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Journal ArticleDOI

Computationally efficient winding loss calculation with multiple windings, arbitrary waveforms, and two-dimensional or three-dimensional field geometry

01 Jan 2001-IEEE Transactions on Power Electronics (IEEE)-Vol. 16, Iss: 1, pp 142-150
TL;DR: The squared-field-derivative method for calculating eddy-current (proximity effect) losses in round-wire or litz-wire transformer and inductor windings is derived in this paper.
Abstract: The squared-field-derivative method for calculating eddy-current (proximity-effect) losses in round-wire or litz-wire transformer and inductor windings is derived. The method is capable of analyzing losses due to two-dimensional and three-dimensional field effects in multiple windings with arbitrary waveforms in each winding. It uses a simple set of numerical magnetostatic field calculations, which require orders of magnitude less computation time than numerical eddy-current solutions, to derive a frequency-independent matrix describing the transformer or inductor. This is combined with a second, independently calculated matrix, based on derivatives of winding currents, to compute total AC loss. Experiments confirm the accuracy of the method.
Citations
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Proceedings ArticleDOI
15 Jun 2003
TL;DR: In this paper, the Ferreira method and Dowell method were compared to evaluate the accuracy of each method for predicting proximity-effect losses in round-wire windings and found that the Dowell algorithm can have substantial errors, exceeding 60%.
Abstract: The two best-known methods for calculating high-frequency winding loss in round-wire windings-the Dowell method and the Ferreira method-give significantly different results at high frequency We apply 2-D finite-element method (FEM) simulations to evaluate the accuracy of each method for predicting proximity-effect losses We find that both methods can have substantial errors, exceeding 60% The Ferreira method, which is based on the exact Bessel-function solution for the eddy current in an isolated conducting cylinder subjected to a time-varying magnetic field, is found to be most accurate for loosely packed windings, whereas the Dowell method, which approximates winding layers comprising multiple turns of round wire with a rectangular conducting sheet, is most accurate for closely-packed windings To achieve higher accuracy than is possible with either method alone, we introduce a new formula, based on modifying the Dowell method Parameters in the new formula are chosen based on fitting our FEM simulation data By expressing the results in terms of normalized parameters, we construct a model that can be used to determine proximity-effect loss for any round-wire winding with error under 2%

246 citations

Journal ArticleDOI
TL;DR: In this article, the relationship between wire size, normalized cost, and normalized loss is shown to have a general form that applies to a wide range of designs, and a practical design procedure is provided, applied to an example design, it leads to less than half the original loss at lower than the original cost, or, alternatively, under one fifth the original costs with the same loss as the original design.
Abstract: Design of litz-wire windings subject to cost constraints is analyzed. An approximation of normalized cost is combined with analysis of proximity effect losses to find combinations of strand number and diameter that optimally trade off cost and loss. The relationship between wire size, normalized cost, and normalized loss is shown to have a general form that applies to a wide range of designs. A practical design procedure is provided, Applied to an example design, it leads to less than half the original loss at lower than the original cost, or, alternatively, under one fifth the original cost with the same loss as the original design.

233 citations

Journal ArticleDOI
TL;DR: A new single-layer winding array and receiver coil structure with cylindrical ferrite cores for planar contactless battery charging systemsplying with the “Qi” standard, this design enables multiple devices to be placed and charged simultaneously on the wireless charging pad in a free-positioning manner.
Abstract: The planar contactless battery charging system is an emerging technology that can be applied to a wide range of portable consumer electronic products. Beginning with a brief historical background, this paper presents a new single-layer winding array and receiver coil structure with cylindrical ferrite cores for planar contactless battery charging systems. Complying with the “Qi” standard, this design enables multiple devices to be placed and charged simultaneously on the wireless charging pad in a free-positioning manner. The charging flux is totally localized within the covered area between the selected primary winding and the secondary winding inside the load. The electromagnetic characteristics of such winding design are studied in finite-element analysis and confirmed by practical implementation.

226 citations


Cites methods from "Computationally efficient winding l..."

  • ...Here, litz wire is used in the coils, and thus, the method reported in [28] can be used for calculating the ac resistance with the aid of finite-element magnetostatic analysis....

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Journal ArticleDOI
TL;DR: The major advantages and disadvantages in the use of planar magnetics for high-frequency power converters are covered in this paper, and a detailed survey of winding conduction loss, leakage inductance, and winding capacitance for planar magnetic technologies is presented.
Abstract: The momentum toward high efficiency, high frequency, and high power density in power supplies limits wide use of conventional wire-wound magnetic components This paper gives an overview of planar magnetic technologies with respect to the development of modern power electronics The major advantages and disadvantages in the use of planar magnetics for high-frequency power converters are covered, and publications on planar magnetics are reviewed A detailed survey of winding conduction loss, leakage inductance, and winding capacitance for planar magnetics is presented so power electronics engineers and researchers can have a clear understanding of the intrinsic properties of planar magnetics

208 citations


Cites background from "Computationally efficient winding l..."

