Basin stability of the Kuramoto-like model in small networks

Power system stability is quantified as the ability to regain an equilibrium state after being subjected to perturbations. We start by investigating the global basin stability of a single machine bus-bar system and then extend it to two and four oscillators. We calculate the basin stability of the stable fixed point over the whole parameter space, in which different parameter combinations give rise to a stable fixed point and/or a stable limit cycle depending crucially on initial conditions. A governing equation for the limit cycle of the one-machine infinite bus system is derived analytically and these results are found to be in good agreement with numerical simulations.