Inernaonal Journal of Scenfc & Engneerng Research, Volume 5, Issue 7, July-204 723 ISS 2229-558 Secury Consraned Un Commmen Based Load and Prce Forecasng Usng Evoluonary Opmzed LSVR Ehab E. Elaar, Member, IEEE, and Tamer A. Farrag Absrac In hs paper, a local predcor approach based on proven powerful regresson algorhm whch s suppor vecor regresson (SVR) combned wh space reconsrucon of me seres s nroduced. In addon, real value genec algorhm (GA) has been ulzed n he proposed mehod for opmzaon of he parameers of he SVR. In he proposed approach, he embeddng dmenson and he me delay consan for he load and prce daa are compued frsly, and hen he connuous load and prce daa are used for he phase space reconsrucon. Subsequenly, he reconsruced daa marx s subjec o he local predcon algorhm. Then he forecased loads and prce are fed no IEEE 30 bus es sysem for secury consran un commmen o show he reacons of un commmen o load and prce forecasng errors. The proposed model s evaluaed usng real world daase. The resuls show ha he proposed mehod provdes a much beer performance n comparson wh oher models employng he same daa. Index Terms Load forecasng, prce forecasng, local predcors, secury consraned un commmen, suppor vecor regresson, genec algorhm, sae space reconsrucon. ITRODUCTIO HORT erm load forecasng (STLF) s a val par of he op- of power sysems. STLF very valuable ool. Ths s because of he upheaval of deregulaon n elecrcy marke. Shor-erm prce forecasng n a Seraon ams o predc elecrc loads for a perod of mnues, hours, days, or weeks. STLF has always been a compeve elecrcy marke s sll a challengng ask because of he specal elecrc prce characerscs [7], [8], such as very mporan ssue n economc and relable power sysems operaon such as un commmen, reducng spnnng reserve, manenance schedulng, ec. calendar effec, hgh volaly, hgh percenage of unusual hgh-frequency, non-saonary behavor, mulple seasonaly, Several STLF mehods ncludng radonal and arfcal prces, hard non-lnear behavor ec. nellgence-based mehods have been proposed durng he In he leraure, several echnques for shor-erm elecrcy prces forecasng have been repored, namely radonal las four decades. The relaonshp beween elecrc load and s exogenous facors s complex and nonlnear, makng and AI-based echnques. The radonal echnques nclude auoregressve negraed movng average (ARIMA) [9], wavele-arima [0] and mxed model [] approaches. Alhough, que dffcul o be modeled hrough radonal echnques such as lnear or mulple regresson [], auoregressve movng average (ARMA), exponenal smoohng mehods [2], hese echnques are well esablshed o have good performance, hey canno always represen he non-lnear characerscs of he complex prce sgnal. Moreover, hey requre a lo Kalman-fler-based mehods [3], ec. On he oher hand, varous arfcal nellgence echnques were used for STLF; of nformaon, and he compuaonal cos s very hgh. among hese mehods, arfcal neural neworks (As) have On he oher hand, AI-based echnques have been used by receved he larges share of aenon. The As ha have many researchers for he prce forecasng n elecrcy markes. These mehods can deal wh he non-lnear relaon be- been successfully used for STLF are based on mullayered perceprons [4]. The neural fuzzy nework has also been used ween he nfluencng facors and he prce sgnal, herefore for load forecasng [5]. Radal bass funcons (RBFs) [6] have he forecasng precson s rased. These echnques nclude been also used for day-ahead load forecasng, gvng beer neural nework () [2], radal bass funcon [3], fuzzy resuls han ha of he convenonal neural neworks. neural nework (F) [4] and hybrd nellgen sysem (HIS) Accurae forecasng of he elecrcy prce has become a [5] Recenly, SVR [6], [7] has also been appled successfully o STLF and prce forecasng. SVR replaces he emprcal rsk mnmzaon whch s generally employed n he classcal Ths work was suppored bytaf Unversy, KSA under gran 3267-435-. mehods such as As, wh a more advanageous