Intermittently renewable energy, optimal capacity mix and prices in a deregulated electricity market. Irena Milstein a and Asher Tishler b.

Transcription

1 Inermenly renewable energy, opmal capacy mx and prces n a deregulaed elecrcy marke Irena Mlsen a and Asher Tshler b a Holon Insue of Technology, 52 olomb., Holon 58102, Israel (renam@h.ac.l) b Faculy of Managemen, Tel Avv Unversy, Tel Avv 69978, Israel (ashler@pos.au.ac.l) Absrac Ths paper assesses he effec of nermenly renewable energy on generaon capacy mx and marke prces. We consder wo generang echnologes: (1) convenonal fossl-fueled echnology such as combned cycle gas urbne (CCT), and (2) sunshne-dependen renewable echnology such as phoovolac cells (PV). In he frs sage of he model (game), when only he probably dsrbuon funcons of fuure daly elecrcy demand and sunshne are known, producers maxmze her expeced profs by deermnng he CCT and PV capacy o be consruced. In he second sage, once daly demand and sunshne condons become known, each producer selecs he daly producon by each echnology, akng he capaces of boh echnologes as gven, and subjec o he avalably of he PV capacy whch can be used only f he sun s shnng. Usng real-world daa for Israel, we confrm ha he nroducon of PV echnology amplfes prce volaly. A large reducon n PV capacy cos ncreases PV adopon bu may also rase he average prce. Thus, when consderng he promoon of renewable energy o reduce CO 2 emssons, regulaors should assess he behavor of he elecrcy marke, parcularly wh respec o characerscs of renewable echnologes and demand and supply unceranes. Keywords: Elecrcy markes, renewable echnologes, endogenous capacy mx JEL codes: D43, L11, L94, D24 We are graeful o I. pekerman and C.K. Woo for valuable commens and suggesons. 1

2 1. Inroducon Besdes nuclear energy expanson, commonly acceped remedes for he problem of global warmng due o greenhouse gases (H), whch wll lkely domnae publc polcy debaes n he comng decade (Weyan e al., 2006; Tol, 2006; Lor, 2010; Cansno e al., 2010), nclude ncreased conservaon and renewable energy o dsplace he use of fossl fuels (Traner, 2010; Lor, 2010; Traber and Kemfer, 2010). Renewable energy s becomng an ever-ncreasng feaure of he landscape worldwde. For nsance, [2009] was a record-seng year for wnd energy n he IEA Wnd member counres, whch nsalled more han 20 ggawas (W) of new wnd capacy. Ths growh led o a oal of 111 W of wnd generang capacy, wh more han 2 W operang offshore (IEA, 2010a, p.2). In 2008, renewable energy also me 7.3% of ermany's prmary energy consumpon, a fgure ha s predced o ncrease o 33% by 2020 (Burgermeser, 2009). "I's ambous, bu ermany can be runnng on renewable energy by 2050 f here s he polcal wll", sad Davd Wormann, Drecor of Renewable Energy and Resources a ermany Trade and Inves, a governmen body supporng he counry s renewable energy secor (Burgermeser, 2009). However, recen research on nuclear energy (Kessdes, 2010; NEA, 2010; Lor, 2010), carbon capure and sorage (CC) (MIT, 2007; IEA, 2010b) and ncenves o promoe green elecrcy (Cansno e al., 2010; Badcock and Lenzen, 2010) suggess ha he road o a "green world" s no fully paved and he poenal and lms of renewable energy are nsuffcenly explored and undersood (Traner, 2010; Lor, 2010). I also suggess ha recen European polces o reduce H 2

