Inductance Calculation Research Articles

Bayesian neural network based inductance calculations of wireless power transfer systems

This letter proposes a new method for obtaining self and mutual inductances in wireless power transfer (WPT) systems using a Bayesian neural network (BNN). Generally, inductance calculations using a field solver take a huge amount of time. Moreover, due to the complexity of WPT systems, there is no approximate equation for calculating inductances including ferrite shields. In this letter, nine structural parameters of a WPT system are experimentally used as inputs. The experimental results demonstrate that inductances obtained by the proposed method are within 5.1% in the maximum errors and within 1.1% in the mean absolute errors. The proposed method is about 748k times faster than the field solver in the CPU time required to obtain the inductances of one structure.

Mutual Inductance Calculation of Circular Coils for an Arbitrary Position With a Finite Magnetic Core in Wireless Power Transfer Systems

Mutual inductance can be increased, and magnetic leakage can be reduced by adding finite magnetic core materials to the coil structure. However, the problem of the calculation of the mutual inductance between two arbitrarily positioned circular coils with a finite magnetic core has not been resolved. In this article, an analytical formula for calculating the mutual inductance between two circular coaxial coils on a finite magnetic core is obtained based on regional hierarchical expansion analysis (RHEA), the Maxwell equation, the Bessel function, and the boundary conditions for electromagnetic fields. The mutual inductance between two arbitrarily positioned coils is obtained by using the analytical geometry method. A series of experiments are carried out to verify the analytic calculations. The experimental results for each misalignment case are compared with the calculated results and simulated results. The theoretical results and simulated results are in good agreement with the experimental data, which verifies the validity of the proposed method.

Method of calculation of the magnetic induction of the stator winding of a spiritual synchronous motor

This article discusses the calculation of the magnetic fields of the differential scattering of the stator, passing in the radial direction (penetrating the body of the rotor core), taking into account the saturation nonlinearities of the tooth zones of the magnetic circuit. The results of the method for calculating the magnetic permeability of the final values of the steel sections of the magnetic circuit in the stator and rotor of a salient-pole synchronous motor for its spatial harmonic fields in the air gap are presented.

Inductance Calculation for the Power Net Area Fill of Packages and PCBs Based on Plane-Pair PEEC

The inductance of the power/ground planes is an integral contributor to the input impedance of a power delivery network for high-speed printed circuit boards (PCBs) and packages. Conventionally, differential-equation (DE) circuit and cavity type models have been applied to compute the inductive behavior of the plane-to-plane inductance. However, these methods are not suitable for the case where the structures are perforated or involve other uneven structures. In this article, a new partial-element-equivalent-circuit (PEEC)-based method is presented to compute the inductance of parallel plate-like planes and other structures. Examples are given to show that the new method can efficiently compute inductances for multiple integrated circuit power vias, power/ground planes, and multiple decoupling capacitors. The proposed model is validated with both full-wave CEM simulations as well as with measurements. Further, the speed and the accuracy for real PCB and package designs are presented to validate the efficiency as well as the accuracy of the proposed approach. An important aspect of any approach is the limitations for solving real life problems. In this article, we consider important issues related of plane-pair PEEC to power distribution evaluations. Specifically, we show that large holes in planes can accurately be modeled. This is a difficult issue for DE methods. Another surprising practical issue is the accuracy obtained even if the planes are not of the same size. We also consider the speedup, which can be obtained in comparison to solutions for other approaches. This is due to the sparsity of the coupling for the rapid coupling decrease with distance. This short-distance coupling also increases the maximum frequency for which the method can be applied.

Research on Output Power of Series–Series Resonance Wireless Power Transmission System

The popularization of smart mobile devices has led to the research on wireless power transfer (WPT) technology. Previous research shows that increasing the excitation coil or the energy transfer coil can increase the energy transmission distance of the WPT system. But the mutual inductance calculation of coils is not accurate enough when the distance is close. This paper presents an improved formula to calculate the mutual inductance between two round inductance coils. Contrasts with the previous calculation methods, computer simulation and experimental results are done to validate the accuracy of the formula, especially when the two inductance coils are close together. On the basis of this formula, the maximum output power (MOP) and the maximum output power distance (MOPD) of the two-, three- and four-coil series–series resonance WPT systems based on circuit models are studied and compared. The simulation and experimental results show a high consistency with the theoretical calculation results. We can find that the farther the MOPD of the system is, the smaller the MOP is. Moreover, when the operating frequency increases, the MOPD of the two-coil conformation increases, while the four-coil conformation is just opposite.

