Sparse Continuation-Based Eigenvalue Tracking for Power System DDAEs

Abstract

In this paper, we formulate a continuation method for tracking eigenvalue trajectories in power system models with time-delayed measurement and control signals. Such delays are known to weaken damping and reduce stability margins if not properly accounted for in stability analysis and control design. The proposed formulation follows selected eigenpairs directly from sparse delay differential-algebraic equation (DDAE) models with one or multiple delayed variables, avoiding repeated eigensolutions as system conditions or parameters vary. The continuation parameter can represent system and control parameters, constant delay magnitudes, or parameters governing nonconstant wide-area measurement system (WAMS) delays. The proposed method is validated on a modified IEEE 39-bus system and on a real-world-scale dynamic model of the Irish transmission network, demonstrating accurate tracking of critical eigenvalue trajectories and clear computational advantages over repeated eigensolution-based analysis.