Ene gy Con e sion and Managemen 283 (2023) 116890
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Ene gy Con e sion and Managemen
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Pa adigma ic case o long- e m coloca ed wind–wa e ene gy index end in
Cana y Islands
Alain Ulaziaa,∗, Jon Sáenzb,d, Ai o Saenz-Agui ea, Gab iel Iba a-Be as eguic,d,
Sheila Ca eno-Madinabei iae
aEne gy Enginee ing Depa men , Uni e si y o he Basque Coun y (UPV/EHU), Enginee ing School o Gipuzkoa-Eiba , Spain
bDepa men o Physics, Uni e si y o he Basque Coun y (UPV/EHU), Sa iena Auzoa z/g, 48940 Leioa, Spain
cEne gy Enginee ing Depa men , Uni e si y o he Basque Coun y (UPV/EHU), Alda, U kijo, 48013 Bilbao, Spain
dPlen ziako I sas Es azioa, PIE (BEGIK), Uni e si y o he Basque Coun y (UPV/EHU), A ea za Pasealekua, 48620 Plen zia, Spain
eDepa men o Ma hema ics, Uni e si y o he Basque Coun y (UPV/EHU), Paseo de la Uni e sidad, 01006 Vi o ia-Gas eiz, Spain
ARTICLE INFO
Keywo ds:
Wa e ene gy
Wind ene gy
Co-loca ion index
ERA5
Long- e m ene gy end
Fluid mechanics
ABSTRACT
P e ious s udies based on emo e sensing da a and eanalysis ha e iden i ied s ong his o ical inc emen s
o wind speed in he a ea a ound he Cana y Islands (Spain) wi hou app ecia ing any inc emen o wa e
heigh . This decoupling o long- e m ends o wind and wa e da a is no e y common, and can be
conside ed pa adigma ic o an inno a i e s udy, wi h impo an implica ions o wind and wa e hyb id o
co-loca ed ene gy p oduc ion. In his s udy, wind and wa e da a om ERA5 eanalysis in he a ea a ound he
Cana y Islands ha e been used o compu e a wind–wa e ene gy co-loca ion easibili y index be ween 1981–
2020 showing an inc emen o he index abo e +5%/decade. Fu he mo e, ealis ic wind and wa e ene gy
p oduc ion has been calcula ed a an in e es ing ho -spo using a speci ic loa ing wind u bine co-loca ed
aside a oscilla ing buoy ype wa e ene gy con e e . The co esponding capaci y ac o end o wind ene gy
(+0.8%/decade) and cap u e wid h a io e olu ion o wa e ene gy (−1.5%/decade) shows also he wind–wa e
decoupling, which cons i u es a signi ican esul o an o iginal app oach.
1. In oduc ion
Renewable ene gy is showing a signi ican inc ease, almos doubling
he sha e o ene gy om enewable sou ces in g oss inal ene gy
consump ion in he case o Eu ope [1]. Howe e , 80% o cu en
ene gy supply is s ill deli e ed by ossil uels [2], and each coun y
mus include a deca boniza ion policy based on enewable ene gy
sou ces o ob ain a ca bon-neu al socie y h ough u he de elopmen
o clean echnologies and sus ainable mul i-pe iod selec ion o loca-
ions [3]. Fo ins ance, Ibe ian Peninsula and Cana y Islands cons i u e
a pa adigma ic case due o he hei high wind and sola ene gy
po en ial, showing e y good p e isions o hei echno-economic
assessmen [4]. This will ce ainly con ibu e o mee he Spanish C02-
educ ion objec i es. This is an impo an issue since by 2030 Spain is
commi ed o gene a e mo e han 74% o i s elec ici y om enewable
sou ces [5].
Among enewable ene gy sou ces, Ocean Renewable Ene gy (ORE)
can o e a huge po en ial o elec ici y gene a ion, mainly using he
∗Co esponding au ho .
E-mail add esses: [email p o ec ed] (A. Ulazia), [email p o ec ed] (J. Sáenz), [email p o ec ed] (A. Saenz-Agui e), [email p o ec ed]
(G. Iba a-Be as egui), [email p o ec ed] (S. Ca eno-Madinabei ia).
combina ion o wind and wa e ene gy, as i was shown in speci ic ge-
og aphical a eas such as he Medi e anean [6] o he Chinese Sea [7],
o wi hin sus ainable de elopmen objec i es using enewable ene gy
s a egies in Eu ope [8].
In gene al e ms, cu en ly wa e ene gy exhibi s a he low Tech-
nology Readiness Le el (TRL) alues [9] and is no so echnically
de eloped as o sho e wind echnology. Howe e , ecen inno a ions
ha e shown he po en ial o wa e a ms nea he coas a p o iding
a con inuous appo ion o ene gy in o he g id [10]. In he case o a
pa icula echnology – Oscilla ing Wa e Column (OWC) – he TRL is
cu en ly a a alue o 8 [11].
