Georgi Shilyashki

Rotational Magnetization in Transformer Cores—A Review

Usually, rotational magnetization (RM) is associated with rotating machine cores. However, in more restricted ways, it also arises in three-phase transformer cores. Modern designs of T-joint yield detours of flux, as a source of RM in the T-joint, the middle limb ends, as well as in the yokes. Simulation of RM is possible by means of so-called rotational single sheet testers which should consider the large grains of highly grain oriented materials. Their high effective anisotropy yields induction patterns of rhombic or lancet-like type with maximum values of axis ratio a up to 0.5, and very high angular velocity round the materials hard directions. Compared to elliptic RM-as arising in non-oriented materials-the corresponding losses are lower due to restricted induction in the hard direction. But they show strong increase with (i) rising a and (ii) rising angular velocity of the induction vector. The magnetostrictive strain shows a pronounced (negative) maximum in the rolling direction with values up to 10 ppm, the transverse direction and normal direction exhibiting positive maxima of lower extent. With respect to industrial relevance, significant RM effects are restricted to the vicinities of T-joints. They represent the location of maximum core loss and also of maximum magnetostrictive strain as a source of audible core noise.

Magnetostriction of Transformer Core Steel Considering Rotational Magnetization

As it is well known, the power loss of transformer core steel depends on a series of parameters which vary in the final core in complex ways. The aim of the present study was to investigate the corresponding dependencies for the second key characteristic, i.e., magnetostriction (MS), as the most significant source of no-load noise. The MS-performance of core material was investigated by means of a rotational single sheet tester (RSST). Compared to loss, the peak-to-peak MS in rolling direction (RD; as the direction of strongest strain) shows similar increases with increases of both induction and axis ratio a. On the other hand, the shape of induction pattern B (t) proves to be rather insignificant, MS being similar for elliptic and rhombic magnetization. While increased dynamics of the pattern yields rising eddy current loss, MS remains unaffected. However, the harmonics show increases as being of relevance for audible noise. While mechanical tension in RD yields slight decreases of MS for alternating magnetization, MS for rotational magnetization increases for both tension and compression. As in the case of loss, MS shows significant increases for DC-bias which correlates with reports of increased noise. The study also included local measurements on a 2-limb, 1-phase model core and on a 3-limb, 3-phase core. MS remains in the order of 0.5 ppm for the 1-phase core, except from its corners. On the other hand, T-joint regions of the 3-phase core show values up to the order of 6 ppm, in accordance to RSST-results. Moderate DC magnetization, as being possible in practice as a long term phenomenon, yields distinct increase of MS intensity and MS harmonics with strong regional differences.

Automatic 3-D Building Factor Analyses of a Grain-Oriented Model Transformer Core

The literature reports various transformer model core studies on local values of the building factor (BF), which consider the core as a 2-D single-package object. For the first time, we report 3-D BF analyses of a three-phase core that exhibits three different widths of packages. The inner BF values were determined by taking advantage of 25 channels of 2.5 mm width through the entire core. BF profiles along the channels were measured by means of a thermistor sensor that was controlled by a 3-D scanning system. For a nominal induction of 1.7 T, the results indicate that the main package of maximum width and thickness behaves similarly to one-package cores, with minimum BF in outer limbs and maximum BF (however, of reduced intensity) in the T joint. On the other hand, outer packages of reduced width and thickness show distinctly reduced BF, especially in the T joints. The results indicate that 2-D studies are not representative of peripheral packages. They show specific performance, especially due to the usual combination of circular limbs with semicircular yokes. The resulting regional off-plane z -flux seems to have a balancing function which reduces the effects of overlaps. However, low BF in the peripheral packages does not indicate good performance. Rather, it indicates poor exploitation of the core material.

