The aim of this paper is presentation and comparison of calculation methods of the inductance matrix of a 3-column multi-winding autotransformer. Main and leakage autotransformer inductance was obtained using finite elements method. Static calculations were made at the current supply for 2D and 3D models, and mono-harmonic calculations were made at the voltage supply. In the mono-harmonic calculations the eddy current losses were taken into account, this made it possible to study relationship between the autotransformer parameters and the frequency. Calculations were made using Ansys and the authors' own programs in Matlab.

The 15-winding and 3-column autotransformer supplying an 18-pulse rectifier circuit was developed. Presented methods can be used also for the autotransformers of other topologies supplying different kinds of converters. Presented methods make it possible to exactly calculate main and leakage inductances of the multi-winding autotransformer. The presented analysis of the eigenvalues and eigenvectors of the inductance matrix makes it possible to identify the influence nature of individual modes on the inductance matrix, and to compare the calculation results obtained using the presented methods. Frequency dependence of autotransformer parameters was shown. Also modes of the impedance matrix of the multi-winding autotransformer was investigated, this made it possible to identify the influence nature of individual modes on the inductance matrix. Using presented methods one can exactly calculate main and leakage inductances of the autotransformer. Thanks to this, one can design in optimal way autotransformers for supplying, for example, rectifier circuits, THD coefficients. The results of the measurements and simulations were also shortly presented at the end of the article.

The optimization method using the ON/OFF sensitivity analysis has an advantage hat an epoch-making construction of magnetic circuit may be obtained. Therefore, it is attractive for designers of magnetic devices. We have already developed the ON/OFF method for the optimization of a static magnetic field problem, and the effectiveness is verified by applying it to the optimization of magnetic recording heads. In this paper, the ON/OFF sensitivity method is extended to the optimization of the eddy current problem using the adjoint variable. The newly developed ON/OFF method is applied to the determination of the optimal topology of the yoke of the billet heater for rolling wire rod. As a result, the optimal shape of yoke, which we could not imagine beforehand can be obtained. It is shown that the local heating of the yoke was reduced without decreasing the heating efficiency.

Harmonic flux penetrating solid conductive material causes eddy currents inside. It seems plausible that its magnitude does not exceed the exciting magnetomotive force (mmf). However, under certain circumstances the opposite occurs. This article deals with a special case in which the eddy current is approximately 13% higher than the exciting mmf. An analytical field solution, a finite element calculation and a measurement proving this phenomenon are presented. A special flux linkage is turned out to be the reason for this phenomenon. Finally, another example with higher pronounced mmfexceeding in a coil is presented.

The results of the eddy currents losses calculations with using electrodynamics scaling were presented in this paper. Scaling rules were used for obtain the values of the eddy currents losses. For the calculations Finite Element Method was used. Numerical calculations were verified by measurements and a good agreement was obtained.

Precise measurement of rail vehicle velocities is an essential prerequisite for the implementation of modern train control systems and the improvement of transportation capacity and logistics. Novel eddy current sensor systems make it possible to estimate velocity by using cross-correlation techniques, which show a decline in precision in areas of high accelerations. This is due to signal distortions within the correlation interval. We propose to overcome these problems by employing algorithms from the field of dynamic programming. In this paper we evaluate the application of correlation optimized warping, an enhanced version of dynamic time warping algorithms, and compare it with the classical algorithm for estimating rail vehicle velocities in areas of high accelerations and decelerations.

The current passed by the stator coil of the permanent magnet synchronous motor (PMSM) provides rotating magnetic field, and the number of turns will directly affect the performance of PMSM. In order to analyze its influence on the PMSM performance, a 3 kW, 1500 r/min PMSM is taken as an example, and the 2D transient electromagnetic field model is established. The correctness of the model is verified by comparing the experimental data and calculated data. Firstly, the finite element method (FEM) is used to calculate the electromagnetic field of the PMSM. The performance parameters of the PMSM are obtained. On this basis, the influence of the number of turns on PMSM performance is quantitatively analyzed, including current, no-load back electromotive force (EMF), overload capacity and torque. In addition, the influence of the number of turns on eddy current loss is further studied, and its variation rule is obtained, and the variation mechanism of eddy current loss is revealed. Finally, the temperature field of the PMSM is analyzed by the coupling method of electromagnetic field and temperature field, and the temperature rise law of PMSM is obtained. The analysis of this paper provides reference and practical value for the optimization design of PMSM.

