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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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Proceedings ArticleDOI
21 Nov 2011
TL;DR: In this article, a medium frequency dc/dc-converter design procedure is presented that allows a clear representation of transformers total mass and efficiency under consideration of thermal aspects.
Abstract: A converter system based on medium frequency dc/dc-converters can replace the conventional traction transformer saving both mass and energy. A medium-frequency-transformer design-procedure is introduced that allows a clear representation of transformers total mass and efficiency under consideration of thermal aspects. measurements with a prototyped mf-transformer verify the calculated results.

22 citations

Journal ArticleDOI
10 May 2019-Energies
TL;DR: In this article, a light emitting diode (LED) driver containing an integrated transformer with adjustable leakage inductance in a high-frequency isolated LLC resonant converter was proposed as an LED lighting power converter.
Abstract: In this study, a light emitting diode (LED) driver containing an integrated transformer with adjustable leakage inductance in a high-frequency isolated LLC resonant converter was proposed as an LED lighting power converter. The primary- and secondary-side topological structures were analyzed from the perspectives of component loss and component stress, and a full-bridge structure was selected for both the primary- and secondary-side circuit architecture of the LLC resonant converter. Additionally, to achieve high power density and high efficiency, adjustable leakage inductance was achieved through an additional reluctance length, and the added resonant inductor was replaced with the transformer leakage inductance without increasing the amount of loss caused by the proximity effect. To optimize the transformer, the number of primary- and secondary-side windings that resulted in the lowest core loss and copper loss was selected, and the feasibility of the new core design was verified using ANSYS Maxwell software. Finally, this paper proposes an integrated transformer without any additional resonant inductor in the LLC resonant converter. Transformer loss is optimized by adjusting parameters of the core structure and the winding arrangement. An LLC resonant converter with a 400 V input voltage, 300 V output voltage, 1 kW output power, and 500 kHz switching frequency was created, and a maximum efficiency of 97.03% was achieved. The component with the highest temperature was the transformer winding, which reached 78.6 °C at full load.

22 citations

Journal ArticleDOI
TL;DR: In this article, a fast numerical method is presented for the simulation of complicated 3D structures, such as inductors constructed from Litz or stranded wires, above or sandwiched between the planar lossy magnetic media.
Abstract: A fast numerical method is presented for the simulation of complicated 3-D structures, such as inductors constructed from Litz or stranded wires, above or sandwiched between the planar lossy magnetic media. Making use of its smoothness, the quasi-static multilayer Green's function is numerically computed using finite differences, and its source height dependence is computed using an optimal Toeplitz-plus-Hankel decomposition. We show that a modified precorrected fast Fourier transform method can be applied to reduce the dense linear algebra problem to near-linear time, and that frequency-dependent setups can be avoided to result in a considerable speed-up. Experimental verifications are made for a 16-strand Litz wire coil realistically modeled down to each individual strand. Results are obtained in 2-3 h, showing an excellent agreement to measurements, and can be used to study the impact of transposition patterns in Litz wire construction.

22 citations

Proceedings ArticleDOI
03 Oct 1999
TL;DR: In this paper, a method for calculating eddy-current (proximity effect) losses in transformer and inductor windings is introduced, which is capable of analyzing losses due to two-and three-dimensional field effects in multiple windings with arbitrary waveforms in each winding.
Abstract: A method for calculating eddy-current (proximity-effect) losses in transformer and inductor windings is introduced. The new method is capable of analyzing losses due to two- and three-dimensional field effects in multiple windings with arbitrary waveforms in each winding. It uses a simple set of numerical magnetostatic field calculations to derive a matrix describing the transformer or inductor. This is combined with a second matrix calculated from derivatives of winding currents to computer total AC loss. Experiments show the method is accurate for coils that are not in or close to self-resonance.

22 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