Traditional methods of determining steady-state power system operating points are not applicable to droop-controlled microgrids. The conditions of an islanded microgrid, including the absence of a slack bus and inherent coupling of complex power, frequency, and bus voltage, require new tools to properly analyze. In this study, a method of determining the operating points of droop-controlled microgrids is proposed. The procedure is similar in form and function to a traditional power flow analysis, but is performed in the synchronous reference frame to ensure compatibility with conventional inverter models. A quasi-Newton iterative process is used to solve the nonlinear equations pertaining to each generation unit and load bus. The method provides a structured approach to determining the consistent system-level linearization points required for large-scale microgrid studies. Grid-forming, grid-feeding, and grid-supporting generation units are supported, along with both constant impedance and constant power loads. The method is validated in hardware experiments, simulations, and comparisons to results of existing power flow algorithms. As an example of the method's potential applications, a procedure for determining droop constants that ensure equal Q sharing between generation units is constructed around the proposed method's basic functionality.