Ene gy Con e sion and Managemen 271 (2022) 116303
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Floa ing wind u bine ene gy and a igue loads es ima ion acco ding o
clima e pe iod scaled wind and wa es
Ai o Saenz-Agui e a,∗, Alain Ulazia a, Gab iel Iba a-Be as egi b,c, Jon Saenz c,d
aEne gy Enginee ing Depa men , Uni e si y o he Basque Coun y (UPV/EHU), O aola 29, 20600 Eiba , Spain
bEne gy Enginee ing Depa men , Uni e si y o he Basque Coun y (UPV/EHU), Alda, U kijo, 48013 Bilbao, Spain
cPlen ziako I sas Es azioa (BEGIK), Uni e si y o Basque Coun y (UPV/EHU), A ea za Hi ibidea 47, 48620 Plen zia, Spain
dDepa men o Physhics, Uni e si y o he Basque Coun y (UPV/EHU), Sa iena, 48940 Leioa, Spain
ARTICLE INFO
Keywo ds:
Wind ene gy
Floa ing O sho e
Fa igue loads
Clus e analysis
ERA5
ABSTRACT
O sho e wind powe is one o he as es -g owing enewable ene gy sou ces, as i is expec ed o play a majo
ole in he ansi ion owa ds sus ainabili y and ne ze o emissions. Despi e i s po en ial, he in e ac ion o
he u bines wi h he oceanic wa es, especially in case o loa ing u bines, is one o he main d awbacks
associa ed o i . In ac , mechanical oscilla ions caused by he wa es could po en ially al e he ope a ion
and li e ime o he u bines. Hence, while he cha ac e iza ion o he wind is su icien o he long- e m
design o onsho e wind u bines, he p ocedu e is mo e complex in case o o sho e u bines, since he heigh ,
pe iod and di ec ion o he wa es will a ec he li e ime o he u bine. In his pape , a me hodology o
he e alua ion o he ene gy gene a ion and a igue mechanical loads o a Floa ing O sho e Wind Tu bine
(FOWT) conside ing a 30-yea pe iod is p oposed. To ha end, me eo ological da a om 1991 o 2020 a e
cha ac e ized using a clus e analysis and educed in o a compu a ionally a o dable numbe o simula ion
cases. Resul s show negligible ene gy loss o a FOWT due o in e ac ion wi h he oceanic wa es. Howe e , a
subs an ial inc emen o he mechanical a igue in he side-side and o e-a bending momen s o he owe
a e de ec ed. Such analyses migh be applied o he p edic abili y o he li e ime o an o sho e wind u bine,
as well as he selec ion o po en ial op imal wind a m loca ions, based on clima ic pa e ns and he e olu ion
o me eo ological da a.
1. In oduc ion
The apidly inc easing numbe o o sho e wind u bines is a clea
ep esen a ion o he g ow h o his echnology in he ecen yea s. A -
e he ins alla ion o he i s o sho e u bine in 1990, he cumula i e
o sho e wind powe capaci y had al eady inc emen ed o 1471 MW
by 2008 [1]. F om ha momen on, he endency has been exclusi ely
inc emen al and by 2017 a 1.5% (43 TWh) o he ene gy p oduc ion in
he Eu opean Union p esen ed o sho e wind o igin [2]. The p ognosis
is he sho - e m expansion and se lemen o ma ine enewable ene gy
sou ces, especially wind and wa e powe , as he p incipal d i e s o he
deca boniza ion and ne ze o emission p ocess in he ene gy gene a ion
in as uc u e [3].
The main ad an ages o o sho e wind powe in compa ison o on-
sho e wind echnology a e ela ed o he wind speed esou ce a oceanic
loca ions [4], whe e usually highe mean wind speed alues and lowe
u bulence and wind shea a e ound. Highe wind speed alues allow
imp o ed ene gy gene a ion, and lowe u bulence is ansla ed in o a
educ ion o he mechanical loads in he wind u bine. Addi ionally,
∗Co esponding au ho .
E-mail add ess: [email p o ec ed] (A. Saenz-Agui e).
depending on he dis ance o he sho e, o sho e wind u bines a e
un es ic ed in e ms o isual o noise impac , which inc eases he
a ailabili y o a eas o he ins alla ion o wind u bines. Expensi e
ounda ions o moo ing sys ems, cos ly main enance, di icul ies e-
la ed o g id in eg a ion and hyd odynamic in e ac ion wi h he ocean
wa es a e he mos impo an d awbacks associa ed o o sho e wind
echnology. A de ailed compa ison be ween onsho e and o sho e wind
echnologies is p o ided in [1].
Conce ning loca ion, o sho e wind u bines migh be ins alled ei-
he nea -sho e o a -o sho e [5]. S ic egula ions in some coun ies,
ega ding noise o isual impac o he wind u bines, as well as he
p o ec ion o nea -sho e ma ine ecosys ems, ha e led o he ins alla ion
o a -o sho e wind a ms, which, as a consequence o he la ge wa e
dep h, equi e Floa ing O sho e Wind Tu bines (FOWTs). Addi ionally,
in some cases, he ins alla ion o FOWTs is a di ec esul o he ab up
coas al loo in some a eas, whe e he la ge wa e dep h nea -sho e
p e en s he ins alla ion o bo om- ixed wind u bines. In his con ex ,
h ps://doi.o g/10.1016/j.enconman.2022.116303
Recei ed 23 July 2022; Recei ed in e ised o m 27 Sep embe 2022; Accep ed 28 Sep embe 2022
