A Hierarchical Fuzzy Linear Regression Model for Forecasting Agriculture Energy Demand: A Case Study of Iran

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1 3rd Iteratoal Coferee o Iformato ad Faal Egeerg IPEDR vol. ( ( IACSIT Press, Sgapore A Herarhal Fuzz Lear Regresso Model for Foreastg Agrulture Eerg Demad: A Case Stud of Ira A. Kazem, H. Shakour.G, M.B. Meha 3, M.R. Mehrega ad N. Neshat Fault of Maagemet, Uverst of Tehra, Tehra, Ira Departmet of Idustral Egeerg, Uverst of Tehra, Tehra, Ira 3 Departmet of Eletral Egeerg, Amrkabr Uverst of Teholog, Tehra, Ira Departmet of Idustral Egeerg, Sharf Uverst of Teholog, Tehra, Ira Abstrat. The am of ths paper s to develop a predto model of eerg demad of agrulture setor Ira. A fuzz-based approah s appled for the agrulture eerg demad foreastg usg soo-eoom dators. Ths approah s strutured as a fuzz lear regresso (FLR. A herarhal FLR model s desged properl. Ths paper deed proposes a herarhal FLR model b whh the puts to the edg level are obtaed as outputs of the startg levels. Atual data from s used to develop the herarhal FLR ad llustrate apablt of the approah ths regard. The estmato fuzz problem for the model s formulated as a lear optmzato problem ad s solved usg the lear programmg based smple method. Furthermore, havg obtaed the fuzz parameters, the agrulture eerg demad s predted from 7 to.the results provde setf bass for the plaed developmet of the eerg suppl of agrulture setor Ira. Kewords: Eerg osumpto, Agrulture setor, Foreastg, FLR. Itroduto Aordg to the eoomal theores ad vews, eerg s oe of the ma ad the most mportat produto fators agrulture setor. Predtg ts future osumpto s a mportat step maroplag agrultural ad eerg setos. Covetoal regresso aalzes s oe of the most used statstal tools to epla the varato of a depedet varable Y terms of the varato of eplaator varables X as: Y = f (X where f (X s a lear futo. The use of statstal ovetoal regresso s bouded b some strt assumptos about the gve data. Ths model a be appled ol f the gve data are dstrbuted aordg to a statstal model ad the relato betwee X ad Y s rsp. Overomg suh lmtatos, fuzz regresso s trodued whh s a eteso of the ovetoal regresso ad s used estmatg the relatoshps amog varables where the avalable data are ver lmted ad mprese ad varables are teratg a uerta, qualtatve ad fuzz wa []. Durg the past deades, the applatos of fuzz regresso models for eerg foreastg problems have bee resulted several researh papers [-3]. I a fuzz lear regresso model had bee developed b Al-Kadar et al for eletr load foreastg. The estmato fuzz problem for the model s tured out to a lear optmzato problem, fuzz lear regresso. It has bee foud usg suh fuzz model; a relable operato for the eletr power sstem ould be obtaed []. I 9, Taghzadeh et al. have formulated a foreastg mult-level fuzz lear regresso model to predt the trasport eerg demad of Ira up to usg soo-eoom ad trasport related dators [3]. Also ths a Correspodg author. E-mal address: alehkazem@ut.a.r 9

