Efficient T-A-ϕ formulation applied to the modeling of 3D HTS devices

Abstract

Abstract

Abstract The increasing demand for compact, high-efficiency energy systems has elevated the importance of accurate and computationally efficient models for high-temperature superconducting (HTS) devices, particularly in the context of intricate 3D geometries. Traditional formulations such as the T-A formulation, while accurate, often involve high computational costs in large-scale simulations. In the present work, a 3D version of the T-A-ϕ formulation is presented to simulate complex 3D HTS systems, coupling the current vector potential T, the magnetic vector potential A, and the magnetic scalar potential ϕ in a domain-decomposed framework. The method is validated using racetrack and non-planar coils, demonstrating excellent agreement with the standard T-A formulation in terms of instantaneous AC losses, with a coefficient of determination R² larger than 0.9993 and a maximum relative error below 4%. The maximum errors in the current density normalized to the field-dependent critical current density are below 15% for the racetrack coil and 1% for the non-planar coil, while reducing the simulation time by 36% for the racetrack coil and by about 41.5% for the non-planar coil. These results highlight the ability of the 3D T-A-ϕ method to provide reliable solutions with significant performance gains, making it a promising tool for simulating HTS devices with convoluted 3D geometries under realistic operating conditions.