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 Apr 2018
TL;DR: In this paper, a toroidal gapped-core shape has been made up with silicon steel alloy, and the power losses of the inductor have been determined with finite element analysis (FEA) based co-simulations, and then its thermal behaviors have been investigated with the calculated heat sources for different ambient temperatures.
Abstract: The main factor that has to be considered in the inductor designing is the power losses occurred in the core and windings, and temperature rise released depend on these power losses. In addition to worsening efficiency, temperature rise due to the power losses reduce lifespan of the isolation materials and cause significant change on electromagnetic behavior of the core. These effects become more important for the high power medium frequency inductors. Therefore, the cooling conditions have to be considered during the designing stage to keep the temperature rise of the inductors at a certain level. In this study, medium frequency inductor of an LCL filter used in the grid interactive inverter output has been designed. The toroidal gapped-core shape has been made up with silicon steel alloy. The core and the winding power losses of the inductor have been determined with finite element analysis (FEA) based co-simulations, and then its thermal behaviors have been investigated with the calculated heat sources for different ambient temperatures.
1 citations
DOI•
15 Feb 2020TL;DR: In this article, a novel method for loss reduction and efficiency optimization of the high frequency flyback transformers is proposed based on rearrangement of the windings, which shows 3.3% improvement in total efficiency of the converter and 41.78% loss reduction in the flyback transformer.
Abstract: In this paper, a novel method for loss reduction and efficiency optimization of the high frequency flyback transformers is proposed based on rearrangement of the windings. According to detailed analysis of the high frequency flyback transformer using FEM technique, a novel and simple approach for its design improvement and loss reduction is introduced. It is shown that leakage flux scattering in core air-gap is one of the main reasons for hot-spot point generation in the windings. So, this problem and its possible solutions are analyzed in more detail. Moreover, FEM analysis is used for investigation of the developed method and rearrangement of the winding structure. In fact, some winding structures for efficiency improvement of the flyback transformer is presented and analyzed. Finally, in order to verify accuracy and effectiveness of the developed approach, simulation and experimental results are presented. Experimental results show 3.3% improvement in total efficiency of the converter and 41.78% loss reduction in the flyback transformer.
1 citations
21 Jun 2021
TL;DR: In this article, a transformerless DC EV battery charger with Litz wire inductors and printed circuit boards was evaluated with respect to power loss and difficulty of the fabrication process, and the results showed that the PCB design can provide similar performance to the Litz wires at higher cost and increased manufacturing complexity.
Abstract: Inductor design can be a process of repetitive core searching and iterative turn and airgap calculation, where every decision to be made involves a trade-off in terms of power loss, cost and power density. This paper deeply discusses the inductor design for a transformerless DC EV battery charger where inductance and operating DC bias are required to be high ( $\mathrm{500}\ \ \mu \mathrm{H}$ and 32 A). The design of the charger's filter is discussed to provide the values of the passive components and to motivate the inductor design. Two commonly used but seldom compared winding options, Litz wire and printed circuit board, are both designed and examined with respect to power loss and difficulty of the fabrication. Through tuning of the trace width and copper weight, the PCB design can provide similar performance to the Litz wire configuration, at higher cost and increased manufacturing complexity. In order to verify the text-colorblacktheoretical calculations, high-fidelity 3D finite element analysis is performed for both inductor types. After comparison, the Litz wire implementation was chosen for its reduction in power losses, cost and manufacturing complexity. The Litz wire inductor is assembled and tested on a transformerless DC charger platform with ≥ 99% efficiency at 11 kW and ≥98% efficiency at up to 22 kW.
1 citations
Proceedings Article•
06 Sep 2021
TL;DR: In this paper, a detailed case study of optimally designed foil-winding medium-frequency transformers, for the relevant range of standardized medium voltage levels, and considering state-of-the-art materials and technologies, is presented.
Abstract: In this paper, the challenges tied to the design of foil windings for medium-frequency medium-voltage transformers for solid-state transformer applications, are addressed. Besides the core losses, winding losses represent the most important design challenge of any transformer, limiting its efficiency and power-processing capability. This is especially true for transformers operating at medium frequency, where additional winding losses are unavoidable and cooling surfaces are decreased due to frequency scaling. While litz-wire windings can help to overcome this challenge to some extent, foil windings remain a technology of choice in many industrial applications due to their low cost, easy manufacturability, good fill factor and high temperature class. A detailed case study of optimally designed foil-winding medium-frequency transformers, for the relevant range of standardized medium voltage levels, and considering state-of-the-art materials and technologies, is presented in this paper. This is done using a custom developed design optimizer that employs 2D finite-element simulations for accurate modeling of AC effects within the foil windings. The analysis of the mentioned results provides valuable insights, highlighting the influence of the selected insulation technology and a strong correlation between the rated insulation voltage and the additional frequency-dependent foil-winding losses.
1 citations
TL;DR: In this article, a semi-numerical method based on the mirroring method is proposed to calculate eddy current losses in foil windings exposed to a 2D fringing field.
Abstract: The calculation of eddy current losses in foil windings exposed to a 2-D fringing field is a complex task because of the current displacement along the height of the foil. For model-based optimization of magnetic components, loss calculation with 2-D finite element method simulation is not an option because of the high computational effort. The existing alternative calculation methods with low computational effort, rely on approximations applicable only to a certain geometrical arrangement of the windings and the air gap. Therefore, in this study, a new semi-numerical method was developed to overcome these limitations. The method is based on the mirroring method and is applicable to arbitrary air gaps and winding arrangements. The accuracy of the new method was verified by measurements, and the deviation of the model results from the measured losses was found to be below 15%.
1 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