Evaluation of Advanced Wind Power Forecasting Models Results of the Anemos Project

Transcription

1 Evaluation of Advancd Wind Powr Forcasting Modls Rsults of th Anmos Projct Ignacio Marti, Gorgs Kariniotakis, Pirr Pinson, I. Sanchz, T.S. Nilsn, Hnrik Madsn, Grgor Gibl, Julio Usaola, Ana Maria Palomars, R. Brownsword, t al. To cit this vrsion: Ignacio Marti, Gorgs Kariniotakis, Pirr Pinson, I. Sanchz, T.S. Nilsn, t al.. Evaluation of Advancd Wind Powr Forcasting Modls Rsults of th Anmos Projct. Europan Wind Enrgy Confrnc, EWEC 26, Fb 26, Athèns, Grc. 9 p., 26. <hal > HAL Id: hal Submittd on 28 Dc 21 HAL is a multi-disciplinary opn accss archiv for th dposit and dissmination of scintific rsarch documnts, whthr thy ar publishd or not. Th documnts may com from taching and rsarch institutions in Franc or abroad, or from public or privat rsarch cntrs. L archiv ouvrt pluridisciplinair HAL, st dstiné au dépôt t à la diffusion d documnts scintifiqus d nivau rchrch, publiés ou non, émanant ds établissmnts d nsignmnt t d rchrch français ou étrangrs, ds laboratoirs publics ou privés.

2 Evaluation of Advancd Wind Powr Forcasting Modls Rsults of th Anmos Projct I. Martí 1, G. Kariniotakis 2, P. Pinson 2, I. Sanchz 5, T. S. Nilsn 3, H. Madsn 3, G. Gibl 4, J. Usaola 5, A.M. Palomars 6, R. Brownsword 7, J. Tambk 8, U. Fockn 9, M. Lang 9, G. Sidratos 1, G. Dscombs CENER, 2 Ecol ds Mins d Paris, 3 IMM-DTU, 4 RISOE, 5 Univ. Carlos III d Madrid, 6 CIEMAT, 7 RAL- CCLRC, 8 Univ. Oldnburg, 9 EMSYS, 1 UA, 11 ARIA. imarti@cnr.com & gorgs.kariniotakis@nsmp.fr Abstract An outstanding qustion posd today by nd-usrs lik powr systm oprators, wind powr producrs or tradrs is what prformanc can b xpctd by stat-of-th-art wind powr prdiction modls. This papr prsnts rsults of th first vr intrcomparison of a numbr of advancd prdiction systms prformd in th fram of th Europan projct Anmos. A framwork for rror charactrization has bn dvlopd consisting by a masur- and a distribution-orintd approach. This comparison has givn a prspctiv of th possibilitis and limitations of th forcasts in th diffrnt tst cass that wr dfind. At a scond stag, th homognous comparison procss has prmittd to valuat th possibility of obtaining bttr prformanc by xploiting th mrits of individual modls through modl combination. Th papr prsnts th mthodology and rsults from th combination approach. 1. Introduction Th Europan projct Anmos [1] has dvlopd a wid rsarch on svral topics rlatd to wind powr forcasting such as physical and statistical modling, uncrtainty stimation, upscaling and othrs. From a vry first stag of th projct it was rcognizd by both nd-usrs and modlrs th ncssity to map th xisting wind powr forcasting tchnology both in trms of rsarch approachs and also in trms of prformancs. Initially an xtnsiv litratur rviw was dvlopd and rportd in [4]. Thn, a comparison of a numbr of stat of th art prdiction modls has bn carrid out in ordr to know what ar th possibilitis of th forcasting modls undr diffrnt situations. This comparison has givn a prspctiv of th possibilitis and limitations of th forcasts in th diffrnt tst cass that wr dfind. This is th first comparison of wind powr prdiction modls that is mad at Europan lvl; th rsults ar valuabl information for th potntial usrs of th prdiction modls about th typical rangs of rror lvl, and th rlation of th accuracy with th wind farm charactristics. It is shown that th accuracy of powr production forcasts as wll as wind spd forcasts dpnds on th faturs of th wind farm as wll as on th prdiction modl. This intrcomparison xrcis has bn dsignd to covr diffrnt typs of wind farms and stat of th art forcasting modls, thrfor th rsults ar a valid rfrnc of th analysd prdiction modls prformanc for th final usrs. Th tst cass dfind