Peter Hamberger

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.

Design optimization of power transformers. Part 2. Eddy current analyses for tank wall and core clamping parts

For pt.1 see ibid., p.1365-1370, (2004). To maintain quality, performance and competiveness, finite element analyses are increasingly utilized for the initial design, the design review and the design optimization of power transformers. The detailed geometry of windings, core, tank wall as well as insulation and clamping parts requires 3D numerical calculation methods in order to obtain high accurate values for the material utilization. The paper presents 3D finite element analyses for the distribution of eddy currents in the core clamping parts and the tank wall of power transformers. Since these eddy current losses are obviously different between measurements of load losses and normal operational conditions, the calculation shows the regions of possible hot-spot temperatures with normal operational conditions.

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.

Finite element analyses in the design optimization of winding support and tank wall of power transformers

Short-term customer deadlines, ambitious technical specifications and individual customer demands require high levels of precision and reliability in calculating the results for power transformers. Therefore, finite element analyses are increasingly utilized with initial design, design review and design optimization. The paper presents 3D finite element calculations with the intent of an optimization of winding support, core clamping system and tank wall shape regarding the electric field distribution in the winding support.

Investigation of surface velocity pattern of power transformers tanks

It is common knowledge, that the surface velocity pattern of power transformers tanks and therefore the sound pressure level (SPL) are very sensitive to environmental influences, for example a temperature rise or a simple displacement, so a precalculation of the surface velocity and the SPL seem not to be feasible. By means of an experimental tank it is demonstrated, that the surface velocity pattern can be broken down into a linear combination of resonant modes near the excitation frequency. The magnitude and phase between the resonant modes are influenced by the environmental changes, but the shapes of the involved resonant modes are widely independent of the environmental influence. Therefore the resonant modes can be predicted with numerical simulation.

Analytical approach for the calculation of the stray field of large power transformers

The paper discusses a novel analytic method for determining the stray field of the windings of large power transformers. Taking into account the detailed arrangements of low and high voltage windings as well as tapping windings, the algorithm utilizes series expansions of orthonormal Eigenfunctions for the Laplacian equation of a gauged 3D magnetic vector potential. In order to fulfill the appropriate boundary conditions at the boundaries of the high permeable laminated iron core, fictious surface currents at these boundaries are introduced. Thus, a very fast evaluation of the stray field suitable for an inclusion with the initial design of large power transformers within an industrial environment is achieved.