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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01 Jan 2014
TL;DR: This paper aims at efficiency optimization of MF transformers and studies the relation between efficiency and core materials, operating parameters, and geometric parameters to give MF transformer designs some useful references.
Abstract: Power electronics transformers (PETs) have the advantages of small volume and light weight, so they have promising applications in rail transit traction systems substituting traditional transformers. The PET consists of the medium frequency transformer (MF transformer) and power electronic converters on the primary and secondary sides. Among these components, the MF transformer efficiency affects overall system power transfer capacity, and plays an important role as it determines whether the PET system could work with high performance. This paper aims at efficiency optimization of MF transformers and studies the relation between efficiency and core materials, operating parameters, and geometric parameters to give MF transformer designs some useful references.
01 Nov 2020
TL;DR: In this article, a cooling scheme and a corresponding thermal design method for high power high frequency transformer, which is used in power electronic transformer device for railway traction applications, is proposed and verified through the experiment on a 5.5kHz 140kVA transformer.
Abstract: In this paper, a cooling scheme and the corresponding thermal design method is proposed for high power high frequency transformer, which is used in power electronic transformer device for railway traction applications. Particularly, to address the overheating problem resulting from dimensional restriction and electrical insulation in railway applications, the cooling scheme based on actively cooled system with R245fa refrigerants is further enhanced by 2-phase flow cooling. The mathematic model of transformer copper and iron loss is first introduced. Subsequently, the required cooling area of transformer core is quantitatively calculated using thermal network method and the total pressure loss and heat transfer in two-phase flow is determined accordingly. Finally, the proposed thermal design method and corresponding cooling scheme are verified through the experiment on a 5.5kHz 140kVA transformer.
29 Nov 2019-Compel-the International Journal for Computation and Mathematics in Electrical and Electronic Engineering
TL;DR: An electrical equivalent circuit for inductive components as well as the methodology for electrical parameter extraction by using a 3 D finite element analysis (FEA) tool are presented.
Abstract: The purpose of this paper is the presentation of an electrical equivalent circuit for inductive components as well as the methodology for electrical parameter extraction by using a 3 D finite element analysis (FEA) tool.,A parameter extraction based on energies has been modified for three dimensions. Some simplifications are needed in a real model to make the 3 D finite element method (FEM) analysis operative for design engineers. Material properties for the components are modified at the pre-modeling step and a corrector factor is used at the post-modeling step to achieve the desired accuracy.,The current hardware computational limitations do not allow the 3 D FEA for every magnetic component, and due to the component asymmetries, the 2 D analysis are not precise enough. The application of the new methodology for three dimensions to several actual components has shown its usefulness and accuracy. Details concerning model parameters extration are presented with simulation and measurement results at different operation frequencies from 1 kHz to 1 GHz being the range of switching frequencies used by power electronic converters based on Si, SiC or GaN semiconductors.,This new model includes the high-frequency effects (skin effect, proximity effect, interleaving and core gap) and other effects can be only analyzed in 3 D analysis for non-symmetric components. The electrical parameters like resistance and inductance (self and mutual ones) are frequency-dependent; thus, the model represents the frequency behavior of windings in detail. These parameters determine the efficiency for the inductive component and operation capabilities for the power converters (as in the voltage boost factor), which define their success on the market.,The user can develop 3 D finite element method (FEM)-based analyses with geometrical simplifications, reducing the CPU time and extracting electrical parameters. The corrector factor presented in this paper allows obtaining the electrical parameters when 3D FE simulation would have developed without any geometry simplications. The contribution permits that the simulations do not need a high computational resource, and the simulation times are reduced drastically. Also, the reduced CPU time needed per simulation gives a potential tool to optimize the non-symmetric components with 3 D FEM analysis.
09 Dec 2022
TL;DR: In this paper , the authors presented the parameters affecting the parasitic capacitance of the inductor and compared with finite element analysis (FEA) to present the effects of the minor parameters.
Abstract: This paper presents the parameters affecting the parasitic capacitance of the inductor. These parameters are categorized into major and minor parameters. The conductor size, number of turns, distance between turns, and the number of layers are the major parameters. The minor parameters of the parasitic capacitance include permittivity of the bobbin material, the bobbin material responses about the temperature and operating frequency, the size of the bobbin, the insulated material of the wire, and the thickness of the insulated material. The simulation results are compared with finite element analysis (FEA) to present the effects of the minor parameters on the parasitic capacitance of the inductor. The results show that the parasitic capacitance of the inductor can be reduced by optimal selection of the parameters that contribute to the parasitic capacitance during the design stage.
19 Mar 2023
TL;DR: In this paper , an extended Cauer circuit model of power inductors that can represent both eddy current effects and capacitive properties is presented. But the model is valid from DC to higher frequencies beyond the resonance because it considers the skin and proximity effects of windings as well as the parasitic capacitance.
Abstract: This study presents an extended Cauer circuit model of power inductors that can represent both eddy current effects and capacitive properties. This model is valid from DC to higher frequencies beyond the resonance because it considers the skin and proximity effects of windings as well as the parasitic capacitance. The inductive part is represented by a Cauer circuit whose circuit parameters are recursively determined from the frequency properties of the inductor obtained through measurements or simulations. Moreover, the impedance profile around the resonance is expressed by introducing hierarchical RLC series circuits to the Cauer circuit. The extended Cauer circuit can be embedded in circuit simulators once constructed to perform time-domain simulations.
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