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Multi-Grid Schemes for Multi-Scale Coordination of Energy Systems

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Book cover Energy Markets and Responsive Grids

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 162))

Abstract

We discuss how multi-grid computing schemes can be used to design hierarchical coordination architectures for energy systems. These hierarchical architectures can be used to manage multiple temporal and spatial scales and mitigate fundamental limitations of centralized and decentralized architectures. We present the basic elements of a multi-grid scheme, which includes a smoothing operator (a high-resolution decentralized coordination layer that targets phenomena at high frequencies) and a coarsening operator (a low-resolution centralized coordination layer that targets phenomena at low frequencies). For smoothing, we extend existing convergence results for Gauss-Seidel schemes by applying them to systems that cover unstructured domains. This allows us to target problems with multiple timescales and arbitrary networks. The proposed coordination schemes can be used to guide transactions in decentralized electricity markets. We present a storage control example and a power flow diffusion example to illustrate the developments.

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Acknowledgements

We acknowledge funding from the National Science Foundation under award NSF-EECS-1609183.

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Authors and Affiliations

  1. Department of Chemical and Biological Engineering, University of Wisconsin-Madison, 1415 Engineering Dr, Madison, WI, 53706, USA

    Sungho Shin & Victor M. Zavala

Authors
  1. Sungho Shin
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  2. Victor M. Zavala
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Corresponding author

Correspondence to Victor M. Zavala .

Editor information

Editors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Florida, Gainesville, Florida, USA

    Sean Meyn

  2. Technological Leadership Institute, University of Minnesota, Minneapolis, Minnesota, USA

    Tariq Samad

  3. Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, Michigan, USA

    Ian Hiskens

  4. Department of Electronic Systems, Aalborg University, Aalborg, Denmark

    Jakob Stoustrup

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Shin, S., Zavala, V.M. (2018). Multi-Grid Schemes for Multi-Scale Coordination of Energy Systems. In: Meyn, S., Samad, T., Hiskens, I., Stoustrup, J. (eds) Energy Markets and Responsive Grids. The IMA Volumes in Mathematics and its Applications, vol 162. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-7822-9_9

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