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On the Generalized Gardner Problem for Phase-Locked Loops in Electrical Grids

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Abstract

Methods of nonlinear analysis and synthesis of synchronization control systems for electrical grids have been developed. The use of averaging methods and Lyapunov-type stability criteria for the cylindrical phase space have made it possible for the first time in the Gardner problem to obtain analytical estimates of the system parameters to ensure acceptable values of phase errors and to take into account changes in the reference signal amplitude.

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Notes

  1. The solution of the problem for such parameter values is used, for example, in the design of electric equipment in the Transconverter and Siemens companies.

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Funding

This work was supported by the Ministry of Science and Higher Education of the Russian Federation in the framework of the program “Advanced Digital Technologies” of St. Petersburg Polytechnic University, agreement no. 075-15-2020-934 of November 17, 2020.

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Authors and Affiliations

  1. St. Petersburg State University, St. Petersburg, Russia

    N. V. Kuznetsov, M. Yu. Lobachev, M. V. Yuldashev & R. V. Yuldashev

  2. Mechanical Engineering Research Institute, Russian Academy of Sciences, St. Petersburg, Russia

    N. V. Kuznetsov

  3. Peter the Great St. Petersburg Polytechnic University, St. Petersburg, Russia

    N. V. Kuznetsov

  4. Moscow Aviation Institute (National Research University), Moscow, Russia

    S. I. Volskiy & D. A. Sorokin

Authors
  1. N. V. Kuznetsov
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  2. M. Yu. Lobachev
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  3. M. V. Yuldashev
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  4. R. V. Yuldashev
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  5. S. I. Volskiy
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  6. D. A. Sorokin
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Corresponding author

Correspondence to N. V. Kuznetsov.

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Translated by I. Ruzanova

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Kuznetsov, N.V., Lobachev, M.Y., Yuldashev, M.V. et al. On the Generalized Gardner Problem for Phase-Locked Loops in Electrical Grids. Dokl. Math. 103, 157–161 (2021). https://doi.org/10.1134/S1064562421030108

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  • DOI: https://doi.org/10.1134/S1064562421030108

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