Medium and long term. Equilibrium models approach

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1 Medum and long term electrcty prces forecastng Equlbrum models approach J. Vllar, A. Campos, C. íaz, Insttuto de Investgacón Tecnológca, Escuela Técnca Superor de Ingenería-ICAI Unversdad ontfca Comllas J. González, A. íaz, M. A. Rodríguez,. Rodríguez Subdreccón de Métodos y Medos Endesa ISF-21, San ego, June 21

2 Contents Short vs long term prces forecastng Nash equlbrum approaches Morse: Endesa tools for strategc long term analyss Some forecastng scenaros and results Conclusons ISF 21 -José Vllar - Long term electrcty prces forecastng - 2

3 Need of fundamental models For the short term, tme seres well suted: Account for most relevant factors mplct n hstorc data Uses a reduced d set of external nputs demand, d wnd forecasts, often avalable from the SO. For the medum and long term, fundamental approaches become essental f hypothess nvolvng structural changes must be analyzed snce they make almost useless recent past hstory. Fundamental models can account for: partcpant mergng or new partcpants generaton capacty expanson, technologcal changes hedgng contracts new regulaton polces nteracton t wth other busness/sectors gas retal, etc ISF 21 -José Vllar - Long term electrcty prces forecastng - 3

4 Need of fundamental models For a gven demand, several factors serously affect electrcty prces, and can be grouped nto several categores: Cost structure techncal and economc features of the generaton unts. Indeed electrcty prces depends very much on the margnal cost of the system at each demand level. Strategc behavor of the agents: for a same system cost structure, dfferent regulaton polces, or dfferent number and sze of agents lead to dfferent prces. Typcally long term models are based on Nash equlbrums, and can account for most of those factors. Snce the cost structure s needed, they need a more detaled representaton of generaton unts, although, for the long or very long term, technologes nstead of ndvdual d unts can be used. Long term forecastng becomes a multple scenaro analyss, more than producng a unque tme seres, as t s n the short term. ISF 21 -José Vllar - Long term electrcty prces forecastng - 4

5 Nash equlbrum approaches Nash equlbrum: partcpants maxmze smultaneously ther profts wth ther compettors strateges supposed to be fxed and at the equlbrum at the equlbrum ndvdual moves are unproftable. Equlbrum computaton provdes market prce and partcpants p equlbrum strateges productons, supply functons, etc. Among the equlbrum approaches are: Cournot Equlbrum, where generators strateges are represented n terms of quanttes and do not react to compettors moves. Conjectural Varaton Equlbrum that consders the reacton of the compettors. Conjectured Supply Functon Equlbrum that assumes a local frst- order approxmaton of the supply functons. Supply Functon Equlbrums where generator s strateges are represented by supply functons. ISF 21 -José Vllar - Long term electrcty prces forecastng - 5

6 Nash equlbrum formulaton Agent proft: B C Market prce roductons Agent cost functon C assumed to be known generaton unts, techncal data, fuel costs, etc. Techncal constrants: max Balance equaton: + j j emand curve: + emand curve: ISF 21 -José Vllar - Long term electrcty prces forecastng - 6

7 Nash equlbrum formulaton At the equlbrum ndvdual moves are unproftable. B B,, * * * Nash, 195 Equlbrum smultaneous proft optmzaton:,, wth respect to the strategc varables C B Equlbrum equatons: C +, max + Resoluton by MC or equvalent optmzaton problem ISF 21 -José Vllar - Long term electrcty prces forecastng - 7 Resoluton by MC or equvalent optmzaton problem. ay, Hobbs, 22 Barquín, Centeno, et al. 24

8 Nash equlbrum formulaton Equlbrum equatons: C Cournot approach ay, Hobbs, 22 Barquín Centeno et al 24 χ Barquín, Centeno, et al α θ + emand must be elastc wth Hgher prces and too sensble to demand elastcty α ISF 21 -José Vllar - Long term electrcty prces forecastng - 8 Hgher prces and too sensble to demand elastcty

9 Nash equlbrum formulaton Equlbrum equatons: C Conjectural-varaton approach tt t ay, Hobbs, 22 compettors react prce response conjecture χ θ y Barquín, Centeno, et al. 24 prce response conjecture θ S RC 1 S RC θ 1 θ 1 RC ISF 21 -José Vllar - Long term electrcty prces forecastng - 9 Conjecture estmaton s the major drawback

