Closed-form determination of fault current limiter (FCL) impedance for symmetrical faults was reported previously using a mathematically rigorous method. In this paper, extensions of the method to asymmetrical faults are presented. Single line-to-ground faults and line-to-line faults are studied. As shown in this paper, although the material corresponding to asymmetric faults use the same basic concepts described before, the different nature of asymmetrical faults and application of symmetrical components theory lead to a different formulation. Also, the graphical representation of asymmetrical faults is as contour plots instead of the circle diagrams for three-phase faults. A three-bus and the IEEE 39-bus systems are used to illustrate the virtues of the method for the proper selection of FCLs impedance. Results demonstrate that the FCL designed, as shown in this paper, works properly for asymmetrical faults. The new formulation and graphical representation for asymmetrical faults are compatible with traditional power system short-circuit analysis software. An example with both symmetrical and asymmetrical faults is presented to illustrate how a full FCL impedance design can be achieved with the method.

中文翻译：

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故障限流器阻抗轨迹图的闭式确定：不对称故障

先前使用数学上严格的方法报告了对称故障的故障限流器 (FCL) 阻抗的闭合形式确定。在本文中，介绍了该方法对不对称故障的扩展。研究了单线对地故障和线对线故障。如本文所示，虽然非对称断层对应的材料使用了与之前描述的相同的基本概念，但非对称断层的不同性质和对称分量理论的应用导致了不同的表述。此外，不对称故障的图形表示是等高线图，而不是三相故障的圆形图。三总线和 IEEE 39 总线系统用于说明正确选择 FCL 阻抗的方法的优点。结果表明，FCL 设计的，如本文所示，适用于不对称故障。非对称故障的新公式和图形表示与传统的电力系统短路分析软件兼容。提供了具有对称和非对称故障的示例，以说明如何使用该方法实现完整的 FCL 阻抗设计。