Module 50: Theoretical Conditions for the Regions of Attraction in Kuramoto Systems

Faculty Contact: Francesco Bullo

Research Areas:


One of the key problems in power systems is “transient stability analysis.” If the system suffers some perturbation—for example, a generator goes offline or a line is cut—then the 60 Hz electricity for which our devices are designed will suddenly drop. The frequencies will then evolve in horribly complex ways until they reach a stable point, hopefully of 60 Hz everywhere in the grid. If some nodes end up far above or far below 60 Hz, then there is a risk of equipment damage and cascading failures in the grid. To avoid this risk, system operators perform transient stability analysis by simulating how the system would respond to possible disturbances; and they deploy generating resources to minimize the likelihood of leaving the 60 Hz equilibrium.

Unfortunately, simulations take a long time to run and are prone to numerical error. Furthermore, it is difficult to use them for planning future control systems to bring in renewables or other smart grid tech. To deal with this, we are working on “direct methods” for transient stability analysis, which provide theoretical conditions for stability (as opposed to the current numerical approaches). Specifically, we are studying the regions of attraction of equilibrium points in first-order and second-order Kuramoto systems. Kuramoto systems are networks of coupled oscillators, which provide a simplified model for power system dynamics. By developing theoretical conditions for the regions of attraction in Kuramoto systems, we can estimate how “bad” of a disturbance a (simplified) power system can handle and still return to its 60 Hz equilibrium… without running any costly simulations.


Active Quarters:

  • Summer 2018: Kevin Smith
  • Fall 2018: Kevin Smith