Ene gy Con e sion and Managemen : X 23 (2024) 100650
A ailable online 22 June 2024
2590-1745/© 2024 The Au ho (s). Published by Else ie L d. This is an open access a icle unde he CC BY-NC license (h p://c ea i ecommons.o g/licenses/by-
nc/4.0/).
A bi-le el mode decomposi ion amewo k o mul i-s ep wind powe
o ecas ing using deep neu al ne wo k
★
Jingxuan Wu
a
,
*
, Shu ing Li
b
,
**
, Juan C. Vasquez
a
, Josep M. Gue e o
a
,
b
,
c
a
Aalbo g Uni e si y, Pon oppidans aede 111, Aalbo g 9220, Denma k
b
Ba celonaTech (UPC), Ba celona Eas School o Enginee ing (EEBE), Ba celona 08019, Spain
c
Ca alan Ins i u ion o Resea ch and Ad anced S udies (ICREA), Pg. Lluís Companys 23, Ba celona 08010, Spain
ARTICLE INFO
Keywo ds:
BiLSTM
Deep lea ning
Mode decomposi ion
Wind powe p edic ion
ABSTRACT
The p opo ion o wind ene gy in global ene gy s uc u e is g owing apidly, p omo ing he de elopmen o wind
powe o ecas ing (WPF) echnologies o sol e he unce ain y and in e mi ence o wind powe gene a ion.
Howe e , he nonlinea and s ochas ic ea u es o wind powe ime se ies es ain he accu acy o mul i-s ep
p edic ion pe o mance. A mul i-s ep WPF (MS-WPF) app oach based on a ime se ies bi-le el empi ical mode
decomposi ion (BLEMD) me hod and BiLSTM neu al ne wo k is p oposed in his pape o imp o e he WPF
accu acy o egional wind powe gene a o s. Since he unce ain y is always gene a ed h ough coupled ac o s
om bo h wind and wea he - o-powe con e sion, he linea i y ea u e is i s in oduced as an aspec apa om
he equency in he p oposed app oach o decompose he wind powe ime sequence da a. The p oposed BLEMD
in oduces Pea son p oduc -momen co ela ion coe icien o e alua e he linea i y o ime se ies and a linea i y-
based decomposi ion algo i hm is designed acco dingly. To u he enhance he p ecision and elease compu-
a ion bu dens, a DL-based p edic ion s a egy, including a BiLSTM ne wo k, a CNN-BiLSTM ne wo k, and a
mean weigh es ima ion me hod a e implemen ed o p edic he componen s sepa a ely. The p oposed me hod
only elies on local da a, g ea ly educing he da a acquisi ion and compu a ion cos . The p ecision o he p o-
posed MS-WPF is e i ied by a 2.5 kW wind u bine wi h ho izons om 5 s o 30 s, a 1.5 MW wind u bine wi h
ho izons om 10 min o 1 h, and a 51 MW wind a m wi h ho izons om 1 h o 6 h. The compa a i e expe -
imen al esul s wi h o he cu ing-edge me hods indica ed ha he p oposed MS-WPF has supe io p edic ion
accu acy and s able pe o mance o mul i-s ep p edic ion.
1. In oduc ion
Wind ene gy has eme ged as a highly sough -a e o m o enewable
ene gy due o he inc easing awa eness o en i onmen al conse a ion.
The de elopmen o wind powe gene a ion has become one o he mos
widely discussed opics a ound he wo ld. Besides he supe io i ies o
non-pollu ion and enewabili y, wind powe gene a ion p omo ing is
g ea ly es ic ed by he unce ain y and in e mi ence o wind powe .
This p oblem becomes much mo e c i ical in some pa icula small-scale
applica ions like egional Mic og id applica ions. Di e en om la ge-
scale wind a m scena ios [1], he wind in Mic og ids becomes a mo e
complex na u al phenomenon. No only wind oscilla ion, including
speed, di ec ion, and gus bu also he mechanical and elec ical pa o
he wind u bines (WTs), o ins ance, deg ada ion and ic ion o he
gene a o , ene gy con e sion, and ansmission losses, migh aise he
powe oscilla ion in Mic og id sys ems [2]. In his sense, wind powe
o ecas ing (WPF) becomes an impo an pa o ene gy managemen
s a egies o Mic og ids [3,4]. The dynamic cha ac e is ics o wind
powe and wind speed ac as chao ic ime se ies wi h high s ochas ic
ea u es, wind p edic ion is consequen ly ega ded as a complex
eg ession ask. Exis ing WPF esea ch can be classi ied in o model-
based and da a-d i en me hods.
Model-based me hods include nume ical wea he p edic ion (NWP)-
based physical me hods and pe sis ence models (PM). NWP can gi e
egional long- e m wea he o ecas s (wind speed, cloud co e , em-
pe a u e, ai p essu e, e c.) acco ding o a la ge amoun o wea he da a
★
This wo k was suppo ed in pa by he China Schola ship Council (CSC).
* Co esponding au ho .
** P incipal co esponding au ho .
E-mail add esses: [email p o ec ed] (J. Wu), [email p o ec ed] (S. Li).
Con en s lis s a ailable a ScienceDi ec
Ene gy Con e sion and Managemen : X
jou nal homepage: www.sciencedi ec .com/jou nal/ene gy-con e sion-and-managemen -x
h ps://doi.o g/10.1016/j.ecmx.2024.100650
Ene gy Con e sion and Managemen : X 23 (2024) 100650
2
[5]. I s pe o mance on WPF is highly es ic ed by he addi ional un-
ce ain y caused by he wea he - o-powe con e sion. Besides, he high
compu a ion bu den o his me hod also es ains i s applica ion on
ul a-sho - e m [6]. The pe sis ence model, on he con a y, is a
s aigh o wa d me hod. The p edic ion alue equals he la es obse -
a ion alue. The pe o mance o he pe sis ence model deg ades as he
ime ho izon ex ends. Hence, i p o ides highe accu acy in he ul a-
sho - e m o ecas and he pe o mance is limi ed in medium- e m
and long- e m p edic ion asks [7].
