Investigating Power Factor Definitions in the Context of Unbalanced Loads and Voltages

The power factor (PF), an indicator of how efficiently the load is drawing energy from the grid and whether load compensation is necessary, should not be influenced by unbalances and harmonics present in the voltages. However, these phenomena can affect the readings of each PF definition, potentially leading to unfair scenarios for the customer or the utility. In the literature, the PF billing of unbalanced loads has not been evaluated considering unbalanced non-sinusoidal voltages. To address this gap, this paper investigates five definitions (per-phase fundamental PF, and three-phase fundamental arithmetic, geometric, and positive-sequence PFs, and effective PF) when an extensive set of unbalanced non-sinusoidal voltage conditions are applied to balanced and unbalanced constant impedance loads via computational simulations and experimental tests, which reveals that all definitions, except the fundamental geometric and positive-sequence PFs, are sensitive to unbalances present in the supply voltage when applied to unbalanced constant resistive loads. Analytical expressions are developed for each PF definition, revealing that they are non-linear functions of the VUF and the load's admittances. It is also proposed admittance factors that can be employed for billing purposes because they do not depend on the voltages but solely on the load's characteristics.