Synchronization stability of lossy and uncertain power grids

Direct energy methods have been extensively developed for the transient stability analysis and contingency screening of power grids. However, there is no analytical energy functions proposed for power grids with losses, which are normal in practice. This paper applies the recently introduced Lyapunov Functions Family approach to the certification of synchronization stability for lossy power grids. This technique does not rely on the global decreasing of the Lyapunov function as in the direct energy methods, and thus is possible to deal with the lossy power grids. We show that this approach is also applicable to uncertain power grids where the stable equilibrium is unknown due to possible uncertainties in system parameters. We formulate this new control problem and introduce techniques to certify the robust stability of a given initial state with respect to a set of equilibria.