3 emssons 1 and conform o he Kyoo Proocol wll lkely rase elecrcy prces subsanally, unless new approaches o elecrcy generaon are adoped (Lnares e al., 2006; Reedman e al., 2006; Odenberger and Johnsson, 2007; Marnsen e al., 2007; Cansno e al., 2010). Ths paper offers a formal model o ad regulaory undersandng of he relaonshp beween renewable energy, opmal generaon mx, and elecrcy prce level and volaly. In parcular, demonsraes ha weaher dependence of renewable energy sources (usng he example of phoovolac cells) and he fac ha elecrcy power canno be economcally sored and he demand sde canno be suffcenly managed (Traber and Kemfer, 2010) can cause prce spkes and ncrease he average prce and prce volaly, parcularly when PV adopon rses due o s declnng cos. 2 Furhermore, hese prce effecs worsen wh he nroducon of CO 2 axes, a polcy ha ams o reduce emssons, as requred by he Kyoo proocol (Cansno e al., 2010; Badcock and Lenzen, 2010). To be far, enforcng hgh elecrcy prces va H axes s lkely o boos R&D expendure by governmens and prvae frms on producve, safe and new echnologes whch wll, evenually, brng abou cleaner and more envronmen-frendly elecrcy generaon. To smplfy he exposon, our model only employs combned cycle gas urbne (CCT) and PV plans. However, s resuls equally apply o oher fossl as well as weaher-dependen renewable energy sources such as wnd, solar-hermal 1 The quanes of CO 2 emssons by echnology are dealed n Lse and Kruseman (2008) and Kessdes (2010). The cos of reducng H n he elecrcy secor depends on he counry s exsng and fuure mx of generaon echnologes (Baalle e al., 2007; Tshler e al., 2007). amuelson (2007) dscusses he praccal dffcules of mgang H emssons. 2 ubsanal prce volaly due o sudden and unexpeced change n wnd generaon s repored by ERCOT n Texas (Hardy and Nelson, 2010). 3

4 echnologes, and sea waves. In parcular, more effcen elecrcy producon by PV echnology wll enhance he followng effecs: In he shor erm, when mos of he generaon capacy s gven, wll shf producon away from CO 2 -nensve (fossl) echnologes o PV echnology. In he md and long erm, opmal capacy mx wll shf new capacy consrucon away from CO 2 -nensve echnologes o PV echnology and, possbly, cause early reremen of CO 2 -nensve echnologes. An ncrease n he share of elecrcy producon by PV echnology wll rase he equlbrum elecrcy prce durng perods n whch weaher condons lm s use. nce elecrcy demand s very "nelasc", parcularly n he shor run, elecrcy prces wll spke subsanally durng hese perods, and wll lkely rase he average prce and prce volaly. Ths paper conrbues o he leraure by presenng an analycal model of endogenous nvesmens and operaons n an elecrcy marke wh CCT and PV echnology under demand and supply unceranes. 3 Formally, n he frs sage of he game, when only he probably dsrbuon funcons of fuure daly elecrcy demands and weaher condons are known, prof-seekng producers maxmze her expeced profs by deermnng he amoun of generaon capacy o be consruced for each echnology. In he second sage, afer daly demand and sunshne-deermned PV avalably become known, each producer selecs s daly elecrcy producon, hereby deermnng he equlbrum marke prces. Lke many oher sudes of he 3 Alhough he analyss becomes more complcaed, s sraghforward o demonsrae he naure of he soluon s unchanged by addng more generang echnologes (Mlsen and Tshler, 2009). 4

