Do costs fall faster than revenues? Dynamics of renewables entry into electricity markets

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1 Do costs fall faster than revenues? Dynamcs of renewables entry nto electrcty markets Rchard J. Green Thomas-Olver Léauter November 6, 217 Abstract In many countres, entry of Renewable Energy Sources nto power markets has been supported by subsdes and fnanced by a tax on electrcty consumed. Prevous works have descrbed ths phenomenon through numercal smulatons. Ths artcle s the frst to analytcally derve the mpact of renewable capacty ncreases on the long-term equlbrum generaton mx, subsdy, and tax. Ths enables us to provde analytcal expressons for prevously obtaned smulaton results, but also derve addtonal results. The analyss yelds two man fndngs. Frst, the subsdy to Renewable Energy Sources may never stop, as the value of the energy produced may decrease faster than the cost as renewable capacty ncreases. Second, hgh Renewable Energy Sources penetraton leads to a dscontnuty n the rate at whch ther margnal values fall, after whch the subsdy and tax grow extremely rapdly. Keywords: electrc power markets, renewables, publc polcy JEL Classfcaton: L11,L94,D61 1 Introducton In many European countres and Amercan states, support for renewable electrcty producton has been an essental energy polcy ntatve of the last decade. In the Unted States, 3 states and the Dstrct of Columba have renewable portfolo standards that requre electrcty retalers to procure a mnmum percentage of ther supples from renewable generators, whle seven states have voluntary goals. The European Unon s clmate-energy package requres 2% of all the energy consumed n the EU to come from Renewable Energy Sources (RES) n 22. The most cost-effectve way of meetng ths goal wll be to source much more than 2% of electrcty from RES. As a result of such polces, the share of non-hydro RES n world electrc power producton has grown tremendously, from 1.7% n 2 to 9.1% n Through a varety of mechansms, governments have subsdzed the nstallaton of RES. The smplest justfcaton for subsdzng RES s that they contrbute to reducng carbon emssons. Imperal College, London. r.green@mperal.ac.uk Correspondng author. Toulouse School of Economcs (IAE, IDEI, CRM). thomas.leauter@tse-fr.eu 1 1

2 The correct economc argument s more subtle and reles on learnng. The most effcent approach to reduce carbon emssons s to prce carbon, ether through a tax or an emssons market (see Goller and Trole, 215 for a recent and comprehensve dscusson of the tax vs. market debate). However, even wth a hgh carbon tax, the frst MW of most types of RES costs more to nstall than the market value of the electrcty t produces. On the other hand, nstallng that frst MW generates a postve externalty, snce learnng-by-dong reduces the cost of nstallng the next MW. Furthermore, f equpment manufacturers antcpate that a large volume of RES wll be nstalled, they nvest n large facltes, whch can also sgnfcantly reduce the cost of nstallng future MW of RES. Ths argument justfes subsdzng at least the frst MW of RES. It s wdely antcpated that the requred subsdy wll decrease over tme as costs decrease and f fuel and (partcularly) carbon prces rse over tme, and drop to zero when the cost of RES capacty s equal to the market value of the electrcty produced. Therefore, polcy makers n many jursdctons have mplemented RES support mechansms. The magntude of these subsdes s sgnfcant: the Internatonal Energy Agency 2 estmates $ 11 bllon was spent on RES subsdes n 212, ncludng $ 57 bllon n the European Unon, and $ 21 bllon n the Unted States, and antcpates subsdes wll rse to $ 22 bllon by 235. These subsdes are usually fnanced through a unt tax on power consumed or ts economc equvalent. For example, the renewable energy levy n Germany s around 62 /MWh n 215, twce the level of the wholesale power prce. The rrupton of RES has had a sgnfcant mpact on the electrcty ndustry, and generated a rch academc lterature, revewed n Secton 2. Some observers beleve t completely transforms the economcs of the power ndustry. For example Keay (216) consders that (...) electrcty markets are desgned to reflect and optmze the cost structures of the conventonal technologes we are famlar wth from 2th century electrcty systems. They are not suted to the systems we are developng to meet 21st century needs and crcumstances, and they do not gve effectve sgnals n stuatons where, as at present, one set of technologes s recevng support from outsde the market, whle other technologes are expected to remunerate themselves from the market yet both sets of technologes are operatng n the same market. Ths artcle examnes rgorously ths clam, showng how RES and ncumbent generators coexst n a market where the former receve subsdes. It s the frst to derve analytcally the laws of moton of the generaton mx, subsdy, tax, and resultng net surplus. Thus t complements and extends prevous work by provdng analytcal expressons for prevously obtaned smulaton results, hence furtherng our understandng of these evolutons. In addton we test these results and provde emprcal estmates for the specfc case of Great Brtan. Ths artcle models the prmary RES support regme used n Europe, characterzed by fxedprce payment (.e., RES receve a pre-agreed fxed payment per MWh to cover ther cost) and 2 2

