Extraction of low-order non-linear inductor models from a high-order physics-based representation

A method to extract low-order dynamic models of nonlinear magnetic devices from a high-order physics-based model is presented. The model includes saturation, skin effect, and eddy current. The physics-based model is derived from finite-element analysis, using only geometry and materials data. A nonlinear model order reduction method based on the Krylov subspace projection is used to extract the low-order model. A linear system is set up at each interpolation point along a training trajectory. Each linear system is reduced by the corresponding projection matrix. The resulting reduced linear systems are used to approximate the original system within each region, yielding accurate local simulation results. Good global properties are achieved by the use of piecewise simulation and weighting. Simulation results demonstrate that the original, nonlinear high-order system can be represented by a set of connected low-order, piecewise-linear systems with satisfactory agreement. This method can be automated and should provide a foundation for more complicated magnetic devices, such as multiphase coupled inductors, actuators, and rotary machines