Passivity properties for regulation of DC networks with stochastic load demand

TL;DR

This paper introduces stochastic passivity properties for DC power networks with unpredictable, time-varying loads modeled by stochastic differential equations, ensuring stability through a distributed control scheme.

Contribution

It extends existing passivity results to stochastic load models in DC networks and proves stability of a control scheme under these conditions.

Findings

Distributed control achieves current sharing and voltage regulation.

Ensures asymptotic stochastic stability of the network.

Models loads with stochastic differential equations.

Abstract

In this paper we present new (stochastic) passivity properties for Direct Current (DC) power networks, where the unknown and unpredictable load demand is modelled by a stochastic process. More precisely, the considered power network consists of distributed generation units supplying ZIP loads, i.e., nonlinear loads comprised of impedance (Z), current (I) and power (P) components. Differently from the majority of the results in the literature, where each of these components is assumed to be constant, we consider time-varying loads whose dynamics are described by a class of stochastic differential equations. Finally, we prove that an existing distributed control scheme achieving current sharing and (average) voltage regulation ensures the asymptotic stochastic stability of the controlled network.