  The emergence of second-generation high temperature superconducting tapes has
favored the development of large-scale superconductor systems. The mathematical
models for superconductors have evolved from simple analytical models to
complex numerical models. The available analytical models are just capable of
estimating electromagnetic quantities in single wires or small arrays. The
numerical models like the H formulation finite element models are useful for
the analysis of more medium-size systems, but their application in large-scale
systems is problematic due to the excessive cost in terms of memory and the
computation time. Then it is necessary to devise new strategies to tackle this
challenge. The homogenization and the multi-scale approach are methodologies
that have successfully simplified the description of the systems allowing the
study of large-scale systems. Recently, efficient calculations have been
achieved using the T-A formulation. In this manuscript, we analyze the adequate
order of the elements used in the T-A formulation. More importantly, we propose
a series of adaptations to the homogenization and multi-scale methodologies in
order to allow their implementation to the T-A formulation models. The proposed
strategies are validated by means of comparing them with the H reference model
of a racetrack coil. The computation time and memory demand are substantially
reduced up to a point that makes it possible to perform real-time simulations
for slow ramping cycles. At the same time the comparison demonstrates a very
good agreement with respect to the reference model, both at a local and global
level, is achieved.