srucural The Auhors are wh he deparmen of he Elecrcal Engneerng, Faculy of Engneerng, Taf Unversy, Kgdom of Saud Araba. rsk mnmzaon prncple. SVR has been shown o be very Ehab E. Elaar on leave from he Deparmen of Elecrcal Engneerng, ressan o he over fng problem and gve a hgh generalzaon performance n forecasng problems [8]. Faculy of Engneerng, Menofa Unversy, Shebn El-Kom, Egyp (e-mal: Udr.elaar0@yahoo.comU5T). All he above echnques are known as global predcors n Tamer A. Farrag s on leave from he Deparmen of Communcaons and whch a predcor s raned usng all daa avalable bu gve a Elecroncs, Msr hgh nsue of Engneerng and Technology, Egyp. predcon usng a curren daa wndow. The global predcors suffer from some drawbacks whch are dscussed n our prevous work [9], [20]. To overcome hese drawbacks, he local 204 hp://www.jser.org
Inernaonal Journal of Scenfc & Engneerng Research, Volume 5, Issue 7, July-204 724 ISS 2229-558 SVR predcor s proposed n our prevous work [9] [2] and can be used o solve he STLF and prce forecasng problem. Phase space reconsrucon s an mporan sep n local predcon mehods. The radonal me seres reconsrucon echnques usually use he coordnae delay (CD) mehod [22] o calculae he embeddng dmenson and he me delay consan of he me seres [23]. Alhough local SVR (LSVR) mehod gves good predcon accuracy when s appled o STLF and prce forecasng, has a serous problem. Ths problem s ha here s a lackng of he srucural mehods for confrmng he selecon of SVR s parameers effcenly. So, n hs paper, a local predcor approach based on proven powerful regresson algorhm whch s SVR combned wh space reconsrucon of me seres s nroduced. In addon, real value genec algorhm (GA) has been ulzed n he proposed mehod for opmzaon of he parameers of he SVR. The proposed algorhm s called evoluonary opmzed LSVR (EOLSVR). Un commmen problem (UC) s a nonlnear, mxed neger combnaoral opmzaon problem. The UC problem s he problem of decdng whch elecrcy generaon uns should be scheduled economcally n a power sysem n order o mee he requremens of load and spnnng reserve. I s a dffcul problem o solve n whch he soluon procedures nvolve he economc dspach problem as a sub-problem. Snce UC searches for an opmum schedule of generang uns based on load forecasng daa, he mprovemen of load forecasng s frs sep o enhance he UC soluon [24]. In hs paper, we propose secury consraned un commmen (SCUC) mehod o reduce he producon cos by combnng load and prce forecasng wh UC problem. Frs, shor-erm loads and prce are forecased usng EOLSVR, local 2 TIME SERIES RECOSTRUCTIO onlnear me seres analyss and predcon have become a relable ool for he sudy of complex me seres and dynamcal sysems. A commonly used ool s he phase space reconsrucon echnque whch sems from he embeddng heorem developed by Takens and Sauer [22], [25]. I llusraes clearly he phase space rajecory of a me seres n he 204 hp://www.jser.org embedded space nsead of he rajecory n he me doman. The heorem regards an -dmensonal me seres x() for =, 2,..., as compressed hgher dmensonal nformaon and, hus, s feaures can be exraced by exendng x() o a vecor X() n a d-dmensonal space as follows: [ x( ), x( m), x( 2m),..., x( ( d ) )] X ( ) = m where d denoes he embeddng dmenson of he sysem and m s he delay consan. Based on Takens heorem [22], o oban a fahful reconsrucon of he dynamc sysem, he embeddng dmenson mus sasfy d 2 D a +, where D a s he dmenson of he aracor. In order o oban an approprae model reconsrucon, s necessary o esmae d and m. The correlaon dmenson mehod [26] s he mos popular mehod for deermnng d because of s compuaonal smplcy. The muual nformaon mehod proposed n [27] usually provdes a good creron for he selecon of m. In general, he proper value of m corresponds o he frs local mnmum of muual nformaon. In hs paper, he correlaon dmenson mehod [26] and he muual nformaon mehod [27] are used o calculae d and m respecvely. The deals of how o choose he proper values of d and m usng hese wo mehods have been repored n [9]. 