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A no e on lexible hyd opowe and secu i y o supply: Spain beyond 2020
Luis Mª Abadie a, José M. Chamo o b*, Sébas ien Huclin a, Di k-Jan an de Ven a
a Basque Cen e o Clima e Change (BC3), Sede Building 1, 1s loo ,
Scien i ic Campus, Uni e si y o he Basque Coun y UPV/EHU, 48940 Leioa, Spain. E-mails:
[email p o ec ed], sebas ien.huclin@bc3 esea ch.o g, [email p o ec ed]
b Uni e si y o he Basque Coun y UPV/EHU, Dp . Financial Economics II,
and Ins i u e o Public Economics, A . Lehendaka i Agui e 83, 48015 Bilbao, Spain.
E-mail: jm.chamo [email protected]
*Co esponding au ho .
Oc obe 2nd 2019
ABSTRACT
Gene a ion adequacy is a key ing edien o secu i y o elec ici y supply (SoS). Some na ional plans
en isage a u u e dec ease in he numbe o coal- i ed s a ions and an inc ease in enewable ins alled
capaci y. This o ecas , along wi h he u u e educ ion o nuclea capaci y, will lead o a combina ion o
less baseload plan s and sizeable in e mi en gene a ion. Hence he e is a isk ha supply will be unable o
mee demand and gene a ion adequacy will su e .
We assess how he lexible managemen o hyd o esou ces can alle ia e his isk by adjus ing
powe gene a ion o peak demand. Indeed he e is empi ical e idence ha hey a e posi i ely co ela ed. We
compu e his co ela ion in he case o Spain (an ‘elec ic island’). Besides, hyd o plan s ope a e in
combina ion wi h o he non-dispa chable echnologies wi hin he sys em. The e o e, we also ake hei
hou ly seasonali y in o accoun . Nex we un a Mon e Ca lo simula ion o de i e he isk p o ile o se e al
adequacy me ics in he coming decades. Ou esul s show ha lexible hyd o gene a ion ce ainly mi iga es
he isk bu is insu icien o b ing an adecua e le el o SoS when he enhanced enewable capaci y goes
hand in hand wi h a dec eased baseload capaci y. The isk u he dec eases a e accoun ing o seasonal
non-dispa chable gene a ion, ye i s ill looms la ge. These esul s can be impo an o policy make s,
sys em ope a o s, and powe companies when analizing in es men s in enewable ene gy wi h a long
li espan.
Keywo ds: secu i y o elec ici y supply, gene a ion adequacy, hyd o s a ions, unce ain y, Mon e
Ca lo, los load.
1 INTRODUCTION
As he o e all demand o elec ici y is an icipa ed o inc ease in he u u e, secu i y o elec ici y
supply (hence o h SoS) is elici ing e e mo e a en ion om all he s akeholde s in ol ed. I seems ai o
claim ha he e is ha dly a widely accep ed de ini ion o SoS. None heless, a common h ead a ises om
he di e en e sions, namely he abili y o powe supply o mee e ec i e demand on a con inuous basis.
In a sense his is a ‘na ow’ de ini ion since powe demand and supply do no ope a e in a acuum. [1] goes
beyond i by encompassing also en i onmen al and socie al conce ns. This makes sense because SoS is
a ec ed by a numbe o ac o s, among hem echnology, ma ke s, poli ics, and he en i onmen .
The powe supply in pa icula is a complex chain ha is na u ally exposed o a numbe o isks and
unce ain ies. As a dema ca ion c i e ion, he p obabili ies and/o impac s o he o me can be mo e
eliably compu ed han hose o he la e . Sou ces o unce ain y a e ypically ad essed by means o
scena io analysis. Ins ead, ega ding isks, he s anda d p ac ice is o de ine and compu e a numbe o isk
me ics. This said, supply is only 50 pe cen o he s o y. [2] de ines sys em adequacy as he exis ence
wi hin a sys em o su icien gene a ion and ansmission capaci y o mee he load, whe he unde no mal
o unusual condi ions. I subsequen ly in oduces di e en app oaches o measu e adequacy and a lis o
ela ed me ics.
[3] de elop a s ochas ic model ha explici ly ma ches powe demand and supply (i possible).
F om his in e play i is possible o assess gene a ion adequacy by means o se e al me ics ha accoun o
di e en a ibu es o po en ial supply sho alls. Nex hey demons a e he model by example.
*Re ised Manusc ip wi h No Changes Ma ked
Click he e o iew linked Re e ences
This documen is he Accep ed Manusc ip e sion o a Published Wo k ha appea ed in inal o m in:
Abadie L.M., Chamo o J.M., Huclin S., Ven D.-J.V.D. 2020. On lexible hyd opowe and secu i y o supply: Spain beyond 2020. ENERGY. 203. DOI (10.1016/
j.ene gy.2020.117869).
© 2020 Else ie B.V.
This manusc ip e sion is made a ailable unde he CC-BY-NC-ND 3.0 license h p://c ea i ecommons.o g/licenses/by-nc-nd/3.0/
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Speci ically, hey look a Spain (an ‘elec ic island’ igh now and in he nea u u e a leas ) beyond he yea
2020. Mon e Ca lo (MC) simula ion allows hem de i e he isk p o ile o se e al key a iables. Taken
oge he hey cha ac e ize he isk p o ile o SoS in g ea de ail.