Recen s udies on a ully ope a ional wa e a m [12], indica e ha
he ene gy gene a ed by wa es a e p edic able o a high ex en in he
sho e m, hus allowing he de elopmen o elec ici y managemen
p o ocols o be applied in he o e all ene gy ma ke . An impo an
challenge is he de e mina ion o how clima e-d i en changes in wa e
ene gy, will impac on he u u e elec ici y gene a ed a a wa e a m
designed unde cu en -day condi ions. Simila ly, u u e changes o
h ps://doi.o g/10.1016/j.enconman.2023.116890
Ene gy Con e sion and Managemen 283 (2023) 116890
2
A. Ulazia e al.
Lis o Abb e ia ions
C3S Cope nicus Clima e Change Se ice
ECMWF Eu opean Cen e o Medium-Range
Wea he Fo ecas s
ERA5 5 h eanalysis by ECMWF
ERA-In e im 4 h eanalysis by ECMWF
FB Floa ing Body wa e ene gy con e e
IFS In eg a ed Fo ecas ing Sys em
LCOE Le elized Cos o Ene gy
NCAR Na ional Cen e o A mosphe ic Resea ch
NCEP Na ional Cen e s o En i onmen al P edic-
ion
NREL Na ional Renewable Ene gy Labo a o y
ORE Ocean Renewable Ene gy
OWC Oscilla ing Wa e Column
TRL Technology Readiness Le el
WEC Wa e Ene gy Con e e
WT Wind Tu bine
Nomencla u e
𝐴𝐸𝑃 Annual Ene gy P oduc ion (kWh)
𝐵F on al abso p ion wid h and diame e o
he WEC
𝑐(0) Ins an aneous Co ela ion
𝐶𝐿𝐹 Coloca ion Feasibili y Index
𝐶𝐹 Capaci y Fac o
𝐶𝐼 Con idence In e al
𝐶𝑊 𝑅 Cap u e Wid h Ra io (m)
𝐷𝑏Diame e o he loa ing body
𝑔Accele a ion o g a i y (9.8 m/s2)
𝐻𝑠Signi ican wa e heigh (m)
𝑀Molecula mass o d y ai (28.9 kg/kmol)
𝑁Numbe o hou s pe yea (8760 h)
𝑝P essu e (Pa)
𝑃(𝑈𝑖)Wind u bine powe o wind speed 𝑈𝑖(kW)
𝑃𝑎𝑏𝑠 Abso bed Powe o he WEC (kW)
𝑃𝑤𝑎𝑣𝑒 Theo e ical Powe o he wa e on (kW)
𝑃𝑅Ra ed powe o he wind u bine (kW)
𝑅Cons an o ideal gases
𝑡Tempe a u e (K)
𝑇𝑚Mean wa e pe iod (s)
𝑇𝑒Ene gy pe iod o wa es (s)
𝑈Wind speed (m/s)
𝑈𝑥Wind speed a 𝑥m heigh (m/s)
𝑊 𝐸𝐹 Wa e Ene gy Flux (kW/m)
𝑊 𝑃 𝐷 Wind Powe Densi y (W/m2)
𝑧0Sea oughness (m)
𝛼𝑖,𝑗 𝐶𝐿𝐹 index weigh coe icien s
𝜌Real ai densi y (kg/m3)
𝜌0S anda d ai densi y (kg/m3)
𝜌𝑤sea wa e densi y (kg/m3)
𝜎S anda d de ia ion
𝛥𝑇 Time esolu ion (1 h)
sea le el could also ha e an impac on he u u e elec ici y ou pu
some decades om now. Al hough unce ain ies emain abou hese
wo issues, a leas Oscilla ing Wa e Column (OWC) ype con e e s –
mainly due o hei egula ion mechanisms – seem o exhibi an excel-
len obus ness and adap abili y o wa e clima e changes [13]. Coming
o he impac o sea-le el ise on wa e a ms a ecen s udy [14]
sugges s ha i may be negligible. The e o e, p edic abili y in he sho
e m and obus ness be o e long- e m changes seem o be wo majo
cha ac e is ics o wa e ene gy.
The combined exploi a ion o wind and wa e ene gy is he e o e
d awing inc easing a en ion in he ecen scien i ic li e a u e, showing
s ong syne gies no only o ene gy p oduc ion, bu also o ope a ion,
main enance, and p o ec ion o loa ing wind u bines and i s s uc u es
agains ex eme e en s [15]. Al hough ocean ex eme e en analysis
is an impo an aspec , i alls ou o he scope o his s udy. Ex eme
e en ela ed index es ablishes a cu -o o he ins alla ion o o sho e
s uc u es due o secu i y issues. I is he e o e a disc e e indica o
ins ead o a con inuous one like a easibili y index ela ed o he
op imal combina ion o wind–wa e. I is supposed ha be o e a wind–
wa e easibili y s udy, o any o he kind o wind and wa e ene gy
po en ial s udy, an ex eme e en assessmen should e i y whe he an
o sho e ins alla ion is bo h, echnologically and economically iable o
no . Beyond hese secu i y and su i al p oblems, his s udy is ela ed
o he op imal combina ion and hyb idiza ion o wind ene gy and wa e
ene gy.
This combined app oach [16] can play a key ole a mee ing he
Eu opean objec i e o hyd ogen p oduc ion [17]. The p esen s udy
emphasizes he impo ance o long- e m wind [18] and wa e ene gy
end analysis de eloped by he au ho s o Mu iku wa e plan [13],
Gul o Biscay [19], I eland [20] o Iceland [21], now, in a comple ely
di e en en i onmen . Now, ins ead o ca ying ou wo independen
analyses o wind and wa es, his wo k cons i u es a no el app oach
o he es ima ion o his o ical ends o he combined esou ce. To
ha pu pose, a pa adigma ic oceanic a ea such as he Cana y Islands
has been selec ed o his s udy, whe e he p edominan wind ( ade
winds) and he swell ( om he A lan ic Ocean) a e aligned in opposi e
di ec ions.
All he se en islands o he Cana y A chipelago show a g ea po-
en ial in OREs. El Hie o is e e en ial in his sense, being a ele an
case a ound he wo ld o a o ally independen elec ical ene gy
sys em based on wind ene gy wi h he wind-hyd o p ojec Go ona del
Vien o [22], and also wi h a high wa e ene gy po en ial [23]. O he
islands such as Tene i e and G an Cana ia also exhibi an impo an o -
sho e wind and wa e ene gy po en ial [24,25], and i can be concluded
ha his hyb id po en ial is gene ally s ong o he se en islands.
The s udy o his o ical wa e ene gy and wind ene gy ends a
he global scale ha e commonly shown a combined inc emen o bo h
esou ces in he las decades, which has been hypo he ically ela ed
o he e ec s o clima ic change. This synch onized inc emen o bo h
esou ces is well known based on eanalysis da a o emo e sensing
da a. Young e al. [26] used sa elli e da a since he 80 s o he 90 s
o compu e global ends o wind speed and wa e heigh , and his
synch onized inc emen is gene al in he A lan ic Ocean wi h he
excep ion o Maca onesian a ea and he Guinean Gul . In o he A lan ic
egions like he Bay o Biscay in he las decades, he obse a ions
indica e a combina ion o posi i e ends o wa e ene gy and a no
clea pa e n o wind speed [13]. All his makes Cana y Islands an a ea
o scien i ic in e es o his ype o s udies. The special cha ac e o
he Cana ian ma ine clima e wi hin he in e ac ion o wind and wa es
is also shown by he in luence o ade winds on ans-hemisphe ic
swell wa es [27], o by singula ocean cu en s de i ed om a s ong
con inen al slope [28].