The Structure and Its Leakage Inductance Model of Integrated LLC Transformer With Wide Range Value Variation

The integrated magnetics technology is famous in academic and industrial applications to achieve low profile and high power density of switch-mode power supply (SMPS). The integrated LLC transformer is widely used in LLC converter, where the transformer and resonant inductor are integrated into a magnetic component. However, the value Variation range of leakage inductance of conventional integrated transformer structures is limited due to the low profile and small volume in some planar applications. In this paper, a new integrated LLC transformer structure and its leakage inductance adjustment method are proposed. Based on the two-dimensional equivalent model of the structure, the distribution of the leakage magnetic field and the leakage inductance calculation model of the proposed transformer structure are established. The proposed structure can improve the value variation range of leakage inductance in some special applications and is easily achieved in the planner structure. Finally, the design guideline of the proposed integrated LLC transformer is obtained. Simulation results and prototype experiment results verify the correctness and flexibility of the theoretical analysis.

Variation Regularity and Measurement of Zero-Sequence Inductance of Fractional Slot Concentrated Winding PMSMs

The zero-sequence inductance is a vital parameter for the performance analysis of permanent magnet machines, especially under faulty conditions or in open-winding machines. This paper focuses on the zero-sequence inductance calculation of fractional slot concentrated winding permanent magnet synchronous machines (FSCW-PMSMs), and reveals the variation regularity of this kind of inductance and its various components against pole/slot combinations, using the winding function and finite element methods. Moreover, based on the analysis of 36-slot FSCW-PMSMs with different pole numbers, the dependency of each inductance component on the pole/slot combination is discussed in detail. To validate the regularities, experimental measurements of zero-sequence inductance are implemented in the prototype of the 36-slot stator. It is found that the regularities are independent of specific slot or pole numbers, which provide guidelines for optimum pole/slot combination selection, to mitigate the problems caused by zero-sequence current.

Optimal Design with Generalized Inductance Calculation for IPTs Using a Spiral Rectangular Coil Pair

It is important to analytically and accurately calculate the self-inductance of the primary and secondary coils and the mutual inductance between them, in order for the optimization algorithm of the Inductive Power Transmission (IPT) system. In this paper, the inductance calculation methods used in the IPT designs at different power levels are examined. The performances of these methods have been evaluated according to the experimental results of these IPTs using rectangular coil pairs. Inductance results were obtained with Finite Element Analysis (FEA) for IPTs without experimental results. Accordingly, a 120 W IPT has been designed to be used for wireless charging of the Electric bicycle (e-bike). Rectangular spiral coil pair with 75 mm distance between them was fabricated according to the design result. Analytical and experimental inductance values are compatible with each other for the optimal IPT design. The efficiency between the DC power supply to the load has been achieved as 92.1672% in approximate load conditions.

Transformer Leakage Inductance Calculation Method with Experimental Validation for CLLLC Converter Topology

Leakage inductance is one of the key parameters of a transformer, and it is often intentionally integrated into transformers. Rogowski’s equation is generally used for leakage inductance calculation; however, it is only applicable to concentric winding transformers where windings have the same height. Consequently, it has limited applications. This paper proposes a transformer leakage inductance calculation method using a double Fourier series. The limitation of Rogowski’s leakage inductance equation was analyzed in practical applications, and a new model for calculating the leakage inductance of a double-group-overlapping winding transformer was derived. Experimental prototypes of transformers were developed, and their simulation models were built in Ansys. The correctness of the proposed calculation method for transformer leakage inductance using a double Fourier series was verified by comparing the calculation results with the simulation and measured ones. A sensitivity analysis was also conducted by studying the variations in different parameters that might affect the leakage inductance value. The proposed calculation model gives an intuitive and simple method with less calculation and design effort while maintaining reasonable accuracy for leakage inductance calculation. In addition, the featured double Fourier series approach has a wider range of applications than Rogowski’s equation.

