  The modeling and analysis of superconducting coils is an essential task in
the design stage of most devices based on high-temperature superconductors
(HTS). These calculations allow verifying basic estimations and assumptions,
proposing improvements, and computing quantities that are not easy to calculate
with an analytical approach. For instance, the estimation of losses in HTS is
fundamental during the design stage since losses can strongly influence the
cooling system requirements and operating temperature. Typically, 2D finite
element analysis is used to calculate AC losses in HTS, due to the lack of
analytical solutions that can accurately represent complex operating conditions
such as AC transport current and AC external applied magnetic field in coils.
These 2D models are usually a representation of an infinitely long arrangement.
Therefore, they cannot be used to analyze end effects and complex 3D
configurations. In this publication, we use the homogenization of the T-A
formulation in 3D for the analysis of superconducting coils with complex
geometries where a 2D approach can not provide accurate analyses and
verification of assumptions. The modeling methodology allows an easier
implementation in commercial software (COMSOL Multiphysics) in comparison with
the currently available 3D H homogenization, despite the complexity of the
geometry. This methodology is first validated with a racetrack coil (benchmark
case) by comparing the results with the well-established H formulation. Then,
the electromagnetic behavior of coils with more complex geometries is analyzed.
