Differentiation and power loss computation of classical Preisach model

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In certain applications of hysteresis, the differentiated output is of interest rather than the output described by a model of hysteresis. Instead of numerical backward differentiation, a direct differentiation of the classical Preisach model is presented here. This gives rise to five cases depending on the hysteresis history. An energy state for the hysteresis model is defined in the paper. The power loss can then be computed by differentiating the energy state, whereby the same five cases occur. Moreover, the computation time of the energy loss is considerably reduced when applying numerical integration of this power loss, compared to methods in the literature. The derived expressions have been employed in simulations of an equivalent circuit for superconductors using standard simulation tools.