Data-Driven Voltage Regulation in Radial Power Distribution Systems

In this paper, we develop a data-driven framework for controlling distributed energy resources (DERs) in a balanced radial power distribution system with the objective of regulating voltages across the whole system. The objective is to determine optimal DER power injections that minimize the voltage excursions outside a desirable voltage range without knowing a complete model of the power distribution system. To this end, we approximate the nonlinear relationship between the voltage magnitudes and the power injections by a linear model. The parameters of this linear model - referred to as the voltage sensitivities - can be computed using information on the network topology and the line parameters, the values of which will be estimated. Assuming the knowledge of feasible network topology configurations and distribution line resistance-to-reactance ratios, we propose a framework for identifying the true network topology configuration and the corresponding line parameters using only a few measurements of voltage magnitudes and power injections. Utilizing the estimated voltage sensitivities, the optimal DER power injections can be readily determined by solving a convex optimization problem. Due to its data-driven nature, the proposed framework is intrinsically adaptive to changes in system conditions such as unknown topology reconfiguration. The effectiveness of the proposed framework is validated via numerical simulations on the IEEE 123-bus distribution test feeder.