DOI: 10.1111/jiec.13536
RESEARCH ARTICLE
Designing ci cula economy s a egies in dis ibu ed
gene a ion o small- and medium-sized en e p ises using
Mon e Ca lo simula ion
Jaime González-Domínguez1Gonzalo Sánchez-Ba oso1
F ancisco Zamo a-Polo2Jus o Ga cía-Sanz-Calcedo1
1Depa amen o de Exp esión G á ica,
Uni e sidad de Ex emadu a, Badajoz, España
2Depa amen o de Ingenie ía del Diseño,
Escuela Poli écnica Supe io , Uni e sidad de
Se illa, Se illa, España
Co espondence
Jus o Ga cía-Sanz-Calcedo, Depa amen o de
Exp esión G á ica, Uni e sidad de
Ex emadu a, A enida de El as, Badajoz,
España. Email: [email protected]
Edi o Managing Re iew: Jooyoung Pa k
Funding in o ma ion
In e eg VA España-Po ugal P og am,
G an /Awa d Numbe : 0475_LOCALCIR_4_E;
Jun a de Ex emadu a (co ounded by
Eu opean Regional De elopmen Fund),
G an /Awa d Numbe : GR21098
Abs ac
The ci cula economy (CE) s a egies in ene gy communi ies enable i ms o e i-
cien ly manage he excess o pho o ol aic ene gy hey p oduce, and he eby enhance
hei sus ainabili y. Thus, he p esen esea ch aims o compa e he economic and
inancial p o i abili y and g eenhouse gas (GHG) emissions o sha ed pho o ol aic
sel -consump ion e sus indi idual sel -consump ion in he egion o Ex emadu a
(Spain). Six i ms wi h complemen a y ene gy p o iles we e selec ed, analyzing hei
hou ly ene gy consump ion. In addi ion, he Mon e Ca lo me hod was used o gen-
e a e 30,000 simula ions, educing he unce ain y caused by he a iabili y o he
i ms’ ene gy consump ion. The esul s show ha collec i e gene a ion co e s he
ene gy needs mo e e icien ly, educing he cos o ene gy consumed by 14.38% and
gene a ing be e cos –bene i a io. They also show ha he CE s a egy o he
ene gy communi y allows i ms o ob ain a conside able educ ion o GHG emissions
associa ed wi h he pho o ol aic ene gy consumed.
KEYWORDS
ci cula economy, ene gy communi y, indus ial ecology, Mon e Ca lo, pho o ol aic ene gy, SMEs
1INTRODUCTION
The ci cula economy (CE) ep esen s a new model o p oduc ion and consump ion, lea ing a linea economy o p oduc ion, use, and disposal (López
Ruiz e al., 2020) wi h he aim o educing esou ce consump ion, was e, and minimizing en i onmen al impac (Mome e, 2020). I s inclusion in
ene gy communi ies signi ican ly a ec s he way ene gy is managed in cascades, ansi ioning owa d a collabo a i e economy (Gomes e al., 2022).
Ene gy communi ies p o ide suppo o his ene gy ansi ion. The ene gy ansi ion and he ci cula economy sha e a simila ocus on such con-
cep s as sus ainable g ow h while espec ing he en i onmen and he economy (Chen & Kim, 2019). Implemen ing ci cula economy s a egies in
ene gy communi y p ojec s could acili a e he ene gy ansi ion and enhance he o e all ci cula i y o hese ini ia i es (Mish a e al., 2022).
In his con ex , some au ho s ha e ca ied ou esea ch on ene gy-based indus ial symbiosis (F accascia e al., 2021). This s a egy is based on
educing he amoun o ene gy coming om ex e nal indus ial sys ems, allowing concomi an educ ions in en i onmen al impac (Aissani e al.,
2019) and ene gy dependence (Liu e al., 2017). Mo e speci ically, he aim is o euse he was e ma e ials and ene gies ob ained du ing di e en
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2GONZÁLEZ-DOMÍNGUEZ ET AL.
p oduc ion p ocesses, allowing ene gy cos s o be educed h ough a ci cula app oach (Shah e al., 2020). In his con ex , he e appea s he concep
o ene gy cascade models which allow he esidual ene gy o one i m o be used by ano he (Kikuchi e al., 2016). Ts e ko a e al. (2015) designed
a biogas-based dis ibu ed ene gy sys em o be eplica ed in six loca ions in o de o achie e economy o eplica ion. Li e al. (2015) de eloped
indica o s o e alua e he e iciency o indus ial symbiosis and ound ha hese s a egies imp o e he i ms’ ene gy e iciency and inancial cos s.
