Safe Data-Driven Secondary Control of Distributed Energy Resources

In this paper, we present a data-driven secondary controller for regulating to some desired values several state variables of interest in an inverter-based power system, namely, electrical frequency, voltage magnitudes at critical buses, and active power flows through critical lines. The secondary controller is based on online feedback optimization, leveraging the learned sensitivities of changes in the state variables to 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 or compromising system operational reliability. To ensure safe and reliable operation, we present an approach based on Gaussian process regression that, by making an inference about the modeling uncertainties not accounted for in the sensitivity-based prediction model, allows the controller to correct the predictions and find safe control actions, for which the prediction errors are more likely to be small. 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.