RENEWABLE POWER GENERATION: DEVELOPMENT, ECONOMICS
AND INVESTMENT VALUATION METHODS
ENERGY ECONOMICS
ARTICULO DE INVESTIGACION
Luis Ma ía Abadie, José Manuel Chamo o,
Renewables
Publicaciones DYNA SL -- c) Maza edo nº69 - 4º -- 48009-BILBAO (SPAIN)
Tel +34 944 237 566 – www. e is adyna.com - email: dyna@ e is adyna.com
Pag. 1 / 12
ESTIMACIONES DEL COSTE DE LA ELECTRICIDAD: FACTORES
DETERMINANTES Y MÉTODOS DE VALORACIÓN
Luis Ma ía Abadie1, José Manuel Chamo o2
1Basque 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,
48940 Leioa, Spain. E-mail: lm.aba[email p o ec ed] g
2Uni 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]
Recei ed: 24/Ap /2019--Re iewing: 6/Sep/2019--Accep ed: 13/Sep/2019—DOI: h p://dx.doi.o g/10.6036/9223
LEVELIZED COST OF ELECTRICITY: KEY DRIVERS AND VALUATION
METHODS
ABSTRACT:
The aim o his pape is o p opose an imp o emen o e
adi ional app oaches o he le elized cos o elec ici y (LCOE).
Basically he e a e wo me hods a ailable. The i s one
conside s a yea ly ime ame, so i yields a yea ly es ima e o he
LCOE. The second one, ins ead, keeps he whole li e ime o he
acili y when compu ing i s LCOE; i hus esul s in a li e-cycle
es ima e. This said, hey sha e some ea u es, o example, hei
eliance on he ne -p esen - alue me hodology and he scan use
o ma ke p ices. Un o una ely, hey also s umble on some
common issues, such as he p ope way o accoun o isk.
The ocus he e alls on wo powe gene a ing echnologies om
enewable sou ces, namely wind and sola . Sec ion 1 gi es a
quick o e iew o hei widesp ead deploymen ac oss he
wo ld. Sec ion 2 p o ides a ho ough e iew o he wo
app oaches o he LCOE a a heo e ical le el. I also includes
some ema ks abou hei unde lying assump ions and pinpoin s
some o hei limi a ions. Sec ion 3 shows nume ical es ima es
o LCOE o di e en echnologies and coun ies ollowing he
wo app oaches. I also looks a ecen ends o LCOE es ima es
o e ime. Then Sec ion 4 p esen s a p oposal o an imp o ed
LCOE, one ha uses public in o ma ion a ailable on he ma ke s
and deals wi h he discoun ing o isk mo e p ope ly. The e is
also a nume ical applica ion o a s anda d wind pa k. Sec ion 5
concludes.
Key Wo ds: Elec ici y gene a ion, enewable ene gies, sola
a ms, wind a ms, in es men alua ion, u u es ma ke s
RESUMEN:
Es e abajo p esen a una al e na i a al cálculo adicional del cos e de
la elec icidad, ambién conocido como LCOE po sus siglas en inglés
(le elized cos o elec ici y). Den o de la p ác ica adicional se
pueden dis ingui dos en oques. El p ime o de ellos conside a un
ho izon e empo al de un año en sus cálculos (y apo a una es imación
anual). El segundo, en cambio, aba ca oda la ida de la ins alación (y
da una es imación de ciclo i al). Es os en oques ienen a ios asgos
comunes. Po ejemplo, ambos se basan en la noción del alo ac ual
ne o y hacen un uso limi ado de los p ecios de me cado. En pa e po
ello, ambos adolecen de limi aciones impo an es, como la mane a en
que a an y alo an el iesgo.
Es e a ículo se cen a p incipalmen e en la es imación del LCOE en el
caso pa icula de las ecnologías eólica y sola . La Sección 1
p esen a el desa ollo de las ecnologías eno ables a ni el mundial.
La Sección 2 analiza los dos en oques del LCOE a ni el eó ico,
p es ando especial a ención a los supues os subyacen es y las
debilidades que de ahí se de i an. La Sección 3 mues a es imaciones
numé icas del LCOE pa a di e en es ecnologías y países en base a
los dos mé odos. También analiza las endencias ecien es de las
es imaciones del LCOE. La Sección 4 p esen a una p opues a pa a el
cálculo de un LCOE mejo ado. La mejo a pasa po hace más uso de
la in o mación pública disponible en los me cados y abo da el
descuen o del iesgo de mane a más adecuada. La p opues a se
ilus a po medio de una aplicación a un pa que eólico ípico. Las
conclusiones se encuen an en la Sección 5.
