## 4 Practical Experiments
### Real-World Electrical Network  
This experiment aimed to also verify Equations (25) and (26) in real-world installations, and not only in controlled conditions at the laboratory. Additionally, the experiment was used to prove that measuring only the load powers is enough to determine the apparent powers of the source (the transformer, in this case) with very good approximation.  
An electrical network of the utility Electrica de Vinalesa SCV, Valencia, Spain, was used for this practical experience. The waves of the line currents and source voltages, as well as the source and load powers registered by the SIMPELEC power analyzer, are shown in Figure 13a,b. The network power was supplied by a 400-kVA 20-kV/400-V Dyn11 three-phase transformer through a three-phase four-wire balanced buried line of cross-section 25 mm\({}^{2}\) and length 28 m (from the transformer to the load distribution panel). The power consumptions of each phase of the load are shown in Figure 14. The line currents were distorted and strongly unbalanced (Figure 13b), while the voltages were hardly distorted (Figure 13a).  
It should be noted that, as shown in Table 8, the apparent powers measured at the PCC when the neutral point of the load (n) was used as the voltage reference point (58,385.30 VA) were slightly higher than the apparent powers measured at the PCC using the source neutral point (N) as the voltage reference point (58,382.40 VA). The differences between the measured apparent powers were due to the neutral-point displacement of the load and source, caused by the non-negligible neutral conductor impedance.  
Figure 14: Screenshots of the active and reactive power consumptions in each phase of the load of the real-world electrical network measured by the SIMPELEC power analyzer.  
Figure 13: Main screens of the SIMPELEC power analyzer for measurement of the (**a**) source (with representation of line-to-neutral voltages), and (**b**) load (with representation of line currents) of the real-world electrical network.  
The source and load voltages show the effects of the neutral displacement phenomenon. While the source voltages stayed quasi-balanced, with values around 230 V (Figure 13a), the load voltages became unbalanced, with over-voltages greater than 231 V in phases A and B, and sub-voltages (228.21 V) in phase C. The power effects caused by the non-negligible neutral conductor impedance were determined by the neutral-displacement powers, which were 575.81 VA for the load and only 107.19 VA for the source (Table 8).  
We knew the values of the apparent and neutral-displacement powers in the source and load (represented in Table 8), because we measured these powers in both subsystems (source and load) of the real-world installation. However, usually, the powers are measured at only one part (source or load) of the power systems, making it difficult to measure two sides at once. In these cases, the procedure proposed in this paper could be very useful, because it enables determining the source apparent power, with great approximation, measuring only the load powers. Indeed the neutral-displacement power of the source (\(S_{ns}=107.19\) VA, Table 8) was negligible in comparison to the load neutral-displacement power (\(S_{nl}=575.81\) VA, Table 8), which is true in most power systems, since the sources are usually more balanced and less distorted than the loads, as may be obtained from Equations (25) and (26).  
\[S_{s}\equiv\sqrt{S_{l}^{2}-S_{nl}^{2}}=\sqrt{58385.3^{2}-575.81^{2}}=58,382.46\ \text{VA}.\]  
This result is very close to the measured value of the source apparent power (\(S_{s}=58,382.4\) VA, Table 8). The findings of this example are of great practical significance, particularly for the possibility of estimating the source apparent power of a system using only the powers measured in the load of that system, because the source neutral point is inaccessible or to save measuring instrumentation on the source.