## 5 Conclusions  
The phenomenon associated with the apparent power differences measured in each subsystem of a three-phase star-configured power system, depending on the point used as the voltage reference, was examined in this paper. The phenomenon was determined to be due to the power effects caused by the neutral-point displacement voltage difference between the different voltage reference points. A proposed power that represents the effect of this phenomenon, referred to as the neutral-displacement power (\(S_{n}\)), was developed, and its expressions were derived based on Buchholz's apparent power. In each subsystem (source or load) of a three-phase star-configured power system, the value of the neutral-displacement power is determined by the adopted voltage reference point. When the voltage reference point is an ideal grounding point, the neutral-displacement power is zero, and the measured apparent power has the minimum possible value, including when the subsystem is unbalanced and/or distorted. If the voltage reference point is the neutral point of an unbalanced and/or a distorted subsystem, the neutral-displacement power would be non-zero. This is because of the existence of a voltage difference between the neutral point of the subsystem and the ideal reference point, resulting in an increase in the value of the apparent power relative to the value measured using the ideal reference point. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Reference Point** & **Apparent (VA)** & **Neutral (\(S_{n}\))** \\
**Source** & **(VA)** & **(VA)** \\
**(ref. pt. N)** & 58,382.40 & 107.19 \\
**Load** & **(ref. pt. \(n\))** & 58,385.30 & 575.81 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Apparent and neutral-displacement powers measured by the SIMPELEC power analyzer for the PCC of the real-world installation with respect to the selected voltage reference point (N or n). The apparent power measured by a power analyzer when a real grounding point is used as the voltage reference point is slightly higher than that measured using an ideal grounding point as the reference point. This is because the neutral-displacement power for a real grounding point is non-zero, although very small. The neutral points of quasi-balanced and barely distorted subsystems in a three-phase power system can be considered as real grounded points. This enables the apparent powers of the subsystems to be determined with great precision using any real grounding point as the voltage reference point. This affords a practical means of measuring the apparent powers of the subsystems when their neutral points are not easily accessible, because they are very far from the measurement point, or when we want to save in power measurement instrumentation. The apparent powers of unbalanced and/or distorted subsystems measured using real grounding points as the voltage reference points instead of the neutral points of the subsystems contain errors, the magnitudes of which increase with increasing imbalance and/or distortion of the subsystems. Nevertheless, the errors can be avoided using Equations (37) and (39), presented in this paper, as demonstrated by the second and third application examples considered in the present study. The Buchholz apparent powers of most power sources can be determined with great precision by measuring only the load powers and using Equations (25) and (27). This was also demonstrated by the first and fourth (real-world) application examples considered in our study. This procedure is based on the fact that the power source of an electrical system is usually less unbalanced and distorted than the load, and the neutral-displacement power of the former is, thus, not as influential as that of the latter.