5 elecrcy secor, we employ he Courno conjecure o deermne equlbrum quanes and prces n he second sage of he game, where elecrcy s sold smulaneously by all producers o mee marke demand (Carpo and Perera, 2007; Borensen and Bushnell, 1999; reen, 1996, 2004; Newbery, 1998; Tshler and Woo, 2006; Puller, 2007; Murphy and meers, 2005, 2007; Tshler e al., 2008; Bushnell e al., 2008). We show ha he opmal soluon s very sensve o PV's sunshnedependen avalably and capal cos. These heorecal properes of he model are llusraed usng daa for he Israel elecrcy marke Model Consder wo ypes of generang echnologes: (1) CCT, o be denoed, whch exhbs "low" capacy cos and "hgh" varable cos; and (2) PV, o be denoed, wh hgh capacy cos and zero varable cos. 5 The olgopoly marke consss of N dencal frms, each employng boh echnologes. Each frm bulds generang capacy and hen uses o generae and sell elecrcy on each day of an operaon horzon of T days (e.g., T = 365 for a 1-year horzon). 6 Le P and Q denoe he elecrcy prce and oupu on day. Followng Wolfram (1999) and Tshler e al. (2008), daly elecrcy demand s: 4 Tshler e al. (2008) presen recen daa on four major elecrcy markes n he UA (New England; Calforna; PJM Pennsylvana, New Jersey and Maryland; and ERCOT, Texas) demonsrang ha he characerscs of he dsrbuon of elecrcy prces over me n hese markes and n Israel s very smlar. Thus, he resuls n hs paper lkely apply o hose, and oher, markes. 5 Neher of hese wo echnologes domnaes he oher. ee Chao (1983) and Mlsen and Tshler (2009) on hs ssue and he general use of he concep "mer order" n elecrcy markes. 6 Elecrcy demand can be defned for any lengh of me. I s sraghforward, for example, o solve he model for 8760 hours or half-hours of he year. The model assumes ha consumers are nformed abou elecrcy prces and can respond, a leas o some exen, o elecrcy prce changes. 5

6 P a, (1) bq where N (Q Q ) 1 Q and Q and Q denoe he CCT and PV producon on day of he -h frm. The parameers a 0 and b 0 are assumed o be known consans. In equaon (1), s a random varable accounng for he effec of a random demand facor such as emperaure. s revealed o he elecrcy producers on day and he prce s deermned each day accordng o he Courno conjecure. 7 Only f ( ), he (probably) densy funcon of, and he probably funcon of daly sunshne are known o he frms when hey choose her capacy. Followng Murphy and meers (2005, 2007) and Mlsen and Tshler (2009), he annual producon cos of he -h frm employng echnology (echnology ) and a generaor of K ( K ) MW of capacy s: C ( K,Q ) K c Q (2a) C ( K,Q ) K c Q (2b) where T Q Q and 1 T Q Q denoe he annual CCT and PV producon by 1 frm. Capacy cos s U$ ( ) per MW-year and varable (margnal) cos s U$ c ( c ) per MWH for echnology (echnology ). By assumpon, echnology s more expensve n operaons, c c 0, and echnology s more expensve 7 Puller (2007) shows ha he conduc of he frms n he resrucured elecrcy marke n Calforna durng Aprl 1998 unl lae 2000 s conssen wh a Courno prcng game. Bushnell e al. (2008) fnd ha a Courno-compeon predced equlbrum prces are good approxmaons for acual elecrcy prces durng he summer of 1999 n hree U markes. 6

7 n capacy,. The parameers consans. c, c, and are assumed o be known The avalably of PV capacy on day, =1,,T, s condonal on wheher he sun s shnng. We suppose ha he sun s shnng wh probably. If he sun s shnng on day, all of PV capacy s avalable on ha day; oherwse he avalable PV capacy s zero. For exposonal smplcy, we assume ha he avalably of he sun and are ndependen. 8 Ths assumpon reflecs our conenon ha demand s manly drven by emperaure, much less so by daly cloudness. Fnally, we assume ha E( ) 0, Var ( 2 ) and c a. 9 The decson process of hs wo-sage game s as follows: age 1: Each of he N frms decdes on s capacy nvesmen, K and K, o maxmze s expeced profs over T days, akng he capaces of he oher N - 1 frms and he probably funcons of and daly sunshne as gven. age 2: Once he frms know and he sunshne condon on day, each frm decdes how much elecrcy o produce (and sell) o maxmze s daly operang prof. The frm's decson s based on he Courno conjecure, reang he quany produced by he oher N - 1 frms and he capacy of all N frms as gven. Ths sage s repeaed T (ndependen) mes. The game s solved recursvely usng backward nducon. The daly elecrcy producon of each frm s found by solvng he second sage of he game. The opmal 8 The naure of he resuls s unchanged f hese wo varables are correlaed. Prce volaly ends o be hgher f hey are posvely correlaed. 9 If E( ) 0, we add µ o he consan a n expresson (1), hus seng E( ) 0. 7

