REDESIGNING ADEQUACY PERFORMANCE MEASURES IN THE PRESENCE OF DEMAND ELASTICITY IN ELECTRICITY MARKETS. Pablo Rodilla* & Carlos Batlle*

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1 IIT Workng Paper IIT A. Frs verson: February Ths verson: March Submed o XXX. REDESIGNING ADEQUACY PERFORMANCE MEASURES IN THE PRESENCE OF DEMAND EASTICITY IN EECTRICITY MARKETS Pablo Rodlla* & Carlos Balle* The ably o analyze and assess he elecrcy marke performance n erms of he resulng generaon adequacy level s essenal for boh marke agens and regulaors. Tradonally, n he conex of elecrc power sysems, hs assessmen has been carred ou based on he so-called relably ndexes, such as he oss of oad Probably (OP) or he Expeced Non-Served Energy (ENSE). However, as we dscuss, hese ndexes are no well sued when a non-neglgble par of he demand s elasc (.e. prce responsve). The objecve of hs paper s o llusrae and deal wh he proper defnon of mercs amed o evaluae wheher, n he presence of demand elascy, he marke s reachng an effcen generaon adequacy level. To suppor and beer llusrae he dscusson, we propose an exenson of he convenonal Probablsc Producon Cosng model (PPC) ha allows akng no accoun a prce responsve demand curve. The model developed, as well as he mercs proposed, are esed wh a case example. Keywords Elecrcy markes, generaon adequacy, Probablsc Producon Cosng models, demand elascy 1 INTRODUCTION 1.1 Movaon The ably o analyze he elecrcy marke performance n erms of he resulng generaon adequacy level 1 s essenal for boh marke agens and regulaors. In order o carry ou hs adequacy assessmen s usually necessary o defne mercs and reference values (also known as benchmark values). Tradonally, n he conex of elecrc power sysems, hese mercs have been expressed n erms of pure relably, for nsance, based on he values of oss of oad Probably (OP), oss of oad Expecancy (OE) and/or Expeced Non-Served Energy (ENSE). The cos effcency creron s mplcly nroduced when defnng he benchmark reference value. For nsance, he well-known reference of he one day n en years (a FERC relably sandard) ndrecly acknowledges ha achevng a larger level of relably would be no cos effecve 2. In he conex of hs adequacy concern, smulaon models have proved o be valuable suppor ools. One of he smulaon ools whch has served (among oher uses) o carry ou smplfed 1 Tha s, he marke performance wh respec o wheher or no ensures enough avalable generaon capacy o effcenly mee demand n he long erm. 2 These reference values should be every now and hen updaed, so as o properly ake no accoun he echnology and cos evoluon ha may affec he elecrcy ndusry. Unforunaely n he majory of power sysems hs has no been he case. The auhors are wh he Insue for Research n Technology (IIT), Comllas Ponfcal Unversy, Sa. Cruz de Marcenado 26, Madrd, Span. (e-mal: 1

