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

Abstract

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 non-active 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, firstly, 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. Secondly, 3-D FEA solutions are computationally-slow and therefore inefficient as an "internal routine" of an optimization procedure. This paper 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.

A Combined 3-D Geometric and Magnetic Modeling Approach of Coils in Air-Cored Resonant Induction Machines

“…3(a), the end face of 𝔸, ABCD, is transformed to EFGH with different depth and width, both ABCD and EFGH are rectangles and parallel to the yz plane. To avoid coil-end clashing, the two-layer end-winding arrangement is adopted [13], [14]. A step is connected right after 𝔸𝔼 which joins the axial and end parts, denoted as 𝕁𝔸.…”

“…Periodicity and symmetry in three-phase winding layout can be invoked so that only mutual inductances of independent coil pairs are computed and repeated evaluations are eliminated, which further accelerates the calculation. The collection routine of phase inductances for single-layer lapwindings as well as the equivalent-circuit inductances has been discussed in [13], so will not be repeated here.…”