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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06 Jun 2019
TL;DR: In this paper, a study of the skin effect influence in the AC machines for electric drives is presented, and the different approaches for the Field coefficient are compared and the influence of different geometrical parameters of the stator winding on the field coefficient for different frequencies of stator currents is studied.
Abstract: The paper presents a study of the skin effect influence in the AC machines for electric drives. First the theory background from different sources is presented. Then the different approaches for the Field coefficient are compared. Finally the influence of different geometrical parameters of the stator winding on the Field coefficient for different frequencies of the stator currents is studied.
5 citations
01 Jan 2005
TL;DR: In this paper, a homogenization method for the inclusion of skin and proximity effect in windings in finite-element (FE) models of electromagnetic devices is proposed, where the conductors are characterized in the frequency domain by means of a reduced FE model.
Abstract: This paper deals with novel homogenization methods for the inclusion of skin and proximity effect in windings in finite-element (FE) models of electromagnetic devices. A general frequency-domain approach and its original extension to the time domain are proposed. In a preprocessing step the conductors (i.e. type of cross-section and packing, and fill factor) are characterized in the frequency domain by means of a reduced FE model, producing six dimensionless and frequency-dependent skin- and proximity-effect coefficients. The latter coefficients are readily taken into account in a frequency-domain FE analysis of a complete device. A time-domain FE analysis with homogenized winding requires the introduction of additional unknowns and equations; this extension to the time domain is analogous to the approximation of a frequency-dependent inductive impedance by a ladder circuit consisting of constant resistances and inductances. By way of illustration and validation, the homogenization methods are applied to a 2D FE model of an inductor. For the winding, different types of wire cross-section and packing, viz round/hexagonal and rectangular/rectangular, are considered. A precise reference solution is obtained with a FE model in which all wires are finely discretized. An excellent agreement is achieved while reducing the computation time considerably
5 citations
01 Jun 2017
TL;DR: In this article, a population-based genetic algorithm was used to design inductors implementing powdered iron core (FeSi) with rectangular wire and ferrite core with litz wire at different operating frequencies and for different number of phases for a 40kW nominal, 60kW peak bidirectional DC-DC boost converter.
Abstract: Magnetics design is a major factor within the design of any high-power converter due to its large volume, weight, and cost. Typically inductor design is a time-consuming iterative process. Therefore, any technique which speeds this process up will help reducing the time spent for the design. As such this paper discusses typical inductor design, and proposes a population based optimization technique for a high power inductor for an EV/HEV application. The Genetic Algorithm (GA) optimization technique will be used to design inductors implementing powdered iron core (FeSi) with rectangular wire and ferrite core with litz wire at different operating frequencies and for different number of phases for a 40kW nominal, 60kW peak bidirectional DC-DC boost converter. The comparison will show what phase number at what operating frequency provides the lowest inductor volume. This paper will also discuss a lumped parameter thermal network for the core temperature estimation which will be used within the Genetic Algorithm.
5 citations
27 Jul 1999
TL;DR: In this article, a new design and fabrication method for planar windings is presented, which can automatically series-connect each layer of the winding, and virtually eliminate external soldering or conductive vias, thus reducing the DC resistance and increasing the reliability.
Abstract: A new design and fabrication method for planar windings is presented. This method can automatically series-connect each layer of the winding, and virtually eliminate external soldering or conductive vias, thus reducing the DC resistance and increasing the reliability. Compared with the previously reported folding method for winding fabrication, this method maximizes the use of window height and minimizes the wastage of copper area in manufacturing. Practical examples of low-profile transformers and inductors were constructed and tested in an active-clamped DC-DC converter with self-driven synchronous rectifiers. Experimental results are presented to show that such transformers/inductors are particularly useful for the design of low-profile and high-power-density converter modules. Finally, a new and easy-to-implement algorithm is presented for minimum core volume design of high-frequency planar transformers. Given a set of specifications, such as transformer efficiency, converter topology, output power and voltage, etc., the PC-based program can search for a core with minimum volume, and provide such transformer parameters as core and winding geometry, etc. Unlike the conventional design, the new design approach considers the high frequency effect, and offers more flexibility in design.
5 citations
01 Sep 2019
TL;DR: In this article, an equivalent π-model of a two-winding transformer is derived using circuit synthesis method, which conserves the intertwined effects among the transformer parasitics over a wide frequency range.
Abstract: In literature, experiment based methods are met, which postulates circuit behavior of a two-winding transformer using empirical formulae based on impedance measurement and parameter extraction. Alternately in this paper, an equivalent π-model of a two-winding transformer is derived using circuit synthesis method. Individual branch impedances of π-model are expressed using the lumped circuit parameters, which conserve the intertwined effects among the transformer parasitics over a wide frequency range. Proposed π-model permits to find the open-circuit and short-circuit impedances of transformer and forecast its parallel and serial resonance frequencies. Any anomaly, e.g. close proximity of the resonance and switching frequencies, can be avoided prior to transformer prototyping, saving time, effort and cost. Accuracy of the proposed π-model is verified with the help of an exact circuit of a two-winding transformer, modeled in MATLAB. Performance of the equivalent π-model is further validated experimentally using frequency response analysis (FRA) of a 1.5 kW, 200/100 V, 15 kHz, EE8020×2 ferrite core transformer. Close agreement is noted among analytical, simulation and experimental results, which substantiates accuracy of the proposed π-model and its utility for transformer designs at medium/high frequency.
5 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