Large signal nonlinear model of anisotropic transformers for nonsinusoidal operation. I. λ-i characteristics

Single-phase, nonlinear transformers with anisotropic iron cores are modeled for nonsinusoidal (consisting of fundamental and low-order harmonics) terminal conditions based on design data through a quasi three-dimensional magnetic field analysis. This analysis includes the effects of the interlamination and butt-to-butt air gaps, the exchange of flux between any two neighboring anisotropic laminations, and the influences of the end windings. It is shown that the B-H characteristics of cross and with-grain iron core samples, obtained from Epstein measurements, are not valid for anisotropic iron cores. However, these characteristics can be used to compute, through a quasi-three-dimensional magnetic field analysis, appropriate B- H characteristics for anisotropic iron core samples. Based on such newly defined B-H characteristics for λ- i functions representing the saturation-dependent magnetizing inductance as well as saturation-dependent leakage inductances are calculated from design data. Calculated and measured characteristics corroborate well for a 1 kVA single-phase transformer