Non-convex Feedback Optimization with Input and Output Constraints for Power System Applications

Abstract

In this thesis, we present a novel control scheme for feedback optimization. That is, we propose a discrete-time controller that can steer the steady state of a physical plant to the solution of a constrained optimization problem without numerically solving the problem. Our controller can be interpreted as a discretization of a continuous-time projected gradient flow and only requires reduced model information in the form of the steady-state input-output sensitivity of the plant. Compared to other schemes used for feedback optimization, such as saddle-point flows or inexact penalty methods, our scheme combines several desirable properties: It asymptotically enforces constraints on the plant outputs, and temporary constraint violations along the trajectory can be easily quantified. Further, as we prove in our main result, global convergence to a minimum is guaranteed even for non-convex problems, and equilibria are feasible regardless of model accuracy. Additionally, our scheme is straightforward to tune, since the step-size is the only tuning parameter. Finally, we numerically verify robustness (in terms of stability) of the closed-loop behavior in the presence of model uncertainty. For the envisioned application in power systems, we use our novel feedback approach to steady-state optimization for time-varying AC power flow optimization. In numerical experiments, we show that our scheme scales nicely for larger power system setups and exhibits robustness with respect to time-varying generation limits, unobserved demand variations, and a possible model mismatch.