Electricity consumption prediction using a neuralnetwork-based

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1 Journl of the Opertionl Reserch Society (207) 68, ª 206 The Opertionl Reserch Society. All rights reserved /7 Electricity consumption prediction using neurlnetwor-bsed grey forecsting pproch Yi-Chung Hu,2 * College of Mngement nd College of Tourism, Fujin Agriculture nd Forestry University, Fuzhou City, Chin; nd 2 Deprtment of Business Administrtion, Chung Yun Christin University, 200 Chung Pei Rd., Chung Li Dist., Toyun City, Tiwn Electricity consumption is n importnt economic index nd plys significnt role in drwing up n energy development policy for ech country. Multivrite techniques nd time-series nlysis hve been proposed to del with electricity consumption forecsting, but lrge mount of historicl dt is required to obtin ccurte predictions. The grey forecsting model ttrcted reserchers by its bility to chrcterize n uncertin system effectively with limited number of smples. GM(,) is the most frequently used grey forecsting model, but its developing coefficient nd control vrible were dependent on the bcground vlue tht is not esy to be determined, wheres neurl-networ-bsed GM(,) model clled NNGM(,) hs been presented to resolve this troublesome problem. This study hs pplied NNGM(,) to electricity consumption nd hs exmined its forecsting bility on electricity consumption using smple dt from the Turish Ministry of Energy nd Nturl Resources nd the Asi Pcific Economic Coopertion energy dtbse. Experimentl results demonstrte tht NNGM(,) performs well. Journl of the Opertionl Reserch Society (207) 68(0), doi:0.057/s y; published online 22 December 206 Keywords: electricity consumption; neurl networ; grey forecsting; GM(,). Introduction Over the pst few decdes, continuous economic development nd popultion increse worldwide hve led to rpid growth in electricity demnd. The verge nnul growth rte of globl electricity demnd ws 2.6% for nd 3.3% for It is expected to rech 2.8% for (Liu, 205). Electricity plys very importnt role mong energy sources. Therefore, electricity consumption is importnt for every ntionl uthority when ming energy policy. An energy policy hs gret impct on industril development in country, especilly for developing countries. Mny forecsting methods, such s computtionl intelligence methods, multivrite regression nd time-series nlysis, hve been frequently used for electricity consumption prediction (Nogles et l, 2002; Cost et l, 20; Tutun et l, 205; Abdoos et l, 205). A lrge number of smples re required for multivrite regression nd time-series nlysis (Wng nd Hsu, 2008). The performnce of computtionl intelligence methods cn be significntly ffected by the number of trining ptterns (Pi et l, 200). Beyond this, sttisticl methods usully require tht the dt conform to sttisticl ssumptions, such s hving norml distribution *Correspondence: Yi-Chung Hu, Deprtment of Business Administrtion, Chung Yun Christin University, 200 Chung Pei Rd., Chung Li Dist., Toyun City, Tiwn. E-mil: ychu@cycu.edu.tw (Lee nd Tong, 20). However, using long-term dt to build electricity consumption prediction models my be imprcticl becuse the verge nnul growth rte of electricity consumption is high nd unstble. In ddition, the dt collected on energy consumption often do not conform to sttisticl ssumptions (Lee nd Tong, 20). Therefore, to construct n electricity consumption prediction model, forecsting method is needed tht wors well with smll smples nd without ming ny sttisticl ssumptions (Feng et l, 202; Li et l, 202). The grey system theory proposed by Deng (982) ws developed to void the inherent defects of sttisticl methods nd requires