term load forecastng wth auto regressve and artfcal neural network models. Int. J. Comput. Intel. Res., : Harun, M.H.H., M.M. Othman and I. Musrn, 009. Short Term Load Forecastng (STLF) Usng artfcal neural network based multple lags of tme seres. Lecture Note Comput. Sc., 5507: DOI: 0.007/ _54 INC Hebdo, 006, Electrcté : la résoluton de l équlbre Offre-Demand. Insttut natonal de la consommaton. Jan, A., E. Srnvas and R. Rauta, 009. Short term load forecastng usng fuzzy adaptve nference and smlarty. Proceedngs of the World Congress Nature and Bologcally Inspred Computng, Dec. 9-, IEEE Xplore Press, Combatore, Inda, pp: DOI: 0.09/NABIC James, W.T., L.M. De Menezes and E. Patrck McSharry, 005. A comparson of unvarate methods for forecastng electrcty demand up to a day ahead. Int. J. Forecast., : -6. DOI: 0.06/j.jforecast Jang, J.S.R., 993. ANFIS: Adaptve-network-based fuzzy nference system. IEEE Trans. Syst. Man Cybernetcs, 3: DOI: 0.09/.5654 Lu, Z.Y. and F. L, 006. Fuzzy-rule based load pattern classfer for short-tern electrcal load forecastng. Proceedngs of the IEEE Internatonal Conference on Engneerng of Intellgent Systems, Apr. -3, IEEE Xplore Press, Islamabad, Pakstan, pp: -6. DOI: 0.09/ICEIS Mordjaou, M., B. Boudjema, M. Bouabaz and R. Dara, 00. Short term electrc load forecastng usng neuro-fuzzy modellng for nonlnear system dentfcaton. Proceedng of the 3rd Conference on Nonlnear Scence and Complexty, Jul. 8-3, Ankara, Turkey.

7 Senabre, C., S. Valero and J. Aparco, 00. Usng a self organzng map neural network for short-term load forecastng, analyss of dfferent nput data patterns. Adv. Soft Comput., 79: DOI: 0.007/ _5 Song, K.B., Y.S. Baek, D.H. Hong and G. Jang, 005. Short-term load forecastng for the holdays usng fuzzy lnear regresson method. IEEE Trans. Power Syst., 0: DOI: 0.09/TPWRS