Real-time simulation of large-scale HTS systems: multi-scale and homogeneous models using T-A formulation

The emergence of second-generation high temperature superconducting (HTS) tapes has favored the development of large-scale superconductor systems. The mathematical models capable of estimating electromagnetic quantities in superconductors have evolved from simple analytical models to complex numerical models. The available analytical models are limited to the analysis of single wires or infinite arrays that, in general, do not represent actual devices in real applications. The numerical models based on the finite element method using the H formulation of Maxwell's equations are useful for the analysis of medium-size systems, but their application in large-scale systems is problematic due to the excessive computational cost in terms of memory and computation time. Therefore it is necessary to devise new strategies to make the computation more efficient. The homogenization and the multi-scale methods have successfully simplified the description of the systems allowing the study of large-scale systems. Also, efficient calculations have been recently achieved using the T-A formulation. In the present work, we propose a series of adaptations to the multi-scale and homogenization methods so that they can be efficiently used in conjunction with the T-A formulation to compute the distribution of current density and hysteresis losses in the superconducting layer of superconducting tapes. The computation time and the amount of memory are substantially reduced up to a point that it is possible to achieve real-time simulations of large-scale HTS systems under slow ramping cycles of practical importance on personal computers.