Bagagiolo, F. and Bauso, D. (2014) Mean-Field Games and Dynamic Demand Management in Power Grids. Dynamic Games and Applications, 4 (2). 155 - 176. ISSN 2153-0785
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 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. © 2013 Springer Science+Business Media New York.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © Springer Science+Business Media New York 2013. This is an author produced version of a paper subsequently published in Dynamic Games and Applications. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Mean field games; Dynamic demand management; Viscosity solutions; Distributional solutions |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Automatic Control and Systems Engineering (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 08 Oct 2015 15:25 |
Last Modified: | 24 Mar 2018 20:19 |
Published Version: | http://dx.doi.org/10.1007/s13235-013-0097-4 |
Status: | Published |
Publisher: | Springer Verlag |
Refereed: | Yes |
Identification Number: | 10.1007/s13235-013-0097-4 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:89664 |