Transformer Sheets Research Articles

Determination of Changes in Flux Density of Transformer Steel Sheets

Magnetic fields in transformer cores are typically assumed to be one-dimensional fields, thus allowing magnetization processes to be regarded as axial magnetization. However, in the core corners or T-joint points of medium- and high-power rating transformers, the magnetic lines have different directions with respect to the rolling direction. This paper describes a method that allows changes in the flux density of transformer steel sheets to be calculated for any magnetization direction. These changes are assumed to depend only on certain limiting hysteresis loops assigned separately to the rolling and transverse directions of a tested transformer sheet, where these loops depend on the magnetization direction on the sheet plane. The selection of coefficients that define the limiting hysteresis loops for several magnetization directions is described, and the condition for the flux density saturation is considered. The resultant flux density in a specified magnetization direction is the geometric sum of the corresponding flux densities assigned to both the rolling and transverse directions. The limiting and partial hysteresis loops determined based on the proposed method for several magnetization directions are compared with analogous measured loops. Additionally, a comparison of the calculated hysteresis loops with loops showing changes in the resultant flux density for several magnetization direction is presented.

Driving Signal and Geometry Analysis of a Magnetoelastic Bending Mode Pressductor Type Sensor.

The paper deals with a brief overview of magnetoelastic sensors and magnetoelastic sensors used in general for sensing bending forces, either directly or sensing bent structures, and defines the current state of the art. Bulk magnetoelastic force sensors are usually manufactured from transformer sheets or amorphous alloys. In praxis, usually, a compressive force is sensed by bulk magnetoelastic sensors; however, in this paper, the sensor is used for the measurement of bending forces, one reason being that the effect of such forces is easily experimentally tested, whereas compressive forces acting on a single sheet make buckling prevention a challenge. The measurement of the material characteristics that served as inputs into a FEM simulation model of the sensor is presented and described. The used material was considered to be mechanically and magnetically isotropic and magnetically nonlinear, even though the real sheet showed anisotropic behavior to some degree. A sinusoidal magnetizing current waveform was used in the experimental part of this paper, which was created by a current source. The effects of various frequencies, amplitudes, and sensor geometries were tested. The experimental part of this paper studies the sensors' RMS voltage changes to different loadings that bend the sheet out of its plane. The output voltage was the induced voltage in the secondary coil and was further analyzed to compute the linearity and sensitivity of the sensor at the specific current characteristic. It was found that for the given material, the most favorable operating conditions are obtained with higher frequency signals and higher excitation current amplitudes. The linearity of the sensor can be improved by placing the holes of the windings at different angles than 90° and by placing them further apart along the sheet's length. The current source was created by a simple op-amp voltage-to-current source controlled by a signal generator, which created a stable waveform. It was found that transformer sheet bending sensors with the dimensions described in this paper are suitable for the measurement of small forces in the range of up to 2 N for the shorter sensors and approximately 0.2 N for the longer sensors.

A measuring setup for testing the mechanical stress dependence of magnetic properties of electrical steels

Measurements of mechanical stress dependence of magnetic properties of electrical steels are significant from both theoretical and application points of view. The paper presents a novel measuring setup for testing the magnetoelastic properties of electrical transformer sheets made of grain-oriented and non-grain-oriented steel. The proposed method takes into consideration the angle between the easy electrical steel magnetization axis and the mechanical stress direction. Due to the innovative 3D self-adjustment mechanism of the yoke position, measurements may be taken for different magnetization strengths and angles. The paper also presents detailed uncertainty analyses and examples of results of magnetoelastic measurements for grain-oriented electrical steel M120-27s. The presented results validate the method and confirm its usability for further detailed studies of mechanical stress dependence of magnetic properties of electrical steels.

