Diagonal Stability of Systems with Rank-1 Interconnections and Application to Automatic Generation Control in Power Systems

TL;DR

This paper establishes a simple necessary and sufficient condition for the diagonal stability of matrices with rank-1 interconnections and applies this to analyze the stability of automatic generation control in power systems, providing theoretical insights.

Contribution

It introduces a novel stability criterion for rank-1 interconnection matrices and applies it to the first theoretical stability analysis of AGC in nonlinear power systems.

Findings

Derived a necessary and sufficient condition for diagonal stability.

Provided the first theoretical stability analysis of AGC in nonlinear power systems.

Offered insights into tuning and dynamic performance of AGC.

Abstract

We study a class of matrices with a rank-1 interconnection structure, and derive a simple necessary and sufficient condition for diagonal stability. The underlying Lyapunov function is used to provide sufficient conditions for diagonal stability of approximately rank-1 interconnections. The main result is then leveraged as a key step in a larger stability analysis problem arising in power systems control. Specifically, we provide the first theoretical stability analysis of automatic generation control (AGC) in an interconnected nonlinear power system. Our analysis is based on singular perturbation theory, and provides theoretical justification for the conventional wisdom that AGC is stabilizing under the typical time-scales of operation. We illustrate how our main analysis results can be leveraged to provide further insight into the tuning and dynamic performance of AGC.