An Algorithm for Calculating Cournot Mixed Strategy Equilibrium with Transmission Constraints

In this paper, at first two properties of Cournot mixed strategy Nash equilibrium with considering the transmission grid constraints are proved, and then a novel method of computing mixed strategy equilibrium is suggested. For a transmission grid, transmission congestion states and non-congestion state constitute transmission states. The generators each randomize over their pure strategies as some probability vector, such that the selected pure strategies combined with other generators' strategy combinations keep some specific transmission states of power system and attain their maximal expected profits. A method based on this characteristic and two properties mentioned above is provided. Congestion influence on bidding strategies is taken into account in this method. Since this method does not continuously tune discretization of strategy space as usually, the computation burden can be released. Several illustrative examples are given to show the process and effectiveness of this method