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The quasi-static approximation that considers inductive–capacitive–resistive effects is referred to as the Darwin model of Maxwell’s equation. However, numerical analysis of the Darwin model is computationally expensive on account of large ill-conditioned equations. In this article, we proposed a new model order reduction technique for the Darwin model of Maxwell’s equations to drastically reduce the computational cost. In this method, four symmetric non-gauged equations were solved to obtain the basis vectors and avoid solving the non-symmetric equations. The reduced-order model (ROM) was obtained through congruent transformation, and time-domain analysis was performed using the time-difference method. We observed that the symmetric ROM was superior to the asymmetric ROM, in terms of accuracy and stability of the time-domain analysis. [ABSTRACT FROM AUTHOR]

Topology optimization (TO) has been formulated as a quadratic unconstrained binary optimization (QUBO) problem that can be solved by Digital Annealer (DA) and quantum computers, which can realize massive parallelization. It is shown that the 3-D TO of a permanent magnet (PM), with 600 unknowns, is successfully performed by the DA with the aid of the finite element method (FEM) for field computations. Moreover, it is shown to perform TO of a magnetic core, with 758 unknowns, in such a way that the QUBO and field problems are iteratively solved to determine the optimal solution in which the magnetic field and optimal core structure are self-consistent. [ABSTRACT FROM AUTHOR]

This article presents a fast population-based multi-objective optimization of electromagnetic devices using an adaptive neural network (NN) surrogate model. The proposed method does not require any training data or construction of a surrogate model before the optimization phase. Instead, the NN surrogate model is built from the initial population in the optimization process, and then it is sequentially updated with high-ranking individuals. All individuals were evaluated using the surrogate model. Based on this evaluation, high-ranking individuals are reevaluated using high-fidelity electromagnetic field computation. The suppression of the execution of expensive field computations effectively reduces the computing costs. It is shown that the proposed method works two to four times faster, maintaining optimization performance than the original method that does not use surrogate models. [ABSTRACT FROM AUTHOR]

This article proposes a novel analysis method for the losses in a litz wire considering the circulating and eddy currents. In the proposed method, the macroscopic complex permeability is introduced to evaluate the eddy current loss owing to the proximity effect. Homogenization-based finite element analysis using the macroscopic complex permeability can effectively compute the proximity effect loss. The loss owing to the circulating currents is evaluated by solving the corresponding circuit equation. It is shown that the eddy current loss is dominant for the solenoidal and spiral coils without magnetic cores because of the uniform magnetic field distribution along the wire. Moreover, the magnetic reactors in which the circulating current loss cannot be ignored are analyzed using the proposed method. It is shown that the losses computed by the proposed method agree well with the measured results. [ABSTRACT FROM AUTHOR]

This article proposes a method based on 3-D discrete element and finite element methods to numerically evaluate the effects of the particle size distribution of soft magnetic composite (SMC) on the electromagnetic property. The three SMC models which obey Gaussian, homogeneous, and twin-peak distributions are compared using the proposed method. It is shown that the Gaussian model has the highest permeability and the lowest loss at high frequencies under the condition that the three models have the same filling rate. [ABSTRACT FROM AUTHOR]

This study presents a novel two-step optimization method that incorporates explainable neural networks into topology optimization. The deep neural network (DNN) is trained to infer the torque performance from the input image of the motor cross section. The sensitive region that has a significant influence on the average torque is extracted using gradient-weighted class activation mapping (Grad-CAM) constructed from the DNN. Then, the optimization with respect to the torque ripple is performed only in the incentive region with little influence on the average torque. The proposed method is shown to increase the average torque of an interior permanent magnet (IPM) motor by 14% and reduce the torque ripple by 79% compared with the original model. [ABSTRACT FROM AUTHOR]

