Short-Term Power Load Forecasting Based on a Combination of VMD and ELM

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1 Pol. J. Evro. Stud. Vol. 7, No. 5 (08), DOI: 0.544/pjoes/7844 ONLINE PUBLICATION DATE: Orgal Research Short-Term Power Load Forecastg Based o a Combato of VMD ad ELM We L*, Cogx Qua, Xuyag Wag, Shu Zhag Departmet of Ecoomcs ad Maagemet, North Cha Electrc Power Uversty, Baodg, Cha Receved: 3 August 07 Accepted: 3 October 07 Abstract Accurate short-term power load forecastg s becomg more ad more mportat for the stable operato ad mproved ecoomc beefts of electrc power systems. However, whe affected by varous factors the power load shows o-lear ad o-statoary characterstcs. I order to forecast power load precsely, we propose a extreme learg mache (ELM) combed wth varatoal mode decomposto (VMD), as a ew hybrd tme seres forecastg model. I the frst stage, sce decomposed modes ad hdde layer odes have great fluece o predcto accuracy, a three-dmesoal relatoshp has bee establshed to determe them advace. I the secod stage, usg VMD, the tme seres of power load s decomposed to predetermed modes that are the used to costruct trag parts ad forecast outputs. The every dvdual mode s tae as a put data to the ELM. Evetually, the thrd stage, the fal forecasted power load data s obtaed by aggregatg the forecastg results of all the modes. To testfy the forecastg performace of the proposed model, a fve-mute power load data Hebe of Cha s used for smulato, ad comprehesve evaluato crtera s proposed for quattatve error evaluato. Smulato results demostrate that the proposed model performs better tha some prevous methods. Keywords: short-term power load forecastg, extreme learg mache (ELM), varatoal mode decomposto (VMD) Itroducto I recet years, short-term power load forecastg s playg a creasgly mportat part the stable operato of electrcal power systems, whch s essetal for the developmet of prevetve mateace plas [-]. Wth creasgly maret-oreted electrc power producto ad cosumpto, more accurate short-term power load forecastg s eeded for matag the secure ad stable operato of the electrcal power grd, whch ca also promote the sustaable developmet of *e-mal: cepulw@6.com the electrcty dustry [3]. Therefore, t s dspesable to develop power load forecastg techques to acheve a more accurate smulato result [4-5]. Thus far, short-term power load forecastg methods maly clude covetoal methods, tellget methods, ad hybrd forecastg methods. Covetoal methods maly clude may mathematcal statstcs methods such as multple lear regresso aalyss [6], the grey-forecastg model [7], autoregressve tegrated movg average (ARIMA) [8-9], state space model [0], box-jes model [], geeral expoetal smoothg [], ad so o. Although these methods have the advatage of capturg lear characterstcs, they caot accurately forecast short-term power load

2 44 L W., et. al. showg o-lear ad o-statoary characterstcs. To capture olear characterstcs ad obta accurate predcto results, may tellget methods such as artfcal eural etwor (ANN) [3], support vector regresso (SVM) [4-5], ad tellget evolutoary algorthms [6] have bee proposed to forecast shortterm power loads. ANN ad SVM are well-ow models, ad they have obvous predcto advatages compared wth covetoal methods. Tag to accout the fact that each sgle forecastg model has ts ow predcto shortcomgs, a creasg umber of researchers are adoptg hybrd forecastg methods because they ca avod the shortcomgs of each sgle forecastg model ad deal wth the complex problem more effectvely. ARIMA ad Grey predcto models, as typcal represetatves of covetoal methods, have bee wdely used ad appled to solve may forecastg problems. The ma dea of these models s to loo for the tred of data chages, accordg to the tred equato, to forecast future data [7]. They are sutable to smooth ad lear tme seres predcto, ot good at graspg the tred of olear sequece chages. Wth the rapd developmet of the