Palab as Cla e: Gene ación de elec icidad, ene gías eno ables,
pa ques eólicos, pa ques sola es, alo ación de in e siones,
me cados de u u os
1.- INTRODUCTION
Du ing he las i een yea s, enewable ene gy has played an e e mo e p ominen ole. In he pa icula case
o elec ici y, his ac can be obse ed bo h in e ms o ins alled capaci y and gene a ion le els [1]. Se e al
ac o s ha e con ibu ed o he b oade deploymen o hese echnologies: g ow h in wo ld elec ici y demand
[2], conce ns abou secu i y o supply and clima e change, ene gy p ices, echnological p og ess, public
suppo …
RENEWABLE POWER GENERATION: DEVELOPMENT, ECONOMICS
AND INVESTMENT VALUATION METHODS
ENERGY ECONOMICS
ARTICULO DE INVESTIGACION
Luis Ma ía Abadie, José Manuel Chamo o,
Renewables
Publicaciones DYNA SL -- c) Maza edo nº69 - 4º -- 48009-BILBAO (SPAIN)
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Pag. 2 / 12
Fig. 1. Renewable elec ici y gene a ion (pe cen age sha e o wo ld o al). Sou ce: Own elabo a ion on da a
om In e na ional Ene gy Agency [2].
Figu e 1 shows he pe cen age o enewable elec ici y deli e ed by he wo ld gene a ion pa k. I s ela i e
sha e has isen om 18% in 2003 o 24.4% in 2016, making i easie o mee he g owing ene gy demand.
Only since 2013 he sha e o coal-based gene a ion s a ed o decline signi ican ly ( om 41.1% in ha yea o
38.3% in 2016). I will ake ime o enewable elec ici y o each a highe ma ke sha e o o al gene a ion
han 24.4%. Ye i s de elopmen will no come wi hou i s own se o p oblems, e.g. he in e mi en ,
unp edic able na u e o enewable sou ces, in addi ion o hei a ia ions o e space and ime (e.g. seasonal
beha io ). These ea u es, coupled wi h insu icien s o age capaci y, can gi e ise o powe sho ages a imes
o peak demand [3] i enewable gene a ion al e s.
RENEWABLE POWER GENERATION: DEVELOPMENT, ECONOMICS
AND INVESTMENT VALUATION METHODS
ENERGY ECONOMICS
ARTICULO DE INVESTIGACION
Luis Ma ía Abadie, José Manuel Chamo o,
Renewables
Publicaciones DYNA SL -- c) Maza edo nº69 - 4º -- 48009-BILBAO (SPAIN)
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Pag. 3 / 12
Fig. 2. Dis ibu ion o wo ld enewable powe gene a ion in 2016. Sou ce: Own elabo a ion on da a om
In e na ional Ene gy Agency [2].
Figu e 2 displays he wo ld mix o enewable gene a ion in 2016. Hyd opowe gene a ion p o ided 4,170,035
GWh, abou 68% o o al enewable gene a ion. Wind gene a ion came second, wi h 957,694 GWh, o 15.6%.
Sola (bo h pho o ol aic, PV, and he mal) accoun ed o 5.5% o o al. O he echnologies like liquid bio uels,
indus ial was e, and ide, wa e and ocean ell s ill u he behind in he wo ld elec ici y gene a ion pa k.
A he wo ld le el, he ins alled capaci ies o bo h wind and sola PV a e g owing o e ime, bu hei capaci y
ac o is ela i ely low (i measu es a plan ’s ac ual powe gene a ion compa ed o he maximum amoun i
could gene a e in a gi en pe iod o ime wi hou any down ime); in he case o wind, i can be abou 30%
depending on he plan ’s loca ion. In 2017 he gene a ion capaci y o o sho e wind was 18.8 GW, a me e
3.5% o o al wind powe capaci y; none heless i also displays an accele a ion. This is due o some posi i e
cha ac e is ics, o example s onge and less in e mi en winds a sea, which in u n enables la ge u bines.
Ye ins alla ion cos s (depending on sea loo dep h and si e cha ac e is ics), he need o g id in as uc u e, and
main enance cos s a e majo d awbacks. The chie law o sola is ha i wo ks only when he sun shines.
