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Journal ArticleDOI

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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Dissertation
25 Jun 2012
TL;DR: In this paper, the authors present a methode qui consiste premierement, a alleger l'ACV a l'aide d'un logiciel de gestion environnementale and d'en profiter pour construire un modele malleable pour calculer les differents impacts.
Abstract: Avec l’apparition des differentes normes et reglementations telles que les normes ISO 14001, les preoccupations industrielles y compris ferroviaires sont de plus en plus orientes vers l’eco-conception. La problematique la plus importante dans l’eco-conception des produits ferroviaires est de reduire leurs impacts environnementaux tout en maintenant leurs performances fonctionnelles et en maitrisant le cout. La solution pour surmonter ce probleme est de trouver un ensemble de compromis entre les deux objectifs (impacts et cout).L’eco-conception des produits ferroviaires presentent plusieurs difficultes parce que, d’une part, leur analyse de cycle de vie est tres lourde. D’autre part, l’integration de leurs impacts dans la phase de conception est delicate vu leur nombre. Enfin, ces composants ont parfois differents types de modeles a exploiter car ils presentent des compromis entre la precision et le temps de calcul. Pour surmonter ces problemes nous avons presente dans cette these une methode qui consiste premierement, a alleger l’ACV a l’aide d’un logiciel de gestion environnementale et d’en profiter pour construire un modele malleable pour calculer les differents impacts. Deuxiemement, a agreger ces impacts pour obtenir un seul indice qui sera considere comme notre critere environnemental. Pour exploiter les outils d’optimisation, le probleme d’eco-conception est traduit par un probleme d’optimisation. Les algorithmes d’optimisation sont capables de trouver l’ensemble de compromis optimaux entre le critere environnemental et la masse (cout) sous forme d’un graphe appele front de Pareto. Certains algorithmes ont ete adaptes pour mieux servir dans l’eco-conception

8 citations

Proceedings ArticleDOI
20 Mar 2006
TL;DR: The presented design method is based on a restatement of the traditional transformer design equations to include non-sinusoidal switching waveforms and high frequency skin and proximity effects to reach a transformer with high power density and admissible temperature rise.
Abstract: In this paper a new approach for optimization of high frequency transformer design is presented. The presented design method is based on a restatement of the traditional transformer design equations to include non-sinusoidal switching waveforms and high frequency skin and proximity effects. In this optimization procedure both electric and thermal effects in the transformer is considered. Wave form of voltage and current, and maximum acceptable temperature rise, are used as input data. The aim of this procedure is the selection of the smallest core that can deliver desired power, and determination of optimum flux density and current density to reach a transformer with high power density and admissible temperature rise. Since the transformer is the major contributor to the volume and weight of the Power Supply, the results of this transformer analysis can be used for entire power supply optimization as well. Finally the validity of presented method is analyzed.

8 citations

Proceedings ArticleDOI
22 Apr 2013
TL;DR: In this article, the effect of different geometrical parameters at a wide range of frequencies was investigated in order to propose a pseudo-empirical formula for winding loss calculation in high frequency transformers.
Abstract: When operating higher up in frequency, the copper losses in transformer windings will significantly rise due to enhanced skin and proximity effect. This leads to a high need to propose and develop new methods to accurately evaluate winding losses at higher frequencies. This paper investigates the effect of different geometrical parameters at a wide range of frequencies in order to propose a pseudo-empirical formula for winding loss calculation in high frequency transformers. A comprehensive analysis of the edge effect and AC resistance is done by performing more than 12300 2-D finite element simulations on foil and round conductors. Unlike previous studies which mostly focused on specific case studies with limited applications, this model provides very high accuracy, especially where the most common analytical models drastically underestimate the winding losses. Moreover the model has a wide-range applicability which could be of interest for designers to avoid time consuming FEM simulation without compromising with the accuracy.

8 citations

Proceedings ArticleDOI
29 Sep 2014
TL;DR: In this paper, the accuracy of typical AC resistance calculation methods in gapped inductors is discussed and it is shown that despite the additional losses caused by fringing flux induced eddy currents, the calculated resistances can be overestimated considerably due to non-tangential field distribution and reduced winding proximity losses.
Abstract: This paper discusses the accuracy of typical AC resistance calculation methods in gapped inductors. It is shown that despite the additional losses caused by fringing flux induced eddy currents, the calculated resistances can be overestimated considerably due to non-tangential field distribution and reduced winding proximity losses. However, this phenomenon is not so significant with windings having only a few winding layers; in such cases 1D calculation methods can be useful in predicting the winding resistances. It is also demonstrated how the fringing flux induced losses affect the calculated results and how they can be taken into account when using the 1D methods.

8 citations

Journal ArticleDOI
TL;DR: This paper reviews the most known analytical models that are used to calculate the medium-frequency resistance for several winding technologies and compares the analytical model results with measurements and 3-D finite-element electromagnetic simulations and the impact on the warming.
Abstract: In the future, medium-frequency transformers (with a frequency range of 5–100 kHz) will be major components in dc–dc converter applications, for both medium-voltage direct current and high-voltage direct current networks. Importantly, the corresponding power losses should be accurately calculated in order to reach performance targets (very high efficiency). This paper reviews the most known analytical models that are used to calculate the medium-frequency resistance for several winding technologies. In order to qualify these models in a future design flow, we compare the analytical model results with measurements and 3-D finite-element electromagnetic simulations and the impact on the warming. The adopted design flowchart has been tested on a 17-kHz 180-kVA prototype transformer that will be used in a dual active bridge.

8 citations

References
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Journal ArticleDOI
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

Journal ArticleDOI
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

Journal ArticleDOI
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

Journal ArticleDOI
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