The computational cost of topology optimization based on the stochastic algorithm is shown to be greatly reduced by deep learning. In the learning phase, the cross-sectional image of an interior permanent magnet motor, represented in RGB, is used to train a convolutional neural network (CNN) to infer the torque properties. In the optimization phase, all the individuals are approximately evaluated by the trained CNN, while finite element analysis for accurate evaluation is performed only for a limited number of individuals. It is numerically shown that the computational cost for the topology optimization can be reduced without the loss of optimization quality. [ABSTRACT FROM AUTHOR]

The soft magnetic composite (SMC), which consists of insulated iron particles, has been used for electric machines and devices. The magnetic permeability of SMC is underestimated when it is assumed that SMC is composed of homogeneous particles without magnetic contact. In this paper, SMC is modeled by the discrete element method, considering the inhomogeneity in particle size and contact among particles. It is shown that the measured permeability of SMC can be reproduced by considering these effects. Moreover, the frequency characteristics of SMC are evaluated by the proposed method, and the Ollendorff formula modified with an anomaly factor is introduced. [ABSTRACT FROM AUTHOR]

This paper presents the fast topology optimization methods for rotating machines based on deep learning. The cross-sectional image of electric motors and their performances obtained during a multi-objective topology optimization based on the finite-element method and genetic algorithm (GA) is used for training of the convolutional neural network (CNN). Two different approaches are proposed: 1) CNN trained by preliminary optimization with a small population for GA is used for the main optimization with a large population and 2) CNN is used for screening of torque performances in the optimization with respect to the motor efficiency. [ABSTRACT FROM AUTHOR]

A new method is introduced to evaluate the macroscopic permeability of a litz wire which is composed of stranded conductors. In this method, an integral equation is solved for the complex magnetization in the litz wire generated due to the proximity effect. The macroscopic permeability computed from the magnetization is used in the homogenization-based finite-element analysis of eddy currents in a litz-wire coil. It is shown that the wire twist has a little effect on the complex permeability. [ABSTRACT FROM AUTHOR]

In this paper, the multi-turn coil used in a wireless power transfer (WPT) device is modeled as a uniform material using the homogenization method to consider the proximity effect. By fitting the coil impedance to the numerical results, the Cauer equivalent circuit of the multi-turn coil is synthesized for the design and optimization of the power circuits in the WPT device. It is shown that the results obtained from the equivalent circuit and measurement are in good agreement. Moreover, the impedance of a flat WPT coil composed of a Litz wire is shown to be accurately evaluated by the proposed method when the contribution of capacitance is negligible. [ABSTRACT FROM AUTHOR]

Eddy current loss in a litz wire which has 3-D structure is analyzed using the integral equation method considering the proximity effect. In the present method, each wire is modeled as a polygonal line. 1-D integral equation is solved for the dipole magnetization generated by the anti-parallel eddy currents in the wire. The discretized integral equation can effectively be solved using an iterative method solver to compute the eddy current distribution in the wire due to the proximity effect. [ABSTRACT FROM AUTHOR]

The Cauer-equivalent circuit of electric apparatus is synthesized by applying the model order reduction to the finite-element equations. In this method, the admittance function of a given electric apparatus is expressed by a rational polynomial from which the Cauer-equivalent circuit is directly synthesized. Magnetic saturation in the magnetic core is considered by introducing nonlinearity in the primal inductance of the circuit. The synthesized circuit is shown to express the input–output properties of inductors and induction heating devices in good accuracy. [ABSTRACT FROM AUTHOR]

Mesh quality strongly affects the solution accuracy in electromagnetic finite-element analysis. Hence, the realization of adequate mesh generation becomes a very important task. Several adaptive meshing methods for automatic adjustments of the mesh density in accordance with the shape and complexity of the analyzed problem have been proposed. However, the most of them are not enough robust, some are quite laborious and could not be universally used for adaptive meshing of complex analysis models. In this paper, a new adaptive mesh refinement method based on magnetic field conservation at the border between finite elements is proposed. The proposed error estimation method provides easy mesh refinements, and generates smaller element within regions with large curvature of the magnetic flux lines. The proposed adaptive mesh refinement method based on non-conforming edge finite elements, which could avoid generation of flat or ill-shaped elements, was applied to a simple magnetostatic permanent magnet model. To confirm the validity and accuracy, the obtained results were compared with those obtained by means of the Zienkiewicz–Zhu (ZZ) error estimator. The results show that the computational error using the proposed method was reduced down to 1% compared with that of the ZZ method, which yields error of 8.6%, for the same model. [ABSTRACT FROM AUTHOR]

