Mathematical Model of a Three-Phase Induction Machine in a Natural abc Reference Frame Utilizing the Method of Numerical Integration of Average Voltages at the Integration Step and Its Application to the Analysis of Electromechanical Systems

摘要

Recent advances in the real-time simulation of electric machines are linked with the increase in the operation speed of the numerical models retaining the calculation accuracy. We propose utilizing the method of average voltages at the integration step (AVIS) for the design of a three-phase induction machine's model in its natural abc reference frame. The method allows for avoiding rotational e.m.f. calculation at every step; in turn, the electromagnetic energy conversion is accounted by the change of flux-linkage. The model is integrated into the object-oriented environment in C++ for designing the computer models of electromechanical systems. The design of the model of an electromechanical system utilizing the proposed approach is explained in an example. The behavior of the numerical models of a three-phase IM has been compared for the set of conventional numerical methods as well as first- and second-order AVIS. It has been demonstrated that both first- and second-order AVIS methods are suitable tools for high-speed applications, namely, AVIS provides higher maximum possible integration step (e.g., first-order AVIS provides 4 times higher than the second-order Runge-Kutta method, and the second-order AVIS provides 2.5 times higher than the first-order method). Therefore, we consider the most preferable order of the AVIS method for the high-speed applications is the second order, while the first order may be a suitable alternative to increase the calculation speed by 30% with the acceptable decrease in the accuracy.