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 Sep 2020
TL;DR: A comprehensive comparison of four loss models with respect to general mathematical approach, computational effort, as well as the impact of different parameters on the accuracy of the different models is presented.
Abstract: Litz wire (LW) is essential for reducing HF winding losses in medium frequency transformers and inductors. In order to predict the losses and optimise the parameters of LW, several analytical loss models have been presented. However, a detailed comparison of the models and the accuracy is missing. Therefore, this paper presents a comprehensive comparison of four loss models with respect to general mathematical approach, computational effort, as well as the impact of different parameters on the accuracy of the different models. Guidelines and insights for choosing the most suitable model are also provided.
11 citations
01 Nov 2015
TL;DR: A unified inductor model is first developed and a novel inductor design methodology is proposed, which makes it possible to easily introduce all the phenomena present in the inductor operation in the design process, including winding high-frequency effects and fringing flux in the gap.
Abstract: DC inductor design has recently drawn the attention of magnetic designers due to the rise in the number of DC-DC power converter applications, such as electric vehicles and renewable distributed generation systems. The design methods found in the literature are highly iterative and make it difficult to assess the design trends and optimize the power converter as a whole. In this paper, the DC gapped inductor design problem is analyzed. A unified inductor model is first developed and a novel inductor design methodology is then proposed. The comprehensive inductor model makes it possible to easily introduce all the phenomena present in the inductor operation in the design process, including winding high-frequency effects and fringing flux in the gap. With this so-called analytical inductor design methodology, the inductor energy density can be maximized while achieving high efficiencies. Finally, an inductor for a fuel cell 2.4 kW-22 kHz boost converter is optimally designed reaching an energy density of 0.61 J/dm3 and an efficiency of 99.04%.
10 citations
Dissertation•
11 Aug 2011
10 citations
TL;DR: A design by optimization process is used to size a 10-kW three-phase pulse width modulation (PWM) inverter for aeronautic application and several optimization results using different AC inductor solutions are compared.
Abstract: In this paper, a design by optimization process is used to size a 10-kW three-phase pulse width modulation (PWM) inverter for aeronautic application. The objective function is the converter weight, which has to be minimized. Sizing constraints are the efficiency, alternating current (AC) and direct current (DC) harmonics, and thermal constraints on all devices. A deterministic algorithm is chosen since it allows obtaining quick results and dealing with a large number of variables. All equations are analytical, in order to comply with this gradient-based optimization strategy, which imposes the derivability of the models. Several optimization results using different AC inductor solutions (iron powder and ferrite) are compared. The optimized converters were built and tested experimentally to verify their performances. Semiconductor and inductor losses were measured accurately using calorimetric test benches. The optimality of the solutions was carefully verified by changing parameters.
10 citations
TL;DR: In this paper, a simple closed-loop control algorithm with online tuning of the controller parameters is proposed to improve the utilisation of the isolation transformer in DC-AC applications, where the authors investigate the nature of the problem with experimental determination of approximate lumped parameter modelling and saturation behaviour (B-H curve) of the HF transformer.
Abstract: Power conversion using high frequency (HF) link converters is popular because of compact size and light weight of high-frequency transformer. This study focuses on improved utilisation of HF transformer in DC–AC applications. In practical application, the operating condition of the power converter deviates significantly from the designed considerations. These deviating factors are commutation requirements (dead-time, overlap), mismatch in device drops and presence of the fundamental frequency in load current. As a result, the HF transformer handles some amount of low-frequency components (including DC) other than desired HF components. This causes the operating point in B-H curve to shift away from its normal or idealised position and hence results poor utilisation of the HF transformer and unwanted losses. This study investigates the nature of the problem with experimental determination of approximate lumped parameter modelling and saturation behaviour (B-H curve) of the HF transformer. A simple closed-loop control algorithm with online tuning of the controller parameters is proposed to improve the utilisation of the isolation transformer. The simulation and experimental results are presented.
10 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