Singular Perturbation and Small-signal Stability for Inverter Networks

Saber Jafarpour, Victor Purba, Brian Johnson, Sairaj Dhople, Francesco Bullo

Research output: Contribution to journalArticlepeer-review


This paper examines small-signal stability of electrical networks composed dominantly of three-phase grid-following inverters. We show that the mere existence of a high-voltage power flow solution does not necessarily imply small-signal stability; this motivates us to develop a framework for stability analysis that systematically acknowledges inverter dynamics. We identify a suitable time-scale decomposition for the inverter dynamics, and using singular perturbation theory, obtain an analytic sufficient condition to verify small-signal stability. Compared to the alternative of performing an eigenvalue analysis of the full-order network dynamics, our analytic sufficient condition reduces computational complexity and yields insights on the role of network topology and constitution as well as inverter-filter and control parameters in small-signal stability. Numerical simulations for a radial network validate the approach and illustrate the efficiency of our analytic conditions for designing and monitoring grid-tied inverter networks.

Original languageEnglish (US)
JournalIEEE Transactions on Control of Network Systems
StateAccepted/In press - 2021

Bibliographical note

Publisher Copyright:


  • Analytical models
  • Circuit stability
  • Inverters
  • Numerical stability
  • Perturbation methods
  • Power system stability
  • Stability analysis


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