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Control of HVDC Transmission Systems: From Theory to Practice and Back

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Mathematical Control Theory I

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 461))

Abstract

The problem of modeling and control of multi-terminal high-voltage direct-current transmission systems is addressed in this chapter, which contains three main contributions. First, to propose a unified, physically motivated, modeling framework—based on port-Hamiltonian systems representations—of the various network topologies used in this application. Second, to prove that the system can be globally asymptotically stabilized with a decentralized PI control that exploits its passivity properties. Close connections between the proposed PI and the popular Akagi’s PQ instantaneous power method are also established. Third, to reveal the transient performance limitations of the proposed controller that, interestingly, is shown to be intrinsic to PI passivity-based control. The performances of the controller are verified via simulations on a three-terminal benchmark example.

This work is dedicated to Arjan van der Schaft, excellent teacher and dearest friend.

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Notes

  1. 1.

    A directed graph is an ordered 3-tuple, \(\mathcal {G}=\{\mathcal {\mathcal V,\mathcal E},\varPi \}\), consisting of a finite set of nodes \(\mathcal {V}\), a finite set of directed edges \(\mathcal {E}\) and a mapping \(\varPi \) from \(\mathcal {E}\) to the set of ordered pairs of \(\mathcal {V}\), where no self-loops are allowed.

  2. 2.

    Synchronized operation of the VSRs is usually achieved via robust phase-locked-loop detection of the latching frequencies [35].

  3. 3.

    Unless indicated otherwise all physical parameters of the system are positive constants.

  4. 4.

    For ease of presentation we restrict the discussion here to a single VSR. The extension to multiple VSRs being straightforward.

  5. 5.

    This well-known phenomenon of nonlinear systems [16] is akin to cancellation of unstable zeros of the plant with the unstable poles of the controller in linear systems.

  6. 6.

    This discussion pertains only to the behavior of the adopted mathematical model of the VSR. In practice, other dynamical phenomena and unmodeled effects may trigger instability even for the PI–PBC.

  7. 7.

    With some abuse of notation, the zero dynamics is represented using the same symbols of the system dynamics.

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Acknowledgments

This work was supported by the Ministry of Education and Science of Russian Federation (Project 14.Z50.31.0031), Alstom Grid and partially supported by the iCODE institute, research project of the Idex Paris-Saclay.

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Authors and Affiliations

  1. Laboratoire des Signaux et Systèmes, 3, rue Joliot Curie, 91192, Gif-sur-Yvette, France

    Daniele Zonetti & Romeo Ortega

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  1. Daniele Zonetti
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  2. Romeo Ortega
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Correspondence to Daniele Zonetti .

Editor information

Editors and Affiliations

  1. Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen, Groningen, The Netherlands

    M. Kanat Camlibel

  2. Department of Electrical, Computer and Systems Engineering, Rensselaer Polytechnic Institute, Troy, New York, USA

    A. Agung Julius

  3. Department of Electrical Engineering, Indian Institute of Technology, Chennai, Tamil Nadu, India

    Ramkrishna Pasumarthy

  4. Engineering and Technology Institute Groningen, University of Groningen, Groningen, The Netherlands

    Jacquelien M.A. Scherpen

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Zonetti, D., Ortega, R. (2015). Control of HVDC Transmission Systems: From Theory to Practice and Back. In: Camlibel, M., Julius, A., Pasumarthy, R., Scherpen, J. (eds) Mathematical Control Theory I. Lecture Notes in Control and Information Sciences, vol 461. Springer, Cham. https://doi.org/10.1007/978-3-319-20988-3_9

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  • DOI: https://doi.org/10.1007/978-3-319-20988-3_9

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  • Online ISBN: 978-3-319-20988-3

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