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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01 Aug 2019
TL;DR: In this paper, an optimized high-frequency transformer design for a 6 kV, 100 kW Isolated Modular Multilevel DC-DC (iM2DC) converter for shipboard application with 50 kHz transformer ac frequency is presented.
Abstract: This paper presents an optimized high-frequency transformer design for a 6 kV, 100 kW Isolated Modular Multilevel DC-DC (iM2DC) converter for shipboard application with 50 kHz transformer ac frequency. The Phase Shifted Square Wave Modulation (PS-SWM) scheme produces an unconventional, non-sinusoidal ac voltage waveform that makes the high-frequency transformer design challenging. This paper proposes an optimized transformer design method by accurately estimating the transformer’s power loss for iM2DC converter while still utilizing the advantages associated with PS-SWM modulation. The findings are later validated by a down scaled prototype.
14 citations
18 May 2014
TL;DR: In this article, the authors presented a winding design procedure for minimizing the power losses using foils and solid round wires under sinusoidal excitation to limit the temperature rise, and compared the windings losses between foil windings and round conductors.
Abstract: High frequency transformers are widely used in Switched-mode power supplies and now are being proposed to be used with power electronic converters to replace line-frequency transformers. This paper presents a winding design procedure for minimizing the power losses using foils and solid round wires under sinusoidal excitation to limit the temperature rise. This paper derives the range from which the thickness of the layers can be chosen to obtain the minimum power loss. This thickness range is a function of the number of layers and does not include the “optimum” based on the previous literature. Using this design procedure, it is shown that interleaving is not necessary in foil-wound transformers to obtain the minimum loss. A comparison of winding losses between foil windings and round conductors is also given. The analytical results are verified by designing six different winding configurations for the same specifications using 2-D Ansys Maxwell finite element design package.
14 citations
CERN1
TL;DR: In this article, an analysis of the effect of high-frequency phenomena on the I2PS functioning is described, where the key element is the modeling of the resistance as a function of the frequency, which starts from the analytical resolution of Maxwell's equations in the coil's geometry.
Abstract: The ironless inductive position sensor (I2PS) is a five-coil air-cored structure that senses the variation of flux linkage between supply and sense coils and relates it to the linear position of a moving coil. In air-cored structures, the skin and proximity effect can bring substantial variations of the electrical resistance, leading to important deviations from the low-frequency functioning. In this paper, an analysis of the effect of high-frequency phenomena on the I2PS functioning is described. The key-element is the modeling of the resistance as a function of the frequency, which starts from the analytical resolution of Maxwell's equations in the coil's geometry. The analysis is validated by means of experimental measurements on custom sensor coils. The resulting model is integrated with the existing low-frequency analysis and represents a complete tool for the design of an I2PS sensor, framing its electromagnetic behavior.
14 citations
TL;DR: In this paper, a procedure based on 2D finite element models for accelerating the calculation of additional losses in large foil windings of dry-type distribution transformers is presented, and different levels of simplification proposed are compared with a detailed 2D simulation of the windings.
14 citations
15 May 2013
TL;DR: In this article, thermal analysis of a 35kW wireless power transfer (WPT) pickup module to keep the system's efficiency at different temperatures is presented. But the authors do not consider the effect of temperature on the performance of the WPT system.
Abstract: This paper reports thermal analysis of a 35kW wireless power transfer (WPT) pickup module to keep the system's efficiency at different temperatures. Temperature effects are first considered by looking at change in efficiency of the system which is influenced by change in resistance and capacitance at different temperatures. Then, we introduce methods to improve the overall performance of a high powered WPT system by utilizing appropriate wires and capacitors, and cooling the device by means of an optimized heat sink.
14 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