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

Air-cored resonant induction machines normally have flat cross-sectional coils because of the air-cored and toothless magnetic structure. Since the precision in the geometry modeling is vital to the inductance-estimation accuracy, a combined geometry modeling and inductance calculation method is proposed. The coil geometry construction process can handle non-circular cross-sections and complex coil shapes, it generates a single- or multi-filament model ready for analytic inductance calculation and coordinates information for 3-D FEA modeling. Using closed-form solutions for the mutual inductance of two straight segments placed at any orientation in 3-D, the filament-level, conductor-level, coil-level and winding-level inductances can be calculated quickly and accurately and avoids numerical singularities so is suitable for incorporating into an optimization program. Good correlation is confirmed in validation against 3-D FEA results on an air-cored resonant induction machine design.