only limited mount of dt to estimte the behviour of n uncertin system (Wen, 2004). The GM(,) model, which is primry time-series forecsting model in grey theory, is one pproch tht hs the merit of effectively constructing prediction model for short-term problems (Liu nd Lin, 2006). In ddition, it only needs four recent dt points to chieve relible nd cceptble ccurcy for future prediction (Wng nd Hsu, 2008; Wng et l, 2008). The GM(,) hs been widely used in mny fields such s mngement, economics nd engineering, nd the relted models hve been developed (Feng et l, 202; Li et l, 202; Pi et l, 200; Lee nd Tong, 20; Mo nd Chirw, 2006; Hu et l, 205; Hu, 203; Tsur nd Lio, 2007; Chng et l, 205, 206; Wng nd Ho, 206; Luet l, 206; Mo et l,

2 260 Journl of the Opertionl Reserch Society Vol. 68, No ; Yun et l, 206). Moreover, grey prediction hs been gining in populrity in the pst decde becuse of its simplicity nd bility to chrcterize unnown systems by few dt points (Sugnthi nd Smuel, 202). Trditionl GM(,) model uses the lest squre method to obtin the developing coefficient nd the control vrible using grey difference equtions. However, these equtions cn be ffected by the bcground vlue tht is not esy to be determined. Hu et l (200) thus presented novel neurlnetwor-bsed GM(,) model clled NNGM(,) to resolve such troublesome problem. This study contributes to verify the usefulness nd pplicbility of the NNGM(,) by pplying this grey prediction model to electricity consumption forecsting. The experimentl results indicte tht NNGM(,) performs well compred to other vrints of GM(,). The reminder of the pper is orgnized s follows. Section 2 introduces trditionl GM(,) nd NNGM(,). Section 3 exmines the electricity consumption forecsting performnce of NNGM(,) by mens of two experiments on rel-world dt. Section 4 includes discussion nd conclusions. 2. Neurl-Networ-Bsed GM(,) From the perspective of grey system theory, the originl dt provided by most systems re finite, insufficient nd chotic, but the potentil regulrity hidden in these dt sequences cn be identified by generting new sequences through the ccumulted generting opertion (AGO) (Liu nd Lin, 2006; Deng, 982). Let ¼ð ; xð0þ 2 ;...; xð0þ n Þ consisting of n smples denote n originl sequence. A new sequence x ðþ ¼ðx ðþ ; xðþ 2 ;...; xðþ n Þ cn be generted from x(0) by AGO s follows: x ðþ ; xðþ 2 x ðþ ¼ X j¼ j ; ¼ ; 2;...; n ðþ ;...; xðþ n function, which is first-order differentil eqution. cn be pproximted by n exponentil dx ðþ þ x ðþ ¼ b ð2þ dt where nd b re the developing coefficient nd the control vrible, respectively. The predicted vlue, ^x ðþ, for x ðþ cn be obtined by solving the differentil eqution with initil condition x ðþ = : ^x ðþ ¼ b e ð Þ þ b ð3þ As for nd b, both prmeters cn be estimted by mens of grey difference eqution: where the bcground vlue z ðþ z ðþ ¼ x ðþ þ z ðþ ¼ b ð4þ cn be formulted s follows: þð Þx ðþ is usully specified s 0.5 for convenience. Trditionl GM(,) uses the lest squre method to obtin nd b using n - grey difference equtions ( = 2, 3,, n). This mens tht the determintions of both developing coefficient nd control vrible re fully dependent on the bcground vlue. Finlly, by mens of the inverse ccumulted generting opertion (IAGO), the predicted vlue, ^ generted s follows: Therefore, ^ ^ ¼ ^x ðþ,of ð5þ cn be ^x ðþ ; ¼ 2; 3;...; n ð6þ ¼ð e Þ b e ð Þ ; ¼ 2; 3;...; n ð7þ Note tht ^x ðþ ¼ ^ holds. Becuse z ðþ is not esily determined, it is quite resonble to find nd b without the interference coming from z ðþ (Hu et l, 200). A cost function E(, b) of NNGM(,) ws built on this rgument. Eð; bþ ¼ X 2; ^ ¼ 2; 3;...; n ð8þ 2 As shown in Figure, NNGM(,) is estblished by wellnown neurl networ, nmely single-lyer perceptron (SLP), in which nd b re connection weights. The lerning rules D nd Db with respect to nd b, respectively, cn be esily obtined by implementing the grdient descent method on the cost function (Hertz et l, 99): oe½; bš D ¼ g ¼ g X o oe½; bš Db ¼ g ¼ g X ob Figure (0) xˆ ^ ^ b V V b Single-lyer perceptron for NNGM(,). ð9þ ð0þ