Da a-d i en me hods, using lagged obse a ion as inpu , ge
inc easing a en ion due o he popula i y o supe iso y con ol and
da a acquisi ion (SCADA) sys ems. Da a-d i en me hods can be di ided
in o con en ional s a is ical and machine lea ning-based ypes. The
au o eg essi e mo ing a e age (ARMA) model is o g ea impo ance in
s a is ical me hods [8], and he NWP model is u he deployed based on
he ARMA model o p o ide inpu da a [9]. The ec o au o eg essi e
(VAR) model wi h he Leas Absolu e Sh inkage and Selec ion Ope a o
is also e i ied as an e ec i e way o enhance he accu acy [10]. In-
o ma ion usion is ano he solu ion o enhance p edic ion pe o mance
by me ging mul i-sou ces da a [11]. Fo wind powe in e al p edic ion,
uzzy models [12], Ma ko chain [13], and Lo enz dis u bance sequence
[14] can be e ec i e solu ions. Howe e , he pe o mance o hese
s a is ical me hods is highly dependen on he accu acy o s a is ical
models and he non-linea i y o he inpu ime se ies will dec ease he
p edic ion accu acy [15]. The machine-lea ning-based me hod is
de eloped o sol e he nonlinea ime-se ies p oblem. Thanks o i s da a
mining and ea u e ex ac ion abili ies, i ou pe o ms s a is ical
me hods in mos cases. Since adi ional machine lea ning-based p e-
dic ion, including suppo ec o machine, decision ee, o neu al
ne wo k [16], equi es lo s o expe ience and skill o de elop shallow
models, deep lea ning (DL) [17] shows i s ad an ages in au oma ion and
high gene aliza ion e iciency [18]. Plen y o esea ch is o ganized wi h
a i icial neu al ne wo k (ANN) [19], con olu ional neu al ne wo k
(CNN) [20], au oencode [21], ecu en neu al ne wo k (RNN) [22],
e c. In DL app oaches, RNN is heo e ically designed o ime se ies
eg ession asks due o i s sequence da a memo y. Long sho - e m
memo y (LSTM), bidi ec ional LSTM (BiLSTM) and ga ed ecu en
uni s (GRU) [23,24], as a ian s o RNN, inhe i he ad an age and sol e
he exploding o g adien anishing p oblem by in oducing an ex a
o ge ga e o he memo y cell, making hem he mos e icien neu al
ne wo k a chi ec u es o ime-sequence da a o ecas ing [25]. How-
e e , he signi ican cha ac e is ic o wind, unce ain y, is s ill oo s o-
chas ic o be i ed.
In his sense, decomposi ion me hods a e deployed o spli ime-
se ies signals in o wo o mo e sub-signals and p edic hem sepa-
a ely. Empi ical mode decomposi ion (EMD), a ia ional mode
decomposi ion (VMD), wa ele decomposi ion (WD), and Fou ie
decomposi ion (FD) a e he mos common me hods o wind da a
decomposi ion. EMD spli s he ime-se ies signal acco ding o he da a
ea u e [26]. A complemen a y ensemble EMD is p oposed o decom-
pose he wind powe da a in o ou in insic mode unc ions (IMFs) [27]
and build he long- e m p edic ion wi h he sigma poin Kalman il e
and sho - e m p edic ion wi h ein o cemen lea ning. EMD can also be
used o wind speed p edic ion [28]. A s uc u ing elemen is in oduced
o ex ac ea u es om he o iginal wind speed signal. Howe e , he
main sho coming o EMD is he lack o ma hema ic heo y, which
makes his me hod highly dependen on expe ience. VMD decomposes
he o iginal signal in o se e al subse ies wi h limi ed bandwid h in he
spec al domain [29], while WD and FD do i acco ding o he equency
ea u e o he o iginal signal [30]. Based on he assump ion ha he
wind ime se ies con ain di e en equencies, hese me hods will lead
o an o e all imp o emen in o ecas ing. While conside ing he wind is
a non-s a iona y andom p ocess, decomposi ion acco ding o equency
and bandwid h migh ace he challenge o de ining a undamen al wa e
o wa ele basis.
To sol e his p oblem, his pape p oposes a mul i-s ep BiLSTM-
based WPF (MS-WPF) me hod, including a Bi-le el EMD (BLEMD) wi h
ma hema ical analysis and coope a ed DL-based p edic ion app oaches.
The main con ibu ions o his app oach can be summa ized as ollows.
1. A BLEMD conside ing bo h linea i y and equency ea u es o ime
se ies is p oposed o assign he eg ession algo i hm and compu a-
ion esou ce. The design o he BLEMD is suppo ed by igo ous
ma hema ical analysis, and a no el linea i y e alua ion me hod
based on Pea son p oduc -momen co ela ion coe icien (PCCs) is
p oposed o ex ac he linea end o he ime se ies.
2. A MS-WPF s uc u e is p oposed o handle he eg ession ask o ime
se ies componen s. The MS-WPF, including a BiLSTM ne wo k, a
CNN-BiLSTM ne wo k, and a weigh mean es ima ion (WME), p o-
ides high-p ecision o ecas ing esul s and educes he compu a ion
bu den.
3. The p oposed MS-WPF is alida ed wi h ealis ic da a om dis inc
a eas. The mul i-s ep p edic ion pe o mance is e i ied by
compa ing i wi h cu ing-edge app oaches. The esul s indica e ha
he p oposed app oach can achie e a high p edic ion accu acy.
The es o he a icle is o ganized as ollows. The amewo k o he
mul i-le el WPF me hod is p esen ed in Sec ion 2. The p oposed BLEMD
algo i hm is discussed in Sec ion 3. The s uc u e and algo i hm o he
BiLSTM ne wo k, CNN-BiLSTM ne wo k, and he p oposed WME a e
p esen ed in Sec ion 4. In Sec ion 5, he expe imen al esul s wi h h ee
dis inc scena ios a e analyzed, and he compa ison be ween he p o-
posed app oach and exis ing me hods is s udied. A conclusion is d awn
in Sec ion 6.