The Impact of Off-Plane Flux on Losses and Magnetostriction of Transformer Core Steel

Transformer cores are assembled from several packages of different widths. Furthermore, circular limbs tend to be combined with semicircular yokes. These characteristics mean that the core represents a complex 3-D system. A consequence is balancing off-plane flux (z-flux) perpendicular to the core plane. Measurements of z-induction on model cores show that mere inhomogeneity of stacking may yield significant values of flux density Bz in the normal direction. Close to overlapping regions of corners and T-joints, the order of 10 mT was observed. Losses prove to increase in a nonlinear way with increasing Bz for both alternating magnetization (AM) and rotational magnetization (RM). Effects become significant for Bz = 10 mT, with losses showing increases of order of 30%. The corresponding increases of magnetostriction are much more pronounced, reaching 100%. These increases are clearly supported by the results of Kerr effect studies of domains. They reveal distinct increases of oblique domains. For 1-D AM, they are restricted to inner lancet slopes. For 2-D RM, the latter merge to inner plate domains. For the 3-D case of additional z-flux, the formation of plates is significantly enhanced. Plates can be assumed as a main source of both rising hysteresis losses and increasing magnetostriction.

Pin Sensor for Interior Induction Measurements in Transformer Cores

This paper concerns, the problem to assess 3-D distributions of magnetic induction in soft magnetic systems like machine cores of transformers or generators. Within bulk material, estimations of distributions are restricted to numerical methods like FEM, the application of sensors being hard. On the other hand, in laminated material, the conventional method is to use single-turn search coil sensors arranged in holes through the laminations. As drawbacks, the method is extremely laborious, and it causes artifacts due to the formation of interlaminar air gaps. This paper presents a completely novel alternative that is applicable in systems of both laminated and bulk material. Instead of single holes, measurement channels (e.g., 3 mm width) are established through the whole system. A soft magnetic pin (e.g., 2.5 mm diameter) with pickup coil is used as an a priori calibrated dummy sensor. It determines an induction profile along the channel in a fully automatic way. The effectiveness is demonstrated for the case of a 3-phase transformer core. Induction profiles through a core-limb of three packages of different width are presented in correlation with corresponding loss profiles, as detected in an analogous way.

A Tangential Induction Sensor for 3-D Analyses of Peripheral Flux Distributions in Transformer Cores

This paper concerns the detection of local magnetic induction in peripheral regions of transformer cores. Induction distributions are important for the interpretation of local losses and magnetostriction. Most authors use advanced numerical modeling-like FEM for the computation of local induction values. However, effective estimations tend to be impossible due to non-linearity, extreme anisotropy, and complex effects of hysteresis. As an alternative to FEM, the conventional method for local measurements is to use arrays of single-turn search coils. However, this method is laborious, and it affects the measured values in strong ways due to the thickness of the arranged wires and artifacts from the drilled holes. This paper presents a novel approach for peripheral core regions based on measurements with a tangential induction coil, i.e., a field coil with a ferromagnetic core. The sensor was tested on a model transformer core stacked from three packages of different widths of grain-oriented electrical steel, for the nominal induction of 1.7 T. As an advantageous effect, the sensor does not cause any interlaminar air gaps and detects the amplitude of the induction not only in planar, but also in lateral positions. Results from ~100 measuring positions are presented. They show that the induction distribution is inhomogeneous with variations up to ~15%. High induction values were measured in the widest main package of the core, in contrast to much lower ones in the outer packages. On the other hand, the corners, yokes, and T-joints show much more uniformly flux distribution. The findings of this paper can be assumed to be relevant for industry in order to optimize the construction of cores for the purpose of their uniform utilization.

