The interconnection of quadratic droop voltage controllers is a Lotka-Volterra system: implications for stability analysis
Abstract
This paper studies the stability of voltage dynamics for a power network in which nodal voltages are controlled by means of quadratic droop controllers with nonlinear AC reactive power as inputs. We show that the voltage dynamics is a Lotka-Volterra system, which is a class of nonlinear positive systems. We study the stability of the closed-loop system by proving a uniform ultimate boundedness result and investigating conditions under which the network is cooperative. We then restrict to study the stability of voltage dynamics under a decoupling assumption (i.e., zero relative angles). We analyze the existence and uniqueness of the equilibrium in the interior of the positive orthant for the system and prove an asymptotic stability result.
Keywords
Cite
@article{arxiv.1710.09636,
title = {The interconnection of quadratic droop voltage controllers is a Lotka-Volterra system: implications for stability analysis},
author = {Matin Jafarian and Henrik Sandberg and Karl H. Johansson},
journal= {arXiv preprint arXiv:1710.09636},
year = {2018}
}
Comments
Submitted to The IEEE Control Systems Letters