Cauer Ladder Network Representation of a Nonlinear Eddy-Current Field Using a First-Order Approximation

Abstract

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.

Model order reduction of nonlinear eddy-current field using parameterized CLN

“…To improve the representation accuracy in the low current region, we can (a) parameterize not only with I 1 but also with I 3 , or (b) use the total current I t (=Σ n I 2 n +1 ) instead of I 1 as the parameter α when solving the state equations. The second method appeared to be effective in the study by Eskandari and Matsuo (2020).…”

“…Assuming that the first mode current I 1 has a huge impact on the saturation, we approximate it as a function of I 1 by choosing α = I 1 , which was also referred to as the first-order approximation in the study by Eskandari and Matsuo (2020). Thus, we have: …”

“…Equations ( 34), ( 38) and (39) correspond to the nonlinear Cauer network equations examined by Eskandari and Matsuo (2020).…”

“…In recent years, several model order reduction (MOR) methods have been developed to provide reduced systems, wherein the number of unknown variables for electromagnetic field representations is reduced without the loss of accuracy. To handle the reduced systems under multiple states, some MOR methods have parameterized representation depending on the degree of magnetic saturation (Sato et al , 2017; Hasan et al , 2018; Eskandari and Matsuo, 2020), temperature and the rotational angle of the motors (Henneron and Clenet, 2014; Shimotani et al , 2016). The dynamical behavior of such reduced systems, however, has not been rigorously discussed with time-varying orthogonal basis functions.…”

Model Order Reduction of an Induction Motor Using a Cauer Ladder Network

“…The application of the developed method to rotational machines is straightforward. The non-linearization of CLN method [9] will be combined for practical motor analyses.…”