A Methodology of Power Demand Prediction

Transcription

1 A Methodolog of Power Demad Predcto Cora MARTINEAC, Oaa ONET, Smoa ARDELEAN, Claudu VERMEŞAN, Mha HOPÎRTEAN, Tudor VESA Techcal Uverst of Cluj-Napoca,FDEE Electrca DstrbuŃe Traslvaa Nord, Utrecht Uverst str.c.dacovcu r.5, RO-00 Cluj-Napoca, str. I. Măcelaru r 8 A, RO- 38 Cluj-Napoca, Hedelberglaa,3584CS Utrecht, THE NETHERLANDS Cora.Marteac@eps.utcluj.ro, oetz_oaa@ahoo.com, Smoa.Ardelea@eps.utcluj.ro, Claudu.Vermesa@td.electrca.ro, M.I.Hoprtea@studets.uu.l, Tudor.Vesa@staff.utcluj.ro Abstract The ed use cosumers of eerg coverso, trasport ad dstrbuto determe maret demad of eerg. Ths should be balaced b the offer provded b producers the eerg sstem. Esurg the balace betwee demad ad suppl electrct s a complex process of damc ature ad requres a strct balace of electrcal power at each momet for esurg a stable eerg sstem, sce the electrct ca ot be stored. Ths balacg of suppl ad demad of eerg must be fulflled both techcall ad ecoomcall. Recordg actvt ad eerg cosumpto parameters that deped o them s followed b a predcto of cosumpto ad a aalss of the results to mprove the fal formato qualt. The stud preseted the paper focuses o predctg treds eerg cosumpto, holdg for database real-tme readgs of eerg cosumpto related to a caledar ear, fled for a dstrbuto operator. The chose predcto mechasm s the smple lear regresso method, sce the ol varable that was cosdered s the hstor of cosumpto. The preseted predcto methodolog uses the regresso strumet of Excel rug lear regresso aalss usg least squares method to fd a le that correspods to a set of observatos. It was teded that the dexes of qualt of eerg cosumpto tred s as good as the ca be order to crease the chaces that forecast made to adequatel reflect the future actual data ad the maxmum percetage error s as small as t ca be. Idex Terms load curves, power demad, predcto, statstcal dcators, tred I. LOAD CURVES A. Dal load curves. Problems ad ma dexes. Usuall, the dal load curves represet the actve power demaded b the cosumers. The problems of dal load curves: Classfcatos, crtera: the buldg tpe, the d of cosumer, the d of load, determato methods, (measurg, calculato, forecast); Ma dexes: dal eerg; maxmal, mmal, medum power, flatteg coeffcet, durato of use of the dal pea power, tme losses, power factor; mea square root, power varato coeffcet, correlato coeffcet; Load curves modelg: determst; probablstc (probablstc hourl level, the ormal dstrbuto law s respected, dexes: average, rregulart, dsperso, stadard devato) Load curves forecast: classcal methods (drectl: statc, damc: drect); moder methods (heurstc; artfcal tellgece: euroal etwor, expert sstems, decso tree). II. POWER DEMAN PREDICTION A. The eed for power demad predcto Predctg eerg ad power cosumpto ams to atcpate eerg ad power cosumpto calculatos based o the aalss ad terpretato of.dverse data set, order fall to acheve a accurate match betwee estmated ad actual cosumpto. The actvt of power demad predcto volves solvg the followg problems: Idetfg the power demad causes order of mportace. Determato qualtatve ad quattatve shape of the law (correlato) betwee cause ad effect. Usg the correlato prevousl establshed for effectve future power demad predcto. Checg tme predcted results. Balacg eerg suppl wth demad s made o two dstct levels: techcal (at the desg stage ad the the operatoal phase); ecoomcal. B. Mathematcal model of power demad predcto Followg the phase of collecto, selecto ad processg the orgal data from the database, the mathematcal model of power demad s establshed. Power demad