2. F amewo k o he p oposed MS-WPF
Due o he da a mining abili y, DL me hods always pe o m well
wi hin long- e m o sho - e m ime se ies p edic ion. BiLSTM p o ides
sa is ying accu acy due o i s memo y cell and bidi ec ional aining o
Fig. 1. S uc u e o he p oposed MS-WPF.
J. Wu e al.
Ene gy Con e sion and Managemen : X 23 (2024) 100650
3
imp o e sequence lea ning. Howe e , o sho - e m WPF, he in luence
o unce ain y migh lead o he p edic ion e o being ampli ied. The
MS-WPF app oach is p oposed o enhance he p edic ion accu acy. The
main s uc u e is shown in Fig. 1. The o line pa upda es he eg ession
model o online p edic ion wi h his o ical da a and he online pa
conduc s he mul i-s ep p edic ion in eal ime. Real- ime (RT) da a is
s o ed in a da abase o deep neu al ne wo k aining. In he o line
aining pa , he wind powe ime se ies will be no malized and
decomposed by he BLEMD. The wind powe da a will be spli in o h ee
pa allel ime se ies acco ding o equency ea u e and linea i y.
Componen 1 (C1) desc ibes he end o wind powe . Componen 2 (C2)
and Componen 3 (C3) ollow no mal dis ibu ion a ound ze o wi h
egula ed equency. The o line aining p ocess implemen s a BiLSTM
ne wo k and a CNN-BiLSTM ne wo k o C1 and C2 eg ession model
aining. Meanwhile, he dis ibu ion o C3 is analyzed o p o ide he
es ima ion pa ame e s o WME. The Mul i-s ep WPF DL Ne wo k ma ix
is he amewo k o he eg ession model, which consis s o mul iple
laye s de ined by he look-ahead s eps. The DL ne wo k ma ix will be
gene a ed by he o line aining p ocess and each laye includes wo DL
ne wo ks and a WME algo i hm o he h ee componen s. The mul i-
le el eg ession model will be upda ed in a long- e m ho izon. In he
sho - e m ho izon, RT da a would be sampled and s o ed in a da a
bu e and hen decomposed in o h ee elemen s as in he o line aining
p ocess. The mul i-le el eg ession model ou pu s he p edic ed wind
powe using he componen s and wind speed da a, inally, he esul s o
he componen s p edic ion will be combined in o he WPF ou pu .
3. P oposed BLEMD algo i hm
The unce ain y o wind powe and wind speed signi ican ly inhibi s
he WPF accu acy. In he ime se ies o wind powe sampling da a, he
unce ain y ac s like a andom e o , and he ampli ude inc eases as he
ime ho izon dec eases. This Sec ion will in oduce he BLEMD algo-
i hm o wind powe da a and analyze he equency and linea i y
ea u es o componen s.
3.1. F equency and linea i y-based BLEMD
BiLSTM ne wo k ou pe o ms o he DL me hods on ime sequence
eg ession and p edic ion, bu s ochas ic componen s migh inc ease he
non-linea i y and lead o he pe o mance deg ada ion o BiLSTM. To
es ain he in luence o s ochas ic componen s and alloca e he
compu a ion esou ce app op ia ely, he equency and linea i y-based
BLEMD is implemen ed o di ide he ime se ies in o h ee compo-
nen s, he p ocess is shown in Fig. 2.
To ex ac he unp edic able unce ain y om he wind powe da a, a
lowpass il e is deployed o spli he high- equency componen s. The
i e a ion p ocess o he il e can be desc ibed as
{LFS(n) = TS
ω
cP(n) + (1−TS
ω
c)LFS(n−1);
C3(n) = P(n) − LFS(n).
(1)
in which low- equency sequence (LFS) is he componen ex ac ed by
he il e , he P is he wind powe ime se ies, Ts ep esen s he sample
ime, and
ω
c means passband equency.
The di e ence be ween he aw signal and he ou pu LFS is he C3.
The
ω
c mus be se as high as possible o limi he ampli ude o C3 since
i s mean and s anda d de ia ion a e in e sely p opo ional o
ω
c. He e
he
ω
c is de ined acco ding o he look-ahead s eps and i should be less
han hal o he sample a e.
A e he equency decomposi ion, he ime se ies is di ided in o
wo sub-signals wi h speci ic equency cha ac e is ics, and he esidual
will be u he decomposed acco ding o he linea i y ea u es. A
Gaussian-weigh ed mo ing mean (GWMM)-based da a smoo he [31] is
deployed he e o ex ac he end o wind powe ime se ies, which is
C1, and he C2 is he emainde . The window mus be igh -aligned as
⎧
⎪
⎨
⎪
⎩
C1(n)=Σn
i=n−m+1LFS(i)wi
Σn
i=n−m+1wi
;
C2(n) = LFS(n) − C1(n).
(2)
whe e C1(n)dona es he ou pu alue o GWMM, also he C1 ime se ies,
a n h da a poin , he LFS is he low- equency sequence de ined in (1).
The wi is he weigh calcula ed by he a e age alue and s anda d de-
ia ion o he sliding window, and m is he leng h o he window. The
window leng h is he c i ical pa ame e o he GWMM, i a ec s he
linea i y o C1 and he co ela ion be ween C1 and C2. The p edic ion o
C1 and C2 will bene i om a alid choice o window leng h m.
3.2. F equency and linea i y analysis
The main pa ame e s o he p oposed BLEMD a e he
ω
c and he m,
which a e ela ed o he equency and linea i y sepa a ely. The
ω
c will
comp ess he equency o C1 and C2 in a limi ed egion, which will
g ea ly bene i he pe o mance o he deep lea ning-based p edic ion
me hod. Howe e , he ampli ude o C3 g ows as he
ω
c dec eases, so he
ω
c is se as
ω
c=1
2
α
Ts
(3)
ω
c is ela ed o he maximum obse a ion ime Ts in he aining
p ocess and he look-ahead s eps
α
. The
α
mus be smalle han he look-
ahead s ep o enhance he pe iodici y o C1 and C2 wi h a cycle ime
equal o he look-ahead ho izon. Hence, he p edic ion pe o mance o
C1 and C2 can be imp o ed. Besides, he ampli ude o C3 inc eases as
he
α
dec eases, which will gene a e inc easing andom e o s in he
p edic ion o C3. In his sense, he
α
should be as la ge as possible. By
join ly conside ing he e ec s on he wo aspec s, he
α
should be equal
o he look-ahead s ep.
