Game Theoretic Equilibrium Analysis of Energy Auction in Microgrid

The future energy grid is expected to be a decentralized network where household units acting as agents can trade energy with others within local neighborhoods by means of an action mechanism. When agents can establish their own price of energy, it is essential to analyze the auction from a market equilibrium standpoint. This paper provides a proof that such a mechanism, although previously formulated as a gradient ascent algorithm to maximize the welfare (i.e. the sum of the utilities of all the agents), converges to the generalized Nash equilibrium (GNE) under physical grid operating constraints, where no agent is incentivized to deviate from its bid. The theoretical analysis is accompanied by simulations of a modified IEEE 37 node system showing convergence towards the equilibrium.