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The emergence of second-generation high temperature superconducting tapes hasfavored the development of large-scale superconductor systems. The mathematicalmodels for superconductors have evolved from simple analytical models tocomplex numerical models. The available analytical models are just capable ofestimating electromagnetic quantities in single wires or small arrays. Thenumerical models like the H formulation finite element models are useful forthe analysis of more medium-size systems, but their application in large-scalesystems is problematic due to the excessive cost in terms of memory and thecomputation time. Then it is necessary to devise new strategies to tackle thischallenge. The homogenization and the multi-scale approach are methodologiesthat have successfully simplified the description of the systems allowing thestudy of large-scale systems. Recently, efficient calculations have beenachieved using the T-A formulation. In this manuscript, we analyze the adequateorder of the elements used in the T-A formulation. More importantly, we proposea series of adaptations to the homogenization and multi-scale methodologies inorder to allow their implementation to the T-A formulation models. The proposedstrategies are validated by means of comparing them with the H reference modelof a racetrack coil. The computation time and memory demand are substantiallyreduced up to a point that makes it possible to perform real-time simulationsfor slow ramping cycles. At the same time the comparison demonstrates a verygood agreement with respect to the reference model, both at a local and globallevel, is achieved.

T-A homogenized and multi-scale models with real-time simulation capabilities for large-scale HTS systems