Efficient Energy Distribution in a Smart Grid using Multi-Player Games

TL;DR

This paper models energy sharing among smart houses in a micro-grid as a multi-player game, proving the existence of Nash equilibria and designing controllers that optimize local energy use and reduce reliance on the global grid.

Contribution

It introduces a game-theoretic framework for energy distribution in smart grids, demonstrating the existence of Nash equilibria with coalition-based punishment strategies and applying it to real-world smart house scenarios.

Findings

Nash equilibria always exist in the modeled game.

Strategies with retaliation mechanisms can enforce compliance.

Controllers can maximize local energy consumption and reduce grid dependency.

Abstract

Algorithms and models based on game theory have nowadays become prominent techniques for the design of digital controllers for critical systems. Indeed, such techniques enable automatic synthesis: given a model of the environment and a property that the controller must enforce, those techniques automatically produce a correct controller, when it exists. In the present paper, we consider a class of concurrent, weighted, multi-player games that are well-suited to model and study the interactions of several agents who are competing for some measurable resources like energy. We prove that a subclass of those games always admit a Nash equilibrium, i.e. a situation in which all players play in such a way that they have no incentive to deviate. Moreover, the strategies yielding those Nash equilibria have a special structure: when one of the agents deviate from the equilibrium, all the others form a coalition that will enforce a retaliation mechanism that punishes the deviant agent. We apply those results to a real-life case study in which several smart houses that produce their own energy with solar panels, and can share this energy among them in micro-grid, must distribute the use of this energy along the day in order to avoid consuming electricity that must be bought from the global grid. We demonstrate that our theory allows one to synthesise an efficient controller for these houses: using penalties to be paid in the utility bill as an incentive, we force the houses to follow a pre-computed schedule that maximises the proportion of the locally produced energy that is consumed.