The interconnection of quadratic droop voltage controllers is a Lotka-Volterra system: implications for stability analysis

摘要

This paper studies the stability of voltage dynamics for a distribution powernetwork in which nodal voltages are controlled by means of quadratic droopcontrollers where the injected power is assumed to be either reactive power orthe sum of active and reactive power. We assume that the nodal power flows obeythe AC nonlinear model and show that the voltage dynamics is a Lotka-Volterrasystem, which is a class of nonlinear positive systems. We study bothtime-invariant (i.e., constant relative angles, droop gains, and references)and time-varying power networks. For the time-invariant system, we analyze theexistence and uniqueness of the equilibrium and prove an asymptotic stabilityresult. For the time-varying system, a uniform boundedness result is proved.