3 Yi-Chung Hu Electricity consumption prediction using neurl-networ 26 where g is the lerning rte. V nd V b re derived s follows: V ¼ ð e Þ b e ð Þ þ ð e b Þ e ð Þ 2 þ ð e Þ ðþ b ð þ Þe ð Þ ðþ V b ¼ e e ð Þ ð2þ It is obvious tht the determintions of nd b re dependent on D nd Db insted of on z ðþ. The steps for estblishing NNGM(,) cn be described s follows:. Present rndomly selected sequence (,,)( = 2, 3,, n) with s its desired output to NNGM(,). 2. Clculte the ctul output ^ of NNGM(,). 3. Adjust the connection weights only for (,, ) so tht nd b cn be djusted to be? D nd b? Db, respectively. The modifictions of D nd Db below re performed for (,, ): D ¼ g ^ V ð3þ Db ¼ g ^ V b ð4þ 4. Repet the bove steps until pre-specified number of itertions hve been performed. Figure 2 illustrtes the flow chrt of constructing NNGM(,). 3. Computer simultions Flse True Strt Prepre originl dt sequences Present rndomly selected sequence Clculte the ctul output Adjust the connection weights Rech pre-specified number of itertions? End To exmine the electricity consumption forecsting bility of NNGM(,), the first experiment involved compring its results with those from GM(,) with rolling mechnism (GPRM) s described in Ay nd At (2007) on dt set collected from 970 to 2004 nd obtined from the Turish Ministry of Energy nd Nturl Resources (MENR). The second experiment involved compring the results with those from the dptive GM(,) (AGM(,)) proposed by Li et l (2009) on smple of twenty-one countries in the Asi Pcific region from 2000 to 2007, which ws obtined from the Asi Pcific Economic Coopertion (APEC) energy dtbse. Detils of these dt sets cn be obtined from the relevnt publictions. As for prmeter specifictions for trining NNGM(,), becuse g should be specified s smll vlue to void generting excessive perturbtions of D nd Db, g ws initilly specified s 0-2. Next, the initil vlues of nd b were rndomly given. Considering the vilble computing time, the mximum number of itertions ws set to Figure 2 Although these prmeter specifictions re somewht subjective, the experimentl results show tht they re cceptble. 3.. Appliction to Turish MENR dt GM(,) cn use only recent dt with smll smple size to increse forecsting ccurcy in future prediction in cse of hving chotic dt. The rolling mechnism cn implement concretely this unique chrcteristic of GM(,). The mechnism wors s follows: ^ Flow chrt of construction of NNGM(,). is obtined by using ; xð0þ 2 ;...; corresponding to 970, 97,, 970? ( - 2), respectively, to construct forecsting model, wheres ^ þ is obtined from 2 ; xð0þ 3 ;...; xð0þ corresponding to 97, 972,, 970? ( - ), respectively, nd so on. In other

4 262 Journl of the Opertionl Reserch Society Vol. 68, No. 0 words, s the prediction model develops further, the significnce of the older dt is reduced (Liu nd Lin, 2006). The term GPRM refers to trditionl GM(,) using the rolling mechnism. As in Ay nd At (2007), this study pplied NNGM(,) seprtely to totl nd industril sector electricity consumption for Turey nd used the rolling mechnism to build NNGM(,). Four smples were used s the trining dt, nd the incoming dtum ws predicted. For instnce, ^ 5 cn be produced by the model build using, xð0þ 2, xð0þ 3, xð0þ 4, wheres 2, xð0þ 3, xð0þ 4, xð0þ 5 re used to obtin ^ 6. The men bsolute percentge error (MAPE) used