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 Jan 2005
TL;DR: In this paper, an infinite-dimensional model for discrete track EDS magnetic levitation (EDS) has been presented, which can be truncated to an ODE for numerical evaluation that yields accurate predictions of dynamic stability.
Abstract: Since the dawn of maglev transportation technology in the 1970’s, a great variety of models for electrodynamic suspension (EDS) magnetic levitation (maglev) have been presented. This article unifies these models by deriving equations for discrete track EDS maglev (with stranded or solid conductors), and introduces criteria required to justify the approximation of track currents by current filaments. Parallels to the diffusion equation governing continuous tracks are also provided. Our EDS analyses are careful to clarify the validity of the modelling assumptions, and strive to maintain accurate static and dynamic properties in the reduced order equations. The development starts with the derivation of a general diffusion equation (with source) describing the evolution of current fields in an arbitrary track. We then simplify the track current fields to filaments reducing the Laplacian in the diffusion equation to a discrete convolution operator. The final result, the key contribution of this paper, is an infinite-dimensional model that can be truncated to an ODE for numerical evaluation that yields accurate predictions of dynamic stability. In addition, the infinite-dimensional model is amenable to harmonic analysis and, hence, the computation of lift, drag and other static properties. Although we derive a 2DOF (heave, propulsion) model, the modelling approach applies to 6DOF systems.
6 citations
01 May 2000
TL;DR: Based on approximative equations for single step calculation design procedures, a simple method is proposed in this paper to adopt the most suitable topology in low power DC to DC conversion is derived from the volume calculation of the magnetic cores needed.
Abstract: Based on approximative equations for single
step calculation design procedures, a simple method
useful to adopt the most suitable topology in low power
DC to DC conversion is derived from the volume
calculation of the magnetic cores needed
Eletronica de Potencia, revista de la SOBRAEP, (ISSN 1414-8862), vol 5, no 1, Brasil, mayo 2000, p 16 - p 27
6 citations
01 Jan 2000
TL;DR: In this article, the relationship between K-factor and AC winding resistance is investigated and test procedures for checking the linearity and su-perposition assumptions are also developed, and it is found that linearity holds very well for the test transformers while the k-factor overestimates the losses in transformer windings.
Abstract: Transformer loading with harmonic-rich current and subsequent overheating is an ongoing concern of electric utilities and consumers. UL Standards 1561 and 1562 suggest using a K-factor for determination of transformer capacity with nonlinear loads. This work focuses at investigating the concept of K-factor and the relationship between K-factor, transformer derating, and the transformer winding eddy-current loss. The relationship between K-factor and AC winding resistance is investigated. Laboratory test procedures for measuring the AC winding resistance of two type of distribution transformers are developed and explained. Test procedures for checking the linearity and su-perposition assumptions are also developed. From the test results, it is found that linearity and superposition holds very well for the test transformers while the K-factor overestimates the losses in transformer wind-ings. The difference between K-factor results and lab test results is explained. Another approach for estimating the total stray loss in transformer winding, the Harmonic Loss Factor, is discussed and found to be a better solution. ii ACKNOWLEDGEMENTS
6 citations
17 Mar 2019
TL;DR: In this paper, a high frequency planar transformer intended to be used in a 4 kW 500 kHz DAB converter is presented, and the experimental measurements are compared with experimental measurements.
Abstract: Increasing electrification in transport sectors, from automotive to aerospace, highlights the need for low size and high power density components. The recent advent of planar technology theoretically allows to reduce considerably the size of the magnetic components. This article focuses on the design of a high frequency planar transformer intended to be used in a 4 kW 500 kHz DAB converter. In particular, the inter-winding capacitances are assessed, as they have a strong influence on the behaviour of the DAB, and in some extreme cases may impede operation entirely. Analytical and finite element models are used to evaluate the stray elements of the transformer (resistance of the conductors, inter-winding capacitance and leakage inductance), and the resulting circuit model is compared with experimental measurements. This work focuses on influences of design parameters on the transformer stray elements.
6 citations
TL;DR: In this paper, the authors presented a study to improve the inductance calculation of magnetic components in power converters, of particular interest, in the case of applications using variable inductors.
Abstract: This article presents a study to improve the inductance calculation of magnetic components in power converters, of particular interest, in the case of applications using variable inductors. In order to increase the accuracy of the estimation of the reluctance paths, several factors have been taken into consideration, such as the permeability definition under saturation, the temperature effect on the magnetic material behavior, and the distribution of saturated regions in the magnetic core. The methodology of the present study is to compare the analytical models derived from circuital equivalents against finite-element analysis numerical techniques, in order to validate the proposed model of a variable inductor, including the effects of the mentioned factors. The proposed model is then compared with experimental measurements to prove its validity. Finally, a design example for the variable inductor is presented.
6 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