artfcal tellgece method, artfcal tellgece forecastg techology has bee gradually replacg covetoal forecastg techology the feld of power load forecastg. Bac propagato (BP) eural etwor, as a commo ANN, has the ablty to lear by tself, ad t has bee proposed by may researchers to apply to the short-term power load forecastg problem [8]. But the BP eural etwor s easly trapped local mmum value [9]. Hece, may optmzato algorthms have bee proposed, but the computato burde s greatly creased. Compared wth the BP eural etwor, the SVM algorthm has advatages of good robustess ad strog geeralzato ablty, avodg fallg to local mmum [0]. But the trag tme of the SVM creases expoetally by creasg the dmeso of put vector. A ew learg algorthm for the sglehdde-layer feed-forward eural etwor (SLFN) called the extreme learg mache (ELM) has recetly bee proposed []. I the learg process of ELM, sce ELM requres oly a sgle-pass trag stage wthout ay terato for weght adjustmet, t has very fast learg processg []. Ad t s able to solve the problem of stoppg crtera, learg rate, learg epochs, ad local mmum [3]. I recet years, the ELM has bee appled varous felds ad has become a sgfcat method olear modelg [4-6]. Cosderg the o-statoary ad chaotc propertes of short-term power load data, the tme seres decomposto techque s appled to decompose the orgal power load sequece to several subsequeces. Emprcal mode decomposto (EMD), based o Hlbert-Huag trasform (HHT), ca effectvely extract the compoets of the basc mode from o-lear or o-statoary tme seres. Owg to ts attractve features, t has bee appled to may ecoomc ad facal ssues such as predctg crude ol prces [7], electrcty prces [8], ad so o. But EMD has may dsadvatages, cludg lac of exact mathematcal model, terpolato choce, ad sestvty to both ose ad samplg [9]. The a ew multresoluto called varatoal mode decomposto (VMD) was troduced as a alteratve to the EMD algorthm to overcome ts lmts. VMD has the ablty to separate toes of smlar frequeces, cotrary to EMD [30]. Ad much lterature [3-33] has come to the cocluso that VMD was more effectve modelg ad forecastg ecoomc ad facal data compared wth EMD. The ths paper, hybrd ELM-VMD tellgece s proposed for forecastg short-term power load. I partcular, the umber of modes decomposed by the VMD model maes a great fluece o aalyss, ad the umber of hdde layer odes plays a mportat role predcto accuracy. Ad both of them must be predetermed. So, how to determe the umber of modes ad the umber of hdde layer odes s a hghlght of ths paper. The pot s specfcally made the remader of ths paper. After determg the umber of modes ad the umber of hdde layer odes, the VMD s appled to decompose power load data to several modes that have specfc sparsty propertes. The ELM s costructed to forecast these modes dvdually. Ad all of these forecastg values are aggregated to produce the fal power load forecastg results. Evetually, by cotrast, the proposed method s compared wth other alteratve models such as the GM (,), ARIMA, sgle BP, sgle SVM, sgle ELM, hybrd BP-EMD, hybrd BP-VMD, ad ELM- EMD models. Smulato results demostrate that the proposed model performs more effectvely ad obtas more accurate predcto results. Materal ad Methods Varatoal Mode Decomposto (VMD) The purpose of the VMD s to decompose the orgal sgal to K dscrete umber of modes that have specfc sparsty propertes whle producg the ma sgal. Thus, each mode u s requred to be mostly compact aroud a ceter pulsato ω determed alog wth the decomposto. Compared wth EMD, VMD has the ablty to separate toes of smlar frequeces. Meawhle, the VMD model searches for a umber of modes ad ther respectve ceter frequeces, such that the bad-lmted modes reproduce the put sgal exactly or a least-squares sese. The VMD algorthm to assess the badwdth of a oe-dmesoal sgal s as follows [4]: ) For each mode u, compute the assocated aalytc sgal by meas of the Hlbert trasform to obta a ulateral frequecy spectrum.

