Calculation Of Eddy Current Losses Research Articles

Calculation of eddy current losses in metal parts of power transformers

To maintain quality, performance and competitiveness, the eddy current losses in metal parts of power transformers in the range of 50‐200 MVA are investigated in a more detailed form. The finite element calculations utilize different modelling strategies for the current carrying metal parts. Several global and local results are further used to obtain simplified calculation approaches for an inclusion in the initial design and the design optimization. The results from two finite element approaches using nodal and edge based formulations will be compared with measurements.

Calculation of eddy current losses and temperature rises at the stator end portion of hydro generators

This paper deals with a calculation method of eddy current losses and temperature rises at the stator end teeth of hydro generators. It can be used for analysing and evaluating different design variants when optimising the stator core end portion. The calculation method simulates the three‐dimensional local core end field, but uses only a two‐dimensional calculation model. Amongst all the stator teeth it treats the tooth with the highest axial and radial magnetic flux impact. The paper presents a collection of calculation algorithms of the method and provides some results gained for two different stator core end designs.

Analysis of effective resistance and eddy-current losses in multiturn winding of high-frequency magnetic components

This paper develops a numerical model for calculation of eddy-current losses in a multiturn winding of a high-frequency transformer. The model assumes periodic arrangement of conductors, and uses the repeat elementary cell concept. The paper proposes analytical expressions and graphic dependences to determine effective frequency-dependent resistance of the winding. It computes the leakage field in the transformer window, taking into consideration the effective magnetic permeability of the multiturn winding as a heterogeneous medium. Finally, it analyzes the values of the resistance at various frequencies for two types of winding (solid conductor winding and Litz wire winding) by numerical and experimental methods.

Eddy Current Losses: A Theoretical Discussion of Dowell’s Layer Copper Factor

In ID analytical models aimed at calculating eddy current losses in magnetic devices subject to high-frequency effects, the “layer copper factor” is classicaly used to take layers composed of several conductors into account. In this paper, we discuss the theoretical base of this factor, showing that the equations used in Dowell’s basic paper are inconsistent with Ampere’s law. As a conclusion, the layer copper factor is re-interpreted as a true empirical correcting factor which can be used to model several 2D effects of the fields inside the windings.

直流送電用フィルタリアクトルの巻線内渦電流損の計算

直流送電用フィルタリアクトルの巻線内渦電流損の計算

Eddy-current losses in magnetic conductors with abrupt magnetic transitions

This paper presents an analysis of eddy-current losses in magnetic conductors with abrupt magnetic transitions. The study of the linear polarization of the magnetic flux is based on the Preisach model representation of eddy-current hysteresis. By using this representation, analytical formulas for the calculation of eddy-current losses in terms of simple experimental data are derived. The analysis of the circular polarization of the magnetic flux is carried out through the exact analytical solution of the corresponding nonlinear vector diffusion equation. It is shown that the f/sup 2/ law for eddy-current losses has a universal character.

Nonlinear diffusion and the Preisach model of hysteresis

Subtle and interesting connections between the Preisach model of hysteresis and nonlinear diffusion are discussed. On this basis, Preisach modeling of eddy current hysteresis and superconducting hysteresis is presented. It is stressed that rate-dependent eddy current hysteresis can be fully characterized by its step response. Preisach representation of eddy current hysteresis is then used for the calculation of eddy current losses and the universality of the ‘ f 2 -law’ for these losses is emphasized. Experimental results that provide evidence for remarkable accuracy of the Preisach description of superconducting hysteresis are presented.

Eddy current losses in anisotropic media subject to rotating magnetic fluxes

In the article, the analysis of “rotational” eddy current losses is carried out for elliptical polarizations of magnetic flux and magnetically nonlinear anisotropic media. Elliptical polarizations of magnetic flux and constitutive relations for anisotropic media are treated as perturbations of circular polarizations of the magnetic flux and constitutive relations for isotropic media, respectively. By using the mathematical machinery of perturbation technique, simple expressions for electromagnetic fields are derived and applied to the calculation of eddy current losses.

Improved design of cover plates of power transformers for lower eddy current losses

Due to the heavy current passing through the steel cover plates of power transformers, some areas are subject to serious local overheating. This affects the safety and reliability of the expensive equipment and power delivery. In this paper, the improved design of cover plates is presented to reduce eddy current losses and to protect them from local overheating. For the accurate calculation of eddy current losses and power loss density distribution in the cover plates, the indirect BIEM (boundary integral equation method) is applied to the 3D open boundary problem caused by the heavy current of leads in a three-phase power transformer. The numerical results by the indirect BIEM are compared with experimental values.

Eddy-current calculation of statistically distributed material

In this paper the calculation of eddy current loss of a statistically distributed material is presented. For loss calculation two FE and one semi-analytical formulation are compared. The distribution of the material, which is only known by some global parameters, is generated by a Monte Carlo approach, so that a large number of calculations describe one system state. The results are evaluated by means of probability theory. >

Eddy current loss calculation in thin rectangular plates at cryogenic temperatures and its experimental verification

Eddy current losses in conducting plates placed in a non-uniform alternating magnetic held at cryogenic temperatures have been calculated taking into account temperature dependencies of resistivity, heat capacity and heat-transfer coefficient. The calculation method is based on a coupled solution of a quasi-stationary electromagnetic problem and a non-stationary heat-conduction equation. A simplification of the task is achieved by neglecting eddy current reaction and free space charge. In this case the problem is solved in two stages: (1) the calculation of electromagnetic field; (2) the determination of a temperature distribution in the plate. As the first boundary condition for heat-conduction equation it is assumed that the heat transfer from edges of the plate equals zero. The second boundary condition is determined as a solution of the integral equation describing the law of conservation of energy relevant to the plate. The nonlinear two-dimensional heat conduction equation has been solved using partition of coordinates, implicit difference approximation and modified Thomas algorithm for obtained finite-difference equations. The numerical results remain in good agreement with data obtained by means of an experimental model of the cryogenic device, while neglecting thermal processes results in substantial errors amounting up to several hundreds percent. >