In he end, [3] simula e he pe o mance o he Spanish peninsula gene a ing sys em unde en
di e en scena ios. Rega ding he ins alled gene a ion capaci ies om 2020 h ough 2050, hey basically
d aw on [4]. Impo an ly, [3] assume ha coal- i ed and nuclea s a ions a e kep cons an om 2017 o
2020 bu dec ease signi ican ly in 2030 and comple ely cease o ope a e om 2040 onwa ds; na u al gas
plan s, ins ead, a e assumed o emain cons an a hei 2017 le el h ough 2050. Unlike he mal s a ions,
enewable powe echnologies g ow in all o he scena ios, be i ei he slowe o as e depending on he
g ow h o powe demand (ei he 1.36% o 1.72%). Acco ding o hei esul s [3], he sys em’s adequacy
wo sens in 2020 and does so d ama ically in 2040 and 2050, when coal and nuclea s a ions a e comple ely
eplaced by enewable plan s.
The ea lie esul s in [3] conside all powe echnologies as eeding hei po en ial ou pu in he
sys em i espec i e o demand; his gene al ule applies o hyd o powe in pa icula oo. Because o he
ea h’s g a i a ional ield he e is ene gy s o ed in he wa e ha lows in i e s om ups eam egions
owa d he sea. So-called di e sion o un-o - i e hyd opowe e e s o ex ac ing a po ion o he ene gy
con ained in lowing wa e i sel o p oduce elec ici y. Ano he possibili y is o use he po en ial ene gy
con ained by a dam s uc u e o he same pu pose; his is equen ly called impoundmen hyd opowe ; [5].
Impo an ly, his ype o acili ies can egula e he low o be u bined a any p ecise ime. Despi e he
di e ences be ween bo h ypes, [3] conside all hyd opowe plan s (HPPs) as a whole. Thus, he esul s in
[3] ake mon hly seasonali y o hyd o’s load ac o in o accoun , bu he e is no oom o s a egic
managemen o hyd o plan s (i.e. no aim a maximizing p o i s by p oducing mo e elec ici y a demand
peaks wi hin he mon h).1 By no means his is exclusi e o [3]; indeed i seems o be he usual p ac ice. Fo
example, [2] p esen s he indings om an empi ical analysis on adequacy me ics and s anda ds adop ed in
Eu ope. F om he esea ch conduc ed ia public sou ces, one o he gene al conclusions d awn eads as
ollows: “In no case was i men ioned how he ope a ion o hyd opowe plan s wi h ese oi s is
conside ed. In coun ies wi h medium o high pa icipa ion o hyd opowe in he gene a ion mix, his ac o
is c ucial o sys em secu i y. In ac , in some o hese coun ies, a d y yea may be he mos s ess ul
si ua ion in ela ion o gene a ion adequacy. The use o his o ical se ies o gene a ion da a would igno e
he possibili y o ope a ing ese oi s in a conse a i e manne , in o de o inc ease gene a ion adequacy
(o equi alen ly, o educe he isk o load shedding)”. In iew o his, he EC u ges o conside a leas he
p obabilis ic cha ac e iza ion o a numbe o ac o s, among hem: “Hyd oelec ic ene gy a ailabili y
depends on he ese oi ope a ion s a egies es ablished by he owne s o plan s”.
Hyd opowe plan s wi h ese oi s can in p inciple se e se e al pu poses, o example i iga ion
needs o looding con ol. HPPs can be managed as SoS de ices also. They a e no mally designed o
gene a ion du ing peak hou s.2 Fu he , some HPPs a e equipped wi h e e sible u bines o sepa a e
gene a ing and pumping equipmen (so-called pumped s o age hyd opowe ).3 They enable he sys em o
pump wa e (using elec ici y) om a lowe ese oi up o a highe one when powe demand (and
p esumably p ice) is low; when demand (p ice) inc eases, he low is e e sed. This ‘load le eling’ is a
widesp ead ype o load managemen ; [7]. ‘Ramping and load ollowing’ a e o he ypes o load
1 No e ha deciding when i will be mo e p o i able o p oduce elec ici y is no easy ask. A one le el, supplie s d aw on limi ed
hyd o ene gy esou ces a ailable. On he o he hand, u u e in lows a e unce ain and he e is a isk o spillage. Acco ding o [6],
gene a o s y o hedge agains isk and a e usually conse a i e. Fo example, hey gene ally op o deploying limi ed wa e
esou ces when p ices a e mode a ely high, ins ead o wai ing o a possible (unce ain) sca ci y o gene a ing esou ces (when he
peak p ice would be e y high) in he u u e.
2 The lexibili y o hyd o ese oi s is o en seen as he pe ec complemen o a sys em domina ed by in e mi en enewable
sou ces; [7], [8]. [9] and [10] e en claim ha a sys em based on only wind, wa e and sola powe could se e 100% o ene gy
pu poses by 2050 in a eliable and a o dable way. Howe e , his claim has ecei ed a ious c i iques, e.g. ha hese au ho s a e oo
op imis ic abou he balancing ole o hyd opowe [11].
3 Pumped hyd o s o age is he majo ene gy s o age echnology. I accoun s o 96% o he wo ld s o age capaci y [9]; comp essed
ai , ba e ies, he mal and lywheel ene gy s o age play e y mino oles. [7] and [12] highligh some o i s applica ions (along wi h
some ba ie s o i s de elopmen ), such as o se ing he in e mi ence o enewable sou ces and p o iding ancilla y se ices o he
powe sys em (e.g. ol age egula ion).
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managemen , in which ene gy s o age is used o assis gene a ion o ollow he load changes. In his ega d,
[13] poin ou ha he business case o p ice a bi age has anished pa ly owing o he injec ion o
subsidized enewable elec ici y du ing peak demand pe iods. To a oid becoming uneconomic, pumped
s o age s a ions ha e o ind addi ional sou ces o e enue. [14] conside he Aus ian-Ge man spo powe
ma ke and he Aus ian balancing ene gy ma ke h ough he yea s 2012-2015. They ind ha ea nings
om he la e may exceed hose om he o me many imes o e .
