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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01 Mar 1987TL;DR: In this article, a micromachine is described for use in studies of standstill (particularly frequency-response) test methods for obtaining the transient impedance parameters of a tubogenerator.
Abstract: A micromachine is described for use in studies of standstill (particularly frequency-response) test methods for obtaining the transient impedance parameters of a tubogenerator. The severe design compromises associated with dynamic micromachines are completely avoided, rotor induced-current field and magnetic nonlinearity being correctly scaled. Advantages for the micromachine are listed and a detailed specification provided. First tests, in open-circuit field configuration, have shown the effect of surface contact resistance of aluminium wedges to be very pronounced, as is coming to be recognised in turbogenerator studies. Tests with wedges removed are compared with field computations, and with new data (obtained from installed probes) on the measured effectiveness of inducedcurrent paths in wedges and teeth. Standstill frequency-response measurements are possible in the micromachine up to 20% current, contrasting with 0.5% in a turbogenerator. Measurements of operational inductance and transfer function, over a full frequency range, thus show for the first time the changes that occur as excitation increases above the low-B range of magnetic nonlinearity. It becomes clear that the standard procedure for adjusting only the mutual branches of the d- and q-axis equivalent circuits, to allow for this nonlinearity, is inadequate.
1 citations
01 Jan 2020
TL;DR: In this paper, an open-source robust design optimization framework process based medium frequency transformer design process is introduced and the magnetic field is calculated directly by the builtin FEM solver.
Abstract: Nowadays, there is a huge interest in the design of medium frequency transformers. Due to their high power density and relatively good efficiency. These transformers are still used in wind farms and traction, where not only the efficiency, but the overall size and weight of the transformer are important design criteria. However, the determination of the load losses is based on analytical or pseudo-empirical formulations during the design optimization process. In this paper, an open-source robust design optimization framework process based medium frequency transformer design process is introduced. During the solution of this process, the magnetic field is calculated directly by the builtin FEM solver.
1 citations
23 Jun 2020
TL;DR: An optimization design tool is developed to minimize both the volume and losses of high-frequency transformers, by optimizing the maximum flux density, by selecting the maximum switching frequency.
Abstract: Power density and efficiency are the main concerns in power electronic converters of electric aircraft. Transformers are major contributors to the size of isolated converters. In this paper, an optimization design tool is developed to minimize both the volume and losses of high-frequency transformers, by optimizing the maximum flux density. Optimum switching frequency selection is considered for different core materials and number of cores in parallel. The analysis shows the trade-offs involving the selection of the switching frequency and the effects on the transformer weight and volume, and the overall converter efficiency. Numerical simulations are performed in JMAG to validate the analytical models.
1 citations
01 Sep 2019
TL;DR: An ac winding loss formula based on the vector form is derived, which can decouple the skin and proximity effect concisely, and is convenient to be applied for the design of the switching transformers in power adapters.
Abstract: The paper proposes a technique to calculate the ac winding loss of transformer windings with arbitrary phase-shifted current waveforms. An ac winding loss formula based on the vector form is derived, which can decouple the skin and proximity effect concisely, and is convenient to be applied for the design of the switching transformers in power adapters. Based on the technique, a guideline to optimize the transformer winding structure is introduced and applied to an active-clamp Flyback power converter. The auxiliary, cancellation and shielding windings which are commonly used in power adapters products are also taken into consideration. Simulation verifies the theory and technique.
1 citations
DOI•
TL;DR: In this paper , a two-stage factorized power architecture (FPA) dc-dc converter is proposed, which caters to applications that require high efficiency, high power density, low ripple, and high dynamic response of space-borne low-voltage and high-current power supply.
Abstract: In this article, we propose a two-stage factorized power architecture (FPA) dc–dc converter, which caters to applications that require high efficiency, high power density, low ripple, and high dynamic response of space-borne low-voltage and high-current power supply. The first-stage 48 V intermediate bus converter (IBC) adopts the six-phase interleaving magnetic integration buck converter (IMIBC). A new array high symmetry multi-phase coupled inductor (CI) is constructed, and a general zero-voltage switching (ZVS) control strategy is proposed. The designed IBC provides 2.4 kW power with a density of up to 1400 W/in3 and efficiency up to 97.15%. The second-stage point of load converter (POLC) adopts the four-phase interleaving magnetic integration LLC dc/dc transformer (DCX). A new method of current sharing, which is based on the inverse coupling resonant inductor, is proposed. This method yields good current sharing under a 15% mismatch of resonance parameters. A highly symmetrical four-phase resonant CI and a four-phase magnetic integration transformer are developed; the design of magnetic components is optimized by constructing a high-precision magnetic circuit mode. The designed POLC has a power density of up to 700 W/in3 and an efficiency of up to 97.1%. Finally, the experimental prototype is fully tested against a similar type of Vicor’s products. According to the results, the power supply designed in this article has several benefits with regard to efficiency, power density, transient response speed, and ripple.
1 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