POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 20 |NUMBER: 4 |2022 |DECEMBER
Da a-D i en Hype pa ame e Op imized Ex eme
G adien Boos ing Machine Lea ning Model o
Sola Radia ion Fo ecas ing
Man osh KUMAR1, Kuma i NAMRATA1, Nishan KUMAR2
1Depa men o Elec ical Enginee ing, Na ional Ins i u e o Technology,
Adi yapu , 831014 Jamshedpu , Jha khand, India
2Depa men o Elec ical Enginee ing, B. K. Bi la Ins i u e o Enginee ing & Technology,
BKBIET Campus, CEERI Road, 333031 Pilani, Rajas han, India
man[email p o ec ed], [email p o ec ed], k nishan[email p o ec ed]
DOI: 10.15598/aeee. 20i4.4650
A icle his o y: Recei ed Jul 31, 2022; Re ised Sep 07, 2022; Accep ed No 23, 2022; Published Dec 31, 2022.
This is an open access a icle unde he BY-CC license.
Abs ac . The unce ain y o he non-con en ional
sou ces especially sola ene gy caused due o spa io-
empo al ac o s like empe a u e, p essu e,
ela i e humidi y e c. is con inuously dis up ing
he p oduc i i y and eliabili y o an in eg a ed
powe sys em which mo i a es he esea che o
ene gy indus y o s a egic o ecas ing solu ions o
enhance he p ope scheduling and con ol o sola
gene a ion powe plan s. Se e al s udies ha e been
ca ied ou ; bu s ill he objec i e o achie ing accu a e
o ecas ing dependen on he spa io- empo al ea u es
is no achie ed. To add ess his c i ical o ecas ing
issue in his esea ch a icle a hype pa ame ic
uning o he Ex eme G adien Boos ing (XGB)
machine lea ning model has been ca ied ou using
wo me heu is ic algo i hms: Mo h Flame Op imiza-
ion (MFO) and G ey Wol Op imiza ion (GWO).
The da ase comp ises i e yea s o me ological a -
ibu es collec ed om he Na ional Renewable Ene gy
Labo a o y (NREL) o analysis. The alida ion
o he p oposed model has been done based on he i e
s a is ical e o s: Max E o (ME), Mean Absolu e
E o (MAE), Coe icien o De e mina ion (R2),
Mean Squa e E o (MSE) and Roo Mean Squa e
E o (RMSE). The eg essi e assessmen o all h ee
models has con i med ha he XGB-MFO model ou -
pe o med he o he s as showing he highes R2sco e
o 0.9337, 0.9011, 0.8744 and lowes RMSE alues
o 76.29 W·m−2, 41.90W·m−2and 95.94W·m−2 o
Global Ho izon al I adiance (GHI), Di use Ho izon-
al I adiance (DHI) and Di ec No mal I adiance
(DNI) espec i ely which ensu es he p oposed model
implemen a ion o he p edic ion and p oduc ion
o sola powe .
Keywo ds
Ex eme G adien Boos ing, o ecas ing, G ey
Wol Op imiza ion, Mo h Flame Op imiza ion,
sola i adiance.
1. In oduc ion
1.1. Mo i a ion
The consis en a ailabili y o ene gy supply ac oss
he na ion is essen ial o a na ion’s economic p os-
pe i y [1]. Wi h he apid de elopmen o echnology
and u baniza ion [2], he need o a s able powe sup-
ply is also inc easing p opo ionally, pushing he powe
indus y o comple e shi on he Renewable Ene gy
Sou ces (RES) in he long un-in o de o ul il he is-
ing powe consump ion and educe he g eenhouse
e ec . As pe ecen In e na ional Ene gy Agency
(IEA) analysis, he amoun o ene gy p oduced ia
enewable sou ces su passed 8,000 TWh in 2021,
a eco d 500 TWh mo e han in 2020. A he same ime
hyd opowe dec eased by 15 TWh, and wind and
sola Pho o ol aic (PV) ou pu climbed by 270 TWh
and 170 TWh, espec i ely.
©2022 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 549
POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 20 |NUMBER: 4 |2022 |DECEMBER
The g ow h in wo ldwide CO2emissions in 2021
would ha e been 220 M g ea e wi hou inc eased ou -
pu om nuclea and enewable ene gy sou ces [13].
The o al ins alled and pipelined sola capaci y o
India has been shown in Fig. 1 which depic s he p o-
g essi e beha iou o he sola ene gy sys em [14].
Though he PV sys em is pa ing he pa h o clean
ene gy, i s in e mi en na u e makes i s pe o mance
highly elian on he wea he and en i onmen [15]
and [16]. Fo he s eady and secu e in eg a ion o g een
ene gy sou ces in o he p esen ene gy ne wo k accu-
a e o ecas ing echniques ha e become essen ial [17]
and [18]. Nume ical Wea he P edic ion (NWP), s a-
is ical and Machine Lea ning (ML), and image-based
me hods a e he h ee p ima y ca ego ies o sola o e-
cas ing echniques [19]. The NWP s udies he o e-
