Risk Sharing Under Renewable Portfolio Standards

Transcription

1 Risk Saing Unde Renewable Potfolio Standads Becky A. Lafancois PD Candidate, Syacuse Univesity Depatment of Economics 110 Egges Hall, Syacuse, NY Pone: (401)

2 Intoduction Feed-in Taiffs and Renewable Potfolio Standads (RPS) ae two of te most popula policy tools cuently being used to pomote te use of enewable esouces in electicity geneation. Feed-in Taiffs egulate te pice at wic utilities must pucase enewable electicity fom supplies, usually above maket value. Feed-in Taiffs ave been especially successful in Gemany and Spain, but ae not widely used in te United States. An RPS establises a minimum level (quantity) o pecentage of etail electicity sales tat must come fom eligible enewable souces. Suc standads ave been implemented in Japan, Austalia, and te Euopean Union, as well as in tity states in te USA. In addition, tee as been ecent discussion in te United States on te establisment of a nationwide RPS. Despite te gowing populaity of Renewable Potfolio Standads, few economists ave conducted eseac on te impacts of tese standads on electicity makets and investment in enewable tecnology. Fisce (2006) develops a teoetical model of te electicity maket in wic se examines ow te establisment of an RPS affects electicity pices. Se finds tat te elative supply elasticities of fossil and enewable fuels ae te diving foces influencing electicity pices. Tis pape extends te wok of Fisce (2006) by consideing te fact tat many enewable enegy souces ae intemittent and non-dispatcable. Using tis fact, tis pape examines ow socks in te availability of enewable esouces (e.g. wind, sola enegy) impact electicity pices wen an RPS is in place. Tis pape analyzes ow te featues and stuctue of an RPS affect te incentives and beavio of agents in te maket. In addition, te pape will lay te foundation fo fute analysis of ow an RPS inteacts wit ote types of enegy policies. Fo expositional ease, tis pape will employ wind as te only souce of enewable electicity. Ote enewable esouces 2

3 (e.g. sola) possess simila caacteistics as wind, so te esults of te analysis can be genealized to some ote types of enewable electicity. Te next section of te pape develops a model of te electicity maket. Te emainde of te pape is devoted to analyzing te incentives te RPS places on te utility. Model An electicity maket tat is govened by an RPS is compised of seveal impotant paticipants including electicity poduces, electicity distibutos, te end uses of electicity, and maket egulatos. Te cental paticipant in te maket is te electicity distibuto, wo will be denoted as te utility. Te utility is esponsible fo pucasing electicity fom vaious supplies and distibuting tat electicity to te end use in excange fo payment. In addition, te utility is subject to egulation fom two egulatoy bodies. Te legislatue enacts policies egulating te composition of electicity tat can be sold by te utility, and it also establises penalties fo noncompliance to its standads. Te public utilities commission egulates te pice tat te utility can cage its end use fo electicity. Te utility satisfies te demand of te end uses toug electicity pucases fom vaious types of poduces. In te cuent model, tee ae tee classes of electicity geneatos. Conventional poduces satisfy baseload powe consumption using taditional tecnologies suc as coal fied, gas, and nuclea plants. Renewable poduces, including wind and sola, ae used to meet electicity demand tat exceeds te baseload. A key featue of enewable electicity is tat it is intemittent, so te utility must ave access to anote souce of electicity in te case of a sotfall fom enewable poduces. Te utility tus employs poduces of gas-fied powe to cove any deficiencies fom enewable output. Figue 1 povides an illustative intepetation of 3

4 te paticipants in te electicity maket. Key assumptions and attibutes of te vaious paticipants will be developed as te model demands. Renewable (Wind) Supplies Conside an investo wo is delibeating investing in a single wind tubine. Unde te existing maket conditions, te pice of enewable electicity is significantly ige tan te pice of conventional electicity, eflecting te ige costs equied in poducing enewable electicity. Given suc cicumstances, a viable maket fo enewable electicity would be nonexistent wit te absence of policies pomoting enewables. Te tubine as a pesent value cost c wic encompasses all costs of investment, including capital costs, maintenance costs, and a equied etun on te investment. As a esult of te vaiability of wind, te tubine poduces an uncetain amount of electicity, q. Te output is distibuted unifomly ove te ange a to b, and tee is te cance tat a could equal 0. Tat is, if te wind does not blow, no electicity is poduced by te tubine. Fo eac unit of electicity tat is poduced by te tubine, te poduce eceives a fixed pice 1, p. Te pofit function fo a tubine can be epesented by π = p q c (0.1) Te expected pofit fo an investo in enewable enegy, given te andom distibution of wind is π = p q c (0.2) Wee te expected output of electicity q is b 1 ( b+ a) q = q dq = (0.3) b a 2 a 1 Te detemination of te pice of enewable electicity is a subject of ongoing eseac. 4