2 Redesgnng relably measures n he presence of demand elascy n elecrcy markes elecrc power generaon relably assessmens s he so-called Probablsc Producon Cosng (PPC) model. In hs paper, our purpose s wo-folded: we frs am o conrbue o he refnemen of he classc adequacy mercs, and second we am o exend he PPC modelng approach: We propose an algorhm ha allows exendng he classc PPC models desgn o explcly represen a sep-wse prce responsve demand curve (.e. an elasc demand). The mehodology proposed s a smple and robus soluon whch clears up he ask whou complcang he orgnal approach. Ths exended model wll serve us o suppor he major dscusson developed here, ha s, how classc relably ndexes are no longer suable mercs o measure adequacy performance when demand s prce responsve. Indeed, as we wll laer dscuss, n an fully elasc demand conex 3, he OP or he ENSE value as radonally defned, would ake a zero value, no maer whch he generaon avalably would be. Fnally, a refnemen of hese classc ndexes s proposed, so as o more suably evaluae he level of adequacy of an elecrcy sysem n he presence of demand elascy. A case example wll be presened. I s mporan o clarfy ha n hs paper we wll no model, neher consder n he compuaon of he dfferen relably ndexes, he poenal relably falures due o oher causes dfferen from generaon forced ouages (as for nsance a forced ouage on a nework ransmsson lne). The paper s srucured as follows. Nex, n he remander of hs nroducon, we brefly revew he mos basc and elemenal PPC model, snce represens he sarng pon of he refnemen descrbed laer. Then, n secon II, he algorhm o model demand elascy s developed n deal. In secon III, we dscuss he reasons why we sae ha classc relably measures are no suable mercs n a conex n whch demand elascy s sgnfcan. Ths wll lead o he dscusson on he necessy o redefne he classc relably mercs o beer assess o wha exen he marke oucomes are adequae n erms of generaon adequacy. A basc case example serves o llusrae hs dscusson. Fnally we have gahered he mos mporan conclusons n secon IV. 1.2 Probablsc Producon Cosng Models PPC models have been radonally used as a suppor ool n he cenralzed long-erm decson-makng process n elecrc power sysems. These models are characerzed for represenng he random naure of some of he mos relevan varables nvolved n he longerm plannng problem (ypcally he demand values and he generaon avalably). They allow for calculang, among ohers, producon coss, and relably assessmens of real-sze elecrc power sysems wh lle compuaonal effor. However, snce PPC are based on a me absraced smulaon, hs s acheved a he cos of makng srong smplfcaons regardng shor- and medum-erm operaonal and plannng consrans of he generaon plans. 3 Nowadays hs full elasc demand conex s jus an deal heorecal scenaro; however, he full lberalzaon of real markes, n whch no regulaed arff prce s admnsravely deermned, and he ncreasng peneraon of acve demand response facles also a he resdenal level (elecronc meers and equpmen ha allows dscrmnang and sheddng any ype of cusomer based on prce crera), may urn hs deal scenaro no a real one n he fuure. 2

3 IIT Workng Paper IIT Ths approach has araced consderable effors from academa snce he lae 60 s, see for nsance he poneerng works of Baleraux e al. (1967) and Booh e al. (1972). The mos basc and elemenary model corresponds o s applcaon o a non-consraned hermal sysem, where hermal plans are characerzed by means of a smple wo-sae model,ha s, plans are supposed o be able o produce a full capacy a any me unless hey are ou-of-order due o a forced ouage. Ths basc approach wll serve as he sarng pon o llusrae how o model demand elascy n hs conex. The major oupus ha were frs calculaed usng PPC models were: Relably measures: OP, OE, ENSE, ec. Expeced producon schedules, ha s, he expeced energy suppled by each generang un. Expeced producon coss. There are dozens of papers where many remarkable developmens have been nroduced o he basc PPC approach. For nsance, here are some works focused on nroducng smplfed alernaves o nclude lmed energy plans, as hydro uns (Bllnon & Harrngon, 1978), (Fnger, 1979), (Malk, 2004), (Gonzalez e al., 2005), or sorage uns (Conejo, 1987), (Invernzz e al., 1988), me dependen uns (Conejo e al., 1985), nermen generaon (Be, 2009), frequency and duraon consderaons (Ayouh & Paon, 1976) or more han one nework node and ransmsson falures, see for nsance (Cho e al., 2008). There are also dfferen approaches o compue some addonal resuls, for nsance n ee da Slva e al. (1988) or n ee e al. (1990) a means o calculae he underlyng varance of he resuls s provded. A descrpon on how o esmae dervaves (e.g. margnal values), can be found n (Ramos e al., 1994) and also n Macera & Perera (1996). However, o our knowledge, he leraure has lacked of an effcen algorhm o negrae a prce-response demand elascy curve n PPC models. Two relaed approaches can be referred n hs respec, bu as we nex dscuss, none of hem were amed a solvng he problem of modelng a prce-responsve demand curve: In Malk (2001), an approach amed o represen he mpac of demand-sde programs s descrbed. The chef objecve of hs approach s o nroduce and assess he effec of load shfng programs, whch are demand sde-managemen programs ha seek o move he load consumpon from peak o off-peak hours (.e. an ner emporal shfng 4 ). Ths s carred ou by breakng down he load shfng operaon no wo operaons ha can be separaely modeled whn he PPC conex by means of lmed energy generaors. Ths way he model separaes peak clppng (reducon of he consumpon on he peak) and valley fllng (ncreasng on off-peak hours), and models he frs operaon as an equvalen hydro un and he second as he process of loadng a pump sorage un. However, n Malk s model, he energy o be shfed from peak load o valley load s nroduced as an exogenous parameer; so n rgor no explc response o prces s modeled on he demand sde. In Chowdhury & Bllnon (1989), a probablsc relably analyss s carred ou dsngushng beween wo ypes of loads: he frm load (he nelasc load) and he 4 Iner emporal consrans are consdered o fall ousde of he scope and purposes pursued n hs paper. 3

