Mutual Inductance Calculation of Circular Coils Sandwiched between 3-Layer Magnetic Mediums for Wireless Power Transfer Systems

The mutual inductance between coils directly affects many aspects of performance in wireless power transmission systems. Therefore, a reliable calculation method for the mutual inductance between coils is of great significance to the optimal design of transmission coil structures. In this paper, a mutual inductance calculation for circular coils sandwiched between 3-layer magnetic mediums in a wireless power transmission system is proposed. First, the structure of circular coils sandwiched between 3-layer magnetic mediums is presented, and then a mutual inductance model of the circular coils is established. Accordingly, a corresponding magnetic vector potential analysis method is proposed based on Maxwell equations and the Bessel transform. Finally, the mutual inductance calculation method for circular coils between 3-layer magnetic mediums is obtained. The correctness of the proposed mutual inductance calculation method is verified by comparing the calculated, simulated, and measured mutual inductance data.

Calculation of the Eddy Current Losses in a Laminated Open-Type Transformer Core Based on the A→,T→−A→ Formulation

Losses due to eddy currents in an open-type transformer core are significantly reduced by the lamination of the transformer core. In order to further reduce the eddy current losses, the open-type core often has a multi-part structure, i.e., it is composed of several more slender cores. The complete homogenization of such a core is not possible when an A→,V−A→ formulation is used, where A and V represent the magnetic vector potential and electric scalar potential, respectively. On the other hand, an A→,T→−A→ formulation, where T represents the electric vector potential, enables the complete homogenization of the general open-type core, but the simulation converges poorly due to the large number of degrees of freedom. By eliminating the redundant degrees of freedom, the convergence rate is significantly improved, and is at least twice as good as the convergence rate of the simulation based on the A→,V−A→ formulation. In this paper, a method for the calculation of the eddy current losses in an open-type core based on the A→,T→−A→ formulation with the elimination of redundant degrees of freedom is presented. The method is validated by comparison with a brute force simulation based on the A→,V−A→ formulation, and the efficiency of the method is determined by comparison with the standard homogenization method based on the A→,V−A→ formulation.

A Comparison of Sparse and Non-sparse Techniques for Electric-Field Inversion from Normal-Component Magnetograms

An important element of 3D data-driven simulations of solar magnetic fields is the determination of the horizontal electric field at the solar photosphere. This electric field is used to drive the 3D simulations and inject energy and helicity into the solar corona. One outstanding problem is the localisation of the horizontal electric field such that it is consistent with Ohm’s law. Yeates (Astrophys. J.836(1), 131, 2017) put forward a new “sparse” technique for computing the horizontal electric field from normal-component magnetograms that minimises the number of non-zero values. This aims to produce a better representation of Ohm’s law compared to previously used “non-sparse” techniques. To test this new approach we apply it to active region (AR) 10977, along with the previously developed non-sparse technique of Mackay, Green, and van Ballegooijen (Astrophys. J.729(2), 97, 2011). A detailed comparison of the two techniques with coronal observations is used to determine which is the most successful. Results show that the non-sparse technique of Mackay, Green, and van Ballegooijen (2011) produces the best representation for the formation and structure of the sigmoid above AR 10977. In contrast, the Yeates (2017) approach injects strong horizontal fields between spatially separated, evolving magnetic polarities. This injection produces highly twisted unphysical field lines with significantly higher magnetic energy and helicity. It is also demonstrated that the Yeates (2017) approach produces significantly different results that can be inconsistent with the observations depending on whether the horizontal electric field is solved directly or indirectly through the magnetic vector potential. In contrast, the Mackay, Green, and van Ballegooijen (2011) method produces consistent results using either approach. The sparse technique of Yeates (2017) has significant pitfalls when applied to spatially resolved solar data, where future studies need to investigate why these problems arise.

