It is known that the occurrence and existence of ferroresonant oscillations at the subharmonic frequency (SHC) in power transmission lines (TL) and in power supply systems is extremely undesirable, since they cause ferroresonant overvoltages at different frequencies. At the same time, there is a wide class of nonlinear electrical circuits, in which the excitation of autoparametric oscillations (AIC) at the frequency of the SHC forms the basis of frequency converting devices serving as secondary power sources. It is shown that three-phase nonlinear systems are in one way or another equivalent circuits for power transmission lines, the main elements of which are: longitudinal compensation capacitors, transverse compensation reactors, and transformers with a nonlinear characteristic. To study the regularities of the excitation and maintenance of SHC at a frequency in three-phase electro-ferromagnetic circuits (EFMC), theoretical and experimental studies of an equivalent model of a three-phase circuit with nonlinear inductance were carried out. For the analysis of the steady-state mode of the SHC at the frequency, the method of a small parameter (averaging) was applied. A shortened differential equation of motion for a three-phase nonlinear circuit is obtained. By solving them, the regions of existence of the SHC and the critical parameters of the chain were determined. The obtained results of theoretical research are confirmed by experimental studies.

It is known that the occurrence and existence of autoparametric oscillations (AIC) at the subharmonic frequency (GHC) in power lines (power lines) and in power supply systems is extremely undesirable, since they cause ferroresonant overvoltages at different frequencies. At the same time, there is an extensive class of nonlinear electric circuits in which the excitation of the AIC at the frequency of the SGC forms the basis of frequency-converting devices serving as secondary power sources. It is shown that single-phase-three-phase nonlinear systems are, to one degree or another, equivalent circuits of power lines, the main elements of which are: longitudinal compensation capacitors, transverse compensation reactors, and transformers with non-linear characteristics. The regularities of the excitation of the GCC at the frequency (ω / 3) of the power lines were studied, theoretical and experimental studies of the equivalent model of single-phase-three-phase circuits with nonlinear inductance were carried out. For a theoretical analysis of the steady-state mode of SGK at a frequency (ω / 3) with inductive coupling, the frequency- energy approach is used. The conditions of existence and critical parameters of the circuit are determined, and the mechanism of the appearance of the SGC at the frequency (ω / 3) is also studied.

In the theory of nonlinear electrical circuits, the analysis of physical processes occurring in three-phase Ferroresonant circuits during excitation of subharmonic oscillations (SHO) of the second order is of particular importance in the design and creation of various converter devices. From the point of view of creating multi-phase secondary power sources (phase-discrete devices, frequency dividers, switching elements, automation and relay protection devices, etc.), the study of second-order SHO excitation in three-phase Ferro resonant circuits with bias is of greatest interest. The article deals with the excitation of second-order subharmonic oscillations in three-phase self-oscillatory circuits with common magnetic circuits with a bias winding. Shortened equations are derived using the averaging method with appropriate phases. From the condition for the existence of a periodic solution, the phase and amplitude relationships of the excited oscillations are determined, which are different from three-phase circuits with a separate ferromagnetic element. In the steady state, the conditions of excitation, the region of existence are determined depending on the parameters of the circuit, the bias current and the applied action. The stability of the solution of the original system of nonlinear differential equations of the second order is also studied by analyzing the roots of the characteristic equation by a qualitative method. Numerical realization of the initial considered system of equations described, self-oscillatory processes is given.

This article considers the mode of excitation of sub harmonic oscillations of the third order in a three-phase circuit consisting of active, capacitive and inductive elements having a common magnetic bond, which are analogous to the power line "line -unloaded transformer".Equations of motion are derived from the method of averaging with the corresponding phases.From the condition of the existence of the periodic solution, phase relations are determined that are different from the phase ratios for three-phase circuits with group Ferro magnetic elements. In the stationary mode, the conditions of excitation, the scope of existence, the dependence of the output values on the parameters of the circuit and the applied effect are determined.

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