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 thermal modeling method based on a lumped elements thermal network model is proposed for planar magnetic components made of double planar E shaped cores (EE) and PLT combined with plate one (E/PLT).
Abstract: Thermal performance of power converters is a key issue for the power integration. Temperatures inside the active and passive devices can be determined using thermal models. Modelling the temperature distribution of high-frequency magnetic components is quite complex due to the diversity of their geometries and used materials. This study presents a thermal modelling method based on lumped elements thermal network model, applied to planar magnetic components made of double planar E shaped cores (EE) and planar E core combined with plate one (E/PLT). The 3D model is automatically generated from the component's geometry. The computation enables to obtain 3D temperature distribution inside windings and core of planar transformers or inductors, in steady state or in transient case. This study details the proposed modelling method as well as the automated tool including the problem definition and the solving process. The obtained temperature distributions are compared with finite-element simulation results and measurements on different planar transformers.
4 citations
TL;DR: In this paper, the authors presented an analytical approach to the determination of power losses in a high-frequency transformer operating in the dual active bridge (DAB), which couples two DC circuits that significantly differ in voltages (280 V and 51 V ± 20%).
Abstract: *e-mail: piotr.grzejszczak@ee.pw.edu.pl Abstract. The paper presents an analytical approach to the determination of power losses in a high-frequency transformer operating in the dual active bridge (DAB). This transformer, having two single-phase transistor bridge inverters, couples two DC circuits that significantly differ in voltages (280 V and 51 V ±20%). Power losses in the core and windings of the planar transformer 5600 VA /100 kHz were calculated taking into account changes in the value and direction of the energy flow between the coupled DC circuits. These circuits represent storage or renewable energy sources and intermediate circuits of the converters used in distributed generation systems. Calculations were performed using the Steinmetz’s and Dowell’s equations. The analytical results have been verified experimentally.
4 citations
05 Oct 1997
TL;DR: The aim of this paper is to investigate the consequences of first, the multi-layer structure of each winding and second, the observed behavior of Mn-Zn magnetic cores.
Abstract: A previous paper established the link between the electromagnetic power propagation and electrical equivalent circuit of the two-winding transformer. This study pointed out that an electrical equivalent circuit can be associated with each layer (conductor, insulator, ferrite) gone through, and that linking all these elementary circuits together leads to the equivalent circuit of the entire component. Propagation is assumed to be 1D and each winding is supposed by a single layer of turns. The aim of this paper is to follow the same approach to investigate the consequences of first, the multi-layer structure of each winding and second, the observed behavior of Mn-Zn magnetic cores. Theoretical results are compared to experimental data.
4 citations
TL;DR: In this paper, a simplified 2-D winding loss analytical model for flyback transformers considering the effects of low-order harmonics is proposed, which has an acceptable accuracy and a simple form that is similar to the conventional 1-D model.
Abstract: The winding loss analysis of a flyback transformer is difficult and ambiguous because the primary side current and the secondary side current differs both in shape and phase, especially for DCM (Discontinuous Conduction Mode) operation. Meanwhile, the fringing field caused by the air gaps further makes the traditional 1-D loss analysis model not directly applicable. The paper gives a thorough investigation into the phase shift of winding currents, which indicates that the phase shift of the high order harmonics is still close to 180o out-of-phase. Based on the analysis, a simplified 2-D winding loss analytical model for flyback transformers considering the effects of low order harmonics is proposed. By neglecting the y components of the fringing field, the proposed model has an acceptable accuracy and a simple form that is similar to the conventional 1-D model. The power loss calculated with the proposed analysis model is verified by FEA (Finite Element Analysis) simulations and experimental results.
4 citations
Dissertation•
28 Jul 2017
TL;DR: In this paper, three methods for field attenuation are discussed for the synergetic attenuation of stray magnetic field which is optimized simultaneously with the efficiency, and the optimization is realized with Pareto front.
