Linear Phase Balancing Scheme using Voltage Unbalance Sensitivities in Multi-phase Power Distribution Grids

Power distribution networks, especially in North America, are often unbalanced due to the mix of single-, two- and three-phase networks as well as due to the high penetration of single-phase devices at the distribution level such as electric vehicle (EV) chargers and single-phase solar plants. However, the network operator must adhere to the voltage unbalance levels within the limits specified by IEEE, IEC, and NEMA standards for the safety of the equipment as well as the efficiency of the network operation. Existing works have proposed active and reactive power control in the network to minimize imbalances. However, these optimization problems are highly nonlinear and nonconvex due to the inherent non-linearity of unbalanced metrics and power-flow equations. In this work, we propose a linearization approach of unbalance metrics such as voltage unbalance factors (VUF), phase voltage unbalance rate (PVUR), and line voltage unbalance rate (LVUR) using the first order Taylor's approximation. This linearization is then applied to the phase balancing control scheme; it is formulated as a feedback approach where the linearization is updated successively after the active/reactive control setpoint has been actuated and shows improvement in voltage imbalances. We demonstrate the application of the proposed scheme on a standard IEEE benchmark test case, demonstrating its effectiveness.