Multifrequency nonlinear model of magnetic material with artificial intelligence optimization

Magnetic rings are extensively used in power products where they often operate in high frequency and high current conditions, such as for mitigation of excessive voltages in high-power switchgear equipment. We provide a general model of a magnetic ring that reproduces both frequency and current dependencies with the use of artificial intelligence (AI) optimization methods. The model has a form of a lumped element equivalent circuit that is suitable for power system transient studies. A previously published conventional (non-AI) model, which we take as a starting point, gives a good fit of parameters but uneven characteristics as a function of current, which pose numerical instabilities in transient simulations. We first enforce the Langevin function relationship to obtain smooth characteristics of parameters, which reduces the number of parameters and ensures their even characteristics, however, compromises fit quality. We then use AI metaheuristic optimization methods that give a perfect fit for the model in the whole range of frequency up to 100 MHz and current up to saturation, with smooth characteristics of its parameters. Additionally, for such fitted parameters, we show that it is feasible to find a frequency dependence for the magnetic saturation parameter of the Jiles-Atherton (JA) model, thus enabling frequency-dependent JA.