Three-dimensional flux distributions in transformer cores as a function of package design

In spite of extensive optimizations of transformer core designs, investigations of full sized cores showed distinct inhomogeneities of flux density B. Limbs showed discontinuous variations of B in peripheral packages and minima of B in thick central ones. The latter are not caused by global eddy currents but rather by localized flux components Φ_z normal to the sheet plane. Attempts to determine the respective effective ac-permeability μ_z yielded values below 100, i.e., almost three orders below μ_x of the rolling direction. For given B, (planar) eddy current losses P_z proved to exceed the respective values P_x by two orders, a ratio which increases with increasing length L of the magnetized sheet region. The low ratio μ_z/μ_x yields a tendency of constant package flux throughout the whole core. A key criterium for Φ_z-components between packages proved to be the overlap regions which were studied in a comparative way for several step-lap configurations. Distinct differences of respective values of lap-region excitation V_L were observed as a function of air gap lengths and the step number N, respectively. Variations of V_l-and especially overlaps of high V_L in connection with shifted overlap regions-proved to yield Φ_z-components including flux transfer between packages. In a complex way, shifts yielded decreasing excitation power, but increased core losses due to planar eddy currents. In addition, package shifts cause both the discontinuities of B of thin peripheral packages and the minima of local B in thick central ones. With respect to core design, it can be assumed that small shifts favor take over of flux without causing significant planar eddy current losses (due to small L), while large shifts increase total losses in a disadvantageous way. With increasing N, these effects become less significant