includ complx trrain and rlativly flat aras to tak into account th ffcts of th topography; distanc to th shor, diffrnt altituds and climatic conditions. A databas has bn dvlopd including wind masurmnts, powr production, and othr mtorological data; numrical wathr prdictions wr also includd as wll as th charactristics of th wind farm for ach tst cas (powr curvs, digital maps of th trrain and roughnss, tc). This databas has providd all th ncssary data for ach modl. From th point of viw of th prdiction modls, this xrcis covrs a wid varity of tchnical approachs, from autorgrssiv modls to fuzzy logic nural ntworks, including MOS systms and boundary layr physical modls. A numbr of "baslin" modls wr run for th tst cass, such as Prdiktor, WPPT, Prvinto, Siprolico, CENER s LocalPrd, th Armins AWPPS, RAL's modl, ARIA wind, and UA's. Most of ths systms ar oprational today and usd by systm oprators or in markt trading in Spain, Grmany, Dnmark, Irland and Grc. Apart from th powr prdiction modls, th xrcis was also xtndd to th comparison of numrical wathr prdictions from diffrnt systms. Dtaild rsults of this task ar prsntd in [2]. In ordr to b abl to compar rsults by diffrnt modls for th various tst cass an appropriat 1

3 framwork was dfind charactrizd by a masurorintd approach and a distribution approach for charactrizing th dviations of th forcasts in rlation to th masurmnts. Th masur-orintd approach gathrs a st of statistical rror masurs in th form of an valuation protocol dfind in [6]. Using this protocol on can driv conclusions on th prformanc of prdiction mthods and on what affcts this prformanc (trrain, sason, horizon tc). Th distribution-orintd approach aims to focus on th analysis of th joint distributions of prdictions and obsrvations. It invstigats th influnc of crtain variabls (i.. lvl of prdictd powr, spd, a.o.) on th momnts of rror distributions (from th bias to kurtosis). This analysis is valuabl to charactriz prdiction rrors and rlat waknsss of modls to spcific causs. In this sns, it is a prrquisit for idntifying aras of modl improvmnt. Dtaild rsults ar prsntd in [12]. Finally, th homognous comparison procss has prmittd to valuat th possibility of obtaining bttr prformanc by xploiting th mrits of individual modls through modl combination. Th papr prsnts th mthodology and rsults from th combination approach. 2. Slctd wind farms Th objctiv of th bnchmark was to study th prformanc of th prdiction modls undr typical wind farm locations. Six tst cass wr slctd to covr a wid rang of conditions with rspct to climatology and trrain and ar locatd in four diffrnt countris: Wustrhusn wind farm in Grmany (flat trrain), Alaiz (vry complx trrain) and Sotavnto (complx trrain) wind farms in Spain, Klim (flat trrain) and Tunø (offshor) wind farms in Dnmark, Golagh wind farm in Irland (complx trrain). For th bnchmarking 11 stat of th art powr prdiction modls [4] hav bn tstd in th slctd wind farms. In ordr to nsur that vry prdiction modl run undr th sam conditions, a common databas was cratd for ach wind farm. Databass includ datasts of wind and powr masurmnts, as wll NWP and all th ncssary information about ach wind farm (digital trrain maps with lvation and roughnss, wind farm layout, wind turbin powr and thrust curvs). Th following NWP modl outputs wr usd as inputs for th powr prdiction modls: High Rsolution Limitd Ara modl (HIRLAM): o.2º grid rsolution in Spain. Th forcasts ar updatd four tims a day with a lad-tim of 24 hours. o.15º grid rsolution in Dnmark and Irland. Th forcasts ar updatd four tims a day with a lad-tim of 48 hours. Dutschland-Modll (DM).15º grid rsolution in Grmany. Th forcasts ar updatd onc a day with a lad-tim of 72 hours. Tst cas Tunoknob Klim Wustrhusn Golagh Sotavnto Alaiz Classification Offshor Flat Flat Complx Complx Vry complx Training priod Mar 22 Dc 22 Jan 1999 Fb 21 Jan 1999 Jun 2 Aug 22 Jan 23 May 21 Aug 21 Jan 21 Aug 21 Nominal Validation powr priod [MW] Dc 22 Apr 23 5 Mar 21 Apr Jul 2 Dc 2 1 Fb 23 Mar Sp 21 Nov Sp 21 Dc Tabl I: Charactristics of th wind farms slctd as tst cass. Slction of rprsntativ wind farms Offshor Flat trrain Complx trrain Highly complx trrain Tunø Knob (Dnmark) Klim (Dnmark) Wustrhusn (Grmany) Golagh (Irland) Sotavnto (Spain) Alaiz (Spain) Figur 1: Tst cass in Spain, Irland, Dnmark and Grmany. 2

