Online Feedback Optimization with Applications to Power Systems

Online feedback optimization refers to the design of feedback controllers that asymptotically steer a physical system to the solution of an optimization problem while respecting physical and operational constraints. For the considered optimization problem many parameters might be unknown, but one can rely on real-time measurements and the underlying physical system enforcing certain constraints. This problem setup is motivated by applications to electric power systems and has historic roots in communication networks and process control. In comparison to other optimization-based control strategies, transient optimality of trajectories is not the primary goal, and no predictive model, running costs or exogenous setpoints are required. Hence, one aims at controllers that require little model information, demand low computational cost, but that leverage real-time measurements. We design such controllers based on optimization algorithms that take the form of open and discontinuous dynamical systems. In this talk we discuss different algorithms such as projected gradient and saddle-point flows, their closed-loop stability when interconnected with physical systems, robustness properties, regularity conditions, and implementation aspects. Throughout the talk we demonstrate the potential of our methodology for real-time operation of power systems.