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Journal ArticleDOI

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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Journal ArticleDOI
TL;DR: In this article, an analytical expression for the optimum conductor size of rectangular litz-wire conducting harmonic currents, which ensures best use of the available copper is proposed, and an insulation design scheme considering the influence of short-term power frequency sinusoidal wave and long-term square wave voltage excitations is put forward.
Abstract: A comprehensive design methodology is required to maximize the power capacity, the efficiency, and the power density of medium-frequency transformer (MFT), while complying with material, insulation, leakage inductance, and temperature limits. Different from the previous work, an analytical expression for the optimum conductor size of rectangular litz-wire conducting harmonic currents, which ensures best use of the available copper is proposed. A method to tune the leakage inductance with different winding configurations is presented. An insulation design scheme considering the influence of short-term power frequency sinusoidal wave and long-term square wave voltage excitations is put forward. Method to acquire the optimal dimension of fin array heat exchanger under forced air-cooling condition is presented. On this basis, the design methodology is established using the multiobjective nondominated sorting genetic algorithm II. A 1 kV, 200 kVA, 10 kHz nanocrystalline core MFT is designed and prototyped for a 10 kV, 2.5 MW solid-state transformer. The optimal design achieves an efficiency of 99.45%, a power density of 8 MW/m3, and a forced air-cooling temperature of 62 °C.

32 citations

Journal ArticleDOI
TL;DR: In this article, the design and development of a transformer isolated high-power dc-dc converter is presented, where an energy recovery passive snubber circuit and the selection of pulsewidth modulation control methods are first introduced to reduce the voltage spike and power loss across switching devices.
Abstract: This paper presents the design and development of a transformer isolated high-power dc-dc converter. There are several design issues and challenges. In this paper, we focus on three major issues in high-power dc-dc converters. 1) An energy recovery passive snubber circuit and the selection of pulsewidth modulation control methods are first introduced to reduce the voltage spike and power loss across switching devices. 2) Interleaved winding method is then employed to reduce proximity effect in the transformer winding. 3) The voltage oscillation problem in the secondary rectifier diode is addressed, and solutions are provided.

32 citations

Journal ArticleDOI
19 Aug 2019
TL;DR: The proposed method aims at creating computationally efficient 3-D multiphysics models of electrical machines with liquid cooled jacket based on the assumption of a fully developed flow in the cooling jacket which allows to scale the computational fluid dynamics (CFD) simulation to 1-D.
Abstract: Modeling of electrical machines is a multiphysics problem. Depending on the phenomena of interest and the computational time constraint, this can be done at different levels of detail. In this article, the main approaches to model the thermal behavior of electrical machines with a liquid cooled casing around the stator (often referred to as cooling jacket) are analyzed and a novel approach is presented. The proposed method aims at creating computationally efficient 3-D multiphysics models of electrical machines with liquid cooled jacket. This model is based on the assumption of a fully developed flow in the cooling jacket which allows to scale the computational fluid dynamics (CFD) simulation to 1-D. The slot with a two layer concentrated winding and potting material is modeled using a composite material comprising of both the conductors and slot filler. Similarly, a unified material is used to model the end-windings. Experimental results on a traction machine for vehicle applications are presented showing good agreement with the simulations. Also, a comparison with a 3-D CFD is presented to verify the pressure drop in the pipe bend. Finally, the model is used to simulate a dynamic load cycle, which would be computationally extremely demanding with combined 3-D CFD and thermal FEA of the machine and its cooling.

32 citations

Journal ArticleDOI
23 Apr 2018
TL;DR: In this paper, an improved model is proposed for calculating the eddy current distribution in litz-wire windings due to the skin and proximity effects, which can have much more accurate prediction of eddy currents in the cross-section of a round litzwire conductor, and can be used for electromagnetic design of high frequency devices.
Abstract: The winding power loss of a high frequency transformer is strongly influenced by the high frequency eddy current skin and proximity effects. The litz-wire can reduce effectively the eddy current effects. The precise loss calculation method of litz-wire remains however a difficulty. At present, the Dowell model [1] and Ferreira model [2], [3] are two commonly used methods to calculate the winding loss. The Dowell model is originally derived to calculate the eddy current effects in foil conductors and later on extended to packed windings composed of litz-wire by introducing a porosity factor [4]. The accuracy however declines quickly when porosity factor reduces, and the characteristics of eddy current distribution is not adapted to the litz-wire. On the other hand, the magnetic field of round conductors analyzed by Ferreira model is excellent, but the error become significate at high frequency at high porosity factor [5] because it neglects the interaction between conductors in the same layer [6]. In this paper, an improved model is proposed for calculating the eddy current distribution in litz-wire windings due to the skin and proximity effects. This model can have much more accurate prediction of eddy current distributions in the cross-section of a round litz-wire conductor, and can be used for electromagnetic design of high frequency devices.

32 citations

Proceedings ArticleDOI
08 Oct 1995
TL;DR: In this article, the various loss mechanisms of a foil winding are analyzed and quantified and the results show a strong correlation between the current and field distributions within the windings where the current is always attracted to the high field regions.
Abstract: The design of high power and high frequency foil wound inductors is not a straightforward task. At high frequencies, additional losses occur within the foil windings due to the eddy currents induced by skin, proximity, fringing and other AC effects. In addition, the winding structure greatly affects the distribution of losses within the windings. In this paper, the various loss mechanisms of a foil winding are analyzed and quantified. Both analytical and finite element analysis tools are utilized to investigate and understand the different loss mechanisms. The results show a strong correlation between the current and field distributions within the windings where the current is always attracted to the high field regions. By shaping and controlling the field distribution in a given design, the current distribution can be improved which results in an improvement in the winding losses.

32 citations

References
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Journal ArticleDOI
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

Journal ArticleDOI
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

Journal ArticleDOI
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

Journal ArticleDOI
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