INDIAN INSTITUTE OF MANAGEMENT CALCUTTA WORKING PAPER SERIES. WPS No. 739/ January 2014

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1 IDIA ISTITUTE OF MAAGEMET CALCUTTA WORKIG PAPER SERIES WPS o. 739/ January 2014 Impact of Tme of Use (TOU) Retal Prcng n an Electrcty Market wth Intermttent Renewable Resources by Balram Avttathur Professor, IIM Calcutta, Damond Harbour Road, Joka P.O., Kolkata Inda

2 Impact of Tme of Use (TOU) Retal Prcng n an Electrcty Market wth Intermttent Renewable Resources Abstract The share of renewable energy n the overall producton of electrcty has been ncreasng n recent years. However, there are worres that ncrease n share of solar and wnd power could destablze the grd owng to ther beng ntermttent resources. We explore the mpact of a Tme of Use (TOU) retal prcng n a capactated and deregulated electrcty market that s suppled from a fnte mx of ntermttent renewable and steady non-renewable resources. Our modellng attempts to address a research vod by consderng both demand (retal) and supply (renewable energy) as varable. An effcent feed-n-tarff (FIT) as dentfed n lterature, where the FIT s lnked to the wholesale prce, s consdered for energy procured from renewable sources. The FIT so consdered ensures that that demand s met frst by electrcty from renewable sources, whch s n lne wth sustanable energy arguments. Through a set of experments the TOU retal prcng s compared wth fxed retal prcng. Our models and the numercal experments renforce the exstng lterature that ncreasng share of renewable energy reduces energy prces under both prcng schemes. Our experments ndcate that wth ncreasng share of renewable energy, and demand and supply uncertantes, TOU retal prcng results n hgher meetng of demand, hgher expected revenues for the energy frms and hgher utlzaton of non-renewable supply. Our experments also ndcate that fall n prces that occurs as a consequence of ncreasng share of renewable energy s lesser n TOU prcng compared to fxed prcng, whch makes t less dsadvantageous to exstng non-renewable energy supplers and potental nvestments n non-renewable energy. Through these results and arguments we conclude that TOU retal prcng s superor to fxed retal prcng n the context of ncreasng share of renewable energy, and uncertantes n demand and supply. Keywords: capactated, deregulated, electrcty market, ntermttent resources, sustanable renewable energy, Tme of Use (TOU), retal prcng, uncertan supply, varable demand 1. Introducton The atmospherc CO 2 level s at a record hgh of close to 400 ppm and s expected to contnue wth ts steady clmb as fossl fuels contnue to be the prncpal energy source n most parts of the world. The Avttathur (2014): Impact of TOU retal prcng n an electrcty market wth ntermttent renewable resources 1

3 resultng changes to clmate and ocean levels have been a topc of consderable global debate. A response to ths has been the encouragement provded by governments across the world to nvestments n renewable energy. It was recently reported that the worth of the top 20 energy utltes of Europe declned from roughly 1 trllon n 2008 to less than half of that n 2013 (Economst, 2013). Ths has been attrbuted to the ncreasng share of renewable energy, whch has helped push wholesale electrcty prces down. However, the artcle also ponts to the worry that ncrease n share of solar and wnd power could destablze the grd owng to ther beng ntermttent and n turn ncrease the chances of blackouts or brownouts. Also n the news are countres wth severe energy shortage lke Inda, where the share of renewable energy s much lesser than n Europe, but stll sees many of ts energy utltes n poor fnancal health owng to low tarff and dependence on costly mported fuels (Economst, 2012; Jayaram and Avttathur, 2012). Despte consderable progress n technology, management and regulaton, electrcty markets world over contnue ther quest n resolvng many of the challenges they face. Whle provdng a relable network at reasonable prce, producers look for best returns on ther nvestments. Owng to envronmental consderatons, the share of renewal energy n the total electrcty producton s expected to ncrease n comng years n both developng and developed countres. Though renewal energy helps n reducng the carbon emssons per dollar of GDP, they have also contrbuted to a set of uncertantes, whch s expected to ncrease as ther share of total producton ncreases. At the core of the problem s the fact that electrcty demand n not unform and could fluctuate wthn the day as well between dfferent tmes of the year. However, energy sources lke coal-based and nuclear power plants are not techncally suted for operatng under wdely fluctuatng loads whle energy sources lke solar and wnd are ntermttent. Apart from ts greater avalablty drven by the shale gas revoluton n the USA, the mportance of gas as an energy source s also because of the flexblty of gas-based utltes to operate easly at dfferent utlzaton levels (Economst, 2013). However, ths would mply that these utltes would also operate at lower utlzaton levels compared to when share of ntermttent resources was neglgble, whch would result n hgher cost of electrcty generaton. We explore the mpact of a Tme of Use (TOU) retal prcng n a capactated and deregulated electrcty market that s suppled from a fnte mx of ntermttent renewable and steady non-renewable resources. The ntermttent renewable resources are sources lke solar and wnd, and the steady non-renewable resources are Avttathur (2014): Impact of TOU retal prcng n an electrcty market wth ntermttent renewable resources 2