Howe e , mos esea ch in his a ea has ocused on he use o was e and hea o gene a e ene gy o o he i ms a he han on he use o su plus
dis ibu ed ene gy.
Dis ibu ed sola powe gene a ion (Robe s e al., 2019) inc eases sus ainabili y and con ibu es o compliance wi h new en i onmen al mea-
su es. The p oduc ion o elec ici y close o he company educes he losses associa ed wi h i s dis ibu ion (Ruiz-Rome o e al., 2013). One op ion
o he use o su plus pho o ol aic (PV) ene gy gene a ed is o sell i o he elec ici y ma ke (S a e Go e nmen , 2018, 2019). Howe e , his is a
less han op imal op ion economically and en i onmen ally. In his sense, ano he op ion is o gene a e elec ici y collec i ely in wha a e known
as ene gy communi ies which can maximize he bene i s o PV ins alla ion. In his way, collec i e dis ibu ed powe gene a ion has he po en ial
o minimize elec ici y consump ion and en i onmen al impac h ough he op imal sha ing o su plus PV ene gy. As an ins umen o collec i e
ene gy gene a ion, ene gy communi ies a e de ined in Di ec i e (EU) 2018/2001 as a legal en i y open o olun a y pa icipa ion and con olled
by s akeholde s, whose pa icipan s a e na u al pe sons, small and medium-sized en e p ises (SMEs), and local au ho i ies (Eu opean Pa liamen
and o he Council, 2018). These ini ia i es seek o p o ide he pa icipan s wi h economic, social, and en i onmen al bene i s. P e ious esea ch
has add essed he ela ionship be ween he ci cula economy and ene gy communi ies. Thus, his s a egy allows o he app op ia e use and op i-
miza ion o su plus ene gy and con ibu es o he p inciples o ci cula ene gy (Mish a e al., 2022). The e o e, collec i e dis ibu ed gene a ion
con ibu es o economic g ow h, social de elopmen , and en i onmen al esponsibili y (Pala ox-Alcan a e al., 2020).
The po en ial o dis ibu ed ene gy gene a ion has been analyzed o in di e en ypes o buildings. Yan e al. (2021) es ablished he mos
app op ia e echnology combina ions o dis ibu ed ene gy gene a ion in h ee ypes o comme cial buildings and di e en clima e zones, using
mul idisciplina y design op imiza ion (MDO). López P ol and S eininge (2020) de e mined he economic p o i abili y o pho o ol aic ins alla ions
in esiden ial, comme cial, and indus ial buildings in Spain, es ablishing he oppo uni ies o sel -consump ion o sha ed s o age. Fina e al. (2019)
e alua ed he p o i abili y o ene gy communi ies made up o mos ly esiden ial buildings in compa ison wi h he sola ene gy gene a ion o indi-
idual buildings. Li and Ma (2020) de e mined he bene i s and limi a ions o pee - o-pee (P2P) elec ici y ading in esiden ial communi ies,
analyzing he ac o s ha in luence his new o m o in e -communi y ene gy ading. The e a e p eceden s on collec i e PV powe gene a ion in
esiden ial buildings. Howe e , ew o hem a e applied o dis ibu ed PV gene a ion in a clus e o i ms.
Analyzingscien i iccon ibu ions, his esea chaims o ill hescien i icgapin hee alua iono dis ibu ed powe gene a ions a egyinSMEsin
an a ea wi h high sola adia ion. In his way, i will analyze and quan i y he p o i abili y and he educ ion o he en i onmen al impac (g eenhouse
gas[GHG]emissions)whenSMEsdecide o p oduce ene gy collec i ely. The Mon e Ca lo me hod is implemen ed in o de o educe he unce ain y
associa ed wi h he a iabili y o he i ms’ ene gy demand, inc easing he applicabili y o he esul s and allowing use ul in o ma ion o be ob ained
o he scien i ic communi y.
