Transforaton of Coercal Flows nto Physcal Flows of Electrcty Marek ADAMEC, Mchaela INDRAKOVA, Pavel PAVLATKA Dept. of Econocs, Manageent and Huantes, Czech Techncal Unversty, Zkova 4, 166 27 Praha, Czech Republc arek_adaec@sezna.cz, ndrakova@post.cz, ppavlatka@centru.cz Abstract. We are wtnesses of large scale electrcty transport between European countres under the ubrella of the ENTSO-E organzaton. Ths s due to the nablty of generators to satsfy the growng consupton n soe regons. In ths content, we dstngush between two types of flow. The frst type s physcal flow, whch causes costs n the transsson grd, whlst the second type s coercal flow, whch provdes revenues for the arket partcpants. The old ethods for allocatng transfer capacty fal to take ths dualty nto account and allocate transsson border capacty to vrtual coercal flows whch, n fact, wll not flow over ths border. Ths stuaton obvously does not lead to an optal transsson capacty allocaton. Soe flows are ncorrectly and needlessly rejected (wthout real congeston) and conversely, soe accepted flows can cause congeston on another border. The Flow Based Allocaton (FBA) s a ethod, whch should solve ths proble because t would provde allocaton accordng to real physcal flows. Another goal of FBA s to ensure sustanable developent of expanson of transsson capacty. Transsson capacty s portant, because t represents a way to establsh better transsson syste stablty, and t provdes a dstrbuton channel for electrcty to custoers abroad. For optal developent, t s necessary to ensure the rght dvson of revenue allocaton aong the arket partcpants. Ths paper contans a bref descrpton of the FBA ethod. Probles of revenue axzaton and optal revenue dstrbuton are entoned. Keywords Flow based allocaton, cross border tradng, TBC, NTC, explct aucton, plct aucton, physcal flow of electrcty, coercal flow, CAO, day ahead aucton, PTDF. 1. Why Physcal and Coercal Flow Should Be Dstngushed The proble s that today no correspondence has been reached between coercal flows, whch brng revenues, and physcal flows, whch cause costs. The theoretcal prncple states that captal should be allocated nto areas where t s necessary to nvest. A dfference between physcal and coercal flows consequently does not lead to optal captal allocaton. Socal Welfare s an dea that s often entoned n the context of FBA and future grd developent. Grd developent should lead to greater transsson capacty. Ths capacty enables larger energy transports and levelng of electrcty prces. Ths produces greater socal welfare for areas where the electrcty prce (after FBA pleentaton) falls, and t brngs less socal welfare to areas where the electrcty prce rses. In general however, global socal welfare should grow. Our assupton s that
the econocal beneft for one area (consuers surplus) s greater than the econoc losses for the second area. 2. The Relatonshp between Physcal and Coercal Flows Electrc energy flows fro a source to a snk (slarly to lquds). In the nterconnected grd there are any sources and snks. In addton the current can be conducted va nuerous conductors (nterconnectons). The nterconnected grd s a very coplcated syste, and superposton of any flows s always presented n every connectng lne. Fgure 1 llustrates the dfference between coercal flow (blue arrow) and the resultng physcal flows (orange arrows). If an ATC-based syste of capacty allocaton was used, the avalable transfer capacty, between CZ and DE, would decrease by 100 MW. If an FBA-based syste of capacty allocaton was used, the sae transsson capacty would decrease only by 30 MW. But n addton, all free border capacty n the area decreases accordng to the real physcal flows. 5 PL 5 100 DE CZ 30 SK 30 30 10 31 4 2 CH 2 63 2 AT 5 3 HU 1 4 IT 6 SL Fg. 1. Dfference between coercal and physcal flows. The used values of capacty are only exeplfcatve. 3. Converson between Coercal and Physcal Flows FBA allocaton coprses two necessary steps. The frst s real flow evaluaton, and the second s physcal lt quantfcaton. For both very coplex atheatcal odels are needed. The atheatcal prncple for flow converson s very sple. For ths purpose we use a PTDF (Power Transfer Dstrbuton Factors) atrx. The sae prncple s used for transsson between lnear spaces n the algebra. An exaple of the frst colun of such a atrx s gven n Fgure 1, on the rght. When we deal wth real purpose of nubers fro ths colun ore detaled, they present a bass. A coercal flow between CZ and DE s dvded accordng ths bass. It ust be ephaszed, that ths exaple supposes splfed presupton, that any other coercal flow s presented. A generalzed equaton s followng.
