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
06 Mar 2011
TL;DR: In this paper, a planar integrated magnetics (PIM) design approach for primary parallel isolated boost converters is presented, where all magnetic components in the converter including two input inductors and two transformers with primary-parallel and secondary-series windings are integrated into an E-I-E core geometry.
Abstract: A high efficient planar integrated magnetics (PIM) design approach for primary parallel isolated boost converters is presented. All magnetic components in the converter including two input inductors and two transformers with primary-parallel and secondary-series windings are integrated into an E-I-E core geometry. Due to a low reluctance path provided by the shared I-core, the two transformers as well as the two input inductors can be integrated independently, reducing the total ferrite volume and core loss. AC losses in the windings and the leakage inductance of the transformer are kept low by interleaving the primary and secondary turns of the transformers. To verify the validity of the design approach, a 1-kW prototype converter with two primary power stages is implemented for a fuel cell fed battery charger application with 20–40 V input and 170–230 V output. An efficiency of 96% can be achieved during nominal operating conditions. Also experimental comparisons between the PIM module and two separate cases have been done in order to illustrate the advantages of the proposed method.
15 citations
11 Sep 2006
TL;DR: In this paper, the authors considered the possibility of increasing the power density of high-power dc-dc converters with galvanic isolation, and three cornerstones for reaching high power densities are identified: size reduction of passive components, reduction of losses particularly in active components and thermal management.
Abstract: This thesis is concerned with the possibilities of increasing the power density of high-power dc-dc converters with galvanic isolation. Three cornerstones for reaching high power densities are identified as: size reduction of passive components, reduction of losses particularly in active components and thermal management. In addition to the cornerstones, the spatial integration of converter components is considered as it is also important for high power density. The size reduction in passives is obtained by increasing the operating frequency. On the other hand, an increase of operating frequency yields also higher losses in passive components themselves. Therefore, the thesis addresses the power loss in windings of magnetic components with special attention to the transformer windings. Integration of several passive components into a single component is also considered as the means to increase the power density. The main challenge is the integration of components at the considered high power levels. A high operating frequency results in a substantial increase of switching losses in active components. The higher losses yield reduced efficiency and require larger heatsinks which consequently reduce the effect of the higher operating frequency on the overall power density. In this thesis, the power loss in active components is reduced by applying so called Zero-Voltage-Switching Quasi-Zero-Current-Switching topology. The heat generated inside converter components must be removed to prevent them from overheating. Performing this task becomes more difficult as the power density increases because of higher power dissipated in a smaller volume. The thesis considers thermal management of a power converter on component, converter and system level. Each of the levels is addressed separately and adequate heat removal methods and concepts are proposed. Spatial integration of converter components is important to obtain a high power density as well. The key to the successful integration of components is to make design choices which result in components of compatible dimensions and shapes. Basic guidelines that should serve as an aid in the design of high power density high-power converters are discussed in this thesis. The operating conditions and requirements vary with the power level processed by a power converter. Therefore, the scalability of the design concepts and approaches is important for their practical implementation in the wide range of considered applications. This thesis briefly discusses scaling up with respect to power density and performance of the converter components. The ability of achieving high power densities in high power is demonstrated on a 50 kW converter prototype. The reached power density is in order of 11.2 kW/litre with water cooling and 6.6 kW/litre with forced air cooling. It is also shown that by designing for high power density, the efficiency might not need to suffer. The measured efficiency of the final converter prototype is as high as 97.5 % in a broad load range.
15 citations
TL;DR: In this article, the authors derived a mathematical expression to calculate the evolution, in the time domain, of the magnetic field during the switching, which will later used to obtain the current density distribution and copper losses in the component.
Abstract: High-frequency copper losses, or copper losses produced during switching in switching-mode power supplies, are very much related to variations of the magnetic field distribution within the core window. When operating at high frequency, the current flowing through the windings of a magnetic component experiences redistribution across the section of the conductor due to skin and proximity effects. Current redistribution depends not only on actual frequency, but also on conductor size and layer distribution. While previous works aim to optimize windings size by considering just the current flowing through that winding, this paper shows that, in most of the cases, current redistribution is strongly affected by the currents at the other transformer windings, which should also be taken into account. This paper derives a mathematical expression to calculate the evolution, in the time domain, of the magnetic field during the switching, which will be later used to obtain the current density distribution and copper losses in the component. An easy-to-calculate expression will be derived that allows magnetic windings to be analyzed and/or optimized, because losses are expressed as a function of the winding geometry and position. An application example is also included. All the equations derived are verified by comparing them with the results obtained from a differential equations solver, and with previous works when applicable. Experimental results are also provided.
15 citations
01 Jan 2013
TL;DR: In this article, the influence of the coil and work piece geometry on the effect of induction heating on billets is discussed. But the effect on the billet is not discussed.
Abstract: Induction heating is a common industrial process used for the reheating of billets before extrusion or forging. In this work the influence of the coil and work piece geometry, the effect of the ele ...
15 citations
TL;DR: A multi-physics model of a BIPV integrated DC/DC converter is developed in the Modelica language, taking into account the thermal and electrical couplings inherent to power electronic systems.
15 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