The empi ical e idence shows ha hyd o ope a ion does ollow demand o some ex en .
Speci ically, hese s a ions gene a e ela i ely mo e powe du ing peak hou s and less in non-peak ones. On
he o he hand, hese plan s ope a e alongside o he (non-dispa chable) echnologies in a sys em. Fo
example, wind ene gy blows du ing he nigh , when powe demand is ela i ely lowe ; pump s a ions can
a oid was ing his ene gy by s o ing i . Consequen ly, a de ailed analysis o he con ibu ion o hyd opowe
o SoS calls o aking due conside a ion o non-dispa chable sou ces.4 This no e is an ex ension o [3] on a
leas h ee accoun s. Fi s , i aims o accoun o ha posi i e co ela ion be ween maximum hou ly
demand and hyd opowe gene a ion o check he po en ial o lexible managemen o ein o ce SoS.
Second, we disagg ega e hyd o s a ions be ween un-o - i e (RoR) s a ions and he emainde (non-RoR)
s a ions.; his way we wan o accoun o he di e en deg ee o eedom be ween he wo ypes when i
comes o lexible managemen . Thi d, we also conside he hou ly seasonali y in gene a ion om
non-dispa chable echnologies du ing peak hou s. In addi ion, o hese h ee easons, now he nume ical
applica ion ( ia MC simula ion) ge s mo e complex han in [3]. Thus, ela i e o [3], his pape con ibu es
in scope, me hod, and policy implica ions. To ou knowledge, no o he pape on applied SoS adequacy
me ics add esses he ole o hyd o-based gene a ion in mi iga ing powe supply sho alls o he po en ial
o seasonal non-dispa chable gene a ion in mee ing peak demands (le alone in he way we do).
In 2017 hyd o s a ions (including pumped s o age) ep esen ed abou 20% o he o al capaci y
ins alled in he Spanish mainland sys em (20,331 MW ou o 99,311 MW); in e ms o powe gene a ion,
hey p o ided a ound 8.3% o he o al. Would he lexibili y o hyd opowe alle ia e es ima es o supply
sho ages in [3]? How e ec i e is i in enhancing SoS in mainland Spain? In he same ein, does
conside a ion o seasonal non-dispa chable gene a ion con ibu e o quell SoS conce ns? I so, o wha
ex en ? Acco ding o ou esul s, he posi i e co ela ion be ween hou ly peak demand and lexible
hyd opowe ’s gene a ion signi ican ly empe s he se e i y o he nega i e impac s o demand su ges. The
si ua ion u he imp o es when hou ly seasonali y o non-dispa chable gene a ion is conside ed.
None heless, he expec ed ene gy no se ed (EENS) jumps abo e his o ical le els in 2030 and uns in o he
ens o housands megawa s-hou he ea e . The issue is o in e es no only o Spanish consume s and
u ili ies, bu also o o he s akeholde s in ol ed in he cons uc ion o he Eu opean in e nal powe ma ke .
Fu he , clima e change migh exace ba e he high a iabili y ha cha ac e izes enewable ene gy sou ces
in gene al and hyd o powe gene a ion in pa icula ; [15].
The emainde o he pape is o ganized as ollows. Sec ion 2 ex ends he model in [3] o accoun
o he lexible ope a ion o hyd opowe s a ions in mainland Spain and also he seasonal pa e n o
enewable gene a ion. The esul ing impac on he adequacy me ics is analyzed in Sec ion 3. Sec ion 4
concludes.
2 ACCOUNTING FOR HYDROPOWER FLEXIBILITY AND SEASONAL
NON-DISPATCHABLE GENERATION
2.1. Model ex ension
[3] p opose a model o e alua ing gene a ion adequacy in he long un om he iewpoin o he
acili ies ins alled. E en hough powe demand can be ela i ely p edic able a his ime scale, unexpec ed
peak loads can ce ainly occu also in he sho un; [16].
Gi en hei ocus on gene a ion adequacy hey na u ally pay special a en ion o peak demand.
Typically demand su ges a e sho li ed. Publicly a ailable eco ds on powe demand s e ch back o e
4 We hank an anonymous e iewe o b inging his issue o ou a en ion.
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many yea s, e en decades. Un o una ely, howe e , hei sample da a on peak demand a e e y limi ed.
They eso o an indi ec app oach ha elies on yea ly da a; speci ically, hey ela e he hou ly peak
demand in a u u e yea (, in MWh) o he annual demand in ha yea (, in MWh):
lnln
; (1)
s ands o an independen and iden ically dis ibu ed andom shock. By assump ion, he na u al loga i hm
o maximum hou ly demand e e y yea ollows a No mal dis ibu ion wi h a e age αβElnQ
(whe e E deno es he ma hema ical expec a ion ope a o ) and s anda d de ia ion equal o he s anda d e o
o he eg ession. This is a s ochas ic equa ion: hough he a e age g ow h a e o q depends on he a e age
g ow h a e o Q
, by i s e y na u e q will g ow abo e i some imes, and below i some o he s.