8 second-sage soluons (he reacon funcons) are hen used o deermne he expeced prof-maxmzng generaon capaces n he frs sage. Formally, he objecve of he -h frm n sage 2 s o maxmze s operang profs,, condonal on, appearance of he sun, K and K ( = 1,..., N ), Q k and Q ( k 1,...,N ;k ). When he sun s shnng, he maxmzaon problem of k frm on day s: max ( P c Q,Q s.. Q K, )Q Q ( P c K, Q )Q,Q 0, 1,...,N (3) When here s no sun, he maxmzaon problem of frm on day s: max ( P c Q,Q s.. Q K, )Q Q 0, 1,...,N (4) The soluon of (3) s gven n Mlsen and Tshler (2009) and he soluon of (4) s gven n Tshler e al. (2008). To deermne opmal capaces, he -h frm uses he second-sage reacon funcons o solve he sage 1 expeced prof maxmzaon problem: max K,K E [ T T ( K,K )] (1 )E [ ( K )] K K. (5) 1 1 There s no closed form soluon of problem (5) and he opmal capaces, * K, are obaned by numercal mehods. * K and 8

9 3. Applcaon o real-world daa To llusrae s real-world relevance, we apply our model o Israel daa. Table 1 lss descrpve sascs of he hourly elecrcy use n Israel durng 2009 and Fgure 1 presens he hsogram of hese daa (IEC, 2010). The daa n Fgure 1 and Table 1 show ha he dsrbuon of he hourly elecrcy use n 2009 s close o symmercal, wh mos of he mass around he mean. Table 1: Daly averages and maxmal values of hourly elecrcy use n Israel durng 2009 (1000 MWH) Average hourly use Maxmal hourly use Mean Medan ample sandard devaon Mnmum Maxmum

10 More Percen n % 10.0% 8.0% 6.0% 4.0% 2.0% 0.0% Hourly elecrcy use (1000 MWH) Fgure 1: Hsogram of hourly elecrcy use n 2009 Compuaon of he opmal capaces s based on esmaes of he demand parameers, a and b, he cos parameers,,, c, and c, he parameers of he probably funcon f ( ) and on ρ. Usng he average generaon prce n 2009 (66.4 $/MWH) and a (shor-run) prce elascy of for he daly demand funcon for elecrcy, 10 hese esmaes are as follows (Tshler e al., 2008): 11 a , b , T , c 40, c 0. To llusrae he properes of he equlbrum soluon of he model, we consder hree PV o CCT capacy cos raos: (1) 10, (2) 6 and 10 The naure of he resuls of hs sudy does no change when prce elascy s -0.1 or ee Khab (2010) and Lor (2010) and references heren for he coss of elecrcy generaon by varous echnologes. 10

