  In this paper, we present a data-driven secondary controller for regulating
to some desired values several variables of interest in a power system, namely,
electrical frequency, voltage magnitudes at critical buses, and active power
flows through critical lines. The power generation system is based on
distributed energy resources (DERs) interfaced with either grid-forming (GFM)
or grid-following (GFL) inverters. The secondary controller is based on online
feedback optimization leveraging the learned sensitivities of the changes in
the system frequency, voltage magnitudes at critical buses, and active power
flows through critical lines to the changes in inverter active and reactive
power setpoints. To learn the sensitivities accurately from data, the feedback
optimization has a built-in mechanism for keeping the secondary control inputs
persistently exciting without degrading its performance. The feedback
optimization also utilizes the learned power-voltage characteristics of
photovoltaic (PV) arrays to compute DC-link voltage setpoints so as to allow
the PV arrays to track the power setpoints. To learn the power-voltage
characteristics, we separately execute a data-driven approach that fits a
concave polynomial to the collected power-voltage measurements by solving a
sum-of-squares (SoS) optimization. We showcase the secondary controller using
the modified IEEE-14 bus test system, in which conventional energy sources are
replaced with inverter-interfaced DERs.
