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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TL;DR: In this paper, the 1D Dowell's method is modified and supplemented with a component called intra-layer proximity effect loss by considering the interaction between conductors in the same layer, which gives much accurate prediction of 2D eddy current distribution in the crosssection of a round conductor with a wider band of frequency than Ferreira's method.
Abstract: With the switching frequency of power electronic devices increasing rapidly, the high-frequency loss in windings is becoming significant The one-dimensional (1D) Dowell's method and 2D Ferreira's method are the most accepted methods used for winding loss calculation Ferreira's method is used to calculate high-frequency loss in windings composed of round conductors In this study, this method is modified and supplemented with a component called intra-layer proximity effect loss by considering the interaction between conductors in the same layer The improved model gives much accurate prediction of 2D eddy current distribution in the cross-section of a round conductor with a wider band of frequency than Ferreira's method On the basis of the eddy current distribution, the AC-to-DC winding resistance ratio is derived The results of the improved method are verified by finite element method, and the error of loss calculation is <;06% when skin effect and proximity effect are very significant
11 citations
TL;DR: This paper proposes a novel index named Total Financial Losses (TFL) to compare different inverter topologies from reliability and energy losses points of view, and selects the optimal photovoltaic inverter of the 150 kW power range out of commonly used two-level and three-level topologies.
Abstract: Inverters are the most vulnerable parts of the photovoltaic (PV) power plants. Therefore, choosing an appropriate inverter topology to maximize the reliability and availability of the PV power plants is very important, especially in the large scale power plants. This paper proposes a novel index named Total Financial Losses (TFL) to compare different inverter topologies from reliability and energy losses points of view. Initial cost, repair cost, financial losses due to the downtime and element losses, and environmental conditions are considered in evaluating the TFL index. Using this universal index, the optimal inverter topology and its switching frequency are determined when the TFL is minimized. Considering the fact that the reliability of power electronic devices is strongly dependent on their power losses and ambient conditions, the exact failure rates of vulnerable elements such as capacitors, switches, diodes, and cooling system are calculated. The system availability and frequencies of encountering the failure states are determined using the Markov method. Finally, the optimal photovoltaic inverter of the 150 kW power range is selected out of commonly used two-level and three-level topologies.
11 citations
DOI•
01 Jan 2018
Abstract: This work has been triggered by an industrial project targeting the development of a novel regulation system for a mechanical watch. Mechanical watches have been known for over a century as one of the finest example of energy autonomous devices, embodying an exceptional amount of human knowledge and high craftsmanship. Nevertheless, the accuracy of a mechanical timepiece keeps being significantly lower with respect to a quartz watch powered by a chemical battery. The aim of the study is thus filling such gap without compromising energy independence. The new regulation concept revolves around a small scale electromagnetic generator, the development of which is severely constrained at different levels. A major key point is miniaturization, which is needed in order allow the embedding of the generator in a watch movement. In fact, the overall size of the generator falls in the millimeter range, while some inner features might reach a micrometric critical dimension. A first important consequence is that not all the mathematical models that are used for conventional scale applications are suitable when it comes to the design of small scale devices. Another fundamental aspect concerns the technology associated to the fabrication of the device, which heavily affects the solutions that can actually be considered. In this sense, the adoption of the ensemble of the latest MEMS (acronym for Micro Electro-Mechanical System) technologies plays a fundamental role. The research presented within this thesis aims to address such topics in the most comprehensive way as possible, with the ambition of providing scientific tools of general use. After a brief review of the state of art in the vast domain of microscale power generation, an electromechanical model for the time-dependent description of the dynamics of synchronous machines is derived. In this context, the main issues associated with size reduction are discussed in detail, with a particular emphasis on how the manufacturing technique affects the overall functionality of this class of devices. The model is then refined accordingly and used for the analysis of an existing MEMS machine. Then, the design of the MEMS generator for the watchmaking application is addressed. On the basis of the theoretical structure defined, an algorithm is conceived in order to perform the optimization of the device. The dissertation will then digress on the modeling and manufacturing of single layer planar coils. In this framework, two different fabrication
11 citations
TL;DR: In this paper, models that account for the duty cycle and phase shift angle of the applied phase voltages in coupled stripline microinductors are presented and are shown to have a significant impact on harmonic current amplitudes and therefore microinductor efficiency.
Abstract: In this paper, models that account for the duty cycle and phase shift angle of the applied phase voltages in coupled stripline microinductors are presented and are shown to have a significant impact on harmonic current amplitudes and therefore microinductor efficiency. The impact of a high coupling factor between two windings surrounded by a single core is also investigated. The models are validated using finite-element analysis and measurements. A three-phase-coupled microinductor has been fabricated with a Ni45Fe55 core and analyzed for a number of operating conditions. A prototype 1.6 W, three-phase converter utilizing this inductor has also been measured and is discussed in detail. The coupled microinductor is predicted to have a peak efficiency of 86.6% at 20 MHz in the prototype circuit.
11 citations
01 Jan 2007
TL;DR: Abdelbagi et al. as mentioned in this paper investigated the skin and proximity effects of two parallel plate conductors while a laminated core was designed to reduce the power losses and showed that the eddy current power loss in a sold core is greater than loss in an oxide core by a factor of K, where K is the number of sheets in the laminate core.
Abstract: Abdelbagi, Hamdi. M.S., Department of Electrical Engineering, Wright State University, 2007. SKIN AND PROXIMITY EFFECTS IN TWO PARALLEL PLATES Time varying currents within winding and core conductors induce magnetic fields. When more than one conductor is present the resultant magnetic field can be found by adding the individual magnetic fields by superposition. The resultant magnetic field in turn induces eddy currents within each electrical component within the vicinity of the resultant magnetic field. Eddy currents flow in the opposite direction of the primary current and increase the resistance by reducing the area in which the primary current has to travel. Eddy currents also reduce the effectiveness of the conductors to conductor high frequency currents. Skin and proximity effects were numerically investigated for two parallel plate conductors while a laminated core was designed to reduce the power losses. Maxwell’s equations were solved to obtain analytical equations for magnetic fields eddy current distribution and power losses. These equations were illustrated in MATLAB for various frequencies to validate the theoretical analysis. Results demonstrate current within an isolated conductor flows near the surface. However, when the same conductor is placed near another conductor the flow path is affected. For the case when the current is flowing in the opposite direction, the magnetic fields are added in the area between the conductors and subtracted on the outer side of the conductor. This causes an increase of the current density within the conductor areas, where the conductors are close to each other. This is the proximity effect. The anti-proximity effect occurs when two conductors carry current in the same direction. In this case the magnetic fields are subtracted from each other in the area between the conductors and are added to each other in the area outside the conductors resulting in a higher current density in these areas. The eddy currents iii can be reduced in two ways. Using a highly resistant material for the core increases the skin depth making the distribution of the magnetic flux more uniform. Laminating the core with an oxide film can be used to reduce the eddy current loss as well. The study shows that the eddy current power loss in a sold core is greater than loss in a laminated core by a factor of K, where K is the number of the sheets in the laminated core.
11 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