In his pape he adi ional me hods o es ima ing he le elized cos o elec ici y (LCOE) a e analyzed and
an al e na i e is p oposed, which is based on elec ici y u u es ma ke quo es (i.e. obse ed ma ke p ices o
u u e deli e y o elec ici y). The LCOE is an es ima e o he a e age cos o p oducing elec ici y wi h a
pa icula echnology. I can be use ul when making in es men decisions (especially in egula ed, e ically
in eg a ed powe sys ems). Sec ion 2 p o ides a ho ough e iew o he wo app oaches o he LCOE a a
heo e ical le el. I also includes some ema ks abou hei unde lying assump ions and pinpoin s some o hei
limi a ions. Sec ion 3 shows nume ical es ima es o LCOE o di e en echnologies and coun ies ollowing
he wo app oaches. I also looks a ecen ends o LCOE es ima es o e ime. Then Sec ion 4 p esen s a
p oposal o an imp o ed LCOE, one ha uses public in o ma ion a ailable on he ma ke s and deals wi h he
discoun ing o isk mo e p ope ly. The e is also a nume ical applica ion o a s anda d wind pa k. Sec ion 5
concludes.
RENEWABLE POWER GENERATION: DEVELOPMENT, ECONOMICS
AND INVESTMENT VALUATION METHODS
ENERGY ECONOMICS
ARTICULO DE INVESTIGACION
Luis Ma ía Abadie, José Manuel Chamo o,
Renewables
Publicaciones DYNA SL -- c) Maza edo nº69 - 4º -- 48009-BILBAO (SPAIN)
Tel +34 944 237 566 – www. e is adyna.com - email: dyna@ e is adyna.com
Pag. 4 / 12
2. APPROACHES TO THE LEVELIZED COST OF ELECTRICITY (LCOE)
The e a e a numbe o al e na i e powe gene a ion echnologies. Consequen ly, powe companies and/o
policy make s ha e looked o me ics ha allow ank hose echnologies acco ding o hei gene a ion cos .
The me ics o choice has ypically been he so-called le elized cos o elec ici y (LCOE). I was i s
p oposed in 1984 by he In e na ional A omic Ene gy Agency [4] o compa e cos s ac oss gene a ing uni s.
The LCOE aims o measu e he uni cos o he powe gene a ed a a gi en acili y in a pa icula sys em. The
concep looks a he simple in p inciple, ye di e en ins i u ions de ine i in a di e en way. Hence one mus
be ca e ul o a oid he ‘easy o use, easy o con use/misuse’ ap. Besides, one mus ensu e ha i is measu ed
uni o mly ac oss he echnologies being compa ed.
Fo his pu pose, wo di e en c i e ia o classi y hem a e adop ed, namely cos s base and ime dimension. A
one le el, he calcula ion can be amed ei he in a single yea o ope a ion (which gi es ise o an annual cos )
o he whole li e o he p ojec (a li e ime cos ). On he o he hand, he calcula ion can well ake in o accoun
only he cos s incu ed by he acili y’s owne , in which case a na ow-based es ima e o he LCOE a ises;
none heless, any powe gene a ion asse is a me e pa o a b oade sys em, and he p ojec ’s impac a he
sys em le el oo could be conside ed when compu ing he LCOE. An e en b oade es ima e would include he
cos s o socie y o wha e e ‘ex e nal e ec s’ emana e om powe gene a ion (e.g. g eenhouse gas emissions,
impac s on public heal h). In his pape he issue is add essed om he owne ’s iewpoin using ma ke p ices
o u u es con ac s on elec ici y.
2.1.- SINGLE-PERIOD PLANT-LEVEL LCOE
Fi s he single-pe iod plan -le el calcula ion o LCOE is e iewed, which is a s anda d o en used in he
elec ical indus y. The US Na ional Renewable Ene gy Labo a o y (NREL) [5] de ines he ‘simple LCOE
(sLCOE)’, which is measu ed in $/kWh, and allows he compa ison o he combina ion o capi al cos s,
ope a ions and main enance, pe o mance, and uel cos s:
𝑠𝐿𝐶𝑂𝐸=𝑜𝑣𝑒𝑟𝑛𝑖𝑔ℎ𝑡 𝑐𝑎𝑝𝑖𝑡𝑎𝑙 𝑐𝑜𝑠𝑡∗𝐶𝑅𝐹+𝐹𝑂𝑀
8760∗𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 𝑓𝑎𝑐𝑡𝑜𝑟 + 𝑓𝑢𝑒𝑙 𝑐𝑜𝑠𝑡∗ ℎ𝑒𝑎𝑡 𝑟𝑎𝑡𝑒+ 𝑉𝑂𝑀. (1)
O e nigh Capi al Cos is measu ed in dolla s pe ins alled kilowa ($/kW). CRF is he capi al eco e y ac o .
