When designing a tariff for the transport of electricity, the main difficulty

Transcription

1 Chapter 4 COST RECOVERY AND SHORT-RUN EFFICIENCY Claude Crampes Grema ad Ide, Uversty of Toulouse, Frace Whe des a tarff for the trasport of electrcty, the ma dffculty s that the trasport dustry apparetly curs hh fxed costs ad o real varable cost. I effect, he the frastructure s stalled ad he the operators are at ther orkplace, the oly put hch s ecessary to delver electrcty at a ve thdraal ode s electrcty at some jecto ode sce electrcty s flo by tself. Coseuetly, at frst sht the problem s just to allocate fxed costs, maly frastructure mateace costs, aes ad facal chares, amo the dfferet types of users of the rd. As a matter of fact, the trasport of electrcty creates to sfcat varable costs. 1 Oe s a teral cost, that s, a cost terms of electrcty: a fracto of the eery hch s jected to the rd ll be lost dur trasport. It results that the cosumpto of 1 MWh of electrcty reures the eerato of (1+L) MWh, ad ths extra L MWh s a real cost for hch producers must be compesated. Addtoally, because the les ad odes used for trasport have a lmted capacty, the optmal allocato of producto ad cosumpto s ot as effcet as t ould be, abset ay rd costrat. Ad prc must clude ths ecoomc cost due to coesto. Whe trasport prces are computed us the maral values of these to costs (the so-called odal prces ), they provde a reveue larer tha the losses of eery. Ths surplus ca be used to pay for fxed costs of trasport but, most cases, t s ot lare eouh to balace the budet of the operator. Ths explas hy trasport tarffs must be ether secod-best lear prces (Ramsey prces) or o lear prces. The chapter presets the ormatve prcples of the ecoomc aalyss of prc electrcty trasport. It s exclusvely dedcated to short-term

2 106 Trasport prc of electrcty etorks aalyss, that s to the operato of a ve electrcty etork. The developmet of the trasport frastructure s aalysed Chapter 5. I Secto 1, e defe the varable cost of trasport as the sum of the cost of coesto ad the cost of ohmc losses. I Secto 2, e sho ho odal prces ca be used to des tarffs for trasport. Secto 3 s dedcated to the problem of fud rs order to balace the budet of the trasport operator. Frstly, e focus o Ramsey prces, hch are the secod-best lear prces he oe tres to reach effcecy thout mpar the budet eulbrum of the trasport frm. Secodly, e cosder a specal class of o-lear prces, amely, to-part tarffs. We coclude Secto 4. We do ot dscuss ho to defe trasmsso rhts o the trasport frastructure ad the coflct betee the supporters of physcal rhts ad the supporters of facal rhts. 2 Nether do e cosder the oershp ad the overace of the trasport frm. We suppose that users face o barrer to a access to the rd. The reulato of the trasport operator uder alteratve hypotheses cocer vertcal terato ad competto betee rd users s scrutsed Chapter 6. Whle the follo sectos e have adopted a o-techcal presetato, the reader ca fd the appedx a formal modell of the ma results. 1. FIRST-BEST DISPATCH IN AN ELECTRICITY NETWORK 1.1 The trasport of electrcty I ecoomc terms, a ood s defed by: () some trsc characterstcs (eht, sze, ualty, etc.); () the locato; () the date; ad (v) the state of ature here t s avalable. Trasport s the actvty that maly cossts modfy attrbute (), eve f, as sde effects, the three other attrbutes are also modfed most cases. It results that, to aalyse the utlty of trasport a specfc ood, e eed to aalyse the utlty ad the cost of that ood at the departure ad arrval locatos. The dfferece betee the et utlty of the ood at the arrval locato ad at the departure locato s the ross utlty from trasport t. Ths dfferece s to be compared th the cost of trasport order to decde f the ood s to be dsplaced or f t should rema at the tal locato. Ths s the ormatve prcple that e have to apply he aalys electrcty trasport. The start pot s to determe the uattes to

3 Cost recovery ad short-ru effcecy 107 eerate ad to cosume order to maxmse the elfare of all the aets that use the trasport frastructure. I the short ru, the eupmet for eerato, trasportato ad dstrbuto s fxed. The prefereces of cosumers also are fxed. The optmal allocato s lmted to decd ho much to eerate at each ode ad ho much to cosume at each ode, ve the restrats mposed by the topolocal characterstcs of the etork ad the techcal capablty of each pece of eupmet (see Box 4-1 for detals o the objectve to maxmse elfare uder alteratve sets of costrats). Box 4-1: Frst-best, secod-best, ad costrats to maxmse elfare I the short ru, the hole eerato ad trasportato eupmets are fxed, as ell as all the eeds. The rd-free frst best allocato s the set of uattes of electrcty eerated ad cosumed at each ode that maxmses the et elfare, that s, the sum of the dfferece betee the utlty of electrcty for cosumers ad the cost to eerate t, a fcttous stuato here eery ca flo from oe ode to others thout ay costrat ad thout ay loss. The rd-costraed frst best allocato also maxmses the et elfare, but tak to accout the physcal characterstcs of the rd. I ths case: () some eery s lost dur trasport; ad () because some les ad termedary odes have lmted capacty, the rd-free optmal flos are o loer feasble, hch creates a coesto cost. I ecoomc theory, secod-best maly refers to a stuato here the beevolet plaer has to balace the budet of the producers he supervses. Actually, ths expresso ca be used ay stuato here a costrat s added to a tal allocato problem. I that respect, the rd-costraed frst-best s a secod-best th respect to the rd-free frst best allocato. Whe a costrat s added to a ve optmsato problem, ether that costrat s ot bd ad the tal allocato does ot chae, or t s bd ad t results a decrease of the tal performace. The e allocato ca ever ve a hher performace sce, f feasble o, t as feasble before the e costrat s added ad t ould have bee chose. The dfferece betee the performace thout ad the performace th the costrat s the ecoomc cost of the costrat. For example, the ecoomc cost of the trasport rd s the dfferece betee the rd-free socal elfare ad the rd-costraed socal elfare. I the same ay, oe ca measure the cost of addtoal costrats, such as: the oblato to balace budet;