3 physcal dspatch nsurance (.e., RES are always dspatched, unless system securty s threatened). Alternatve support mechansms are analyzed n our companon artcle (Green and Léauter, 216). For ths support mechansm, we frst derve the law of moton of equlbrum conventonal capacty (Proposton 1). As RES capacty ncreases, two effects (usually) reduce conventonal capacty: () RES capacty replaces conventonal capacty, and () the RES tax (usually) ncreases, hence reduces demand. We then derve the law of moton of the margnal value of RES capacty (Proposton 2). As the capacty of RES j ncreases, the margnal value of RES decreases proportonally to the covarance between the avalabltes of RES and j on the vertcal segments of the supply curve. The covarance captures the combned effect of the short term prce decrease caused by hgher producton by RES j and the long-term prce ncrease as ncumbent technologes are pushed out by RES j. We then examne the evoluton of RES subsdes. For a margnal RES, the subsdy s the dfference between ts cost, whch s decreasng through the learnng effect as RES capacty ncreases, and the value of the energy t produces, whch s also decreasng as RES capacty ncreases (by Proposton 2). As long as the nstalled RES capacty s small, the cost reducton effect domnates and the subsdy to the margnal unt decreases. However, when the nstalled RES capacty s large enough the second effect may domnate and the subsdy to the margnal unt may ncrease, contrary to prevous expectatons. Ths argument s formalzed n Proposton 3. Furthermore, nstallng a margnal RES reduces the value of all (nfra-margnal) energy produced by ths technology, and may reduce the value of all energy produced by other renewable technologes. For example, nstallng a new off-shore wnd farm reduces the market value of wnd energy produced, hence ncreases the subsdy requred by for all wnd farms. Therefore, the tax requred must ncrease to cover the subsdy of the margnal unt as well as the change of subsdy for all nframargnal unts (Proposton 4). We also derve the margnal net surplus loss (Proposton 5). We prove t s the margnal subsdy, plus the deadweght loss resultng from the margnal demand reducton, and use the prevous results to derve an analytcal expresson. Fnally, we characterze a dscontnuty n the economc representaton of power markets. For low to moderate RES entry, conventonal generaton capacty s reduced at the long-term equlbrum to accommodate RES producton, and the standard analyss apples, wth a few modfcatons. For hgh RES entry, a dscontnuty occurs: no technology s able to operate as baseload,.e., to produce every hour. Ths leads to a dscontnuty n the slope of prces and margnal values, that profoundly transforms the economcs of baseload generaton technologes. We derve ths result under two polar stuatons: () fully nflexble baseload technology,.e., baseload producers are wllng to receve a prce lower than margnal costs for some hours to avod shut-down and start-up costs, n whch case hgh RES entry may lead the baseload technology to dsappear from the long-term equlbrum (Proposton 6); and () fully flexble baseload technology, n whch case hgh RES entry may lead the (former) baseload technology to stop producng every hour, even f t remans ncluded n the long-term equlbrum generaton mx (Proposton 7). 3

4 Untl ths dscontnuty, markets provde adequate nvestment sgnals, even wth the presence of subsdy, hence Keay (216) s observaton s not rgorously exact. However, t becomes true after the dscontnuty. Applyng ths analyss, we compute the mpact of renewable subsdes n Great Brtan, usng the model developed by Green and Vaslakos (211), wth an updated dataset. It s essental to specfy that the value of renewable generaton s boosted by our ncluson of a 7 /ton carbon prce n the model, reflectng projectons whch see ths prce rsng sgnfcantly from current levels over the lfetme of power statons now beng planned. We nclude two renewable technologes: onshore and offshore wnd turbnes. We frst consder entry of 3 GW renewable capacty, leadng to 25% of electrcty beng produced from renewables, the level mpled by the more ambtous UK targets for the early 22s. The market value of the frst ncrement of onshore wnd capacty s 2 /kw per year, decreasng to 15 /kw per year for 3 GW renewable capacty, and 28 /kw per year decreasng to 22 /kw per year for offshore wnd capacty. 3 The margnal subsdy remans around 3 /kw per year for onshore wnd, and decreases from 28 to 11 /kw per year for offshore wnd. The cumulatve subsdy s fnanced by a unt tax on all MWh sold, whch ncreases to 1 /MWh. The nflexble baseload technology (nuclear) s drven out of the market when renewable entry reaches 45 GW, whch corresponds to 38% of electrcty produced from renewables. As suggested by Proposton 6, margnal values vary sgnfcantly when ths occurs. For example, when renewable capacty ncreases from 4 GW to 5 GW, the margnal subsdy ncreases from 3 to 13 /kw per year for onshore wnd, from 9 to 2 /kw per year for offshore wnd, whle the unt tax more than doubles from 13 /MWh to 32 /MWh, and contnues to ncrease to 121 /MWh for 6 GW. The cumulatve loss n net surplus ncreases to 9 bllons per year. Ths artcle yelds clear polcy recommendatons. Frst, the current support mechansm cannot be used to accommodate large scale RES entry. Ths vew s not orgnal to ths work: dfferent stakeholders have voced concerns n the past. However, ths artcle s the frst to analytcally prove ths pont. If socetes agree to contnue supportng RES entry, possbly ndefntely, alternatve mechansms are requred, whch are analyzed n our companon artcle (Green and Léauter, 216). Second, polcy makers should nclude the mpact of a margnal RES on the subsdy to all nframargnal RES when settng targets. Ths would reduce the rsk of explodng subsdes, whch would weaken the poltcal acceptablty of RES support. Ths artcle s structured as follows: Secton 2 brefly dscusses renewables support polces mplemented n Europe and the Unted States. Secton 3 presents the general model. Secton 4 derves the margnal mpact of renewables. Secton 5 apples the analyss to Great Brtan. Techncal proofs are presented n the Appendx. 3 Market values and subsdes are rounded up to the nearest 1. 4

5 2 Renewable support polces Hydro-electrc generators have been a feature of the electrcty ndustry snce ts earlest days, but the large-scale adopton of other types of RES s a relatvely recent phenomenon. It has nspred a very large lterature, summarzed n Edenhofer et al. (211) and Bruckner et al. (214). Ths Secton summarzed key themes relevant to ths paper. 2.1 Justfcaton for renewable support Several arguments are used to justfy renewable support. Snce the focus of ths work s the mpact of the support mechansm, not ther justfcaton, t s worth summarzng them. The obvous argument s that renewable energy dsplaces carbon emssons and reduces the rsk of severe clmate change. Ths s n fact a second-best argument, snce the effects of carbon emssons are a negatve externalty that ought to be corrected drectly wth a carbon prce arsng from a tax or a market for emssons (Goller and Trole, 215). Ths advce may not be poltcally feasble, however, snce t would lead to sgnfcant ncreases n the prce of energy, wth costs to consumer-voters. Fabra and Reguant (214) show that the pass-through of emssons costs n a European electrcty market has been close to 1%. Rghtly or wrongly, the rsk of carbon leakage, drvng producton to countres that have not mposed carbon prces s also perceved to be sgnfcant. In ths paper, however, we assume that a carbon prce s n effect and need other justfcatons for separately supportng renewable energy. Cullen (213) found that most estmates of the socal cost of carbon and other pollutants were lower than hs measures of the cost of reducng emssons through wnd power n Texas, mplyng that such addtonal support would be needed. As mentoned n the ntroducton, the most common argument for supportng renewables n the presence of a carbon prce arses from the magntude of the learnng curve to develop the renewable technologes (reported for example by Baker et al., 213, Lndman and Söderholm, 212, and van der Zwaan et al., 212). The frst unts deployed cost more than the conventonal technology, but as more renewable generators use new technologes, learnng by dong and the chance of obtanng economes of scale means that future unts wll cost less. Neuhoff (28) shows that f at some future date t wll be optmal to deploy large amounts of renewable capacty, but that there are lmts to the rate at whch nvestment can rse, a further justfcaton for subsdy now s that ths wll create a larger renewable ndustry, better able to expand producton n future. Proponents of ndustral polcy argue that supportng renewable energy can create jobs n manufacturng wnd turbnes or solar panels. Ths s most lkely to be a good polcy where a strong exportng ndustry can be establshed, as wth the Dansh wnd turbne company Vestas. Makng renewable generators purely for the domestc market wll create jobs n that sector, but the resultng hgher prce of power rsks destroyng jobs n energy-usng sectors, and t s unclear whether the net gan s postve. 4 4 A report by UKERC n 214 revewed the scentfc lterature on ths queston, and concluded the long-run mpact was ambguous. 5

