Tracking of Kuramoto oscillators with input saturation and applications in smart grids

The Kuramoto oscillator has been widely studied because it can model biological, social, chemical, and engineering problems. Conditions for frequency synchronization of a network of Kuramoto oscillators have been well established, but it depends on the connectivity of the network and on the natural frequencies. In this work we propose a consensus-based control strategy that forces the network to follow a virtual agent with constant frequency. Besides, we consider that the control input is constrained and we establish the limits of the set of inputs that assure frequency tracking. The results are extended to the smart grid case, where the nodes of a power network are modeled as Kuramoto oscillators that synchronize to a desired frequency using the injection/absorbsion of power according to a consensus based control. We show that our results are feasible when isolated group of nodes are taken into account, and they can be connected or disconnected to the main grid. Finally, the effects of time-varying sampling are analyzed and sampling period independence is demonstrated.