4 Redesgnng relably measures n he presence of demand elascy n elecrcy markes nerrupble load. In hs analyss s gven prory o he frm consumpon over he nerrupble one, bu he approach does no model an explc prce response. As prevously poned ou, n hs paper we propose a mehodology ha allows solvng he problem of modelng a sep-wse prce response demand curve n a smple and compac way. In order o ease and clarfy he descrpon, we frs presen he proposed new formulaon on he bass of he smples PPC model desgn (where jus wo-sae non-energy-lmed hermal generang plans are modeled). As s laer shown, hanks o he conssency and sraghforwardness of he algorhm proposed, he mehodology allows furher complcaon of he sysem represenaon on exacly he same bass as he radonal approach self, hus beng compable wh any of he refnemens developed n hs parcular PPC mehodology. Addonally, s noeworhy ha PPC models have been somemes used o deermne he margnal conrbuon of each generang un o he relably objecves. One of he frs works n hs respec s he one developed n Garver (1966). A more recen work ryng o deermne hs conrbuon o relably objecves (n hs case, he conrbuon of wnd energy) by means of a PPC model can be found n Kahn (2004). In hs sense, he mehodology presened n hs paper could serve as a sarng pon o assess he conrbuon n erms of relably of ncreasng he percenage of prce-responsve demand. 1.3 Bref descrpon of he mos basc PPC Model The smples PPC model ha can be devsed would be he one bul upon wo major assumpons: frs, demand s consdered o be nelasc and sochasc, and second, all generaon plans can produce a full capacy unless hey are ou-of-order due o a forced ouage. Even wh such a smple approach, can be checked a basc relably condon: whenever he sysem s (nelasc) demand exceeds he avalable generang capacy a loss of load akes place. The probably of such an even happenng, he OP, and he correspondng ENSE, are wo relably resuls ha can be easly obaned from hs PPC model. In such a conex, he loss of load probably dsrbuon can be evaluaed by means of he dsrbuon of he dfference beween wo random varables: 1) he nelasc demand consumpon and 2) he oal generaon avalable. If all he random varables nvolved (he nelasc demand and he avalably of each generang un n he smples case) are sascally ndependen, hen he compuaon of he former dfference consderably smplfes, snce he probablsc dsrbuon funcon of he sum (or dfference) of wo ndependen random varables s equal o he convoluon of her probably dsrbuon funcons. oadng crera: he mer order When operang consrans are no consdered, he loadng order ha resuls n he mnmum operang cos s he one n whch generaors are loaded n order of ncreasng margnal cos (n pracce, based on heursc algorhms, hs loadng order can be modfed n order o consder approxmaely he effec of some operang consrans, such as hgh sar-up, hgh on-lne or shu-down coss, nework ransmsson consrans, ec.). Ths rankng of he generaors s usually known as he mer order or he loadng order. 4

5 IIT Workng Paper IIT The Equvalen oad Duraon Curve concep The EDC( x ) (Equvalen oad Duraon Curve a ), represens he probably of havng a load greaer han x o be served afer loadng un (whose avalably s a random varable). The EDC0 ( x ) represens he cumulave dsrbuon funcon of he load random varable. The plans are loaded followng he mer order ha has jus been descrbed. The loadng of hermal plan, modeled by means of he aforemenoned wo-sae model, can be mahemacally saed hrough he followng recursve expresson (whch represens he convoluon): where EDC ( x ) = q EDC ( x ) + (1 q ) EDC ( x C ) (1) 1 1 q s he forced ouage probably of hermal plan, C s he generang capacy of hermal plan. The expeced non-served energy afer loadng hermal plan ( ENSE ) s he amoun of energy whch s expeced no o be served f no more generang plans were avalable o produce. Ths value can be easly obaned by negrang he resulng EDC( x ) curve, and hen mulplyng hs resul by he duraon of he perod T whn whch he resulng ENSE s beng evaluaed: ENSE= T EDC ( x ) dx (2) 0 The expeced energy generaed by hermal plan, E, can be compued by akng he dfference beween he wo values of unserved energes before and afer he loadng of he hermal plan : E= T EDC 0 1( x) EDC ( ) 0 x (3) Probably 1 EDC 8 EDC 4 EDC0= DC OP 0 oad [MW] Fgure 1. Equvalen load duraon curve concep, OP and ENSE Fgure 1 llusraes he prevous loadng procedure and he resulng EDCs. The las EDC represens he dsrbuon of he load (n MW) ha remans o be served when all uns have been loaded. The expeced non-served energy afer loadng all uns can be obaned as prevously nroduced. Addonally, from hs Equvalen oad Duraon Curve, we can also exrac 5

