Assessment of a Global-to-Direct empirical model for the long-term characterization of Direct Normal Insolation

Ene gy P ocedia 49 ( 2014 ) 2377 – 2386 A ailable online a www.sciencedi ec .com ScienceDi ec 1876-6102 © 2013 The Au ho s. Published by Else ie L d. This is an open access a icle unde he CC BY-NC-ND license (h p://c ea i ecommons.o g/licenses/by-nc-nd/3.0/). Selec ion and pee e iew by he scien i i c con e ence commi ee o Sola PACES 2013 unde esponsibili y o PSE AG. Final manusc ip published as ecei ed wi hou edi o ial co ec ions. doi: 10.1016/j.egyp o.2014.03.252 Assessmen o a Global- o-Di ec empi ical model o he long- e m cha ac e iza ion o Di ec No mal Insola ion S. Mo eno-Teje aa, E. Pé ez-Apa icioa, J. M. Ba ea-Ga cíaa, I. Lillo-B a ob, M. A. Sil a-Pé ezb aAICIA / G upo de Te modinámica y Ene gías Reno ables. Add ess: A da. de los descub imien os s/n, 41092 Se illa (Spain) bUni e si y o Se ille. G oup o The modynamics and Renewable Ene gies. Abs ac The s a is ical cha ac e iza ion o he sola esou ce (di ec no mal sola adia ion) is a key poin in he ini ial phases o a sola he mal elec ici y (STE) plan p ojec . Ideally, his cha ac e iza ion should be based on long ime se ies (a leas 8 yea s) o on-si e measu ed da a o Di ec No mal Insola ion (DNI) and o he me eo ological pa ame e s. Un o una ely, he e a e e y ew places a ound he wo ld whe e such ime se ies a e a ailable, so al e na i e me hods ha e o be used. Mos o hem ely on he applica ion o global- o-di ec con e sion models o long ime se ies o Global Ho izon al Insola ion (GHI), measu ed o de i ed om sa elli e images, o es ima e he long- e m esou ce. Usually, a me eo ological s a ion including senso s o he measu emen o DNI is ins alled a he selec ed p ojec si e a he beginning o he p ojec . The da a collec ed du ing he measu emen campaign, which no mally ex ends be ween a ew mon hs and 2 yea s, a e used o adjus he con e sion models and o co ec he es ima es. In his pape , a simple empi ical model ha ela es mon hly clea ness index and mon hly di ec no mal ac ion is used o es ima e mon hly and annual long- e m DNI om s a is ically ep esen a i e mon hly alues o GHI. This model is adjus ed wi h GHI and DNI da a collec ed du ing measu emen campaigns o di e en du a ions. We show ha he accu acy o he p oposed model is unde 5% and ha his accu acy imp o es sha ply wi h he du a ion o he es campaign. Fo his pu pose, we ha e used 13 yea s o high quali y DNI and GHI da a om he adiome ic s a ion o he G oup o The modynamics and Renewable Ene gies (GTER) o he Uni e si y o Se ille, Spain. The esul s sugges ha , his simple empi ical model is a good al e na i e o he p esen me hodologies when sho DNI measu emen campaign bu long- e m GHI alues a e a ailable. © 2013 The Au ho s. Published by Else ie L d. Selec ion and pee e iew by he scien i ic con e ence commi ee o Sola PACES 2013 unde