Title: Synchronization and Kron Reduction in Power Networks Speaker: Francesco Bullo http://motion.me.ucsb.edu Joint work with: Florian Dorfler Abstract: We discuss the modelling and synchronization problem for network-reduced and structure-preserving power system models. First, we focus on the network-reduced power system model with non-trivial transfer conductances - the classic swing equations. We exploit the relationship between the network-reduced power system model and a first-order model of coupled oscillators. Extending methods from transient stability, synchronization theory and consensus protocols, we establish sufficient conditions for synchronization of non-uniform Kuramoto oscillators. These conditions reduce to and improve upon previously-available tests for the well-known Kuramoto model. Combining our singular perturbation and Kuramoto analyses, we derive concise and purely algebraic conditions that establish synchronization and transient stability in a network-reduced power system. Second, we analyze the network-reduction process relating the network-reduced and the more detailed structure-preserving power system model. The network reduction process, termed Kron reduction, is characterized by iterative Schur complementation of the admittance matrix. A detailed algebraic and graph-theoretic analysis of the Kron reduction process allows us to extend the synchronization conditions obtained for the network-reduced model to the structure-preserving model. In the end, we are able state one spectral and one resistance-based condition that relate synchronization in a power network to the underlying network state, parameters, and topology.