Three-dimensional analysis of magnetodynamic fields in electromagnetic devices taken into account the dynamic hysteresis loops

A new magnetic field equation exhibiting dynamic hysteresis loops is proposed. Based on this magnetic field equation, a system of two-dimensional magnetic circuit equations taken into account the dynamic hysteresis loops is derived by the method of magnetic circuits. By means of magnetic power invariant transformation, a system of two-dimensional magnetic circuit equations is transformed into a system of three-dimensional magnetic circuit equations. This system of three-dimensional magnetic circuit equations is discretized in time by a finite difference method. A system of three-dimensional magnetic circuit equations discretized in time is solved by a simple iteration method, using a relaxation parameter. As an example, a system of three-dimensional magnetic circuit equations of a simple saturable reactor is derived. Also, the numerical solutions of dynamic hysteresis loops in a saturable reactor are presented together with those of experimental results.