LONG TERM ELECTRIC PEAK LOAD FORECASTING OF KUTAHYA USING DIFFERENT APPROACHES

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1 Iteratoal Joural o Techcal ad Physcal Problems of Egeerg (IJTPE) Publshed by Iteratoal Orgazato o TPE (IOTPE) ISSN IJTPE Joural jtpe@otpe.com Jue 0 Issue 7 Volume 3 Number Pages 87-9 LONG TERM ELECTRIC PEAK LOAD FORECASTING OF KUTAHYA USING DIFFERENT APPROACHES Y. Asla S. Yavasca C. Yasar Electrcal Egeerg Departmet, Uversty of Dumlupar, Kutahya, Turkey yasla@dpu.edu.tr, serkayavascaoglu@hotmal.com, cyasar@dpu.edu.tr Abstract- I the system plag, cotrol ad maagemet of power dstrbuto compaes the log term peak load demad projectos has a mportat role. I geeral, the load forecastg s performed by studyg the past evets. Log term forecastg of future peak load demad s very mportat for the ecoomc ad secure operato of power systems. I ths study the log term peak load forecastg s performed for the cty of Kutahya wth the least squares regresso based methods ad artfcal eural etworks (ANN) usg the load, temperature ad populato growth data from 000 to 008. The results attaed are valdated wth the real data obtaed from the Turksh Electrcty Dstrbuto Corporato (TEDAS) whch represets the mothly peak load electrc cosumpto Kutahya, Turkey. By comparg the forecasted results wth the real data the most sutable method s proposed. Keywords: Load Forecastg, Least Squares Regresso, Artfcal Neural Networks. I. INTRODUCTION Load forecastg s of the most dffcult problems dstrbuto system plag ad aalyss. However, ot oly hstorcal load data of a dstrbuto system play a very mportat role o peak load forecastg, but also the mpacts of meteorologcal ad demographc factors must be take to cosderato [, ]. For plag, maagemet ad effectve operato of electrc power systems, load forecastg should be accomplshed over a broad spectrum of tme tervals [3]. Load forecastg methods are dstgushed o the bass of forecastg perods. I geeral, the requred load forecastg ca be categorzed to short, medum ad log term forecasts. Short term forecastg (half hour to oe week ahead) represets a great savg potetal for ecoomc ad secure operato of power systems. Medum term forecastg (oe day to several moths) deals wth the schedulg of fuel supples ad mateace operatos, ad log term forecastg (more tha a year ahead) s useful for plag operatos [-3]. Majorty of the electrc load forecastg methods are dedcated to short term forecastg ad relatvely less work has bee doe o log or medum term load forecastg. To date o specfc methodology has bee developed by whch projectos regardg atcpated electrcty cosumpto ca be made accurately specally over a log-term tme frame [4, 5]. Geerally, load forecastg methods are maly classfed to two categores: classcal approaches ad ANN based techques. Classcal approaches are based o statstcal methods ad forecast future value of a varable by usg a mathematcal combato of the hstorc formato [6]. For stace wth tme seres model of auto regressve tegrated movg average (ARIMA) whch corporates the kowledge of expereced huma operators short term load forecastg s carred out by usg a lear combato of the past values of the varable [6]. I [5, 7] log-term ad mdterm electrc load forecastg s preseted whch corporates daly ad weekly smple lear regresso models wth aual load growth to predct the future load demad. Meawhle, for dfferet resdetal areas by usg ANN based techques short ad log term load forecastg s performed [, 3, 8-] ad [] respectvely. I aforemetoed studes, the results attaed from dfferet approaches are compared ad dscussed. I these studes, t s poted out that, whle ANN ca yeld satsfactory results wth relatvely lmted formato, the case of statstcal methods loger put data s requred. I ths study, by usg the peak load data whch s recorded from 000 to 007 ad employg the least squares regresso based methods ad ANN, peak load demad for 008 s forecasted. The results are valdated by usg the real data of 008. II. FORECASTING METHODS I the forecastg process of log term electrc peak load, least squares regresso based methods ad ANN are used. A. Least Squares Regresso Methods I regresso based models, the predcto error s mmsed to zero by usg the least squares approach as gve Equato (). S = ( y, y, ) () real value approxmate 87

