## 4 Practical Experiments
### Laboratory Applications with Three-Phase Voltage Source
#### 4.1.3 Distorted Voltage Source  
In this practical application, the three-phase source was programmed to supply balanced and distorted line-to-neutral voltages formed by a 230-V 50-Hz fundamental-frequency harmonic and a 23-V 150-Hz third harmonic. The registrations of the Fluke 437 and SIMPELEC power analyzers are shown in Figures 11 and 12. The load and neutral path resistances were maintained at the same values as in the previous tests. The RMS results for the different parts of the circuit are presented in Table 6.  
Figure 11: Screenshots of Fluke 437 power analyzer showing the currents and [PERSON]’s powers measured under supply of distorted voltage: (**a**) source power, (**b**) load power, and (**c**) line and neutral currents. Figure 12: Main screens of the SIMPELEC analyzer when the source is distorted and with representation of the line-to-neutral voltage waves, using the voltage reference point as (**a**) the neutral point of source (N), (**b**) the neutral point of load (n), and (**c**) a real grounding point (G). The total RMS values of the voltages and currents in the tested circuit were obtained by applying Fourier series to the harmonic components presented in Table 6. Hence, using Equation (24), the RMS values of the zero-sequence line-to-neutral voltages at the source, load, and PCC for the use of a real grounding point as the voltage reference point were respectively as follows:  
\[V_{AN0}=\sqrt{0.07^{2}+23^{2}}=23\;\text{V},\quad V_{An0}=\sqrt{45.08^{2}+9.508 ^{2}}=46.07\;\text{V},\]  
\[V_{AG0}=\sqrt{0.07^{2}+0.23^{2}}=0.24\;\text{V}.\]  
The apparent powers measured by the analyzers are presented in the third column of Table 7. The neutral-displacement powers in the fourth column of Table 7 were measured at the PCC by the SIMPELEC power analyzer using the neutral points of source (N) and load (n), as well as with a real grounding point (G), as the voltage reference points, respectively, according to Equations (27), (28), and (35). The source and load apparent powers indicated in the fifth column of Table 7 were obtained from the apparent powers measured at the PCC using a real grounding point (\(G\)) and Equations (37) and (39). Hence, for example, to calculate the load apparent power (\(S_{l}^{*}\)) from PCC apparent power (\(S_{pcc}^{*}=403.8\) VA, Table 7, measured by the Fluke 437 power analyzer), the load and PCC neutral-displacement powers (\(S_{nl}=80.95\) VA, \(S_{n,pcc}=0.42\) VA) in Equation (37) should be used. \[S_{l}^{*}=\sqrt{\left(S_{pcc}^{*}\right)^{2}+S_{nl}^{2}-S_{n,pcc}^{2}}=\sqrt{4 03.8^{2}+80.95^{2}-0.42^{2}}=411.83\;\text{VA}.\]  
This result is very close to the real value of 411.7 VA (third column of Table 7), measured by the Fluke 437 power analyzer using the neutral point of the load as voltage reference. The general results obtained for the tested circuit when it was supplied with the distorted voltage (Table 7) are comparable with those obtained when the circuit was supplied by an unbalanced voltage (Table 5). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Source Voltage**} & \multicolumn{2}{c}{**Load Voltage**} & \multicolumn{2}{c}{**Real Grounding Point Voltage**} & \multicolumn{2}{c}{**Line Current**} \\ \cline{2-7}  & **50 Hz** & **150 Hz** & **50 Hz** & **150 Hz** & **50 Hz** & **150 Hz** & **50 Hz** & **150 Hz** \\ \hline
**A-phase** & 230.0 & 23.0 & 189.69 & 9.536 & 231.2 & 0.275 & 0.78 & 0.04 \\ \hline
**B-phase** & 230.0 & 23.0 & 239.32 & 9.49 & 231.2 & 0.211 & 0.565 & 0.023 \\ \hline
**C-phase** & 230.2 & 23.0 & 267.85 & 9.5 & 231.3 & 0.211 & 0.315 & 0.011 \\ \hline \(V_{0}\)/\(I_{N}\) & 0.07 & 23.0 & 45.08 & 9.508 & 0.07 & 0.23 & 0.246 & 0.071 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Harmonic voltages and currents measured by the SIMPELEC power analyzer using different voltage reference points (\(V_{0}\) = zero-sequence voltage, \(I_{N}\)= neutral current).