Comparison and Combination of Techniques for Determining the Parameters of a Magnetic Hysteresis Model

Filomena B R Mendes,Nelson J Batistela,Fredy M S Suárez,Nelson Sadowski,João P De Barros Neto,Jean V Leite

doi:10.1590/2179-10742019v18i31513

Abstract

The Jiles-Atherton scalar hysteresis model presents five parameters used to represent the material tested and used to calculate the magnetic losses. This article presents a comparative analysis of the performance of two methods of identifying these parameters. In the first method, the equations of Jiles-Atherton were assembled into a single non-linear ordinary differential equation as a function of the variables of interest. An algebraic system of five equations with five unknowns is obtained by evaluating the non-linear ordinary differential equation in five points belonging to the branch of the experimental hysteresis loop. The parameters are obtained by solving this system of equations using the method of Non-Linear Least Squares (NLLS). In the second method, the inverse model of Jiles-Atherton is used to calculate the magnetic field H from the experimental values of magnetic induction B. Using the method of genetic algorithms (MGA), the objective function given by the sum of the relative error of calculated magnetic field and experimental magnetic field along the hysteresis loop is minimized. To validate methods the experimental curves were compared with calculated ones. When applying the methods, it was verified that NLLS besides providing more accurate results, it is faster when compared to MGA. In the MGA the convergence of the calculated magnitudes to the experimental magnitudes improves when one of the chromosomes of the initial population is the solution obtained applying NLLS.

Highlights

Ferromagnetic materials are used in electrical engineering applications to provide a robust structure to electrical machines, to conduct magnetic flux and mainly to amplify the magnetic inductions up to a limit value imposed by the saturation of the material
The inability to traverse the same paths of flux in the material, the need for energy to reorient the magnetic domains of the material, the delay considering the magnetic induction B and the magnetic field H and the pinning points that hinder the movement of the domain walls originate the phenomenon of hysteresis in ferromagnetic materials
The calculated parameters x, the number of iterations required for the algorithm to converge, the mean squared error (MSE), the percentage error considering the measured magnetic loss and the calculated magnetic loss, the simulation time t, the type and the cutting direction of the sample, the test instrument used, the test conditions, the simulated hysteresis loop and the experimental hysteresis loop can be seen in Fig. 3- 11

Summary

INTRODUCTION

Ferromagnetic materials are used in electrical engineering applications to provide a robust structure to electrical machines, to conduct magnetic flux and mainly to amplify the magnetic inductions up to a limit value imposed by the saturation of the material. The proposed methodology to determine the parameters of the model consists in transforming the non-linear ordinary differential equation obtained in an algebraic equation as a function of B and H In this regard, it is necessary to choose five points of the experimental hysteresis loop; and numerically calculate the derivatives at these points. Random values are mapped within the allowed range

CHARACTERIZATION RESULTS

WORKBENCH USED TO ACQUIRE EXPERIMENTAL DATA

CONCLUSION

Descending