11 (3) The frs sage of he game s solved under he assumpon ha f ( ) follows he unform dsrbuon, f ( ) 1/( ), wh 317 and We also assume = and N = Fgure 2 presens he ndusry s opmal capacy as a funcon of. I shows ha producers wll no buld PV capacy a he prevalng (very hgh) capacy cos of he PV echnology, mrrorng he realy repored n Traner (2010), Lor (2010), and Badcock and Lenzen (2010). The share of PV capacy n he ndusry s oal capacy ncreases when PV capacy cos decreases. 16 Uncerany n daly PV capacy, however, reduces s profably. Hence, a large PV capacy cos reducon only leads o a moderae ncrease n PV adopon. As shown n Fgure 2, PV capacy s abou 22% of oal capacy when PV capacy cos s reduced by 80%. Mlsen and Tshler (2009) show ha he frequency of prce spkes does no depend on he fxed cos of he base echnology (PV n our model) when s capacy s always avalable (ρ = 1). Ths resul does no hold when ρ < 1. Fgure 3 presens he dsrbuon of daly equlbrum elecrcy prces n he year. 12 The frs case, where he PV capacy cos s 10 mes ha of he CCT capacy cos, reflecs he curren rao n he Israel marke (Lor, 2010 and Traner, 2010). The laer wo cases represen echnology mprovemens. 13 Though he normal dsrbuon seems o be a more reasonable approxmaon (see Fgure 1), he unform dsrbuon s smpler o use n our case (a smlar assumpon s made, for example, n Wang e al., 2007). Tshler e al. (2008) show ha employng he emprcal, a unform, or a normal dsrbuon yelds almos dencal opmal capacy. 14 Ths value seems o be realsc for Israel: nghs consue abou one hrd of he year and he sun may appear parally or no a all durng 5-15% of he year - mosly, bu no only, durng he wner. 15 Daly prces are somewha lower (hgher) when N ncreases (decreases), bu he naure of he resuls does no change for larger (smaller) N. 16 PV s he mos-run echnology snce s margnal producon cos s zero. The ndusry s oal capacy s lower n a compeve marke han under regulaon due o he prce spkes, whch shave demand durng peak hours, hus reducng he need for capacy durng peak hours (Tshler e al., 2008). 11

12 U$ per MWH Indusry capacy (1000 MW) 7.5 Capacy of echnology Capacy of echnology % 21.6% / =10 / =6 / =2 Fgure 2: Indusry capacy Capacy s 10 mes more expensve han capacy Capacy s 6 mes more expensve han capapcy Capacy s 2 mes more expensve han capacy Days Fgure 3: Prce dsrbuon over he year Equlbrum prces are sable when producon s below full capacy and sar o rse a an ncreasng rae once full capacy s reached. Full capacy s reached 12

13 earler, he hgher s he share of PV n oal capacy, whch occurs due o lower PV capacy cos. In our example, when PV capacy s zero because he sun s no shnng, he CCT echnology reaches full capacy for 17, 35 and 96 days of he year when 10, 6 and 2, respecvely. 17 Moreover, full capacy s reached on he 318h day of he year when 10and on he 266h day when 2. Thus, prce spkes are larger and more frequen under rsng PV adopon due o declnng PV capacy cos. Fgure 4 presens he average and maxmal elecrcy prces for 10, 6 and 2. The average equlbrum prces ncrease from 179 $/MWH when 10 o 206 $/MWH when 2. The maxmal prce ncreases from 528 $/MWH when 10 o 704 $/MWH when 2. Thus, he larger PV capacy share yelds hgher elecrcy prce spkes on days whou sun, when all he demand mus be me by CCT. Very hgh prce spkes ogeher wh very low prce elascy gve producers some monopoly power, poenally rasng he average elecrcy prce over he year. Ths phenomenon does no happen when ρ = 1 (he sun s always shnng), and he average elecrcy prce decreases when PV capacy cos declnes n hs case (Mlsen and Tshler, 2009). 17 Prce spkes may no occur f he value of he random varable, ε, s suffcenly small. For example, echnology reaches full capacy on 96 days when 2. On sx of hese days we do no observe prce spkes, due o small realzaons of ε. 13