4 sources lke gas and coal. In our modellng, consumer demand and renewable energy supply are varable. We compare TOU retal prcng aganst fxed retal prcng wth the objectve of understandng ts potental advantages n () matchng demand and supply, () managng the demand and supply varabltes and () better utlzaton of the energy resources. Secton 2 descrbes the lterature, secton 3 descrbes the retal prcng models, secton 4 descrbes the numercal experments and ther results, and conclusons are descrbed n secton Lterature An argument common n much of the lterature on electrcty markets s the fact that electrcty cannot be stored. Hence, supply must equal demand at a gven pont n tme and has been one of the major manageral and technologcal challenges faced by ths ndustry. Before the arrval of compettve prcng, the electrcty sector was consdered a natural monopoly where effcent producton requred a monopoly suppler that was subject to government regulaton of prces, entry, nvestment, servce qualty and other aspects of frm behavor (Joskow, 1997). The author argues that tradtonal regulatory prcng prncples based on the prudent nvestment standard and recovery of nvestment costs, mplctly allocates most of the market rsks assocated wth nvestments n generatng capacty to consumers rather than producers. Oum, Oren and Deng (2006) s one of a stream of electrcty market lterature reportng ther transt n the past decade from regulated monopoles to deregulated compettve ones where generaton, transmsson and dstrbuton are no more by the same frm. They state that electrcty s now bought and sold n the wholesale market by numerous market partcpants such as generators, load servng enttes (LSEs), and marketers at prces set by supply and demand equlbrum. Prcng has been an mportant tool n attractng new nvestments n energy utltes and managng demand n electrcty markets. Borensten (2000) argues n favor of competton nstead of regulaton n determnng prces n wholesale electrcty markets. Descrbng market power as the ablty of a frm to ncrease prce and proft by reducng supply, he argues that t should not be confused wth compettve peak-load prcng. However, the market equlbrum through compettve prcng s stll pertanng largely to the wholesale markets only. Borensten and Holland (2005) descrbe the strong dsconnect between retal prcng and wholesale costs n restructured electrcty markets, where retal prces reman steady even though wholesale prces fluctuate extremely. They argue that flat-rate retal prcng has the problem of preventng hour-by-hour Avttathur (2014): Impact of TOU retal prcng n an electrcty market wth ntermttent renewable resources 3

5 prces that reflect wholesale costs and fals n a compettve market n mzng customer welfare. They also argue that ncreasng the share of customers on real tme prcng (RTP) would mprove effcency though t need not reduce capacty nvestment. Allcott (2011) evaluates a program to expose resdental consumers to RTP and found that enrolled households are prce elastc. They responded by conservng energy durng peak hours but dd not ncrease average consumpton durng off-peak tmes. The program ncreased consumer surplus by $10 per household per year whch s one to two percent of the electrcty costs. Chao (2010) explores the benefts of demand-response programs that pay consumers to reduce ther demand durng hgh-prce perods aganst a baselne, whch s the demand had t not been reduced. They dscuss the varous problems assocated wth the use of an admnstratve customer baselne that could create adverse ncentves and cause neffcent prce formaton. He dentfes fxed unform retal rate as a barrer to prce-responsve demand, whch s essental for realzng the beneft of a smart grd. Yang et. al. (2013) report varous studes on electrcty prcng and report that whle some nvestgated peak prcng consderng demand uncertanty only others nvestgated peak prcng consderng supply uncertanty only. They argue that most studes focused on prcng n the peak perod only and thereby gnored the possblty of consumpton shfts from peak hours to off-peak hours. They propose a tme-of-use tarff wth consderaton of consumer behavor that could create a wn-wn stuaton for both the producer and consumers. Smart Grd and Smart Meterng are necessary for the mplementaton of real-tme or tme-of-use tarff n retal markets. Blumsack and Fernandez (2012) descrbe the rapd advent of the smart grd and dscuss ts potental to act as an enablng technology for renewable energy ntegraton, prce-responsve electrcty demand and dstrbuted energy producton. Allcott (2011) report that though the customer surplus from RTP s meagre compared to the $150 per household nvestment n retal smart grd applcatons, many utltes are nvestng n them as they offer substantal cost savngs and provde the opton of offerng RTP. The lterature on renewable energy has two streams relevant to our study. The frst one s regardng feed-n-tarff (FIT) that s necessary to encourage nvestment n renewable energy. Frondel et. al. (2010) whle crtqung the German renewable energy model argue that supportng renewable technologes through FITs mposes hgh costs wthout any of the alleged postve mpacts on emssons reductons, employment, energy securty, or technologcal nnovaton. Garca et. al. (2012) argue that nether a FIT nor a renewable portfolo standard are ndependently capable of nducng the socally optmal level of nvestment n Avttathur (2014): Impact of TOU retal prcng n an electrcty market wth ntermttent renewable resources 4

