Background. When analyzing symmetrical three-phase circuits of sinusoidal current, the equation of the connection between complex phase voltages and current in the transformer windings is represented as Ohm's law, while the value of the complex impedance of all phases of the nominal mode can be determined from the transformer nameplate data. In the case of symmetry breaking, the voltages and currents of transformer branches will be connected by matrix equations. In this case, the determination of the complex impedance matrix elements of transformer branches becomes problematic and can only be performed if the magnetic system parameters are taken into account. This is one of the reasons for applying the method of symmetrical components to calculating the asymmetric modes of circuits with power transformers. However, this method is only applicable to linear systems, which makes it scientifically relevant to find theoretical approaches to the determination of complex impedance matrix elements of transformers in any asymmetric modes, taking into account magnetic circuit saturation, hysteresis and eddy current losses in steel, and windings asymmetry.
Materials and methods. The research is founded on the symbolic method of analysis of branched electric and nonlinear magnetic circuits using the concept of complex magnetic permeability and matrix methods based on complete three-phase equivalent circuits of network objects.
Results. A mathematical model has been developed for analyzing nonlinear circuits with power transformers taking into account changes in their parameters in asymmetric operating modes.
Conclusion. The proposed model allows calculating transformer asymmetric operation modes accounting for the discreteness and asymmetry of the winding structure, magnetic circuit saturation, and hysteresis and eddy current losses in steel, as well as the influence of technological factors in symmetrical and asymmetrical operation modes without using the method of symmetrical components. The proposed algorithms can be used to simulate asymmetric and emergency operation modes of power systems containing a large number of transformers, which is a prerequisite for the development of intelligent power networks with active-adaptive connections.