Ene gy Con e sion and Managemen 271 (2022) 116303
2
A. Saenz-Agui e e al.
Lis o Abb e ia ions
AEP Annual Ene gy P oduc ion
CF Capaci y Fac o
DEL Damage Equi alen Load
DLC Design Load Case
ECMWF Eu opean Cen e o Medium-Range Wea he
Fo ecas s
FAST Fa igue, Ae odynamics, S uc u es and Tu -
bulence
FOWT Floa ing O sho e Wind Tu bine
HAWT Ho izon al Axis Wind Tu bine
LCA Li e Cycle Assessmen
LSS Low Speed Sha
NREL Na ional Renewable Ene gies Labo a o y
NTM No mal Tu bulence Model
SSP Sha ed Socioeconomic Pa hway
SWL Su ace Wa e Le el
TMD Tuned Mass Dampe
Nomencla u e
𝑈10 Wind speed a 10 m heigh om ERA5
𝑈100 Wind speed a 100 m heigh om ERA5
𝑈90 Wind speed a 90 m heigh
𝑧0Roughness o he sea
𝑈𝑑𝑖𝑟 Incoming di ec ion o wind (deg ees clock-
wise om No h)
𝜌0S anda d ai densi y
𝜌Real ai densi y
𝐻𝑠Signi ican wa e heigh
𝑇𝑝Peak wa e pe iod
𝐻𝑠𝑑𝑖𝑟 Incoming di ec ion o wa es (deg ees clock-
wise om No h)
𝑚Ma e ial exponen o a igue calcula ion
𝑘Weibull scale pa ame e
𝑐Weibull o m pa ame e
𝑃𝑈P obabili y o occu ence o wind speed o
he con idence in e al o he cen oid in
each clus e
𝑃𝑠𝑡 S anda d p obabili y o occu ence o wind
speed o he con idence in e al o he
cen oid in each clus e
𝑃𝑐P obabili y o occu ence o each clus e
ba hyme y s udies mus be conduc ed o cha ac e ize he coas al loo
p io o selec ion o o sho e wind a m loca ions [6].
The loca ion o a wind a m, nea -sho e o a -o sho e, will a ec
he cos s associa ed o i . A compa ison be ween a 20 yea long Li e
Cycle Assessmen (LCA) o a a -o sho e wind a m ( o med by 40–
50 FOWTs) [7] and he LCA o an equi alen nea -sho e wind a m
o med by bo om- ixed wind u bines [8] indica e ha he inc eased
economical cos associa ed o ma e ials, ins alla ion and main enance
o FOWTs is compensa ed by a highe capaci y ac o . As a esul ,
he LCA and he en i onmen al impac o he elec ici y gene a ion is
simila in bo h cases.
Besides ins alla ion, main enance and s uc u al design o he wind
u bine, wind a m loca ion will also ha e an impac on he ope a ion
and mechanical loading o he wind u bines, as a esul o hei
in e ac ion wi h he oceanic wa es. Nume ical me hods o s udy hese
hyd odynamic p ocesses ha e been widely s udied in li e a u e [9]. In
addi ion, as a esul o he mechanical oscilla ions gene a ed by he
wa es, hei in luence on he pe o mance o he u bine migh be
ampli ied in case o FOWTs [10]. This could lead o powe losses due o
pla o m-pi ch in e ac ions [11], exci a ion o mechanical equencies
o he wind u bine componen s o he educ ion o he expec ed
li e ime o hese componen s due o a igue ailu e [12]. Inc easing
he ae odynamic damping ia con ol unc ionali ies [11], o wi h
he in oduc ion o addi ional Tuned Mass Dampe (TMD) [12] a e
solu ions p oposed and nowadays used o FOWTs.
The e o e, a p e ious assessmen o he wind and wa e esou ces
[13], as well as hei coupling [14], a po en ial wind a m ins alla ion
loca ions is c ucial as i can help cha ac e ize he e ec o he en i on-
men al condi ions on he pe o mance o he wind u bines [14], he
inc emen o hei a igue mechanical loads as a esul o he hyd ody-
namic in e ac ion wi h he oceanic wa es a ha speci ic loca ion o
e en op imize main enance p ocedu es [15]. On ha accoun , op imal
loca ions o he ins alla ion o wind a ms based on he e olu ion o
his o ical me eo ological da a could be selec ed.
While he cha ac e iza ion o he wind esul s su icien o he long-
e m design and analysis o onsho e wind u bines, he p ocedu e ge s
complica ed in case o o sho e u bines, since he heigh , pe iod and
di ec ion o he p edominan wa es need o be conside ed o such
long- e m ho izon analyses. In his pape , a me hodology is p oposed
o he es ima ion o he ene gy gene a ion and he a igue mechanical
loads o FOWTs a speci ic o sho e loca ions and unde conside a ion
o clima ological no mal pe iods as ime ho izon used in he calcula-
ions. This me hodology shall be alid o analyse he e ec o long- e m
clima e change pa e ns on he wind u bine ene gy gene a ion and
hei a igue mechanical loads, as well as he p edic abili y o u u e
mechanical a igue a ec ion o he wind u bines based on me eo ologi-
cal p ojec ions and he selec ion o op imal loca ions based on his o ical
o p ojec ed e olu ions o me eo ological condi ions.
In his case, he wind and wa e ene gy esou ce a e ob ained
using i h gene a ion ERA5 Reanalysis [16] a he g id poin closes
o Hywind-Sco land [−1.5◦E, 57.5◦N], i.e. i s loa ing wind a m in
he wo ld. The ime esolu ion o his s udy is 1 h and he s udied
pe iod is 30 yea s (1991–2020), ha is, he da abase includes 262 968
hou ly cases. The selec ion o his e e ence pe iod (30 yea s o da a
s a ing in 1991) co esponds o he cu en guidelines by he Wo ld
Me eo ological O ganiza ion [17] in he de ini ion o clima ological
s anda d no mals. This is he same pe iod cu en ly used by majo
me eo ological da a p o ide s such as he Cope nicus Clima e Change
Se ice in hei clima ological analyses [18].
The wind u bine model used o he calcula ion o he mechanical
loading is he baseline NREL 5 MW u bine wi h OC3-Hywind spa -
ype lo a ion sys em. This model is s uc u ed a ound he open-sou ce
ae oelas ic model OpenFAST 2.6.0 [19] and p esen s he same lo a-
ion de ice as he wind u bines in he Hywind wind a m [20]. Open-
FAST ool, de eloped by he Na ional Renewable Ene gies Labo a o y
(NREL), combines ae odynamics, hyd odynamics o o sho e s uc-
u es, con ol and s uc u al dynamics. I o e s, hence, a high-de ailed
simula ion en i onmen o bo h onsho e and o sho e wind u bines,
which ha e been widely-used and accep ed in he li e a u e [21].
