Distributed Generalized Nash Equilibrium Seeking for Energy Sharing Games

TL;DR

This paper introduces a distributed algorithm for prosumers in energy sharing games to find the generalized Nash equilibrium, enhancing decentralized energy management with proven convergence and scalability.

Contribution

It proposes a novel distributed Krasnosel'ski{}}-Mann iteration algorithm for GNE seeking in energy sharing games, with rigorous convergence proof and scalability validation.

Findings

Algorithm converges reliably to GNE

Validated with experiments on 3 prosumers

Scalable to 123 prosumers

Abstract

With the proliferation of distributed generators and energy storage systems, traditional passive consumers in power systems have been gradually evolving into the so-called "prosumers", i.e., proactive consumers, which can both produce and consume power. To encourage energy exchange among prosumers, energy sharing is increasingly adopted, which is usually formulated as a generalized Nash game (GNG). In this paper, a distributed approach is proposed to seek the Generalized Nash equilibrium (GNE) of the energy sharing game. To this end, we convert the GNG into an equivalent optimization problem. A Krasnosel'ski{\v{i}}-Mann iteration type algorithm is thereby devised to solve the problem and consequently find the GNE in a distributed manner. The convergence of the proposed algorithm is proved rigorously based on the nonexpansive operator theory. The performance of the algorithm is validated by experiments with three prosumers, and the scalability is tested by simulations using 123 prosumers.