## 4 Practical Experiments
### Laboratory Applications with Three-Phase Voltage Source  
Figure 4 is a photo of the three-phase circuit used for the laboratory applications. The three-phase voltage source (1) supplied an unbalanced load (5) consisting of De Lorenzo resistances [37] with practical equivalent phase resistances of \(R_{a}=241.58\ \Omega\), \(R_{b}=419.31\ \Omega\), _and_\(R_{c}=840.62\ \Omega\). To achieve significant differences between the source and load apparent powers, a neutral path was formed by a resistance \(r_{n}=185.33\ \Omega\) (4). The Fluke 437 (2) and SIMPELEC (3) analyzers were series-connected between the source and the load. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Analyzer** & **Voltage** & **Current Clamp** \\  & **Accuracy \%** & **Accuracy \%** \\ \hline
**Fluke 437-II** & \(\pm 0.1\) & 1 \\
**SIMPELEC** & \(\pm 0.9\) & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of the transducer features used by the Fluke 437 series II and SIMPELEC analyzers. Figure 4: Montage of the testing circuit: **(1)** Chroma source; **(2)** Fluke 437; **(3)** SIMPELEC analyzer; **(4)** neutral resistances and ammeter clamps; **(5)** load resistances. The source and load apparent powers in the third column of Table 3 were measured by the Fluke 437 and SIMPELEC power analyzers using the neutral point (N or n) of the corresponding subsystem (source or load) as the voltage reference point. The source and load neutral-displacement powers in the fourth column of Table 3 were measured by the SIMPELEC power analyzer (Figure 7a,b). The fifth column of Table 3 gives the source and load apparent powers determined using the neutral point of the opposite subsystem as the voltage reference point. As an example of how the values of the fifth column were calculated, we wanted to determine [PERSON]'s source apparent power, but the source neutral point (N) was not accessible and, thus, we used the load neutral point (n) as the voltage reference. The apparent power measured by the Fluke 437 power analyzer using n as the voltage reference point was the load apparent power (412.3 VA, third column in Table 3), while the measured load neutral-displacement power was 78.8879 VA (fourth column in Table 3). Thus, if the source neutral-displacement power was known (0.0666 VA, Table 2), the source apparent power according to [PERSON] could be determined from Equations (25) and (26) as follows:  
\[S_{s}=\sqrt{S_{l}^{2}-S_{nl}^{2}+S_{ns}^{2}}=\sqrt{\left(412.3\right)^{2}- \left(78.8976\right)^{2}+\left(0.0686\right)^{2}}=404.68~{}VA.\]  
This result is only slightly less than 404.8 VA, which was the real value obtained using the source neutral point (N) as the voltage reference point. A comparison of the real values of the source and load apparent powers measured by the SIMPELEC power analyzer (third column in Table 3) with the values calculated using Equations (25) and (26) reveals that they are very close. This verifies the validity of Equations (25) and (26). However, because the sources are generally quasi-balanced and hardly distorted, their neutral-displacement powers are usually less than the load neutral-displacement powers (Table 3). The source apparent powers can, thus, be estimated with great precision exclusively from the measured load apparent and neutral-displacement powers. This was also confirmed by the experimental results for the real-world electrical network (Section 4.2) The procedure has significant potential in practical applications since it reduces the number of power analyzers required to measure the apparent powers in different parts of a power system.