I measu es he a io o a cons an annui y o he p esen alue o ecei ing ha annui y o a gi en leng h o
ime [6]; he inancial o mula o compu ing i wi h an in e es a e i o e he nex yea s is:
𝐶𝑅𝐹=1
1
𝑖−1
𝑖(1+𝑖)𝑡=𝑖(1+𝑖)𝑡
(1+𝑖)𝑡−1 (2)
Fixed Ope a ion and Main enance (FOM) cos s a e in dolla s pe kilowa -yea ($/kW-y ). Va iable Ope a ion
and Main enance (VOM) cos s a e in dolla s pe kilowa -hou ($/kWh). In he denomina o , 8760 = 365 × 24
is he numbe o hou s in a yea . The Capaci y Fac o is he po ion o a yea ha he powe plan is gene a ing
powe (0≤CF≤1).
Equa ion (1) is a s anda d one o LCOE. I s a es he equali y be ween he p esen alue o income (o
e enue) and he p esen alue o cos s when calcula ing he LCOE. Howe e , as NREL poin s ou , his
me ics does no include inancing issues, discoun issues, u u e eplacemen o deg ada ion cos s, e c.
2.2.- MULTI-PERIOD PLANT-LEVEL LCOE
Unlike he U.S. NREL, he In e na ional Ene gy Agency [7] ollows a le elized a e age li e ime cos
app oach; in common wi h he o me , i uses he discoun ed cash low (DCF) alua ion me hod. Fo his
pu pose, i adop s h ee discoun a es (3%, 7% and 10%). T ansmission and dis ibu ion cos s a e le aside.
RENEWABLE POWER GENERATION: DEVELOPMENT, ECONOMICS
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The esul s include a ca bon cos o US $30/ onne; beyond his, LCOE calcula ion does no cap u e o he
ex e nali ies o sys emic cos s.
The ounda ion o LCOE compu a ion is he equi alence o he p esen alue o he sum o discoun ed
e enues and he p esen alue o he sum o discoun ed cos s:
∑𝑃𝑀𝑊ℎ×𝑀𝑊ℎ
(1+𝑟)𝑡
𝑛
𝑡=1 =∑𝐶𝑡+𝑂&𝑀𝑡+𝐹𝑢𝑒𝑙𝑡+𝐶𝑂2𝑡+𝐷𝑡
(1+𝑟)𝑡
𝑛
𝑡=1 . (3)
He e, PMWh deno es he cons an li e ime emune a ion o he supplie o elec ici y; MWh is he amoun o
elec ici y p oduced (in MWh), assumed cons an ; (1+ )- is he discoun ac o o yea ( e lec ing paymen s
o capi al); C s ands o o al capi al cons uc ion cos s in yea ; CO2 e lec s ca bon cos s in yea ; and D
cap u es decommissioning and was e managemen cos s in yea ; O&M a e he ope a ion and main enance
cos s in yea ; Fuel is he uel p ice in yea . All o he a iables a e eal, i.e. ne o in la ion. Discoun ing
akes place on a yea ly basis ( he discoun a e mus be eal o consis ency). Since PMWh is cons an o e
ime i can be b ough ou o he summa ion; his yields:
𝐿𝐶𝑂𝐸≡𝑃𝑀𝑊ℎ=∑[(𝐶𝑡+𝑂&𝑀𝑡+𝐹𝑢𝑒𝑙𝑡+𝐶𝑂2𝑡+𝐷𝑡)×(1+𝑟)−𝑡]
𝑛
𝑡=1 ∑𝑀𝑊ℎ×(1+𝑟)−𝑡
𝑛
𝑡=1 . (4)
This is he o mula used by IEA o calcula e he le elized cos o p oducing baseload elec ici y a he plan
le el.
On he o he hand, he Cali o nia Ene gy Commission [8] has de eloped i s Cos o Gene a ion Model
(CGM). I is an Excel sp eadshee model ha calcula es LCOE o u ili y-scale elec ic gene a ing
echnologies. These le elized cos s a e mean o be he o al cos s o building and ope a ing a powe plan o e
he economic li e con e ed o equal annual paymen s in bo h ene gy (dolla s pe megawa -hou ) and capaci y
(dolla s pe kilowa -yea ) e ms.
