A Markov Chain Grey Forecasting Model: A Case Study of Energy Demand of Industry Sector in Iran

Transcription

1 0 3d Iteatoal Cofeece o Ifomato ad Facal Egeeg IED vol. (0) (0) IACSIT ess, Sgapoe A Makov Cha Gey Foecastg Model: A Case Study of Eegy Demad of Idusty Secto Ia A. Kazem +, M. Modaes, M.. Mehega, N. Neshat ad A. Foough.A 3 Faculty of Maagemet, Uvesty of Teha, Teha, Ia Depatmet of Idustal Egeeg, Shaf Uvesty of Techology, Teha, Ia 3 Natoal Iaa Ol Compay, Teha, Ia Abstact. The am of ths pape s to develop a pedcto model of eegy demad of dusty secto Ia. A Makov cha gey model (MCGM) s poposed to foecast the eegy demad of dusty secto. It s the compaed to gey model (GM) ad egesso model. The compaso eveals that the MCGM has hghe pecso tha GM ad egesso model. The MCGM s the used to foecast the aual eegy demad of dusty secto Ia up to the yea 00. The esults povde scetfc bass fo the plaed developmet of the eegy supply of dusty secto Ia. Keywods: Eegy demad, Idusty secto, Foecastg, GM, MCGM, egesso. Itoducto I today's compettve wold, the bette a ogazato ca pedct ad aalyze the developg ted futue based o past facts, the bette chace t has to suvve. Vaous techcal ad statstcal methods fo eegy demad foecastg have bee poposed the last few decades wth vayg esults. GM s sutable fo foecastg the compettve evomet whee decso makes ca efe oly to a lmted hstocal data. But the foecastg pecso fo data sequeces wth lage adom fluctuato s low. The Makov-cha foecastg model ca be used to foecast a system wth adomly vayg tme sees. It s a dyamc system whch foecasts the developmet of the system accodg to tasto pobabltes betwee states whch eflect the fluece of all adom factos. So the Makov-cha foecastg model s applcable to poblems wth adom vaato, whch could mpove the GM foecastg model []. The applcatos of gey model fo eegy foecastg poblems have esulted seveal eseach papes [-3]. I 00, Zhag ad He have developed a Gey Makov foecastg model fo foecastg the total powe equemet of agcultual machey Shag ovce []. I 007, Akay ad Atak have fomulated a Gey pedcto model wth ollg mechasm fo electcty demad foecastg of Tukey [3]. A Gey Makov foecastg model has bee developed by Huag, He ad Ce 007. Ths pape was based o hstocal data of the electc-powe equemet fom 985 to 00 Cha, ad foecasted ad aalyzed the electc- powe supply ad demad Cha []. I ths pape eegy demad of dusty secto Ia has bee foecasted usg the MCGM fo the tme spa 009 to 00. Fo the estmato, tme sees data coveg the peod 990 to 008 have bee used. Ths model s compaed wth GM ad egesso model. The emag pats of the pape ae ogazed as follows. I the secod ad thd sectos, GM ad MCGM ae peseted. Detals of applyg GM, MCGM ad egesso model fo eegy demad of dusty secto Ia ad obtaed umecal esults ae descbed the secto. Secto 5 aalyzes ad compaes the empcal esults obtaed fom the thee foecastg models. A bef evew of the pape ad the futue eseach ae Secto 6. + Coespodg autho. E-mal addess: alyehkazem@ut.ac. 3

