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Journal ArticleDOI

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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Journal ArticleDOI
TL;DR: In this article , a modified Preisach model of hysteresis for a 3-phase medium frequency transformer in a 100 kW dual active bridge converter is presented, where the transformer magnetic core is assembled out of ferrite I-cores, which results in multiple parasitic air gaps.
Abstract: This article presents the modified Preisach model of hysteresis for a 3-phase medium frequency transformer in a 100 kW dual active bridge converter. The transformer magnetic core is assembled out of ferrite I-cores, which results in multiple parasitic air gaps. For this transformer, the hysteresis loops were measured and parameters of the Preisach model were determined. The Preisach distribution function is approximated with a two-dimensional Gauss function series and the feedback function is a 3rd-degree polynomial. The optimized identification of Preisach distribution function parameters was prepared. Two sets of parameters were determined based on the analysis of major and minor hysteresis loop. The developed model is used to analyze the transformer core power loss. A new set of Steinmetz equation parameters for multi air gap ferrite core MFT is proposed.

1 citations

Journal ArticleDOI
TL;DR: In this paper , the authors proposed an analytical model that considers the 2-D characteristic of the magnetic field and the geometrical particularities of toroidal windings, which provides an easy-to-use method, which avoids the unaffordable computational cost of FEA software.
Abstract: Toroidal inductors are used in many industrial applications in which they are key components regarding cost and volume. In the inductor design process, it is paramount to accurately estimate its high-frequency winding loss. Finite element analysis (FEA) software and analytical models can be used for this purpose. However, the former employs too much time and the latter lacks accuracy when applied to toroidal windings, leading to an overestimation that can exceed 200%. As a consequence, designers would benefit from a reliable method to calculate high-frequency loss in toroidal windings. This paper proposes an analytical model that considers the 2-D characteristic of the magnetic field and the geometrical particularities of toroidal windings. Furthermore, it provides an easy-to-use method, which avoids the unaffordable computational cost of FEA software. Simulations and experimental measurements are carried out for six toroidal power inductors, from 10 Hz up to 200 kHz. Three different well-known state-of-the-art analytical models are used for comparison purposes. The results obtained with the proposed model are in good agreement with those from FEA and the experiments. The proposed model shows a maximum deviation below 20%, while the overestimation of the existing analytical methods reaches values from 93% to 226%.

1 citations

01 Jan 2017
TL;DR: This master thesis proposes methods of measurement, simulation model adjustments, and usage of the finished model based on curve fitted parameters, and compares the simulated properties to current and voltage levels measured in real vehicles.
Abstract: Current ripple can cause a lot of problems as it spreads in the DC-side of the TVS of electric and electric hybrid vehicles. Fully knowing the properties of the TVS can be used to build a simulation model to determine the spreading of current ripple beforehand, which in turn is useful for calculating component placement, optimal filter sizes, and component lifetime. Being the second in line of an ongoing chain of thesis projects at Volvo buses, this master thesis proposes methods of measurement, simulation model adjustments, and usage of the finished model. Using an LCR meter, the impedance of several components was measured and modeled in LTSpice based on curve fitted parameters. Comparing the simulated properties to current and voltage levels measured in real vehicles, the accuracy of the models of different buses is presented and validated. (Less)

1 citations

Proceedings ArticleDOI
20 Mar 2022
TL;DR: In this article , the analytical models and optimization procedure for the design of high-power matrix core transformer (MCT) aiming at isolated DC/DC converter applications, especially for dual active bridge (DAB) converters, are proposed.
Abstract: In this work, the analytical models and optimization procedure for the design of high-power matrix core transformer (MCT) aiming at isolated DC/DC converter applications, especially for dual active bridge (DAB) converters, are proposed. The loss models, leakage inductance and thermal network models of MCT are presented, and a multi-variable, multi-objective optimization methodology of MCT is proposed. A 100 kW/50 kHz MCT design is selected and prototyped based on the optimization results. An additive manufactured bobbin design is also presented to control the leakage inductance and the path of the airflow. The electrical, magnetic, and thermal performance of the prototype are validated using by experimental studies.

1 citations

Journal ArticleDOI
01 Feb 2003
TL;DR: It is argued that coming to grips with the electromagnetic operation of switch-mode power conversion presents a barrier of knowledge that will have to be crossed in order to achieve future meaningful innovation in switch- mode power conversion.
Abstract: Historically, it came about that the analysis and design of the power electronic converter center around currents and voltages in the circuits. During the last decade, the electromagnetic character of power electronic converters became more important due to the noise that the switches generates and electromagnetic interference (EMI) and electromagnetic compatibility (EMC) standards have been put in place to control the electromagnetic noise levels. In this contribution, it is argued that coming to grips with the electromagnetic operation of switch-mode power conversion presents a barrier of knowledge that will have to be crossed in order to achieve future meaningful innovation in switch-mode power conversion. Rigorous electromagnetic analysis using realistic parameters are used to indicate important issues relating fundamental limits and technological paths for future generations of power electronic converters. Electromagnetic integration in three dimensions creates new possibilities to increase power densities.

1 citations

References
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Journal ArticleDOI
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

Journal ArticleDOI
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

Journal ArticleDOI
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

Journal ArticleDOI
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