esponsibili y o PSE AG. Keywo ds: Sola Resou ce Assessmen ; Di ec No mal Insola ion; Clea ness Index model, Sola The mal Elec ici y © 2013 The Au ho s. Published by Else ie L d. This is an open access a icle unde he CC BY-NC-ND license (h p://c ea i ecommons.o g/licenses/by-nc-nd/3.0/). Selec ion and pee e iew by he scien i ic con e ence commi ee o Sola PACES 2013 unde esponsibili y o PSE AG. Final manusc ip published as ecei ed wi hou edi o ial co ec ions. 2378 S. Mo eno-Teje a e al. / Ene gy P ocedia 49 ( 2014 ) 2377 – 2386 1. In oduc ion The cha ac e iza ion o he di ec no mal sola adia ion is one o he key poin s in he ini ial phases o a sola he mal elec ici y (STE) plan p ojec . Di ec no mal insola ion (DNI) se ies, which s a is ically ep esen he sola esou ce o he plan si e, a e commonly used o analyze he inancial easibili y o STE p ojec s. These da a se s in ol e an unce ain y ha depends, among o he ac o s, on he numbe o he DNI yea s measu ed on si e, he quali y o hese measu emen s and he me hodology used o es ima ing hem. Fo he pu pose o educing he unce ain y, a DNI measu emen campaign s a s up on he chosen si e a he beginning o he p ojec [1]. DNI da abases co e ing a pe iod long enough o apply he con en ional me hodologies [2] a e no e y common. In consequence, he need o cha ac e ize his a iable has s imula ed he de elopmen o al e na i e me hodologies adap ed o he a ailable in o ma ion wi h unce ain ies associa ed [3,4]. Mos o hese me hodologies a e based on global ho izon al insola ion da a; ei he measu ed a nea by s a ions o es ima ed om sa elli e images, co ec ed wi h sho DNI measu emen campaign on si e. S udies show ha GHI da ase s es ima ed om sa elli e images could supply a easonable esul o long- e m es ima es in mon hly and annual equency, and e en mo e i ha da ase s we e co ec ed wi h measu emen s on si e [5]. Ne e heless, ha is no he case o DNI da ase s es ima ed om sa elli e images. A c oss compa ison o a ew o hem in Eu ope showed ha wi hin 90% o he s udy a ea he annual unce ain y o DNI may go up o 17% [6]. O he alida ion s udies based on g ound measu emen s e eal a numbe o p oblems in geog aphical a eas whe e signi ican disag eemen exis be ween he es ed da ase s. Un o una ely, some o hese geog aphical a eas a e wi hin hose wi h a e y high po en ial in e ms o DNI. O e all annual di e ences wi hin ±10% and mon hly di e ences o mo e han 30 % ha e been epo ed o Eu ope. Rega ding No h A ica, he di e ences each signi ican alues in some a eas highe han 100% [7]. The possibili y o es ima ing a s a is ically ep esen a i e DNI se using only on-si e measu emen s and an empi ical simple model de eloped om hese eco ded da a is explo ed in his wo k. The basic assump ion o his me hodology is ha enough in o ma ion o cha ac e ize he GHI om he si e [8] and a minimum pe iod o a yea o DNI measu emen s on si e a e a ailable. To quan i y he