Physics-Informed Graph Neural Networks for Power-Grid Stability

Abstract

The transition of modern transmission grids toward inverter-based generation is steadily eroding the rotational inertia that has historically anchored small-signal stability. As synchronous machines are displaced, frequency deviations evolve faster, damping margins shrink, and the network becomes increasingly fragile under topology changes, contingencies, and the operational stress imposed by extreme weather events. At the same time, the streaming data now available from modern grid sensors is largely underused because prediction, stability assessment, and control are still treated as separate pipelines rather than as a single decision process. This thesis closes that gap by developing a unified, closed-loop framework for online stability support in low-inertia, topology-varying power grids, addressing three coupled objectives: online stability assessment under uncertainty, adaptive virtual inertia allocation under topology change, and integration of prediction with control under formal stability guarantees. At the core of the framework is a spectral-sensitivity-based virtual inertia allocator, derived from swing-equation dynamics and eigenvalue perturbation analysis, which identifies the buses whose inertia most strongly influences the damping of critical electromechanical modes and concentrates allocation at those locations. A spatio-temporal physics-informed graph neural network (ST-GNN) forecasts near-future grid states and reproduces these allocation targets, with Kirchhoff's laws and operational limits enforced as physics-informed penalties during training. A reinforcement-learning policy then issues coordinated control actions spanning generator re-dispatch, demand response, and inertia updates, and a supervisory coordination layer blends these actions with the spectral reference and projects them onto the feasible set prior to execution. A Lyapunov-based analysis establishes that, provided inertia stays within design bounds and the network remains connected between switching events, the closed-loop electromechanical dynamics preserve uniform asymptotic stability. Validation on the IEEE 118-bus system under N--2 contingencies not seen during training demonstrates accurate state tracking, topology-aware inertia redistribution, and sustained operational security across extended simulations, while saliency-based diagnostics expose the structural drivers of each control decision. The result is an interpretable, computationally efficient framework that brings physics-based guarantees and learning-based adaptability into a single coherent control loop for stability-aware operation of future smart grids.