Shor-Term Load Forecasng usng PSO Based Local Lnear Wavele Neural Newor Prasana Kumar Pany DRIEMS, Cuac, Orssa, Inda E-mal : Prasanpany@gmal.com Absrac - Shor-erm forecasng (STLF plays an mporan role n he operaonal plannng secury funcons of an energy managemen sysem. The shor erm forecasng s amed a predcng elecrc s for a perod of mnues, hours, days or wee for he purpose of provdng fundamenal profles o he sysem. The wor presened n hs paper maes use of PSO based local lnear wavele neural newors (LLWNN o fnd he elecrc for a gven perod, wh a ceran confdence level. The resuls of he new mehod show sgnfcan mprovemen n he forecasng process. Keywords - Elecrc, forecas, wavele neural newor (WNN, local lnear wavele neural newor (LLWNN, Parcle Swarm Opmzaon,arfcal neural newor (ANN, arfcal nellgence,,weely mean absolue percenage error (WMAPE. I. INTRODUCTION Elecrc forecasng s used by power companes o ancpae he amoun of power needed o supply he demand. In he las few years, varous echnques for he STLF have been proposed and appled o power sysems. Convenonal mehods based on me seres analyss explo he nheren relaonshp beween he presen hour, weaher varables and he pas hour. Auo regressve (AR and movng average (MA and mxed Auo regressve movng average(arma models[] are promnen n he me seres approach. The man dsadvanage s ha hese models requre complex modelng echnques and heavy compuaonal effor o produce reasonably accurae resuls []. Bascally, mos of sascal mehods are based on lnear analyss. Snce he elecrc s non lnear funcon of s npu feaures, he behavor of elecrc sgnal can no be compleely capured by he sascal mehods. So sascal mehods are no adapve o rapd varaons. Anoher dffculy les n esmang and adjusng he model parameers, whch are esmaed from hsorcal daa ha may no reveal shor erm paern change[3]. The emergence of arfcal nellgence (AI echnques has led o her applcaon n STLF as exper sysem ype models. These mehods are dscree and logcal n naure. By smply learnng he hsorcal samples, hese mehods can map he npu-oupu relaons and hen can be used for he predcon. Among he AI echnques avalable, dfferen models of NNs due o flexbly n daa modelng have receved grea deal of aenon by he researchers n he area of STLF. Many ype of NN models whch are characerzed by her opology and learnng rules have been successfully for STLF problems [4,5,6,7,8,9,,,,3,4]. A comprehensve revew of he leraure on he applcaon of NNs o he forecasng can be found n [9]. Anoher useful echnque for STLF, proposed n he recen years s wavele based NN mehod. In hs mehod wavele s merged wh NN and ermed as wavele neural newor (WNN. The WNN has been emerged as a powerful new ype of ANN. Bu he major drawbac of he WNN s ha for hgher dmensonal problems many hdden layer uns are needed. Curse of dmensonaly s an unsolved problem n WNN heory whch brngs some dffcules n applyng he WNN o hgh dmensonal problem. So he applcaons of WNN are usually lmed o problems of small npu dmensons. The man reason s ha hey are composed of regularly dlaed and ranslaed waveles. The number of waveles n he WNN drascally ncreases wh he dmenson. In order o ae he advanages of local capacy of he wavele basc funcon whle no havng oo many hdden uns, he archecure of LLWNN has been used n hs paper for STLF. Inernaonal Journal of Insrumenaon, Conrol and Auomaon (IJICA ISSN : 3-89 Volume-, Issue-, 58
Shor-Term Load Forecasng usng PSO based Local Lnear Wavele Neural Newor II. LOAD-DATA ANALYSIS To develop an approprae model for forecasng, we examne he man characerscs of he seres n hs Secon. To llusrae he forecasng procedure he elecrc for he hub of he New England pool from July 8 o 3 Augus, 8 s used for predcon. Accordng o he daa samples for each hour of he day and each day of he monh, s clear ha he dynamcs have mulple seasonal paerns, correspondng o a daly and weely perodcy, respecvely, and are also nfluenced by a calendar effec,.e. weeends and holdays. These properes are jus he same as hose of prce. I s well-nown ha he