  The emergence of second-generation high temperature superconducting 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 real devices in real
applications. The numerical models based on finite element method using the H
formulation of the Maxwells 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. Then 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 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 HTS
large-scale systems under slow ramping cycles of practical importance on
personal computers.
