Re-stabilization of power network systems using high-dimensional, low-sample-size data

Power grids are complex network systems that exhibit critical transitions before dramatic deterioration. Early detection of such transitions is crucial, since it enables operators to prevent cascading failures, reduce the risk of large-scale blackouts, and maintain system reliability in a cost-efficient manner. However, existing anomaly detection methods typically identify problems only after significant degradation has already occurred, resulting in substantial economic losses and system downtime. Moreover, the intrinsic characteristics of both the system dynamics and the available data make early detection and intervention particularly challenging. To overcome these limitations, this paper proposes a model-free approach that leverages the sensitivity of dynamical network markers to capture pre-transition signals, enabling proactive system management. Specifically, we develop a framework for early detection and re-stabilization using High-Dimensional, Low-Sample-Size (HDLSS) data. We first detect the pre-deteriorating stage using Dynamical Network Marker theory. We then propose a model-free pole placement approach that shifts the maximum eigenvalue by allocating control inputs to a few selected nodes. Finally, we demonstrate through numerical simulations on a 10-generator swing-equation model that the proposed method achieves early detection and re-stabilization with energy-efficient control achieved by applying control inputs to a small number of generators.