3 GEETIC ALGORITHM The GA s a search algorhm for opmzaon, based on he mechancs of naural selecon and genecs [28], [29]. The GA s able o search very large soluon spaces effcenly by provdng a lower compuaonal cos, snce hey use probablsc ranson rules nsead of deermnsc ones. GA has a SVR and local RBF models. Then UC problem s solved usng number of componens or operaors ha mus be specfed n he dynamc programmng mehod. We have chosen he hsorcal daa for he Souh Ausrala elecrcy marke, whch ncludes he power demand and prce for he perod of 2003-2005. Hsorcal weaher daa was colleced from Macquare Unversy Web Se. Then he forecased loads and prce are fed no IEEE 30 bus es sysem for un commmen o show he reacons of un commmen o forecasng errors. The paper s organzed as follows: Secon 2 revew he me seres reconsrucon mehod. Secon 3 gves a bref dscrbon abou GA. A revew of he SCUC problem and s formulaon are presened brefly n Secon 4. The proposed mehod s presened n deals n Secon 5. Applcaons and smulaons for load and prce forecasng and UC problem are gven n Secons 6. Fnally, Secon 7 concludes he work. order o defne a parcular GA. The mos mporan componens are represenaon, fness funcon, selecon mehod, crossover, muaon and ermnaon. The GA sars wh an nal populaon of ndvduals (generaon) whch are generaed randomly. Every ndvdual (chromosome) encodes a sngle possble soluon o he problem under consderaon. The fes ndvduals are seleced by rankng hem accordng o a pre-defned fness funcon, whch s evaluaed for each member of hs populaon. The ndvduals wh hgh fness values herefore represen beer soluon o he problem han ndvduals wh lower fness values. There are many dfferen selecon operaors presened by some researchers such as sochasc samplng wh replacemen roulee wheel selecon and ournamen selecon [30]. Followng hs nal process, he crossover and muaon operaons are used where he ndvduals n he curren populaon produce he chldren (offsprng). The dea behnd he crossover operaor s o combne useful segmens of dfferen parens o form an offsprng ha benefs from advanageous b combnaons of boh parens [3]. Whle, by muaon, ndvduals are randomly alered. These varaons (muaon seps) are mosly small [3]. ormally, offsprng are muaed afer beng creaed by crossover. I s nended o preven ()
Inernaonal Journal of Scenfc & Engneerng Research, Volume 5, Issue 7, July-204 725 ISS 2229-558 premaure convergence and loss of genec dversy. A new populaon of ndvduals (generaon) s hen formed from he ndvduals n curren populaon and he chldren. Ths new populaon becomes he curren populaon and he erave cycle s repeaed unl a ermnaon condon s reached [28]. 4 SECURITY COSTRAIT UIT COMMITMET (SCUC) The objecve of secury-consraned un commmen (SCUC) dscussed n hs work s o oban a un commmen schedule a mnmum producon cos whou compromsng he sysem relably. The relably of he sysem s nerpreed as sasfyng wo funcons: adequacy and secury. In several power markes, he ndependen sysem operaor ISO plans he day-ahead schedule usng (SCUC)[32], [33]. The radonal un commmen algorhm deermnes he un schedules o mnmze he operang coss and sasfy he prevalng consrans such as load balance, sysem spnnng reserve, ramp rae lms, fuel consrans, mulple emsson requremens and mnmum up and down me lms over a se of me perods. The scheduled uns supply he load demands and possbly manan ransmsson flows and bus volages whn her permssble lms [34]. However, n crcumsances where mos of he commed uns are locaed n one regon of he sysem, becomes more dffcul o sasfy he nework consrans hroughou he sysem. Mahemacally, he objecve funcon, or he oal operang cos of he sysem can be wren as follows [32], [33]: HS, f X T off, [ F ( P ) + S ( u ) ] S = T mn u (2) P u = = where P s he oupu power of un a perod, u s he commmen sae of un a perod, F ( P ) s he fuel cos of un a oupu power P, S s he sar up prce of un a perod, s he number of generang