quali y o he esul s, 13 comple e and quali y-con olled yea s o GHI and DNI measu emen s om he adiome ic s a ion o he G oup o The modynamics and Renewable Ene gies si ed in Se ille a e used. As a esul o his s udy, he annual and he mon hly e o s –de ined as he di e ence be ween he e e ence se ies, ob ained as he a e age om he 13-yea DNI measu emen s and he es ima es ob ained when applying his me hodology- a e shown, wi h di e en measu emen campaigns o di ec no mal adia ion om 1 o 12 yea s. Nomencla u e Hg0,m mon hly ho izon al global adia ion H0,m mon hly ho izon al ex a e es ial adia ion Hn,m mon hly no mal ex a e es ial adia ion Hbn,m mon hly di ec no mal adia ion k mon hly clea ness index kbn mon hly di ec no mal ac ion S. Mo eno-Teje a e al. / Ene gy P ocedia 49 ( 2014 ) 2377 – 2386 2379 2. Backg ound 2.1. Da a collec ion and p ocessing The adiome ic s a ion o he G oup o The modynamics and Renewable Ene gies (GTER) o he Uni e si y o Se ille, si ed a he Enginee ing School o Se ille, has eco ded adiome ic and me eo ological measu es since 1984. Du ing i s li e ime, he adiome ic s a ion has been eloca ed and he senso s upg aded se e al imes. Du ing he pe iod 2000-2012 he s a ion was si ed in 37.40º N, 6.01ºE and collec ed accu a e and high esolu ion DNI and GHI da a in 5 seconds in e als, wi h a seconda y s anda d py anome e and a i s class py heliome e , acco ding o ISO speci ica ions. The da a collec ed du ing he pe iod 2000-2012 ha e been checked, co ec ed, and alida ed h ough a p ocedu e de eloped by GTER, esul ing in a high quali y ime se ies o DNI, GHI and o he me eo ological pa ame e s ha cons i u es he basis o he p esen wo k. The quali y con ol and co ec ion p ocess is b ie ly desc ibed below: x Quali y con ol: The p elimina y s ep includes a daily isual inspec ion o he g aphical ep esen a ions, he cen e ed o days i necessa y, he loca ion o gaps a he eco ds and, inally, he classi ica ion o days depending on he cloudiness le el [9,10]. x Classi ica ion o days: In his sec ion he days a e classi ied as shown in igu e 1. This classi ica ion has been done a ending o he alidi y o da a, loca ion o e o s and kind o days. Fig 1. Classi ica ion o days. x Co ec ion: A his poin he co ec ion me hods a e de eloped o each case. The e a e wo main g oups o days ha need o be modi ied; disca ded and co ec able. Co ec able days a e hose ha complemen he da abase using mainly adia ion models [11] and heo e ical ela ionships widely ecognized [12]. Rega ding o disca ded days, depending on which adiome ic componen is he anomaly de ec ed, nea by da abases o DNI models de eloped o he si e a e used. F om he o al eco ded days du ing he pe iod 2000-2012, only 8% we e classi ied as disca ded days and 18% as co ec able days. The es o he days, a 74 % we e eco ded wi hou any anomalies. 