This ac makes he Cana y Islands a pa adigma ic case o s udy
he his o ical e olu ion o wind and wa e ene gy combina ion, which
in his wo k, will be s udied using eanalysis da a and decadal ends
o bo h esou ces. The ocus will be o use a ine esolu ion analysis
a p e iously iden i ied ho spo s based on a wind–wa e co-loca ion
index [29] and he consequen op imal s a egies o deploymen o co-
loca ed wind–wa e ene gy a ms [16]. The discussion on he adop ion
o an analy ical o a subjec i e index o measu e he easibili y o he
Ene gy Con e sion and Managemen 283 (2023) 116890
3
A. Ulazia e al.
Table 1
Compa ison be ween he p ope ies o ERA5 and he p e ious ECMWF’s eanalysis ERA-In e im.
P ope ies ERA-In e im ERA5
A ailabili y 1979 onwa ds 1950 onwa ds
IFS model cycle 31 2 (2006) 41 2 (2016)
Da a assimila ion 12-hou 4D-Va 12-hou 4D-Va ensemble
Spa ial esolu ion 79 km (TL255) 60 le els o 10 Pa 31 km (TL639) 137 le els o 1 Pa
Ocean wa es 1 deg ee 0.5 deg ee
Ou pu equency 6-hou ly o analyses 3-hou ly o o ecas s Hou ly h oughou (unce ain y 3-hou ly)
Ou pu pa ame e s Ex ensi e Ex ended (e.g. 100 m wind)
hyb idiza ion o bo h OREs is beyond his a icle due o i s ma hema -
ical na u e, bu i opens a ich esea ch line in analogy o o he kind
o indexes o measu e echno-economic aspec s such as ene gy po e y,
as i is desc ibed in Sec ion 4[30].
The eminde o he pape is s uc u ed as ollows: a e he in o-
duc ion on he s a e o a o he hyb idiza ion o wa e ene gy and wind
ene gy, he speci ic ERA5 da a used o his s udy will be explained
(Sec ion 2.1); hen he me hodology on he compu a ion o decadal
e olu ion in Sec ion 2.2.2, and he desc ip ion abou he co-loca ion
easibili y index (CLF) in Sec ion 2.2.3 will be shown. A speci ic sec ion
will be de o ed o he me hod o compu a ion on eal ene gy p oduc-
ion based on he powe cu e o speci ic u bine (Sec ion 2.4.1) along
wi h he powe model o a speci ic wa e ene gy de ice (Sec ion 2.4.2);
Sec ion 3shows he decadal esou ce maps, he e olu ion o co-loca ion
index, and he e olu ion o eal wa e and wind ene gy p oduc ion. The
Discussion Sec ion 4in e p e s quali a i ely hese esul s, and inally,
Sec ion 5concludes wi h a undamen al summa y and ou looks o
u u e de elopmen s.
2. Da a and me hods
The ollowing sec ions desc ibes he da a sou ces used o he s udy
and he co esponding me hods o de elop he esul s.
2.1. Da a
The ollowing sec ions desc ibe he ERA5 eanalysis and he s udy
a ea a ound Cana y Islands, whe e he da a sou ces a e implemen ed.
2.1.1. ERA5 eanalysis
Long- e m a ia ions o he wa e and wind esou ce ha e been
analysed employing ERA5 eanalysis da a [31]. The Eu opean Cen e
o Medium-Range Wea he Fo ecas s (ECMWF) p ocesses all da ase s
using hei Ea h Sys em model In eg a ed Fo ecas ing Sys em (IFS) and
he esul s a e dis ibu ed by he Cope nicus Clima e Change Se ice
(C3S) and i al eady co e s he pe iod om 1950 o p esen [32].
This eanalysis combines huge amoun s o his o ical obse a ions om
sa elli es, in-si u me -ocean da a (onsho e me eo ological s a ions and
o sho e buoys), and snow da a.
The ERA5 eanalysis is he i h majo global eanalysis p oduced
by he ECMWF (a e ERA-In e im, see Table 1), and p o ides 1-hou ly
da a a a spa ial esolu ion o a ound 30 km all o e he wo ld o
downloaded me eo ological da a:
1. Fo a mosphe e and wind ene gy analysis hese pa ame e s a e
used: wind speed (𝑈), p essu e (𝑝), and empe a u e (𝑡).
2. Howe e , in he case o wa e da a, he spa ial esolu ion a ail-
able is abou 50 km, whe e hese pa ame e s a e used: signi ican
wa e heigh (𝐻𝑠) and mean wa e pe iod (𝑇𝑚) o peak wa e
pe iod (𝑇𝑝).
Recen li e a u e desc ibes good e alua ions o ERA5 agains wind
and wa e obse a ions, and no only o low oughness and u bulence
a eas o he ocean, bu also o less p edic able onsho e loca ions in
case o wind a ms:
•Ve sus wind a m da a in he No h o Eu ope [33];
•In he Ibe ian Peninsula e sus o sho e buoys anemome e s [18];
•Fo Ibe ian and Cana ian buoy wa e da a [34];
•Fo swell wa e da a [35];
•Fo global wa e da a e sus al ime e measu emen s [36] ;
•In China wa e s o wa e da a [37].
2.1.2. S udy a ea
The clima e o he Cana y Island has long ago been iden i ied as
e y in e es ing o wind ene gy due o he ac ha he islands a e
loca ed, especially du ing summe , unde a s ong in luence o No h-
Eas e ly ade winds associa ed o he Azo es high p essu e sys em.
These summe ade winds a e e y egula and e y equen ly blow
wi h speeds be ween 7 m/s and 11 m/s [38]. The Azo es high ep-
esen s du ing summe he su ace esponse o he p essu e ield o
he subsidence associa ed o he Hadley Ci cula ion in he A lan ic
sec o , and some s udies show ha he e is a posi i e end in he
a ea-a e aged p essu e o he Azo es High [39], which makes he
a ea in e es ing o a s udy like his one, which add esses he long-
e m beha iou o ene gy esou ces o he a ea. Fu he mo e, gi en
i s poli ical membe ship o he Eu opean Union (Spain) in con as
o i s geog aphical A ican o igin in he o m o olcanic islands, i
cons i u es a e y in e es ing a ea o a isola ed elec ical g id based
on enewable ene gies wi h ew in e connec ions [40].