Rega ding powe supply, hey dis inguish wo g oups o gene a ion echnologies. The i s g oup
comp ises he mal echnologies: coal () , na u al gas (), and nuclea (). Each s a ion has a pa icula
ins alled capaci y (MW) and a ailabili y a e (%). A ailabili y is ep esen ed by a bina y a iable (). A
pa icula s a ion o ype ∈,, is in se ice o a ac ion Λ o he yea (i can ei he ac ually un
o emain idle depending on powe demand); i is ou o se ice o ano he ac ion 1-Λ (because o
ailu es and main enance wo ks):
0,′o s a ewi hp obabili y1Λ
1,′ons a ewi hp obabili yΛ. (2)
The second g oup o gene a ion echnologies includes hyd o, wind, sola (bo h pho o ol aic and
he mal), cogene a ion, and o he s. The ime se ies o powe p oduced/consumed by hese s a ions
subsumes bo h he usual pa e n o ailu es and hei in e mi en na u e. Consequen ly, [3] adop he load
ac o o desc ibing hese in e mi en echnologies and assume ha hese show a s ochas ic beha io wi h
bo h he mon hly a e age and he ola ili y changing om one mon h o ano he .5 They adop he Weibull
dis ibu ion o desc ibe his a iable ac oss all o he echnologies in his g oup.6 The p obabili y densi y
unc ion o he load ac o () is:
i 0
0i 0 , (3)
whe e ∈0,∞ is he scale pa ame e and ∈0,∞ is he shape pa ame e . The cumula i e
densi y unc ion is:
1
i 0
0i 0 . (4)
The a e age and he a iance a e gi en by:
Γ1
, (5)
Γ1
Γ1
, (6)
whe e deno es he gamma unc ion.
This pa e n o he gene a ion echnologies in he second g oup applies o hyd opowe gene a ion.
In his sense, Eqs. (3)-(6) may be a easonable app oach as long as [3] conside hyd o gene a ion as a single
powe sou ce o echnology. None heless, unlike [3], he e we a e going o disagg ega e hyd o s a ions
be ween RoR s a ions and non-RoR s a ions. The o me a e ela i ely mo e dependen on na u al
( e)cha ge and less amenable o s a egic managemen . Consequen ly, we a e going o es ima e an
independen Weibull dis ibu ion o RoR s a ions acco ding o Eqs. (3)-(4). Hence we can ge nume ical
es ima es o he a e age () and he a iance () ollowing Eqs. (5)-(6); he subindex R e e s o hese
pa icula s a ions. Non-RoR s a ions include con en ional ese oi s (o seasonal, annual o plu iannual
egula ion) and pumped s o age s a ions (o daily, weekly o seasonal cycle). In p inciple hey a e mo e
amenable o s a egic ope a ion and lend hemsel es mo e easily o ack demand su ges. Again, we assume
ha he load ac o o hese s a ions can be cha ac e ized by a Weibull dis ibu ion, Eqs. (3)-(4), wi h
5 Mul iplying he load ac o imes he ins alled capaci y allows de i e samples o mon hly powe gene a ion la e on.
6 No e ha he Weibull dis ibu ion does no admi nega i e alues, which is jus igh when dealing wi h load ac o s.
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associa ed a e age () and () acco ding o Eqs. (5)-(6); we adop he subindex P o hese hyd o plan s.
Unlike RoR, howe e , he Weibull dis ibu ion o non-RoR s a ions is going o be co ela ed wi h peak
demand.
Now he in o ma ion a ailable di e s om da a in [3] in h ee key espec s: (a) we know he
maximum hou ly demand in each single day o he yea s 2015, 2016, and 2017, i.e. we ha e 365+366+365
= 1,096 da a; (b) we know hyd o-based powe gene a ion du ing he hou s o peak demand o e hose
yea s; (c) we also ha e hyd o-based ins alled capaci y e e y day ( om linea in e pola ion be ween
mon hly alues); he combined in o ma ion o (b) and (c) allows compu ing his echnology’s load ac o on
a daily basis. Figu e 1 displays he ime pa h o hou ly peak demand (a) along wi h non-RoR s a ions’ load
ac o in Janua y o e he sample pe iod. I sugges s ha hese se ies a e posi i ely co ela ed. As a ma e
o ac , he co ela ion coe icien is 0.256 ( he las column in Table 3 below shows he coe icien in he
o he mon hs). In June i eaches he lowes alue, close o ze o. The uppe bound is almos 45% and applies
in Ma ch. The main d i e behind his como emen is ha powe u ili ies manage hese plan s in an
oppo unis ic o s a egic way since peak demands a e usually associa ed wi h highe p ices (indeed hyd o
is he ‘ma ginal’ echnology on he wholesale powe ma ke in many ins ances).
FIGURE 1: Maximum hou ly demand and non-RoR s a ions’ load ac o in Janua y 2015-2017.
La e on we will un a numbe o simula ions (no e ha he main adequacy me ics in [3] d aw on a
p obabilis ic MC app oach). Rega ding RoR s a ions, o his end we will use he a e age () and he
a iance () es ima ed acco ding o Eqs. (5)-(6). Howe e , in he case o non-RoR s a ions we will need o
gene a e co ela ed samples. We s a by de i ing wo independen samples
∗ and
∗ o non-RoR
s a ions’ load ac o and hou ly peak demand (no e he subindex D). In a second s ep we no malise each
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se ies by sub ac ing i s a e age and di iding by i s ola ili y. Thus we ob ain wo independen , no malised
samples and o he load ac o and peak demand, espec i ely. In a hi d s ep we cons uc
co ela ed samples, and , acco ding o he scheme:
;1, (7)
whe e s ands o he co ela ion coe icien be ween he wo daily se ies.
2.2. Pa ame e es ima ion in add essing co ela ion
Ou sample da a include daily powe gene a ion and ins alled capaci y o he wo ypes o hyd o
s a ions. Da a on hese a iables (b) and (c) allow compu ing sepa a e, speci ic load ac o s on a daily basis.
Nex we a ange all o he daily load ac o s by mon h. Thus, he e a e 31+31+31=93 daily ac o s in
Janua y, 28+29+28=85 ac o s in Feb ua y, and so on. Wi h he daily ac o s in any single mon h we
es ima e a Weibull dis ibu ion o ha pa icula mon h, i.e. we es ima e he scale () and shape ()
pa ame e s o e e y mon h.
