Nash equilibria in electricity pool markets with large-scale wind power integration

Abstract

This work investigates the interaction between power producers with conventional and wind generation portfolios participating in a network-constrained pool-based market. A stochastic bi-level problem is introduced to model the strategic behavior of each single producer. The upper-level problem maximizes the producers’ expected profits and the lower-level problem optimizes the jointly cleared energy and balancing market under economic dispatch. Market participants’ offers are modeled using linear stepwise curves, and the stochastic wind power generation is realized through a set of plausible wind scenarios. The bi-level problem is recast into a single-level mathematical problem with equilibrium constraints with primal-dual formulation using the Karush-Kuhn-Tacker first order optimality conditions and the strong duality theorem. The joint solution of all strategic producers’ problems constitutes an equilibrium problem with equilibrium constraints. The latter is reduced into an equivalent mixed integer linear program by using disjunctive constraints. Different objective functions are applied to the final program to define the range of market equilibria, and a single-iterate diagonalization process is used to justify those equilibria that are meaningful. The model addresses several cases considering different types of market competition, transmission line congestions, and different levels of wind power penetration and volatility.