Solving stochastic complementarity problems in energy market modeling using scenario reduction

European Journal of Operational Research

Volumn 197, Issue 3, 2009, Pages 1028-1040

  Gabriel, Steven A ^a   Zhuang, Jifang ^b   Egging, Ruud ^a  

^a UNIVERSITY OF MARYLAND   (United States)

^b CHEVRON ENERGY TECHNOLOGY COMPANY   (United States)

Author keywords

Complementarity problems; Scenario reduction; Stochastic programming

Indexed keywords

MARKETING; NUMERICAL METHODS; RANDOM PROCESSES; STOCHASTIC PROGRAMMING;

COMPLEMENTARITY PROBLEMS; ENERGY MARKET MODELING; ENERGY MARKETS; MARKET EQUILIBRIUM; MARKET MODELS; NUMERICAL RESULTS; SCENARIO REDUCTION;

STOCHASTIC MODELS;

EID: 61849127756     PISSN: 03772217     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ejor.2007.12.046     Document Type: Article

References (37)

1. Altman E., Pourtaillier O., Haurie A., and Moresino F. Approximating Nash equilibria in nonzero-sum games. International Game Theory Review 2 2-3 (2000) 155-172
2. Bazaraa M.S., Sherali H.D., and Shetty C.M. Nonlinear Programming Theory and Algorithms (1993), John Wiley & Sons Inc., New York
3. Birge J.R., and Louveaux F. Introduction to Stochastic Programming (1997), Springer-Verlag, New York
4. Boots M., Rijkers F.A.M., and Hobbs B.F. A two-level oligopoly analysis of the European gas market. The Energy Journal 25 3 (2004) 73-102
5. Cabero, J., Baillo, A., Ventosa, M., Cerisola, S., 2005. Electricity market equilibrium with risk constraints via benders decomposition. In: INFORMS San Francisco Meeting.
6. x permits. IEEE Transactions on Power Systems 20 1 (2005) 119-129
7. Dupačová J., Gro{combining double acute accent}we-Kuska N., and Ro{combining double acute accent}misch W. Scenario reduction stochastic programming. Mathematical Programming 93 3 (2003) 493-511
8. Directive 2003/55/EC Concerning Common Rules for the Internal Market in Natural Gas.
9. Directive 2004/67/EC Concerning Measures to Safeguard Security of Natural Gas Supply.
10. Egging R., and Gabriel S.A. Examining market power in the European natural gas market. Energy Policy 34 17 (2006) 2762-2778
11. Egging, R., Gabriel, S.A., Holz, F., Zhuang, J., 2008. A complementarity model for the European natural gas market. Energy Policy, accepted for publication.
12. Energy Information Administration, 2006. U.S. Department of Energy, www.eia.doe.gov.
13. Facchinei F., and Pang J.-S. Finite-Dimensional Variational Inequalities and Complementarity Problems vol. 1 (2003), Springer, New York
14. Gabriel S.A., Kiet S., and Zhuang J. A mixed complementarity-based equilibrium model of natural gas markets. Operations Research 53 5 (2005) 799-818
15. Gabriel S.A., Zhuang J., and Kiet S. A large-scale complementarity model of the North American natural gas market. Energy Economics 27 (2005) 639-665
16. http://www.math.hu-berlin.de/ ̃nicole/scenred/.
17. Genc T., Reynolds S.S., and Sen S. Dynamic oligopolistic games under uncertainty: A stochastic programming approach. Journal of Economic Dynamics and Control 31 1 (2007) 55-80
18. Gröwe-Kuska, N., Heitsch, H., Römisch, W., 2003. Scenario reduction and scenario tree construction for power management problems. In: Borghetti, A., Nucci, C.A., Paolone, M. (Eds.), IEEE Bologna Power Tech Proceedings.
19. Gürkan G., Özge Y.A., and Robinson S.M. Sample-path solution of stochastic variational inequalities. Mathematical Programming 84 2 (1999) 13-333
20. Haurie A., and Moresino F. S-adapted oligopoly equilibria and approximations in stochastic variational inequalities. Annals of Operations Research 114 (2002) 183-201
21. Haurie, A., Zaccour, G., 2005. S-adapted equilibria in games played over event trees: An overview. In: Nowak, A.S., et al. (Eds.), Advances in Dynamic Games, Annals of the International Society of Dynamic Games 7, 417-444.
22. Haurie, A., Zaccour, G., Legrand, J., Smeers, Y., 1987. A stochastic dynamic Nash Cournot model for the European gas market. Technical Report HEC Montreal. http://citeseer.ist.psu.edu/haurie98computation.html.
23. Haurie A., Zaccour G., and Smeers Y. Stochastic equilibrium programming for dynamic oligopolistic markets. Journal of Optimization Theory and Applications 66 (1990) 243-253
24. Heitsch H., and R ömisch W. Scenario reduction algorithms in stochastic programming. Computational Optimization and Applications 24 (2003) 187-206
25. Holz, F., von Hirschhausen, C., Kemfert, C., 2006. A strategic model of the European gas supply (GASMOD), Discussion Paper 551, German Institute for Economic Research (DIW), http://www.diw.de.
26. Horn R.A., and Johnson C.R. Matrix Analysis (1985), Cambridge University Press, Cambridge
27. IEA Energy Statistics, 2001, www.iea.org/Textbase/stats/index.asp.
28. UNFCCC, 1998. Kyoto Protocol to the United Nations Framework Convention on Climate Change (COP 3 report, document FCCC/CP/1997/7/Add.1 (18.03.98)).
29. Metzler C., Hobbs B.F., and Pang J.-S. Nash-Cournot equilibria in power markets on a linearized dc network with arbitrage: Formulations and properties. Networks & Spatial Economics 3 2 (2003) 123-150
30. Murty K.G. Linear Programming (1983), John Wiley & Sons, New York
31. Plazas M.A., Conejo A.J., and Prieto F.J. Multimarket optimal bidding for a power producer. IEEE Transactions on Power Systems 20 4 (2005) 2041-2050
32. Römisch, W., Dupačová, J., Gröwe-Kuska, N., Heitsch, H., 2003. Approximations of stochastic programs. Scenario tree reduction and construction. GAMS Workshop, Heidelberg, September 1-3, 2003. DFG Research Center, Berlin.
33. Salant S.W. Imperfect competition in the international energy market: A computerized Nash-Cournot model. Operations Research 30 2 (1982) 52-280
34. Shanbhag, U., Glynn, P., Infanger, G., 2005. A complementarity framework for forward contracting under uncertainty. In: INFORMS San Francisco meeting.
35. Wei J.-Y., and Smeers Y. Spatial oligopolistic electricity models with Cournot generators and regulated transmission prices. Operations Research 47 1 (1999) 102-112
36. Zhuang, J., 2005. A stochastic equilibrium model for the North American Natural Gas Market. Ph.D. Thesis. Department of Civil & Environmental Engineering, University of Maryland, College Park, MD, USA.
37. Zhuang J., and Gabriel S.A. A complementarity model for solving stochastic natural gas market equilibria. Energy Economics 30 1 (2008) 113-147