6 Another argument for supportng renewable energy s that ncreased use of domestcally-generated renewable power can reduce the amount of fuel that must be mported from abroad, wth benefts for energy securty. Ths s true, but t s also the case that the avalablty of many renewable generators depends on the weather, and ths can create a securty rsk of ts own, unless adequate backup s avalable. 2.2 Renewable support approaches There are two key questons for polcymakers who wsh to support renewable generaton. Frst, should generators receve a guaranteed prce, or receve some support on top of the ncome that they can obtan from the electrcty market? Second, should the government offer a gven level of support to all the elgble generators that wsh to enter the scheme, or should t attempt to fx the quantty of generaton that t supports? The predomnant model n Europe takes the frst choce n both cases: all elgble generators can receve a guaranteed, pre-fxed prce, whch s usually called a Feed-n Tarff (FT). The prce s set admnstratvely, and the local grd company (or some other agency) s requred to purchase all the output from a renewable generator at a fxed prce and to sell t on to retalers and ultmately to consumers. The cost of these purchases s added to consumers blls. Countres such as France and Germany have explct taxes; n Great Brtan, the cost of a FT for small-scale generators s passed on to retalers n proporton to ther sales, and they n turn pass t on to ther customers. A FT gves prce securty to the generator, but has often created an open-ended promse to pay ths prce to any generator that meets the elgblty condtons. An over-generous prce can lead developers to add a large amount of capacty n a short perod of tme, rskng the affordablty of the scheme. If a government wshes to lmt the amount of generaton supported by a guaranteed-prce scheme, t can aucton contracts to sell renewable electrcty, wth bdders competng on the prce that they are wllng to accept. The Non Fossl Fuel Oblgaton auctons used n Great Brtan n the 199s offered a FT equal to the wnnng bd. More recently, that government has auctoned Contracts for Dfference (CfDs) that requre generators to sell ther output n the wholesale market but offer a top-up nversely lnked to the out-turn level of market prces. 5 Snce the generator may earn slghtly more or less from the market than the prces assumed n ts CfD, ts revenues are not qute guaranteed, but they should be relatvely stable. The government need not offer a guaranteed prce, however. It could requre the generator to sell ts power n the wholesale market (or va a contract) but top up ths revenue wth addtonal payments. In Europe, ths s typcally n the form of a fxed payment derved from electrcty consumers, a premum FT or Feed-n Premum (FIP). In the Unted States, a renewable tax credt gves a rebate on corporate taxes for each MWh generated, and comes at the expense of taxpayers. In ts renewable support gudelnes 6 publshed n 214, the European Commsson s recommendng 5 The Department of Energy and Clmate Change publshed on 26 February 215 the result of the frst aucton, avalable at Contracts_for_Dfference_-_Aucton_Results_-_Offcal_Statstcs.pdf 6 6

7 a move towards FIPs, and many countres, such as Span and Germany, already use both FITs and FIPs. Another varant, advocated for example by Newbery (212), s to offer support lnked to renewable capacty rather than output. The US has gven renewable generators the choce between a tax credt per MW of capacty and one per MWh of generaton. These schemes are open to all elgble generators that choose to enter the market, but the government can also concentrate on the quantty of renewable power to be procured, rather than ts prce. The US Renewable Portfolo Standards requre retalers to procure output from renewable generators but need not lay down any condtons on how ths s done. In Europe, tradable green certfcate schemes requre retalers to acqure certfcates equal to a set proporton of ther sales, or to pay a buy-out fee. Generators are gven certfcates for each unt of renewable power they produce, whch they can sell to retalers; they also have to sell ther power n the wholesale market or through long-term contracts. Long-term contracts can gve revenue securty to the renewable generator, but sellng n the wholesale market creates a prce rsk that may affect the generator s cost of captal. Ths artcle examnes the frst two approaches, of a guaranteed prce. In a world wthout uncertanty, any chosen level of capacty could be delvered by settng a seres of approprate prces for all generators, and reducng the prce to unattractve levels once the target has been ht. A seres of auctons to decde on the guaranteed prces for a fxed amount of capacty would be equvalent and run less rsk of over-supply, but requre a defnte choce as to the amount of capacty to procure. The companon artcle Green and Leauter (216) examnes the other approaches n whch the prce s not guaranteed. 2.3 Impact on electrcty markets Impact on average prces Over the last few years, the rapd rse n renewable capacty n Europe has depressed market prces. Snce the margnal cost of wnd (or solar) generaton s effectvely zero, t pushes the ndustry s supply curve to the rght, so that ths ntersects wth demand at a lower equlbrum prce, a feature named the mert-order effect. The mert-order effect s a dsequlbrum phenomenon, however, because the lower prces mean that some (or all) conventonal statons wll be unable to recover ther full economc costs. Ths may lead to retrements, or at the very least a shortage of new nvestment, and so the ndustry s conventonal capacty should adapt to ths new realty over tme. As long as there s baseload producton n the market, the tme-weghted average prce of power n a long-run equlbrum should not depend on the amount of renewable capacty, snce ths prce wll tend to the average cost of ths baseload technology. The demand-weghted average prce mght change. If there s more renewable output, on average, at tmes of hgh demand (for example, solar power n a system wth summer-peakng demands) then the demand-weghted prce wll be reduced as renewable capacty grows. 7