6 renewable energy. Couture and Gagnon (2010) descrbe dfferent ways to structure FITs. These could broadly be categorzed nto two groups based on whether the remuneraton s dependent or not on the electrcty prce. Whle the former encourage electrcty generaton when t s needed most, the latter has the advantage of lowerng nvestment rsks. Thus FITs that are dependent on electrcty prce help n easng peak supply pressures and mproves market ntegraton of renewable energy sources. Lesser and Su (2008) argue that a FIT structure should be economcally effcent and propose a two-part FIT consstng of a capacty payment and an energy payment that s ted drectly to the market prce of electrcty. The second stream of lterature on renewable energy addresses the ssues assocated wth ts beng an ntermttent resource. Woo et. al. (2011) show that though ncreasng wnd generaton could reduce spot prces, t could also ncrease the spot-prce varance. Chao (2011) propose an effcent prcng and nvestment model for electrcty markets wth ntermttent resources. A contrbuton of ths paper s that both demand and supply are consdered to be varable, wth the supply uncertanty ncludng the varablty from ntermttent renewable energy sources. Hs smulaton study, based on ths modelng, shows that the ntroducton of renewable energy and dynamc prcng reduces the average cost of electrcty. Ambec and Crampes (2012) analyze the nteracton between a relable source of electrcty producton and ntermttent sources such as wnd or solar power. They argue that fxed retal prcng dstorts the optmal mx of energy sources and that a large share of renewable energy would be sustanable only wth a structural or fnancal ntegraton of the two types of technology. Lastly we revew some lterature on hour-ahead and day-ahead forecastng of renewable energy. Potter et. al. (2009) suggest that the smart grd operatons can be consderably mproved by accessng nformaton about the lkely behavor of renewable energy. Apart from longer-term assessments they hghlght the value of hour-ahead and day-ahead forecasts n better management of a grd. Kavasser and Seetharaman (2009) use fractonal-arima or f-arima models to forecast wnd speeds wth reasonable accuracy one day n advance. Foley et. al. (2012) revew dfferent wnd power forecastng methods and ther performance over dfferent forecast horzons. They report that wth wnd farm poolng and hour-ahead or day-ahead forecastng t s possble to predct wnd energy accurately. Mellt and Pavan (2010) study the 24 hour solar rradance forecast usng artfcal neural network and report a hgh forecast correlaton (above 94%) wth actual rradance. Perez et. al. (2013) too report the advances n solar rradance forecastng. Avttathur (2014): Impact of TOU retal prcng n an electrcty market wth ntermttent renewable resources 5

7 3. The Model We extend the lterature n ths feld by modellng a capactated and deregulated electrcty market wth multple supplers (generatng frms) and buyers (dstrbuton frms) for a partcular tme horzon. The supplers comprse of renewable and non-renewable energy frms. Lke Chao (2011) we too consder uncertan demand and supply. However, the supply varaton s only owng to the ntermttent renewable energy sources. The demand varaton s modelled explctly wth two components an nter-day varaton and an ntra-day varaton. Based on the ntra-day demand varaton, a day s dvded nto I equal duraton tme perods that are denoted by ( = 1, 2,, I). The tme horzon could be a perod of three, sx or twelve months, whch would be referred now onwards as the plannng perod. There s no electrcty storage faclty wth the dstrbuton frms and ther purchase of electrcty from the generatng frms durng any tme perod s equal to the demand for electrcty durng that perod. The electrcty demand at retal prce p durng perod of a day, Q (p), s a varable that s expressed as ( p), where s a varable ndcatng nter-day varaton ( > 0 and = 1) and Q ( p) s Q the expected demand at retal prce p durng perod. Let Q ( p) ndcate the expected demand at retal prce p at any nstant durng the plannng perod and Q ( p) Q ( p). As all perods are of same duraton t s easy to note that I. We assume a mum retal prce that the consumers are wllng to pay, ndcated by p. The stochastc demand curves could then be expressed as ( p p), where b s the slope of the demand curve n perod. Then, Q ( p) and Q ( p) can be expressed as b ( p p) and b b ( p p), respectvely. From the defnton of, t can be seen that b b or b b I. The generatng frms produce electrcty from both non-renewable and renewable sources. We assume that durng the plannng perod the non-renewable supply does not exhbt varaton whle the renewable supply exhbts varaton that s a functon of the tme of the day and day of the plannng perod. C R and C are the aggregate generaton capactes from renewable and non-renewable sources, respectvely, of all the supplers that s avalable for sale n ths market, and we assume that C s fully avalable at all tmes. The electrcty avalable for sale from renewable sources durng perod of a day, A ( A C, ), s a varable R that s expressed as A, where s a varable ndcatng nter-day supply varaton n perod ( > 0 and Avttathur (2014): Impact of TOU retal prcng n an electrcty market wth ntermttent renewable resources 6