10 Nash equlbrum formulaton Equlbrum equatons: C Conjectural-supply functon approach Local lnear approxmaton of SF: + α ay, Hobbs, 22 If nelastc demand, then θ 1 α ' ' In the lterature ether s taken as gven and α are computed, ether α are taken as gven and are computed. Solvng for both requres addtonal assumptons. ISF 21 -José Vllar - Long term electrcty prces forecastng - 1

11 Nash equlbrum formulaton Equlbrum equatons: C az et al Conjectural-supply functon approach n MORSE + α θ 1 α ' ' + α { } Robustness assumpton: same holds for very close demand scenaros ε ε 1, ε 2 Endogenous teratve conjecture estmaton: ε ε C + 1 ˆ α' ' ε 2 ε1 ε ε ε ε ε, ε { ε, ε } ˆ α untl ˆ α convergence ISF 21 -José Vllar - Long term electrcty prces forecastng - 11

12 Long term forecastng tools for Endesa Workng on medum and long term electrcty sector forecastng for Endesa snce 2, developng MORSE from 25. Vllar et al, 21 MORSE, set of tools and models for long term forecastng and strategc analyss of the Spansh electrcty sector: Models the man busness of the sector, such as electrcty pool, commercalzaton, regulated actvtes, etc. Computes electrcty sector balance yearly accumulated surplus or defct annual sector settlement by energy commsson. ool electrcty market prces and productons solved wth EQUITEC: conjectural supply functon market equlbrum where GENCO's are represented at a technology level. compute agent conjectures lnear the supply functon approxmaton at the equlbrum under smple hypothess of robustness. ISF 21 -José Vllar - Long term electrcty prces forecastng - 12

13 Long term forecastng tools for Endesa MIX, Logístc, etc rces and energes of the contracts, wth or wthout hedgng ennsula Contracts Islands Energy commercalzed Market share of retaler and dstrb.cmpny Total demand rofle and kurtoss Total energes and profles Non dspatchable Energes mp, exp, tur, bomb, hdr, re Lberalzaton % ennsula emand Islands hyscal and fnancal contracts network losses Energy per retaler, dstrb. Cmpny Types of clents SB energy RE Incomes Inter.n Ext. Incomes SB demand em. growng Fuels costs Caract. Empresas conjeturas,... Tech costs Generaton Module ennsula Islands Tech data: costs, avalablty. Agents data: nstalled capactes, conjectures, etc. rces, productons, ncomes, costs, margns Brent, Uranum, Carbon, Change rate,.. agos bombeo, Energía RO, Ingresos GSL, prmas y Fn CN, recos electrcdad EQUITEC GAMS Et Extra charges Man results: -rces and producctons -Incomes, costs and margns of every agent -Sector balance Interests, amortzaton efct efct ennsula Interest rate, years ennsula Clents Islands Tolls and Tarfs Coste from other markets and servces ancllary servces, peower rces, GSL, IC ower plant changes ennsula Regulated busness Island Incomes form clents Transportaton ncomes strbuton ncomes Fnal sector balance Islands Sector balance Island compensaton ISF 21 -José Vllar - Long term electrcty prces forecastng - 13

14 emand representaton emand often represented by the load duraton curve, and smplfed nto blocks. Equlbrum solved for each block. Blocks can represent demand levels, and could dstngush between workng and weekend days. Currently explorng demand representaton wth daly patterns wth hourly detal. Real values Step wse approxmaton emand Blocks sp p ll1 ll2 v sv ISF 21 -José Vllar - Long term electrcty prces forecastng - 14

15 Generaton unts or technologes For the long term, generaton unts can be grouped nto technologes The resultng margnal cost curves can be lnearly approxmated Less unts, less data, faster computaton Technology changes appled to all agents, or agent by agent For every agent For every technology Generaton unt Generaton unt Generaton unt Generaton unt Agents technologes Margnal Cost Margnal Cost Max-MC Mn-MC rod Generaton unts grouped by tech and agent Lnear approxmaton of MC ISF 21 -José Vllar - Long term electrcty prces forecastng - 15