14 U$ per MWH 800 max prce 600 average prce / =10 / =6 / =2 Fgure 4: Average and maxmal prce Table 2 presens he maxmal daly elecrcy prces as a funcon of for dfferen values of ρ. A hgher value of ρ mples a hgher share of PV capacy n oal capacy whch, n urn, mples hgher elecrcy prce spkes on days whou sunshne, as all he demand mus be me by CCT capacy nsalled. When he capacy cos of PV s large, producers buld PV capacy only when he sun shnes on a suffcen number of days. Ths happens when 10 and ρ = 0.9 or hgher (he opmal PV capacy s zero when 10 and ρ < 0.9) A he pon a whch producers sar o buld some PV capacy, whch s 10 and ρ = 0.9 n our case, oal capacy ncreases, PV capacy s very low, CCT capacy s sll "large", and prce spkes may occur on days on whch s "large" (raher han on days on whch he sun s no shnng). Consequenly, he maxmal elecrcy prce may declne n hs suaon relave o he maxmal prce when ρ < 0.9 (see he frs column of Table 2). 14

15 Table 2: Maxmal elecrcy prces as a funcon of and ρ ρ Do Fgure 4 and Table 2 mean ha R&D mprovemens or governmen subsdes o PV echnology are no socally desrable? No necessarly. Fgure 5 shows ha he ndusry s prof ncreases when decreases. One reason for he prof ncrease s lower oal generaon cos. Anoher reason s hgher olgopoly profs due o he low prce elascy of elecrcy demand, whch enables producers o gan more on rsng marke prces han hey lose on fallng marke prces. Fgure 6 shows ha he ndusry s producon ends o declne as PV capacy cos falls. Ths mrrors rsng PV adopon due o declnng PV capacy cos, whch n urn rases he average marke prces, hus reducng marke demand. Fnally, he ndusry s elecrcy producon n a compeve marke s lower n comparson o producon under marke regulaon (abou 53 mllon MWH n 2009; see IEC, 2010). 15

16 Indusry producon (1000 MWH) Indusry profs ($ bllon) 8 Indusry profs: echnology Indusry profs: echnology % 17.0% / =10 / =6 / =2 Fgure 5: Indusry profs 60,000 50,000 Indusry producon usng echnology Indusry producon usng echnology 49,139 49,155 47,979 40,000 30,000 20,000 10, % 16.1% / =10 / =6 / =2 Fgure 6: Indusry producon 16

17 4. Concluson Ths paper analyzes he relaonshp beween nermenly renewable energy and opmal endogenous generang capacy mx, energy producon by echnology, and marke prces n a Courno marke wh CCT and PV generaon. The soluon o a wo-sage game shows ha rsng adopon of PV due o declnng PV capacy cos can ncrease he average marke prce and prce volaly. Ths resul s confrmed by an applcaon o real-world daa for he Israel elecrcy secor. I arses because marke prces spke o balance he prce-nelasc demand and CCT capacy nsalled when PV oupu dsrups due o a lack of sunshne. The paper hghlghs ha gh generang capacy and frequen elecrcy prce spkes n compeve elecrcy markes are due no only o demand varably over me (day, season and year), he hgh cos of consrucng capacy and he long lead me requred o add new capacy, bu also o supply uncerany, an nevable oucome n markes wh subsanal renewable generaon capacy (Hardy and Nelson, 2010; Traner, 2010, Lor, 2010). To be sure, an ndependen sysem operaor may mgae prce spkes by mananng capacy reserves ha wll no be par of he daly marke operaons (Tshler e al., 2008). However, he analyss of hs paper underscores he fac ha effcen use of renewable capacy requres an negraed approach o he managemen of elecrcy markes, one ha accouns for modern and properly dsrbued T&D nfrasrucure, balancng generaon, smar grds, and mplemenaon of approprae fnancal and oher ncenve sysems (Lor, 2010, Hardy and Nelson, 2010 and references heren). 17

18 Fnally, hs paper accenuaes he mporance of regulaors undersandng he behavor of he elecrcy marke when consderng he promoon of renewable energy for he purpose of reducng CO 2 emssons, parcularly wh respec o he characerscs of renewable echnologes, demand and supply unceranes, and marke srucure. Absen such an undersandng, successful promoon ha resuls n a generaon mx domnaed by nermen capaces can have unnended consequences, ncludng rsng average marke prce level and worsenng prce volaly. 18

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