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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28 Jun 2010
TL;DR: In this paper, the buck PFC has a better CM EMI performance than the boost PFC under critical conduction mode (CRM) and is more attractive in low power applications which meet the IEC61000-3-2 Class D standard.
Abstract: This paper presents a detailed performance comparison (including efficiency, EMC performance and component electrical stress) between boost and buck type PFC under critical conduction mode (CRM). In universal input (90–265Vac) applications, the CRM buck PFC has around 1% higher efficiency compared to its counterpart at low-line (90Vac) condition. Due to the low voltage swing of switch, buck PFC has a better CM EMI performance than boost PFC. It seems that the buck PFC is more attractive in low power applications which only need to meet the IEC61000-3-2 Class D standard based on the comparison. The experimental results from two 100-W prototypes are also presented for side by side comparison.
44 citations
TL;DR: In this paper, the authors proposed a high-power density 1.8 kW auxiliary power module (APM) for electric vehicles (EVs) based on gallium nitride devices.
Abstract: This article proposes a high-power density 1.8 kW auxiliary power module (APM) for electric vehicles (EVs) based on gallium nitride devices. A design procedure for the high-frequency phase-shift full-bridge with current-doubler rectifier using printed circuit board (PCB)-based planar magnetics is proposed. Leakage inductance analysis of the high-frequency pulsewidth-modulation converter is given to achieve both regulation and zero-voltage-switching turn- on . Then, the magnetics optimization procedure for the customized planar core is proposed with a magnetic figure-of-merit concept to meet the high-power density target. Technical considerations are detailed to meet the extreme temperature constraint imposed on the EVs components. Finally, the proposed APM is demonstrated with a switching frequency of 700 kHz and a power density of 8.1 kW/L (132.8 W/in3).
44 citations
18 Mar 2010
TL;DR: In this article, a modular dual-half-bridge (MDHB) bidirectional dc-dc converter is proposed for future renewable electric energy distribution and intelligent power management systems, which consists of multiple low-voltage modules connected in input-series and output-parallel mode.
Abstract: This paper presents the development of modular dual-half-bridge (MDHB) bidirectional dc-dc converter as the dc-dc stage of 10 kVA single phase solid state transformer (SST) for future renewable electric energy distribution and intelligent power management systems. The dc-dc converter, connected to 12 kV DC bus generated by an ac-dc rectifier interfacing with 7.2 kV electric utility grid, is to provide galvanic isolation function as well as 400 V DC bus for DC loads. The dc-dc converter consists of multiple low-voltage modules connected in input-series and output-parallel mode so that low-voltage commercial silicon MOSFETs, which usually have low conduction losses and high switching speed, can be adopted. Besides bidirectional power flow capability, the phase-shift dual-half-bridge (DHB) can realize zero-voltage-switching for all the switching devices without auxiliary switch devices, which enables the high switching frequency operation with low switching losses. As a result, high efficiency and high power density can be achieved. Other advantages of DHB topology have also been investigated for this application. A planar transformer adopting printed-circuit-board (PCB) winding is designed to realize high voltage solid isolation and identical parameters in multiple modules. The power loss of each main component has been analyzed for DHB converter under high frequency operation. Finally, the experimental results of two modules operating at 50 kHz switching frequency are presented with 97% efficiency.
43 citations
06 Oct 1996
TL;DR: In this article, a method for predicting the stray capacitances of HF inductors is presented, which is based on an analytical approach to obtain the turn-to-turn and turnto-shield capacitance of coils.
Abstract: A method for predicting stray capacitances of HF inductors dependent on their geometry is presented The analysis is performed for inductors made of one layer of turns with circular and rectangular cross-sections The wire is uniformly wound around a cylindrical nonferromagnetic core The method is based on an analytical approach to obtain the turn-to-turn and turn-to-shield capacitances of coils The influence of insulating coatings of the wire is also taken into account An overall equivalent stray capacitance is derived according to the typical HF equivalent lumped parameter circuit of inductors The method was tested with experimental measurements and the accuracy of the results was good in most cases The derived expressions are useful for designing of HF inductors and can be also used for simulation purposes
43 citations
TL;DR: In this article, a dc-dc boost composite converter architecture is introduced that can lead to optimized efficiency over a range of operating points dictated by the application requirements, which is composed of three converter modules: buck converter, boost converter, and a dual active bridge converter that operates as a dc transformer.
Abstract: A dc–dc boost composite converter architecture is introduced that can lead to optimized efficiency over a range of operating points dictated by the application requirements. The composite converter system employs dissimilar modules to minimize the ac power losses in the indirect power conversion paths. It is composed of three converter modules: buck converter, boost converter, and a dual active bridge converter that operates as a dc transformer (DCX). Each module processes partial power, with reduced voltage rating. With the same semiconductor area and same magnetics volume, substantial efficiency improvements and reductions in capacitor size are achieved relative to a conventional boost architecture. It is possible to design each module to optimize efficiency over a wide operating range, including pass-through modes that exhibit very low loss. A 10-kW boost composite converter is experimentally demonstrated having 98.7% efficiency at a critical partial power point, with similar very high efficiencies achieved over a wide operating range.
43 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