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: An extension to dispersive media of a subgridding hybrid implicit–explicit algorithm finite difference time domain (FDTD) devised by the authors to deal with that kind of materials is presented and applied to the FDTD method.
Abstract: In this paper, we show a simulation strategy for composite dispersive thin-panels, starting from their microscopic characteristics and ending into a time-domain macroscopic model. In a first part, we revisit different semianalytic methods that may be used to obtain the S-parameter matrices. The validity of them is assessed with numerical simulations and experimental data. We also include some formulas that may be used to tailor the shielding effectiveness of panels in a design phase. In a second part, we present an extension to dispersive media of a subgridding hybrid implicit–explicit algorithm finite difference time domain (FDTD) devised by the authors to deal with that kind of materials. The method, here presented and applied to the FDTD method, is a robustly stable alternative to classical impedance boundary condition techniques. For this, a previous analytical procedure allowing to extract an equivalent effective media from S-parameters is presented, thus making this road map able to simulate any kind of dispersive thin layer. A numerical validation of the algorithm is finally shown by comparing with experimental data.
5 citations
08 Jul 2020
TL;DR: In this article, an improved version of the equation for determining the series resistance of a single wire is proposed, and a mathematical approximation to calculate the conductor resistance for any operation frequency is provided.
Abstract: Efficiency of the power converters is an important specification that determines their success on the market, being the losses a critical part that influences greatly the operation capabilities of the converter. To analyse with the required precision, the losses of magnetic component, both magnetic core and electric winding losses, usually Finite Element Method (FEM) analysis is carried out. The eddy currents effects are divided primordially in skin and proximity effects. The attention is focused on single wire alone case to better understanding the skin effect influence, proposing an improved version of the equation for determining the series resistance of a single wire. It also introduces a mathematical approximation to calculate the conductor resistance for any operation frequency. All the theoretical assumptions and conclusions are supported by numerical simulations using Finite Element Method analysis.
5 citations
TL;DR: In this article , a bidirectional resonant dc-dc converter is proposed to solve the contradiction among wide voltage gain range, squeezed dc-link voltage span, and narrow switching frequency band.
Abstract: Plug-in electric vehicles’ charger is preferred to cover an ultrawide battery voltage range with the vehicle-to-grid capability. Conventional bidirectional resonant dc–dc converters suffer from the contradiction among wide voltage gain range, squeezed dc-link voltage span, and narrow switching frequency band. To solve the issue, this article proposes a novel H5-bridge-based bidirectional $CLLC$ on and zero-current turn- off are achieved in the rectifying mosfet s. The prototype exhibits 98.04% peak efficiency and good overall efficiency performance.
5 citations
Dissertation•
19 Apr 2006
Abstract: The demand for high power density keeps driving the development of electromagnetic integration technologies in the field of power electronics. Based on planar homogeneous integrated structures, the mechanism of the electromagnetic integration of passives has been investigated with distributed-parameter models. High order modeling of integrated passives has been developed to investigate the electromagnetic performance. The design algorithm combining electromagnetic design and loss models has been developed to optimize and evaluate the spiral winding structure. High power density of 480 W/in has been obtained on the prototype. Due to the structural limitation, the currently applied planar spiral winding structure does not sufficiently utilize the space, and the structure is mechanically vulnerable. The improvement on structures is necessary for further application of integrated passives. The goal of this research is to investigate and evaluate alternative structures for high-powerdensity integrated passives. The research covers electromagnetic modeling, constructional study, design algorithm, loss modeling, thermal management and implementation technology The symmetric single layer structure and the stacked structure are proposed to overcome the disadvantages of the currently applied planar spiral winding structure. Because of the potential of high power density and low power loss, the stacked structure is selected for further research. The structural characteristics and the processing technologies are addressed. By taking an integrated LLCT module as the study case, the general design algorithm is developed to find out a set of feasible designs. The obtained design maps are used to evaluate the constraints from spatial, materials and processing technologies for the stacked structure. Based on the assumption of one-dimensional magnetic filed on the cross-section and linear current distribution along the longitudinal direction of the stacked structure, the electromagnetic field distribution is analyzed and the loss modeling is made. The experimental method is proposed to measure the loss and to verify the calculation. The power loss in the module leads to thermal issues, which limit the processed power of power electronics modules and thus limit the power density. To further improve the power handling ability of the module, the thermal management is made based on loss estimation. The heat extraction technology is developed to improve the heat removal ability and further improve the power density of integrated passives. The experimental results verify the power density improvement from the proposed stacked structure and the applied heat extraction technology. The power density of 1147 W/in (70 W/cm) is achieved in the implemented LLCT module with the efficiency of 97.8% at output power of 1008W.
5 citations
TL;DR: In this paper, an analysis technique is presented that can be used to determine the current density, as well as the electric field and magnetic field distributions, within multipath conductive structures.
Abstract: An analysis technique is presented that can be used to determine the current density, as well as the electric field and magnetic field distributions, within multipath conductive structures. A multipath conductor has several different conductive materials that are configured in parallel and carry a total known terminal current at a known frequency. The conductivity and permeability of the materials in the multipath conductor may take on arbitrary values. Knowledge of the different field and current distributions is important as it then becomes possible to determine the resistance and internal inductance of the multipath conductor as a function of frequency. The technique is initially developed for an arbitrary number of stacked planar conductors; however, it is also extended to multilayer coaxially arranged cylindrical conductors. Verification of the proposed technique is achieved through comparison against finite element method eddy current simulations as well as experimental structures and demonstrates excellent agreement.
5 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