The paper conducts a comparison study of the different feasible approaches that are available for implementation of the first-order approximation of a nonlinear eddy current field using the Cauer ladder network (CLN) method. The study comprises a comparison of the different definitions used for the reluctivity, the circuit equations, and the various saturation indexes used in the different approximations. A nonlinear laminated iron core is selected as an appropriate numerical example. Comparisons are carried out with sinusoidal and pulse excitations at high frequencies.
An approximation approach is proposed for the analysis of nonlinear quasi-static eddy currents adopting a Cauer ladder network (CLN). When there are nonlinear magnetic materials in the analysis domain, the electric and magnetic modes and their corresponding values for resistors and inductors in the CLN may vary according to the level of saturation in the core. Considering the effects of the modes and their magnitudes on the saturation imposes a heavy computational burden, which brings the efficiency of the CLN method into question. This paper studies a first-order approximation of the nonlinear CLN method to keep the nonlinearization procedure computationally effective, simple, and accurate. Numerical tests are carried out for a two-dimensional nonlinear inductor excited with rectangular and sinusoidal excitations to show the accuracy of the proposed nonlinear resolution method.
This paper develops a multi-scale Model Order Reduction (MOR) method including both material and machine scale MOR. The material-scale MOR homogenizes the eddy-current (EC) field in laminated cores using the Legendre expansion of magnetic induction along the stacking direction within each steel sheet. The machine-scale MOR represents the EC field in electromagnetic devices with their equivalent Cauer Ladder Network (CLN). The former MOR is built into the latter by applying the CLN procedure to the homogenized EC field equation.
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