Stochastic optimal day-ahead bid with physical future contracts

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1 Introducton Stochastc optmal day-ahead bd wth physcal future contracts C. Corchero, F.J. Hereda Departament d Estadístca Investgacó Operatva Unverstat Poltècnca de Catalunya Ths work was supported by the Mnstero de Educacón y Cenca of Span Project DPI C02-01 June 6, 2008 C. Corchero, F.J. Hereda IWOR Madrd 1/27

2 Introducton 1 Introducton MIBEL Physcal Futures Contracts n the MIBEL 2 Problem defnton Optmal bddng Two-stage stochastc program formulaton 3 characterstcs Stablty analyss Futures Contracts Quantty Results 4 C. Corchero, F.J. Hereda IWOR Madrd 2/27

3 Introducton Electrc Energy Iberan Market: MIBEL MIBEL Physcal Futures Contracts n the MIBEL Organzed markets -Vrtual PowerPlantsauctons(EPE) - Dstrbuton auctons(sd) - Internatonal Capacty Interconnecton auctons - Internatonal Capacty Interconnecton nomnaton Non organzed markets Medum/ Long Term DayD-1D-1 Blateral Contracts Dervatves Market Day-Ahead Market DayD Intradaly Markets Dervatves Market Blateral Contracts Day-Ahead Market - Natonal BC beforethe spot market - InternatonalBC beforethe spot market -NatonalBC afterthespotmarket Physcal Futures Contracts Fnancal and Physcal Settlement. Postons are sent to OMEL s Mercado Daro for physcal delvery. Fnancal Futures Contracts OMIClear cash settles the dfferences between the Spot Reference Prce and the Fnal Settlement Prce Organzed markets -Vrtual PowerPlantsauctons(EPE) - Dstrbuton auctons(sd) - Internatonal Capacty Interconnecton auctons - Internatonal Capacty Interconnecton nomnaton Non organzed markets - Natonal BC beforethe spot market - InternatonalBC beforethe spot market -NatonalBC afterthespotmarket Organzed markets -Vrtual PowerPlantsauctons(EPE) - Dstrbuton auctons(sd) - Internatonal Capacty Interconnecton auctons - Internatonal Capacty Interconnecton nomnaton Non organzed markets - NatonalBC beforethe spot market - InternatonalBC beforethe spot market - NatonalBC afterthe spot market Physcal Futures Contracts Fnancal and Physcal Settlement. Postons are sent to OMEL s Mercado Daro for physcal delvery. Fnancal Futures Contracts OMIClear cash settles the dfferences between the SpotReference Prce and the Fnal Settlement Prce Day-Ahead Market Hourly acton. The matchng procedure takes place 24h before the delvery perod. Physcal futures contracts are settled through a zero prce bd. Day-Ahead Market Physcal Futures Contracts Hourly acton. The matchng procedure takes place Fnancal and Physcal Settlement. Postons are 24h before the delvery perod. C. Corchero, F.J. Hereda IWOR Madrd 3/27

4 Introducton Electrc Energy Iberan Market: MIBEL MIBEL Physcal Futures Contracts n the MIBEL Organzed markets -Vrtual PowerPlantsauctons(EPE) - Dstrbuton auctons(sd) - Internatonal Capacty Interconnecton auctons - Internatonal Capacty Interconnecton nomnaton Non organzed markets Medum/ Long Term DayD-1D-1 Blateral Contracts Dervatves Market Day-Ahead Market DayD Intradaly Markets Dervatves Market Blateral Contracts Day-Ahead Market - Natonal BC beforethe spot market - InternatonalBC beforethe spot market -NatonalBC afterthespotmarket Physcal Futures Contracts Fnancal and Physcal Settlement. Postons are sent to OMEL s Mercado Daro for physcal delvery. Fnancal Futures Contracts OMIClear cash settles the dfferences between the Spot Reference Prce and the Fnal Settlement Prce Organzed markets -Vrtual PowerPlantsauctons(EPE) - Dstrbuton auctons(sd) - Internatonal Capacty Interconnecton auctons - Internatonal Capacty Interconnecton nomnaton Non organzed markets - Natonal BC beforethe spot market - InternatonalBC beforethe spot market -NatonalBC afterthespotmarket Organzed markets -Vrtual PowerPlantsauctons(EPE) - Dstrbuton auctons(sd) - Internatonal Capacty Interconnecton auctons - Internatonal Capacty Interconnecton nomnaton Non organzed markets - NatonalBC beforethe spot market - InternatonalBC beforethe spot market - NatonalBC afterthe spot market Physcal Futures Contracts Fnancal and Physcal Settlement. Postons are sent to OMEL s Mercado Daro for physcal delvery. Fnancal Futures Contracts OMIClear cash settles the dfferences between the SpotReference Prce and the Fnal Settlement Prce Day-Ahead Market Hourly acton. The matchng procedure takes place 24h before the delvery perod. Physcal futures contracts are settled through a zero prce bd. Day-Ahead Market Physcal Futures Contracts Hourly acton. The matchng procedure takes place Fnancal and Physcal Settlement. Postons are 24h before the delvery perod. C. Corchero, F.J. Hereda IWOR Madrd 4/27

