Distributed Nash Equilibrium Seeking for a Dynamic Micro-grid Energy Trading Game with Non-quadratic Payoffs

Abstract

To model energy trading interactions among prosumers, a generic non-quadratic dynamic game model is proposed and solved for a stable Nash equilibrium. The framework is modeled as a non-cooperative, infinite strategy, multiplayer game where the participating players can possess a non-quadratic payoff function. Moreover, the market framework realizes a dynamic mapping from strategy set to payoffs of the participating players. It also carries an embedded notion of reliability and fairness by utilizing the concept of market reputation index. The existence of multiple Nash equilibria is discussed as well as the criteria for stability of Nash equilibrium. It is demonstrated that when an extremum seeking approach is used to model Nash seeking behavior of the players, the system converges to one of the stable Nash equilibriums depending on the initial condition. Simulation results are presented to verify the theoretical results, and a complete day with multiple prosumers is simulated to demonstrate effectiveness of the approach. The results are evaluated using several reliability matrices to show that the proposed framework results in an increased local generation, increased payoffs for prosumers, lower market clearing prices, and higher reliability.