Vector Potential, Magnetic Field, Mutual Inductance, Magnetic Force, Torque and Stiffness Calculation between Current-Carrying Arc Segments with Inclined Axes in Air

In this paper, the improved and the new analytical and semi-analytical expressions for calculating the magnetic vector potential, magnetic field, magnetic force, mutual inductance, torque, and stiffness between two inclined current-carrying arc segments in air are given. The expressions are obtained either in the analytical form over the incomplete elliptic integrals of the first and the second kind or by the single numerical integration of some elliptical integrals of the first and the second kind. The validity of the presented formulas is proved from the particular cases when the inclined circular loops are addressed. We mention that all formulas are obtained by the integral approach, except the stiffness, which is found by the derivative of the magnetic force. The novelty of this paper is the treatment of the inclined circular carting-current arc segments for which the calculations of the previously mentioned electromagnetic quantities are given.

Real-time computation of transcranial magnetic stimulation electric fields using self-supervised deep learning

Background: Electric fields (E-fields) induced by transcranial magnetic stimulation (TMS) can be modeled using partial differential equations (PDEs) with boundary conditions. However, existing numerical methods to solve PDEs for computing E-fields are usually computationally expensive. It often takes minutes to compute a high-resolution E-field using state-of-the-art finite-element methods (FEM). Methods: We developed a self-supervised deep learning (DL) method to compute precise TMS E-fields in real-time. Given a head model and the primary E-field generated by TMS coils, a self-supervised DL model was built to generate a E-field by minimizing a loss function that measures how well the generated E-field fits the governing PDE and Neumann boundary condition. The DL model was trained in a self-supervised manner, which does not require any external supervision. We evaluated the DL model using both a simulated sphere head model and realistic head models of 125 individuals and compared the accuracy and computational efficiency of the DL model with a state-of-the-art FEM. Results: In realistic head models, the DL model obtained accurate E-fields with significantly smaller PDE residual and boundary condition residual than the FEM (p<0.002, Wilcoxon signed-rank test). The DL model was computationally efficient, which took about 0.30 seconds on average to compute the E-field for one testing individual. The DL model built for the simulated sphere head model also obtained an accurate E-field whose difference from the analytical E-fields was 0.004, more accurate than the solution obtained using the FEM. Conclusions: We have developed a self-supervised DL model to directly learn a mapping from the magnetic vector potential of a TMS coil and a realistic head model to the TMS induced E-fields, facilitating real-time, precise TMS E-field modeling.

Analytical model of a T-core coil above a multi-layer conductor with hidden hole using the TREE method for nondestructive evaluation

Purpose In eddy current nondestructive testing, a probe with a ferrite core such as an E-core coil is usually used to detect and locate defects such as cracks and corrosion in conductive material. However, the E-core coil has some disadvantages, such as large volume and difficulty in the process of winding the coils. This paper aims to present a novel T-core probe and its analytical model used for evaluating hidden holes in a multi- layer conductor. Design/methodology/approach By using a cylindrical coordinate system, the solution domain is truncated in the radial direction. The magnetic vector potential of each region excited by a filamentary coil is derived, and the expansion coefficients of the solutions are obtained by matching the boundary and interface conditions between the regions. By using the truncated region eigenfunction expansion method, the final expression in closed form for the impedance of the multi-turn coil is worked out, and the impedance calculation is performed in Mathematica. For frequencies ranging from 100 Hz to 100 kHz, both the impedance changes of the T-core coil above the multi-layer conductor without a hidden hole and in the absence of the layered conductor were calculated, and the influence of a hidden hole in the multi-layer conducting structure on the impedance change was investigated. Findings The correctness of the analytical model of the T-core coil was verified by the finite element method and experiments. The proposed T-core coil has higher sensitivity than an air-core coil, and similar sensitivity and smaller size than an E-core coil. Originality/value A new T-core coil probe and its accurate theoretical model for defect evaluation of conductor were presented; probe and analytical model can be used in probe design, detection process simulation or can be directly used in defect evaluation of multi-layer conductor.