4 Wustrhusn wind farm is placd in th northastrn part of Grmany 2 km southast of th town of Grifswald and 8 km from th shorlin of th Baltic Sa. Th wind farm consists of 2 Nordtank K5/41 turbins with a total ratd capacity of 1. MW. Th RIX valu is for this wind farm, maning that no slop is highr that th rfrnc valu (3%). Sotavnto wind farm is placd in Galicia rgion in th North Wstrn part of Spain approximatly 4 km from th coastlin of th Atlantic Ocan. Th sit is locatd 6-7 m abov sa lvl in smi-complx trrain. Th wind farm is a tsting sit and consists of larg numbr of diffrnt turbins with a ratd capacity ranging from 6 kw to 132 kw. Th total ratd capacity of th Sotavnto wind farm is MW. Th RIX valu for this wind farm is 7. Alaiz wind farm is situatd 15km south of Pamplona in th Navarra rgion of Spain in vry complx trrain 91 m 112 m abov sa lvl. Alaiz is a larg wind farm with a ratd capacity of 33.9 MW distributd on 49 Gamsa G47-66 wind turbins and on Lagrwy LW75 turbin. Th RIX valu for this wind farm is 15. Klim wind farm is locatd in th northwstrn part of Jutland approximatly 8 km from th north coast and 5 km wst of th city of Aalborg. Th wind farm consists of 35 Vstas V44 6 kw turbins with a total ratd capacity of 21. MW. Th RIX valu for this wind farm is. Tunø Knob wind farm is situatd offshor, 6km of th ast coast of Jutland and 1km wst of th island of Samsø. This is on of th first offshor wind farms in th world and consists of 1 Vstas V39 5 kw turbins with a total ratd capacity of 5. MW. Th RIX valu for this wind farm is. Golagh wind farm is locatd in th northwstrn part of Irland (Dongal County) 37 m abov sa lvl. Th turbins ar 25 Vstas V42 6 kw machins corrsponding to a ratd capacity of 15. MW. Th RIX valu for this wind farm is Dsign a virtual laboratory for th bnchmarking In ordr to compar th prformanc of th powr prdiction modls a bnchmarking structur was dsignd. Th objctiv was to charactris th prformanc of th modls undr th sam input conditions: Th diffrnt NWP and wind farm data wr stord to a common databas aftr convrsion to a common format ("Dpri") that was dfind for this purpos. A wb scurd srvic was st-up to manag th availabl fils and th rsults. Common NWPs wr usd for ach tst cas. Common wind farm masurmnts (powr production, wind spd and dirction in som cass). A training priod in th data st was dfind for ach tst cas in ordr to train thos powr prdiction modls that nd it. An indpndnt tsting priod was dfind for ach tst cas. Th rsults prsntd in this papr corrspond to th tsting priod of th tst cass. A forcast rror valuation protocol was dvlopd [6] for valuating th prformanc of th prdiction mods in a standardisd way. In ordr to prsnt homognous rsults, th following forcasts hav bn analyzd: Prdictions calculatd at UTC. +12 hours forcasts horizons for th comparison of modl prformanc. Figur 2 summarizs th structur of th bnchmarking. This structur has actd as a "virtual laboratory" in th fram of th projct. Wind farm masurmnts NWP Databas Wind powr forcasting modls WPPT LocalPrd Prdiktor AWPPS Prvinto ARIA RAL Siprólico Forcast rror valuation protocol Comparison Figur 2: Dsign a virtual laboratory for th bnchmarking. 4. Evaluation rsults Training Validation UA This Sction prsnts rprsntativ rsults of th bnchmarking xrcis from th Alaiz and Golagh tst cass charactrizd by vry complx and complx trrains rspctivly. Complt rsults ar givn in [2]. Th Alaiz tst cas is th on with highr trrain complxity, as indicatd by th RIX valu (15). This has bn provn th most difficult wind farm to prdict, with high valus of th NMAE (Normalisd Man Squar Error) critrion and high disprsion among th prformancs of th prdiction modls 3

