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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22 Jun 2014
TL;DR: In this article, an analytical sizing methodology for inductive power transfer (IPT) systems is proposed based on the inductance coupling principle, which allows to obtain the geometry (dimension of the coil, number of turns, according to the geometry type: circular, rectangular, square...) and the performance of an IPT system from just a few parameters: nominal power, nominal voltage in primary and secondary winding, air gap and operation frequency.
Abstract: In this paper an analytical sizing methodology for inductive power transfer (IPT) systems is proposed. The methodology is based on the inductance coupling principle. It allows to obtain the geometry (dimension of the coil, number of turns, according to the geometry type: circular, rectangular, square...) and the performance of an IPT system from just a few parameters: nominal power, nominal voltage in primary and secondary winding, air gap and operation frequency. This procedure has been implemented using Matlab, where different prototypes can be obtained in a very short time, reducing significantly the effort during the design process. The validation of the methodology has been carried out through finite element method (FEM) software and the construction and experimentation on a prototype. This paper includes a sensitivity analysis regarding coil sizing methodology, with the introduction of misalignment between windings.
2 citations
Dissertation•
18 Nov 2008
TL;DR: In this article, the authors propose an integration magnetique of a transformateur with inductance on a seul noyau magnetique, baptisee LT, for augmenting the densite de puissance.
Abstract: L'integration magnetique d'un transformateur avec une inductance sur un seul noyau magnetique, baptisee LT, se presente comme une solution prometteuse pour augmenter la densite de puissance. Une formule generale de dimensionnement a ete etablie pour un composant integre. En respectant quelques hypotheses, les pertes cuivre peuvent etre estimees en appliquant la methode de Dowell ou celle de Ferreira. Ainsi, la methode d'homogeneisation pour un fil de Litz a ete validee experimentalement et numeriquement a fin de calculer les pertes par effet de proximite dans un prototype integre. Finalement, le transfert de la chaleur d'une forme cubique par la convection naturelle et le rayonnement a ete analyse numeriquement et analytiquement a fin de construire un modele thermique pour les composants magnetiques.
2 citations
23 Apr 2013
TL;DR: In this paper, the concept of varying conductor thickness is further used to achieve substantial reduction in overall losses with the further advantage of drastically reducing the time needed for obtaining the optimal winding shape.
Abstract: This paper further elaborates on the topic of conductor optimization for planar helical foil windings. Part 1 of this work briefly covers the classical design methods and new schemes suggested for ac-inductors supported by two case studies. Optimisation of the windings used in filter inductors, carrying both ac- and dc-currents simultaneously, are handled in Part 2 of the publication. Winding shaping techniques, formerly used for cylindrical conductor windings, are adapted for helical foil windings placed in gapped cores. The concept of varying conductor thickness is further used here to achieve substantial reduction in overall losses with the further advantage of drastically reducing the time needed for obtaining the optimal winding shape. The calorimetric methods used to verify results experimentally are also included in this part.
2 citations
Dissertation•
27 May 2015
TL;DR: Acknowledgements and Declaration of Authorship as discussed by the authors were given by the author and his co-authors in their book "A Declaration of Authorhip" and their list of publications.
Abstract: ......................................................................................................................vi! Acknowledgements ................................................................................................... vii! Declaration of Authorship ...................................................................................... viii! List of Publications .................................................................................................... ix!
2 citations
01 Jan 2011
TL;DR: In this paper, a wide-band three phase transformer model is proposed to support the physical interpretation of frequency response analysis (FRA) through the development of a wideband transformer model, which can be used for parameter sensitivity analysis.
Abstract: Research Doctorate - Doctor of Philosophy (PhD)%%%%A power transformer will yield a frequency response which is unique to its mechanical geometry and electrical properties. Changes in the frequency response of a transformer can be potential indicators of winding deformation, as well as other structural and electrical problems. A diagnostic tool which can be used to detect such changes is Frequency Response Analysis (FRA). To date, FRA has provided only limited insight into the underlying physical cause of the change. There is now a growing research interest in identifying the physical change in a transformer directly from its FRA signature. The aim of the research in this thesis is to support the physical interpretation of FRA through the development of a wide-band three phase transformer model. The resulting model can be used for parameter sensitivity analysis, hence providing greater insight into the effects geometric change can have on transformer FRA. The research validates the proposed modelling approach by fitting the model to FRA data, without a priori knowledge of the internal dimensions, and then quantitatively assessing the accuracy of key geometric parameters. Finally, the ability of the model to support the interpretation of FRA is demonstrated. This is achieved by modifying a power transformer to emulate winding deformation and using the model to detect and quantify the degree of change.
2 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