Effects of eddy currents in transformer windings
01 Aug 1966-Vol. 113, Iss: 8, pp 1387-1394
TL;DR: In this article, the effect of eddy currents on transformer windings is considered and a method is derived for calculating the variation of winding resistance and leakage inductance with frequency for transformers with single-layer, multilayer and sectionalised windings.
Abstract: The effects of eddy currents in transformer windings are considered, and a method is derived for calculating the variation of winding resistance and leakage inductance with frequency for transformers with single-layer, multilayer and sectionalised windings. The method consists in dividing the winding into portions, calculating the d.c. resistances and d.c. leakage inductances of each of these portions, and then multiplying the d.c. values by appropriate factors to obtain the corresponding a.c. values. These a.c. values are then referred to, say, the primary winding and summed to give the total winding resistance and leakage inductance of the transformer. Formulas are derived and quoted for calculating the d.c. resistances and leakage inductances of the winding portions. Theoretical expressions are derived for the variation with frequency etc. of the factors by which the d.c. values must be multiplied to obtain the corresponding a.c. values. These expressions are presented in the form of graphs, permitting the factors to be read as required.
Citations
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DOI•
01 Jan 2016
TL;DR: In this paper, different integrated inductor solutions are presented with an objective to reduce the overall size of the magnetic component, so that the power density can be further improved or for the given filter size, the switching frequency can be reduced.
Abstract: The two-level Voltage Source Converters (VSCs) are often connected in parallel to increase the current handling capability. In such systems, the multi-level voltage waveforms can be obtained by interleaving the carrier signals of the parallel connected two-level VSCs. The multi-level voltage waveform facilitates reduction in both the switching frequency and the size of the harmonic filter components. This leads to the improvement in both the system efficiency and power density. However, when VSCs are connected in parallel and share the same dc-link, the circulating current flows through the closed path due to the control asymmetry and the impedance mismatch. When the carriers are interleaved, the pole voltages (switched output voltage of the VSC leg) of the interleaved parallel legs are phase shifted and it creates instantaneous potential difference across the closed path, formed due to the parallel connection. This instantaneous potential difference further aggravates the circulating current, which results in increased losses and unnecessary oversizing of the components present in the circulating current path. Therefore, the circulating current should be suppressed to realize the full potential of the carrier interleaving. The formation of the circulating current path can be avoided by using the line frequency isolation transformer. However, it increases the overall size of the system and should be avoided. The use of the Common-Mode (CM) inductor in series with the line filter inductor for each of the VSCs is proposed in literature. Another approach proposes the use of the Coupled Inductor (CI) to suppress the circulating current by providing magnetic coupling between the parallel interleaved legs of the corresponding phases. Although the interleaved carrier signals lead to the reduction in the value of the harmonic filter components, additional filter components (CIs) are often required to suppress the circulating current. The volume of these inductive components can be reduced by integrating both of these functionalities into a single magnetic component. Different integrated inductor solutions are presented in this thesis with an objective to reduce the overall size of the magnetic component, so that the power density can be further improved or for the given filter size, the switching frequency can be further reduced. The advantages achieved by
1 citations
01 Sep 2020
TL;DR: An adequate loss model is established and an optimal design approach for inductors for buck or boost converters is presented and a test inductor is realized and characterized.
Abstract: In this work an optimal design approach for inductors for buck or boost converters is presented. The optimization routine is based on Non-Dominated Sorting Genetic Algorithm (NSGA2) which is well suited for such multi objective optimization applications with discrete design parameters. The optimization objectives are size and loss. Therefore an adequate loss model is established. The whole algorithm and the results are presented. To verify the models a test inductor is realized and characterized.
1 citations
TL;DR: In this paper , an air-core transformers for electric vehicles was developed for medium-power (tens of kWs) converter applications specifically used at a high frequency, with the advantage of lacking magnetic saturation and iron losses, making them suitable for high frequency applications.
Abstract: This paper presents the study of air-core transformers for electric vehicles, developing them for medium-power (tens of kWs) converter applications specifically used at a high frequency. Air-core transformers have the advantage of lacking magnetic saturation and iron losses, making them suitable for high-frequency applications. We designed and manufactured a transformer for a determined frequency and inductance value. The design of this passive component aims to both keep the magnetic field inside the transformer and manage the thermal energy efficiently. The electrical, magnetic, and thermal properties are simulated and then verified by experiments with a specific test bench. The transformer reaches high performances for a higher frequency than usual for an equivalent power transfer in automotive applications.