8 Impact on operatng reserves Electrcty must be generated (or taken from storage) at the exact moment that t s requred, but the output of many knds of renewable generator s ntermttent, dependng on the varyng strength of the wnd or the sun. Ths means that t s not possble to retre 1 GW of conventonal capacty when 1 GW of wnd capacty s added to the ndustry s captal stock, snce the wnd statons may not generate at the tme of peak demand. Furthermore, f the wnd changes over a large area of the country at once, ths could lead to a sgnfcant and rapd fall n the amount of wnd generaton. System Operators (SOs) cope wth unpredctable unavalablty by securng operatng reserves: they always run some statons part-loaded so that they can ncrease output f another staton fals. It s expected that ncreasng the share of renewables n a market wll ncrease the requred operatng reserves. Recent engneerng studes (for example, Bertsch et al., 215) suggest that the avalablty of these operatng reserves should not be an ssue: renewables wll lead to a hgher share of md-mert and peakng-plants, whch wll be able to provde the requred flexblty. However, the costs of provdng these reserves s not neglgble. Gowrsankaran et al. (213) show that the cost of ntermttency for solar power n Arzona s around 12 $/MWh f the SO adjusts ts reserve levels to cope wth the fluctuatons (partcularly short-term changes) n solar output, but far hgher f the SO contnues wth tradtonal levels of reserves. A well-connected country lke Denmark can manage ths ssue by tradng power wth ts neghbors, although at a cost of between 4 and 8 per cent of the value of the energy produced (Green and Vaslakos, 212). Impact on the value of renewable generaton The reason that Denmark loses money when tradng wnd wth ts neghbors s the negatve short-run correlaton between wholesale electrcty prces and the amount of wnd energy generated. If renewable generaton s above average for the tme of day and the season, then the market prce wll be below average (ceters parbus), creatng ths negatve correlaton. The greater the renewable capacty, the stronger ths effect wll be (Twomey and Neuhoff, 21). The pattern of average output may counteract ths correlaton for small amounts of renewable capacty. For example, the average wnd speed n Great Brtan s hgher n the wnter than n the summer, and so are average electrcty prces, so that the average prce receved by a wnd farm wll be hgher than the tme-weghted average wholesale prce - as long as there s not too much renewable capacty. As the level of capacty grows, however, the negatve correlaton brought about by shortrun varatons around the seasonal average becomes more mportant and the wnd farms average revenues wll fall. Joskow (211) ponts out that these nteractons between the tme of generaton and the value of the electrcty produced mean that ther levelzed costs of generaton are a very poor measure of the relatve compettveness of dfferent technologes. Numercal estmates of the sze of these effects have been estmated for Calforna by Mlls and Wser (212) and for Germany by Hrth (213), among other studes. Whether t starts above or below the tme-weghted average prce, the average market prce weghted by renewable output wll fall as renewable capacty ncreases. A rch lterature, revewed 8

9 for example by Hrth (215) has characterzed ths value drop of renewables as ther penetraton ncreases. These works dffer from ours n several mportant dmensons: () they rely on numercal smulatons, whle we provde analytcal results, () most consder nelastc demand, hence mnmze generaton costs, whle we consder elastc demand, hence maxmze net surplus and nclude the mpact of the renewable tax, and () most do not nclude learnng-by-dong, whle we do. 3 A model of the electrc power market wth renewables 3.1 Demand To smplfy the exposton, ths artcle assumes all customers face the spot prce of electrcty. Aggregate electrcty demand s thus D (p +, ), where p s the wholesale electrcty prce, s a per-unt tax leved to cover the cost of subsdzng renewable generators, and s the state of the world, dstrbuted on R + accordng to cumulatve densfy functon F (.), andprobablty densty functon f (.) =F (.). The dstrbuton of states of the world combnes two effects. Frst, demand vares across the year: demand s hgher durng the week than durng the weekend, hgher n the wnter than n the summer n Europe due to electrc heatng, hgher n the summer than n the wnter n the Unted States due to ar condtonng. Second, demand for a gven hour vares randomly, for example due to temperature varatons. Inverse demand P (Q, ) s assumed to be downward slopng: 8, 8Q, P q (Q, ) <. Ths condton s met for example f nverse demand s lnear wth constant slope P (Q, ) =a ( ) bq, wth b>. Recognzng that a fracton of customers face a prce constant across states of the world would lead to smlar economc nsghts at the cost of more complex notaton (see for example Borensten and Holland, 25, Joskow and Trole, 27, and more recently Léauter, 216). 3.2 Supply (N + I) generaton technologes are avalable: N ncumbent technologes ndexed by n 2 [1,N], and I renewable technologes correspondng to n =and ndexed by 2 [1,I]. Incumbent technologes nclude thermal and nuclear generaton. For n 1, c n s the constant margnal operatng cost and r n s the constant hourly margnal fxed cost of technology n (.e., annual margnal annutsed captal cost plus fxed annual operatng and mantenance costs expressed n /M W/year dvded by 8, 76 hours per year), both expressed n /M W h. Wthout loss of generalty, ncumbent generaton technologes are ordered by ncreasng operatng cost: c n >c m 8 n m. There s a trade-off between captal and operatng costs: f a technology requres lower captal cost, t then produces at hgher operatng cost,.e., r n <r m 8 n m. In general, not all avalable technologes are present at the long-term equlbrum. To smplfy the exposton, n =1(resp. n = N) denotes the frst (resp. the last) ncumbent technology present n the long term equlbrum before RES are ntroduced. For ncumbent technologes n 1, k n s the nstalled capacty of technology n, andk n = P n m=1 k m s the cumulatve nstalled ncumbent capacty up to technology n. 9