6 Redesgnng relably measures n he presence of demand elascy n elecrcy markes anoher valuable pece of nformaon: he loss of load probably (OP). The OP can be calculaed as he pon where hs las curve nerceps he y-axs (probably). I represens he probably ha here wll sll be non-served demand lef o be sasfed afer all he generaors have been loaded (.e. he probably of havng a load greaer han x= 0 o be served afer loadng he las un n he mer order). Thus, he OP can be expressed as: where N sands for he number of generang plans. OP= EDCN ( x= 0) (4) 2 INTRODUCING DEMAND EASTICITY IN PPC MODES To nroduce demand response o prces n a PPC model we propose o use an equvalen represenaon of demand. Ths equvalen formulaon consss n nroducng a se of fcous hermal uns. Ths mehodology has been prevously used n oher modelng approaches, see for nsance Balle & Barquín (2005). As we show nex, hs soluon can be easly appled n he conex of PPC models, allowng clearng up he ask whou complcang he convenonal approach. We frs descrbe he basc dea of he equvalen formulaon of he problem, ha s, how an elasc (prce responsve) demand bddng block can be modeled as an nelasc demand block and a fcous hermal un. For he sake of clary we frs graphcally llusrae hs equvalence usng boh a deermnsc demand curve and a se of he hermal uns whose falure rae s zero (deermnsc avalably). Once we have presened he equvalen formulaon and analyzed how o nerpre he resuls n he deermnsc case, s sraghforward o formulae he PPC algorhm proposed by followng a compleely analogous reasonng. 2.1 The equvalen approach n a deermnsc conex: modelng demand prceresponsve bds by means of equvalen hermal generaors e us consder a smple deermnsc case, n whch here s a demand bd curve gven by he red sep-wse curve shown n Fgure 2. The avalable generaors capaces (MW) and her correspondng margnal coss ( /MWh) have been represened by he blue slashed sep-wse offer curve n he same char. 6

7 IIT Workng Paper IIT [ /MWh] In 4 Demand's bd Generaor's offer In [MWh] Fgure 2. Demand and generaon offer curves n he orgnal problem Noe ha n he demand represenaon here are wo dfferenaed pars whch generally speakng can be emprcally found n real markes demand bds: The nelasc (or frm) load consumpon. The correspondng nelasc demand quany s denoed here by In. The assocaed bd prce represenng hs poron of he consumpon s assumed o be much hgher han he varable cos of any of he generaors, and usually, also suffcenly above any of he oher demand bddng blocks. The bddng blocks correspondng o elasc demand consumpon. e us denoe he quany correspondng o each bd of he elasc curve by. The proposed algorhm consss n solvng an equvalen problem, see Fgure 3, n whch he orgnal demand bd curve s replaced by: A new fcous nelasc demand, whose quany F In, s compued followng he expresson: F In = In+ (5) A se of fcous generang uns. For each demand elasc block, we nroduce a fcous generang hermal un f n he equvalen formulaon The correspondng capacy (MW) and margnal cos ( /MWh) of f are respecvely he quany and he prce bd n he orgnal elasc demand block ( ). Ths way, he algorhm represens ha when he marke prce rses up o he level of an elasc bddng block of demand, hs block of energy s rered (n he equvalen formulaon s absorbed by he new fcous hermal un). 7