predcto hghlghts the exstece of four ma compoets whch determe the eerg curve show fgure : the tedec or tred, T, (the ma compoet that establshes the essetal form of eerg chage), the cclcal compoet, C, (due to fluctuatg ad slow-actg causes), the seasoal compoet, S, (caused b certa parameters that have seasoal fluctuatos) ad the radom compoet ε (due to accdetal causes). B projectg the power demad, the varato of each compoet s estmated separatel, achevg the fal result b summg the results of the predcted compoets. If cclcal compoets, seasoal ad radom are small compared to the tred, the fluece o varato power demad ca be eglected ad all s related just about tred predcto. Ths s most commo practce, beg further developed ths paper. 80

2 a= bx x b= x x ( x ) (6) (7) Fgure. Compoets of mathematcal model of power demad curve. III. METHODS USED IN PREDICTION A. Regresso method The method mplemets b meas of aaltcal expressos, ow as regresso fuctos, show how the depedet varable evolves relato wth chages of oe or more depedet varables X. The geeral form of the regresso fucto s: ( X,X,, X ) e Yx = f K + () where "e" s the perturbg radom varable, or error, represetg the effect of all uspecfed factors that are dffcult to quatf or are sgfcat. The ma tpes of regresso models are: ufactoral regresso; Smple curvlear regresso ad correlato; Multple regresso ad correlato ca be expressed b a lear fucto or a curvlear fucto. B. Smple lear regresso It s a regresso model whch the depedet varable () chages learl uder sgfcat fluece of a sgle depedet varable (x). Aalss ad predcto model used wll be the ufactoral lear regresso: Y = a + bx x + e () where "a" ad "b" are uow parameters of the fucto, whch are to be estmated C. Smple lear regresso ad regresso model valdato Estmato of parameters "a" ad "b" of the lear regresso equato s acheved b the method of least squares. Ths method s based o mmzg the sum of squared errors, meag the mmzato of the observed squared devatos values sum (Y) from the theoretcal values (Yx): (3) Normal equato sstems become: a+ b x = = = (4) a + = x b x x = = = B solvg the sstem of equatos the parameters a ad b are obtaed, as follows a= x x x ( x ) x (5) IV. STUDY CASE ON LOAD CURVES A. Load curves correspodg to characterstc wees For ths case stud hourl readgs of power demad for the ears 006, 007 ad 008 are used. A frst selecto ad processg of collected data s made, followed b vewg them graphcal form, trough the average load curves specfc to a partcular perod. The cocepts of mothl tpcal wee ad aual tpcal wee are troduced ths paper. Mothl tpcal wee presets load curves for each da of a tpcal wee of a moth. The are obtaed b mag the average cosumpto for 4 hours for all the das wth the same ame wth a moth. Thereb oe ca spea about a tpcal wee of Jauar, Februar, etc. Aual tpcal wee shows the tpcal average load curves for each da of a tpcal wee of a ear, metog that the are obtaed b mag the average cosumpto durg the 4 hours for all 5 das wth the same ame durg a ear. B. Mothl tpcal wee - load curves Graph of fgure presets da load curves characterstc of "Moda" the mothl tpcal wees. The preseted graphs correspod to the das of moths related to the mothl tpcal wee of Jauar, Februar, etc. It s otced that o Moda the power demad eep the same shape. Each graph s obtaed b performg the power demad average for the das of "Moda" of the moth. Based o the same prcple all weedas for each moth separatel s represeted graphcall t, h Jauar Februar March Aprl Ma Jue Jul September November December Fgure. Moda load curves from the mothl tpcal wee of the ear 006. A mothl tpcal wee covers average hourl eerg cosumpto for the da Moda, Tuesda, Wedesda, etc. for the specfc moth. Oe ca cosder a mothl tpcal wee for "Jauar", "Februar", "March", "Aprl", etc. As show power demad creases the morg pea area ad eveg pea area as the ste of these peas should be provded adequate reserves of eerg. These load curves provde formato o power demad aspect both for a perod of 4 hours ad depedg o the seaso. Fgure emphases that the wter moths 8

