On The Relationships Among Different Voltage Unbalance Definitions

Growing penetrations of distributed energy resources (DERs) increase the power injection variability in distribution systems, which can result in power quality issues such as voltage unbalance. To measure unbalance, organizations such as IEC, NEMA and IEEE define phase unbalance in their power quality standards. However, the definitions in these different standards are not consistent, and voltages that are considered acceptable by one standard may violate good practices defined by another standard. To address this issue, this paper provides analytical comparisons of the most common voltage unbalance definitions, which are supplemented with numerical simulations. The analytical relationships suggest that it is possible to approximately bound the symmetrical-component-based voltage unbalance factor (which depends on the magnitude and relative phase angle) by limiting the line-to-line voltage unbalance, whereas applying line-to-ground voltage unbalance definitions neglects all information about phase angle offsets.