10 In practce, the base load technology 1 has often very hgh startup costs, whch reduces ts startup and shutdown flexblty. For example, nuclear unts are extremely costly to start up after shuttng down, hence ther operators attempt to run them permanently. A full representaton of these startup costs requres complex modelng. Green and Vaslakos (211) propose a smplfyng approach: nflexblty s represented by a mnmum producton level m 1 k 1. Ths artcle follows the same approach. The base case s no baseload flexblty,.e., m 1 =1. Ths reflects the past stuaton n the UK, when t was dffcult to operate gas-cooled reactors at less than full capacty. On the other hand, pressurzed water reactors used n the US and France can be ramped down to relatvely low levels of output. The cost of dong so s an ncomplete fuel burn, reducng the total output avalable from a gven set of fuel rods. We have no data on the sze of ths effect, whch would tend to reduce the margnal cost of generaton and rase the fxed cost by an offsettng amount. We choose to model the case of full flexblty,.e., m 1 =, wth no change n costs, even though we are aware that ths over-estmates the actual stuaton. Snce realty s somewhere between the two extremes we consder and our results are smlar for both of these cases, we are therefore confdent that they are robust. 3.3 Renewable Energy Sources We consder I renewable technologes, for example onshore wnd, offshore wnd, and photovoltac panels. For =1,...,I, denote by K the nstalled capacty of RES, K 2 R I the vector of nstalled RES capactes K, r K the margnal captal cost of RES, R K = R K r (x) dx the cumulatve captal cost of RES capacty K,andR (K )= P I =1 R K the aggregate cumulatve captal cost of RES capactes K. For all renewable technologes, varable operatng cost s neglgble,.e., c =. Learnng by dong and economes of scale mply that r (.) s decreasng n K :nstallnganaddtonaloffshore wnd turbne reduces the cost of the next offshore wnd turbne. We assume that there are no cross-technology externaltes from learnng or economes of scale: nstallng an addtonal onshore wnd turbne does not sgnfcantly reduce the cost of the next offshore wnd turbne. Thus, R (K )= IX =1 Z K r (x) = r K. Ths assumpton can be relaxed n further work, should emprcal evdence prove t does not hold. RES are often ntermttent (e.g., wnd and solar). Avalablty of RES n state s ( ) 2 [, 1], hence avalable producton from RES n state s ( ) K. Ths could reflect two dmensons of ntermttency. Frst, RES can be predctably unavalable, for example, the sun does not shne at nght, or the wnd may be forecasted to be low. The mpact on the resdual demand,.e., demand net of renewable producton, vares wth the type of RES avalable and the shape of the demand curve. For example, n Calforna or Arzona, demand s hghest when the sun shnes and Ar Condtonng s on, whch precsely concdes wth the hghest producton from solar panels (Gowrsankaran et al., 215). Ths s not the case n northern Europe, where most (nstalled) RES are wnd turbnes, 1

11 whch produce more n wnter than n summer (wth hgher average wnd speeds then) but generate very lttle on the cold, calm days whch often see the very hghest demands (Oswald et al., 28 ). Ths mples that addng 1 MW of RES capacty does not lead to a E ( ) MW reducton n ncumbent generaton capacty (let alone a 1 MW reducton). Ths substtuton effect s captured n equatons (8) derved below. Second, RES may be unpredctably unavalable to an extent whch requres the SO to procure addtonal flexblty. Includng ths dmenson n the model would add sgnfcant complexty, hence s left for further work. 3.4 Wholesale market structure and equlbrum Ths artcle assumes polcy makers set a target RES capacty K. Ths s consstent wth observed practces n most European countres. Some countres set a target share of RES n electrcty producton, whch s equvalent to a target capacty snce RES are gven dspatch prorty. Whle K s set exogenously, nstalled capactes of ncumbent technologes are determned endogenously by long-term free entry condtons descrbed later. Formally, each K n s therefore a functon of the vector K of RES capacty. Ths artcle assumes the market s centralzed,.e., an SO receves bds from all producers and consumers, selects the optmal dspatch (defned later), and declares a unque market prce. Ths consttutes an adequate descrpton of US markets. European markets are decentralzed, hence buyers and sellers transact ether n power exchanges or blaterally, then communcate ther negotated transactons to the SO, who takes any actons needed to ensure a feasble and secure dspatch. Snce we focus ths analyss on the dstortons caused by renewables support polcy, we assume competton s perfect, hence both approaches are equvalent. We also abstract from transmsson constrants. In every state of the world, the SO assgns the dspatch rate u n ( ) 2 [, 1] to each technology n. Producton from technology n 1 s u n ( ) k n, and producton from renewable technology s u ( ) ( ) K. If technology 1 nflexble, u 1 ( ) =1. In ths artcle, RES receve physcal dspatch nsurance,.e., they have dspatch prorty,.e., u ( ) =1. Ths s the case n most jursdctons, where the SO can cut renewables off only when the operatonal securty of the system s threatened, a stuaton we do not model. Green and Léauter (216) dscusses an alternatve approach, that allows the SO to cut renewables off when prce drops down to zero, whle stll payng for the energy they would have produced. The analyss follows the standard peak load prcng model (see for example Boteux, 1949). The man dfference wth the standard model s that a tax on the electrcty prce s leved to fnance the subsdy. The tax covers only the cost of the renewable producton. The cost of grd enhancements requred to accommodate renewables are ncluded n the grd rate, hence not covered by ths analyss. For the reader s convenence, the dervatons are presented n Appendx A. The economc optmum would be for the SO to set the retal prce (whch determnes consumpton) equal to the margnal cost of power. The wholesale prce would then be the retal prce mnus 11