emperaure s he mos domnan weaher facor ha drves he shor erm. The sascal correlaon coeffcen beween emperaure and s found o be.745. I can be observed ha he seres presens mulple perodces and hence, he pas demand could affec and mply he fuure demand. If he a hour h s o be forecased, he nformaon of prevous hours up o m hours should be aen as a par of he npu of shor erm forecasng(stlf model. The auo correlaon funcon (ACF can be used o denfy he degree of assocaon beween daa n he seres separaed by dfferen me lags.e. prevous. The hsorcal of 7 days pror o day whose s o be predced have been consdered o buld he proposed forecasng model. Hence he oal daa pons are equal o 7*4=68. Snce he proposed model uses daa of 7 hours ago o predc he a hour h, 68-7=6 npu vecors are used o develop he forecas model. III. ELECTRIC LOAD FORECASTING USING PSO BASED LLWNN The srucure of LLWNN model s shown n Fg.. I comprse of npu layer, hdden layer and lnear oupu layer. The npu daa n npu layer of he newor are drecly ransmed no he wavele layer. As he hdden layer neurons mae use of waveles as acvaon funcons, hese neurons are usually called wavelons. Snce forecasng s used by power companes o ancpae he amoun of power needed o supply he demand, accurae esmaes are crucal for producers o maxmze her profs and for consumers o maxmze her ules. In sead of usng mul layered neural newors and s several varans a LLWNN s used for forecasng he nex day and nex wee elecrc n a deregulaed envronmen. In he proposed model, one hour ahead forecasng usng seven hours before daa and weny four hours ahead forecasng usng seven days.e. 68 hours before daa have been used. Accordng o wavele ransformaon heory, waveles n he followng form s a famly of ψ = / n { ψ = a ψ : a, b R, z} x b a x = ( x, x,... xn a = ( a, a,... a n b = ( b, b... bn funcons, generaed from one sngle funcon ψ(x by he operaon of dlaon and ranslaon ψ(x. ψ(x whch s localzed n boh me space and he frequency space, s called a moher wavele and he parameers a and b are he scale and ranslaon parameers, respecvely. Insead of he sragh forward wegh w (pecewse consan model, a lnear model v = w + w x +... + wn xn s nroduced. The acves of he lnear models v (=,,-------- n are deermned by he assocaed locally acve wavele funcons ψ (x (=,,-------,n, hus v s only locally sgnfcan.non-lnear wavele bass funcons (named waveles are localzed n boh me space and frequency space. Fg. : General srucure of a local lnear wavele neural newor. Here m = n and oupu (Y of he proposed model s Calculaed as follows: M ( Y= ( w + w x + + wnxn x ψ (x ( = The moher wavele s Inernaonal Journal of Insrumenaon, Conrol and Auomaon (IJICA ISSN : 3-89 Volume-, Issue-, 59
Shor-Term Load Forecasng usng PSO based Local Lnear Wavele Neural Newor ψ (x = x x σ e x c σ (3 ψ ( x = e (4 where x = d + d +... + dn IV. TRAINING The usually used learnng algorhm for LLWNN s graden decen mehod o ge all he unnown parameers of newor.e. ranslaon and dlaon coeffcens, weghs whch are randomly nalzed a begnnng snce he funcon compued by he LLWNN model s dfferenable wh respec o all menoned unnown parameers. Bu s dsadvanages are slow convergence speed and easy say a local mnmum. Hence he proposed model s raned by he PSO algorhm. Parcle swarm opmzaon s bascally developed hrough smulaon of brd flocng n wo-dmenson space. The poson of each agen s represened by XY axs poson and also he velocy s expressed by vx and vy. Modfcaon of he agen poson s realzed by he poson and he velocy nformaon. Brd flocng opmzes a ceran objecve funcon. Each agen nows s bes value so far (pbes and s XY poson. Moreover, each agen nows he bes value so far n he group (gbes among pbes. Manly each agen res o modfy s poson usng he followng nformaon. (a The dsance beween curren poson and pbes. (b The dsance beween he curren poson and gbes. Velocy of each agen can be modfed by he followng equaon: + v = wv + c rand ( pbes s + c rand ( gbes s where, v s he velocy of agen a eraon, w s weghng funcon, c s weghng facor, s