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• Interlaminar faults cause additional losses in magnetic cores. • Fractional derivative operators are used to model these additional losses. • The magnetic core is represented as an equivalent thick lamination. • A pseudo-conductivity is introduced to account for these additional losses. Stacks of grain-oriented silicon steel (GO FeSi) laminations play a crucial role as magnetic cores of power transformers. These cores undergo degradation over time due to corrosion, thermal cycles, etc. Geometrical abnormalities and residual stress from manufacturing processes exacerbate these degradation processes. Edge burrs can form around cut edges and lead to InterLaminar Faults (ILFs). In a recent work, we described an innovative method for simulating dynamical GO FeSi lamination hysteresis cycles. This method can be applied without any change to a stack of electrically isolated laminations, like in a magnetic core. It is especially easy when the working conditions impose a homogeneous behavior (B-imposed conditions). The simulation technique combines the resolution of the magnetic diffusion equation and a fractional differential equation as material law, yielding excellent simulation results across a broad frequency range with only two parameters accounting for the dynamic contribution. This new article outlines the successful extension of this simulation method to consider ILFs and predict their impact on the performances. For this, lamination stacks were initially simulated under full short-circuit conditions. Then, we used linear combinations between responses from these stacks and flawless ones. The simulation successfully reproduced the experimental data obtained for one or three aligned ILFs on several conditions. Then it was used to predict the behavior of additional aligned ILFs and/or different numbers of laminations in the simulated stack. [ABSTRACT FROM AUTHOR]

Mechanical characterization of electrical steels in an attempt to predict component fatigue has drawn more and more attention to magneto-mechanical coupling in ferromagnetic materials. In this paper, experimental evidence on the magneto-mechanical coupling of a thin Fe-Ni50 sheet subject to multiaxial stress due to electromagnetic peening-induced residual stresses is presented. A comprehensive model of the stress-dependent magnetostriction is validated using the Jiles–Atherton–Sablik (JAS) model for scalar ferromagnetic hysteresis. The JAS parameters are determined from an optimization algorithm, and the dependence of the model accuracy regarding its own parametrization is analyzed. Good correlation of experimentation data with the JAS model was obtained upon careful optimization of the model parameters. [ABSTRACT FROM AUTHOR]

Electric steel is widely used for magnetic conversion of electrical energy such as in electric motors and power transformers. Electric steel sheets are cut using mechanical methods (such as punching) during manufacturing. These methods induce local plastic strains, which lead to overall degradation in magnetic performance. Plasticity and magnetic losses are physically related in electrical steel. It is impossible to measure the magnetic losses on the production line using standard methods. Non-destructive testing (NDT) based on magnetization mechanisms is a promising alternative, giving access to local plastic strains and indirectly to local magnetic losses. In this study, a setup was designed to stimulate the magnetization mechanisms separately while maintaining the same experimental conditions. The magnetization processes related to the domain wall kinetics were revealed to be more correlated to plastic strain. The magnetic incremental permeability hysteresis area and maximal value, and the coercivity associated with Barkhausen noise were found to be the best plastic strain indicators. Additional tests in an NDT context confirmed the correlations, the equal applicability of the proposed indicators, and their viability in predicting static hysteresis loss. [ABSTRACT FROM AUTHOR]

• Fractional derivative methods for the magnetic core loss simulation are reviewed. • Lump methods like STL are faster but unable access to local information. • The physical meaning of the fractional diffusion equation is questionable. • An original combination diffusion equation/fractional material law is proposed. The core losses prediction in laminated magnetic circuits has generated relentless scientific research efforts. In this domain, the almost forty years old Statistical Theory of Losses (STL) is still prevailing. Modern electrical energy conversion exposes laminated magnetic circuits to higher frequencies and larger excitation fields. STL, which requires a full flux penetration, poorly considered these intense stimuli. Recent studies proposed upgrading STL by modifying the classical eddy current loss term using fractional derivative operators. Excellent predictions were observed, but the lumped aspect inherent to STL means working with averaged quantities which constitutes a limitation. Alternatively, local predictions and good simulation trajectories were obtained for the frequency dependence of hysteresis by replacing the classic magnetic diffusion equation with a fractional one. Still, the physical origin of the fractional diffusion equation remains questionable. In the light of these results, we propose in this new study to review the use of the fractional derivative operators for the core losses prediction. We eventually revealed an alternative way to combine the classic diffusion equation to a fractional material law, leading to the ultimate fractional method, with physical fundaments, few parameters, and accurate results on significant frequency bandwidths. [ABSTRACT FROM AUTHOR]