5 NMAE (% nominal powr) R2 (Figur 3). Th scal of th rrors is highr than common cass of complx trrain; it rangs from 2% to 35% for th diffrnt modls and horizon 24. Th dtrmination cofficint R2 also prsnts a high disprsion and rlativly low valus for som of th prdiction modls. NMAE (% nominal powr) R M2 NMAE M3 NMAE M4 NMAE M5 NMAE M7 NMAE M8 NMAE M9 NMAE M1 NMAE M11 NMAE Forcast horizon (hours) Forcast horizon (hours) Figur 3: NMAE and R2 for Alaiz tst cas. M2 R2 M3 R2 M4 R2 M5 R2 M7 R2 M8 R2 M9 R2 M1 R2 M11 R M1 R2 M2 R2 M4 R2 M5 R2 M6 R2 M7 R2 M8 R2 M9 R2 M1 R2 M11 R2 Forcast horizon (hours) M1 NMAE M2 NMAE M4 NMAE M5 NMAE M6 NMAE M7 NMAE M8 NMAE M9 NMAE M1 NMAE M11 NMAE Forcast horizon (hours) Figur 4: NMAE and R2 for Golagh tst cas. Avrag NMAE (% nominal powr) Th NMAE valus for Golagh wind farm ar lss dpndnt on th forcast horizon than for th othr sits. Th rang of variation of NMAE for 24 hours horizon is 1% - 16%, bing comparabl for longr forcast horizons. Similar bhavior can b sn for R2 valus (Figur 4). In gnral, it can b sn in th figurs that for th first forcast horizons, thos modls with autoadaptivity capabilitis show bttr rsults (lowr NMAE and highr R2 valus). This improvmnt is mor vidnt in th first 6 hours. This study rvald both in a qualitativ and quantitativ way how prformanc of th prdiction modls is rlatd to th complxity of th trrain. Figur 5 rprsnts th variation of th avrag valu of th NMAE for th 12 hours forcast horizon, for ach tst cas. Figur 5 rprsnts th prformanc of th studid powr prdiction modls, showing th bst, th wors and th avrag prformanc at ach tst cas. It can b sn that thr is a significant incras in th NMAE valus as th complxity of th trrain incrass (highr RIX valus). Th offshor wind farm (Tunø) has slightly highr valus of NMAE but similar to th ons obtaind for th flat trrain wind farms. 5 TUN (offshor) KLI WUS FLAT TERRAIN SOT GOL COMPLEX TERRAIN RIX (%) ALA HIGHLY COMPLEX TERRAIN Figur 5: Avrag NMAE for 12 hours forcast horizon vs RIX at ach tst cas. Qualitativ comparison. NMAE (% nominal powr) ALA SOT KLI GOL WUS TUNO Tst cas Max Min Avrag Figur 6: Avrag NMAE for 12 hours forcast horizon vs RIX at ach tst cas ordrd by RIX valu. Qualitativ comparison. 4

6 5. Distribution-orintd valuation. In a scond stag a distribution-orintd approach for forcast vrification was dvlopd for highlighting th charactristics of forcast uncrtainty. This approach is basd on th notion that it is th joint distribution of forcasts ^ q pˆ, p which contains all th non-tim-dpndnt information about a prdiction mthod s quality [8]. Such a distribution-orintd approach is also known as th Murphy-Winklr vrification framwork. Whil it is rathr hard to dirctly study this joint distribution, on can instad focus on th various conditional and marginal distributions for driving th ncssary conclusions on th joint distribution proprtis. Ths various distributions includ th conditional distributions of th obsrvations givn th q p pˆ, th conditional distributions of th forcasts ( ) p and obsrvations p, ( ) forcasts givn th obsrvations q( pˆ p), th marginal distribution of th obsrvations q ( p) and finally th marginal distribution of th forcasts q( pˆ ). For all th various aspcts of forcast quality and th way thy can b assssd from th analysis of ths distributions, w rfr to [9]. Som of ths aspcts will b mntiond throughout th prsnt papr. Following a distribution-orintd approach, w hav applid in th fram of th bnchmarking xrcis of th Anmos projct a mthodology consisting in studying th influnc of a givn variabl (.g. prdictd powr) on th momnts of prdiction rror distributions (from th first to fourth ordr). Dnot by t+ k t th prdiction rror rlatd to th powr / ^ prdiction p t+ k / t mad at tim t for lad tim t+k. This is bcaus ths momnts corrspond to diffrnt charactristics of prdiction rrors: Th man µ k locats th cntr of gravity of a distribution and provids information on th systmatic part of th rror. It is givn by th bias, as dfind in [3]. Th standard dviation σ k rflcts th disprsion of a distribution, thus tlling on th lvl of prdiction uncrtainty. It is givn by th Normalizd Standard Dviation of th Errors (NSDE) as dfind in [1]. Th skwnss ν k dscribs th lack of symmtry of a distribution. It givs th most likly dirction of xpctd prdiction rrors. A distribution with an asymmtric tail xtnding out to th right is rfrrd to as positivly skwd. Th skwnss is oftn stimatd following Fishr s formula: ν k = ( t + k / t µ k 1 σ k T N N T )( 2) = t 1 3 whr N T is th numbr of availabl prdiction sris in th valuation st. th xcss kurtosis κ k informs on th shap of a givn distribution, compard to th shap of normal distributions. Th xcss kurtosis for a normal distribution is qual to zro. Thn, a positiv xcss kurtosis translats to a sharpr pak and havir tails. This momnt is stimatd by: N ( / T = + 1) κ k ( 1)( 2)( 3) = t 1 4 3( 1) 2 t + k t µ k σ k ( 2)( 3) Application of th distribution-orintd approach for highlighting th ffct of th powr curv. It is known that th contribution of th powr curv to th powr forcasting rrors is to amplify or dampn wind spd prdiction rrors dpnding on th lvl of prdictd wind spd. Th powr curv thus altrs th shap of th wind spd rror distributions. Whil prvious studis [11] hav only focusd on th ffct of th powr curv on th gnral lvl of prdiction rror (xprssd with masurs), w want to go furthr hr by basing our study on th distributionorintd approach introducd abov for bttr showing how th lvl of prdictd powr impacts rror charactristics. W concntrat on th Tunø Knob tst cas which consists in fact an illustrativ xampl of th conclusions that wr drawn from th whol valuation study. Th analysis is basd on 536 forcasts ovr a priod of four and a half months. Wind powr prdictions ar providd by 5 stat-ofth-art mthods (dnotd by M1, M2,, M5), with HIRLAM mtorological forcasts as input. M1, M2 and M3 ar statistical prdiction mthods, whil M4 and M5 blong to th family of physical prdiction approachs. A first invstigation consists in studying th conditional distributions of th masurs givn th q p pˆ. This prmits to assss th rliability forcasts ( ) of wind powr forcasts [8]. Rliability is dfind as th corrspondnc btwn th man of th obsrvations associatd to a particular forcast and that forcast. It thrfor translats to studying th dpndnc of th systmatic rror to th lvl of th prdictand., 5

7 For this purpos, th rang of forcast powr valus is split in 1% sub-rangs. In Figur 7, th normalizd biass for th various prdiction mthods ar givn for ach of th 1%-rangs of forcast valus, for 18- hour ahad prdiction. This horizon is chosn randomly sinc w hav not obsrvd significant diffrncs as a function of th horizon. W will also concntrat on that particular prdiction horizon in th rmaining of th paragraph, kping in mind that drivd conclusions can b gnralizd ovr th whol rang of look-ahad tims. Bias valus xhibit significant variations ovr th rang of possibl prdictd outcoms. Ths valus ar comprisd btwn -7% and 9% of P n, and sm to hav a gnral trnd to b positiv in th lowr part of th powr curv and ngativ in its highr