4 108 Trasport prc of electrcty etorks the prohbto to dscrmate o prces; restrctos o tarff classes (lear, to-part, etc.); the ablty of the operator to collect formato o prefereces ad costs; the uversal servce oblato; etc. Short-ru decsos are costraed by the capacty to adapt the trasport frastructure ad the eerato plats. For ths reaso, the short-ru cost, hch there are sfcat fxed costs, s hher tha the lo-ru cost exclusvely made of optmally chose varable puts. To uderstad hy the optmal allocato ca be defed that smple ay, t s terest to stress some mportat dffereces betee the trasport of electrcty ad other trasport actvtes, for example freht or passeers trasport. Frstly, electrcty s hhly stadardsed, hch meas close substtutablty betee eerato odes for a ve eed ad, symmetrcally, close substtutablty betee cosumpto odes for a ve producto. Ths homoeety property allos to pool uattes. Secodly, for electrcty, the tme attrbute of the ood s ot modfed by trasport. Poer flos stataeously throuh les ad termedary odes. (See Box 4-2 for some llustratos of etork topoloes). Ths explas hy, the optmal dspatch, jectos ad thdraals are cotemporaeous. For the same reaso, the dspatcher ca ko for sure the state of ature at a thdraal ode he ject poer at aother locato, hch reatly reduces the radomess of et locatoal utltes. The thrd dfferece th most trasport etorks s that, for electrcty, the techoloy does ot allo to cotrol the physcal flo of eery throuh the rd (see Box 4-2 for a llustrato). Coseuetly, the actual flo o each le caot be a cotrol varable. Fourthly, a ve rd, oe ca predct very precsely the amout of trasport losses because they follo ell ko physcal las. To sum up, trasport electrcty cossts cotroll modfcatos ts attrbutes () ad (v) thout modfy attrbute () ad provok a udesrable but predctable chae attrbute (). The physcal path folloed because of the trasformato attrbute () caot be cotrolled; t results that trasport betee to odes a meshed etork creates exteraltes o all les ad odes tetoally ad utetoally crossed by the eery flo. I the optmal allocato defed by a beevolet socal plaer, at each ode, maral utlty s eual to maral cost. If, at oe ode, maral cost ere hher tha maral utlty, the last kwh ould be eerated at loss ad, symmetrcally, f maral cost ere less tha maral utlty, t ould mea that the etre potetal socal surplus s ot created. At each

5 Cost recovery ad short-ru effcecy 109 ode, ths eualty of maral cost ad maral utlty ll most lkely reure a trasfer of eery. Some odes ll have to export eery ad others ll be et mporters, deped o the cost structure of eerato ad ve the cosumers' prefereces for electrcty. Whe o pece of frastructure exhbts coesto, ad he there s o ohmc loss, the optmal allocato s such that eery has oe sle value throuhout the hole etork, hch ca be veed as a at uue ode or as a plate. To see ths, observe that f there remaed a dfferece betee to odes, t ould be easy to crease the lobal surplus by trasferr some kwh from the ode th the loer maral valuato toards the ode th the hher valuato. Box 4-2: Of odes ad les A electrc rd ca be veed as a set of odes, ether fal (jecto ad thdraal odes) or termedary (trasformers, meters, cotrollers, etc.), tercoected by les. The smplest etork s made of oe sle le coect to fal odes. The orth-south etork represeted belo (see Fure 4-1) s a useful theoretcal cofurato to uderstad coesto ad losses, but t also ves a reasoably ood pcture of the rd some coutres. 3 Sce there exsts a sle le, there s oe uue possble path for trasport electrcty from orth to south or from south to orth. Abset ay eery loss, the physcal eulbrum of the electrc dustry mposes s s, here (respectvely ) stads for the uatty eerated (respectvely cosumed) at the orth ode ad s (respectvely s ) stads for the uatty eerated (respectvely cosumed) at the south ode. Coseuetly, the uatty of electrcty flo o the le s. s s But may coutres, partcularly cotetal Europe, electrc etorks are meshed. The coseuece s that there s ot oe uue path for electrcty to o from oe ode to aother. Ths s llustrated the three-ode etork hereafter (see Fure 4-2). Eery flos follo paths of least resstace determed by Krchhoff's las. Suppose a eerato ode ad a cosumpto ode are coected by to les, oe th a resstace tce the other's. Whe eerators ject uatty at oe ode ad, assum o losses, cosumers thdra the same uatty at the other ode, the flos o the lo resstace le ad o the hh resstace le are respectvely 2/3 ad /3. I a 3-le etork th the same resstace o each le, lke Fure 4-2, f there are to eerators stalled at odes 1 ad 2 respectvely, ad cosumers are located at the thrd ode, the smultaeous jecto of 1 ad 2 ll eerate a superposto of flos o the les coect cosumers to eerators. For example, the le betee ode 1 ad ode 3 trasports to thrds of the eery jected at ode 1 plus oe thrd of the eery jected at ode 2. By cotrast, oly oe thrd of the et flo crculates o the le betee the to eerators.

6 110 Trasport prc of electrcty etorks orth s south s Fure 4-1. Oe le etork ode 1 jecto ode 2 jecto ode 3 cosumpto Fure 4-2. Three-le etork But, as explaed belo, because of losses ad because of some scarce capacty trasport, trasfers from oe ode to aother caot be doe for

7 Cost recovery ad short-ru effcecy 111 free. It meas that the very-frst-best allocato (or rd-free allocato) s ot feasble. The dspatcher ca oly reach the rd-costraed optmal allocato ad, coseuetly, eery valuato result from ths dspatch ll dffer amo the odes. 1.2 The cost of coesto Assume frst that losses ca be elected. At mport odes, the com eery s lmted by the capacty of les ad trasformers alo the physcal path folloed by eery. As a result, electrcty s relatvely scarce ad t s more valued tha f there ere o capacty costrat. Recprocally, at export odes, eery s relatvely excess ad lo valued because the outo eery s lmted by the capacty of les ad trasformers. The more coested the etork, the hher the dscrepacy betee odal valuatos. The lmt case s the autarky case here les are cut sot that each ode s solated from the others. The dfferece betee to odal valuatos of eery, abset ay loss, s a dex of the thtess of the trasport costrat. It reflects the capacty of the operator to crease eerato at lo-cost odes ad to decrease t at hh-cost odes as ell as ts capacty to crease cosumpto at hh-utlty odes ad to decrease t at lo-utlty odes. The mert order commads that o eerator should be dspatched f there remas some avalable capacty th a loer cost. It s o loer mplemetable. I the smplest case of Box 4-3, th oe sle le coect effcet orther eerators th a south ode here there are effcet eerators ad the load, oe ca easly dra the rd-costraed optmal uattes ad measure ho they depart from the rd-free optmal uattes. The dfferece odal valuatos exactly reflects the socal cost of hav a out-of-mert-order dspatch because of the lmted capacty for trasport betee orth ad south. The dfferece s the shado value of the trasport le that sals by ho much socal elfare ould be creased f the costrat could be relaxed. I meshed etorks, eery flos alo least resstace paths thout the possblty to cotrol them. 4 As a result, ay jecto ad thdraal of a ve uatty at to dstct odes ll provoke a trast of electrcty throuh all the les of the etork. If oe le s coested, all paths ll appear coested. Coseuetly, a meshed etork, coesto o oe le s suffcet for odal values to dffer throuhout the etork. Because of ths cotao effect, the dual value of the coested le s larer tha the mere dfferece betee the maral values at the to eds of the coested le. 5 The dfferece betee these to values reflects the

