A methodology for researching asymmetric modes of synchronous machines based on the Volterra integral equations of the second kind
In industry, the solution to many problems is directly related to the development and research of synchronous machines, which operate into a rectifier (asymmetric) load. Transients, which are described by a system of nonlinear differential equations in synchronous machines, play a fundamental role in it. In the study of synchronous machines, it suffices to consider electromagnetic transients due to the large inertial constant of the machine. The equations become linear, but with periodic coefficients, which also do not have a common solution, since they contain periodic coefficients. The possibilities for the practical application of such equations are generally limited by the difficulties associated with the determination of eigenvalues. In this work, we apply the transformation of differential equations with periodic coefficients to equations with constant coefficients based on the representation of a system with periodic coefficients by the Volterra matrix integral equation of the second kind. The consideration is carried out by the example of a three-phase magnetoelectric generator operating on an active-inductive load. Based on a comparison with the classical theory of systems with periodic coefficients, the article established that the constant matrix B is not strictly defined in the considered method. The proposed modeling method allows us to study both symmetric and asymmetric transients in synchronous machines. The method does not have a limitation associated with the sinusoidal spatial distribution of the magnetic driving force of the synchronous machine windings and can be applied taking into account the higher harmonics of the inductances of synchronous machines.