5 Regulato Te egulato plays two oles in te model, setting te enewables taget fo te RPS and detemining te noncompliance fine fo utilities tat ave a sotfall of enewables. Te egulato detemines a goal fo enewable electicity pucases by its utility companies. In geneal, te goal can be expessed as a fixed quantity o as a pecentage of total electicity sales. Tis pape will assume tat te mandated RPS isφ, wic can be intepeted as eite a quantity d goal o as te esult fom a pecentage RPS, wee φ = ψq. Te egulato sets a fine F suc tat wee F = f + f ( φ Nq ) F can be tougt of as a two pat taiff wit a fixed penalty a (0.4) f a fo failing to comply wit te egulation and a pe unit fine f on te ange of noncompliance ( φ Nq ). Fo tis model, we will assume tat f a equals 0, and te utility pays fines only on tose units fo wic it did not comply wit te RPS 2. Public Utility Commission Te ole of te public utility commission is to set te maket pice fo electicity p d. It is assumed in tis model tat te commission sets te pice of electicity so tat wen enewable electicity is at its aveage, te utility eans zeo pofits 3. Electic Utility Te electic utility as two main esponsibilities. Te fist is to satisfy te demand of its customes, d Q, and te second is to comply wit te RPS egulation, φ. As peviously discussed, te utility pocues electicity fom tee distinct supplies. Te utility buys c Q units 2 Altenative fine stuctues ae te subject of late wok. 3 Fute analysis of te maket pice of electicity is ongoing in concuent eseac. 5

6 of electicity fom conventional supplies to satisfy its baseload demand. Te utility also pucases Q units of powe fom enewable supplies to satisfy te RPS equiements. In addition, te utility needs access to an amount of dispatcable electicity tat matces te potential enewable capacity. Tis is equied to make up fo any supply sotfall fom enewables. Te utility acquies g Q fom wat will be temed gas-based supplies. To induce investment in enewable electicity, te utility engages in contacts wit a poduce and offes a fixed pice p fo its output. Te pice tat is offeed by te utility is te pice tat just induces investment in enewable electicity and yields te investo zeo economic pofits. 4 Te utility selects te numbe of contacts N to enact wit te enewable supplie. Te cuent analysis will use a single site model 5 in wic te utility selects te numbe of tubines to be constucted on a single site. Eac contact epesents te constuction of an additional tubine by te enewable supplie. Eac tubine poduces q units of electicity wee q is unifomly distibuted between a and b. Since all of te tubines ae located on te same site, eac tubine eceives te same amount of wind, tus output is pefectly coelated acoss te tubines. Te R total enewable electicity pucased by te utility is Q = Nq. Maket Definitions: Te maket cleaing condition fo electicity is d c Q = Q + Q + Q g (0.5) wee te total quantity of enewable electicity pucased by te utility is found by aggegating te output of all N tubines Q = Nq (0.6) 4 Tis seems to be wat is done in pactice. 5 Multi site model is te subject fo futue eseac. 6

7 and te total quantity of gas based electicity employed is found by aggegating te sotfall of enewable electicity ove te N tubines g Q = N( b q ) (0.7) Te sotfall in enewable electicity fom a paticula tubine is epesented by ( b q ) given te assumption tat if te tubine opeated at full capacity b te demand in excess of baseload would be fully satisfied. Using te definitions fom (0.6) and (0.7), te equilibium in te maket fo electicity can be expessed as Q = Q + Nq + N( b q d c ) (0.8) Total Revenue: Te total evenue function fo te utility is defined as TR = d d p Q (0.9) d d wee p is te maket pice fo electicity tat is set by te public utilities commission and Q is te maket demand. Total Cost: Te utility s total cost function is defined as TC = TCE + F (0.10) wee te total cost TC can be split into two components, te total cost of electicity TC, wic E is paid to supplies, and any noncompliance fines F tat must be paid to te egulato. Te total cost of electicity is defined as TC = pq + pq + pq E c c g g (0.11) wee c p, p, and g p ae te pices te utility pays to te conventional, enewable, and gas- based supplies, espectively. Substituting in fo te quantities of enewable and gas-based electicity defined in equations (0.6) and (0.7), te total cost of electicity can be expessed as c c g TC = p Q + p Nq + p N( b q ) E (0.12) 7

