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This study extracts effective loading constraints for synchronous machine-based distributed generators (SMDGs) in a micro-grid to ensure their post-fault first swing stability. The notion of trajectory sensitivity is used to determine the sensitivity of the SMDGs rotor angles and velocities with respect to the mechanical input power. Then, appropriate loading constraints for SMDGs are calculated for a set of pre-specified faults. The proposed methodology can be used for a micro-grid with an arbitrary number of SMDGs, under various fault scenarios, as well as both grid-connected and autonomous (islanded) modes of operation. The proposed methodology is verified using time-domain simulation of a modified benchmark system of the IEEE standard 399-1997.