A graph theoretic view on small signal stability of inverter-based power grids
Provides a necessary and sufficient stability criterion for inverter-based power grids, enabling decentralized stability assessment and quantification of conservatism, which is important for grid operators transitioning to renewable energy.
The paper derives a necessary and sufficient small-signal stability criterion for lossless inverter-based power grids, showing that stability is equivalent to the positive definiteness of a single matrix combining network topology, operating point, and droop gains. Graph-theoretic criteria based on an augmented cone graph are presented, with cycle contributions shown to be small in IEEE test cases.
Dynamic grid stability is traditionally ensured with synchronous generators. Modern grids rely substantially more on inverter-based resources, which require grid-forming control to guarantee adequate system-wide synchronization and stability. Small-signal stability has granted various centralized and decentralized stability certificates - but these have primarily been limited to sufficient criteria only. In this work, we construct a necessary and sufficient small-signal stability criterion for lossless inverter-based power grids with arbitrary topology. We show that asymptotic stability is equivalent to the positive definiteness of a single matrix that combines network topology, operating point, and effective droop gains. We derive graph-theoretic stability criteria based on an augmented cone graph and show that the contribution of graph cycles is typically small, as illustrated for three IEEE test cases. The resulting framework yields decentralized stability criteria, quantifies the conservatism introduced by decentralization, and may support the development of future grid codes.