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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09 Oct 2022
TL;DR: In this paper , a hybrid model was proposed that combines a modified Dowell's model with the double-2-D model to calculate the low-frequency leakage inductance of a variable inductance transformer.
Abstract: Skin and proximity effects can cause a significant drop in the effective leakage inductance of a transformer when the operating frequency is increased. Although the magnetic image method-based double-2-D model can calculate the low-frequency leakage inductance with sufficient accuracy, it is inherently a frequency-independent model. While Dowell's 1-D model uses frequency-dependent relations to account for both skin and proximity effects, its accuracy is severely affected by the assumed winding geometry. In this paper, a hybrid model is proposed that uses superposition to combine a modified Dowell's model with the double-2-D model. The proposed model is investigated on a variable inductance transformer (VIT)-a partially-filled transformer whose leakage inductance can be varied by moving one of the windings mechanically. The frequency-dependent leakage inductances of the VIT evaluated using the hybrid model are in excellent agreement with the corresponding finite element method (FEM) simulated and experimentally measured values, thereby validating the proposed hybrid model.
1 citations
01 Jan 2020
TL;DR: In this paper, the authors explore the impedance for a standard round conductor winding silicon steel, by also considering parasitic components, which increase with the operating frequency due to skin effect and proximity effect.
Abstract: Impedance behavior of laminated core inductor is studied at different frequency. Winding parasitic parameters which increase with the operating frequency due to skin effect and proximity effect are considered. These parameters can be modelled with dc resistance, winding dielectric capacitance, and magnetic core loss. These parameters may be calculated from standard data sheet parameters of the copper conductor and laminated sheets. The windings of electrical machines such as transformers, rotating machines, have been studied by various researchers to determine its state of health during operation. Different methods have been employed such as Sweep Frequency Response Analysis (SFRA), Motor Current Signature Analysis (MCSA) etc., to determine its condition at different frequencies. SFRA can offer detailed insight into condition of the winding insulation by analyzing the impedance of the winding over its bandwidth, however it is limited to offline implementation due to the invasiveness of the technique. The purpose of this paper is to lay the foundation for further development of the technique towards online implementation using an inverter, by firstly considering the case of an inductor. This will allow for a better understanding of the bandwidth and impedance model (including parasitic parameters, associated with the device) before translating the model and implementation to a rotating electric machine. Therefore, this paper sets out to explore the impedance for a standard round conductor winding silicon steel, by also considering parasitic components.
1 citations
TL;DR: An optimization process applied to the sizing of high-power silicon carbide inverters, the design of an aeronautical converter, with the goal of minimizing the global mass of the converter is presented.
Abstract: This article presents an optimization process applied to the sizing of high-power silicon carbide inverters. The case study is the design of an aeronautical converter. A gradient-based optimization method is chosen for its ability to explore a wide solution space with a large amount of constraints, which is the case during the predesign phase. Many topologies are selected and the associated models are developed. Among all these models, active and passive component design and spectral analysis of voltages and currents are presented. The optimization results, with the goal of minimizing the global mass of the converter, are provided. The different topologies are compared to find the best one for the selected case study. The relevance of the optimization result is evaluated with the study of the optimality of the solution. Finally, the experimental results are compared with the optimization ones, which validates the good accuracy of analytical models.
1 citations
TL;DR: In this article , an approach combining semi-empirical equations and the method of images is proposed for round conductor layer windings with un-gapped core, which can convert the constant field strength from the magneto-motive force (MMF) across the core window into a frequency-dependent uniform background magnetic field strength.
Abstract: In this article, an approach combining semi-empirical equations and the method of images is proposed for round conductor layer windings with un-gapped core. The new equation for proximity effect can convert the constant field strength from the magneto-motive force (MMF) across the core window into a frequency-dependent uniform background magnetic field strength, which can take partly the interaction between conductors into account. Geometric factors are introduced by fitting the finite element method (FEM) results to improve the accuracy. The method of images is used to calculate the field strength in order to counteract the impact of the 2-D edge effect. The new method is compared with the 2-D FEM, analytical methods, and is also validated by measurements with EE core transformers. The proposed method shows good accuracy (< 10% error) compared with 2-D FEM for both high and low porosity factor windings. Therefore, it can handle more winding configurations than other 1-D analytical methods.
1 citations
TL;DR: In this paper , a semi-analytical method for calculating ac copper loss of stator form-wound windings is presented, which is capable of simulating circulating current effect between parallel strands with torsion transposition in the end region.
Abstract: This article presents a semi-analytical method for calculating ac copper loss of stator form-wound windings. The proposed method is capable of simulating circulating current effect between parallel strands with torsion transposition in the end region, as well as skin and proximity effect inside the strand. The solution model of circulating current is first derived, and the key parameter, namely the slot leakage inductance matrix, is also obtained by analytical method. Then, with the calculated current of each strand, the current density distribution inside the strand is induced. Finally, the calculated copper loss of a permanent magnet generator is compared with the finite element result, which validates the accuracy of the proposed model.
1 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