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.
