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Conventional droop-based techniques have widely been used in controlling Voltage Source Inverter (VSI) based on distributed generation units within a Micro-Grid (MG). Despite the simplicity and high reliability of the controller, the low-inertia nature of VSIs threatens the system stability against probable disturbances. Thus, from the stability viewpoint, it is essential to carefully monitor the system operating point to determine the stable region of the parameters affecting the micro-grid stability. To this end, a complete dynamic model for an inverter-based micro-grid has been derived. According to this model, states affecting the dominant eigenvalues of the system are identified using eigenvalues analysis and modal analysis. Then, bifurcation theory is used to predict the parameter stability margin and identify the type of bifurcation. In this paper, by introducing a bifurcation index, the appropriate virtual impedance X/R ratio is selected from the viewpoint of both small-signal analysis and bifurcation analysis. Finally, a multi-objective optimization framework is presented to prevent such a problem in parallel to other operational goals. [ABSTRACT FROM AUTHOR]