The influence of a random domain size distribution on the eddy-current contribution to hysteresis in transformer steel

A modified Pry and Bean domain-wall eddy-current model (1958) is proposed in which the domain widths are Poisson distributed in the demagnetized state. The statistics of the domain population and eddy-current interactions of the domain walls are followed as magnetization proceeds. Instantaneous and average loss-anomaly ratios eta R, eta R are tabulated as functions of mean domain size and polarization for comparison with the corresponding eta PB and eta PB. eta R rises sharply as polarization increases owing mainly to progressive annihilation of domain walls. However, even near B=0, eta R> eta PB because of increased eddy-current overlap associated with random bunching of walls. In contrast to the PB model, this random width model accords well with 120 Hz sinusoidal hysteresis data for 0.15 mm electrical steel reported by Siventsev et al. (1974) for which wall bowing (ignored in both models) should be negligible. Improved agreement is found even with 120 Hz sinusoidal H data for which wall bowing is expected to be severe.