Distributed stability analysis for power systems with grid-following and grid-forming devices

Distributed stability analytics are receiving growing attention in modern power systems due to the employment of numerous devices with heterogeneous control strategies. Based on their synchronization control strategies, devices can be categorized as grid-following (GFL) or grid-forming (GFM). A distributed stability analytics based on the concept of output-differential passivity (ODP) and ODP index shows promise, yet it falls short in addressing systems with GFL. In this paper, we propose input-differential passivity (IDP) as the dual concept of ODP, and leverage IDP index to reflect GFL device’s contribution to stability. Furthermore, utilizing both IDP and ODP, we propose a sufficient condition for system-wide stability of systems with both GFL and GFM, which requires each device to possess a large enough passivity index. An algorithm based on linear matrix inequality (LMI) is developed for distributed assessment of system stability. Finally, simulations on a 3-bus system validate our results and demonstrate the correctness of the proposed stability condition.