Abstract
On current electricity markets the electrical utilities are faced with very sophisticated decision making problems under uncertainty. Moreover, when focusing in the short-term management, generation companies must include some medium-term products that directly influence their short-term strategies. In this work, the bilateral and physical futures contracts are included into the day-ahead market bid following MIBEL rules and a stochastic quadratic mixed-integer programming model is presented. The complexity of this stochastic programming problem makes unpractical the resolution of large-scale instances with general-purpose optimization codes. Therefore, in order to gain efficiency, a polyhedral outer approximation of the quadratic objective function obtained by means of perspective cuts (PC) is proposed. A set of instances of the problem has been defined with real data and solved with the PC methodology. The numerical results obtained show the efficiency of this methodology compared with standard mixed quadratic optimization solvers.
Similar content being viewed by others
References
Anderson E, Philpott A (2002) Optimal offer construction in electricity markets. Math Oper Res 27(1):82–100
Anderson E, Xu H (2002) Necessary and sufficient conditions for optimal offers in electricity markets. SIAM J Control Optim 41(4):1212–1228
Bjorgan R, Liu CC, Lawarrée J (1999) Financial risk management in a competitive electricity market. IEEE Trans Power Syst 14(4):1285–1291
BOE (2006a) Boletin Oficial del Estado n.128 30/5/2006
BOE (2006b) Boletin Oficial del Estado n.158 4/7/2006
Carrión M, Arroyo J (2006) A computationally efficient mixed-integer linear formulation for the thermal unit commitment problem. IEEE Trans Power Syst 21(3):1371–1378
Chen X, He Y, Song YH, Nakanishi Y, Nakahishi C, Takahashi S, Sekine Y (2004) Study of impacts of physical contracts and financial contracts on bidding strategies of GenCos. Electr Power Energy Syst 26:715–723
Conejo AJ, Nogales FJ, Arroyo JM (2002) Price-taker bidding strategy under price uncertainty. IEEE Trans Power Syst 17(4):1081–1088
Conejo AJ, García-Bertrand R, Carrión M, Caballero A, de Andrés A (2008) Optimal involvement in futures markets of a power producer. IEEE Trans Power Syst 23(2):703–711
Corchero C, Heredia FJ (2011) A stochastic programming model for the thermal optimal day-ahead bid problem with physical futures contracts. Comput Oper Res 38(11):1501–1512. doi:10.1016/j.cor.2011.01.008
CPLEX (2009) IBM ILOG CPLEX V12.1 user’s manual for CPLEX. International Business Machines Corporation
Dahlgren R, Liu CC, Lawarree J (2003) Risk assessment in energy trading. IEEE Trans Power Syst 18(2):503–511
Escudero L, Garín M, Merino M, Pérez G (2009) A general algorithm for solving two-stage stochastic mixed 0–1 first-stage problems. Comput Oper Res 36:2590–2600
Fleten SE, Kristoffersen TK (2007) Stochastic programming for optimizing bidding strategies of a Nordic hydropower producer. Eur J Oper Res 181(2):916–928
Frangioni A, Gentile C (2006) Perspective cuts for a class of convex 0–1 mixed integer programs. Math Program 106:225–236
Frangioni A, Gentile C (2009) A computational comparison of reformulations of the perspective relaxation: SOCP vs. cutting planes. Oper Res Lett 37:206–210
Gountis VP, Bakirtzis AG (2004) Bidding strategies for electricity producers in a competitive electricity marketplace. IEEE Trans Power Syst 19(1):356–365
Guan X, Wu J, Gao F, Sun G (2008) Optimization-based generation asset allocation for forward and spot markets. IEEE Trans Power Syst 23(4):1796–1807
Heredia FJ, Rider M, Corchero C (2010) Optimal bidding strategies for thermal and generic programming units in the day-ahead electricity market. IEEE Trans Power Syst 24(4):1–9. doi:10.1109/TPWRS.2009.2038269
Heredia FJ, Rider MJ, Corchero C (2011) A stochastic programming model for the optimal electricity market bid problem with bilateral contracts for thermal and combined cycle units. Ann Oper Res (in press). doi:10.1007/s10479-011-0847-x
Hiriart-Urruty JB, Lemaréchal C (1993) Convex analysis and minimization algorithms I. Fundamentals. Springer, Berlin
Hull J (2002) Options, futures and other derivatives, 5th edn. Prentice Hall International, Englewood Cliffs
Luenberger DG (2004) Linear and nonlinear programming, 2nd edn. Kluwer Academic, Boston
Ni E, Luh PB, Rourke S (2004) Optimal integrated generation bidding and scheduling with risk management under a deregulated power market. IEEE Trans Power Syst 19(1):600–609
Nowak MP, Schultz R, Westphalen M (2005) A stochastic integer programming model for incorporating day-ahead trading of electricity into hydro-thermal unit commitment. Optim Eng 6(2):163–176
Tawarmalani M, Sahinidis N (2001) Semidefinite relaxations of fractional programs via novel convexification techniques. J Glob Optim 20:137–158
Acknowledgements
This work was supported by the Ministry of Science and Technology of Spain through MICINN Project DPI2008-02153.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Corchero, C., Mijangos, E. & Heredia, FJ. A new optimal electricity market bid model solved through perspective cuts. TOP 21, 84–108 (2013). https://doi.org/10.1007/s11750-011-0240-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11750-011-0240-6