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.
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01 Sep 2020
TL;DR: In this paper, the authors present a methodology to evaluate and analyze the volumetric power density of planar magnetics used in power electronics converters, considering optimal configurations for the planar transformers' design and for its cooling heatsink.
Abstract: This paper presents a methodology to evaluate and analyze the volumetric power density of planar magnetics used in power electronics converters. The power density is computed for various EE and E/PLT cores considering optimal configurations for the planar transformers' design and for its cooling heatsink. The analysis is performed for three cooling configurations: natural convection without heatsink, single sided cooled component with one heatsink, and double sided cooled with two heatsinks. This study can be very useful for designers to evaluate their design specifications and to adapt their technological choices to achieve the desired planar magnetics' characteristics.
5 citations
TL;DR: In this paper, the authors showed that the magnetic flux in the space between two parallel conductors approaches zero when parallel currents are frequency independent and proved theoretically and demonstrated experimentally that the current distribution is constant from medium frequency (MF) to high frequency (HF).
Abstract: The momentum to achieve high efficiency, high frequency, and high power density in power supplies limits the use of conventional wire-wound transformers, but widely employs planar transformers. Planar transformers intrinsically benefit from low profile, predictable parasitic components, ease of manufacture, and excellent repeatability of construction, which are generally applied to high frequency and high current applications, such as data centers and telecoms. Reducing the current density through parallel connections is becoming common practice in planar transformers. However, the current on every parallel conductor is usually unbalanced and hard to be predicted. Start from the motivation to predict parallel current distribution, a phenomenon is discovered in this article that the parallel current distribution is constant from medium frequency (MF) and follows the same pattern in higher frequency range. Besides, this article points out that the insulation thickness also affects the current distribution. Furthermore, the phenomenon that the magnetic flux in the space between two parallel conductors approaches zero when parallel currents are frequency independent is proved theoretically and demonstrated experimentally. Together with Ampere's circuital law, which links the current to the magnetic field, the current distribution can be derived. No complex mathematical calculation or simulation tool is required. Any applications using planar transformers with parallel conductors at MF or higher frequency can adopt this method to predict the parallel current distribution for design optimization.
5 citations
15 Mar 2020
TL;DR: In this paper, the authors evaluated the performance of a 10kV SiC MOSFET based direct medium voltage (MV) connected Extreme Fast Charger (XFC) for electric vehicle (EV) charging applications.
Abstract: This paper evaluates the performance of a 10kV SiC MOSFET based direct Medium Voltage (MV) connected Extreme Fast Charger (XFC) for Electric Vehicle (EV) charging applications Two-stage converter topology is considered, where the Active Front End (AFE) is directly connected to the 416kV MV grid The MVDC output of the AFE is processed by the isolated DC-DC converter to achieve the output voltage that is compatible with the EV battery Thanks to the reconfiguration capability, the proposed XFC can charge both 400V and 800V EVs without any significant performance degradation The data collected through experimental characterization of the 10kV SiC MOSFETs is used for simulating the complete converter of MV-XFC and performing loss analysis through MV SiC modeling in PLECs software Analytical transformer losses and multiobjective design optimization are obtained using MATLAB Based on the outcome of the multiobjective design optimization, the converter design parameters are selected and the trade-off between the loss and volume of the proposed design has been evaluated
5 citations
16 Mar 2014
TL;DR: In this paper, an analytical modeling of conductor physical behavior was developed to match optimization requirements, and used to compare various components with different cores - coils geometries and wire technologies.
Abstract: An optimize design process of inductors and transformers used in switching power converters is presented in this paper An analytical modeling of conductor physical behavior was developed to match optimization requirements, and used to compare various components with different cores - coils geometries and wire technologies Rigorous analytical modeling was applied to achieve minimization of the losses, using homogenization of the stack of wires in equivalent conductive layers of the coils, first introduced by Dowell and improved here The resolution has been carried out for many different shapes of conductors All the results are compared to FEM simulations ones and both are analyzed to compare in a quantitative way proximity and skin-depth effects Then, taking into account the harmonic content of current waveforms, conductor's losses are minimized It is highlighted that losses could largely be reduced by improvements of coil structure and the choice of conductor's shapes The benefit of using an optimized design procedure to select best industrial solution has been proven
5 citations
18 May 2014
TL;DR: In this paper, a closed form approximate expression for power loss for a particular range of diameters of round wire was presented, which does not require a large series summation and is shown to have reasonable accuracy in comparison to the fourier series method.
Abstract: One of the limiting factor in the course of reducing the size of high frequency transformer is the temperature rise. The knowledge of transformer power loss is important to make an estimate of the temperature rise. The transformer winding loss due to a duty-cycle regulated square current waveform can be estimated by summing the copper loss due to each harmonic using Dowell's formula. The paper shows that a large number of harmonics have to be considered for the loss computation. It is shown that for solid-round wire conductors the losses decrease with increasing diameter and there is no optimal diameter for which the losses are minimum. This paper presents a closed form approximate expression for power loss for a particular range of diameters of round wire that does not require a large series summation. Results from this closed form expression are shown to have reasonable accuracy in comparison to the fourier series method and also validated using 2-D finite element method.
5 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