Mean-Field Games and Dynamic Demand Management in Power Grids

Abstract

This paper applies mean field game theory to dynamic demand management. For a large population of electrical heating or cooling appliances (called agents), we provide a mean field game that guarantees desynchronization of the agents thus improving the power network resilience. Second, for the game at hand, we exhibit a mean field equilibrium, where each agent adopts a bang-bang switching control with threshold placed at a nominal temperature. At the equilibrium, through an opportune design of the terminal penalty, the switching control regulates the mean temperature (computed over the population) and the mains frequency around the nominal value. To overcome Zeno phenomena we also adjust the bang-bang control by introducing a thermostat. Third, we show that the equilibrium is stable in the sense that all agents' states, initially at different values, converge to the equilibrium value or remain confined within a given interval for an opportune initial distribution.

Mean-field games and two-point boundary value problems

“…In essence, by using tools from differential game theory, mathematical physics, and H ∞ -optimal control, mean-field dynamical games provide a modeling framework that allows to study the interaction between a mass of players and each individual. Such problems arise in several application domains such as economics, physics, biology, and network engineering, to mention a few [3], [4], [7], [12], [14], [17], [20], [23]. T Obtaining the solution of a mean-field game boils down to solving a system of two coupled partial differential equations (PDEs), namely the Hamilton-Jacobi-Bellman (HJB) equation and the Fokker-Planck-Kolmogorov (FPK) equation, which describes the density of the players [18], [22].…”

Game Theoretic Decentralized Feedback Controls in Markov Jump Processes

“…Decision problems with mean-field coupling terms have also been formalized and studied in [21], and application to power grid management are recently provided in [22]. The literature provides explicit solutions in the case of linear quadratic structure.…”

Mean field game based control of dispersed energy storage devices with constrained inputs

“…However, the cited literature does not consider constraints on control inputs when deriving optimal control laws. In contrast, [Bagagiolo et Bauso, 2013] and [Grammatico et al, 2015] study controls of the power demands of a large number of home appliances under an MFG framework, in the presence of saturated controls. A chattering switching control is implemented in [Bagagiolo et Bauso, 2013], and at equilibrium the mean temperature and the main frequency are regulated at the desired values.…”