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Background: The paper analyses symmetrical three-phase circuits of sinusoidal current with induction motors and considers an equivalent machine with a stationary rotor, where the stator and rotor currents are changed at the same frequency. If the circuit becomes assymetrical, the voltage at the induction motor terminals is determined by the currents of all branches of the stator and rotor. In this case, the determination of the elements of the complex resistance matrix of a rotating machine becomes problematic and can only be performed based on magnetic field in the core. This is one of the main reasons why the method of symmetric components is still applied to the calculation of asymmetric operation modes of three-phase circuits. All this makes it an urgent problem to find theoretical approaches to determining, with small computational costs, the complex resistances matrix elements of an induction motor in any symmetric or asymmetric modes, taking into account the discreteness and unbalance of the structure of windings, induced currents and mutual displacement of serrated cores. Materials and methods: The study is based on the method of tooth contours (or the so-called universal method), which is currently one of the most effective and universal methods for analyzing fields and processes of rotating electrical machines. Results: By employing a unified symbolic method we have developed a mathematical model for calculating steady-state modes of rotating induction motors, in which the flux-coupling and stator and rotor branch currents change with different frequencies over time. The model allows investigating three-phase circuits containing induction machines in both symmetrical and any asymmetrical, including emergency, conditions. Conclusion: The proposed model allows modelling any symmetrical and asymmetrical modes of circuits with rotating induction machines by a symbolic method.

Application of a symbolic method to calculating circuits with rotating induction motors