Compositional and Equilibrium-Free Conditions for Power System Stability -- Part I: Theory

Traditional centralized stability analysis struggles with scalability in large complex modern power grids. This two-part paper proposes a compositional and equilibrium-free approach to analyzing power system stability. In Part I, we prove that using equilibrium-free local conditions we can certificate system-wide stability of power systems with heterogeneous nonlinear devices and structure-preserving lossy networks. This is built on a recently developed notion of delta dissipativity, which yields local stability conditions without knowing the system-wide equilibrium. As a consequence, our proposed theory can certificate stability of equilibria set rather than single equilibrium. In Part I, we verify our theory and demonstrate promising implications by the single machine single load benchmark, which helps to better explain the compositional and equilibrium-set-oriented stability analysis. Part II of this paper will provide methods for applying our theory to complex power grids, together with case studies across a wide range of system scales. Our results enable a more scalable and adaptable approach to stability analysis. It also sheds light on how to regulate grid-connected devices to guarantee system-wide stability.