Validation of wind turbine wake models

Imagem An ónio Nunes Vicen e Valida ion o wind u bine wake models Disse ação de Mes ado em Engenha ia Mecânica na Especialidade de Ene gia e Ambien e July/2018 DEPARTAMENTO DE ENGENHARIA MECÂNICA Valida ion o wind u bine wake models Submi ed in Pa ial Ful ilmen o he Requi emen s o he Deg ee o Mas e in Mechanical Enginee ing in he speciali y o Ene gy and En i onmen Validação de modelos de es ei a pa a u binas eólicas Au ho An ónio Hen ique Seab a Nunes Vicen e Ad iso s PhD. An ónio Manuel Gamei o Lopes PhD. Oma He e a Sanchez (menzio GmbH) Ju y P esiden PhD. Ped o de Figuei edo Viei a Ca alhei a Assis an P o esso , Uni e si y o Coimb a Vowel PhD. Alme indo Domingues Fe ei a Assis an P o esso , Uni e si y o Coimb a Ad iso PhD. An ónio Manuel Gamei o Lopes Assis an P o esso , Uni e si y o Coimb a Uni e sidade de Coimb a menzio GmbH Coimb a, July, 2018 Acknowledgemen s An ónio Nunes Vicen e i ACKNOWLEDGEMENTS Fi s o all, I would like o hank my ad iso , P o esso An ónio Gamei o, o ha ing gi en me he oppo uni y o wo k on an in e es ing and ele an opic. His dedica ion and guidance we e c ucial o my hesis wo k. I much app ecia e he ac ha I ha e always been able o made p og ess in a simple and s eady way. I would also like o hank my co-ad iso , P o esso Oma He e a Sanchez, o his use ul ad ice and con inued suppo . My ime a Uni e si y o Coimb a has jus come o an end, and hus I would like o exp ess my g a i ude o my dea es classma es who ha e made my jou ney a pleasan one. Las , bu no he leas , I would like o hank my Pa en s o always belie ing in me and pushing me o do my bes , and my siblings Lau a and Vasco o ne e le ing he e be a dull momen . EVALUATION OF WIND TURBINE WAKE MODELS ii 2018 ABSTRACT An ónio Nunes Vicen e iii Abs ac Wind u bine wakes ha e a s ong impac on wind a ms gi en ha hey a ec he powe ou pu and he le el o u bulence ha de e mines he u bines li e ime. Thus, wake modelling is o c i ical impo ance o he wind ene gy indus y, ha ing a cen al ole in he op imiza ion o wind a m layou s. The main objec i e o his wo k is he alida ion o he analy ical wake models implemen ed in he so wa e package WindS a ion. Such alida ion was based on measu emen da a eco ded in an onsho e wind a m wi h eigh wind u bines, and suppo ed by esul s ob ained by he so wa e package WindSim. Conclusions we e d awn by analyzing he compu ed eloci y de ici o he ai low downs eam o he wind u bines and he e ec i e powe o a single wind u bine. Keywo ds: Wind, Tu bine, Wake, Tu bulence, WindS a ion, WindSim. EVALUATION OF WIND TURBINE WAKE MODELS x 2018 LIST OF TABLES Table 4.1 – Wind u bine echnical speci ica ions .............................................................. 28 Table 5.1 - TI co ec ion ...................................................................................................... 42 Table 5.2 – E o ob ained o all i e wake models. .......................................................... 45 Table 5.3 – O se co ec ion: upda ed e o ob ained o all i e wake models ................ 50 Table 0.1 – Wind u bines de ails: ow numbe , u bine name, u bine ype, al i ude (z) in me e s and coo dina es .......................................................................................... 57 Wind a m and measu emen da a An ónio Nunes Vicen e 11 SIMBOLOGY AND ACRONYMS Simbology  – Wind u bine o o swep a ea  – Th us coe icien  – Wind u bine o o diame e  – Tu bulence kine ic ene gy  – Wake adius  – Tu bulence in ensi y  – Wind speed  – Wind speed co ec ed wi h he wake e ec  – Wind speed de ici  – F ee s eam wind speed  – Wake decay cons an  – Wind di ec ion Ac onyms GWEC – Global Wind Ene gy Council SCADA – Supe iso y Con ol And Da a Acquisi ion WFDT – Wind Fa m Design Tool WMM – Wind Me eo ological Mas wspd – Wind speed EVALUATION OF WIND TURBINE WAKE MODELS 12 2018 Wind a m and measu emen da a An ónio Nunes Vicen e 13 1. INTRODUCTION Al ough ossil uels a e s ill he dominan sou ce o ene gy, he e has been a g adual shi owa ds enewable ene gies. One o he mos eliable sus ainable ene gy is wind ene gy, which nowadays is used in la ge scale o elec ical powe p oduc ion. The global cumula i e ins alled wind powe capaci y in 2017 has o e come he alue o 500,000 MW (see Figu e 1.1). This powe is p oduced in onsho e and o sho e wind a ms con aining la ge numbe s o wind u bines. Figu e 1.1 – Global cumula i e ins alled wind capaci y. Adap ed om GWEC (2018) The concep o ene gy conse a ion dic a es ha i a wind u bine ex ac s kine ic ene gy om he wind, hen he downs eam low will diminish in momen um. The u bine