Stability of Dynamic Feedback Optimization with Applications to Power Systems

TL;DR

This paper analyzes the stability of feedback optimization methods when applied to dynamic systems like power grids, ensuring that online optimization does not destabilize the system by using a specialized singular perturbation approach.

Contribution

It introduces a tailored stability analysis for feedback optimization in dynamic systems, especially power systems, accounting for the interaction between slow optimization and fast system dynamics.

Findings

Stability conditions for feedback optimization in power systems.

Convergence guarantees under certain dynamic assumptions.

Applicability of the analysis to real-world power system scenarios.

Abstract

We consider the problem of optimizing the steady state of a dynamical system in closed loop. Conventionally, the design of feedback optimization control laws assumes that the system is stationary. However, in reality, the dynamics of the (slow) iterative optimization routines can interfere with the (fast) system dynamics. We provide a study of the stability and convergence of these feedback optimization setups in closed loop with the underlying plant, via a custom-tailored singular perturbation analysis result. Our study is particularly geared towards applications in power systems and the question whether recently developed online optimization schemes can be deployed without jeopardizing dynamic system stability.