  • ...multiwinding transformers with 2-D and 3-D field effects and arbitrary waveforms in each winding [36]....

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Journal ArticleDOI
TL;DR: In this article, a three-coil wireless power transfer system is proposed to maximize the magnetic coupling with the receiver coil for efficient power transfer, and the theoretical proof and the conditions for meeting the objective are derived and practically verified in a practical prototype.
Abstract: A new methodology for ensuring that a three-coil wireless power transfer system is more energy efficient than a two-coil counterpart is presented in this paper. The theoretical proof and the conditions for meeting the objective are derived and practically verified in a practical prototype. The key features of the magnetic design are to: 1) shift the current stress from the primary driving circuit to the relay resonator; and 2) generate a large relay current for maximizing magnetic coupling with the receiver coil for efficient power transfer. Consequently, the current rating and cost of the driving circuit can be reduced and the overall quality factor and system energy efficiency are improved. This approach utilizes the combined advantages of the maximum efficiency principle and the use of relay resonator to overcome the energy efficiency problem for applications with extended energy transfer distances.

188 citations

References
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Book
01 Jan 1939

2,503 citations

Journal ArticleDOI
01 Aug 1966
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.

1,246 citations

Journal ArticleDOI
22 Jun 1997
TL;DR: In this paper, the number and diameter of strands to minimize loss in a litz-wire transformer winding is determined, and a power law to model insulation thickness is combined with standard analysis of proximity effect losses to find the optimal stranding.
Abstract: The number and diameter of strands to minimize loss in a litz-wire transformer winding is determined. With fine stranding, the AC resistance factor can be decreased, but DC resistance increases as a result of the space occupied by insulation. A power law to model insulation thickness is combined with standard analysis of proximity-effect losses to find the optimal stranding. Suboptimal choices under other constraints are also determined.

683 citations


"Computationally efficient winding l..." refers background or methods in this paper

  • ...5 and 6 also include loss predictions from simple 1-D analysis [15], [21], as detailed in Appendix II....

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  • ...In the case of litz wire, construction can guarantee current sharing between strands independent of frequency [21]....

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  • ...struction, bundle-level effects can be made negligible [21]....

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  • ...AC resistance factor is modeled by [15], [21]...

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  • ...In the case of litz wire, we have assumed that bundle-level effects are negligible, a valid assumption for well-designed litz constructions [21]....

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Journal ArticleDOI
TL;DR: In this paper, the authors propose an orthogonality between skin effect and proximity effect to calculate the AC resistance of round conductor windings, which gives more accurate answers than the basic one-dimensional method because the exact analytical equations for round conductors can be used.
Abstract: The one well-known one-dimensional method for calculating the AC resistance of multilayer transformer windings contains a built-in orthogonality which has not been reported previously. Orthogonality between skin effect and proximity effect makes a more generalized approach for the analytical solution of AC resistance in windings possible. This includes a method to calculate the AC resistance of round conductor windings which is not only convenient to use, but gives more accurate answers than the basic one-dimensional method because the exact analytical equations for round conductors can be used. >

546 citations


"Computationally efficient winding l..." refers methods in this paper

  • ...If it is not, a similar approach could be used, combining magnetostatic field calculations with Besselfunction analysis of the loss in the winding [6], [17], [18]....

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  • ...For designs in which 1-D field analysis is accurate, and where wire strands are not large compared to a skin-depth, these various methods are approximately equivalent [6], despite...

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  • ...The most rigorous approach uses an exact calculation of losses in a cylindrical conductor with a known current, subjected to a uniform external field, combined with an expression for the field as a function of 1-D position in the winding area [6], [18]....

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Journal ArticleDOI
TL;DR: In this article, the authors present a new formula for the optimum foil or layer thickness, without the need for Fourier coefficients and calculations at harmonic frequencies, which is simple, straightforward and applies to any periodic wave shape.
Abstract: AC losses due to nonsinusoidal current waveforms have been found by calculating the losses at harmonic frequencies when the Fourier coefficients are known. An optimized foil or layer thickness in a winding may be found by applying the Fourier analysis over a range of thickness values. This paper presents a new formula for the optimum foil or layer thickness, without the need for Fourier coefficients and calculations at harmonic frequencies. The new formula requires the RMS value of the current waveform and the RMS value of its derivative. It is simple, straightforward and applies to any periodic waveshape.

316 citations


"Computationally efficient winding l..." refers methods in this paper

  • ...The squared field derivative, or corresponding squared winding current derivatives, have been used by many authors, including [19]–[21], [23]....

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