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This study extends the methodologies presented in other study concerned with the modelling and stability analysis of autonomous microgrids. It elaborates on a continuation method for finding the equilibria states through the entire loading range of an autonomous microgrid. The continuation method is based on the conventional continuation power flow (CPF) employed in the analysis of large power systems. However, the dissimilarities between conventional, simplified models of large power systems employed in CPF and those of detailed dynamics employed in microgrids make it necessary to reinterpret the CPF methodology. The methodology followed employs modelling procedures of microgrids previously published so as to build the Jacobians required by the predictor step. The procedure is quite expeditious, speeding up the solutions. The study also discusses revisions conducted on the CPF to warrant convergence of the corrector step to the particular case of islanded microgrids.