Stability of Dynamic Feedback optimization with Applications to Power Systems

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.

Timescale Separation in Autonomous Optimization

“…In this paper, we extend and generalize the results in [25]. Namely, we consider nonlinear physical systems instead of LTI plants and we study a variety of optimization dynamics other than mere gradient flows.…”

“…Relation between Stability and Optimality: The fact that asymptotically stable equilibria are strict local minimizer has been shown in [25] for LTI plants and the standard metric. The proof extends to the present case without major modifications.…”

Distributed Control and Optimization for Autonomous Power Grids

“…We will not cover the dynamic part of the control design in this section, which is a thriving topic on its own. We can refer the reader to some very recent works on this matter [67]- [73].…”

“…Price-based control strategies have been proposed in [114], [125]- [127], and an approximate decentralized approach was studied in [128]. Finally, we note that there is an emerging line of theoretical research on steady-state optimizing feedback control which encompasses some (or all) of the control schemes discussed in this section; see [70]- [73] for different formulations.…”

Steady-State Optimal Frequency Control for Lossy Power Grids with Distributed Communication

“…A class of distributed control concepts that has recently been very popular in terms of frequency regulation and balancing is real-time dynamic pricing (see [2] for a detailed survey on current research directions). Dynamic pricing is particularly advantageous in large scale networks as it enables implicit communication of momentary imbalances via a price signal, resulting in a dynamic feedback minimization [3]- [6] of the overall costs. The price signal represents an aggregated information about current imbalances between generations and consumptions.…”