Finally, on accoun o he high numbe o me eo ological esou ce
da apoin s in a clima ological no mal pe iod o 30 yea s (262 968
hou ly cases) and he compu a ional un easibili y o simula e and pos -
p ocess all he cases using a high-de ailed wind u bine model such
as OpenFAST, a cha ac e iza ion me hod o he clima ological no mal
pe iod in o a educed numbe o da apoin s is p oposed in his pape .
Thus, hou ly wind and wa e da a in Hywind ha e been classi ied in o
20 clus e s using Wa d’s minimum a iance me hod [22]. Nex , he
a mosphe ic-sea combined s a e ep esen ing each o he clus e s has
been used o a simula ion using he ae oelas ic code OpenFAST in
o de o analyse he ope a ion and calcula e he powe p oduc ion
and he mechanical loads o a FOWT ope a ing a such en i onmen al
condi ions.
Ene gy Con e sion and Managemen 271 (2022) 116303
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A. Saenz-Agui e e al.
Table 1
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
The pape is s uc u ed as ollows: The wind and wa e ene gy
esou ce da a and he analysis me hod o ERA5 a e in oduced in
Sec ion 2.1. The wind u bine model and he simula ion en i onmen
used in he analysis a e desc ibed in Sec ion 2.2. In Sec ion 2.3 a de-
ailed explana ion o he me hodology ollowed by he cha ac e iza ion
o he clima ological no mal pe iod using a clus e analysis and he
calcula ion o he powe p oduc ion and he a igue mechanical loads
o he FOWT is gi en. In Sec ions 3and 4, he esul s and discussion a e
p esen ed, espec i ely. Finally, he conclusions and he u u e ou look
a e explained in Sec ion 5.
2. Da a and me hodology
The wind and wa e da a used in he analysis and he me hodology
o he assessmen o he powe p oduc ion and he a igue mechanical
damage in a FOWT o e a clima ological no mal pe iod a e desc ibed
in he ollowing sec ions.
2.1. ERA5 eanalysis a Hywind-Sco land loca ion
The i h gene a ion ERA5 Reanalysis [16] one-hou ly da a a he
nea es g id poin o Hywind-Sco land ha e been used in his s udy.
These da a ha e been downloaded om he Cope nicus Clima e Change
Se ice’s Clima e Da a S o e (h ps://cds.clima e.cope nicus.eu/) o Eu-
opean Cen e o Medium Wea he Fo ecas ing (h ps://www.ecmw .
in /) (ECMWF) o he 1991–2020 ime pe iod, i.e. conside ing 30 yea s
in o de o comp ehend he a ia ions o long- e m clima ic pa e ns,
as also ecommended by he Wo l Me eo ological O ganiza ion [17].
Such da a ha e shown e y good alida ions o wind ene gy applica-
ions [23], and also o wa e ene gy esou ce assessmen [24].
Speci ically, wind speed a 10 m heigh (𝑈10), wind speed a 100 m
heigh 𝑈100, peak wa e pe iod (𝑇𝑝) and signi ican wa e heigh (𝐻𝑠)
ha e been objec o s udy. Addi ionally, he incoming di ec ion o he
wind 𝑈𝑑𝑖𝑟 and he wa es 𝐻𝑠𝑑𝑖𝑟, by means o zonal and me idional
wind speed and wa e di ec ion, ha e also been inco po a ed in o he
analysis. Being he ocus o his pape he es ima ion o he ene gy
gene a ion and he a igue mechanical damage o a FOWT, his was he
se o a iables ha could be expec ed o ha e he bigges in luence.
A mosphe ic da a om ERA5 a e dissemina ed by de aul a an
ho izon al esolu ion o 0.25◦× 0.25◦, while he de aul g id o ocean
da a shows a wide esolu ion o 0.50◦×0.50◦. Tha is why he common
nea es g id poin o bo h a mosphe ic and oceanic da a has been
selec ed, which is loca ed a (−1.5◦W,57.5◦N), 12 km dis ance om he
wind a m. The exac posi ion o he loa ing wind a m a he Eas o
Sco land and he Wes o he No h Sea is shown in Fig. 1(b).
The wind ose and he wa e ose ( o he zonal and me idional
p ojec ions o signi ican wa e heigh ) diag ams o he speci ied lo-
ca ion a e p esen ed, espec i ely, in Figs. 2(a) and 2(b), which show
he main pa e ns o wind and wa e clima e in a single ep esen a ion.
Besides he conside able mean wind speed alue a he hub heigh
(abo e 9 m/s), he main cha ac e is ic o his si e is he misalignmen
be ween he p edominan wind di ec ion (No h) and wa e di ec ion
(Sou hwes ), consis en wi h he ela i e o ien a ion o he coas wi h
espec o he main wind-wa e gene a ion a eas and he p opaga ion
o he wa es [26]. Tha means, ha he cu en analysis poses a new
Table 2
Main cha ac e is ics o he OC3-Hywind spa - ype lo a ion sys em.
Value Uni
Technology Spa –
Dep h o pla o m base below SWL 120 m
Dep h o ancho s below SWL 320 m
Numbe o moo ing lines 3 –
Pla o m mass, including ballas 7466.33 onnes
Wa e displaced olume 8029 m3
challenge since he di ec ional e ec o wind and wa es need o be
inco po a ed in o he analysis.
Gi en ha he hub heigh o he baseline NREL 5 MW wind u bine
is 90 m, e e o Table 1, wind speed da a a 10 m (𝑈10) and a 100 m
(𝑈100) a e used o compu e he one-hou ly oughness o he sea (𝑧0)
using he loga i hmic law ha de e mines he e ical p o ile o he
wind shea [27], see Eq. (1).
𝑈100
𝑈10
=log(100∕𝑧0)
log(10∕𝑧0)⇒𝑧0=𝑒(((log(2)+log(5))(2𝑈10−𝑈100))∕(𝑈10−𝑈100)) [m]
(1)
By using he ob ained 𝑧0 ime-se ies, loga i hmic law can be applied
again o calcula e he wind speed a he hub heigh o he u bine
(90 m) s a ing om 𝑈10, see Eq. (2).
𝑈90 =𝑈10
log(90∕𝑧0)
log(10∕𝑧0)[m∕s] (2)
Fu he mo e, wind speed da a ha e been no malized acco ding o
he ins an aneous ai densi y compu ed om empe a u e and p essu e
as desc ibed in [28]. In summa y, 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, see Eq. (3).
