Transient stability of a power grid via robust mean-field games

The transient stability of a power grid characterized by regional aggregations is studied via robust mean-field games. The model involves a set of coupled Hamilton-Jacobi-Bellman-Isaacs equations and Fokker-Planck-Kolmogorov equations. The former describe the behavior of each single machine, while the latter model the population behavior in aggregate form. The model sheds light on a multi-scale phenomenon including a fast synchronization within the same population and slow inter-cluster oscillations between geographically sparse grids.