A mixed strategy Nash Equilibrium of multi-player games with a transmission congestion considering PTDF

Nash Equilibrium (NE) is essential to investigate a participantpsilas offer strategy in a competitive electricity market. The transmission line constraints make it difficult to compute the NE due to causing a mixed strategy NE instead of a pure strategy NE. Computing a mixed strategy is more complicated in a multi-player game. The competition among multiple participants is modeled by a two-level hierarchical optimization problem. A mathematical programming approach is widely used in finding this equilibrium. However, there are difficulties in solving a mixed strategy NE. This paper presents two heuristics applied to the mathematical programming method. The heuristics are based on empirical studies of mixed strategies in numerous sample systems. Based on the heuristics, a new formulation is provided with a set of linear and nonlinear equations, and an algorithm is suggested for using the heuristics and the newly-formulated equations. The effectiveness of the heuristics and the algorithm is illustrated through application of IEEE 30 bus system with 6 generating firms. The equilibrium is verified to satisfy the NE condition.