𝑈90𝑛=(𝜌
𝜌0)1
3
𝑈90 [m∕s] (3)
2.2. Floa ing o sho e wind u bine model
The i s loa ing wind a m in he wo ld is loca ed in Hywind-
Sco land and ope a es wi h a ins alled capaci y o 30 MW, co e ing
an a ea o 4 km2[29]. Hywind is o med by 5 equal OC3-Hywind
spa - ype FOWTs (see Fig. 1(a)), each wi h a o o diame e o 154 m
and a a ed powe o 6 MW. A high- ideli y model o a FOWT o
e y simila cha ac e is ics and using he same OC3-Hywind spa - ype
lo a ion sys em is a ailable in OpenFAST [19]. Hence, his model will
be used in he analysis p oposed in his pape . Gene al cha ac e is ics
o he wind u bine model and he OpenFAST simula ion en i onmen
employed o he ae oelas ic simula ions a e p esen ed in Sec ions 2.2.1
and 3.2, espec i ely.
2.2.1. Cha ac e is ics o he baseline NREL 5 MW OC3-Hywind spa - ype
wind u bine
The baseline NREL 5 MW wind u bine [30] wi h a OC3-Hywind
spa - ype lo a ion sys em [31] will be used in his pape o he
high- ideli y e alua ion o he e ec o he wind and wa e cha ac e -
is ics co esponding o a clima ological no mal pe iod on he ene gy
gene a ion and he a igue mechanical damage o a FOWT.
The main cha ac e is ics o he baseline NREL 5 MW wind u bine
modelled in OpenFAST a e p esen ed in Table 1. Addi ional cha ac e -
is ics o he wind u bine can be ound in [30].
Simila ly, he main cha ac e is ics o he OC3-Hywind spa - ype
lo a ion sys em a e shown in Table 2. Addi ional in o ma ion abou he
pla o m and he moo ing o his wind u bine a e p esen ed in [32].
Ene gy Con e sion and Managemen 271 (2022) 116303
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A. Saenz-Agui e e al.
Fig. 1. (a) OC3-Hywind spa - ype FOWT ins alled in Hywind-Sco land [25]. (b) Geog aphical loca ion o he Hywind-Sco land pionee ing loa ing wind a m.
Fig. 2. Wind and wa e ose diag ams a he nea es g id poin om Hywind-Sco land [−1.5◦E,57.5◦N].
2.2.2. OpenFAST simula ion en i onmen
OpenFAST [19] is an open-sou ce, high- ideli y and mul i-physics
(includes ae odynamics, hyd odynamics o o sho e s uc u es, con ol
and s uc u al dynamics) ae oelas ic simula ion en i onmen o he
e alua ion o he coupled dynamic esponse o a la ge a ie y o wind
u bine con igu a ions, including onsho e, bo om- ixed o sho e and
loa ing o sho e opologies. An o e iew o he a ious componen s
conside ed in an OpenFAST simula ion is p esen ed in Fig. 3
OpenFAST 2.6.0 ool, as well as i s p e ious eleases FAST, ha e
been widely-used in he li e a u e o he simula ion and analysis
o Ho izon al Axis Wind Tu bines (HAWTs), bo h onsho e and o -
sho e, wi h a high deg ee o de ail and accep ance [33]. The e ec
o wind-wa e misalignmen s on he ope a ion and mechanical loads
o an o sho e wind u bine is s udied in [34] using FAST. Simila ly,
mechanical loads educ ion a e in oduc ion o passi e s uc u al
elemen s [35] o ac i e indi idual pi ch ac ua ion [36] ha e also been
analysed in he li e a u e using his same ae oelas ic code.
As pa o OpenFAST simula ions, he cha ac e is ics o en i on-
men al condi ions, bo h wind and wa e, can be ex e nally de ined,
see Fig. 3, wi h espec o he scope o he conduc ed analysis. In his
case, he objec i e o he p esen analysis is o make an assessmen o
he e ec o wind and wa e cha ac e is ics, a clima ological no mal
pe iod le el, on he ene gy gene a ion and a igue mechanical loads
o a spa - ype FOWT. Fo ha , nume ous ae oelas ic simula ions ha e
been conduc ed using di e en wind speed (p incipally de ined by he
mean wind speed a hub heigh 𝑈90) and sea s a e (p incipally de ined
by he signi ican heigh 𝐻𝑠, he peak pe iod 𝑇𝑝and he di ec ion 𝐻𝑠𝑑𝑖𝑟
o he wa es) condi ions.
Tu bulen wind speed ields o he simula ion a e gene a ed using
he s ochas ic u bulence emula o Tu bsim [37]. As de ined in he s an-
da d IEC 61400-3 [38], Kaimal spec um, No mal Tu bulence Model
Ene gy Con e sion and Managemen 271 (2022) 116303
5
A. Saenz-Agui e e al.
Fig. 3. O e iew o he mul i-physic componen s in ol ed in a FOWT simula ion using OpenFAST.
(NTM), and Cwind class a e selec ed o he simula ion o he FOWT.
In addi ion, i egula wa es a e gene a ed based on he JONSWAP
spec um, wi h a peak enhancemen ac o calcula ed ollowing he
me hodology in IEC 61400-3 Annex B, i.e. using peak wa e pe iod 𝑇𝑝
and signi ican wa e heigh 𝐻𝑠, as explained in [39].
Finally, i is o be no ed ha OpenFAST simula ions a e conduc ed
using an ex e nal con ol sys em in Ma lab-Simulink, which p o ides
e ec i e pi ch and o que egula ion o op imize he pe o mance o he
wind u bine a below a ed wind speeds, limi i a beyond a ed wind
speeds and p o ide limi ed load educ ion handles, since no addi ional
owe damping is p o ided.
2.3. Me hodology o powe p oduc ion and mechanical a igue loads as-
sessmen
The me hodology o he e alua ion o he ene gy gene a ion and
he a igue mechanical loads is di ided in o se e al s eps, which a e
desc ibed in he ollowing subsec ions. The cha ac e iza ion o he
me eo ological da a in o a educed numbe o clus e s is desc ibed
in Sec ion 2.3.1. The me hodology o calcula e powe p oduc ion o
he FOWT is desc ibed in Sec ion 2.3.2. Finally, he me hodology o
es ima e he a igue mechanical loads o he FOWT is explained in
Sec ion 2.3.3.
