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 article, a high-density transformer using nanocrystalline core for a 30 kW, 200 kHz resonant converter is developed, and the important parasitic models are also developed considering litz wire effects.
Abstract: A high-density transformer using nanocrystalline core is developed for a 30 kW, 200 kHz resonant converter. Loss models are established for nanocrystalline cores through experimental characterization. The important parasitic models are also developed considering litz wire effects. Following a minimum size design procedure, several transformers with both nanocrystalline and ferrite cores are designed and prototyped. While all transformers meet the converter performance requirement during testing, using nanocrystalline core can achieve a significantly higher power density even at 200 kHz.
104 citations
04 Mar 2001
TL;DR: In this article, an extensive survey of techniques and technologies used to implement planar magnetic structures in modern DC to DC converters is presented, emphasizing the practical applications of these devices.
Abstract: This paper presents an extensive survey of techniques and technologies used to implement planar magnetic structures in modern DC to DC converters. The survey emphasises the practical applications of these devices. The trends are analyzed in the context of the marketplace and some predictions of future direction are attempted.
102 citations
TL;DR: In this article, a wideband three-phase transformer model is developed based on three types of frequency response analysis (FRA) tests, which can be used as a flexible test bed for parameter sensitivity analysis, leading to greater insight into the effects that geometric change can have on transformer FRA.
Abstract: A power transformer will yield a frequency response which is unique to its mechanical geometry and electrical properties. Changes in the frequency response of a transformer can be potential indicators of winding deformation as well as other structural and electrical problems. A diagnostic tool which leverages this knowledge in order to detect such changes is frequency-response analysis (FRA). To date, FRA has been used to identify changes in a transformer's frequency response but with limited insight into the underlying cause of the change. However, there is now a growing research interest in specifically identifying the structural change in a transformer directly from its FRA signature. The aim of this paper is to support FRA interpretation through the development of wideband three-phase transformer models which are based on three types of FRA tests. The resulting models can be used as a flexible test bed for parameter sensitivity analysis, leading to greater insight into the effects that geometric change can have on transformer FRA. This paper will demonstrate the applicability of this modeling approach by simultaneously fitting each model to the corresponding FRA data sets without a priori knowledge of the transformer's internal dimensions, and then quantitatively assessing the accuracy of key model parameters.
102 citations
20 Jun 2004
TL;DR: In this paper, a parametric set of finite-element analysis (FEA) simulations was used to give proximity-effect loss for a large range of frequencies, using the parameters from a lookup table based on winding geometry.
Abstract: It has recently been shown that the most commonly used methods for calculating high-frequency eddy-current loss in round-wire windings can have substantial error, exceeding 60%. Previous work includes a formula based on a parametric set of finite-element analysis (FEA) simulations that gives proximity-effect loss for a large range of frequencies, using the parameters from a lookup table based on winding geometry. We improve the formula by decreasing the number of parameters in the formula and also, more importantly, by using simple functions to get the parameters from winding geometry such that a large lookup table is not needed. The function we present is exact in the low frequency limit (diameter much smaller than skin depth) and has error less than 4% at higher frequencies. We make our new model complete by examining the field expression needed to get the total proximity-effect loss and by including the skin-effect loss. We also present experimental results confirming the validity of the model and its superiority to standard methods.
102 citations
TL;DR: In this article, a high-frequency gallium nitride (GaN)-based three-phase LLC converter is employed to address these aforementioned challenges, where all magnetic components, namely, three inductors and three transformers, can be integrated into one common structure while all magnetic windings implemented in a compact four-layer PCB with 3oz copper.
Abstract: The LLC converter is deemed the most widely used topology as dc/dc converter in server and telecom applications. To increase the output power and reduce the input and output current ripples, three-phase interleaved LLC converter is becoming more and more popular. It has been demonstrated that three interleaved LLC converter can achieve further efficiency improvement at the 3-kW power level. However, the magnetic components for multiphase LLC converter are complex, bulky, and difficult to manufacture in a cost-effective manner. In this paper, a high-frequency gallium nitride (GaN)-based three-phase LLC converter is employed to address these aforementioned challenges. With GaN operating at 1 MHz, all magnetic components, namely, three inductors and three transformers, can be integrated into one common structure while all magnetic windings implemented in a compact four-layer PCB with 3-oz copper. The proposed structure can be easily manufactured cost-effectively in high quality. Furthermore, shielding techniques for full-bridge secondary have been investigated, and additional two-layer shielding has been integrated to reduce common-mode noise. A 1-MHz 3-kW 400 V/48 V three-phase LLC converter is demonstrated, and the peak efficiency of 97.7% and power density of 600 W/in3 (37 kW/L) are achieved.
100 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