Comparison Study of First-Order Approximations of Nonlinear Eddy-Current Field Using Cauer Ladder Network Method

Abstract

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.

Nonlinear Multi-Scale Model Order Reduction of Eddy-Current Problems

“…The linearization in the machine scale in the CLN context is investigated in [8], [9]. Sato and Igarashi [8], considered the magnetic saturation by imposing the nonlinearity on the first inductor L 1 , only.…”

“…Sato and Igarashi [8], considered the magnetic saturation by imposing the nonlinearity on the first inductor L 1 , only. In [9], the nonlinearity was extended to all the circuit elements similar to (12) except that all of the magnetic modes are interpolated with µ or µ d only.…”

“…The close analogy in the microscopic linearization [3] and the macroscopic one [9] brings up the nonlinear multi-scale MOR procedure summarized in algorithm 1. A table of parametric CLN elements are computed with respect to the coil current I 1 in line 4.…”

“…The superscript (d) represents either apparent of differential definitions. By neglecting the transition of magnetic modes at two consecutive time-steps, the network equations become identical to that of the first-order approximation method (FO-CLN) [9].…”

“…Some of the MOR approaches are capable of generating equivalent circuit models such as Padé via Lanczos (PVL) approximation to Krylov subspace [6] or the Cauer Ladder Network (CLN) method [7]. Several extensions were proposed to the CLN method, including nonlinear CLN [8], [9] and multi-scale MOR [10], [11]. The multi-scale MOR combines the homogenization method as a microscopic MOR and the CLN method as a machine scale MOR to construct an efficient and accurate reduced system including the laminated core [10].…”