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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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01 Jan 2013
TL;DR: Forest et al. as discussed by the authors presented Forest, Professeur des universites, IES -Universite de Montpellier 2 Rapporteur Eric Laboure, Professeur des universités, LGEP- Universite de Paris SUD, G2ELab - Grenoble INP Examinateur Ambroise Schellmanns, Maitre de conferences.
Abstract: President Francois Forest, Professeur des universites, IES – Universite de Montpellier 2 Rapporteur Eric Laboure, Professeur des universites, LGEP – Universite de Paris SUD 11 Rapporteur Jean-Luc Schanen, Professeur des universites, G2ELab – Grenoble INP Examinateur Ambroise Schellmanns, Maitre de conferences, LMP – Universite de Tours Examinateur Christian Martin, Maitre de conferences, Ampere – Universite de Lyon 1 Directeur de these Nadir Idir, Professeur des universites, L2EP – Universite de Lille 1 Co-encadrant de these Xavier Margueron, Maitre de conferences, L2EP – Ecole Centrale de Lille

1 citations

24 Aug 2012
TL;DR: In this paper, the authors explored design optimization of dual active bridge (DAB) DC/DC converter components: the capacitors, the cooling system and the transformer, and found that the three interleaved DAB is the best in terms of volume, mass and thermal management.
Abstract: The use of power electronics DC/DC converters in aircraft has increased due to the state-of-art converters developments. However, the volume, efficiency and mass of such converters are critical issues. Each component of the DC/DC converters contributes to the total mass of the system. By designing each component, optimized to have small volume, high efficiency and small mass, the total system can have small volume, small mass and high efficiency. This master project explores design optimization of dual active bridge (DAB) DC/DC converter components: the capacitors, the cooling system and the transformer. Different types of capacitors are compared in terms of mass, volume and loss for the input and output capacitors. After selecting the types of capacitors, the number, volume and mass of the input and output filter capacitors are optimized by interleaving two and three dual active bridge DC/DC converters. The thermal resistance of external cooling system for the selected switches is optimized by a trade-off between the junction temperature of the switches and the losses induced. The transformer is optimized by an evolutionary algorithm, particle swarm optimization, for volume, power loss and required maximum allowable thermal resistance for cooling. The three interleaved DAB is found to be attractive in terms of less capacitor number which leads to a small volume and mass. It is also found to be attractive in terms of thermal management of the transformers designed using the particle swarm optimization. This decreases the volume of cooling systems needed for the transformer. Interleaved three DAB is selected as best in terms of volume, mass and thermal management.

1 citations

Journal ArticleDOI
TL;DR: In this article , the authors proposed an analytical model that considers the 2-D characteristic of the magnetic field and the geometrical particularities of toroidal windings, and provided an easy-to-use method, which avoided the unaffordable computational cost of FEA software.
Abstract: Toroidal inductors are used in many industrial applications in which they are key components regarding cost and volume. In the inductor design process, it is paramount to accurately estimate its high-frequency winding loss. Finite-element analysis (FEA) software and analytical models can be used for this purpose. However, the former employs too much time and the latter lacks accuracy when applied to toroidal windings, leading to an overestimation that can exceed 200%. As a consequence, designers would benefit from a reliable method to calculate high-frequency loss in toroidal windings. This article proposes an analytical model that considers the 2-D characteristic of the magnetic field and the geometrical particularities of toroidal windings. Furthermore, it provides an easy-to-use method, which avoids the unaffordable computational cost of FEA software. Simulations and experimental measurements are carried out for seven toroidal power inductors, from 10 Hz up to 200 kHz. Three different well-known state-of-the-art analytical models are used for comparison purposes. The results obtained with the proposed model are in good agreement with those from FEA and the experiments. The proposed model shows a maximum deviation below 20% while the overestimation of the existing analytical methods reaches values from 93% to 226%.

1 citations

Journal ArticleDOI
TL;DR: This article proposes a unique solution that would make the power converters low profile by split the main bulky transformer into a number of low profile transformers, which reduces the total weight and volume of the converter but also the total transformer losses.
Abstract: Compact and low profile power converters are the main business of today’s power industry. A significant volume of a power converter is occupied by the power transformer. This article proposes a unique solution that would make the power converters low profile. Instead of designing a power converter by using a single bulky transformer, the solution proposed is to split the main bulky transformer into a number of low profile transformers. This not only reduces the total weight and volume of the converter but also the total transformer losses. The use of more than one transformer in series reduces the applied voltage on the transformers, which minimizes the required turns ratio and decreases the stress on the secondary rectifiers and filter elements. Moreover, the decrease in the applied voltage reduces the proportional loss per transformer and makes it possible to design a hybrid transformer by combining Litz wire and traces of a printed circuit board. The reduced copper loss and lower heat dissipation per transformer simplify thermal management. An analytical comparison is made between the utilization of a single transformer or a number of transformers. The procedure of splitting a volume of a single transformer into a number of small transformers has been comprehensively discussed. The idea is investigated both experimentally and in computer simulation for an example application of a phase shifted full bridge dc-dc converter. The converter is characterized up to a load power of 2.2 kW at $V_{in} =400\,\,\text{V}_{\mathrm {dc}}$ and $\text{V}_{out} =48\,\,\text{V}_{\mathrm {dc}}$ .To make the approach more practical, the transformers are modeled using the traditional analytical method. The design of the example application using the split transformer approach reduces the total transformer weight by 45%, compared to the traditional approach with a single transformer. The converter also shows good performance with a maximum efficiency of 96%.

1 citations

Journal ArticleDOI
TL;DR: A learning outcomes assessment proves the validity of the magnetic design course, specifically designed for PEs education, and reveals that enhanced skills in magnetic design are acquired in comparison with general PEs courses.
Abstract: Contribution: This article proposes a comprehensive graduate course on magnetic design that addresses existing gaps in current power electronics (PEs) education, provides theoretical foundations and hands-on skills, and matches syllabi coverage with current societal needs for electronic energy conversion. Background: A growing worldwide interest in electronic energy conversion in recent years has led to a remarkable development of the PEs knowledge field. Currently, PEs are at the heart of popular applications, such as wireless energy transference for electrical vehicles or energy conversion associated with renewable energies. Environmental and economic factors contribute to this trend. Magnetic elements are an inherent part of PEs converters, and some experts have expressed the need for specific magnetic design courses, to supplement PEs curricula. Intended Outcomes: A comprehensive approach to magnetic design education, mainly focused on filling identified gaps in PEs curricula at the graduate level. Application Design: The design of the proposed course includes lectures, laboratory sessions, and a wireless inductive power transfer (IPT) project as a representative application of electronic energy conversion. Topics include a review of electromagnetism principles, magnetic materials, loss mechanisms, and the design of inductors, transformers, and IPT systems. Societal needs (such as those demanded by the PEs industry, the research sphere, or academia) are addressed through a focus on topic selection, acquisition of specific skills, and developing representative applications pertaining to the electronic energy conversion field. Findings: A learning outcomes assessment proves the validity of the magnetic design course, specifically designed for PEs education. The assessment of the effectiveness of this approach reveals that enhanced skills in magnetic design are acquired in comparison with general PEs courses.

1 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