wake is he egion a ec ed by his momen um de ici . Due o wake e ec s, wind u bines posi ioned downs eam o o he s will ha e i s pe o mance conside ably a ec ed: lowe wind speeds educe he u bine powe gene a ion, and he aise o u bulence in ensi y causes a igue loads, sho ening he u bine li e span. Owing o he cos o land, wind u bines a e being g ouped oge he in igh e spacing, which leads o inc eased wake e ec s. Hence, wake modelling plays a cen al ole in de eloping op imized wind a m layou s. The goal o his wo k is o alida e and e alua e he wake models included in he so wa e package WindS a ion. Measu emen da a om a small onsho e wind a m will be used o assess he p edic ion o he eloci y de ici o each wake model. The alida ion o hese models is hen co obo a ed by he so wa e package WindSim. The ou line o his hesis is as ollows. Chap e 2 will gi e an in oduc ion o u bine wakes and i s modelling backg ound. Chap e 3 will p o ide a desc ip ion o WindS a ion and i s a ailable wake models, as well as a sho o e iew o WindSim. The EVALUATION OF WIND TURBINE WAKE MODELS 14 2018 measu emen da a o he wind a m will be p esen ed in Chap e 4, oge he wi h he il e ing p ocess made wi h such da a. Chap e 5 hen discusses he alida ion o he wake models: he ocus is on compa ing he eloci y de ici esul s ob ained by a pano ama calcula ion in WindS a ion and WindSim wi h measu emen da a. Bo h single wake and mul iple wake si ua ions a e analysed. The e ec i e powe o single u bines will also be analysed. TURBINE WAKES An ónio Nunes Vicen e 15 2. WIND TURBINE WAKES This chap e will p o ide a b ie desc ip ion o he wake beha io , om i s beginning o a u he downs eam posi ion, as well as a summa y o he wake modelling backg ound. 2.1. Wake beha io As he ai low app oaches a wind u bine, i s a s o slow down and he p essu e inc eases. Then, when i c osses he u bine o o , he e is a sudden p essu e d op (see Figu e 2.1, cu A-A). Figu e 2.1 – Wind speed and p essu e a ia ion. Adap ed om Janssen (2012). A u bine wake egion is commonly di ided in o a nea wake and a a wake. The egion immedia ely downs eam o he o o is called he nea wake and i ex ends o 2 o 5 o o diame e s. This egion is domina ed by he u bulence c ea ed by he u bine i sel : he e a e non-uni o m de ici s o p essu e and wind speed associa ed wi h he axial h us and o que o he machine. The ai ci cula ion along he u bine blades leads o he o ma ion o o ices wi h helical ajec o ies ha quickly expand, o ming a cylind ical shea laye . This shea laye is wha sepa a es he inside o he wake om he ou side ambien low. EVALUATION OF WIND TURBINE WAKE MODELS 16 2018 Figu e 2.2 depic s a ske ch o his si ua ion. The wake g ow h and shea laye expansion a e ep esen ed based on an axisymme ic low. Figu e 2.2 – Wake g ow h based on an axisymme ic low. Adap ed om C espo e al. (1999). Fu he downs eam, he wake s a s o eco e : he p essu e inc eases and he eloci y inside he wake dec eases un il ambien p essu e is eached (Figu e 2.1, cu B-B). As u bulen di usion o momen um becomes he dominan mechanism, he nea wake egion ends when he shea laye hickness inc eases un il i eaches he wake axis. The a wake egion s a s app oxima ely 5 diame e s behind he o o , whe e he wake low is comple ely de eloped. The wind eloci y s a s hen o eco e and he low will decay o i s ee s eam condi ions. The opog aphic e ec s and ambien u bulence become dominan o e he u bulence caused by he o o . 2.2. Wake modelling A signi ican amoun o esea ch has been done o e he pas 50 yea s in wake modelling. A comp ehensi e li e a u e su ey on wake models can be ound in C espo e al. (1999). They dis inguished wo classic app oaches o he p oblem. A common app oach was o assume ha he u bines ac ed as dis ibu ed oughness elemen s. These models used a loga i hmic wind p o ile, modi ied by an inc ease in oughness due o he p esence o he u bine i sel ; see, e.g., Bossanyi e al. (1980), Emeis and F andsen (1993). TURBINE WAKES An ónio Nunes Vicen e 17 Howe e , he adi ional app oach o wake modelling is based on he desc ip ion o a single wake, succeeded by a calcula ion o i s in e ac ion wi h he neighbou ing ones. These ype o models a e known as indi idual models. The classical wo k by Lissaman (1979) was one o he pionee s o his me hod. The au ho desc ibed a compu e model o an a bi a y a ay o u bines, using basic luid mechanics exp essions and sel -simila wake p o iles de i ed om he expe imen al wo k done by Ab amo ich (1963) on co- lowing je s. Indi idual wake models a e di ided in o wo ca ego ies: analy ical models and compu a ional models. O he au ho s call hem