5 Introducton MIBEL Physcal Futures Contracts n the MIBEL Characterstcs of Physcal Futures Contracts Man characterstcs Base load Physcal or fnancal settlement. Delvery perod: years, quarters, months and weeks. Defnton A Base Load Futures Contract conssts n a par (L f, λ f ) L f : amount of energy (MWh) to be procured each nterval of the delvery perod. λ f : prce of the contract (ce/mwh). C. Corchero, F.J. Hereda IWOR Madrd 5/27

6 Introducton MIBEL Physcal Futures Contracts n the MIBEL Characterstcs of Physcal Futures Contracts Man characterstcs Base load Physcal or fnancal settlement. Delvery perod: years, quarters, months and weeks. Defnton A Base Load Futures Contract conssts n a par (L f, λ f ) L f : amount of energy (MWh) to be procured each nterval of the delvery perod. λ f : prce of the contract (ce/mwh). C. Corchero, F.J. Hereda IWOR Madrd 5/27

7 Introducton MIBEL Physcal Futures Contracts n the MIBEL Physcal Futures MIBEL : futures contracts Contracts & day ahead market and Day Ahead Market - 1 futures contract - 1st stage varables - 2nd stage varables DM FC Day D-3 RCCF ( Lmn, RCCF ( Lmn, UCP1 UCPj. IPO IPO IPO IPO IPO IPO Day D-1 DAM D DAM: Day-Ahead Market DM: Dervatves Market FC: Futures Contract UCP: Term contract unts FCMR: Futures contracts matchng result IPO: Instrumental Prce Offer C. Corchero, F.J. Hereda IWOR Madrd 6/27

8 Problem defnton Introducton Problem defnton Optmal bddng Two-stage stochastc program formulaton The objectve of the study s to decde: the optmal economc dspatch of the physcal futures contract among the thermal unts the optmal bddng at Day-Ahead Market abdng by the MIBEL rules the optmal unt commtment of the thermal unts maxmzng the expected Day-Ahead Market profts takng nto account futures contracts. C. Corchero, F.J. Hereda IWOR Madrd 7/27

9 Problem defnton Introducton Problem defnton Optmal bddng Two-stage stochastc program formulaton The objectve of the study s to decde: the optmal economc dspatch of the physcal futures contract among the thermal unts the optmal bddng at Day-Ahead Market abdng by the MIBEL rules the optmal unt commtment of the thermal unts maxmzng the expected Day-Ahead Market profts takng nto account futures contracts. C. Corchero, F.J. Hereda IWOR Madrd 7/27

10 Problem defnton Introducton Problem defnton Optmal bddng Two-stage stochastc program formulaton The objectve of the study s to decde: the optmal economc dspatch of the physcal futures contract among the thermal unts the optmal bddng at Day-Ahead Market abdng by the MIBEL rules the optmal unt commtment of the thermal unts maxmzng the expected Day-Ahead Market profts takng nto account futures contracts. C. Corchero, F.J. Hereda IWOR Madrd 7/27

11 Problem defnton Introducton Problem defnton Optmal bddng Two-stage stochastc program formulaton The objectve of the study s to decde: the optmal economc dspatch of the physcal futures contract among the thermal unts the optmal bddng at Day-Ahead Market abdng by the MIBEL rules the optmal unt commtment of the thermal unts maxmzng the expected Day-Ahead Market profts takng nto account futures contracts. C. Corchero, F.J. Hereda IWOR Madrd 7/27

12 Problem defnton Introducton Problem defnton Optmal bddng Two-stage stochastc program formulaton The objectve of the study s to decde: the optmal economc dspatch of the physcal futures contract among the thermal unts the optmal bddng at Day-Ahead Market abdng by the MIBEL rules the optmal unt commtment of the thermal unts maxmzng the expected Day-Ahead Market profts takng nto account futures contracts. C. Corchero, F.J. Hereda IWOR Madrd 7/27

