Temperature-Dependent Extension of a Static Hysteresis Model

Abstract

Some soft magnetic materials are strongly dependent of the temperature, because of their low Curie temperature. In order to predict their behavior in electrical devices, engineers need hysteresis models able to take into account the temperature. This paper is an attempt to take into account the temperature in an existing model of static hysteresis through its parameters. Variations of some parameters with temperature are issued or build thanks to the literature. At the end, all needed parameters have an analytical law versus temperature. Simulation results are compared to measurements and discussed.

Numerical model of static hysteresis taking into account temperature

“…To this aim, we developed formulation to identify the parameters of the VPM. Conversely to existing works, this formulation has as unknowns only the parameters ( χ k ), whereas ω k ≡ 1/ N is fixed a priori.…”

“…The terms are the internal state of each cell. They are upgraded as a function of the applied magnetic field h and of their current value according to where χ k is a parameter linked to the coercivity . The relationship between h , h r e , and h i r is depicted in Figure .…”

“…The parameters ω k and χ k must verify the following constraints: In the work of Henrotte et al it is proposed to determine these parameters basing on the experimental curve H c ( H p ), where H c is the coercive field corresponding to a minor symmetric closed loop, for which the peak magnetic field is H p . The same approach is followed in the works of François‐Lavet et al and Sixdenier et al However, this approach requires a specific set of measurements (ie, symmetric closed loops at many peak levels), which have to be performed purposely. Conversely, it would be interesting to explore the possibility of being able to identify model parameters from a generic set of measurements.…”

“…Therefore, the only parameters that have to be identified are ω k and χ k (at a given temperature T ) with k spanning from 1 and the (unknown) number of cells N . According to the work of Sixdenier et al these parameters have been fitted for a single temperature T 0 = 298K; their variation with temperature is as described in Section 2. For the sake of simplicity, let us define the vectors Y = ( ω 1 … ω N ) and X = ( χ 1 … χ N ).…”

“…The same authors also proposed a method where they considered linear variations of saturation magnetisation and coercive field to take into account the temperature for permanent magnets. In a previous paper, variations of some parameters of the VPM were identified thanks to different papers in the literature . This last approach gave mixed results.…”