This paper presents the placement and sizing of the hybrid superconducting fault current limiters (SFCLs) to restore the protection coordination of the distribution system with the synchronous distributed generations (SDGs). Therefore, the normalized objective function considers minimizing the size of the hybrid SFCLs and the total operation time of overcurrent relays (OCRs) for two primary and backup protection models in the fault conditions. This function is selected to achieve the optimal protection coordination (OPC) for the distribution network with SDGs considering low installation cost for SFCLs. Constraints include limits of coordination time interval (CTI), protection coordination restoration (PCR), size of the switches coupled with OCRs, setting parameters of OCRs, and size of the SFCL, and equations concerning the calculation of the fault current flowing through OCRs. This scheme has a nonlinear programming (NLP) framework. Also, the hybrid differential equations (DE) and crow search algorithm (CSA) are utilized to obtain the reliable optimal solution. Finally, the scheme is applied to the standard distribution network, so that the numerical results obtained from various case studies confirm the capability of the suggested strategy in improving the protection coordination of the distribution system with SDGs using the optimal size and location of SFCLs.

本文介绍了混合超导故障限流器 (SFCL) 的位置和尺寸，以恢复配电系统与同步分布式发电 (SDG) 的保护协调。因此，归一化目标函数考虑在故障条件下最小化混合 SFCL 的大小和过流继电器 (OCR) 的总运行时间，用于两个主要和备用保护模型。考虑到 SFCL 的低安装成本，选择此功能是为了实现具有 SDG 的配电网络的最佳保护协调 (OPC)。约束包括协调时间间隔 (CTI)、保护协调恢复 (PCR)、与 OCR 耦合的开关大小、OCR 设置参数和 SFCL 大小的限制，和有关计算流过 OCR 的故障电流的方程。该方案具有非线性规划 (NLP) 框架。此外，利用混合微分方程（DE）和乌鸦搜索算法（CSA）来获得可靠的最优解。最后，将该方案应用于标准配电网络，因此从各种案例研究中获得的数值结果证实了所建议的策略在使用 SFCL 的最佳大小和位置改善配电系统与 SDG 的保护协调方面的能力。