Nonlinear modeling of magnetic materials for circuit simulations

Magnetic materials in the form of magnetic rings are widely used in power engineering products. In many cases, they operate in high frequency and in nonlinear conditions, e.g., as damping elements in electrical power substations equipped with Gas-Insulated Switchgear (GIS) where they provide suppression of Very Fast Transient Overvoltages (VFTOs). To model phenomena in GIS with magnetic rings it is required to have realistic time-dependent models of magnetic materials operating in a wide frequency range and nonlinear conditions. Nowadays, this has become even more relevant due to the actual trend in the industry to create digital twins of physical devices. Models composed of high-precise discrete lumped nonlinear elements are in demand in circuit simulators like SPICE. This work introduces a method based on classical algorithms that find equivalent lumped models of magnetic cores based on frequency-dependent measurements of impedance under DC-bias current. The model is specifically designed to have smooth behavior in the current domain and thanks to that to improve numerical stability in the time domain simulations.