Cluster-Based Distributed Small-Signal Stability Certificates for Grid-Forming Inverter Networks

Bhathiya Rathnayake, Sijia Geng

Large-scale power networks are often organized by geography, ownership, or control authority, making stability certificates that require a fully assembled global model challenging. This paper develops a time-domain small-signal stability certification framework for grid-forming inverter networks with selectable clustering resolution. The objective is to certify stability at the same scale at which the network is organized and operated: each cluster verifies conditions using intra-cluster and limited boundary information, and these checks collectively yield a network-level stability certificate without requiring a global eigenvalue computation. After linearization about a phase-cohesive synchronized operating point, a small-angle approximation decomposes the model into a voltage subsystem and an angle-frequency subsystem, where the latter is certified by an energy argument using the symmetric weighted-Laplacian network structure. For the voltage subsystem, node-to-node gains are introduced and a cyclic small-gain argument yields a family of sufficient exponential stability certificates ranging from fully decentralized to cluster-based and centralized. For an arbitrary network partition, each cluster verifies intra-cluster directed-cycle conditions and inter-cluster path conditions. The singleton- and single-cluster limits recover the decentralized and centralized certificates, respectively. The resulting stability indices provide diagnostic information beyond a pass/fail verdict by localizing the limiting margin to individual nodes, internal feedback loops, and inter-cluster channels.