3 approachg cosumpto of MWh ad the summer moths power demad reduces b aroud MWh. Shape of load curves specfc of worg das are ver dfferet tha shape of the load curves for Saturdas ad Sudas or holdas over ear, as show fgure t, h Jauar Februar March Aprl Ma Jue Jul September Fgure 3. Suda load curves from the mothl tpcal wee of the ear 006. Smlarl correspodg graphs for average hourl chage power demad for all das of the mothl tpcal wees for the ears 007 ad 008 are preseted, fgures 4 ad 5 showg ol specfc curves for the das of Moda t, h Jauar Fe bruar M arch Aprl M a Jue Jul Septem be r Octobe r Fgure 4. Moda load curves from the mothl tpcal wee of the ear t, h Jauar Februar M arch Aprl M a Jue Jul Septem ber Fgure 5. Moda load curves from the mothl tpcal wee of the ear 008. It ma be otced that for the same da, load curves have smlar shape whether s part of the mothl tpcal wee, or aual tpcal wee. Also dfferet cosumpto pea loads da ad ght depedg o seaso appear. C. Aual tpcal wee load curves Studg the varato of specfc average power demad, durg the seve das of aual tpcal wee, other tpes of graphcs are obtaed. Chart of fgure 6 presets the load curves specfc for aual tpcal wee correspodg to the three studed ears 006, 007 ad 008. Each load curve s obtaed b performg the average eerg cosumpto for all the das of "Moda" durg that ear. Ad t s obvous to otce that a of the three ears o "Moda" the varato of eerg cosumpto has the same shape. Same aalss was doe for load curves of the das of "Tuesda", "Wedesda", "Thursda", etc. ad these das together form a aual tpcal wee. Ths method of overlappg the profles of eerg cosumpto s a method used practce qute frequetl. It ma also appl to a mothl tpcal wee. Wth ths overlap of load curves s observed that all Modas have a smlar allure, ad t s assumed that the da "Moda" of the followg ear, 009, power demad eeps the same shape. I fact t sees the dett betwee hourl cosumer behavor of ear ad ear -, our case 009 compared to the ears MONDAY 006 MONDAY 007 MONDAY Fgure 6. Moda load curves from the auall tpcal wee. V. APPLICATION OF A SIMPLRE LINEAR REGRESSION A. Predctg the tred power demad Ths stud s based o the tred progoss of the power demad. The smple lear regresso method has bee chose as a predcto strumet because the ol varable tae to accout s the hstorcal cosumpto. The hstorcal cosumpto s based o the 5 wees of the ear, a specal atteto pag to the (holdas) feastdas: Chrstmas, Easter, Jauar the st, the st of Ma ad December the st. Due to the fact that these das the power demad s reduced, the are cosdered as das wth low cosumpto, correspodg to the das of Suda. For the followg predcto the Excel s smple lear regresso method s used, based o least-squares method for fdg a fucto that correspods to a observed data base. A Regresso aalss tool, cluded b request Mcrosoft Excel Aalss Tool Pac applcato s used. I ths case the depedet varable s the eerg, W, ad the depedet varable s the tme, t. The predcto s made for two radom wees of 006 ad oe wee of 007, as well as 008. For a good approxmato of the tred t s recommeded to respect the codto: 5 where s the umber of data cosdered for the prevous perod before forecastg. The value = 0 s chose ad the am s to predct the value of da. Twet cosecutve values correspodg to the power demad for the das of "Moda" are chose t, h 8