3 Short-Term Power Load Forecastg Based ) For each mode, shft the mode s frequecy spectrum to basebad (arrow frequecy) by mxg wth a expoetal tued to the respectve estmated ceter frequecy. 3) Estmate the badwdth through Gaussa smoothess of the demodulated sgal; for example, the squared L-orm of the gradet. The, the decomposto process s realzed by solvg the followg optmzato problem [4]: ω + ω u ω d ˆ ( ) + ω 0 = + uˆ ( ω) dω 0 ˆ ˆ λ + ( ω) = λ ( ω) + τ f ( ω) uˆ + ( ω) (5) (6) j jω m = t δ ( t) * u ( t) e u, ω + πt Subject to u = f t () where f s the sgal to be decomposed, u s ts mode, ω represets the frequecy, δ s the Drac dstrbuto, t represets tme scrpt, * deotes covoluto, j =, ad s the umber of modes. I ths framewor, the mode u wth hgh-order expresses low frequecy compoets. To address the costraed varatoal problem oted above, a quadratc pealty factor α ad Lagrage multplers λ(t) are troduced. The combato of these two terms beefts from both cosderable covergece propertes of the quadratc pealty at fte weght ad the strct eforcemet of the costrat by the Lagraga multpler. Therefore, the above optmzato problem s chaged to a ucostraed oe as below [4]: () where represets the terato umber ad τ devotes the tme step of the dual ascet. Ad the cocrete procedures of the VMD algorthm are llustrated Fg.. Extreme Learg Mache The extreme learg mache (ELM) was a ew method for learg the sgle-layer feed-forward eutral etwor (SLFNs), whch was frst troduced by Huag et al. []. It teds to provde superor geeralzato performace ad extremely fast learg speed by j L( { u},{ ω}, λ ) = α t σ ( t) + * u ( t) e πt e jw t + f ( t) u ( t) + λ( t), f ( t) u ( t) The optmzato methodology deoted as the alterate drecto method of multplers (ADMM) s the used to obta the saddle pot of the augmeted Lagraga by updatg u, ω, ad λ alterately. The covergece crtero of the algorthm + ( u ˆ uˆ / uˆ ) < ε s, where ε s the covergece tolerace. So, the fal updated equatos are gve as follows [4]: (3) ˆ ˆ λ ( ω ) f uˆ u + + ( ω) ( ω) ( ω) + < > ω = + α( ω ω ) uˆ ( ) (4) Fg.. Cocrete procedures of the VMD algorthm.

4 46 L W., et. al. where H ( W, W,..., W, b, b,..., b,x,x,..., X ) = l l N f ( W, b, X)... f ( Wl, bl, X) M M M L f ( W, b, X N ) f ( Wl, bl, X N ) N l T η η= M, T η l l m T T t = M T t N N m. Fg.. Typcal structure of the ELM. radomly choosg the put weghts ad aalytcally determg the output weghts [4]. Ad oly the umber of hdde layer euros s set, whch case the uque optmal soluto wll be obtaed. The typcal structure of ELM s show Fg., whch cludes put, hdde, ad output layers. Assumg that the etwor has p put layer euros ad l hdde layer euros, for N arbtrary dstct samples m ( X, t ) R R the SLFN wth hdde euros ca be descrbed as: l j= f ( W, b, X ) η = o =,,..., N j j j where W j = [W, W,...,W ] T s the put weght vector coectg the put odes ad the j th hdde ode, η j = [η j, η j,...,η j ] T s the weght vector coectg the jth hdde euro ad output euro, X s the th trag example, o j = [o, o,...,o ] T s the output vector, b j s the bas of the j th hdde ode, ad f(.) deotes the actvato fucto of the hdde euro. If the above ELM ca approxmate the N samples wth a zero error, the we ca obta: N = o y = 0 Hece parameters η j, b j, ad W j meet the codtos: l j= (7) (8) f ( Wj, bj, X ) η j = t =,,..., N (9) The above equato ca be descrbed as aother form: Hη = T (0) Dfferet from the tradtoal fucto approxmato theory, the put weghts ad hdde bases of the ELM are radomly geerated. Thus, trag the ELM s approprately equal to fd a least-square soluto of the lear fucto Hη = T[]. H ˆ η T = m Hη T The the soluto of the above form s η + ηˆ=h T () () where H + represets the Moore-Perose geeralzed verse of the hdde layer s output matrx H. Evaluato Crtero To quattatvely measure the performace of the proposed model, mea absolute percetage error (MAPE), root mea square error (RMSE), ad the coeffcet of determato (R ) are used to calculate forecastg accuracy. The overall fttg effect of the proposed model ca be evaluated by RMSE ad R. The MAPE s also oe mportat dcator, ad the smaller the MAPE values, the closer the predcted power load tme seres values to those of the actual value. The deftos of the above-metoed crtera are: y ˆ y MAPE = y = RMSE = (y yˆ ) R = (3) (4) ( y ˆ y ) = = (y % ˆ y ) = (5)