8 112 Trasport prc of electrcty etorks eatve exteraltes electrcty trasport, that s, the addtoal coesto cost due to loop-flos. Box 4-3: Out-of-mert-order optmal dspatch Cosder the orth-south etork Box 4-2 (see Fure 4-1). Assume that all cosumers are south ad ther maral utlty from thdra the uatty s of electrcty s ve by the decreas fucto U '( ) 10 s s (see Fure 4-3). I orth, electrcty ca be eerated at a costat maral cost eual to 1 ad, south, there exst plats th a costat maral cost eual to 4. There s o costrat of capacty for eerato ad there s o eery loss o the le. Let K deote the capacty of the le. ode 1 jecto ode 2 jecto ode 3 cosumpto Fure 4-3. Out-of-mert-order optmal dspatch If K s very lare, the optmal dspatch cossts produc oth south here eerato s very costly. The hole eery comes from orth. The optmal cosumpto s such that U '( ) 1, that s the rd-free optmal uatty s =9. If K < 9, the capacty of the le does ot allo to mport ths uatty of eery from orth. The dspatch frst cossts saturat the le to trasfer as much eery as possble from orth, hch s K. After that, there are to possbltes: () f the maral utlty from cosum K s stll hher tha the maral cost of eerato south, use the south plat up to the pot here the maral utlty of electrcty s eual to the maral cost of eerato, that s U '( K s ) 4. Otherse, do ot dspatch the costly plat. I the frst case, the rd-costraed optmal allocato s K, s 6 K (as lo as K 6 ) ad the total cosumpto s 6. s

9 Cost recovery ad short-ru effcecy 113 I the secod case, that s for K betee 6 ad 9, the total output s the costraed flo com from orth, K, s 0. These uattes are raphed the mddle pael of Fure 4-3 as fuctos of the capacty of the le K. Because of the effcet dspatch created by the lmted capacty of the le, elfare caot be as hh as t ould be f lo-cost eerators ere located at the south ode th cosumers. The loer pael of Fure 4-3 represets the maral value of the capacty costrat, hch represets the maral cost of coesto. Whe K s smaller tha 6, oe addtoal ut of capacty ould allo to substtute oe orth kwh to oe south kwh, that s to save = 4-1 = 3 for a uchaed total output. Whe K s betee 6 ad 9, oe addtoal ut of capacty allos to crease the cosumpto by meas of more mports from orth, so that ts value s the et maral utlty of electrcty; = U'(K) - 1 = 9 - K. Fally, he K s larer tha 9, ay developmet ould be useless, hch s salled by = 0. As sho Chapter 5, the shado prce of the les s to be compared th the real prce of oe ut of eupmet to ko hether the trasport capacty s to be creased or decreased. Whe the dual value of the costrat s hher tha the cost of oe addtoal ut of eupmet, the trasport le should be developed. Ad t should be doszed the opposte case. I actual etorks, the frastructure s almost alays larer tha ts optmal sze. The coseuece s that the shado prce of les ad trasformers s less tha ther ut cost. Ad t s eve eual to zero he there s o coesto at all. 1.3 The cost of losses Suppose o that there s o coesto. The ma cost of delver 1 MWh at oe ode start from a specfc jecto ode results from the fact that a uatty L of the eery jected ll be lost trasport. It meas that 1+L MWh are to be eerated. As a result, a optmsed etork the maral valuato of 1 MWh ll dffer from oe ode to the other by the value of the lost eery. Note that t s ot a cost curred by the trasport rd tself. It s a cost due to the dstace betee jecto ad thdraal odes. It drectly cocers eerators ad cosumers. I electrc etorks, losses crease proportoally to the suare of the eery jected. The coseuece of ths precse fuctoal form s that maral losses are tce hher tha averae losses. 6

10 114 Trasport prc of electrcty etorks 1.4 The short-ru maral cost of trasport To sum up, because mata ad develop the frastructure s costly, t s optmal to keep some coesto most peces of the trasport rd. As a result, the dspatch that ould maxmse et socal elfare thout ay referece to the rd (lke f all eerators ad cosumers ere located at the same place) s ot feasble. The actual dspatch s sub-optmal as compared th the fcttous oe-ode dustry. The cost due to coesto s eual to the dfferece betee the maxmum elfare obtaed thout trasport costrats ad the elfare that results from the actual dspatch. I addto to coesto costs, oly a fracto of the uatty jected ca be cosumed. The cumulatve effects of these elemets s that a etork bult for electrcty trasport, the optmal allocato of uattes to eerate ad to thdra at each ode s such that maral valuatos ll be dfferet from oe ode to others. The odal valuato of eery s a atural by-product of the optmsato alorthms used by system operators. Whe a Idepedet System Operator computes the feasblty of a ve dspatch o the rd he cotrols, the value of eery at each ode ca be publshed stataeously. The dfferece betee odal valuatos that cludes a real cost (the value of lost eery) ad a shado cost (the value of lost effcecy), s to be veed as the short-ru maral cost of trasport. Yet, ote that oe of the to compoets of the short-ru maral cost ca be drectly related to a ecoomc or accout expedture curred by the operator of the trasport frastructure. 1.5 Tme varato The eeds for electrcty are stroly varable tme. They are both cyclcal (accord to ell ko daly, eekly ad yearly varatos) ad radom (for example because of chaes temperature). There occur other types of tme varablty o the eerato sde, due to the scarcty of hydro resources, the fluctuatos of fuel prces ad the avalablty of plats (mateace ad repar). I cotrast, the trasport frastructure s almost fxed for the medum ru. The optmsato of a stroly varable elfare fucto uder varable trasport costrats obvously results a cotuously vary optmal allocato ad, coseuetly, a cotuously vary maral value of eery at each ode. Dur lo actvty perods, the capacty of the les ad trasformers s ot bd. The odal valuatos dffer oly by the maral value of losses, hch are rather lo sce the level of cosumpto s lo. I cotrast, dur peak perods, the dfferece betee odal valuatos s very hh. Note that the last asserto s ot alays true. I some crcumstaces, the dfferece betee peak load

