Effects of DC Bias on Regional Flux and Magnetostriction of a Single-Phase Transformer Core Modeled by 3-D MACC

Traditionally, flux distributions in transformer cores are modeled as a 2-D problem. However, experimental studies indicate that 3-D models are needed. The main reason is that limbs of circular cross section are combined with roughly semi-circular yokes. At the joints, this yields shifts of overlap regions as a reason of significant (off-plane) normal direction (ND) induction BND. This paper reports a first corresponding 3-D modeling of a two-package one-phase core with the consideration of non-linear characteristics of material. For corners, the so-called critical induction BCRIT of joints-as arising close to 1.4 T-is considered. Two instants of the cycle of global magnetization are addressed, i.e., B
_GL
= 1.7 T for normal operation and 1.9 T as a value that may arise for dc bias. For 1.7 T, the results indicate strong inhomogeneity, in particular in the wide main package of the core. On the other hand, 1.9 T is characterized by distinct homogenization. As 3-D effects, the cycle of magnetization involves distinct changes of flux in ND, with values up to more than 0.2 T. Half-cycle saturation is indicated especially for inner (window-sided) corner regions. The corresponding consequences on local magnetostriction (MS) values are over-proportional due to the complex dependence of strain λ and induction. The so-called butterfly curve is dynamically passed beyond the turn point and even into its positive range. In particular, this yields distinct distortion of λ, which can be assumed as a source of over-proportional rises of A-weighted noise. Apart from MS, further enhancement is to be expected from inter-laminar forces.