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.
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Dissertation•
28 May 2015
TL;DR: In this paper, the authors present a model of an HVDC/DC system for a multicellulaire DC/DC, isolee pour l’application proposee.
Abstract: L’electricite prend une place de plus en plus importante dans les systemes energetiques embarques. L’electricite est une forme d’energie tres malleable, facile a transporter et reglable ou transformable avec un tres faible taux de pertes. L’energie electrique, associee a des convertisseurs statiques, est plus facile a maitriser que, par exemple, l’energie hydraulique et/ou pneumatique, permettant un reglage plus fin et une reduction des couts de maintenance. L’evolution de la puissance dans les modeles avioniques est marquante. Avec le nombre croissant de charges electroniques, un avion plus electrique avec un reseau a courant alternatif inclurait un grand nombre de redresseurs AC/DC qui devront respecter les normes de qualite secteur. Une solution pour la reduction de la masse serait de preferer un reseau HVDC (High Voltage DC Bus). Sur les futurs modeles avioniques plus electriques, les concepteurs envisageront des conversions HVDC/DC a partir de l’unite appelee BBCU (Buck Boost Converter Unit). Dans ce cas d’etude, un reseau de distribution en tension continue (±270Vdc) est connecte a un reseau de securite basse tension (28Vdc) avec un echange bidirectionnel de puissance pouvant atteindre 10kW. Le convertisseur statique assurant cette liaison represente de nouveaux defis pour l’electronique de puissance en termes de fiabilite, surete, detection de panne, rendement et reduction de masse et de cout. Le dimensionnement du convertisseur doit prendre en compte une conception optimale, en aeronautique ce critere est la masse. Dans le processus de dimensionnement et d’optimisation du convertisseur, il est donc imperatif de prendre en compte trois facteurs principaux : 1) l’evolution des topologies de conversion, 2) l’evolution des composants actifs et passifs et 3) l’integration de puissance. La reunion de ces trois facteurs permettra ainsi la miniaturisation des convertisseurs statiques. Dans un premier temps, nous preciserons la demarche adoptee pour le dimensionnement d’un convertisseur en prenant en compte : les topologies actives, les filtres differentiels et le systeme de refroidissement. Les differents elements qui composent le convertisseur sont decrits dans un langage informatique oriente objet. Des facteurs de performances seront egalement introduits afin de faciliter le choix des semi-conducteurs, des condensateurs et du dissipateur pour un convertisseur statique. Dans un deuxieme temps, nous presenterons le fonctionnement d’une topologie multicellulaire DC/DC, isolee pour l’application proposee. Nous presenterons les avantages du couplage de differentes phases de ce convertisseur. Nous introduirons les differentes associations des cellules et leurs avantages, possibles grâce a l’isolement, comme la mise en serie et en parallele. Puisque la caracterisation des pertes des semi-conducteurs est essentielle pour le dimensionnement du convertisseur statique, nous proposerons deux approches : un modele de simulation relativement simple et parametre a l’aide de seules notices constructeurs ; et une methode de mesure des pertes dans les semi-conducteurs qui est a la fois precise et compatible avec les composants les plus rapides. En ce qui concerne les composants magnetiques, une surface de reponse des materiaux ferrites sera presentee. Nous allons decrire, par le biais analytique et de simulation, des modeles pour la determination du champ magnetique a l’interieur du noyau et des ondulations de courant engendres. Finalement, en profitant des modeles et des resultats obtenus dans les sections precedentes, nous montrerons le dimensionnement et la realisation de chaque partie du convertisseur BBCU 100kHz / 10kW. Une perspective d’un design ideal est egalement presentee.
16 citations
TL;DR: The results of the energy efficiency and power loss measurements of a 16 kVA customer-end inverter (CEI) unit are analyzed and the efficiency optimization goals are discussed and set.
Abstract: In this paper, the results of the energy efficiency and power loss measurements of a 16 kVA customer-end inverter (CEI) unit are analyzed. The CEI is part of the low-voltage dc (LVDC) distribution network. The efficiency of the CEI power conversion significantly affects the energy efficiency of the LVDC distribution network and the electricity supply chain. The efficiency of the CEI and its components is measured by applying calorimetric and electrical input-output methods. The power loss measurement results are analyzed, and the power loss mechanisms are described. The efficiency optimization goals are discussed and set.
16 citations
01 Oct 2017
TL;DR: In this article, a symmetrical resonant converter as well as a symmetric PCB transformer structure is proposed to cancel the common mode current brought by the large inter-winding capacitor and therefore the total system common mode noise is significantly reduced.
Abstract: Wide-band-gap devices can provide much faster switching speed. But the dv/dt of switching node voltage also becomes much higher, causing potential common mode noise issue. On the other hand, PCB winding transformer has significant large inter-winding capacitance, which provides a low impedance path for common mode noise. In this paper, a symmetrical resonant converter as well as a symmetrical PCB transformer structure is proposed. By using cancellation concept, common mode current brought by the large inter-winding capacitor is cancelled out and therefore the total system common mode noise is significantly reduced. No additional hardware implementation is required and the system structure is simple. A 6.6kW 500kHz WBG based CLLC resonant converter prototype with 97.8% efficiency and 130W/in3 power density is built to verify the superior performance and feasibility of the proposed concept.
16 citations
TL;DR: In this paper, a study of stator losses for three different commercially available nonoriented silicon-iron steel grades (with lamination thicknesses 0.1, 0.2, and 0.3mm) is presented.
Abstract: The recent emergence of wide-bandgap power transistors enables higher switching frequencies in electrical motor drives. Their full utilization from a system point of view requires quantification of the corresponding time-harmonic motor losses. As an initial step, this paper presents a unique study of stator losses for three different commercially available nonoriented silicon–iron steel grades (with lamination thicknesses 0.1, 0.2, and 0.3 mm). The investigations cover a wide frequency range (10–100 kHz) at different levels of dc bias (up to 1.6 T). Iron losses are identified from measurements on fully assembled stators deploying a novel technique. By utilizing fully assembled stators, no additional samples are required. Manufacturing influence is inherently incorporated. Results show that measured iron losses are twice as high at 10 kHz compared with Epstein test results, which emphasizes the need to incorporate manufacturing influence on iron losses at high frequencies. The level of dc bias is also observed to have a significant impact on iron losses (up to 30%). Even though thinner laminations are known for reducing iron losses, the reduction is much lower than anticipated in the studied frequency range due to skin effect. Using a 0.1-mm lamination gauge instead of 0.3 mm reduces losses by 50% at 10 kHz, while the same substitution at 100 kHz only reduces losses by 30%. Future work includes loss separation in complete converter-fed machines.
16 citations
Proceedings Article•
15 Sep 2011TL;DR: In this paper, a 10 kW current-fed DC-DC converter using resonant push-pull topology is demonstrated and analyzed and the grounds for component dimensioning are given and the advantages and disadvantages of the resonant Push-Pull topology are discussed.
Abstract: In this paper, a 10 kW current-fed DC-DC converter using resonant push-pull topology is demonstrated and analyzed. The grounds for component dimensioning are given and the advantages and disadvantages of the resonant push-pull topology are discussed. The converter characteristics and efficiencies are demonstrated by calculations and prototype measurements.
16 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