11 Cost recovery ad short-ru effcecy 115 ad off-peak load ca be larer at a export ode tha at a mport ode. I that case the electrcty flo o the le at peak perods ca be smaller tha at off-peak perods ad the odal dfferece electrcty valuato ca be hher at off-peak perods. 2. NODAL PRICES 2.1 Eery prces The frst-best allocato ca be decetralsed by meas of prces hch reflect the maral value of electrcty. It meas that the frst-best eerato levels ad cosumpto levels ould be freely chose by dvdual eerators ad dvdual cosumers f they ere fac prces eual to the maral value of electrcty the optmal allocato. Ad sce, as sho formerly, maral valuatos chae from oe ode to the other (ad from tme to tme), the decetralsato of frst-best ecesstates odal prces. If perfect competto mechasms preval at each ode (rouhly sad, f there exsts a lare umber of small buyers ad supplers of electrcty at each ode ho behave as prce-takers), the eulbrum ll aturally determe eery prces eual to the maral values obtaed formerly. Coseuetly, oraz competto s a ood ay to reach effcecy. Hoever, eve he the umber of eerators ad the umber cosumers are reasoably lare, the decetralsato of decsos reures some publc terveto, for example to oraze the match of demad ad supply holesale markets. I cotrast, f there s oly a small umber of lare supplers ad/or buyers, the eulbrum prce ould reflect the market poer of these aets. 7 To mplemet the frst-best, odal prces are to be reulated by the overmet or, more precsely, by a reulato etty or a attrust authorty. I ay case, he cosumers at ode ca buy electrcty ayhere ad pay electrcty com from ay ode j at a prce p eual to the optmal maral valuato of ode, they cosume the optmal uatty. Ad he eerators at ode are authorsed to sell electrcty ayhere ad receve p for ay kwh sold to ay ode j, they produce the optmal uatty Trasport prces For a ve trasacto, he the buyer ad the seller are located at the same ode, they trasact at the same prce p that covers oly eerato

12 116 Trasport prc of electrcty etorks costs. If the seller s at ode ad the buyer at ode j, the former receves p ad the latter pays p j. The problem s to ko hat to do th the dfferece. To ve a aser, ote that aother ay to decetralse the frst-best s to dstush the prce of eery ad the prce of trasport. Whe there are to separate blls, the prce for trasport 1 MWh from ode to ode j s to be t j= p j - p. As a matter of fact, the cosumer at ode j must be dfferet betee buy ts eery at ode j at prce p j o the oe had ad, o the other had, buy t at ode at prce p ad the pay t j for ts trasport to ode j. Smlarly, the eerator at ode must be dfferet betee sell ts eery at ode at prce p o oe had ad, o the other had, sell t at ode j at prce p j hle pay t j for ts trasport to ode j. Coseuetly, e ca coclude that, from the pot of ve of cosumers ad producers, the dfferece t j= p j - p really appears as a trasport fee. For ths reaso, t s atural to pay t to the operator of the trasport frastructure eve f the costs covered are o the users' sde. Note that f the et flo of eery s from (the export ode) to j (the mport ode), ay dvdual trasacto from to j creases coesto ad must be chared t j >0. I cotrast, assume p j < p so that ode j s a et exporter to ode ad there occurs a dvdual trasacto betee a eerator located at ad a cosumer located at j. Ho ca t be possble sce the eerator receves more tha hat s pad by the cosumer? Because the dvdual trasacto creates a couter-flo, t allevates the coesto o trasport les. Coseuetly, the trasport prc system should promote ths type of trasacto by reard the partes stead of char them for trasport. Ad ths actually occurs th odal prces sce the trasport of 1MWh from to j ould the be chared t j= p j - p <0. I other ords, the couter-flo trasactos ould be ecouraed. The total value of the flos of eery us the trasport prces derved from odal prces s the merchadz surplus. Eve f couter-flos are to be rearded, the merchadz surplus s obvously postve 9 for the follo reaso. Recall that odal prces reflect optmal valuatos of eery. Coseuetly, the merchadz surplus s made of to elemets. The frst pece s a et surplus due to the specfc fuctoal form of the losses of eery ad ther coverae by a maral prc rule. Actually, the eerator must be pad for the electrcty he produces, eve f t caot be cosumed. But because losses crease th the suare of the load, ther maral value s tce ther averae value. Coseuetly, after compesat the eerator for ts losses, t remas a eual sum that ca be used to pay for trasport. The secod part s the cost of coesto, ad ts overall value caot be eatve. Ether some les or odes are coested ad the the surplus s postve, or there s o coesto ad the the

13 Cost recovery ad short-ru effcecy 117 surplus s zero. By ts very defto, the merchads surplus does ot correspod to the paymet of costs curred by the operator. The trasport prces calculated us odal prces vary th the date, the tal ode ad the termal ode of the trasacto. All the users ho trasact at the same date, the same tal ode ad the same termal ode should pay (or should be pad for couter-flos) the same ut prce. Therefore, e ca assert that the odal prce system s objectvely odscrmatory (see Chapter 1). 3. CONSTRAINED AND UNCONSTRAINED PRICING 3.1 Effcecy cocer vs. fud-ras cocer Frst-best prc allos pay for all the costs of a dustry he the eupmet s optmally desed ad there are o creas returs to scale the lo ru. I ths hypothetcal stuato, o the oe had the short-ru maral cost ad the lo-ru maral cost are eual ad, o the other had, the lo-ru maral cost s at least eual to the lo-ru averae cost. Coseuetly, a prce eual to maral cost caot be belo the loru averae cost. But these optmal codtos are practcally mpossble to meet actual etorks, because of the follo reasos: 10 () dscrepacy betee lo-ru ad short-ru eeds The optmal dyamc expaso of the trasport frastructure does ot amout to the mere coecto of may statc plas. Most etork facltes are bult for 20 or 30 years ad t s ulkely for ay oe of the facltes to have exactly the optmal statc capacty for a ve year. Addtoally, devatos from the optmal pla are due to errors the forecast of demad ad eerato costs. () techcal o covextes For trasport facltes, decsos are dscrete optos rather tha cotuous varables. For a ve reforcemet, the feasble set s very small, e.., les of 220 kv or 400 kv. Coseuetly, as compared th the maral optmum, the result of proramm th teer umber ll be a apparetly ether overszed or uderszed etork, th a atural tedecy toards oversz he demad s expected to crease.

