CDS Seminar: Synchronization of Power Networks and Non-uniform Kuramoto Oscillators

Professor Francesco Bullo, Department of Mechanical Engineering, University of California at Santa Barbara

ABSTRACT: Motivated by recent interest for multi-agent systems and smart power grid architectures, we discuss the synchronization problem for the network-reduced model of a power system with non-trivial transfer conductances.  Our key insight is to exploit the relationship between the power network model and a first-order model of coupled oscillators. Assuming overdamped generators (possibly due to local excitation controllers), a singular perturbation analysis shows the equivalence between the classic swing equations and a non-uniform Kuramoto oscillator model. Here, non-uniform Kuramoto oscillators are characterized by multiple time constants, non-homogeneous coupling, and non-uniform phase shifts. 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 standard Kuramoto model. Combining our singular perturbation and Kuramoto analyses, we derive concise and purely algebraic conditions that relate synchronization and transient stability of a power network to the underlying system parameters and initial conditions.    

Joint work with: Florian Dorfler
http://motion.me.ucsb.edu


Francesco Bullo received the Laurea degree in Electrical Engineering from the University of Padova in 1994, and the Ph.D. degree in Control and Dynamical Systems from the California Institute of Technology in 1999. From 1998 to 2004, he was affiliated with the Coordinated Science Laboratory at the University of Illinois at Urbana-Champaign. He is currently a Professor with the Mechanical Engineering Department at the University of California, Santa Barbara.  His students' papers were finalists for the Best Student Paper Award at the IEEE Conference on Decision and Control (2002, 2005, 2007), and the American Control Conference (2005, 2006, 2010).  He is the coauthor of the book "Geometric Control of Mechanical Systems" (Springer, 2004) and of the book "Distributed Control of Robotic Networks" (Princeton, 2009).  His main research interest is multi-agent networks with application to robotic coordination, distributed computing and power networks. Other interests include vehicle routing, geometric control, and motion planning problems.