5 Short-Term Power Load Forecastg Based y ad ˆ where y represet the actual ad forecastg power load values at tme, respectvely; y~ s mea value of the predcted value; ad s the umber of the all load data. Approaches of ELM-VMD Model It s worth otg that both the umber of hdde layer odes l ad the umber of decomposed subsgal K play a mportat role predcto accuracy. Thus, ths paper t maes sese to fd ther optmal combatos, whch ths secto dscusses detal. Sce the umber of sub-sgals decomposed by VMD requres t to be gve advace, the rage of chage vares depedg o the umber of IMFs obtaed by EMD. For stace, f the umber of IMFs s, the parameter K used to determe the umber of decomposto to obta by EMD s 3,,,, +, +, ad +3 [34]. I order to avod mssg the optmal umber of hdde layer odes, ths paper the umber of hdde layer odes s set wth a wde rage from 5 to 00. I ths paper, predetermed trag samples are dvded to sub-trag samples ad subtestg samples. MAPE, a bechmar for evaluatg predcto accuracy, s used to determe the optmal combatos. Thus, there s a three-dmesoal relatoshp amog them. The specfc steps are preseted as follows: ) Determe sub-trag samples ad sub-testg samples. ) Apply VMD to decompose the orgal power load data to K statoary modes wth dfferet frequeces. 3) A rollg forecastg process s studed, ad ELM s used to forecast each mode decomposed by VMD; order to mprove the forecastg accuracy of the ELM, all the orgal power load seres ad decomposed sub-seres must be ormalzed prmarly as follows: Fg. 3. Forecastg procedures of the ELM-VMD forecastg model. (6) where x s orgal sample data, represets ormalzed sample data, ad x max ad x m represet the maxmum ad mmum of the data 4) The fal power load forecastg result s obtaed by aggregatg all de-ormalzed values of the ELM outputs. 5) Calculate MAPE ad obta l ad K wth the mmum value of MAPE; the l ad K are determed. I fact, parameters l ad K are obtaed after 7 96 = 67 calculatos. The, usg the parameters already obtaed, repeat steps (), (3), ad (4) to forecast short-term power load. The flowchart of the forecastg procedure s show Fg. 3. Results ad Dscusso Descrpto of Data To verfy the effectveess of the proposed ELM-VMD model, fve-mute load data from Hebe Provce Cha was used ths case study. The power load data obtaed from oe day, wth a total of 88 data pots, was selected as expermetal samples. A rollg forecastg process s studed whch the prevous half-hour data s used to forecast the ext data. That s, the frst sx load data pots are used to forecast the seveth data, amely the last fve load data (x 6, x 5, x 4, x 3, x, x ) are used as the put varables of the ELM, ad the output varable s x. The detals are show Fg. 4.

6 48 L W., et. al. Fg. 4. A rollg-forecastg mechasm for short-term power load forecastg: a) for trag set ad b) for testg set. I ths paper, the prevous hours of data, cludg 5 data pots, were used as the trag set, ad the remag 36 data pots were used as the testg set. To determe the parameters l ad K, the prevous 8 hours of the trag set data were selected as sub-trag set ad the remag data pots were used as the sub-testg set. All computatos are mplemeted a MATLAB (05a) evromet o a computer wth Itel core 5,.6 to.3 GHz CPU, ad 4 GB of RAM. Fg. 5. Orgal short-term power load tme seres. Determe Parameters l ad K The fluctuato of short-term power load s severe, as s show Fg. 5. Thus, EMD s exploted to decrease the o-statoary characterstcs of the orgal shortterm power load tme seres. The results are show Fg. 6, whch the short-term power load data s decomposed to sx dfferet IMFs ad oe resdue. It ca be clearly see that the frequeces of IMF ad IMF are too hgh, whch maly dcates the radom formato of power load. The frequeces of IMF3 to IMF6 are moderate, whch actually are the perodc compoets of the orgal short-term power load seres. Ad the resdue represets the log-term varato tedecy of the orgal power load seres. The, parameter K the umber of decomposed modes vares from 3 to 9, accordg to the umber of IMFs decomposed by EMD. Sce the decomposed modes are ormalzed betwee 0 ad, the sgmod s selected as actvato fucto ths paper. The subtrag power load data s used to tra ELM, ad the sub-testg sample s used to calculate MAPE. Because the mmum value s ot easy to observe the mage, the verse of MAPE s troduced to have