8 Te utility s total cost of noncompliance depends on te penalty system establised by te egulato f and te degee of violation ( φ Nq ), and is defined as F = f ( φ Nq ) (0.13) Using te definitions fom (0.9) and (0.10), te utility s pofit function is defined as te diffeence between total evenue and total cost u d d π = p Q TCE F (0.14) Substituting in te components fom (0.12), te utility s pofit can be expessed as π u = p d Q d p c Q c p Nq p g N( b q ) F (0.15) Te pofit fo te utility depends on te pices and quantities of te vaious types of electicity and wete o not te utility is subject to a non-compliance fine by te egulato. Expected pofits and analysis of te fine: In te context of tis analysis, I assume tat te utility is isk neutal, and teefoe is concened only about its expected etun 6. Te utility s expected pofit is defined as π u = p d Q d p c Q c p Nq p g N( b q ) F (0.16) wee q is te expected quantity of enewable electicity geneated by a tubine and F is te expected noncompliance fine. Recall tat output of electicity fom a given tubine is unifomly distibuted ove te ange fom a to b and te output is pefectly coelated among te N tubines at te site. Tus, te expected enewable electicity available fo pucase by te utility is Nb ( + a) E( Nq ) = = Nq (0.17) 2 6 A isk avese utility is a subject of futue eseac. 8

9 Te utility is concened about wete it will be subject to a fine F if it does not satisfy te equiements of te RPS. Te pobability tat te utility company is subject to a noncompliance fine is te cance tat its enewable pucases ae less tan amount equied by te RPS. In ote wods, it is te pobability tat Nq < φ, wic can altenatively be expessed as te pobability tat q φ <. Define N φ = qˆ ( N) (0.18) N Te pobability tat te utility is subject to a noncompliance fine can be expessed as qˆ ( N) ˆ 1 q ( N) a P( q < qˆ ( N)) = dq = (0.19) b a b a a wee qˆ ( N) can be intepeted as te output of electicity equied by eac tubine to satisfy te RPS. Teefoe, qˆ ( N) ais te ange of output fo wic te RPS is not satisfied. Te potential output by eac tubine anges fom a to b, so te atio of te anges yields te cance tat te utility is in violation of te policy. If te utility violates te RPS, it is subject to a fine. As defined in equation (0.13), te utility is equied to pay a pe unit fine f ove te sotfall φ Nq utility is teefoe Te utility s expected fine is. Te fine to be paid by te F = f ( φ Nq ) (0.20) qˆ( N) 1 F = f ( φ Nq ) dq (0.21) b a a 9

10 Evaluating te integal and substituting in fo qn ˆ( ) yields an expected fine of 2 f φ 2 φ Na φ Na F = 2φ a+ Na = f (0.22) 2( b a) N Nb Na 2 wic can be intepeted as te expected magnitude of noncompliance aggegated ove te N tubines multiplied by te pe unit fine f. Te magnitude of noncompliance is te pobability tat te utility does not satisfy te RPS multiplied by te aveage level of noncompliance. Te utility s goal is to select te numbe of tubines N tat will maximize its expected pofit π defined in equation (0.16). Te fist ode condition fo te utility is d d c c g max π = p Q p Q p Nq p N( b q ) F (0.23) N df dn g = ( pq + p ( b q )) (0.24) Te fist ode condition indicates tat te utility company pucase tubines until te eduction in te expected fine is just equal to te expected cost of executing anote contact wit te enewable supplie. Te expected cost of executing an additional contact is compised of te expenditues by te utility on te enewable electicity and te supplementay gas. Te cange in te expected fine given a cange in te numbe of tubines is df qˆ a qˆ+ a = f if ˆ q < q ( N) (0.25) dn b a 2 wic can be intepeted as a combination of te cange in te cance of being fined and te cange in te seveity of te fine multiplied by te size of te fine. Te sign of te deivative indicates tat te size of te fine is invesely elated to te numbe of tubines. Solving te fist ode condition fo N sows tat te utility will maximize expected pofits by selecting te numbe of tubines suc tat 10