8 Redesgnng relably measures n he presence of demand elascy n elecrcy markes F In [ /MWh] f 4 f 2 f 3 f 1 Demand's bd Fcous generaor offer Generaor s offer In [MWh] Fgure 3. The equvalen model formulaon In he prevous fgure has been represened he equvalen formulaon of he orgnal problem (shown n Fgure 2). I can be easly checked how he marke oucome remans unchanged. I s worh nong ha n he equvalen problem, he producon of he fcous generang uns corresponds o hose blocks of he demand whch were no suppled, ha s, corresponds o he energy ha was no purchased by he demand because he prce bd was below he resulng marke prce. 2.2 Inroducng an elasc demand n he conex of he PPC approach The aforemenoned mehodology allows ncludng demand elascy n he PPC framework by performng some well-known operaons (he prevously descrbed loadng of he hermal uns). For he sake of smplcy we have nroduced wo addonal smplfyng hypoheses boh n he descrpon of he algorhm and n he case example: We have consdered a unary value for all he avalably raes of he fcous generang uns. However, noe ha by means of he avalably falure rae of he fcous generang uns we can represen sochasc demand elascy (exacly n he same way ha he avalably of he hermal generang uns s modeled). We have also consdered ha demand elascy s consan 5. Algorhm descrpon The PPC algorhm proposed follows a compleely analogous reasonng. Ths way, he necessary seps are: 1.- Calculae he dsrbuon funcon of he new fcous equvalen load duraon curve F EDC ( x ). As prevously descrbed, he elasc demand bds have been modeled wh an In 5 Demand elascy dependence upon me of day can be aken no accoun by splng he whole me scope no mulple smaller-scale smulaons. In parcular, a dfferen PPC smulaon would be needed for each me perod n whch a unform behavor could be consdered as a reasonable hypohess for he elasc demand, for more deals, see Balle & e al. (2010). 8

9 IIT Workng Paper IIT avalably of 1 and hey are also assumed o be me ndependen. Thus, n hs parcular case, he calculang he resulng dsrbuon s sraghforward. 2.- Inroduce he se of fcous hermal generaors f as prevously descrbed. These fcous generaors wll have o be aken no accoun as convenonal hermal plans when deermnng he economc loadng order 3.- oad he generaors followng expresson (1), proceedng wh he fcous generaors f he same way we would proceed wh a real hermal generaor. 2.3 Addonal relevan resuls ha can be obaned wh he exended PPC mehodology: In addon o he classc resuls obaned wh he PPC modelng approach (expeced producon of he hermal plans, he ENSE, he OP, ec.), wo addonal resuls relaed o each parcular demand elasc bd block can be easly compued: The expeced value of he energy non-commed n he marke o a parcular demand bd block. We have prevously seen n he deermnsc example ha, n he equvalen formulaon, he energy produced by a fcous hermal un corresponds o he amoun of energy non-commed o he demand bd block he fcous un represens. Ths concep can be analogously appled n he probablsc formulaon allowng us o compue he expeced value of he energy ha a ceran demand bd block wll no be capable o purchase n he marke (for he bd prce falls below he sysem margnal prce). In order o calculae hs expeced value of non-commed energy n he equvalen formulaon, we jus need o apply expresson (3) o he fcous generaor ha s used o model he demand block of neres. The probably of no commng a ceran demand bd block. The probably ha an elasc demand bd block does no resul commed, whch wll be denoed as he Non Served Probably of block ( NSP ), can be compued n he exended PPC formulaon as he resulng OP afer dspachng he equvalen hermal generaor f. Nex we solve a case example o beer llusrae boh he mehodology and he addonal resuls ha can be compued. 2.4 Numercal case example To beer llusrae he procedure, we resor o a case example. In Table we ls he hermal plans characerscs consdered n hs analyss. We have nroduced he demand elasc offers n he model by means of he fcous generang uns, whch are also nsered n he able accordng o he new mer order of he equvalen problem. 9

10 Redesgnng relably measures n he presence of demand elascy n elecrcy markes Insalled capacy [MW] Table. Case Example: Thermal Uns and Fcous Generang Uns Avalably [p.u.] Varable coss [ /MWh] Insalled capacy [MW] Avalably [p.u.] Varable coss [ /MWh] f f f In Fgure 4 we presen he F DC In as well as he demand elascy. The mnmum demand value (ncludng boh he nelasc and elasc consumpon) s equal o MWh, and he maxmum MWh. Resuls Prob mn= max = [ /MWh] CDF [MWh] In 3 2 max = [MWh] Fgure 4. DC and demand elascy funcon used n he case example In he nex fgure we have represened he resuls obaned from loadng probablscally each one of generaors consdered n he equvalen problem. The srped areas correspond o he probablsc loadng of he fcous generang uns. 10

