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Methods for Efficient Stability Analysis of Future Power Systems

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Methods for Efficient Stability Analysis of Future Power Systems

Abstract: This talk presents two geometric methods—based on normal vectors and differential geometry—for efficient stability analysis of future power systems characterized by high complexity and uncertainty. The first part of the talk focuses on using normal vectors to analytically describe the stability margin to Hopf and saddle-node bifurcations, addressing oscillatory instability and voltage collapse, respectively. We apply this theory to assess the parameter sensitivities of grid-forming and grid-following inverters and identify the most effective control parameters for enhancing stability margins. In particular, the impacts of line dynamics are investigated. It is observed that line dynamics introduce a uniform reduction in the stability margin to Hopf bifurcation across all parameters. However, the reduction is generally small. The second part introduces a novel differential geometry-based method to approximate the singular solution space boundary (SSB) of power systems under high renewable generation variability. By extracting geometric information from the power flow manifold, we approximate geodesics originating from an operating point in any interested directions corresponding to generation and load fluctuations. Using these geodesic curves, we predict voltage collapse points by solving a few univariate quadratic equations. Compared to conventional methods that rely on optimization or computationally expensive numerical continuation, this approach is efficient and well-suited for handling the high-dimensional variability introduced by large-scale renewable integration.

Bio: Sijia Geng is an Assistant Professor in the Department of Electrical and Computer Engineering at Johns Hopkins University. She is a Core Faculty with the Ralph O’Connor Sustainable Energy Institute (ROSEI) and co-PI of the NSF EPICS Global Center. Before joining JHU, she was a Postdoctoral Associate at the Laboratory for Information & Decision Systems (LIDS) at MIT. Dr. Geng received her Ph.D. in Electrical and Computer Engineering from the University of Michigan, Ann Arbor, where she also obtained two M.S. degrees in Mathematics and in ECE. Her research interests include dynamics, control and stability of inverter-based smart grids and optimization of electrified transportation systems. She is the recipient of a Best Paper Award at the MIT/Harvard Applied Energy Symposium in 2022 and was named a Barbour Scholar and Rising Star in EECS in 2021.