13 Introducton Problem defnton Optmal bddng Two-stage stochastc program formulaton Optmal bd curve wthout future contracts (I/II) For a gven spot prce λ, the beneft functon of the commtted unt t s: B t (p t ) = λ p t ( c t b + ct l pt + c t q(p t ) 2), p t [P t, P t ] (1) and the generaton p d,t that maxmzes B t(pt ) s: P t f p p d,t t (λ ) P t (λ ) = P t f p t (λ ) P t p t (λ ) otherwse (2) where p t (λ ) = ( λ cl t ) /2c t q s the unconstraned maxmum of the beneft functon (1) C. Corchero, F.J. Hereda IWOR Madrd 8/27

14 Introducton Problem defnton Optmal bddng Two-stage stochastc program formulaton Optmal bd curve wthout future contracts (II/II) The day-ahead optmal bd curve λ o,t (p o,t ) that maxmzes the beneft functon (1) for any gven spot prce λ s the expresson derved from (2) : graphcally: λ o,t (p o,t ) = { 0 f 0 p o,t P t 2cqp t o,t + cl t f P t < p o,t P t (3) o λ o (p ) λ o ( P ) d λ λ o ( P ) P p d P po C. Corchero, F.J. Hereda IWOR Madrd 9/27

15 Introducton Problem defnton Optmal bddng Two-stage stochastc program formulaton Optmal bd curve wth future contracts (I/II) Let q t be the generaton of thermal t at tme allocated to all the physcal contracts of the portfolo. The market rules forces each generator to send the amount q t to the Day-Ahead Market through an nstrumental prce bd (bd at zero prce). For a gven value q t, the optmal bd curve s the functon λ o,t (p o,t ; q t ) that provdes the energy-prce pars (po,t, λ o,t ) that maxmze the beneft functon for any gven spot prce λ. C. Corchero, F.J. Hereda IWOR Madrd 10/27

16 Introducton Problem defnton Optmal bddng Two-stage stochastc program formulaton Optmal bd curve wth future contracts (II/II) The expresson of the optmal bd curve for thermal unt t at tme nterval, for a gven q t, s: { graphcally: λ o,t (p o,t ; q t ) = 0 f 0 p o,t q t 2cqp t o,t + cl t f q t < p o,t P t (4) pgflastmage C. Corchero, F.J. Hereda IWOR Madrd 11/27

17 Matched energy Introducton Problem defnton Optmal bddng Two-stage stochastc program formulaton Gven a spot prce λ s, correspondng to scenaro s, and a value qt, the matched energy p ts s completely determned through expresson (4), and depends on the comparson between q t and p ts : p ts = { q t p d,ts f q t p d,ts otherwse where the constant p d,ts s the generaton that maxmzes the beneft functon for a gven spot-prce λ s (2). (5) C. Corchero, F.J. Hereda IWOR Madrd 12/27

18 Problem defnton Introducton Problem defnton Optmal bddng Two-stage stochastc program formulaton Model characterstcs Stochastc mxed nteger quadratc programmng model Prce-taker generaton company Set of thermal generaton unts, T Optmzaton horzon of 24h, I Set of physcal futures contracts, F Set of day-ahead market prce scenaros, λ s R I, s S C. Corchero, F.J. Hereda IWOR Madrd 13/27

19 Varables Introducton Problem defnton Optmal bddng Two-stage stochastc program formulaton Frst stage varables: t T, I Unt commtment: u t, at, et {0, 1} Instrumental prce offer bd : q t Scheduled energy for contract j: f t j j F Second stage varables t T, I, s S Matched energy: p ts C. Corchero, F.J. Hereda IWOR Madrd 14/27

20 Varables Introducton Problem defnton Optmal bddng Two-stage stochastc program formulaton Frst stage varables: t T, I Unt commtment: u t, at, et {0, 1} Instrumental prce offer bd : q t Scheduled energy for contract j: f t j j F Second stage varables t T, I, s S Matched energy: p ts C. Corchero, F.J. Hereda IWOR Madrd 14/27

21 Varables Introducton Problem defnton Optmal bddng Two-stage stochastc program formulaton Frst stage varables: t T, I Unt commtment: u t, at, et {0, 1} Instrumental prce offer bd : q t Scheduled energy for contract j: f t j j F Second stage varables t T, I, s S Matched energy: p ts C. Corchero, F.J. Hereda IWOR Madrd 14/27