11 IIT Workng Paper IIT [Prob] f [MWh] Fgure 5. Case example resuls We calculae now he probably ha each one of he offers does no resul acceped for fallng below he marke prce. We have ermed hs probably assocaed o each demand bd block as he Non Served Probably (NSP). I s also possble o calculae he ENSE correspondng o each one of he demand bds (whch corresponds o In he followng able we have gahered hese resuls. Table. Case Example Resuls: Elasc offers Quany [MWh] Prce [ /MWh] E f n he equvalen problem). NSP [p.u.] Resuls E f [MWh] 1 f f f Ths way, he frs block s never mached n he marke, snce he probably of non commng such block s 1, and he value of he E f s equal o he quany bd. On he oher exreme, he block bd a he hghes prce s no dspached 6% of he me, and he expeced energy no beng commed s 102 MWh. The classc relably measures ake he followng values: Table. Case Example: OP and ENSE OP [p.u.] ENSE [MWh] 1.8E WHY REDEFINING CASSIC REIABIITY INDEXES? In real markes, he regulaor has been (and sll s) parcularly concerned abou guaraneeng he elecrcy supply for he nelasc (non prce responsve) demand. Ths happens for several reasons, among whch we can hghlgh he followng: The nelasc consumpon sll represens a que large percenage of overall energy consumpon, 11

12 Redesgnng relably measures n he presence of demand elascy n elecrcy markes The underlyng margnal demand uly (deally, he demand s bd prce) s consdered o be much hgher han he one correspondng o he elasc demand. Usually, hs uly s referred o as he VO 6. For he reasons jus menoned, radonally he regulaor has defned s relably objecves n erms of he sysem capably o supply he nelasc consumpon. Ths capably o provde hs crcal fracon of he demand s wha s usually analyzed by he dfferen socalled relably measures. Ths way, he OP represens he probably of no beng able o supply hs nelasc consumpon and he Non-Served Energy (NSE) he non-suppled energy correspondng o hs nelasc consumpon. 3.1 Relably measures n he presence of demand elascy The non-served consumpon correspondng o he elasc demand blocks no beng commed n he marke does no nervene a all n he classc relably measures. We nex show he fac ha, when assessng he sysem adequacy by means of hese relably measures, snce we are jus akng no accoun he nelasc consumpon, we may be leavng asde relevan nformaon. e us now consder wo dfferen deermnsc scenaros. In he frs one a fully nelasc demand has been represened, whle n he second has been consdered a fully elasc scenaro. Boh scenaros have been confroned wh hree deermnsc scenaros of generaon avalably, one presenng a suffcen reserve margn, one n whch several groups are unavalable and also a las one represenng a severe scarcy (jus a few groups are avalable). Ths s wha we can observe: In he case of he fully nelasc demand scenaro, see Fgure 6, here are wo generaon avalably scenaros whch lead o non-served energy. NSE 3 NSE 2 Prce VO Quany (1) All generaors are avalable (2) Hgh number of forced ouage (3) Severe scarcy Fgure 6. Fully nelasc demand scenaro In he case of he fully elasc demand scenaro, see Fgure 7, when resorng o he classc defnon of he aforemenoned relably measures, he NSE s equal o zero. 6 There are many analyss amed a calculang hs VO, see for nsance AIM (2007) or Cramon & en (2000). 12

13 IIT Workng Paper IIT Prce Quany Fgure 7. Fully elasc demand scenaro Does hs mean ha n an deal conex where demand would be fully elasc, relably would no longer be a problem? Resorng o he defnon provded prevously he answer s ha effecvely, relably as classcally defned would no longer a problem, snce he reference ndex would ake a zero value. However, noe ha n hs deal fully elasc demand case, a permanen scenaro of severe scarcy (scenaro 3) could by no means be consdered as desrable from he regulaor perspecve. The objecve of he regulaor s o maxmze he ne socal benef, whch mples assessng f (and o wha exen) he marke mechansm performance may no be yeldng he expeced/requred oucomes. Ths does no jus mean accomplshng wh a relably sandard based jus on he nelasc consumpon (lke he one day n en years), bu raher meeng a suffcenly cos effecve supply for all consumpon (hrough he mos effcen nvesmens, resource managemen, schedulng, ec.). 3.2 Redefnng he mercs o evaluae he marke performance n erms of generaon adequacy In order o ake no accoun hs elasc demand consumpon, we propose o nclude n he ndexes he nformaon derved from all he blocks of non-served demand, and no jus hose correspondng o he nelasc (or frm) consumpon. Ths way, he mercs would provde a more precse dea of how well he marke s performng s job han he mere consderaon of he classc relably crera, based on he sysem s capacy o supply he nelasc demand. Redefnng he expeced non served energy value: Ths way, he expeced non served energy value (ENSEV, measured n [$]) should be equal o: where ENSEV= ENSE VO+ ENSE p (6) ENSE sands for he expeced non served energy of an elasc block. 13