A Fast 3-D Winding Inductance Estimation Method for Air-Cored Resonant Induction Machines

The air-cored resonant induction machine removes the magnetic core, so the fields produced by the windings are truly 3-D in nature. The end-windings normally regarded as a nonactive and leakage source in conventional iron-cored machines now become an active part and contribute to the torque production. Therefore, the electromagnetic modeling can no longer be reduced to a 2-D analysis, and the 3-D inductance calculation becomes a key problem. The 3-D finite element analysis (FEA) can solve the 3-D magnetic field, but, first, the validity of its solution depends on the precision in geometry modeling. In particular, representing the end-winding region avoiding conductor clashing can be very complicated. Second, 3-D FEA solutions are computationally slow, and therefore inefficient as an “internal routine” of an optimization procedure. This article proposes a fast analytic 3-D winding inductance estimation method for air-cored resonant induction machines. The approach breaks down the real coils into straight conductors and represents them by single filaments located at their centers, then uses closed-form expressions derived from Neumann integrals to calculate the coil self and coil-to-coil mutual inductances, which are then collected into winding phase self and mutual inductances. All the independent coil-pair contributions are isolated, so as to eliminate redundant calculations. Good accuracy of the calculated results is confirmed by validation against both 3-D FEA and experimental results, including winding inductance breakdown and overall machine tested performance.

Modeling of Magnetic Anisotropy Due to Compression Molding of Soft Magnetic Composite for Inductance Calculation

A modeling method of the anisotropic magnetic characteristics due to compression molding of a soft magnetic composite (SMC) for inductance calculation of an SMC inductor is proposed. First, a particle model with a flattened iron particle and a uniform layer of insulation is constructed to simulate the anisotropic <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">BH</i> curves in arbitrary directions using the measured limited two <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">BH</i> curves in the compress and vertical directions under compression. Then, the proposed particle model is expanded to include the dc-biased characteristic of permeability. Moreover, the proposed model is applied to two inductors with legs having different compress directions. It is shown that the proposed method can be applied to the optimal design of inductors taking account of the compress direction of SMC.

Analysis and Verification of Leakage Inductance Calculation in DAB Converters Based on High-Frequency Toroidal Transformers under Different Design Scenarios

High-frequency transformers are becoming an essential component in the integration of power resources that rely on power electronic converters; their efficiency and performance are influenced by parasitic characteristics in the interface. In this article, the design of a high-frequency toroidal transformer has been explained in detail using the ANSYS Maxwell platform. Various parameters, such as leakage inductance, magnetic flux density, magnetic field strength and uniform magnetic flux line are analyzed using Finite element analysis. High-frequency transformers using a toroidal core with different winding configurations are examined and all parameters obtained through simulation are validated by an analytical approach. Analysis of each design is based on its leakage inductances, which will aid in the appropriate selection of transformers as a function of their operating frequency. This analysis is expected to guide designers to optimize the high-frequency transformer parameters based on practical applications. The optimized parameters are then applied for a dual active bridge (DAB) converter within MATLAB/Simulink to verify the design process. A prototype has been built to validate the simulation and design procedure. The results obtained from both simulation and experiments are compared and show great correlation.

Immunological characteristics of tobacco samples of competition and breeding variety testing in the conditions of Prydnistrovia of Ukraine

