This paper investigates the voltage and phase dynamics of a low inertia inverter based Microgrid in islanded operation. In such case, the network is less robust to disturbances due to the lack of associated inertia within an inverter. In islanded operation the assumption of a stiff grid is no longer valid and the voltage and phase adjustment based on conventional droop control have a resulting effect on the power flows throughout the network where voltage and frequency stability of the network

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... ay be compromised. Other approaches neglect the network dynamics when there are power imbalances in the system and how each node is affected and if the resulting increase in demand can be met with the available generation. This paper uses the fact that the phase dynamics of coupled inverters that employ droop control closely resemble the phase dynamics proposed by the Kuramoto model. Using this model allows the network stability to be analysed under the true nonlinear operation. We find through the strong coupling impedance of the primary distribution transmission lines and the implementation of robust droop control provides an appropriate means for rural and suburban neighbourhoods to operate independently.