14 Redesgnng relably measures n he presence of demand elascy n elecrcy markes p sands for he bddng prce of he elasc load block 7. Redefnng he OP Noe ha he OP would no longer make sense n he fully elasc demand scenaro. In hs new conex can raher be calculaed he probably of no supplyng a ceran demand block, or he probably of no supplyng demand above a ceran prce. The need o recalculae he radonal reference values In he nroducon we poned ou ha reference values o compare hose obaned wh he chosen merc are necessary. We also poned ou ha he cos effcency creron was mplcly nroduced when defnng hese benchmark reference values. The same sll apples when redefnng hese mercs. A reference value would be necessary o acknowledge ha s no cos effecve o supply all ypes of elasc consumpon. 3.3 Numercal case example The expeced value of he non served energy n he prevous case example could hen be compued followng he prevous expresson. In he case example we have consdered a VO equal o /MWh. 4 ENSEV= ENSE VO+ E p = 0, = CONCUSION We have developed he Probablsc Producon Cosng model approach by exendng he classc formulaon on he bass of a novel algorhm ha allows modelng a sep-wse demand elascy funcon n a smple and robus way. Then, we have aken advanage of hs model formulaon o show how he radonal relably measures, such as he OP or he ENSE, as a measure o assess he level of secury of supply should be reconsdered n he presence of sgnfcan demand elascy. Ths has led us o propose a way o more suable redefne hese mercs. Acknowledgemens The auhors wan o hank Sanago Cersola, uz A. Barroso and Professors Ignaco J. Pérez- Arraga and Andrés Ramos for her valuable commens and suggesons, as well as he suppor of Mkel Ayala. 5 REFERENCES AIM, All Island Projec, The Value of os oad, he Marke Prce Cap and he Marke Prce Floor. A Response and Decson Paper. AIP-SEM Sepember When a perfec compeve envronmen can be assumed on he demand sde, hs prce deally represens he demand s margnal demand uly. 14

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16 Redesgnng relably measures n he presence of demand elascy n elecrcy markes Invernzz, A., Manzon, G. & Rvoro, A., Probablsc smulaon of generang sysem operaon ncludng seasonal hydro reservors and pumped-sorage plans. Elecrcal Power and Energy Sysems. Vol. 10, no. 1, pp Kahn, E.P., Effecve oad Carryng Capably of Wnd Generaon: Inal Resuls wh Publc Daa, Elecrcy Journal, December ee, F. N., n, M., and Brepohl, A. M., Evaluaon of he varance of producon cos usng a sochasc ouage capacy sae model, IEEE Transacons on Power Sysems, Vol. 5, No. 4, November ee da Slva, A. M., Pazo Blanco, F. A. F., & Coelho, J., Dscree Convoluon n Generang Capacy Relably Evaluaon- OE Calculaons and Uncerany Aspecs. Paper 88 WM IEEE PES Wner Meeng New York, USA. January Macera, M. E. P & Perera, M-V. F., Analycal modelng of chronologcal reservor operaon n probablsc producon cosng [of hydrohermal power sysems], IEEE Transacons on Power Sysem, Vol. 11, No. 1, February Malk, A. S., Modellng and economc analyss of DSM programs n generaon plannng, Inernaonal Journal of Elecrcal Power & Energy Sysems, Volume 23, Issue 5, June Malk, A. S., Smulang lmed energy uns whn he framework of EDC and FD mehods, Inernaonal Journal of Elecrcal Power & Energy Sysems, Volume 26, Issue 8, Ocober Ramos, A., Muñoz-Moro,. & Pérez-Arraga, I. J., Drec compuaon of dervaves n producon cos models based on probablsc smulaon. Conference on Probablsc Mehods Applcaons n Power Sysems, PMAPS-94. pp Ro de Janero, Brazl. Sepember