Native application of finite-element method (FEM) to the analysis of skin and proximity effects in multi-turn coils results in large equation systems, whose solution needs long computational time. This paper proposes a semi-analytical approach to overcome this problem. For the analysis of the proximity effect, the complex permeability of a round conducting wire immersed in uniform time-harmonic magnetic fields is represented in a closed form. Then, the homogenized complex permeability over the cross section of the multi-turn coil is analytically evaluated using the Ollendorff formula. The magnetoquasistatic problem is thus replaced by the magnetostatic one, in which the multi-turn coil is treated as a uniform material with the homogenized complex permeability. The skin effect is taken into consideration by introducing the corresponding impedance in the circuit equation. The proposed method is shown to give the impedance of multi-turn coils, which is in good agreement with that obtained by the conventional FEM as well as experiments. [ABSTRACT FROM AUTHOR]

It is revealed that the contact of magnetic particles in soft magnetic composite (SMC) significantly increases the macroscopic permeability. It is shown that Ollendorff’s formula, which assumes homogenous magnetic particles and insulation layers, underestimates the macroscopic permeability of SMC. It is suggested that the excess in the permeability is due to the local contacts among the magnetic particles. The effect of the magnetic contact is evaluated using a magnetic circuit model. [ABSTRACT FROM AUTHOR]

This paper proposes an equivalent-circuit generation from the finite-element (FE) model of electromagnetic devices using a model order reduction (MOR). In this method, an equivalent circuit is directly generated from the reduced transfer function obtained using MOR based on Padé approximation via the Lanczos process. It is shown that the generated circuit yields sufficiently accurate results in both frequency and time domains. Moreover, the computational time of the present method is much shorter than that of the circuit generation based on frequency sweep using the conventional FE analysis. [ABSTRACT FROM AUTHOR]

The visualization of magnetic flux lines is one of the most effective ways to intuitively grasp a magnetic field. The depiction of continuous and smooth magnetic flux lines according to the magnetic field is of paramount importance. Thus, it is important to adequately allocate the distribution of magnetic flux lines in the analyzed space. We have already proposed two methods of determining the allocation of magnetic flux lines in 3-D space. However, both the methods exhibited a long computation time to determine the allocation of magnetic flux lines. For solving this problem, in this paper, we propose a new improved method for the correct allocation of magnetic flux lines in the 3-D space with modest computational cost. The main advantages of this method are shorter computation time, correct allocation of the magnetic flux lines, and, especially, short computation time for the visualization of magnetic flux lines when changes in the number of depicted flux lines are requested. [ABSTRACT FROM AUTHOR]

This paper presents a novel adaptive subdomain model order reduction (MOR) based on proper orthogonal decomposition (POD) and discrete empirical interpolation (DEI) methods for nonlinear magneto-quasi-static (MQS) problems. In this method, a nonlinear region is decomposed into two regions, where one of the regions includes all those finite elements that have a particularly strong saturation and the other region does not. MOR based on POD and DEI methods is applied only to the latter region. Both the regions are determined automatically at each time step. It is shown that this method can effectively reduce the computational time to solve the nonlinear MQS problems without losing the quality of accuracy. [ABSTRACT FROM AUTHOR]