One-hou ly da a om 1981 o 2020 (40 yea s) ha e been down-
loaded in he Cana y Islands o he p esen s udy, meaning ha
350640 cases a e analysed a each g idpoin in he analysed a ea,
which co e s longi udes in he in e al [−19◦E, −13◦W] and la i udes
in [27◦N, 30◦N], which is composed o 91 g idpoin s in o al o
he geog aphical window ha co e s he se en Cana y Islands: El
Hie o, La Palma, La Gome a, Tene i e, G an Cana ia, Lanza o e and
Fue e en u a.
The s eep ba hyme y a ound he islands due o i s olcanic o igin
is shown using shaded a eas in Fig. 1, which eaches up o −5000 m
dep h in ew kilome e s [41]. In Sec ion 3.2, a poin o in e es is
selec ed o he beha iou o CLF a he Sou h o Tene i e, whe e a zonal
ba hyme y ansec (unde he map) and me idional ansec (on he
le ) a e plo ed as whi e lines h ough he poin −17◦E and 27.5◦N. Bo h
show ha he sea deepens o housands o me e s in ew kilome e s
om he coas and ha he ho -spo dep h is a ound −3500 m.
2.2. Me hods
The ollowing sec ions de i e he main pa ame e s ha in e p e
he esul s om he basic pa ame e s o ERA5, desc ibe he me hod
o compu a ion o hese pa ame e s’ end pe decade, and de ines he
CLF ha de e mines he pe o mance o wind–wa e combina ion a a
gi en loca ion.
2.2.1. De i ed magni udes
The Wa e Ene gy Flux (𝑊 𝐸𝐹 ) is he usual indica o o cha ac e ize
he ene gy anspo ed by wa es. I is s a ed in [kW/m], and is de i ed
om he 𝐻𝑠and ene gy (mean) wa e pe iod (𝑇𝑒) [42,43] acco ding
o Eq. (1).
𝑊 𝐸𝐹 =𝜌𝑤𝑔2
64𝜋𝐻2
𝑠𝑇𝑒= 0.49𝐻2
𝑠𝑇𝑒(1)
Ene gy Con e sion and Managemen 283 (2023) 116890
4
A. Ulazia e al.
Fig. 1. Map o he Cana y Islands, wi h black labels showing he main islands (EH: El Hie o, LP: La Palma, LG: La Gome a, TE: Tene i e, GC: G an Cana ia, F: Fue e en u a and
L: Lanza o e). The ba hyme y a ound he islands is shown using shaded a eas and he loca ion o he buoys used in he s udy a e shown by s a s and labelled in ed (TS: Tene i e
Su , SCT: San a C uz de Tene i e, GC: G an Cana ia, LPE: La Palma Eas ). One me idional (zonal) ansec h ough he poin −17◦E and 27.5◦N is shown o he le (unde ) he
map o e e ence and as whi e lines d awn in he map.
I is o be aken in o accoun ha ERA5 denomina es mean wa e
pe iod o he ene gy pe iod 𝑇𝑒[44] so he calcula ion o 𝑊 𝐸𝐹 is
s aigh o wa d using (1) unde he assump ion o deep wa e s condi-
ions. In he case o Cana y Islands, his condi ion is me gi en i s deep
ba hyme y as shown in Fig. 1.
On he o he hand, he magni ude ha de ines he kine ic powe o
he wind is he Wind Powe Densi y (𝑊 𝑃 𝐷), and is gi en by Eq. (2):
𝑊 𝑃 𝐷 =1
2𝜌𝑈3(2)
whe e 𝜌is he ai densi y, calcula ed e e y hou om 𝑝and 𝑡,
oge he wi h he molecula mass o he ai 𝑀=28.9 kg/kmol, and he
cons an o he ideal gases 𝑅=8314 KJ/kgK.
𝜌=𝑝𝑀
𝑅𝑡 (3)
A e de eloping speci ic ools o educe he huge compu a ional
e o in ol ed [45,46], i is o be highligh ed ha he au ho s ha e
shown in many p e ious s udies he impac o ai densi y changes in
wind ene gy p oduc ion. Ins ead o conside ing he s anda d alue o
1.225 kg/m3as a cons an in wind ene gy s udies, au ho s ha e shown
he impac o seasonal 𝜌 a ia ions as well as he small in luence o hu-
midi y changes in he WPD a a gi en heigh and loca ion annually [47]
and seasonally [48].
2.2.2. Decadal e olu ion
The decadal e olu ion o 𝑊 𝐸𝐹 and 𝑊 𝑃 𝐷 densi y has been com-
pu ed in pe cen age e ms in bo h cases, by compa ing he di e ences
o he decadal a e ages o 𝑊 𝐸𝐹 (i.e., las decade 𝑊 𝐸𝐹4 o 2011–
2020 minus i s decade 𝑊 𝐸𝐹1 o 1981–1990) wi h espec o he i s
decade:
100 𝑊 𝐸𝐹4−𝑊 𝐸𝐹1
𝑊 𝐸𝐹1
(4)
The same can be done o he 3 h and 2nd decades, and o he
𝑊 𝑃 𝐷 end (see Fig. 3).
2.2.3. Coloca ion index o wind and wa es
The 𝐶𝐿𝐹 o wind and wa e ene gy de ined by As a iz e al. is
used in his s udy [29]. I depends on 𝑊 𝐸𝐹 and 𝑊 𝑃 𝐷, and on
he ins an aneous co ela ion (𝑐(0)) o he s anda d de ia ion o bo h
magni udes (𝜎𝑊 𝐸𝐹 and 𝜎𝑊 𝑃 𝐷). Fo he sake o b e i y in his a chi al
pape , he equa ion is no de ined, bu he gene al in e p e a ion is
simple, since i cons i u es a sco e be ween 0 and 1, wi h 1 a he
maximum co-loca ion easibili y o he combina ion o wind and wa e
ene gy. Acco ding o Eq. (5), he e a e s a is ically weigh ed i e e ms
in he equa ion o a gi en s udy a ea anged be ween 0 and 1.