kinema ic models and ield models, espec i ely. Compu a ional models a e e y ime consuming and compu a ionally expensi e, as hey make he leas simpli ica ions o he Na ie -S okes equa ions o ully cha ac e ize he u bine wake and u bulence. These models calcula e he low magni udes a e e y poin o he low ield, wi h esou ce o Compu a ional Fluid Dynamics (CFD). Rele an ield models we e de eloped by Taylo (1980), Ainslie (1985), and C espo and He nández (1989). Acco ding o Ré ho é (2009) he e a e h ee main CFD wind u bine wake models: ull- o o compu a ions, he ac ua o line me hod and he ac ua o disk me hod. Howe e , hese ype o models will no be s udied in his wo k. Analy ical wake models a e based on semi-empi ical unc ions and simpli ica ions o he Na ie -S okes equa ions. They apply analy ical exp essions o calcula e he wind speed de ici s a e he calcula ion o wind ields. Di e en models ha e been p esen ed in he pas yea s; see, e.g., Lissaman (1979), Jensen (1983), F andsen (2007) and Ishiha a e al. (2004). These models can be e y e ec i e in modelling he wake expansion and he eloci y de ici , and a e usually p e e ed due o i s compu a ional e iciency and as es esolu ion. Howe e , as he change in ambien u bulence is no conside ed, a u bulence model has o be coupled wi h analy ical models. WindS a ion p o ides h ee (analy ical) wake models: Jensen, Jensen 2D and La sen. These models will be in oduced in he ollowing chap e . EVALUATION OF WIND TURBINE WAKE MODELS 18 2018 SOFTWARE PACKAGES An ónio Nunes Vicen e 19 3. SOFTWARE PACKAGES In his chap e he so wa e packages ha we e used on his wo k a e desc ibed: WindS a ion and WindSim. The main ocus is on desc ibing WindS a ion, wi h e e ence o he main heo e ical ounda ion concep s and a ailable wake models. 3.1. WindS a ion WindS a ion is a so wa e package o he nume ical simula ion o u bulen low o e complex opog aphy, complemen ed wi h a ecen upda e o u bine wake modelling. The nume ical wind ields a e calcula ed wi h p o ided solu ions o he non-linea luid dynamics equa ions, coupled wi h u bulence models. De ailed in o ma ion abou WindS a ion is a ailable in he WindS a ion manual by Lopes (2018). 3.1.1. Theo e ical backg ound 3.1.1.1. T anspo equa ions The nume ical calcula ion is suppo ed by he non-linea luid dynamics equa ions, mo e speci ically he Na ie -S okes equa ions, he con inui y equa ion and he ene gy equa ion. A summa y o hese equa ions will be made nex . The Na ie -S okes equa ion desc ibes he conse a ion o momen um o a luid low, wi h he assump ion ha i is a unc ion o a p essu e e m and a di usion iscous e m. The gene ic WindS a ion s eady s a e o mula ion o hese equa ions is:            = −     +     󰇩 Γ 󰇧 2       − 2 3   󰇍  󰇨 󰇪 +     󰇩 Γ 󰇧 2       +       󰇨 󰇪 + 󰇡    −    󰇢    +   +   (3.1) whe e  [kg/m3] is he luid densi y,  [m] is a gene ic Ca esian coo dina e,  [N/m2] is he p essu e, and Γ==+ [N s/m2] is he ime di usion coe icien o momen um, i.e., he e ec i e iscosi y. EVALUATION OF WIND TURBINE WAKE MODELS 26 2018  Wind Resou ces – he wind ield nume ical esul s a e coupled wi h clima ology da a o p o ide a wind esou ce map;  Ene gy – he annual ene gy p oduc ion, AEP, is calcula ed o all u bines, including wake losses. In his wo k, WindSim was used as an al e na i e app oach o WindS a ion o assessing he wake models. The p ocedu e was o eplica e, as a as possible, he simula ion pa ame e s used on WindS a ion. WindSim p o ides h ee wake models: Jensen, La sen, and a hi d one wi h a u bulen dependen a e o wake expansion (which was no used in his wo k). Mo e de ails abou WindSim can be ound in he WindSim Ge ing S a ed manual by Meissne (2015). WIND FARM AND MEASUREMENT DATA An ónio Nunes Vicen e 27 4. WIND FARM AND MEASUREMENT DATA 4.1. Wind a m The wind a m unde s udy in his wo k is loca ed in no he n F ance and is composed by eigh wind u bines and one me eo ological mas (WMM), displayed as in Figu e 4.1. A 3D layou om WindSim o he wind a m is also a ailable in Figu e 0.1 o APPENDIX A. The u bines a e a anged in wo ows: ow 1 (composed by 21,20,9,6) and ow 2 (composed by 22,0,8,23). The me eo ological mas is placed sou hwes o he a ay. De ailed in o ma ion ega ding u bine coo dina es and mean sea le el heigh is a ailable in Table 0.1 o APPENDIX A. Figu e 4.1 – Wind a m layou . The u bine ypes a e  90 − 2.0 MW and  112 − 3.075 MW. Row 1 is composed by he 90 ype and ow 2 by 112. I s main echnical speci ica ions a e displayed in he ollowing able: EVALUATION OF WIND TURBINE WAKE MODELS 28 2018 Table 4.1 – Wind u bine echnical speci ica ions Tu bine Ra ed powe (kW) Cu - in