2METHODS
2.1 Gene al o e iew
To de elop he ene gy communi y, six SMEs om di e en economic sec o s we e selec ed. They we e loca ed close o each o he in he
Ex emadu a egion (Spain). Ex emadu a is in he wes o Spain and bo de s wi h Po ugal, a longi ude −6.15◦and la i ude 39.2◦. I has an a ea o
41,635 km2and a o al o 1,054,245 inhabi an s. Figu e 1shows he map o he egion o Ex emadu a.
Two scena ios o dis ibu ed pho o ol aic ene gy gene a ion we e conside ed o his esea ch. Each o he s eps o he me hodology,
applica ions, and scena io conside ed will be de ailed below. Figu e 2shows a low cha o each scena io in his esea ch.
The Mon e Ca lo me hod allows he inhe en unce ain y due o he a iabili y o he i ms’ ene gy demand o be educed (Monie e al., 2021)
since i gene a es a mul i ude o simula ions o hei ene gy consump ion o di e en load si ua ions: low, medium, and maximum (Díaz López,
2018). In his way, he esul s will no be a ec ed by changes in he i ms’ ene gy demand.
2.2 Fi m selec ion and acili y design
The i ms selec ed ha e o be loca ed close enough oge he o o m pa o an ene gy communi y. While he numbe o i ms ha cons i u e ha
communi y can a y, i mus be su icien o gua an ee he complemen a i y o he ene gy low du ing he hou s o pho o ol aic p oduc ion. Fi s ,
he i ms’ ene gy p o ile was d awn up based on he hou ly ene gy consump ion da a supplied di ec ly by hem. This was ollowed by he selec ion
o i ms wi h complemen a y pa e ns o ene gy consump ion o ensu e collec i e pho o ol aic sel -consump ion. Fo his pu pose, he ene gy
15309290, 0, Downloaded om h ps://onlinelib a y.wiley.com/doi/10.1111/jiec.13536 by Uni e sidad De Se illa, Wiley Online Lib a y on [26/08/2024]. See he Te ms and Condi ions (h ps://onlinelib a y.wiley.com/ e ms-and-condi ions) on Wiley Online Lib a y o ules o use; OA a icles a e go e ned by he applicable C ea i e Commons License
GONZÁLEZ-DOMÍNGUEZ ET AL.3
FIGURE 1 Map o he egion o Ex emadu a (Google, 2005).
consump ion was obse ed du ing he hou ly pe iod s udied o his esea ch which co esponded o he daily hou s in which pho o ol aic ene gy
can be gene a ed. This pe iod depends on he season o he yea and includes a pa o he o al i ms’ daily consump ion. The case analyzed in
his esea ch had six i ms o ensu e an e icien ene gy low wi hin he ene gy communi y. The selec ed i ms we e SMEs in acco dance wi h he
Eu opean Union c i e ia as hey had a size o 0 o 250 employees and a u no e o less han 50 million eu os (The Commission o he Eu opean
Communi ies, 2003). Thus, he pa icipan s o he ene gy communi y comply wi h he de ini ion o he Eu opean Di ec i e (Eu opean Pa liamen
and o he Council, 2018). Fi ms 1 and 2 we e es au an s, which all wi hin he indus ial sec o o ho el and ca e ing ac i i ies. Fi ms 3 and 4 we e
ca epai i ms, whose indus ial sec o is he sale and epai o mo o ehicles and mo o bikes. Fi m 5 deal wi h he sale o ood p oduc s and
is included in he indus ial sec o o e ail ade o ood, d inks, and obacco p oduc s in specialized es ablishmen s. Finally, i m 6 was inancial
b oke age and i s indus y sec o is inancial and insu ance ac i i ies.
Once he complemen a i y o he ene gy p o iles o he selec ed i ms was ensu ed; he mean mon hly ene gy demand o e 1 yea was quan-
i ied. To ob ain his alue, he ene gy demanded by each i m o e 3 yea s was used. In addi ion, he mon hly consump ions we e used o see he
economic and inancial iabili y o each o he scena ios. The pho o ol aic sys em was sized o co e he ene gy demand du ing he pe iod s udied.
The pa ame e s and da a used in his esea ch o calcula e he mean mon hly p oduc ion o he pho o ol aic ins alla ion a e gi en in Suppo ing
In o ma ion S2 (Appendix 1).
