Distributed Stability Analysis for Power Systems Under Persistent Disturbance

The continued growth of renewable energy penetration in power systems calls for an efficient and scalable approach for stability analysis. This paper proposes a new stability index called
$\mathcal{L}_{2}$
stability index (LSI) for power systems under persistent disturbance by combining the concepts of
$\mathcal{L}_{2}$
gain and output-differential passivity (OD-passivity). The proposed stability index provides a quantitative way to measure the power system stability under external disturbances such as power fluctuations due to renewable generation. We also put forward a distributed approach to computing LSI and implement it in three typical power devices, i.e., synchronous generators (SGs), conventional droop-controlled inverters, and quadratic droop-controlled inverters. Case studies on two IEEE 39-bus systems verify the theoretical analysis in this paper.