Stochastic bilevel games applications in electricity markets
- Autores: David Pozo Camara
- Directores de la Tesis: Javier Contreras Sanz (dir. tes.)
- Lectura: En la Universidad de Castilla-La Mancha ( España ) en 2013
- Idioma: inglés
- Tribunal Calificador de la Tesis: Antonio Jesús Conejo Navarro (presid.), Julián Barquín Gil (secret.), João Paulo da Silva Catalão (voc.)
- Materias:
- Enlaces
- Tesis en acceso abierto en: TESEO
- Resumen
This thesis addresses the subject of bilevel games and their application for modeling operational and planning problems in restructured power systems. Such games are well fitted to model hierarchical competition but they are hard to solve in general. Bilevel games set new challenges for power system operators and planners and they constitute an ongoing topic for many researchers.
Bilevel games are generally modeled as equilibrium programs with equilib- rium constraints (EPEC) within the operations research field. EPEC problems are highly non-linear and non-convex, and the existence of global and unique solutions is not guaranteed even in the simplest instances of EPECs. Hence, a generalized theory and solution algorithms for solving EPECs have not been firmly established so far. Only a few and specific instances of EPECs have been shown to have equilibria. In many of these instances, the solution is stated as a stationary equilibrium, which is not necessarily a global solution. Additionally, most of the proposed solution techniques do not guarantee finding all pure Nash equilibria. The difficulties both from a theoretical and a numerical point of view arise because EPEC problems inherit the bad properties of the set of MPEC problems that conform the corresponding EPEC.
In this thesis, we propose a special case of EPECs where leaders compete among themselves at the upper level in a Nash equilibrium setting by making decisions in finite strategies constrained by the solution of the lower level problem, where the followers compete among themselves in a Nash equilibrium setting by making continuous decisions. The upper and lower level problems are linear and uncertainty is included at the lower level. Then, the bilevel game is stated as a finite stochastic EPEC with the possibility of multiple equilibria. This specific EPEC structure is appropriate for many problems that appear in restructured power systems. We devote two chapters of this thesis to show the applicability of this game structure in both operational and planning frameworks.ii To overcome the difficulties described above, we propose a mixed integer lin- ear reformulation (convexification) of the corresponding stochastic finite EPEC problem. The advantage of this approach is two-fold. First, the linearized formulation can be solved with standard mixed integer linear programming (MILP) solvers and a global solution can be guaranteed for moderately-sized problems. Second, the discrete strategies at the upper level problem allow us to find all (pure) Nash equilibria. This is done by including a set of linear constraints in the problem that represent ¿holes¿ in the feasible region for the known Nash equilibria.
Finally, although the proposed methodology has several advantages, it is important to recall its limitations. First, the linearization (convexification) approach proposed in this thesis requires the inclusion of binary variables into the model, which increases its complexity. And second, the lower-level problem has to be a convex optimization problem (linear in this thesis) in order to transform it into its equivalent and sufficient first-order optimality conditions.