2.2. Co ela ion be ween clea ness index and di ec no mal ac ion The aim o his wo k is o assess he unce ain y o a simple empi ical model ha ela es mon hly GHI alues wi h mon hly DNI alues and allows he es ima ion o long- e m mon hly DNI da a om long e m GHI da a unde he ollowing assump ions: x Enough in o ma ion o cha ac e ize he GHI om he si e. x A minimum pe iod o a yea o DNI measu emen s on si e is a ailable. 2380 S. Mo eno-Teje a e al. / Ene gy P ocedia 49 ( 2014 ) 2377 – 2386 The model chosen o his pu pose is based in an empi ical ela ion be ween he mon hly clea ness index, k (1) and he di ec no mal ac ion kbn de ined in (2). The clea ness index is well documen ed in li e a u e and widely used o cha ac e ize sola adia ion in di e en imescales. Howe e he di ec no mal ac ion is no so used, being in mos cases he di use ac ion he chosen index.  ݇௧ൌு೒బǡ೘ ுబǡ೘  (1) ݇௕௡ ൌு್೙ǡ೘ ு೙ǡ೘ (2) As i s s ep, he whole selec ed pe iod (2000-12) o bo h a iables eco ded by GTER s a ion is conside ed o e alua e wi h he bes scena io he ype o eg ession model p ope ly o he s udy. Among he eg ession es ed models, linea and second o de polynomial i s p o ide a easonable esul . Inc easing he complexi y o he model does no esul in a signi ican imp o emen . Fig 2. Linea (a) and second o de polynomial (b) i s om k and kbn alues. The es ima ed equa ion o he linea i is: ݇௕௡ ൌͳǤͲͻͺ͵ ή݇ ௧െͲǤ͵ͳͶͳ (3) The es ima ed equa ion o he polynomial i is: ݇௕௡ ൌͳǤ͵͹͹ͳ ή݇ ௧ ଶെͲǤͷͳͷ͵ ή݇ ௧൅ͲǤͳͷͳ (4) Al hough, he linea i is less sa is ac o y o he ex eme alues, bo h eg essions p o ide easonable esul s. The polynomial coe icien o co ela ion R2 is 0.95, e y simila o he linea coe icien co ela ion 0.94. In o de o analyze he possible e ec in he mon hly unce ain y o he di e en seasons, bo h i s will be used o his s udy. 3. Me hodology When a sola esou ce assessmen s udy is add essed, he on-si e measu emen campaign a ely exceeds wo yea s. Consequen ly, an al e na i e me hodology has o be use o es ima e a ep esen a i e DNI da ase , and quan i y he unce ain y om he me hodology is no an easy ask because a e e ence esul is no a ailable. In his s udy, he mon hly a e age GHI and DNI measu es om he 2000-12 pe iod a e conside ed he long e m ep esen a i e alues and hey a e used as a e e ence o e alua e he unce ain y o he models when sho e pe iods o DNI measu emen s a e a ailable. To co e a ep esen a i e numbe o possible cases and, a he same ime, habi ual scena ios, pe iods o eco ds ha e been selec ed based on he c i e ia desc ibed bellow: S. Mo eno-Teje a e al. / Ene gy P ocedia 49 ( 2014 ) 2377 – 2386 2381 x Pe iods include consecu i e mon hs. x The numbe o selec ed mon hs is mul iple o 12: om 1 yea o 12 yea s. x All he possible combina ions a e assessed o e e y pe iod. The able 1 shows se e al examples o he analyzed cases. Once selec ed he pe iod o measu emen s (inpu da a o he model), he linea and polynomial k -kbn models a e adjus ed om DNI and GHI measu emen