[ PTDF atrx] [ BID] = [ Power Flow], (1) where [BID] s the vector of coercal bds and [Power Flow] s the vector of real physcal flows. 3.1 PTDF Matrx Coeffcent Calculaton Every poston n the PTDF atrx (coeffcent) shows whch part of partcular coercal flow wll flow va the concrete border. The atrx sze (n the ost general stuaton wthout nettng) s N (N-1)x I, where N s the nuber of partcpatng TSOs and I s the nuber of borders. In ore obvous pont of vew N could be nuber of areas, whch are bounded by connectons wth nsuffcent transsson capacty (states) and I s nuber of these congested connectons (borders between states). In other words every PTDF coeffcent explans how large physcal flow wll flow between the par of neghborng TSOs as a result of partcular trade (coercal flow). Borders 1 2 3 N.(N-1) A 1 A B 2 B C 3 C I Coercal Flows PTDF Coercal Flows X = Real Border Load Fg. 2. Graphcal nterpretaton of equaton 1. Sultaneously, every coeffcent expresses the senstvty of the approprate border to generaton or consupton shfts. The currently used quantfcaton ethod akes use of ths fact. Theoretcally, a shft of 1 kw on the deand or supply sde, results n a physcal flow shft. PTDF A B P = = P P [%], (2) where PTDF A B s the coeffcent of the PTDF atrx correspondng to energy transfer fro A to B, P s a shft of coercal flow, and P s the real shft of physcal flow between A and B, whch s ndependent fro the P value. It s obvous, that the process of coeffcent quantfcaton s qute senstve for grd data valdty. Therefore t s napproprate to use the FBA ethod for yearly and onthly auctons. It s explotable only for short-ter tradng, e.g. day ahead aucton (D-1). Valdty of the grd data decreases wth ncrease of the te perod. 3.2 Splfcaton for the ore countres For the calculatons wth PTDF atrxes can be used uch known atheatcal prncples. These prncples are explotable especally for stuatons, where fgure ore countres.
PTDF( A B) = PTDF( A C) + PTDF( C B) (3) PTDF( A B) = PTDF( B A) (4) 4. Man Features of FBA ethod Possble future pleentaton of the FBA ethod represents a sgnfcant change n the aucton procedure. The an dfference s n ndspensablty of very exact grd odel. In addton ths ethod needs soe authorty, whch wll deal wth as uch data. Ths authorty s a coordnated aucton offce (CAO). 4.1 Coordnated Aucton Offce As t was ndcated above, t s necessary to collect and cople the nforaton fro all TSOs, and also fro all arket partcpants. For ths purpose CAO would be durng FBA pleentaton establshed. Its sson s to collect, analyze and store data fro all arket partcpants and to provde feedback for the. As a result of analyss ths offce evaluates portant coeffcents e.g. PTDF, TBC, FRM Base case etc... The proposed procedure for each analyss before any allocaton (aucton) could be dvded nto followng steps: Each TSO coples odels of ts grd and afterwards CAO forulates odel of ths grd. A result of ths very frst step s the PTDF atrx. Ths odel ust count wth real stuaton wth power generaton and consupton. Any falure ust be nvolved as soon as possble. TSO calculates the techncal lts of each lne n ts grd. It ust be underlned, that the bottlenecks, where congeston could occur, can also be presented nsde the natonal grd and not only on the borders. Consequently the TBC (Total Bottleneck/Border Capacty) would be calculated by the CAO. Lots of flows wll be presented n the grd before the FBA process. Therefore these flows ust be also calculated and subtracted fro TBC. Ths s also responsblty of the CAO. The portant coeffcents (PTDF, TBC, FRM ) are ade publc. 4.2 The Startng Descrpton of the Grd (Base Case) For the sooth calculaton of all paraeters of the grd odel s necessary to forulate Base Case. The Base Case descrbes the whole grd wth all generators and places of consupton of electrcty. Ths base case serves as a bass before the FBA. The ore exact the base case s, the ore exactly wll FBA transt coercal flows nto the physcal ones. Because of the fact, that stuaton n the grd s stll changng the ost exact base case ust be publshed every day and can be used for the short ter tradng. Ths Grd descrpton ust be done ex ante and t ust contan: Detaled grd descrpton wth locatons of portant power plants, types of the power plants and nforaton about predcted shut downs. Predcted supply of these sources wth nforaton about the control range.
