Direct approach in computing robust Nash strategies for generating companies in electricity markets

• A new analytic method for computing Nash equilibrium.
• Conditions for convergence and uniqueness of the solution.
• Extending the basic approach to consider constraints.
• Introducing and computing a new concept of robust Nash equilibrium.

Supply function equilibrium (SFE) is often used to describe the behavior of generating companies in electricity markets. However, comprehensive analytical description of supply function models is rarely available in the literature. In this paper, using some analytical calculations, a novel direct approach is proposed to compute the Nash equilibrium (NE) of the supply function model under uniform marginal pricing mechanism. An explicit mathematical proof for its existence and uniqueness is also presented. The proposed methodology is then generalized to accommodate practical market constraints. In addition, a new concept of robust NE is introduced and calculated based on this approach. Finally, numerical simulations demonstrate the applicability and effectiveness of the proposed solution scheme.