2.3.1. Clus e analysis o wind and sea s a es
As in oduced in Sec ion 1, in o de o ensu e compu a ional sim-
ula ion easibili y o he one-hou ly obse a ions aken du ing he
clima ological no mal s anda d pe iod 1991–2020, hey a e g ouped
in o a educed numbe o clus e s. To ha pu pose, he Wa d’s min-
imum a iance me hod is p oposed, since i aims a inding compac ,
sphe ical clus e s. This algo i hm has been used in se e al wind s udies
o simila clus e ing pu poses [22] and e e ences he ein.
Con en ional simila s udies a e s uc u ed a ound he clus e ing o
he wind [40]. While ha app oach migh esul alid o onsho e wind
powe gene a ion sys ems, addi ional a iables a e necessa y o ensu e
eliabili y o an analysis o an o sho e wind u bine. Due o he hyd o-
dynamic in e ac ion be ween he oceanic wa es and he wind u bine,
he cha ac e is ics o he wa e esou ce will in luence he ope a ion
o a FOWT and mus , he e o e, be included in he clus e ing, which
inc eases i s complexi y bu is equi ed o gua an ee he eliabili y o
he esul s. Consequen ly, in his s udy, he hype space o each case is
de ined by he ollowing 5 dimensions:
•𝑈90 [m] wind speed a hub heigh .
•𝑈𝑑𝑖𝑟 [◦] incoming di ec ion o wind.
•𝐻𝑠[m] signi ican wa e heigh .
•𝐻𝑠𝑑𝑖𝑟 [◦] incoming di ec ion o wa es.
•𝑇𝑝[s] peak wa e pe iod.
A e s anda diza ion o he a iables, he selec ion o he numbe
o clus e s is made by examina ion o he agglome a ion ee o he
indi idual obse a ions in he 5-D hype space ob ained wi h he Wa d
algo i hm. The dis ance be ween wo cases is calcula ed as he squa e
o he Euclidean dis ance. Going upwa ds in he agglome a ion ee, he
mos simila cases (e.g hose ha exhibi he smalles dis ance among
hem) end o clus e oge he . In Fig. 4, i can be obse ed, ha a
numbe o 20 clus e s easonably ep esen s he mos impo an g oups
o simila indi idual obse a ions. Addi ionally, he wind and wa e
oses o he 20 clus e s (no included in he pape ), exhibi a clea
p edominan di ec ion o mos indi idual hou ly cases belonging o
hose clus e s.
2.3.2. Calcula ion o p oduced powe
Powe p oduc ion o he baseline NREL 5 MW wind u bine wi h
OC3-Hywind spa - ype lo a ion sys em is e alua ed conside ing 10 min
simula ions using OpenFAST amewo k, see Sec ion 3.2. As speci ied in
he s anda d IEC 61400-3 [38], 10 min simula ions a e ecommended
o powe p oduc ion scena ios. i.e. DLC 1.2 cases, conside ing a leas
6 andom seeds, hus esul ing in 60 min o s ochas ic wind and wa e
inpu s o each en i onmen al condi ion. Plus, he low peak wa e
pe iod 𝑇𝑝 alues o he sea s a es conside ed in he simula ions suppo
he use o 10 min simula ions.
The e o e, he ope a ion o he wind u bine, and especially i s
powe p oduc ion, a e analysed o all 20 clus e cases ob ained in
Sec ion 2.3.1. Mo eo e , o be consis en wi h he equi emen s in
he s anda d IEC 61400-3, 10 di e en NTM wind speed seeds a e
simula ed and pos -p ocessed o each clus e case. The inclusion o
nume ous seeds in he calcula ions educes a iabili y and inc eases o-
bus ness o he esul s, as i minimizes he isk o eaching conclusions
based on isola ed e en s.
Addi ionally, he Capaci y Fac o (CF) o he analysed FOWT is
es ima ed and compa ed o CF alues p esen ed in ela ed s udies in he
li e a u e. A cohe en CF alue shall alida e he en i onmen al da a
conside ed, as well as he conduc ed powe p oduc ion calcula ions.
Ene gy Con e sion and Managemen 271 (2022) 116303
6
A. Saenz-Agui e e al.
Fig. 4. Iden i ica ion o clus e s. Agglome a ion ee ob ained a e execu ion o Wa d’s algo i hm.
2.3.3. Es ima ion o a igue mechanical loads
The es ima ion o he a igue mechanical damage in he main com-
ponen s o he wind u bine is accomplished by pos -p ocessing o
OpenFAST simula ion esul s using so wa e ool MLi e [41]. The ap-
plica ion o his ool o he calcula ion o a igue mechanical loads
associa ed o ac i e con ol s a egies in a HAWT [42] o o de e mine
mechanical sho - e m a ec ion o oceanic wa es in he owe o a
FOWT [43] can be ound in he li e a u e.
Fa igue damage es ima ion is undamen ally based on he calcu-
la ion o mechanical loads in he ime domain, he applica ion o a
ain low coun ing algo i hm o de e mine he numbe o cycles and
a la e cumula i e damage calcula ion based on he S-N cu e co e-
sponding o he ma e ial o he mechanical componen [44]. In his
case, as i is p esen ed in Fig. 5, he mechanical loads in he ime
domain a e ob ained h ough simula ion o DLC 1.2 cases conside ing
he 20 clus e s ob ained in Sec ion 2.3.1 and using OpenFAST ame-
wo k, see Sec ion 3.2. Again, acco ding o he s anda d IEC 61400-3,
he leng h o he simula ion has been se o 10 min and 10 di e en
NTM wind speed seeds a e simula ed and pos -p ocessed, in o de o
educe a iabili y o he ob ained esul s.
