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
04 Mar 2018
TL;DR: In this article, the authors derived the resistance matrix for a closed core transformer accounting for the two-dimensional fields present, which can then be used to analytically calculate AC winding loss for arbitrary current waveforms such as those found in Flyback converters.
Abstract: Traditionally, Dow ell's one-dimensional method is used to calculate the AC winding loss factor for transformers with reasonable accuracy in most cases. However, for thin film transformers there can be significant two-dimensional fields which, if ignored will lead to erroneous results. The problem is exacerbated for transformers used in Flyback DC-DC converters which are exposed to arbitrary current waveforms. In this paper we derive the resistance matrix for a closed core transformer accounting for the two-dimensional fields present. The derived resistance matrix can then be used to analytically calculate AC winding loss for arbitrary current waveforms such as those found in Flyback converters.
2 citations
Dissertation•
01 Jan 2018
TL;DR: The focus of this work is in the reduction in volume of ac/dc converters while keeping efficiency constant or improving it, which is challenging to achieve while meeting all the specifications.
Abstract: In this thesis we present a two-stage ac/dc grid-connected converter for computer applications. Also known as off-line power supplies, these converters have to meet various demanding specifications such as a wide input voltage range (typically 0-376 V), large voltage step down (typical output voltages range from 12-48 V), harmonic current limits and galvanic isolation. The focus of this work is in the reduction in volume of ac/dc converters while keeping efficiency constant or improving it, which is challenging to achieve while meeting all the specifications. The thesis breaks down the converter in subsystems and explores architectural and topological trade-offs, modeling, component selection and control methods. The performance of each individual subsystem is experimentally verified. The first stage of the converter is a step-down power factor correction (PFC) converter. This stage interacts with the grid and draws the necessary ac power from the line and rectifies it. Following the PFC is a capacitor bank, which is used to both buffer the ac power from the line and to provide hold-up energy to the output. The capacitor selection process is detailed in the thesis. The second stage of the converter provides isolation and regulation to the output. Two different approaches to the second stage converter are presented: using commercially available, “plug and play” converters and developing a custom converter. The full system is evaluated with both solutions and is compared to other state of the art converters. The final prototype achieves an efficiency of 95.33% at full power (250 W) and 230 Vac input, and a power density of 35 W/in. Thesis Supervisor: David J. Perreault Title: Professor of Electrical Engineering and Computer Science Thesis Supervisor: Khurram K. Afridi Title: Assistant Professor of Electrical, Computer and Energy Engineering University of Colorado Boulder Thesis Reader: Jeffrey H. Lang Title: Professor of Electrical Engineering and Computer Science
2 citations
25 Jun 2010
TL;DR: Improved methods of the hardware interface circuit and micro-controller programming were presented to achieve an agreement between the remote meter reading data and the register displaying to show that the method can be widely applied in centralized multi-users electronic energy meters.
Abstract: The basic error of ADE7755 and its application in the remote meter reading system were introduced. The error between the remote meter reading data and the register displaying was detailed analyzed in centralized multi-users electronic energy meters. The power down test simulated work-site condition showed that frequent power down was the main factor causing the error. New improved methods of the hardware interface circuit and micro-controller programming were presented to achieve an agreement between the remote meter reading data and the register displaying. The application example analysis showed that the method can be widely applied in centralized multi-users electronic energy meters.
2 citations
29 Oct 2015
TL;DR: In this paper, an improved 3-level flying capacitor inverter topology was proposed to reduce the reverse recovery related losses in PV inverters, which benefits from the latest superjunction (SJ) MOSFET devices.
Abstract: This paper investigates an improved 3-level flying capacitor inverter topology allowing a drastic reduction of reverse recovery related losses. It benefits from the latest superjunction (SJ) MOSFET devices. The presented 2kW inverter was designed for Japanese PV market (200Vrms). It allows non unitary power factor operations with peak and European efficiency of 98.0% and 97.6% respectively. Thanks to SJ MOSFET implementation, it outperforms state-of-art configuration using IGBTs and SiC diodes in terms of efficiency.
2 citations
TL;DR: In this study, a specific methodology to analyze inductors and transformers by thermal networks and a simplification based on the Thevenin’s theorem leading to a simple equation are proposed.
Abstract: The volume of magnetic components for space applications, directly related to the launch cost, and their performance are critically influenced by their capability to dissipate the internal electromagnetic power losses. This is the reason why accurate thermal models are required. Furthermore, these models need to be simple and versatile to allow a fast analysis of many different designs. In this study, a specific methodology to analyze inductors and transformers by thermal networks and a simplification based on the Thevenin’s theorem leading to a simple equation are proposed. The specific details to address thermal modelling for space magnetic components are discussed. A generic 50 W Flyback transformer for space applications is analyzed in this study and experimental validation is provided, showing that the proposed method leads to a deviation in the temperature estimation between 1 °C and 5 °C, which is considered quite a good result from the literature review carried out.
2 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