𝐶𝐿𝐹𝑖=𝛼𝑊 𝐸𝐹
𝑊 𝐸𝐹𝑖−𝑊 𝐸𝐹min
𝑊 𝐸𝐹max −𝑊 𝐸𝐹min
(1)+
𝛼𝑊 𝑃 𝐷
𝑊 𝑃 𝐷𝑖−𝑊 𝑃 𝐷min
𝑊 𝑃 𝐷max −𝑊 𝑃 𝐷min
(2)+
𝛼𝑐(0)
𝑐(0)max −𝑐(0)𝑖
𝑐(0)max −𝑐(0)min
(3)+
𝛼𝜎𝑊 𝐸𝐹
𝜎𝑊 𝐸𝐹 ,max −𝜎𝑊 𝐸𝐹 ,𝑖
𝜎𝑊 𝐸𝐹 ,max −𝜎𝑊 𝐸𝐹 ,min
(4)+
𝛼𝜎𝑊 𝑃 𝐷
𝜎𝑊 𝑃 𝐷,max −𝜎𝑊 𝑃 𝐷,𝑖
𝜎𝑊 𝑃 𝐷,max −𝜎𝑊 𝑃 𝐷,min
(5)
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Table 2
Main cha ac e is ics o he baseline NREL 5 MW wind u bine.
Value Uni
Ra ed powe 5 MW
Ro o diame e 123 m
Hub heigh , diame e 90, 3 m
Cu -in, a ed, cu -ou wind speed 3, 11.4, 25 m/s
Cu -in, a ed o o speed 6.9, 12.1 pm
1. The a io be ween he di e ence o mean 𝑊 𝐸𝐹 wi h espec o
he minimum 𝑊 𝐸𝐹 o he egion and he di e ence be ween
he maximum and minimum 𝑊 𝐸𝐹 .
2. The a io be ween he di e ence o mean 𝑊 𝑃 𝐷 wi h espec o
he minimum 𝑊 𝑃 𝐷 o he egion and he di e ence be ween
he maximum and minimum 𝑊 𝑃 𝐷.
3. The empo al co ela ion o 𝑊 𝑃 𝐷 and 𝑊 𝐸𝐹 a each g idpoin .
4. The a io be ween he di e ence o he s anda d de ia ion o
𝑊 𝐸𝐹 wi h espec o he maximum s anda d de ia ion o he
egion and he di e ence be ween he maximum and minimum
s anda d de ia ions.
5. The a io be ween he di e ence o he s anda d de ia ion o
𝑊 𝑃 𝐷 wi h espec o he maximum s anda d de ia ion o he
egion and he di e ence be ween he maximum and minimum
s anda d de ia ions.
Ob iously, he i e e ms should be be ween [0,1], and being 𝑖
subs i u ed by 𝑊 𝐸𝐹 ,𝑊 𝑃 𝐷,𝑐(0),𝜎𝑊 𝐸𝐹 , o 𝜎𝑊 𝑃 𝐷,
∑
𝑖
𝛼𝑖= 1 (6)
In his way, acco ding o he poin s 1 and 2 he a e age alue o
𝑊 𝑃 𝐷 and 𝑊 𝐸𝐹 a he loca ion should be as high as possible (nea
he maximum o he egion) o imp o e 𝐶𝐿𝐹 . The same can be said
o he co ela ion be ween 𝑊 𝑃 𝐷 and 𝑊 𝐸𝐹 . Howe e , he poin s 4
and 5 es ablish ha he s anda d de ia ions o 𝜎𝑊 𝐸𝐹 and 𝜎𝑊 𝑃 𝐷 should
be as low as possible (low a iabili y nea he minimum o he egion)
in o de o aise he alue o 𝐶𝐿𝐹 .
2.3. Annual ends a a selec ed loca ion
The p e ious spa ial me hod will be used o selec a ho spo and
in e es ing loca ion due o 𝑊 𝑃 𝐷 and 𝑊 𝐸𝐹 a ia ions. A e his
selec ion, a ine me hodology is used a his loca ion o ind he annual
a ia ions o co-loca ion easibili y and eal ene gy p oduc ion.
The compu a ion o he annual ends o 𝐶𝐿𝐹 and eal p oduc ions
using Capaci y Fac o (𝐶𝐹 ) and Cap u e Wid h Ra io (𝐶𝑊 𝑅) (see
Sec ions 2.4.1 and 2.4.2) will be ep esen ed by linea eg ession and
Theil–Sen me hod [49], which is a obus es ima o which educes he
sensi i i y o he end o ou lie s by conside ing he medians ins ead
o geome ical a e ages.
2.4. Real ene gy p oduc ion
The heo e ical me hods de eloped p e iously will be u he de el-
oped in oducing wind and wa e da a in powe cu es and powe ma-
ices o eal wind u bines and Wa e Ene gy Con e e s (WECs). This
inal app oach can he e o e o e s ong comme cial in e p e a ions in
he esul s.
2.4.1. Wind u bine
The wind da a a he iden i ied ho -spo ha e been implemen ed
on he powe cu e o he Na ional Renewable Ene gy Labo a o y
(NREL) 5 MW wind u bine [50] o he compu a ion o he Annual
Ene gy P oduc ion (𝐴𝐸𝑃 ) and he 𝐶𝐹 .Table 2 desc ibes he main
cha ac e is ics o he u bine.
Howe e , p e iously, he wind speed a 10 m has o be aised o
he wind speed a he hub heigh (90 m) by he log law [51]. The
ins an aneous one-hou ly oughness (𝑧0) o he sea is ob ained om
wind speed a 10 m (𝑈10) and a 100 m (𝑈100) by Eq. (7).
𝑈100
𝑈10
=log(100∕𝑧0)
log(10∕𝑧0)⇒𝑧0=𝑒
log(10)(2𝑈10−𝑈100)
𝑈10−𝑈100 (7)
A e ha , wind speed a he hub heigh is ob ained using he log
law in Eq. (8).