cas s o i adiance and wea he while image-based
app oaches ack and ad ec ion clouds using sky cam-
e as, sa elli e pho os, o shadow came as o an icipa e
sola i adiance. S a is ical and machine lea ning mod-
els ‘ ain’ hemsel es using pas da a and makes o e-
cas s based on new inpu a iable alues. S a is ical
and ML me hods can be used o a a ie y o ime
spans, bu hey a e mos ly used in hou ly o ecas ing
s udies. Au ho s in [20] gi e an o e iew o ends
in sola o ecas ing echniques.
This epo is o use only by au ho ised, paying subsc ibe s o BRIDGE TO INDIA Ene gy P i a e Limi ed.
Unau ho ised use, ep oduc ion, p oduc ion, dis ibu ion and ansmission o his epo is exp essly no
pe mi ed. | © BRIDGE TO INDIA Ene gy P i a e Limi ed, 2022
1
Figu e: To al ins alled and pipeline capaci y as on 31 Ma ch 2022, MW
Sou ce: BRIDGE TO INDIA esea ch, MNRE
Execu i e summa y
Q1 2022 was ano he bumpe qua e as India added 4,418 MW sola
powe capaci y, he second highes e e . Capaci y addi ion was spli
85:13:2 be ween u ili y scale, oo op sola and o -g id sola a 3,759 MW,
575 MW and 84 MW espec i ely. To al ins alled capaci y eached 56,812
MW by 31 Ma ch 2022. To al commissioned u ili y scale, oo op sola and
o - g id sola capaci y is es ima ed a 45,692 MW, 9,563 MW and 1,557
MW espec i ely.
To al p ojec pipeline – p ojec s alloca ed o p ojec de elope s and a
a ious s ages o de elopmen – s ands a 53,119 MW.
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COMMISSIONED
56,812 MW
PIPELINE
53,119 MW
Fig. 1: To al ins alled and pipelined capaci y by 31s Decembe
2021, in (MW) [2].
Se e al esea che s ha e p oposed a ious ML mod-
els wi h de aul hype pa ame ic alues which p o-
ide di e en p edic ion ou comes. In he p esen sce-
na io, he hyb idisa ion o me aheu is ic algo i hms
wi h he ML model is being ca ied ou o imp o e
he accu acy o he a ious ange o hype pa ame-
e s [21] and [22]. Al hough XGB has a conside ably
good pe o ming model, he pa ame ic sea ch is essen-
ial o he de elopmen o he basic s uc u e o any
ML model which can be pe o med by inco po a ing
he op imiza ion me hods. To add ess his hype pa a-
me ic sea ch and de elop an e ec i e ML model o
accu a e sola i adiance o ecas ing, in his esea ch
a icle he hype pa ame ic uning o he basic model
o he XGB eg esso has been pe o med by hyb idiza-
ion o he wo op imiza ion algo i hms namely mo h-
lame op imiza ion and g ey wol op imiza ion me hod
based on he 5 yea s da ase aken om NREL.
1.2. S a us Quo o Sola Fo ecas ing
Using AI
O e he las ew decades, many a emp s ha e been
made o o ecas Sola Radia ion using di e en so s
o empi ical models, such as cloudiness-based mod-
els [23], sunshine-based models [24], and hyb id models
ha es ima e global sola adia ion by inco po a ing
o he me eo ological ac o s. I has been p edic ed us-
ing ANN [25] and SVM [26] and he ecen s udies ha e
been abula ed in Tab. 1.
1.3. Con ibu ions o he Pape
The main objec i es o ou s udy a e:
1. To c ea e and analyze he XGB model o o e-
cas ing sola adia ion u ilizing web-based da a,
including.
2. To op imize he hype pa ame e s o he XGB
model using MFO and GWO algo i hms.
3. To compa e all he h ee machine lea ning models
accu acies and o ind he bes model among hem
o sola o ecas ing.
The emaining sec ion o he esea ch a icle has
been s uc u ed as ollows: Sec. 2. illus a es
he da ase used and p oposed me hodology applied
while he desc ip ion o he algo i hms inco po a ed
has been b ie ly explained in Sec. 3. Sec ion 4.
desc ibes he pe o mance me ics used o he de e mi-
na ion o he bes model and Sec. 5. b ie ly explains
he o e all esul analysis o all he ML models. Finally,
he a icle has been concluded wi h he u u e scope
in Sec. 6.
2. Me hodology
2.1. Si e Selec ion
As pe he Ci y Mayo s Founda ion, Jamshedpu , wi h
coo dina es (22◦47’33 “N, 86◦11’03 “E) is he 84 h
as es - ising ci y globally. The Indian Me eo ological
Depa men Cen e in Ranchi epo s ha Jamshedpu
was he s a e’s ho es loca ion in 2022, wi h a sco ch-
ing empe a u e o up o 43 ◦C [27]. Tempe a u es
ange om a minimum o 5 ◦C in win e o a maximum
o abou 43 ◦C in summe , and he a e age empe a-
u e o Jamshedpu is 25.7 ◦C [28].