Design and Evaluation of a Magnetoelastic Tensile Force Sensor

Abstract This paper introduces the basic theory behind magnetoelastic sensors which are based on the change of magnetic properties (permeability) due to mechanical stress (Villari effect). A well-known magnetoelastic sensor, the Pressductor, is described. A simulation model of a sensor is created, described, and evaluated by computing the static transfer characteristic of RMS secondary coil voltage change due to tensile stress. A real sensor is then manufactured from a polycrystalline transformer sheet and experimentally tested by using a tensile load created by water weight. The simulation and experiment show similar behavior but are not completely identical which is most likely since some material properties were taken from literature rather than from experimental measurements, like the magnetostriction coefficient and initial magnetic susceptibility.

Calculations of eddy currents in electrical steel sheets taking into account their magnetic hysteresis

PurposeThe purpose of this paper is to present the method which relatively easily allows to approximate the hysteresis loop of the dynamo or transformer steel sheets. The paper also looks into the formulation of an equation allowing determination of distribution of the flux density and eddy currents in cross-section of these sheets.Design/methodology/approachAn exponential function was applied in the presented method relating to the approximation of the hysteresis loop. When the field strength changes its value, then, the flux density are the sum or difference of a function, describing the lower or upper hysteresis curve and some “ransient” component. On the basis of Maxwell’s equations and Amper’s law, one non-linear differential equation was formulated which allows to calculate the flux density and eddy currents in a cross-section of a transformer sheet.FindingsThe method which relatively easily allows approximation of the hysteresis loop of ferromagnetic material is presented in the paper. The paper presents the derivation of one non-linear differential equation, allowing calculation of the flux density and eddy currents in the cross-section of the transformer sheets, taking into account the hysteresis phenomenon.Practical implicationsThe paper presents the method that can be used in modeling of the hysteresis loops of dynamo or transformer sheets, and the final non-linear differential equation can be applied in calculations of the magnetic field and eddy currents in cross-section of the transformer sheets.Originality/valueThe paper refers to important issues of modeling and calculations of the magnetic and eddy current field distribution in transformer steel sheets.

Measurement uncertainty of the instantaneous characteristics of non‐linear coil obtained by Dommel's method

The characteristics of coil are obtained through the following measurement: the root mean square (RMS) coil current, as a function of RMS coil voltage, and the coil loss, as a function of RMS coil voltage. These values were then transformed, using Dommel's method, into instantaneous characteristics of non-linear coil, in a form of a non-linear inductance, representing saturation effect; in parallel with the non-linear resistance representing coil loss. The instantaneous characteristics are composed of peak values of resistance current and voltage, and inductance current and flux. The uncertainties of the characteristics are defined through the uncertainty of the peak values. The uncertainty of instantaneous characteristics is calculated on an example of a coil realised as unloaded iron-cored toroid transformer with a strip-wounded core made of oriented transformer sheets (M5-type) using the adaptive Monte-Carlo method (MCM) and uncertainty framework of ‘Guide to the expression of uncertainty in measurement’ (GUM). Results reveal the peculiarities of both methods and the impact of the uncertainty of measured values on the uncertainty of instantaneous characteristics.

Experimental investigation of impact of remnant flux on the ferroresonance initiation

Objective: The paper presents an experimental and numerical investigation carried out on a ferroresonant circuit in order to determine to what extent the initiation of ferroresonance depends on remnant flux.Methods: In order to gain the full insight of impact of initial conditions on the initiation of ferroresonance in general, the investigation was carried out varying the initial capacitance voltage and the phase shift as well. Ferroresonant circuit under study comprises a linear capacitor, sinusoidal voltage source and a coil designed for 30V nominal primary voltage with the core made of oriented transformer sheets (M5-type). Additionally, the response of the circuit was obtained using a coil with the same core type (M5-type), but designed for higher nominal primary voltage (36V) and a coil designed for 30V nominal primary voltage, but with the core made of Ni–Fe alloy (Trafoperm N3).Results/Conclusions: Based on measurements and simulation results, it is shown that the remnant flux and initial conditions in general, as well as phase shift have significant impact on initiation of ferroresonance for all used coil types. Thereby, the odd-symmetry of responses was observed as a consequence of odd-symmetric characteristics of passive circuit elements. The impact of initial conditions is explained theoretically as well, using a bifurcation diagram and calculation of Floquet multipliers.

