On the impact of different voltage unbalance metrics in distribution system optimization

With increasing penetrations of single-phase, rooftop solar PV installations, the relative variations in per-phase loading and associated voltage unbalance are expected to increase. High voltage unbalance may increase network losses and lead to failure of three-phase equipment such as motor loads. However, solar PV panels are connected to the grid through inverters, which can provide reactive power support and may mitigate some of these negative effects. In this paper, we utilize a three-phase AC optimal power flow (OPF) formulation to minimize voltage unbalance using reactive power from solar PV inverters. When considering actions to reduce voltage unbalance, it is important to recognize that various organizations such as IEC, NEMA and IEEE provide different and partially inconsistent definitions of voltage unbalance in their power quality standards. This paper analyzes the impact of the different voltage unbalance metrics using different combinations of voltage unbalance objectives and constraints. For our analysis, the optimization scheme is tested on two unbalanced low-voltage distribution networks. We observe that minimizing voltage unbalance defined by one standard might actually increase voltage unbalance as defined by another standard, potentially resulting in equipment damage. We also observe that minimizing voltage unbalance does not always lead to lower network losses. However, considerable reduction in voltage unbalance with low network losses can be achieved by minimizing the losses while simultaneously enforcing limits on multiple definitions of voltage unbalance.