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This paper proposes an algorithm for designing a fixed shunt capacitive compensator to improve first swing stability margin of a micro-grid including synchronous machine-based distributed generators (SMDGs). The notion of trajectory sensitivity analysis is used to determine the sensitivity of the SMDGs' relative rotor angles and velocities with respect to the compensator susceptance. For a given fault contingency, the minimum required susceptance and compensator location are determined to maintain the first swing stability of SMDGs. The proposed methodology can be used for a micro-grid with an arbitrary number of SMDGs, various fault scenarios, and both grid-connected and autonomous (islanded) modes of operation. The proposed algorithm is verified using time-domain simulation of a modified benchmark system of the IEEE standard 399-1997.