Comparison of three eddy current formulations for superconductor hysteresis loss modelling

Abstract

As is well known, the superconductor hysteresis loss modelling problem may be formulated as an eddy current (EC) problem in which the resistivity of the superconducting region is modelled with a power law. We compare three EC formulations suitable for the modelling of superconductor hysteresis losses. Namely, the a–v–j-, T–φ- and h-formulations are discussed. We review these formulations, and through simulation results the properties of these formulations are discussed and their suitabilities for different modelling situations are compared. Special attention is paid to the h-formulation: we investigate the effects of the modelling decisions related to resistivity of the air region in an h-formulation based EC solver. According to the results, these decisions affect the energy distribution of the field solution and may even lead to seemingly contradictory behaviour.