Predcted deand of large custoers connected to the grd. Schedule of flows orgnated fro realzed deals fro the past (yearly and onthly aucton). Predcted flows for external areas (OF) fro countres not nvolved n the FBA allocaton ethod. Predcted natural flows fro the grd regulaton 4.2.1 The ost portant nfluences on Base Case Majorty of the base case paraeters are very well descrbed. These are consupton n the ndustry and generaton n the conventonal power plants (nuclear, coal, gas, ol etc ), whch s well predctable. Ther values are very well known for every day te except of soe accdents. The rest are unpredctable nfluences. These are ostly generaton n the renewable resources (ostly n the wnd power plants) and possble accdents. Such unpredcted effects nfluences ostly PTDF coeffcents, Bottlenecks capactes and F REF. Renewable resources nfluence In general there s a proble to predct exact value of generaton n the renewable resources (except of resources powered by renewable fuel lke boass or bogas or geotheral, because n such resources perforance anageent s possble). The rest of the renewables are very bad predctable. Because these resources are sgnfcantly nfluenced by the weather, t s possble to predct t s generaton n very short te perod (ostly ax. 2 days). Longer perods could be predcted only wth larger uncertantes. 4.2.2 Possble splfcatons n the Base Case odel The splfcatons are ostly necessary for utlzaton of the FBA echans. Wthout these splfcatons the grd odel would be too dffcult and unable to effectvely descrbe. On the other hand such splfcatons could cause also large stakes n the grd descrptons and n ts consequence they could cause large uncertantes durng the FBA process. The possble splfcatons for the Base case are that not every lttle generator or every lttle custoer ust be descrbed. Also not every lne of the dstrbuton grd s necessary to be descrbed. On the other hand soe exaple of the nadssble splfcaton s a erge of soe country n a sple knot. Each country has not only border connectons, but also nternal connectons. On such connectons the bottleneck and congestons could also occur. Therefore t s nadssble to descrbe country lke a sple knot. 4.3 Ltaton of Cross Border Flows As t s entoned above, lts for the electrcty transportaton are n the nternatonal connected grd presented. Ths s precsely why any capacty allocaton s carred out. These lts are called bottlenecks. The capacty avalable for the electrcty transsson s set partly by the physcal constrant and partly by the flows, whch are on the lne presented. Two types of flow can be dstngushed n the Grd. The frst group has natural character and these flows are presented n the Grd ndependently of any coercal flow. Ther orgn s n the Grd
regulaton. Another group s flows orgnated fro coercal electrcty transport. These flows are ajorly nfluenced by electrcty tradng. The procedure, entoned above s necessary for real physcal flow evaluaton. The second step s of course to evaluate the physcal lt on every border. Every transsson lne s lted by ts techncal potentaltes. 4.3.1 The already presented flows These flows are probles (cause lts) only n the bottlenecks. The Already Nonated Flow (ANF) These flows orgnate fro long ter contracts and the yearly and onthly auctons. These long ter flows are and also wll be nonated by classcal (not FBA) ethods, because t s possble to forulate any base case one year or onth ago. Natural Flow (NF) Ths flow s presented n the grd always. It orgnates ostly fro the grd regulaton and has no connecton wth any coercal flow. In other words ths flow s necessary for the grd stablty. Fro the hstorcal experence ths flow s alost constant. Outsde Flow (OF) It s obvous, that not all of bottlenecks n the nternatonal grd are nvolved n the FBA echans. There are flows n the grd that orgnate n the areas, where FBA ethod s not used. The OF are flows, that have t s orgn n the areas out of the FBA area. CAO ust therefore descrbe such flows, because they could nfluence the whole FBA process largely. It s truth, that because of dupng n the grd, such flows are ore portant near to the edge of the FBA area, but for all that t reans as very portant nfluence n whole FBA area. 4.3.2 Capactes Total Border/Bottleneck Capacty (TBC) Ths s the capacty of soe bottleneck that s possble for electrcty transsson. Mostly are such bottlenecks on the borders between two neghborng countres. Generally such bottlenecks could occur also nsde of soe natonal transsson grd. Therefore the nae bottleneck capacty s ore coon. The lt of ths capacty s ostly caused by the physcal features of the concrete lne. It ust be specfed regardng to axal current that could flow through the lne, to axal teperature of the lne and to axal potental drop. Flow Relablty Margn (FRM) Every projecton and every odel ncludes soe uncertanty. Hence t s nevtable to establsh soe securty nterval that wll decrease the capacty usable for the transport. Ths securty nter al s broadly naed flow relablty argn. Fro the experence, the FRM s quantfed based on TBC.