un and T s he oal number of schedulng perods. The consrans are as follows: Power balance: u P = where D s he cusomers demand n me nerval. Generang lms: These lms defne he regon whn whch a un mus be dspached. u P mn P Mnmum up me: Once he un s commed, mus be kep runnng for ceran number of hours, called he mnmum up me, before allowng urnng off. Ths can be formulaed as follows: up ( X on T )( u u ) X ( ) on, = X on, + u D u P, 0 max (3) (4) (5) 204 hp://www.jser.org X, where, on s he number of hours he un has been on up lne and T s he mnmum up me. Mnmum down me: Once he un s urned off, s no allowed o be brough onlne agan before spendng ceran number of hours called mnmum down me. Ths can be formulaed as follows: down ( X T )( u u ) X off, 0 off, = ( X + )( u ) off, where X off, s he number of hours he un has been off down lne and T s he mnmum down me. Spnnng reserve: I can be modeled as follows: u P max D + R (7) where R s he spnnng reserve requremens. Transmsson flow lm from bus k o bus m: max P km P km ( ) = f where P() s he real power generaon vecor and φ() s he phase shfer conrol vecor a me T. The Sar up cos whch can be modeled by he followng form: CS, f X > T down + CH (9) off, where, HS, CS s he un s ho/cold sar up cos and CH s he cold sar hour. F P s frequenly represened by he followng polynomal funcon: Fuel cos funcons ( ) F P = a + b P + c P (0) where a, b, c are he coeffcens for he quadrac cos curve of generang un. 5 EVOLUTIOARY OPTIMIZED LOCAL SUPPORT VECTOR REGRESSIO (EOLSVR) 5. Suppor Vecor Regresson (SVR) The basc dea of SVR s o map he daa x no a hgh dmensonal feaure space va a nonlnear mappng, and perform a lnear regresson n ha feaure space [7] as: ( x) w x b f =, + () max ( P( ), ϕ( ) ) p down ( ) ( ) 2 + CH km (6) (8)
Inernaonal Journal of Scenfc & Engneerng Research, Volume 5, Issue 7, July-204 726 ISS 2229-558 Where.,. denoes he do produc, w conans he coeffcens ha have o be esmaed from he daa and b s a real consan. Usng Vapnk s ε nsensve loss funcon [6], he overall opmzaon s formulaed as: mn w, b, ξ, ξ 2 T w w + C = ( ξ + ξ ) T y ( w φ( x ) + b) ( ( ) ) ε + ξ 5.2 Local predcors Local predcon s concerned wh predcng he fuure based only on a se of K neares neghbors n he reconsruced embedded space whou consderng he hsorcal nsances whch are dsan and less relevan. Local predcon consrucs he rue funcon by subdvson of he funcon doman no many subses (neghborhoods). Therefore, he dynamcs of me seres can be capured sep by sep locally n he phase space and he drawbacks of global mehods can be overcome. The local SVR (LSVR) and local RBF (LRBF) mehods can be summarzed as follows [9]: 204 hp://www.jser.org Frs, reconsruc he me seres as descrbed n he prevous secon. For, each query vecor q, he K neares neghbors {z q,z q 2,...,z q K} among he ranng npus s choosng usng he Eucldan dsance as he dsance merc beween he q and each z n he reconsruced me seres. Usng hese Kneares neghbors, ran he SVR (or RBF) o obansuppor vecors and correspondng coeffcens. Fnally, he oupu of SVR (or RBF) can be compued. T 5.3 EOLSVR subjec o w φ x + b y ε + ξ (2) There are some key parameers for SVR, whch are C, ε ξ, ξ 0, =,..., and σ n he Gaussan kernel funcon. The selecon of hese parameers s mporan o he generalzaon of he predcon. Inapproprae parameers n SVR lead o overfng or where, x s mapped o hgher dmensonal space by he funcon φ, ε s a real consan, ξ and ξ are slack varables under-fng [35]. Therefore, hese parameers mus be chosen subjec o ε-nsensve zone and he consan C deermnes he carefully. However choosng he opmal parameers s a very rade-off beween he flaness of f and ranng errors. mporan sep n SVR, here are no general gudelnes avalable o selec hese parameers ll now. The problem of opmal Inroducng Lagrange mulplers α and α wh α α =0 and α, α =0 for =,,, and accordng o he Karush-Kuhn- parameers selecon s very complcaed because he complexy of SVR (and hence s generalzaon