On the Applicability of Kuramoto Model to Microgrid Technologies

The synchronisation of coupled Kuramoto oscillators has been widely studied by the mathematics and control systems communities and some recent works investigated the close relationship between the Kuramoto oscillators and the power system networks. This paper presents more in-depth analysis of the application of the Kuramoto model to the microgrid technologies. First, the characteristics of the first-order and second-order Kuramoto models are analysed to find the explicit and implicit conditions, which the power system components must satisfy to achieve the synchronisation. Then the models of different components of microgrid are derived by using the Kuramoto model characteristics. The developed models are applied to a modified WSCC 9-bus test system for stability analysis and is simulated under different scenarios. It can be concluded that the Kuramoto coupled oscillator is not applicable to the distribution level microgrid where the line impedances are mainly resistive, however; if the line impedances are assumed to be inductive, it is applicable.