wind speed (m/s) Cu - ou wind speed (m/s) Ro o diame e (m) Hub heigh (m) V90 2000 4 25 90 105 V112 3075 3 25 112 94 The wind a m a ay is i egula ly spaced. The spacing be ween u bines in a ow ange om a minimum dis ance o 548 m o 21−20, which co esponds o 4.9 o o diame e s (4.9 ), o a maximum dis ance o 601 m (6.2 D) o 0−8 (see Figu e 4.1). On he o he hand, adjacen u bines a e sepa a ed by a minimum dis ance o 1642 m (14,7 ) o 6−23 and a maximum dis ance o 1872 m (16,7 ) o 21−22. As o he me eo ological mas , i s closes wind u bine is 21 a 1599 m. No e ha his wind a m is neighbo ed by 3 o he ones, which will no be conside ed h oughou his s udy due o inexis en measu emen da a. 4.2. Measu emen da a Fo his in es iga ion, he a ailable da a was SCADA da a, eco ded du ing he mon h o Augus 2016. The da ase is composed by 10-minu e mean alues measu ed in he 8 wind u bines and in he me eo ological mas . The wind u bine measu emen s we e made a hub heigh . The a iables measu ed o each u bine we e he ollowing:    [m/s]    [°󰇠     [°󰇠    [kW]        ℎ  [°󰇠     [ pm]    [°C] The me eo ological mas measu emen s we e made a 5 di e en heigh s: 40 m, 60 m, 80 m, 99 m and 101 m. The a iables measu ed o each heigh we e he ollowing:     [m/s]    [°󰇠 WIND FARM AND MEASUREMENT DATA An ónio Nunes Vicen e 29           The u bulence in ensi y in he me eo ological mas a a heigh o  can be de ined by equa ion 4.1:   ,  =  (  )   (  ) (4.1) whe e () is he wind speed s anda d de ia ion and () is he ee s eam wind speed, bo h a heigh . This way o compu ing he u bulence in ensi y will be discussed la e . Fu he mo e, wo  iles wi h in o ma ion abou he 90 and he 112 wind u bines we e p o ided. The in o ma ion included he hub heigh , a ed powe , o o diame e , and measu ed alues o bo h powe and h us coe icien cu es as unc ion o wind speed. 4.2.1. Fil e ing measu emen da a Fil e ing measu emen da a is an impo an pa o he alida ion p ocess. I is known ha se e al ex e nal ac o s can in luence he measu emen s accu acy, such as u bulence, ai densi y, wind speed g adien s, wind u bine echnical p oblems, e c. In a epo o low and wakes in la ge wind a ms by Ba helmie e al. (2011), a desc ip ion is p o ided o he au ho s’ expe ience in o ganizing and il e ing da a om la ge wind a ms. A p e ious pape (Ré ho é e al., 2009) p oposed a gene al guideline o da a alida ion. This sec ion desc ibes all he il e ing p ocess made in his wo k when using SCADA da a. The s a ing poin was o elimina e all wind speed alues lowe han he cu - in wind speed, i.e., <3 m/s o 112 u bines and <4 m/s o 90 u bines. The nega i e powe p oduc ion alues we e also all elimina ed. Nacelle misalignmen is an impo an ac o o ake in conside a ion. I can be de ined as he di e ence be ween he ambien wind di ec ion a hub heigh and he nacelle di ec ion. Time eco ds wi h egis e ed alues abo e 5° we e elimina ed. Fu he mo e, a compa ison be ween he eal powe cu e o each wind u bine (ob ained wi h measu emen da a) and he one p o ided by he b ile was made. Taking u bine 22 as an example, Figu e 4.2 shows bo h powe cu es ( eal and b ile) in one cha . The poin s away om he powe cu e we e elimina ed. EVALUATION OF WIND TURBINE WAKE MODELS 30 2018 Figu e 4.2 – Powe cu e o u bine T22. O he pa ame e s aken in o conside a ion we e he o o o a ion speed and he blades pi ch angle. By plo ing hese a iables wi h ambien wind speed, one can e alua e whe he he u bine is wo king no mally. See o ins ance he o o o a ion speed in Figu e 4.3 - he poin s away om he cu e we e elimina ed. Figu e 4.3 – Ro o pm a e age o u bine T22. -200 300 800 1300 1800 2300 0 5 10 15 Powe p oduc ion (kW) Wind Speed (m/s)  22 - Powe cu e T22 SCADA da a . b ile 0 2 4 6 8 10 12 14 16 0 2 4 6 8 10 12 14 Ro o pm a e age ( pm) Wind speed (m/s)  22 - Ro o pm a e age SIMULATION OVERVIEW An ónio Nunes Vicen e 31 5. SIMULATION OVERVIEW 5.1. Inpu da a The inpu da a o bo h WindS a ion and WindSim consis ed on he e ain da a o he si e, he me eo ological mas da a, and he wind u bine da a s o ed in he b iles al eady men ioned in Sec ion 4.2. The e ain da a was composed by he ele a ion and oughness iles which we e con e ed om WindS a ion ile o ma , A cIn o ASCII, o WindSim o ma gws, using he Global Mappe so wa e package (see Global Mappe 19.1). In WindS a ion, he ini ializa ion o he wind ields is done by assigning eloci y, u bulence and empe a u e alues o he whole domain. In his case, hose alues a e based on he me eo ological mas da a. Then, a econs uc ion o he e ical p o iles is done o bo h wind speed and u bulence quan i ies. This econs uc ion may be done wi h wo di e en app oaches, depending whe he he Co iolis o ces a e conside ed o no . In his wo k, Co iolis o ces we e always conside ed. The emaining calcula ion p ocess depends on he bounda y condi ions and o he pa ame iza ion. Fo mo e de ails please see Lopes (2018). 