2 fleble fuzz regresso model have bee formulated b Azadeh et al. to foreast ol osumpto based o stadard eoom dators []. I ths paper agrulture eerg demad of Ira s foreasted usg FLR model osderg eoom ad soal dators for the tme spa 8 to. For the estmato, tme seres data overg the perod 993 to 7 are used. The remag parts of the paper are orgazed as follows. I seto, FLR model s trodued. Detals of the proposed foreast strateg ad umeral results are desrbed seto 3. A bref revew of the paper s gve seto.. Fuzz lear regresso model Fuzz lear regresso model was proposed b Taaka et al []. Ths method s wdel appled to varous applatos ludg marketg, maagemet ad sales foreastg. It a also be appled for eerg foreastg problems. I ths seto, a formulato for fuzz lear regresso estmato problem s preseted. I ths model, the outputs are o-fuzz observatos. Also, the puts are o-fuzz puts. The base model s assumed to be a fuzz lear futo as below: f ( A ~ A ~ A ~ X A ~ X A ~ =, =... ( X where A ( =,,..., are the fuzz oeffets the form of ( p, where p s the mddle ad s the spread. The membershp futos for eah tpe of A ~ are assumed a tragular membershp. So t a be epressed b defto as: a p ~, p a p A a = ( (, otherwse B applg the Eteso Prple [5] the membershp futo of fuzz umber ~ s gve b: { } ~ ~ ma(m { } A ( a a = f (, a ( = φ (3 otherwse From ( ad (3 we get: ( p p = ~ ( ( = = =, = =, The spread of ~ s ad the mddle of ~ s p. = ~ = We seek to fd the oeffets A = ( p, that mmze the spread of the fuzz output for all data sets. Eq. (5 shows the obetve futo [6]. M m ( = = = ad the ostrats requre that eah observato has at least h degree of belogg to ~ (, that s:[7] ~ ( h m (6 =,,..., The degree h s spefed b the user. B substtutg Eq. ( to Eq. (6, t s obtaed: p p = = p p ( h( ( h( = =,, =,,..., m =,,..., m The above aalzes leads to the followg lear programmg problem []: (5 (7

3 M s. t. m ( = = = p p, = = p p p ( h( ( h( = = =,,..., m =,,..., m (8 3. The herarhal FLR model developmet ad applato I ths seto agrulture eerg demad of Ira from 8 to s foreasted regardg sooeoom dators usg a herarhal fuzz lear regresso model. The struture of the desged herarhal FLR s gve Fg.. Fg. : Struture of the desged herarhal FLR for agrulture eerg demad The ma FLR (FLR5 takes agrulture eerg demad the last, value added of agrulture setor, growth rate of populato, growth rate of gas ol pre ad growth rate of eletrt pre as puts ad produes the agrulture eerg demad. The puts to edg level are obtaed as outputs of the startg levels. The value added of agrulture setor, populato, gas ol pre ad eletrt pre are foreasted usg FLRs. Table summarzes the FLRs puts ad output. TABLE I. FLRS INPUTS AND OUTPUT. FLR Iputs Output value added of agrulture setor the last, value added of agrulture setor value added of agrulture setor two last populato the last, populato two last, Populato 3 Gas ol pre the last, gas ol pre two last gas ol pre eletrt pre the last, eletrt pre two last eletrt pre 5 value added of agrulture setor, growth rate of populato, agrulture eerg demad growth rate of gas ol pre, growth rate of eletrt pre, agrulture eerg demad the last B ths wa fuzz lear regresso models are developed for foreastg of value added of agrulture setor, populato, gas ol pre, eletrt pre ad agrulture eerg demad. The FLR models are preseted Table. where AGVA s value added of agrulture setor, POP s populato, AGPGO s gas ol pre, AGPEL s eletrt pre, AGENG s agrulture eerg demad, α s growth rate.

4 Data related wth agrulture eerg demad model s olleted from Isttute for Iteratoal Eerg Studes (IIES ad Ira Mstr of Eerg. All values gve for the eoom varables are ormalzed based o the fed pres of 997 (997=. TABLE II. FLR MODELS FOR AGRICULTURE ENERGY DEMAND FORECASTING. FLR FLR models AGVA = ( p, ( p, AGVA( t ( p, AGVA( t POP = ( p, ( p, POP( t ( p, POP( t 3 AGPGO = ( p, ( p, AGPGO( t ( p, AGPGO( t AGPEL = ( p, ( p, AGPEL( t ( p, AGPEL( t 5 AGENG = ( p ( p 3, 3, αagpgo ( p ( p, AGVA ( p,, αagpel ( p 5 αpop, 5 AGENG ( t B usg the past hstor data fuzz lear regresso equato of agrulture eerg demad of Ira s as bellow: AGENG = (7 / 57, ( / 3, AGVA (,/ 3 αpop ( / 68, / αagpgo ( /, αagpel ( /9, AGENG ( t Average absolute error peretage (AAEP rtera s used for valdt vestgato of the model. The AAEP s alulated from the followg equato: ˆ( ( AAEP = ( = ( where ˆ( s the estmated data ad ( s the atual data. The AAEP value s.98%. That s aeptable. For foreastg agrulture eerg demad future, value added of agrulture setor, populato, gas ol pre ad eletrt pre are foreasted. The fuzz lear regresso s arred out to fd fuzz parameters. The results are show Table 3. FLR TABLE III. Fuzz parameters FUZZY PARAMETERS OF FLR,,3, MODELS. FLR Fuzz parameters = = = = = = p p p p The AAEP values of value added of agrulture setor, growth rate of populato, growth rate of gas ol pre ad growth rate of eletrt pre related to fuzz models a be see Table. The AAEP values are aeptable. TABLE IV. AAEP VALUES OF FLR,,3, MODELS. FLR 3 AAEP /3%.68% 3.6%.% The the fuzz models are used to predt value added of agrulture setor, populato, gas ol pre ad eletrt pre from 7 to. The estmato of value added of agrulture setor, populato, gas ol pre ad eletrt pre are gve Fg., 3, ad 5. These graphs show the atual data versus the FLR results. The value added of agrulture setor wll reah to a level of 976 ^9 R, populato s about 85 mllo, gas ol pre s about 65 R/L ad eletrt pre s about 6 R/KWH mddle level. (9