14 118 Trasport prc of electrcty etorks The tedecy toards over vestmet s tesfed because of scale ecoomes: the larer the capacty of the vestmet the smaller the captal cost per ut of capacty. () addtoal costrats Netork expaso pla s subject to relablty costrats hch create the eed for extra capacty th respect to the optmal pla uder strct ecoomc terms. Facal, evrometal, techcal or eve poltcal restrctos are also mposed o the expaso of the etork eeral or of a ve corrdor. We coclude that, because the frastructure s overszed as compared th short-ru eeds ad because there exst lo-ru ecoomes of scale, coesto rets calculated o the bass of short-ru maral costs ll be rather lo, ad the rets from losses ll ot be hh eouh to cover all the fxed costs curred by the rd operator. 3.2 Budet costrat Several solutos are avalable to balace the budet of the trasport frm. If publc subsdes are alloed, they ca be used to pay the dfferece betee the merchads surplus ad the fxed costs of the frastructure. But the taxes leved to fud the subsdes create ecoomc dstortos ad the result allocato of cosumpto ad producto caot be the frst-best. Because of the cost of publc fuds, e ca oly reach a secod best. Addtoally, th the Europea lberalsed frameork, the State-ad soluto s ot authorsed. Therefore, prces are to be adjusted to cover all the costs. Whe costraed to balace the budet of the trasport operator, the optmal tarffs ll depart from frst-best f specfc restrctos are mposed ther computato. Whe ay fuctoal form ca be mplemeted, that s he the bll s ot ecessarly proportoal to the uatty of eery that s trasported (o lear prces), the frst-best allocato remas feasble. 11 Amo o-lear tarffs e ll oly dscuss to-part prces. O the cotrary, f prces are restrcted to be lear, the best oes are Ramsey prces, ad the result allocato of eerato ad cosumpto ll oly be a secod best. We frst cosder the case here oly lear prces are feasble. 3.3 Secod-best lear prces Ramsey prces are the best lear prces he the balac of budet s madatory. They cover maral cost (coesto ad losses) plus a mar computed to pay for the fxed costs. I methods for prc appled by practtoers, fxed costs are allocated accord to some proportoalty rule

15 Cost recovery ad short-ru effcecy 119 (for example the cost share pad by aet he cosum the uatty s:, or C( )/ C j( j), j / j j here C( ) s the drect cost to produce, or ay other rato 12 ). I Ramsey prces, oe takes to accout the reacto of the frastructure users he they are blled or pad. Prc above maral cost s effcet because t provokes a decrease cosumpto. Smlarly, he a producer s pad less tha maral utlty, he decreases hs producto. Coseuetly, the am of secod-best prc s to lmt ths bas uattes produced ad cosumed. It s easy to uderstad that, f some cosumers react to prce creases less tha others, t s optmal to make them pay more tha more reactve cosumers. Ad symmetrcally, f some eerators decrease ther output more tha other producers he the sell prce s decreased, t s optmal to modfy ther sell prce less. Ths explas that Ramsey prces are versely related to the elastcty of demad ad to the elastcty of supply. As a coseuece, they are dscrmatory: each semet of users that ca be solated from the others ll pay or ll be pad a dfferet Ramsey odal prce. I the smple case here, at each ode, oe caot dstush betee dfferet types of cosumers ad betee dfferet types of producers, t remas true that oe ca dstush a roup of cosumers o oe sde ad a roup of producers oe the other sde. Coseuetly the Ramsey demad prce p ll be dfferet from the Ramsey supply prce p : because of the eed to levy fuds to cover fxed costs, e lose the property of prce uueess at oe ode. Whe eery ad trasport of eery from to j are blled separately, the eulbrum codto s that pay p j to cosume at ode j s to be euvalet to buy at prce p at ode ad trasport toards j, that s pj p tj. It results that the Ramsey prce for trasport tj pj p s the ehted sum of to elemets: () the cost terms of effcecy due to eery losses ad coesto e already had Secto 1; ad () the cost terms of effcecy due to the budet costrat. The frst part ca be postve or eatve deped o the drecto of dvdual operatos as compared th the et flo betee ad j. The secod part s ecessarly postve: t depeds o the elastcty of the eery supply fucto at the jecto ode ad o the elastcty of the eery demad fucto at the thdraal ode. The smaller these elastctes, the hher the Ramsey prce for trasport betee ad j, hatever the costs of ohmc losses ad coesto.

16 120 Trasport prc of electrcty etorks Note that Ramsey prc commads a lobal allocato of fxed costs based o demad elastcty, but trasparecy ad poltcal arumets mpose some frametato of fxed costs. Actually, the oblato to balace the budet ca be solved may dfferet ays. Oe possblty s to mpose a lobal budet costrat to the trasport operator. I ths case, Ramsey prces allocate all the fxed costs of frastructure to all users. Les ad trasformers lo voltae are pad by all users, clud lare cosumers ad eerators ho use oly hh or medum voltae eupmet. Aother soluto s to exempt lare users from pay for the fxed cost of the lo voltae system. I ths case, the optmal allocato of cosumpto ad eerato amo odes ad the result flos o les s to be calculated subject to several budet costrats. As explaed Box 4-1, the larer the umber of costrats, the hher the effcecy loss. It meas that, he prce dscrmato s alloed, dscompos the cost recovery costrat to several user-tareted costrats caot be justfed terms of effcecy. 3.4 To-part tarffs The drabacks of Ramsey prces are obvous: () a lare uatty of formato s ecessary to compute the elastctes; () dscrmato s forbdde by la, () the result uattes devate from frst best. For these reasos, mult-part prces ca be preferred. I the smple case of to-part prces, the cosumer pays a fxed amout of moey depedet of the uatty of trasport he ll reure ad, the, he pays a maral prce for each ut he ats to trasport. Sce the maral prce ca be set eual to the maral cost of coesto ad losses, ths tarff allos mplemet the frst-best allocato, provded that the fxed part of the tarff does ot exclude ay user th a maral lless to pay hher tha the maral cost. I effect, the rsk th oe uue topart prce s that the fxed fee must be hh eouh to cover all the fxed costs, so that users th lo come ll ot be able to pay for t. If these lo-come users ca be easly detfed, a soluto s to propose them a specfc to-part prce, for stace th a zero fxed part. The fla s that e are back to dscrmato. Eve a sle to-part prce s dscrmatory sce the ut prce pad s decreas th the uatty cosumed. Isofar as to-part prces are acceptable o leal rouds, t s effcet to propose to users ot oe but a hole set of to-part prces, lett each user choose th the meu the tarff he prefers. It s a very effcet ay to collect fuds for fxed costs cover. It s also a ood ay to oraze secod deree prce dscrmato he the prce maker lacks formato about the lless to pay of users. 13