4 to predct the power demad for the st da of "Moda". The same wa has bee appled to predct the st da of Tuesda, Wedesda, etc, thus obtag a predcto for the etre wee. Ths wee correspods to the thrd wee of Ma. Data from table represet the results acheved through progoss strumet regresso of Excel for Moda. It maes a comparso betwee forecast (usg tme tervals - 4 hours of the da) ad effectve cosumpto values. These are followed b error, ad statstcal dcators. These tables clude also mmum values, maxmum ad average of the errors absolute ad percetage. Smlar tables for each da of the wee have bee obtaed. Fgure 7 represets the power demad predcto for the whole wee (the st wee of the ear 006) accordg wth these tables. TABLE I. POWER DEMAND FOR THE ST DAY OF MONDAY FOR THE YEAR 006. Therefore t s recommeded that a moths whch the progoss s made, to tae to accout a small umber of readgs cosumpto <0. W, MWH Power demad predcto Power demad March 3, 006 March 4, 006 March 5, 006 March 6, 006 March 7, 006 March 8, 006 March 9, 006 March 0, 006 Fgure 8. Power demad predcto for the th wee of the ear 006. Predcto made o the bass of pror readg for power demad both of the th wee of the ears 007 ad 008 are show fgures 9 ad 0. t, das Power demad predcto Power demad Fgure 7 presets the varato of power demad predcto for the st wees of the ear 006. Power demad predcto Power demad March, 007 March 3, 007 March 4, 007 March 5, 007 March 6, 007 March 7, 007 March 8, 007 March 9, 007 t, das Fgure 9. Power demad predcto for the th wee of the ear 007. Power demad predcto Power demad Ma, 006 Ma 3, 006 Ma 4, 006 Ma 5, 006 Ma 6, 006 Ma 7, 006 Ma 8, 006 Ma 9, 006 t, das Fgure 7. Power demad predcto for the st wee of the ear 006. It s poted out that the expected values preset a certa dfferece wth real cosumpto, oes whch ca lead to some losses, especall ecoomcal, for the dstrbuto operator. If cosumpto are uderestmated the cost are curred through cover damages caused b o-eerg, the problems assocated wth mproper szg of the trasport capact ad a overload of exstg equpmets. If cosumpto are overvalued, the ujustfed fuds are allocated to addtoal vestmets led to crease the producto capact, trasmsso ad creasg stocs of eerg carrers. Smlarl predcto s doe for the th wee of 006, correspodg to the thrd wee of March. The predcto graph s show fgure 8. Ule power demad predcto Ma, t ca be see that for a smaller umber of cosumpto readgs, the accurac s much hgher. March 0, 008 March, 008 March, 008 March 3, 008 March 4, 008 March 5, 008 March 6, 008 March 7, 008 t, das Fgure 0. Power demad predcto for the th wee of the ear 008. B. Statstcal dcators Tme seres cotas observatos made for each predcto ad there are predcto errors; ths case = 4 (hours). The statstcal dcators are: ME - mea error: ME = = ( ˆ ) MAD - Mea absolute devato: MAD= ˆ = MAPE mea percetage error: ˆ MAPE= = 00 (8) (9) (0) 83