𝑈90 =𝑈10
log(90∕𝑧0)
log(10∕𝑧0)(8)
Fu he mo e, he no maliza ion o he wind speed is gi en by he
cubic oo o he a io be ween ai densi ies, being 𝜌0 he s anda d ai
densi y, and 𝜌 he eal ai densi y [48] (see Eq. (9)).
𝑈90𝑛=(𝜌
𝜌0)1
3
𝑈90 (9)
Finally, he annual p oduc ion 𝐴𝐸𝑃 (kWh) is gi en by Eq. (10),
whe e N=8760 is he hou s pe yea , 𝑃(𝑈𝑖)is he powe p oduced in kW
by he u bine o each wind-speed 𝑈𝑖o he ime se ies, and 𝛥𝑇 = 1ℎ,
he ime esolu ion o he ime se ies.
𝐴𝐸𝑃 =
𝑁
∑
𝑖=1
𝑃(𝑈𝑖)𝛥𝑇 (10)
𝐴𝐸𝑃 is di ided by he ideal p oduc ion a a ed powe 𝑃𝑅= 5000
kW o ob ain 𝐶𝐹 acco ding o he Equa ion
𝐶𝐹 =𝐴𝐸𝑃
𝑃𝑅⋅365.25 ⋅24 (11)
This pa ame e 𝐶𝐹 is selec ed as an adimensional a io in o de o
no malize he eal p oduc ion o he wind u bine and compa e i wi h
o he a io (𝐶𝑊 𝑅) ha exp esses an simila concep o he selec ed
WEC, see Sec ion 2.4.2.
2.4.2. Poin abso be wa e ene gy con e e
A WEC model o loa ing body ype o de eloped by Oiga den and
Olsen was used in deep wa e condi ion [52,53], ha ing he abso bed
wa e powe 𝑃𝑎𝑏𝑠 in kW as a unc ion o 𝐻𝑠and 𝑇𝑝:
𝑃𝑎𝑏𝑠 = 4.5𝐷2.4
𝑏𝐻1.7
𝑠𝑇−0.9
𝑝(12)
. whe e 𝐷𝑏deno es he diame e o he loa ing body. 𝐷𝑏= 2 m is
adop ed in he i s app oxima ion by he in en o s [52], and in he
40 yea s e olu ion p esen ed in Sec ion 3.3.3.
This WEC was designed o be pa ially illed wi h wa e , changing
he wa e olume wi hin, hus adap ing he na u al equency o he
de ice o he inciden wa e pe iod.
The e o e, 𝐶𝑊 𝑅 can be ob ained conside ing 𝑃𝑎𝑏𝑠 as he eally
abso bed powe , and 𝑃𝑤𝑎𝑣𝑒 he heo e ical wa e powe gi en by 𝑊 𝐸𝐹
along he ans e sal longi ude o he wa e o 𝐷𝑏( on al wid h o he
de ice 𝐵=𝐷𝑏).
𝐶𝑊 𝑅 =𝑃𝑎𝑏𝑠
𝑃𝑤𝑎𝑣𝑒
=𝑃𝑎𝑏𝑠
𝑊 𝐸𝐹 ⋅𝐵(13)
This pa ame e , 𝐶𝑊 𝑅, is selec ed as an adimensional a io in o de
o no malize he eal p oduc ion o he WEC de ice and compa e i wi h
wind u bine’s 𝐶𝐹 , which is also a a io.
3. Resul s
The Table 3 summa izes all he main esul s and he con idence
in e als a 95% con idence le el o 𝐶𝐿𝐹 ,𝐶𝐹 ,𝐶𝑊 𝑅, and he eal
powe p oduc ion o he wind u bine and he WEC. In he nex
sec ions, he o igin and isual ep esen a ions o hese inal alues a e
shown wi h a b ie in e p e a ion o hese p e ious esul s.
Ene gy Con e sion and Managemen 283 (2023) 116890
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A. Ulazia e al.
Fig. 2. Absolu e a e age alue in he 1980–1989 ini ial decade o 𝑊 𝐸𝐹 (le in kW/m) and 𝑊 𝑃 𝐷 ( igh in W/m2).
3.1. Resou ce maps o decadal di e ences
Fig. 2 shows he a e age 𝑊 𝐸𝐹 (le ) and 𝑊 𝑃 𝐷 ( igh ) om 1980
o 1989, he i s e e en ial decade wi h espec o which he ela i e
a ia ions o he ollowing decades will be compu ed. Fo he ollowing
in e p e a ion o he inal esul s i should be no ed he s ong educ ion
o wind ene gy po en ial in he Sou hwes o Tene i e (a ound 200
W/m2a 10 m heigh ), unde he p o ec ion o No heas e n ade
winds (a ound 500 W/m2in he No h wi h peaks o 900 W/m2
be ween islands), an e ec ha is also conside able o 𝑊 𝐸𝐹 , bu in a
weake way ( om 15 kW/m o 10 kW/m). These spa ial dis ibu ions
a e e y simila o alues ound in p e ious li e a u e o wa e ene gy
assessmen and o sho e wind ene gy assessmen [25,54].
The decadal di e ences in pe cen o 𝑊 𝐸𝐹 and 𝑊 𝑃 𝐷 (Fig. 3)
show a ele an inc ease, which each up o 15% and 18% be ween he
main islands o Tene i e and G an Cana ia o he las decade du ing
he 2010s. In he case o 𝑊 𝑃 𝐷, he e is e en a dec ease nea he coas
o A ica ha eaches -5%, bu he gene al end is clea ly inc emen al
du ing he decades.
Howe e , he inc emen di e ence be ween 𝑊 𝐸𝐹 and 𝑊 𝑃 𝐷
(Fig. 4) is he ele an ques ion he e, in o de o analyse he decadal
a ia ion o he easibili y o wind and wa e ene gy combina ion. This
s udy shows a huge di e ence o 18% be ween bo h his o ical ends a
a g idpoin in he sou h o Tene i e and La Palma (longi ude = −17◦E,
la i ude = 27.5◦N), due o he high inc ease o 𝑊 𝐸𝐹 and he educ ion
o 𝑊 𝑃 𝐷 om he decade o 1980s o he las decade o 2010s. This
loca ion also co esponds o he highly p o ec ed a ea om ade winds
acco ding o ene gy po en ial maps o Fig. 2.
