| Abstrakt: |
Currently, despite the abundance of publications on subharmonic oscillations in three-phase circuits, the processes in them are illuminated based on purely experimental data, and theoretical analysis bas been carried out for the single-phase analogue of a three-phase circuit, distorting the quantitative and qualitative aspects of the process. This is due to the solution of nonlinear systems of inhomogeneous differential equations, the right-band side of which bas fixed phase shifts. These equations describe nonlinear three-phase systems. On the other hand, in all published works, subharmonic oscillations have been studied in three-phase circuits without ferromagnetic coupling between phases. The issues of exciting such oscillations in three-phase circuits with a three-phase ferromagnetic element with magnetic coupling between phases have not been sufficiently studied to date. This article discusses the excitation mode of third-order subharmonic oscillations in a three-phase circuit consisting of active, capacitive, and inductive elements with common magnetic linkage, which is an analogue of a transmission line with an unloaded transformer. The equation of motion is derived. Using the averaging method with corresponding phases, shortened equations are obtained. From the condition of the existence of a periodic solution, phase relationships are determined, different from phase relationships for three-phase circuits with group ferromagnetic elements. In the steady-state mode, conditions for excitation, existence regions, dependencies of output parameters on circuit parameters and applied influence are determined. [ABSTRACT FROM AUTHOR] |
