Applied Math Seminar: Shriya Nagpal (Pitzer College)

Title: Designing Robust Networks of Coupled Phase Oscillators with Applications to the High-Voltage Electric Grid

Abstract: A network is any collection of objects, called nodes, in which some pairs of these objects are connected by links, called edges. In a network of coupled phase-oscillators, each node represents a phase-angle (or an angle with periodicity) whose long-term dynamics is determined by a differential equation governed by the node’s connectivity to the rest of the network and the phase-angle’s inherent natural frequency. Networks of coupled phase-oscillators have been of great interest to the scientific community in the last decade because of their ability to model a broad array of applications including circadian rhythms, flashing fireflies, and high voltage electric grids. In many of these applications, synchronization is a coordinated behavior that emerges over time and is of interest to optimize for. To this end, we introduce a mathematical framework for designing robust networks of coupled phase-oscillators. Robustness, in this context, denotes the ability of the phase-oscillators to maintain synchronized behavior despite minor system perturbations. We then apply this mathematical framework to address challenges impacting the functionality of high voltage electric grids, particularly in the context of integrating renewable energy.