Geometric Decentralized Stability Certificate for Power Systems Based on Projecting DW Shells

Abstract

The development of decentralized stability conditions has gained considerable attention due to the need to analyze multi-agent network systems, such as heterogeneous multi-converter power systems. A recent advance is the application of the small-phase theorem, which extends the passivity theory. However, it requires the transfer function matrix to be sectorial, which may not hold in some frequency range and will result in conservativeness. To address this issue, this paper proposes a geometric decentralized stability condition based on Davis-Wielandt (DW) shell and its projections. Our approach provides a geometric interpretation of the small-gain and small-phase theorems and enables decentralized stability analysis of power systems. It serves as a visualization method to understand the closed-loop interactions and assess the stability of large-scale network systems in a scalable and modular manner.