©2022 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 550
POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 20 |NUMBER: 4 |2022 |DECEMBER
Tab. 1: Li e a u e su ey o la es sola o ecas ed me hods.
Au ho s Objec i e Solu ion
Jebli e al. [3] ML models wi h he Pea son coe icien used o p edic he eal- ime
and sho ime sola powe .
Linea Reg ession (LR), Sup-
po Vec o Reg ession model
(SVR), Random Fo es (RF),
Mul ilaye Pe cep on (MLP)
Kuma i e al. [4] An ensemble XGB-DNN me hod p oposed o he es ima ion
o he GHI on an hou ly basis
Ex eme G adien Boos ing
(XGB), Deep Neu al Ne wo k
(DNN)
T izoglou, e al. [5] Au ho s ha e applied he XGB and LSTM in associa ion wi h
he SCADA sys em o wind u bines o o ecas ing o aul s and e-
duce he ope a ion and main enance cos .
XGB, Long Sho -Te m Mem-
o y (LSTM)
Lee e al. [6] An ensemble echnique o o ecas ing he sola adia ion o a sho
du a ion used which shows mo e eliable ou pu s as compa ed o indi-
idual ML models.
Ensemble Me hod Bagged-
T ees, Boos ed-T ees, RF,
Suppo Vec o Machines
(SVM), Gaussian P ocess
Reg ession (GPR)
Massaoudi e al. [7] A S acking me hod used o combine he h ee ML models (XGB-
LGBM-MLP) o o ecas he g id load o sho du a ion.
S acking (XGB-LGBM-MLP)
Mokbal e al. [8] Ex eme G adien Boos ing C oss-Si e Sc ip ing (XGBXSS) me hod
used o de ec ing he C oss-Si e Sc ip ing a acks whe e XGB has
been applied wi h he ea u e selec ion and a ecu si e op imiza ion.
XGB, G id Sea ch
Fan e al. [9] ML models we e used o p edic he anspi a ion o daily maize and i
was concluded ha he DNN model is mo e e icien o daily maize T
es ima e.
XGB, A i icial Neu al Ne -
wo ks (ANN), DNN, SVM
Nguyen e al. [10] XGB applied o o ecas he punching shea esis ance o R/C in e io
slabs. The designed XGB model’s p edic ion accu acy o punching
shea s eng h was in es iga ed and compa ed o o he machine lea n-
ing models and empi ical models.
XGB, ANN, RF
Chia e al. [11] XGB wi h me heu is ic models i.e. MFO, Whale Op imiza ion Al-
go i hm (WOA) and Pa icle Swa m Op imiza ion (PSO) ha e been
used o e apo anspi a ion es ima ion
XGB wi h PSO, MFO, WOA
Rui Liu e al. [12] GWO has been inco po a ed wi h ML models o g oundwa e po en-
ial p edic ion.
GWO wi h RF and SVM
2.2. Da a P e-p ocessing
The me eo ological da a is in i s aw s a e and mus
be p e-p ocessed be o e i can be used. In he da a
p e-p ocessing, he e is a combina ion o he ollowing
ou p ocesses. Figu e 2 depic s he wo k low o ou
expe imen .
1. Da a Cleaning: I in ol es checking o
epea ed, duplica e, and No Applicable (NA)
en ies in he da a.
2. Da a No maliza ion: He e, all da a a iables a e
no malized o a common in e al, which is o en
be ween 0 and 1. This phase compa es he alues
o nume ous a iables.
3. Fea u e Ex ac ion: He e, only impo an ea-
u es a e picked, as including unnecessa y ea u es
inc eases da a size and slow down a o ecas ing
algo i hm’s lea ning speed and accu acy. I is
done h ough Explo a o y Da a Analysis (EDA)
p ocess.
4. Da a Spli ing: The p e-p ocessed da ase is
di ided in o es and aining se s and sen
o he o ecas ing phase.
Me ological
Da a Da a Cleaning Da a No maliza ion Fea u e Ex ac ion
Da a P ep ocessing
T ainig
Da a
Tes ing
Da a
P ep ocesssed Da a
XGB Model
MFO
GWO
Pe o macne Pa ame e s
MSEMAE
MAPERMSE
R2 Sco e
Bes ML Model
Fig. 2: Me hodology o he p oposed wo k.
©2022 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 551
POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 20 |NUMBER: 4 |2022 |DECEMBER
3. Fo ecas ing Algo i hm Used
3.1. Ex eme G adien Boos ing
(XGB) ML Model
Chen and Gues in de eloped he XGB algo i hm as
a e olu iona y implemen a ion app oach o G adien
Boos ing Machines, namely Reg ession T ees and K
Classi ica ion [29]. XGB is designed o a oid o e
i ing and op imizing compu a ion esou ces
a he same ime. Du ing he aining phase o XGB,
calcula ions a e also pe o med synch onously and
au oma ically o all he unc ions. The model’s inal
p edic ion is calcula ed as he sum o each model’s
p edic ions. The pseudo-code desc ip ion o XGB is
gi en by Algo i hm 3 and he schema ic diag am o
he XGB algo i hm is shown in Fig. 3.
)(y
ˆ
1
x
n
ii



