3D Modeling of AC Loss in D-Shaped HTS Coils Using $H$ and $T$-$A$ Formulation-Based Finite Element Methods

The D -shaped coil is employed in the design of the hybrid toroidal magnet for 10 MJ high-temperature superconducting magnetic energy storage (HTS-SMES) to mitigate the huge bending moment on the coil. During the power compensation process of the SMES system, the time-varying currents induce AC losses within the magnet, leading to heating and temperature rise. Excessive temperature rise can result in the magnet experiencing a quench or even damage. Therefore, accurately calculating the AC losses generated by the magnet for HTS-SMES is crucial for the stable operation of the system. Generally, 2D models cannot accurately simulate the complex geometric shapes of superconducting coils with non-axisymmetric properties. This paper applies the \boldmath $H$ -formulation and $T$ - $A$ formulation and their homogeneous method to the 3D finite element method (FEM) models of a D -shaped double-pancake coil (DPC). The effectiveness of the established 3D FEM models has been verified through AC loss measurement experiments on a D -shaped HTS DPC at 77 K temperature. The application strategies of $T$ - $A$ full, $T$ - $A$ homogenization, and $H$ homogenization in the 3D FEM models have been comprehensively compared under different sizes of D -shaped HTS DPCs. Subsequently, the distribution characteristics of AC losses in a D -shaped DPC have been analyzed. The research findings reveal that the distribution of AC losses exhibits non-uniformity along the arc direction of the coil. The difference between the maximum and minimum values in this coil is approximately 15.1% in the \boldmath $H$ homogeneous model and 14.0% in the $T$ - $A$ homogeneous model. This work holds significant guidance for the computational assessment of AC losses in the hybrid toroidal magnet for 10 MJ HTS-SMES.