This paper deals with the incorporation of a vector hysteresis model in 2D finite‐element (FE) magnetic field calculations. A previously proposed vector extension of the well‐known scalar Jiles‐Atherton model is considered. The vectorised hysteresis model is shown to have the same advantages as the scalar one: a limited number of parameters (which have the same value in both models) and ease of implementation. The classical magnetic vector potential FE formulation is adopted. Particular attention is paid to the resolution of the nonlinear equations by means of the Newton‐Raphson method. It is shown that the application of the latter method naturally leads to the use of the differential reluctivity tensor, i.e. the derivative of the magnetic field vector with respect to the magnetic induction vector. This second rank tensor can be straightforwardly calculated for the considered hysteresis model. By way of example, the vector Jiles‐Atherton is applied to two simple 2D FE models exhibiting rotational flux. The excellent convergence of the Newton‐Raphson method is demonstrated.
Gyselinck, J., Dular, P., Sadowski, N., Leite, J. and Bastos, J.P.A. (2004), "Incorporation of a Jiles‐Atherton vector hysteresis model in 2D FE magnetic field computations: Application of the Newton‐Raphson method", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 23 No. 3, pp. 685-693. https://doi.org/10.1108/03321640410540601
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