X, y
T1TkT n
1 k
esul
Fig. 3: XGB model.
3.2. Mo h Flame Op imiza ion
(MFO)
In 2015, au ho in [30] p oposed he MFO
algo i hm, which was mo i a ed by he mi o ing
beha iou o mo hs. These mo hs employ a peculia
kind o noc u nal iangula ion known as ans e se
o ien a ion, which allows mo hs o ho e in a s aigh
line by emembe ing he s a iona y pe spec i e
pa allel o he moon. Mo hs loa in spi al pa e ns
in he la ency o an un eal sou ce o ligh ha is close
o he moon by ocusing upon he sou ce o ligh .
AM =




AM1
AM2
.
.
.
AMa





.(5)
Mo hs and lames a e wo signi ican componen s
o he MFO s uc u e. The mo hs ha ho e
in a deeply engaged, d-dimensional plane ac as sea ch
media o s. In he Mma ix, he dwelling is ese ed.
The i ness alue ele an o each mon h is subse-
quen ly s o ed in a ay AM. The size o a mo h
Algo i hm 1 Implemen a ion o XGB.
1: Inpu : Da ase D, X (Fea u es) and y (Ta ge )
loaded wi h aining labelled da a, pa ame e s (es-
ima o s, lea ning a e, maximum dep h e c.).
Ou pu : Sys em accu acy in e ms o pe o mance
me ics.
2: Ini ialize a base model wi h:
0(x) = a g min
γ
m
X
i=1
L(yi, γ)+Ω.(1)
3: while (s opping c i e ion) do
4: o = 1, + + do
5: o i= 1 o mdo
6: Compu e esidual, i :
i =−∂L (yi, (xi))
∂ (xi) − i−1
.(2)
7: end o
8: o j= 1 o J do
9: Fi he weak ee o i .
10: Compu e e ised loss unc ion:
γj = a g min
γX
xi
L(yi, −1(xi) + γ).(3)
11: Upda e model unc ion:
(x) = −1(x) +
Jm
X
j=1
γjmI(x∈Rjm).(4)
12: end o
13: end o
14: end while
15: Model i ing wi h aining da a.
16: Model alida ion wi h es ing da a.
and a lame a e he same. Mo h and lame bo h unc-
ion as pa s o he algo i hmic solu ion. Flame deno es
he mo h’s ideal posi ion, whe eas he mo h deno es
he hun ing agen . Mo hs e ol es a ound he lames
ha se e as lag h oughou he sea ch p ocess.
As a esul , bo h posi ions a e being upda ed, dec eas-
ing he likelihood ha one would be los . Acco ding
o Eq. (6), he mo h’s loca ion is upda ed.
Mj=SF (Mj, Fj),(6)
whe e Mjindica es he j h mo hs, whe eas Fj ep e-
sen s he j h lames and SF is o spi al unc ion which
is exp essed in Eq. 7.
SF (Mj, Fj) = Dj
∗eb ∗cos(2π ) + Fj,(7)
whe e, bis spi al cons an , is he a bi a y alue
(−1,1) and Djis j h mo h and j h lame Euclidean
©2022 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 552
POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 20 |NUMBER: 4 |2022 |DECEMBER
dis ance. Djis ep esen ed as Eq. (8).
Dj=|Fj−Mj|.(8)
In he ini ial s age, lames and mo hs emain o be
he exac numbe , which may educe he po en ial
o sophis ica ed solu ions o be di e se due o mo hs’
conscious choice o ndis inc loca ions in he ques
o oom o upda ing. Eq. (9) is used o upda e
he lames.
Fno = ound F−j∗F−1
i max
O.(9)
3.3. G ey Wol Op imiza ion (GWO)
GWO, modelled on he na u al hun ing ac ics o g ey
wol es is a me a-heu is ic op imiza ion echnique p o-
posed in 2014 by au ho s in [31]. E e y wol in GWO
symbolizes a sea ch agen (po en ial solu ion). GWO
classi ies he wol es in o ou ca ego ies alpha (α), be a
(β), gamma (δ) and omega (ω) by eplica ing he g ey
wol popula ion’s hie a chy. The wol es in he i s
h ee g ades co espond o he cu en h ee bes solu-
ions. The cu en h ee bes solu ions a e ep esen ed
by he wol es in he i s h ee ca ego ies (α,β,δ).
The (ω) wol es ollow he pack’s s onges wol es.
1) Enci cling
G ey wol es su ound hei p ey as pa o he hun ing
p ocess. So, he ini ial phase o he ma hema ical mod-
elling o he GWO is o su ound he a ge , which may
be exp essed by he ollowing o mulas [16] and [17].

