Calculation Of Mutual Inductance Research Articles

Mutual Inductance Calculation of Rectangular Coils at Arbitrary Position With Bilateral Finite Magnetic Shields in Wireless Power Transfer Systems

Mutual Inductance Calculation of Rectangular Coils at Arbitrary Position With Bilateral Finite Magnetic Shields in Wireless Power Transfer Systems

An approach of dynamic wireless charging structure for an electric vehicle based on mutual inductance calculation

An approach of dynamic wireless charging structure for an electric vehicle based on mutual inductance calculation

Analytical Calculation of Mutual Inductance of D-Shaped Coils Applied to High-Temperature Superconducting Magnet

Analytical Calculation of Mutual Inductance of D-Shaped Coils Applied to High-Temperature Superconducting Magnet

Analytical method of mutual inductance for T-R rectangular coils perpendicular to the planar medium

Some studies indicate that for specific defect detection in eddy current testing (ECT), the transmitter-receiver (T-R) probe models with tangential rectangular transmitter coil exhibit effective detection performance. In this context, mutual inductance being a crucial parameter. The calculation of mutual inductance for vertically oriented T-R coils is more intricate compared to that of parallel T-R coils, which is currently predominantly focused on circular mutual inductance analysis. This paper presents a closed-form formula for the mutual inductance of rectangular T-R coils oriented vertically to the conductor based on the method of the second-order vector potential approach. In this model, a form function concerning the coil's position and shape is defined, allowing convenient extension to T-R coils of arbitrary shapes and positions. Simultaneously, the validity of the theory is tested against experimental measurements on different positions and frequencies of coil systems above an aluminum plate. The results indicate good agreement between theoretical and experimental results within the 100 Hz to 100 kHz range. Consequently, this model can offer guidance for the calculation of mutual inductance for vertically oriented rectangular T-R coils in ECT.

Calculation of mutual inductance between arbitrarily positioned planar spiral coils for wireless power applications

Mutual inductance is one of the main parameters required to determine the power link’s performance (output voltage, efficiency) in wireless power transfer. The coils are often misaligned angularly in these applications, which affects the mutual inductance and thus the performance. Hence, an accurate calculation of mutual inductance is necessary to decide the working region of the coil. This paper presents an analytical calculation of mutual inductance between two planar spiral coils under angular misalignment conditions. By solving the Neumann integral formula, mutual inductance is derived for constant current-carrying coils, and the final mutual inductance value is calculated numerically. The influence of angular misalignment of the coil, which can be due to nutation and spin angles, on mutual inductance is studied in detail. The mutual inductance of the spiral coil is calculated for different misalignment cases. The accuracy of the calculation results is verified by comparing it with conventional formulas (mainly the Liu, the Babic formula, and the Poletkin formula) and by simulation using the finite element method. The proposed method is a more generalized and simpler one that can be used to calculate the mutual inductance of any size of coils, either spiral or circular, with any lateral and angular misalignments. Finally, a couple of spiral coils are fabricated to validate it experimentally. The comparison of the simulation and experiment results with the calculation result shows its accuracy. Thus, the proposed method can be applied to compute mutual inductance in any angularly misaligned coupling coils for the optimization of the wireless power transfer and their design.

Analysis on Transmission Characteristics of Dynamic Magnetic Coupling Mechanism of Racetrack Coil with Deflection Angles

In dynamic magnetically coupled contactless power transmission, the fluctuation of mutual inductance is caused by the relative motion between transmission and receiving coils, which affects the stability of power transmission. In order to reduce the fluctuation characteristics of power transmission, the mutual inductance calculation model of transmission mechanism including a racetrack coil with deflection angle is established by using Neumann formula, and the influence of different deflection angle and layout on mutual inductance fluctuation characteristics is analyse and compare. Then the power transmission system with LCC-S compensation for the transmission mechanism is established. The transmission characteristics of the racetrack coil with deflection angle are studied. The results show that reasonable design of the deflection angle can reduce the fluctuation of the mutual inductance and the power output in dynamic transmission. The fluctuation of power output can also be reduced by changing the distance between transmission coils and the length of straight side of receiving coils.

Calculation and regulation of mutual inductance of wireless charging coils with metal shielding materials based on multiple intelligent optimization algorithms

SummaryIn wireless charging systems for electric vehicles, fluctuations in coil mutual inductance can affect both system output power and efficiency. This paper introduces a coil mutual inductance model that accounts for metal shielding material. The formula for coil mutual inductance is derived using Maxwell's equations and boundary conditions. Additionally, the paper presents a tactic for adapting the mutual inductance with the aid of an intelligent optimization algorithm, which is utilized for steadying the mutual inductance of the transmission coil. Lastly, a model of the transmission coil is developed to authenticate the practicality of the mutual inductance equation and the adaptation scheme. Measurement and calculation results indicate that the difference between the calculated value of the mutual inductance formula and the actual mutual inductance value of the coil, following deflection and offset, is below 5%. Moreover, the algorithm, along with the employed adaptation strategy, consistently demonstrates effectiveness in maintaining the mutual inductance value within a predefined range. The temporal efficiency of the algorithm, as measured by the time taken to determine this coordinate position, is consistently under 1 s. This ensures that the algorithm exhibits a rapid response time, a crucial attribute in ensuring its practical utility.

