A critical condition for the operation of a power grid network is that its power generators must remain synchronized. Disturbances can, however, prompt desynchronization, which is a process that has been involved in large power outages. In this work we first derive the condition under which the synchronous state of a power grid is stable, and compute the basin stability to quantify the stability of a node to recover its synchronization when perturbed. We also investigate the action of the frequency controller on the improvement of the basin of stability for an elementary network of two nodes, and then we apply random fluctuations of the electrical power to study the effects of Dynamics Demand Control (DDC) on the frequency and synchrony stabilization.
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