Enhancement of mathematical models for AC electromechanical converters
DOI:
https://doi.org/10.15588/1607-6761-2025-4-4Keywords:
induction motor, resulting vector, mathematical models, polar coordinates, rotational speedAbstract
Purpose. Development of mathematical models of electromechanical AC converters invariant to the speed of rotation of the coordinate system using as state variables of electromechanical converters the modules of the resulting vectors of three-phase variables and their phase shifts relative to each other for the development of new structures of automated asynchronous electric drives.
Methodology. Mathematical modeling methods for electromechanical systems, numerical methods for solving systems of first-order differential equations for the development of mathematical models of AC electromechanical converters invariant to the rotational speed of the coordinate system.
Findings. The reviewed mathematical models of electromechanical converters made it possible to reproduce their steady-state and dynamic processes with the same accuracy as models in Cartesian coordinates. The use of phase shifts of the resulting vectors relative to each other as state variables for the electromechanical converter allowed for the derivation of mathematical models in which all variables are limited in magnitude and have constant values in the steady-state mode, regardless of the coordinate system's rotational speed. Studies performed using the proposed models indicate that the vector and circular diagrams, which are traditionally used for analyzing the steady-state modes of electromechanical converters, characterize the angular position of some vector variables with an accuracy of a multiple of 2πK.
Originality. The proposed mathematical model of AC electromechanical converters is invariant to the rotational speed of the coordinate system, which allows the use of the modules of the resulting vectors of three-phase variables and their phase shifts relative to each other as state variables of electromechanical converters.
Practical value. The proposed mathematical models make it possible to obtain the amplitude values of the vector variables, their angular position relative to one another, instantaneous cosφ values (and so on), without additional calculations.
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