Authors

T.W. Stegink, C. De Persis, A.J. van der Schaft

Abstract

The gradient method is a well-known tool for solving convex optimization problems. This paper shows that the gradient method admits a Brayton-Moser and a port-Hamiltonian representation. In fact, its dynamics can be interpreted as a interconnection of multiple (port-Hamiltonian) passive systems, which plays a key role in proving asymptotic stability of the method. As an application to smart grids, this paper studies the problem of frequency regulation in power grids, while maximizing the social welfare. By applying the gradient method, we obtain a real-time dynamic pricing model in port-Hamiltonian form. By coupling with the port-Hamiltonian description of the physical network we obtain a closed-loop port-Hamiltonian system, which properties are exploited to prove asymptotic stability to the set of optimal points.

Keywords

gradient method; port-Hamiltonian; passivity; convex optimization; power networks; frequency regulation; social welfare problem; dynamic pricing.

Citation

  • Journal: IFAC-PapersOnLine
  • Year: 2015
  • Volume: 48
  • Issue: 13
  • Pages: 13–18
  • Publisher: Elsevier BV
  • DOI: 10.1016/j.ifacol.2015.10.207
  • Note: 5th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2015- Lyon, France, 4–7 July 2015

BibTeX

@article{Stegink_2015,
  title={{Port-Hamiltonian Formulation of the Gradient Method Applied to Smart Grids}},
  volume={48},
  ISSN={2405-8963},
  DOI={10.1016/j.ifacol.2015.10.207},
  number={13},
  journal={IFAC-PapersOnLine},
  publisher={Elsevier BV},
  author={Stegink, T.W. and Persis, C. De and van der Schaft, A.J.},
  year={2015},
  pages={13--18}
}

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References