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On the use of conformai mapping in the analysis of electric machines

Conformal mapping is a widespread mathematical technique to approach the electromagnetic study of electric machines. In its practical application, however, it is relatively easy to incur in errors which make results unreliable. In this paper, some fundamental but possibly deceitful facts in conformal mapping application are described, focusing in particular on: energy conservation in magnetostatic and time-harmonic problems; current source assignment in the transformed domain; transformation of the flux density components through conformal mapping. The addressed topics are first investigated from a theoretical point of view; then some application examples, based on Finite Element Analysis are provided for illustration and validation purposes.