Controllability and Observability with Confidence: From Gramians to Guarantees for Refined Power Systems

This NSF project aims to develop new mathematical tools that help power grid operators understand, in real time, whether they can steer the grid where it needs to go, see what is happening inside it, and keep it stable. The nation's electric grid is rapidly changing: power electronics and inverter-based resources are transforming how electricity is generated and delivered, and the decades-old mathematical theory that operators rely on was not designed for this new reality. Recent large-scale blackouts, including the April 2025 event that left the Iberian Peninsula without power, illustrate what can happen when protective devices act on incomplete information of grid behavior. The project will bring transformative change by replacing snapshot-based grid analytics with methods that track the grid as it actually behaves---continuously, nonlinearly, and under uncertainty. This will be achieved by building algorithms that keep grid models calibrated using live sensor data, compute trustworthy measures of grid controllability and observability, and translate those measures into operator actions that prevent blackouts. The intellectual merit of the project includes new theory and scalable computation for fundamental system properties of realistic power grid models, a long-standing open problem in the field. The broader impacts of the project include a more reliable and secure national electricity systems, open-source software and datasets, graduate student training alongside educational workshops, and methods transferable to other infrastructure like water, gas, and traffic networks. The technical foundation of this project lies in nonlinear differential-algebraic equations (NDAEs), the mathematical models that couple generator and inverter dynamics with the physics of power flow. Classical measures of controllability, observability, and stability are well understood only for simplified linear models tied to a single operating point, and such linearizations become stale within minutes as operating conditions, network topology, and equipment parameters shift. This project develops an NDAE-aware analytics framework with three components. First, live model refinement algorithms jointly estimate dynamic and network parameters from phasor measurement unit and supervisory control and data acquisition streams, while enforcing power flow constraints and quantifying uncertainty. Second, new tangent-space Gramians, energy-based metrics computed directly on the power flow manifold, and polytopic certificates deliver controllability, observability, and stability guarantees valid across forecasted load ranges and contingencies. Third, optimization layers translate these metrics into grid interventions, including load shedding, flexible AC transmission system dispatch, and synthetic inertia allocation. Deliverables include open-source software and reproducible benchmarks on networks with thousands of buses. 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.