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
More filters
23 May 2010
TL;DR: In this paper, a new compact high power capacitor charger with modular topology for rep. rated high power Microwave generators and other Pulsed power applications is reported. And the charger is capable of using a number of synchronized H-Bridge inverters feeding into a common transformer.
Abstract: We are reporting on a new compact high power capacitor charger with modular topology for rep. rated High Power Microwave generators and other Pulsed Power Applications. The charger is capable of using a number of synchronized H-Bridge inverters feeding into a common transformer. The common transformer uses litz wire windings [1] and a nano-crystalline core to reduce losses and AC impedance. The H-Bridge inverter modules are individually controlled using peak current mode control which assures proper current sharing and protects the H-Bridge modules from overload while achieving the maximum current handling capacity. To assure stability of the current loops for peak current mode control, slope compensation [2] is used. Major advancements over previous designs [4] are the ability to use multiple H-Bridge inverters with proper synchronization, improved efficiency through advanced transformer design and improved current mode control.
5 citations
22 Jul 2015
TL;DR: This paper discusses the identification of Ferrite Core (FC) power inductors parameters in the real operating conditions relevant to Switch-Mode Power Supplies starting from experimental measurements using a novel method based on Evolutionary Algorithms and the analysis of inductors non-linear behavior.
Abstract: This paper discusses the identification of Ferrite Core (FC) power inductors parameters in the real operating conditions relevant to Switch-Mode Power Supplies starting from experimental measurements. A novel method for parameters identification is proposed, based on Evolutionary Algorithms (EAs) and on the analysis of inductors non-linear behavior. Two EAs, the Genetic Algorithm and the Differential Evolution, are investigated and compared. The results of the proposed method are experimentally validated by means of a buck converter evaluation board.
5 citations
01 Apr 2017
TL;DR: In this paper, a simplified method to compute the frequency-dependent coupling resistances inside high-current instrument transformers (HCTs) is presented, where the solution of the 1-D Helmholtz equation is used to estimate the losses inside the winding layers dependent on the frequency of the exciting current.
Abstract: This paper presents a simplified method to compute the frequency-dependent coupling resistances inside high-current instrument transformers (HCTs). The solution of the 1-D Helmholtz equation is used to estimate the losses inside the winding layers dependent on the frequency of the exciting current. The resistive couplings inside the HCT are determined by computing the total winding losses inside the HCT and differentiating the loss equation. An equivalent proximity depth for HCTs is defined by assessing the losses component of skin and proximity effect. This quantity, which only depends on the skin depth and the number of winding layers, enables to estimate the limit beyond which the proximity effect causes high losses inside the winding. A computation example shows the results of the model.
5 citations
5 citations
TL;DR: A novel class of neural-network-inspired statistical data-driven models, especially derived for the purpose of design optimization of medium-frequency transformers, allow for an efficient yet sufficiently accurate and numerically stable estimation of the complex effects, with otherwise impractically high computational cost and/or convergence issues.
Abstract: This article proposes a novel class of neural-network-inspired statistical data-driven models, especially derived for the purpose of design optimization of medium-frequency transformers. These models allow for an efficient [three to four orders of magnitude faster compared to a finite-element method (FEM)] yet sufficiently accurate (within 5–10% error relative to the FEM) and numerically stable estimation of the complex effects, with otherwise impractically high computational cost and/or convergence issues. The application of the proposed modeling framework is described in detail on two characteristic examples of the complex electromagnetic phenomena occurring within the medium-frequency transformers. The performance of the derived models is verified both with detailed FEM simulations and experimental results.
5 citations
References
More filters
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