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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14 Sep 2020
TL;DR: In this article, a comprehensive review of high frequency (HF) converters is presented, the essential challenges are analyzed such as topology selection, soft-switching technologies, resonant gate drivers, magnetic components design and optimization.
Abstract: Development of power electronic converters tend to achieve high efficiency and at the same time high power density in many industrial applications. In recent years, with emerging third-generation semiconductor materials i.e. Silicon Carbide (SiC) and Gallium Nitride (GaN), the switching frequency of several MHz has become a widely studied frequency band, therefore traditional technology can no longer meet the demand, and many new challenges appear. This paper presents a comprehensive review of high frequency (HF) converters, the essential challenges are analyzed such as topology selection, soft-switching technologies, resonant gate drivers, magnetic components design and optimization.
23 citations
18 May 1993
TL;DR: In this paper, an equivalent diagram with localized constants has been created to represent the two winding transformer, and the experimental method which allows all the diagram constants to be determined with impedance measurements outside the component is described.
Abstract: An equivalent diagram with localized constants has been created to represent the two winding transformer. The equivalent diagram with localized constants is practically independent of the transformer construction. Only the numeric constants change from one component to another. This circuit can be introduced into converter simulation software, and leads to very realistic forecasts even when working at high frequency. The authors describe, taking a classical transformer as an example, the experimental method which allows all the diagram constants to be determined with impedance measurements outside the component. The features and advantages of this diagram are discussed. >
23 citations
TL;DR: In this paper, a large-scale 3D computer model for calculating magnetic fields in a transformer and evaluating effective parameters (inductance and resistance) of its windings and losses is presented.
Abstract: This part of the paper focuses on implementation of hierarchical multi-scale approach for modeling high frequency electromagnetic processes in power transformers. A large-scale 3D computer model for calculating magnetic fields in a transformer and evaluating effective parameters (inductance and resistance) of its windings and losses is presented. The model accounts for complex, anisotropic and frequency-dependent effective diamagnetic properties of the windings, which were obtained by solving small-scale 2D field problems as described in Part I of this paper. Results of the computations performed for a test transformer are analyzed in the frequency range 10 Hz – 10 MHz. Effects of windings conditions (open and short-circuited) and their location on the transformer core are discussed.
23 citations
12 Nov 2012
TL;DR: In this paper, the skin and proximity effect losses for Litz wire winding used in wireless power transfer system is calculated using exact 2-D method, based on those losses the equivalent complex permeability and conductivity are calculated for each strand in the bundle.
Abstract: In this paper the skin and proximity effect losses for Litz wire winding used in wireless power transfer system is calculated using exact 2-D method. Based on those losses the equivalent complex permeability and conductivity are calculated for each strand in the bundle. Due to specific properties of Litz wire, the whole bundle is homogenized using isotropic complex permeability and conductivity and is simulated numerically in Finite Element (FE) verifying the analytical and experimental results.
23 citations
IBM1
TL;DR: In this article, the authors examined high-frequency losses of wire windings due to the fringing fields of an air gap and derived formulas for the losses and validated them numerically using the 2D finite element method (FEM).
Abstract: This paper examines high-frequency losses of thick rectangular and round wire windings due to the fringing fields of an air-gap. It derives formulas for the losses and validates them numerically using the 2-D finite-element method (FEM). It also provides a procedure for including the effect of self and proximity fields in the loss calculations, using the principle of superposition and a one-dimensional model of self and proximity fields. The paper validates the latter procedure numerically, using a 2-D finite element model.
23 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