7 Short-Term Power Load Forecastg Based Fg. 6. EMD decomposto results for short-term power load tme seres; from top to bottom: frst IMF to resdue. a better represetato ad uderstadg of obtaed results, whch s show Fg. 7. It s clearly observed that the verse of MAPE reaches a maxmum wth 8 decomposed modes together wth 6 hdde layer odes, amely achevg the best performace ths case. The other coclusos we ca draw are that wth the crease of decomposto levels, the predcto accuracy s bascally creasg. After 8 decomposed levels, the predcto remas almost costat. Therefore, the decomposto of sgal to 8 levels s the best choce, whch smply creases the computatoal burde wth more decomposto levels. Ad wth the umber of hdde layer odes creasg, the predcto error frst creases ad the decreases. We ca observe that the predcto effect wll eep well whe the hdde odes rage approxmately from 0 to 50. The the orgal short-term power load seres was decomposed to 8 modes by VMD (Fg. 8). Fgure 8 shows that the frst ad secod modes prmarly represet the log-term tred of power load seres. Whle the last two modes, wth hgh frequecy, capture short varatos of power load seres. Fg. 7. Results of determg parameters usg MAPE as error dex. Short-Term Power Load Forecastg Results To verfy the effectveess of the ELM as forecastg part ths paper, may forecastg models exstg other lterature such as GM (,), ARIMA, BP eutral etwor, ad SVM are appled as cotrast. The the forecastg results are obtaed by usg orgal power load data that has ot bee decomposed. The parameters of BP eutral etwor are set as follows. Obvously, the put layer ode ad output layer ode were set to 6 ad, respectvely. As a geeral rule of thumb, the hdde layer ode was set to 0 ths paper. The maxmum umber of trag steps was set to 00, the learg rate was set to 0., ad the error precso was set to As for SVM model, the sgmod erel fucto s selected to map the orgal feature space to a hgh-dmesoal space. The epslo loss fucto of epslo-svm s set to 0.0. Owg to the radomess of predcto results for BP eural etwor, the BP eural etwor rus 0 tmes ad the average value of the predcted results s used as the fal result. The, the obtaed results are show Table ad the absolute error values are depcted Fg. 9 for the above-metoed forecastg tools. The forecastg errors of ARIMA ad GM (,) are too large, so ther absolute error values are ot show the above Fgure 9 for the rederg effects of the whole mage. As ca be see from Table, the ELM has the best forecastg accuracy amog all forecastg tools. The forecastg accuracy of GM (,) ad ARIMA s far lower tha other forecastg tools because they are sutable for stable ad smooth tme seres. Compared wth them, tellgece algorthms such as BP eutral etwor, SVM, ad ELM are able to eep o learg, the they ca deal wth o-lear ad o-statoary tme seres more effectvely. The MAPE, RMSE, ad R of the ELM are superor to the BP eutral etwor because the heret characterstcs of the BP eutral etwor may fall

8 50 L W., et. al. Fg. 8. VMD decomposto results for short-term power load tme seres; from top to bottom: frst mode to eghth. to local optmum ad the hdde odes of BP eural etwor hghly deped o tral ad error procedure. The SVM usually has very good forecastg performace whe the put ad output dmesos are hgh, but the SVM does ot wor well ths rollg predcto. Ad t eve performs worse tha the BP eutral etwor. From the stadpot of computg tme usg ELM, the computg tme of the forecastg process s s, whch s very short amog all appled forecastg tools. Although the computg tme of GM (,) s rather short ( s), t has large forecastg errors. What s more, the SVM has the logest forecastg tme of s. If SVM combed wth the VMD s proposed, the