Lyapunov stability of smart inverters using linearized distflow approximation

Shammya Shananda Saha, Daniel Arnold, Anna Scaglione, Eran Schweitzer, Ciaran Roberts, Sean Peisert, Nathan G. Johnson

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


Fast-acting smart inverters that utilize preset operating conditions to determine real and reactive power injection/consumption can create voltage instabilities (over-voltage, voltage oscillations and more) in an electrical distribution network if set-points are not properly configured. In this work, linear distribution power flow equations and droop-based Volt–Var and Volt–Watt control curves are used to analytically derive a stability criterion using Lyapunov analysis that includes the network operating condition. The methodology is generally applicable for control curves that can be represented as Lipschitz functions. The derived Lipschitz constants account for smart inverter hardware limitations for reactive power generation. A local policy is derived from the stability criterion that allows inverters to adapt their control curves by monitoring only local voltage, thus avoiding centralized control or information sharing with other inverters. The criterion is independent of the internal time-delays of smart inverters. Simulation results for inverters with and without the proposed stabilization technique demonstrate how smart inverters can mitigate voltage oscillations locally and mitigate real and reactive power flow disturbances at the substation under multiple scenarios. The study concludes with illustrations of how the control policy can dampen oscillations caused by solar intermittency and cyberattacks.

Original languageEnglish (US)
Pages (from-to)114-126
Number of pages13
JournalIET Renewable Power Generation
Issue number1
StatePublished - Jan 2021

ASJC Scopus subject areas

  • Renewable Energy, Sustainability and the Environment


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