A tutorial review of complementarity models for decision-making in energy markets

Elsevier BV - Tập 2 - Trang 91-120 - 2013
Carlos Ruiz1, Antonio J. Conejo2, J. David Fuller3, Steven A. Gabriel4, Benjamin F. Hobbs5
1Universidad Carlos III de Madrid, Leganés, Spain
2University of Castilla La Mancha, Ciudad Real, Spain
3University of Waterloo, Waterloo, Canada
4University of Maryland, College Park, USA
5The Johns Hopkins University, Baltimore, USA

Tóm tắt

Complementarity models can represent the simultaneous optimization problems of one or several interacting decision-makers, and thus they have become an increasingly important and powerful tool for formulating and solving bottom-up energy market models. This paper provides an overview of the full range of complementarity-based formulations and how these can be applied to assist the different market participants and organizations with their decision-making processes. To this end, the first part of the paper introduces the mathematical formulation of some basic complementarity models, which are illustrated by highly simplified but illustrative energy market applications. Considering these models, the second part of the paper is devoted to describing in broad terms four areas of their potential application: electricity markets, emission markets, natural gas markets and economies comprising several interacting markets.

Tài liệu tham khảo

Abada I (2012) Modélisation des Marchés du Gaz Naturel en Europe en Concurrence Oligopolistique. Le Modè le GaMMES et Quelques Applications. Ph.D. thesis, Université Paris Ouest, Nanterre–La Défense Abada I, Briat V, Gabriel SA, Massol O (2012) A generalized Nash–Cournot model for the Northwestern European natural gas markets with a fuel substitution demand function: the GaMMES model. Netw Spat Econ. doi:10.1007/s11067-012-9171-5 AIMMS (2013) Advanced interactive multidimensional modeling system. http://www.aimms.com. Feb. 2013 AMPL (2013) A modeling language for mathematical programming. http://www.ampl.com. Feb. 2013 Arroyo JM, Conejo AJ (2000) Optimal response of a thermal unit to an electricity spot market. IEEE Trans Power Syst 15(3):1098–1104 Bautista G, Anjos MF, Vannelli A (2006) Formulation of oligopolistic competition in ac power networks: an NLP approach. IEEE Trans Power Syst 22(1):105–115 Bertsekas DP (1999) Nonlinear programming, second edition. Athena Scientific, Belmont, MA Boots MG, Hobbs BF, Rijkers FAM (2004) Trading in the downstream European gas market: a successive oligopoly approach. Energy J 25(3):73–102 Bowley AL (1924) The mathematical groundwork of economics: an introductory treatise. Oxford University Press, Oxford Chen YH, Hobbs BF (2005) An oligopolistic power market model with tradable NO x permits. IEEE Trans Power Syst 20(1):119–129 Chen Y, Hobbs BF, Leyffer S, Munson TS (2006) Leader–follower equilibria for electric power and NO x allowances markets. Comput Manag Sci 3:307–330 Chen YH, Sijm J, Hobbs BF, Lise W (2008) Implications of CO2 emissions trading for short-run electricity market outcomes in northwest Europe. J Regul Econ 34(3):251–281 Chen YH, Liu AL, Hobbs BF (2011) Economic and emissions implications of loadbased, source-based and first-seller emissions trading programs under California AB32. Oper Res 59(3):696–712 Chyong C-K, Hobbs BH (2011) Strategic Eurasian natural gas model for energy security and policy analysis. EPRG Working Paper 1115, Cambridge Working Paper in Economics, 1134 Conejo AJ, Castillo E, Mínguez R, García-Bertrand R (2006) Decomposition techniques in mathematical programming: engineering and science applications. Springer, New York Cottle RW, Pang J-S, Stone RE (1992) The linear complementarity problem. Academic Press, San Diego Cournot AA (1838) Researches into the mathematical principles of the theory of wealth. (translated by Nathaniel T. Bacon, 1927) Macmillan, New York Daxhelet O, Smeers Y (2001) Variational inequality models of restructured electric systems. In: Ferris MC, Mangasarian OL, Pang J-S (eds) Applications and algorithms of complementarity. Kluwer, Dordrecht de Wolf D, Smeers Y (1996) Optimal dimensioning of pipe networks with application to gas transmission networks. Oper Res 44(4):596–608 DeMiguel V, Xu H (2009) A stochastic multiple-leader Stackelberg model: analysis, computation, and application. Oper Res 57(5):1220–1235 Dieckhöner C (2012) Simulating security of supply effects of the Nabucco and South Stream projects for the European natural gas market. Energy J 33(3):155–183 Dietsch M (2012) The next global energy cartel. http://www.forbes.com. April 2012 Dirkse SP, Ferris MC (1995) The PATH solver: a nonmonotone stabilization scheme for mixed complementarity problems. Optim Methods Softw 5:123–156 Department of Energy (2012) Natural gas vehicle emissions. http://www.afdc.energy.gov Direct Emissions from Stationary Combustion Sources (2012) http://www.epa.gov Egging R, Gabriel SA (2006) Examining market power in the European natural gas market. Energy Policy 34(17):2762–2778 Facchinei F, Kanzow C (2007) Generalized Nash equilibrium problems. 