DGW =

C·
Xp
GW ( )−
XGW ( ),(10)

XGW ( + 1) = 

Xp
GW ( )−
A·
D,(11)
whe e, 
Aand 
Ca e no ed as he coe icien ec o s
and is symbolised as he cu en i e a ions. 
XGW
signi ies g ey wol posi ion ec o and P ey’s posi-
ion ec o is indica ed by 
Xp
GW whe eas, he 
DGW
is he ec o which depends on 
Xp
GW . Compu a ion
o he coe icien ec o s 
Aand 
Ca e as ollows:

A= 2a · 1−a, (12)

C= 2 · 2,(13)
a = 2 −2i
i max ,(14)
whe e,  1and  2a e andom a iables in he in e al
[0, 1] and alues o a a e linea ly dec easing om 2 o 0
h oughou he span o i e a ions. Concisely,  1and  2
ec o s enable wol es o ex end o any loca ion. Ac-
co dingly, Eq. (13) and Eq. (14) indica es ha he g ey
wol may upda e hei posi ion inside he sea ch space
(space ci cling p ey) a any andom poin . The same
app oach could be employed in a sea ch space wi h
dimension n, whe e he g ey wol es will ci cle he bes
ou come hus a in hype -cubes o hype -sphe es.
2) Hun ing
The αusually leads he hun while he βand δmay
occasionally engage in hun ing. We pos ula e ha he
alpha (bes solu ion), be a, and del a ha e supe io in-
o ma ion abou he p obable loca ion o p ey o ma h-
ema ically imi a e he hun ing beha iou o g ey
wol es. The e o e, we ese e he i s h ee bes
esponses. Thus, o compel he o he sea ching agen ,
along wi h omegas and o upg ade hei posi ions in
acco dance wi h he s a us o he op sea ch agen s.
The below men ioned Eq. (15), Eq. (16), Eq. (17)
and Eq. (18) a e ollowed o abo e s a ed con ex :

XGW ( + 1) = 
X1
GW +
X2
GW +
X3
GW
3,(15)

X1
GW =
Xα
GW −
A1·

C1·
Xα
GW −
XGW ,(16)

X2
GW =
Xβ
GW −
A2·

C2·
Xβ
GW −
XGW ,(17)

X3
GW =
Xδ
GW −
A3·

C3·
Xδ
GW −
XGW .(18)
3) Sea ching and A acking P ey
G ey wol es p ima ily use he (α), (β), and (δ) posi-
ions o guide hei sea ch. They dispe se om one
ano he o look o p ey and hen eassemble o
a ack i . We use 
Awi h andom alues highe han
1 o less han −1 o o ce he sea ch agen o di-
e ge om he p ey o ma hema ically simula e di e -
gence. This encou ages explo a ion and enables a wide
sea ch o he GWO algo i hm. As al eady men ioned,
a e he p ey s ops mo ing, he g ey wol es a ack i
o end he hun . We lowe he alue o a o ma hema -
ically simula e app oaching he p ey. Keeping in mind
he educ ion occu ing in 
Amay also dec ease by a .
In o he espec s, a dec eases om 2 o 0 h oughou
he du a ion o i e a ions, and 
Ais a andom num-
be in he ange [2a, 2a]. 
Asea ch agen ’s u u e
posi ion may be anywhe e be ween i s p esen posi ion
and he p ey’s posi ion when andom numbe s o 
Aa e
in he ange [1, 1].
4. Pe o mance Pa ame e s
To quan i y he pe o mance and hei a ia ion
om he eal alue o he ML models, we p o ide
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Algo i hm 2 Pseudo code o GWO.
1: Inpu : Wol Popula ion (N), 
A,a, and 
C.
Ou pu : Op imal solu ion (R2).
2: Fi ness Calcula ion o sea ch agen (i.e G ey
wol es).

Xα
GW bes op imal solu ion (sea ch agen ).

Xβ
GW second bes op imal solu ion (sea ch agen ).

Xδ
GW hi d bes op imal solu ion (sea ch agen ).
3: while (i < i max)do
4: o i= 1,2,3,...N do
5: Upda e cu en posi ion using Eq. (18).
6: end o
7: Upda e 
A,a, and 
C.
8: Fi ness Calcula ion o sea ch agen .
9: Upda e 
Xα
GW ,
Xβ
GW and 
Xδ
GW .
10: i =i + 1.
11: end while
12: e u n 
Xα
GW .
se e al common s a is ical me ics. The di e ence
be ween he es ima ed (o an icipa ed) and ac ual
ou pu pa ame e is known as he de ia ion some-
imes e e ed o as he e o s o esidue. Fo example,
he e o o GHI can be exp essed as:
δ=GHIobs −GHIp ed .(19)
These can be used o assess he deg ee o di e -
gence and co ela ion be ween he p edic ed and ac ual
da a. Figu e 4 depic s he exp essions o o ecas ing
he e ec i eness o ML models in ou esea ch.
ME
MAE
MSE
RMSE
R2
Mean Absolu e E o helps use s
o o mula e lea ning p oblems
in o op imiza ion p oblems. I
also se es as an easy- o-
unde s and quan i iable
measu emen o e o s o
eg ession p oblems.
Mean Squa ed E o is he
a e age o he squa ed
de ia ion be ween he
obse ed and expec ed alues
ac oss all ins ances in a da a
se .
Roo Mean Squa e E o is he
s anda d de ia ion o he
esiduals (p edic ion e o s), i.e.
a measu e o how a om he
eg ession line da a poin s a e.
R-Squa ed is a s a is ical
measu e o i ha indica es
how much a ia ion o a
dependen a iable is
explained by he independen
a iable(s) in a eg ession
model.
Max E o is he absolu e
alue o he mos
signi ican di e ence
be ween a p edic ed
a iable and i s eal alue.
Whe e is obse ed alue is p edic ed alue and is mean alue.
i
y
j
y
ˆ
j
y
jj
j
ME Max y y
 
