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.