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Microgrids can be operated either grid-connected to reduce system losses and for peak shaving or islanded to increase reliability and provide backup power during utility outage. Such dual configuration capability imposes challenges on the design of the protection system. Fault current magnitudes will vary depending on the microgrid operating mode. In this paper, a microgrid protection scheme that relies on optimally sizing fault current limiters and optimally setting directional overcurrent relays is proposed. The protection scheme is optimally designed taking into account both modes of operation (grid-connected and islanded). The problem has been formulated as a constrained nonlinear programming problem and is solved using the genetic algorithm with the static penalty constraint-handling technique. The proposed approach is tested on two medium-voltage networks: a typical radial distribution system and on the IEEE 30-bus looped power distribution system equipped with directly connected conventional synchronous generators.