Improved analytical modeling of conductive losses in magnetic components
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. >
Citations
More filters
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
Cites background or methods from "Improved analytical modeling of con..."
...If there are significant harmonics for which the skin depth is small compared to wire diameter, then the analysis in [27] can facilitate 1-D analysis of nonsinusoidal waveforms, or for more accuracy Bessel-function analysis [17] with a Fourier decomposition of the waveform can be used....
[...]
...are small compared to the skin depth [17]....
[...]
...Other methods of calculating loss in litz wire also assume equal current in all strands [17], [19], [22]....
[...]
...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 one-dimensional (1-D) position in the winding area [17]....
[...]
..., [17]) is important when...
[...]
15 Jun 2003
TL;DR: In this article, the design considerations of the output filter for the grid-interconnected inverter were comprehensively discussed and different passive damping filter solutions were compared and the optimized design guidelines were also proposed.
Abstract: Traditionally, LC filter is used for an inverter power supply. A grid-interconnected inverter, however, has some unique requirements that an LC filter may not be sufficient. This paper comprehensively discusses the design considerations of the output filter for the grid-interconnected inverter. Different passive damping filter solutions are compared and the optimized design guidelines are also proposed. Simulation results are provided to validate the design.
360 citations
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.
344 citations
Cites methods from "Improved analytical modeling of con..."
...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]....
[...]
...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...
[...]
...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]....
[...]
TL;DR: The LCL filter design procedure from the point of view of power loss and efficiency is analyzed, and LCL parameter values which give the highest efficiency while simultaneously meeting the stringent standard requirements are identified.
Abstract: Higher order LCL filters are essential in meeting the interconnection standard requirement for grid-connected voltage source converters. LCL filters offer better harmonic attenuation and better efficiency at a smaller size when compared to the traditional L filters. The focus of this paper is to analyze the LCL filter design procedure from the point of view of power loss and efficiency. The IEEE 1547-2008 specifications for high-frequency current ripple are used as a major constraint early in the design to ensure that all subsequent optimizations are still compliant with the standards. Power loss in each individual filter component is calculated on a per-phase basis. The total inductance per unit of the LCL filter is varied, and LCL parameter values which give the highest efficiency while simultaneously meeting the stringent standard requirements are identified. The power loss and harmonic output spectrum of the grid-connected LCL filter is experimentally verified, and measurements confirm the predicted trends.
334 citations
Cites methods from "Improved analytical modeling of con..."
...The analytical equation for the ac resistance of an inductor with round wire was specified in [13] and modified in [14] to improve accuracy....
[...]
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
Cites background from "Improved analytical modeling of con..."
...The orthogonality of skin and proximity effects in wire windings is described by Ferreira [13]....
[...]
...1, a detailed treatment of wire conductors is given by Ferreira [13] and Jongsma [14]....
[...]
...[17] J. A. Ferreira,Electromagnetic Modeling of Power Electronic Converters....
[...]
...[13] J. A. Ferreira, “Improved analytical modeling of conductive losses in magnetic components,”IEEE Trans....
[...]
References
More filters
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
TL;DR: In this article, a graphical and numerical method of calculating and minimizing losses in windings, that generalizes previous findings, has been introduced using electromagnetic theory and MMF diagrams in both space and time.
Abstract: A graphical and numerical method of calculating and minimizing losses in windings, that generalizes previous findings, has been introduced Using electromagnetic theory and MMF diagrams in both space and time a method is proposed that provides insight into the mechanism of skin and proximity effect losses and that also yields quantitative results Using this method, several winding geometries for various topologies are covered The analysis and optimization process is experimentally verified using an interleaved flyback transformer The mathematical treatment justifying the use of the field method and which is essential in arriving at any numerical result is presented are more general equations for the calculation of copper losses are derived The relation between the fields in the transformer and copper losses is emphasized Also, the tools necessary to derive optimization diagrams are provided >
233 citations
TL;DR: In this paper, the effect of curvature on the power consumption of a series-connected multiple-layer coil has been investigated with respect to power losses with the windings. But the authors did not consider the effects of the curvature of the coils.
Abstract: The classical one dimensional magnetic field and eddy current distribution ("proximity effect") within a series connected multiple layer coil is reexamined with regard to power losses withinthe windings. When the lengthand number of layers ina coilare fixed, the power dissipation within each layer can be minimized by choosing a specific radial thickness for each layer. Above or below this thickness, the losses within the winding increase. The conductor thickness which results in minimum dissipation depends on the relative position of the layer. When compared to a design having a constant thickness for each layer (chosen for minimum total dissipation), it is found that substantial savings in power consumption can be realized by employing a variable thickness of conductor. The one dimensional solution in cylindrical coordinates for the eddy current and skin effect in amultiple layer series connected coil is alsopresented. By solving the problem n cylindrical coordinates, the effect of curvature on the power consumption within each layer is apparent. This analysis should have application to the design of power transformers, armature windings, and inductors for power transmission lines.
144 citations
13 Mar 1989
TL;DR: Several papers pertaining to the design and modeling of high-frequency transformer windings are reviewed in this paper, stressing their significant contributions and their relationship to the others, and the understandability and applicability are evaluated.
Abstract: Several papers pertaining to the design and modeling of high-frequency transformer windings are reviewed. Each paper is summarized, stressing its significant contributions and its relationship to the others. The emphases and relative merits of each are discussed, and the understandability and applicability are evaluated. >
137 citations