Aim. Investigate competition and selection material of tobacco for resistance to major diseases for immunological characterization of samples and use of results in practical selection.General scientific and special work methods: field, laboratory, selection that use induction apomixis, calculation, mathematical and statistical. The use of apomixis in tobacco breeding helps shorten the selection process by 4–6 years. During the assessment of the selection material for the resistance of tobacco to harmful organisms, we have used the results substantiated by us during 2011−2015 scales for assessing the intensity of damage by the most common and harmful diseases and the settlement and damage by pests. Results. Tobacco varieties and hybrids with individual and complex resistance to diseases, that are common in the Transnistria region of Ukraine, were selected for the purpose of using them in selection work. On the basis of these samples, a characteristic collection of tobacco was created and registered on resistance to biotic and abiotic factors.Conclusions. During the years of research (2016−2020), varieties and hybrids of tobacco were selected in competitive and selective variety tests (Ternopilsky 7, Berley 38, Berley 46, Ukrainsky Novy, Fn Banat × Ukrainian new, An Berlei 46 × Ternopil 7, Zhovtolisty 36, Ukrainian sharp-leaved, Fn [(Banat × Ukrainian new) × Polish burley)] × Yellow-leaved 36, Fn Temp 321 × Sharp-leaved 451, Fn Virginia 23 × Virginia 401) with complex and individual resistance to the main diseases common in Transnistria of Ukraine. On the basis of these samples, a characteristic collection of tobacco was created and registered on resistance to biotic and abiotic factors in the National Center of Plant Genetic Resources of Ukraine.

Decoupled Estimation Scheme for PMSMs Toward Accurate Inductance Modeling

Parameter identification of permanent magnet synchronous machines (PMSMs) is critical toward building an accurate machine model, achieving precise control, and improving operational reliability. This article proposes a decoupled estimation scheme for interior PMSM with consideration of magnetic saturation as nonlinear functions of current to improve the inductance estimation accuracy. An improved machine model considering magnetic saturation and cross-coupling effects by utilizing a quadratic model in inductance calculation is developed. Furthermore, the decoupled estimation scheme with considering stator resistance and iron loss resistance can effectively reduce the interaction in the process of parameter identification, and the least square algorithm is employed to improve the computational efficiency. Moreover, this proposed method is especially dedicated to the modern testing solutions that require complex hardware and extensive machine operation while being noninvasive by nature.

A New Analytical Study on Mutual Inductance Calculations for Wireless Power Transfer Using Magnetic Vector Potential

This article presents a new analytical approach for the calculation of mutual inductance based on magnetic vector potential (MVP). To demonstrate the proposed mutual inductance calculation method, planar spiral coils of polygonal shape with an arbitrary number of sides are discussed. The coils considered in this work are coaxial and assumed to be composed of concentric filaments. The flux produced by the primary and linking the secondary is calculated by the line integral of the MVP. In order to simplify the calculation strategy, the MVP contribution of only one side of each single-turn filament of the primary is considered due to the symmetry of the coils’ shapes. Accordingly, coupling flux across the surface surrounded by each turn of the secondary is calculated by the line integral of the MVP over half path of the filament’s turn. The accuracy of the new analytical approach is confirmed by examining coil systems with a different primary and secondary in terms of the number of sides, the number of turns, and size. Results of the new approach are compared with those obtained from Ansys Maxwell, analytical studies in the literature, and experimental to demonstrate the validity of the proposed method. Results from this work are in good agreement with those obtained from simulation, studies in the literature, and experiment that proves the feasibility of formulas used in this work.

3-D Analytical Model of Bipolar Coils With Multiple Finite Magnetic Shields for Wireless Electric Vehicle Charging Systems

The bipolar pad is one of the most promising topologies in inductive power transfer (IPT) systems for electric vehicles. However, there is scant literature on the analytical model of the bipolar pad. In this article, a three-dimensional (3-D) analytical model of the IPT system including a bipolar transmitter and a square receiver is developed based on the superposition of two 2-D subdomain analytical models. Ferrite and the aluminum shields with finite dimension are taken into account on the transmitter and receiver sides. An analytical calculation of the mutual inductance is then carried out with respect to the main parameters of the IPT system, namely the dimension of the coils, the conductivity, and the permeability of the shield. Three study cases are demonstrated to highlight how the proposed method can accelerate speed up the pad design process. Calculation results of the proposed model are compared with both a finite-element analysis (FEA) model and experimental measurements, demonstrating that the proposed model is nine times faster than the FEA method. When comparing with the experimental results, computational error of the proposed model is less than 6% in most of the study cases.