16 Forecastng scenaros and results emand System demand RE Renewable GWh GWh ECOALTO: hgh demand, renewables, and Brent and CO 2 prces MAXIMUM MINIMUM BASE ECOALTO ECOBAJO MAALTO MABAJO 2 p ECOBAJO: low demand, renewables, and Brent and CO 2 prces MAXIMUM MINIMUM BASE ECOALTO ECOBAJO MAALTO MABAJO $/BBL GWh MAALTO: low demand but hgh renewables and Brent Brent and CO 2 prces MABAJO: hgh demand but low 7 renewables and CO2 2 Brent and CO 2 prces /t GWh CO MAXIMUM MINIMUM BASE ECOALTO ECOBAJO MAALTO MABAJO MAXIMUM MINIMUM BASE ECOALTO ECOBAJO MAALTO MABAJO ISF 21 -José Vllar - Long term electrcty prces forecastng - 16

17 Forecastng scenaros and results Market prce ECOALTO: hgh demand, renewables, and Brent and CO 2 prces /MWh ECOBAJO: low demand, renewables, and Brent and CO 2 prces MAALTO: MAALTO: low demand but hgh 6 renewables and Brent and CO 2 prces 4 2 MABAJO: hgh demand but low renewables and Brent and CO 2 prces MAXIMUM MINIMUM BASE ECOALTO ECOBAJO MAALTO MABAJO ISF 21 -José Vllar - Long term electrcty prces forecastng - 17

18 Conclusons Long term forecastng requres fundamental models, snce past hstory becomes very often useless. Fundamental models allow to: defne complex future scenaros wth structural market changes: new regulaton polces partcpant mergng or new partcpants generaton capacty expanson, technologcal changes hedgng contracts nteracton wth other busness/sectors gas commercalzaton, etc account for many nputs hypothess or estmatons, such as: Fuel prces Lberalzed demand Renewable and G penetraton, etc. Many of them based on dfferent formulatons of a Nash equlbrum proft functon, strategc t varables. Our approach MORSE mplements a CSFE market model wth endogenous conjecture computaton, developed for Endesa. Runnng wth satsfactory results for more than 4 years. ISF 21 -José Vllar - Long term electrcty prces forecastng - 18

19 Conclusons Long term forecastng becomes a multple scenaro analyss exercse. Indeed, s long term forecastng a real forecastng exercse? Other mportant ssues n electrcty prce forecastng are related wth network constrants and ancllary servces markets new terms n proft functon, new constrants, network constrants. Currently workng on: emand representaton wth daly patterns wth hourly detal for jont energy and reserve equlbrum. Endogenous conjecture computaton wth capacty network constrants t ISF 21 -José Vllar - Long term electrcty prces forecastng - 19

20 References J. F. Nash, Equlbrum onts n N-erson Games, roceedngs of the Natonal Academy of Scences, vol. 36, No. 1, 195, pp M. Ventosa, A. Baíllo, A. Ramos, and M. Rver, "Electrcty Markets modellng trends," Energy olcy, vol. 33, 7, pp , 25 J. Barquín, E. Centeno, and J. Reneses, "Medum-term generaton programmng n compettve envronments: A new optmsaton approach for market equlbrum computng," IEE roceedngs on Generaton Transmsson and strbuton, vol. 151, 1, pp , 24. C. ay, B. F. Hobbs, and J. S. ang, "Olgopolstc Competton n ower Networks: A conjectured Supply Functon Approach," IEEE Transactons on ower Systems, vol. 17, 3, pp , 22. J. Vllar, F. A. Campos, C. A. íaz, J. González, A. íaz, M. A. Rodríguez,. Rodríguez, MORSE: Tools for long-term strategc analyss of the Spansh electrcty sector, 7 th European Energy Markets Conference, Madrd 21. C. A. íaz, J. Vllar, F. A. Campos, and J. Reneses, "Electrcty Market Equlbrum Based on Conjectural Varatons," Electrc ower Systems Research, n 2 nd revson, 21. C. A. íaz, J. Vllar, F. A. Campos, and M. A. Rodríguez, "A new Algorthm to compute Conjectured Supply Functon Equlbrum n Electrcty Markets," n revew process. ISF 21 -José Vllar - Long term electrcty prces forecastng - 2

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