8 = 1) and A s the expected supply from renewable sources durng perod ( A C, ). Let A ndcate R the expected supply from renewable sources at any nstant durng the plannng perod ( A A I ). Owng to dfferent types of non-renewable fuels and technologes, the supplers of electrcty from nonrenewable sources are assumed to be havng dfferent margnal costs and a partcular suppler would be n the market only f the wholesale prce covers ts margnal cost. Wholesale prce of electrcty from nonrenewable sources s expressed as Q, where Q s the demand met from non-renewable sources (Q C ), s the margnal cost of the most effcent non-renewable source and s the slope of the electrcty supply curve from non-renewable source. We assume p and 0. The margnal cost of electrcty suppled from any renewable source s assumed to be lesser than. Owng to ths assumpton and an envronmental regulaton mandate argument, the demand s met frst by electrcty from renewable sources. Ths consderaton s smlar to Chao (2011) and Ambec & Crampes (2012) who have assumed that margnal cost of renewable sources s less than that of the non-renewable ones. Electrcty from renewable sources s purchased at an effcent feed-n-tarff (FIT), F, that s lnked to the wholesale prce of electrcty from nonrenewable sources. In our model F Q, whch s smlar to the energy payment suggested by Lesser and Su (2008). Whle model n Chao (2011) looks at the optmal nvestment n capacty, the objectves of our modellng s to understand the advantages of TOU retal prcng aganst fxed retal prcng n () matchng demand and supply, () managng the demand and supply varabltes and () achevng better utlzaton of the energy resources. If Q s the total demand, the wholesale prce durng perod can be expressed as w (Q) for Q A and Q A ) for A < Q A + C (1) ( The dstrbuton frms charge ther customers a retal prce that s ether constant throughout the plannng perod or varyng wthn (the dfferent perods of a day) and between days. They wll be referred to as fxed retal prcng and tme of use (TOU) retal prcng, respectvely. A compettve dstrbuton market s assumed n both retal prcng scenaros. Accordngly, at equlbrum the retal prce s equal to the wholesale prce. In fxed retal prcng (Fgure 1), the prce at whch expected retal demand durng the plannng perod Avttathur (2014): Impact of TOU retal prcng n an electrcty market wth ntermttent renewable resources 7

9 equals the expected supply s taken as the retal prce. In ths model, we assume that the prce at whch expected retal demand durng the planned perod equals A s greater than the wholesale prce at ths supply, whch s. Ths mples that expected retal demand s greater than the expected supply of electrcty from renewable sources. Smlarly, we assume that the prce at whch expected retal demand durng the plannng perod equals the mum expected supply, A + C, s always less than the wholesale prce at ths supply. Ths mples that expected retal demand s lesser than the expected supply of electrcty from both renewable and non-renewable sources. These assumptons mply that b p A and bp C A C... (2) Prce Lean perod expected demand Peak perod expected demand Prce Scenaro 1 demand Scenaro 2 demand Wholesale prce Sc 1 wholesale prce Sc 2 wholesale prce p 1 F p 2 α F + C Fgure 1: Fxed Retal Prcng Demand (MW) α A 1 A 2 A 1 + C Demand (MW) A 2 + C Fgure 2: TOU Retal Prcng Scenaro 1: Hgh demand, low supply from renewable sources Scenaro 2: Low demand, hgh supply from renewable sources In TOU retal prcng (Fgure 2), the equlbrum retal prce vares contnuously from one perod to another. The lterature regardng renewable energy forecastng ndcates hgh accuracy n predctng supply one day ahead. Hence, we assume that the market has accurate nformaton regardng supply before a perod commences. As s common today n energy tradng, we also assume that the market has reasonably accurate demand nformaton before a perod commences. Hence, the wholesale prces are known wth reasonable accuracy before the start of a perod. Chao (2011) consders the retal prce to be equal to wholesale prce when the retal prcng s dynamc. We too make a smlar assumpton and also assume that the dstrbuton frms have a smart grd mechansm of communcatng ths retal prce to ther customers just before start of the perod, whch enables them to adjust demand accordng to the TOU prce. In TOU retal prcng, the equlbrum retal prce at an nstant s same as the wholesale prce at that nstant. It s equal to and Avttathur (2014): Impact of TOU retal prcng n an electrcty market wth ntermttent renewable resources 8

10 Q A for Q A and A Q A C, respectvely (Scenaro 2 n Fgure 2). At Q A C, the wholesale prce curve becomes a vertcal lne. In scenaro 1 (see Fgure 2), the supply curve s vertcal when t ntersects the demand curve. The equlbrum demand and prce are A1 C and p 1, respectvely. Fxed Retal Prcng Inverse of the expected retal demand durng any perod, Q ( p) b ( p p), can be expressed as p p Q b. Let Q F and p F be the demand and prce at equlbrum. From Fgure 1 and (2), t can be seen that we need to consder only A Q A C for fxed retal prcng. For A Q A C, the wholesale prce by (1) s w ( Q A). Equatng p and w, we get the expressons Q p F F b p A 1 b and bp A 1 b for A Q A C (3) From (3), t can be seen that p F s decreasng wth A. If there s no electrcty supply from renewable sources, then A = 0 and soluton of (3) s Q F p b and p F bp 1 b b 1 (4) For fxed retal prcng model, the demand and total electrcty avalable for sale n perod of a partcular day can be expressed as Q (p F ) and A C, respectvely, or Q( p F ) and A C, respectvely. In ths model, dstrbuton frms cannot exercse a prcng based strategy to manage demand. Ths mples that when Q ( p ) A C, the excess demand s ether not met (dstrbuton frms would F resort to electrcty ratonng) or s met through back-up sources whose margnal costs are far hgher than the margnal cost of any of the regular supples. Whle the former results n lesser customer welfare, the latter results n economc loss for the dstrbuton frms. Understandng the mpact of avalable supply s an objectve of studyng a capactated electrcty market. Ths s facltated by the assumpton that demand n excess of A C s lost and dstrbuton frms resort to ratonng on such occasons. Let dfference between avalablty and demand n perod for fxed retal prcng model be g F, whch can be expressed as A C Q( p F ). As and are defned as equal to 1 and Q( pf ) b( p pf ), the expected value of ths dfference, g F E, s A C b p p ). As the varaton n demand s ndependent of ( F Avttathur (2014): Impact of TOU retal prcng n an electrcty market wth ntermttent renewable resources 9

