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The tensor complex permeability of a multi-turn coil with elliptic cross-section is analytically expressed. In field analysis, a multi-turn coil can be modeled by the uniform material that has the present tensor complex permeability. It is shown that the frequency characteristic of the present tensor complex permeability is in good agreement with that evaluated by finite element method applied to a unit cell of the multi-turn coil region.

The authors introduce a new method to evaluate the complex permeability of a multi-turn rectangular coil. To obtain the complex permeability of a rectangular coil in a closed form, it is approximated as an elliptic coil. Because the rectangular coil has different complex permeabilities in the vertical and horizontal directions, the complex permeability have to be defined in a tensor form. It suffices to discretize the coil region into rather coarse finite elements without considering the skin depth in contrast to the conventional finite element method.

The proposed method is shown to give the impedance of multi-turn coils which is in good agreement with results obtained by the conventional finite element (FE) analysis. By extending the proposed approach, the authors can easily perform 3D FE analysis without difficulty in discretization of the coil region with fairly fine finite elements. Moreover, they found that the approximation of rectangular coils as the elliptic coils is valid for analysis of quasi-static fields using this homogenization method.

The novelty of this study is in the approximation of the rectangular coils with elliptic coils, and the complex permeability for them is formulated here in a closed form. The proposed formula includes that for the round coils. Using the present method, the authors analyze the rectangular coils without fine discretization.

This paper aims to present a SPICE model to represent antennas in receiving mode. The model can be used to evaluate the performance of the antenna when it is coupled to several different nonlinear electric circuits. The proposed methodology is particularly suitable for rectenna applications, as it allows the analysis of different configurations for a rectenna more efficiently than using full-wave analysis simulators coupled directly to each rectifier circuit.

The model presented uses reciprocity theory to calculate the ideal voltage source of the Thevenin-equivalent circuit for an antenna. Vector fitting is then used to approximate the model to rational functions that can be converted to Resistor, Inductor and Capacitor circuits. Additional components are added to the circuit to prevent numerical instability.

Two rectennas are used to illustrate the performance of the proposed model, one based on a 2.45-GHz rectangular patch antenna and another based on a planar spiral antenna. The second antenna has impedance with positive and negative real parts along the frequency range, which could lead to numerical instabilities. The proposed method is shown to be stable while working with these negative resistance values, which may appear during circuit parameterization.

The equivalent SPICE circuit model for the antenna makes it easy to simulate nonlinear circuits connected to the antenna and perform transient analyses. The computational cost of antenna analysis is reduced, being more computationally efficient than methods that involve full-wave simulation. This characteristic makes it an interesting approach for working with rectennas, or any application where the time constant of the circuit is much longer than the period of the incident wave.

For most antenna applications, the numerical stability of the circuit can be achieved using passive enforcement. However, depending on the phase response of the antenna, the impedance that represents its far-field characteristic may present a negative real part, in which case, passive enforcement will fail. In this paper, the problem of numerical instability is solved by introducing an offset resistance and a current-controlled voltage source to the model.

The purpose of this paper is to propose a fast synthesis method of the equivalent circuits of electromagnetic devices using model order reduction. Finite element method (FEM) has been widely used to design electromagnetic devices. For FE analysis of these devices connected to control and deriving circuits, FE equations coupled with the circuit equations have to be solved for many times in their design processes. If the FE models are replaced by equivalent circuit models, computational time could be drastically reduced.

In the proposed method, a reduced FE model is obtained using proper orthogonal decomposition (POD) in which the size of FE equation is effectively reduced so that the computational time for FE analysis is shortened. Then, the equivalent circuits are directly synthesized from the admittance function of the reduced system.

Accuracy and computational efficiency of the proposed method are compared with those of another POD-based method in which the equivalent circuits are synthesized from fitting of frequency characteristics using optimization algorithm. There are no significant differences in the accuracy of both methods, while the speedup ratio of the former method is found larger than that for the latter method for the same sampling points.

The equivalent circuits of electric machines and devices have been synthesized on the basis of physical insight of engineers. This paper proposes a novel method by which the equivalent circuits are automatically synthesized from FE model of the electric machines and devices using POD.

The purpose of this study is to search for an optimal core shape that is robust against misalignment between the transmitting and receiving coils of the wireless power transfer (WPT) device. During the optimization process, the authors maximize the coupling coefficients while minimizing the leakage flux around the coils to ensure the safety of the WPT device.

In this study, a novel topology optimization method for WPT devices using the geometry projection method is proposed to optimize the magnetic core shape. This method facilitates the generation of bar-shaped magnetic cores because the material distribution is represented by a set of elementary bars.

It is shown that an optimized core shape, which is obtained through topology optimization, effectively increases the net magnetic flux interlinked with the receiving coil and outperforms the conventional core.

In the previous topology optimization method, the material distribution is represented by a linear combination of Gaussian functions. However, this method does not usually result in bar-shaped cores, which are widely used in WPT. In this study, the authors propose a novel topology optimization method for WPT devices using geometry projection that is used in structural optimization, such as beam and cantilever shapes.

