Magnetic hysteresis model

A dynamical model is described which permits calculation of the excitation current
I
as a function of time in a laminated grain-oriented (G-O) steel transformer core. The independent variable is the magnetic flux density or, equivalently, the coil voltage less the
IR
drop associated with the resistance
R
of the windings. Recent observations on flux reversal mechanisms in GO steel indicate that, in the range of magnetic field intensities typically present in transformer cores, the important reversal processes are the motion of long 180° domain walls continuous across grain boundaries and the motion of 90° walls within individual grains. These processes are represented in the model by two subcircuits connected in series. Each subcircuit consists of an inductive element in parallel with a linear resistor which accounts for the eddy current losses accompanying the flux change. The properties of each inductive element (flux vs. current) reflect the two wall motion mechanisms, respectively, in the limit of zero frequency. This model is capable of faithfully simulating minor loop behavior as well as the response to complex waveforms; e.g., the superposition of two or more frequencies. The circuit equations are solved, and some results of computer calculations using a program that implements this model are presented.