2.3 Scena io desc ip ion
The i s scena io consis ed o an indi idual ins alla ion o each i m so ha he excess p oduced is sold on he elec ici y ma ke h ough he
ading co po a ion, in acco dance wi h he egula o y no m (S a e Go e nmen , 2019). In o de o size he ins alla ion, each i m’s ene gy p o ile
was s udied. In his i s scena io, he ins alla ion was sized o co e a leas 50% o he ene gy demand du ing he leas a o able mon hs in he
pe iod s udied. In his way, mos o he ene gy demand was co e ed du ing he mos a o able mon hs, gene a ing ew su pluses, and ob aining a
highe p o i abili y o he PV ins alla ion. This is due o he ac ha he sale o su plus ene gy in he elec ici y ma ke does no allow he p o i o
he PV ins alla ion o be op imized.
In hesecond scena io, o op imize hepho o ol aicene gy low in he ene gycommuni y, he i mswe eg ouped oge he ollowing woc i e ia.
Fi s , he i ms we e g ouped acco ding o he complemen a i y o hei ene gy p o ile and he seasonali y o hei ene gy demand. Thus, he hou ly
ene gyp o ile and he in luenceo he seasonso heyea onene gydemandwe e analyzedino de og oup ene gycomplemen a y i ms oge he .
The second c i e ion was based on ene gy demand alues. In pa icula , he excess o PV ene gy was es ablished o i o be used by he company
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4GONZÁLEZ-DOMÍNGUEZ ET AL.
FIGURE 2 Flow cha o he wo scena ios.
wi h he highes le el o ene gy consump ion. Due o he p oximi y o he i ms, no p oximi y c i e ia we e conside ed o clus e ing. Rega ding he
pho o ol aicins alla ion in Scena io 2, i wassized o y o co e asmuch o he ene gy demando he hou ly pe iod s udied as possible,conside ing
he limi a ions o he space a ailable o he pho o ol aic ins alla ion. In con as o Scena io 1, in Scena io 2 he su pluses can be used o co e he
ene gy demand o he i ms in he clus e , esul ing in a e y cos -e ec i e al e na i e.
The pho o ol aic ene gy low be ween he i ms o Scena io 2 depends on hei ene gy consump ion du ing he hou ly pe iod s udied. Thus,
he Mon e Ca lo me hod was applied o conside he andomness o ene gy consump ion, which is essen ial o analyze he collec i e gene a ion
(Scena io 2) p ope ly. The indi idual gene a ion (Scena io 1) does no ha e his p oblem, as he e is no pho o ol aic ene gy low be ween he i ms.
2.4 Economic and inancial analysis
Aneconomic and inancials udy wasca iedou ode e mine he economicad an agesand disad an ageso he woscena ios p oposed (Almak a
e al., 2021). On he one hand, he economic s udy made i possible o calcula e an annual balance a e implemen ing he pho o ol aic ins alla ion,
o de e mine he economic sa ings o e 1 yea . In his way, he bene i s and e enues gene a ed h ough excess ene gy om indi idual gene a ion
(Scena io 1) and he elec ici y bill sa ings gene a ed by he ene gy sha ing in collec i e gene a ion (Scena io 2) we e quan i ied. On he o he hand,
he inancial iabili y s udy allowed he ad an ages and disad an ages o he in es men o be analyzed unde he wo scena ios. In Scena io 1,
he in es men made by each i m depends on he cos o each i m’s PV ins alla ion. Howe e , in Scena io 2 he cos o he dis ibu ed gene a ion
ins alla ion is sha ed among all he i ms, wi h hei sha e being p opo ional o hei ene gy demand, so ha hey sha e ene gy a no cos . Fo he
economic and inancial analysis, all cos s ela ed o he pho o ol aic ins alla ion we e conside ed, including ma e ial and human esou ces cos s.A
se ice li e o he ins alla ions o 25 yea s was conside ed (Ganesan & Valde ama, 2022). Table2lis s he main pa ame e s and cos s conside ed in
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GONZÁLEZ-DOMÍNGUEZ ET AL.5
TABLE 1 Cha ac e is ics o he i ms’ oo s.