11 the varaton n renewable energy avalablty, the varance of ths dfference, Var g F, s A b ( p pf ), where and are the standard devatons of and, respectvely. If (.) and (.) are general representaton of probablty densty functon and cumulatve dstrbuton functon, respectvely, then the expected unmet demand as a proporton of expected demand n perod, E L F, the expected utlzaton of non-renewable supply n perod, E U F share of renewable supply n the total supply n perod, E R F, are: E 0 L g g dg b p p ) F mn gf F (5) F F ( F (6) C C gf EU F 1 g F g F dg F C g F dg F C 0 and ER EU C 1 EL Q( p ) F (7) 1 F F F, and the expected As per our assumptons mentoned earler, the calculatons n (6) and (7) assume that when demand n a perod s less than the total electrcty avalable for sale t s frst met through renewable sources and only after exhaustng ths source would electrcty be purchased from non-renewable sources. Tme of Use (TOU) Retal Prcng In TOU retal prcng model, the demand and total electrcty avalable for sale n perod of a partcular day can be expressed as Q (p) and Prce ε ε A, respectvely or ( p p) and C b A C, respectvely. In ths model, the dstrbuton frms employ prcng as a strategy to manage demand wth supply. The shaded zone n α Demand (MW) Fgure 3 s the area n whch the equlbrum les for a gven C and gven range of and. A A A +C A +C Fgure 3: TOU retal prcng equlbrum zone for perod Inverse of the retal demand durng perod, Q ( p) b ( p p), can be expressed as p p Q b. For a gven C, and, equatng p and w, we get: ( p Q b ) for Q A Avttathur (2014): Impact of TOU retal prcng n an electrcty market wth ntermttent renewable resources 10

12 ( p Q b ) Q A for A Q A C and Let Q T and p T be the demand and prce at equlbrum n perod.then, Q T b ( p ) and p for Q A (9) T and Q p T T b ( p ( b p A ) A ) 1 b and 1 b for A Q A C (10) Beyond A C, the equlbrum retal prce s such that b ( p pt) A C or Q T A C pt p A C b and (11) Let / and // / ( be such that b p ) A // and b ( p A ) 1 b A C. Then, E / // b ( p ) d b ( p A ) d d / 0 1 b d A C // ( QT ) and 1 b d p A C // / // E( pt ) d ( b p A b d d / ) (12) 0 As prcng s a tool to manage demand, there s no unmet demand n TOU retal prcng model. From (9) to (11), the expresson for demand met through non-renewable energy sources, 0 for Q A b ( p ) A 1 b C for Q A C Q T, s for A Q A C and (13) Avttathur (2014): Impact of TOU retal prcng n an electrcty market wth ntermttent renewable resources 11 The expected utlzaton of non-renewable supply n perod, E U T, and the expected share of renewable supply n the total supply n perod, E R T, are: // T b p ) A 1 b d C d d C / // E U ( (14) and ER EU C EQ T 1 (15) T T Lemma 1: Movng from fxed retal prcng to TOU prcng decreases the potental demand for an electrcty market that s not capactated. Proof: Refer Appendx 1 Lemma 2: As the share of renewable energy ncreases, the utlzaton of non-renewable supply ncreases n both the prcng scenaros. Proof: Refer Appendx 2