FRM = TBC k, (5) where k s a coeffcent that expresses whch part of TBC s reserved and cannot be allocated. k has usually been at the value of 10%. Ths securty buffer should prevent falures and t s possble consequences black outs caused by several uncertantes or phenoena. Uncertantes n the data used for grd flow predcton. Every odel of a real grd has soe uncertantes. Its relablty s negatvely nfluenced by nconsstences n soe splfyng presuptons. Unpredctable s a alforaton of flows resultng fro frequency alternatons n soe parts of a connected grd. Unpredctablty of soe possble generator falure and resultng shut down. Unpredctablty of extree weather phenoena. Net Border Capacty (NBC) The NBC s the axu net capacty that s usable for the FBA process. It s the TBC decreased by FRM and by the flows already presented n the lne or flows out of TSO s control. NBC TBC FRM ANF ( NF + OF) = (6), As a result of above otoned already presented flows the CAO wth TSOs wll calculate followng flows Reference Flow (F REF ): s an estaton of flows whch are ndependent fro the FBA allocaton process and are presented n the grd. These are ANF, NF a OF. Maxu Allowable Flow (F MAX ): s the axal total flow that s allowable on soe bottleneck as a result of coercal flow. In other words ths physcal flow wll cause any proble n the grd. 5. Iplct and Explct Aucton Coparson Slarly as n classcal non flow-based ethods, two dfferent ways n the FBA echans are dstngushed. Dfferences between these ethods are very slar as n the classcal non flow-based ethods. 5.1 Explct FBA Method Electrcty s traded n the separate aucton fro capacty for ts transport. On each border, the nfluence of every coercal flow s calculated. Afterwards the transsson capacty for each successful coercal flow (trade) s auctoned. If congeston occurs, capacty bds wth the lowest prce wll be rejected.
n 1 P Q [0] [ Q] [ Q = MAX = arket value =. (7) B ] where P s the prce of transsson capacty bd, Q s transsson capacty allocated to P, [Q] s a vector of really allocated capacty, [Q B ] s a vector of all bds before rejecton, n s the nuber of successful bds. 5.2 Iplct FBA Method Electrcty s traded n only one aucton. If soe congeston appears, electrcty wth the lowest prce s rejected. Therefore prce of the transsson capacty s plctly ncluded n the electrcty prce. After the process of allocaton soe prce dfferences between partcular areas settle down, and ths s called prce balance. n = 1 Q ( P = Q 0 Q port port port P = exp ort = Q n = 1 exp ort Q ) Q port = MAX ;0 Q exp ort = arket value = n = 1 Q exp ort port where P s the prce of electrcty resultng fro the ntersecton of deand and supply n the portng area, Q port s the aount of ported electrcty resultng fro the ntersecton of deand export and supply n the portng area, P s the prce resultng fro the ntersecton of deand and supply n the exportng area, Q export s the aount of exported electrcty resultng fro the ntersecton of deand and supply n the exportng area, and Q s aount of electrcty transtted between the areas resultng fro -BID. (8) NTC based ethods (ATC) Flow-Based Explct aucton Iplct aucton Explct Iplct (FBA MC) Frst coe, frst served Pro - rata Explct aukcon Blateral aucton Multlateral: Market Couplng, Market Splttng Coordnated Non - arket based ethods Market - based ethods Fg. 3. Graphcal dvson of used allocaton ethods.
