Eigenvalue Tracking of Large-Scale Systems Impacted by Time Delays

Abstract

The paper focuses on tracking eigenvalue trajectories in power system models with time delays. We formulate a continuation-based approach that employs numerical integration to follow eigenvalues as system parameters vary, in the presence of one or multiple delayed variables. The formulation is compatible with sparse delay differential-algebraic equation (DDAE) formulations of the system model and allows treating the delay magnitude itself as a varying parameter with implementation aspects discussed in detail. The proposed approach is illustrated on a modified IEEE 39-bus system, as well as on a real-world-scale dynamic model of the Irish transmission network.