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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TL;DR: In this article, a planar transformer structure with reduced winding length on the secondary side is proposed, which utilizes flux cancellation and reduces core loss while maintaining a low core volume, and the path of the secondary winding is a fraction of a full turn.
Abstract: This article proposes an isolated LLC resonant converter with MHz-level switching frequency that can achieve zero-voltage switching in the full-load range. In the proposed converter, conventional silicon devices are replaced with wide band-gap gallium nitride devices to reduce switching losses in the power device. A planar transformer structure with reduced winding length on the secondary side is proposed, which utilizes flux cancellation and reduces core loss while maintaining a low core volume. The path of the secondary winding is a fraction of a full turn, which reduces secondary-side losses while maintaining a turns ratio of 16:1. This planar transformer achieves the goals of decreasing core loss and volume while increasing power density. Within a limited circuit layout area, optimal points for the efficiency of core loss and copper loss were calculated. The magnetic simulation software ANSYS Maxwell was employed to verify whether the actual circuit behavior of this planar transformer conformed to the design theory. Finally, a resonant converter was achieved with a switching frequency operating at 1 MHz, input voltage of 380 V, output voltage of 12 V, output power of 800 W, power density of 55 W/cm3, and maximum efficiency of 96.5%.
16 citations
01 Sep 2018
TL;DR: The basic idea is to solve the current sharing problem between parallel strands in 2D without any influence of the core, but with an imposed external flux, representing the slot leakage flux.
Abstract: In the design process of electrical machines, the frequency dependence of the winding resistance is often neglected, although previous investigations have shown that losses can drastically increase due to eddy current effects. On the other hand, simulations using Finite Element Analysis (FEA) with every single strand modeled and connected together in an external circuit are time consuming and therefore not practicable. To address this issue, this paper proposes an analytical method for calculating the AC losses of arbitrarily arranged and connected conductors. The basic idea is to solve the current sharing problem between parallel strands in 2D without any influence of the core, but with an imposed external flux, representing the slot leakage flux. The model was validated using a permanent magnet synchronous machine (PMSM). Although the results of the analytical model only deviate slightly compared to FEA results, the computation time is considerably reduced.
16 citations
TL;DR: In this article, it was shown that, by adding some components to the classical circuit, eddy currents in windings can be taken into account, which enabled the above circuit to be justified and expressions for the supplementary components values.
Abstract: The precision of the classical equivalent circuit of a transformer is not sufficient for the software simulation of a high frequency power supply to be true. In this paper we show that, by adding some components to the classical circuit, eddy currents in windings can be taken into account. First, this modification was deduced from experimental results. Then, thanks to an homogeneous layer model, an analytical study was carried out. This enabled the above circuit to be justified and expressions to be derived for the supplementary components values. Finally, a more exact geometry was investigated thanks to an electromagnetic software simulation. The corresponding results agree well with analytical and experimental ones.
16 citations
Proceedings Article•
15 Sep 2011TL;DR: In this article, the authors present a tool for the design of isolated dc-dc converters based on multiobjective optimization (MO) using genetic algorithms (GAs), which performs search and optimization whereas analytical models are used to model the power converters.
Abstract: This paper presents a computer-aided design (CAD) tool for the design of isolated dc-dc converters. This tool, developed in Matlab environment, is based on multiobjective optimization (MO) using Genetic Algorithms (GAs). The Elitist Nondominated Sorting Genetic Algorithm (NSGA-II) is used to perform search and optimization whereas analytical models are used to model the power converters. The design problem requires minimizing the weight, losses and cost of the converter while ensuring the satisfaction of a number of constraints. The optimization variables are, as for them, the operating frequency, the current density, the maximum flux density, the transformer dimensions, the wire diameter, the core material, the conductor material, the converter topology (among Flyback, Forward, Push-Pull, half-bridge (HB) and full-bridge (FB) converters), the number of semiconductor devices associated in parallel, the number of cells (each of them corresponding to a topology) associated in serial or parallel as well as the kinds of input and output connections (serial or parallel) of these cells and the semiconductor devices (among diodes, IGBTs and MOSFETs). Finally, a design example is presented and the results show that such tool to design dc-dc power converters presents several advantages. In particular, it proposes to the designer a set of solutions — instead of a single one — so that he can choose a posteriori which solution best fits the application under consideration. Moreover, interesting solutions not considered a priori can be found with this tool.
16 citations
02 Mar 2012-Compel-the International Journal for Computation and Mathematics in Electrical and Electronic Engineering
TL;DR: In this paper, the authors present a computer-aided design tool for the design of isolated dc-dc converters, which is based on multi-objective optimization (MO) using genetic algorithms.
Abstract: Purpose – This paper presents a computer‐aided design (CAD) tool for the design of isolated dc‐dc converters.Design/methodology/approach – This tool, developed in Matlab environment, is based on multiobjective optimization (MO) using genetic algorithms. The Elitist Nondominated Sorting Genetic Algorithm is used to perform search and optimization whereas analytical models are used to model the power converters. The design problem requires minimizing the weight, losses and cost of the converter while ensuring the satisfaction of a number of constraints. The optimization variables are, as for them, the operating frequency, the current density, the maximum flux density, the transformer dimensions, the wire diameter, the core material, the conductor material, the converter topology (among Flyback, Forward, Push‐Pull, half‐bridge and full‐bridge topologies), the number of semiconductor devices associated in parallel, the number of cells associated in series or parallel as well as the kinds of input and output c...
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