forecastg tme wll be approxmately 44 8 = 35 s. Compared wth the ELM-VMD, ts forecastg tme s much greater tha the computg tme of the ELM-VMD (approxmately = 0.48 s). Thus, the SVM model combed wth other sgal decomposed techques was ot tae to cosderato because of ts too-log calculato tme. Moreover, to demostrate the superorty of applyg VMD to sgal aalyss, EMD as a sgal processg tool s troduced to provde comparso results. Whe t comes to the ELM-EMD model, to be cosstet wth the proposed method, usg sub-trag set ad sub-testg set to ga the predetermed optmal hdde odes. The result s show as Fg. 0. Thus, ths codto the hdde odes of the ELM were set to. Whe t comes to the BP-VMD model, the predetermed umber of decomposto K rages from 3 to 9, the BP eural etwor also rus 0 tmes ad obtas average value. The obtaed forecastg errors of hybrd forecastg methods are gve Table. It ca be see that the MAPE ad RMSE of the hybrd ELM-VMD model are the smallest ad the goodess of ft reaches 0.998, whch s the best of all models. As Tables ad show, the hybrd models have better predcto accuracy tha the correspodg sgle format. Ths dcates that the forecastg performace wll be mproved after Table. Error statstcs for sgle forecastg model. Forecastg model Error dex MAPE (%) RMSE (MW) R (MW) Computg tme (s) GM(,) ARIMA BP SVM ELM (proposed model)

9 Short-Term Power Load Forecastg Based... 5 Fg. 9. Absolute error of sgle models the short-term power load forecastg. orgal data are decomposed by sgal processg tools. It s worth otg that the BP-EMD model has worse performace tha the sgle BP model because the BP eutral etwor may fall to the local mmum value. The forecastg fte IMFs ad resdue are added to obta the fal result, ad the forecastg error may crease. As show Table, the VMD-based approach performs better tha the EMD-based approach terms of MAPE ad RMSE, whch llustrates the advatage of the VMD-based approach for forecastg short-term power load. Oe possble reaso s that the EMD has the dsadvatage of mode mxg, whle the EMD has the ablty to separate toes of smlar frequeces. Table also showed that the ELM-VMD model outperformed the BP-VMD model terms of MAE, RMSE, ad R for all values of K. The BP-VMD model performs better tha the ELM-EMD model terms of MAPE ad RMSE, wth K = 6,7,8,9. Ths also meas that sgal preprocessg has great fluece o predcto accuracy. The absolute error values are also depcted Fg.. For dverse decomposed modes, t has dfferet forecastg results of the BP-VMD. The case of the best performace wth K = 8, as the represeted case of all cases for the BP-VMD model s show Fg.. I summary, the expermetal results fully demostrate the effcecy of ELM power load forecastg ad the advacemet of VMD sgal processg. At the same tme, t cofrms that establshg three-dmesoal relatoshps to determe coeffcets l ad K s a good dea to obta Fg. 0. Result of determg hdde odes usg MAPE as error dex.

10 5 L W., et. al. Table. Statstcs error for all hybrd forecastg models. Error dex Hybrd model MAPE (%) RMSE (MW) R (MW) BP-EMD K = K = K = BP-VMD K = K = K = K = ELM-EMD ELM-VMD (proposed hybrd model) accuracy forecastg results. Ad t also dcates that the proposed model s effectve ad effcet for shortterm power load forecastg. I fact, the forecastg process tme of ELM-VMD s approxmately 0.48s, ad ts computatoal tme s much smaller tha other hybrd models. Coclusos I ths paper, a ew hybrd short-term power load forecastg model based o ELM ad VMD has bee proposed. Frst of all, t uses a sub-trag set ad subtestg set, establshg three-dmesoal relatoshps, to obta the umber of varatoal modes ad hdde odes of ELM. The, cosderato of the volatlty of power load, the orgal load seres s decomposed to predetermed modes. Next, rollg predcto s studed step by step ad the ELM s appled to forecast dvdual modes. Fally, the dfferet forecastg seres are recostructed to get the fal forecastg results. Expermets wth dfferet statstcal crtera (MAPE, RMSE, R ) clearly testfy that the ELM- VMD model acheved the lowest forecastg error. Fg.. Absolute error of all hybrd models short-term power load forecastg.

