The Mathematical Models of a Saturated Induction Machine in Polar Coordinates
Abstract
This study is aimed at filling a certain gap in the mathematical modeling of steady-state and transient processes in induction machines. A set of mathematical models written in polar coordinates that take into account the machine main magnetic circuit saturation is proposed. For solving the formulated problems, methods of the complex variable theory were used. The proposed mathematical models were implemented by means of software, and the processes simulated using them were investigated in the MATLAB computation environment (using the SIMULINKpackage of application computer programs). Two versions of induction machine mathematical models written in polar coordinates are presented, which take into account saturation of the main magnetic circuit and differ from each other in the set of machine state variables. The specific features of implementing such models by means of software are determined. It has been found that these models describe the processes in an induction machine in the working part of its mechanical characteristic with sufficient accuracy. It is shown that the mathematical models written in polar coordinates simulate the processes in an induction machine on the whole with the same accuracy as the widely used similar models written in the Cartesian coordinates. At the same time, by using the models written in polar coordinates, it is possible to observe induction machine state variables that cannot be observed in the case of using the mathematical models written in the Cartesian coordinates.
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