Peng Yang, Liaoyuan Yang, Feng Liu
Conventional power-system stability analysis is largely centralized and centered on a single equilibrium point, which becomes increasingly restrictive in the presence of large-scale fluctuating renewable generation. This paper develops a decentralized framework for stability analysis and control that certifies the asymptotic stability of an equilibrium set rather than that of a given single operating point. To this end, we introduce a new notion termed input--output differential passivity (IODP), which decomposes equilibrium-set stability of the interconnected system into local requirements imposed on individual devices. These requirements are formulated without embedding a particular operating equilibrium into the local conditions; once the certified regions are constructed, stability verification for a given operating scenario reduces to checking whether its equilibrium lies in the certified set. The proposed conditions require each bus to possess a sufficient level of IODP, quantified by an IODP index. To compensate for an IODP shortage, we further develop an I/O-transformation-based passivation controller that reshapes the local input--output behavior of the corresponding device. In this way, all grid-connected components can be made to satisfy the decentralized conditions for system-wide stability. The proposed framework is validated on a modified IEEE 39-bus system. Simulation results demonstrate that it provides a scalable and equilibrium-set-oriented solution for stability certification and control under highly variable operating conditions.