13 4. umercal Experments and Results For the experments we consder sx tme perods per day, each of four hours duraton (see Table 1). These perods were dentfed based on the Table 1: The Perods Perod 02:00a-06:00a dstnct ntra-day demand and renewable supply patterns notced n the 06:00a-10:00a Indan context. The demand s hghest after sunset whle renewable supply 10:00a-02:00p :00p-06:00p avalablty, whch s a mx of wnd and solar power, s hghest durng md- 06:00p-10:00p :00p-02:00a day. When faced wth power shortage the evenng hours, when the demand s hghest, are typcally chosen for ratonng by the dstrbuton frms. Based agan on estmates n the Indan context, the values of p,, b and are taken as $250/MW-hr, $25/MW-hr, 50 and 0.01, respectvely. We consder two levels of overall Table 2: The Experments avalablty (8500 MW, 9000 MW) and four levels of renewable energy as Avalablty Renewable Share of Experment a proporton of total energy (0%, 10%, 20%, 30%) for our experments. (MW) Energy % Ths mples eght experments (see Table 2). For each experment we study % % the dfferent measures for two levels of nter-day demand uncertanty % % (coeffcent of varaton values of 0.05 and 0.10) and two levels of nter-day % renewable energy uncertanty (coeffcent of varaton values of 0.10 and % % 0.20). We use the terms L, L, L, H, H, L and H, H to ndcate the dfferent combnatons of nter-day A rato demand and renewable energy uncertantes, where L ndcates low and H ndcates hgh. In each term, the frst letter ndcates the demand uncertanty level and the second letter ndcates the renewable energy uncertanty. Based on our assumpton ndcated by (2), an overall avalablty of at least 8333 MW s to be consdered for the parameters assumed above. Though the avalablty levels consdered may appear to be values close to each other, they are dfferent enough to ndcate ther effects on the varous measures that we would be studyng. By (4), the equlbrum demand and prce n the absence of renewable energy supply would be 7500 MW and $100/MW-hr, respectvely. In all the experments, TOU prcng results n hgher meetng of demand (see Fgure 4). Ths s n spte of the expected demand potental beng lesser for TOU prcng (see Lemma 1). Explanaton for ths observaton s the loss of demand that occurs n fxed retal prcng, ndcated by (5) and Fgure 11. Fgure 4 shows that the excess demand met under TOU prcng ncreases wth both the uncertantes as well as wth ncreasng share of renewable energy. The hgher meetng of demand wth TOU prcng ndcated n Fgure 4 Avttathur (2014): Impact of TOU retal prcng n an electrcty market wth ntermttent renewable resources 12

14 s explaned strongly by the hgher demand met n the lean perods (see Fgure 5). In the lean perods, the lower TOU prces results n hgher generaton of demand. Fgure 4: Hgher demand met under TOU prcng 240 MW Experment L, L L, H H, L H, H Fgure 5: Hgher lean demand met under TOU prcng Experment L, L L, H H, L H, H MW The average prce falls wth ncreasng share of renewable energy and total avalable supply n both fxed retal prcng and TOU prcng. For an avalable supply of 8500 MW, the average prce n fxed prcng falls from $100/MW-hr for no renewable energy supply to $83/MW-hr when renewable energy s 30% of the total supply. Smlar observatons are seen for TOU prcng. Ths renforces the observaton of Chao (2011) and others that ncreasng share of renewable energy results n lowerng of energy tarff. Except n Experment 5, the average prce was hgher wth TOU prcng, wth the dfferental ncreasng wth ncreasng share of renewable energy (see Fgure 6). Uncertanty has no mpact on fxed retal prcng but has an effect on TOU prcng. The dfferental ncreases faster wth hgher uncertanty and lower avalable supply. The 17% drop n average prce that s mentoned above for fxed prcng results only n a 11.33% ncrease n demand potental, mplyng a revenue reducton to the dstrbuton Fgure 6: Dfferental n expected (average) prce Experment $/MW-hr L, L L, H H, L H, H Fgure 7: Dfferental n expected revenue $ '000s frms wth ncreasng share of renewable energy. Smlar observatons are seen for TOU prcng. Ths phenomenon n realty s rasng Experment L, L L, H H, L H, H Avttathur (2014): Impact of TOU retal prcng n an electrcty market wth ntermttent renewable resources 13

15 questons on the vablty of nvestments n the energy sector as a whole n the lght of ncreasng thrust of governments on nvestments n renewable energy. Though the nvestments n renewable or non-renewable energy, or the fnancal vablty of energy frms are not study objectves of ths paper, the results ndcate that TOU prcng results n hgher expected revenue for the dstrbuton frms (see Fgure 7). Ths can be explaned by the hgher average prce and the absence of lost demand n the case of TOU prcng. The dfferental n expected revenue ncreases wth ncreasng share of renewable energy and uncertantes, but decreases as the total avalable energy supply ncreases. Fgure 8: Dfferental n supply utlzaton 4% 3% 2% 1% % of total supply Fgure 9: Dfferental n lean tme supply utlzaton 4% 3% 2% 1% % of total supply 0% Experment L, L L, H H, L H, H 0% Experment L, L L, H H, L H, H The decrease n retal prce assocated wth the ncrease n share of renewable energy contrbutes to an ncrease n the demand n both the prcng scenaros. By Lemma 2, ths mples that the utlzaton of nonrenewable supply ncreases n both the prcng scenaros. Referrng to Fgures 8 and 9, t s seen that the utlzaton of the non-renewable supply s always hgher wth TOU prcng at the overall level as well as n the lean tme perods. Ths dfferental ncreases wth ncrease n the share of renewable energy and the uncertantes but decreases as the overall energy supply ncreases. The dfferental s negatve n the peak tme perods, when the utlzaton s hgh n both the prcng scenaros. Fgure 10: Prce Varablty (SD) under TOU prrcng Experment L, L L, H H, L H, H $/MW-hr Fgure 11: Peak demand not met under fxed retal prcng 30% 20% 10% 0% Experment L, L L, H H, L H, H % of potental demand Avttathur (2014): Impact of TOU retal prcng n an electrcty market wth ntermttent renewable resources 14

