Comparison of the Finite Element Method and High-Order Isogeometric Analysis for Modeling Magnetic Vector Hysteresis

Modeling the full vector hysteresis relation provides critical insight in the magnetic behavior of the core of an electric machine. Yet, including a vector hysteresis model comes at the cost of a significant extra computational load, that grows with the size of the electromagnetic problem. Therefore, high-order methods, which achieve similar accuracy as the well-known finite element method for a smaller problem size, are potentially very interesting when modeling vector hysteresis.<br/

Comparison of the Finite Element Method and High-Order Isogeometric Analysis for Modeling Magnetic Vector Hysteresis

Modeling the full vector hysteresis relation provides critical insight in the magnetic behavior of the core of an electric machine. Yet, including a vector hysteresis model comes at the cost of a significant extra computational load, that grows with the size of the electromagnetic problem. Therefore, high-order methods, which achieve similar accuracy as the well-known finite element method for a smaller problem size, are potentially very interesting when modeling vector hysteresis.<br/

Effects of DC-Field Excitation on the Incremental Inductance of a Variable Flux Reluctance Machine

This paper presents a method for the computation of the incremental inductances in a 12/10 variable flux reluctance machine using the hybrid analytical modeling coupled with a fixed-point nonlinear solver. The variation of incremental and apparent inductance with respect to the dc-field excitation is investigated for both zero and non-zero ac-field excitations. The results show that the difference between both inductance values is not negligible after 25 A/mm2 dc-current density for the investigated benchmark without the ac field. Moreover, when a non-zero ac field is introduced in addition to the dc-field, the apparent inductance becomes misleading not only under magnetic saturation but also under low excitation in the linear region of the saturation curve. The results obtained with the proposed nonlinear hybrid model are compared with the finite element method in terms of magnetic flux density distribution and incremental inductance value. The root-mean-square discrepancy of magnetic flux density distribution is found to be 37.6 mT. Furthermore, the discrepancy between incremental inductance results of the proposed method and the finite element model is calculated as 1.43%, while the proposed approach requires less post-processing and necessitates ten times less number of degrees-of-freedom

Convergence analysis of the fixed-point method with the hybrid analytical modeling for 2-D nonlinear magnetostatic problems

This paper presents the convergence analysis of the fixed-point method (FPM) to model the nonlinear magnetic characteristics of a 2-D magnetostatic problem. In this study, FPM is used as the iterative nonlinear solver of the hybrid analytical modeling (HAM) technique for the accurate computation of the magnetic field distribution. The benchmark consists of a stator with excitation windings, an airgap, and a slotless mover. The relative errors between two successive iterations are calculated using different error estimators: the attraction force on the mover, the Fourier coefficients defined in the airgap, the magnetic flux density, and the magnetic scalar potential distributions. The effect of the number of mesh elements and harmonics on the accuracy and computational cost of the model is investigated for different levels of magnetic saturation. It is observed that the maximum rate of change in the relative difference of attraction force during the iterations is found to be 0.52 under the magnetic saturation. In addition, the absolute error of the attraction force between the developed hybrid model with FPM and the finite element method (FEM) is achieved to be 0.18%, while HAM has approximately three times less number of degrees-of-freedom compared to FEM

Magnetodynamic finite element analysis coupled with a vector hysteresis model applied to a variable flux reluctance machine

This article presents an extended magnetodynamic finite element modeling technique for 2-D time-dependent electromechanical problems with soft-magnetic laminated steels. The proposed modeling technique includes magnetic vector hysteresis, eddy-current, and excess field components in the system of equations instead of obtaining them in the post-processing. A transient finite element solver is coupled with the Jiles-Atherton vector hysteresis model, while the dynamic components, i.e. eddy current and excess field, are modeled in a weak formulation. The proposed method is experimentally verified using a laminated transformer core similar to TEAM problem 32. It is demonstrated that the proposed magnetodynamic model with vector hysteresis characteristics calculates the flux linkage and iron loss more accurately than magnetostatic and magnetodynamic models coupled with the single-valued magnetization curve. The proposed method estimates the iron loss with a discrepancy of less than 15 % up to an excitation frequency of 1500 Hz when it is compared to the transformer core measurements. Later, the experimentally verified magnetodynamic model is employed to model a 48 V, 5 kW variable flux reluctance machine with 16 Nm peak torque under various excitation levels. The machine is tested in laboratory conditions utilizing a field-oriented control algorithm in motor mode at 1000 rpm rotor speed. The average percentage error of the magnetodynamic model with vector hysteresis characteristics is found to be 14 % compared to the iron loss measurements while the magnetodynamic and magnetostatic models coupled with the single-valued curve exhibit 25 % and 45 % average percentage errors, respectively

Discovering Sparse Hysteresis Models: A Data-driven Study for Piezoelectric Materials and Perspectives on Magnetic Hysteresis

This article presents an approach for modelling hysteresis in piezoelectric materials that leverages recent advancements in machine learning, particularly in sparse-regression techniques. While sparse regression has previously been used to model various scientific and engineering phenomena, its application to nonlinear hysteresis modelling in piezoelectric materials has yet to be explored. The study employs the least-squares algorithm with sequential threshold to model the dynamic system responsible for hysteresis, resulting in a concise model that accurately predicts hysteresis for both simulated and experimental piezoelectric material data. Additionally, insights are provided on sparse white-box modelling of hysteresis for magnetic materials taking non-oriented electrical steel as an example. The presented approach is compared to traditional regression-based and neural network methods, demonstrating its efficiency and robustness

A Comparative Study of Finite Element Method and Hybrid Finite Element Method–Spectral Element Method Approaches Applied to Medium-Frequency Transformers with Foil Windings

This study aims to improve the computational efficiency of the frequency domain analysis of medium-frequency transformers (MFTs) with the presence of large clearance distances and fine foil windings. The winding loss and magnetic energy in MFTs in the medium-frequency range are calculated utilizing a finite element method (FEM) using common triangular and alternative rectilinear mesh elements. Additionally, in order to improve the computational efficiency of the calculations, a spectral element method (SEM) is coupled with a FEM, thus creating a hybrid FEM–SEM formulation. In such a hybrid approach, the FEM is used to calculate the current density distribution in the two-dimensional (2D) cross-section of the foil conductors to achieve reliable accuracy, and the SEM is adopted in the nonconducting clearance distances of the winding window to reduce the system of equations. The comparative analysis of the calculated resistance and reactance of the under-study models showed that the FEM with rectilinear mesh elements and the FEM–SEM model outperformed the FEM with triangular mesh elements in terms of accuracy and computational cost. The hybrid FEM–SEM model enables a reduced system of equations for modeling the electromagnetic behavior of MFTs. This research provides valuable insights into both the computational approaches and meshing challenges in the analysis of MFTs and offers a foundation for future research on the design and optimization of MFT