Development of Nash Equilibrium for Profit Maximization Equilibrium Problem in Electricity Market

In a competitive electricity market, it is unpredictable to analyze the behavior of participants from the view-point of another participant. In this case, the market can be realized by solving the individual's problem collectively, known as Equilibrium Problem (EP). The paper proposes a mathematical technique, called complementarity modeling, to solve an EP. Nash Equilibrium (NE) point is calculated, which gives the best possible solution for every participating player who is solving an interlinked optimization problem. A Cournot duopoly model is considered to frame the EP with the objective of profit maximization. Results are derived at NE using complementarity modeling and validated by solving the problem graphically using a derivative method. EP is also solved for Cournot duopoly and oligopoly test models using commercial software.