Fi m Type
RA
(m2)
OA
(m2)
Inclina ion
(◦)
Azimu h
(◦)
1 Gabled 150 0 12 24
2Fla 609 86.8 0 9
3 Gabled 920 0 18 9
4 Gabled 945 018 7
5 Gabled 2463 267 15 −7
6 Gabled 717 121 13 7
Abb e ia ions: OA, obs acle a ea; RA, oo a ea..
TABLE 2 Main pa ame e s and cos o economic and inancial analysis.
Name Desc ip ion
Main enance cos Annual cos o 3% o he o al cos o he ins alla ion (Muñoz-Ce ón
e al., 2018)
Deg ada ion o PV p oduc ion Dec ease 0.8% each yea (Domingos & Pe ei a, 2021)
Discoun a e (k) Discoun a e o 3.4%
In e es a e 4% in e es a e on he o al in es men
Sale a e 7% o sale he ene gy o he elec ici y g id
Sola panels €128.04 (CYPE P ices Gene a o , 2021)
Adjus able suppo s €70-144.70 (CYPE P ices Gene a o , 2021)
In e e s €1985.34-4630.28 (CYPE P ices Gene a o , 2021)
his esea ch o he economic and inancial analysis.
To ca y ou hese analyses, a ious inancial a ios we e calcula ed. The ne p esen alue (NPV) allows one o de e mine he bene i s o losses
o he in es men o yea n(Pon a e al., 2018), acco ding o Equa ion (1).
NPV =−I0+
n
∑
=1
F
(1+k) (1)
whe e I0is he ini ial in es men , F is he cash lows in each pe iod ,kis he discoun a e, and nis he numbe o ime pe iods o e which he
in es men analysis is pe o med.
The in e nal a e o e u n (IRR) is an indica o o he p o i abili y o he in es men . I is de e mined when Equa ion (1) is equal o 0. The bene i
cos a io(BCR) ep esen s he bene i ob ained o eacheu ospen in he pho o ol aicins alla ion.Thisindica o is complemen a y o he NPVand
p o ides use ul in o ma ion o in es o s abou how much bene i can be ob ained wi h he economic unds spen (F ej e al., 2021). The calcula ion
o he BCR is shown in Equa ion (2) (Malka e al., 2022).
BCR =∑bene i s
∑cos =
∑n
=1
F
(1+k)
I0
(2)
whe e he ini ial in es men , I0, includes he cos s associa ed wi h he main enance o he pho o ol aic sys em. The las a io used in inancial
analysis is he payback pe iod (PP), which is he numbe o pe iods needed o eco e he ini ial capi al in es ed. Equa ion (3) shows he calcula ion
o he payback pe iod.
PP =I0
AR (3)
whe e PP is he payback pe iod, I0is he ini ial in es men made in he ins alla ion, and AR is he annual e enue ob ained by he ins alla ion. This
las pa ame e is ob ained when ca ying ou he p e ious economic analysis.
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6GONZÁLEZ-DOMÍNGUEZ ET AL.
2.5 Mon e Ca lo simula ion me hod
The Mon e Ca lo s a is ical me hod allows one o simula e a pa ame e ha is andom in na u e, aking i s beha io o be ep esen ed by ha o
a p obabili y densi y unc ion (PDF) o a andom a iable (Bel án e al., 2020). I is he eby possible o cons uc a da abase ha is la ge enough
o mi iga e he p oblems de i ing om he unce ain y o he a iables o which he s udy is sensi i e. Following he Cen al Limi Theo em, he
Mon e Ca lo me hod shows con e gence a 1
√n,whe enis he numbe o cases analyzed (Ballio & Guadagnini, 2004).
The e a e di e en a iables ha apply unce ain y o he esul s ob ained in ene gy communi y esea ch. Howe e , ene gy demand is consid-
e ed o be a a iable whose andomness signi ican ly a ec s he dis ibu ion o su plus pho o ol aic ene gy. I a ec s he ene gy low wi hin he
ene gy communi ies. Thus, he Mon e Ca lo me hod is used o gene a e a sequence o andom numbe s o simula e a ia ions in ene gy demand.
