A Fast 3-D Winding Inductance Estimation Method for Air-Cored Resonant Induction Machines

The air-cored resonant induction machine removes the magnetic core, so the fields produced by the windings are truly 3-D in nature. The end-windings normally regarded as a nonactive and leakage source in conventional iron-cored machines now become an active part and contribute to the torque production. Therefore, the electromagnetic modeling can no longer be reduced to a 2-D analysis, and the 3-D inductance calculation becomes a key problem. The 3-D finite element analysis (FEA) can solve the 3-D magnetic field, but, first, the validity of its solution depends on the precision in geometry modeling. In particular, representing the end-winding region avoiding conductor clashing can be very complicated. Second, 3-D FEA solutions are computationally slow, and therefore inefficient as an "internal routine" of an optimization procedure. This article proposes a fast analytic 3-D winding inductance estimation method for air-cored resonant induction machines. The approach breaks down the real coils into straight conductors and represents them by single filaments located at their centers, then uses closed-form expressions derived from Neumann integrals to calculate the coil self and coil-to-coil mutual inductances, which are then collected into winding phase self and mutual inductances. All the independent coil-pair contributions are isolated, so as to eliminate redundant calculations. Good accuracy of the calculated results is confirmed by validation against both 3-D FEA and experimental results, including winding inductance breakdown and overall machine tested performance.