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The large increase in wind generation could improve the final development of wind systems with brushless doubly-fed induction machines (BDFIM) as an alternative to the doubly-fed asynchronous machines. For this reason, a detailed study of several aspects of the BDFIM design, as well as of its rotor configuration, is absolutely essential. In this paper, the authors present an alternative formulation of the BDFIM operating principle in synchronous mode. Besides the basic equation of the machine operation, it presents as main advantage the precise characterization of all the magnetic field components in a BDFIM with idealized stator windings and an idealized rotor cage. Based on this formulation, the paper provides a standard that may be used to compare the fields created by different real BDFIMs. This standard has been validated by laboratory tests.