3.2. E olu ion o he co-loca ion index a a ele an loca ion
The iden i ied ho spo a he men ioned g idpoin (−17◦E, 27.5◦N)
will be used o he s udy o he annual e olu ion o 𝐶𝐿𝐹 du ing he
40 yea s o analysis. Thus, he i e e ms o he 𝐶𝐿𝐹 equa ion ha e
been compu ed o each yea om 1980 o 2019 wi h a ound 350400
cases analysed, and s a is ical weigh o each e m has been subjec i e
keeping he alues o he o iginal wo k o As a iz e al. [29], and
weigh ing abo e all he index o he alues o wa e ene gy and wind
ene gy, lowe o he co ela ion, and gi ing a low speci ic weigh o
he a iabili y o he wo s anda d de ia ions (see Exp ession (14)).
𝛼𝑊 𝐸𝐹 = 0.35; 𝛼𝑊 𝑃 𝐷 = 0.35; 𝛼𝑐(0) = 0.2; 𝛼𝜎𝑊 𝐸𝐹 = 0.05; 𝛼𝜎𝑊 𝑃 𝐷 = 0.05;
(14)
This elec ion acco ding o [29], es ablishes he same index weigh
o 𝑊 𝐸𝐹 and 𝑊 𝑃 𝐷, no only o hei absolu e alues (𝛼𝑊 𝐸𝐹 and
𝛼𝑊 𝑃 𝐷), bu also o hei a iabili y wi hin he s anda d de ia ion o
he signals (𝛼𝜎𝑊 𝐸𝐹 and 𝛼𝜎𝑊 𝑃 𝐷 ).
Fig. 5 shows a clea inc emen o 𝐶𝐿𝐹 along he 40 yea s om
0.44 o 0.51, showing also he con idence in e al o he end a a
95% con idence le el using Theil–Sen me hod [49]. Al hough he alue
o 𝑊 𝑃 𝐷 emains almos cons an a his poin , his posi i e e olu ion
is due o he s ong inc emen o 𝑊 𝐸𝐹 a his poin , which has a
high s a is ical weigh (0.35). The low a ia ions o he co ela ion and
s anda d de ia ions does no a ec he inal p oduc o 𝐶𝐿𝐹 .
3.3. Real ene gy p oduc ion
The e alua ion o he annual eal p oduc ion conside ing he powe
cu e o he NREL 5 MW wind u bine o he compu a ion o 𝐶𝐹 (see
Sec ion 2.4.1), and he loa ing de ice model’s annual a e age 𝐶𝑊 𝑅
(see Sec ion 2.4.2), show app oxima ely a simila beha iou : posi i e
in he case o he wind u bine (Fig. 7), and nega i e in he case o he
WEC (Fig. 8). The selec ed g idpoin using he desc ibed 𝐶𝐿𝐹 me hod
shows he e o e a long- e m wind–wa e ene gy compensa ion also o
ealis ic elec ical ene gy p oduc ion. Fo ha , p e ious o he ene gy
p oduc ion es ima ions, he i s ollowing Sec ion 3.3.1 analyzes he
ins an aneous wind and wa e powe in kW conside ing he en i e ime
se ies o ou decades 1-hou ly.
3.3.1. Powe p oduc ion by decades
Fi s ly, Fig. 6 shows he decade boxplo s o each de ice, he loa ing
body (a) and he wind u bine (b), acco ding o hei ins an aneous
p oduc ion in kW a each momen o he ime se ies (40 yea s, 1
hou ly). Al hough he e is a ele an inc emen o powe p oduc ion
o wa es, i is no clea he end o wind powe p oduc ion. This
ins an aneous powe will be he base o he compu a ion o 𝐶𝐹 and
𝐶𝑊 𝑅 in he ollowing sec ions.
3.3.2. E olu ion o he annual capaci y ac o o he wind u bine
The selec ed g idpoin does no show a good 𝐶𝐹 , since he bes
o sho e loca ions’ 𝐶𝐹 each 0.40–0.50, bu i is abo e a easonable
limi app oxima ing 0.30 [55]. Howe e , he 40-yea end is posi i e,
showing a ele an inc emen a a 95% con idence le el desc ibed by
he shaded a ea (See Table 3). The linea i ing me hod o he Theil–
Sen me hod [49] show a simila slope alue and con idence in e al,
wi h a ise o 𝐶𝐹 a ound 0.02 s a ing om 0.27 in 40 yea pe iod.
Table 3 in Sec ion 4shows he exac alues o he con idence in e al.
3.3.3. E olu ion o he annual a e age cap u e wid h a io o he loa ing
de ice
The selec ed g idpoin shows a easonable 𝐶𝑊 𝑅 o a loa ing
de ice a ound 0.40–0.50 [56]. The 40-yea end is again ele an a
a 95% con idence le el, bu he e is a educ ion o he alue (See
Table 3). The nega i e slope compu ed by he linea me hod o he
Theil–Sen me hod [49] a e simila , showing an absolu e educ ion o
𝐶𝑊 𝑅 a ound 0.02 s a ing om 0.45.
Ene gy Con e sion and Managemen 283 (2023) 116890
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A. Ulazia e al.
Fig. 3. Decadal di e ences wi h espec o 1980s ini ial decade in pe cen (by ows) o 𝑊 𝑃 𝐷 (le column) and 𝑊 𝐸𝐹 ( igh column).
4. Discussion
A s a is ical summa izing o he p e ious g aphical esul s shows he
signi icance o he ob ained con idence in e als and ends. Table 3
esumes he con idence in e als (CI 95%) calcula ed by means o he
Theil–Sen me hod o he end analysis o 𝐶𝐿𝐹 ,𝐶𝐹 and 𝐶𝑊 𝑅 pe
decade (by columns). Wind u bine’s (WT) and loa ing body’s (FB)
powe (kW) is also shown in he inal ows. The las column shows
he slope in pe cen pe decade acco ding o he cen al alue.
