  In this paper we propose an approach based on an Online Feedback Optimization
(OFO) controller with grid input-output sensitivity estimation for real-time
grid operation, e.g., at subsecond time scales. The OFO controller uses grid
measurements as feedback to update the value of the controllable elements in
the grid, and track the solution of a time-varying AC Optimal Power Flow
(AC-OPF). Instead of relying on a full grid model, e.g., grid admittance
matrix, OFO only requires the steady-state sensitivity relating a change in the
controllable inputs, e.g., power injections set-points, to a change in the
measured outputs, e.g., voltage magnitudes. Since an inaccurate sensitivity may
lead to a model-mismatch and jeopardize the performance, we propose a recursive
least-squares estimation that enables OFO to learn the sensitivity from
measurements during real-time operation, turning OFO into a model-free
approach. We analytically certify the convergence of the proposed OFO with
sensitivity estimation, and validate its performance on a simulation using the
IEEE 123-bus test feeder, and comparing it against a state-of-the-art OFO with
constant sensitivity.