4OR Q J Oper Res 5(3):173210 Ferris MC, Pang J-S (1997) Complementarity and variational problems: state of the art. SIAM Publications, Philadelphia, vol 92, pp 40–61 Fishbone LG, Abilock H, Markal (1981) A linear-programming model for energy systems analysis—technical description of the BNL Version. Int J Energy Res 5(4):353–375 Fortuny-Amat J, McCarl B (1981) A representation and economic interpretation of a two-level programming problem. J Oper Res Soc 32(9):783–792 Fountain H (2012) Ohio: sites of two earthquakes nearly identical. The New York Times Gabriel SA, Smeers Y (2006) Complementarity problems in restructured natural gas markets. In: Seegger A (ed) Recent advances in optimization. Lecture Notes in Economics and Mathematical Systems, Springer, Berlin, vol 563, pp 343–373 Gabriel SA, Vikas S, Ribar D (2000) Measuring the influence of Canadian carbon stabilization programs on natural gas exports to the United States via a “bottom-up” intertemporal spatial price equilibrium model. Energy Econ 22(5):497–525 Gabriel SA, Kydes A, Whitman P (2001) The National Energy Modeling System: a largescale energy-economic equilibrium model. Oper Res 49(1):14–25 Gabriel SA, Manik J, Vikas S (2003) Computational experience with a large-scale, multi-period, spatial equilibrium model of the North American natural gas system. Netw Spat Econ 3(2):97–122 Gabriel SA, Kiet S, Zhuang J (2005a) A mixed complementarity-based equilibrium model of natural gas markets. Oper Res 53(5):799–818 Gabriel SA, Zhuang J, Kiet S (2005b) A large-scale linear complementarity model of the North American natural gas market. Energy Econ 27(4):639–665 Gabriel SA, Siddiqui S, Conejo AJ, Ruiz C (2012a) Solving discretely-constrained Nash–Cournot games with an application to power markets. Netw Spat Econ (accepted, Nov. 2012) Gabriel SA, Rosendahl KE, Egging R, Avetisyan H, Siddiqui S (2012b) Cartelization in gas markets: studying the potential for a gas OPEC. Energy Econ 34(1):137–152 Gabriel SA, Conejo AJ, Hobbs BF, Fuller D, Ruiz C (2013a) Complementarity modeling in energy markets. International Series in Operations Research and Management Science, Springer, New York Gabriel SA, Conejo AJ, Ruiz C, Siddiqui S (2013b) Solving discretely-constrained, mixed-linear complementarity problems with applications in energy. Comput Oper Res 40(5):1339–1350 GAMS (2013) General algebraic modeling system. http://www.gams.com. Feb. 2013 Golan M, Whitson CH (1991) Well performance, second edition. Prentice-Hall, New Jersey Guldmann J-M (1983) Supply, storage, and service reliability decisions by gas distribution utilities: a chance-constrained approach. Manag Sci 29(8):884–906 Harker PT (1991) Generalized Nash games and quasi-variational inequalities. Eur J Oper Res 54(1):81–94 Hobbs BF, Nelson SK (1992) A nonlinear bilevel model for analysis of electric utility demand-side planning issues. Ann Oper Res 34:255–274 Hobbs BF, Helman U (2004) Complementarity-based equilibrium modeling for electric power markets. In: Bunn DW (ed) Modeling prices in competitive electricity markets. Wiley Series in Financial Economics, London, chap 3 Hobbs BF, Pang JS (2004) Spatial oligopolistic equilibria with arbitrage, shared resources, and price function conjectures. Math Program Ser B 101(1):57–94 Hobbs BF, Metzler CB, Pang J-S (2000) Strategic gaming analysis for electric power networks: an MPEC approach. IEEE Trans Power Syst 15(2):638–645 Hobbs BF, Bushnell J, Wolak FA (2010) Upstream vs. downstream CO2 trading: a comparison in the electricity context. Energy Policy 38(7):3632–3643 Hogan WW (1975) Energy policy models for Project Independence. Comput Oper Res 2:251–271 Hogan WW (2002) Energy modeling for policy studies. Oper Res 50(1):89–95 Holz F, von Hirschhausen C, Kemfert C (2008) A strategic model