Equilibria among strategic producers and strategic consumers: a solution approach relying on a single optimization problem
本文提出一种系统方法，将批发电力市场中战略生产者和消费者的均衡问题转化为单一优化问题，通过松弛和凸锥规划求解，并应用于实际案例验证。
Finding general Nash equilibria involving strategic producers and strategic consumers in a wholesale electricity market is a complex problem. In this paper, this problem is addressed by formulating an equilibrium problem with equilibrium constraints, which involves the joint solution of several mathematical programming with equilibrium constraints. These mathematical programming with equilibrium constraints result from bilevel problems associated with strategic producers and strategic consumers. In previous approaches, the mathematical programming with equilibrium constraints constituting the equilibrium problem with equilibrium constraints have not been represented by their primal-dual optimality constraints, as they do not have exact dual counterparts. Primal-dual optimality constraints are preferable to Karush-Kuhn-Tucker conditions for representing the mathematical programming with equilibrium constraints in the equilibrium problem with equilibrium constraints formulation, as they replace all complementarity constraints with the strong duality equality. In this paper, we propose a systematic solution approach for solving the equilibrium problem with equilibrium constraints in which, mathematical programming with equilibrium constraints is relaxed and recast as convex rotated quadratic conic problems, enabling the derivation of their dual counterparts and the application of primal-dual optimality constraints. The proposed methodology is applied to a realistic case study, and different market setups are analyzed where potential market power may be exerted by producers and/or consumers, or by none of them. The results of the proposed methodology are compared to those provided by other approaches.