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Optimization and Stabilization of Hierarchical Electrical Networks

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Mathematical Modeling, Simulation and Optimization for Power Engineering and Management

Part of the book series: Mathematics in Industry ((MATHINDUSTRY,volume 34))

Abstract

Triggered by the increasing number of renewable energy sources, the German electricity grid is undergoing a fundamental change from mono to bidirectional power flow. This paradigm shift confronts grid operators with new problems but also new opportunities. In this chapter we point out some of these problems arising on different layers of the grid hierarchy and sketch mathematical methods to handle them. While the transmission system operator’s main concern is stability and security of the system in case of contingencies, the distribution system operator aims to exploit inherent flexibilities. We identify possible interconnections among the layers to make the flexibility from the distribution grid available within the whole network. Our presented approaches include: the distributed control of energy storage devices on a residential level; transient stability analysis via a new set-based approach; a new clustering-based model-order reduction technique; and a modeling framework for the power flow problem on the transmission level which incorporates new grid technologies.

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Acknowledgements

The authors collaborate within the project KONSENS: Konsistente Optimierung uNd Stabilisierung Elektrischer NetzwerkSysteme funded by the German Federal Ministry of Education and Research (BMBF, grants 05M18OCA, 05M18SIA, and 05M18EVA).

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Authors and Affiliations

  1. Automatic Control and System Dynamics Laboratory, Technische Universität Chemnitz, Chemnitz, Germany

    Tim Aschenbruck, Willem Esterhuizen & Stefan Streif

  2. Faculty of Mathematics, Technische Universität Chemnitz, Chemnitz, Germany

    Bartosz Filipecki & Christoph Helmberg

  3. Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany

    Manuel Baumann, Sara Grundel & Tobias K. S. Ritschel

  4. Faculty of Mathematics and Natural Sciences, Technische Universität Ilmenau, Ilmenau, Germany

    Philipp Sauerteig & Karl Worthmann

Authors
  1. Tim Aschenbruck
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  2. Manuel Baumann
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  3. Willem Esterhuizen
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  4. Bartosz Filipecki
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  5. Sara Grundel
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  6. Christoph Helmberg
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  7. Tobias K. S. Ritschel
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  8. Philipp Sauerteig
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  9. Stefan Streif
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  10. Karl Worthmann
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Corresponding author

Correspondence to Bartosz Filipecki .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Scientific Computing Research Group, University of Mannheim, Mannheim, Germany

    Simone Göttlich

  2. Department of Mathematics, Group Continuous Optimization, RWTH Aachen University, Aachen, Nordrhein-Westfalen, Germany

    Michael Herty

  3. Computing Centre (URZ), Unit Technology Transfer and Cooperation, Heidelberg University, Heidelberg, Germany

    Anja Milde

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Aschenbruck, T. et al. (2021). Optimization and Stabilization of Hierarchical Electrical Networks. In: Göttlich, S., Herty, M., Milde, A. (eds) Mathematical Modeling, Simulation and Optimization for Power Engineering and Management. Mathematics in Industry, vol 34. Springer, Cham. https://doi.org/10.1007/978-3-030-62732-4_8

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