Dynamic Passivity Multipliers for Plug-and-Play Stability Certificates of Converter-Dominated Grids

Abstract: Ensuring small-signal stability in power systems with a high share of inverter-based resources (IBRs) is hampered by two factors: (i) device and network parameters are often uncertain or completely unknown, and (ii) brute-force enumeration of all topologies is computationally intractable. These challenges motivate plug-and-play (PnP) certificates that verify stability locally yet hold globally. Passivity is an attractive property because it guarantees stability under feedback and network interconnections; however, strict passivity rarely holds for practical controllers such as Grid Forming Inverters (GFMs) employing P-Q droop. This paper extends the passivity condition by constructing a dynamic, frequency-dependent multiplier that enables PnP stability certification of each component based solely on its admittance, without requiring any modification to the controller design. The multiplier is parameterised as a linear filter whose coefficients are tuned under a passivity goal. Numerical results for practical droop gains confirm the PnP rules, substantially enlarging the certified stability region while preserving the decentralised, model-agnostic nature of passivity-based PnP tests.