s. Subsequen ly and using he i ed models, he long- e m mon hly DNI alues a e es ima ed om he mon hly a e age GHI measu emen s o he comple e ime se ies (2000-2012). The ela i e e o be ween he long- e m mon hly es ima ed DNI alues and he mon hly a e age DNI measu emen s om he whole pe iod is conside ed he unce ain y o he models. These s eps a e epea ed o e e y pe iod and e e y p e iously desc ibed case. Se e al examples o he numbe o cases o each analyzed pe iod a e shown in he ollowing able. Table 1. Pe iods o DNI measu emen s used o quan i y he unce ain y o he model. 1 yea 2 yea s 3 yea s … 10 yea s 11 yea s 12 yea s Case 1 Ene00-Dic00 Ene00-Dic01 Ene00-Dic02 … Ene00-Dic09 Ene00-Dic10 Ene00-Dic11 Case 2 Feb00-Ene01 Feb00-Ene02 Feb00-Ene03 … Feb00-Ene10 Feb00-Ene11 Feb00-Ene12 … … … … … … … … Case n Ene12-Dic12 Ene11-Dic12 Ene10-Dic12 … Ene03-Dic12 Ene02-Dic12 Ene01-Dic12 n 145 133 121 … 37 25 13 4. Resul s and discussion The ela i e e o o he long- e m es ima ed DNI yea s om he me hodology wi h espec o he a e age DNI yea om he whole pe iod o measu emen s a e compa ed in his sec ion. As al eady s a ed abo e, his pa ame e is assumed as he unce ain y o he models. 4.1. Annual unce ain y: The annual DNI unce ain y alues o each pe iod analyzed by means o he linea and he polynomial model a e ep esen ed in he igu es 2 and 3. Fo bo h eg ession models, he maximum annual unce ain y is eached o one yea o DNI measu emen s and clea ly dec eases when he measu emen pe iod inc eases un il 9 yea s. Fo campaigns be ween 9 and 13 yea s he unce ain y end changes e y sligh ly, bu always keeping a alue inside ± 1%. This ac is a consequence o he mon hly e o s ob ained. These ones, as show he ables 2 and 3, always dec ease when he pe iod o yea s inc eases bu wi h di e en sign, causing hese changes o end in he annual e o s. As shown he igu e 3, he annual unce ain y when i ing he linea model om one yea o DNI measu emen s eaches alues be ween -6 % and 5% and his in e al sligh ly dec eases wi h he polynomial model p esen ing alues be ween 3.4% and -5%, as shown he igu e 4. In his case, he polynomial model p o ide mo e accu a e esul s, bu when he measu emen campaign is longe han one yea bo h ype o eg essions p esen simila esul s. Fo pe iods equal o o highe han 3 yea s, bo h models show an unce ain y equal o lowe han 3%. These esul s indica e he possibili y o an annual long- e m DNI es ima ion on his si e wi h a k -kbn model, wi h an accep able unce ain y when a sho pe iod o DNI measu emen s is a ailable and e y low unce ain y when his pe iod is highe han wo yea s. 2382 S. Mo eno-Teje a e al. / Ene gy P ocedia 49 ( 2014 ) 2377 – 2386 Fig 3. Rela i e e o s be ween annual long- e m DNI es ima ed alues by means o he linea model and annual a e age DNI measu emen s agains he numbe o cases s udied (a) and o each analyzed pe iod (b). Fig 4. Rela i e e o s be ween annual long- e m DNI es ima ed alues by means o he polynomial model and annual a e age DNI measu emen s agains he numbe o cases s udied (a) and o each analyzed pe iod (b). 