Application of a Calculation Formula for the Self‐Inductance of an Arbitrary‐Shaped Single‐Layer Coil (Derivation of Shape Functions and Inductance Caluculations for Regular Polygonal Coils)

In the design and production of electrical and electronic devices and circuits, it is desirable to have a calculation formula for obtaining exact inductance values, which are generally fundamental for coils. In this paper, a formula that can be applied to the exact calculations of the self-inductance of arbitrary-shaped single-layer coils is presented, and its application to the several types of coils that are technologically valuable is reported. Specifically, the formula employs a new coefficient corresponding to the Nagaoka coefficient and the shape function determined by the coil. Moreover, it realizes a versatile and convenient inductance calculation method. In addition, as the formula is derived via an analytical method, it has the advantage that it can be calculated with a short-time numerical integration. As examples of the application of the formula, rhombic, race-track, elliptic, and regular polygonal coils were discussed, and the process and result of deriving the shape function and new coefficient for each coil were presented. Furthermore, regarding the calculation formula for regular polygonal coils, we made a regular pentagonal coil and conducted an experiment, and the validity of the calculation formula was confirmed. © 2022 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

A Practical Guide to Estimating Coil Inductance for Magnetic Resonance Applications

Radiofrequency (RF) coils are employed to transmit and/or receive signals in Magnetic Resonance (MR) systems. The design of home-made, organ-specific RF coils with optimized homogeneity and/or Signal-to-Noise Ratio (SNR) can be a plus in many research projects. The first step requires accurate inductance calculation, this depending on the conductor’s geometry, to later define the tuning capacitor necessary to obtain the desired resonance frequency. To fulfil such a need it is very useful to perform a priori inductance estimation rather than relying on the time-consuming trial-and-error approach. This paper describes and compares two different procedures for coil inductance estimation to allow for a fast coil-prototyping process. The first method, based on calculations in the quasi-static approximation, permits an investigation on how the cross-sectional geometry of the RF coil conductors affects the total inductance and can be easily computed for a wide variety of coil geometries. The second approach uses a numerical full-wave method based on the Finite-Difference Time-Domain (FDTD) algorithm, and permits the simulation of RF coils with any complex geometry, including the case of multi-element phased array. Comparison with workbench measurements validates both the analytical and numerical results for RF coils operating within a wide field range (0.18–7 T).

Fast and Precise Calculation of Mutual Inductance for Electrodynamic Suspension: Methodology and Validation

The mutual inductance is the core parameter of electrodynamic suspension (EDS) as it couples the onboard coils and ground coils to realize the stable suspension. The precise and efficient calculation of mutual inductance is therefore of great significance to understand and optimize the characteristics of EDS train, which has achieved a manned speed in excess of 600 km/h. In this article, we proposed a calculation method of mutual inductance, considering the geometrical details of coils and the attitude of bogie, by means of the 3-D discretization of coils and the spatial coordinate transformation of discrete units. Based on this methodology, the analytical model was established, and the dependence of computation time and precision on the discretization degree is intensively discussed. Afterward, the finite-element analysis (FEA) was adopted to check the accuracy and effectiveness of the proposed methodology. Compared with FEA, the computation time has been reduced by 97% with accuracy reserved. Finally, a testing platform was constructed to further verify the availability of the proposed model. In summary, the proposed methodology can realize efficient calculation of mutual inductance in consideration of more realistic situations, providing an invaluable tool for the complex studies of superconducting EDS train.

Module Integral Method for the Calculation of Frequency-Dependent Leakage Inductance of High-Frequency Transformers

The accurate calculation of frequency-dependent leakage inductance of high-frequency transformers is critical for the optimized design of power electronic transformers. The leakage inductance can be obtained through the magnetic energy, usually calculated by the phasor integral of the magnetic energy density in the literature. This article analyzes the difference between the module and the phasor integral based on frequency-domain energy and proposes to take the module integral of magnetic energy density as the periodic averaged magnetic energy. Furthermore, the closed-form formula of the leakage inductance is given accordingly. The modules under different frequencies correspond to the intrinsic constant magnetic densities. Thus, the proposed method has a better physical interpretation compared with the previous phasor integral method. The finite element method simulation and experimental results of five transformers are taken as benchmarks to compare the proposed method with the phasor integral method. The comparison shows that the proposed module integral method has satisfying effectiveness and accuracy in the whole frequency band for all the cases involving both noninterleaved and interleaved windings.