A rational decentralized generalized Nash equilibrium seeking for energy markets

TL;DR

This paper introduces a decentralized energy market design that ensures individual rationality and system constraints are met, using a game-theoretic approach and a distributed algorithm with proven convergence.

Contribution

It formulates a welfare maximization problem with IR constraints as a non-cooperative game and develops a distributed algorithm to find the unique GNE.

Findings

The proposed algorithm converges to the GNE in simulations.

The market design guarantees individual rationality in expectation.

The approach effectively incorporates grid constraints into decentralized market mechanisms.

Abstract

We propose a method to design a decentralized energy market which guarantees individual rationality (IR) in expectation, in the presence of system-level grid constraints. We formulate the market as a welfare maximization problem subject to IR constraints, and we make use of Lagrangian duality to model the problem as a n-person non-cooperative game with a unique generalized Nash equilibrium (GNE). We provide a distributed algorithm which converges to the GNE. The convergence and properties of the algorithm are investigated by means of numerical simulations.