A Column-and-Constraint Generation Algorithm to Find Nash Equilibrium in Pool-Based Electricity Markets.

• We design a methodology to find specific Nash equilibrium in electricity markets. • We devise an efficient column-and-constraint generation method to solve the EPEC. • We benchmark the proposed solution method with the state-of-the-art methodology. • The proposed algorithm is 20 times faster than current state-of-the-art on average. Equilibrium analysis is crucial in electricity market designs, with Nash equilibrium recognized as the most powerful one. Its most prominent hindrance, however, is an efficient methodology to compute an equilibrium point in large-scale systems. In this work, a Column-and-Constraint Generation (CCG) algorithm is proposed to tackle this challenge. More precisely, the master problem finds a candidate for Nash equilibrium and the oracle identifies whether this candidate point is indeed an equilibrium. A set of numerical experiments was conducted, comparing its computational performance with the solution of an Equilibrium Problem with Equilibrium Constraint (EPEC). We identify that the proposed algorithm overcomes the benchmark in the magnitude of 20 times on average and more than 30 times in the most demanding instances. Furthermore, the scalability of the EPEC formulation is challenged even for medium-scale instances, whilst the proposed algorithm was able to handle all tested instances in a reasonable computational time. [ABSTRACT FROM AUTHOR]