  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.
