Peculiarities of mathematical modeling of an induction motor taking into account its nonlinearities

Abstract

The choice of the mathematical description of the induction motor has been made. Modeling of an induction motor in three-phase natural axes A, B, C is proposed, taking into account the nonlinearity of the parameters of an induction motor. The purpose of the study is aimed at improving the correspondence of the model of an induction motor to a real motor by taking into account the nonlinearities of its parameters. The mathematical model, obtained taking into account assumptions and idealization, is a system of differential, algebraic and logical equations that reflect the conditions of electrical and mechanical equilibrium and the conditions of electromechanical energy conversion. The electrical equilibrium equations are compiled according to Kirchhoff’s laws and Maxwell’s equations, and the mechanical ones – according to the d’Alembert and Lagrange equations. As state variables, the stator and rotor flux links are used, which are determined at each step of numerical integration. For the adequacy of the model in the calculations, it is necessary to take into account a number of non-linearities of the IM – the effect of current displacement and machine saturation, losses in steel, changes in operating temperature. The choice of the parameter nonlinearity to be taken into account, as well as the accounting methods, are individual and are determined by the complexity of the tasks that are set for the model. The completeness of taking into account the non-linear parameters of the IM is determined by the requirements for the accuracy of the study and necessarily provides for taking into account the most influencing the performance of the machine.