s he j curren poson of agen I a eraon, pbes s he pbes of agen and gebs s he gbes of he group. Usng he above equaon, a ceran velocy, whch gradually ges close o pbes and gbes can be calculaed. The curren poson (searchng pon n he (5 soluon space can be modfed by he followng equaon: s + = s + v + (6 The frs erm of (5 s he prevous velocy of he agen. The second and hrd erms are used o change he velocy of he agen. The general flow char of PSO for opmzng a local lnear wavele neural newor can be descrbed as follows: Sep. Generaon of nal condon of each agen : Inal searchng pons (s and velocy (v of each agen are usually generaed randomly whn he allowable range. Noe ha he dmenson of search space s consss of all he parameers used n he local lnear wavele neural newor as shown n equaon (. The curren searchng pon s se o pbes for each agen. The bes-evaluaed value of pbes s se o gbes and he agen number wh he bse value s sored. Sep. Evaluaon of searchng pons of each agen : The objecve funcon value s calculaed for each agen. If he value s beer han he curren pbes of he agen, he pbes value s replaced by he curren value. If he bes value of pbes s beer han he curren gbes, gbes s replaced by he bes value and he agen number wh he bes value s sored. Sep. 3 Modfcaon of each searchng pon: The curren searchng pon of each agen s changed usng (5 and (6. Sep. 4 Checng he ex condon: The curren eraon number reaches he predeermned maxmum eraon number, hen ex oherwse go o sep. V. ACCURACY MEASURES Mean absolue percenage error (MAPE s used o assess predcon accuracy of he developed models n he paper. The absolue error (AE s defned as da, d f, AE = (7 d a, The daly mean absolue error (DMAE can become compued as follows. DMAE = 4 4 = AE (8 Inernaonal Journal of Insrumenaon, Conrol and Auomaon (IJICA ISSN : 3-89 Volume-, Issue-, 6
Shor-Term Load Forecasng usng PSO based Local Lnear Wavele Neural Newor The daly mean absolue percenage error 4 (DMAPE = AE (9 4 = The weely mean absolue error (WMAE = 68 68 = AE ( And, The weely mean absolue percenage error 68 (WMAPE = AE ( 68 = Predced.667.46.3.48.88.44.34.4.34.4983 ly -.8 -.4 -.3.5.78.379.389.9.584.76 Predced.587.49.9.99.6.78.694.49.3985.659 ly -.5 -.34 -.6.78.5.55.459.89.64.367 VI. RESULTS & ANALYSIS To llusrae he forecasng procedure, he elecrc for he hub of New England Pool from s June, 6 o 3 s July, 6 s used for predcon. The forecased obaned wh proposed Model s shown n Fg. and he correspondng error s shown n Fg. 3 for ranng daa se. The forecased obaned wh proposed model by usng PSO algorhm as learnng algorhm and he acual are shown n Fg. 4 and Fg-5 shows he error for es daa se.. TABLE - Resuls obaned by proposed model for 4 hours of a day. Tes wee daa se Tranng wee daa se Predced.675.754.7.7333.7458.6976.6653.66.6439.698.667.63.6499.75 ly. -.534 -.7 -.5 -.443 -.4.84.766.998.533.496.833.6.365 Predced.6836.698.74.784.75.697.6837.698.7438.745.73.734.765.748 ly.5 -.94.67 -.4 -.69.48.464.5.48.58 -.379.3.859 -.668 Table I provdes he predced n erms he maxmum and relave error for s 4 hrs. of he ranng daa se and es daa se ang d_daa as npu vecors n proposed model by usng PSO algorhm as learnng algorhm. Where d_daa=( daa-mnmum /(maxmum -mnmum for a gven perod. Local Lnear Wavele Neural Newor raned by PSO algorhm was convergen a eraon 94 wh WMAPE 7.56 for ranng daa se and he WMAPE for es daa se s 8.63. I can be seen from Fg. 4 and Table ha predcaed of he es wee are que close o he acual. Very less ranng me as compared o he oher forecasng mehods shows he hgher convergence rae of PSO based LLWNN model o predc he elecrc wh hgher accuracy. A PSO based LLWNN performs beer han all consdered mehods, because boh smooh global and sharp local varaons of sgnal can be effecvely represened by he wavele bass acvaon funcon for hdden layer neurons whou any exernal decomposer / composer and also no havng oo many hdden uns. VII. CONCLUSION In hs paper, elecrc forecasng by usng a PSO based local lnear wavele neural Ne wor (LLWNN model