2 . GM foecastg model Gey pedcto (G) has thee basc opeatos: accumulated geeatg opeato (AGO), vese accumulatg opeato (IAGO) ad gey model (GM). The steps of G ae show below. Step : Ogal tme sequece wth samples (tme pot) s epessed as = {, (),..., ( )} AGO opeato s used to covet chaotc sees to mootocally ceasg sees j = {, (),..., ( )}, whee ( j) = = ( It s obvous that the ogal data ( ca be easly ecoveed fom ( as whee ( = ( ( ) ( ) =, (. Ths opeato s called IAGO []. Step : Fom the GM model by establshg a fst ode gey dffeetal equato ( + az ( = b whee z ( = ( ( + ( + ) I Eq. (3), ( =,..., ) s a tme pot. a s called the developmet coeffcet ad b s called dvg T coeffcets. Usg least mea squae estmato techque coeffcets, [ a, b] ca be estmated as a = ( A' A) b A' X ', z () z (3) A = z ( ), X = () (3) ( ) Step 3: Accodg to the estmated coeffcets a ad b, G equato ca be obtaed by solvg dffeetal equato Eq. (3). By IAGO, the pedcted equato s (0 b ( + ) = ˆ ( + ) ˆ ( = ( )( e a ) e a ) ˆ 3. MCGM foecastg model a I ths secto, Makov cha s peseted to ehace the pedcted accuacy of GM. The ew model s defed as MCGM. The ogal data ae fst modelled by the GM, the the esdual eos betwee the pedcted values ad the actual values fo all pevous tme steps ae obtaed. The dea of the MCGM s to establsh the tasto behavo of those esdual eos by Makov tasto matces, the the possble coecto fo the pedcted value ca be made fom those Makov matces. The detaled pocedue s show as follows []. 3.. The dvso of state Fo ogal data sees, use GM foecastg model to obta the pedcted value ˆ (. The, the esdual eo e( = ( ˆ ( ca also be obtaed. Assume that thee ests some egula fomato the esdual eo sees of GM. We ca establsh Makov state tasto matces; states ae defed fo each tme step. Thus the dmeso of the tasto mat s. The esdual eos ae pattoed to equal potos called states. Each state s a teval whose wdth s equal to a fed poto of the age betwee the mamum ad the mmum of the whole esdual eo. The, the actual eo ca be classfed to those states. Let s j be the j th state of the th tme step Sj [ Lj, U j ], j =,,..., whee L j ad U j ae the lowe bouday ad uppe bouday of the j th state fo the th tme step of the esdual eo sees. e( s esdual eo of GM. j j Lj = m e( + (ma e( m( ), U j = m e( + (ma e( m( ) (6) () (3) () (5)

3 3.. Establshmet of tasto pobablty mat of state M j If the tasto pobablty of state s j =, j =,,...,, whee M tasto fom state to j by m steps. (m) j s the pobablty of (m) M j s the tasto tmes fom state to j by m steps ad M s the umbe of data belogg to the th state. Because the tasto fo the last m etes of the sees s defable, M should be couted by the fst as m etes; s the quatty of etes of the ogal sees. The, the tasto pobablty mat of state ca be wtte as ( ( = ( m) m) m) 3.3. Obtag the pedcted value The esdual eo sees e ( s dvded to states, the thee s tasto pobablty ow vectos. The possbltes of a ceta eo state fo the et step ae obtaed by the pobabltes ow vectos, deoted as { a ( T ), =,,..., } at tme step T. Defe the cetes of states as v ( =,,..., ). The, the pedcted value fo the et step s ~ T = ( ) ˆ ( T + ) + a ( T ) v (8) whee a a a ( T + ) ( T + ) ( T + k ) + ( T ) a [ a ( T ), a( T = a = a = a ( T ) = ),..., a ( T )] = a ad ( T ) ( T + ) whee m =. ( T + k ). Eegy demad foecastg of dusty secto Ia I 008, total eegy cosumpto of dusty secto was 36.3 mllo bael of ol equvalet. Ths fgue equals of the 9.9% total fal eegy cosumpto Ia. Thus, the dusty secto has bee hghest poty fom cosevato polcy pespectve. Because of may udemg factos, cludg ecoomcal developmet, dustes techology, the atoal polcy, etc., fluctuato the eegy cosumpto of dusty secto appeaed obvous. As Table shows, the hstocal data sees of the eegy cosumpto of dusty secto Ia fom 990 to 008 s sg, but fluctuatg adomly. Theefoe, ths pape poposed a MCGM foecastg model to foecast eegy demad of dusty secto Ia. Ths model wll compae wth GM ad egesso foecastg model. (7) (9) TABLE I. STATISTICS OF THE ENEGY CONSUMTION OF INDUSTY SECTO IN IAN FOM 990 TO 008 [5] Eegy cosumpto Eegy cosumpto Eegy cosumpto Eegy cosumpto Establshmet of pedcto model GM ad MCGM Based o the hstocal data of the eegy cosumpto of dusty secto Ia fom 990 to 008, a ted cuve equato s bult by GM foecastg model. GM foecastg model was establshed by Eq. (5). As ˆ (, =,,..., ad ogal data ae plotted the esults, the ftted ad pedcted geeated data sees { } 5

