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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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Proceedings ArticleDOI
24 May 2019
TL;DR: In this paper, the authors proposed a transformer design that maximizes the value of the secondary leakage inductance and minimizes the primary leakage induction value to avoid the voltage drop caused by the relatively large value of magnetizing current.
Abstract: Minimizing the transformer magnetizing inductance is essential for the soft switching operation of the LLC resonant converter, despite the fact that it results in higher values of magnetizing current, which deteriorates the converter efficiency. Furthermore, it is a well-known practice to utilize the transformer leakage as an inductive component in the resonant tank to improve the power destiny. This paper reveals that the transformer voltage gain can be improved when the transformer leakage inductance in concentrated on the secondary side to avoid the voltage drop inflicted by the relatively large value of the magnetizing current (im), especially at light load condition. The theoretical discussion relies on the asymmetry of the EI core by placing the secondary winding in a close contact with the magnetic core and placing the primary winding in the vicinity of the air gap. Moreover, noise absorber had been utilized to control the leakage inductance value. The proposed transformer design maximizes the value of the secondary leakage inductance and minimizes the primary leakage inductance. Alongside with the theoretical discussion, experimental tests had been conducted to evaluate the proposed method using a 390V-12V, 220W LLC resonant converter.

6 citations

Proceedings ArticleDOI
B. Ackermann1, A. Lewalter
22 Oct 2001
TL;DR: In this article, a two-dimensional analytical model for planar magnetic components is presented that overcomes the shortcomings of the one-dimensional models, and its accuracy is corroborated by a comparison with results obtained from finite element calculations.
Abstract: Calculating the winding losses is of major importance for the design of magnetic components for power electronics. Two-dimensional finite element programs provide sufficiently accurate results. However, using them is cumbersome. Therefore there is a considerable need for efficient analytical models suitable to assess a large number of design alternatives. State of the art one-dimensional models fail in many situations. A two-dimensional analytical model for planar magnetic components is presented that overcomes the shortcomings of the one-dimensional models. Its accuracy is corroborated by a comparison with results obtained from finite element calculations. Quantifying the tradeoff between the building height and winding losses of a planar inductor is discussed as a design example.

6 citations

Proceedings ArticleDOI
09 Jul 2017
TL;DR: In this article, a new analytical model is proposed which makes it possible to carry out a straightforward and accurate calculation of the winding loss in high-frequency low-permeability inductors.
Abstract: Traditional winding loss estimation models lead to unacceptable estimation errors when applied to low-permeability inductors. This is due to the highly two-dimensional character of the magnetic field in these inductor windings. In this paper, a new analytical model is proposed which makes it possible to carry out a straightforward and accurate calculation of the winding loss in high-frequency low-permeability inductors.

6 citations

Proceedings ArticleDOI
13 Nov 2014
Abstract: Proper use of winding area and conductor layout in resonating coils of Inductive Power Transfer (IPT) systems is of great importance to achieve high efficient systems. In this paper a simple adaptable analytical method is investigated that can be implemented on variety of coil layout optimization problems to increase the resonator performance and the system efficiency. The method is frequency independent and overcomes the difficulties associated with the prediction of high frequency field distributions in IPT systems. In this study the procedure is applied to optimize a one-turn circular foil resonator operating at 13.56 MHz, with the Finite Element (FE) results showing of up to 30% increase in resonator quality factor and 1.73% increase in link efficiency of the IPT system.

6 citations

Journal ArticleDOI
14 Feb 2022-Energies
TL;DR: In this article , a concentric-winding (CW) enhanced leakage-inductance-integrated (ELII) structure, which includes an additional core, was proposed for dual active bridge (DAB) converters.
Abstract: For dual active bridge (DAB) converters, integrating the phase-shifting inductance (PSI) in the medium-frequency transformer (MFT) is an effective way to improve the overall power density. Different from the existing leakage-inductance-integrated (LII) structure, a concentric-winding (CW) enhanced leakage-inductance-integrated (ELII) structure, which includes an additional core, is proposed in this paper. In order to explain the operating mode of CW ELII MFT, a magnetic circuit model is established, and the analysis is carried out under the typical DAB excitation. The total leakage inductance of CW ELII MFT is divided into the winding leakage inductance and the additional leakage inductance for calculation. The integrated structure makes the heat dissipation of the MFT challenging. Therefore, the air–water combined cooling method is adopted in the design. A thermal resistance model is built for the winding air channel under forced convection. On this basis, MFT designs with different integration structures for different leakage inductance requirements are compared. Finally, a 200 kW/4 kHz/200 μH MFT prototype was designed and manufactured, which achieved the power density of 5.16 kW/dm3 and the efficiency of 99.30%. The prototype was tested in a DAB converter, which is a module of a 2 MW modular multilevel converter-bidirectional DC–DC converter (MMC-BDC).

6 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