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Multi-Resolution Large Population Stochastic Differential Games and Their Application to Demand Response Management in the Smart Grid

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Abstract

Dynamic demand response (DR) management is becoming an integral part of power system and market operational practice. Motivated by the smart grid DR management problem, we propose a multi-resolution stochastic differential game-theoretic framework to model the players’ intra-group and inter-group interactions in a large population regime. We study the game in both risk-neutral and risk-sensitive settings, and provide closed-form solutions for symmetric mean-field responses in the case of homogeneous group populations, and characterize the symmetric mean-field Nash equilibrium using the Hamilton–Jacobi–Bellman (HJB) equation together with the Fokker–Planck–Kolmogorov (FPK) equation. Finally, we apply the framework to the smart grid DR management problem and illustrate with a numerical example.

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Notes

  1. Allowing the demand to take negative values captures the possibility of the scenario that users can act as a power supplier in the smart grid, that is, they can generate their own energy from renewable sources. Users can sell their excess energy when energy generated exceeds the load of the users while they can also buy energy from the market if their load exceeds self-generated energy. Hence, \(d_{i}^{k}\) here captures this effect and users would want to sell excess energy when \(d_{i}^{k}\) becomes negative. A detailed discussion of this can be found in [27].

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Acknowledgements

This is an expanded revised version of a paper that was presented at the International Conference on Network Games, Control, and Optimization (NetGCOOP 2011), Oct. 12–14, 2011; Paris, France.

The research was partially supported by an AFSOR MURI Grant (FA9550-10-1-0573).

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Authors and Affiliations

  1. Coordinated Science Laboratory and the Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, 1308 West Main Street, Urbana, IL, 61801, USA

    Quanyan Zhu & Tamer Başar

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  1. Quanyan Zhu
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  2. Tamer Başar
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Correspondence to Quanyan Zhu.

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Zhu, Q., Başar, T. Multi-Resolution Large Population Stochastic Differential Games and Their Application to Demand Response Management in the Smart Grid. Dyn Games Appl 3, 68–88 (2013). https://doi.org/10.1007/s13235-013-0072-0

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