The CGM i s calcula es he cos s o a echnology on an annual basis, inds he p esen alue o each yea ly
cos , sums he p esen alues o he cos componen s, and hen calcula es he le elized cos he eo , i.e. he
annual paymen (unde he in e es , o discoun , a e ) equi ed o pay o ha p esen alue o e he speci ied
pe iod T. The o mula is as ollows ( he capi al eco e y ac o shows up he e again):
𝐿𝐶𝑂𝐸=∑𝐶𝑜𝑠𝑡𝑡
(1+𝑟)𝑡
𝑇
𝑡=1 𝑟(1+𝑟)𝑡
(1+𝑟)𝑡−1 (5)
The esul s a e p esen ed as a cos pe uni o gene a ion o e he pe iod conside ed (in $/MWh o cen s/kWh).
These calcula ions a e done by di iding he cos s by he sum o all he expec ed gene a ion o e he ime
ho izon being analyzed.
LCOE es ima es accoun o he o al cos s o gene a ing powe . To al cos s a e he sum o ixed cos s (i.e.
independen o he numbe o ope a ing hou s) and a iable cos s. In he end, o al LCOE es ima es a e
calcula ed as a unc ion o who he de elope is: me chan , in es o -owned u ili y, o publicly owned u ili y
( inancing cos s and co po a e axes change depending on he ype o de elope ).
Now, he UK Depa men o Business, Ene gy and Indus ial S a egy [9] de ines he LCOE as “ he
discoun ed li e ime cos o owne ship and use o a gene a ion asse , con e ed in o an equi alen uni o cos
o gene a ion in £/MWh”: 𝐿𝐶𝑂𝐸= 𝑃𝑉(𝑡𝑜𝑡𝑎𝑙 𝑐𝑜𝑠𝑡𝑠)
𝑃𝑉(𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑖𝑡𝑦 𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑖𝑜𝑛) (6)
RENEWABLE POWER GENERATION: DEVELOPMENT, ECONOMICS
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Luis Ma ía Abadie, José Manuel Chamo o,
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To al cos s a e he sum o ‘Capex cos s’ and ‘Opex cos s’. Capi al expendi u e cos s comp ise: p e-
de elopmen cos s, cons uc ion cos s, and in as uc u e cos ( he las wo adjus ed o e ime o lea ning).
Ope a ion expendi u e cos s comp ise: ixed opex (adjus ed o lea ning), a iable opex, insu ance, connec ion
cos s, ca bon anspo and s o age cos s, decommissioning und cos s, hea e enues ( o combined hea -and-
powe plan s), uel p ices, and ca bon cos s. Rega ding he denomina o , expec ed gene a ion da a ake in o
accoun : capaci y o plan , expec ed a ailabili y, expec ed e iciency, expec ed load ac o (all assumed
baseload). Bo h o al cos s and elec ici y gene a ion a e exp essed in ne p esen alue e ms (i.e. u u e cos s
and ou pu s a e discoun ed a a a e when compa ed o cos s and ou pu s oday).
Following Alde sey-Williams and Rube [10], in inance he in e nal a e o e u n (IRR) on an in es men
p ojec is he discoun a e ha makes i s Ne P esen Value (NPV) equal o ze o:
𝑁𝑃𝑉=𝑃𝑉(𝑟𝑒𝑣𝑒𝑛𝑢𝑒𝑠)−𝑃𝑉 (𝑐𝑜𝑠𝑡𝑠)=0→𝑃𝑉(𝑐𝑜𝑠𝑡𝑠)=𝑃𝑉(𝑟𝑒𝑣𝑒𝑛𝑢𝑒𝑠) (7)
Hence, when = IRR he LCOE can be equi alen ly de ined as:
𝐿𝐶𝑂𝐸=𝑃𝑉(𝑟𝑒𝑣𝑒𝑛𝑢𝑒𝑠)
𝑃𝑉(𝑒𝑛𝑒𝑟𝑔𝑦) =𝑃𝑉(𝑒𝑛𝑒𝑟𝑔𝑦×𝑝𝑟𝑖𝑐𝑒)
𝑃𝑉(𝑒𝑛𝑒𝑟𝑔𝑦) . (8)
Thus, he LCOE can na u ally be in e p e ed as he elec ici y p ice equi ed o he p ojec o ha e a ze o
NPV, o , in o he wo ds, o he e enues om he p ojec o p o ide a e u n (IRR) ha exac ly ma ches he
discoun a e ( ). This same easoning unde lies he calcula ion o LCOE acco ding o NREL [11].
