Research of Ferr-Resonance Oscillations at the Frequency of Subharmonics in Three-Phase Non-Linear Electric Circuits and Systems

Abstract

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.

Keywords

• ferroresonance
• self-oscillation
• subharmonic
• approximation
• lowest harmonic
• small parameters
• ferromagnetic element