Apa om he equency, linea i y is also an essen ial ea u e
a ec ing he p ecision o DL-based p edic ion me hods. Howe e , he e
a e s ill no widely accep ed linea i y e alua ion me hods, so a PCC-
based linea i y analysis is designed o guide he linea i y-based
decomposi ion. I is de ined as he PCCs be ween he aw signal and
Fig. 2. wind powe da a BLEMD p ocess.
J. Wu e al.
Ene gy Con e sion and Managemen : X 23 (2024) 100650
4
i s 2-o de polynomial eg ession i ing cu e in a sliding window. The
ma hema ical p ocedu e o he p oposed linea i y e alua ion includes
wo s eps. Fi s ly, a sliding window is ac i a ed o he local i ing. A 2-
o de polynomial i ing cu e in each window is gene a ed h ough
o dina y leas squa es. As he window mo es, a new disc e e signal wi h
he same end as he aw signal is p oduced as he linea i y e e ence.
The second s ep is calcula ing he PCCs be ween he aw da a and he
e e ence, which can be deno ed as
C1= [C1(1),C1(2),…,C1(n)]; (4)
and
C1 e =[C1 e (1),C1 e (2),…,C1 e (n)]; (5)
The linea i y l can be calcula ed by
l=Σn
i=1(C1(i)−C1)(C1 e (i)−C1 e )

Σn
i=1(C1(i) − C1)2Σn
i=1(C1 e (i)−C1 e )2
√(6)
whe e l anges in (0, 1], and he close l app oaches 1, he highe he aw
da a’s linea i y.
C2 is de ined as he emainde o he LFS a e ex ac ing C1. The
co ela ion be ween hem can be e alua ed by hei co ela ion coe i-
cien 1−2,
1−2=
Σn
i=1(C2(i)−C2)(C1(i)−C1)

Σn
i=1(C2(i) − C2)2Σn
i=1(C1(i) − C1)2
√
(7)
The ange o 1−2 is (0, 1], and he highe he 1−2, he close he
co ela ion be ween he wo elemen s.
The BLEMD could be designed based on he linea i y e alua ion l o
C1 and co ela ion coe icien 1−2 be ween C1 and C2. I is easie o he
DL me hods o ain an accu a e eg ession model wi h a linea and
highly co esponding inpu , which means highe l and 1−2. The sliding
window leng h o he smoo he is an essen ial ac o o hem. The l is
ising while he 1−2 is alling wi h he sliding window leng h inc easing.
To balance he l and 1−2, a p edic abili y coe icien
ε
is de ined as,
ε
=lΣC1+ 1−2Σ|C2|
ΣC1+ 1−2Σ|C2|(8)
he
ε
is a ma hema ical unc ion o he GWMM window leng h m, he
op imal window leng h m is he index o he maximum p edic abili y
coe icien .
m∈ [2,3,4,…]:
ε
(m)⩾
ε
(x), o ∀x∈ [2,3,4,…](9)
The p edic abili y o he ain da a will be analyzed and he op i-
mized window leng h will be igu ed ou o he BLEMD in each aining
p ocess.
4. P oposed DL-based p edic ion and e o compensa ion
s a egy
The h ee componen s o wind powe will be p edic ed sepa a ely.
The eg ession model o C1 will be gene a ed by a BiLSTM ne wo k, and
he inpu in ol es wind speed. The o ecas ing o C2 is ealized ia a
CNN-BiLSTM ne wo k o achie e be e accu acy, he inpu in ol es
wind speed and C1. The C3 is p edic ed using a WME me hod o sa e
compu a ion esou ces.
4.1. BiLSTM-based sequence o sequence DL ne wo k
The BiLSTM is a u he s uc u e based on LSTM, which is an
enhanced RNN wi h a memo y cell and a o ge ga e. The i e a ion
p ocess o LSTM, which is al eady well-known, can be summa ized as
ou s eps. Fi s ly, he o ge ga e o k h cycle is igu ed by,
(k)=
σ
(W ⋅[h(k−1),x (k)]+b )(10)
In (10), he x is he inpu ime sequence, he h is he hidden laye
s a us o LSTM,
σ
is he passing a e wi hin [0, 1], hen W will decide
which pa o he memo y and inpu sequence should be o go en.
Secondly, he memo y ga e is calcula ed,
i (k) =
σ
(Wi⋅[h(k−1),x (k)] + bi)(11)
whe e i is he memo y ga e. The 
C is he empo a y cell s a us, and he
cell s a us C could be upda ed in he hi d s ep as,

C (k)= anh(Wc⋅[h(k−1),x (k)]+bc)(12)
and
C (k)= (k)⋅C (k−1)+i (k)⋅
C (k)(13)
A e he cell s a us is upda ed, he ou pu ga e o is calcula ed, and
hen he hidden laye is upda ed as,
o (k) =
σ
(Wo⋅[h(k−1),x (k)] + bo)(14)
and
h(k) = o (k)⋅ anh(C (k)) (15)
The his o ical inpu and cell s a us will be condi ionally conside ed
du ing he i e a ion. Howe e , he e is s ill one sho coming: he e ec
o he nex cycle is no conside ed. As a esul , BiLSTM is de eloped o
sol e his p oblem. The p oposed sequence- o-sequence BiLSTM
ne wo k is es ablished based on he LSTM, as shown in Fig. 3. The inpu
sequence o he C1 ne wo k includes wo dimensions which a e wind
Fig. 3. A chi ec u e o he p oposed BiLSTM aining ne wo k.
J. Wu e al.
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5
speed and i s his o ical sequence, while he inpu sequence o he C2
ne wo k con ains one mo e dimension: C1. The BiLSTM laye has a
o wa d LSTM and a backwa d one, he hidden laye o he wo LSTM
ma ked as h and hb will be combined o achie e he imp o ed hidden
laye sequence h . Then he d op laye will dele e some cells andomly o
p e en o e i ing. The ully connec ed laye is employed o e ch he
ea u e and a e he ac i a ion o he anh Laye , ano he is deployed o
achie e he mapping be ween he hidden laye and esponses.
