Abstract
This tutorial paper presents the mathematics behind the widely observed air-gap field modulation phenomena in electrical machines and derives the duality between electrical machines and switching converters. A bibliometric analysis of the existing research on various machine types is presented to show the historical development of electrical machines from the perspective of the number of publications, showing the necessity and urgency of unifying the analysis of operating principles/torque production mechanisms before the development of the general air-gap field modulation theory in 2017. The theoretical framework and its applications are reviewed. Detailed examples of how to use the developed theory to analyze the operating principle/torque production, conduct the quantitative analysis of parameters and basic performance, and make innovations from topologies of typical electrical machines are also included for verification as well as self-study.
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