performance) depends Tucker opmaly condons [7], he SVR ranng procedure amouns o solvng he convex quadrac problem: on all hree parameers ogeher. Thus, a separae selecon of each parameer s no adequae o ge an opmal regresson model. mn ( α α )( α j α j ) Q( x, x j ) + α, α 2, j= There are many rals o choose he SVR s parameers. Varous auhors have seleced hese parameers by experence ( ε α + α ) y ( α α ) [6], [36] bu hs mehod s no suable for nonexper users. = = The grd search opmzaon mehod has been proposed by 0 α Scholkopf and Smola [37] o ge he opmal parameers of, α C subjec o (3) SVR. However, hs mehod s me consumng. The cross valdaon mehod has been also used o selec he SVR s parame- = ( α α ) = 0, =,..., ers [36]. Ths mehod s very compuaonally nensve and The oupu s a unque global opmzed resul ha has daa-nensve. Pa and Hong proposed a GASVR model [38] he form: o opmze he SVR s parameers n whch he parameers are (4) ( α ) f ( x) = α = where, Q(x,x)= φ(x). φ (x). Usng kernels, all necessary compuaons can be calculaed drecly n he npu space, whou compung he explc map φ(x). Varous kernel ypes exs such as lnear, hyperbolc angen, Gaussan, polynomal, ec. [7]. Here, we employ he commonly used Gaussan kernel whch can be as defned as followng: x x Q( x = (5), x) exp 2 2σ Q( x, x ) + b j encoded as a bnary code. Ths mehod suffers from some problems. The frs one s ha encodng he parameers as bnary code wll lead o neger valued soluons and may suffer from he lack of accuracy [29]. In addon, f he lengh of he srng s no long enough, mgh be possble for he GA o ge near o he regon of he global opmum bu never wll arrve a. As evden from above, here s a lackng of he srucural mehods for confrmng he selecon of SVR s parameers effcenly. Therefore, a real value GA s proposed n hs work o selec he SVR s parameers of local SVR mehod whch smulaneously opmzes all SVR s parameers from he ranng daa. The seps for load and prce forecasng based on he proposed mehod can be summarzed as followng: Sep : Reconsruc he me seres: Load he mulvar ae me seres daase X = (x (), x 2(),..., x M()), ( =, 2,...,). Usng he correlaon dmenson mehod and he muual nformaon mehod, calculae he embeddng dmenson d and he me delay consan m for each me seres daa se. Then, reconsruc he mulvarae me seres usng hese values. Sep 2: Form a ranng and valdaon daa: The npu daase afer reconsrucon X ~ s dvded no wo pars, ha s a ranng X ~ daase and valdaon r X ~ daase. The va
Inernaonal Journal of Scenfc & Engneerng Research, Volume 5, Issue 7, July-204 727 ISS 2229-558 6 EXPREMET RESULTS sze of he ranng daase s r whle he sze of he valdaon daase s va. Sep 3: For each query pon xq, choosng he K neares neghbors of hs query pon usng he Eucldan dsance beween x q and each pon n X r ( < K<<< X ~ r ). Sep 4: Represenaon and generaon of nal populaon: In real value GA he real value parameers can be used drecly o form he chromosome. Ths means ha he chromosome represenaon n real value GA s sraghforward. In hs case, he hree parameers C, ε and σ are drecly coded o generae he chromosome CH = {C, ε, σ}. These chromosomes are all randomly nalzed. Sep 5: Evaluaon: each chromosome s evaluaed usng he fness funcon whch measures he performance of he model. I s que mporan for evolvng sysems o fnd a good fness measuremen. The fness (F) of each chromosome evaluaed usng mean absolue percenage error (MAPE) defned as: where A and F are he acual value and he forecased value, respecvely, va s he valdaon daase sze, and denoes he es nsance ndex. Sep 6: Selecon: A sandard roulee wheel selecon mehod s employed o selec he fes chromosomes from he curren populaon. Sep 7: Crossover: The operaor of crossover can now be mplemened o produce wo offsprng from wo parens whch are chosen usng he roulee wheel selecon mehod. In hs work, he lne arhmecal crossover s used [28]. Sep 8: Muaon: Smlarly, he muaon operaon can conrbue effecvely o he dversy of he populaon. In hs work, he Gaussan muaon [28] s used. Sep 9: Els sraegy: The chromosome ha has he wors fness value n he curren generaon s replaced by he chromosome ha has he bes fness value n he old generaon Sep 0: Check he soppng creron: The modellng can be ermnaed when he soppng creron s reached. In hs work, we use a predeermned maxmum number of generaons as a ermnaon condon. If he soppng creron s no sasfed, he model has o be expanded, he seps 5 o 9 can be repeaed unl he soppng creron s sasfed. Sep : Afer he ermnaon condon s sasfed, he chromosome whch gves he bes performance n he las generaon s seleced as he opmal values of SVR s parameers. Sep 2: Tran SVR: The K neares neghbors of he query pon and he opmzed parameers are used o ran he SVR algorhm. Sep 3: Calculae he predcon value of he curren query pon usng equaon (4). Sep 4: Then, he seps 3 o 3 can be repeaed unl he fuure values of dfferen query pons are all acqured. 204 hp://www.jser.org In hs paper, he performance of he EOLSVR s esed and compared wh local SVR and local RBF usng hourly load prce and emperaure daa n Souh Ausrala. The load daa used ncludes hourly load and prce for he perod of 2003-2005 for he Souh Ausrala elecrcy marke. Whle he hourly emperaure for he same perod s colleced from Macquare unversy web se. 6. Parameers To mplemen a good model, here are some mporan parameers o choose. Choosng he proper values of d and m s a crcal sep n he algorhm. The correlaon dmenson mehod and he muual nformaon mehod are used o selec d and m, respecvely, and he opmal values of hese parameers are shown n Table. Usng he obaned values of d and m, he mulvarae me seres can be reconsruced as descrbed n Secon 2. va TABLE A F MAPE = 00 (6) PHAE RECOSTRUCTIO PARAMETERS va = A Load daa Temperaure daa Prce daa Daase d m d m d m Souh Ausrala elecrcy marke 4 3 4 2 5 3 Choosng K s very mporan sep n order o esablsh he local predcon model. There are some mehods used n leraures o fnd hs parameer. In hs paper K s calculaed usng a sysemac mehod whch s proposed by us n [20]: kmax α (7) K round k = max D max = k = D k ( x ) where, s he number of ranng pons, k max s he maxmum number of neares neghbors, D k(x) s he dsance beween each ranng pon x and s neares neghbors whle D max s he maxmum dsance, kmax = = D k k ( x ) kmax Dmax s he average dsance around he pons whch s nversely proporonal o he local denses and α s a consan. The wo consans k max and α are very low sensvy parameers. k max can be chosen as a percenage of he number of ranng pons () for effcency whle α can be chosen as a percenage. In hs paper, k max and α are always fxed for all es cases a 70% of and 95, respecvely. 6.2 Forcasng Accuracy Evaluaon For all performed expermens, we quanfed he predcon performance wh he Mean Absolue Error (MAE) and Mean Absolue Percenage Error (MAPE). They can be defned as follows: MAE = n MAPE = n n = n = A( ) F( ) A( ) F( ) 00 A( ) (8)
Inernaonal Journal of Scenfc & Engneerng Research, Volume 5, Issue 7, July-204 728 ISS 2229-558 (9) TABLE 5 IMPROVEMET OF THE EOLSVR OVER OTHER APPROACHES where, A and F are he acual and he forecased loads, respecvely, n s he esng daase sze, and denoes he es nsance ndex. 6.3 Resuls and Dscusson The performance of he evoluonary opmzed local SVR (EOLSVR) s esed and compared wh local SVR and local RBF usng hourly load, prce and emperaure daa n Souh Ausrala. To make resuls comparable, he same expermenal seup s used for he hree predcors. Tha s he week of February 5-2, 2005 has been used as a esng week. The avalable hourly load and emperaure daa (for he perod of 2003-2005) are used o forecas he load of esng week. Also, he avalable hourly prce and emperaure daa (for he perod of 2003-2005) are used o forecas he prce of esng week. Frs, we calculae he MAE and MAPE of each day durng he esng week. Then he average MAE and MAPE values of each mehod for he esng week are calculaed. The resuls are shown n Tables 2 and 3. These resuls show ha, he EOLSVR mehod