A Neural Network Modeling of Stress Behavior in Nonlinear Magnetostrictive Materials

Using accurate magnetostriction simulation models during the various design stages of their related devices can positively contribute to the enhancement of their precision. These models are indispensable to different crucial computational activities such as those dealing with active vibration damping devices and optimum clamping stresses for transformer sheets. In this paper, we present a new contribution for the dynamic hysteresis behavior of magnetostrictive materials. To do this, we have used a neural network to model the relationship between the elongation λ and the magnetization M for different loads σ. The derivative of λ according to M is then calculated numerically and integrated in the Jiles–Atherton model for calculating the hysteresis loops.

Vibration of transformer sheets using non-linear characteristics

Intensive research has been carried out over the years to reduce acoustic noise resulting from the vibration of transformer plates. The noise of transformer sheets excited by electromagnetic field can be mostly attributed to induced forces between the plates. The vibration generated from transformer structures causes abnormal vibration, breakage of the machine, and noise. Vibration measurement and analysis of the structure is important to prevent this phenomenon. This chapter presents the research resulted by measurement and Finite Element Method of the resonance of the transformer sheets.The goal of this research is to introduce the coupling of the developed nonlinear hysteresis model and the Finite Element Method. The COMSOL and MATLAB based finite element simulation method combines the electromagnetic, structural mechanics and acoustic models. The moving mesh (ALE) geometry of the transformer sheets leads on a valid model and assures the calculations of the electromagnetic properties in different deformed shapes. The measurement of the natural frequencies of the plates yields the relation between the excitation frequency and the resonance of the system.The goals of the developed model are:to derive the magnetic field intensity H and with hysteresis nonlinearity the magnetic flux density B properties inside the transformer sheets with d = 0.35 mm and I = 150 mm;to compute the induced current density J; inside the plates;to calculate the Lorentz force F distribution along the sheets;to derive the plane stresses the horizontal and vertical displacements along the sheets are calculated;applying the ALE moving mesh the deformation of plates can be simulated.For modelling the nonlinear characteristic of the magnetic material M = H{H} a novel developed hysteresis model is used. The advantages of the hysteresis model are its easy identification, past memory representation and numerical simplicity [1]. So, the hysteresis characteristic can be determined as

Experimental Characterization of Interlamination Shorts in Transformer Cores

Burr-induced interlamination shorts in magnetic circuits increase eddy current loss. In large transformer cores, the short-circuit currents can become so high as to even damage the core. This paper presents contributions to modeling an individual short circuit between two transformer sheets. The aim of the model is to predict the additional eddy current loss caused, depending on the excitation conditions, the placement of the contact points, and the contact resistances. Measurements have been conducted on artificial short circuits between single pairs of transformer sheets. Findings prove that the interlaminar short can be modeled with good approximation by a resistive equivalent circuit, even when the core is saturated. The influence of different parameters on the elements of the equivalent circuit is discussed.

Effect of the cutting technique on the residual stress distribution of cut edges in FeSi3 transformer sheets

AbstractSamples of laser‐scratched FeSi3 transformer sheets have been investigated. The investigations were carried out by using the Kossel and EBSD techniques in our self‐designed multifunctional system. The results show residual stress mappings of the cut edges of FeSi3 transformer sheets and their dependence on the cutting process (conventional plate shears, abrasive water‐jet technique, laser cutting). (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Identification and testing of an efficient hopfield neural network magnetostriction model

Magnetostriction models are indispensable to different crucial computational activities such as those dealing with active vibration damping devices and optimum clamping stresses for transformer sheets. This paper presents an efficient magnetostriction Preisach-type model based on the effective field approach. According to this approach, the total applied field may be regarded as a super position of the actual magnetic field and a stress-dependent feedback term. Construction and identification of the model is carried out by providing experimental training data to a modular discrete Hopfield neural network–linear neural network combination. Experimental testing suggests that this model can lead to good qualitative and quantitative simulation results.