 
2
1
2
1
1
n
jj
j
n
jj
j
yy
R
yy







 
1
1n
jj
j
MAE y y
n
  

 
2
1
1n
jj
j
MSE y y
n
  

 
2
1
1n
jj
j
RMSE y y
n
  

Fig. 4: Pe o mance E alua ion pa ame e used in ou wo k.
5. Resul s and Discussion
The objec i e o he s udy is o de elop an op imized
sys em o o ecas ing sola i adiance using he XGB
model o he selec ed egion, as well as wo op imiza-
ion echniques ha e been inco po a ed o op imize
he pa ame e s o he XGB o enhance he pe o -
mance o p edic ion. Nume ous esea ch pape s ha e
been published abou he s udy o his kind o model.
Due o he complexi y o he ime se ies and he
accumula ion o o ecas ing mis akes, i is s ill di icul
o de e mine how o bes op imize he XGB model,
using he me heu is ic op imiza ion echniques o
he p edic ion o sola i adia ion.
Hence, wo hyb id model XGB-MFO and XGB-
GWO ha e been analysed o he o ecas ing pu -
pose. Ini ially he 70 % o da ase i.e., aining da a
has been used o he aining he wo hyb id models
and he unc ions buil in o he sys em a e e alua ed by
compa ing he o ecas ed esul s o he eal ou comes
based on s a is ical e o s. This alida es he ecom-
mended me hodological app oach used. On he alida-
ion da ase , which includes 30 % o he da ase , i e
e alua ion me ics MAE, MSE, RMSE, ME and R2
sco e is u ilised o de e mine he bes hype pa a-
me ic op imized model. The model wi h he lowes
e o and highes accu acy is inally no ed as he bes
p edic i e model.
I ’s c ucial o keep in mind ha he popula ion
size o each hyb id model a ies and changing his
pa ame e ’s alue will ha e an immedia e impac
on he model’s unning du a ion and abili y o iden-
i y he o e all bes solu ion. A la ge popula ion will
g ea ly leng hen he unning ime, which will make
i di icul o apply he models o enginee ing p ob-
lems, while a small popula ion would esul in uns able
i ness alues. Fi e popula ion sizes - 50, 100, 150, 200
and 500 we e used in his s udy o cons uc he wo
hyb id models.
The whole sys em has been designed using Py hon
language whe e he sys em has been ained o 3 yea s
and alida ed o he nex 1 yea i.e., 35,078 en ies
ha e been used o model aining and 4,922 en ies
applied o alida ing he model o ob ain he op imum
esul .
5.1. Pe o mance o XGB ML Model
Tab. 2: Selec ed alues o XGB Hype -pa ame e s.
Sl. No. Desc ip ion Value
1 Maximum no. o ees 100
2 Maximum dep h 5
3 Lea ning a e 0.001
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Tab. 3: Pe o mance e alua ion pa ame e s ou comes o XGB wi hou op imiza ion.
MAE MSE RMSE ME R2sco e
(W·m−2) (W·m−2) (W·m−2) (W·m−2) T ain Tes
GHI 38.144 6449.03 80.30 791.74 0.9720 0.9278
DHI 25.265 2317.48 48.14 363.31 0.9611 0.8751
DNI 50.471 9318.99 96.53 692.92 0.9189 0.8527
Gene ally subsampling happens once o e e y ee
in XGB. Inc easing he dep h o he ee makes
he model mo e complica ed and p one o o e i ing.
To p e en o e i ing, s ep size sh inking is
employed in he weigh upda e wi h he help o lea n-
ing a e. We may immedia ely ob ain he new weigh s
o he ea u es a e each boos ing s ep, and he lea n-
ing a e, he e, lowe s he weigh s o he ea u e o make
he boos ing me hod mo e conse a i e. The pa ame-
e s selec ed o he analysis he XGB model wi hou
op imiza ion has been shown in Tab. 2 whe e hype
pa ame e s has been ixed.
The e alua ion pa ame e s ob ained using he
selec ed hype pa ame ic alues ha e been abula ed
in Tab. 3 which shows he highe e o alues o DNI
han GHI and DHI while he R2sco e o GHI is app ox-
ima ely 8 % highe as compa ed o he DHI and DNI
pa ame e . The e iciency o he model can be im-
p o ed using he p ope pa ame e s o he XGB model.
To op imize he model, he ange o a ious in e -