16 The prce varablty under TOU prcng s descrbed n Fgure 10. Ths ncreases wth ncreasng share of renewable energy and uncertantes. The effect of demand uncertanty s clearly hgher than that of the renewable supply uncertanty. It s also nterestng to note that ncreasng total supply of energy reduces prce volatlty only at lower levels of renewable energy. Fgure 11 descrbes the demand that s not met by the dstrbuton frms n the peak perods under fxed retal prcng as a percentage of the potental demand. Ths ncreases wth ncreasng share of renewable energy. The demand and renewable supply uncertantes have a neglgble mpact on the demand that s not met. 5. Conclusons A capactated and deregulated electrcty market wth energy suppled from renewable and nonrenewable sources s modeled n ths paper to examne the advantages of TOU retal prcng over fxed retal prcng. The numercal experments based on the models clearly ndcate that n the context of ncreasng share of renewable energy TOU retal prcng s superor to fxed retal prcng on a varety of measures. Electrcty from renewable sources s procured n our models at an effcent FIT nstead of at constant prces. By assumng a lower margnal cost for generatng electrcty from renewable sources, demand s met frst by electrcty from renewable sources n our models. Ths s clearly algned wth sustanable energy arguments. Our models and the numercal experments renforce the exstng lterature that ncreasng share of renewable energy reduces energy prces under both prcng schemes. Our experments also ndcate that wth ncreasng share of renewable energy, and demand and supply uncertantes, TOU retal prcng results n hgher meetng of demand, hgher sale of electrcty n lean perods, hgher expected revenues for the energy frms, hgher utlzaton of non-renewable supply and hgher utlzaton of non-renewable supply durng lean perods. These dfferences decrease as the overall supply of electrcty ncreases. Hgher expected revenue for the energy frms under TOU prcng does not mply hgher costs for the consumers. Fxed retal prcng results n demand not beng met fully, specfcally n the peak perods. In our experments, the TOU average prces are hgher than fxed retal prces except when the overall supply s hgher and t s fully suppled from non-renewable sources. Ths dfferental ncreases wth ncreasng share of renewable energy and uncertantes. Rather than nterpretng ths as a dsadvantage of TOU prcng, we argue that ths result s explaned by the fact that the fall n prces that occurs as a Avttathur (2014): Impact of TOU retal prcng n an electrcty market wth ntermttent renewable resources 15

17 consequence of ncreasng share of renewable energy s lesser n TOU prcng compared to fxed prcng. The fall n prces as a result of ncreasng share of renewable energy has been hghlghted n recent tmes as detrmental to new nvestments n non-renewable energy. Hence, the hgher TOU average prces could be vewed as more encouragng for non-renewable energy nvestments. We assume that even wth ncreasng share of renewable energy, many parts of the world would stll be seeng new nvestments n non-renewable energy n the comng years. Through these results and arguments we conclude that TOU retal prcng s superor to fxed retal prcng. Our models have not consdered the nvestment costs n swtchng over to TOU retal prcng. Ths s a lmtaton of ths study. We also recognze that creaton of a smart grd that ncludes all the consumers could stll be many years n the watng, partcularly n lower ncome countres lke Inda and Chna. However, a hybrd model could be conceved n the nterm that allows smaller consumers, for whom the swtchng cost relatve to the consumpton s hgh, to contnue wth fxed retal prce. Such a hybrd model would exhbt the characterstcs of a TOU prcng model, f the consumpton by the large consumers wth smart meters s a substantal proporton of the total consumpton. References 1. Allcott, H. (2011). Rethnkng real-tme electrcty prcng. Resource and Energy Economcs, 33(4), Ambec, S., & Crampes, C. (2012). Electrcty provson wth ntermttent sources of energy. Resource and Energy Economcs, 34(3), Blumsack, S., & Fernandez, A. (2012). Ready or not, here comes the smart grd!. Energy, 37(1), Boden, T.A., G. Marland, and R.J. Andres (2013). Global, Regonal, and atonal Fossl-Fuel CO 2 Emssons. Carbon Doxde Informaton Analyss Center, Oak Rdge atonal Laboratory, U.S. Department of Energy, Oak Rdge, Tenn., U.S.A. do /CDIAC/00001_V Borensten, S. (2000). Understandng compettve prcng and market power n wholesale electrcty markets. The Electrcty Journal, 13(6), Borensten, S., & Holland, S. (2005). On the effcency of compettve electrcty markets wth tmenvarant retal prces. The Rand Journal of Economcs. 36(3), Chao, H. P. (2010). Prce-responsve demand management for a smart grd world. The Electrcty Journal, 23(1), Chao, H. P. (2011). Effcent prcng and nvestment n electrcty markets wth ntermttent resources. Energy Polcy, 39 (7), Couture, T., & Gagnon, Y. (2010). An analyss of feed-n tarff remuneraton models: Implcatons for renewable energy nvestment. Energy Polcy, 38(2), Avttathur (2014): Impact of TOU retal prcng n an electrcty market wth ntermttent renewable resources 16

