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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20 Jun 1994
TL;DR: In this article, an analysis of the edge effect in high-frequency transformers is performed by modeling the winding as either allfoil or wire-foil, and the effects of the winding positions in the core and the winding widths on the AC resistance and leakage inductance of the transformer are investigated by using the two-dimensional finite element method.
Abstract: An analysis of the edge effect in high-frequency transformers is performed by modeling the winding as either all-foil or wire-foil. The effects of the winding positions in the core and the winding widths on the AC resistance and leakage inductance of the transformer are investigated by using the two-dimensional finite element method (FEM). An optimal distance between the windings is found, which results in a minimum resistance for each particular frequency. It is demonstrated that the winding has the lowest AC resistance and leakage inductance when the primary and secondary have equal winding width. >
49 citations
TL;DR: The design and detailed operation of a Ćuk derived, common-ground PV microinverter in continuous conduction mode operation is presented and the inverter is shown to be compatible with both linear and nonlinear loads, in stand-alone and grid-connected modes of operation.
Abstract: Photovoltaic (PV) microinverters dispense with the line frequency transformer, however at the cost of system grounding and ground leakage current problems. These have been erstwhile resolved by the topologies derived from buck, boost, buck–boost, Zeta, Watkins–Johnson, and Cuk converters, or combinations of these. The Cuk derived inverters, employing second-order input and output filters, offer the most efficient, lightweight, and economical solution in the class. This paper presents design and detailed operation of a Cuk derived, common-ground PV microinverter in continuous conduction mode operation. The inverter is shown to be compatible with both linear and nonlinear loads, in stand-alone and grid-connected modes of operation. Optimal design rules of passive components are rigorously derived to ensure attenuation of input voltage ripples arising from the twin effects of switching and double-frequency output power oscillation. Additionally, the design rules also incorporate considerations of efficiency maximization and some aspects of easing control complexity. Inverter performance is experimentally validated with a 300 VA, 110 V, and 50/60 Hz laboratory prototype.
48 citations
TL;DR: In this paper, a review of derating of transformers under non-sinusoidal operation is presented, for which all available approaches are classified into four major methods including IEEE recommended, analytical, experimental and finite elements based methods.
Abstract: The increasing application of non-linear loads in power system causes additional losses in transformers resulting in premature damage Manufactures and users of transformers realise the importance of this phenomenon and it is vital to adopt a procedure to prevent it thereby enhancing the reliability of power system To achieve this, the most common method is derating of transformers This paper intends to review derating of transformers under non-sinusoidal operation, for which all available approaches are classified into four major methods including IEEE recommended, analytical, experimental and finite elements based method For each method, the fundamental theory, significant factors related to derating, test techniques as well as advantages and disadvantages are discussed The methods are then evaluated and compared with each other from different points of view Moreover, the overall trend of a more precise derating method is suggested This review clarifies the research areas which require attention in the future to advance the subject
47 citations
TL;DR: In this article, the authors present several approaches to reduce the use of Cu wire in high-frequency transformers and inductors, including careful winding design, trading winding volume for core volume, replacing Cu with Al, and using Cu-clad Al (CCA) windings.
Abstract: Recent Cu price increases motivate careful examination of approaches to minimize Cu use in high-frequency transformers and inductors. Approaches that can reduce Cu use without increasing losses include careful winding design, trading winding volume for core volume, replacing Cu with Al, and using Cu-clad Al (CCA) windings. Al wire is particularly attractive. The cost of Al is lower than it might appear from the cost per unit mass when the much lower density of Al is also considered, and the disadvantage of higher resistivity becomes less important when high-frequency effects are considered.
47 citations
TL;DR: A new and practical measurement method is proposed to characterize the planar transformer copper loss operating in a high-frequency switching mode power supply (SMPS) and good matching between the simulation and measurement results is achieved.
Abstract: In this paper, a new and practical measurement method is proposed to characterize the planar transformer copper loss operating in a high-frequency switching mode power supply (SMPS). The scheme is easy to set up, and it provides an equivalent winding alternating current resistance, which is the result of all the field effects on the transformer windings to achieve more accurate copper loss characterization. A detailed error analysis for the proposed copper loss measurement method is conducted. The analysis results can provide useful guidelines on the SMPS transformer copper loss measurement scheme design. Measurement results on the copper loss of a planar transformer in a high-frequency dc/dc converter are presented. In order to verify the measurement results, a time-domain finite-element analysis transient solver is adopted to analyze the transformer copper loss. Good matching between the simulation and measurement results is achieved.
47 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