ouperforms local SVR and local RBF. Table 4 shows he MAE mprovemens of he EOLSVR mehod over local SVR and local RBF. Whle Table 5 shows he MAPE mprovemens of he EOLSVR mehod over local SVR and local RBF. These resuls show he TABLE 2 LOAD FORECASTIG RESULTS Local RBF Local SVR EOLSVR MAE (GW) 0.034 0.023 0.032 MAPE (%) 2.3.55 0.94 superory of he proposed mehod over oher mehods. TABLE 3 Prce Forecasng Resuls Local RBF Local SVR EOLSVR MAE (GW) 0.0322 0.0220 0.040 MAPE (%) 3.79 2.96.90 REGARDIG MAPE Load Forecasng Prce Forecasng MAPE Improvemen MAPE Improvemen EOLSVR 0.94 --.90 -- Local RBF 2.3 59.3% 3.79 49.86% Local SVR.55 39.35% 2.96 35.8% Fg. Forecased and acual hourly load from 5h o 2s February 2005 usng local RBF Fgures -3 show he acual load and forecased load values usng local RBF, local SVR and EOLSVR, respecvely for he esng week. TABLE 4 IMPROVEMET OF THE EOLSVR OVER OTHER APPROACHES REGARDIG MAE Load Forecasng Prce Forecasng MAE Improvemen MAE Improvemen EOLSVR 0.032 -- 0.040 -- Local RBF 0.034 57.96% 0.0322 56.52% Local SVR 0.023 38.02% 0.0220 36.36% Fg. 2 Forecased and acual hourly load from 5h o 2s February 2005 usng local SVR 204 hp://www.jser.org
Inernaonal Journal of Scenfc & Engneerng Research, Volume 5, Issue 7, July-204 729 ISS 2229-558 The resuls of load and prce forecasng are fed no he IEEE 30 bus es sysem. The IEEE 30 bus es sysem s used wh a oal of 6 generaors and 4 lnes. Table 6 shows he es sysem daa. The spnnng reserve s assumed o be 0% of he demand. The acual loads (24 hour) as well as he forecased loads are gven n Table 7. If he nal commmen sae of a generaor s, means hs generaor s on and zero ndcaes hs generaor s off. The IEEE 30 bus es sysem has 4 lnes. Each lne can ransm a maxmum power flow n MW. Table 8 shows he maxmum power flow for each lne Feasble un combnaon and oal cos (TC) values of he es sysem usng dynamc programmng mehod for load values and forecasng load values are gven n Table 9. I s clear ha accurae load forecasng s very mporan for he UC soluon. The oal cos of he forecasng load values for local RBF mehod s more han ha of acual load values by $340.6. Addonally, he oal cos of he forecasng load values for local SVR s more han ha of acual load values by $506. Whereas he oal cos of he forecasng load values for EOLSVR s more han ha of acual load values by $334.. 7 COCLUSIO In hs paper, we have proposed EOLSVR mehod for elecrcal load and prce forecasng. Afer ha he resuls of load and prce forecasng are used o solve he secury consran un commmen problem. The proposed mehod combnes a proven powerful regresson algorhm whch s SVR wh a local predcon framework. For daa preprocessng, he embeddng dmenson and he me delay consan for he npu daa are compued frsly, and hen he connuous load and prce daa are used for he phase space reconsrucon. In addon, he neghborng pons are presened by Eucldan dsance. Accordng o hese neghborng pons, he local model s se up. The local predcors can overcome he drawbacks of he global predcors by nvolvng more han one model o ulze he local nformaon. Therefore, he accuracy of he local predcor s beer 204 hp://www.jser.org han he global predcor n whch only one model s engaged for all avalable daa ha conans rrelevan paerns o he curren predcon pon. In addon, o se he SVR s parameers appropraely, a new mehod s proposed. Ths mehod adops real value GA o seek he opmal SVR s parameers values and mproves he predcon accuracy. Then he forecased loads and prce are fed no IEEE 30 bus es sysem for secury consran un commmen o show he reacons of un commmen o load and prce forecasng errors. Dynamc programmng mehod s used for solvng he UC problem. Toal coss are calculaed for load daa whch s aken from Souh Ausrala elecrcy marke and forecasng load and prce daa compued by local RBF, local SVR and EOLSVR, separaely. Comparng hese oal coss show ha accurae load forecasng s mporan for UC. Over-predcon of STLF wases resources snce more