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.
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20 Jun 1993
Abstract: Analytical two-dimensional (2-D) field solutions produced by conductors located in magnetic cores are developed. The problem of arbitrarily placed rectangular conductors in the window of a ferrite core is solved by deriving analytical field solutions based on combining multiple sets of eigenfunctions in the window space and in each conductor into the 2-D Poisson equation with dynamic source terms. This technique extends classical, high frequency, one-dimensional (1-D) solutions and 2-D, DC solutions, to high frequency, two-dimensional problems. Results show higher accuracy over 1-D methods in computing AC resistance and fields. Improvements are significant due to the incorporation of various 2-D effects, not previously possible in 1-D solutions. >
22 citations
TL;DR: Power losses in high-efficiency dc-dc step up converters based on the synchronous three-level neutral-point-clamped (TLNPC) configuration were investigated and a thorough loss analysis is reported, extended to subtle power dissipation processes, which in high efficiency converters grow in relevance after weakening of the major loss mechanisms.
Abstract: Power losses in high-efficiency dc–dc step up converters based on the synchronous three-level neutral-point-clamped (TLNPC) configuration were investigated. TLNPC converters benefit from the reduced stress on components and from the non-insulated stacked-boost output stage to provide reduced power losses and large voltage gains. Several prototypes with increasing efficiency were produced and tested; voltage gains larger than $20\times$ were achieved by means of hard-switched prototypes with composite switches consisting of both low- $R_{ds(ON)}$ and high-speed MOSFETs. At lower voltage gains conversion efficiencies exceeding 98% were demonstrated. A thorough loss analysis is reported, extended to subtle power dissipation processes, which in high efficiency converters grow in relevance after weakening of the major loss mechanisms. The related model is proven capable to accurately predict circuit performance in a wide range of operating conditions.
22 citations
TL;DR: In this article, the authors present a state-of-the-art numerical modeling of the coupled problems involving heat, fluid flow and electromagnetic phenomena in electrical transformers, and a coupling procedure of both Computational Fluid Dynamics (CFD) and EMAG solutions to examine the specific power losses within coils and a core is outlined.
Abstract: The paper presents a state-of-the-art of the numerical modeling of the coupled problems involving heat, fluid flow and electromagnetic phenomena in electrical transformers. Mathematical descriptions of both Computational Fluid Dynamics (CFD) and electromagnetic (EMAG) models are given. Since these models include other submodels for a definition of boundary conditions as local and temperature-dependent convective and radiative heat fluxes, heat generation terms, temperature-dependent and effective values of material properties for different constructions of coils etc., the component problems published in a subject literature are also reported. Moreover, a coupling procedure of the CFD and EMAG solutions to examine the specific power losses within coils and a core is outlined. On the basis of the mathematical model, a numerical example of a three phase medium-power dry-type electrical transformer is presented. A validation of the numerical calculations is performed using the experimental transformer temperature tests in the short-circuit, open-circuit, and under rated parameters according to the current European Standards for dry-type transformers. During the tests, temperatures were measured at selected points on transformer elements using thermocouples and thermometers, while on the external tank walls an infrared thermography was employed.
22 citations
TL;DR: In one-dimensional analytical theories aimed at calculating winding losses in magnetic devices, one usually introduces a "layer copper factor" to take layer porosity into account, which leads to nonphysical equations.
Abstract: In one-dimensional analytical theories aimed at calculating winding losses in magnetic devices, one usually introduces a "layer copper factor" to take layer porosity into account. The existence of this factor has been accepted since 1966 although it leads to nonphysical equations. This paper is a short theoretical discussion explaining: 1) how the layer copper factor comes from neither a one-dimensional nor two-dimensional model; 2) the true meaning of this factor; and 3) how an erroneous justification has propagated since 1966 in scientific literature.
22 citations
TL;DR: In this article, a thermal camera was used for the quantitative estimation of power losses in a high frequency planar transformer (100 kHz/ 5600 VA) based on the observation of the transient temperature rise and determination of the power losses by means of curves representing the derivative of temperature as a function of power dissipated in the transformer.
Abstract: This paper presents the implementation of a thermal camera for the quantitative estimation of power losses in a high frequency planar transformer (100 kHz/ 5600 VA). The methodology is based on the observation of the transient temperature rise and determination of the power losses by means of curves representing the derivative of temperature as a function of power losses dissipated in the transformer. First, the thermal calibration characteristics had to be obtained from a simple experiment, where power losses are generated by DC current in the ferrite core and windings. Next, experimental investigations focused on the determination of the transformer power losses for a short circuit and no load, with a resistive load and with the rectifier as a load were carried out. Finally, to verify the obtained results, analytical calculations based on Dowell’s and modified Steinmetz’s equations were additionally made, which showed a good convergence. The proposed method is easy to implement and can be used as an alternative to the calorimetric method which is time-consuming and requires a complicated measurement setup.
21 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