Mutual Inductance Calculation Method of Rectangular Coils with Bilateral Bounded Single-hole Type Magnetic Medium in Wireless Power Transfer Systems

Mutual Inductance Calculation Method of Rectangular Coils with Bilateral Bounded Single-hole Type Magnetic Medium in Wireless Power Transfer Systems

CALCULATION OF POWER TRANSFORMER INDUCTANCE MATRIX

Practical calculations of electric equipment and electric networks are performed using equivalent circuits. Without taking into account saturation phenomena, electromagnetic processes in a power transformer are described by a system of linear equations, which can be represented in matrix form. The transformer inductance matrix contains self and mutual winding inductances, whose values for one phase are determined directly from the passport data containing the results of no-load and short circuit experiments. Mutual inductances between phases depending on the type and size of the magnetic core are not usually given in the transformer documentation. It does not allow to simulate the operating modes that differ from the steady state with uniform phase load.
 
 The purpose of the work is to develop an algorithm for calculating elements of the power transformer inductance matrix according to its passport data and magnetic circuit parameters.
 
 The scientific novelty lies in use of information about magnetic circuit type and size to determine elements of the inductance matrix.
 
 Materials and methods. Methods of linear electric and magnetic circuit theory are used in the work.
 
 Results. The proposed algorithm for calculation of power transformer inductance matrix includes three stages: calculation of self and mutual inductances for one phase; construction of an equivalent circuit for a magnetic circuit and calculation of magnetic fluxes in order to take into account the mutual influence of windings on various phases; assembly of the inductance matrix of three-phase transformer. A method is proposed for constructing the transformer inductance matrix with an arbitrary type of magnetic circuit, phases and windings quantity. The method involves preliminary calculation of the coefficient matrix that characterizes the magnetic circuit and depends mainly on its type and, to a less, on the ratio of geometric dimensions in rods and yokes. The coefficient matrix can be calculated in advance and used to determine the inductance matrix of a wide range of transformers.
 
 Conclusions. 1. The passport data of the transformer do not allow to model transformer operation at unbalanced load validly. 2. An algorithm for determining the inductance matrix of transformers has been developed. 3. A method for compilation of a transformer inductance matrix with an arbitrary type of magnetic circuit, the number of phases and windings is introduced. The practical significance of the algorithm is determined by the simplicity of algorithmizing, as well as by the possibility of using it in computer simulation of electrical circuits with transformers, for example, using the modified nodal analysis method.

Calculation of Mutual Inductance between Two Planar Coils with Custom Specifications and Positions Using a Machine Learning Approach

Wireless power transmission systems enable the transfer of electricity between grids without the use of physical wires. Different methods are employed for wireless power transfer, each suited to different distances. Inductive coupling, the subject of this study, is typically used for shorter distances. The effectiveness of inductive coupling systems is evaluated using a parameter called mutual inductance. In the present study, an attempt is made to provide a model for calculating mutual inductance in wireless power transfer systems using a machine learning approach. To achieve this goal, finite element simulations are employed, and 64 datasets are generated from mutual inductance calculations in various scenarios. These datasets are used to train machine learning regression algorithms, including linear regression, support vector regression, decision tree regression, and artificial neural networks. The evaluation results, using performance metrics such as R-squared, mean absolute error, and root mean square error, confirm that among these four algorithms, the artificial neural network exhibits higher computational accuracy with an R-squared value of 0.950 for predicting test data.

Design Optimization of Null-Flux Superconducting Electrodynamic Suspension for Cost-Saving and Performance Improvement

The onboard superconducting magnets and null-flux coils (NFCs) on the track side are the crucial components for realizing the null-flux superconducting electrodynamic suspension (EDS). In this article, the multiobjective optimization of a null-flux EDS system was investigated to improve the performance using the nondominated sorting genetic algorithm-II (NSGA-II) method. First, a precise mathematical model of the superconducting EDS was established by adopting mutual inductance calculation method we proposed before. Then, the comprehensive sensitive analysis was carried out to analyze the influence of variables on different objectives. The ratio of levitation force to drag force (drag ratio), the ratio of levitation force to mass of NFCs (mass ratio) as well as the fluctuation of levitation force, were defined to be the optimization objectives. Third, an optimization scheme employing NSGA-II method was built, and the Pareto front was obtained. Afterward, the effectiveness of optimized results was verified by the finite element analysis. Finally, an equivalent experimental method was used to characterize the performance of a down-scale EDS system to confirm the proposed optimization methodology. To conclude, the optimal method can greatly improve the performance of EDS, and provide diverse design scheme choices.

