Lyapunov Stability of Smart Inverters Using Linearized DistFlow Approximation

TL;DR

This paper develops a Lyapunov-based stability criterion for smart inverter control in power distribution networks using linearized power flow equations, enabling local adaptive control to prevent voltage instability.

Contribution

It introduces a novel stability analysis method incorporating Lipschitz constants and local control policies for smart inverters based on the linearized DistFlow model.

Findings

The stability criterion effectively predicts voltage stability under various conditions.

Local control policies can mitigate voltage oscillations without centralized communication.

Simulation results confirm improved voltage stability and disturbance mitigation.

Abstract

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 \lyapnouv 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 cyber-attacks.