Abstract: Significant stray magnetic field exists around the coils when charging the electric vehicles (EVs) with inductive power transfer (IPT), owning to the large air gap between the transmitter and receiver. The methods for field attenuation usually introduce extra losses and reduce the efficiency. This study focuses on the synergetic attenuation of stray magnetic field which is optimized simultaneously with the efficiency. The optimization is realized with Pareto front. In this dissertation, three methods are discussed for the field attenuation. The first method is to tune the physical parameters of the winding, such as the inner radii, outer radii, distribution of the turns, and types of the litz wires. The second method is to add metal shields around the IPT coils, in which litz wires are used as shields to reduce the shielding losses. The third method is to control the phases of winding currents, which avoids increasing the size and weight of the IPT coils. To attenuate the stray magnetic field by tuning the physical parameters, the conventional method is to sweep all the physical parameters in finite-element simulation. This takes thousands of simulations to derive the Pareto front, and it’s especially timeconsuming for three-dimensional simulations. This dissertation demonstrates a faster method to derive the Pareto front. The windings are replaced by the lumped loops. As long as the number of turns for each loop is known, the efficiency and magnetic field are calculated directly from the permeance matrices and current-to-field matrices. The sweep of physical parameters in finite-element simulation is replaced by the sweep of the turns numbers for the lumped loops in calculation. Only tens of simulations are required in the entire procedure, which are used to derive the matrices. An exemplary set of coils was built and tested. The efficiency from the matrix calculation is the same as the experimental measurement. The difference for stray magnetic field is less than 12.5%. Metal shields attenuate the stray magnetic field effectively, but generates significant losses owning to the uneven distribution of shield currents. This dissertation uses litz wires to replace the conventional plate shield or ring shield. Skin effect is eliminated so the shield currents are uniformly distributed and the losses are reduced. The litz shields are categorized to two types: shorted litz shield and driven litz shield. Circuit models are derived to analyze their behaviors. The concept of lumped-loop model is applied to derive the Pareto front of efficiency versus stray magnetic field for the coils with litz shield. In an exemplary IPT system, coils without metal shield and with metal shields are optimized for the same efficiency. Both the simulation and experimental measurement verify that the shorted litz shield has the best performance. The stray magnetic field is attenuated by 65% compared to the coils without shield. This dissertation also introduces the method to attenuate the stray magnetic field by controlling the phases of winding currents. The magnetic field around the coils is decomposed to the component in the axial direction and the component in the radial direction. The axial component decreases with smaller phase difference between windings’ currents, while the radial component exhibits the opposite property. Because the axial component is dominant around the IPT coils, decreasing the phase difference is preferred. The dual-side-controlled converter is applied for the circuit realization. Bridges with active switches are used for both the inverter on the transmitter side and the rectifier on the receiver side. The effectiveness of this method was verified both in simulation and experiment. Compared to the conventional series-series IPT with 90° phase difference between winding currents, stray magnetic field was attenuated by up to 30% and 40% when the phase differences of winding currents are 50° and 40°, respectively. Furthermore, an analytical method is investigated to calculate the proximity-effect resistance of the planar coils with ferrite plate. The objective of this method is to work together with the fast optimization which uses the lumped-loop model. The existence of the ferrite plate complicates the calculation of the magnetic field across each turn which is critical to derive the proximity-effect resistance. In this dissertation, the ferrite plate is replaced by the mirrored turns according to the method of image. The magnetic fields are then obtained from Ampere’s Law and Biot-Savart Law. Up to 200 kHz, the difference of the proximity-effect resistance is less than 15% between calculation and measurement. Synergetic Attenuation of Stray Magnetic Field in Inductive Power Transfer Ming Lu General Audience Abstract Inductive power transfer for the battery charging of electric vehicles uses loosely coupled coils to replace the cables and plugs. The power is transferred from transmitter to receiver across tens of centimeters. Significant stray magnetic field exists around the coils owning to the large gap, which should be attenuated for the safety consideration of human beings. Three methods are discussed for the field attenuation. The first method is to tune the physical parameters of the winding, such as the inner radii, outer radii, distribution of the turns, and types of the litz wires. The second method is to add metal shields around the IPT coils, in which litz wires are used as shields to reduce the shielding losses. The third method is to control the phases of winding currents, which avoids the increase of the size and weight of the IPT coils. However, the field attenuation usually comes with reduced efficiency of the system. The work in this dissertation is focused on the synergetic attenuation of stray magnetic field in inductive power transfer for electric vehicles. The optimization is realized with Pareto front. The coils are optimized for low stray magnetic field and high efficiency simultaneously.
4 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