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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TL;DR: In this paper, the authors proposed an approach to identify intrinsic power losses of the medium frequency transformer that interfaces two modular multilevel converters (MMC) operated with phase-shifted square wave modulation (PS-SWM) to form a DC solid state transformer (DC SST) module.
Abstract: This article proposes an approach to identify intrinsic power losses of the medium frequency transformer that interfaces two modular multilevel converters (MMC) operated with phase-shifted square wave modulation (PS-SWM) to form a DC solid state transformer (DC SST) module. Cascaded MMC module based DC SST architecture is an excellent choice for HVDC to MVDC conversion for DC grid application as well as for renewable and distributed energy resource integration into the DC grid. Operation with PS-SWM allows reduced cell capacitor size and lower total semiconductor device ratings. However, this modulation generates a unique quasi-square waveform at the SST internal medium frequency (MF) AC interface, which differs from other known square-wave modulation types. This produces a similarly unique transformer flux density, resulting in a transformer core loss that cannot be predicted by existing methods which makes it challenging to identify. In the interest of presenting a useful and optimizable MF transformer design methodology, this article develops a tool to predict the loss of the MF transformer subjected to PS-SWM. The proposed loss estimation technique is validated through an experimental testbed operated in two different configurations and is demonstrated to provide a valid basis for the use of the proposed MF transformer design methodology. Furthermore, this article provides an analysis of the load-dependent MF transformer core loss, which demonstrates a secondary usefulness of the proposed loss prediction tool in identifying load-dependent converter losses
9 citations
TL;DR: In this article, the authors proposed a homogenization method to minimize the cost of the expensive 3D finite element (FE) computation in the frequency domain, where the originality lies in the non-homogeneous TET geometry during the meshing process.
Abstract: Transcutaneous Energy Transmitters (TETs) transfer wireless energy through an inductive link established between two pancake coils placed, respectively, outside and inside the body of a patient. The simulation of the misalignment between the coils must be performed in 3-D, e.g., with a Finite Element (FE) method. This paper introduces a homogenization method to minimize the cost of the expensive 3-D FE computation in the frequency domain. Its originality lies in the non-homogeneous TET geometry during the meshing process. The results of this technique are compared with those obtained by considering regular stranded TET coils. They showed improvements mainly at kilohertz frequencies, the typical TET operating frequency range.
9 citations
Proceedings Article•
15 Sep 2011
TL;DR: In this article, the thermal management of a high frequency power transformer is investigated and the total power loss of such a device can be easily predicted based on the results, the temperature distribution inside the transformer is simulated.
Abstract: In this paper the thermal management of a high frequency power transformer is investigated. To begin with, it is shown how the total power loss of such a device can be easily predicted. Based on the results, the temperature distribution inside the transformer is simulated. It is demonstrated how different cooling conditions affect the hot-spot temperature. Copper coil formers to improve the thermal connection between coil/core and the bottom plate of the transformer are presented. Further, the effect of insulation material with improved thermal conductivity is investigated. Different transformer prototypes were realized to illustrate the practical capability of the applied thermal model. All simulation is based on finite element method (FEM) and verified by means of experimental data drawn from various electrical and thermal measurements.
9 citations
TL;DR: In this article, the skin and proximity effects of isolated and in-bundle coated strands are studied for various coating properties and dimensions, and a new method is proposed for calculation of proximity losses inside coated-strand litz wire, which enables simple systematic approach for proximity loss and ac resistance determination.
Abstract: Substantial induced eddy-current losses and the need for skin-depth-size strands leave litz wire out as an option for inductive applications at multi-megahertz frequencies. To address this, we analyze and minimize the litz-wire eddy-current losses by adding a coating layer to each strand while keeping the wire dimensions and packing factor constant. The skin and proximity effects of isolated and in-bundle coated strands are studied for various coating properties and dimensions. A new method is proposed for calculation of proximity losses inside coated-strand litz wire, which enables simple systematic approach for proximity loss and ac resistance ( ${R} _{\mathrm{ac}}$ ) determination. Three types of pure copper (Cu), silver-coated copper (Ag/Cu), and nickel-coated copper (Ni/Cu) strands are studied in isolation and inside a litz wire. The litz wires associated with these strands are fabricated and their power dissipations are measured. Analytical results followed by finite-element modeling and experimental results show 26% reduction in Ni/Cu litz wire ${R} _{\mathrm{ac}}$ , and 3% reduction in Ag/Cu litz wire ${R} _{\mathrm{ac}}$ at 13.56 MHz compared with same-size Cu litz wire.
9 citations
19 Mar 2006
TL;DR: In this paper, a model of the frequency-dependent resistance in round-wires planar windings is developed based on the superposition of the different loss effects (DC, skin, and proximity) in the wire.
Abstract: In this paper a model of the frequency-dependent resistance in round-wires planar windings is developed. The model is completely analytical and based on the superposition of the different loss effects (DC, skin, and proximity) in the wire. The model also includes the field changes caused in the conductors by the induced currents in the neighbouring conductors. In order to verify the model some tests have been performed, so several inductors were constructed and results with both non-loaded and loaded inductors are compared with theoretical predictions.
8 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