reserves are avalable han needed and, n urn, ncreases he operang cos. On he oher hand, under-predcon of STLF leads o a falure o provde he necessary reserves whch s also relaed o hgh operang cos due o he use of expensve peakng uns. ACKOWLEDGMET The auhors graefully acknowledge he Taf Unversy for s suppor o carryou hs work. I funded hs projec wh a fund number 3267-435-. REFERECES [] A. D. Papalekopulos and T. C. Heserberg, A regresson-based approach o shor-erm sysem load forecasng, IEEE Trans. Power Sys., 5 (4), 535 547, ov. 990. [2] J. W. Taylor, L. M. de Menezes, and P. E. McSharry, A comparson of unvarae mehods for forecasng elecrcy demand up o a day ahead, In. J. Forecasng, 22 (), 6, 2006. [3] J. H. Park, Y. M. Park, and K. Y. Lee, Compose modelng for adapve shorerm load forecasng, IEEE Trans. Power Sys., 6 (2), 450 457, May 99. [4] H. S. Hpper, C. E. Pedrera, and R. C. Souza, eural neworks for shor erm load forecasng: A revew and evaluaon, IEEE Trans. Power Sys., 6 (), pp. 44 55, Feb. 200. [5] C. J. Ln, C. H. Chen, and C. T. Ln, A hybrd of cooperave parcle swarm opmzaon and culural algorhm for neural fuzzy neworks and s predcon applcaons, IEEE Trans. Sys.,Man, Cyber. C, Appl. Rev., 39 (), 55 68, Jan. 2009. [6] S. Sheng and C. Wang, Inegrang radal bass funcon neural nework wh fuzzy conrol for load forecasng n power sysem, n Proc. IEEE Trans. Ds. Conf. Exhb. Asa and Pacfc, 2005, pp. 5. [7] C. Maros, J. Rodrguez, and M. Sanchez, Forecasng elecrcy prces by exracng dynamc common facors: applcaon o he Iberan Marke, IET Gener. Transm. Dsrb., 6, (), 20, 202. [8] L. San, S. Aggarwal, and A. Kumar, Parameer opmsaon usng genec algorhm for suppor vecor machne-based prce forecasng model n aonal elecrcy marke, IET Gener. Transm. Dsrb., 4, (), 36 49, 200. [9] T. Jakasa, I. Androces,and P. Sprcc, Elecrcy prce forecasng ARIMA model approach. Eghh In. Conf. Eur. Energy Marke (EEM), 20, pp. 222 225 [0] A. Conejo, M. Plazas, R. Espnola, and A. Molna, Day-ahead elecrcy prce forecasng usng he wavele ransform and ARIMA models, IEEE Trans.
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Inernaonal Journal of Scenfc & Engneerng Research, Volume 5, Issue 7, July-204 73 ISS 2229-558 TABLE 6 TEST SYSTEM DATA Un Un 2 Un 3 Un 4 Un 5 Un 6 Pmax (MW) 500 400 250 250 200 350 Pmn (MW) 200 50 50 50 25 50 a ($/h) 0 0 20 0 20 0 b ($/MWh) 200 50 80 00 80 50 c ($/MWh2) 00 20 40 60 40 00 up T (h) 5 4 3 3 4 down T (h) 3 2 2 2 2 Sar up cos 200 00 80 80 30 95 Inal sae 0 0 0 TABLE 7 ACTUAL LOAD OF 6 UITS 24 HOUR TEST SYSTEM AD THE FORECASTED LOADS USIG LRBF, LSVR AD EOLSVR Loads (GW) Hour 2 3 4 5 6 7 8 9 0 2 3 4 5 6 7 8 9 20 2 22 23 24 Acual.33.9.05.00 0.96 0.98.00.04.2.9.24.30.32.32.30.3.34.36.35.35.38.32.28.38 LOCAL RBF.37.28.4.05 0.96 0.98.04.0.2.23.28.39.32.3.3.34.36.37.32.34.39.33.22.40 LOCAL SVR.35.24.09.03 0.96 0.98.03.08.5.23.28.33.30.3.30.29.35.36.33.34.38.33.30.40 EOLSVR.34.20.07.00 0.96 0.98.03.06.5.20.28.33.30.3.30.30.34.36.35.34.38.32.27.39 TABLE 8 MAXIMUM POWER FLOW FOR EACH LIE I THE TEST SYSTEM (MW) L 650 L 325 L2 80 L3 80 L4 60 L2 650 L2 60 L22 80 L32 80 L3 325 L3 325 L23 80 L33 80 L4 650 L4 325 L24 80 L34 80 L5 650 L5 325 L25 80 L35 80 L6 325 L6 325 L26 60 L36 325 L7 450 L7 60 L27 60 L37 80 L8 350 L8 60 L28 60 L38 80 L9 650 L8 60 L29 60 L39 80 L0 60 L20 80 L30 80 L40 60 204 hp://www.jser.org
Inernaonal Journal of Scenfc & Engneerng Research, Volume 5, Issue 7, July-204 732 ISS 2229-558 TABLE 9 FEASIBLE UIT COMBIATIO OF TEST SYSTEM FOR ACTUAL LOAD AD FORECASTIG LOAD VALUES USIG LOCAL RBF, LOCAL SVR AD EOLSVR Hour Feasble UC (Acual load) Feasble UC (Local RBF) Feasble UC (Local SVR) Feasble UC (EOLSVR) 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 9 0 0 0 0 0 0 0 0 0 0 0 0 0 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 23 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 24 0 0 0 0 0 0 0 0 0 0 0 0 TC $ 60665.3 $ 69305.9 $ 68.5 $ 609506.4 204 hp://www.jser.org