part. Howvr, it dos not appar possibl to stablish a clar rlation btwn lvl of prdictd powr and prdiction bias. Such bhaviour has also bn noticd for th othr cas-studis considrd in th Anmos projct with highr bias valus for th wind farms locatd in smi-complx and complx trrain. Figur 7: Normalizd bias of th forcasting rror distributions dpnding on th prdictd powr rang. In a gnral way, vn if mthods rliability is not prfct, w cannot idntify a systmatic lack of rliability in crtain zons of th powr curv or for a givn mthod, apart from th trnd w hav xprssd abov. Th nxt stp is to valuat what ar th variations in th shap of rror distributions dpnding on th prdictand valu. First, th nonlinar and boundd natur of th nrgy convrsion procss maks that th skwnss of rror distributions volvs with th lvl of prdictd powr. Figur 8 dpicts this volution. Distributions ar positivly skwd for low prdictd valus and thn ngativly skwd whn ths valus ar in th high part of th powr curv. Morovr, th nonlinar procss acts on both th sprad and pakdnss of rror distributions. Th sprad dpndnc to th lvl of prdictd powr is shown in Figur 9, in which th sprad is quantifid by th standard dviation. Rmmbr that th uncrtainty of a givn procss is usually sn as th variability of its rlatd obsrvations. Thn, studying th volution of th sprad of conditional distributions of th masurs givn th forcasts q p pˆ rlats to valuating th prdictand-dpndnt ( ) uncrtainty. In paralll, xcss kurtosis, as a function of prdictd powr, is dpictd in Figur 1. Figur 8: Skwnss of th forcasting rror distributions dpnding on th prdictd powr rang Figur 9: Normalizd standard dviation (quantifid by th NSDE) of th forcasting rror distributions dpnding on th prdictd powr rang. 6

8 In this work, a nw adaptiv combination mthod, calld AEC, is proposd. Th mthod is calld Adaptiv Exponntial Combination (AEC) and is similar to always using th bst individual prdictor. Figur 1: Excss kurtosis of th forcasting rror distributions dpnding on th prdictd powr rang. High xcss kurtosis valus corrspond to prdictd powr valus clos to minimum and maximum wind gnration. Error distributions ar highly pakd in ths zons of th powr curv. And, in th mdium powr rang, slightly ngativ xcss kurtosis valus indicat that distributions ar mor flat than Gaussian distributions. At th sam tim, NSDE curvs ar almost symmtric with rspct to th 5% powr valu. In th rang of valus rlatd to th stp part of th powr curv, th standard dviation is largr than for powr valus clos to th powr curv plataus (say two or thr tims largr). Also, it can b sn that th standard dviations for ths two plataus ar rathr similar. Th ratio btwn th uncrtainty in th stp part of th powr curv and th on in th low and high parts is approximatly th sam for all th prdiction mthods and th tst cass considrd in th full valuation study, vn if th shap of th standard dviation curvs slightly diffrs from on tst cas to anothr. This tlls us that th variations of th wind powr forcasting uncrtainty ar similar whatvr th wind farm and ar in fact du to th wind-spd-to-powr convrsion procss. Uncrtainty lvls may b highr whn it is hardr to prdict wind spd (.g. for complx trrain or offshor), but th way forcast uncrtainty will vary as a function of th lvl of prdictd powr will b similar. 