Abstract: Prior research has shown that spectral decomposition of the reduced power flow Jacobian (RPFJ) can yield participation factors that describe the extent to which particular buses contribute to particular spectral components of a power system. Research has also shown that both variance and autocorrelation of time series voltage data tend to increase as a power system with stochastically fluctuating loads approaches certain critical transitions. This paper presents evidence suggesting that a system's participation factors predict the relative bus voltage variance values for all nodes in a system. As a result, these participation factors can be used to filter, weight, and combine real time PMU data from various locations dispersed throughout a power network in order to develop coherent measures of global voltage stability. This paper first describes the method of computing the participation factors. Next, two potential uses of the participation factors are given: (1) predicting the relative bus voltage variance magnitudes, and (2) locating generators at which the autocorrelation of voltage measurements clearly indicate proximity to critical transitions. The methods are tested using both analytical and numerical results from a dynamic model of a 2383-bus test case.
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Bongard's work focuses on understanding the general nature of cognition, regardless of whether it is found in humans, animals or robots. This unique approach focuses on the role that morphology and evolution plays in cognition. Addressing these questions has taken him into the fields of biology, psychology, engineering and computer science.
Danforth is an applied mathematician interested in modeling a variety of physical, biological, and social phenomenon. He has applied principles of chaos theory to improve weather forecasts as a member of the Mathematics and Climate Research Network, and developed a real-time remote sensor of global happiness using messages from Twitter: the Hedonometer. Danforth co-runs the Computational Story Lab with Peter Dodds, and helps run UVM's reading group on complexity.
Laurent studies the interaction of structure and dynamics. His research involves network theory, statistical physics and nonlinear dynamics along with their applications in epidemiology, ecology, biology, and sociology. Recent projects include comparing complex networks of different nature, the coevolution of human behavior and infectious diseases, understanding the role of forest shape in determining stability of tropical forests, as well as the impact of echo chambers in political discussions.
Hines' work broadly focuses on finding ways to make electric energy more reliable, more affordable, with less environmental impact. Particular topics of interest include understanding the mechanisms by which small problems in the power grid become large blackouts, identifying and mitigating the stresses caused by large amounts of electric vehicle charging, and quantifying the impact of high penetrations of wind/solar on electricity systems.
Bagrow's interests include: Complex Networks (community detection, social modeling and human dynamics, statistical phenomena, graph similarity and isomorphism), Statistical Physics (non-equilibrium methods, phase transitions, percolation, interacting particle systems, spin glasses), and Optimization(glassy techniques such as simulated/quantum annealing, (non-gradient) minimization of noisy objective functions).