2.2.1. Run-o - i e s a ions
The le block in Table 1 shows he mon hly es ima es o he Weibull pa ame e s o RoR s a ions
along wi h hei 95 pe cen con idence in e als. Fo he scale pa ame e () he in e als a e a he na ow.
The di e ence be ween he uppe and lowe bounds is minimum in Ma ch (4.07%) and maximum in May
(10.7%). Ins ead, he in e als a e wide o he shape pa ame e (). The di e ence anges be ween 33.1%
(Oc obe ) and 40.2% (Janua y).
The nex s ep is o subs i u e he mon hly alues o and in Eqs. (5)-(6) o compu e he mon hly
a e age and s anda d de ia ion o RoR s a ions’ load ac o ; see he igh block in Table 1. Looking a ,
he mean is highes in Ma ch; hence o h i declines consis en ly un il Oc obe and hen ises. Simila ly, he
highes ola ili y is eached in Ap il and he lowes one in Sep embe . The e o e, h ough he h ee
sample yea s, he ex eme alues o he mean and he ola ili y a e a he con empo aneous. The maximum
gene a ion akes place om Feb ua y o May. In 2017 he ins alled capaci y o RoR s a ions was 2,104 MW
[17]; see Table A1 in he Appendix.
Table 1. Run-o -Ri e (RoR) load ac o : Pa ame e es ima es (daily da a 2015-17).
Mon h Scale () Shape () A e age Vola ili y
Value 95% in . Value 95% in .
Janua y 0.520 0.499—0.542 5.163 4.360—6.114 0.479 0.106
Feb ua y 0.668 0.651—0.684 9.178 7.766—10.846 0.633 0.083
Ma ch 0.734 0.717—0.751 9.330 8.019—10.854 0.696 0.089
Ap il 0.715 0.680—0.750 4.424 3.767—5.195 0.652 0.167
May 0.659 0.626—0.693 4.241 3.624—4.961 0.599 0.160
June 0.531 0.507—0.555 4.825 4.153—5.606 0.486 0.115
July 0.412 0.398—0.426 6.364 5.482—7.386 0.384 0.070
Augus 0.358 0.347—0.370 6.680 5.759—7.747 0.335 0.059
Sep embe 0.303 0.293—0.313 6.418 5.500—7.487 0.282 0.051
Oc obe 0.270 0.258—0.281 4.962 4.301—5.723 0.248 0.057
No embe 0.369 0.351—0.387 4.457 3.802—5.224 0.337 0.086
Decembe 0.407 0.390—0.424 5.156 4.454—5.968 0.375 0.083
2.2.2. Non-RoR s a ions
Fo he es o hyd o (non-RoR) s a ions, as s a ed ea lie , we assume ha he Weibull dis ibu ion
desc ibing hei load ac o is co ela ed wi h peak demand; see Figu e 1. In 2017 he capaci y ins alled
amoun ed o 18,227 MW; see Table A1 in he Appendix. We display he Weibull pa ame e es ima es in
Table 2. Again, he con idence in e als a e hinne o he scale pa ame e han o he shape pa ame e .
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Hence we u he compu e he a e age and he ola ili y o he load ac o (, ) by means o Eqs.
(5)-(6).
Table 2. Res o hyd o (non-RoR) load ac o : Pa ame e es ima es (daily da a 2015-17).
Mon h Scale () Shape () A e age Vola ili y
Value 95% in . Value 95% in .
Janua y 0.406 0.385—0.427 4.113 3.513—4.813 0.368 0.101
Feb ua y 0.447 0.421—0.475 3.692 3.080—4.425 0.404 0.122
Ma ch 0.470 0.448—0.492 4.584 3.903—5.383 0.430 0.107
Ap il 0.374 0.343—0.406 2.585 2.198—3.039 0.332 0.138
May 0.355 0.325—0.386 2.492 2.117—2.933 0.315 0.135
June 0.285 0.264—0.306 2.951 2.500—3.483 0.254 0.094
July 0.251 0.230—0.272 2.535 2.153—2.982 0.223 0.094
Augus 0.225 0.208—0.243 2.837 2.418—3.327 0.201 0.077
Sep embe 0.222 0.207—0.237 3.146 2.678—3.694 0.199 0.069
Oc obe 0.252 0.232—0.271 2.758 2.336—3.256 0.224 0.088
No embe 0.262 0.239—0.288 2.343 1.981—2.770 0.233 0.105
Decembe 0.266 0.244—0.289 2.598 2.202—3.065 0.236 0.098
Table 3 shows he desc ip i e s a is ics o hou ly peak demand and u he in o ma ion abou he
co ela ion wi h powe gene a ion o m non-RoR s a ions.7 The la e sheds ligh on he s a is ical
signi icance and accu acy o he mon hly es ima es. We s a om he s anda d (Pea son) o mula ( hus
assuming a linea ela ionship be ween bo h a iables). As a sa egua d agains sampling e o we conduc a
es . The null hypo hesis is 0. The al e na i e hypo hesis is 0 (which equi es a wo- ail es ). The
- es o he co ela ion obse ed is:
√
, (8)
whe e n s ands o he numbe o obse a ions; his - es has n-2 deg ees o eedom. As o he con idence
in e al we i s u n he obse ed co ela ion in o Fishe ’s ans o m:
. (9)
Hence he in e al o he z’ ans o m is compu ed as:
1.96
√;1.96
√. (10)
And he esul ing in e al o he co ela ion obse ed is calcula ed as:
.
√
.
√;.
√
.