6. Combination of forcasts It is not infrqunt in wind nrgy to hav accss to mor than on prdictions of th wind farm production for th nxt hours. This has bn th cas in th Anmos projct. In thos cass, th adaptiv combination of forcasts might b a usful mthodology to gnrat an fficint singl forcast. Figur 11: Exampl of individual prdiction modls (dottd lins) and th xpctd ffct of rror rduction by prdiction combination in Golagh wind farm. Combination dpnds on forcast horizon. It is basd on a two stp combination mthodology to combin a st of altrnativ prdictions. This two stp procdur aims to tak th advantag of th diffrnt approachs of forcast combination. In th first stp, svral combination mthods ar usd, bing th AEC on of thm. In th scond stp, th AEC mthod is usd to combin th altrnativ combinations of th first stp. Th application to a ral data st illustrats th usfulnss of th proposd mthods to obtain th bst output from a st of altrnativ prdictions. Two diffrnt typs of combination approachs in a unifid mthod Thr ar many approachs in th litratur to prform combination of forcasts. For convninc, hr w will classify th altrnativ approachs into two main classs dpnding on th goal of th combination. Th first class of combination mthods will b dnotd as combination for improvmnt. In this class, w targt th bst (constraind) linar combination of a st of forcasts. Mthods to prform this combination for improvmnt can b basd on th rgrssion mthodology, aimd at minimizing th rsidual varianc of th linar combination. Idally, th optimal linar combination would outprform th individual forcasts. In a practical situation, it is unclar how far w ar of th idal prformanc that can b obtaind by combination. It is thn possibl that such combination is wors than som of th individual forcasts. 7

9 Th scond class of combination mthods is calld combination for adaptation. In this class w look for th combination that prforms as wll as th bst individual procdur. This scond class can thn b intrprtd as similar to a dynamic modl slction, whr th combination tnds to put all th wigh to th bst prdictor, whnvr it is clar that on of th prdictors is th bst on. Two-stps combination of forcasts In a practical situation w will not know in advanc whthr it would b bttr to us a combination for improvmnt mthod or, convrsly, a combination for adaptation mthod. In ordr to bnfit from both typs of approachs w will apply thm for wind nrgy forcast in a two stp procdur. In a first stp, w will apply altrnativ combination procdurs basd on th two mntiond approachs: on or mor mthods of adaptiv combination for improvmnt, and also th AEC mthod of combining for adaptation. In a scond stp, w will trat ths altrnativ combinations of th first stag as a nw combination problm, and will combin thm to obtain th final combination. In this scond stp w will not xpct to improv ovr th combind prdictions of th first stp, but only to assur that th final combination is as good as th bst of th compting combind prdictions. Thn, it is a combination for adaptation problm and only th AEC mthod will b usd. W will rfr to this practic as a two-stps combination of forcasts. Application to wind nrgy prdictions W will compar th prformanc of diffrnt combination schms applid to a st of altrnativ forcasts of hourly wind nrgy production. W hav 9 altrnativ sris of forcasts producd with th prdiction modls tstd in Anmos projct, dnotd as P1 to P9 as wll as th tim sris of ral obsrvations for Golagh wind farm. Th tim span is thr months, with a total of 2118 tim priods. Th 9 forcastrs hav had th opportunity to build and train thir rspctiv mthods using a larg nough portion of oldr data from th wind farm. For th xrcis, ach hour th 9 forcastrs had to supply prdictions for th nxt 48 hours. Tabl II shows th root man squard rror (RMSE) normalisd with nominal powr of ach forcastr for slctd horizons. This tabl displays th minimum RMSE across th forcastrs, and thn th diffrnc btwn th RMSE of ach forcastr and th minimum. W can s from this tabl that th bst prdictor (bold numbrs) is diffrnt at ach horizon. As mntiond abov, w prform a two-stps combination of forcasts. In a first stp w combin th 9 compting forcast using th combination for improvmnt mthod (dnotd as C1) and th combination for adaptation (AEC). In th scond