An accurate fourier-series expansion for round-rotor electric machine permeance function including large eccentricity effects

One of the key tasks in the modeling of electric machines is the analytical expression of self and mutual phase inductances as a function of the rotor position. Winding and permeance functions are a powerful tool for this purpose. This paper investigates the expression of the air-gap permeance function for a round rotor machine subject to pronounced eccentricity. An expression is sought in the form of a Fourier series expansion in order to make it suitable for modeling purposes. Although derived through non trivial algebraic passages, the final expression proposed is proved to be accurate and computationally efficient as the theoretically infinite sums involved in it exhibit a very rapid convergence to their asymptotical values.