√. (11)
The in o ma ion abo e allows assess he osbus ness o ou nume ical es ima es.
Table 3. Basic s a is ics o hou ly peak demand and co ela ion wi h non-RoR’s load ac o .
Hou ly peak demand Co ela ion Coe icien
Mon h # Obs. p- alue 95% con . in .
Janua y 35,424 3,207 93 0.256 0.0132 0.055—0.437
Feb ua y 35,280 2,528 85 0.381 0.0003 0.183—0.550
7 We hank an anonymous e e ee o aising his poin .
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Ma ch 33,340 2,563 93 0.449 0.0000 0.270—0.598
Ap il 30,715 2,338 90 0.326 0.0017 0.128—0.499
May 30,572 2,251 93 0.101 0.3364 -0.105—0.299
June 33,048 2,953 90 -0.012 0.9115 -0.219—0.196
July 35,290 3,158 93 0.369 0.0003 0.179—0.533
Augus 33,186 2,954 93 0.215 0.0382 0.012—0.401
Sep embe 32,236 2,766 90 0.194 0.0674 -0.014—0.386
Oc obe 31,087 2,335 93 0.179 0.0869 -0.026—0.369
N
o embe 33,174 2,903 90 0.152 0.1514 -0.057—0.348
Decembe 33,654 2,998 93 0.101 0.3370 -0.105—0.299
We a e going o simula e a Weibull dis ibu ion 50,000 imes each mon h using he pa ame e
alues o and and hen compu e he a e age load ac o and i s ola ili y. P o ided he la e closely
mi o hose de i ed om ou sample da a, he nume ical es ima es o he MC-based adequacy me ics can
be conside ed eliable. Table A2 in he Appendix shows he esul s om bo h he sample da a and he
simula ion uns in each mon h. The (negligible) di e ences obse ed can be a ibu ed o he limi ed
numbe o uns and he e y na u e o andom numbe s.
Rega ding he maximum hou ly demand, we eso o Eq.(1). As in [3], we ake andom samples o
he shock e m and shi he maximum demand cu e in 2017 acco dingly. Speci ically we use 50,000
simula ion uns (i.e. yea s, each comp ising 365 days). We g oup hem by mon h and compu e he mon hly
a e age and ola ili y, and , espec i ely; see he le block columns in Table 3. Peak demand su ges
ypically in Janua y (35,424 MWh) and July (35,290); hese mon hs a e also he mos ola ile ones (3,207
MWh and 3,158, espec i ely).
The igh block in Table 3 p o es he impo ance o ex ending [3] along he lines d awn in his no e.
To begin wi h, a he yea ly le el (i.e. neglec ing di e ences ac oss mon hs) he co ela ion be ween
non-RoR s a ions’ load ac o and hou ly peak demand is 0.214 (s a is ically di e en om ze o a he 5%
con idence le el). The analysis on a mon hly basis shows ha , o mos o he yea , he e is a mild
co ela ion. I anges om abou 0 o 25% in eigh ou o wel e mon hs, sligh ly alle ia ing powe supply
sho ages ( he compu a ion d aws on all he daily alues o bo h a iables in any single mon h).
None heless, he lexibili y ad an age o hyd opowe ge s la ge in mon hs wi h a high load ac o (Janua y
o Ap il), wi h he co ela ion coe icien ising up o 45%; his sugges s ha highe wa e le els in
ese oi s do allow a mo e lexible and s a egic managemen o hose ese oi s; [18], [19]. Jus hal o he
mon hly es ima es o a e s a is ically di e en om ze o (again, a he 5% con idence le el).
In e es ingly, hey a e signi ican om Janua y o Ap il along wi h July and Augus , p ecisely he mon hs
when he coe icien eaches i s highes alues. This said, we can also obse e ha he con idence in e als
a e wide, he uppe bound being se e al imes highe han he lowe one on many occasions. This con i ms
he use ulness o accoun ing o he seasonal beha io o he co ela ion be ween non-RoR’s load ac o and
peak demand, and o using mon hly pa ame e s in his analysis.
Mon hly di e ences in co ela ion can be aced back o se e al issues.8 On he supply side, wi hin
non-RoR s a ions he e a e HPPs wi h ese oi s (ins alled capaci y 11,900 MW) and pumped s o age
s a ions (6,327 MW). Spain has 20 pumped s o age plan s.9 They we e commissioned h ough he 20 h
cen u y mainly o add ess ain all a iabili y. So-called Hyd og aphic Con ede a ions ule he basins; hey
a e legally abo e hyd opowe ope a o s since hey se limi s on he use o wa e . F om his pe spec i e,
somehow he e is an uppe bound on powe gene a ion om non-RoR s a ions which is a ec ed by bo h
8 We hank an anonymous e e ee once mo e o b inging his issue o ou a en ion.
9 They can be u he subdi ided in o wo ypes: pu e o closed-loop (whe e wa e is i s pumped o an uppe ese oi and hen
eleased o gene a e powe ) and mixed o open-loop (when he e a e wa e con ibu ions om i e s). Pu e pumped s o age
accoun s o 53% o he o al (3,337 MW) while mixed pumped s o age akes he emaining 47%.
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ac ual ain all and wa e needs. The so-called ‘hyd opowe po en ial’ measu es he maximum amoun o
elec ici y ha could be heo e ically p oduced om he wa e con ibu ions du ing a pa icula pe iod o
ime a e sub ac ing he wa e di e ed o i iga ion o o he uses di e en om powe gene a ion. Table
A3 and Figu e A1 in he Appendix show ha he highes hyd opowe po en ials a e a ailable du ing he
i s h ee o ou mon hs o he yea . They subsequen ly decline h ough summe and s a ising in au umn.
