A comprehensive modular state-space model of a microgrid is developed that handles basic components and loads, as well as inverter-based generation, such as PQ inverter and voltage-source inverter (VSI). Specifically, the developed model is suitable for control design utilizing the nominal set-point values of frequency and voltage of the VSI inverters, and active and reactive power set points of the PQ inverters. The model is also useful for small-signal stability assessment and enhancement. It is shown that when a PQ inverter is added to the system, the low-frequency modes of the power-sharing dynamics drift to new locations and the relative stability is improved. Meanwhile, to preserve the power-sharing stability, a decentralized droop controller of paralleled VSI inverters is designed. Finally, the dynamic model is used to design and implement distributed secondary frequency controllers taking into consideration the characteristics of storage devices. The proposed modeling and control methodologies are demonstrated using an 11 bus microgrid with and without PQ inverters.