Equations of magnetic field of transformer steel sheets

This study described a method for determining the magnetic field in transformer steel sheets for any magnetisation direction. In the proposed approach, limiting hysteresis loops for the rolling and transverse directions were used. These loops, which were determined separately in both directions, were modified depending on the direction of magnetisation. The assumed area of the magnetic field occurrence was divided into elementary segments, and the appropriate components of field strength and flux density were assigned to the edges and elementary segments of the grid dividing this area. The relationships between the flux density and field strength along both the rolling and transverse directions in the elementary segments were introduced into the equations of the magnetic field distribution, which were based on Maxwell’s equations in the integral form. These equations facilitated the determination of changes in the magnetic field, considering the magnetic hysteresis. The correctness of these equations was validated through comparisons of the results of numerical calculations with the analogous results of measurements performed using a laboratory package of transformer sheets.