4.2. Mon hly unce ain y In he ables 2 and 3, he maximum and minimum mon hly and annual ela i e e o s ob ained o each pe iod and each mon h wi h linea and polynomial model a e shown. The maximum mon hly ela i e e o s o bo h models co espond o Decembe (18.3 % wi h he linea model and 21.6 % wi h he polynomial model) bu as shown in igu e 5, hese alues only appea in a ew o he 145 cases. Discoun ing Decembe and conside ing he ela i e e o s as he unce ain y models, he polynomial model p o ides easonable esul s wi h an unce ain y lowe han 10 % wi h only one yea o measu emen s and his unce ain y dec eases when he eco ded pe iod inc eases. Pe iods o 3 yea s and longe p o ide unce ain ies lowe han 6 % in he highes adia ion mon hs wi h his eg ession model. In a i s imp ession, he polynomial model p esen s he bes mon hly esul s, mainly when he campaign is composed o one yea o DNI measu emen s, bu a mo e de ailed analysis show ha he lineal model p o ides lowe e o s in Janua y, Oc obe and No embe when pe iods a e longe . Ne e heless, bo h models show simila beha io in mon hs wi h highes DNI o summe mon hs. This ac sugges s a dependence o he ype o model wi h he ype o clima e. Figu es 6 (a) and (b) illus a e his ac . S. Mo eno-Teje a e al. / Ene gy P ocedia 49 ( 2014 ) 2377 – 2386 2383 Table 2. Rela i e e o s be ween annual and mon hly long- e m DNI es ima ed wi h he linea model and measu ed o each mon hs and analyzed pe iod. Pe iod (yea s) Anual Jan. Feb. Ma . Ap il May June July Aug. Sep . Oc . No . Dec. 1 Min. -6,0% -12,8% -7,2% -4,2% -4,4% -1,4% -3,7% -8,4% -5,4% -3,0% -9,7% -12,3% -18,3% Max. 4,7% 2,2% 5,7% 9,6% 7,5% 8,4% 5,8% 2,5% 5,2% 7,1% 4,3% 3,6% 0,4% 2 Min. -2,6% -6,1% -2,0% 1,5% 0,0% 0,9% -2,6% -7,1% -4,1% -0,4% -3,7% -5,2% -11,4% Max. 4,1% 0,5% 4,6% 8,3% 6,6% 8,1% 5,1% 0,9% 3,8% 6,6% 2,9% 1,8% -1,8% 3 Min. -1,6% -5,6% -0,9% 2,5% 1,1% 1,8% -1,8% -6,4% -3,4% 0,5% -2,8% -4,6% -10,0% Max. 2,9% -0,5% 3,5% 7,2% 5,4% 6,8% 4,3% 0,3% 3,3% 5,3% 1,9% 0,8% -2,9% 4 Min. -0,7% -4,9% -0,2% 3,3% 1,9% 2,9% -0,5% -5,1% -2,0% 1,6% -2,0% -4,1% -9,5% Max. 2,2% -1,5% 2,6% 6,2% 4,7% 6,2% 3,6% -0,5% 2,5% 4,7% 0,9% -0,3% -3,5% 5 Min. -0,5% -4,7% -0,4% 3,1% 1,8% 3,3% 0,0% -4,4% -1,4% 2,0% -2,2% -3,7% -8,3% Max. 1,8% -1,8% 2,3% 5,9% 4,3% 5,9% 3,5% -0,6% 2,4% 4,4% 0,6% -0,6% -4,1% 6 Min. -0,3% -4,5% -0,1% 3,4% 2,0% 3,6% 0,4% -4,0% -1,0% 2,2% -1,9% -3,5% -8,5% Max. 1,6% -2,3% 1,9% 5,5% 4,0% 5,7% 3,2% -0,8% 2,1% 4,3% 0,2% -1,1% -4,9% 7 Min. -0,2% -4,7% -0,2% 3,3% 2,0% 3,7% 0,5% -3,8% -0,8% 2,3% -2,0% -3,7% -8,6% Max. 1,5% -2,3% 1,9% 5,4% 3,9% 5,5% 2,7% -1,5% 1,5% 4,1% 0,1% -1,2% -5,1% 8 Min. -0,1% -3,9% 0,4% 3,9% 2,4% 3,7% 0,8% -3,5% -0,6% 2,4% -1,4% -2,8% -7,4% Max. 1,2% -2,5% 1,7% 5,2% 3,7% 5,2% 2,3% -1,8% 