Efficient numerical models are required for the design of systems with high temperature superconductor (HTS) coils, as fully resolved finite element simulations of individual coated conductors become computationally prohibitive. This work applies the foil conductor model (FCM) to insulated HTS coils using magnetic field conforming h-(full), h-$φ$, and t-$ω$ formulations. The approach replaces individual turns by a homogenized bulk and ensures physically consistent current density distributions in the coils by using additional voltage basis functions in the finite element formulations. The models are verified in 2D axisymmetric and 3D geometries with a pancake coil simulation under AC transport current excitation. All FCM formulations show excellent agreement with reference detailed simulations, with coefficients of determination above 0.99 for instantaneous AC losses. In 3D, the h-$φ$ and especially the t-$ω$ formulation substantially reduce the number of degrees of freedom by using the magnetic scalar potential in non-conducting regions. Scalability is demonstrated with a 3D stack of racetrack coils model with a field- and angle-dependent critical current density. For the stack of racetrack coils, while maintaining accurate loss prediction, the t-$ω$ FCM achieves a speedup factor of 22 and reduces degrees of freedom by 78 % with respect to a detailed reference model.

翻译：针对高温超导（HTS）线圈系统的设计，需要高效的数值模型，因为对单个涂层导体进行完全解析的有限元仿真在计算上变得不可行。本工作将箔导体模型（FCM）应用于绝缘HTS线圈，采用磁场相容的h-（全量）、h-$φ$和t-$ω$公式。该方法用均匀化体替代单个匝，并通过在有限元公式中引入附加电压基函数，确保线圈中电流密度分布的物理一致性。通过盘式线圈在交流传输电流激励下的二维轴对称和三维几何仿真对模型进行了验证。所有FCM公式与参考详细模型均表现出高度一致性，交流损耗瞬态值的决定系数超过0.99。在三维情形下，h-$φ$公式，尤其是t-$ω$公式，通过在非导电区域使用磁标势大幅减少了自由度数量。通过包含场强和角度依赖临界电流密度的三维跑道型线圈堆叠模型验证了可扩展性。对于跑道型线圈堆叠，在保持精确损耗预测的同时，t-$ω$ FCM相对于参考详细模型实现了22倍的加速比，并将自由度减少了78%。