The effect of high-penetrating emission on the growth, superoxide accumulation and ATP/ADP ratio in Saccharomyces cerevisiae

Many kinds of physical field are able to affect the biological activity, such as electromagnetic field, magnetic field, scalar wave, magnetic vector potential and so on. Some works investigated a high-penetrating emission (HPE) generated by a LED generator that can affect the conductivity of water and the growth of dry yeast. In this research, the biological effect of the HPE of LED generator on S. cerevisiae was studied. The results showed that this kind of HPE could promote the growth of S. cerevisiae. With the decrease of initial concentration and the extension of exposure time, the growth promoting effect of HPE increased significantly. When the initial cell concentration was 2 × 102 cell/ml and exposed for 24 h, the number of yeast cells increased by 19.5% compared with the control group. Further studies showed that adenosine triphosphate (ATP) content and the ratio of ATP and adenosine diphosphate (ADP, ATP/ADP ratio) of exposed cells were higher than those of unexposed cells, indicating that exposed cells had higher cell viability and energy status. In addition, the intracellular superoxide (O2−) content decreased significantly after the HPE exposed. In this study, the stainless steel box acts as a Faraday cage to shield the electromagnetic field, so the biological effect of the HPE is not produced by the electromagnetic field. Nevertheless, the mechanism of the HPE is still unknown and needs further research. This is the first report on the effect of HPE on mitochondrial parameters, contributing to further study on HPE and revealing potential for future medical applications.

Vector Potential, Magnetic Field, Mutual Inductance, Magnetic Force, Torque and Stiffness Calculation between Current-Carrying Arc Segments with Inclined Axes in Air

In this paper we give the improved and new analytical and semi-analytical expression for calcu-lating the magnetic vector potential, magnetic field, magnetic force, mutual inductance, torque, and stiffness between two inclined current-carrying arc segments in air. The expressions are ob-tained either in the analytical form over the incomplete elliptic integrals of the first and the sec-ond time or by the single numerical integration of some elliptical integrals of the first and the second kind. The validity of the presented formulas is proved from the special cases when the inclined circular loops are treated. We mention that all formulas are obtain by the integral ap-proach except the stiffness which is found by the derivative of the magnetic force.

A problem of thermo-magnetoelasticity for a system of parallel electrical conductors by Cartesian harmonic polynomials and rational functions

A method proposed earlier, relying on the use of harmonic Cartesian polynomial and rational functions, is extended here to find a semi-analytical solution to the uncoupled, two-dimensional problem of thermo-magnetoelasticity for a system of long parallel, non-intersecting, transversely isotropic elastic cylindrical electrical conductors. Results are presented for two conductors of equal circular normal cross-sections carrying currents of equal densities flowing along the same direction, subjected to Robin-type thermal boundary conditions. Quantities of practical interest are represented graphically and discussed. Consideration of a system of electrical conductors is of practical importance in power plants and in various technological instruments, where it is required to assess the interaction between conductors. The obtained formulas for the magnetic vector potential may be of importance for the determination of the coefficients of self- and mutual inductance of long electric conductors, otherwise difficult to calculate by standard methods. Comparing the results with those of a single conductor allows us to assess the interaction between conductors.

Accounting for Slot Harmonics and Nonsinusoidal Unbalanced Voltage Supply in High-Speed Solid-Rotor Induction Motor Using Complex Multi-Harmonic Finite Element Analysis

Solid rotor induction machines are still used in high-speed systems. A two-dimensional field-circuit model based on the finite element method and the complex magnetic vector potential has been shown as a very time-effective tool in the analysis of their steady states compared to time-domain models. This continuation work presents a validated computational algorithm that enables the inclusion of the nonsinusoidal and/or asymmetrical voltage supply in the multi-harmonic field-circuit model of these machines that was presented in the previous works by the authors. The extended model accounts for both spatial harmonics due to slotting and/or winding distribution and the time-harmonics due to voltage waveform. The applicability range of the model therefore increases to cases when the machine is supplied with a nonsinusoidal three-phase system of voltages with symmetry or asymmetry that can be decomposed into three symmetrical components. Its short execution time characteristic allows for much more insightful design studies of the contribution of voltage supply- and slotting-related harmonics to the overall efficiency of the machine than is possible with the time-consuming time-domain models. The proposed computational framework has never been presented in the literature. The model is verified positively by the comprehensive time-domain model. It is especially useful in design studies on solid rotor induction motors related to the optimisation of the efficiency of induction motor-based drive systems.