stp, w combin ths two combinations of forcasts of th first stp using th AEC mthod. W will trat ach prdiction horizon as an indpndnt combination problm. Th rsults ar displayd in Tabl III. Th column of Minimum RMSE is th sam as in th prvious tabl. Minimum Diffrnc from minimum RMSE H RMSE P1 P2 P3 P4 P5 P6 P7 P8 P Tabl II: Minimum RMSE along th altrnativ prdictors at ach horizon, and diffrnc of th RMSE of ach prdictor to that minimum. Diffrnc from minimum RMSE First Stp Scond Stp H Min. RMSE C1 AEC AEC Tabl III: Minimum RMSE along th altrnativ prdictors at ach horizon, and diffrnc of th RMSE of ach combination with rspct to that minimum. W s in this tabl that th proposd two stps combination mthodology, togthr with th us of th proposd AEC mthod, hlps to tak th bst 8

10 prformanc of a st of compting prdictions for this wind farm. 7. Conclusions Nin stat of th art wind powr prdiction modls hav bn compard in six wind farms. This is th first comparison that is carrid out at Europan lvl on short trm prdiction. A framwork has bn dvlopd for th bnchmarking of th modls, including a protocol for rror analysis, common databass for ach tst cas and th dfinition of a standard format for data and prdictions xchang. Th rsults showd a dpndncy of th prdiction rrors on th complxity of th trrain as wll as on th forcast horizon. Th distribution of rrors was studid and also th rlation of th rrors with th powr curv. Finally an algorithm to combin powr prdiction forcasts was dvlopd and analysd, bing possibl to optimis th prformanc of a st of forcasts for a givn wind farm. 8. Acknowldgmnts This work was prformd in th fram of th ANEMOS Projct (ENK5-CT ) fundd in part by th Europan Commission. Acknowldgmnts ar du to EDF, EHN, ELSAM, ESB, EWE, IDAE & PPC for providing th data for this work. Spcial thanks to th National Mtorological Institut of Spain for providing HIRLAM NWP of Spain. 9. Rfrncs [1] [2] Kariniotakis, G., Marti, I., t al What prformanc can b xpctd by short-trm wind powr prdiction modls dpnding on sit charactristics?. Procdings of th 24 Europan Union Wind Enrgy Confrnc and Exhibition, London, UK, Novmbr 22-25, 24. [3] Bown, A.J., Mortnsn, N.G., Exploring th limits of WAsP: th Wind Atlas Analysis and Application Program. Procdings of th 1996 Europan Union Wind Enrgy Confrnc and Exhibition, Götborg, Swdn, May 2-24, 1996, pp [4] Gibl, G., G. Kariniotakis, R. Brownsword: Th Stat-of-th-Art in Short-Trm Prdiction of Wind Powr A Litratur Ovrviw. Position papr for th ANEMOS projct, download from [5] Gibl, G., Boon, B., A Comparison of th DMI- Hirlam and DWD-Lokalmodll for Short-Trm Forcasting. Procdings of th EWEC, London (UK), Novmbr 24. [6] Madsn, H., Kariniotakis, G., Nilsn, H.Aa., Nilsn, T.S., Pinson, P., "A Protocol for Standardising th Prformanc Evaluation of Short- Trm Wind Powr Prdiction Modls", CD-rom Procd. of th Global WindPowr 24 Confrnc, Chicago, USA, Mar , 24. [7] Papadopoulos, A., Katsafados, P., Kallos, G., Rgional wathr forcasting for marin application. Global Atmos. Ocan Syst., 8, No 2-3, 21, [8] A. H.Murphy and R. L.Winklr. A gnral framwork for forcast vrification. Monthly Wathr Rviw, 115: , [9] A. H. Murphy. What is a good forcast? An ssay on th natur of goodnss in wathr forcasting. Wathr Forcasting, 8(2): , [1] H. Madsn, P. Pinson, T.S. Nilsn, H.Aa. Nilsn, G. Kariniotakis. Standardizing th prformanc valuation of short-trm wind powr prdiction modls. Wind Enginring, 26. In Prss. [11] M. Lang. On th uncrtainty of wind powr prdictions - Analysis of th forcast accuracy and statistical distribution of rrors. Trans. of th ASME, J. Solar Enrgy Eng., 127(2): , May 25 [12] P. Pinson. Estimation of th uncrtainty in wind powr forcasting, PhD thsis, Ecol ds Mins d Paris, Cntr for Enrgy & Procsss, 23 March 26. 9