Finding Multiple Nash Equilibria in Pool-Based Markets: A Stochastic EPEC Approach

We present a compact formulation to find all pure Nash equilibria in a pool-based electricity market with stochastic demands. The equilibrium model is formulated as a stochastic equilibrium problem subject to equilibrium constraints (EPEC). The problem is based on a Stackelberg game where the generating companies (GENCOs) optimize their strategic bids anticipating the solution of the independent system operator (ISO) market clearing. A finite strategy approach both in prices and quantities is applied to transform the nonlinear and nonconvex set of Nash inequalities into a mixed integer linear problem (MILP). A procedure to find all Nash equilibria is developed by generating "holes" that are added as linear constraints to the feasibility region. The result of the problem is the set of all pure Nash equilibria and the market clearing prices and assigned energies by the ISO. A case study illustrates the methodology and proper conclusions are reached.