4.2. CNN-BiLSTM-based DL ne wo k
The C2 sequence is p edic ed h ough a CNN-BiLSTM ne wo k since
i con ains mo e mu a ions han C1. The C2 p edic ion p ocess in ol es
C1, C2, and wind speed sequences, a con olu ion il e will scan he
inpu ma ix and de ec he lead and lag o di e en sequences. The
esul is ansmi ed o he BiLSTM ne wo k o ime sequence da a
mining. The C2 sequence has limi ed equency and ollows no mal
dis ibu ion, an essen ial challenge o i s p edic ion ask is a oiding
o e - i ing. Apa om employing d op laye s in he DL ne wo k
s uc u es, he lea ning a e is se o dec ease piecewise and a alida ion
p ocess is es ablished o p e en o e - i ing p oblems.
4.3. High- equency componen es ima ion me hods
Since he C3 is s ochas ic and unp edic able, an es ima ion me hod is
designed ins ead o compensa e o he andom e o in he WPF. Based
on he wo ea u es o he C3: 1) The equency o he C3 has limi ed
abo e he pass-band equency; 2) The dis ibu ion o C3 ollows he
no mal dis ibu ion a ound ze o; he WME is designed. The p ocedu e
has h ee s eps.
S ep 1: e ch a da a window o his o ical da a wi h he leng h o nWME
and s o e i in ma ix X (So by ime in descending o de ), he es ima-
ion elemen s ma ix 
E will be calcula ed by,
{
E= [e(1),e(2),…,e(nWME −1)];
e(k)=(k+1)
μ
−Σk
i=1X(i).
(16)
whe e
μ
ep esen s he long ho izon mean.
S ep 2: The ma ix E is he absolu e es ima ion e o o each elemen
in he p e ious cycle, and he weigh ma ix W is de ined by he accu acy
o each elemen in he las i e a ion,
{E= [e(1),e(2),…,e(nWME −1)];
e(k)= |X(1)−(k+1)
μ
+Σk+1
i=2X(i)|.
(17)
⎧
⎪
⎨
⎪
⎩
W= [w(1),w(2),…,w(nWME −1)];
w(k)=ΣE−E(k)
(nWME −2)ΣE.
(18)
S ep 3: calcula e he WME ou pu as,
WME =WET(19)
Bo h he long ho izon and sho ho izon mean a e calcula ed in 
E,
and he weigh ma ix W will adjus he dynamic esponse o WME
acco dingly. The accu acy o he p oposed WME elies on he dis ibu-
ion o C3.
5. Case s udy
Compu a ional expe imen s a e implemen ed o alida e he pe -
o mance o he p oposed MS-WPF on di e en look-ahead s eps and
ho izons agains exis ing me hods. Th ee da ase s wi h di e gen sce-
na ios, lis ed in Table 1, a e u ilized o es he ad ance o he p oposed
me hod. Da a om scena io 1 comes om he eal- ime da a acquisi ion
sys em o he IoT labo a o y, Aalbo g Uni e si y, Denma k, in which a
2.5 kW WT is es ablished and analyzed in his scena io. Scena ios 2 and
3 a e ex ac ed om a public da ase om KDD Cup 2022 [9], he da a
comes om he SCADA sys em o a wind a m in China. Scena io 2 is he
ou pu powe o one single WT. Scena io 3 uses he o al wind a m
ou pu powe and a e age wind speed da a o 34 WTs. The ho izons o
he scena ios a e dis inc , om ul a-sho - e m (5s) o long- e m (1 h).
The pe sis ence model is deployed as one o he baselines o p edic ion
me hodology due o i s high pe o mance in sho - e m and ul a-sho -
e m p edic ion. The o he baselines include ARIMA [28,32], GRU [24],
CNN-BiLSTM [20,23] and WD-BiLSTM [30]. Fo all he DL-based
me hods, 80% o da a is alloca ed o aining, 1% o alida ion du -
ing he aining and 19% o es ing. Mean absolu e pe cen e o
(MAPE) and nominal oo mean squa ed e o (nRMSE) a e he wo
c i ical pa ame e s o WPF accu acy e alua ion.
MAPE =1
NΣN
i=1
yi−yi
yi(20)
in which yi is he ac ual wind powe and yi is he wind powe p edic ion.
The nRMSE is de ined by,
nRMSE =
ΣN
i=1(yi−yi)2
ΣN
i=1(yi−y)2
√(21)
y is he mean o ac ual alue. MAPE is a e y in ui i e in e p e a ion
o ela i e e o , and nRMSE is mo e sensi i e o ou lie s.
Addi ionally, he coe icien o de e mina ion, R2, is deployed o
e alua e he eg ession pe o mance, which is de ined as,
R2=1−ΣN
i=1(yi−yi)2
ΣN
i=1(yi−y)2(22)
when he R2 app oaches 1, he p edic ion is posi i ely co ela ed o he
o iginal signal. I he R2 app oaches −1, he p edic ion is nega i ely
co ela ed o he o iginal signal. R2=0 indica es ha y and y a e no
ela ed.
Table 1
Con igu a ion o he expe imen al da ase s.
Pa ame e s Scena io 1 Scena io 2 Scena io 3
Ho izon 6*5 s 6*10 min 6*1 h
Nominal powe 2.5 kW 1.5 MW 1.5 MW*34
Loca ion Denma k China China
Fig. 4. The wind powe ime se ies and ou pu componen s o BLEMD in 5-s,
10-min, and 1-h scena ios.
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5.1. 6-s ep p edic ion esul s o he p oposed MS-WPF
The pe o mance o he MS-WPF is e i ied in h ee di e en sce-
na ios wi h di e en scales and ho izons. An abla ion expe imen is
conduc ed o alida e he e ec i eness o he p oposed BLEMD. A con-
en ional EMD using he de end unc ion, which also decomposes he
o iginal signal in o h ee componen s, is deployed o coope a e wi h he
same DL amewo k.