A he same ime, powe demand also plays a ole he e; i changes seasonally o e ime (Table A3
and Figu e A1 in he Appendix). The a e age peak demand in pa icula is highes in Janua y and July
(Table 3) ollowed by Feb ua y (which lags close behind, wi h 35,280 MWh). In gene al, he i s mon hs o
he yea end o be also he mon hs when he co ela ion be ween peak demand and hyd o’s load ac o is
ela i ely highe (as shown in Table 3); his also applies o July (maybe in an e o o make ends mee ).
Anyway, a cau iona y no e seems in o de .Wa e ese es a he end o 2017 we e a hei lowes
le el on eco d (s a ing 1990); [20]. Hyd o-based gene a ion dec eased almos in hal wi h espec o 2016,
and eached i s lowes alue since 2005. Hyd o was he hi d powe gene a ion sou ce in 2016 bu d opped
o he six h in 2017. The d ough in 2017 d agged enewable gene a ion down om 40.3% o o al in 2016
o 33.7% in 2017. This episode a es s o he high a iabili y o enewable esou ces, bo h a yea ly and
mon hly le els ( o one, hyd o-based gene a ion con ibu ed 26% o o al powe in May 2016 bu 10.1% in
May 2017, i s lowes le el on eco d).
Annual a iabili y ce ainly complica es d awing conclusions om jus h ee yea s o obse a ions.
Ye a ac speaks o i sel : in 2017 he a e age con ibu ion o pu e pumped s o age o powe gene a ion
was jus 0.9%; none heless, i jumped o 6.7% in he day o peak demand (Janua y 25 h); [20]. This ac
highligh s i s ole in add essing SoS conce ns.
2.3. Pa ame e es ima ion in add essing seasonali y
Ou ini ial model does no accoun o any hou ly seasonali y. No e, howe e , ha we do no use he
24 hou ly demands in any single day, bu only he maximum hou ly demand in ha day. We p oceed as
ollows.
We conside he wel e mon hs o 2017, ou base yea . E e y day in e e y mon h has a maximum
hou ly demand a a pa icula ime. We ake each mon h in isola ion and iden i y he mos equen hou a
which he maximum hou ly demand akes place. Thus, in he case o Janua y, he ypical hou wi h
maximum demand is 21:00; ins ead, in July i is 14:00.
We ha e hou ly powe gene a ion by all o he non-dispa chable echnologies o he han non-RoR
(i.e. RoR, wind, sola , cogene a ion, and o he s) om 2015 h ough 2018, i.e. ou yea s. Now, le ’s hink o
a pa icula enewable echnology, say wind, and a pa icula mon h, say Janua y. The e a e ou such
mon hs in he sample, each unning om day 1 o day 31. We hus ha e 4×31= 124 Janua y days; we adop
he sub-index k o each one o hem, wi h k =1, 2,…, 124. On he o he hand, each day comp ises 24 hou s,
deno ed by sub-index i, wi h i =1, 2,…, 24. The e o e, we ha e 142 obse a ions o hou 1 in Janua y,
ano he 142 obse a ions o hou 2 in Janua y, 142 obse a ions o hou 3 in Janua y, and so on un il hou
24 in Janua y.
Ini ially we compu e he hou ly a e age gene a ion in each day (μk) summing up i s 24 hou ly
le els and hen di iding by 24. Nex , we di ide each o hese 24 hou ly le els in day k by he hou ly a e age
ha day (μk) jus calcula ed. This way we de i e a se ies o seasonal ac o s o each hou , wi h each se ies
comp ising 124 e ms. We deno e each ac o by φik (again, wi h i =1, 2,…, 24 and k =1, 2,…, 124).
D awing on he 124 alues o hou i, he i- h seasonal ac o o wind in Janua y is jus hei a e age:
∑,
,1,2,…,24. (12)
Thus we ge a se ies o 24 ac o s (φi, wi h i=1, 2,…24), one o each hou o he day in Janua ies; hey can
be in e p e ed as ep esen ing hou ly seasonali y (in gene a ion om wind). Some o hem a e highe han 1,
and some o he s a e lowe han 1; hey sum o 24:
∑
24. (13)
Hence o h, we ollow his p ocedu e: we simula e he daily a e age gene a ion in any single
Janua y day om wind (μ). Then we use he abo e ac o s φi (based on empi ical/his o ical e idence) o
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[24] Red Eléc ica de España (2014): Impo ancia del Equipo Gene ado Hid oeléc ico en la
Ope ación del Sis ema Eléc ico. Mad id.
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[26] Spanish Go e nmen (2019): Plan Nacional In eg ado de Ene gía y Clima, 2019. A ailable a :
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y-clima.aspx(accessed 04/30/2019).
[27] McPhe son M., Ka ney B. (2017): “A scena io based app oach o designing elec ici y g ids
wi h high a iable enewable ene gy pene a ions in On a io, Canada: De elopmen and applica ion o he
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[28] Schlach be ge D.P., B own T., Sch amm S., G eine M. (2017): “The bene i s o
coope a ion in a highly enewable Eu opean elec ici y ne wo k”. Ene gy 134, 469-481.
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Appendix
Table A1 displays he o al ins alled capaci ies (in MW) o powe echnologies in mainland Spain and he
peninsula o al annual demand (in GWh). Sou ce: [3].
Table A.1. Peninsula Spanish powe sys em.
