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Searching for Frontiers in Contemporary Eddy Current Model Based Hysteresis Loss Modelling of Superconductors

Research output: Book/ReportDoctoral thesisCollection of Articles


Original languageEnglish
PublisherTampere University of Technology
Number of pages97
ISBN (Electronic)978-952-15-3352-5
ISBN (Print)978-952-15-3334-1
Publication statusPublished - 1 Sep 2014
Publication typeG5 Doctoral dissertation (article)

Publication series

NameTampere University of Technology. Publication
PublisherTampere University of Technology
ISSN (Print)1459-2045


Alternating current (AC) or magnetic field leads to heat generation in otherwise lossless superconducting materials. Such heat generation is called AC loss. AC loss of special type that occurs in the superconducting material itself, and not in the normal-conducting parts of the superconducting wire is called hysteresis loss. Hysteresis loss is a restricting factor for the feasibility of many superconducting applications, and hence, having reliable and efficient models for predicting hysteresis losses in devices is crucial for the design process. In this thesis, we first introduce the readers to the mathematical structures that are essential for simulating AC losses. The level of abstraction deviates from what is typical in this field, but it allows us to present the models and formulations we use in a structured manner and naturally program simulation tools, which are independent of the dimension of the modelling domain. We also discuss the background of the research by presenting important aspects of our research philosophy and the framework inside which the research in this field is conducted. Then, we briefly present two formulations implemented in our AC loss simulation tool, the so called H-formulation and the so called T-Phi-Psi-formulation, and compare their properties through simulations. The latter of the formulations exploits the topology of the modelling domain to reduce the number of required equations, and it is superior to the former in terms of running times of the simulations. Furthermore, we discuss the properties of two widely used models, the critical state model and the eddy current model, through particular case studies of superconductors under direct current bias and an alternating magnetic field. Neither one of the models is fully able to reflect the intrinsic properties of high-temperature superconductors. Finally, the possibilities of our simulation tool are investigated: we study the potential of the tool in question to yield predictions of multifilamentary twisted superconductors with partially coupled filaments in external magnetic field in two dimensions. We present a simple algorithm for this, and the obtained simulation results show good agreement with results of three-dimensional simulations.

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