12 the tax, lower than the short-term margnal cost c n when technology n s margnal. Ths s unrealstc. Producers are unwllng to partcpate n a market that guarantees prce lower than c n when they are margnal. Therefore we nclude a producers partcpaton constrant for n>1: (p (K, ) c n ) u n ( ). The resultng supply curve s a "starcase" (Fgure 1): on the horzontal portons, the wholesale prce s the margnal cost of the margnal technology producng; on the vertcal portons, the margnal technology produces at capacty, and the wholesale prce s set by the ntersecton of the demand curve and the vertcal supply curve, mnus the tax. Fgure 1 about here The long-run equlbrum wholesale prce n state when K has already been nstalled s p (K, ). Recallng that c =andusngtheconventon c N+1! +1, the steps of the starcase are formally defned for apple n apple N by v n = { : c n <p(k, ) <c n+1 } and h n = { : p (K, )=c n }. The sets v n and h n are functons of K. To smplfy the notaton, the reference s omtted. Whle technology 1 earns a negatve operatonal margn when p (K, ) <c 1, t stll produces snce t cannot reduce ts output. As we wll see below, nvested capacty n technology 1 s determned to precsely balance the postve and negatve margns. When baseload generaton s nflexble, h 1 = Ø snce prce s never set at c 1.Smlarly,h = Ø snce prce s never set at. On h n for n 2 technology n produces at the margn, and IX K n 1 + u n ( ) k n + ( ) K = D (c n +, ). =1 =1 =1 On v n, technology n 1 produces at capacty and technology (n + 1) does not produce, prce s determned by the ntersecton of the vertcal supply curve and the demand curve:! IX IX K n + ( ) K = D (p (K, )+, ), p (K, )=P K n + ( ) K,. Fnally, n a compettve equlbrum, nvestors n non-renewable generators nvest untl ther margnal proft s equal to zero, whch yelds E [(p (K, ) c n ) u n ( )] = r n,forn 1. (1) The free-entry condtons above yeld a unque vector of ncumbent capactes. Defne (K, c, r, ) =E " P K n +! IX ( ) K, =1 ( + c)! I P I {P(Kn+ =1 ( )K, ) ( +c)} # r. 12

13 Appendx A proves that cumulatve ncumbent capacty s unquely defned by (K N,c N,r N, )=, (2) whle K n for n 2 s unquely defned by (K n,c n,r n,) (K n,c n+1,r n+1, )=. (3) Inflexble technology 1 s slghtly dfferent, for t faces sgnfcant startup costs. To avod shuttng down, producer 1 s wllng to accept a prce lower than c 1 for a few hours. Therefore, the baseload capacty (when postve) s unquely defned by h E P K 1 + P I =1 ( ) K, 3.5 Renewable support polcy ( + c 1 ) I P I {P(Kn+ + (K 1,c 1,r 1,) (K 1,c 2,r 2, ) =1 ( )K, )<( +c 1)} =. (4) The market value of energy produced by renewable technology s E ( ) p (K, ). In many cases, t s less than the generator s cost, and t would not be vable wthout some knd of state support. The smplest method, used n many markets, s for polcy makers to commt to purchase power generated by renewables at a pre-agreed rate, whch nsulates them from the wholesale market and ts prce rsk. We assume that ths rate can be exactly adjusted as capacty s added and renewable costs fall. For example, the SOs (or a government agency) runs a seres of calls for tenders for capacty ncrements dk untl cumulatve capacty s K. For each ncrement, competton among developers s perfect, hence the fxed prce f K for the margnal nvestor s the mnmum requred amount to precsely cover the margnal captal cost: f K E ( ) = r K. Ths model s statc: polcy makers set a target renewable capacty K, and perfectly adjust the subsdy to cover the margnal nvestment cost r (x) for all x apple K. Thus, we gnore the temporal dmenson: all perods are collapsed nto one. Extendng the model to dfferent perods would smply make the notaton more complex, and lead to the same economc ntuton. Ths approach consttutes a frst-best benchmark. In realty, when FITs are used, polcy makers fnd t hard to control capacty ncrements. If the FIT s set to cover r (), a very large number of producers wll wsh to enter, snce by constructon r K <r (). Ths creates rents for renewable nvestors who can add capacty before the FIT s reduced, whch reduce net surplus, snce the taxes to pay for them create a Dead Weght Loss. We therefore estmate a lower bound of the net surplus loss from supportng RES. For nstalled renewable capacty K, the cumulated expected revenues from the fxed prce 13

14 contracts cover exactly the cumulatve captal cost Z K f j (x) E ( ) dx = R K. The subsdy requred by a margnal unt of technology when K has been nstalled, denoted ' (K ), s the dfference, when postve, between the margnal cost and the margnal value: ' (K ) = max r K E ( ) p (K, ),. (5) As was dscussed, the subsdy s postve for the frst unts for all consdered RES technologes. It s expected that margnal RES unts wll no longer requre subsdes after suffcent capacty has been nstalled. For ease of exposton, we present frst the case where all RES technologes receve a postve subsdy, then examne the stuaton where subsdes are no longer requred. For technology, the cumulatve subsdy up to K, denoted (K ), s the dfference between the fxed payments to producers and the revenues from sale of renewable energy: (K )=R K E ( ) p (K, ) K. Ths relaton can be aggregated over all renewable technologes. The cumulatve subsdy up to K s the dfference between the fxed payments to producers and the revenues from sale of renewable energy: (K )=R (K ) IX E ( ) p (K, ) K. (6) =1 Ths subsdy s fnanced through a unt tax on the retal power prce of pad by all users. Denotng the expected demand by D (K )=E [D (p (K, )+ (K ), )], the unt tax s determned by (K ) E [D (p (K, )+ (K ), )] = (K ). (7) If the elastcty of demand s very hgh, ncreasng the tax may sgnfcantly reduce demand, and equaton (7) may not have a soluton. Ths artcle assumes ths stuaton never occurs, and that equaton (7) always admts a unque soluton. Equaton (7) shows that the tax level s a functon of prces, hence nstalled capactes K n.on the other hand, equatons (2), (3), and (4) show that, for a gven vector of RES capactes K equlbrum cumulatve capactes K n are a functon of the tax. The long-term equlbrum wth the unt tax s therefore a fxed pont problem. Appendx A proves that f equaton (7) always admts a unque soluton, the long-term equlbrum exsts and s unque. In practce, the realzed avalablty rate and demand may be hgher or lower than expected, and the tax may adjust for the prevous year s out-turn. We abstract from ths ssue, as we gnore potental rsk averson. 14

