Distributed Voltage Unbalance Mitigation in Distribution Systems With Grid-Forming Control

This paper proposes a distributed voltage balancing control to mitigate voltage unbalance in three-phase distribution networks with grid-forming converters. The proposed distributed balancing control is designed based on partitioning the overall network into subnetworks that each contain one grid-forming converter and can be implemented without knowledge of branch impedances. Notably, the proposed control only requires knowledge of the type of network branches (e.g., transformer, line) and voltage measurements from within the subnetwork. Based on this information, the distributed control adjusts the phase differences of voltages of grid-forming converters. Timescale separation arguments are used to establish that the proposed control is input-to-state stable. Moreover, an analytical bound on the suboptimality of the distributed control relative to a centralized optimal control is obtained. We illustrate and validate our analytical results and efficacy of the proposed voltage balancing control using EMT simulations of a modified IEEE 13 bus feeder.