Design of the magnetic hysteresis mathematical model based on Preisach theory

In the frame of the constantly increasing in electric power systems (EPSs) complexity, the challenge of ensuring adequacy of relay protection (RP) devices operation becomes more and more urgent. The authors propose to use the detailed mathematical models of the combination «instrument transformers (IT)—RP» with modern EPS simulators as the solution. It is very important to adequately simulate IT, in particular, the magnetic core magnetization process, because IT largely determines the shape of the RP-controlled signal and affects on its operation. However, in practice simplified models are currently used due to the lack of an accurate mathematical description of the IT core magnetization characteristics. Such models do not reflect all processes in the magnetic core. The aim of this work is to develop a hysteresis mathematical model, which will have a high accuracy in reproducing the magnetization processes of transformer core. The main research method is mathematical modeling of the ferromagnetic material magnetization processes in the MathCAD software. The article presents main development principles of the mathematical model with magnetic hysteresis memory based on the Preisach theory, which reproduces with high accuracy both the major and minor hysteresis loops.