Random alues o ene gy demand will be gene a ed based on a PDF ha desc ibes he unce ain y o he a iable (Wang e al., 2022). The i ms’
ene gydemandsa e assumed o be ep esen ableasa andompa ame e ,anda emodeled usingPDFs (Uniyal& Kuma , 2018).O hemanypossible
PDFs (Weibull, no mal, be a, e c.), i is ound (Bo dba i e al., 2018) ha he unce ain y o elec ical ene gy demand ollows a no mal dis ibu ion. A
building’s ene gy consump ion can be p edic ed by assigning a sui able p obabili y dis ibu ion unc ion (Kang & Wang, 2018). I is also possible o
model his pa ame e wi h a be a dis ibu ion since i s co esponding PDF has shape and ange pa ame e s ha allow i o ep esen p ac ically any
o he PDF (Yu e al., 2018). The mean o he no mal dis ibu ion es ablishes he loca ion o he p obabili y mass unc ion, and he s anda d de ia ion
allows one o limi he ange o alues o he a iable. Equa ion (4) gi es he no mal PDF o m used in he Mon e Ca lo simula ions.
(x, m, 𝜎)(4)
whe e xis he sequence o numbe s gene a ed in he simula ions, and mis he mean and σ he s anda d de ia ion o he ene gy consump ion
(exp essed in kWh). S ochas ic Mon e Ca lo simula ions a e a sui able al e na i e o es ima ing exp essions ha do no ha e analy ical solu ions
(López-Agüí, 2008). Equa ion (5) lacks an analy ically exp essible p imi i e, so i canno be sol ed wi h analy ical me hods.
b
∫
a
(x)dx (5)
whe e xis a con inuous andom a iable dis ibu ed o e he in e al [a,b]and (x) is he no mal dis ibu ion exp essed in Equa ion (4). The solu ion
o his p oblem can be es ima ed om andom alues by de e mining which a e below he unc ion (x). Thus, Equa ion (5) can be app oxima ed by
he exp ession in Equa ion (6).
b
∫
a
(x)dx ≈N
D(b−a)M(6)
whe e Nis he numbe o andom alues below he unc ion (x),Dis he numbe o o al andom alues, (b–a) is he in e al o alues o he a iable
x, M is he heigh o a ec angle con aining all he poin s o he unc ion (x) in he in e al (b,a). Fo a no mal dis ibu ion, he alue o Mco esponds
o he mean o he PDF, as his is he highes alue o he unc ion (x).
2.6 G eenhouse gas emissions
The ma ke ’s elec ici y consump ion gene a es an en i onmen al impac ha depends on he na u e o he egion’s ene gy mix (Wil ing e al.,
2021). When he ene gy is enewable, he en i onmen al impac is ze o (Guillén-Lambea e al., 2023). The dis ibu ed gene a ion o Scena ios 1
and 2 educes he GHG emissions o he i ms since hey s op consuming ene gy om he ma ke powe g id. To calcula e he educ ion o GHG
emissions in each scena io, he o al ene gy compensa ed wi h he pho o ol aic ins alla ion is ob ained and i s en i onmen al impac is quan i ied
based on he ene gy mix o he egion. Equa ion (7) is he exp ession applied in his esea ch o ob ain he GHG emissions educ ion.
GH G educ ion =Ene gyPV ×Femission (7)
whe e GHG educ ion (exp essed in CO2eq/yea ) a e he me ic ons o CO2equi alen ha a e educed each yea due o dis ibu ed pho o ol aic
gene a ion; Ene gyPV (exp essed in kWh) is he ene gy compensa ed annually wi h pho o ol aic p oduc ion; Femission (exp essed in CO2eq/kWh)
is a ac o ha quan i ies he amoun o CO2equi alen ha is emi ed in o he a mosphe e when consuming 1 kWh in he egion o Ex emadu a.
The CO2eq is he olume o GHG emissions equi alen o 1 me ic on o CO2. Analyzing he mos impo an ene gy supplie s in he Ex emadu a
egion, 41.2% o he ene gy mix comes om enewable ene gy, 1.93% om high e iciency cogene a ion, 26.33% om na u al gas combined cycle,
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GONZÁLEZ-DOMÍNGUEZ ET AL.7
FIGURE 3 Mean elec ical ene gy consump ion pe i m. Unde lying da a a e a ailable in Table S1 o Suppo ing In o ma ion S1.
2.93% om coal, 1.13% om uel oil/gas, 21.20% om nuclea , and 5.27% om o he non- enewable sou ces. The alue o Femission is 165 ×10−6
CO2/kWh acco ding o he Na ional Commission o Ma ke s and Compe i ion (Comisión Nacional de los Me cados y la Compe encia, 2022).
