Two-Dimensional Fourier-Based Modeling of Electric Machines—An Overview

An increasing need for fast and reliable models has led to a continuous development of Fourier-based (FB) analytical modeling. This paper presents an overview of the techniques that are currently available in FB modeling for electric machines. By coupling that overview to the most relevant literature related to the subject, an interesting starting point is provided for anyone who wants to use or improve FB models. The following seven aspects of FB models are discussed in detail: 1) the magnetic potential (scalar or vector potential); 2) the coordinate system and the solution of the partial-differential equations for each magnetic potential and for each coordinate system; 3) the way in which time dependence is accounted for; 4) the implementation of the source terms; 5) the possibilities to account for slotted structures; 6) the modeling of eccentricity; and 7) the post-processing computation of physical quantities, such as flux density, electromotive force, torque, losses, and eddy currents in conductive objects. Furthermore, this paper gives the closed form solution of the Laplace, Poisson, and Helmholtz equations in each coordinate system. In addition, this paper tackles other important features of FB models such as computational time reduction and coupling the machine model to an electric circuit.