The wind powe ime se ies aw da a should be p ep ocessed h ough
he BLEMD. The ou pu is h ee componen s wi h di e en linea i y and
complemen a y equency ea u es. The ou pu o BLEMD o MS-WPF o
he h ee scena ios is p esen ed in Fig. 4. The pa ame e s o he BLEMD
a e op imized by he me hodology p oposed in Sec ion 3. The sliding
window leng h is 39 o scena io 1, 5 o scena io 2, and 35 o scena io
3, as Fig. 4 shows, C1 has he same end as wind powe , C2 and C3
oscilla e a ound 0.
The h ee componen s a e ansmi ed o he pa allel DL ne wo ks o
ain he eg ession models, he hype pa ame e s a e p esen ed in
Table 2. The 1-s ep p edic ion esul s o he MS-WPF and he EMD-
BiLSTM o he h ee componen s a e p esen ed in Fig. 5. The p edic-
ion esul s p esen ed by he do s a e compa ed wi h he ac ual wind
powe alue in he same igu e, and he dis ance be ween he do s and
he e e ence line ep esen s he p edic ion e o . I is e iden ha he
BiLSTM and he CNN-BiLSTM ne wo k ha e sa is ying accu acy wi h he
p edic ion ask o C1 and C2. In Fig. 5(g–i), he p oposed WME me hod
also shows p omising pe o mance.
Table 2
Hype pa ame e s o he p oposed MS-WPF
Laye s BiLSTM CNN-BiLSTM
Con olu ion Laye NA C[4,1] – F[256]
BiLSTM B[128] B[256]
D op Laye 0.1 0.1
Fully connec Laye 1 F[256] F[512]
Lea n a e/D op ac o 0.005/0.5 0.005/0.5
Fig. 5. 1-s ep componen s p edic ion esul s o 5-s scena io, 10-min scena io and 1-h scena io.
J. Wu e al.
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The dis ibu ion o black do s and blue do s indica es he esul s o
he MS-WPF and he EMD-BiLSTM. In bo h decomposi ion me hods, he
gene al end o he wind powe ime se ies is ex ac ed as C1. The
p oposed BiLSTM and CNN-BiLSTM can e ec i ely es ima e he C1 and
C2. Howe e , con en ional EMD canno ensu e he equency and
linea i y ea u es o he C1 and C2, so he accu acy is es ained. The
p oposed BLEMD decomposes he wind powe ime se ies in o h ee
componen s wi h speci ic cha ac e is ics: C1 (high linea i y, low e-
quency), C2 (low linea i y, low equency), and C3 (low linea i y, high
equency). The accu acy o he wind powe end is g ea ly enhanced
i s by p edic ing he C1. The p edic ion accu acy o C2 bene i s om
he egula ed equency o C2. The ampli ude o he C3 is es ained by
he BLEMD and will ha e a limi ed e ec on o e all pe o mance.
The 6-s ep p edic ion esul s o he p oposed MS-WPF e alua ed
h ough MAPE, nRMSE, and R2 a e shown in Fig. 6. The p edic ion
p ecision deg ades as he look-ahead s ep g ows as expec ed, and he
MAPE is es ained by he p oposed me hodology. The MAPE o 1-s ep
p edic ion is below 10 %, which g ea ly bene i s om he high p eci-
sion o C1 and C2 p edic ion, as shown in Fig. 5. The in luence o C3
p edic ion e o is es ained by he low ampli ude o C3. As he look-
ahead s ep g ows, he
ω
c o equency decomposi ion mus inc ease
o achie e be e C1 and C2 p edic ion esul s. Hence he ampli ude o
Fig. 6. S a is ical p edic ion esul e alua ion o a) 5-s scena io, b) 10-min scena io, and c) 1-h scena io.
Fig. 7. Mul i-s ep p edic ion esul s o he p oposed MS-WPF and exis ing app oaches.
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C3 is ising, which leads o he educ ion o o ecas ing accu acy. The R2
indica es a good eg ession pe o mance. The p edic ion esul s ack
he ealis ic wind powe well.
The p edic ion accu acy o he 10-min scena io is he bes among
he h ee cases. Scena io 1 ep esen s he ul a-sho - e m p edic ion
which in ol es d ama ic wind dynamics. The dynamics ga he in he C3
ime se ies and di ec ly a ec he p ecision o he MS-WPF. Scena io 3 is
a long- e m p edic ion case ha indica es a long- e m ho izon. The 1-
s ep p edic ion in scena io 3 eaches an accu a e le el (MAPE =
0.056,nRMSE =0.059,R2=0,996). Howe e , he p ecision deg ades
exponen ially as he ho izon g ows due o he s ochas ic o wind.
In summa y, he p oposed MS-WPF p o ides high-pe o mance
p edic ion o wind powe in di e en scena ios and ho izons. The 1-
Table 3
Hype pa ame e s o he benchma ks
Benchma ks Hype pa ame e s
PM NA
GRU G[1024] – D op[0.1] – F[1024]
Lea n a e/D op ac o – [0.001/0.2]
CNN-BiLSTM C[4,32] – B[512] – D op[0.1] – F[512]
Lea n a e/D op ac o – [0.001/0.5]
WD-BiLSTM WD[‘db3’, 9]
B[128, 128] – D op [0.3, 0.7]
Lea n a e/D op ac o – [0.01/0.5]
ARIMA P[4] – D[0] – Q[5]
Table 4
Mul i-s ep p edic ion esul s e alua ion o p oposed MS-WPF and exis ing app oaches.
