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This paper investigates the problem of appropriate load sharing in an autonomous microgrid. High gain angle droop control ensures proper load sharing, especially under weak system conditions. However, it has a negative impact on overall stability. Frequency-domain modeling, eigenvalue analysis, and time-domain simulations are used to demonstrate this conflict. A supplementary loop is proposed around a conventional droop control of each DG converter to stabilize the system while using high angle droop gains. Control loops are based on local power measurement and modulation of the d-axis voltage reference of each converter. Coordinated design of supplementary control loops for each DG is formulated as a parameter optimization problem and solved using an evolutionary technique. The supplementary droop control loop is shown to stabilize the system for a range of operating conditions while ensuring satisfactory load sharing.