Optimal Power Flow for resistive DC Networks: a Port-Hamiltonian approach

Authors

Ernest Benedito, Dunstano del Puerto-Flores, Arnau Dòria-Cerezo, Jacquelien M.A. Scherpen

Abstract

This paper studies the optimal power flow problem for resistive DC networks. The gradient method algorithm is written in a port-Hamiltonian form and the stability of the resulting dynamics is studied. Stability conditions are provided for general cyclic networks and a solution, when these conditions fail, is proposed. In addition, the results are exemplified by means of numerical simulations.

Keywords

Optimal power flow; port-Hamiltonian systems; gradient method; DC networks; cyclic networks

Citation

• Journal: IFAC-PapersOnLine
• Year: 2017
• Volume: 50
• Issue: 1
• Pages: 25–30
• Publisher: Elsevier BV
• DOI: 10.1016/j.ifacol.2017.08.005
• Note: 20th IFAC World Congress

BibTeX

@article{Benedito_2017,
  title={{Optimal Power Flow for resistive DC Networks: a Port-Hamiltonian approach}},
  volume={50},
  ISSN={2405-8963},
  DOI={10.1016/j.ifacol.2017.08.005},
  number={1},
  journal={IFAC-PapersOnLine},
  publisher={Elsevier BV},
  author={Benedito, Ernest and Puerto-Flores, Dunstano del and Dòria-Cerezo, Arnau and Scherpen, Jacquelien M.A.},
  year={2017},
  pages={25--30}
}

Download the bib file

References

• Arrow, (1958)
• Benedito, E., del Puerto-Flores, D., Doria-Cerezo, A., van der Feltz, O. & Scherpen, J. M. A. Strictly convex loss functions for port-Hamiltonian based optimization algorithm for MTDC networks. 2016 IEEE 55th Conference on Decision and Control (CDC) 7483–7488 (2016) doi:10.1109/cdc.2016.7799425 – 10.1109/cdc.2016.7799425
• Biggs, (1974)
• Cherukuri, A. & Cortés, J. Asymptotic stability of saddle points under the saddle-point dynamics. 2015 American Control Conference (ACC) 2020–2025 (2015) doi:10.1109/acc.2015.7171030 – 10.1109/acc.2015.7171030
• Feijer, D. & Paganini, F. Stability of primal–dual gradient dynamics and applications to network optimization. Automatica vol. 46 1974–1981 (2010) – 10.1016/j.automatica.2010.08.011
• Gavriluta, C., Candela, I., Luna, A., Gomez-Exposito, A. & Rodriguez, P. Hierarchical Control of HV-MTDC Systems With Droop-Based Primary and OPF-Based Secondary. IEEE Transactions on Smart Grid vol. 6 1502–1510 (2015) – 10.1109/tsg.2014.2365854
• Rosen, A new network theorem. Journal IEE (1924)
• Stegink, T. W., Persis, C. D. & van der Schaft, A. J. Port-Hamiltonian Formulation of the Gradient Method Applied to Smart Grids. IFAC-PapersOnLine vol. 48 13–18 (2015) – 10.1016/j.ifacol.2015.10.207
• van der Schaft, A. Characterization and partial synthesis of the behavior of resistive circuits at their terminals. Systems & Control Letters vol. 59 423–428 (2010) – 10.1016/j.sysconle.2010.05.005
• Van Hertem, D. & Ghandhari, M. Multi-terminal VSC HVDC for the European supergrid: Obstacles. Renewable and Sustainable Energy Reviews vol. 14 3156–3163 (2010) – 10.1016/j.rser.2010.07.068
• Chung Wang & Tokad, Y. Polygon to Star Transformations. IRE Transactions on Circuit Theory vol. 8 489–491 (1961) – 10.1109/tct.1961.1086831
• Zhang, A real-time control framework for smart power networks: Design methodology and stability. Automatica (2015)