The lis o mechanical bending momen elemen s selec ed o a igue
pos -p ocessing, as well as a b ie desc ip ion o each o hem, is p e-
sen ed in Table 3. These elemen s a e a e lec ion o he mos impo an
mechanical momen s in he co e componen s o a HAWT, i.e. owe ,
LSS and blades, and shall he e o e be used as pe o mance indica o s
o he main subsys ems in a HAWT. Same pe o mance indica o s
a e used in simila mechanical a igue loads es ima ion s udies in he
li e a u e [45].
Ma e ial exponen s 𝑚selec ed o he calcula ion o he a igue
damage (in a ime ho izon o 30 yea s) a e 3,4,5 o he owe and he
LSS and 8,10,12 o he blades. This selec ion esponds o he ma e ial
o each componen , s eel o he owe and he LSS and composi e o
he blades [45].
Finally, MLi e weigh s he a igue Damage Equi alen Load (DEL)
o each bending momen elemen by he s a is ical e ms gi en by he
Weibull dis ibu ion and i s cha ac e is ic pa ame e s, scale 𝑘and o m
𝑐, which de e mine he equency o occu ence o each wind speed
bin in e al [27]. In case o onsho e wind u bines, he p obabili y o
Table 3
Lis o bending momen elemen s selec ed o a igue pos -p ocessing, named a e hei
abb e ia ions in OpenFAST.
Name Desc ip ion Uni
Roo Mxb1 Edgewise bending momen a he blade oo [kN m]
Roo Myb1 Flapwise bending momen a he blade oo [kN m]
Roo Mzb1 Pi ch bending momen a he blade oo [kN m]
Ro To q Ro o o que, cons an along he LSS [kN m]
LSSGagMya Ro a ing y-axis bending momen a he LSS s ain gage [kN m]
LSSGagMza Ro a ing z-axis bending momen a he LSS s ain gage [kN m]
Tw BsMx Side-side (o oll) bending momen a he owe base [kN m]
Tw BsMy Fo e-a (o pi ch) bending momen a he owe base [kN m]
Tw BsMz To sional (o yaw) bending momen a he owe base [kN m]
occu ence o he wind migh su ice o he long- e m a igue damage
calcula ion. Ne e heless, o o sho e wind u bines, he s a is ical
dis ibu ion o he sea s a es mus also be conside ed in o de o achie e
eliable esul s.
On accoun o he es ic ions o conside he s a is ical dis ibu ion
o he sea s a es in he MLi e pos -p ocessing, he a igue DEL calcula-
ion is done in wo s eps. Fo ha , he p obabili y o occu ence o each
clus e wind speed 𝑃𝑈is compu ed conside ing he 95% con idence
in e al o i s cen oid, i.e. 𝑈90𝜖[𝑈90,𝑞05, 𝑈90,𝑞95], as i is shown in
Eq. (4).
𝑃𝑈,𝑖 =𝑒−( 𝑈𝑞05,𝑖
𝑐)𝑘−𝑒−( 𝑈𝑞95,𝑖
𝑐)𝑘(4)
whe e 𝑁 e e s o he o al numbe o clus e s and 𝑖𝜖 {1,…, 𝑁}.
In he i s s ep, he scale and o m ac o s a e de ined wi h hei
s anda d alue, 𝑘= 2 and 𝑐= 6 m∕s, and he s anda d p obabili y o
occu ence 𝑃𝑠𝑡 is calcula ed. Howe e , he eal s a is ical con ibu ion
o each clus e 𝑖is p o ided by i s p obabili y o occu ence 𝑃𝑐, which
is shown in he las column in Table 4. The e o e, he o iginal a igue
DEL alues p o ided by MLi e a e no malized by 𝑃𝑠𝑡 and e-weigh ed
by 𝑃𝑐, which al eady conside s he s a is ical dis ibu ion o 𝑈90,𝑈𝑑𝑖𝑟,
𝐻𝑠,𝐻𝑠𝑑𝑖𝑟 and 𝑇𝑝 o each clus e . This p ocedu e gi es he inal a igue
DEL alue by he ponde ed con ibu ions o all clus e s, see Eq. (5).
Ene gy Con e sion and Managemen 271 (2022) 116303
7
A. Saenz-Agui e e al.
Fig. 5. Schema ic diag am o he p ocedu e o he es ima ion o he a igue mechanical damage o he FOWT.
𝐷𝐸𝐿𝑓=
𝑁
∑
𝑖=1
𝐷𝐸𝐿𝑖
𝑃𝑐,𝑖
𝑃𝑠𝑡,𝑖
(5)
whe e 𝑁 e e s o he o al numbe o clus e s and 𝑖𝜖 {1,…, 𝑁}.
3. Resul s
The esul s o he clus e analysis and he subsequen cha ac e i-
za ion o he me eo ological da a in o a educed numbe o cases is
desc ibed in Sec ion 3.1. Sec ion 3.2 shows he esul s ela ed o he
e alua ion o he powe and ene gy p oduc ion o he FOWT. Finally,
esul s co esponding o he es ima ion o he a igue mechanical loads
a e p esen ed in Sec ion 3.3.
3.1. Iden i ica ion o clus e classes
The cen oids o he clus e s desc ibed in Sec ion 2.3.1 can be
conside ed as he majo wind-sea combined s a e- ypes in which all
he obse a ions in he a ea o he analysed 30 yea s pe iod can be
g ouped. The lis o 20 clus e classes ob ained a e execu ion o he
clus e ing p ocess using Wa d’s minimum a iance me hod is p esen ed
in Table 4. All hou ly clima e obse a ions in he analysed 30 yea s
exhibi he smalles dis ance o one o his pa icula cen oids o , in
o he wo ds, belong o one o he clus e s.
As ep esen a i es o he majo wind-sea combina ions in Hywind-
Sco land o he las clima ological no mal s anda d pe iod (30 yea s,
1991–2020), he en i onmen al condi ions de ined by he clus e s in
Table 4 a e simula ed using he ae oelas ic code OpenFAST 2.6.0 in
o de o e alua e in de ail he powe p oduc ion and a igue mechanical
loads (wi h he same ime ho izon o 30 yea s) o a FOWT in such
en i onmen al condi ions.
The las column in Table 4 ep esen s he p obabili y o occu ence
o he clus e du ing he analysed 1991–2020 pe iod. This p obabili y
mus be conside ed in he es ima ion o he a igue mechanical damage,
in o de o success ully ma ch each se o en i onmen al condi ions o
hei ac ual occu ence, and compu e long- e m damage in a ealis ic
way.
