PRZEGLĄD ELEKTROTECHNICZNY (Electrical Review), ISSN 0033-2097, R. 88 NR 4a/2012 253 Abdelaziz LADJIMI 1,2 , Mohamed Rachid MÉKIDECHE 2 Laboratoire L.G.E.G, Université de Guelma, Algérie (1), Labortoire (L.A.M.E.L) université de Jijel, Algérie (2) Modeling of Thermal effects on Magnetic Hysteresis using the Jiles-Atherton Model Abstract. The present paper deals with a temperature dependent modelling approach for the generation of hysteresis loops of ferromagnetic materials. The physical model is developed to study the effect of temperature on the magnetic hysteresis loop using JA model. The thermal effects were incorporated through temperature dependent hysteresis parameters of JA model. The temperature-dependent JA model was validated against measurements made on the ferrite material and the results of proposed model were in good agreement. Streszczenie. Zaprezentowano metodę modelowania pętli histerezy z uwzględnieniem wpływu temperatury. Do tego celu wykorzystano model Jiles- Atherton włączając do modelu parametry zależne od temperatury. Model sprawdzono na materiałach ferrytowych. (Modelowanie wpływu temperatury na pętlę histerezy przy wykorzystaniu modelu Jlies-Atherton) Keywords: Jiles-Atherton model, Magnetic hysteresis, Temperature, Modeling. Słowa kluczowe: Model Jiles-Atherton, pętla histerezy. 1. Introduction Magnetic hysteresis is encountered in the operation of most Electrical Engineering devices (motors, transformers, magnetic recording, and components for power electronics). The development of a model can accurately describe this cycle and its variation depending on the operating regime that is still an issue that inspires researchers. Amongst these models, we find the Jile-Atherton model which is based on energy considerations, that is on the movement of Bloch walls within the material. Its inconvenience lies in the identification of parameters and especially in case of temperature change. All machines are electric seat Joule losses, hysteresis and eddy currents, making these devices heat up. For instance, the temperature can be very high in case of heating induction furthermore, the integration of the temperature in the hysteresis model is imperative for a reliable estimate of losses related to this phenomenon. Taking into account the variation of the five parameters model depending on the temperature during the integration of this model in a computer code by finite element field is a formidable task, especially in the study of magnetic electromagnetic device. In this paper, we propose the introduction of temperature effect for the generation of hysteresis loops in the Jiles-Atherton model. In this paper, we adopt a different approach of [1]. We introduced the two thermal behavior of the spontaneous magnetization M s and coercive H c in the parameter k of the Jiles-Atherton model. 2. The Jiles Atherton model According to the Jiles–Atherton (JA) model [2], the total magnetization of a ferromagnetic material can be represented as the sum of contributions of irreversible, irr M , and reversible, rev M , magnetization components [2]: irr rev M M M   ) 1 ( The reversible component is the combination of the reversible translation and rotation of the walls in ferromagnetic materials. But the irreversible component represents the irreversible displacement of the magnetic domains. The differential equation describing the dependence of magnetization on magnetic field can be constructed as   irr an irr M M c M M    ) 2 ( e dH irr dM an k M M    ) 3 ( where M an is the anhysteretic curve, which follows the Langevin function                           e e s an H a a H M M coth ) 4 ( where M H H e    is the effective field taking into account the domain interactions,  is the molecular field parameter, k parameter is linked to the coercitive field, c Reversibility coefficient and  parameter is 1    when 0  dt dH and 1    when 0  dt dH [3]. The differential susceptibility according to the JA model can be expressed as follows [4]. e irr e an e an e irr dH dM c dH dM c dH dM c dH dM c dH dM ) 1 ( 1 ) 1 ( ) 5 (         3. Temperature Dependence of JA Thermal effects can be incorporated into the model through the temperature dependence of hysteresis parameters in (5): spontaneous magnetization M s , parameter  , reversibility factor c and parameter k. a. Spontaneous magnetization M s The temperature dependence of spontaneous magnetization M s can be expressed using Weiss theory of ferromagnetism [5]. )) exp( 1 ( ) ( ) 6 ( s M c Ta s s T T M T M     Where Ta s M is the value of spontaneous magnetization at room temperature, c T is the Curie temperature, and s M  is the constant defined on the experimental curve of spontaneous magnetization with temperature . b. Parameter a The parameter a, is treated as a constant in this model because its variation with temperature is negligible [6]. c. Parameter  The parameter  , can be expressed in an isotropic material as [7]