15 4 Margnal mpact of renewables Ths Secton derves the margnal mpact of renewable capacty on ncumbent capactes, subsdes, taxes, and net surplus. Two mutually exclusve stuatons are possble: postve nvestment n the baseload technology occurs at the long-term equlbrum, or renewables entry s so large that no baseload technology s present at the long-term equlbrum. The economc ntuton s dentcal, but the detals of the analyss are slghtly dfferent for each case. For ease of exposton, we examne each n turn. Fnally, we extend the results to flexble baseload. 4.1 Baseload technology present at the long-term equlbrum Throughout ths subsecton, renewable capacty s assumed to be small enough that baseload technology s present at the equlbrum. We frst establsh the followng: Lemma 1. The expected prce on the vertcal segments of the supply curve does not vary wth nstalled renewable capacty. Specfcally, for all 1, ) The tme weghted average prce s constant: ) p (K, ) <c 2 =, and 8n 2, E v n E [p (K, )] =. Proof. The results are standard n the peak load prcng lterature. For the reader s convenence, formal proofs are presented n Appendx B.1. At the long-run equlbrum, the expected prce on the vertcal segments of the supply curve s set to yeld profts equal to the captal cost of the margnal technology, and hence does not depend on the renewable capacty. Smlarly, snce the baseload technology cannot be turned off, t produces all the tme. At the long-run equlbrum, the tme-weghted average prce s equal to the long-run margnal cost of the baseload technology, hence does not depend on the renewable capacty Margnal mpact on ncumbent capacty Lemma 1 yelds the followng: Proposton 1. Installed ncumbent capacty changes as RES capacty ncreases for two reasons: RES capacty substtutes for ncumbent capacty, and demand changes through the change n unt tax. 1 E P q ( ) p <c 2 = E [P q p<c 2 ], and 8n n E P q ( ) v n = E [P q v n ]. (8) 15

16 Proof. For n h 2, v n =yelds 2 E 4@P n + 1 IX j ( ) K j, j=1 + ( ) 1 3 A v n 5 =. Rearrangng yelds equatons (8). The same argument apples for n =1on the vertcal { : p (K, ) <c 2 }. Intuton for equaton (8) s easer to obtan when assumng nverse demand s lnear wth constant slope, P (Q, ) =a ( ) for n 2. bq, n whch case t smplfes n = E ( ) v n 1 b The change n K n s the sum of two effects. Frst, technology n s replaced by the renewable technology. Cumulatve capacty K n s determned by the expected margn when technology n produce at capacty. If ( ) s constant, ncreasng K by 1 reduces K n by. If ( ) s not constant, ncreasng K by 1 reduces K n by the expectaton of ( ) on v n. Second, the tax usually ncreases, hence demand decreases, and so does K n. If demand s not lnear wth constant slope, these substtuton effects are weghted by the slope of the demand functon. Prevous numercal studes have also found that, as RES enter the market, ncumbent technologes retreat n the long-term equlbrum. Proposton 1 enhances our understandng of these dynamcs, by specfyng how dfferent RES technologes mpact dfferent ncumbent technologes. Consder a smple example of two ncumbent technologes, baseload and peakng. Suppose frst RES are equally avalable n all states of the world whch occurs f RES avalablty s not correlated to demand. Thus ( ) =, and equaton (8) shows 1 2. Snce peakng capacty s cumulatve capacty K 2 mnus baseload capacty K 1, peakng capacty s unchanged and baseload capacty s reduced at the long-term equlbrum. Suppose now RES produce only durng peak hours, for example solar panels produce when the sun s shnng and Ar Condtonng demand s hghest. Then, E ( ) p <c 2 =< E ( ) v 2. Ignorng the tax effect, baseload capacty s unchanged, whle peakng capacty s reduced. If renewable capacty s very large, we may reach a pont where K n (K )=. Ths s examned n Secton 4.2. Fnally, Proposton 1 enables us to determne the mpact of renewable capacty on expected demand D (K ): Corollary 1. The margnal mpact of K on expected demand D (K ) D = 1 B 16 +, (9)

17 where and 1 B = N X n=2 = (cn +, ) E h n Pr (h n )+ Pr (v E [P q v n ] NX E E! ( ) P q v n ( ) v n Pr (v n ) E [P n=2 q v n ] + E E! ( ) P q p<c 2 ( ) p <c 2 E [P q p<c 2 ] Pr (p <c 2 ) E [P q p<c 2 ], Pr (p <c 2 ). Proof. The proof s presented n Appendx B.2. Suppose agan nverse demand s lnear wth constant slope P (Q, ) =a ( ) bq. Then, B = b, =, and equaton (9) smplfes D = 1 b. An ncrease n K leads to a change n tax. If demand s lnear wth constant slope, ths leads to a proportonal change n expected demand. As wll be shown later, under reasonable assumptons, : the tax ncreases to fnance an ncrease n renewable target capacty. The tax effect s thus negatve: as renewable capacty ncreases, so does the tax, and demand decreases Margnal mpact on the value of renewable capacty We now determne the mpact of the level of renewable capacty on ts margnal value: Proposton 2. The margnal mpact of K on the margnal value of renewable technology j E j ( ) p (, K ) apple = E j ( = j E j, (1) where E j = NX n=2 E P q v n E Pq j v n E [P q v n ] + E P q p<c 2 E Pq j p<c 2 E [P q p<c 2 ] E P q, j v n! Pr (v n ) E P q, j p<c 2! Pr (p <c 2 ). Proof. The proof s presented n Appendx B.3. If demand s lnear wth constant slope, E j = b NX cov, j v n Pr (vn )+cov!, j p<c 2 Pr (p <c2 ) n=2 17 = bcov c K ( ), j ( ),