11 Short-Term Power Load Forecastg Based... Compared wth other hybrd or sgle models, t has a very fast forecastg process ad saves sgfcat computatoal tme, whch meas that the ELM-VMD model ca be used as a very promsg methodology for short-term power load predcto. I ths paper, several other coclusos ca be acqured as follows: A) Establshg three-dmesoal relatoshps to obta the umber of varatoal modes ad hdde odes of ELM, as a hghlght of ths paper, acheves fe performace. B) As a ew adaptve multresoluto techque, VMD has better performace ad t s more robust for aalyzg osy sgals tha EMD. C) The tellget algorthm s more sutable for predctg the o-statoary ad olear tme seres tha covetoal method. D) Compared wth other forecastg algorthms the hybrd models, the ELM has the lowest forecastg error ad the shortest computato tme. As a result, the proposed hybrd model ths paper s smple to mplemet ad t provdes fast learg ad covergece whe the sample sze s large. The whole process from selectg optmal parameters to obtag the fal forecastg result s easy to uderstad. Thus, all of these reasos mae t more sutable for forecastg short-term power load ad eve other tme seres. However, ths paper, oly the oe-step-ahead forecastg model s costructed, wth regards to future research drectos, to costruct the mult-step-ahead forecastg model should also be tae to accout. Besdes, short-term power load forecastg s equvalet to tme seres forecastg ths paper, ad other factors such as temperature, wd power, ad precptato are excluded from the proposed hybrd model. Thus, a future study should verfy the superorty of the proposed model mult-step-ahead forecastg ad corporate those fluecg factors to develop the comprehesve hybrd forecastg model. Acowledgemets The curret wor s supported by the Natoal Socal Scece Foudato of Cha (grat No. 5BGL45), the Natoal Natural Scece Foudato of Cha (grat No ), the Fudametal Research Fuds for the Cetral Uverstes (No. 06MS5), ad the Phlosophy ad Socal Scece Research Base of Hebe Provce. Refereces. Sastad A.H., McMeam S., Sue A., Barbose G.L., Goldma C.A. Modelg a aggressve eergy-effcecy scearo log-rage load forecastg for electrc power trasmsso plag. Appled Eergy, 8 (3), 65, L C., L, S., Lu Y. A least squares support vector mache model optmzed by moth-flame optmzato algorthm for aual power load forecastg. Appled Itellgece 45 (4), 66, Wag J., L L., Nu D., Ta Z. A aual load forecastg model based o supportvector regresso wth dfferetal evoluto algorthm. Appled Eergy, 94 (6), 65, Nu D., Wag Y., Dua C., Xg M. A New Shortterm Power Load Forecastg Model Based o Chaotc Tme Seres ad SVM. Joural of Uversal Computer Scece, 5 (3), 76, Zhou X., Zhou X., Zhag Z.M., Tetzers M.M. Short-term power load forecastg usg grey corelato cotest modelg. Expert Systems wth Applcatos, 39 (), 773, Hog T., Gu M., Bara M.E., Wlls H.L. Modelg ad forecastg hourly electrc load by multple lear regresso wth teractos. Power & Eergy Socety Geeral, Meetg, -8, L W., Ha Z.H. Applcato of mproved grey predcto model for power load forecastg. Iteratoal Coferece o Computer Supported Cooperatve Wor Desg, 6, Ne H., Lu G., Lu X., Wag Y. Hybrd of ARIMA ad SVMs for Short-Term Load Forecastg. Eergy Proceda, 6 (5), 455, Nazaro J., Jurczu A., Zalews W. ARIMA models load modellg wth clusterg approach. Power Tech, IEEE Russa, -6, Dordoat V., Koopma S.J., Ooms M., Dessertae A., Collect J. A hourly perodc state space model for modellg Frech atoal electrcty load. Iteratoal Joural of Forecastg, 4 (4), 566, Vähäyla P., Haoe E., Léma P. Short-term forecastg of grd load usg Box-Jes techques. Iteratoal Joural of Electrcal Power & Eergy Systems, (), 9, Chrstaase W.R. Short-term load forecastg usg geeral expoetal smoothg. IEEE Trasactos o Power Apparatus & Systems, 90 (), 900, Xa F., Fa L. Applcato of Artfcal Neural Networ (ANN) for Predcto of Power Load. Sprger Berl Hedelberg, 5, 673, Wu Q. Power load forecasts based o hybrd PSO wth Gaussa ad adaptve mutato ad W v -SVM. Expert Systems wth Applcatos, 37 (), 94, Lu B., Yag R. A ovel method based o PCA ad LS- SVM for power load forecastg. Iteratoal Coferece o Electrc Utlty Deregulato & Restructurg & Power Techologes, 759, Tzafestas S., Tzafestas E. Computatoal Itellgece Techques for Short-Term Electrc Load Forecastg. Joural of Itellgece & Robotc Systems, 3 (-3), 7, Heg J., Wag C., Zhao X., Wag J. A Hybrd Forecastg Model Based o Emprcal Mode Decomposto ad the Cucoo Search Algorthm: A Case Study for Power Load. Mathematcal Problems Egeerg, L L.J., Huag W. A Short-Term Power Load Forecastg Method Based o BP Neural Networ. Appled Mechacs & Materals, , 647, Hog W.C. Chaotc partcle swarm optmzato algorthm a support vector regresso electrc load

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