(demand g ow h: +1.36%) (demand g ow h: +1.73%)
2017 2020 2030 2040 2050 2020 2030 2040 2050
Nuclea 7,117 7,117 3,040 0 0 7,117 3,040 0 0
Coal 9,536 9,536 6,642 0 0 9,536 6,642 0 0
Na u al Gas 24,948 24,948 24,948 24,948 24,948 24,948 24,948 24,948 24,948
Hyd o: 20,331 20,331 21,900 24,700 25,600 20,331 23,300 25,900 28,600
RoR 2,104 2,104 2,104 2,104 2,104 2,104 2,104 2,104 2,104
Non-RoR 18,227 18,227 19,796 22,596 23,496 18,227 21,196 23,796 26,496
Wind 22,863 26,000 28,700 32,100 35,800 24,500 32,600 39,800 44,400
Sola 6,730 16,000 20,500 24,600 29,400 15,100 20,300 27,300 39,300
Cogen. 6,373 8,100 9,900 10,800 11,600 8,100 10,800 13,200 16,100
O he s 1,413 1,200 2,800 3,800 5,300 1,200 2,000 3,500 6,200
To al(MW) 99,311 113,232 118,430 120,948 132,648 110,832 123,630 134,648 159,548
Demand
(GWh) 253,082 263,621 302,026 346,026 396,436 266,564 316,909 376,762 447,920
Table A2 displays he basic s a is ics de i ed om ou sample da a o non-RoR s a ions (le block)
and hose esul ing om 50,000 simula ion uns (on he igh ). They a e almos iden ical, which ende s ou
MC-based adequacy me ics ela i ely eliable. In o he wo ds, his able basically se es as a c oss-check
o ou non-RoR pa eme e s in he simula ions abo e. Fo pumped-s o age s a ions we use an a ailabili y
a e o 60.66% o hei ins alled capaci y; his is he 95 h pe cen ile o he 2015-2017 daily se ies.
Table A2. Non-RoR: Es ima ed Weibull pa ame e s and hose om Mon e Ca lo simula ion.
Es ima ed Simula ed
Mon h Mean Vola il. Mean Vola il.
Janua y 0.368 0.101
0.256 0.368 0.101 0.256
Feb ua y 0.404 0.122
0.381 0.404 0.122 0.382
Ma ch 0.430 0.107
0.449 0.430 0.107 0.451
Ap il 0.332 0.138
0.326 0.332 0.138 0.326
May 0.315 0.135
0.101 0.315 0.135 0.100
June 0.254 0.094
-0.012 0.254 0.094 -0.013
July 0.223 0.094
0.369 0.223 0.094 0.368
Augus 0.201 0.077
0.215 0.201 0.077 0.216
Sep embe 0.199 0.069
0.194 0.199 0.069 0.193
Oc obe 0.224 0.088
0.179 0.224 0.088 0.180
No embe 0.233 0.105
0.152 0.232 0.105 0.153
Decembe 0.236 0.098
0.101 0.235 0.098 0.100
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Table A3 shows he maximum gene a ion po en ial om hyd o s a ions (in Spanish, ‘p oducible
hid áulico’) and powe demand as an app oach o explaining he ac o (s) behind he mon hly changing
co ela ion be ween he o me ’s load ac o and he la e .
Table A3. Behind he co ela ion be ween demand and hyd o’s load ac o .
Mon h
Hyd opowe po en ial (GWh) Powe demand (GWh)
2015 2016 2017 2015 2016 2017
Janua y 2,612 6,024 1,124 22,694 21,470 23,109
Feb ua y 4,204 4,889 3,802 21,013 20,848 19,912
Ma ch 4,133 4,603 2,667 21,184 21,477 21,128
Ap il 2,913 6,105 1,546 18,851 19,931 18,833
May 2,576 5,483 1,990 19,832 19,732 20,242
June 1,535 2,112 1,074 20,377 20,247 21,709
July 578 915 557 23,470 22,235 22,401
Augus 647 367 253 20,880 21,464 21,809
Sep embe 877 470 287 19,591 20,845 20,215
Oc obe 1,503 729 411 19,728 19,852 20,252
No embe 1,980 1,592 528 19,880 20,663 20,950
Decembe 1,314 1,378 1,734 20,897 21,336 22,181
Sou ce: Red Eléc ica de España (REE).
Figu e A1 displays bo h se ies om Jan 2015 o Dec 2017. Hyd o po en ial is measu ed along he
le e ical axis; demand goes along he igh one. In bo h cases, mon hly alues ep esen pe cen ages, i.e.
he abosul e le els a e di ided by he yea ly o als. Fo ins ance, demand in Jan 2015 accoun ed o 9.14%
o o al demand in 2015; hyd o po en ial in he same mon h ep esen ed 11.31% o o al po en ial in ha
yea . A clea seasonal pa e n a ises, pa icula ly in hyd o po en ial, which is a i s highes in win e and
lowes in summe ; ins ead, demand peaks in Janua y and July. O e all he wo (whole) se ies seem p e y
much unco ela ed ( he coe icien is -0.14); di e en seasonal pa e ns can explain his o some ex en .
The e a e wide gaps and end misma ches in summe , bu he wo se ies como e a numbe o mon hs.
FIGURE A1: Hyd opowe po en ial and powe demand in mainland Spain 2015-2017.
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Figu e A2 below displays he ac ual ope a ion p o ile o pu e pumped s o age (PHES) plan s in
Spain. We ha e collec ed hei hou ly gene a ion o e he pe iod 2014-2018, i.e. 43,824 obse a ions. Each
ba shows he numbe o hou s when hei ne gene a ion le el alls be ween he bounds shown on he
ho izon al axis. E en hough hei agg ega e ins alled capaci y amoun s o 3,337 MW, hei usual ne ou pu
is qui e a om ope a ion a ull capaci y.
FIGURE A2: Hou s wi h posi i e ne gene a ion om PHES s a ions, 2014-2018. Sou ce: Own elabo a ion
on REE da a.
