On the Stability of Networked Nonlinear Negative Imaginary Systems with Applications to Electrical Power Systems

TL;DR

This paper introduces a stability analysis framework for networked nonlinear negative imaginary systems, applying it to power grids with battery-based control to facilitate renewable integration and grid expansion reduction.

Contribution

It develops a novel Lyapunov function for stability of interconnected nonlinear NI systems and applies this to power grid control with batteries, enabling gradual grid transition.

Findings

Stability results for interconnected nonlinear NI systems.

Output feedback consensus for networked systems.

Framework supports incremental power grid upgrades.

Abstract

In the transition to achieving net zero emissions, it has been suggested that a substantial expansion of electric power grids will be necessary to support emerging renewable energy zones. In this paper, we propose employing battery-based feedback control and nonlinear negative imaginary (NI) systems theory to reduce the need for such expansion. By formulating a novel Lur\'e-Postnikov-like Lyapunov function, stability results are presented for the feedback interconnection of two single nonlinear NI systems, while output feedback consensus results are established for the feedback interconnection of two networked nonlinear NI systems based on a network topology. This theoretical framework underpins our design of battery-based control in power transmission systems. We demonstrate that the power grid can be gradually transitioned into the proposed NI systems, one transmission line at a time.