17 Cost recovery ad short-ru effcecy 121 Apply these prcples to the trasport of eery, the tarff to trasport a ve uatty form ode to ode j should have a frst part proportoal to the uatty (here the proportoalty coeffcet s the maral cost of coesto ad losses) ad a secod part, fxed, computed after the fxed parts of the eery tarffs for cosumers at ode j ad eerators at ode. The fxed part of the tarffs for eery must be adjusted ot oly to pay for the fxed costs of eerators but also to pay for the fxed costs of the rd operator. By defto, the fxed part of to-part tarffs does ot dstort effcecy. Therefore, the tarff maker has some derees of freedom to calculate them. He maly has to avod the excluso of some aets, dvdually or collectvely. I electrcty trasport, the ma cocer s that lare cosumers have alteratve opportutes to the use of the rd, for example by stall eerato plats at ther locato. To prevet ths by-pass, several to-part tarffs must be proposed. Each tem the meu s talored so that o oe s excluded (partcpato costrat) ad each aet chooses the tarff calculated for hm (self-selecto costrat). Whe also tak to accout the possblty of coalto betee several producers or lare cosumers, or betee a producer ad oe of ts clets order to bypass the trasport frastructure, t s ecessary to have recourse to cooperatveames theory to optmally des the fxed part of the tarff. 14 Fally, ote that devces able to cotuously meter the flo of electrcty o a le are very expesve ad, may coutres, they are stalled oly o the hh voltae rd. Addtoally, he avalable, t ould be very costly both at the operator level ad at the user level to process all the formato they collect. As a result, stead of sed voces based o the tme profle of the demad for trasport, most coutres oe uses to calculate the areate uatty trasported dur a ve perod (for example, oe year) ad to chare a uform maral prce of trasport all the year lo. The draback s that the same total uatty of eery ca be trasferred th stro tme reularty or th a hh rreularty. Ad the rreular load profle s much more demad terms of trasport capacty tha the reular oe. Oe soluto s to dstush a eery compoet ad a capacty compoet the demad for trasport, each th a specfc costat maral prce. But t remas true that these to elemets are to be desed to sed accurate sals of scarcty to users. A fxed part remas ecessary to cover the fxed costs of the frastructure thout dstort the decso of the users.

18 122 Trasport prc of electrcty etorks 4. CONCLUDING COMMENTS To calculate the tarffs to trasport electrcty, the trade-off betee effcecy, budet reuremets, leal costrats ad practcablty, results a o lear tarff based o the odal prces of eery ad o the fxed costs of the frastructure. The smplest s to-part. The total bll to be pad to the trasport frm s made of a effcecy-oreted part, varable th the uatty trasported, ad a cost-recovery part, depedet of the uatty trasported. The frst part s amed at sall the cost of physcal losses ad the cost of coesto. It should vary th tme ad locato ad should be creas th the uatty of eery trasported. 15 Practcally, t should be a fucto of the jecto ad thdraal odes (ot o the physcal path of eery sce t actually caot be cotrolled) ad o the drecto of the flo. For practcal reasos, ths frst part of the tarff ca be dscomposed to a eery term ad a capacty term, both lear fuctos, provded that the scarcty sals they trasmtted are smlar to the oes that allo a effcet use of the rd. The fxed part of the tarff s amed at pay for the frastructure costs. Because ts purpose s purely budetary, t should ot terfere th the scarcty sals set by the varable part(s). I partcular, he the trasport tarff dstushes betee a eery compoet ad a capacty compoet, the latter should ot be veed as the fxed part of the tarff. I most coutres, actual trasport tarffs are to-part but the ay they balace the varable part(s) ad the fxed part s very heteroeeous. 16 APPENDIX MODEL SETTING To odes, (for orth) ad s (for south), are coected by a le of capacty K. The ut cost of capacty s r. The uatty of electrcty trasported throuh the le s measured the same ut as K. We ote of electrcty at ode ad U the utlty derved from the cosumpto of a uatty C the cost of eerat at ode (, s). Let W,,,, K U C U C rk stad for the s s s s s s elfare fucto of ths dustry, here superscrpt stads for thdraal ad superscrpt stads for eerato. We cosder oly short-ru decsos, that s, K s ot a cotrol varable. The optmal allocato s the soluto to:

19 Cost recovery ad short-ru effcecy 123,,, s s max W,,,, K (1) s.t. s s s s (2) def s z K (3) Provsoally, e assume there s o loss, hch s reflected by (2). To smplfy otatos, e assume that prefereces ad costs are such that the orth ode ll alays export a et flo of electrcty z toards south. For ths reaso, z 0. s s THE SOCIAL COST OF CONGESTION Let deote the dual varable assocated to costrat (3). The frst-order codtos that o o o o characterse the soluto (,,, ) to the above problem are: s s C C U C (4) ' o o s s s s U C (5) ' o o (6) o o o s s (7) o o o o s s o 0, K o o, o. K o o 0. (8) By (4) ad (5), at each ode maral utlty ad maral cost are to be eual. If the o capacty of the le s very lare, e obta the rd-free allocato. I ths case, z s K o so that 0 by the complemetary slackess codto (8). The, by (6), the maral valuato of electrcty s the same at both odes. The seres of eualtes U o C o U ' o C o, toether th s s s s codto (7), fully descrbe the optmal allocato. (see Fure 4-4). ' U North South exports= z o s ' U s C s C mports= z o s o o o s o s s Fure 4-4. No capacty costrat, same valuato at both odes