to mesure the prediction performnce with respect to ( = 5, 6,, 35) cn be clculted s follows: MAPE ¼ X35 ¼5 ^ 3 00% ð5þ The MAPE vlues obtined by NNGM(,) for totl nd industril electricity consumptions were 3.4 nd 4.76%, respectively, wheres those obtined by GPRM for totl nd industril electricity consumptions were 3.69 nd 5.70%, respectively. Besides, the forecsting results obtined by two well-nown neurl networs, multi-lyer perceptron using bc-propgtion trining (i.e. BP networ, BPN) nd rdil bsis function networ (RBFN), re included. To trin the neurl networs, for instnce, the inputs with respect to the desired outputs, xð0þ 2, xð0þ 3 nd 4 re, 2, 3 nd 4, respectively. Then, n ctul output ^ 5 for 5 cn be obtined by using 5 s n input. A two-lyer perceptron with one input node, two hidden nodes nd single output for totl nd industril electricity consumptions ws 4.48 nd 7.26%, respectively, wheres tht obtined by RBFN with one receptive field unit, two hidden nodes nd single output for totl nd industril electricity consumptions ws 7.9 nd 7.68%, respectively. Therefore, the prediction ccurcy of NNGM(,) is superior to tht of GPRM, BPN nd RBFN. Additionlly, MENR hs used the Model of Anlysis of the Energy Demnd (MAED) to crry out energy forecsting studies (Ay nd At, 2007). The forecsting results reported by MENR for for totl nd industril electricity consumptions re summrized in Tbles nd 2, respectively. It is obvious tht NNGM(,) performs well nd outperforms MAED, GPRM nd RBFN. Furthermore, GPRM, NNGM(,), BPN nd RBFN show much better prediction ccurcy thn MAED Appliction to APEC Dt Li et l (202) explored the forecsting performnce of novel dptive GM(,) clled AGM(,) using electricity consumption dt from the Asi Pcific Economic Coopertion (APEC) energy dtbse. Similrly to Ay nd At (2007), AGM(,) nd NNGM(,) were built by the rolling mechnism nd by selecting 4 yers of recent dt 4, xð0þ 3, 2, xð0þ to predict ^ ( C 5) for ech country. For instnce, for Austrli, forecsting model ws constructed using dt from 2000 to 2003 to predict vlue for 2004, wheres the predicted vlue for 2005 ws obtined using dt from 200 to 2004, nd so on. The forecsting results mesured using MAPE, including two-lyer BPN nd support vector regression (SVR) s reported in Li et l (202), re summrized in Tble 3. It is pprent tht NNGM(,) gives stisfctory performnce compred to the other forecsting methods considered. 4. Discussion nd conclusions Electricity consumption forecsting plys n importnt role in ming energy policy. Either overestimtion or underestimtion of electricity demnd will led to excessive operting costs (Nogles et l, 2002). GM(,) is n pproprite pproch for electricity demnd prediction becuse it cn use limited number of smples to construct prediction model without sttisticl ssumptions. This study hs pplied NNGM(,) to Tble Absolute percentge errors obtined by different methods for totl electricity consumption Yer Actul vlue (TWh) MAED GPRM BPN RBFN NNGM(,) MAPE

5 Yi-Chung Hu Electricity consumption prediction using neurl-networ 263 Tble 2 Absolute percentge errors obtined by different methods for industril electricity consumption Yer Actul vlue (TWh) MAED GPRM BPN RBFN NNGM(,) MAPE Tble 3 Absolute percentge errors obtined by different methods for electricity consumption of countries in the Asi Pcific region Country AGM(,) BPN SVR NNGM(,) Austrli Brunei Drusslm Cnd Chile Chin Hong Kong, Chin Indonesi Jpn Republic of Kore Mlysi Mexico New Zelnd Ppu New Guine Peru Philippines Russi Singpore Chinese Tipei Thilnd USA Vietnm Averge electricity consumption. Compred to trditionl GM(,), NNGM(,) hs the convenience of determining directly the developing coefficient nd the