Design of the magnetic hysteresis mathematical model based on Preisach theory

  • Mikhail Andreev
  • Alisher Askarov
  • Aleksey SuvorovEmail author
Original Paper


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.


Relay protection Magnetic hysteresis Mathematical simulation Inverse hysteresis model Preisach theory Major hysteresis loop Minor hysteresis loop 



This work was supported by the Ministry of Education and Science of the Russian Federation under the governmental Grant “Science” No. 13.5852.2017/8.9 (Development of the concept for comprehensive validation of calculating modes and processes in electric power system and tools of its realization).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Division for Power and Electrical Engineering, School of Energy and Power EngineeringTomsk Polytechnic UniversityTomskRussia

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