3RESULTS
3.1 Scena io 1: Indi idual p oduc ion
Suppo ing In o ma ion S2 (Appendix 2) shows Figu e 3, which p esen s he mean mon hly consump ion o he six i ms. Also, a desc ip ion o
Figu e 3is gi en in ha appendix. The da a used o p oduce Figu e 3a e shown in Table S1 o Suppo ing In o ma ion S1.
The mean mon hly p oduc ion o he pho o ol aic ins alla ions was calcula ed o each company. Conside ing he da a in Table 1,Fi m1had
an ins alla ion o 30 panels, Fi m 2 o 43 panels, Fi m 3 o 61 panels, Fi m 4 o 49 panels, Fi m 5 o 246 panels, and Fi m 6 o 46 panels. This
co esponds o ins alla ions o 9.9, 15.3, 20.13, 16.17, 81.8, and 15.18 kW, espec i ely. Wi h hese alues, i is possible o de e mine he amoun o
ene gy co e ed by each i m’s ins alla ion (Figu e 4). The da a used o p oduce Figu e 4a e shown in Table S2 o Suppo ing In o ma ion S1.
F om Figu e 4, i can be in e ed ha he ene gy p oduc ion o he ins alled panels co e s app oxima ely 50% o he ene gy consumed du ing he
pe iod s udied in he leas a o able mon hs in all he companies excep Fi m 1. This is because his i m’s oo a ea does no allow mo e panels o
be ins alled, and i he e o e canno co e e en hal o he win e mon hs’ ene gy demanded. This solu ion co esponds o a scena io in which he
pho o ol aic ins alla ion is done indi idually o each i m.
3.2 Scena io 2: Collec i e p oduc ion
The g ouping o i ms in Figu e 5has been ca ied ou ollowing he c i e ia se ou in Sec ion 2. Thus, h ee g oups ha e been o med, each wi h a
pho o ol aic ins alla ion designed acco ding o i s ene gy p o ile.
These g oupings we e made based on he complemen a i y o hei ene gy p o ile, he alues o he ene gy consump ion, and he seasonali y
o hei ene gy demand. In his way, an adequa e low o su plus ene gy is achie ed. In ac , Fi ms 3, 4, and 5 had a high ene gy demand du ing he
summe season, while Fi ms 1, 2, and 6 did no p esen his beha io du ing hese mon hs. Thus, he su pluses gene a ed by Fi ms 1, 2, and 6 can be
used o co e he ene gy demand o Fi ms 3, 4, and 5, as hese i ms had a complemen a y ene gy p o ile. By analyzing he ene gy demand alues,
h ee g oups we e ob ained. G oup 1 comp ised Fi ms 2 and 3; G oup 2 comp ised Fi ms 1 and 4; and G oup 3 comp ised Fi ms 5 and 6. Finally,
i was obse ed ha Fi m 5 o G oup 3 was he one wi h he highes ene gy consump ion o all he i ms. The su pluses o each g oup we e used
by he i ms wi h he highes consump ion. In sum, Fi m 5 could use he su pluses o Fi m 6 and he o he wo g oups. The i s wo g oups had a
pho o ol aic ins alla ion wi h a peak powe o 86.79 kW, and he hi d had one o 125.07 kW peak powe . The 86.79 kW ins alla ion consis ed o
263 sola panels, and he 125.07 kW ins alla ion had 379 panels. While hese 379 panels we e ins alled on he oo s o Fi ms 5 and 6, he 86.79kW
ins alla ion equi ed no only he oo s o Fi ms 2 and 4 bu an addi ional space. This addi ional space was an a ailable plo o land nex o he clus e
and clea ed o buildings, wi h a o al o 2600 m2.
As can be seen om Figu e 3(Suppo ing In o ma ion S2), he mean mon hly ene gy demand is di e en o each o he i ms in he same g oup,
allowing he ene gy p oduced in he ins alla ions o adequa ely co e he demand. A no mal dis ibu ion was used o model he unce ain y o he
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8GONZÁLEZ-DOMÍNGUEZ ET AL.