control vrible using SLP without using the bcground vlue. Besides, one merit of NNGM(,) is tht it is simple enough to implement s computer progrm. Note tht lthough Wng nd Hsu (2008) proposed genetic-lgorithm-bsed GM(,) to determine the developing coefficient nd the control vrible, it should be stressed tht NNGM(,) is the first pproch to use n optimiztion technique to obtin these two prmeters in grey prediction. Note lso how to optimize the relted prmeters of grey forecsting models to increse prediction ccurcy using different computtionl intelligence tools hs become n importnt issue. For instnce, Hsu (2009) used genetic lgorithm to determine the development coefficient nd the grey input coefficients for GM(,N). Hsu nd Chen (2003) used neurl networs to estimte the signs for residul models. Similrly, Lee nd Tong (20) incorported genetic progrmming into residul GM(,) for energy demnd forecsting. In this study, two dt sets were used to exmine the forecsting performnce of NNGM(,). The experimentl results show tht NNGM(,) outperformed GPRM on the Turish energy dt for totl nd industril electricity consumptions. NNGM(,) lso outperformed AGM(,), BPN nd SVR on the Asi Pcific energy dt by the verge MAPE. It cn be seen tht BPN nd SVR re inferior to AGM(,) nd NNGM(,) becuse the trining smple size hs significnt impct on the forecsting performnce of computtionl intelligence methods. Their forecsting performnce would be improved by incresing the mount of trining dt. This demonstrtes the usefulness of NNGM(,) for electricity forecsting problems. It should be noted tht the SLP in this study ws trined on the bsis of the BP using grdient descent. The lerning is continued until convergent

6 264 Journl of the Opertionl Reserch Society Vol. 68, No. 0 condition is reched. It is nown tht one disdvntge of using BP is tht locl minimum [4] is liely to be stuc during the lerning process. However, it seemed not to be serious problem for NNGM(,) in view of the forecsting performnce on electricity consumption. Energy demnd forecsting cn be regrded s grey system problem (Pi et l, 200; Sugnthi nd Smuel, 202) becuse few fctors such s income nd popultion hve influence on energy demnd, but how exctly these fctors ffect energy demnd is not cler. Therefore, on the bsis of the remrble forecsting performnce of NNGM(,) for electricity consumption, it would be interesting to explore the pplicbility of NNGM(,) to other energy forecsting problems such s totl energy production in certin developing countries. Moreover, it is nown tht the prediction ccurcy of the trditionl GM(,) cn be improved by the residul GM(,) (Liu nd Lin, 2006; Deng, 982). The two models comprise grey residul modifiction model, nd both models re usully constructed in the sme wy s the trditionl GM(,) model. To further improve the prediction ccurcy of residul modifiction model, how NNGM(,) cn combine with the residul GM(,) becomes n interesting issue for energy demnd forecsting. These remin for the future wor. Acnowledgements The uthor would lie to thn the nonymous referees for their vluble comments. This reserch is prtilly supported by the Ministry of Science nd Technology, Tiwn, under Grnt MOST H MY2. References Abdoos A, Hemmti M nd Abdoos AA (205). Short term lod forecsting using hybrid intelligent method. Knowledge-Bsed Systems 76: Ay D nd At M (2007). Grey prediction with rolling mechnism for electricity demnd forecsting of Turey. Energy 32(9): Chng CJ, Di WL nd Chen CC (205) A novel procedure for multimodel development using the grey silhouette coefficient for smll-dt-set forecsting. 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Energy 00: Received Jnury 206; ccepted 8 November 206