This paper aims to present a deep learning–based surrogate model for fast multi-material topology optimization of an interior permanent magnet (IPM) motor. The multi-material topology optimization based on genetic algorithm needs large computational burden because of execution of finite element (FE) analysis for many times. To overcome this difficulty, a convolutional neural network (CNN) is adopted to predict the motor performance from the cross-sectional motor image and reduce the number of FE analysis.

To predict the average torque of an IPM motor, CNN is used as a surrogate model. From the input cross-sectional motor image, CNN infers dq-inductance and magnet flux to compute the average torque. It is shown that the average torque for any current phase angle can be predicted by this approach, which allows the maximization of the average torque by changing the current phase angle. The individuals in the multi-material topology optimization are evaluated by the trained CNN, and the limited individuals with higher potentials are evaluated by finite element method.

It is shown that the proposed method doubles the computing speed of the multi-material topology optimization without loss of search ability. In addition, the optimized motor obtained by the proposed method followed by simplification for manufacturing is shown to have higher average torque than a reference model.

This paper proposes a novel method based on deep learning for fast multi-material topology optimization considering the current phase angle.

This study aims to realize a sensorless metal object detection (MOD) using machine learning, to prevent the wireless power transfer (WPT) system from the risks of electric discharge and fire accidents caused by foreign metal objects.

The data constructed by analyzing the input impedance using the finite element method are used in machine learning. From the loci of the input impedance of systems, the trained neural network (NN), support vector machine and naive Bayes classifier judge if a metal object exists. Then the proposed method is tested by experiments too.

In the test using simulated data, all of the three machine learning methods show high accuracy of over 80% for detecting an aluminum cylinder. And in the experimental verifications, the existence of an aluminum cylinder and empty can are successfully identified by a NN.

This work provides a new sensorless MOD method for WPT using three machine learning methods. And it shows that NNs obtain high accuracy than the others in both simulated and experimental verifications.

The prolonged training time of the neural network (NN) has sparked considerable debate regarding their application in the field of optimization. The purpose of this paper is to explore the beneficial assistance of NN-based alternative models in inductance design, with a particular focus on multi-objective optimization and uncertainty analysis processes.

Under Gaussian-distributed manufacturing errors, this study predicts error intervals for Pareto points and select robust solutions with minimal error margins. Furthermore, this study establishes correlations between manufacturing errors and inductance value discrepancies, offering a practical means of determining permissible manufacturing errors tailored to varying accuracy requirements.

The NN-assisted methods are demonstrated to offer a substantial time advantage in multi-objective optimization compared to conventional approaches, particularly in scenarios where the trained NN is repeatedly used. Also, NN models allow for extensive data-driven uncertainty quantification, which is challenging for traditional methods.

Three objectives including saturation current are considered in the multi-optimization, and the time advantages of the NN are thoroughly discussed by comparing scenarios involving single optimization, multiple optimizations, bi-objective optimization and tri-objective optimization. This study proposes direct error interval prediction on the Pareto front, using extensive data to predict the response of the Pareto front to random errors following a Gaussian distribution. This approach circumvents the compromises inherent in constrained robust optimization for inductance design and allows for a direct assessment of robustness that can be applied to account for manufacturing errors with complex distributions.

The calculation of magnetic shielding with ferromagnetic material by an effective reluctivity method and a time step method based on the finite element calculation is investigated. The calculation results of both methods are compared with measurement results and with each other in order to check their reliability and accuracy. It turns out that both methods give similar results for the field inside the shielding material, whereas in the surrounding air the effective reluctivity method gives more accurate results than the present time step method.

It is important to investigate large‐scale numerical analyses of electromagnetic fields in design processes of electromagnetic machines. Thus, faster solvers for eddy current analyses are necessary. Parallel computation methods for linear solvers in electromagnetic field analyses have been investigated. These methods have gained importance due to the diffusion of PC clusters and multi‐core CPUs in recent years.

This paper discuses linear solvers for the finite element method in eddy current analyses on parallel computers. The preconditioned conjugate gradient method with overlapping domain decomposition is treated. Some techniques treated to improve the convergence was investigated.

The numerical results show that the overlapping effect results in good convergence in eddy current analyses.

The preconditioned conjugate gradient method with overlapping domain decomposition has been treated. The numerical results show that the overlapping method works more efficiently for eddy current analyses. Moreover, this method enables large‐scale analyses on popular computers such as PC clusters.

The purpose of this paper is to present a new method to obtain robust solutions to electromagnetic optimization problems, solved with evolutional algorithms, which are insensitive to changes in design parameters such as spatial size, positioning and material constant.

Adjoint variable method is employed to evaluate the sensitivity of individuals in evolutional processes.

It is shown in the numerical examples, where the present method is applied to optimization of a superconducting energy storage system and C‐shape magnet, that robust solutions are actually obtained which are insensitive to deviations in spatial sizes.

Unlike usual optimization methods, the present method takes into account deviation in the design parameters due to production errors and long‐term changes. Moreover, the present method is limited to about twice the computational cost of non‐robust optimization methods.