Toward Distributed Stability Analytics for Power Systems with Heterogeneous Bus Dynamics

The stability issue emerges as a growing number of diverse power apparatus connecting to the power system. The stability analysis for such power systems is required to adapt to heterogeneity and scalability. This paper derives a local passivity index condition that guarantees the system-wide stability for lossless power systems with interconnected, nonlinear, heterogeneous bus dynamics. Our condition requires each bus dynamics to be output feedback passive with a large enough index w.r.t. a special supply rate. This condition fits for numerous existing models since it only constrains the input-output property rather than the detailed dynamics. Furthermore, for three typical examples of bus dynamics in power systems, we show that this condition can be reached via proper control designs. Simulations on a 3-bus heterogeneous power system verify our results in both lossless and lossy cases. The conservativeness of our condition is also demonstrated, as well as the impact on transient stability. It shows that our condition is quite tight and a larger index benefits transient stability.

💡 Research Summary

The paper addresses the growing challenge of stability analysis in modern power systems that are increasingly populated by heterogeneous devices such as synchronous generators, inverter‑based resources, and diverse loads. Traditional centralized methods (time‑domain simulation, eigenvalue analysis, direct methods) become impractical due to computational burden, communication constraints, and privacy concerns. To overcome these limitations, the authors propose a distributed stability framework based on passivity theory and the concept of a passivity index.

System Modeling
The network‑reduced power system is represented as an undirected graph with n buses. Each bus i is equipped with a dynamic device whose state evolves according to a generic nonlinear input‑output model
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