Phenomenological modelling of ferromagnetic hysteresis using three dimensional dipole collectives

Knowing the magnetic properties of electrical steel is very important to build highly efficient electrical machines. Many approaches, which are either of mathematical, physical or phenomenological kind, were developed in the past in order to predict the phenomenon of hysteresis in case of unmeasured conditions. In this paper, a phenomenological 3D hysteresis model using magnetic dipoles, which are mechanically supported on a 3-dimensional grid, is presented. The different interactions between these dipoles are based on the equations of micromagnetism. Instead of minimizing the free energy in the system by mathematical optimization methods, each elementary dipole is able to rotate into an individual energetically favourable positon due to its mechanical mounting. In the following sections the model, its parameters and the identification process are presented. Afterwards, the results of the parameter identification process for a measured hysteresis are shown. Furthermore the predictive abilities of the model in case of unmeasured conditions are discussed.