The ongoing Energy Transition in many regions of the world creates changes in the patterns of consumption and production, and of power flows on the electrical network. Understanding the stability characteristics of the electrical distribution and transport networks is then of major importance nowadays to ensure a secure supply of electricity.
We investigate the stability properties of electrical networks, based on models of coupled oscillators. Such models are simplifications of the Swing Equations able to capture complex synchronization phenomena.
We identify and characterize the various synchronous states of a given system. The number of such synchronous states strongly depends on the number and length of cycles in the network [Del16,Del17a]. We identify mechanisms leading to transition from a synchronous state to another. Some topological changes such as lines openings and/or closings might bring the system to undesirable synchronous states [Col16]. Noisy power injections can as well bring the system to a new synchronous state on the long run [Tyl18].