nal pa ame e s o he XGB has been aken as shown
in Tab. 4 which will be op imized using he wo op i-
miza ion me hods i.e., MFO and GWO. The i e a ion
o bo h op imiza ion me hods has been ixed o 100
o analyse he e ec o inc easing he popula ion size.
The e alua ion pa ame e s o de e mining he e ec
o he MFO and GWO op imiza ion on he XGB
model has been shown in Tab. 5 and Tab. 6, whe e all
he i e pa ame e s o he a ge a iable GHI, DHI
and DNI ha e been calcula ed o he a ious popula-
ion size o check he bes popula ion o he na u e-
based algo i hm wi h espec o he ixed i e a ion
coun . The bes alues o each pa ame e ha e been
highligh ed in bold which shows ha he model has
been op imized as he s a is ical e o s ha e been
educed and he accu acy o he model has been
conside ably imp o ed. The g aphical ep esen a ion
o he accu acy o he XGB-MFO model o a ious
popula ion sizes has been shown in Fig. 5.
Tab. 4: Selec ed alues o XGB hype -pa ame e s.
Sl. No. Desc ip ion Uppe Lowe
bound bound
1 Maximum no. o ees 100 1000
2 Maximum dep h 5 50
3 Lea ning a e 0.001 0.1
Addi ional es ing o he no el app oach will be
necessa y o da a de i ed om wea he o ecas s.
Howe e , he model mus employ p edic ed wea he
in o ma ion o be use ul. The model would be
especially help ul o applica ions on a wide scale
(i.e., coun y, o egional scale). This is possible due
o he abili y o smoo h ou he quick change in local
me eo ological condi ions ha causes he in a-hou ly
luc ua ion in sola i adiance. La ge -scale PV ou -
pu es s in conjunc ion wi h an icipa ed wea he da a
encou age he p ope use o he p oposed model.
DNI
DHI
0.85
N=50 N=100 N=150 N=200 N=500
Popula ion size
T ain
Tes
0.9
T ain
Tes
T ain
GHI
Tes
R2 sco e
T ain
Tes
T ain
0.95
Tes
1
Fig. 5: R2sco e analysis using XGB-MFO (100 i e a ions).
5.2. Compa a i e Analysis
In his sec ion, all h ee models i.e., XGB, XGB-
MFO and XGB-GWO a e compa ed wi h he bes
pa ame e s o iden i y he well-sui ed ML model o
o ecas ing sola i adiance. The o e all bes com-
pa a i e pe o mance analysis has been ep esen ed
in Tab. 7, which shows ha he XGB-GWO has an
accu acy o 0.63 %, 2.88 % 2.48 % and XGB-MFO
has 0.53 %, 2.73 % and 2.40 % accu acy mo e han
ha o he unop imized XGB model o GHI, DHI
and DNI espec i ely. The RMSE alues ha e also been
educed by 4.98 %, 12.94 %, 0.61 % using XGB-GWO
and 4.35 %, 12.31 % and 0.30 % using XGB-MFO p e-
dic ed model o he h ee a ge pa ame e s which
clea ly signi ies he con ibu ion he me a-heu is ic
algo i hms wi h he ML models. The co esponding
popula ion sizes we e 100, 200 and 150 which shows
he impo ance o he p ope selec ion o popula ion
sizes. The bes ou comes in he able ha e been high-
ligh ed. O e all, we can s a e ha XGB-GWO ou -
pe o ms he o he wo models o he gi en da ase s
and loca ion. The compa a i e analysis has also been
ep esen ed in Fig. 6.
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Tab. 5: Pe o mance e alua ion pa ame e s ou comes o XGB-MFO.
I e a ions Popula ion MAE MSE RMSE ME R2sco e
size (W·m−2) (W·m−2) (W·m−2) (W·m−2) T ain Tes
GHI 100
50 33.8953 5947.45 77.0114 726.15 0.9611 0.9314
100 33.4033 5899.41 76.8076 738.05 0.9678 0.9328
150 32.8728 5939.38 77.0674 748.90 0.9744 0.9323
200 33.2459 5983.11 77.3505 743.24 0.9584 0.9318
500 33.2469 6023.76 77.6128 750.95 0.9514 0.9314
DHI 100
50 20.1519 1841.72 42.9153 361.75 0.9459 0.8963
100 20.0928 1834.19 42.8274 364.53 0.9384 0.8968
150 20.8935 1859.86 43.1260 361.86 0.9368 0.8953
200 20.7235 1781.66 42.2097 349.77 0.9637 0.8997
500 20.1217 1838.93 42.8827 365.12 0.9432 0.8965
DNI 100