3.2. E alua ion o powe and ene gy p oduc ion
As desc ibed in Sec ion 2.3.2, he e alua ion o he powe p oduc-
ion o he FOWT is based on he simula ion o DLC 1.2 cases, wi h a
Table 4
Clus e cen oids and pe cen age o occu ence.
Clus e # 𝑈90 [m/s] 𝑈𝑑𝑖𝑟 [◦]𝐻𝑠[m] 𝐻𝑠𝑑𝑖𝑟 [◦]𝑇𝑝[s] 𝑃𝑐[% o
occu ence]
1 11.2 119.8 2.2 93 7.8 6.6
2 14.9 169.6 2.3 161.1 6.5 7.1
3 6 92 1.1 167.4 8.6 0.3
4 8 181.7 0.8 153.6 4.8 10.6
5 11.9 189.1 2.7 120.3 8.8 1.4
6 7.9 249.4 0.9 254.3 4.8 4.8
7 4.7 184.8 1 97.1 8.6 10.1
8 8.7 205.1 1.4 172.8 11.5 1.1
9 13.8 223.2 2.3 187.5 6.9 4.7
10 13.8 232.2 2.1 230.5 5.9 14.5
11 7.7 232.7 1 135.9 5.9 0.98
12 10.4 225.1 1.9 54.8 8.6 0.04
13 14 252.9 2.8 297 8.1 0.3
14 12 317.6 2.2 285.6 7 9.7
15 6 125 0.9 96.4 5.5 9.6
16 12.5 200 2.9 57.4 9.4 4.5
17 7 304.1 1.2 153.2 6.5 1.4
18 14.7 300.2 3 225 8.3 0.1
19 8.7 82.2 2.2 85.2 8.5 2.6
20 7.1 241.6 1.7 192.7 11.3 9.5
simula ion ime o 600 s. A e ha , he p oduced powe and gene al
ope a ion a iables o he FOWT a all se o en i onmen al condi ions
de ined in 3.1 can be analysed. Addi ionally, in o de o assess he
e ec o he wa es on he ope a ion and powe p oduc ion o he wind
u bine, he ope a ion o he same FOWT ha e been simula ed a s ill
wa e s a e, bu conside ing he same wind condi ion o each clus e .
No e ha o all 20 clus e s 10 di e en u bulen wind speed seeds
ha e been simula ed, in o de o educe a iabili y o he esul s and
inc ease obus ness o he conclusions.
The negligible a ec ion o he wa es on he powe p oduc ion and
o e all ope a ion o he FOWT is shown in Fig. 6. Fo ha , he ollowing
simula ion cases a e shown:
•Wind condi ions in clus e 1, u bulen seed 1 and s ill wa e
(s aigh blue line).
•Wind and wa e condi ions in clus e 1, u bulen seed 1 (dashed
yellow line).
•Wind condi ions in clus e 1, u bulen seed 3 and s ill wa e
(s aigh pu ple line).
Ene gy Con e sion and Managemen 271 (2022) 116303
8
A. Saenz-Agui e e al.
Fig. 6. OpenFAST based ime-domain ope a ion and powe p oduc ion o he FOWT in a ious en i onmen al condi ions.
•Wind and wa e condi ions in clus e 1, u bulen seed 3 (dashed
o ange line).
Besides wind speed and ins an aneous wa e ele a ion, o o speed,
pi ch angle and elec ical powe a e analysed as majo ep esen a i es
o he ope a ion o he wind u bine. While elec ical powe p oduc ion
is usually he inal and mos -widely analysed concep , as i de ines
Annual Ene gy P oduc ion (AEP), o o speed and pi ch angle a e
necessa y o e alua e he co ec ope a ion o he wind u bine and
in e p e he ins an aneous elec ical powe p oduc ion alue.
The simula ion esul s show ha he ope a ion o he wind u bine
is no ema kably al e ed by he in e ac ion wi h he wa es, as he e
is no ob ious di e ence in any o he ope a ional a iables, including
elec ical powe p oduc ion. In addi ion, he conclusion is alid o bo h
u bulen wind speed seeds ha ha e been ep esen ed in Fig. 6, which
in e s ha i is no an isola ed coincidence.
Howe e , in o de o demons a e he gene al alidi y o he conclu-
sions, he de ia ion (in [%]) be ween he elec ical powe p oduc ion in
case o s ill wa e and in case o in e ac ion wi h wa es is ep esen ed in
Fig. 7, o each clus e and each u bulen wind speed seed. Finally, he
s a is ical mean de ia ion alue o each one o he clus e s is calcula ed
and ep esen ed using he dashed black line.
I is o be obse ed ha he mean de ia ion in he elec ical powe
p oduc ion does no exceed 0.2% in any o he clus e s, which migh
e en be a ec ed by simula ion unce ain ies o he ae oelas ic code
OpenFAST. Hence, in ligh o he lack o a pa e n ha explains a
sys ema ical powe loss due o he in e ac ion o he FOWT wi h he
wa es, i can be concluded ha he e will be no e ec o Hywind-
Sco land wa es on he AEP o he FOWTs.
The e o e, con en ional Weibull dis ibu ion based calcula ions can
be used o he es ima ion o he ene gy gene a ion o a FOWT ins alled
in Hywind-Sco land wind a m and du ing he s udied clima e pe iod
(1991–2020). Those calcula ions can be summa ized as a i ing o he
scale and o m (𝑘and 𝑐) pa ame e s ela ed o he Weibull dis ibu ion
o ma ch he 30 yea wind speed da a, and a la e implemen a ion o
he powe cu e o he FOWT on he i ed his og am o es ima e i s
ene gy p oduc ion. No e ha , in his case, he powe cu e o he FOWT
has been calcula ed using he same simula ion en i onmen desc ibed
in Sec ion 2.2.2 and conside ing 10 di e en u bulen wind speed
seeds o educe a iabili y. The esul s o he i ing p ocedu e on he
his og am ( he alues o he Weibull pa ame e s), he AEP and he
co esponding CF a e shown in Fig. 8.