6. Revenue Dstrbuton The optal way of aucton revenue dstrbuton should ensure the followng. On the one hand, captal allocaton nto areas where nvestent s necessary, and on the other hand sutable ncentves for TSO. Through ths the current transsson capacty enlargeent should be enabled. There are any possble transsson allocaton ethods. 6.1 Dstrbuton Based on Shadow Prce Each border obtans a fracton of overall revenues accordng to ts shadow prce. The shadow prce presents the revenue growth after 1kW ncreent of electrcty transsson. MPj S( j) = R (9) = 0 MP = 0 where S(j) s the fracton of overall aucton revenue for the j-border, MP s the argnal prce of capacty on the border, s the nuber of all borders ncluded n FBA. The advantage of ths ethod s that captal s allocated to the borders where the greatest aount of nvestent n new lnes s needed. A dsadvantage s that t gves bad ncentves to TSOs. A lack of transsson capacty s rewarded and there s no otvaton for grd developent. 6.2 Dstrbuton Based on Real Lne Usage The revenues are dstrbuted accordng to the real physcal use of the power lnes. In ths ethod two partal varants are dstngushed. Absolute usage: The key to revenue dstrbuton s only the sze of absolute power lne usage. TSO s rewarded for absolute transtted electrcty. The dsadvantage s that captal s allocated to borders where a large aount of electrcty s transtted, regardless of whether s congeston. Therefore the largest fracton of captal s not allocated to connectons, where new nvestent s needed. Q j S( j) = R (10) = 0 Q = 0 where S(j) s the fracton of overall aucton revenue for the j-border, Q j s aount of electrcty R = 0 transported over the j border, ncluded n FBA. s total FBA revenue and s the nuber of all borders Relatve usage: Ths allocates revenues accordng to the relatve usage of the border. The bgger part of border capacty s used the bgger porton of total FBA revenues the partcular border obtans. Ths presents soe knd of coprose between the above-entoned ethods. Each
TSO has the certanty that t wll obtan soe revenues, and t s sultaneously otvated to enlarge ts transsson capacty. More captal s also allocated to areas where nvestent s needed. S( j) = = 0 R = 0 Q j TBC j Q TBC where TBC j s total capacty on the border j. (11) 7. Conclusons The FBA ethod sees to be convenent for day-ahead aucton or real te tradng. In ths case every arket partcpant has ore of less certan nforaton about the real grd stuaton, and there s alost real te nforaton about electrcty generaton and consupton. The relablty of any nforaton (predcton) s uch hgher one day ahead than one or ore onths ahead. One portant consderaton s that every coercal flow results n a physcal flow change on every border n the area. The low bds fro areas where a petty congeston s and where the prce of transsson n classcal NTC-based aucton would not be hgh enters nto copetton wth bds fro areas where sgnfcant congeston presents a ajor obstacle. It s pretty clear that prces fro congested areas are uch hgher than prces fro less congested areas. After pleentaton of the FBA ethod, ths would enhance the transsson costs for traders n areas where transsson has been cheap so far. Iplct FBA has one portant feature. Nettng s plctly ncluded n t. Ths advantage can be utlzed only f t were to becoe the duty of every arket partcpant to use the capacty allocated to t. Ths should result n enlargeent of capacty n coparson wth NTC-based ethods. Another advantage of FBA s that coercal flow s accepted or rejected n one step. In older NTC-based ethods t can happen that transport over ore than one border s accepted on one border and rejected on another. Experence wth FBA results shows that every splfcaton of the grd odel and any neglect of soe portant event causes nfluental alforatons of the results. Ipleentaton of FBA would therefore need very good and relable nforaton fro each arket partcpant n the real te. Another proble presents fact, that pleentaton of the FBA wll need to establsh new tradng odels for all arket partcpants. Ther experences wth classcal ethods would have to be odfed and t of course presents sgnfcant ncreental costs especally for traders. In y opnon, the FBA ethod sees to be nterestng, and n the future t could be well pleented. On the other hand any probles connected wth FBA have not yet been resolved. Solutons present a challenge for future research. Acknowledgeents The author would lke to express hs grattude to hs supervsor, Prof. Ing. Oldřch Starý, CSc for valuable coents and contrbutons.
References [1] CH. DUTHALER, M. EMERY, G. ANDERSSON, M. KURZIDEM. Analyss of the use of PTDF n the UCTE Transsson Grd. [2] ETSO: Regonal Flow-Based Allocatons State of Play, 2007 [3] Tranng docuents of the Departent of Econocs, Manageent and Huantes, under FEE ČTU n Prague. [4] M. ADAMEC, M. INDRÁKOVÁ, P. PAVLÁTKA. Prncples of Market Couplng on the Electrcty Market, 2008 [5] M. ADAMEC, M. INDRÁKOVÁ, P. PAVLÁTKA. Flow-Based Allocaton, 2008 [6] E. ANDERSON, X. HU, D. WINCHESTER. Forward Contracts n Electrcty Markets: The Australan Experence, Energy Polcy 35, 2007 (Elsever) [7] M. ADAMEC, M. INDRÁKOVÁ, M.Karajca. European Schedulng Overvew (Tranng docuent ČEZ a. s.), 2007 [8] ETSO European Transsson Syste Operator [9] ETSO: Flow-Based Coordnated Aucton Dry-Run n SEE-Regon, 2006 About Authors... Marek ADAMEC was born n Hořovce n 1982. He was awarded a aster s degree n February 2008. He s currently a doctoral student at the Departent of Econocs, Manageent and Huantes, FEE, CTU n Prague.