Mathematical and visual models of asynchronous electric machines energy fields

Abstract

The research considers the development of topological theory of asynchronous electric machines (AEM). The results of the development of energy aspects of the topological theory are presented in the article. The facts proving the actuality of the research are also given. The central notion giving the topological theory the characteristic of being systematic is the vector space notion. The definition of AEM vector space, its dimension, canonical basis, power and energy field of AEM are presented. Mathematical and visual models of AEM energy fields are analyzed. Energy fields of electric losses and magnetic field dissipation having the spherical symmetry are analyzed in particular. Energy and visual models of the main magnetic field are analyzed using AEM with a short circuited rotor and linear AEM as examples. It is established that this field obtains cylindrical or elliptical symmetry. In general the main magnetic field and the main matrix of winding make AEM vector space fully or partially heterogeneous. Energy efficiency is analyzed and its differences for vector space currents are revealed. The areas of vector spaces with high and low energy currents efficiency are defined. According to this indicator longitudinal and transvers subsets of current having, correspondingly, high and zero energy efficiency are distinguished in the vector space. The description of practical application spheres of AEM topological theory is given.