2 Iteratoal Joural o Techcal ad Physcal Problems of Egeerg (IJTPE), Iss. 7, Vol. 3, No., Ju. 0 I the equato; s the umber of data, y realvalue, s the exstg recorded data, y, approxmate s the type of the fucto used ad S s the sum of the squared predcto errors. I ths method, the varable S s equalsed to zero after dfferetated to each coeffcet. By ths way the ormal equatos are attaed [3, 4]. I the least squares method, regresso models whch are explaed detal below ad used as y, approxmate Equato (). The smple lear regresso The smple lear regresso model s based o the lear relatoshp betwee the depedet varable y ad depedet varable x as show Equato () [4, 3, 4]. y = a + bx () Ths s the equato of a straght le whch tercepts y axes at a wth a slope of b [4]. I order to atta zero error, by usg the least squares errors method, Equatos (3) ad (4) are obtaed. a + b a x + b x = y x = x y I the equatos the varables y, x ad represet the peak load, the years ad the umber of years whch the forecastg s based o respectvely. The a ad b coeffcets are calculated from the Equatos (3) ad (4) ad replaced Equato () for the load forecastg [4]. Multple lear regresso Ths approach shows a plae the space wth three dmesos whch ca be expressed as gve Equato (5) [3, 4]. y = a + bx + cx (5) I the equato, a, b, ad c are regresso parameters relatg the mea value of y to x ad x. Whe the least squares method s appled (to atta zero error), Equato (6) s obtaed [5]. x x y a = x x x x b x y. (6) c x x. x x x y By solvg the Equato (6); a, b ad c parameters are calculated; where y s the peak load, x s the temperature, x s the populato data ad s the umber of years the forecastg algorthm based o. By replacg the regresso parameters Equato (5) the peak load forecastg s performed. The quadratc regresso I ths approach the parabolc fucto whch s gve Equato (7) s used [4]. y = a + bx + cx (7) (3) (4) The a, b ad c coeffcets of the parabolc fucto ca be obtaed from Equato (8) whch s wrtte matrx form. x x x a 3 = x x x b x y (8) c 3 4 x x x x y The load forecastg s performed by replacg the calculated coeffcets Equato (7). The expoetal regresso I ths approach, the tred equato s formed by usg a expoetal fucto as gve Equato (9) [4, 4]. x y = ab (9) By wrtg the Equato (9) logarthmc form ad the applyg the least squares approach, Equatos (0), () ad () are formed. log y = log a + x log b (0) log y = loga + ( x logb) () x log y ) = ( x loga) + ( ( x logb) () Sce the Equato (0) s lear, by applyg lear tred aalyss a ad b coeffcets are foud as show Equatos (3) ad (4). log a = log y (3) log b = x log y x (4) By replacg a ad b coeffcets Equato (9) the peak loads are predcted. B. ANN Fgure depcts the archtecture of typcal feedforward multed eural etwork cosst of a put, (oe or more) hdde s ad a output. The umber of hdde s ad euros s s subject to problem studed ad decded upo tral-error. Iputs Iput Hdde Output Fgure. Feed forward mult ANN Outputs The put receves the sgal from outer evromet ad dstrbutes t to the euros the hdde s. The hdde s have computatoal euros ad the umber of s depeds o the fuctos to be used. The etwork computes the actual 88

3 Iteratoal Joural o Techcal ad Physcal Problems of Egeerg (IJTPE), Iss. 7, Vol. 3, No., Ju. 0 outputs of the euros the hdde ad output by usg the actvato fucto. The error gradet for the euros the output s calculated ad the weghts the back-propagato etwork propagatg backward the errors assocated wth output euros are adjusted. The total error at the output s the reduced by redstrbutg the error backwards through the hdde s utl the hdde s reached. The process updatg the weghts utl the desred output s reached defed as trag. Ths process s called as geeralsed delta rule ad repeated utl the error crtero for all datasets s reached. I geeral each ANN s traed o a dfferet 80% of the trag data ad the valdated o the remag 0%. Sce each addtoal expoetally creases the computg load, practce mostly 3- ANNs are preferred [3,, 5]. I ths work, the mplemetato stage of the ANN Matlab 6.5 software s used. I the program; three s ANN model cludg oe hdde wth feed forward ad back-propagato algorthm has bee traed by usg Leveberg Marquardt (LM) algorthm. The etwork used ths study has euros the hdde wth the logarthmc sgmod actvato fucto whch s o-lear cotuous fucto betwee 0 ad as expressed Equato (5) where, β s the slope costat ad geeral assumed equal to [5]. f( x) = (5) + x