Al hough he posi i e end o WT’s 𝐶𝐹 is no s a is ically signi -
ican , he nume ic alues o he in e se ends o wa e ene gy and
wind ene gy a e cohe en wi h he p e ious g aphical ep esen a ions,
and he inal esul in pe cen pe decade show e y ele an a ia ions
mainly o he nega i e slope o 𝐶𝑊 𝑅 and he posi i e alue o 𝐶𝐿𝐹
ha eaches he 5%. This is a e y impo an alue, since a p ojec ion
o his end along a cen u y would inc emen he co-loca ion index
om 0.4–0.5 o 0.7–0.8. I should be no ed also he s ong inc emen
in pe cen o FB’s powe due o he inc emen o 𝑊 𝐸𝐹 , which is o se
in he calcula ion o 𝐶𝑊 𝑅 due o he inc ease o he di iso in Eq. (13).
These s ong ends a e no s ange, because p e ious li e a u e
on global his o ical ends o wind speed and wa e heigh shows a
Ene gy Con e sion and Managemen 283 (2023) 116890
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A. Ulazia e al.
Fig. 4. Inc emen di e ence in ou decades (2011–2010 minus 1980–1989) be ween 𝑊 𝐸𝐹 and 𝑊 𝑃 𝐷.
Fig. 5. CLF end a he iden i ied ho spo .
Table 3
This able summa izes he main esul s o his a icle, showing
he nume ical alues o he ends pe decade wi h hei
con idence in e als. In columns, con idence in e als (CI 95%)
o he Theil–Sen me hod o he in e io , cen al and supe io
alue (pe decade). In ows, he Co-loca ion Feasibili y index,
Capaci y Fac o , cap u e wid h a io, and he Wind u bine and
loa ing body powe in kW. The las column shows he decadal
inc emen in pe cen based on he cen al alue.
CI 95% In e io Cen al Supe io %/10y
CLF 0.01 0.020 0.025 +5.6
CF 0.000 0.0017 0.0040 +0.8
CWR −0.010 −0.007 −0.005 −1.5
WT (kW) −2.3 21.7 26.6 +1.6
FB (kW) 0.13 0.16 0.27 +17
synch onized gene al inc emen in he A lan ic Ocean wi h he ex-
cep ion o he No h-Wes A ican coas , Guinea Gul , and Cana y
Islands [26,57]. This ac has been also co obo a ed by his s udy
showing no only he decoupling o 𝑊 𝐸𝐹 and 𝑊 𝑃 𝐷, bu also he
co esponding decoupling o wind ene gy and wa e ene gy p oduc ion
by a selec ed wind u bine and WEC acco ding o 𝐶𝐹 and 𝐶𝑊 𝑅 (see
Figs. 7 and 8).
High esolu ion Global Wind A las [58] also alida es he 𝐶𝐹 alues
iden i ied a he ho -spo (−17◦E, 27.5◦N), unde he p o ec ion o ade
winds, wi h alues a ound 0.30. This global a las o e s wind esou ce
mapping a 250 m ho izon al g id spacing, and 𝐶𝐹 esou ce mapping a
10, 50, 100, 150 and 200 m abo e g ound/sea le el. Since he ex ension
o he ERA5 g id eaches he 0.5◦ esolu ion, he Global Wind A las
shows ha hese da a co espond o he a ea a he Sou h o La Gome a,
whe e 𝐶𝐹 educes signi ican ly nea he coas e en below 0.20.
The adop ion o subjec i e speci ic weighs o he 𝛼pa ame e s
in Exp ession (14) and Eq. (5) can be imp o ed in he u u e using
analy ic ma hema ical me hodology o index gene a ion, as i is used
in o he kind o ene gy index gene a ion such in he case o ene gy
po e y in a mul idimensional app oach [59]. The inco po a ion o
analy ical c i e ia o axioma ically de e mine he 𝛼pa ame e s can be
e y in e es ing in u u e esea ch, in oducing, o ins ance, Le elized
Cos o Ene gy (LCOE) alues o o sho e wind ene gy and wa e ene gy
o selec a a io be ween 𝛼𝑊 𝐸𝐹 and 𝛼𝑊 𝑃 𝐷. This ac would be impo an
in he cons uc ion o a new analy ical index gi en he lowe LCOE
o o sho e wind ene gy up o 160 e/MWh [60] compa ed o wa e
ene gy’s LCOE, which is be ween 370–1200 e/MWh [61].
Acco ding o hese p elimina y da a, 𝛼𝑊 𝑃 𝐷 and 𝛼𝑊 𝐸𝐹 can be di -
e en in a u u e esea ch ha would modi y he o iginal adop ion
o As a iz e al. [62], bu his app oach would he e o e cons i u e a
new and deepe axioma ic in analy ical hie a chy p ocess desc ibed by
ma hema icians in applica ions o index gene a ion [63]. Anyway, his
new app oach would need o open a u u e esea ch line be ween ma h-
ema ics and echno-economic wa e ene gy enginee ing, in oducing
also he s a is ics abou su i abili y isk and ex eme oceanic e en s as
a p e ious s ep o he ma hema ical modelling o he imp o ed index.
I is no possible cu en ly o a ibu e he de ec ed ends o clima e
change induced by inc eased concen a ion o g eenhouse gases. Local
analyses loca ed no h o he Cana y Islands using Na ional Cen e s o
En i onmen al P edic ion/Na ional Cen e o A mosphe ic Resea ch
(NCEP/NCAR) da a show ha No he n Hemisphe e models o a iabil-
i y such as he No h A lan ic Oscilla ion o decadal signals in he ocean
such as he A lan ic Mul icedal Oscilla ion [64] a ec he a ea. On he
o he hand, e en hough some pape s iden i y a widening (polewa d
shi ) o he Hadley Cell du ing he las decades [65], he e a e s ill
some doub s ega ding he seasonal o egional cha ac e is ics o he
expansion o he opics [66]. Besides ha , he ele an li e a u e has
Ene gy Con e sion and Managemen 283 (2023) 116890
9
A. Ulazia e al.
Fig. 6. Powe p oduc ion in kW o he 5 MW wind u bine and he loa ing body WEC showing he boxplo s co esponding o each decade. Each box shows he i s and he
hi d qua ile in he up and down limi s, and he median is ep esen ed by he line a he middle.
Fig. 7. Capaci y Fac o end a he iden i ied ho spo o he selec ed wind u bine.
Fig. 8. Cap u e Wid h Ra io end a he iden i ied ho spo o he selec ed Wa e Ene gy Con e e .