3D eddy current losses calculation in transformer tanks using the finite element method

The authors discuss the 3-D electromagnetic modeling of a transformer to evaluate eddy current losses in the tank. To achieve this, several numerical methods are used with two 3-D field computation packages. Conventional volume elements and shell elements are used for the modeling of thin conducting regions. Surface elements are used for the modeling of conducting regions with a reduced skin depth. The results, along with several characteristics of the tank and magnetic core, are compared. The influence of the characteristics of these two components is investigated. >

Finite element computation of eddy current losses in nonlinear ferromagnetic sheaths of three-phase power cables

A novel method for the finite element computation of the losses in a three-phase power cable is presented. The phase conductors carry sinusoidal, steady-state, and balanced currents, and the sheath is made of a nonlinear ferromagnetic material. A concept for an effective equivalent magnetic permeability is introduced that allows calculations in the complex domain. Sheath losses are presented and discussed for a symmetrical configuration. >

FEM calculation of eddy current losses and forces in thin conducting sheets of test facilities for fusion reactor components

An efficient finite element formulation of the eddy current field in thin conducting sheets has been developed coupled to a description of the magnetic field by a gauged magnetic vector potential. The numerical problems associated with the thin conductors have thereby been eliminated. Results of computations on a model of the TOSKA Upgrade test facility are presented. The aluminium radiation shields are not in danger; the stresses acting upon them are negligible. This is due to their being located relatively far from the superconducting coil. Only parts of the supply lines near the connecting flange of the vacuum vessel experience considerable stress. Their reinforcement under rapid changes may be necessary. The vacuum vessel is not endangered, since its wall of 20 mm thickness easily withstands the stresses due to the induced eddy currents. Normal pressures of up to about 50 t/m/sup 2/ occur at the LN2 shield. This makes modifications of its structure necessary.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Computation of eddy current losses by heavy current leads and windings in large transformers using IEM coupled with improved R- Psi method

A method combining the improved R- Psi method (in which the electrical vector potential R only exists in the conducting region) and the IEM (integral equation method) is described which synthesizes the advantages of the two methods and reduces the CPU time and the storage space required to solve 3-D eddy-current problems in open regions. The IEM is used to compute the magnetic field and losses due to heavy-current leads and the improved R- Psi method is used to calculate the magnetic field and losses due to windings. The coupled method is used to calculate the three-dimensional sinusoidal eddy-current field related to the open region in a 360 MVA/500 kV power transformer. The eddy current and loss computation and the estimation of the local hot spots makes it possible to prevent a large transmitter from local overheating.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Calculation of eddy current losses in nonlinear ferromagnetic materials

A complex analysis of the nonlinear diffusion problem in ferromagnetic materials under steady-state excitation is presented. The problem is solved by considering an equivalent fictitious material where the relative permeability is assumed to be constant in time but different from point to point and is related to the nonlinear B-H characteristic curve with the help of the stored magnetic co-energy density. Eddy current losses are calculated in a one-dimensional thick steel plate. A comparison made with results obtained from the classical step-by-step method shows a good agreement. >

Harmonic Domain Analysis of Field Variables Related to Eddy Current and Hysteresis Losses in Saturated Laminations

The authors give a detailed analysis of the space and time distribution of the field variables B, H, and E inside saturating laminations, using a harmonic domain modeling method. A simple way has been devised for the representation of hysteresis. It was found that hysteresis affects to a small degree the variation of H and B but has no noticeable influence on E and thus, as expected, does not interact with the corresponding eddy current losses. It is shown that saturation distorts the linear space distribution of the eddy currents but that the assumption of linear distribution still leads to a very simple method for eddy current loss calculation which is remarkably accurate at 60 Hz. >

Eddy current losses in composite and/or multibodies with μr≥1

The paper deals with the computation of eddy current losses in composite and/or multiconducting cylinders due to time-harmonic transverse magnetic fields. The cylinders are linear magnetic or nonmagnetic with an arbitrary cross-section area. Two diffferent formulations in terms of the Fredholm integral equations of the second kind are used. The exact formulation comprises 2N (where N is the number of conductors) coupled one-dimensional integral equations; and the second, where the external impedance boundary condition approach is used, consists of N coupled one-dimensional integral equations. With the proper choices of the equations the highest singularity in both formulations is logarithmic (weak singularity in 2D). Numerical results are computed for the special case of a pair of circular conductors. Magnetic and nonmagnetic materials are considered and the results are compared with the corresponding results for a single circular conductor.

The effect of nonsinusoidal excitation on eddy current losses in saturated iron

Mathematical expressions are presented for the calculation of eddy-current losses in solid and laminated iron cores with the rectangular B-H characteristic. The core was magnetized by forced nonsinusoidal magnetic field or by forced nonsinusoidal flux. The distorted excitation was represented by the function sin/sup m/ omega t. Experimental results are in agreement with the theoretical results and prove that waves of constant RMS but with different harmonic spectra will cause different eddy-current losses. The same conclusion applied to distorted waves with constant amplitude. >

Calculation of extra losses in shell form power transformer windings

Extra losses in shell-form power transformers are calculated. Some analytical methods are proposed for the calculation of eddy-current losses, circulating-current losses, and transpositions. Based on these methods a code has been written. Some calculation and test results are reported for a 13.333-MVA single-phase shell-form power transformer built for this study.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>