Compositional and Equilibrium-Free Stability Certification for Power Systems--Part I: Theory

Abstract

Stability certification for large-scale power systems is challenging due to heterogeneous device dynamics and time-varying operating conditions. This two-part paper develops an equilibrium-free compositional framework based on local delta dissipativity. In Part I, we introduce the concept of local delta dissipativity (LDD), a localized extension of delta dissipativity in which the dissipation inequality is required only on a prescribed local state--input region, thereby relaxing the global requirement of standard delta dissipativity. Using LDD, we establish asymptotic stability with respect to an equilibrium set, rather than with respect to a single equilibrium point, and derive compositional sufficient conditions that decompose into device-level LDD certificates and a network-level coupling inequality. We further specialize the results to structure-preserving power-system models described by differential-algebraic equations, yielding equilibrium-free stability certificates that are verifiable at the device level and composable through a network constraint. Part II of this two-part paper develops the corresponding certificate computational methods and demonstrates, on modified IEEE 9-, 39-, and 118-bus systems, how the compositional theory established here enables scalable stability certification. A single-machine single-load benchmark illustrates the derived conditions and the resulting certified stability region under load variations.