Recently, the two most significant characteristics of power transformer cores, i.e., loss and noise, have been reduced considerably because of improved material and improved core design. An undisputed base value of noise results from magnetostriction (MS) due to the global magnetization of limbs and yokes, whereas excess values are attributed to different mechanisms, such as excess MS and magnetic forces (MF), in a controversial way. However, a multistep lap (MSL; number of overlap steps N>1) yields considerably lower noise than a single-step lap (SSL; N=1), indicating a specific role of joint design. The present work was aimed at a deeper understanding as a tool for further improvements. For a large number of differently built-up single-phase model cores, local distributions of surface displacements d/sub x/, d/sub y/, d/sub z/ and velocities v/sub x/, v/sub y/, v/sub z/ as well as the corresponding noise n were determined. As a major finding, MSL yielded weak reductions of in-plane vibrations v/sub x/ and V/sub y/, considerable reductions of v/sub z/, and strong reductions of n. Interpretations of results were based on numerical Spice modeling of linearized joint vibrations, which were also established experimentally. The results indicate high values of off-plane flux density B/sub z/ and the corresponding Maxwell stress arising at the outermost sheet ends for SSL, and considerably lower values for MSL, provided that B is below its critical value B/sub c/. MSL yielded reductions of d/sub z/, v/sub z/, and n in 80% of all cases. Three additional core parameters-small air gap lengths, high overlap lengths, and high lamination factors A-all lead to reduced n; the use of oil yielded strong reductions. It is concluded that joint designs actually play a predominant role in noise generation. Apart from some contribution from attractive in-plane forces due to B/sub z/, in air gaps, interlaminar flux B/sub z/ yields primary sources of vibrations that propagate to the entire core surface. In core regions of reduced /spl Lambda/, B/sub z/ yields vibrations of sheet ends due to MF according to an experimentally determined effective Young's modulus that considers practical conditions like waviness, burrs, and thickness variations of laminations. For high h, oscillations of the whole core thickness due to B/sub z/-caused MS will arise close to joints. For MSL, all of these mechanisms become less relevant: Gap regions show much lower B/sub x/ and, provided B<B/sub c/, also lower B/sub z/, apart from being regionally distributed. Further, imperfections of joint assembling are less critical. As a consequence, the noise level of modern MSL power transformer cores, as commercially assembled with homogeneous compression and high N, can be well predicted by mere consideration of MS resulting from global magnetization.

Relevance of magnetostriction and forces for the generation of audible noise of transformer cores

With the fast-paced changing technologies in the power industry, new references addressing new technologies are coming to the market. Based on this fact, there is an urgent need to keep track of international experiences and activities taking place in the field of modern transformer design. The complexity of transformer design demands reliable and rigorous solution methods. A survey of current research reveals the continued interest in application of advanced techniques for transformer design optimization. This paper conducts a literature survey and reveals general backgrounds of research and developments in the field of transformer design and optimization for the past 35 years, based on more than 420 published articles, 50 transformer books, and 65 standards.

Transformer Design and Optimization: A Literature Survey

This paper presents an advanced model of the frequency response of a three-phase power transformer for use in conjunction with diagnostic measurements by the method of frequency response analysis (FRA). The model includes high- frequency behavior of the laminated core and the insulation through taking into account the frequency dependencies of the complex permittivity of insulation materials (paper, pressboard, and oil) and of the anisotropic complex permeability of magnetic core and conductors. A lumped parameter circuit model is used to simulate the frequency response of open-circuit impedance, short-circuit impedance, and impedance between primary and secondary windings, in which the characteristics of circuit elements are calculated by means of the finite-element method. The effect of correct representation of each circuit element on the FRA response is analyzed and discussed in comparison to measurement results on a real transformer.

High-Frequency Modeling of Power Transformers for Use in Frequency Response Analysis (FRA)

Because the performance of power transformers is by various distinct parameters of the magnetic core, the prediction of relevant characteristics such as no-load losses P by analytical methods is impractical. This paper reports first attempts to predict the dependence of P on several parameters of core design by means of artificial neural networks (ANN's). Investigations of several ANN versions showed good results for simple backpropagation networks equipped with several output neurons for an adaptive version of Gaussian coarse coding. A main problem arises from the fact that an increase of input parameters is linked with a large increase in training batches established by time-consuming model core experiments. As a compromise, first ANN's were trained for the prediction of the losses P/sub J/ of "linearized" joint regions as a function of the most relevant parameters, including the number of overlap steps and the mean air-gap length of joints. This yields rough estimations of the joint's contribution to the building factor for small cores. For larger cores, an ANN cascade structure was tested. It includes a second ANN that considers indirect effect of joint designs on the global distribution of losses. The major problem with an ANN-based prediction system is establishing representative training data. Modified versions of the ANN method can be applied to various tasks, including the prediction of losses and noises of full-sized cores.

Neural networks for the prediction of magnetic transformer core characteristics

Simple equivalent permeability and reluctance models are obtained for the transformer core joints from the analysis of the magnetic flux. It is shown that the flux variations in the joint zone can be fitted with simple Gaussian expressions suitable for transformer design purposes. These models are derived from 2D and 3D finite element simulations. The magnetic flux distribution in the transformer core joints is studied for wound cores and stacked-lamination cores with step-lap configurations. The models of the study properly account for the effects of core design parameters such as length of air gaps, number of laminations per step and overlap length. The proposed models, which include saturation and anisotropy, are applied to grain-oriented silicon steel (GOSS) and super GOSS. The new models are intended to estimate, right from the design phase, the magnetic flux density, permeability and the reluctance in the joints. The maximum differences between the Gaussian models of this study and finite element simulations are under 6%. The models of this study can be used to improve core designs with the aim of reducing core losses and magnetising current. A comparison of the total losses computed with the model of the study and measurements on a wound core distribution transformer showed differences of about 2.5%.

Modelling transformer core joints using gaussian models for the magnetic flux density and permeability

It has been stated that multistep-lap (MSL) jointed cores show distinct improvements regarding power losses P in comparison to single-step-lap (SSL). On the other hand, model core experiments tend to yield contradictory results. In the paper, special emphasis was put on the underlying physical mechanisms, taking into consideration that model cores usually show 'perfect' stacking, while full-size cores exhibit considerably high air gap lengths g as well as shifts s between the overlap regions of adjoining packages. It is shown that an increase of the number N of steps reduces the sensitivity of the core in respect to variations of g and s. This is due to increasing 'critical induction' BC as of which the excitation VL of the overlap region steeply increases. Low VL corresponds to lower balancing interlaminar flux in the overlap/gap regions and thus to a generally more homogeneous flux distribution linked with lower P. The quantity BC can be assumed to be of high practical relevance for the design of transformer cores.

H. Pfutzner

Papers

Relevance of step-lap joints for magnetic characteristics of transformer cores