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
More filters
09 Nov 2020
TL;DR: In this paper, a detailed design procedure of a 4th order resonance output filter is presented to show the advantages of this filter in terms of passives size and loss reduction for a 5.4 W, 20 MHz buck converter with PCB integrated solenoid inductors.
Abstract: Size reduction of passive components in power converters especially magnetic components is essential to reduce the overall size of the converter and achieve higher power densities. For that purpose, this paper presents a detailed design procedure of a 4th order resonance output filter to show the advantages it provides in terms of passives size and loss reduction. A design study comparison is presented between 2nd order, 4th order and 4th order resonance filters in a 5.4 W, 20 MHz buck converter with PCB integrated solenoid inductors. The comparison considers the same circuit specifications and PCB manufacturing capabilities for the PCB inductors. It is found that there is potential for a total inductor size reduction of 38% with a corresponding increase in full load inductor efficiency of 2.1% and full load circuit efficiency of 1.3% provided by the 4th order resonance filter compared to a standard 2nd order filter in a 5.4 W buck converter switching at 20 MHz.
4 citations
TL;DR: In this article , an 80-kW interleaved boost converter is proposed to step a low battery voltage up to an 800-V dc link, which employs a discontinuous conduction mode (DCM) variable-frequency control strategy to achieve an efficiency increase at low-power levels.
Abstract: High system efficiency at all power levels is desired for electric vehicle (EV) propulsion systems. Conventional boost converters employed in EV traction architectures exhibit significantly lower efficiencies at low-power levels when operated under traditional fixed-frequency pulsewidth modulation (PWM) techniques. Also, low system power densities are associated with conventional boost converters due to their bulky inductors. These two shortcomings are addressed here through a comprehensive design methodology for an 80-kW interleaved boost converter stepping a low battery voltage up to an 800-V dc link. The designed converter employs a discontinuous conduction mode (DCM) variable-frequency control strategy to achieve an efficiency increase at low-power levels and, thus, a fairly constant efficiency throughout the entire drive schedule. A system loss model is developed to decompose analytically the loss mechanisms and, thus, determine the optimized design parameters for the variable-frequency control strategy and converter magnetics. Moreover, a custom inductor design based on distributed air gaps and aggressive thermal management through potting is integrated into the design methodology to further increase the converter power density. An 80-kW prototype is fabricated achieving a total power density of 55.6 kW/L, and experimentally tested, yielding system efficiencies above 96% for all power levels.
4 citations
01 Jan 1989
TL;DR: In this article, it is shown that eddy currents can be described by differential equations appropriately called diffusion equations, which are derived from the electromagnetic theory of the eddy current in conductors.
Abstract: From a mathematical/physical point of view, the eddy current phenomena is governed by Maxwell’s equations. It is shown that eddy currents can be described by differential equations appropriately called diffusion equations. Eddy currents in conductors are investigated, as they establish themselves in power electronic circuits. Thepupose of this chapter is to derive the electromagnetic theory of eddy currents on which subsequent analyses are based.
4 citations
Dissertation•
18 Dec 2012
TL;DR: In this paper, the authors propose a 3D semi-analytique with a thermique and an electromagnetique to combine the properties of the thermique, the bruit, and the PWM.
Abstract: La tendance actuelle des equipements electriques ferroviaires est une concentration de materiels dans des volumes de plus en plus faibles et pour des puissances de plus en plus elevees. Ce progres est permis par des composants a fort rendement (IGBT) qui ont la caracteristique de generer des pertes harmoniques importantes dans les composants magnetiques, provoquant du bruit a forte composante tonale. En consequence, les cahiers des charges deviennent de plus en plus drastiques et augmente la difficulte de conception optimale des transformateurs. C’est pourquoi il est necessaire de developper des modeles multi-physiques afin d’integrer les differents phenomenes tels que la thermique, le bruit ou les effets de la PWM. Cette these porte plus precisement sur le dimensionnement optimal des transformateurs et inductances present dans les convertisseurs auxiliaires ferroviaires. L’interet de la mise en place une boucle d’optimisation sur un modele multi-physique est montree. Pour cela il est important de developper des modeles comportent un bon compromis entre le temps de calcul et la precision. Dans cette these seule les composants magnetiques refroidis par une ventilation forcee sont etudies. Un modele thermique 3D semi-analytique couple avec un modele electromagnetique est utilise. Le choix de l’optimiseur s’est porte sur l’algorithme NSGA-II permettant d’effectuer des optimisations multi-objectifs (poids et pertes) en incluant des contraintes thermiques. Pour finir une etude de sensibilite est effectuee grâce a une methode de plan d’experience afin de juger de la robustesse des solutions optimales
4 citations
References
More filters
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