S eps S ep-1 S ep-2 S ep-3 S ep-4 S ep-5 S ep-6
Case 1 (5s) MAPE MS-WPF 0.067 0.126 0.187 0.232 0.256 0.332
PM 0.281 0.590 0.708 0.781 0.875 0.961
GRU 0.108 0.185 0.376 0.578 0.683 0.744
CNN-BiLSTM 0.152 0.300 0.547 0.734 0.790 0.801
WD-BiLSTM 0.307 0.425 0.547 0.638 0.685 0.740
ARIMA 0.234 0.430 0.712 0.928 1.072 1.169
nRMSE MS-WPF 0.110 0.215 0.312 0.361 0.407 0.451
PM 0.546 0.941 1.039 1.113 1.177 1.236
GRU 0.191 0.288 0.524 0.755 0.843 0.865
CNN-BiLSTM 0.240 0.465 0.766 0.905 0.929 0.936
WD-BiLSTM 0.488 0.630 0.719 0.781 0.819 0.848
ARIMA 0.468 0.905 1.361 1.625 1.802 1.884
R2 MS-WPF 0.987 0.953 0.902 0.869 0.834 0.797
PM 0.702 0.114 −0.079 −0.238 −0.385 −0.528
GRU 0.963 0.917 0.725 0.430 0.289 0.252
CNN-BiLSTM 0.942 0.783 0.413 0.181 0.137 0.123
WD-BiLSTM 0.762 0.602 0.482 0.389 0.329 0.280
ARIMA 0.780 0.180 −0.851 −1.639 −2.245 −2.548
Case 2 (10 min) MAPE MS-WPF 0.067 0.179 0.196 0.223 0.235 0.263
PM 0.291 0.462 0.592 0.664 0.716 0.798
GRU 0.150 0.216 0.344 0.487 0.587 0.642
CNN-BiLSTM 0.149 0.244 0.416 0.570 0.653 0.702
WD-BiLSTM 0.332 0.381 0.450 0.490 0.548 0.589
ARIMA 0.140 0.355 0.504 0.583 0.693 0.823
nRMSE MS-WPF 0.058 0.150 0.154 0.195 0.215 0.237
PM 0.272 0.445 0.561 0.644 0.711 0.767
GRU 0.108 0.163 0.283 0.401 0.468 0.501
CNN-BiLSTM 0.121 0.205 0.355 0.466 0.511 0.541
WD-BiLSTM 0.242 0.309 0.365 0.412 0.458 0.498
ARIMA 0.148 0.352 0.494 0.603 0.697 0.793
R2 MS-WPF 0.996 0.977 0.976 0.962 0.953 0.943
PM 0.925 0.801 0.684 0.584 0.493 0.411
GRU 0.988 0.973 0.919 0.839 0.780 0.749
CNN-BiLSTM 0.985 0.958 0.873 0.782 0.738 0.707
WD-BiLSTM 0.941 0.904 0.867 0.830 0.790 0.752
ARIMA 0.978 0.876 0.755 0.636 0.514 0.371
Case 3 (1 h) MAPE MS-WPF 0.056 0.120 0.163 0.204 0.276 0.437
PM 0.261 0.578 0.828 0.977 1.026 1.022
GRU 0.105 0.181 0.325 0.464 0.564 0.611
CNN-BiLSTM 0.188 0.374 0.544 0.645 0.758 0.852
WD-BiLSTM 0.232 0.330 0.416 0.501 0.574 0.637
ARIMA 0.341 0.676 0.812 0.707 0.670 0.796
nRMSE MS-WPF 0.059 0.116 0.158 0.185 0.249 0.378
PM 0.301 0.595 0.782 0.885 0.942 0.975
GRU 0.097 0.188 0.350 0.504 0.597 0.649
CNN-BiLSTM 0.184 0.353 0.493 0.565 0.619 0.676
WD-BiLSTM 0.238 0.348 0.438 0.516 0.587 0.646
ARIMA 0.300 0.602 0.708 0.636 0.613 0.674
R2 MS-WPF 0.996 0.986 0.975 0.965 0.937 0.856
PM 0.909 0.645 0.388 0.215 0.111 0.049
GRU 0.991 0.964 0.877 0.745 0.643 0.578
CNN-BiLSTM 0.966 0.875 0.756 0.679 0.616 0.541
WD-BiLSTM 0.942 0.878 0.808 0.733 0.655 0.582
ARIMA 0.909 0.637 0.498 0.595 0.623 0.544
J. Wu e al.
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s ep p edic ion e o is supp essed wi hin 7%, and he accu acy deg a-
da ion as he ho izon g ows is e ec i ely es ained by he p oposed MS-
WPF app oach. The p oposed BLEMD, which decomposes he complex
wind powe ime se ies acco ding o linea i y and equency, has a
signi ican e ec on enhancing he accu acy o he MS-WPF.
5.2. Compa ison be ween MS-WPF and exis ing app oaches
The supe io i y o he p oposed MS-WPF me hod is alida ed
h ough compa ison wi h cu ing-edge app oaches in h ee scena ios.
The p edic ion esul s o he p oposed MS-WPF and exis ing app oaches
wi h di e en p edic ion s eps a e shown in Fig. 7. The hype pa ame e s
o he DL-based p edic ion me hod in he p oposed MS-WPF a e p e-
sen ed in Table 2 and hype pa ame e s o exis ing app oaches a e lis ed
in Table 3.
The 1-s ep ahead p edic ion esul s o wo scena ios a e shown in
Fig. 7(a), (d), (g), while he 3-s ep ahead esul s a e shown in (b), (e), (h)
and he 6-s ep ahead in (c), ( ), (i). The blue cu e ep esen ing he e-
sul s o he p oposed me hod always acks he ac ual alue well, he
acking o wind powe end is p ecise, and he esponse o wind powe
co ne s is as . The accu acy o he p oposed MS-WPF deg ades in 3-s ep
and 6-s ep p edic ions due o he dec eased sensi i i y o he wind powe
dynamics. Howe e , he o e all end o he wind powe change can s ill
be e ec i ely acked. The PM esul desc ibes he cha ac e is ics o he
wind powe da ase , which is nonlinea , s ochas ic, and ha d o o ecas .
Mos o he me hods ha e p omising esul s on 1-s ep p edic ion, bu he
p ecision deg ades d ama ically. Fo 6-s ep p edic ion, mos o he
exis ing app oaches al eady lose he end o wind powe da a. The
p oposed MS-WPF ou pe o ms all he exis ing app oaches in e ec i ely
cap u ing he end o wind powe . Hence, he o e all accu acy o MS-
WPF o mul i-s ep p edic ion is he highes among he selec ed
me hods. F om he igu es, i can be ound ha DL-based me hods
handle nonlinea p edic ion asks be e han con en ional ma hema -
ical algo i hms. GRU ne wo k can e icien ly p edic wind powe e en
wi hou any decomposi ion app oaches.
