The Use of Hypergeometric Functions in Hysteresis Modeling

Chwastek, Krzysztof; Herceg, Dejana

doi:10.3390/en13246500

Cited by 4 publications

(4 citation statements)

References 28 publications

(36 reference statements)

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“…A recent contribution [48] which considered a more general transformation based on hypergeometric functions also offered an improved description of minor loops in GO steel. However, to the best of our knowledge, a simple relationship similar to the hyperbolic tangent of a sum/difference of its arguments does not exist for hypergeometric functions.…”

Section: Discussionmentioning

confidence: 99%

The Effective Field in the T(x) Hysteresis Model

et al. 2023

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Hysteresis loops constitute the source of important information for the designers of magnetic circuits in power transformers. The paper focused on the possibility to interpret the phenomenological T(x) model in terms of effective field vs. magnetization dependence. The interdependence of anhysteretic curve and hysteresis loops was emphasized. The concept of the anhysteretic plane introduced at the end of the last century by Sablik and Langman was subject to a tangible interpretation within the hyperbolic model framework. A novel geometric interpretation of the “effective field” related to the concept of affine transformation was introduced. It was shown in the paper that minor hysteresis loops of grain-oriented electrical steel may be described with the proposed formalism.

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Section: Discussionmentioning

confidence: 99%

The Effective Field in the T(x) Hysteresis Model

et al. 2023

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“…Several methods are directly based on the Talukdar-Bailey model. Examples of these are a method using rational fractions based on Rivas [67] by Mukherjee et al [205] and Hypergeometric function by Herceg [206,207]. A similar method was also proposed by Zeinali et al [208].…”

Section: Talukdar-bailey Modelmentioning

confidence: 99%

“…Another generalized alternative to tanh is the Hypergeometric functions studied by Herceg [206,207].…”

Section: Phenomenological Sigmoid Functionsmentioning

confidence: 99%

Review of Hysteresis Models for Magnetic Materials

Mörée

Leijon

2023

Energies

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There are several models for magnetic hysteresis. Their key purposes are to model magnetization curves with a history dependence to achieve hysteresis cycles without a frequency dependence. There are different approaches to handling history dependence. The two main categories are Duhem-type models and Preisach-type models. Duhem models handle it via a simple directional dependence on the flux rate, without a proper memory. While the Preisach type model handles it via memory of the point where the direction of the flux rate is changed. The most common Duhem model is the phenomenological Jiles–Atherton model, with examples of other models including the Coleman–Hodgdon model and the Tellinen model. Examples of Preisach type models are the classical Preisach model and the Prandtl–Ishlinskii model, although there are also many other models with adoptions of a similar history dependence. Hysteresis is by definition rate-independent, and thereby not dependent on the speed of the alternating flux density. An additional rate dependence is still important and often included in many dynamic hysteresis models. The Chua model is common for modeling non-linear dynamic magnetization curves; however, it does not define classical hysteresis. Other similar adoptions also exist that combine hysteresis modeling with eddy current modeling, similar to how frequency dependence is included in core loss modeling. Most models are made for scalar values of alternating fields, but there are also several models with vector generalizations that also consider three-dimensional directions.

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“…The modeling of non-linearity and hysteresis in magnetic materials is achieved with different deterministic approaches, both at the micromagnetic and macromagnetic levels, but also with stochastic approaches based on specific applications of artificial intelligence [17]. The determination of distribution of magnetic field inside an inductor core is also possible by using numerical tools based on finite element methods [18,19].…”

Section: Introductionmentioning

confidence: 99%

Influence of Non-Linearity in Losses Estimation of Magnetic Components for DC-DC Converters

et al. 2021

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In this paper, the problem of estimating the core losses for inductive components is addressed. A novel methodology is applied to estimate the core losses of an inductor in a DC-DC converter in the time-domain. The methodology addresses both the non-linearity and dynamic behavior of the core magnetic material and the non-uniformity of the field distribution for the device geometry. The methodology is natively implemented using the LTSpice simulation environment and can be used to include an accurate behavioral model of the magnetic devices in a more complex lumped circuit. The methodology is compared against classic estimation techniques such as Steinmetz Equation and the improved Generalized Steinmetz Equation. The validation is performed on a practical DC-DC Buck converter, which was utilized to experimentally verify the results derived by a model suitable to estimate the inductor losses. Both simulation and experimental test confirm the accuracy of the proposed methodology. Thus, the proposed technique can be flexibly used both for direct core loss estimation and the realization of a subsystem able to simulate the realistic behavior of an inductor within a more complex lumped circuit.

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The Use of Hypergeometric Functions in Hysteresis Modeling

Cited by 4 publications

References 28 publications

The Effective Field in the T(x) Hysteresis Model

The Effective Field in the T(x) Hysteresis Model

Review of Hysteresis Models for Magnetic Materials

Influence of Non-Linearity in Losses Estimation of Magnetic Components for DC-DC Converters

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