5.2. Pa ame iza ion Domain ex ension. The calcula ion domain is nea ly pa allelepipedic. I is delimi ed a he bo om by he g ound and a he op by a ho izon al plane. The a ea co e ed by he whole e ain da a is huge ( oughly 6659 ), which na u ally led o a educ ion o he calcula ion domain ex ension (in o an a ea o 37 ). Figu e 5.1 shows he op iew o he ac ual calcula ion domain in WindS a ion, and a la e al iew h ough cu A-B. EVALUATION OF WIND TURBINE WAKE MODELS 32 2018 Figu e 5.1 – Top iew and la e al iew o he calcula ion domain. Mesh. The mesh in WindS a ion is de ined by a cons an ho izon al spacing and a a iable e ical spacing. In o de o chose a alue o he ho izon al spacing, a mesh e inemen analysis was pe o med by educing he ho izon al spacing om 1000 m o 20 m. The expec a ion was ha a mesh e inemen would no ha e much in luence on he esul s, because he e ain is a he smoo h and he measu emen s a e done a a ele an dis ance om he g ound. The chosen u bine was 22, wi h an ambien wind di ec ion co esponding o an undis u bed incoming low (=234.2°). Figu e 5.2 plo s bo h he measu ed wind speed and he one ob ained in WindS a ion, oge he wi h he numbe o nodes. As expec ed, he mesh in luence on esul accu acy is ha dly pe cep ible (no e ha he e ical axis alues only ange be ween 4,9 m/s and 5,1 m/s). Howe e , he op imal solu ion ell on a ho izon al spacing o 40 m, wi h a numbe o nodes app oxima ely equal o 500,000. Al hough a 20 m spacing could p o ide a aguely be e ag eemen wi h measu ed da a, one would inc ease signi ican ly he numbe o nodes, leading o an excessi e compu a ional ime. The 40 m spacing showed a good balance be ween accu acy and simula ion ime. SIMULATION OVERVIEW An ónio Nunes Vicen e 33 Figu e 5.2 – Mesh g id analysis. The e ical spacing in WindS a ion is de ined by he al i ude (abo e sea le el) o he calcula ion domain op (Z op), by he e ical dis ance be ween he i s calcula ion poin and he g ound (Fi s node), and by he numbe o calcula ion le els (Le els). The Max e ical spacing is he heigh o las con ol olume. As shown in Figu e 5.3, hese pa ame e s sligh ly di e om WindS a ion o WindSim. The di e ence be ween Z op and Heigh abo e e ain is gi en by:  ℎ    =   −  (5.1) The Heigh dis ibu ion ac o gi es he ac ion be ween he cell a he g ound and he cell a he uppe bounda y:  ℎ    =   Max   (5.2) 1000 m 500 m 400 m 300 m 200 m 100 m80 m 60 m 40 m 20 m 4,9 4,95 5 5,05 5,1 1000 10000 100000 1000000 Wind Speed (m/s) Numbe o Nodes Mesh e inemen - T22 Wind Speed Measu ed WindS a ion EVALUATION OF WIND TURBINE WAKE MODELS 34 2018 5.3. Impo an issue conce ning measu emen da a The majo se back when using he me eo ological WMM mas da a as an inpu pa ame e was dealing wi h disc epancies be ween i s alues and he ones om wind u bines. In ac , i a wind di ec ion measu ed in he mas is conside ably di e en om he one measu ed in he wind u bines, he modelled wind low can accoun o a mul iple wake supe posi ion si ua ion, when in eali y i is no . Figu e 5.4 plo s he    a a heigh o 101 m wi h he    [°󰇠 a u bine 0. This was done o he wind di ec ion in e al o ∈[200°,280°󰇠. The o se in wind di ec ion was ound o be la ge and o same cases eaches a alue o 40°. In his way, i was concluded ha i is a he di icul o use he me eo ological mas da a as a e e ence alue o he wind u bine when analysing he simula ed esul s. Ins ead, he ups eam wind u bine was used. Figu e 5.3 – Calcula ion domain pa ame e s in WindS a ion (le ) and WindSim ( igh ). No e ha he al i ude o he calcula ion domain op is equal o Z op=1200 m. SIMULATION OVERVIEW An ónio Nunes Vicen e 35 Figu e 5.4 – O se in wind di ec ion. 5.4. Pano ama simula ion Figu e 5.5 is a wind ose aken om he clima ology epo o WindSim. I gi es he wind speed dis ibu ion in he WMM a a heigh o 101 m, di ided in bins o 2 m/s and wind di ec ion sec o s o 30°. I is clea ha he mos common wind di ec ion sec o s co espond o an ai low om sou hwes . Figu e 5.5 – WMM wind ose a 101 m (WindSim). Based on he sec o a ailabili y o he WMM measu ed da a (displayed in he wind ose) a pano ama simula ion was pe o med o a wind di ec ion in e al o ∈ [225°;270°󰇠 and he esul s we e sepa a ed in wo wind speed bins: 4−6 m/s and 6−8 m/s. Wind speeds abo e 8 m/s we e no conside ed due o lack o measu emen da a. The goal o his simula ion was o in es iga e he eloci y de ici