5 MSE mea squared error: MSE = ( = ˆ ) = σˆ () The predcto stud s accompaed b the statstcal dcators calculato to evaluate ts performace. Amog the statstcal dcators that descrbe the accurac of a mathematcal model some dcators have bee selected order to observe the umercal accurac of the forecast. Mea error s a estmated value that s teded to be as close to zero as possble. If the mea error of the progoss dffers apprecabl from zero the there s a threshold the dcated progoss (a cotuous dsturbg compoet). It ma be a dcato that the ccle of tme has bee modfed a wa whch was ot otced b the used method. The two dcators MAD ad MSE are measurg the errors of the progoss. The errors are wated to be as small as possble. If the errors are uforml dstrbuted, the stadard devatos of the progoss errors have a coecto wth MAD thru: π σˆ = MAD, 5MAD () ths costtutes a verfcato of the obtaed values for the dcators ad a vew over the progoss performace made the case stud. Tables 5 collate statstcal dcators calculated for eerg forecasts made ths stud. Calculated percetage errors are below the threshold of 0% TABLE II. STATISTICAL INDICATORS FOR ST WEEK OF 006 TABLE III. STATISTICAL INDICATORS FOR TH WEEK OF 006 TABLE IV. STATISTICAL INDICATORS FOR st WEEK OF 007 TABLE V. STATISTICAL INDICATORS FOR th WEEKS OF 008 Comparg tables ad 3 shows a hgher precso for a smaller umber ("") of readgs. I tables 3 5, the values of the last two colums emphaszes that the codto (3) s fulflled. MSE = π MAD (3) The power demad predcto stud was made for the power demad correspodg to the frst moth of the ear. It s recommeded to be exteded for each moth of the ear. VI. CONCLUSIONS The paper s meat to develop both theoretcal ad practcal ssues of power demad predcto whch s curret ad wdel dscussed. Importace of a accurate predcto s ecessar because of ther techcal ad ecoomcal mplcatos. As the dstrbuto operator s forced to trade eerg, due to the dffereces to power demad evaluato, the ow techologcal cosumpto ca be reduced or creased as t estmates. I ths cotext power demad forecast s ver mportat electrct bllg. As oted the curret stud, usg smple lear regresso gves good results for some moths but t s ecessar to mae a aalss for all moths. The purpose of the wor was to obta a maxmum percetage error of up to 0%, so ths performace progoss dcator s as small. Thus, t was teded that the dexes of power demad tred be good eough to crease the chaces that the predcto reflects adequatel the future data. Serous errors the top porto of predcted load curves dcate that some other parameters tha hstor must be tae to accout, whch could fluece the power demad such as temperature, demographc factors, whch lead to use the multple lear regresso method. The power demad predcto s damc ad t must be a permaet, cotuous actvt ad to base a stud of eerg developmet. REFERENCES [] Albert, Herma., Mhălescu A. Perder de putere ş eerge î reńelele electrce. Edtura Tehcă, Bucureşt, 997, ISBN X [] Bacu, A., Bacu, C. I. Eerga electrcă ş medul îcojurător. Edtura Tehcă, Bucureşt, 98. [3] Bott, E. Mcrosoft offce XP. Edtura Teora, Bucureşt, 00.ISBN [4] Carabogda I. Gh., Mhăleau C. BlaŃur eergetce. Edtura Tehcă, Bucureşt, 986 [5] Chdrş, M., Czer, A. C., Mro, Aca, Tomoagă, B. Maagemetul eerge electrce AplcaŃ. Casa CărŃ de ŞtŃă, Cluj-Napoca, 009, ISBN [6] Dare, S., Văda, I. Producerea, Trasportul ş DstrbuŃa Eerge Electrce. IstalaŃ petru trasportul ş dstrbuńa eerge electrce. U.T. PRES, Cluj-Napoca, 003, ISBN [7] Luştrea, B. Progoza cosumulu de eerge. Edtura Agr, Bucureşt, 00 ISBN [8] Motgomer, D.C., Jegs, C.L., Kulahc, M. Itroducto to tme seres aalss ad forecastg. Wle & Sos Ic. Publcato, New Jerse, 008, ISBN [9] Popescu, Th., Demetru, S. Practca modelăr ş predcńe serlor de tmp. Metodologa Box-Jes. Edtura Tehcă, Bucureşt, 99, ISBN [0] Pretl, Ş., Precup, R.E. Itroducere î coducerea fuzz a proceselor. Edtura Tehcă, Bucureşt, 997. [] Studu ANRE realzat de KEMA:. Feasblt of Load Proflg;. Assessg the feasblt of load proflg Romaa, 006 [] Tertşco, M., Stoca, P., ș alń. Modelarea ş predcńa serlor de tmp, Edtura Academe, Bucureşt,