e β For puts, alog the peak load dataset, mothly temperature ad populato growth are take to accout. I ths study, the average mothly temperature values are obtaed from the regoal meteorologcal record offce. The mothly populato growth s calculated from the 997 ad 000 atoal populato statstcs usg Equato (6) whch gves the populato growth o mothly bases [6]. r P = P0. e (6) I ths equato; P 0 s the frst ad P s the secod of the two cosecutve populato statstcs, s the tme terval betwee the statstcs ad r shows populato growth rate. For Kutahya, by takg the 997 ad 000 populato statstcs whch are obtaed from Turksh Statstcal Isttute (TURKSTAT) as 6437 ad respectvely; the value of r s calculated as By usg these values the populato s calculated o mothly bases. All the data whch are used for the trag ad testg of the ANN have bee scaled to a terval of [0.5, 0.75]. III. NUMERICAL EXAMPLE By usg least square regresso based methods ad ANN wth the data from TEDAS, electrc peak load forecastg of 008 has bee carred out for the cty of Kutahya, Turkey. The results attaed are summarsed Table ad llustrated as graphc form Fgure, for smple lear, multple lear, expoetal, quadratc ad ANN approaches. The data used are the mothly averages of the peak loads recorded betwee years 000 ad 008. Table. Forecasted peak load by dfferet approaches for 008 Moths Real load Smple lear Multple lear Expoetal Quadratc ANN Ja Feb March Aprl May Jue July Aug Sept Oct Nov Dec It ca be see from the results that the results attaed wth the lear ad expoetal regresso approach are very close to each other. I both approaches, the mothly peak load s creased cosstetly startg from February ad reached the hghest value August of 008. Estmated peak load Real Lear Expoetal Quadratc Multple regresso ANN Fgure. Real ad forecasted peak load values for 008 Fgure shows the peak load demad predcted wth dfferet forecastg approaches. I multple regresso ad ANN approaches, the puts are suppled wth the hstorc temperature ad populato growth data alog wth the peak load data. I the study, sce the forecastg s carred out o mothly bases, mothly error aalyss performed ad the mea errors are gve Table ad as graphc form Fgure 3. Table. Forecastg errors by dfferet approaches for 008 Moths Moths Smple lear Multple lear Expoetal Quadratc ANN Ja Feb March Aprl May Jue July Aug Sept Oct Nov Dec MAPE(%)

4 Iteratoal Joural o Techcal ad Physcal Problems of Egeerg (IJTPE), Iss. 7, Vol. 3, No., Ju. 0 Error (%) Lear Expoetal Quadratc Multple regresso ANN Moths Fgure 3. Forecastg errors for 008 From the Fgure 3 t s see that, for the peak load forecastg for 008, wth the ANN for te moths, wth the quadratc regresso for eght moths, wth the multple lear regresso algorthm for sx moths, wth the smple lear ad expoetal regresso approaches for three moths the mea error remaed less tha 5%. Whe the approaches are vestgated for the predcto errors betwee 5 to 0%, for e moths wth the smple lear ad expoetal regresso, for two moths wth the multple lear regresso ad ANN approaches ad oly for oe moth for the quadratc regresso the error remaed these lmts. The error remaed betwee 0 to 5%; oly for two moths wth the quadratc regresso ad for four moths wth the multple lear regresso approaches. The error has bee foud betwee 5 to 0% for oly oe moth wth the quadratc regresso. Whe the approaches are compared accordg to ther hghest predcto error; the hghest error for quadratc ad multple lear regresso approaches s August ad September wth a error of 6.98 ad -.40 % respectvely. For expoetal ad smple lear regresso approaches the hghest predcto errors are foud October wth a forecastg error of ad % Jauary respectvely. As for the ANN the hghest forecastg error s December correspodg to %. From these results t s evdet that wth the lowest mea absolute percetage error (MAPE) of 3.53 %, the ANN based algorthm, geeral has relatvely lower forecastg error ad superor to the classcal approaches studed. IV. CONCLUSIONS I order to provde a hgh qualty ad relable servce to the cosumers, t s essetal for electrc power dstrbuto compaes to carry out projectos regardg atcpated electrc peak load demad the future. I the plag ad maagemet of power geerato, trasmsso ad dstrbuto systems, load forecastg s the key factor. The errors the parameters whch are used the load forecastg, the sudde