of European gas supply (GASMOD). Energy Econ 30:766–788 Hu X, Ralph D (2007) Using EPECs to model bilevel games in restructured electricity markets with locational prices. Oper Res 55(5):809–827 Klemperer P, Meyer M (1989) Supply function equilibria in oligopoly under uncertainty. Econometrica 57:1243–77 Kramer A (2006) Gazprom builds wealth for itself, but anxiety for others. The New York Times, January 13 Landler M (2006) Gas halt may produce big ripples in European policy. The New York Times. January 4 Lemke CE (1965) Bimatrix equilibrium points and mathematical programming. Manag Sci 11(7):681–689 Leyffer S, Munson TS (2010) Solving multi-leader-common-follower games. Optim Methods Softw 25(4):601–623 Lise W, Hobbs BF (2008) Future evolution of the liberalised European gas market: simulation results with a dynamic model. Energy 33(7):989–1004 Lochner S (2011) Identification of congestion and valuation of transport infrastructures in the European natural gas market. Energy 36(5):2483–2492 Lochner S, Bothe D (2007) From Russia with gas—an analysis of the Nord Stream pipeline’s impact on the European gas transmission system with the TIGER model. EWI Working Paper 07/2. Institute of Energy Economics at the University of Cologne, Germany Luo ZQ, Pang JS, Ralph D (1996) Mathematical Programs with Equilibrium Constraints. Cambridge Univ. Press, Cambridge, UK McMahon J (2011) Wind power’s future may depend on gas fracking’s fate: panel, Forbes. May 12, 2011, http://www.forbes.com/sites/jeffmcmahon/2011/05/12/wind-powers-future-may-depend-on-gas-frackings-fate-panel/ Midthun KT (2007) Optimization models for liberalized natural gas markets. Ph.D. thesis, Norwegian University of Science and Technology, Trondheim, Norway Midthun KT, Bjørndal M, Tomasgard A (2009) Modeling optimal economic dispatch and system effects in natural gas networks. Energy J 30(4):155–180 MIT Energy Initiatiave (2010) The future of natural gas an interdisciplinary MIT study. Interim Report, ISBN (978-0-9828008-0-5) Model documentation report: international natural gas model (2012) Office of Energy Analysis, Energy Information Administration, US Department of Energy, Washington, DC Motto AL, Galiana FD, Conejo AJ, Arroyo JM (2002) Network-constrained multi-period auction for a pool-based electricity market. IEEE Trans Power Syst 17(3):646–653 Naill R (1992) A system dynamics model for National energy policy. Syst Dyn Rev 8(1):1–19 Nash JF (1951) Non-cooperative games. Ann Math 54(2):286–295 Natural Gas Extraction–Hydraulic Fracturing (2012) http://www.epa.gov/hydraulicfracture O’Neill RP, Williard M, Wilkins B, Pike R (1979) A mathematical programming model for allocation of natural gas. Oper Res 27(5):857–873 Ruiz C, Conejo AJ (2009) Pool strategy of a producer with endogenous formation of locational marginal prices. IEEE Trans Power Syst 24(4):1855–1866 Ruiz C, Conejo AJ, García-Bertrand R (2008) Some analytical results pertaining to Cournot models for short-term electricity markets. Electr Power Syst Res 78(10):1672–1678 Ruiz C, Conejo AJ, Smeers Y (2012) Equilibria in an oligopolistic electricity pool with stepwise offer curves. IEEE Trans Power Syst 27(2):752–761 Scholtes S, Stöhr M (2001) How stringent is the linear independence assumption for mathematical programs with complementarity constraints? Math Oper Res 26(4):851–863 Siddiqui S, Gabriel SA (2012) An SOS1-based approach for solving MPECs with a natural gas market application. Netw Spat Econ 13(2):205–227 Smeers Y (2008) Gas models and three difficult objectives. CORE Discussion paper 2008/9. Université Catholique Louvain, Belgium, February 2008 Stern JP (2005) The Future of Russian Gas and Gazprom. Oxford University Press, Oxford Urbina I (2011) Hunt for gas hits fragile soil, and South Africans fear risks. The New York Times, December 30 Urbina I (2012a) A tainted water well, and concern there may be more. The New York Times, August 3 Urbina I (2012b) New report by agency lowers estimates of natural gas in US. The New York Times, January 28 US Energy Information Administration (2011) World shale gas resources: an initial assessment of 14 regions Outside the United States von Stackelberg H (1934) Marktform und Gleichgewicht. (Market structure and equilibrium). J. Springer, Vienna Yang H, Chung CY, Wong KP (2012) Optimal fuel, power and load-based emissions trades for electric power supply chain equilibrium. IEEE Trans Power Syst 27(3):1147–1157