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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03 Mar 1996
TL;DR: In this paper, a transformer with a height of 6 mm and a power density of 600 W/in/sup 3/ was built for a 100 W, 3.3 V output active-clamped forward converter using self-drive synchronous rectifiers.
Abstract: An algorithm is developed to design a transformer that has the highest power density and meets a given set of specifications. The maximum achievable power density for a given power level and output voltage is computed based on only one fundamental constraint, i.e. the efficiency or temperature rise requirement. A family of curves that present the relationship between the power density and transformer height are developed. It is found that there is an optimum height at which the power density peaks. The maximum achievable power density is determined along with the optimum operating frequency and core geometry. As a result, a transformer with a height of 6 mm and a power density of 600 W/in/sup 3/ was built for a 100 W, 3.3 V output active-clamped forward converter using self-drive synchronous rectifiers.
10 citations
30 Sep 2008
TL;DR: In this paper, a finite element analysis (FEA) software is utilized for the investigation of a series of issues critical for the accurate determination of copper losses in layered coils with round wires or foils.
Abstract: Copper losses in magnetic coils depend on several geometrical parameters, as well as on frequency, in a way that makes their modeling a quite difficult task. In this paper a finite element analysis (FEA) software is utilized for the investigation of a series of issues critical for the accurate determination of copper losses in layered coils with round wires or foils. Some of the issues investigated are the edge effect in foil and round wire windings as well as the effect of the winding pitch on the copper losses. The results that come up from this work help to fully understand the real impact of two dimensional (2D) effects in layered windings of real rather than ideal magnetic components and they consist a tool for the accurate calculation of the encountered losses, which is necessary for an optimized magnetic component design.
10 citations
01 Nov 2011
TL;DR: In this paper, the authors provide a thorough study of transformer design for high-frequency applications, and several novel concepts are proposed to reveal the fundamentals of the transformer design, and the minimum electric and magnetic energy theorem is presented to optimize transformer design.
Abstract: This paper provides a thorough study of transformer design for high-frequency applications. Several novel concepts are proposed to reveal the fundamentals of the transformer design. The minimum electric and magnetic energy theorem is presented to optimize the transformer design. With the utilization of the minimum electric and magnetic energy theorem, the current distribution among high-frequency parallel windings can be identified. Optimal winding structures are proposed to achieve low power losses, and leakage inductance controllability is studied for soft-switching applications. The proposed concepts and theoretical analysis are verified in an LLC resonant dc-dc converter prototype.
10 citations
01 Oct 2017
TL;DR: Close agreement between analytical and simulation results is observed which substantiates proposed thermal model in terms of accuracy and efficacy of computation.
Abstract: A medium/high-power conversion system, using power electronic (PE) converter in conjunction with a medium/high-frequency transformer, has many desirable effects suitably oriented for modern power system architecture. Switching at high frequency results in lesser volume of magnetics but induces higher loss density. Thus design and characterization of a medium-frequency (MF) high-power (HP) transformer has significant ramification on its performance and application. Thermal management of a MF HP transformer is one of key aspects for its characterization. In this paper, an equivalent thermal model of a multi-layer concentrated winding is derived. Core and copper losses are carefully estimated. Thermal resistance and capacitance are accurately calculated. Time-domain response of proposed thermal network is obtained using Heun's method (Modified Euler) and validated with PLECS. Effects of temperature change on thermal properties of material and coolant (transformer oil) are also discussed. Furthermore, accuracy of said thermal network is corroborated through FEM-CFD study of a 10kW, 0.5/2.5kV, 1kHz natural oil-cooled transformer. Close agreement between analytical and simulation results is observed which substantiates proposed thermal model in terms of accuracy and efficacy of computation.
10 citations
Dissertation•
22 Nov 2006
TL;DR: In this article, the authors present three methods to estimate the tension internes of a multicellulaire superpose (SMC) structure: a reconstruction of tension, a structure d'observation basee sur a simulation numerique, and an observateur a modes glissants.
Abstract: Ce manuscrit apporte une contribution a la commande et a l'observation du convertisseur multicellulaire superpose (SMC). Cette nouvelle structure de conversion d'energie, brevetee en 2001, presente des caracteristiques tres interessantes qui lui conferent un interet certain pour les applications industrielles de forte puissance. Les presents travaux ont pour objet principal d'ameliorer le fonctionnement des convertisseurs SMC et de montrer leur competitivite pour ce domaine d'application. Cet enjeu est atteint de deux manieres differentes mais complementaires : en positionnant le SMC dans le domaine basse tension/forte puissance, une gamme de tension reduite par rapport a son domaine de predilection ; en developpant des techniques d'observation des tensions internes de la structure, afin de reduire son cout et d'assurer son fonctionnement optimal et securise. La premiere partie de ce memoire est consacree a la presentation du fonctionnement, de la commande et des proprietes associees aux principales structures multiniveaux. Il s'agit de montrer l'interet que represente la topologie SMC dans les systemes de conversion de puissance vis-a-vis des autres convertisseurs de cette famille. Nous effectuons ensuite une etude comparative des pertes, performances et couts des topologies d'onduleurs 2 et 3 niveaux a base d'IGBT pour une application basse tension/forte puissance. L'enjeu consiste a legitimer l'utilisation du SMC a ce niveau de tension par rapport aux topologies classiques et multiniveaux concurrentes. La deuxieme partie de ce manuscrit est dediee a l'observation fine en temps reel des tensions internes de la structure SMC. Le controle actif de ces dernieres revet en effet un caractere important, car il conditionne la survie du convertisseur en garantissant une repartition equilibree des contraintes en tension sur les semi-conducteurs de puissance. Cet equilibrage actif necessite la connaissance de ces grandeurs a l'echelle de la periode de decoupage. La suppression des capteurs differentiels necessaires permettrait donc de reduire de maniere significative le cout global de ces structures dans le cadre d'applications industrielles. Nous presentons ainsi trois methodes d'estimation : un reconstructeur de tension, une structure d'observation basee sur une simulation numerique en temps reel du systeme associee a une mesure de tension et un observateur a modes glissants. Ces techniques sont toutes validees par simulation sur des structures multicellulaires superposees a 3 cellules de commutation. L'observateur a modes glissants est egalement valide experimentalement pour un onduleur SMC 7 niveaux triphase 15kVA. Son implantation est realisee a l'aide d'une carte numerique associant un DSP et un FPGA.
10 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