a hub heigh o each u bine. 200 210 220 230 240 250 260 270 280 200 210 220 230 240 250 260 270 280 Wind di ec ion (°) Wind di ec ion (°) WMM s T0 WMM wind di ec ion T0 ambien wind di ec ion EVALUATION OF WIND TURBINE WAKE MODELS 42 2018 ep esen i s ansi ion. The inc ease in he no malized wspd alue led o he conclusion ha he u bulence in ensi y in he mas was highe han he one p edic ed by Equa ion 3.8. Whe he his co ec ion is applied in WindSim o no , i is ye unknown. Table 5.1 -  co ec ion WindS a ion  [ ° 󰇠 243.9 246.9 251.9 Modelled   11.6% 12.5% 11.2% Co ec ed   (z=99 m) 22.3% 16.3% 11.8% Modelled no malized wspd 0.78 0.72 0.82 No malized wspd wi h   co ec ion 0.93 0.88 0.86 Figu e 5.13 - La sen (WindS a ion) and La sen (WindSim) pano ama esul s o u bine T20 and wspd bin o 4-6 m/s. 0,40 0,50 0,60 0,70 0,80 0,90 1,00 1,10 1,20 1,30 215 220 225 230 235 240 245 250 255 260 265 270 275 280 No malized Wind Speed Wind di ec ion (°) Tu bine T20 Measu emen Da a La sen (WindS a ion) La sen (WindSim) SIMULATION OVERVIEW An ónio Nunes Vicen e 43 Figu e 5.14 - La sen (WindS a ion) and La sen (WindSim) pano ama esul s o u bine T20 and wspd bin o 6-8 m/s. Finally, in Figu e 5.15 and Figu e 5.16 i was possible o display all he esul s o u bine 20. When compa ing he Jensen 2D (WindS a ion) wi h he La sen (WindS a ion), i is clea ha he La sen cu e has a lowe s eepness and a wide wake wid h. No e ha he e we e no signi ican di e ences in he modelled wake wid h o eloci y de ici when changing om a wind speed bin o 4−6 m/s o 6−8 m/s. Howe e , when looking only a he measu emen da a poin s, he eloci y de ici seems o be highe o 4 − 6 / han o 6 − 8 /. 0,40 0,45 0,50 0,55 0,60 0,65 0,70 0,75 0,80 0,85 0,90 0,95 1,00 1,05 1,10 1,15 1,20 1,25 1,30 215 220 225 230 235 240 245 250 255 260 265 270 275 280 No malized Wind Speed Wind di ec ion (°) Tu bine T20 Measu emen Da a La sen (WindS a ion) La sen (WindSim) Co ec ed TI EVALUATION OF WIND TURBINE WAKE MODELS 44 2018 Figu e 5.15 – Pano ama esul s ob ained in all wake models o u bine T20 and wspd bin o 4-6 m/s. Figu e 5.16 - Pano ama esul s ob ained in all wake models o u bine T20 and wspd bin o 6-8 m/s. 0,40 0,45 0,50 0,55 0,60 0,65 0,70 0,75 0,80 0,85 0,90 0,95 1,00 1,05 1,10 1,15 1,20 1,25 1,30 225 230 235 240 245 250 255 260 265 270 No malized Wind Speed Wind di ec ion (°) Tu bine T20 Measu emen Da a Jensen (WindS a ion) Jensen 2D (WindS a ion) La sen (WindS a ion) Jensen (WindSim) La sen (WindSim) 0,40 0,45 0,50 0,55 0,60 0,65 0,70 0,75 0,80 0,85 0,90 0,95 1,00 1,05 1,10 1,15 1,20 1,25 1,30 215 220 225 230 235 240 245 250 255 260 265 270 275 280 No malized Wind Speed Wind di ec ion (°) Tu bine T20 Measu emen Da a Jensen (WindS a ion) Jensen 2D (WindS a ion) La sen (WindS a ion) Jensen (WindSim) La sen (WindSim) SIMULATION OVERVIEW An ónio Nunes Vicen e 45 In o de o e alua e how each model has adjus ed o he measu emen da a, a polynomial unc ion ha bes i s he co esponding model poin s was i s compu ed. Fo ha pu pose, he Ma lab unc ion poly i was used. Se e al deg ees o he polynomials we e ied and he alue chosen was 6 o e e y model excep o he Jensen (WindS a ion). In his las one, a linea unc ion was enough, since i s alues a e app oxima ely cons an . Then, he polynomial unc ions we e used as a eplacemen o he model poin s, o compu e he co esponding e o o he adjus men o he measu emen da a. This e o was calcula ed by summing up all he absolu e alues o he indi idual e o s o each en y o he measu emen da a, di ided by he numbe o hose en ies: ∑ 󰇻     ,   −   ,  󰇻      (5.3) whe e  is he polynomial co esponding o he model a s ake, (,, ,) a e he measu emen da a poin s and  is he numbe o hose poin s. The ange o he abscissa , o he measu emen da a poin s was es ic ed o he al eady men ioned wind di ec ion in e al [235°,260°󰇠. Table 5.2 shows he esul s ob ained: Table 5.2 – E o ob ained o all i e wake models. T20 Jensen (WindS a ion) Jensen 2D ( = 0 . 