Variation of Transformer Sheet Winding Eddy Current Loss with Frequency

Variation of Transformer Sheet Winding Eddy Current Loss with Frequency

The effect of magnetic field on the recrystallisation of ferromagnetic material with special respect regarding its anisotropy

The properties of soft magnetic material used as transformer sheets strongly depend on the orientation of its crystallites. These thin sheets are manufactured by cold rolling followed by the final technological process (i.e. recrystallisation). The magnetic properties are determined by this last recrystallisation process. In the following rows it will be shown that if the recrystallisation is achieved in a magnetic field the new nuclei having orientation 〈0 0 1〉 have the greatest opportunity to form if the intensity of the magnetic field is higher than that required reaching magnetic saturation.

The importance of textures for determining the mechanical behaviour of intermetallics

In conventional metallurgy it is well accepted that preferred crystal orientations in a polycrystalline material can have significant effects in modifying properties, with notable examples found in γ-γ′ superalloy components and Fe(Si) transformer sheets. The same effects clearly should be obtained in intermetallics, but this aspect has hardly been considered until recently. The influence of textures will be examined in iron aluminide and in γtitanium aluminides. The first compound is highly elastically anisotropic and plastically relatively isotropic. The second compound is elastically more isotropic and shows severe plastic anisotropy, both as single phase γTiAl and in the more common two-phase (γ+α2) form. Control of texture and of its uniformity throughout a component can have a major effect on its response to mechanical stresses.

High temperature magnetization of 3.5% Si steel

Thermomagnetic curves of rapidly solidified ribbons of Fe-3.5 wt% Si prepared using the single wheel and double roller techniques are discussed in comparison with those of commercial grain oriented transformer sheet samples. It is concluded that the arrangement of defect clusters or silicon or impurity atoms, fixed at the temperature of secondary recrystallization, influence the distribution of magnetic moments at high temperature.

The state of order of grain-oriented iron-silicon transformer sheets investigated by neutron scattering

The state of order of commercial high permeability, grain-oriented iron-silicon transformer sheets has been investigated by elastic neutron scattering. The atomic fraction of silicon was 0.061. The sheets had been subjected to the standard heat treatments. They were found to be strongly short-range ordered. The Warren–Cowley parameters αi, 1≤i≤3, were −0.063, −0.100, and +0.056, respectively. For comparison a single crystal grown from the same material was studied. From its neutron scattering data, it is concluded that the state of order of the sheets is that of the single crystal heat-treated at 723 K.

Order in commercial grain-oriented iron-silicon sheets

The state of order of commercial high permeability iron-silicon transformer sheets has been investigated by diffuse elastic neutron scattering. The silicon content was 6.1 at%. The sheets show a high degree of short range order.

Why not use magnetotactic bacteria for domain analyses?

For nondestructive domain analyses of transformer sheets with stress coating, high voltage SEM techniques as well as special colloid techniques have been developed. In the present study, a medium containing magnetotactic bacteria was applied to the sample surface. It was found that the bacteria orient themselves in the stray fields originating from the domain structure, and swim in the field direction. This allows visualization of domains whose stray field is directed into the sheet. Comparisons between the bacteria technique, colloid technique and computer controlled field scanning method are discussed for different kinds of materials.

The effect of small amount of Sb on the texture and magnetic properties of grain-oriented Fe-Si alloys

This paper describes the study of the influence of antimony on the development of the preffered {110} ⟨001⟩ texture in modelling treated Fe-3.1% Si alloys. A small amount of Sb (0.040 and 0.048 wt.%) added to commercial iron-silicon steel leads to more precise (110) [001] texture, higher magnetic induction and to lower core losses in so prepared transformer sheets.