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 a procedure to find an optimized dielectric design of the insulation system of a transformer subjected to fast-front voltage pulses created by power electronic converters, which is based on the interaction between the Finite Element Method, a frequency-domain distributedparameter winding model, and the goal attainment optimization algorithm.
5 citations
01 Jan 2008
TL;DR: In this article, the authors present and evaluate different winding designs for resonant switch mode transformers operating in power supplies with frequencies larger than 500 kHz and show that the revolved parallel design performs best of the tested designs under the given conditions.
Abstract: Switch mode power supplies as a mass produced article leave room for optimization especially at the voluminous magnetic components Hereby planar component designs can reduce the overall height of the power supply and give it a more compact design Since cores are available in standard sizes the optimal winding layout has to be found Due to increased parasitic capacitance interleaving is not a good option to reduce losses in the windings at high frequency resonant power supplies This article presents and evaluates different winding designs for resonant switch mode transformers operating in power supplies with frequencies larger than 500kHz This article shows that the revolved parallel design performs best of the tested designs under the given conditions In addition, the revolved design can compete with solutions as planar litz when it comes to value meaning cost and production complexity Furthermore, the article shows the abilities of a heat measurement prototype
5 citations
01 Jan 2007
TL;DR: In this article, the effects of power loss in power transformers, e.g. winding and core losses, are described, modeled and simulated employing an iterative multi-field coupling scheme.
Abstract: An application-based modelling and simulation scheme for high frequency inductive devices using COMSOL Multiphysics ® 3.3 is presented. The effects of power loss in power transformers, e.g. winding and core losses, are described, modeled and simulated employing an iterative multi-field coupling scheme. Simulation and measurements of temperature rise in the transformer core are consistent. A system simulation comprising voltage source, transformer and discrete electrical components such as resistors, inductors and non-linear elements (e.g. diodes) is performed. Two different transformer winding-schemes are compared using transient current simulations. Keywords: Multi-field coupling, Inductive devices, Power loss, Combined simulation, Optimization. 1. Introduction Nowadays, the demand for an optimal design of products has increased dramatically in the international market all over the world. In most cases, the design process of mechatronic components is lengthy and costly. The still widely used experimental-based design exhibits many disadvantages. Mainly it is very time-consuming, since for each change in the design a new prototype has to be fabricated and the relevant parameters have to be measured. In the design of high frequency inductive devices, e.g. power transformers, performing multi-field simulations of electromagnetical, thermal and possibly structural field interaction is inevitable. For an optimal design of such devices one has to understand the mechanisms of losses within the device and the interaction with electrically connected components. In practice some energy is dissipated due to the resistance of the windings (known as winding or copper losses) and due to magnetic effects mainly attributable to the core (known as core or iron losses). Furthermore, the interaction of the transformer with its surrounding electrical components like resistors, inductors and non-linear elements, e.g. diodes, is important to find an optimum operation for the whole system. This paper is based on a practical configuration of electrical source, transformer and connected electrical components as for example can be found in modern switched-mode power supplies. As a first step we concentrate on the power transformer and its winding losses. An example of two different winding layer configurations will demonstrate the proximity effect and its consequence. To account for the core losses, an iteration-based multiphysics approach is employed and compared to temperature measurements. Finally, the whole system consisting of transformer and electrical components is processed in a combined Finite-Element / discrete component (SPICE) simulation using COMSOL Multiphysics
5 citations
22 Oct 2018
TL;DR: A winding design method is presented by taking all the parasitic parameters, including winding capacitance, ac resistance, and leakage inductance, into consideration in the dual active bridge converter (DAB).
Abstract: The transformer in the dual active bridge converter (DAB) is the key element which provides galvanic insulation and voltage conversion. The parasitic parameters, including winding capacitance, ac resistance, and leakage inductance, are the primary considerations in its winding design. Without proper consideration of those parameters could result in issues on current ringing, high power loss, and overheating. In this paper, a comprehensive study is devoted to those parameters. A winding design method is presented by taking all those parameters into consideration. Special attention is paid to the impact of displacement winding, which is quite often in the manufacture and especially in prototype design phase. Both the normal and displacement winding will be studied and compared, with analytical, simulation, and experimental methods. Through comparison, additional coefficients are introduced to the simple analytical equations so that they could also be applied for displacement windings. Several considerations are given to control those parameters within a reasonable range in the design and manufacture phase. Finally, the analysis and design method are verified by finite element method and the experimental results on a 120 kHz prototype, and can be extended to other high-frequency magnetic designs.
5 citations
04 Dec 2007
TL;DR: In this paper, the effect of air gap in the core on the winding current distribution was investigated and the experimental results confirmed the simulation results and showed that in ordinary paralleling winding, witch is used to decreasing of skin effect, the current is shared unbalance and for perfect paralleling of the winding, interleaved winding must be used.
Abstract: High frequency effects and Current sharing in paralleled winding at high frequency transformers, witch are using in switch mode power supplies, will discuss in this paper. FEM method is used for simulation and shows that in ordinary paralleling winding, witch is used to decreasing of skin effect, the current is shared unbalance and for perfect paralleling of the winding, interleaved winding must be used. Also, the effect of air gap in the core on the winding current distribution will be scrutinized. And therefore, the experimental results confirm the simulation results.
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