Analysis of subharmonic oscillations in three-phase Ferroresonant circuits with bias

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.