This work deals with the inverse problem associated to 3D crack identification inside a conductive material using eddy current measurements. In order to accelerate the time-consuming direct optimization, the reconstruction is provided by the minimization of a last-square functional of the data-model misfit using space mapping (SM) methodology. This technique enables to shift the optimization burden from a time consuming and accurate model to the less precise but faster coarse surrogate model. In this work, the finite element method (FEM) is used as a fine model while the model based on the volume integral method (VIM) serves as a coarse model. The application of the proposed method to the shape reconstruction allows to shorten the evaluation time that is required to provide the proper parameter estimation of surface defects.

The calculations results of the temperature distribution in a 3-phase transformer with modular amorphous core are presented. They were performed for two frequency values which were higher than the power system one. For the 3D field analyses the Finite Element Method (FEM) was used. The calculated temperature at the points of the core surface has been verified using an infrared camera.

This paper considers a Brushless Direct Current (BLDC) machine prototype with six poles and 36 stator slots including a three phase double-layered distributed winding. Presented modifications of rotor construction are identified in order to achieve the best possible compromise of eddy-current losses and cogging torque characteristics. The permanent magnet (PM) eddy-current loss is relatively low compared with the iron loss; it may cause significant heating of the PMs due to the relatively poor heat dissipation from the rotor and it results in partial irreversible demagnetization. A reduction in both losses is achieved by magnet segmentation mounted on the rotor. Various numbers of magnet segmentation is analysed. The presented work concerns the computation of the no-load iron loss in the stator, rotor yoke and eddy-current loss in the magnets. It is shown that the construction of the rotor with segmented magnets can significantly reduce the PM loss (eddy-current loss). The eddy-current loss in PMs is caused by several machine features; the winding structure and large stator slot openings cause flux den sity variations that induce eddy-currents in the PMs. The effect of these changes on the BLDC motor design is examined in order to improve the machine performance. 3-D finite-element analysis (FEA) is used to investigate the electromagnetic behaviour of the BLDC motor.

In this paper we present the results of simulations of the Magnetic Induction Tomography (MIT) forward problem. Two complementary calculation techniques have been implemented and coupled, namely: the finite element method (applied in commercial software Comsol Multiphysics) and the second, algebraic manipulations on basic relationships of electromagnetism in Matlab. The developed combination saves a lot of time and makes a better use of the available computer resources.

Due to the skin effect of eddy currents, the depth of cracks which can be detected by the traditional eddy current probe is very limited. In order to improve the ability of eddy current probes to inspect deep cracks in metal thick-walled structures, a new eddy current probe using an excitation system with phase shifted fields was proposed. Its feasibility for detecting deep cracks was verified by simulation and experiments. The results showed that the penetration depth of eddy currents in austenitic stainless steel is effectively enhanced by using the new probe.

Pot-cored coils are commonly used as probes in eddy current testing. In this paper, an analytical model of such a coil placed over a three-layer plate with a hole has been presented. The proposed solution enables the modelling of both magnetic and non-magnetic conductive plates that contain different types of hole, i.e. a through, a surface, an inner or a subsurface hole. The problem was solved by using the truncated region eigenfunction expansion (TREE) method. The analysis was carried out in a cylindrical coordinate system in which the solution domain was radially limited. With the employment of the filamentary coil, the expressions for the magnetic vector potential, and subsequently for the impedance of the cylindrical coil were obtained. The final formulas were presented in a closed form and then implemented in Matlab. The resistance and reactance values were compared with the results obtained in the experiment and using the finite element method in the Comsol Multiphysics package. In each of the cases, good agreement was obtained.