075 ) La sen (WindS a ion) Jensen (WindSim) La sen (WindSim) 4 - 6 m/s 0.1012 0.1192 0.1011 0.0947 0.1237 6 - 8 m/s 0.0794 0.0894 0.0651 0.0652 0.0708 The la ges e o s we e ound in La sen (WindSim) o a 4− 6 / wind speed bin and in Jensen 2D (WindS a ion) o a 6−8 m/s wind speed bin, wi h alues o 0.1237 and 0.0894 espec i ely. These alues s eng hened he conclusion ha he La sen (WindSim) unde es ima ed he wake e ec s and he Jensen 2D (=0.075) o e es ima ed hem. On he o he hand, lowe alues we e ob ained in he Jensen (WindSim) EVALUATION OF WIND TURBINE WAKE MODELS 46 2018 model han in he Jensen (WindS a ion) model, which can only be explained by he s ep poin s in Jensen (WindSim). As al eady shown by Figu e 5.6−Figu e 5.8, he wind di ec ion sec o ∈ [225°;270°󰇠 accoun s o mul iple wake supe posi ion si ua ions. The esul s ob ained o u bines 9 and 6, which a e espec i ely placed in a double and iple wake egion, a e p esen ed in Figu e 5.17−Figu e 5.20. Na u ally, i he dis ance o he lead u bine inc eases, he wind di ec ion in e al in which he wake e ec o u bine 21 is no iced, dec eases. See o ins ance he example o La sen (WindS a ion) in he 4−6 m/s wspd bin: o u bine 20 (Figu e 5.15) his in e al is app oxima ely [236°,260°󰇠, o u bine 9 (Figu e 5.17) i is educed in o [238°,257°󰇠 and o u bine 6 (Figu e 5.19) in o [238°,256°󰇠. Howe e , he e ec o he wake supe posi ion in he eloci y de ici was ha dly no iced, despi e he sligh inc ease om u bine 20 o u bine 9. O e all, he no malized wind speed alues ob ained in u bines 9 and 6 we e simila o he ones in u bine 20. Figu e 5.17 - Pano ama esul s ob ained in all wake models o u bine T9 and wspd bin o 4-6 m/s. 0,40 0,45 0,50 0,55 0,60 0,65 0,70 0,75 0,80 0,85 0,90 0,95 1,00 1,05 1,10 1,15 1,20 1,25 1,30 225 230 235 240 245 250 255 260 265 270 No malized Wind Speed Wind di ec ion (°) Tu bine T9 Measu emen Da a Jensen (WindS a ion) Jensen 2D (WindS a ion) La sen (WindS a ion) Jensen (WindSim) La sen (WindSim) SIMULATION OVERVIEW An ónio Nunes Vicen e 47 Figu e 5.18 - Pano ama esul s ob ained in all wake models o u bine T9 and wspd bin o 6-8 m/s. Figu e 5.19 - Pano ama esul s ob ained in all wake models o u bine T6 and wspd bin o 4-6 m/s. 0,40 0,45 0,50 0,55 0,60 0,65 0,70 0,75 0,80 0,85 0,90 0,95 1,00 1,05 1,10 1,15 1,20 1,25 1,30 225 230 235 240 245 250 255 260 265 270 No malized Wind Speed Wind di ec ion (°) Tu bine T9 Measu emen Da a Jensen (WindS a ion) Jensen 2D (WindS a ion) La sen (WindS a ion) Jensen (WindSim) La sen (WindSim) 0,40 0,45 0,50 0,55 0,60 0,65 0,70 0,75 0,80 0,85 0,90 0,95 1,00 1,05 1,10 1,15 1,20 1,25 1,30 225 230 235 240 245 250 255 260 265 270 No malized Wind Speed Wind di ec ion (°) Tu bine T6 Measu emen Da a Jensen (WindS a ion) Jensen 2D (WindS a ion) La sen (WindS a ion) Jensen (WindSim) La sen (WindSim) EVALUATION OF WIND TURBINE WAKE MODELS 48 2018 Figu e 5.20 - Pano ama esul s ob ained in all wake models o u bine T6 and wspd bin o 6-8 m/s. 5.4.2. O se in wind di ec ion The same analysis as in he p e ious sec ion was done o ow 2, by no malizing he wind speed wi h espec o u bine 22. The esul s ob ained a e shown in Figu e 0.1−Figu e 0.6 o APPENDIX B. Al hough he same conclusions we e aken, he o se in wind di ec ion was conside ably bigge , due o a la ge dis ance o his ow o he me eo ological mas . This si ua ion is clea ly isible in he esul s ob ained o u bine 0 (wspd bin o 4−6 m/s), displayed in Figu e 5.21. In ac , he a e age alue o he di e ence be ween he measu ed and he modelled wind di ec ion was calcula ed and equals 9.3°. The o se was co ec ed and Figu e 5.21 was upda ed in o Figu e 5.22. The e o was calcula ed like in he p e ious sec ion and upda ed (see Table 5.3); no e ha i dec eased o all models, excep o he La sen (WindSim). 0,40 0,45 0,50 0,55 0,60 0,65 0,70 0,75 0,80 0,85 0,90 0,95 1,00 1,05 1,10 1,15 1,20 1,25 1,30 225 230 235 240 245 250 255 260 265 270 No malized Wind Speed Wind di ec ion (°) Tu bine T6 Measu emen Da a Jensen (WindS a ion) Jensen 2D (WindS a ion) La sen (WindS a ion) Jensen (WindSim) La sen (windSim) SIMULATION OVERVIEW An ónio Nunes Vicen e 49 Figu e 5.21 - Pano ama esul s ob ained in all wake models o u bine T0 and wspd bin o 4-6 m/s. Figu e 5.22 – O se co ec ion: upda ed pano ama esul s ob ained in all wake models o u bine T0 and wspd bin o 4-6 m/s. 0,40 0,45 0,50 0,55 0,60 0,65 0,70 0,75 0,80 0,85 0,90 0,95 1,00 1,05 1,10 1,15 1,20 1,25 1,30 215 220 225 230 235 240 245 250 255 260 265 270 275 280 No malized Wind Speed Wind di ec ion (°) Tu bine T0 Measu ed Da a Jensen (WindS a ion) Jensen 2D (WindS a ion) La sen (WindS a ion) Jensen (WindSim) La sen (WindSim) 0,40 0,45 0,50 0,55 0,60 0,65 0,70 0,75 0,80 0,85 0,90 0,95 1,00 1,05 1,10 1,15 1,20 1,25 1,30 215 220 225 230 235 240 245 250 255 260 265 270 275 280 No malized Wind Speed Wind di ec ion (°) Tu bine T0 Measu emen Da a Jensen (WindS a ion) Jensen 2D (WindS a ion) La sen (WindS a ion) Jensen (WindSim) La sen (WindSim) EVALUATION OF WIND TURBINE WAKE MODELS 50 2018 Table 5.3 – O se co ec ion: upda ed e o ob ained o all i e wake models T0 (4-6 m/s) Jensen (WindS a ion) Jensen 2D (WindS a ion) La sen (WindS a ion) Jensen (WindSim) La sen (WindSim) No mal 0.0935 0.1323 0.1125 0.0925 0.0776 W i h o se co ec ion 0.0928 