I compa ing he 1-s ep p edic ion in he h ee scena ios, i can be
concluded ha he p edic ion ask can be di ided in o wo sub-
objec i es: 1) ollow he end, and 2) de ec he u ning poin . RNN-
based DL app oaches can ollow he end e y well while con en-
ional ma hema ical me hods and CNN-based DL algo i hms a e sensi-
i e o u ning poin s. The p oposed MS-WPF can e ec i ely conside
wo sub-objec i es join ly since he BLEMD has decoupled he end and
oscilla ion componen s. The end is p edic ed by a BiLSTM ne wo k, he
u ning poin is de ec ed by a CNN ne wo k, and he d ama ic oscilla ion
is compensa ed by a ma hema ical app oach. In his way, he in e ac ion
o componen s wi h di e en linea i y and equency in he DL ne wo k
aining p ocess is a oided. The objec i es o he DL ne wo ks a e
simpli ied and conc e ized.
The MAPE, nRMSE, and R2 o he mul i-s ep p edic ion me hods wi h
h ee scena ios a e p esen ed in Table 4. Gene ally, DL-based me hods
ha e highe accu acy and eg ession pe o mance compa ed o con-
en ional ma hema ical app oaches. The p oposed MS-WPF shows he
highes accu acy, and o he DL-based app oaches also show good esul s
wi h one o wo-s ep-ahead p edic ion. Howe e , wi h mo e look-ahead
s eps, mos exis ing me hods will mee a p ecision deg ada ion due o
he o e - i ing p oblem. The s ochas ic and nonlinea componen s in
he ime se ies will a ec he p edic ion o linea componen s, leading o
he algo i hm losing he o e all end o wind powe , u he dec easing
he o e all WPF accu acy. This p oblem is signi ican ly supp essed in he
p oposed MS-WPF, he in e ac ion o he linea and nonlinea compo-
nen s in he p edic ion algo i hm is decoupled by he linea i y- equency
BLEMD. The accu a e p edic ion o linea componen s (C1) ensu es he
s able pe o mance o mul i-s ep o ecas ing.
6. Conclusion
In his pape , an MS-WPF is p oposed o enhance he p edic ion ac-
cu acy o wind powe p edic ion and imp o e he pe o mance as he
look-ahead s ep g ows. The pe o mance o he p oposed me hod is
e i ied h ough h ee c oss-expe imen s. The ad ancemen o he p o-
posed MS-WPF is p o ed by compa ing i o i e con en ional me hods.
The main wo ks o he pape can be summa ized in he ollowing
aspec s.
1. An imp o ed BLEMD wi h igo ous ma hema ical analysis is
designed o wind powe ime se ies decomposi ion. Apa om
equency ea u es, a linea i y ea u e e alua ed by PCCs is p oposed
o decompose he ime se ies legi ima ely. The p oposed BLEMD
e ec i ely decouples he nonlinea and linea componen s in he
wind powe ime se ies and es ains hei in e ac ions, u he
enhancing he accu acy and s abili y o mul i-s ep o ecas ing.
2. A mul i-le el p edic ion s uc u e, including a BiLSTM-based neu al
ne wo k, a CNN-BiLSTM-based neu al ne wo k, and a WME me hod,
is es ablished o sol e he eg ession ask o s ochas ic ime se ies
while e icien ly alloca ing he compu a ion esou ce. The C1, high
linea i y and low- equency componen , is p edic ed wi h less
compu a ion esou ce; he C2, low linea i y and low- equency
componen , is sol ed by a mo e complex neu al ne wo k o ach-
ie e be e esul s; he C3, low linea i y and high- equency
componen , is compensa ed h ough he p oposed WME o elease
compu a ion bu den.
3. The p oposed MS-WPF me hod ou pe o ms he exis ing app oaches
in his pape . The p ecision eaches 93% and emains a ound 70 %
a e 6-s ep-ahead o ecas ing in all cases. The p oposed BLEMD and
DL-based mul i-s ep p edic ion me hod p o ide an essen ial e e -
ence o o ecas ing asks o ime se ies wi h a high p opo ion o
unce ain y.
CRediT au ho ship con ibu ion s a emen
Jingxuan Wu: Concep ualiza ion, Fo mal analysis, Da a cu a ion,
So wa e, In es iga ion, Valida ion, W i ing – o iginal d a . Shu ing Li:
Me hodology, Visualiza ion, W i ing – e iew & edi ing. Juan C. Vas-
quez: Resou ces, W i ing – e iew & edi ing. Josep M. Gue e o:
P ojec adminis a ion, Supe ision.
Decla a ion o compe ing in e es
The au ho s decla e ha hey ha e no known compe ing inancial
in e es s o pe sonal ela ionships ha could ha e appea ed o in luence
he wo k epo ed in his pape .
Da a a ailabili y
Da a will be made a ailable on eques .
Re e ences
[1] Li Menglin, Yang Ming, Yu Yixiao, Lee Wei Jen. A wind speed co ec ion me hod
based on modi ied hidden ma ko model o enhancing wind powe o ecas . IEEE
T ans Ind Appl 2022;58:656–66.
[2] Wang Jianzhou, Qian Yuansheng, Zhang Linyue, Wang Kang, Zhang Haipeng.
A no el wind powe o ecas ing sys em in eg a ing ime se ies e ining, nonlinea
mul i-objec i e op imized deep lea ning and linea e o co ec ion. Ene gy
Con e s. Manage. 2024;299:117818.
[3] Khodaya Mahdi, Wang Jianhui. Spa io- empo al g aph deep neu al ne wo k o
sho - e m wind speed o ecas ing. IEEE T ans Sus ain Ene gy 2019;10:670–81.
[4] Wu Jingxuan, Li Shu ing, Fu Aihui, C e ko ic Miloˇ
s, Palensky Pe e , Vasquez Juan
C, Gue e o Josep M. Hie a chical online ene gy managemen o esiden ial
mic og ids wi h hyb id hyd ogen-elec ici y s o age sys em. Appl Ene gy 2024;
363:123020.
J. Wu e al.