s used. The characersc of he newor s ha he sragh forward wegh s replaced by a local lnear model and hereby needs only smaller waveles for a gven problem han he common wavele neural newors. Hence he proposed model requres smple modelng echnque and lgh compuaonal effor o produce reasonably accurae resul. Snce he proposed model s dscree and logcal n naure, by smple learnng he hsorcal samples, hs mehod can map he npu-oupu relaons and hen can be used for he predcon. The hghes forecas accuracy s aaned by LLWNN model snce boh smooh global Inernaonal Journal of Insrumenaon, Conrol and Auomaon (IJICA ISSN : 3-89 Volume-, Issue-, 6
Shor-Term Load Forecasng usng PSO based Local Lnear Wavele Neural Newor sharp local varaon of elecrc sgnal can be effecvely represened by he wavele bass acvaon funcon for hdden layer neuron whou any decomposer/composer. Ths mehod avers he rs of loosng he hgh frequency componens of elecrc sgnals because proposed model for forecasng s no decomposng me seres daa exernally. I s also observed ha a PSO based LLWNN converges wh hgher rae and ou performed n he forecasng he elecrc compared o oher models because of s favourable propery for modelng he non-saonary and hgh frequency sgnal such as elecrc. REFERENCES [] S.J.Huang and K.R.Shh, Shor erm forecasng va ARMA model denfcaon ncludng non-guassan process consderaon IEEE Trans. On power sysems, vol 8,no, pp 673-679,may 3.. [] I.Maghram and S.Rahman: Analyss and evaluaon of fve shor erm forecasng echnques IEEE Trans. On power sysems, Apr 989,pp 484-49. [3] S.Rahman, O. Hazm, Generalzed nowledge based shor erm forecasng echnque, IEEE Trans. On power sysems, vol. 8,no,pp58-54, May 993. [4] C.N.Lu and S.Vemur, Neural newor based shor erm forecasng IEEE rans. On power sysems, vol 8, no.,pp336-34, Feb 993. [5] T.W.S Chow and C.T. Leung, Non-lnear auoregressve negraed neural newor model for shor erm forecasng, IEE proc. Generaon ransmsson and dsrbuon, vol. 43, no.5, pp5-56, sep 996.. [6] R.Lamedca,A Prudenz, M Sforna, M.Cacoa and V.O Cancell, Neurar newor based echnque for shor erm forecasng of anomalous perods, IEEE Trans. On power sysems, vol no. 4, pp 749-756,Nov 996.. [7] I.Drezga and S.Rahman, Shor erm forecasng wh local ANN predcors. IEEE rans. On power sysems, vol 4, no. 3, pp 844-85, Aug 999.. [8] H.Chen, C.Canzare, and A.Sngh ANN based shor erm forecasng n elecrcy mares, proc. IEEE wner meeng, Columbus, Oho,, pp 4-45, Jan.. [9] H.S.Hpper, C.E.Pedrera and R.C. Souza, Neural newor for shor erm forecasng, arevew andevaluaon, IEEE rans. On power sysems, vol. 6, no., pp 44-55, Feb.. [] T.Senjya, H. Taara, K.Uezao and T. Funabash, One hour ahead forecasng usng neural newor, IEEE rans. On power sysems, Vol. 7, no., pp 3-8,.. [] J.W.Taylor and R.Buzza, Neural newor forecasng wh weaher ensemble predcors, IEEE Transacons on Power sysems, Aug, pp. 66-63.. [] L.M.San and M.K Son, Arfcal neural newor based pea forecasng usng conjugae graden mehods, IEEE Transacons on Power Sysems, Aug vol, no.3, pp. 97-9. [3] P.Mandal, T. Sanjyu, N.urasa and T. Funabash, A neural. newor based several hour ahead elecrc forecasng usng smlar days approach, In. Jouranal of elecrc power and energy sysem, vol 8, no 6, pp367-373, Jul 6. [4] D.Benaouda, F. Muragh, J.L. Sar and O.Renaud, Wavele based non lnear mulscale decomposon model for elecrcy forecasng, Neuro compung vol 7, pp 39-54,dec 6. Predced Tranng.5 4 6 8 4 6 8.5 4 6 8 4 6 8 Fg. : Dynamc sysem oupu and model oupu for ranng wee daa se.3.5..5..5 -.5 -. -.5 -. 4 6 8 4 6 8 Fg. 3 : ly error for ranng wee daa se Inernaonal Journal of Insrumenaon, Conrol and Auomaon (IJICA ISSN : 3-89 Volume-, Issue-, 6
Shor-Term Load Forecasng usng PSO based Local Lnear Wavele Neural Newor Predced Tes.5 4 6 8 4 6 8.5..5..5 Tes.5 4 6 8 4 6 8 -.5 -. -.5 -. 4 6 8 4 6 8 Fg. 4 : Dynamc sysem oupu and model oupu for es wee daa se Fg. 5 : ly error for es wee daa Inernaonal Journal of Insrumenaon, Conrol and Auomaon (IJICA ISSN : 3-89 Volume-, Issue-, 63