Analy ically:
𝐿𝐶𝑂𝐸×∑𝐸𝑡
(1+𝑟)𝑡
𝑛
𝑡=1 =∑𝐶𝑡
(1+𝑟)𝑡
𝑛
𝑡=1 . (9)
In any case, whene e he cos s conside ed a e eal (i.e. as seen om ime 0, in cons an cu ency uni s, o
unadjus ed o u u e in la ion) he LCOE measu es he minimum cons an eal p ice o elec ici y o he
p ojec o make sense economically; needless o say, bo h IRR and a e eal oo o consis ency. By he same
oken, using nominal cos s (i.e. in cu en dolla s, o adjus ed o in la ion) along wi h a nominal discoun a e
yields he a e age nominal p ice o e he p ojec ’s li e ime ha p o ides he equi ed nominal e u n.
Hence o h he ocus is on elec ici y om wo enewable sou ces, namely sola and wind. Thus, in Sec ion 4
only capi al expenses (C ) and ixed ope a ing cos s (O ) a e conside ed in he analysis o LCOE (ins ead,
a iable ope a ing cos s, ca bon cos s, and decommissioning and was e managemen cos s a e le aside).
Speci ically, Equa ion (10) is used, which is a simpli ied e sion o he one used in [7]:
𝐿𝐶𝑂𝐸=∑𝐶𝑡+𝑂𝑡
(1+𝑟)𝑡
𝑛
𝑡=1
∑𝐸𝑡
(1+𝑟)𝑡
𝑛
𝑡=1 . (10)
2.3.- REMARKS ON THE UNDERLYING ASSUMPTIONS
The abo e o mulas o LCOE aise wo impo an s p oblems a leas . The i s one in ol es he beha io o
cos s and p ices o e ime. The second one has o do wi h choice o he app op ia e a e o discoun u u e,
unce ain cash lows back o he p esen when making in es men decisions.
a) Cos in la ion is no much o a p oblem o he LCOE o mula i in la ion is cons an and applies
equally o e e y cos ac o . In his case i is necessa y o u n he eal discoun a e in o a nominal one by
adjus ing he o me o in la ion: (1 + nominal a e) = (1 + eal a e)×(1 + in la ion a e). The LCOE o mula
will hen yield a nominal elec ici y p ice. Ye he ea lie assump ion is an s ingen one.
On he o he hand, in la ion accumula es o e ime. This implies ha powe echnologies wi h he bulk
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o hei cos s ea lie in ime a e less a ec ed by in la ion han hose in which mos o he expendi u e will ake
place u he in o he u u e. Thus, all else equal, enewable s a ions can show a lowe LCOE han he mal
ones (owing o he g ea e impo ance o uel and ope a ion cos s o he la e ).
Besides, he elec ici y p ice is no cons an . S anda d ea u es a e seasonali y, mean e e sion, jumps,
among o he s. The elec ici y p ice can also depend on he coun y/ma ke a hand. Fu he , he elec ici y
p ice (o e enues) and gene a ion cos s can well be a ec ed by di e en in la ion a es.
b) The discoun a e is con o e sial oo. Acco ding o inance heo y, each u u e cash low mus be
dicoun ed a a a e commensu a e wi h i s isk. The e o e, a single discoun a e ( o e e y ou low o cash and
cons an h ough he plan ’s li e ime) is ha dly adequa e. This applies i espec i e o whe he he a e is
‘subjec i e’ (based on managemen ’s expe judgemen ) o ‘objec i e’ (like he weigh ed a e age cos o he
capi al in es ed in he plan ). Anyway, a highe pe cei ed isk (and ensuing discoun a e) in some powe
echnologies will ansla e in o a highe LCOE o hose echnologies.
In his ega d, IEA [7] uses h ee discoun a es ac oss all echnologies: 3% (co esponding o he
social cos o capi al), 7% (ma ke a e in de egula ed o es uc u ed elec ici y ma ke s), and 10% (in es men
in a high- isk en i onmen ). BEIS [9] ocuses on LCOE es ima es using a hu dle a e o 10% along wi h
es ima es a 7% and 3.5% hu dle a es o compa a i e pu poses wi h in e na ional publica ions. CEC [8]
de ines he discoun a e as he a e - ax wigh ed a e age cos o capi al (WACC) and uses a 6.17% eal a e in
i s mid case scena io (changing o 10.57% and 4.28% in he high case and low case, espec i ely). These a es
can be con o e sial and signi ican ly a ec he alua ion p ocess. Below a me hodology o add ess some o
hese p oblems is p oposed.
