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Using EPECs to model bilevel games in restructured electricity markets with locational prices

By Xinmin Hu and Daniel Ralph

Abstract

CWPE0619 (EPRG0602) Xinmin Hu and Daniel Ralph (Feb 2006) Using EPECs to model bilevel games in restructured electricity markets with locational prices We study a bilevel noncooperative game-theoretic model of electricity markets with locational marginal prices. Each player faces a bilevel optimization problem that we remodel as a mathematical program with equilibrium constraints, MPEC. This gives an EPEC, equilibrium problem with equilibrium constraints. We establish sufficient conditions for existence of pure strategy Nash equilibria for this class of bilevel games and give some applications. We show by examples the effect of network transmission limits, i.e. congestion, on existence of equilibria. Then we study, for more general EPECs, the weaker pure strategy concepts of local Nash and Nash stationary equilibria. We model the latter via complementarity problems, CPs. Finally, we present numerical examples of methods that attempt to find local Nash or Nash stationary equilibria of randomly generated electricity market games. The CP solver PATH is found to be rather effective in this context

Topics: Classification-JEL: C61, C62, C72, Q40, electricity market, bilevel game, MPEC, EPEC, Nash stationary point, equilibrium constraints, complementarity problem
Publisher: Faculty of Economics
Year: 2006
OAI identifier: oai:www.repository.cam.ac.uk:1810/131661
Provided by: Apollo

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Citations

  1. (2003). A comparison of electricity market designs in networks. doi
  2. (2003). A note on a class of equilibrium problems with equilibrium constraints. doi
  3. A sequential NCP algorithm for solving equilibrium problems with equilibrium constraints.
  4. (1982). A simpli theory of and second order conditions for extreme problems in topological vector spaces. doi
  5. (1999). A two-level optimization problem for analysis of market bidding strategies. doi
  6. (1995). A unifying approach to existence of Nash equilibria. doi
  7. (1997). An institutional design for an electricity contract market with central dispatch. doi
  8. (2000). Analysis of electricity market rules and their eects on strategic behaviour in a noncongestive grid. doi
  9. (2004). Analysis on forward market equilibrium model. doi
  10. (1992). Contract networks for electric power transmission. doi
  11. (2004). Convergence of a penalty method for mathematical programming with complementarity constraints. doi
  12. (2000). Convergence of a smoothing continuation method for mathematical programs with complementarity constraints. doi
  13. (2001). Convergence properties of a regularization scheme for mathematical programs with complementarity constraints. doi
  14. (1997). Coordinated multilateral trades for electric power networks: theory and implementation. POWER Working Papers PWP-031, doi
  15. (2000). Eciency and income shares in high demand energy networks: who receives the congestion rents when a line is constrained? doi
  16. (1997). Economic ineciency of passive transmission rights in congested electricity systems with competitive generation. doi
  17. (2004). Equilibrium Problems with Equilibrium Constraints and their Application to Electricity Markets.
  18. Finally we have for any di, from principles or by using a chain rule Shapiro (1990), that f0 i(x i;x i;di) = rxi;yi(x;y)(di;y0 i(x;di)): 35With this, the above tangent cone relationship and the MPEC B-stationary condition (21), the result follows.
  19. (1999). Financial transmission rights meet Cournot: how TCCs curb market power. doi
  20. (1991). Game Theory: Analysis of Con ict.
  21. (1992). GAMS A user's guide, release 2.25. The Scienti Press,
  22. (2002). Generation capacity expansion in imperfect competitive restructured electricity markets. doi
  23. (1994). Global convergence of Newton's method for nonsmooth equations, via the path search. doi
  24. (2001). How stringent is the linear independence assumption for mathematical programs with stationarity constraints?
  25. (1999). Interfaces to PATH 3.0: Design, implementation and usage. doi
  26. (2002). Local convergence of SQP methods for mathematical programs with equilibrium constraints. Numerical Analysis Report doi
  27. (2004). Manifolds of multi-leader Cournot equilibria. doi
  28. (1997). Market power and strategic interaction in electricity networks. doi
  29. (2003). Mathematical Programs with Complementarity Constraints and Game Theory Models in Electricity Markets.
  30. (2000). Mathematical programs with complementarity constraints: Stationarity, optimality, and sensitivity. doi
  31. (1996). Mathematical Programs with Equilibrium Constraints. doi
  32. (2005). Modeling and computing two-settlement oligopolistic equilibrium in a congested electricity network. doi
  33. (2001). Nash equilibria for games in competitive electricity markets under network constraints.
  34. (1994). Newton's method for a class of nonsmooth functions. doi
  35. (1993). Nonsmooth Analysis. A Wiley-Interscience Publication,
  36. (2004). Oligopolistic equilibrium analysis for electricity markets: a nonlinear complementarity approach. doi
  37. (1990). On concepts of directional dierentiability.
  38. (1982). On convergence of the PIES algorithm for computing equilibria. doi
  39. (2000). On using the elastic mode in nonlinear programming approaches to mathematical programs with complementarity constraints. doi
  40. (1998). Optimization problems with perturbations: A guided tour. doi
  41. (1999). Power Systems. doi
  42. revised 2004. Electricity generation with looped transmission networks: bidding to an ISO. doi
  43. (2002). SNOPT 6.0 . URL http://www.sbsi-sol-optimize.com/asp/sol product snopt.htm
  44. (2004). Solving mathematical program with complementarity constraints as nonlinear programs. doi
  45. (2005). Solving Multi-Leader-Follower Games. doi
  46. (2000). Strategic gaming analysis for electric power systems: an MPEC approach. doi
  47. (1989). Supply function equilibria in oligopoly under uncertainty. doi
  48. (2001). The New Zealand electricity market (NZEM).
  49. (1998). Transmission congestion contracts and strategic behavior in generation. doi
  50. (1999). Understanding how market power can arise in network competition: a game theoretic approach. doi

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