Winding Inductance Estimations in Air-Cored Resonant Induction Machines

In air-cored machines, there is no magnetic core so the fields produced by the windings are truly 3D in nature, and therefore the end parts of the winding contribute to the torque production. As a result, in the electromagnetic modelling of air-cored machines, the 3D inductance calculations become a key problem. This paper proposes a general and computationally-fast method to calculate the 3D winding inductances in air-cored induction machines. The phase winding self and mutual inductances are derived by collecting the contributions from the coil self and coil-to-coil mutual inductances which in turn are calculated by breaking down the real coils into straight segments and using closed-form expressions. Expressions for three-phase self and magnetizing inductances used in the equivalent circuit are also presented. Good approximations of the calculated results are confirmed in the validation against 3D finite element analysis.