4 Fg.. Accodg to the pedcted data sees { ˆ (, =,,..., + k} by GM foecastg model, ts esdual eo sees e ( ca obtaed as lsted Table. Fom the obtaed esdual eos, the coespodg tevals ae dvded to fou states fo ths study. The fou states ae v = [.8, 6.], v = [ 6., 0.9], v 3 = [ 0.9,5.65], v = [5.65,.60]. The fou states based o the esdual eos ae defed ad the esults ae also lsted Table e( TABLE II TABLE. : STATE TABLE OF MCGM (STATE NUMBE=) e( e( e( I addto, { ˆ ( + v j, fo =,,..., ; j =,,3, } s used to dvde ogal data { ˆ (,,,..., } ad the esults ae plotted Fg.. Eegy demad actual GM foecastg Yea Eegy cosumpto le Ogeal data =, Fg. : The ftted ad pedcted values by GM. Fg.. The state dvso by esdual eos. By the state of each ety as show Table, the tasto pobablty matces of state, m =, ca be evaluated. Accodg to the fou states, we ca calculate the cete values. The model ftted ad pedcted values by MCGM foecastg model, ad the epemetal ogal data ae plotted Fg Establshmet of pedcto model egesso Based o the hstocal data of the eegy cosumpto dusty secto of Ia fom 990 to 008, a ted cuve equato s bult by egesso foecastg model. egesso foecastg model was establshed by ˆ ( = 7.85( -58 whee ( s the actual value ad ˆ( s the pedcted value. As the esults, the model ftted ad pedcted values by egesso foecastg model, ad the epemetal ogal data ae plotted Fg.. Eegy demad actual MCGM foecastg Yea Eegy demad actual egesso foecastg (m) Yea Fg.3: The ftted ad pedcted values by MCGM. Fg.: The ftted ad pedcted values by egesso model. 5. Compaso of foecast pecso betwee the GM, MCGM ad egesso foecastg model 6

5 As the above, the foecast values fom 979 to 006 calculated by GM, MCGM ad egesso model. The foecast values betwee the thee models ae compaed ad the esults ae peseted Table 3. The thee ctea ae used fo compag thee models. They ae the mea squae eo (MSE), absolute mea eo (AME) ad aveage absolute eo pecetage (AAE) whch ae calculated as = ( ) ( ), = ( ), = e MSE e AME e AAE 00 ( = whee e( = ( ˆ( = Table 3 shows that the MCGM foecastg model s bette fo foecastg the eegy demad of dusty secto Ia. The foecast values of MCGM foecastg model ae moe pecse tha GM foecastg model ad egesso foecastg model. = (0) TABLE III. TABLE.3: COMAISON OF FOECAST ESULTS WITH THEE DIFFEENT METHODS. Models Mea Squae Eo (MSE) Absolute Mea Eo (AME) Aveage Absolute Eo ecetage (AAE) egesso % GM % MCGM % The estmated eegy demad of dusty secto by MCGM foecastg model fom 009 to 00 s gve Table. I 00, the eegy demad of dusty secto wll each to a level of 335 MBOE. TABLE IV. THE EDICTED VALUE OF THE ENEGY DEMAND OF INDUSTY SECTO IN IAN BY MCGM FOECASTING MODEL. Eegy demad Eegy demad Eegy demad Coclusos The majo pupose of ths pape was to develop the pedcto model of eegy demad of dusty secto Ia. Though usg the statstcs data of the eegy cosumpto of dusty secto fom 990 to 008, thee foecastg models peseted ad compaed. The esults showed that the accuacy of MCGM foecast eegy demad of dusty secto s hghe tha those of GM ad egesso foecastg model. Also eegy demad of dusty secto Ia fom 009 to 00 was foecasted. The MCGM foecastg model could be appled to foecast othe tme sees poblems wth lage adom fluctuato. 7. Ackowledgemets Ths eseach was suppoted by the Iaa Fuel Cosevato Ogazato (IFCO) ad Ivted Collaboatve eseach ogam (IC). 8. efeeces [] M Huag, Yog He, Haya Ce; "edctve aalyss o electc-powe supply ad demad Cha", eewable Eegy 007; 3(7): [] Zhag SJ, He Y. A Gey Makov foecastg model fo foecastg the total powe equemet of agcultual machey Shag ovce. J Sha Agc Uv (Nat Sc Ed 00; (3): [3] Dya Akay, Mehmet Atak; "Gey pedcto wth ollg mechasm fo electcty demad foecastg of Tukey", Eegy 007; 3(9): [] Guo-Dog L, Dasuke Yamaguch, Masatake Naga; "A GM(,) Makov cha combed model wth a applcato to pedct the umbe of Chese teatoal ales", Techologcal Foecastg & Socal Chage 7

6 007; 7(8): [5] Isttute fo Iteatoal Eegy Studes (IIES), Islamc epublc of Ia (008) Hydocabo Balace, 00. 8