Calculation of a six-phase linear electric circuit by the method of symmetrical components

Abstract

At industrial facilities many problems are associated with synchronous machines that determine the rectifier (unbalanced) load. Transient processes play a fundamental role in them, which are described by a system of nonlinear differential equations in synchronous machines. When studying synchronous machines, it is enough to consider electromagnetic transient processes due to the large inertial constant of the machine. The equations become linear, but with periodic coefficients that also do not have a general solution, since they contain periodic coefficients. The practical applicability of these equations is generally limited by the difficulties associated with determining the eigenvalues. The work uses the method of symmetrical components, which is the main method for calculating asymmetric steady-state modes of linear three-phase (multiphase) circuits containing rotating machines as a source of electrical energy or load. The research is carried out on the example of a six-phase circuit with an unbalanced load. In the considered method, on the basis of Kirchhoff’s laws, a system of equations is drawn up, in which asymmetric systems of variables acting in a linear polyphaser circuit are replaced by symmetric systems, three of which are symmetric systems of direct, reverse and zero sequences. For each of the sequences, the parameters of the electrical circuit (for example, electrical machines) are determined experimentally or by calculation. The system of equations transformed taking into account these parameters is solved with respect to the unknown symmetric components of the variables (currents and voltages). Valid asymmetric currents and voltages are found by the superposition method as vector sums of the corresponding symmetric components of each phase.