18 10. Economst (2012), The future s black, January 21, 2012, 60-62, Prnt. 11. Economst (2013), How to lose half a trllon euros, October 12, 2013, 27-29, Prnt. 12. Foley, A. M., Leahy, P. G., Marvugla, A., & McKeogh, E. J. (2012). Current methods and advances n forecastng of wnd power generaton. Renewable Energy, 37(1), Frondel, M., Rtter,., Schmdt, C. M., & Vance, C. (2010). Economc mpacts from the promoton of renewable energy technologes: The German experence. Energy Polcy, 38(8), Garca, A., Alzate, J. M., & Barrera, J. (2012). Regulatory desgn and ncentves for renewable energy. Journal of Regulatory Economcs, 41(3), Jayaram, J., & Avttathur, B. (2012). Insghts nto Inda. Supply Chan Management Revew, 16(4), Joskow, P. L. (1997). Restructurng, competton and regulatory reform n the US electrcty sector. The Journal of Economc Perspectves, 11(3), Kavasser, R. G., & Seetharaman, K. (2009). Day-ahead wnd speed forecastng usng f-arima models. Renewable Energy, 34(5), Lesser, J. A., & Su, X. (2008). Desgn of an economcally effcent feed-n tarff structure for renewable energy development. Energy Polcy, 36(3), Mellt, A., & Pavan, A. M. (2010). A 24-h forecast of solar rradance usng artfcal neural network: Applcaton for performance predcton of a grd-connected PV plant at Treste, Italy. Solar Energy, 84(5), Oum, Y., Oren, S., & Deng, S. (2006). Hedgng quantty rsks wth standard power optons n a compettve wholesale electrcty market. aval Research Logstcs (RL), 53(7), Perez, R., Lorenz, E., Pelland, S., Beauharnos, M., Van Knowe, G., Hemker Jr, K.,... & Pomares, L. M. (2013). Comparson of numercal weather predcton solar rradance forecasts n the US, Canada and Europe. Solar Energy, 94, Potter, C. W., Archambault, A., & Westrck, K. (2009, March). Buldng a smarter smart grd through better renewable energy nformaton. In Power Systems Conference and Exposton, PSCE'09. IEEE/PES (pp. 1-5). IEEE. 23. Woo, C. K., Horowtz, I., Moore, J., & Pacheco, A. (2011). The mpact of wnd generaton on the electrcty spot-market prce level and varance: The Texas experence. Energy Polcy, 39(7), Yang, L., Dong, C., Johnny Wan, C. L., & To g, C. (2013). Electrcty tme-of-use tarff wth consumer behavor consderaton. Internatonal Journal of Producton Economcs. 146(2), Appendces Appendx 1: Proof of Lemma 1 We prove Lemma 1 usng a two perod model wth zero nter-day demand varablty and zero renewable energy supply that s not capactated. Let the slope of the demand curve n the two perods be b 1 Avttathur (2014): Impact of TOU retal prcng n an electrcty market wth ntermttent renewable resources 17

19 and b 2. By (3), the equlbrum demand for fxed retal prcng s b p 1 b Q F, where b = b1 b 2 2. By (10), the equlbrum demand for TOU retal prcng s Q T 1 b1 ( p ) 1 b1 Q T 2 b and b2 ( p ) 1 2 n perods 1 and 2, respectvely. As the perods are of same duraton, the dfference n demand potental can be expressed as Q Q Q 2 F T1 T 2, whch s p 1 b b ( p ) 1 b b ( p ) 2b b p b 1 b2 b1 b2 2 b1 b2 1 b1 1 b2 Ths smplfes to an expresson that s p b 1 b2 b b 1 b b b b Gven our assumptons that p and 0, the above expresson s always postve and, hence, the lemma. It can be seen that the above result would also hold true for a mult perod model wth nter-day demand varablty and renewable energy supply. 2 Appendx 2: Proof of Lemma 2 We take the case of fxed retal prcng to prove ths lemma. The equlbrum demand for fxed retal prcng s b p A 1 b Q F. As already mentoned n secton 3, the demand s met frst by electrcty from renewable sources. Hence, non-renewable energy consumed, Q F A, can be expressed as b p A 1 b A b p A b 1 Let x be the ncrease n renewable energy n the overall supply. For a gven overall supply, ths mples that the energy avalable from non-renewable sources reduces by x. Referrng to the expresson above, t can be seen that a reducton n avalable non-renewable supply by x reduces non-renewable usage only by x 1 b, whch s lesser than x. Ths mples that utlzaton of the non-renewable supply ncreases wth x and, hence, the lemma. Ths result s vald for TOU prcng too. Avttathur (2014): Impact of TOU retal prcng n an electrcty market wth ntermttent renewable resources 18