22 Varables Introducton Problem defnton Optmal bddng Two-stage stochastc program formulaton Frst stage varables: t T, I Unt commtment: u t, at, et {0, 1} Instrumental prce offer bd : q t Scheduled energy for contract j: f t j j F Second stage varables t T, I, s S Matched energy: p ts C. Corchero, F.J. Hereda IWOR Madrd 14/27

23 Introducton Physcal Future Contracts constrants Problem defnton Optmal bddng Two-stage stochastc program formulaton Physcal future contract coverng: fj t = L j, j F Instrumental prce bd: t T q t j F f t j, t T, I C. Corchero, F.J. Hereda IWOR Madrd 15/27

24 Introducton Physcal Future Contracts constrants Problem defnton Optmal bddng Two-stage stochastc program formulaton Physcal future contract coverng: fj t = L j, j F Instrumental prce bd: t T q t j F f t j, t T, I C. Corchero, F.J. Hereda IWOR Madrd 15/27

25 System constrants Introducton Problem defnton Optmal bddng Two-stage stochastc program formulaton Start-up/Shut-down constrants: I, t T u t u t 1 et + a t = 0 a t + mn{+tm off t, I } k=+1 e t j 1 e t + mn{+tm on t, I } k= a t k 1 Operatonal constrants: I, t T, s S p ts 0 [P t, P t ] q t 0 [P t, p ts ] f t j 0 C. Corchero, F.J. Hereda IWOR Madrd 16/27

26 System constrants Introducton Problem defnton Optmal bddng Two-stage stochastc program formulaton Start-up/Shut-down constrants: I, t T u t u t 1 et + a t = 0 a t + mn{+tm off t, I } k=+1 e t j 1 e t + mn{+tm on t, I } k= a t k 1 Operatonal constrants: I, t T, s S p ts 0 [P t, P t ] q t 0 [P t, p ts ] f t j 0 C. Corchero, F.J. Hereda IWOR Madrd 16/27

27 Objectve functon Introducton Problem defnton Optmal bddng Two-stage stochastc program formulaton mn p,q,f,u,a,e I t T cone t t + coff t at + cb t ut + s S P s [ (c t l λ s )p ts + c t q(p ts ) 2] C. Corchero, F.J. Hereda IWOR Madrd 17/27

28 Introducton Problem defnton Optmal bddng Two-stage stochastc program formulaton Coherency of the model wth the optmal bddng curve It can be proved that at every soluton of the Karush-Kuhn-Tucker system the value of the prmal varables p ts and q t satsfes the same relaton than the matched energy p ts = { q t p d,ts f q t p d,ts otherwse (6) where P t f p p d,ts t (λ ) P t (λ s ) = P t f p t (λ ) P t (λ s cl t) /2ct q otherwse (7) C. Corchero, F.J. Hereda IWOR Madrd 18/27

29 Introducton characterstcs Stablty analyss Futures Contracts Quantty Results characterstcs Real data from the Spansh Market about the generaton company and the market prces. 10 thermal generaton unts (7 coal, 3 fuel) from a Spansh generaton company wth daly bddng n the MIBEL [P P] (MW) mn on/off (h) [P P] (MW) mn on/off (h) Model mplemented and solved wth AMPL/CPLEX CPU tme usng a SunFre V20Z wth two processors AMD Opteron at 2.46Hz and 8Gb of RAM memory. C. Corchero, F.J. Hereda IWOR Madrd 19/27

30 Introducton characterstcs Stablty analyss Futures Contracts Quantty Results characterstcs Real data from the Spansh Market about the generaton company and the market prces. 10 thermal generaton unts (7 coal, 3 fuel) from a Spansh generaton company wth daly bddng n the MIBEL [P P] (MW) mn on/off (h) [P P] (MW) mn on/off (h) Model mplemented and solved wth AMPL/CPLEX CPU tme usng a SunFre V20Z wth two processors AMD Opteron at 2.46Hz and 8Gb of RAM memory. C. Corchero, F.J. Hereda IWOR Madrd 19/27

31 Introducton characterstcs Stablty analyss Futures Contracts Quantty Results characterstcs Real data from the Spansh Market about the generaton company and the market prces. 10 thermal generaton unts (7 coal, 3 fuel) from a Spansh generaton company wth daly bddng n the MIBEL [P P] (MW) mn on/off (h) [P P] (MW) mn on/off (h) Model mplemented and solved wth AMPL/CPLEX CPU tme usng a SunFre V20Z wth two processors AMD Opteron at 2.46Hz and 8Gb of RAM memory. C. Corchero, F.J. Hereda IWOR Madrd 19/27