chages the put parameters or uexpected chages the peak load data may egatvely affect the peak load forecastg process ad cotrbute to further errors. For the cty of Kutahya wth 00,000 habtats whch has a creasg demad electrc power cosumpto, both resdetal ad dustral areas, the factors whch cotrbute to the ucertaty peak load forecastg are very hgh. Hece forecastg methods based o dfferet methodologes may yeld more realstc results. By the comparso of the forecastg for 008 results attaed, t s cocluded that wth the use of loger put data, the forecastg error s decreased. I ths study, whe the dfferet load forecastg techques are compared for Kutahya, t s see that the ANN approach has produced better results. REFERENCES [] M., Beccal, M. Cellura, V. Lo Brao, A. Marvugla, Forecastg Daly Urba Electrc Load Profles usg Artfcal Neural Networks, Eergy Coverso ad Maagemet, Vol. 45, pp , 004. [] M. Djukaovc, B. Babc, D.J. Sobajc, Y.H. Pao, Usupervsed/Supervsed Learg Cocept for 4-Hour Load Forecastg, IEE Proceedgs-C, Vol. 40, No. 4, pp. 3-38, 993. [3] T. Yalcoz, U. Emoglu, Short Term ad Medum Term Power Dstrbuto Load Forecastg by Neural Networks, Eergy Coverso ad Maagemet, Vol. 44, pp , 005. [4] S.C. Trpathy, Demad Forecastg a Power System, Eergy Coverso Maagemet, Vol. 38, No. 4, pp , 997. [5] H.M. Al-Hamad, S.A. Solma, Log Term/Md- Term Electrc Load Forecastg Based o Short-Term Correlato ad Aual Growth, Electrc Power Systems Research, Vol. 74, pp , 005. [6] N. Amjady, Short-Term Hourly Load Forecastg Usg Tme Seres Modelg wth Peak Load Estmato Capablty, IEEE Trasactos o Power Systems, Vol. 6, No. 3, pp , August 00. [7] M.S. Kadl, S.M. El-Debeky, N.E. Hasae, Overvew ad Comparso of Log-Term Forecastg Techques for a Fast Developg Utlty: Part I, Electrc Power Systems Research, Vol. 58, pp. -7, 00. [8] S. Kruc, I. Krcmar, N. Rajakovc, A Improved Neural Network Applcato for Short-Term Load Forecastg Power Systems, Electrc Maches ad Power Systems, Vol. 8, pp , 000. [9] D. Sgh, S.P. Sgh, A Self Selectg Neural Network for Short-Term Load Forecastg, Electrc Power Compoets ad Systems, Vol. 9, pp. 7-30, 00. [0] T. Sejyu, H. Sakhara, Y. Tamak, K. Uezato, Next-Day Load Curve Forecastg usg Neural Network based o Smlarty, Electrc Power Compoets ad Systems, Vol. 9, pp , 00. [] C.C. Hsu, C.Y. Che, Regoal Load Forecastg Tawa Applcatos of Artfcal Neural Network, Eergy Coverso ad Maagemet, Vol. 44, pp , 003. [] S.A. Kalogrou, Applcatos of Artfcal Neural Networks Eergy Systems a Revew, Eergy Coverso ad Maagemet, Vol. 40, pp ,

5 Iteratoal Joural o Techcal ad Physcal Problems of Egeerg (IJTPE), Iss. 7, Vol. 3, No., Ju. 0 [3] S.C. Chapra, R.P. Caale, Numercal Methods for Egeers, McGraw-Hll, 006. [4] B. Bowerma, R.T. O coell, Appled Statstcs, McGraw-Hll, 997. [5] M. Iluga, D. Stepheso, Ifllg Stream Flow Data usg Feed-Forward Back-Propagato (BP) Artfcal Neural NETWORKS: Applcato of Stadard BP ad Pseudo Mac Laur Power Seres BP Techques, Water SA, Vol. 3, No., pp. 7-76, 005. [6] E. Kreyszg, Advaced Egeerg Mathematcs, 6th Edto, Joh Wley ad Sos, Caada, 0-, 988. BIOGRAPHIES Ylmaz Asla was bor Trabzo, Turkey, 965. He receved the B.Sc. Electrcal Egeerg 986 ad the Ph.D. degree Electrcal Egeerg from Uversty of Bath, UK, 997. Curretly, he s a Assstat Professor at electrc ad electroc egeerg departmet of Dumlupar Uversty, Kutahya, Turkey. Hs research terests are aalyss of shut faults power trasmsso ad dstrbuto systems, load forecastg, reewable eergy. Serka Yavasca was bor Bursa, Turkey o Jauary 5, 977. He receved the B.Sc. degree 9999 from Marmara Uversty, Istabul, Turkey. I 007 he started hs master degree the Departmet of Electrcal Egeerg of Dumlupar Uversty, Kutahya, Turkey. Curretly, he works as a structor at Yalova Vocatoal Hgh School. Hs research terests clude load forecastg ad dstrbuto automato. Celal Yasar was bor Kutahya, Turkey, 958. He receved hs B.Sc. degree from Yldz Techcal Uversty, M.Sc. degree from Aadolu Uversty ad Ph.D. degreee from Esksehr Osmagaz Uversty, Turkey, all Electrcall Egeerg 980, 988 ad 999, respectvely. He s curretly workg as a Assstatt Professor at the Electrcal ad Electrocs Egeergg Departmet of Dumlupar Uversty, Kutahya, Turkey. Hs research terests clude aalyss of power systems, ecoomc operato of power systems, power dstrbuto systems ad reewable eergy systems. 9