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 Sep 2020
TL;DR: In this paper, the authors investigated the potential of high extra losses in foil windings with unmitigated circulating currents and proposed to transpose the foil connections between series-connected winding portions.
Abstract: In foil windings of medium-frequency transformers rated for several hundred Amperes and operating at ten or several tens of kHz, parallel connection of foils is necessary to provide sufficient conductor cross-section. In this case, careful winding design is required to keep circulating currents among the foils under control. Such currents were investigated by means of an analytical model, a 2-d finite-element model, and measurements on a reduced-scale transformer for the case of two parallel connected foils. Simulations and measurements yield a consistent picture and show the potential of high extra losses in foil windings with unmitigated circulating currents. In particular, spiral windings of many turns may incur a circulating current that exceeds the useful net current by far if the inductance of the foil connections is small. Practically, it can be expected that the inductance of the foil connections leads to a noticeable reduction of the circulating current. This reduction, however, is not sufficient to bring the AC losses down to acceptable levels, such that it is recommended to transpose the foils between series-connected winding portions. Transposition largely cancels out the axial magnetic flux in the radial gaps between the parallel connected foils. The effectiveness of transposition in balancing the foil currents at frequencies up to 40 kHz is shown both theoretically and experimentally for aluminum foils of 0.2 mm thickness. With proper transposition, the extra AC losses due to circulating currents between foils can be reduced to practically negligible levels.
10 citations
TL;DR: A converter system for high-power applications, connected to a medium-voltage network using a step-up transformer, is presented in this paper, and an integrated inductor is proposed, which suppresses the circulating current in both the converter groups.
Abstract: A converter system for high-power applications, connected to a medium-voltage network using a step-up transformer, is presented in this paper. The converter-side winding of the transformer is configured as an open-end, and both the ends of the windings are fed from two different converter groups. Each converter group comprises of two parallel voltage-source converters (VSCs), whose carrier signals are interleaved to improve the harmonic quality of the resultant switched output voltage of that converter group. However, an additional inductive component is required to suppress the circulating current that flows between the parallel-interleaved VSCs. An integrated inductor is proposed, which suppresses the circulating current in both the converter groups. In addition, the functionality of the line filter inductor is also integrated. Flux in various parts of the integrated inductor is analyzed, and a design procedure is also described. The volume and the losses of the proposed solution are compared with that of the state-of-the-art solution. The control of the proposed converter system is also discussed. The analysis has been verified by the simulation and experimental results.
10 citations
TL;DR: In this paper, a galvanically isolated and scalable three-phase photovoltaic inverter with stacked output cells is proposed, where a distributed ac link composed of small ac capacitors and transformer magnetizing inductances is proposed.
Abstract: Modular converters with stacked cells have an advantage of achieving higher voltage or current levels by using standard low-voltage or low-current switches. This study presents a galvanically isolated and scalable three-phase photovoltaic inverter with stacked output cells. Instead of a dc link with electrolytic capacitors, a distributed ac link composed of small ac capacitors and transformer magnetizing inductances is proposed. Due to nonappearance of a dc link, a fast dynamic response is achievable. The oscillation of the ac link provides soft-switching for all switches in the entire load range without using auxiliary snubbing switches. The transformer core is utilized symmetrically in positive and negative half cycles and the inverter operation is not affected by unequal winding leakage inductances, which makes the transformer design simple. Current symmetry among the windings and voltage symmetry among the ac capacitors is provided naturally. Analytical study, design, and experimental validation of a 750 W prototype is presented.
10 citations
01 Jan 2010
TL;DR: A multi-resonant LLCC-type converter providing galvanic isolation is identified as the best topology, regarding soft-switching of semiconductor devices, high part-load efficiency and controllability.
Abstract: Shaker Verlag Nov 2010, 2010. Buch. Book Condition: Neu. 21x14.8x cm. Neuware Module-integrated photovoltaic (PV) systems show high robustness against mismatching of the PVgenerator, e.g. reasoned by partial shading. Thus, the surface potential for PV can be increased by the unevenly irradiated surfaces using module-integrated PV. Consequently, the important, already sealed surfaces in urban areas can be utilized to contribute to a sustainable energy supply. Different module-integrated system concepts are reviewed and compared. The parallel module-integrated converter concept is identified as the most flexible, safe and cost effective solution. It consists of modules with module-integrated DC-DC converters, feeding into one DC-distribution line in parallel. Since grid connection and metering is performed in a central unit, the critical DC-DC converter is designed to minimum functionality, i.e. maximum power point tracking, safety and efficiency. The system is flexible and scalable for arbitrary modules and can be combined with classical string or central systems. In this work a multi-resonant LLCC-type converter providing galvanic isolation is identified as the best topology, regarding soft-switching of semiconductor devices, high part-load efficiency and controllability. Detailed investigations are carried out for three research foci of the DC-DC converter. With the goal of high converter efficiency, first design...
10 citations
17 May 2016
TL;DR: In this article, a simple and compact formula was developed to select the optimum magnetic core for switching power supplies, including the effects of the frequency and the duty cycle on the magnetic and winding losses.
Abstract: Design an efficient high frequency transformer or inductor is based on accurate core loss and winding loss models. Steinmetz and Dowell's equations are the most common methods used for this purpose. The selection of the optimum magnetic core depends on both: the core and the winding losses. The core geometry coefficient is a popular method which Steinmetz equation, valid for sinusoidal excitation, and the DC copper loss formula are coupled together to determine the suitable magnetic core. However, in switching power supplies, excitation waveforms are non-sinusoidal. This implies that the frequency and the duty cycle can have a great effect on the core and copper losses. As a result, the magnetic core could be undersized which leads to decrease the efficiency. The main contribution of this paper is to develop a simple and compact formula to select the optimum magnetic core. This formula includes the effects of the frequency and the duty cycle on the magnetic and winding losses.
9 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