0.0989 0.0906 0.0917 0.0883 5.4.3. E ec i e powe o a wind u bine As wind lows ac oss a wind u bine, he powe a ailable () in he wind is gi en by (Tong e al., 2012): =12 whe e  is he ai densi y,  is he o o swep a ea and  is he incoming wind speed a hub heigh . Na u ally, no all his powe is gene a ed by he wind u bine. In WindS a ion, he e ec i e wind u bine powe is compu ed by in e pola ing he e ec i e eloci y de ici gi en by Equa ion 3.25 (see Sec ion 3.1.3) in o he measu ed powe cu e o he espec i e wind u bine. I should be in e es ing o compa e esul s ob ained o wind speed de ici s wi h wind u bine e ec i e powe . Figu e 5.23 plo s he powe ob ained in ow 1 wind u bines o he same case showed ea lie in Figu e 5.6−Figu e 5.8, oge he wi h measu emen da a. The alues o e ec i e powe we e no malized wi h he wind u bine a ed powe and a e displayed in pe cen age. SIMULATION OVERVIEW An ónio Nunes Vicen e 51 Figu e 5.23 – No malized e ec i e wind powe compu ed in all wake models = °;,=. /. No e ha o all wake models, he e was a signi ican powe d op be ween u bine 21 and u bine 20. Then, i sligh ly inc eased un il u bine 6. Howe e , he measu emen da a showed an unp edic able powe beha io . I is in e es ing o see ha he Jensen 2D wake model se e ely o e es ima ed he powe loss, which is cohe en wi h he o e es ima ion o eloci y de ici es ima ed in he p e ious sec ions. The opposi e conclusion can be also aken om he La sen (WindSim) wake model. Fu he mo e, a conside able di e ence be ween he Jensen (WindS a ion) and he Jensen (WindSim) wake model was de ec ed, which goes agains he simila i y shown in he wspd de ici esul s. In o de o ha e mo e de ailed conclusions, his analysis should be pe o med o a la ge numbe o cases. 0% 10% 20% 30% 40% 50% 60% No malized Powe Wind Tu bine Measu emen Da a Jensen (WindS a ion) Jensen 2D (WindS a ion) La sen (WindS a ion) Jensen (WindSim) La sen (WindSim) T21 T20 T9 T6 EVALUATION OF WIND TURBINE WAKE MODELS 58 2018 APPENDIX B An ónio Nunes Vicen e 59 APPENDIX B Figu e 0.1 - Pano ama esul s ob ained in all wake models o u bine T0 and wspd bin o 4-6 m/s. 0,40 0,45 0,50 0,55 0,60 0,65 0,70 0,75 0,80 0,85 0,90 0,95 1,00 1,05 1,10 1,15 1,20 1,25 1,30 215 220 225 230 235 240 245 250 255 260 265 270 275 280 No malized Wind Speed Wind di ec ion (°) Tu bine T0 Measu emen Da a Jensen (WindS a ion) Jensen 2D (WindS a ion) La sen (WindS a ion) Jensen (WindSim) La sen (WindSim) EVALUATION OF WIND TURBINE WAKE MODELS 60 2018 Figu e 0.2 - Pano ama esul s ob ained in all wake models o u bine T0 and wspd bin o 6-8 m/s. Figu e 0.3 - Pano ama esul s ob ained in all wake models o u bine T8 and wspd bin o 4-6 m/s. 0,40 0,45 0,50 0,55 0,60 0,65 0,70 0,75 0,80 0,85 0,90 0,95 1,00 1,05 1,10 1,15 1,20 1,25 1,30 225 230 235 240 245 250 255 260 265 270 No malized Wind Speed Wind di ec ion (°) Tu bine T0 Measu emen Da a Jensen (WindS a ion) Jensen 2D (WindS a ion) La sen (WindS a ion) Jensen (WindSim) La sen (WindSim) 0,40 0,45 0,50 0,55 0,60 0,65 0,70 0,75 0,80 0,85 0,90 0,95 1,00 1,05 1,10 1,15 1,20 1,25 1,30 225 230 235 240 245 250 255 260 265 270 No malized Wind Speed Wind di ec ion (°) Tu bine T8 Measu emen Da a Jensen (WindS a ion) Jensen 2D (WindS a ion) La sen (WindS a ion) Jensen (WindSim) La sen (WindSim) APPENDIX B An ónio Nunes Vicen e 61 Figu e 0.4 - Pano ama esul s ob ained in all wake models o u bine T8 and wspd bin o 6-8 m/s. Figu e 0.5 - Pano ama esul s ob ained in all wake models o u bine T23 and wspd bin o 4-6 m/s. 0,40 0,45 0,50 0,55 0,60 0,65 0,70 0,75 0,80 0,85 0,90 0,95 1,00 1,05 1,10 1,15 1,20 1,25 1,30 225 230 235 240 245 250 255 260 265 270 Wind speed a io Wind di ec ion (°) Tu bine T8 Measu emen Da a Jensen (WindS a ion) Jensen 2D (WindS a ion) La sen (WindS a ion) Jensen (WindSim) La sen (WindSim) 0,40 0,45 0,50 0,55 0,60 0,65 0,70 0,75 0,80 0,85 0,90 0,95 1,00 1,05 1,10 1,15 1,20 1,25 1,30 225 230 235 240 245 250 255 260 265 270 Co ec ed Wind Speed Wind di ec ion (°) Tu bine T23 Measu emen Da a Jensen (WindS a ion) Jensen 2D (WindS a ion) La sen (WindS a ion) Jensen (WindSim) La sen (WindSim) EVALUATION OF WIND TURBINE WAKE MODELS 62 2018 Figu e 0.6 - Pano ama esul s ob ained in all wake models o u bine T23 and wspd bin o 6-8 m/s. 0,40 0,45 0,50 0,55 0,60 0,65 0,70 0,75 0,80 0,85 0,90 0,95 1,00 1,05 1,10 1,15 1,20 1,25 1,30 225 230 235 240 245 250 255 260 265 270 No malized Wind Speed Wind di ec ion (°) Tu bine T23 Measu emen Da a Jensen (WindS a ion) Jensen 2D (WindS a ion) La sen (WindS a ion) Jensen (WindSim) La sen (WindSim) E o! A o igem da e e ência não oi encon ada. An ónio Nunes Vicen e 63