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.
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01 Jan 2016
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TL;DR: The new generation of DC/DC converters are characterized with an order of magnitude higher power density, and with higher efficiency and additionally with dramatic reduction of labor contents in the manufacturing process.
Abstract: In today's power electronics products, quality and reliability are given. Great emphases are placed on efficiency, power density and cost. With recent advances made in gallium nitride power devices (GaNs), it is expected that GaNs will make significant impacts to all three areas mentioned above. Thanks to the significantly reduced output capacitance of GaN devices, it enables GaN to operate at a switching frequency more than ten times higher than its silicon counterparts. To illustrate the impact of GaN on efficiency, density and even design practices, three decades of development of LLC resonant converter for computer server are highlighted. By virtue of higher switching frequency beyond 1MHz, the bulky magnetic components for LLC converters are replaced with distributed magnetics and then integrated in a form of matrix transformer with simple PCB winding. The new generation of DC/DC converters are characterized with an order of magnitude higher power density, and with higher efficiency and additionally with dramatic reduction of labor contents in the manufacturing process. Even though this paper only demonstrated the impact of GaN for computer server application, similar can be said for wide range of application for for IT, communication equipment, consumer electronics, lightings and other electronics equipment.
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TL;DR: In this article, the main analysis tools as Finite Element Methods, analytic and measurement-based tools are compared in their application on high-frequency electrical machine analysis, and the influence of the machine design parameters in EMC behavior is outlined for future analysis.
Abstract: Electric drives consume a great amount of the world’s energy, and it will keep increasing due to the electromobility trend. Thus, the efficiency of electric drives must be improved to reach the desired sustainability goal. The Silicon Carbide devices contribute to this objective due to their high working frequency and lower switching losses. However, working at higher frequencies may bring serious Electromagnetic Compatibility (EMC) problems, as well as insulation stress and higher bearing currents. Hence, it is important to have an electrical machine electrical equivalent circuit model to predict the electromagnetic interference levels. This review summarizes the current state of the art in electrical machine modeling and analysis in high frequency. The main analysis tools as Finite Element Methods, analytic and measurement-based tools are compared in their application on high-frequency electrical machine analysis. Then, different machine high-frequency models are reported, detailing their individual features. Additionally, the influence of the machine design parameters in EMC behavior is outlined for future analysis. All in all, Finite Element analysis is the most accurate tool for high-frequency analysis, provided that mesh size is thinner than the skin depth. It is also concluded that the winding placement is an essential parameter to define the high-frequency behavior of the machine.
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TL;DR: In this paper, the authors describe the construction of a thin, flat litz ribbon cable suitable for use in magnetic components such as inductors and transformers where one requires reduced AC losses compared to conventional solid conductor ribbon conductors.
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TL;DR: Simulation is used to analyze total harmonic distortion (THD) as affected by the nonlinear behavior of the magnetic material in a line transformer to predict the level of THD for a variety of core types and configurations.
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10 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