Decentralised Plug-and-Play Stability Conditions for AC Grids-Part II: Unstable Subsystems

RESUMO

Part I of this paper presented a decentralised framework for certifying small-signal stability in AC grids using frequency-domain quadratic constraints on individual grid subsystems. Part II extends the framework to a broader class of networks that contain unstable subsystems. In particular, we show that such unstable subsystems arise in many common scenarios, even when the aggregate system is stable and well behaved. Such subsystems must be stabilised by the closed-loop network interconnection, which complicates decentralised stability analysis. A stable hybrid representation resembling the power (PQ) model at low frequencies and the impedance (IV) model at high frequencies is then defined, to which the stability framework of Part I can be applied, allowing plug-and-play compatible conditions to be formulated. Furthermore, we show that at low frequencies, the characteristic loci in the Nyquist plot of the return ratio in this hybrid representation decouple into unbounded and bounded branches along the classical $P$-$\delta$ / $Q$-$V$ separation, and give sufficient conditions on each branch for ensuring system stability. The results are validated on the Kundur two-area system, where stability is certified, with a decentralised, plug-and-play compatible grid code covering the frequency ranges in which electromagnetic interactions arise.