1,1% 3,8% 0,0% -1,2% -5,4% 9 Min. 0,3% -3,6% 0,8% 4,3% 2,8% 4,2% 1,1% -3,3% -0,3% 2,8% -1,0% -2,5% -7,0% Max. 0,9% -2,6% 1,3% 4,8% 3,3% 4,9% 2,1% -2,0% 0,9% 3,4% -0,4% -1,3% -5,2% 10 Min. 0,1% -3,4% 0,7% 4,2% 2,6% 3,9% 0,9% -3,4% -0,4% 2,5% -1,0% -2,1% -6,5% Max. 0,8% -2,5% 1,4% 5,0% 3,3% 4,7% 1,9% -2,3% 0,6% 3,3% -0,2% -1,2% -5,2% 11 Min. -0,1% -3,6% 0,4% 4,0% 2,4% 3,8% 0,8% -3,5% -0,5% 2,4% -1,2% -2,4% -6,6% Max. 0,8% -2,6% 1,4% 5,0% 3,3% 4,6% 1,6% -2,7% 0,3% 3,3% -0,2% -1,3% -5,3% 12 Min. 0,1% -3,0% 0,8% 4,4% 2,6% 3,8% 0,6% -3,8% -0,8% 2,4% -0,8% -1,8% -5,6% Max. 0,4% -2,7% 1,0% 4,6% 2,9% 4,2% 1,2% -3,2% -0,2% 2,8% -0,5% -1,4% -5,1% 13 0,1% -2,9% 0,8% 4,4% 2,7% 3,8% 0,7% -3,8% -0,8% 2,5% -0,7% -1,6% -5,3% 2384 S. Mo eno-Teje a e al. / Ene gy P ocedia 49 ( 2014 ) 2377 – 2386 Table 3. Rela i e e o s be ween annual and mon hly long- e m DNI es ima ed wi h he polynomial model and measu ed o each mon hs and analyzed pe iod. Pe iod (yea s) Anual Jan. Feb. Ma . Ap il May June July Aug. Sep . Oc . No . Dec. 1 Min. -5,0% -9,6% -5,9% -2,3% -4,3% -3,7% -5,0% -7,9% -5,6% -5,0% -6,7% -8,9% -21,6% Max. 3,4% -0,6% 4,1% 7,2% 7,5% 9,4% 6,3% 5,3% 7,1% 7,9% 1,4% 1,2% 5,4% 2 Min. -3,5% -7,1% -4,2% -0,8% -2,2% -0,9% -3,3% -6,7% -4,1% -2,2% -5,4% -5,5% -12,6% Max. 2,6% -2,4% 1,4% 4,7% 4,1% 6,2% 5,1% 3,0% 5,2% 4,7% -0,4% -0,6% -1,8% 3 Min. -2,5% -6,9% -3,7% -0,3% -1,9% 0,2% -2,1% -5,8% -3,1% -1,3% -5,1% -5,4% -7,3% Max. 1,7% -3,2% 0,1% 3,7% 2,2% 4,6% 4,4% 2,8% 4,9% 3,0% -1,3% -1,7% -2,4% 4 Min. -2,0% -6,5% -3,4% 0,0% -1,5% 0,6% -0,6% -4,2% -1,5% -0,9% -4,8% -5,0% -6,7% Max. 1,2% -3,4% -0,6% 3,1% 1,6% 4,1% 3,9% 2,4% 4,4% 2,5% -1,6% -1,7% -3,8% 5 Min. -1,2% -5,4% -2,3% 1,2% -0,4% 1,5% 0,2% -3,0% -0,4% 0,0% -3,6% -3,9% -6,4% Max. 1,2% -3,6% -0,7% 2,9% 1,2% 3,7% 3,7% 2,1% 4,1% 2,1% -1,9% -2,0% -4,0% 6 Min. -0,9% -5,5% -2,2% 1,2% -0,2% 1,9% 0,5% -2,6% 0,0% 0,3% -3,6% -4,0% -6,0% Max. 1,0% -3,9% -0,8% 2,8% 1,3% 3,9% 3,6% 1,8% 3,9% 2,2% -2,1% -2,3% -3,7% 7 Min. -0,8% -5,6% -2,3% 1,2% -0,3% 1,9% 0,6% -2,4% 0,1% 0,4% -3,7% -4,1% -6,2% Max. 0,9% -4,2% -0,9% 2,6% 1,3% 3,7% 3,3% 1,2% 3,4% 2,1% -2,4% -2,6% -4,5% 8 Min. -0,7% -5,6% -2,4% 1,1% -0,3% 2,0% 0,9% -2,1% 0,4% 0,4% -3,8% -4,1% -6,0% Max. 0,5% -3,9% -0,7% 2,8% 1,1% 3,4% 2,7% 0,6% 2,7% 1,8% -2,0% -2,4% -4,7% 9 Min. -0,5% -5,3% -2,1% 1,4% -0,1% 2,2% 1,1% -2,0% 0,6% 0,6% -3,5% -3,8% -5,7% Max. 0,2% -3,8% -0,7% 2,9% 1,1% 3,1% 2,5% 0,4% 2,6% 1,5% -2,0% -2,3% -4,4% 10 Min. -0,6% -5,2% -1,9% 1,6% 0,1% 2,2% 0,9% -2,1% 0,4% 0,7% -3,3% -3,7% -5,7% Max. 0,0% -4,0% -0,9% 2,7% 0,9% 2,9% 2,3% 0,2% 2,4% 1,3% -2,2% -2,5% -4,7% 11 Min. -0,7% -5,2% -1,9% 1,6% 0,1% 2,2% 0,8% -2,2% 0,3% 0,7% -3,3% -3,7% -5,7% Max. 0,0% -4,3% -1,2% 2,4% 0,7% 2,8% 2,2% 0,1% 2,3% 1,2% -2,5% -2,8% -5,0% 12 Min. -0,7% -5,2% -1,9% 1,6% 0,0% 2,1% 0,8% -2,0% 0,4% 0,6% -3,3% -3,6% -5,6% Max. -0,5% -4,5% -1,4% 2,1% 0,4% 2,3% 1,5% -0,9% 1,4% 