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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TL;DR: In this article, a planar litz wire conductor is constructed by dividing the wide planar conductor lengthwise into multiple strands and weaving these strands in much the same manner as one would use to construct a conventional round litz wires conductor.
Abstract: A new trend in power converters is to design planar magnetic components that aim for low profile. However, at high frequencies, ac losses induced in the planar inductor and transformer windings become significant due to the skin and proximity effects. A planar litz conductor can be constructed by dividing the wide planar conductor lengthwise into multiple strands and weaving these strands in much the same manner as one would use to construct a conventional round litz wire conductor. Each strand is then equally subjected to the magnetic fields in the winding window, thereby equalizing the flux linkage and improving the current distribution. Three-dimensional finite-element modeling was performed for simple models. The simulation results showed that the planar litz conductor can result in lower ac resistance than a solid conductor over a specific frequency range. The performance of the planar litz winding was also verified with measurements on two experimental prototypes.
95 citations
TL;DR: In this paper, the authors proposed an EMI filter embedded into the main high-frequency planar transformer used in the dc/dc converter in plug-in electric vehicles (PIEVs) as a very cost-effective and efficient solution for EVs.
Abstract: Presently, there is an immense impetus in the automotive industry to develop plug-in electric vehicles (PIEVs) to reverse the ever increasing green house gas emissions from fossil fuels and depleting fossil fuel resources. High-frequency ac-dc converters with an isolated output are one of the essential building blocks for transferring power from utility mains to the traction battery packs which store energy for propelling the EV. Generally, the ac/dc converters used in EVs include a PFC stage at the input side and an isolated dc/dc converter at the battery side. Due to the switching nature of the converter, electromagnetic compatibility (EMC) of these converters is an essential requirement, to ensure not only its own operation but also the safe and secure operation of surrounding electrical equipment. EVs possess a lot of sophisticated electronic circuits in the vicinity of the battery charging power converters. Thus, strict EMC standards of the on-board power converters must be met according to the CISPR 12 or SAEJ551/5 relevant EMC standards. Conventional passive filters used for EMI mitigation in power converters, comes at the expense of cost, size and weight, power losses, and printed circuit board real estate. In this paper, an electromagnetic interference (EMI) filter embedded into the main high-frequency planar transformer used in the dc/dc converter is proposed as a very cost-effective and efficient solution for EVs. The proposed structure is able to significantly suppress the common-mode (CM) EMI noise generated in the dc/dc converter. Experimental results have been obtained from a 3-kW prototype in order to prove the feasibility and performance of the proposed EMI filter. The results show that the proposed embedded EMI filter can effectively suppress the CM noise particularly for high switching frequency power converters. The proposed structure can be a very simple and cost-effective EMI filtering solution for future PIEVs.
93 citations
23 Dec 2010
TL;DR: In this article, three cascaded 6.7kVA high-voltage high-frequency transformers operating at 3kHz are employed to convert voltage from 3800V high voltage DC link of each cascaded stage to 400V low voltage dc link.
Abstract: Solid state transformer (SST) exhibits good features such as high power density, small volume and weight, controlled power factor, voltage sag ride through, etc. compared with traditional line frequency transformer. The 7.2kV AC to 120V/240V AC 20kVA solid state transformer is a key component of the future renewable electric energy delivery and management (FREEDM) systems as the interface between the 7.2kV distribution grid and the low voltage residential micro-grid. Three cascaded 6.7kVA high-voltage high-frequency transformers operating at 3kHz are employed to convert voltage from 3800V high voltage DC link of each cascaded stage to 400V low voltage DC link. The transformer is required to withstand at least 15kV high frequency voltage insulation continuously. Transformer magnetic core materials were reviewed and compared. Winding layout alternatives for leakage, magnetizing inductance and insulation were compared. An insulation strategy based on split core and separate winding structure with inserted insulation layer between the C cores was proposed. One 6.7kVA high voltage high frequency transformer prototype was built and the test results were reported.
93 citations
23 Jun 1996
TL;DR: In this article, a design methodology based on a simple model is proposed for a 5 MHz buck power converter application is presented, and a power density of 12.8 W/cm/sup 2/ is achieved for an efficiency of 94%.
Abstract: Possible configurations for microfabricated inductors are considered. Inductance can be set by adjusting permeability through control of anisotropy of a permalloy core, or via a patterned quasi-distributed gap. A design methodology based on a simple model is proposed. Analysis of secondary effects is also developed. A design example for a 5 MHz buck power converter application is presented. A power density of 12.8 W/cm/sup 2/ is possible for an efficiency of 94%.
90 citations
TL;DR: The Biot-Savart law is employed to calculate the magnetic field strength, which results in the proximity-effect resistance in single-layer litz-wire square solenoid coils without a magnetic core, and a strand-number coefficient is introduced to reflect the influence of the strand number inside the wire bundle on the proximity -effect resistance.
Abstract: In order to achieve the highest efficiency of wireless power transfer (WPT) systems, the quality factor of the resonant coil should be as high as possible. Due to the skin effect and the proximity effect, the coil resistance increases with the increase in the frequency. The highest quality factor exists for the optimal frequency together with the corresponding frequency-dependent inductor resistance. This paper employs the Biot–Savart law to calculate the magnetic field strength, which results in the proximity-effect resistance in single-layer litz-wire square solenoid coils without a magnetic core. A strand-number coefficient is introduced to reflect the influence of the strand number inside the wire bundle on the proximity-effect resistance. The coefficient is obtained through simple inductor resistance measurements for various numbers of litz-wire strands. The optimal frequency for the highest quality factor is derived based on the resistance evaluation. Several prototype coils were manufactured to verify the resistance analysis. Two $50\,\rm{cm}\times50\, {\rm cm}$ square coils were employed to construct a WPT prototype. The maximum dc–dc efficiency of this WPT was about 75% at 100-cm distance.
90 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