The utilization of distributed generation (DG) in Microgrids has posed challenges in modeling and operation and has been resolved with power electronic-based interfacing inverters and associated controllers. The inverter controller in both transient and steady states is of paramount importance, as the stability of Microgrid in grid-connected or islanded mode is dependent on inverter control. Again, the type of the network whether low-voltage or high-voltage distribution sector is of prime importance. In high-voltage network, the reactance/resistance ratio is high and hence no issue of decoupling. But in low-voltage networks as this ratio is low and decoupling is an issue. Normally, the Microgrid is located nearer to load centers. Microgrids are active networks with bi-directional current flow. This research work consists of modeling the Microgrid in a transient state, with a special focus on the study of dynamic and static loads pattern in islanded mode. This chapter presents adoptive control of inverter in an islanded Microgrid. A special focus is given to the state space modeling of all the components of the network and then developing linearized models. The sinusoidal time-varying quantities have been transformed into park transformation, to mitigate decoupling.