Threshold stability of the synchronous mode in a power grid with hub cluster topology

The main purpose of this paper is to investigate the dynamics of the power grid model with hub cluster topology based on the Kuramoto equations with inertia. It is essential to study the stability of synchronous grid operation mode and to find conditions of its global stability. The conditions that ensure establishment of the synchronous mode instead of coexisting asynchronous ones are considered. Methods. In this paper we use numerical modelling of different grid operation modes. Also we use an approach based on the second Lyapunov method, which allows to give an estimate of the area of safe perturbations that do not violate the synchronous mode. Results. Various power grid operation modes and boundaries of their existence in the parameter space are considered. An approach allowing to estimate the magnitude of safe disturbances that do not violate the synchronous mode, is described. Conclusion. The paper considers a power grid model with hub cluster topology. For hub-clusters of three and four elements, their parameter spaces are partitioned into areas corresponding to different operation modes. In particular, parameter areas with global asymptotic stability of synchronous modes that is with trouble-free operations under any initial conditions has been identified. To characterize the modes of hub clusters outside the areas of global asymptotic stability, estimates of the areas of safe perturbations that do not violate the synchronous grid operation mode is given