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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01 Feb 2019
TL;DR: An optimization method is described, based on a deterministic strategy, for the design of the filtering inductor of a 3-phase inverter, focusing on the weight minimization and considering a volumetric loss density limitation.
Abstract: This paper introduces an optimization method for the design of the filtering inductor of a 3-phase inverter. The inductor model takes into account saturation, copper and iron losses. The optimization method is described, based on a deterministic strategy. Finally, the optimal design of the inductor is given, focusing on the weight minimization and considering a volumetric loss density limitation.
6 citations
15 Mar 2020
TL;DR: This work demonstrates that the previously-proposed inductor structure with the listed design features can cover a wide range of inductance and power handling requirements with only a few sets of manufactured core pieces, and has potential for commercial adoption to facilitate the design of low-loss HF inductors.
Abstract: Miniaturization and improved performance of power electronics today are limited by magnetic components, which are difficult to scale to small size and high frequencies Inductor structures using field shaping, quasi-distributed gaps, and modular construction have recently been shown to achieve low loss at HF Nevertheless, for widespread adoption, it must be shown that such structures can continue to achieve low loss across applications and can also be produced economically This work demonstrates that the previously-proposed inductor structure with the listed design features can cover a wide range of inductance and power handling requirements with only a few sets of manufactured core pieces In particular, while conventional core sets are usually scaled by roughly 2x in volume, core set components for the proposed structure can be scaled by 4x in volume and still achieve high performance across a large, continuous range of inductor requirements The proposed inductor structure and design techniques thus have potential for commercial adoption to facilitate the design of low-loss HF inductors
6 citations
01 Sep 1993
TL;DR: In this paper, the fundamental equations characterising the full-bridge zero-voltage-switched DC-DC convertor are utilized in a nonlinear design-optimization routine, subject to realistic constraints along with an objective function of minimal total and/or maximum efficiency.
Abstract: The fundamental equations characterising the full-bridge zero-voltage-switched DC-DC convertor are utilised in a nonlinear design-optimisation routine. The design is subject to realistic constraints along with an objective function of minimal total and/or maximum efficiency. The routine is used to study the effects of switching frequency, leakage inductance and load range for zero-voltage switching on the efficiency and size. Maximum efficiency is shown to occur when zero-voltage switching is maintained in the immediate vicinity of full-load operation. Experimental measurements confirm computed predictions.
6 citations
Dissertation•
18 Sep 2014
TL;DR: In this article, the authors developed a high-efficiency, low-cost micro-converter in an effort to increase the output power capability and decrease the cost of modular power conditioning systems.
Abstract: The demand for increased renewable energy production has led to increased photovoltaic (PV) installations worldwide. As this demand continues to grow, it is important that the costs of PV installations decrease while the power output capability increases. One of the components in PV installations that has lots of room for improvement is the power conditioning system. The power conditioning system is responsible for converting the power output of PV modules into power useable by the utility grid while insuring the PV array is outputting the maximum available power. Modular power conditioning systems, where each PV module has its own power converter, have been proven to yield higher output power due to their superior maximum power point tracking capabilities. However, this comes with the disadvantages of higher costs and lower power conversion efficiencies due to the increased number of power electronics converters. The primary objective of this dissertation is to develop a high-efficiency, low cost microconverter in an effort to increase the output power capability and decrease the cost of modular power conditioning systems. First, existing isolated dc-dc converter topologies are explored and a new topology is proposed based on the highly-efficient series resonant converter operating near the series resonant frequency. Two different hybrid modes of operation are introduced in order to add wide input-voltage regulation capability to the series resonant converter while iii achieving high efficiency through low circulating currents, zero-current switching (ZCS) of the output diodes, zero-voltage switching (ZVS) and/or ZCS of the primary side active switches, and direct power transfer from the source to the load for the majority of the switching cycle. Each operating mode is analyzed in detail using state-plane trajectory plots. A systematic design approach that is unique to the newly proposed converter is presented along with a detailed loss analysis and loss model. A 300-W microconverter prototype is designed to experimentally validate the analysis and loss model. The converter featured a 97.7% weighted California Energy Commission (CEC) efficiency with a nominal input voltage of 30 V. This is higher than any other reported CEC efficiency for PV microconverters in literature to date. Each operating mode of the proposed converter can be controlled using simple fixed-frequency pulse-width modulation (PWM) based techniques, which makes implementation of control straightforward. Simplified models of each operating mode are derived as well as control-to-input voltage transfer functions. A smooth transition method is then introduced using a two-carrier PWM modulator, which allows the converter to transition between operating modes quickly and smoothly. The performance of the voltage controllers and transition method were verified experimentally. To ensure the proposed converter is compatible with different types of modular power conditioning system architectures, system-level interaction issues associated with different modular applications are explored. The first issue is soft start, which is necessary when the converter is beginning operation with a large capacitive load. A novel soft start method is introduced that allows the converter to start up safely and quickly, even with a short-circuited output. Maximum power point tracking and double line frequency ripple
6 citations
TL;DR: In this paper, a modified pot core was proposed for low-loss inductance and power handling requirements using only a few sets of manufactured core pieces, which can be scaled by 4× in volume, compared to roughly 2× for conventional core families.
Abstract: Miniaturization and efficiency of power electronics are limited by magnetic components, which are difficult to scale to small size and high frequency (HF). Inductor structures using field shaping, quasi-distributed gaps, and modular construction can achieve low loss at HF (3–30 MHz) without litz wire. For widespread adoption though, these structures must be shown to remain effective across a wide design range and be economical to manufacture. This article investigates the design flexibility of one such previously proposed inductor structure with a modified pot core and demonstrates that this structure can provide excellent performance for a wide range of inductance and power handling requirements using only a few sets of manufactured core pieces. The core pieces used in the modified pot core structure can be scaled by 4× in volume, compared to roughly 2× for conventional core families, and still achieve high performance over a wide design space. Moreover, this approach can achieve about half the loss of conventional designs at HF and, unlike conventional core sets, can provide a range of low-loss form factors with a single family of components. The proposed inductor structure and design approaches, thus, offer new opportunities in the practical production of low-loss HF inductors.
6 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