32 Stochastcty modelng Introducton characterstcs Stablty analyss Futures Contracts Quantty Results Prce Spot Market, λ d,s, s characterzed as a tme seres Tme seres study results n a ARIMA model: ARIMA (23, 1, 13)(14, 1, 21) 24 (0, 1, 1) 168 Prce scenaro constructon: Generaton of 350 scenaros by tme seres smulaton Reducton of the number of scenaros Smulated set of scenaros Reduced set of scenaros Prce(c/MWh) 6 Prce(c/MWh) Hour Hour 1 Gröwe-Kuska et al. Scenaro Reducton and Scenaro Tree Constructon for Power Management Problems C. Corchero, F.J. Hereda IWOR Madrd 20/27

33 Stablty analyss Introducton characterstcs Stablty analyss Futures Contracts Quantty Results 1.4 x 107 Stablty of the objectve functon Expected benefts X Number of scenaros Stablty of frst stage decson varables S c.v. CPU(s) E(benefts)(e) (e)/ (s) , , , , , , ,76 I = 24; T = 10; %P = 40; b.v.= Scenaros C. Corchero, F.J. Hereda IWOR Madrd 21/27

34 Introducton characterstcs Stablty analyss Futures Contracts Quantty Results Optmal bddng strategy by futures contracts quantty % 40% 70% Spot prce (c/kwh) %P E(benefts) I = 24; T = 10; S = 75; c.v. = 720; b.v. = (0,160) (0,186) (0,256) Energy(x1000kWh) C. Corchero, F.J. Hereda IWOR Madrd 22/27

35 Introducton characterstcs Stablty analyss Futures Contracts Quantty Results Results: unt commtment and zero prce bd Energy(x1000kWh) Unt 1 Unt 2 Unt 3 Unt 4 Unt 5 Unt 6 Unt Unt 8 Unt 9 Unt Hour C. Corchero, F.J. Hereda IWOR Madrd 23/27

36 Introducton characterstcs Stablty analyss Futures Contracts Quantty Results Results: procurement of physcal futures contracts Weekly contract MWh Monthly contract MWh thermal 1 thermal 2 thermal 3 thermal 2 thermal 4 thermal 5 thermal 6 Yearly contract MWh Hour thermal 3 thermal 7 thermal 9 thermal 10 C. Corchero, F.J. Hereda IWOR Madrd 24/27

37 Introducton Results: optmal bddng curves characterstcs Stablty analyss Futures Contracts Quantty Results Spot prce (c/kwh) Thermal 1 Thermal 2 Thermal 3 (0,160) (0,250) (0,102) Spot prce (c/kwh) Thermal 4 Thermal 5 Thermal 6 (0,197) (0,30) (0,63) Spot prce (c/kwh) Thermal 7 Thermal 9 Thermal 10 (0,178) (0,110) (0,110) Energy(x1000kWh) Energy(x1000kWh) Energy(x1000kWh) 4 2 C. Corchero, F.J. Hereda IWOR Madrd 25/27

38 Introducton It has been bult an Optmal Bddng Model for a prce-taker generaton company operatng both n the MIBEL Dervatves and Day-Ahead Electrcty Market. The stochastcty of the spot market prce has been taken nto account and t has been represented by a scenaro set. The model developed gves the producer: Optmal bd for the spot market: quantty at 0e/MWh and the rest of the power capacty at the unt s margnal cost Unt commtment Optmal allocaton of the physcal futures contracts among the thermal unts followng n detal the MIBEL rules. C. Corchero, F.J. Hereda IWOR Madrd 26/27

39 Introducton Stochastc optmal day-ahead bd wth physcal future contracts C. Corchero, F.J. Hereda Departament d Estadístca Investgacó Operatva Unverstat Poltècnca de Catalunya Ths work was supported by the Mnstero de Educacón y Cenca of Span Project DPI C02-01 June 6, 2008 C. Corchero, F.J. Hereda IWOR Madrd 27/27

Electricity Market Optimization - F.-Javier Heredia et al. - NUMOPEN CRM Barcelona October 14, /58. gnom.upc.edu

Electricity Market Optimization - F.-Javier Heredia et al. - NUMOPEN 2010 - CRM Barcelona October 14, 2010 1/58 Electricity Market Optimization: finding the best bid through stochastic programming. F.J.