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Basic theoretical foundations and insights on bilevel models and their applications to power systems

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Abstract

Decision making in the operation and planning of power systems is, in general, economically driven, especially in deregulated markets. To better understand the participants’ behavior in power markets, it is necessary to include concepts of microeconomics and operations research in the analysis of power systems. Particularly, game theory equilibrium models have played an important role in shaping participants’ behavior and their interactions. In recent years, bilevel games and their applications to power systems have received growing attention. Bilevel optimization models, Mathematical Program with Equilibrium Constraints and Equilibrium Problem with Equilibrium Constraints are examples of bilevel games. This paper provides an overview of the full range of formulations of non-cooperative bilevel games. Our aim is to present, in an unified manner, the theoretical foundations, classification and main techniques for solving bilevel games and their applications to power systems.

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Notes

  1. Another problem is the ambiguity on the leader’s decision because of the multiplicity of solutions (Leyffer and Munson 2010). This issue is analyzed in Sect. 6.4.

  2. The Nash equilibrium may be referred as global Nash equilibrium or global NEP solution in order to differentiate it from local Nash equilibrium.

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Authors and Affiliations

  1. Department of Electrical Engineering, Pontifical Catholic University of Rio de Janeiro, Rio de Janeiro, Brazil

    David Pozo

  2. Pontificia Universidad Católica de Chile, Santiago, Chile

    Enzo Sauma

  3. University of Castilla–La Mancha, Ciudad Real, Spain

    Javier Contreras

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  1. David Pozo
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  2. Enzo Sauma
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  3. Javier Contreras
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Correspondence to David Pozo.

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This research has been partially supported by the CONICYT, FONDECYT/Regular 1161112 Grant and by the Programa CSF-PAJT, Brazil, under Grant 88887.064092/2014-00.

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Pozo, D., Sauma, E. & Contreras, J. Basic theoretical foundations and insights on bilevel models and their applications to power systems. Ann Oper Res 254, 303–334 (2017). https://doi.org/10.1007/s10479-017-2453-z

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