Mathematical model of an induction machine with consideration of saturation and heating

Abstract

The article discusses the methodology of development of a mathematical model of an asynchronous electric motor. The analysis of some disadvantages of such models, based on an equivalent T-shaped circuit scheme, is carried out. Among these are not always applicable interface variables (input signals), as well as neglect for core magnetization and losses in steel. Dealing with these drawbacks significantly expands the application area of the models considered allowing, in particular, to use them in asynchronous drive control systems based on a sensorless control method. This approach includes no physical sensors of temperature and rotor speed, the signals from which are calculated by indirect parameters. In this regard, it is necessary to take into account nonlinear processes, which increases the accuracy of the calculation. It is shown that among the existing methods of considering of the magnetization, the method of static inductances is preferable. It represents the mutual inductance between the stator and the rotor as a dependency on magnetizing current. The introduction of this dependence will not make the model nonlinear, but it gives a more correct calculation with a minimum of additional parameters. At the same time, losses in steel are accounted for by introducing an active resistance in parallel to the magnetization circuit. This paper provides a detailed description of the development of the model with a theoretical justification for the use of certain assumptions and equations. The input variables of the model are limited by three phase voltages, the speed of rotation of the rotor and the temperature of the outside air. This set can be considered the minimum necessary for using the model as part of a frequency asynchronous drive control system. Such control systems are most sensitive to the resistance of the stator winding of the electric motor. Therefore, a method for calculating its temperature is proposed based on a two-mass model that considers an electric motor in the form of two parts: windings and a core with a casing. At the end of the work, the calculation of the parameters of the equivalent substitution circuit is given on the example of a specific electric motor with the results of its modeling.