Numerical Prediction of Rhombic Rotational Magnetization Patterns in a Transformer Core Package

Evaluations of local induction time patterns B(t) in transformer cores show high relevance for both losses and magnetostriction. This paper presents numerical calculations for a three-phase core package stacked from grain-oriented SiFe for BNOM = 1.7 T. Modeling is based on a novel multi-directionally non-linear magnetic equivalence circuit calculation (MACC). It considers non-linear permeability functions in rolling direction, transverse direction (TD), and diagonal direction in overlaps. MACC yields instantaneous local values B, and the corresponding reluctances and permeabilities as a basis for conclusions. Snapshots of induction distributions for important time instants of zero or maximum limb induction reveal dominant roles of anisotropy and multi-directional non-linearity. Small changes of permeability in the TD yield distinct changes of rotational magnetization (RM) and circulating magnetization. Local dynamic magnetization patterns B(t) are calculated considering 180 instants of time, for sufficient resolution of dynamics. The results confirm the formation of RM patterns of oblique rhombic (or lozenge) shape, in contrast to elliptic patterns as frequently assumed. They also confirm that the induction vector B rotates with maximum angular velocity when passing through the TD.

Rise-of-temperature method for building factor distribution in 1-phase model transformer core interior considering high DC bias

Loss distributions of transformer cores are affected by z-flux effects if considered for the core surface. Here we propose the application of a thermal sensor which is inserted to the core interior through one of 16 channels of 2 mm width. Measurements were made on a 1-phase core assembled from laser-scribed SiFe. Throughout the core, the local building factor BF proved to increase towards the periphery which can be interpreted by interactions of highest anisotropy and non-linearity. Additional DC superposition yields non-uniform increases of BF at different core positions. Local losses tend to become more balanced – measurement locations with a priori high BF experience lower percentage increases, being more robust with respect to DC components.

Automatic 3-dimensional flux analyses of a 3-phase model transformer core

For the development of new strategies for reduction of energy losses and audible noise of transformer cores, the assessment of the induction distribution is essential. The results confirm that the core represents a strongly inhomogeneous 3-dimensional magnetization system. For a full understanding of distributions, measurements in the core interior are necessary. For the first time the paper presents detailed analyses of induction distribution in a multi-package model core. Automatic measurements were performed in 112 local positions within 3-phase, 3-limb transformer core stacked from three packages of different width of grain oriented material. As a completely novel approach, a soft magnetic Fe-pin (of 2.4 mm diameter) with pick up coil was used as an a priori calibrated pin sensor. 25 measurement channels (of 3 mm diameter) were established through the entire core. Z-profiles of the induction through the channels were determined in an automatic way for a nominal induction of 1.7 T. They confirm that the core represents a system that is magnetized in a strong inhomogeneous way. Strong variations of the induction up to 10% were observed not only for the in-plane direction, but also along the normal direction (off-plane). Maximum induction values were detected in the widest main package, minimum ones in the narrowest peripheral package. An exception is the corner area where the inhomogeneity of B decreases, linked with a balancing off-plane flux. The paper proposes a model for the flux distribution through the three packages of the core.

Domain reconstructions of g.o. SiFe during rotational magnetization considering also 3-D flux components

Domain analyses of modern types of grain-oriented (GO) transformer steel are rare, and they are focussed on single grains under academic magnetization patterns. The present Kerr effect study reveals that grains of industrial, polycrystalline materials react in specific ways according to individual crystallographic orientations. The amount of parameters is very large, especially if additional flux components are given as a further impact. The paper reports a procedure for statistical evaluations of quasi-dynamic Kerr effect images. The instantaneous area ratios of bar domain portion BD, oblique domain portion OD and saturation S are determined with consideration of peak induction BRD in the rolling direction (RD), axis ratio a of rotational magnetization, the angle ψ between B and RD, additional flux Bx in RD or Bz in normal direction. Focus is put on OD(t) which is assumed to be ak ey function forλ(t), i.e. the course of time of magnetostriction. As the most distinct tendencies, OD increases strongly with increases of a and ψ. OD(t) shows non-sinusoidal course of time with differences of the two halves of cycle. Rotation out of the RD yields sharp onsets of ODs, especially after half-cycle saturation. Additional off-plane flux enhances ODs in a general way.