1 citations
01 Jan 2014
1 citations
01 Oct 2006-Compel-the International Journal for Computation and Mathematics in Electrical and Electronic Engineering
TL;DR: In this paper, the frequency-domain homogenization method for laminated magnetic cores and multi-turn windings in FE models of electromagnetic devices has been discussed and validated numerically, i.e. by comparison with brute force FE computations where the eddy current effects are directly and accurately taken into account.
Abstract: Purpose – To review and discuss recently proposed homogenization methods for laminated magnetic cores and multi‐turn windings in FE models of electromagnetic devices.Design/methodology/approach – The frequency‐domain homogenization is based on the adoption of complex and frequency‐dependent material characteristics (e.g. reluctivity) in the homogenized domain. The value of the complex quantity is obtained analytically or by means of a simple 2D FE model. The time‐domain counterpart requires the introduction of additional unknowns and equation.Findings – The homogenization methods allow to take into account the global eddy current effect in the individual laminations and wires, with a reasonable precision and computational cost.Research limitations/implications – The homogenization methods have been validated numerically, i.e. by comparison with brute‐force FE computations where the eddy current effects are directly and accurately taken into account. Experimental validation should follow.Originality/value ...
1 citations
References
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TL;DR: In this article, a multilayer winding carrying an alternating current, such as the windings illustrated in figures 1, 2, and 3, each layer of copper lies in the alternating magnetic field set up by the current in all the other layers.
Abstract: IN any multilayer winding carrying an alternating current, such as the windings illustrated in figures 1, 2, and 3, each layer of copper lies in the alternating magnetic field set up by the current in all the other layers. Eddy currents are set up in each layer in a direction to partly neutralize the magnetic intensities in the interior of the copper wire in each layer. As a result of the eddy-current losses in the copper, the effective resistance of the winding to the alternating current it carries may be many times its resistance to continuous currents.
103 citations
TL;DR: In this article, the authors discuss the more important causes of eddy currents in heavy conductors carrying alternating currents and surrounded on three sides by iron, and propose a method to identify the most important causes.
Abstract: The object of the present paper is the discussion of the more important causes of eddy currents in heavy conductors carrying alternating currents and surrounded on three sides by iron.
93 citations
64 citations
TL;DR: In this article, it is shown that a considerable proportion of the effective resistance of inductive coils when used at radio frequencies is caused by the eddy-currents set up in the wires of the coils by the alternating magnetic field in which they are situated, and that in extreme cases the alternating current resistance may amount to more than one hundred times the direct current resistance.
Abstract: It is well-known that a considerable proportion of the effective resistance of inductive coils when used at radio frequencies is caused by the eddy-currents set up in the wires of the coils by the alternating magnetic field in which they are situated, and that in extreme cases the alternating current resistance may amount to more than one hundred times the direct current resistance. It is therefore important to have reliable formulae for the eddy-current resistance of such coils in order to determine the conditions which will reduce the eddy-current losses to a minimum. The simplest case, that of a long straight cylindrical wire under the action of its own current, has been treated by Kelvin, Rayleigh, Heaviside, and others. The general effect is known as the “skin effect,” because the current tends to concentrate more and more upon the skin of the conductor as the frequency increases.
49 citations
TL;DR: In this article, the authors show how hyperbolic functions of complex angles may be applied to the solution of the problem of heat losses in rectangular conductors that are embedded in open slots.
Abstract: The principal object of this paper is to show how hyperbolic functions of complex angles may be applied to the solution of the problem of heat losses in rectangular conductors that are embedded in open slots. A certain knowledge of the functions themselves is presupposed. Inasmuch, however, as they are handled like trigometric functions of real angles?except in regard to the plus and minus signs?it is a simple matter to acquire the requisite technical skill to use them. The hyperbolic function of a complex angle, consisting as it does of a real and an imaginary part, may represent a vector?the real part being the component of the vector along the horizontal, and the imaginary part, component along the vertical. Thus, for example, A sinh (x + j x) represents a vector just as A e j ? A/?, A (cos ? + j sin ?) represent vectors. Considerable experience has shown that the vector method for handling a-c. problems is much superior to the original method in which simple trigonometric functions were used. With this lesson before us, it should require but little contact with the problem at hand to demonstrate the superiority of the vector method, even though it employs the possibly unfamiliar hyperbolic quantities. These hyperbolic vectors have been used for a number of years in the analysis of problems involving a-c. circuits, which have distributed inductance and capacitance, and have proved their usefulness.
27 citations