Mutual inductance calculation for rectangular and circular coils with parallel axes

Mutual inductance calculation for rectangular and circular coils with parallel axes

Calculation of mutual inductance between circular and arbitrarily shaped filaments via segmentation method

In this article, two analytical formulas for the calculation of mutual inductance between a circular filament and line segment arbitrarily positioning in the space are derived by using Mutual Inductance Method (MIM) and Babic’s Method (BM), respectively. Using the fact that any curve can be interpolated by a set of line segments, a method for calculation of mutual inductance between a circular filament and filament having an arbitrary shape in the space is proposed based on the derived analytical formulas. The derived two formulas and the proposed method (Segmentation Method) were numerically validated by using FastHenry software and reference examples from the literature. In particular, the proposed method was successfully applied to the calculation of mutual inductance between the circular filament and the following special curves such as circle, circular arc, elliptic arc, ellipse, spiral, helices and conical helices. All results of the calculation are in good agreement with the reference examples.

Mutual inductance calculations of non-identical n-sided planar coils with arbitrary geometry and spatial orientations

Mutual inductance calculations of non-identical n-sided planar coils with arbitrary geometry and spatial orientations

A Novel Analytical Model for Mutual Inductance Calculations Between Two Nonidentical N-Sided Polygonal Planar Coils Arbitrarily Positioned in 3-D Space for Wireless Power Transfer

Mutual inductance (MI) calculation is of great importance, because there are many systems that operate on the principle of inductive coupling. This paper presents a novel analytical model that calculates the MI between two non-identical n-sided polygonal planar coils located in arbitrary position in 3D space. The model depends upon misalignment of both the primary and the secondary coils of a wireless power transfer (WPT) system operating based on inductive coupling. The polygonal coils used in this model may differ from each other in terms of size, shape and turns number. The misalignment cases considered in the proposed model include lateral, angular, lateral-angular and vertical distance variation between the primary and secondary coils. Based on Stokes Theorem, instead of using the magnetic flux density vector, the magnetic vector potential (MVP) is used to reach the required magnetic flux in the calculation of the MI. A single analytical solution function that can calculate the MI between two planar polygonal coils of any shape in a simple manner and short time duration is obtained by performing difficult mathematical operations through MVP. Results obtained from the developed new model are compared with finite element analysis (FEA), experimental and other studies in the literature. The good agreement of the results of this study with the other results has proved the accuracy and validity of the proposed new analytical model.

Calculations of Self- and Mutual Inductances for Racetrack Coils Using Equivalent Models

This paper presents the calculations of self and mutual inductances for thin racetrack coils using a novel approach. Approximate rectangular and diamond shape models for racetrack coils are used for the analysis with the same cross-sectional area and circumference as the racetrack coils. A 3D analytical method using separation of variables method and Fourier series is developed for the magnetic fields analysis and calculation of self and mutual inductances for thin racetrack coils. The analytical method utilizes magnetic vector potential with two components to solve Maxwell differential equations. Different racetrack coils with different dimensions are considered for the validation of analytical modeling for the inductance calculations. The inductance calculations of circular coils are also presented as special cases for racetrack coils. The approaches for the mutual inductance calculation of racetrack and circular coils could be utilized for wireless power transfer and charging applications.

A novel method for calculating the mutual inductance between two perpendicular coils in wireless power transfer

SummaryThe perpendicular coil is increasingly applied in some wireless power transfer (WPT) systems where space position is limited. The existing method of calculating the mutual inductance between perpendicular coils is mainly applied to rectangular and circular coils. However, the practical rectangular coil often has rounded corners, so it unavoidably introduces systematic errors. Concerning this issue, this paper proposed an analytical method to calculate the mutual inductance between mutually perpendicular round‐corner rectangular (RCR) coils. The proposed method is based on a second‐order vector potential (SOVP) model where the mutual inductance between the coils is described as a double integral formula. In this formula, a novel shape and position function is introduced. This shape and position function describes not only RCR coils but also rectangular (including square), circular, and runway ones. A series of experiments were used to validate the proposed method. According to the consistency validation, the proposed method can be more generalized for calculating the mutual inductance of rectangular and circular coils. Through experimental comparison, the proposed method computes the mutual inductance between the perpendicular coil in excellent agreement with the measured ones. Therefore, the proposed method unifies the mutual inductance calculation of mutually perpendicular circular, rectangular (square), runway, and RCR coils and can provide an important basis for designing WPT systems using the above coils.

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.

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.

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.