Study of eccentric round-rotor synchronous machines through conformal mapping. Part I: Inductances and air-gap field

The study of electric machines subject to rotor eccentricity is usually performed using a winding and permeance function approach. In this paper, an alternative method is investigated based on conformal mapping. The geometry of a an eccentric round-rotor machine is mapped into a uniform air-gap topology by means of Moebius conformal map. The mathematical details of the method are provided along with explicit formulas to compute the air-gap field and inductances of the eccentric machine. It shown how, unlike conventional winding-function theory, the proposed method yields closed-form formulas which do not involve series expansions nor require numerical integrations and are thus particularly fit for implementation into fast simulation programs. Such expressions are assessed by comparison with Finite Element Analysis (FEA).