On the General Theory for Analysis of Subharmonic Oscillations in Three-Phase Ferroresonance Circuits and Systems

  • Muhtarhan IBADULLAEV
  • Akrom N. TOVBAEV
  • Azamat Zh. ESENBEKOV
DOI: https://doi.org/10.24160/0013-5380-2021-12-35-44
Keywords: ferroresonance, self-oscillations, subharmonic, subharmonic oscillations, approximation, small parameters, ferromagnetic element

Abstract

The general theory for analysis of subharmonic oscillations at a frequency of ω/3 in three-phase ferroresonance circuits is presented. The occurrence and existence of ferroresonance oscillations at subharmonic frequencies in power transmission lines and power supply systems is highly undesirable, since they cause overvoltages at various frequencies. At the same time, there is an extensive class of nonlinear electrical circuits in which the excitation of autoparametric oscillations at the frequency of subharmonics forms the basis of phase-discrete frequency converting devices serving as secondary power sources. To study the regularities of excitation and maintaining of subharmonic oscillations at a frequency of ω/3 in three-phase ferroresonance circuits, theoretical and experimental studies of an equivalent model of a three-phase circuit with nonlinear inductance were carried out. A generalized nonlinear differential equation for a three-phase circuit with mixed connection of its elements is derived. The steady-state mode of subharmonic oscillations at a frequency of ω/3 is analyzed using the small parameter (averaging) method, which made it possible to determine their existence domains and circuit critical parameters. A mathematical model and algorithm for calculating autoparametric oscillations have been developed to study the subharmonic oscillation excitation processes at a frequency of ω/3 in three-phase ferroresonance circuits depending on the initial conditions, circuit parameters and input voltage. The theoretical study results have been confirmed experimentally.

Author Biographies

Muhtarhan IBADULLAEV

(Tashkent State Technical University named after Islam Karimov, Tashkent, Uzbekistan) – Professor of the Electrical Engineering Dept., Dr. Sci. (Eng.)

Akrom N. TOVBAEV

(Navoi State Mining Institute, Navoi, Uzbekistan) – Docent of the Electric Power Engineering Dept., Cand. Sci. (Eng.)

Azamat Zh. ESENBEKOV

(Karakalpak State University, Nukus, Uzbekistan) – Senior Lecturer of the Electric Power Engineering Dept

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Published
2021-06-10
Issue
No 12 (2021): Issue № 12
Section
Article