5 value added of agrulture setor s (trllo Rals Atual FLR(Lower FLR(Mddle FLR(Upper Fg. : Estmated value added of agrulture setor populato (mllo (mllo Atual FLR(Lower FLR(Mddle FLR(Upper Fg.3 : Estmated populato gasol pre (R/L(R/L Atual FLR(Lower FLR(Mddle FLR(Upper Fg. : Estmated gas ol pre eletrt pre (R/KWH(R/KW Atual FLR(Lower FLR(Mddle FLR(Upper Fg.5 : Estmated eletrt pre 8 B usg equato (9 ad related data the agrulture eerg demad s estmated. The results a be see Table 5. Agrulture eerg demad wll reah to a level of 7.87 MBOE. Years agrulture eerg demad (MBOE TABLE V. Years ESTIMATED AGRICULTURE ENERGY DEMAND agrulture eerg demad (MBOE Colusos Years agrulture eerg demad (MBOE Ths paper foused o foreastg the aual agrulture eerg demad of Ira regardg sooeoom dators usg herarhal fuzz lear regresso model. A herarhal fuzz lear regresso model was desged to take agrulture eerg demad the last, value added of agrulture setor, growth rate of populato, growth rate of gas ol pre ad growth rate of eletrt pre as puts ad produes agrulture eerg demad. The value added of agrulture setor, growth rate of populato, growth rate of gas ol pre ad growth rate of eletrt pre were foreasted usg FLR models. Atual data from 993 to 7 were used ad agrulture eerg demad of Ira from 7 to was foreasted. 5. Akowledgemets Ths researh was supported b the Iraa Fuel Coservato Orgazato (IFCO ad Ivted Collaboratve Researh Program (ICRP. 6. Referees [] A. Azadeh, M. Khakesta, M. Saber. A fleble fuzz regresso algorthm for foreastg ol osumpto 3

6 estmato. Eerg Pol 9; 37: [] A.M. Al-Kadar, S.A. Solma, M.E. El-Hawar. Fuzz short-term eletr load foreastg. Eletral Power ad Eerg Sstems ; 6(:. [3] M.R. Taghzadeh, H. Shakour G., M.B. Meha, M.R. Mehrega, A. Kazem. Desg of a Mult-level Fuzz Lear Regresso Model for Foreastg Trasport Eerg Demad: A Case Stud of Ira. The 39th Iteratoal Coferee o Computers & Idustral Egeerg (CIE39 9; [] H. Taaka, S. Uema, K. Asa. Fuzz lear regresso model. IEEE Tas Sstem Ma Cberets 98; : [5] B. Heshmat, A. Kadel. Fuzz lear regresso ad ts applatos to foreastg uerta evromet. Fuzz Sets ad Sstems 985; 5(: [6] D.C. Motgomer, E.A. Pek. Itroduto to Lear Regresso Aalss. Wle. New York. 98. [7] D.T. Redde, W.H. Woodall, Further eamato of fuzz lear regresso, Fuzz Sets ad Sstems. 996; 79(: 3-.