The short-circuit levels have increased considerably in transmission and distribution systems in the last years. Fault current limiter (FCL) devices are a potential solution to this problem. Among several FCL topologies, this group has good experience in the use of superconducting fault current limiters (SFCL) to reduce the electrical current during short-circuits. The literature also presents studies of the saturated iron core superconducting fault current limiter (SIC-SFCL) topology employing mathematical modeling and prototypes design. Some of them have shown promising results, including the construction of pilot prototypes in medium and high voltage substations. The SIC-SFCL simulation studies presented optimal topologies that reduce the amount of ferromagnetic material used in the core and represent well the behavior of this limiter. The finite element method and the finite element analysis are suitable to model the SIC-SFCL. However, a more detailed study focusing on the optimization of the DC bias superconducting coil of the SIC-SFCL has not been presented in the literature yet. In this context, this work proposes a multi-objective optimization method using the Nelder–Mead algorithm to find an optimal geometry for the superconducting coil. In this optimization, the objectives functions are: to maximize the critical current density in the high-temperature superconductor (HTS), minimize the voltage drop in the copper winding, minimize the current through the DC biased superconducting winding, and minimize the price of the HTS superconducting winding. Before implementing the multi-objective optimization algorithm, we have tested a non-superconducting saturated iron core prototype and used the results to validate the simulation models. After that, we have replaced the DC copper winding with an HTS coil in the simulations and initiate the optimization process. Results show that constructing the DC bias superconducting coil using the minimum possible fill factor might not be the best choice.

近年来，输配电系统中的短路水平已大大提高。故障电流限制器（FCL）设备是此问题的潜在解决方案。在几种FCL拓扑中，该组在使用超导故障限流器（SFCL）来减少短路期间的电流方面具有丰富的经验。文献还提出了使用数学建模和原型设计对饱和铁芯超导故障限流器（SIC-SFCL）拓扑进行的研究。其中一些已经显示出令人鼓舞的结果，包括在中高压变电站中建造试点原型。SIC-SFCL仿真研究提出了最佳拓扑，可以减少铁心中使用的铁磁材料的数量，并很好地表现了这种限制器的行为。有限元方法和有限元分析适合于对SIC-SFCL进行建模。但是，目前还没有针对SIC-SFCL的直流偏置超导线圈的优化进行更详细的研究。在这种情况下，这项工作提出了一种使用Nelder-Mead算法的多目标优化方法，以找到超导线圈的最佳几何形状。在此优化中，目标功能是：最大化高温超导体（HTS）中的临界电流密度，最小化铜绕组中的电压降，最小化通过直流偏置超导绕组的电流，并最小化其价格。 HTS超导绕组。在实施多目标优化算法之前，我们已经测试了一个非超导饱和铁心原型，并使用结果验证了仿真模型。之后，我们在仿真中将直流铜绕组替换为HTS线圈，并启动优化过程。结果表明，使用最小可能的填充因子构造直流偏置超导线圈可能不是最佳选择。