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.
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15 Oct 2007
TL;DR: This paper presents a detailed analysis to evaluate the performance changes of high power, high frequency inductor with the existence of mounting strap and some guidelines of using the mounting strap in high frequency high power inductors are proposed.
Abstract: This paper presents a detailed analysis to evaluate the performance changes of high power, high frequency inductor with the existence of mounting strap. 2D finite element analysis (FEA) is used thoroughly for the losses calculations of the strap in terms of materials, air gap distance, and mounting strap thickness. After that, an optimal way of selecting the mounting strap material, strap thickness and air gap distance is derived. Then, a simplified equation is created to predict the strap losses and verified by a 2-D FEA simulation. Later on, the existence of the mounting strap to inductance calculation, coil losses and core losses are studied. Dramatic changes can be found on these performances for an inductor with mounting strap. Finally, some guidelines of using the mounting strap in high frequency high power inductors are proposed in the end of the paper.
5 citations
01 Sep 2018
TL;DR: In this paper, a new method to overcome this limitation is proposed that is based on the use of an equivalent layer that behaves as the actual winding, which is accelerated by using an equivalent conductor with homogeneous current distribution.
Abstract: In Wireless Power Transfer system, the optimization of the electromagnetic coupling is one of the main problems. Since the geometry usually is 3D, closed analytical equations cannot be obtained. Due to the small dimensions of the winding's diameters and the high number of conductors compared to the large size of the coupler, the brute force simulations by Finite Element analysis is not feasible. In this work, a new method to overcome this limitation is proposed that is based on the use of an equivalent layer that behaves as the actual winding. Finite Element Simulations are accelerated by the use of an equivalent conductor with homogeneous current distribution. Skin and proximity losses are accounted by the modification of the conductivity and the complex permeability of the new equivalent conductor meanwhile the field energy is accounted by the real permeability. The new electromagnetic parameters are obtained by means of analytical equations.
5 citations
TL;DR: A multi-objective design methodology of a 200-W flyback transformer in continuous conduction mode using genetic algorithms and Pareto optimality concept to minimize loss, volume and cost of the transformer is proposed.
Abstract: Design and optimization of high-frequency inductive components is a complex task because of the huge number of variables to manipulate, the strong interdependence and the interaction between variables, the nonlinear variation of some design variables as well as the problem nonlinearity. This paper proposes a multi-objective design methodology of a 200-W flyback transformer in continuous conduction mode using genetic algorithms and Pareto optimality concept. The objective is to minimize loss, volume and cost of the transformer. Design variables such as the duty cycle, the winding configuration and the core shape, which have great effects on the former objectives but were neglected in previous works, are considered in this paper. The optimization is performed in discrete research space at different switching frequencies. In total, 24 magnetic materials, 6 core shapes and 2 winding configurations are considered in the database. Accurate volume and cost models are also developed to deal with the optimization in the discrete research space. The bi-objective (loss–volume) and tri-objective (loss–volume–cost) optimization results are presented, and the variations of the design variables are analyzed for the case of 60 kHz. An example of a design (30 kHz) is experimentally verified. The registered efficiency is 88% at full load.
5 citations
01 Oct 2017
TL;DR: In this paper, a mission-profile based multi-objective optimization approach for designing power converter is presented, where the objective is to minimize the energy loss for a given load profile as against the conventional approach of minimizing power loss at specific loading conditions.
Abstract: To help mitigate some of the challenges associated with the wide spread adoption of the stochastic wind power, wind turbine with full-scale power converter (Type D) is preferred. Since full power is processed by the power converter in a type D wind turbine, it is important to improve its efficiency and reduce the cost per kW to achieve lower cost of energy. The power produced by the wind turbine varies in a wide range and the conventional design approach of optimizing converter at a specific loading condition may be sub-optimal. To overcome this challenge, a mission-profile based multi-objective optimization approach for designing power converter is presented. The objective is to minimize the energy loss for a given load profile as against the conventional approach of minimizing power loss at specific loading conditions. The proposed approach is illustrated by designing a grid-side power converter for 2 MW, 690 V wind turbine. The loss and volume models of the semiconductor and passive components have been discussed and design procedure has been demonstrated.
5 citations
05 Nov 2015
TL;DR: Etemadrezaei et al. as mentioned in this paper investigated the feasibility of high quality factor resonators at multi-MHz frequency of operation, and new ideas for magnetic link inductive coils were presented.
Abstract: ETEMADREZAEI, MOHAMMAD. High Quality Factor Resonators for Inductive Power Transfer Systems. (Under the direction of Dr. Srdjan M. Lukic). In this dissertation, the Inductive Power Transfer (IPT) systems for multi-MHz frequency of operation are investigated, and new ideas for magnetic link inductive coils are presented. The main focus of the dissertation is to increase the efficiency of the IPT system by investigating various high quality factor inductive coils as the influential components of the system. The challenges and limitations for high quality factor resonators at multi-MHz frequencies are addressed, and several potential coil conductors are explored. The dissertation consists of two general parts: component level, and system level. Each level is investigated individually, and then analyzed together to optimize the whole IPT system. At multi-MHz frequency of operation, choices of inductive coil conductor are limited to the basic types, such as solid round, foil, and tubular conductors. Foil conductor is a potential choice from the manufacturing, thermal behavior and current carrying capability points of view. However, unlike other typical types of conductors, the characteristics of foil conductors are barely expressed in analytical formats due to complexity of electromagnetic field distributions in air core IPT systems. Therefore, in order to optimize the system, link, and resonator for efficiency purposes, a simple fast approach is essential. An optimization approach for foil conductor layout is investigated to maximize the coil quality factor and IPT link efficiency. The optimization approach is fast and frequency independent, and solves the limitations associated with numerical methods. Litz wire is a proper choice of conductor in the KHz frequency range. At multi-MHz frequencies, Litz wire has several drawbacks. One limitation is associated with the uniform current distribution between strands, which increases proximity losses at such high frequencies. A modified type of Litz wire is investigated by adding a coating layer to each strand to reduce the overall Litz dissipation compared to a Litz wire with uncoated strands. A model is developed to simplify the computation of the coated-strand Litz wire, and the reductions in the AC resistance are presented. Another drawback of Litz wire at multi-MHz frequencies is the need for small strand sizes which poses manufacturing issues. This drawback is addressed using a concentric multi-layer tubular conductor as a potential candidate for IPT link resonator. The multi-layer tubular conductor can have lower AC resistance compared to a single layer one. This advantage comes with proper current distribution between the layers. This optimum current distribution is performed using capacitive ballast. Another beneficial role of capacitive ballast is the LC integration and to bring the coil to resonance to reduce the unwanted parasites. Component level optimization cannot guarantee the optimized system level performance at multi-MHz IPT systems. All IPT sub-systems need to be considered simultaneously for efficient system operation. Various system topologies that are commonly used at high frequency IPT systems are investigated. The magnetic link and the system level designs are unified for the IPT design and optimization. In a prototype IPT system, the techniques used for component and system level measurements are discussed, and the system performance is characterized. © Copyright 2015 Mohammad Etemadrezaei
5 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