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Global stability and oscillations of dynamical systems describing synchronous electrical machines

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Abstract

A new mathematical model for a synchronous machine with strong excitation control is proposed. The limit load problem for synchronous machines is considered. The limit admissible load is estimated by the nonlocal reduction method. Criteria for the existence of circular solutions and limit cycles of the second kind for the model of a synchronous machine are obtained.

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References

  1. A. V. Ivanov-Smolenskii, Electrical Machines (Energiya, Moscow, 1980) [in Russian].

    Google Scholar 

  2. G. A. Leonov and N. V. Kondrat’eva, Analysis of Stability of AC Machines (Izd. S.-Peterburg. Univ., St. Petersburg, 2009) [in Russian].

    Google Scholar 

  3. E. A. Barbashin and V. A. Tabueva, Dynamical Systems with Cylindrical Phase Space (Nauka, Moscow, 1969) [in Russian].

    Google Scholar 

  4. A. A. Yanko-Trinitskii, A New Method for Analyzing Synchronous Motors under Abruptly Varying Loads (Gosenergoizdat, Moscow, 1958) [in Russian].

    Google Scholar 

  5. A. Kh. Gelig, G. A. Leonov, and V. A. Yakubovich, Stability of Nonlinear Systems with a Nonunique Equilibrium State (Nauka, Moscow, 1978) [in Russian].

    MATH  Google Scholar 

  6. F. Tricomi, “Sur une equation differetielle de l’electrotechnique,” C.R. Acad. Sci. Paris 193, 635–636 (1931).

    Google Scholar 

  7. F. Tricomi, “Integrazione di unequazione differenziale presentatasi in elettrotechnica,” in Annali della R. Scuola Normale Superiore di Pisa Scienze Fisiche, Matematiche (Piza, 1933), Ser. 2.

  8. M. M. Botvinnik, Excitation Control and the Static Stability of a Synchronous Machine (Gosenergoizdat, Moscow, 1950) [in Russian].

    Google Scholar 

  9. V. A. Venikov, G. R. Gertsenberg, S. A. Sovalov, and N. I. Sokolov, Strong Excitation Control (Gosenergoizdat, Moscow, 1963) [in Russian].

    Google Scholar 

  10. G. A. Leonov, I. M. Burkin, and A. I. Shepelyavyi, Frequency Methods in Oscillation Theory, Vol. 1: Multidimensional Analogues of the van der Pol Equation and Dynamical Systems with Cylindrical Phase Space (Izd. S.-Peterburg. Univ., St. Petersburg, 1992) [in Russian].

    Google Scholar 

  11. G. A. Leonov, D. V. Ponomarenko, and V. B. Smirnova, Frequency-Domain Methods for Nonlinear Analysis. Theory and Applications (World Sci., Singapore, 1996).

    MATH  Google Scholar 

  12. I. G. Petrovskii, Lectures on the Theory of Ordinary Differential Equations (Izd. Mosk. Univ., Moscow, 1984) [in Russian].

    Google Scholar 

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Authors and Affiliations

  1. St. Petersburg State University, Universitetskaya nab. 7/9, St. Petersburg, 199034, Russia

    G. A. Leonov & A. M. Zaretskiy

  2. University of Jyväskylä, Mattilanniemi 2, Jyväskylä, FI-40014, Finland

    A. M. Zaretskiy

Authors
  1. G. A. Leonov
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  2. A. M. Zaretskiy
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Correspondence to G. A. Leonov.

Additional information

Original Russian Text © G.A. Leonov, A.M. Zaretskiy, 2012, published in Vestnik Sankt-Peterburgskogo Universiteta. Seriya 1. Matematika, Mekhanika, Astronomiya, 2012, No. 4, pp. 18–27.

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Leonov, G.A., Zaretskiy, A.M. Global stability and oscillations of dynamical systems describing synchronous electrical machines. Vestnik St.Petersb. Univ.Math. 45, 157–163 (2012). https://doi.org/10.3103/S1063454112040048

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  • DOI: https://doi.org/10.3103/S1063454112040048

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