0,8% -2,7% -2,9% -4,9% 13 -0,7% -4,6% -1,5% 2,0% 0,3% 2,1% 0,7% -2,1% 0,4% 0,6% -2,8% -3,1% -5,1% Fig 5. Rela i e e o s be ween mon hly long- e m DNI es ima ed alues wi h linea (a) and polynomial (b) model and a e age measu ed alues om he whole da abase in Decembe . S. Mo eno-Teje a e al. / Ene gy P ocedia 49 ( 2014 ) 2377 – 2386 2385 In igu e 6 (a), he unce ain y is plo ed agains he du a ion, in yea s, o he measu emen campaign o he mon hs o Janua y, May, June and July. Fo all mon hs, he unce ain y dec eases as he du a ion o he DNI measu emen campaign inc eases. The mon hly unce ain y alues ob ained wi h bo h models i ed om he 13 yea s o DNI measu emen s as a unc ion o he mon hly clea ness index a e shown in igu e 6 (b). This igu e sugges s ha he lineal model p o ides mo e accu a e esul s in mon hs wi h lowe k alues. Fig 6. (a) Maximum and minimum mon hly unce ain y ob ained wi h he polynomial model in Janua y, May, June and July om e e y pe iod analyzed. (b) Mon hly unce ain y ob ained wi h he polynomial and he linea model i ed wi h he 13 yea s o DNI measu emen s agains he mon hly clea ness index om he mon hly a e age GHI measu emen s. 5. Conclusion In his wo k, we ha e p oposed and es ed a simple empi ical model o es ima e mon hly and annual long- e m DNI ep esen a i e alues. The unce ain y o his model has been e alua ed compa ing he DNI alues p o ided by he model, once adjus ed wi h he da a collec ed in measu emen campaigns o di e en du a ion, wi h he a e age alues o a 13-yea ime se ies eco ded a he adiome ic s a ion o he G oup o The modynamics and Renewable Ene gy, Uni e si y o Se ille. The esul s show an annual unce ain y lowe han 5% when one yea o DNI measu emen s is a ailable and lowe han 3% when he DNI campaign is equal o highe han 3 yea om a second o de polynomial model. Rega ding o mon hly esul s, he bes ype o eg ession model is no so clea , sugges ing a di e en ype o eg ession on base o he mon hly k alue. Ne e heless, bo h models p esen easonable mon hly unce ain ies wi h alues lowe han 10 % o he highes adia ion mon hs om one yea o DNI measu emen s and lowe han 6% om h ee yea s o DNI measu emen s. The esul s ob ained on he selec ed si e sugges he use o his kind o model o long- e m DNI es ima ions as a e y good op ion when long DNI da ase s o measu emen s a e no a ailable. The au ho s p opose o ex end his s udy o o he loca ions whe e he equi ed in o ma ion is a ailable. Re e ences [1] Fi ch Ra ings. Ra ing C i e ia o Sola Powe P ojec s. U ili y-Scale Pho o ol aic, Concen a ing Pho o ol aic, and Concen a ing Sola Powe . Global In as uc u e & P ojec Finance; 2013. [2] Wilcox S, Ma ion W. Use s Manual o TMY3 Da a Se s. Na ional Renewable Ene gy Labo a o y. Technical Repo NREL/TP-581-43156; 2008. [3] Hoye -Klick C e al. Cha ac e is ic me eo ological yea s om g ound and sa eli e da a. P oc. Sola PACES 2009 Con . Be lin, Ge many; 2009.