A Framework Leveraging Asymmetry for Synchronization Stability in Networks of Coupled Dynamical Systems

Northwestern University, Evanston IL

Investigators

Abstract

The function of numerous natural and engineered systems depends on the stable synchronization of networks of coupled dynamical entities. An outstanding case is that of power-grid networks, which rely on synchronization among power generators to operate. In the mathematical modeling of such systems, the networks are usually represented by the dynamical entities that define the nodes and the network structure that defines the interactions among nodes. Because contemporary research in network science emphasizes the role of interactions in giving rise to emergent behavior, existing studies have focused mainly on the optimization of the network structure for given nodes. Recent research has shown, however, that in many situations it is more desirable to optimize the node parameters, and this is a problem for which adequate methods do not currently exist. This project will develop and apply mathematical and computational methods to improve synchronization stability of relevance to the U.S. power-grid network by optimizing node parameters. Successful completion of the planned research is expected to lead to design and operation principles that can improve power-grid stability. The project will also provide interdisciplinary research training to one graduate student and several undergraduate students. The project builds on the recent observation that explicit symmetry breaking can often be used to stabilize synchronization states in network systems. Implementation of this idea requires solving a high-dimensional non-convex optimization problem that cannot be satisfactorily addressed by existing linear methods. The project will develop and apply a rigorous nonlinear method tailored to address this class of optimization problems in power-grid networks. The project consists of four parts: 1) the development of a nonlinear, second-order theory, 2) the development of an iterative numerical algorithm implementing the theory, 3) the application of the resulting methods to the U.S. power-grid network, and 4) the application of the methods to study conditions under which explicit symmetry breaking can benefit stability. The expected outcomes will lead to new opportunities for the stabilization of desired synchronous states and an improved understanding of the factors that contribute to stability. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.