20 124 Trasport prc of electrcty etorks Coversely, f K s small, the costrat (3) s bd ad e obta the rd-costraed allocato. The optmal producto orth s ve by U ' o K C o ad, south, by U ' o K C o. s s s s No, the shado prce o U ' o K U ' o K C o C o s s s s s strctly postve. It sals that a larer K ould allo to eerate more eery orth here the cost of oe addtoal ut s smaller tha south ad to cosume more south here the utlty of ths addtoal ut s larer tha orth (see Fure 4-5). ' U C North South K o K C s ' U s o o o s o s s Fure 4-5. Bd trasport capacty, odal maral valuatos of eery dvere THE SOCIAL COST OF LOSSES Assume o that a fracto of the electrcty jected at the orth ode s lost before arrv at the south ode. I the proram to obta the frst-best allocato, e must replace (2) th: L (9) s s s s sce trasmsso losses. L crease th the poer cosumed by the load. The frstorder codtos rema (4), (5) ad (8). But (7) s replaced by (9) th the coseuece that (6) s replaced by: 1 C C L (10) o o o s s here L stads for maral losses. o I the o-coesto case hereafter llustrated by Fure 4-6 ( 0 ), e see that the optmal allocato sets: (1 ) o o o C C L C. s s Ths reflects that t takes (1+L') MWh eerated orth to match the eed for 1 MWh south. As compared th the case here L 0, the volume of trade s reduced ad

21 Cost recovery ad short-ru effcecy 125 cosumpto south s smaller. But eerato orth ca be larer order to compesate for the losses. o C (1 L) ' (1 LU ) ' U o C s s o C (1 L) C C o o C s ' U s s o o s s Fure 4-6. Optmal allocato th eery losses TIME VARIATION For a ve trasport frastructure, the optmal dspatch s tme depedet, follo the chaes cosumers prefereces of ad eerato plats avalablty. The obvous coseuece s that odal valuatos of eery are also tme-depedet. Assume there are o losses ad the trasport le of capacty K s used dur to perods of eual durato: a peak perod (labelled D for day) ad a off-peak perod (labelled N for ht). The problem s to maxmse: [ U C ] rk, DN, s, subject to to costrats of type (2) ad to costrats of type (3), oe par for each perod. 17 From the optmal allocato, e derve the shado prce of the le dur the day C o C o ad the shado prce of the le dur the ht D sd sd D D C o C o. As the eed for trasportato s hher dur the day, e have N sn sn N N o o, here the eualty holds oly the case o o D N D N 0, that s he the le s permaetly o-bd (hch should ever occur sce the ut cost of capacty s postve). Deped o the dscrepacy betee the ht ad day characterstcs of cosumpto ad eerato, e ca have ether a permaetly bd capacty ( o D o N 0 ) or coesto oly dur the peak perod ( o D o 0 ). N I ay case, because the same le s used to satsfy dfferet eeds, t has the features of a publc ood : 18 ths explas hy the test to ko hether the capacty of the le s too o o lare or too small cossts o compar the ut cost of captal r th the sum ( ). D N IMPLEMENTATION The frst-best soluto ca be decetralsed by meas of odal prces. At the south ode ay trasacto ll cost p U ' o C o per ut to a cosumer ad ll retur p s s s s s s

22 126 Trasport prc of electrcty etorks to a producer, hatever the locato of the other sde the trasacto. Smlarly, at the orth ode p U ' o C o ll be chared for ay ut of cosumpto ad ll be pad for ay ut of producto. It s easy to check that cosumers ho solve: max U p o ll choose, ad producers ho solve: max p C ll choose o at, s. Therefore odal prces, ether result from compettve odal markets or mplemeted by a reulato etty, allo to reach the frst-best allocato. Whe eery ad trasport are blled separately, the eulbrum prce for trasport from orth to south must be such that ps p ts; the t s p s p. We coclude that, he losses ca be elected, from (6) the frst-best trasport prce s: t (11) o o s I ords, abset ay ohmc losses, trasport should be free f ad oly f there s o coesto. Where there s coesto, a postve prce s to be chared. Symmetrcally, the eulbrum prce for trasport from south to orth must be such that p p s t s. We o o deduce that reverse flos should be chared ts p ps 0. Ideed, as lo as zs s s 0, dvdual trasactos from south to orth should be rearded sce they reduce the coesto of the le. o o ' Smlarly, tak losses to accout, from (10) e obta ts L' C 0 ad o o ' ts ( L' C ) 0. The latter s oce more justfed because ay et jecto south decreases the uatty of eery that must be jected at the orth ode ad, coseuetly, decreases both the losses of eery ad the coesto o the le. BALANCING THE BUDGET OF THE TRANSPORT OPERATOR Is ths frst-best sustaable o facal rouds? O the eerator s sde, f there are creas returs to scale, maral-cost prc s ot suffcet to break eve. But sce ths report s dedcated to trasport, e assume that eerators do ot lose moey he eerato s valued at frst best 19. What about the resources of the rd operator? The market eulbrum uder odal prces creates a merchads surplus : MS p p p p L. o o o o s s s s o L ' o C. L z o s z s C L K K f the costrat s bd otherse.

23 Cost recovery ad short-ru effcecy 127 Ths surplus s postve for to reasos: o because of the coesto ret K he the le s coested, because losses are creas th the suare of the eery jected. It results that: L L 2, o z s so that the surplus due to losses s CL. I summary, uder odal prc the dfferece MS betee the expedtures of customers ad the as of producers s postve ad t ca be used to cover the cost of the trasport operator. But s t true that MS rk? If the sze of the le could be optmally adjusted to trasport eeds, e ould have o r ad the MS ould leave the operator th a et proft eual to the value of losses (provded there are o-creas returs to scale). But for techcal, ecoomcal ad poltcal o o reasos, most trasport etorks, there s excess capacty so that r, ad eve 0 for absolute excess capacty. I most trasport frastructure, t results that the merchads surplus does ot cover the fxed costs. We successvely cosder secod-best lear prces ad o lear prces. RAMSEY NODAL PRICES To smplfy our aalyss, e come back to the hypothess of o losses. The, the problem s to maxmze (1) th respect to prces ( p, p, p, p ) subject to (2) ad (3), plus the s s addtoal oblato to balace the budet of the trasport frm, that s: p p p p rk 0, (12) s s s s ko that prce-tak cosumers behave optmally U eerators behave optmally C p at each ode =,s. p ad prce-tak Deot by the multpler assocated th the budet costrat (12), by the multpler assocated th the flo costrat (2) ad by the multpler assocated th the capacty costrat (3), from the frst-order codtos, t s strahtforard to rte the secod-best prces as: 20 p p p p orth ps ps ps ps s s south. Where:

