Model-Free Optimal Voltage Phasor Regulation in Unbalanced Distribution Systems

The proliferation of voltage Phasor Measurement Units (PMUs) into electric power distribution grids presents new opportunities for utility operators to manage their systems more effectively. In particular, distribution-level PMUs can serve as proxy measurements for active and reactive power flows, thus alleviating the need for current transformer-based measurements for certain applications. In this work, we explore the use of distribution PMU measurements to optimally control line power flows without explicit measurements of these quantities and without a priori knowledge of the underlying distribution system topology. To do so, we extend a 2 dimensional Extremum Seeking (2D-ES) control paradigm to simultaneously manage Distributed Energy Resource (DER) active and reactive power contributions in unbalanced distribution systems. Simulation results show the ability of the proposed approach to virtually island different portions of a 3-phase unbalanced the network using DER injections while maintaining proper voltage magnitudes in the rest of the network.