18 hence equaton (1) smplfes to apple E j ( = bcov c K ( ), j ( ). (11) A margnal ncrease n RES technology has two effects on prce n state : a short-term prce reducton through the ncreased producton from RES technology, equal to ( ) n state, and a long-term prce ncrease through the reduced ncumbent capacty equal to E ( ) v n on vn f demand s lnear wth constant slope. The change n margnal value of RES technology j s the expectaton of the prce change, weghted by avalablty j ( ). Ths leads the covarance presented n equaton (1). If demand s not lnear wth constant slope, addtonal terms correspondng to the varaton of the slope are added to equaton (1). Prevous numercal studes (for example, Hrt 213 and 215) have already ponted out the declnng margnal value, sometmes called the cannbalzaton effect. Proposton 2 provdes an analytcal descrpton of ths effect, whch, to our best knowledge, s orgnal to ths work, and provdes addtonal nsghts. Frst, t proves that, f demand s lnear, the margnal value of RES evolves almost lnearly as RES capacty ncreases. Second, t shows that, as RES technology capacty ncreases, ts margnal value decreases proportonally to the varance of avalablty (on the vertcal segments of the supply curve). Ths effect can contrbute to makng better nvestment decsons. Consder two felds for wnd turbnes, the frst one n a low but constant wnd envronment, and another one n a hgher but more volatle wnd envronment. The value of the turbne n the frst ste maybe lower than n the second ste. However, the value of margnal turbnes once a sgnfcant capacty has already been nstalled, maybe hgher n the frst than n the second ste. Thrd, t ndcates how to develop hgher value portfolos of RES technologes. Investors should attempt to fnd negatvely correlated technologes. For example, f the wnd n one partcular regon blows mostly at nght, nstallng solar panels ncreases the value of wnd turbnes (and symmetrcally nstallng wnd turbnes ncreases the value of solar panels). Ths s attrbutable to the long-term reducton n ncumbent technologes capacty, whch ncreases the prce receved by RES Subsdy for the margnal unt Proposton 2 leads to the followng: Proposton 3. If demand s lnear wth constant slope, the subsdy requred by a margnal unt of technology may ncrease as renewable capacty ncreases, and ncreases as renewable capacty j ncreases f and only f avalabltes on the vertcal segments of the supply curve are postvely correlated. Proof. The subsdy to the margnal unt s ' (K )=r K E ( ) p (K, ), 18

19 (K ) = d dk r K + bdvar K ( ). The frst term s negatve snce margnal cost s decreasng, whle the second s postve. Ths proves the frst pont. Then, proves the second (K j = bcov c K j ( ), ( ) The frst pont of Proposton 3 llustrates the race between fallng costs and fallng prces. For low capacty, sgnfcant learnng effects are present, hence fallng costs probably outwegh fallng prces. As capacty ncreases, costs fall much more slowly, and maybe not suffcently to compensate the prce decrease. The subsdy may then ncrease. The second pont of Proposton 3 llustrates the complementarty and substtutablty of technologes: f the outputs from two technologes are postvely correlated, ncreasng the capacty of one ncreases the supply and hence reduces the prce avalable to the other one, and so ncreases the requred subsdy. To our best knowledge, ths s the frst tme that these effects are clearly presented Margnal mpact on tax Dfferentaton of equaton (7) wth respect to K yelds D (K D = r K E ( ) p (K, ) IX j=1 apple E j ( K j, D (K )=' D IX j=1 apple E j ( K j. (12) To fnance ncremental renewable capacty, the gross tax recepts D (K ) must change to cover the subsdy to the margnal unt ' K and the reducton n tax recepts, due to the demand D. If ncreasng renewable capacty decreases the value of all nframargnal unts, a thrd cost s added: the reducton n market value of all nframargnal renewables benefttng from the feed-n tarff. Whle the decreasng market value of renewables has been observed n practce and dscussed n the lterature, we beleve the lnk to the subsdy dynamcs s orgnal to ths work. When grantng a fxed prce contract, polcy makers commt the customers to a fxed payment to a renewable producer, hence ther net lablty s ths payment mnus the market value of ths renewable capacty. As more fxed prce contracts are granted, the market value of renewable energy (usually) decreases, and the lablty (usually) ncreases. Usng prevous results, we now establsh the followng: 19

20 Proposton 4. The margnal change n tax s = B ' (K )+ P I j=1 Ej K j + (K ) B D (K ) (K )+B P I j=1 Proof. Insertng equatons (9) and (1) nto expresson (12) D IX B + j=1 whch leads to equaton (13). j K j 1 j K j. (13) A + E p (K, ) ( ) IX E j K j = r K If demand s lnear wth constant slope, equaton (13) yelds D (K ) = 1 1 (K ) b D(K (K )+b j=1 1 IX cov c K ( ), j ( ) K j A, whch llustrates the margnal mpact of K on tax. Frst, the tax must ncrease to cover the margnal subsdy ' (K ). Second, the tax must change to cover the changes n the value of all 1 other renewable capacty. Fnally, ths change s magnfed by the factor > 1 to account for the deadweght loss from taxes. j=1 1 (K ) b D(K ) We expect the tax to ncrease as the capacty of RES ncreases. However, there may be cases when the tax n fact decrease, for example f there are only two renewable technologes, the subsdy to RES s close to zero, and RES s very hghly negatvely correlated to RES j Margnal mpact on net surplus We now compute the change n net surplus caused by a margnal ncrease n renewable capacty. Snce ths analyss focusses on net surplus, and not overall welfare, t gnores dstrbutonal ssues. Sgnfcant rents are beng created and destroyed by the rapd and large ncrease of renewable capacty n Europe. Renewable generators and equpment manufacturers share rents when the prces pad for ther output exceed the true cost of producton. Incumbent generators have lost a sgnfcant amount of money when the expanson of renewable capacty has depressed wholesale market prces and forced them to close exstng capacty before the end of ts techncal lfetme. In a few cases, of course, the same person or company may own both ncumbent and renewable assets. These effects (and the externaltes created for those who lve near wnd farms) are very mportant for the poltcal economy of renewable energy, but are not the prmary focus of ths analyss. Proposton 5. The margnal net hourly surplus, ncludng nvestment cost, (K )+ (K ) + (K ) ' (K )+ P I j=1 Ej K j + (K 1 ) B D (K ) (K )+B P A I j=1 j K j. (14) 2