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APPLICATION OF POSSIBILITY THEORY TO ROBUST COURNOT EQUILIBRIUM IN THE ELECTRICITY MARKET

Published online by Cambridge University Press:  31 August 2005

F. A. Campos ,
J. Villar  and
J. Barquín
F. A. Campos
Affiliation:
Instituto de Investigación Tecnológica, Pontificia Comillas University of Madrid, 28015 Madrid, Spain, E-mail: acampos@iit.upco.es
J. Villar
Affiliation:
Instituto de Investigación Tecnológica, Pontificia Comillas University of Madrid, 28015 Madrid, Spain, E-mail: jose.villar@iit.upco.es
J. Barquín
Affiliation:
Instituto de Investigación Tecnológica, Pontificia Comillas University of Madrid, 28015 Madrid, Spain, E-mail: julian.barquin@iit.upco.es
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Abstract

It is known that Cournot game theory has been one of the theoretical approaches used more often to model electricity market behavior. Nevertheless, this approach is highly influenced by the residual demand curves of the market agents, which are usually not precisely known. This imperfect information has normally been studied with probability theory, but possibility theory might sometimes be more helpful in modeling not only uncertainty but also imprecision and vagueness. In this paper, two dual approaches are proposed to compute a robust Cournot equilibrium, when the residual demand uncertainty is modeled with possibility distributions. Additionally, it is shown that these two approaches can be combined into a bicriteria programming model, which can be solved with an iterative algorithm. Some interesting results for a real-size electricity system show the robustness of the proposed methodology.

Information

Type
Papers from the 8TH International Conference on Probabilistic Methods Applied to Power Systems (PMAPS). Guest editor: James McCalley, Iowa State University
Information
Probability in the Engineering and Informational Sciences , Volume 19 , Issue 4 , October 2005 , pp. 519 - 531
Copyright
© 2005 Cambridge University Press

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References

REFERENCES

Baíllo, A. (2002). A methodology to develop optimal schedules and offering strategies for a generation company operating in a short-term electricity market. Ph.D. dissertation, Departamento de Organización Industrial, Pontificia Comillas University of Madrid.
Barquín, J., Centeno, E., & Guillén, J.R. (2004). Medium-term generation programming in competitive environments: A new optimization approach for market equilibrium computing. IEE Proceedings on Generation Transmission and Distribution 151(1): 119–126.Google Scholar
Brooke, A., Kendrick, D., Meeraus, A., & Raman, R. (1998). GAMS: A user's guide. Washington, DC: GAMS Development Corporation.
Campos, F.A. & Villar, J. (2003). Robust solutions with fuzzy linear chance constrained programming. Presented at the Xth Congress of the International Association for Fuzzy-Set Management and Economy. Leon, Spain.
Cplex (1997). Using the Cplex callable library. Incline Village, NV: ILOG, Inc.
Day, C. & Hobbs, B. (2002). Oligopolistic competition in power networks: A conjectured supply function approach. IEEE Transactions on Power Systems 17(3): 597–607.Google Scholar
Dubois, D. (1987). Linear programming with fuzzy data. Analysis with Fuzzy Information 3: 241–263.Google Scholar
Dubois, D. & Prade, H. (1980). Fuzzy sets and systems: Theory and applications. New York: Academic Press.
Dubois, D. & Prade, H. (1988). Possibility theory. An approach to computerized processing of uncertainty. New York: Plenum.
Dubois, D. & Prade, H. (1993). Fuzzy sets and probability: Misunderstandings, bridges and gaps. Second IEEE International Conference on Fuzzy Systems.
Elishakoff, I. (1999). What may go wrong with probabilistic methods? In: I. Elishakoff (ed.), Whys and hows in uncertainty modelling: Probability, fuzzyness and anti-optimization. CSIM Courses and Lectures, vol. 388. Wien, pp. 265–283.
Inuiguchi, M., Ichihashi, H., & Tanaka, H. (1990). Fuzzy programming: A survey of recent developments. In: R. Slowinski & J. Teghem (eds.), Stochastic versus fuzzy approaches to multiobjective mathematical programming under uncertainty. Dordrecht: Kluwer Academic.
Luhandjula, M.K. (1982). Compensatory operators in fuzzy linear programming with multiple objectives. Fuzzy Sets and Systems 8: 245–252.Google Scholar
Oberguggenberger, O. & Fellin, W. (2002). From probability to fuzzy sets: The struggle for meaning in geotechnical risk assessment. In: R. Pöttler, H. Klapperich, & H.F. Schweiger (eds.), Probabilistics in GeoTechnics: Technical and Economic Risk Estimation. Graz, Austria: Verlag Glückauf Essen, pp. 29–38.
Smets, P. (1997). Imperfect information: Imprecision—Uncertainty. In: A. Motro & P. Smets (eds.), Uncertainty management in information systems. From needs to solutions. Dordrecht: Kluwer Academic, pp. 225–254.
Varian, H. (1992). Microeconomic analysis. New York: Norton.
Yager, R.R. (1986). A characterization of the extension principle. Fuzzy Sets and Systems 18: 205–217.Google Scholar
Zadeh, L.A. (1975). The concept of a linguistic variable and its application to approximate reasoning. Information Sciences 8: 199–249.Google Scholar
Zadeh, L.A. (1978). Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems 1: 3–28.Google Scholar
Zeleny, M. (1973). Compromise programming. In: J.L.C.a.M. Zeleny (ed.), Multiple criteria decision making. Columbia, SC: University of South Carolina Press.