FIGURE 4 Mon hly compa ison o mean elec ici y p oduc ion e sus mean consump ion. Unde lying da a a e a ailable in Table S2 o
Suppo ing In o ma ion S1.
ene gy demand o he i ms. A s anda d de ia ion o 25% was conside ed om he analysis o he ene gyconsump ion o he i ms unde s udy. The
mean ene gy demands conside ed o he Mon e Ca lo simula ions co esponded o he alues gi en in Figu e 3(Suppo ing In o ma ion S2). Wi h
his,30,000caseswe esimula ed oquan i y heunce ain yco esponding o hese i ms’ mon hly consump ion. The 30,000 simula ions allow he
unce ain y gene a ed by he a iabili y o ene gy demand o be educed by mo e han 150 imes, so ha he e o is signi ican ly less han 1%. Fo
hese cases, he pho o ol aic ins alla ions co e on a e age 100% o he annual ene gy consumed in he hou ly pe iod s udied by he i s ou i ms
(G oups 1 and 2). Fi ms 5 and 6 (G oup 3) co e , wi h he PV sys em, 97.38% and 76.68%, espec i ely. By sha ing he o e ages o he collec i e
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GONZÁLEZ-DOMÍNGUEZ ET AL.9
FIGURE 5 G ouping conside ed in he second scena io.
TABLE 3 Economic analysis o Scena ios 1 and 2.
Scena io 1
Economics a ios Fi m 1 Fi m 2 Fi m 3 Fi m 4 Fi m 5 Fi m 6 To al
Annual sa ings
(%)
51.8 74.6 93.64 83.93 90.8 96.05 –
Annual sa ings
(€/yea )
1965.3 2540.8 3995.5 3135.0 16,204.3 3022.6 30,863.5
Su plus ene gy
e enue (€/yea )
–61.67 26.8 12.0 129.7 106.7 336.87
Scena io 2
Economics a ios Fi m 1 Fi m 2 Fi m 3 Fi m 4 Fi m 5 Fi m 6 To al
Annual sa ings
(%)
99.81 99.81 99.81 99.81 99.81 99.81 –
Annual sa ings
(€/yea )
3795.15 3405.75 4266.51 3735.77 17,851.58 3146.71 36,201.47
Su plus ene gy
e enue (€/yea )
1132.10 1132.10 1132.10 1132.10 1132.10 1132.10 6792.6
gene a ion, 99.81% o he ene gy demand o he six i ms is co e ed. Thus, i can be obse ed ha collec i e gene a ion almos comple ely co e s
he mean ene gy demand o he hou ly pe iod s udied o all he i ms in he 30,000 Mon e Ca lo simula ions. Indeed, he main ad an age o e ed
by he g ouping o i ms o he collec i e gene a ion o sola ene gy is he use o such indi idual o e ages o co e he en i e collec i e’s ene gy
demands, hus a oiding o e -sizing he ins alla ions in o de o co e adequa ely he ene gy consumed h oughou he yea (González González
e al., 2018).
3.3 Economic analysis
As desc ibed in Sec ion 2, he economic analysis conside s ene gy consump ion, pho o ol aic ene gy p oduc ion, su pluses gene a ed, and he
ins alla ion main enance. Table 3lis s he annual sa ings on each i m’s elec ici y bill o Scena ios 1 and 2.
The pe cen age annual sa ings was e y high excep o Fi m 1 which had no oo a ea on which o place a pho o ol aic ins alla ion o g ea e
powe . The annual e enues om he o e ages o indi idual gene a ion we e low, and he pe cen age o ene gy co e ed by he six i ms was 85% o
hei ene gy demand du ing he pe iod s udied. This is consis en wi h he sizing o he ins alla ion o co e 50% o he ene gy demand du ing he
leas a o able mon hs, as 100% o he ene gy demand would be co e ed du ing he mos a o able mon hs. This co e s a la ge pa o he ene gy
consumed by he i ms wi hou gene a ing much su plus in o he mo e a o able mon hs. In his scena io, i he pe cen age o ene gy co e ed
du ing he leas a o able mon hs we e o inc ease, he p o i abili y o he ins alla ion would no inc ease. The in es men would be highe , and su -
pluses wi h a lowe economic alue would be p oduced since i s sale o he elec ici y ma ke does no gene a e a high p o i . Collec i e gene a ion
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