50 48.7757 9258.24 96.2197 683.43 0.9602 0.8736
100 49.0448 9276.45 96.3143 694.41 0.9401 0.8735
150 48.9292 9262.21 96.2404 693.43 0.9498 0.8737
200 49.3427 9377.84 96.8392 699.48 0.9340 0.8721
500 49.6549 9446.23 97.1917 697.78 0.9319 0.8712
Tab. 6: Pe o mance e alua ion pa ame e s ou comes o XGB-GWO.
I e a ions Popula ion MAE MSE RMSE ME R2sco e
size (W·m−2) (W·m−2) (W·m−2) (W·m−2) T ain Tes
GHI 100
50 33.4417 5823.47 76.3117 705.48 0.9822 0.9336
100 33.0237 5821.60 76.2994 685.70 0.9884 0.9337
150 33.70866 5906.59 76.8543 739.83 0.96533 0.9327
200 32.7415 5944.24 77.0988 747.75 0.9613 0.9323
500 32.97887 5978.46 77.3205 747.09 0.9604 0.9319
DHI 100
50 19.8547 1805.28 42.4886 361.32 0.9651 0.8984
100 19.9677 1829.09 42.7679 363.31 0.9481 0.8979
150 20.74984 1843.34 42.9342 356.59 0.9441 0.8962
200 20.46198 1756.35 41.9088 352.06 0.9788 0.9011
500 20.1074 1785.00 42.2493 357.94 0.9613 0.8995
DNI 100
50 48.5425 9058.75 95.1774 673.65 0.9674 0.8739
100 48.9012 9241.05 96.1304 687.33 0.9479 0.8740
150 48.8938 9205.37 95.9446 671.52 0.9612 0.8744
200 48.9643 9244.79 96.1498 690.55 0.9434 0.8739
500 49.0030 9392.69 96.9159 692.02 0.9308 0.8719
Tab. 7: XGB models compa a i e analysis.
ML MAE MSE RMSE ME R2sco e
models (W·m−2) (W·m−2) (W·m−2) (W·m−2) T ain Tes
GHI
XGB 38.1442 6449.03 80.3058 791.74 0.9720 0.9278
XGB-MFO 33.4033 5899.41 76.8076 738.05 0.9678 0.9328
XGB-GWO 33.0237 5821.60 76.2994 685.70 0.9884 0.9337
DHI
XGB 25.2654 2317.48 48.1402 363.31 0.9611 0.8751
XGB-MFO 20.7235 1781.66 42.2097 349.77 0.9637 0.8997
XGB-GWO 20.46198 1756.35 41.9088 352.06 0.9788 0.9011
DNI
XGB 50.4714 9318.99 96.5349 692.92 0.9189 0.8527
XGB-MFO 48.9292 9262.21 96.2404 693.43 0.9498 0.8737
XGB-GWO 48.8938 9205.37 95.9446 671.52 0.9612 0.8744
XGB-GWO ( ain)
XGB-MFO ( ain)
XGB ( ain)
XGB-GWO ( es )
XGB-MFO ( es )
XGB ( es )
GHI DHI DNI GHI DHI DNI GHI DHI DNI
0.8
0.85
0.9
0.95
1
R2sco e
Fig. 6: Compa a i e analysis o all models based on R2sco e.
6. Conclusion
The p edic ion o accu a e sola i adiance is e y use-
ul o he o ecas ing o sola ene gy. The main goal
o hese echniques is o modi y he XGB’s combina ion
o hype pa ame e s using mos p ominen op imiza-
ion algo i hms, such as GWO, and MFO, o inc ease
he p edic ion accu acy which can be use ul o engi-
nee ing p ac ise. As a esul , in his s udy, he XGB-
MFO and XGB-GWO hyb id models ha e been c e-
a ed. Fi e s a is ical pa ame e s we e chosen o assess
he consis ency be ween he ac ual alue and he o e-
©2022 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 556
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cas ed alue o examine he pe o mance o each hyb id
model. An unop imized XGB model was also de el-
oped, e i ied, and ained using he NREL his o ical
da ase s o e alua e he pe o mance o he wo op i-
miza ion echniques. The expe imen al indings show
ha bo h in he aining s age and he es s age,
he wo XGB-based hyb id models pe o med much
be e han he unop imized XGB model.
The wo hyb id models’ p edic ion accu acy
exceeded 0.9 du ing es ing, pa icula ly he XGB-
GWO model ( o GHI, R2sco e: 0.9337; MSE:
5821.60; RMSE: 76.2994; ME: 685.70; MAE: 33.0237),
whose p edic ion accu acy eached 0.93 which
ensu es he p oposed model applicabili y o he
u he o ecas ing pu pose.
Au ho Con ibu ions
M.K. has collec ed and analysed he da a along
wi h compu a ion and ma hema ical modelling o
he me hodology adop ed. K.N. supe ised he p ojec
and o ma ed he manusc ip . N.K. has wo ked
in op imiza ion echnique o mula ion and assis ed
in edi ing and o mula ing he manusc ip .
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