3.3. Es ima ion o a igue mechanical loads
In addi ion o he powe p oduc ion o he FOWT, he a igue
mechanical damage in i s main componen s ha e also been calcula ed
and e alua ed. In con as o he elec ical powe p oduc ion, which
ha e been obse ed o emain in a iable, he a igue damage in some o
he mechanical componen s o he wind u bine, especially he owe ,
is expec ed o inc ease as a esul o he hyd odynamic in e ac ion wi h
he oceanic wa es.
As desc ibed in Sec ion 2.3.3, DLC 1.2 cases, wi h a simula ion
ime o 600 s, ha e simula ed o calcula e he ime-domain mechanical
loads necessa y o he es ima ion o he a igue damage o he main
mechanical componen s o he wind u bine. Addi ionally, in o de o
assess he e ec o he wa es on he a igue damage o he wind u bine,
he ope a ion o he same FOWT ha e been simula ed a s ill wa e
s a e, bu conside ing he same wind condi ion o each clus e . Again,
no e ha o all 20 clus e s 10 di e en u bulen wind speed seeds
ha e been simula ed, in o de o educe a iabili y o he esul s and
inc ease obus ness o he conclusions.
A p elimina y analysis o he expec ed a igue mechanical damage
on he wind u bine componen s can be pe o med using he ime-
domain bending momen s p esen ed in Fig. 9. Fo ha , he ollowing
simula ion cases a e shown:
•Wind condi ions in clus e 1, u bulen seed 1 and s ill wa e
(o ange line).
•Wind and wa e condi ions in clus e 1, u bulen seed 1 (blue
line).
I is o be obse ed in Fig. 9 ha he owe side-side is he mos
hea ily a ec ed bending momen due o he hyd odynamic exci a ion
exe ed by he oceanic wa es. In ac , he a ec ion o he wa es on
he blade edgewise bending momen and he o o o que is limi ed,
as no in eg al di e ences be ween he simula ions wi h s ill wa e and
wa es a e de ec ed. Thus, he expec a ion is o no ice ema kable a-
igue damage inc emen p incipally in he owe base bending momen
elemen s.
The equi alen a igue DELs h ough he clima ological pe iod
1991–2020, o bo h s ill wa e and wa e condi ions, a e p esen ed in
Table 5.
Ene gy Con e sion and Managemen 271 (2022) 116303
9
A. Saenz-Agui e e al.
Fig. 7. De ia ion (in [%]) be ween he elec ical powe p oduc ion o he FOWT in case o s ill wa e and conside ing he wa es.
Fig. 8. Weibull i ing and es ima ed ene gy p oduc ion o a FOWT in Hywind-Sco land
du ing he ime pe iod 1991–2020.
Fu he mo e, in o de o acili a e he compa ison and he e alu-
a ion o he a ec ion o he oceanic wa es on he a igue damage o
each one o he componen s, he ela i e inc emen s (in [%]) o each
bending momen a e p esen ed in Table 6.
The la ges ela i e inc emen alues in Table 6 a e highligh ed
in ed, he in ensi y o he colou being p opo ional o he alue o
he inc emen . The esul s suppo he expec ed p emises, as he main
inc emen s a e obse ed in he owe side-side and o e-a bending
momen s, which was o be expec ed a e he p elimina y analysis o
he ime-domain bending momen s p esen ed in Fig. 9. The ela i e
inc emen o he DEL o he es o he bending momen s is negligible,
as such small alues could e en be conside ed o be due o simula ion
unce ain ies.
Fa igue mechanical loads a e hea ily dependen on he cha ac e is-
ics o he wind u bine, he en i onmen al condi ions and he DLCs
conside ed. The e o e, e en hough he ob ained esul s a e ha dly
compa able in absence o ce ain y o iden ical condi ions ha ing been
conside ed in he inpu da a, he simila DEL alues p esen ed in [46]
in calcula ions wi h he same wind u bine shall se e o he alida ion
o he p esen ed esul s. O he s udies in which quad a u e ule ech-
niques a e applied o he a igue load calcula ions [47] also p esen ed
consis en al hough no iden ical esul s.
Table 5
30 yea equi alen a igue mechanical DELs ([kN m]). S ill wa e in black and wa es
conside a ion in blue.
30 yea a igue DELs [kN m]. S ill wa e Wa es
3 4 5 8 10 12
Roo Mxb1 3115.61 3265.20 3376.46
3119.18 3267.48 3377.07
Roo Myb1 2455.86 2762.41 3009.19
2463.14 2775.85 3020.05
Roo Mzb1 49.31 53.71 57.20
49.52 53.95 57.49
Ro To q 208.85 278.45 346.07
210.14 279.92 347.38
LSSGagMya 1679.93 1986.60 2232.31
1681.39 1990.51 2235.15
LSSGagMza 1678.62 1985.89 2225.21
1678.63 1986.65 2224.72
Tw BsMx 2477.95 3029.79 3542.40
6151.60 7542.50 8682.42
Tw BsMy 12 651.56 16 961.72 20 561.73
13 675.49 18 281.12 22 114.09
Tw BsMz 985.59 1135.88 1294.02
986.43 1141.13 1298.43
Table 6
Rela i e inc emen (in [%]) o a igue mechanical DELs due o hyd odynamic
in e ac ion o he FOWT wi h he oceanic wa es.
Compa ison o 30 yea a igue DELs [%]
3 4 5 8 10 12
Roo Mxb1 0.11 0.07 0.02
Roo Myb1 0.30 0.49 0.36
Roo Mzb1 0.44 0.45 0.51
Ro To q 0.61 0.53 0.38
LSSGagMya 0.09 0.20 0.13
LSSGagMza 0.00 0.04 -0.02
Tw BsMx 148.25 148.94 145.10
Tw BsMy 8.09 7.78 7.55
Tw BsMz 0.08 0.46 0.34
4. Discussion
The me hodology p esen ed in his pape educes he compu a ional
cos and simpli ies he es ima ion p ocess o ene gy p oduc ion and
a igue mechanical damage o FOWTs, e en hough he complexi y o
he p oblem is inc emen ed by in oducing new ocean- ela ed a iables,
such as wa e heigh , pe iod and di ec ion, which a e unaccoun able
in case o onsho e wind u bines. This is accomplished by execu ion