This paper proposes a model order reduction (MOR) based on the proper orthogonal decomposition (POD) to perform a fast analysis of motors. When a POD-based MOR is applied to the motor analysis, the number of basis vectors has to be increased to express the changes in the magnetic fields due to a rotational movement. Its computational efficiency is, thus, greatly deteriorated. To overcome this difficulty, the block-MOR is first applied to a motor analysis. In this method, a parameter space is subdivided into several blocks, which correspond to angular ranges in the motor analysis, in each of which the basis vectors are constructed from snapshotted fields. The computational time of the block-MOR is shown to be shorter than that of the conventional MOR, while the accuracy of both the methods is almost identical. [ABSTRACT FROM AUTHOR]

This paper presents the generation of equivalent circuits from a finite-element (FE) model of electromagnetic devices using proper orthogonal decomposition (POD). This method effectively computes the frequency response of the reduced FE model constructed by the POD-based model order reduction. Then, the circuit parameters are determined so as to minimize the error between the frequency responses of the reduced FE model and equivalent circuit. The frequency characteristics of an inductor and the induction heating machine evaluated by the equivalent circuit are shown to be in good agreement with those computed from the original FE model. [ABSTRACT FROM AUTHOR]

This paper presents a fast shape optimization method for antennas using proper orthogonal decomposition (POD)-based model order reduction (MOR). In this method, the finite element region is subdivided into design and ambient regions. The former includes antennas, whose shapes are optimized, whereas the latter includes air and perfect matched layer. Since the electromagnetic fields significantly change in the design region during the optimization process, POD-based MOR is only applied to the ambient region. In addition, MOR for both shape and frequency responses is performed for optimization of wideband antennas. It is shown that the present method can effectively reduce the computational time without deteriorating performance in the optimization. [ABSTRACT FROM PUBLISHER]

High-temperature superconducting quantum interference devices (HTS SQUIDs) have been developed as an extremely sensitive magnetic sensor. The HTS SQUIDs are required to have high robustness with respect to the magnetic noise for stable operation in an unshielded environment and also reduced cost to widen the application range. It is, therefore, necessary to clarify the quantum magnetic behavior of the HTS SQUID. However, a simulation tool, which can consider the quantum magnetic behavior, has not been developed yet. In this paper, an equivalent circuit of a Josephson junction comprising the HTS SQUID is more properly considered to represent the quantum behavior. It can consider the ac and dc Josephson effect. The obtained results are compared with an ordinary simulation using a simplified circuit model, and the results agree well with each other. Using the proposed simulation method instead of the ordinary simulation, the current path is more accurately simulated, so this new method will be used to evaluate the robustness of the SQUID. [ABSTRACT FROM PUBLISHER]

Recently, many investigations about toroidal high-temperature superconducting magnetic energy storage systems have been reported. Some papers reported that there was a possibility that the chain of normal-state transitions occurred on the toroidal HTS-SMES magnet by normal-state-transition simulation. Hence, it should also be investigated that the behavior of unbalanced electromagnetic force during the sequential normal-state transition of the superconducting coil elements. In this paper, we have developed a simulation code to investigate the behavior of the overturning electromagnetic force on the toroidal HTS-SMES system during the normal-state transition. The magnetic field and the circuit analysis were coupled and solved in the previously developed simulation code. Additionally, in order to investigate the normal-state transition more accurately, we also take the thermal analysis into account. Carrying out the newly developed numerical simulation, we investigate the time transition of the transport current, the overturning force, and the magnetic field applied to the superconducting coil elements for a few toroidal HTS-SMESs. [ABSTRACT FROM PUBLISHER]

An automatic mesh generation method employing a dynamic bubble system can provide a high-quality mesh for electromagnetic finite element analysis. However, it takes a very long time to compute bubbles' movement when a mesh with a large number of elements is generated. The bubbles move according to a force among them, such as the van der Waals force. However, the force received from bubbles of very far distance can be ignored. Therefore, it is unnecessary to calculate the force from all the bubbles. In this paper, we propose a subdivided dynamic bubble system in order to shorten the computation time. The proposed method considers the analysis region to be divided into some tetrahedral subdivisions, and then the bubbles move independently in the tetrahedral subdivisions. As a result, acceleration of the computation time is achieved. [ABSTRACT FROM AUTHOR]