Stability and Control of Power Systems using Vector Lyapunov Functions and Sum-of-Squares Methods

TL;DR

This paper introduces a scalable, subsystem-based stability analysis and control method for large power systems using vector Lyapunov functions and SOS techniques, enabling efficient stability verification and control design.

Contribution

It develops a parallel, scalable algorithm for stability analysis of interconnected systems and designs adaptive, distributed control laws for power systems.

Findings

Successful stability analysis of a network-preserving power system

Demonstrated scalability of the subsystem approach for large systems

Designed control laws ensuring asymptotic stability under disturbances

Abstract

Recently sum-of-squares (SOS) based methods have been used for the stability analysis and control synthesis of polynomial dynamical systems. This analysis framework was also extended to non-polynomial dynamical systems, including power systems, using an algebraic reformulation technique that recasts the system's dynamics into a set of polynomial differential algebraic equations. Nevertheless, for large scale dynamical systems this method becomes inapplicable due to its computational complexity. For this reason we develop a subsystem based stability analysis approach using vector Lyapunov functions and introduce a parallel and scalable algorithm to infer the stability of the interconnected system with the help of the subsystem Lyapunov functions. Furthermore, we design adaptive and distributed control laws that guarantee asymptotic stability under a given external disturbance. Finally, we apply this algorithm for the stability analysis and control synthesis of a network preserving power system.