• Inductance spectroscopy (IS) has been used to characterize electrical steel sheets. • Combined with simulations, IS can help predict the hysteresis frequency dependency. • The ferroelectric Cole–Cole model can be used to model IS. • Low- and high-amplitude dynamic behaviors were simulated using the same parameters. Energy conversion is essential to meeting sustainable energy needs. Higher frequencies impart enhanced efficiency. Standard magnetic characterization methods have not been designed for these working conditions, and manufacturers seek alternative solutions. Inductance spectroscopy (IS), which is easy to implement in a production line, relies on impedance measurements during frequency sweeps. IS gives access to dynamic behaviors. Combined with dedicated simulation methods, IS enables parameters that are useful for predicting the hysteresis cycle frequency dependence and the related magnetic losses to be set. We applied IS to oriented grains of electrical steels. We established a correspondence between a lumped model developed to simulate hysteresis cycles and the magnetic version of the Cole–Cole ferroelectric method for IS. We obtained good comparisons with experimental results on large frequency bandwidths for both models and with the same combination of dynamic parameters. We established the uniformity of the dynamic behavior, such as the possibility to characterize this behavior by IS. 1 1 GO: oriented grains; ImS: impedance spectroscopy; IS: inductance spectroscopy; RD: rolling direction; STL: statistical theory of losses; TD: transverse direction. [ABSTRACT FROM AUTHOR]

• Magnetic behaviors are simulated under alternating and rotational magnetization. • The Bergqvist dry-friction model and the multiscale model are combined. • Predictions of the behavior under high amplitude rotating magnetization are obtained. • Highly anisotropic FeSi Go electrical steel is simulated and characterized. Vector quantities and tensorial properties rule the magnetization mechanisms in ferromagnetic materials. Every ferromagnetic material is anisotropic to some degree in its magnetic response, so this anisotropy has to be considered for a general model. In this study, a multiscale approach based on a statistical description of the magnetic domain distribution and the knowledge of the crystallographic texture is used to predict the anhysteretic behavior along an arbitrary space direction. Combined with the vector Bergqvist dry-friction hysteresis model, qualitatively reliable simulation results are obtained under alternating and rotational magnetization. FeSi 3% grain-oriented (FeSi GO) electrical steel is chosen as study material: FeSi GO are widespread so that extensive data are available and strongly anisotropic, forcing the model toward the "worst-case" scenario from the viewpoint of anisotropy. Moreover, under high excitation of rotational magnetization, losses drop due to the disappearance of the magnetic domains. This behavior is represented correctly by the proposed simulation method. In such conditions, the magnetization behavior is led mainly by the anhysteretic behavior, strengthening the predictive ability of the proposed model. In this manuscript, comparisons between simulations and measurements under many amplitudes of alternating and rotational magnetization for different levels of imposed excitation or magnetization are provided and used to validate the simulation method. [ABSTRACT FROM AUTHOR]

• The low-frequency dependence of a ferromagnetic material is investigated. • Standard characterization methods are limited in the low-frequency range. • Magnetic incremental permeability is used to observe the low-frequency dependence. • The quasi-static threshold estimation is refined. The frequency dependence of ferromagnetic hysteresis and the related core losses is still an open question. From scaling relations up to space discretized and simultaneous contributions resolutions, different levels of accuracy in the estimation of these losses can be reached. Below a given frequency known as the quasi-static threshold, it is well admitted that the hysteresis cycle remains unchanged. A precise evaluation of this threshold is fundamental to simulate and evaluate precisely the magnetization behaviors under higher frequencies. But this estimation is complex, especially through the unique observation of the hysteresis cycles and because of instrumentation limitations. In this manuscript, we propose an alternative and simple method to precisely refine this threshold's estimation. By using an alternative magnetic signature known as the magnetic incremental permeability butterfly loop ( μ IP _ (H)), improvements are proposed in observing the very low-frequency magnetization behaviors and assessing the quasi-static threshold. This work constitutes a leap forward in understanding the magnetic low-frequency behaviors of laminated electric steel sheets. [ABSTRACT FROM AUTHOR]