11 N = 2( b a) f φ 2 ( p q + p g ( b q )) + a (0.26) Results Recall tat te utility will maximize its expected pofits by selecting an N suc tat N = 2( b a) f φ 2 ( pq + p g ( b q )) + a φ = (0.27) ψ Te optimal numbe of tubines is dependent upon te stuctue of te RPS (legislative equiement and fine), te pices of enewable and gas-based electicity, and te potential ange of electicity poduced by te enewable tecnology. Tis section of te analysis will examine ow te utility s optimal numbe of tubines esponds to canges in eac of tese paametes. Size of te RPS Requiement Te cange in te optimal numbe of tubines given a cange in te RPS equiement is dn 1 = > 0 (0.28) dφ ψ Ote tings equal, as te RPS becomes moe stingent, moe enewable electicity is equied to avoid te noncompliance penalty. Tus it is advantageous fo te utility to ente into moe contacts fo enewable electicity. Magnitude of te Noncompliance Fine Te cange in te pofit maximizing numbe of tubines given a cange in te noncompliance fine is dn [ ] 3/2 b a g φψ = ( ( )) 2 pq + p b q >0 (0.29) df f 11

12 All else constant, as te legislatue inceases te noncompliance fine, te utility will optimize its expected pofits by inceasing its contacts fo tubines. Analyzing ow te exteme limits of te noncompliance fine impact te optimal numbe of tubines yields a vey intuitive esult. Fist, conside wat would appen if tee wee no fines fo noncompliance, f = 0. Witout a penalty, te utility would not buy any enewable electicity, but would instead fulfill te maket demand using conventional souces of electicity. Te esult is cooboated by computing te limit of te optimal numbe of tubines as te fine goes to zeo. lim N = 0 (0.30) f 0 Convesely, if te noncompliance penalty balloons, it would become extemely expensive fo te utility to fall sot of te RPS equiement. Te ige te penalty, te utility desies moe access to enewables. Tis can be seen by analyzing te limit of te optimal numbe of tubines as te fine goes to infinity. φ lim N = (0.31) f a If te fine fo noncompliance was infinite, ten fims would guaantee compliance by contacting wit enoug tubines so tat wen te output is at its minimum it still satisfies te RPS. Canges in te Costs of Pocuing Electicity Te optimal numbe of tubines esponds to canges in te costs of pucasing enewable and gas electicity fom supplies. Fist, conside a cange in te pice of enewable electicity. dn φ [ ] 3/2 2( b a ) = 0 ψ q < (0.32) dp 2 f 12

13 If te pucase pice of enewable electicity inceases, ceteis paibus, te fim will find it elatively advantageous to educe te numbe of contacts and instead pay te noncompliance fine. A simila esult is seen fo a cange in te pice of gas-based electicity. dn φ [ ] 3/2 2( b a ) = ( ) g ψ b q < 0 (0.33) dp 2 f As it becomes moe expensive to cove te sotfalls in enewable electicity using gas, te fim will be bette off facing te noncompliance penalty. Te esponsiveness of te utility s decision to pocue enewable electicity to canges in te cost of electicity as impotant implications fo policymakes. Any policies, on top of an RPS, tat educe te cost of enewable electicity will aid in inceasing te use of enewables by te utility. Canges in te Range of Renewable Electicity Poduction Te ange of te output of enewable electicity also impacts te utility s optimal coice fo te numbe of tubines it sould employ. Tee ae two distinct ways tat te ange of output can cange. Te fist is an incease in te uppe bound of enewable output b. dn db [ ] 3/2 2 ( 3 g = φ ψ pq + p ( b a) < 0 2 f 2 (0.34) As te uppe bound inceases, te cance tat te utility will satisfy te RPS also inceases. Tus, te utility must contact wit fewe tubines to acieve its pio level of pofit. Te maximum potential output of a tubine could incease due to tecnological impovements in tubine design. Te ote possibility fo a cange in te ange of tubine output is to cange te lowe bound a wile maintaining te size of te output ange (db = da). Tis is equivalent to an upwad tanslation of te output ange. 13

14 dn da [ ] 3/2 2 g φ p = ψ ( b a) + 2a < 2 0 f (0.35) As te ange of output inceases, it becomes less likely tat te utility will violate te RPS, and it is valuable fo te utility to educe te numbe of tubines it employs. A tanslation of te ange is likely if tecnology is constant, but an altenative site is windie tan te cuent site. 14

15 Refeences Fisce, Caolyn How Can Renewable Potfolio Standads Lowe Electicity Pices? RFF Discussion Pape REV. Wasington, DC: Resouces fo te Futue. 15

16 Figue 1- Illustation of te Electicity Maket 16