I is possible o sides ep his issue o some ex en by using obse ed p ices in u u es ma ke s on
commodi ies. These p ices can be discoun ed a he isk- ee a e (because o he hedging po en ial ha hese
ma ke s o e o hei playe s). In he eu o a ea he Ge man deb a e can be adop ed o his pu pose.
c) Ano he p oblem is ha enewable echnologies do no ope a e egula ly h ough ime. In addi ion
o unce ain, hey a e in e mi en and display seasonal beha io s (o e di e en ime ames). Thus, he powe
p ice ha hey ge can well be di e en om he a e age ma ke p ice.
d) Ene gy and en i onmen al policy can also pose a p oblem o using he LCOE o mula. In p inciple,
i he e is a go e nmen push in a o o enewable gene a ion expansion (e.g. eed-in a i s, p oduc ion ax
c edi s, in es men ax c edi s), one can easily add i s p esen alue o Equa ion (10); i public suppo
measu es a e ce ain, he isk- ee a e mus be used o discoun hem. Bu policy measu es canno always be
aken o g an ed o e long ime ho izons as equi ed by ene gy p ojec s.
This said, all o he abo e models accoun o echnological de elopmen o gene a ing echnologies h ough
hei espec i e lea ning cu es. The lea ning ac o ypically esul s in dec easing capi al cos s; he e ec
depends on he ype o echnology and he da e when he plan en e s se ice. Fo example, om 2022 o 2040
NREL [5] p ojec s la ge LCOE educ ions o onsho e wind (9%), o sho e wind (16%), and sola PV (16%).
Simila ly, IEA [7] assumes a lea ning a e o 7% o onsho e wind; o o sho e wind, cos educ ions o abou
40% could be expec ed in he cos o elec ici y gene a ion by 2030, hough unce ain ies emain. Simila ly,
CEC [8] and BEIS [9] use echnology-speci ic lea ning a es.
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3. EMPIRICAL RESULTS
This sec ion p esen s nume ical LCOE es ima es acco ding o he wo me hodologies explained abo e and
analyzes hei ecen ends.
3.1.- SINGLE-PERIOD PLANT-LEVEL LCOE
The analysis in NREL [5] d aws on h ee sou ces, namely he U.S. Ene gy In o ma ion Adminis a ion (EIA)
[7], he Na ional Renewable Ene gy Labo a o y (NREL) [11] o Na ional Ene gy Technology Labo a o y
(NETL) [12], and Laza d [13]. Then NREL compu es U.S. es ima es o LCOEs o selec ed gene a ion
echnologies using cos and hea a e da a anges om hese h ee sou ces (in he case o non-dispa chable
echnologies he hea a e is ze o). Ope a ing cha ac e is ics, such as uel cos s (ze o o non-dispa chable
echnologies) and capaci y ac o s, di e oo o each echnology; he es ima es o LCOE conside he lowes
and highes assump ions epo ed ac oss he h ee p ima y sou ces. On op o his, NREL applies he same
inancial cha ac e is ics ac oss all echnologies; in his ega d, he minimum and maximum cos o capi al
om hese sou ces a e used as inpu s o he LCOE. The esul ing LCOE anges o wind and sola a e shown
in Table 1; hese alues do no include ax c edi s. They e lec wide a ia ion o esou ce quali y ac oss he
U.S.
Table 1. Cu en U.S. LCOE anges o wind and sola echnologies (2013$/MWh). Sou ce: NREL [5].
EIA
NREL
Laza d
Technology
Low
High
Low
High
Low
High
Wind, onsho e
37.09
117.76
35.36
88.87
26.30
81.86
Wind, o sho e
117.22
279.25
114.75
241.09
81.27
218.10
Sola PV, u ili y-scale
80.00
430.52
54.94
171.03
46.06
132.61
Sola CSP
140.20
271.89
82.61
207.35
104.44
249.46
3.2.- MULTI-PERIOD PLANT-LEVEL LCOE
The analysis wi hin IEA [7] d aws on da a o 181 powe plan s in 22 coun ies (19 OECD coun ies plus
B azil, China and Sou h A ica). All cos igu es a e gi en in 2013 US dolla s. The assumed commissioning
da e is 2020. Table 2 displays he LCOE es ima es o onsho e wind, sola he mal, and he h ee ca ego ies o
sola PV in he s udy ( esiden ial, comme cial, and la ge, g ound-moun ed) in he case o Spain.
Table 2. Le elized cos s o elec ici y o gene a ing plan s in Spain (2013$/MWh). Sou ce: IEA [7].
