Calculation of losses in ferro- and ferrimagnetic materials based on the modified Steinmetz equation

This paper discusses the influence of nonsinusoidal flux-waveforms on the remagnetization losses in ferro- and ferrimagnetic materials of inductors, transformers and electrical machines used in power electronic applications. The nonsinusoidal changes of flux originate from driving these devices by nonsinusoidal voltages and currents at different switching frequencies. A detailed examination of a dynamic hysteresis model shows that the physical origin of losses in magnetic material is the average remagnetization velocity rather than the remagnetization frequency. This principle leads to a modification of the most common calculation rule for magnetic core losses, i.e., to the "modified Steinmetz equation" (MSE). In the MSE the remagnetization frequency is replaced by an equivalent frequency which is calculated from the average remagnetization velocity. This approach allows, for the first time, to calculate the losses in the time domain for arbitrary waveforms of flux while using the available set of parameters of the classical Steinmetz equation, DC premagnetization of the material, having a substantial influence on the losses, can also be included. Extensive measurements verify the modified Steinmetz equation presented in this paper.