Electromagnetic modeling of wound rotor induction motors using conformal mappings

Accurate modeling of slotted air-gap electric machines, which has slots on both sides of air-gap, is the main problem which is being addressed in this paper. To this end, conformal mapping (CM) method is presented in this paper for electromagnetic modeling the wound rotor induction motors (WRIM). The CM method can accurately consider the real pathes of flux tubes in the slotted air-gap by using the calculation of air-gap complex permeance. The air-gap complex permeance is really the complex transform function between the slotted air-gap in the physical domain and the slotless air-gap in the canonical domain. In CM method, first of all, the physical slotless air-gap including equivalent line currents is conformally mapped into the canonical slotless domain. Secondly, the air-gap magnetic field is calculated in canonical slotless domain using Hague’s solution, and mapped back into the physical slotless domain. Thirdly, the saturated relative complex permeance function is used to consider the effects of saturated slotted air-gap on the air-gap magnetic field. In final, the results obtained through CM are well verified by comparing with corresponding results obtained from finite element method (FEM) and experiment set-up in terms of accurate prediction of fundamental component and other harmonic components.