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In this paper, we investigate the stability of an islanded AC microgrid (ImG) composed of Distributed generation units (DGUs), dynamic power lines, and loads. Each DGU is equipped with a local controller to ensure desired voltage and frequency in the ImG. Different from the previous works, we account for the dynamics of RL power lines and consider generic interconnections of loads and DGUs. The stability of the ImG hinges on the passivity of all components with specific input-output pairs and the properties of the electrical interconnections. For the DGUs, we provide necessary and sufficient conditions for the existence of control gains guaranteeing passivity. In addition, we show that controllers decoupling the direct- and quadrature axis components of the electric variables can never render the DGU passive. Theoretical results are backed by simulation studies.