24 128 Trasport prc of electrcty etorks def / s the prce elastcty of demad ad p / p def / s the prce elastcty of supply at ode. p / p Both cosumers ad eerators at each ode have to cotrbute to cover the fxed cost of trasport. At ode e observe that: p p p p ( ). 1 It s o loer true that there exsts oe uue prce at each ode. The dfferece betee demad prce ad supply prce creases th the value of the fxed cost of trasport to be pad (hch appears p p throuh the dual varable ) ad t decreases he the demad ad supply elastctes crease. RAMSEY TRANSPORT PRICES It obvously remas true that the eulbrum trasportato chares appled to the domat flo (from orth to south) are such that ps p ts. Us the Ramsey odal prces, e obta: ps p ts ps p 1 1 s (13) As compared th (11), e observe to dstortos: frst, to the maral cost of coesto 21 e have to add the cotrbuto to the recovery of the trasport fxed costs; secod, the maral cost of coesto s tself dstorted. A crease K both creases for facal reasos ad decreases for techcal reasos. It cofrms that the prc of trasport maly appears as the coverae of fxed costs, except he the capacty s very small. Fally, ote that for reverse trasactos (from south to orth) the Ramsey prce shall be: p ps ts p ps 1 1 s (14) It meas that the reard for allevat losses ad coesto ll probably be more tha compesated by the part of the tarff that partcpates to the coverae of fxed costs. If demad s much more elastc south tha orth ad supply much more elastc orth tha south, t ca eve be the case that t s t s, despte the couter-flo effect. Ths s because facal cocers appear as domat as compared th effcecy cocers. I ay case, compar (13) ad (14), e observe that t s t s oly by cocdece. Actually, secod-best prces are drectoal both for techcal ad facal reasos. Also, t

25 Cost recovery ad short-ru effcecy 129 must be recalled that (13) ad (14) the dual varables, the odal prces ad the elastctes are all tme depedet. We coclude that Ramsey trasport prces must be tme depedet. TWO-PART TARIFFS We cosder o the case here prces are ot costraed to be lear. We lmt the aalyss to the to-part tarff here T ( ) = a b s the expedture for cosum at ode ad T ( ) = a b s the reveue he eerat at ode. The oblato to balace the budet of the trasportato frm reads: a a a a ( b b b b) rk 0 (15) s s s s s s ' o ' o By fx a U ( ) a C ( ) at each ode, e obvously mplemet the frstbest allocato of cosumpto ad eerato at each ode. Gve these prces ad ve the flo costrat (2) (assum L=0), (15) reads ( b b b b ) ( o r) K 0. Oe s s obtas a fte set of solutos for the fxed part of the locatoal eery tarffs, eve he tak to accout the partcpato costrats of cosumers U ( ) T ( ) u ad eerators T ( ) C ( ), here u (respectvely ) stads for the reservato o value of cosumers (respectvely, eerators) at ode. Ay rule to share ( r ) K amo the aets by meas of the fxed part of the tarffs that satsfes the above partcpato costrats, plus addtoal costrats due to the formatoal dsadvatae of the prce maker 22, s permtted. Whe the buyer ad the seller of a volume are located at the same ode, they create a surplus: T ( ) T ( ) a b a b = b b To prevet ay arbtrae betee the to odes, the trade of a uatty of eery from orth to south s to be blled T ( ) T ( ) T ( ) a b a b. Therefore: s s s s o T ( ) b b (17) s s Symmetrcally, a dvdual reverse trasacto should be blled: T ( ) T ( ) T o ( ) b b (18) s s s For the sake of trasparecy, oe ca prefer a uform b for all cosumers ad a uform b for all eerators hatever ther locato, but the rsk of excluso (partcpato costrats that ould ot be satsfed) should ot be elected. For the same reasos as the oes metoed formerly, both the maral prce a ad the fxed fee b should be tme depedet. As lo as partcpato costrats are ot bd, the varato of b th the date s superfluous. I cotrast, the varable part of the tarff for o eery a ad, coseuetly, the varable part of the tarff for trasport should be tme depedet order to sed ood scarcty sals to users. MULTIPRODUCT TWO-PART TARIFFS As already metoed, eery prces ad coseuetly trasport prces should be vary th tme. For example, the hourly to-part tarff defed (17) should read:

26 130 Trasport prc of electrcty etorks T (, ( )) A ( ) ( ) B ( ) (18) s s s s s ad the total expedtures pad to the trasport operator by a aet trasferr eery from orth to south, let us say dur oe year, ould be: 8760 ( ) ( ) ( ) s. s s s T A B 1 For the reaso explaed formerly, the fxed part of the tarff ca be chose ute easly 23, for example t ca be a costat. The dffculty s that (18) reures to meter ad to bll the flos from orth to south almost cotuously. Because the trasacto costs ould be very hh, the operator ll stall smple meter ad bll devces that do ot dstush the date of each flo. Ths meas that the maral prce A ( ) ll ot be a cotuous s fucto of tme. I most cases, t ll be a pecese fucto th to seasoal (summer ad ter) ad to daly (day ad ht) values. At orst t ll be uform all the year lo. Assume the latter. I ths case A ( ) A so that: s s (, ( )) 8760 ( ) ( ) e s, s s s s s s s 1 T A B A B 8760 e here ( ) s the total eery cosumed all the year lo. s s 1 The obvous draback of ths to-part prc s that t does ot allo to dscrmate betee reular users ho ca be satsfed th a medum sze rd o oe sde ad, o the other sde, rreular users ho eed lare capacty of trasport for short perods of tme. A soluto s to combe the trasport demad for eery e ad a proxy for the trasport s demad for capacty, for example K max ( ), ad to bll them separately a ay that s s approxmates the optmal tme-depedet to-part tarff. We obta a mult-product to-part tarff: T A A B (19) e e K K s s s s s s LOOP FLOWS Cosder the three-ode etork of Box 4-2 ad suppose that the le betee the to jecto odes s the oly oe th a lmt capacty K. Nelect losses, the optmal dspatch s the soluto to: