Abstract This paper presents the optimal protection coordination (OPC) to grid-connected and islanded micro-grid (MG) consisting renewable energy sources (RESs), and energy storage system (ESS). The proposed approach considers objective function as minimizing the total operation time of the dual setting overcurrent relays (DSORs) in primary and backup protection mode. Problem constraints are the regulation parameters limits of the DSROs, sizing limit of FCLs and also the coordination time interval (CTI) inequality. MG includes generally RESs and ESS, hence, this problem needs to the daily optimal operation results of MG in both grid-connected and islanded modes to obtain the network variables before the fault occurrence. Therefore, it is minimized the MG operation and load shedding costs of islanded MG while it is constrained to MG optimal power flow equation in the presence of RESs and ESS. The proposed OPC includes non-linear model, hence, this paper uses the crow search algorithm (CSA) to obtain a reliable and optimal solution for this formulation. Finally, this strategy is implemented on the 9-bus and 32-bus MGs, thus, it can obtain the high quick protective solution for these MGs by selecting optimal regulation parameters and sizing to DSORs and FCLs, respectively, according to numerical results.