Technology
Capi al cos s
O&M cos s
LCOE
3%
7%
10%
3%-7%-10%
3%
7%
10%
Wind, onsho e
53.65
74.32
92.09
27.86
81.51
102.19
119.96
Sola PV, esiden ial oo op
64.99
100.43
131.11
35.61
100.60
136.02
166.70
Sola PV, comme cial oo op
53.61
82.85
108.16
49.35
102.97
132.01
157.21
Sola PV, la ge, g ound-moun ed
41.57
64.35
84.12
45.75
87.33
109.92
129.57
Sola he mal (CSP) no s o age
175.93
260.88
335.14
87.46
263.39
348.35
422.60
3.3.- EVOLUTION OF LCOE ESTIMATES OVER TIME
As al eady men ioned in Sec ion 2.2, he ocus is on elec ici y om sola and wind ene gies. The e olu ion o
he LCOE in he U.S. has been analyzed by Laza d [13]. I shows a consis en educ ion o e ime, bu a an
e e slowe pace. This sugges s a p oximi y o an equilib ium. The mean alues o 2017 a e 45 US$/MWh o
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onsho e wind and 50 US$/MWh o sola a u ili y scale. The es ima e o o sho e wind in he same yea is
113 US$/MWh.
The IEA [7] shows a numbe o LCOE es ima es o each coun y and echnology in he sample.
These calcula ions depend on he alues o i adia ion and la i ude, bu his in o ma ion, hough used in he
calcula ions, is no supplied by IEA [7].In he Spanish case he LCOE o sola PV (la ge, g ound-moun ed) is
87.33 US$/MWh, o 65.50 EUR/MWh using he exchange a e in he epo [7]. Fo onsho e wind i is 81.51
US$/MWh, o 61.13 EUR/MWh.
Now, hese LCOEs can be compa ed wi h he p ice o elec ici y o u u e deli e y (i.e. he p ice in
he u u es ma ke o elec ici y). The LCOEs a e highe han he u u es p ices. Fo example, Table 3 shows
he annual u u es quo es on 10/31/2018 o elec ici y o be deli e ed in Spain. An open ques ion is i an
inc easing enewable gene a ion can lead o a decline in elec ici y p ices.
Table 3. Fu u es elec ici y p ices (EUR/MWh) o Spain on 10/31/2018. Sou ce: www.omip.p .
Con ac Name
Re e ence P ice
FTB YR-19
60.30
FTB YR-20
53.60
FTB YR-21
50.60
FTB YR-22
48.30
FTB YR-23
46.70
In he case o o sho e wind, he IEA da a [7] also show an impo an dispe sion in LCOE.s This echnology
shows a mean capaci y ac o o 38.72% (i is 34.66 o onsho e wind and 16.66 o sola PV la ge, g ound-
moun ed). Ye i s a e age LCOE is 136.39 US$/MWh, well abo e he u u es p ices on Table 3
4.- A PROPOSAL FOR AN ENHANCED MULTI-PERIOD LCOE
4.1.- PROPOSED METHODOLOGY
Nex , an al e na i e alua ion me hodology o hose in Sec ion 2.2 is p oposed. The s a ing poin is
he s anda d NPV o mula, i.e. he di e ence be ween he p esen alue o cash in lows and he p esen alue
o cash ou lows, bu wi h speci ic discoun a es ha apply o each componen :
𝑁𝑃𝑉=∑ 𝑝𝑡×𝐸𝑡
(1+𝑟1)𝑡− ∑ [𝐶𝑡
(1+𝑟2)𝑡+𝑂𝑡
(1+𝑟3)𝑡] (11)
Equa ion (11) shows he NPV in disc e e ime. This is simila o Equa ion (3), bu in his case he discoun a e
and he u u e elec ici y u u e a e ob ained om ma ke in o ma ion ( hey a e no subjec i e alues). No e
ha when u u es ma ke p ices a e used, e enues can be discoun ed a he iskless a e. No e also ha ,
consis en wi h inancial heo y, he cos s known wi h ce ain y can be discoun ed oo a he isk ee a e.
Al e na i ely Equa ion (12) in con inuous ime can be used:
𝑁𝑃𝑉=∫ 𝑝𝑡×𝐸𝑡×𝑒−𝑟1
∗𝑑𝑡−∫ [𝐶𝑡×𝑒−𝑟2
∗+𝑂𝑡×𝑒−𝑟3
∗] (12)
whe e he discoun a es 𝑟1,𝑟2,𝑟3 co espond o he di e en ma ke s. They a e sligh ly di e en unde
con inuous o disc e e compounding.
Cas illo-Calzadilla e al. [14] assess a sola PV acili y in a s andalone se ices building in Spain. He e
an onsho e wind a m in Spain wi h he ollowing cha ac e is ics is conside ed ( alues o (a)-(g) a e aken
